joint shaft test stand jiří pakosta, gabriela achtenová mecca 01 2017 page 11 10.1515/mecdc-2017-0003 joint shaft test stand jiří pakosta, gabriela achtenová 1. introduction joint shafts of drive axles are increasingly used types of wheel drives in passenger automobile drive trains. in steerable drive axles, constant-velocity joints are the only way how driving power can be transmitted to the driving wheels in a conventional drive train with a combustion engine. thorough description of used types, their design and calculation can be found in [1]. brief overview of joint shaft is covered in [2]. great progress can be seen recently in the area of creation of virtual prototypes where the product designed is replaced with a computer simulation model. the virtual prototype tries to verify the in-service behavior of the real product without having to manufacture it. the virtual prototype is created using mathematic modeling methods which cover stress-strain and dynamic analyses, heat transmission, flow dynamics, acoustics, and a number of other physical processes. each mathematic model, however, is based on simplifying hypotheses which only approximate, to a greater or lesser extent, the actual solution, and much of the input data for the mathematic model is obtained through experiments using simplified realistic models. the mathematic models thus reduce the required number of test prototypes manufactured, although they do not eliminate the need for them entirely. therefore production of realistic prototypes and testing equipment for testing new components is still important today and is covered in this article. the article describes the newly created test stand for testing of joint shafts in the laboratories of the department of automotive, combustion engine and railway engineering. 2. test stand concept in order to use the test stand to simulate the actual behavior of drive shafts in a vehicle as accurately as possible, the stand must imitate the operating conditions as much as possible. in addition, it must include a number of sensors for automation, diagnostics and evaluation of the test. the stand should serve for tests of joint shafts with universal joints as well as shafts with constant velocity joints. as the majority of passenger vehicles are designed with transverse power unit and front axle drive where the use of constant velocity joints is inevitable, the stand was set up and primarily tested for the tests of these shafts. the operating conditions are defined by the torque at specified speed (rpm) and the set bend angle. the joint shaft is loaded jiří pakosta, gabriela achtenová ctu in prague, faculty of mechanical engineering, department of automotive, combustion engine and railway engineering jiri.pakosta@fs.cvut.cz, gabriela.achtenova@fs.cvut.cz abstract the article focuses on description of design of the test stand for shafts with universal joints and constant velocity joints. the shafts can be loaded by torque at specified speed of rotation, while retaining the possibility of setting a variable angle between input and output. all shafts are instrumented with contactless signal transmission. in addition, ventilator simulates the cooling derived from the driving speed. key words: hooke's joint, cv-joint, test stand shrnutí článek popisuje zkušební stav pro měření kloubových hřídelů. hřídele mohou být zatěžovány točivým momentem při různých otáčkách a měnícím se úhlu zlomu. měřené hřídele jsou vybaveny snímaním teploty kloubů s telemetrickou soupravou přenosu signálu. klouby jsou chlazeny náporovým ventilátorem, který simuluje ochlazování kloubů při jízdě vozidla. klíčová slova: křížové klouby, homokinetické klouby, zkušební zařízení joint shaft test stand mailto:jiri.pakosta@fs.cvut.cz joint shaft test stand jiří pakosta, gabriela achtenová mecca 01 2017 page 12 with the driving or braking torque between the engine and the transmission gear and the wheel of the vehicle. the rotation speed of the joint shaft is directly proportional to the driving speed of the vehicle. the bend angle ranges between its minimum and maximum design value. the test stand can be designed as an open or closed test stand. a closed test stand has the advantage consisting of lower energy demand of long-term tests, but its closed space design significantly complicates the tests of various lengths of jointed shafts and a broader range of the bend angles. therefore an open test stand has been selected as a test stand concept. 3. open test stand for joint shaft testing the open test stand consists of the input drive dynamometer which is controlled to constant torque, and the output dynamometer controlled to constant rotation speed. the scheme of the stand is depicted on figure 1. the input dynamometer is placed on the profile rail linear guide in longitudinal direction (in the direction of the dynamometer axis). this dynamometer is a two shafts asynchronous dynamometer. the eddie current output dynamometer is placed on linear guide system in transverse direction (perpendicular to the dynamometer axis). this linear guide system consists of a pair of rails and four ball-bearing carriages. the rails are attached with fasteners to the base plate of the testing site; the ball-bearing carriages are attached with screws to the dynamometer frame. positioning of the dynamometers is facilitated by the use of screw jacks controlling the mechanism of the lead screws. the main parameters of both dynamometers are listed in table 1. figure 1: scheme of the set-up for joint shaft experimental testing obrázek 1: schéma stavu pro zkoušky kloubových hřídelů the position of the shaft in the vertical axis direction in the output dynamometer can be easily set by insertion of calibrated washers between the supporting frame and the dynamometer itself. this resulted in a universal station with the following characteristics: • easy and quick adjustment to different lengths of the joint shafts • easy change of the bend angles of the shafts. if the axis of the movable dynamometer is set at the same height as the axis of the fixed dynamometer the subsequent setting of the bend angle only takes place in-plane, which makes the operation of the stand easier. table 1: dynamometer parametres tabulka 1: parametry dynamometrů parameter input dynamometer output dynamometer type asynchronous eddie current specification asd p200 2vd110/6 maximal rpm 7000 rpm 6000 rpm maximal torque [n.m] 1100 800 maximal power [kw] 200 220 the stand is designed such that the axes of the dynamometers are parallel. it is therefore possible to test joint shafts with universal joints with “z” and “v” bend configuration or, as the case may be, layout with the same space angles. if testing of the joint shaft layout with different joint angles is needed it is possible to deviate the axis of rotation of the output dynamometer to the space. such configuration, however, would substantially complicate the set-up of the bend angles during the tests. the bend axis is changed by the motion of the dynamometer in transversal axis. dependence of the magnitude of the travel on the value of the bend angle is determined by the trigonometric function of transversal displacement of output dynamometer divided the length of the joint shaft. when testing constant bend angles of a joint shaft, it is possible to fix the dynamometer frame to the rail by pneumatically released friction brake. in tests with the changing bend angle, it is possible to drive the screw jack with programming capability using an electric motor. in order to move the dynamometer during operation it was necessary to provide flexible lines of power supply, pressurized air, coolant and sensor conductors. for cooling of the joint shafts, the stand is additionally equipped with fans the cooling effect of which can be adjusted by the distance from the joint shaft or the value of the fan propeller rotation speed. when driving in a vehicle, each joint is blown at by a different air flow. the joint on the gearbox side is typically “shielded” by the shape of the gearbox while the joint on the wheel side is cooled by air with substantially higher velocity. the velocities of the air blowing at each joint have been obtained from the vehicle manufacturers. in laboratory testing, where the joint joint shaft test stand jiří pakosta, gabriela achtenová mecca 01 2017 page 13 shaft is attached with screws directly to the dynamometer flanges, the following solutions are possible: 1. using two fans of different parameters 2. using a fixture for shielding a part of the airflow for the “gearbox joint”, 3. correct positioning of the fan such that greater amount of air would flow to the “wheel” joint. we have opted for the third solution. the correct position of the cooling fan was determined by means of anemometric measurement of the velocity of the air blowing at the two joints. the final position was fixed in order to ensure repeatability of the measurement. 4. magnitudes measured the value of the required load torque is set on the input dynamometer. the load torque corresponds to the one half of the driving torque of the vehicle needed to propel the vehicle on given constant speed on straight flat road. as example we assume the speed of the vehicle equals 175 km/h; the needed torque on one driving wheel equals 248 n.m. the torque measured on the output dynamometer is lower due to the efficiency of the joint shaft. when testing constant-velocity joint shafts, the input and output rotation speed is the same. the necessary speed of rotation n is defined from the given vehicle speed v with help of the dynamic radius of the tire r. the test parameters obtained for the mentioned assumption are listed in table 2. ‐ 5 ‐  1000 60 (1) the devices suitable as joint temperature sensors are, due to their minimal dimensions, thermocouple thermometers which are placed in drill holes in the joint body. signal transmission from the rotating shaft is contactless. in addition, the measuring apparatus attached must be balanced in order to avoid additional load on the joint shaft measured. table 2: example of test parameters tabulka 2: ukázka zkušebních parametrů run-in torque for a bend angle of 7° 50 n.m time of run-in 0,5 h test load torque 248 n.m time of one measuremeng 0,57 h rpm of one half shaft 1441 rpm tested bend angles 7°, 8°, 9°a 10° figure 2: open test stand for testing of joint shafts obrázek 2: otevřený zkušební stav pro zkoušky kloubových hřídelů joint shaft test stand jiří pakosta, gabriela achtenová mecca 01 2017 page 14 various measurements can be performed in the test stand, from functional tests up to lifespan measurements. in the present case, we measured dependence of the joint temperature on the changing bend angle. for one torque and speed level we measured the temperature dependence on the bend angle in most of the operating range of the joint shaft. the joints were cooled down to the original temperature between the individual measurements. the time of the measurement is determined as the necessary time needed to drive with a given speed v the distance of 100 km. for the speed of 175 km/h the measurement time equals 34,2 min. a sample of the temperatures measured during the test defined in table 2 is depicted on figure 3. 5. conclusion the correct design of the stand with mounting of dynamometers on linear sliding system was affirmed as fully functional by a test of different joint shafts focusing on the measurement of the increase of temperature of the joints depending on the changing bend angle. the test stand can be further equipped with the rotary encoder to obtain the value of non-uniform rotation of the joint shafts. as next is investigated the possibility of precise torque measurement to be capable to measure the efficiency of the joint shafts. this measurement with the nowadays equipment is not possible. acknowledgement the authors would like to thank škoda auto, a.s. for provision of joint shafts, and for lending the unique system for measurement of temperatures of rotating shafts. this research has been realized using the support of the ministry of education, youth and sports program npu i (lo), project # lo1311 development of vehicle centre of sustainable mobility. both supports are gratefully acknowledged. references [1] graf can seherr_thoss h. ch.: gelenke und gelenkwellen. springer verlag. 2002. isbn 3-540-41759-1. [2] achtenová g., klír v.: převodná ústrojí motorových vozidel. kloubové hřídele. ctn – nakladatelství čvut. 2012. isbn 978-80-01-05129-0 figure 3: dependence of the temperature of one selected cv joint of the automotive joint shaft on the bending angle. obrázek 3: závislost nárůstu teploty na úhlu zlomu u zkoušeného kloubového hřídele ole_link26 ole_link27 ole_link28 _ref312143099 _goback result_box _ref497901876 result_box2 result_box3 result_box4 result_box5 result_box6 result_box7 result_box8 result_box9 result_box10 result_box11 result_box12 result_box13 _ref498511156 _ref499718432 composite absorber in collision simulations of a bus vít sháněl, miroslav španiel mecca 01 2017 page 1 10.1515/mecdc-2017-0001 composite absorber in collision simulations of a bus vít sháněl, miroslav španiel 1. introduction mass reduction is one of the frequently-mentioned requirements for both current and future vehicles. substitution of various previously steel or alloy parts with composite ones is a commonly accepted approach to this problem. this article presents a numerical study of a specific kind of impact energy absorber made from composite parts. it is based on the experimentally determined response of a single energy absorbing component. the response of the complete absorber, or the vehicle-absorber assembly, has been determined numerically. the purpose of this task was to verify the use of a thin bundle of wound composite tubes to absorb impact energy. the initial task was a series of experimental impact tests on individual tubes and small bunches of tubes in order to determine their response [3]. we have tested several layup options to find the layup that is characterized by stable crushing, a small peak force at the beginning, and a high energy absorption rate. subsequently, we formulated a computational model at the level of the tube with a more complex material model including a description of the damage to the composite [2]. using the abaqus software, we were unable to create a tube model with responses consistent with the experiments. however, such a complicated model at the tube model level would not be applicable to any collision simulation with vehicles containing the absorber (which would consist of a significant number of these composite tubes). for this reason, a simplified tube model as described below was created. this model describes the crushing of the composite tube in a way that is sufficiently accurate and corresponds with the experimentally observed behavior. this tube model is adapted to simulate vehicle collisions containing several tens of composite tubes. vít sháněl faculty of mechanical engineering, czech technical university in prague, technická 4, prague, +420 224 35 2519, vit.shanel@fs.cvut.cz miroslav španiel faculty of mechanical engineering, czech technical university in prague, technická 4, prague, +420 224 35 2561, miroslav.spaniel@fs.cvut.cz abstract this paper details the numerical modeling of composite absorbers and an assessment of the influence of such deformation elements on a bus during frontal collision with a car. the absorber itself is designed as an assembly of thin-walled composite wound tubes oriented in the vehicle direction of travel. during the impact the tubes are crushed, causing energy absorption. crash simulations were performed at various speeds using differing scenarios with the deformational member as well as without it. comparative diagrams of force and velocity of the car and deformation of the bus structure were assessed. key words: absorber, crash, fem, simulation shrnutí článek se zabývá vývojem numerického modelu kompozitního absorbéru a posouzením vlivu celého deformačního členu autobusu při jeho čelním nárazu s osobním automobilem. absorbér je navržen jako soubor tenkostěnných vinutých kompozitových trubek orientovaných ve směru jízdy. v momentě nárazu nastane borcení těchto trubek a tím dojde k významné absorpci energie. byly provedeny simulace nárazu při různých rychlostech ve variantách při použití deformačního členu a bez něj. porovnáním průběhů sil, rychlostí a posuvů osobního automobilu a deformací konstrukce autobusu byla posouzena jeho funkce. klíčová slova: absorbér, náraz, mkp, simulace composite absorber in collision simulations of a bus composite absorber in collision simulations of a bus vít sháněl, miroslav španiel mecca 01 2017 page 2 the objective of the car-bus frontal impact simulation is to assess the impact absorber (i.e. deformational member) composed of composite tubes that serve as deformation elements of the respective member and absorb the kinetic energy. the simulation of this impact is highly complex and thus certain simplifications of the problem are vital. nevertheless, the situation still provides a solid functional rendition of the absorber during a frontal collision between a bus and a car. the crash simulation arrangement is shown in figure 1, where 1 is the car, 2 is the absorber, and 3 is the bus. the simulation was performed using abaqus/explicit. 2. crash situation the crash simulation is performed using three models of interacting bodies: the model of the bus, the model of the vehicle, and the model of the absorber. each model includes a certain degree of simplification compared to reality. the main simplification is an absolutely rigid car model with boundary conditions that prevent it from sliding and turning in other directions than its displacement perpendicular to the bus front. similarly, the properties and the deformation of the absorbers are enabled only in this direction – in figure 1 depicted as the x-direction. only the front half of the bus is used in the simulation. the car has an initial velocity and the bus was fixed at the end of its front half. for this impact simulation, a simplified model of a car was created – figure 1. the car is represented by an absolutely rigid block which is 1188 mm wide, 500 mm high and shaped just like the car bumper. this block is assigned a weight of 1444 kg. the front half of the standard bus model used for crash simulation in the pam-crash software was used. this model is based on shell elements with elastic-plastic behavior. 3. model of the deformation element deformation elements in the absorber are wound composite tubes which are located at the front of the bus. the tubes are made of carbon fiber and an epoxy matrix. mechanical properties (force-displacement diagram) of this composite tube during crushing were obtained from dynamic experiments on a drop tester. a simplification of the recorded behavior is shown in figure 2. the force-displacement behavior shows an apparent initial peak with the maximum force of 25 kn and the force response has a steady value of 20 kn during stable crushing. the behavior of this deformation element can be introduced into the fem model in abaqus using the connector element (connector type translator). using this feature, a forcedisplacement response can be prescribed – but only in a limited way. in order to obtain identical force-displacement response, it is necessary to use two connector elements with different behaviors and join them together. then we can figure 1: crash simulation arrangement. obrázek 1: uspořádání simulace nárazu. figure 2: diagram of the deformation element model and its force-displacement response. obrázek 2: schéma modelu a odezva deformačního elementu. composite absorber in collision simulations of a bus vít sháněl, miroslav španiel mecca 01 2017 page 3 achieve the same deformation element behavior as obtained from the experiments. the first connector element describes the initial peak of the force-deformation behavior, and the second connector displays stable crushing. parallel connection of both connectors (figure 2) ensures a model with the same forcedisplacement behavior as we obtained on a drop tester. the connector element describing the first peak has the following properties. the elastic response is deactivated and all behavior derives from plasticity with some damage. the plasticity limit (yield) is set to 5 kn and initiation of damage is also set at 5 kn. a second connector element simulating stable crushing is also without elastic response and exhibits only plastic behavior, which is set to 20 kn. 4. model of the absorber deformation elements described above are inserted into the deformational member – the absorber (figure 3), which is placed at the front of the bus. the absorber consists of four parts: 1 – front plate, 2 – deformation elements, 3 – rear plate, 4 – supporting structure. the front and back plates do not have a significant impact on absorber behavior – their function is to keep the deformation elements in place and cover them. the supporting structure at the back of the absorber is an intermediate stage between the deformation elements and the bus frame. its function is to ensure uniform transfer of the forces occurring during crushing of the deformation elements into the structure of the bus. the absorber used in the simulations has a width of 2280 mm, a height of 480 mm and a depth between 100 mm and 250 mm. the whole absorber is divided into three parts, two outer and one central part. the central part occupies half the width of the absorber and has a constant depth of 250 mm. the depth of the outer arrays of half the size of the central part varies linearly from 250 mm inside to 100 mm at the edge of the absorber. the absorber is composed of 45 deformable elements described above, which are uniformly distributed over its area. the proposed absorber is theoretically able to absorb an energy of approximately 200 kj, assuming maximum deformation of the deformation elements. this absorber is placed at the frontal bottom part of the bus where it absorbs a significant part of the energy resulting from a frontal impact with a car. 5. results six simulations of impact with different conditions were performed: using different initial car speeds, using the absorber, or omitting the absorber. we monitored the progress of displacement, velocity and acceleration of the car. the monitored variables on the bus were logarithmic deformation and reaction forces in the restrained half of the bus. progress of the car velocity after impact for all variants is shown in figure 9. for all variants velocity reduction is more significant in cases using the absorber. therefore, the impacting bodies achieve zero velocity earlier at all initial speeds than in situations where the absorber is not used. the second graph, figure 9, shows the progress of the reactionary forces in the half of the bus where the boundary condition is applied – these forces are transmitted in the half of the bus frame. the following four images show the distribution of the largest main logarithmic strain in the front of the bus from the bottom view after the impact. all images have the same range of deformations – from zero to two percent of the logarithmic deformation. the displayed situation is captured at the end of the impact – the car is no longer in contact with the bus. grey areas represent a logarithmic deformation greater than two percent. at higher initial velocities (30 and 40 km/h), buckling of the front structure of the bus is clear. the rigidity of this part is not sufficient and thus fails before transmitting the necessary force to support the absorber during its function. this is shown in figure 7 with the logarithmic strain for an impact with initial velocity of 40 km/h. in the case of the 20 km/h initial speed, we could see the loading design nodes responsible for transmitting forces generated by the absorber to the rest of the structure. at this initial speed there was no significant damage, and it was therefore omitted from the list. based on the results, it is evident that the front part of the bus is currently designed as a deformation zone and not as a rigid part of the structure intended to transfer and distribute forces arising from an impact to the rest of the structure. when comparing impact results with and without the absorber, the difference in energy absorption becomes very obvious. when the absorber is not installed on the bus structure (figures 4 and 6) all of the impact energy must be absorbed by the plastic deformation of the bus frame. there is significant deformation and lower rigidity of the front part of the structure as well as a notable bending of the bus structure causing a longer energy absorption time. figure 3: absorber and its parts (top view). obrázek 3: absorber a jeho části (pohled seshora). composite absorber in collision simulations of a bus vít sháněl, miroslav španiel mecca 01 2017 page 4 fi gu re 4 : l og ar ith m ic s tr ai n of th e bu s af te r c ar im pa ct w ith in iti al v el oc ity 3 0 km /h w ith ou t t he a bs or be r. o br áz ek 4 : l og ar itm ic ká d ef or m ac e ko ns tr uk ce a ut ob us u po n ár az u au te m ry ch lo st í 3 0 km /h b ez a bs or bé ru . fi gu re 5 : l og ar ith m ic s tr ai n of th e bu s af te r c ar im pa ct w ith in iti al v el oc ity 3 0 km /h w ith th e ab so rb er . o br áz ek 5 : l og ar itm ic ká d ef or m ac e ko ns tr uk ce a ut ob us u po n ár az u au te m ry ch lo st í 3 0 km /h s a bs or bé re m . fi gu re 6 : l og ar ith m ic s tr ai n of th e bu s af te r c ar im pa ct w ith in iti al v el oc ity 4 0 km /h w ith ou t t he a bs or be r. o br áz ek 6 : l og ar itm ic ká d ef or m ac e ko ns tr uk ce a ut ob us u po n ár az u au te m ry ch lo st í 4 0 km /h b ez a bs or bé ru . fi gu re 7 : l og ar ith m ic s tr ai n of th e bu s af te r c ar im pa ct w ith in iti al v el oc ity 4 0 km /h w ith th e ab so rb er . o br áz ek 7 : l og ar itm ic ká d ef or m ac e ko ns tr uk ce a ut ob us u po n ár az u au te m ry ch lo st í 4 0 km /h s a bs or bé re m . composite absorber in collision simulations of a bus vít sháněl, miroslav španiel mecca 01 2017 page 5 6. conclusion six simulations of a head-on collision between the bus and a car were performed, outlining a possible course of development of the given situation. the aim of the simulations was to assess the impact absorber installation on the front of the bus. this assessment was made by comparing the deformation and forces of the bus and velocity of the car. the simulations do not aim to cover every possible situation that might arise from the collision of a car and a bus. the special case of a direct collision using a simplified model of a car was selected in order to test the absorber effect during the collision. there is a clear positive role of the absorber as a deformation member. however, at higher velocities the rigidity of the front structure of the bus is insufficient. it is necessary to reinforce the front part of the bus structure for the real usage of the absorber on a bus. acknowledgements this study was supported by the grant project josef božek centre of competence of automotive industry (2012 – 2017), te01020020. references [1] abaqus 6.14 documentation. [2] bogomolov s., kulíšek v., španiel m., růžička m. (2011) fe simulation of composite structure, in: calculation of structures using fem, plzeň, pp. 25-32. isbn: 978-80-261-0059-1. [3] sháněl v., kulíšek v., růžička m. (2013) experimental testing of the composite energy absorber, in: advanced materials research, vol. 717, pp 320-324 figure 8: reaction force in the half of the bus over time. obrázek 8: graf závislosti reakční síly ve vetknutí autobusu na čase. figure 9: graph of the car velocity over time for all variants. obrázek 9: graf závislosti rychlosti automobilu na čase pro všechny varianty. ole_link26 ole_link27 ole_link28 _ref312143099 _goback result_box _ref497901876 result_box2 result_box3 result_box4 result_box5 result_box6 result_box7 result_box8 result_box9 result_box10 result_box11 result_box12 result_box13 _ref498511156 _ref499718432 dynamic testing of buses and their components petr záruba, jakub jelínek, michal kalinský mecca 01 2017 page 6 10.1515/mecdc-2017-0002 dynamic testing of buses and their components petr záruba, jakub jelínek, michal kalinský petr záruba tüv süd czech, novodvorska 994/138, 142 21, prague, czech republic, +420 607 068 202, petr.zaruba@tuv-sud.cz jakub jelínek, michal kalinský tüv süd czech, novodvorska 994/138, 142 21, prague, czech republic, jakub.jelinek@tuv-sud.cz, michal.kalinsky@tuv-sud.cz abstract the article gives an overview of a virtual simulation method under ece regulation no. r66 – bus rollover. the first part of the article introduces the process of virtual simulations in terms of homologation. the conclusion is focused on the correlation of physical tests with virtual simulations. key words: ece no. 66, rollover test, fem analysis, crash, physical testing, validation, automotive, tüv süd czech shrnutí článek se věnuje problematice virtuálních simulací dle předpisu ece no. r66 – převrácení autobusů. v jednotlivých kapitolách je rozebrán postup virtuálních simulací z pohledu metodiky a homologačního procesu. závěr je věnován korelaci fyzických testů s virtuálními simulacemi. klíčová slova: ehk 66, pevnost karoserie, převrácení autobusu, mkp analýza, dynamické děje, fyzické testování, validace, automotive, tüv süd czech dynamic testing of buses and their components 1. introduction every year sees an increase in the requirements for passive vehicle safety, and not just in the personal vehicles category, but also for public transport vehicles. tüv süd czech has been certifying m2 and m3 category buses (single deck rigid or articulated vehicles) according to european regulation ece r66 – strength of the chassis large bus, for several years. regulation ece r66 is one of several homologation regulations which can be certified by virtual simulation. virtual simulations are very much required with this regulation, because physical tests take a long time to perform and do not allow many iterations of conceptual design within a very short timeframe. 2. regulation ece r66 regulation ece r66 entered into force in 1989. in 2005, a series of changes included more detailed approval procedures using virtual simulations. regulation r66 requires a manufacturer to construct the chassis of vehicles that will carry more than 22 passengers including driver strong enough so that a survival space clear of any penetration by internal primary structure is preserved when it falls from a platform. this survival space for passengers and driver is defined by the floor structure, the inner cover of the main load structure and by definition of the sr point on the seat, see figure 2. the test is performed with only half the mass of all passengers, which is 34 kg per passenger, located 100mm before and above the r point of the seat. this stricter regulation with added mass is described in r66.01 only for newly certified vehicles with effect from november 2010. in november 2017, however, a new version of regulation r66.02 was introduced that extends compliance with this regulation to smaller buses (16+ passengers). 3. certification process using virtual simulation the process of certification by virtual simulation requires the time consuming and sophisticated preparation of a numerical model. this method depends on having the full set of data mailto:petr.zaruba@tuv-sud.cz mailto:jakub.jelinek@tuv-sud.cz mailto:michal.kalinsky@tuv-sud.cz dynamic testing of buses and their components petr záruba, jakub jelínek, michal kalinský mecca 01 2017 page 7 from manufacturer, such as 3d cad data, real mass of bus components, exact position of the center of gravity, and material characteristics. from the certification point of view the manufacturer may place on the market several variants of the same vehicle type for different numbers of passengers. for this type of global approval, the worst-case configuration for the rollover strength test is considered for the calculation as it covers all other less severe designs. this is the construction with theoretically the worst deformation. the basic structural elements of bus construction are steel beams on the side of the bus and it is, in particular, the number of these beams that determines the stiffness of bus during rollover. from experience the worst variants are those that have a lower number of side beams and the highest center of gravity. when the cog point is high on the z axis, the impact energy and angular speed is also increased and causes bigger deformations. to determine the worst variants, a method based on the calculation of the impact energy and its relationship to specific columns with the inclusion of the cross-sectional characteristic is used. the variant with the highest energy at the column is deemed the worst case. with the updated version of the regulation, the standard now also applies to buses with low transport capacity. these vehicles are conceptually very different because they use self-supporting or additionally reinforced van structures, see figure 3. for these vehicle types it is very difficult to use the simple principle of relative strain energy on a pillar adopted for conventional buses. the choice of the most critical variant is determined primarily by the position of the center of gravity, the transport capacity and the equipment of the bus – its operating mass. the chassis of these bus types (vans) do not perform at their best during the r66 test. the main objective of bus manufacturers is to maximize transporting capacity and, with a typical number of 30 passengers, the vehicle mass of a tested vehicle is increased by more than one ton of additional mass. this is in some cases almost a quarter of the mass of the structure, which is located above the original center of gravity. compared to large buses, it is much more difficult to feasibly design this type of vehicle from the manufacturer’s perspective given the complication of adding additional beams into the existing structure. the manufacturer is required to submit the necessary documentation for this vehicle variant. then the certification process takes place according to the internal methodology. if a manufacturer cannot provide the testing laboratory with approved material data sheets, the window beams have to be physically tested and a material model developed. several tests have to be carried out and these are quasi-static tensile tests, bending tests and dynamic drop tests. dynamic drop tests are primarily performed to determine the response of a material during impact. the mechanical properties of the material vary with the load speed (the strain-rate effect). this figure 1: fem model of bus obrázek 1: mkp model autobusu figure 2: survival space template obrázek 2: vymezení prostoru pro přežití figure 3: van type of vehicle obrázek 3: autobus založený na podvozku dodávky dynamic testing of buses and their components petr záruba, jakub jelínek, michal kalinský mecca 01 2017 page 8 drop test is performed on the characteristic piece of window pillar that the impactor strikes. the impact energy during the test corresponds to the energy in the real test of the entire bus. in the pam-crash simulation software, this test is then replicated and based on the deformation evaluation using the video sequence, the numerical model is validated for the drop test. in the case of small buses, the drop test is applied for more complex parts of the structure. these can, for example, be stamped parts, parts made by hydroforming etc. an example of the drop test for a bus a-pillar of is shown in figure 5. it should be noted that the evaluation and subsequent tuning of the properties of a material model is more complex because deformations occur in several directions. in this case the deformations are measured using 2d tracking points, and plastic deformation is measured after impact by photogrammetry. for validation it is necessary examine the pillar behavior using video footage from a highspeed camera. the creation of a numerical bus model is very time-consuming. it takes one full-time employee about four weeks to prepare a finite element (fe) model of an 18m long bus, and another two weeks is spent connecting and setting up the model. in terms of computational time saving, a 3d cad model that includes volume geometries is converted to mid-surface and the thickness is assigned to 2d elements only computationally. for computation purposes, 2d shell elements are used with five integration points using the bellytschko-tsay uniform reduced integration method. for steel materials, material model type 103 is used – elastic plastic iterative hill with krupkovsky law coefficients. a 3d model also contains a number of radii and holes unnecessary for r66 testing. holes with diameter smaller than 1/5 of the smallest edge are removed and replaced by a mesh (elements), as are radii smaller than 1/5 of the smallest edge. welded joints are largely represented by coincident mesh nodes. this representation method is sufficient and creates smaller strain concentrators than other types of entities. in cases where the direct connection of mesh nodes cannot be used, the welds represent the entity characteristic of pam-crash, plink. for predictable results on all models it is necessary follow the mesh quality and element sizes of the validation model. on parts belonging to the main structure, such as pillars, we use an element size of 8mm, which offers an acceptable combination of size (in terms of computation time) and accuracy. the internal criterion for minimum element length is 5mm for a model consisting of under 1 million elements. it is necessary to keep as many quad elements as possible in order to reduce stress concentrators, which are produced by inconsistent mesh with bad quality elements. when the model is prepared, initial conditions and non-structural masses are added together with the mass balance with respect figure 4: drop test physical and virtual representation obrázek 4: pádová zkouška fyzická a její virtuální reprezentace figure 5: drop test of an a-pillar obrázek 5: pádová zkouška a sloupku figure 6: pillar fem model preparations obrázek 6: příprava mkp modelu sloupku dynamic testing of buses and their components petr záruba, jakub jelínek, michal kalinský mecca 01 2017 page 9 to the center of gravity. the position of the center of gravity in the y and z direction is very important for the simulation. it determines the unstable position when the platform is tilted. from the center of gravity values, this unstable position can be calculated and then the impact angular velocity determined. the accuracy of results is given by the impact kinetic energy of the model calculated from the moment of inertia and angular velocity. the evaluation of the r66 test is rather straightforward. if any part of the internal structure penetrates the survival space, the test is unsuccessful and structural changes are required. 4. correlation process to evaluate the results of the numerical simulation, the validation of partial results is necessary. these validations are performed as the numerical model is being created. individual components are tested both quasi-statically and dynamically as indicated beforehand. one of the purposes of validation is determination of a suitable method for creating a mesh when connecting beams with different cross sections. the purpose, for example, of t-joint weld connections is to find an adequate simplified weld representation. these connections are difficult for the numerical model due to the problematic joining of coincident nodes. the most obvious variation of homologation simulation results is the physical examination of the bus segment. the segment must represent the main structure of the bus chassis, where the r66 test is performed. the most important result is the measurement of the maximum as well as plastic deformation, together with the determination of plastic joints and cracks. the deformation of an entire segment is measured with potentiometers located at the important points of the construction. from these measured points the deformation is evaluated. tests are also captured with high-speed cameras, from which it is possible to determine the behavior of the test sample and deformations are evaluated using a photogrammetric method (2d). accelerometers and other devices can also be used for validation, but this is optional and not every project definition requires such a detailed approach. one of the specialized measurements is, for example, strain gauges placed on washers for the measurement of axial forces in the bolts. these washers are calibrated for axial loads on the tensile test. 5. simulation test parameters and measurement uncertainties physical and virtual test results may be a little different due to model uncertainties. if we include all the model uncertainties of the virtual process and the physical validation, we obtain a total uncertainty in the region of ~ 20%. some uncertainties are caused due mistakes in physical measurement and some come from numerical errors during computation. for example, a slight uncertainty is derived from running the computation on separate processors (parallelization) where each processor has an uncertainty in rounding. so, if computation is split between several processors, it can happen that a slightly different result is obtained with the same simulation. from experience, results from models prepared and validated in pam-crash software are slightly more conservative and show worse results when compared to the physical tests. in the case of homologation calculations, we are on the conservative, i.e. safe side. the calculation results are very dependent on several basic parameters, such as mass, position of the center of gravity, vehicle moment of inertia and impact velocity. there are also many other numerical parameters. among these parameters are, in particular, the coefficient of friction between impact area and tested model. the coefficient of friction must be measured for a specific impact area and given in the technical protocol. figure 9 shows differences between friction coefficients. the y axis indicates the distance of the b pillar from the survival space template. with the improved friction coefficient of real concrete and steel (red line) there is greater deformation – it comes closer figure 7: bus rollover obrázek 7: převrácení autobusu figure 8: t joint with variable pillar height and difference between the plink joint and connecting of adjacent nodes obrázek 8: t spoj s proměnnou výškou profile a rozdíl mezi spojením typu plink a napojení sousedních uzlů dynamic testing of buses and their components petr záruba, jakub jelínek, michal kalinský mecca 01 2017 page 10 to the survival space template. also, the friction coefficient changes the behavior of the whole rollover. boundary conditions are set according to the ece r66 regulation. this means that applied to the model is gravitation and initial angular velocity. the simulation doesn’t run through the whole rollover, but computation starts a few centimeters before first contact with the ground. initial conditions are calculated from the unstable position. 6. conclusion based on correlations between the physical tests and virtual simulations, the czech accreditation institute (čia) acknowledged the internal methodology and subsequently accredited the department of virtual simulations of tüv süd czech for the virtual testing of bus constructions according to r66. tüv süd czech performs about 15 virtual and 5 physical tests per year. there also remains great interest in the testing of entire buses. these tests have moved from pure homologation tests more to validation fe analysis, and are supporting the manufacturer’s r&d department. the requirements for measurement equipment and post processing have increased, due to increased test complexity. in conclusion, however, it is important to note that progress in virtual testing has increased, but it still cannot completely replace physical testing. the best option for the testing departments, and also for the customer, is a suitable combination of both approaches. final homologation can be achieved faster, more effectively and with lower cost. the bus design can be optimized and adapted to load conditions while maintaining all other operating parameters. acknowledgements presented results and procedures had been done with financial support of technology agency of czech republic in framework of project of jozef božek competence centre, work package 23 (wp23) respectively. results of wp23 had been obtained in tight collaboration with faculty of mechanical engineering at čvut, department of automotive, combustion engine and railway engineering and department of mechanics, biomechanics and mechatronics. references [1] černý, ladislav. bezpečnější autobusy. auto profi. 2017, 25(červen), 1. [2] trubač, jiří. analýza komplexnosti modelu na vyhodnocení pevnostní konstrukce autobusů. praha, 2013. bakalářská. čvut. [3] senthil kumar, d. rollover analysis of bus body structure as per ais 031/ece r66. dostupné z: http://www. altairatc.com/india/previous-events/2012/papers-2012/ rnl-a-07_rollover_analysis_of_bus_body_structure_ volvo.pdf [4] dvořák, františek. patrové autobusy by se měly zakázat, říkají odborníci na bezpečnost [online]. dostupné z: https://auto.idnes.cz/patrove-autobusy-by-se-melyzakazat-rikaji-odbornici-na-bezpecnost-1fy-/automoto. aspx?c=a110718_135127_automoto_fdv figure 9: distance of survival space template and b pillar in relation to friction coefficient obrázek 9: graf vzdálenosti prostoru pro přežití a b sloupku v závisloti na třecím koeficientu figure 10: illustration of physical test validation obrázek 10: korelace fyzického testu a virtuální simulace ole_link26 ole_link27 ole_link28 _ref312143099 _goback result_box _ref497901876 result_box2 result_box3 result_box4 result_box5 result_box6 result_box7 result_box8 result_box9 result_box10 result_box11 result_box12 result_box13 _ref498511156 _ref499718432 trends in the development of hybrid drives josef morkus mecca 02 2016 page 01 10.1515/mecdc-2016-0006 trends in the development of hybrid drives josef morkus 1. introduction a combination of combustion engine and electric motor, i.e. a hybrid drive, is one of the ways of reducing the fuel consumption and emissions of motor vehicles. their development has arisen largely due the pressure from emission regulations. although the history of hybrids dates back to the late 19th century, the first modern mass-produced hybrid vehicle, the toyota prius, was introduced as late as in1997 year. at present hybrid vehicles or hybridized models of current production vehicles are appearing in the production programs of most of the major vehicle manufacturers. numerous variations of hybrid drives have been created, which today form a smooth transition between conventional cars with combustion engines, and battery-electric vehicles. sales of hybrid car versions currently represent several percent of total car sales (excluding japan, where it is over 20%), but it has a strong upward trend. in the czech republic only 735 hybrids (excluding microhybrids) were sold in 2015 [1], but this is an increase of about 220% on hybrid sales in 2014. it is expected that after 2020, with an expected tightening of emission regulations, hybrid vehicles will constitute a substantial proportion of cars sold. 2. hybrid types technical development tends to plug-in hybrids, i.e. vehicles rechargeable from a mains socket, which allows a range on one battery charge of several tens of kilometers purely on electricity. this is sufficient for the normal daily mileage of most drivers. the overall range of plug-in hybrids is the same as conventional vehicles. josef morkus ctu in prague, faculty of mechanical engineering, department of automotive, combustion engine and railway engineering e-mail: josef.morkus@fs.cvut.cz shrnutí hybridizace pohonů motorových vozidel je jedním z hlavních trendů v posledních letech. tento článek se zabývá růstem prodejů vozidel s hybridním pohonem a směry jejich technického vývoje, novým řešením převodových mechanismů, kapacitou a umístěním baterií a pokročilou formou řízení hybridního pohonu. specifické trendy se týkají dobíjení elektrických nebo hybridních autobusů na autobusových zastávkách a ovlivnění vývoje soutěžních a závodních vozidel předpisy. hybridní pohony také se objevují v užitkových vozidlech, off-road aplikacích, člunech atd. klíčová slova: hybridní pohony, electromotor, baterie, podpora spalovacího motoru, dojezd, směr vývoje abstract the hybridization of motor vehicle drives is one of the major trends of recent years. this paper deals with the growth in sales of vehicles with hybrid propulsion, the directions of their technological development, new solutions for transmission systems, the capacity and location of the batteries and more sophisticated forms of hybrid drive control. specific trends include the charging of electric or hybrid buses at bus stops and the regulation-influenced development of competitive and racing vehicles. hybrid drives also appear in commercial vehicles, off-road applications, boats etc. keywords: hybrid drives, electric motor, battery, boost, range, trend of the development trends in the development of hybrid drives figure 1: daily mileage of vehicles in germany [3] obrázek 1: denní počet kilometrů vozidel v německu [3] trends in the development of hybrid drives josef morkus mecca 02 2016 page 02 because driving on electricity is significantly cheaper than driving on petrol or diesel, plug-in hybrids use bigger and therefore heavier and more expensive batteries, which increase the range on electricity, but also the price of the vehicle. therefore, if they are not subsidized, simpler version hybrids with smaller and cheaper batteries will prevail in sales. 3. batteries the fundamental problem of all electric vehicles, i.e. hybrids and battery vehicles, is batteries. despite the considerable funds invested into their development and undeniable progress, batteries are still heavy, large and expensive. one kg of petrol or diesel contains approx. 20 to 40 times more energy (with respect to transfer efficiency) than the same mass of an advanced lithium battery, and this proportion increases with the desired range [4]. the result is a small range for battery-vehicles, currently varying depending on many factors and driving style at around 150 km. another issue is where to place large batteries in the vehicle. the trend is to place them under the rear seats or into the floor for suv cars so as not to restrict the usable space in the car. 4.electric motors and transmissions a noticeable trend is the integration of electric motors, most often synchronous permanent magnet motor, into the transmission system. in doing so, we can observe two basic directions: first, the electric motor becomes a part of the gearbox design and it is situated at the front of the step part of the gearbox. this leads to the possibility of the electric motor working in its optimal range and allows electric driving and electric braking (energy recovery) with disconnected combustion engine. sales of hybrids in milions cars share of hybrids on total sales of passanger cars figure 2: sale of hybrid vehicles worldwide [2] obrázek 2: prodej hybridních vozidel na celém světě [2] figure 3: bulky and heavy batteries of full and plug-in hybrids were often placed under the car trunk instead of the spare wheel. together with decreasing the volume of batteries, the trend is to place them under the rear seats (e.g. toyota yaris hybrid) or in the central tunnel (e.g. volvo xc 90 hybrid). the popularity of suvs leads to the possibility of placing the battery in a double floor (e.g. mitsubishi outlander). obrázek 3: objemné a těžké baterie full hybridů a plug-in hybridů byly často umístěny pod kufrem auta namísto rezervního kola. spolu se snížením objemu baterií je trend umístit je pod zadními sedadly (např. toyota yaris hybrid) nebo v centrálním tunelu (např volvo xc 90 hybrid). popularita suv vede k možnosti umístění baterie do dvojité podlahy (např. mitsubishi outlander). trends in the development of hybrid drives josef morkus mecca 02 2016 page 03 the second direction fully replaces a step part of gearbox by an electric motor, uses its characteristics in a wider range and significantly simplifies the transmission. it often uses two electric machines and/or the possibility of switching between serial and parallel connection of the hybrid drive. another significant trend is the addition of an electric motor to the non-driven vehicle axle. adding the electric motor to the rear axle of a conventional vehicle with front-wheel drive simultaneously creates a hybrid and 4x4 vehicle without a complicated transmission. in recent years a combination of hybrid drive unit on one axle and another electric motor on the second axle is more often used, which leads to improved dynamic properties and allows a higher degree of energy recovery during braking (e.g. fig. 7). a similar solution is popular with the sports and racing cars, where ice (sometimes in combination with an electric motor) is usually positioned on the rear axle and another electric motor drives the front axle (e.g. fig. 8). 5. e-boost an alternatively method for using electrical energy to support the engine is the electric drive of a compressor. in this case the electric motor is not connected to the axle, but when support is requested, the motor via the compressor begins to supercharge the engine and thus enhances its power. a substantial advantage of this solution is that it can operate with a low voltage of 48 v and does not require an expensive high voltage battery. on the other hand, it cannot regenerate energy when braking. according to some authors, this solution is not regarded as “real” hybrid. figure 4: six speed automatic gearbox of a truck mercedes-benz atego bluetec hybrid with built-in electric motor obrázek 4: šesti stupňová automatická převodovka nákladního automobilu mercedes-benz atego bluetec hybrid s vestavěným elektromotorem figure 6: hybrid4 models peugeot / citroen uses an electric motor connected to the rear axle via a gear and a clutch. vehicles with this drive may drive in pure electric mode, hybrid mode or as a 4x4 obrázek 6: modely peugeot / citroen hybrid4 používají elektrický motor připojený k zadní nápravě přes převod a spojku. vozidla s tímto pohonem mohou jet v čistě elektrickém režimu, hybridním režimu nebo jako 4x4 figure 7: mitsubishi outlander has a battery built into the floor and electric motors at the front and rear axles. it can drive in pure electric mode on battery power or in so-called serial hybrid mode, where the electric power is supplied by a generator driven by ice or in a parallel hybrid mode, in which ice is mechanically connected to the axle and it is supported by electric motors. obrázek 7: mitsubishi outlander má baterii zabudovanou do podlahy a elektromotory u přední a zadní nápravy. může jet v čistě elektrickém režimu na energii z baterií nebo v tzv sériovém hybridního módu, kdy je elektrická energie dodávána generátorem poháněným spalovacím motorem nebo v paralelním hybridním módu, ve kterém je spalovací motor mechanicky spojen s nápravou a je podporován elektromotory. figure 5: toyota hybrid synergy drive uses a planetary power divider, has no clutch or gear shifting members and continuously varies the gear ratio as a cvt obrázek 5: toyota hybrid synergy drive využívá planetový dělič výkonu, nemá žádné spojky ani řadicí členy a plynule mění převodový poměr jako cvt trends in the development of hybrid drives josef morkus mecca 02 2016 page 04 another version of this solution is connection of the electric motor to a turbocharger. in this case the electric motor can accelerate a turbocharger and thus shorten the engine response (turboeffect) to accelerator action. a turbocharger may also be braked by the electric motor to draw energy from the exhaust gases and to transform it into electric energy. 6. competition and racing cars in the highest categories of competition and racing vehicles a hybrid drive is directly required by regulations. top vehicles for endurance races, such as the le mans 24 hour, have a combustion engine on the rear axle and electric motors on the front axle. in line with regulations introduced in 2014, f1 cars have not only turbocharged six-cylinder engines, but also two energy recovery systems: the first from kinetic energy during braking and the second from exhaust gases energy. drive units are equipped with two electric motors: mgu-k connected to the crankshaft of the engine and mgu-h connected with the turbocharger. in comparison with previous regulations the tenfold increase is permitted in the recovered energy per lap, which leads to significantly higher demands on energy management strategy during a lap. figure 8: new honda nsx acura has three electric motors: one in 9° dual-clutch transmission on the rear axle and two on the front axle. the battery is behind the seats and in the central tunnel. porsche 918 spyder has a v8 engine (4), which drives the rear axle through a dual clutch gearbox (5) with electric motor (6). a second electric motor (2) is on the front axle, the battery (3)behind seats, (1) and (7) are power electronics. obrázek 8: nová honda nsx acura má tři elektrické motory: jeden v 9 ° dvojspojkové převodovce u zadní nápravy a dva na přední nápravě. baterie je za sedadly a v centrálním tunelu. porsche 918 spyder má motor v8 (4), který pohání zadní nápravu přes dvouspojkovou převodovku (5) s elektromotorem (6). druhý elektromotor (2) je na přední nápravě, baterie (3) za sedadly, (1) a (7) je výkonová elektronika figure 10: le mans specials (2015) obrázek 10:speciály pro le mans (2015) figure 9: electric compressor valeo obrázek 9: elektrický kompresor valeo trends in the development of hybrid drives josef morkus mecca 02 2016 page 05 7. urban buses another category of vehicles where hybrid drive often occurs is urban buses. volvo already produces urban buses with only a hybrid version. a number of transport companies are trying to introduce electrobuses, but the basic problem is the discrepancy between bus range and its passenger capacity: when sufficient electric batteries are placed in the bus for the required daily range, there is a problem with exceeding axle load and it is necessary to limit the number of passengers. chinese 12 m electrobus byd has a battery range of up to 250 km, but a capacity of only 54 passengers [5]. a solution is sought in charging batteries at bus stops. the problem, however, is expensive infrastructure with required charging currents up to 1000 a. therefore, many cities choose rather hybrids or a combination of both technologies. 8.commercial vehicles implementation of hybrid drives into commercial vehicles began later, since around 2010, and the number of applications is steadily increasing. hybrid drives are most often used in vehicles for goods distribution in cities. for this vehicles is typically used a parallel hybrid with electric motor between the engine and the gearbox; batteries are placed on the outer side of the vehicle frame. figure 11: f1 energy recovery system obrázek 11: f1 systém pro rekuperaci energie figure 12: city bus volvo 7900 electric hybrid is a combination of an electric bus with a hybrid bus. in the city it can run in pure electric mode and with the recharging of batteries at selected stops; outside the town center it runs in a hybrid mode, whereby the diesel engine is off at the stops, and bus leaves the stop on electric drive only. the diesel engine then starts at a speed of 20 km/h. obrázek 12: autobus volvo 7900 hybrid electric je kombinací elektrického autobusu s hybridním autobusem. ve centru města může jet v čistě elektrickém režimu s dobíjením baterií na vybraných zastávkách; mimo centrum jede v hybridním režimu, přičemž vznětový motor je na zastávkách vypnutý a autobus odjíždí ze zastávky pouze na elektrický pohon. vznětový motor se pak startuje při rychlosti 20 km / h. figure 13: mitsubishi fuso hybrid is produced by a company which is a part of the daimler-benz group. this car is manufactured in both japan and spain. obrázek 13: mitsubishi fuso hybrid vyrábí společnost, která je součástí daimler-benz group. tento vůz je vyráběn jak v japonsku tak i ve španělsku. trends in the development of hybrid drives josef morkus mecca 02 2016 page 06 9. off-road applications a new trend is the use of hybrid drives for off-road applications, for example earthmoving machinery. these solutions may in some cases have significantly higher efficiency (lower fuel consumption) in comparison with the use of a hybrid drive for vehicles. an example is the use of electric propulsion for the rotation of an excavator upper part instead of the usual hydraulic actuator. 10. hybrid drive control a special issue is control software for hybrid or purely electric drives. the purpose is to optimize the course of driving and power split between the combustion engine and the electric motor so as to obtain the lowest energy consumption and at the same time keep battery charge within required limits. therefore, information from gps and clouds is increasingly used for predictive and adaptive control. electronics “see” further than the driver (the socalled electronic horizon). actual driving control is then modified based on data from various sensors (radar, ultrasound, cameras) that monitors the immediate vicinity. however, detailed control procedures are the know-how of manufacturers and are generally not published. 11. conclusion it cannot be said there is a universal solution that could replace internal combustion engines. it can be expected that in the coming years and decades there will be greater diversification of different types of drives depending on the purpose of use of the vehicle, and hybrid drives will also have its role to play. acknowledgement this research has been realized using the support of eu regional development fund in op r&d for innovations (op vavpi) and using the support of eu fp 7 project no. 608756, integration and management of performance and road efficiency of electric vehicle electronics. this support is gratefully acknowledged. references [1] bureš d., český trh v roce 2015: zájem o alternativní paliva roste. jakým modelům se dařilo? auto.cz 19. 1. 2016 [2] morkus j., lectures “hybridní pohony”, fs čvut 2016. data from eevc congress, brusel 2014 [3] mitsubishi motors: elektrické vozy a jejich využití v rámci inteligentních sítí. konference japatech, praha 2011 [4] macek j., general problems of hybrid vehicle design [5] hinčica l., elektrobus byd ebus na zkouškách v dp ostrava. československý dopravák 3/2014 [6] steinbauer p., macek j., morkus j., denk p. at al., „dynamic optimization of the e-vehicle route profile,“ sae technical paper 2016-01-0156, 2016, doi:10.4271/2016-01-0156 figure 14: excavator scoops up earth and turns the tower to the place where the earth is deposited. the drive of rotation is electrical, when rotation is braking the energy is stored in a super-capacitor and subsequently is used for rotation in the opposite direction. obrázek 14: rýpadlo nabere zeminu a otáčí věž na místo, kde zeminu vysype. pohon otáčení je elektrický, při brzdění pohybu je energie uložena v superkondenzátoru a následně je použíta pro otáčení v opačném směru. sl op e [m ] lenght of route sp ee d [m /s ] 35 30 25 20 15 10 5 0 20 10 0 -10 -20 -30 -40 -50 0 1000 2000 3000 4000 5000 6000 7000 8000 figure 15: a sample of the optimum driving speed predictive calculation. the route is divided into sections; in each of them is a constant allowable speed (in red) and road slope (green). blue is the course of optimal driving speed while minimizing energy consumption and with compliance with the required travel time [6]. obrázek 15: příklad prediktivního výpočtu optimální rychlosti jízdy. trasa je rozdělena do sekcí; v každé z nich je konstantní povolená rychlost (červeně) a konstantní sklon silnice (zelená). modrá je průběh optimální rychlosti jízdy s minimalizovanou spotřebou energie a s dodržením požadovaného času jízdy [6]. mecca_20-02_web new advanced methods in side crash testing jakub jelínek, milan r!"i#ka, al"b$ta kafková mecca 02 2020 page 1 10.14311/mecdc.2020.02.01 new advanced methods in side crash testing jakub jelínek, milan r!"i#ka, al"b$ta kafková new advanced methods in side crash testing jakub jelínek tüv süd czech, novodvorská 994/138, +420606613227, jakub.jelinek@tuvsud.com !eské vysoké u"ení technické v praze, fakulta strojní, technická 4, +420606613227, jakub.jelinek@fs.cvut.cz milan r!"i#ka !eské vysoké u"ení technické v praze, fakulta strojní, technická 4, milan.ruzicka@fs.cvut.cz al"b$ta kafková tüv süd czech, novodvorská 994/138, +420725894624, alzbeta.kafkova@tuvsud.com !eské vysoké u"ení technické v praze, fakulta strojní, technická 4, alzbeta.kafkova@fs.cvut.cz abstract this work follows up the previous work [1] regarding the used methodology in the field of passive safety, ie. crash testing. the work is based on experience gained in the active lateral impact simulator (alis) project and describes complete process. the main focus has been given to the fine-tuning of the boundary conditions and loading of the system in order to ensure correct biomechanical loads. key words: crash test, finite element method, design of experiment, biomechanical loads, dycot, alis shrnutí tato práce navazuje na p#ede$lé p#ísp%vky [1] t&kající se metodiky v oblasti pasivní bezpe"nosti, a zejména crash testování. tento "lánek vychází ze zku$enosti získané v rámci projektu bo"ních náraz' a za pou(ití systému active lateral impact simulator (alis) a popisuje cel& postup. hlavní d'raz je kladen na jemné lad%ní po"áte"ních podmínek a náhradního zatí(ení p'sobícího na cel& systém a k dosa(ení po(adovan&ch biomechanick&ch kritérií. klí#ová slova: nárazová zkou%ka, metoda kone#n&ch prvk!, návrh experimentu, biomechanické zatí"ení, dycot, alis 1. introduction this work proposes a new advanced approach of combined virtual and physical testing. the main idea is to reduce development time and associated costs by using sled testing which used to be used mainly for physical simulation of frontal crashes. simulation of side crash in sled environment is not a brand-new topic, but certainly very complex one. this method is not really used on regular basis especially due to predictability issues and low accuracy. this work presents new approach of combination both virtual and physical testing. the whole process starts with full crash simulation, goes through conversion of virtual model to reduced sled model, sled testing and finally is wrapped up with full vehicle crash. 2. main section 2.1 dycot tüv süd czech has recently invested a large sum to test lab equipped with sled system (catapult) – dynamic component testing (dycot) [2]. sled test system consists of sled with grid holes and pusher sled, where all electronics and measurement equipment is mounted as also shown on figure 1. the pusher sled is being pushed by csa catapult, equipped with hydraulic piston that can accelerate the sled by up to 90g to total velocity of 100kph with payload of 1000kg. when fully loaded (payload of 5000kg), the piston is capable of accelerating the sled up to 35g. maximum force is equal to 2.5mn. maximum acceleration gradient is 14g/ms. new advanced methods in side crash testing jakub jelínek, milan r!"i#ka, al"b$ta kafková mecca 02 2020 page 2 figure 1: dycot system during the acceleration of the test sample obrázek 1: systém dycot p#i urychlení zku$ebního vzorku it is usually used for frontal crash test where the occupant safety is being tested. it can also be used for testing of crash-landing of any small airplane that would fit in the lab. latest addition to the service portfolio is battery pack testing for any battery packs up to 1000kg. 2.2 alis the capabilities of dycot sled system have been significantly increased by adding alis into serie, right next to the sled platform see figure 2. it uses up to 6 hydraulic cylinders in order to correctly simulate the door intrusion kinematics during the side crash. it enables one to use only small part of the car together with dummies and restraint systems and carry out simulation of the side crash with focus on restraint system and biomechanical loads. the system may seem as a "train of trolleys". the driven sled trolley is mounted to the main hydraulic system that generates the main acceleration pulse. alis is mounted on the separate trolley, attached to the sled. the whole structure is shown on figure 3, where main components are identified. the lateral system consists of additional pneumatic system directly attached to several pneumatic cylinders, alis primary structure and control system, linear guiding system and "impact break-in structure". the main reason for testing is to fine-tune the restraint system in order to get the best biomechanical loading in cheaper and quicker way – on sled. the fact that sled tests with only several trim parts and seats are used instead of fully equipped crash vehicles makes this approach very effective. we are definitely talking about tens of percents. door structure deforms and biomechanical loads are reached se at , d um m y, c am er as alis sample palette alis actuators g lo ba l a cc p ul se catapult alis on board system and structure im pa ct m ec ha ni sm li ne ar g ui di ng s tr uc tu re figure 3: dycot + alis concept obrázek 3: koncept dycot + alis figure 2: active lateral intrusion simulator (alis) obrázek 2: active lateral intrusion simulator (alis) new advanced methods in side crash testing jakub jelínek, milan r!"i#ka, al"b$ta kafková mecca 02 2020 page 3 2.3 methodology the whole process starts with fe simulation of full vehicle crash and is shown in appendix a. it is also very important to mention that usually testing consists of two sets of tests. the first one inputs are based on virtual model and results only and gets the initial recommendations for the first crash test. the second loop inputs are already based on this crash test and requires further development and tuning of alis. 2.4 design of experiment (doe) [3] the main objective is to develop a virtual method that would allow reducing full crash into sled crash via alis, defining complete alis setup and give highly accurate results, while reducing costs. the doe method is advanced mathematical method that uses n-dimensional mathematical surface for response values prediction based on combination of input parameters. the aim is to get ideally perfect match between full crash model as given at the beginning of the project and alis reduced model. amount of input parameters is very often high. one of the ways how to put up with them might be design of experiment (doe) with response surface creation or "step-by-step" iteration with subsequent physical validation as shown in figure 4. such method would reduce number of runs and predicts multiple results based on input parameter combinations. such pulses have to fulfill feasibility criteria of the cylinders and catapult. 2.4.1 pulse tuning procedure there are several pulses that come into the whole simulation and subsequent physical test. in order to identify and tune pulses two main steps have been chosen. firstly, contribution of every pulse needs to be determined and secondly chosen pulses have to be fine-tuned in a special manner that will ensure both physical feasibility and biomechanical responses. 2.4.2 pulse identification currently there are three hydraulic cylinders available at the alis system. one is 120kn and other two are 60kn and therefore three pulses are available. additional pulse comes from the catapult that represents overall pulses during the side crash. that makes it four pulses available for the first stage of doe testing. each pulse has got several parameters such as scale factor for both abscissa and ordinate and also offset values for both abscissa and ordinate. all four pulses have following set of parameters as shown in figure 5. figure 5: list of design variables obrázek 5: seznam vstupních prom%nn&ch figure 4: doe response surface (top), step-by-step process (bottom) obrázek 4: doe povrch (naho#e), postupn& proces alis #e$ení (dole) new advanced methods in side crash testing jakub jelínek, milan r!"i#ka, al"b$ta kafková mecca 02 2020 page 4 following variable abbreviations are used: • asd_sy – scale factor of sled • asd_oa – pulse offset of sled • dbb_sf – scale factor of actuator at b-pillar bottom • dbb_oa – pulse offset of actuator at b-pillar bottom • dbu_sf – scale factor of actuator at b-pillar upper • dbb_oa – pulse offset of actuator at b-pillar upper • ddd_sf – scale factor of actuator at door structure • ddd_oa – pulse offset of actuator at door structure since there are 8 variables, the resultant design space will be 8d. since there is no simple way of illustrating the 8d interactions, we have to go down to 3d visualisation. when always 3 variables are selected and can be switched for any other variable. all 200 experiments (simulations) have to be run it has to be pointed out that as there are 8 variables, then 8-dimensional surface will be created based on the responses and hence the complete surface is so complex that cannot be displayed. table 1: list of responses tabulka 1: seznam vyhodnocovan&ch odezev id type name component units 90079631 bar first thorax rib compression mm 90079632 second thorax rib compression mm 90079633 third thorax rib compression mm 90079634 first abdomen rib compression mm 90079635 second abdomen rib compression mm 90000002 node head acc acceleration, velocity mm ms-2 / mm ms-1 90015619 t1 lower neck acc acceleration, velocity mm ms-2 / mm ms-1 90021212 t4 first thorax acc acceleration, velocity mm ms-2 / mm ms-1 90023825 t12 second abdomen acc acceleration, velocity mm ms-2 / mm ms-1 90029764 pelvis acc acceleration, velocity mm ms-2 / mm ms-1 figure 6: comparison of initial alis vs full crash results (ribs) obrázek 6: porovnání úvodních v&sledk' alis s fyzickou zkou$kou ((ebra) new advanced methods in side crash testing jakub jelínek, milan r!"i#ka, al"b$ta kafková mecca 02 2020 page 5 2.4.3 responses for response surface determination it is necessary to get responses respective to our objectives. responses are resultants of any measurements such as force, displacement, acceleration, angle, etc. response list is given by the scope of the sensitivity study. in all crash simulations, the most important are biomechanical loads that describes the behaviour of a human body during the crash event. the requirements differ very much from case to case so it is always unique set of criteria that are ideally to be matched. in our pole strike, it is ribs compression. nowadays, most of the dummies and solvers are able to calculate and/or evaluate these criteria directly via sensors/points of interests. in our case several node and bars have been selected. nodes are figure 7: the response trends based on initial variable combination (top) and response trends based on update variable combination (bottom) obrázek 7: trendy odezev v úvodním nastavení (naho#e) a trendy zalo(ené na upraven&ch parametrech (dole) new advanced methods in side crash testing jakub jelínek, milan r!"i#ka, al"b$ta kafková mecca 02 2020 page 6 used for tuning of controlled trim deformation and its velocity. simply the velocity and deformation of the trim ensures the same initial conditions as per full crash. bar then are used for force (shoulder) and displacement (rib compression) evaluation. this metric is the most important for most of the safety crash engineers. responses are used for response surface modelling and results evaluation. in our case there are several responses taken into account. they have been chosen according to the requirements of the customer and also euroncap. responses that have been used are shown in table 1. 3. results of the virtual experiments so far we have been preparing ourselves for the main task. to choose suitable variables from all available sources to achieve the intended responses. now, when the response surface has been created and validated, the selection of variable that would fit the intended values follows. the main reason of the virtual experiments is to perform sensitivity analyses that would later give a good knowledge of the system behaviour. this is particularly useful during the physical testing, when quick response to the current behaviour and recommendation of the next steps is highly expected and table 2: final variable values tabulka 2: seznam finálních hodnot prom%nn&ch label name value initial values asd_sy scale factor of sled 1.02 no asd_oa pulse offset of sled 0 yes dbb_sf scale factor of actuator at b-pillar bottom 1.11 no dbb_oa pulse offset of actuator at b-pillar bottom 0 yes dbu_sf scale factor of actuator at b-pillar upper 1.03 no dbu_oa pulse offset of actuator at b-pillar upper 0 yes ddd_sf scale factor of actuator at door structure 0.98 no ddd_oa pulse offset of actuator at door structure 1 no figure 8: comparison of initial and final alis pulses obrázek 8: porovnání úvodních a finálních puls' alis new advanced methods in side crash testing jakub jelínek, milan r!"i#ka, al"b$ta kafková mecca 02 2020 page 7 there is no time for further simulations. in order to get ideal pulse configurations for respective biomechanical responses, it is necessary to set the target. euroncap assessment is based on scoring system of the maximal biomechanical loads. for illustration there is a comparison of initial alis run, with all variables equal to 1, and full crash model shown on figure 6. the match is not ideal one at the moment and our goal is to get better match. hence there has to be an update done of some or all available pulses (scale factor or offset). the suitable variable combinations can be found by user to achieve his requirements. ls-opt can easily predict response values based when one changes the input variables as indicated on figure 7. this is exactly the way how to better understand mutual interaction between input variables and responses. in our case, when the five ribs are of interest, we get desired response with following variables written in table 2. as these values are predicted, another testing run has to be to verify the suitability. updated three pulses for alis and one for sled are shown on figure 8. updated alis results of dummy biomechanical criteria compared to full crash data are displayed on figure 9. the comparison shows rather good match of both simulation approaches. reduced model is and always will be only approximation and can only get close to the full crash simulation model. four pulses with reasonable match, which is usually considered within deviation of 10%, to the full crash model have been found and hence the first objective is complete. secondary objective was to get a good knowledge of the system behaviour and it has also been done. it will become very useful in upcoming testing. 4. conclusion this paper has shown how to handle alis project within the virtual part. the main objective (pulses identification) has been achieved. controlled pulses have become input parameters into the physical sled test. it is very important to get a good knowledge of the whole system behavior and how biomechanical responses are affected by variation of input as this helps the tuning procedure during early physical testing. without it, one would not be able to recommend further steps to improve the results accuracy. future work is to cover the last remaining part and it is the physical testing and results validation. list of notations and abbreviations alis – active lateral impact simulator asd_sy – scale factor of sled asd_oa – abscissa offset dbb_sf – b-pillar bottom scale factor dbb_oa – b-pillar bottom abscissa offset figure 8: comparison of initial and final alis pulses obrázek 8: porovnání úvodních a finálních puls' alis new advanced methods in side crash testing jakub jelínek, milan r!"i#ka, al"b$ta kafková mecca 02 2020 page 8 dbu_sf – b-pillar upper scale factor dbu_oa – b-pillar upper abscissa offset ddd_sf – door scale factor ddd_oa – door abscissa offset doe – design of experiment dycot – dynamic component testing encap – european new car assessment programme references [1] jelinek j., r'(i"ka m., kalinsk& m. advanced methods in crash safety testing, 56th conference on experimental stress analysis proceedings 2018, isbn 978-80-270-4062-9 [2] )otola m., 2016. dycot presentation, tüv süd czech, pages 3-7 [3] jelinek j., r'(i"ka m. advanced methods in crash safety testing, 24th workshop of applied mechanics 2018, isbn 978-80-01-06453-5 appendix a – methodology output is to be biomechanical loads, intrusion and kinematics of important structural parts such as doors, aand b-pillars. size reduction of fe model comes next. the most important outcome of this phase is determination of the alis settings. this includes number of cylinders used, their timing and also design of the impact structure. amount of input parameters is countless. other two phases are related to the physical testing. figure 10: real crash to alis reduction procedure [3] (courtesy of )koda auto) obrázek 10: proces redukce z reálného crash testu po alis [3] (s laskav&m dovolením )koda auto) full car fe simulation output: biomechanical loads lntrusion kinematics size-reduced fe simulation output: number of cylinders cylinder positions force distribution (shape and magnitude) impact structure design reduced physical crash test output: biomechanical loads physical crash test output: biomechanical loads model reduction alis parameters application correlation mecca_20-01_v10_web testing of automated driving systems ond!ej vaculín, michael gellrich, robert matawa, steffen witschass mecca 01 2020 page 7 10.14311/mecdc.2020.01.02 testing of automated driving systems ond!ej vaculín, michael gellrich, robert matawa, steffen witschass 1. introduction the modern cars were invented as purely mechanical systems more than 130 years ago. however, since introduction of antilock brake systems in 1970s the computerization of the vehicle driving started and computers played more and more significant role in the vehicles. the systems such as antilock brakes, traction control or stability control interrupt the direct connection between the driver and vehicle with the objective to reduce the possible risk, either to avoid the collision or at least to reduce the collision velocity in potentially dangerous situations. in general, four groups of assistance systems can be recognized: 1. comfort systems such as headlight or rain assistant – such systems take duties from drive, which are not directly connected with vehicle dynamic functions, 2. information and warning systems such as driver alert, lane departure warning or traffic sign recognition systems – such systems just inform driver about certain state of vehicle, driver or infrastructure, 3. intervening emergency systems such as stability control or automatic emergency braking – such systems take partial control over the vehicle in critical (near accident) situations, 4. continuously acting systems such as adaptive cruise control of lane keeping assistance – such systems support driver in long time periods by taking part of his duties in standard situations. the increasing computational power together with reducing purchase costs and as well as availability of low cost efficient and reliable sensors allow the manufacturers to implement functions such as lane keeping assistance or emergency braking options even to low cost cars, which are called advance driver assistance systems (adas). the logical consequence of the adas development is a vehicle which is either partly or even fully able to take the driver’s duties. such an automated driving (ad) vehicle will offer a co-pilot functions or drive even autonomously ond!ej vaculín technische hochschule ingolstadt, esplanade 10, 85049 ingolstadt, germany, +420 776 637 352, e-mail: ondrej.vaculin@thi.de (formerly tüv süd czech, novodvorská 994/138, 142 21 praha 4, czech republic) michael gellrich, robert matawa, steffen witschass tüv süd auto service, tüv süd auto service gmbh, 85748 garching, daimlerstraße 11, germany, +49 89 32950-751, e-mail: michael.gellrich@tuv-sud.de, robert.matawa@tuev-sued.de, steffen.witschass@tuev-sued.de abstract the automated driving requires new testing approaches, which are more complex than the current testing systems. the complexity and requirements for accuracy is important, because of interconnection of virtual with physical testing. this paper presents a generic approach to testing of automated driving functions and demonstrates its implementation on measurement of two scenarios. key words: automated driving, testing, testing scenarios shrnutí automatizované !ízení vy"aduje nové testovací p!ístupy, které jsou daleko komplexn#j$í ne" sou%asné testovací systémy. komplexnost a po"adavky na p!esnost jsou d&le"ité z pohledu na propojení fyzického a virtuálního testování. tento %lánek prezentuje obecn' p!ístup k testování funkcí automatizovaného !ízení a demonstruje jeho implementaci na m#!eních dvou scéná!&. klí"ová slova: automatizované !ízení, testování, testovací scéná!e testing of automated driving systems p!ijato k publikaci v roce 2018 testing of automated driving systems ond!ej vaculín, michael gellrich, robert matawa, steffen witschass mecca 01 2020 page 8 table 1: sae levels of automated driving [1]. tabulka 1: úrovn# automatizace !ízení dle sae [1]. sae level name narrative definition execution of steering and acceleration/ deceleration monitoring of driving environment fallback performance of dynamic driving task system capability (driving modes) human driver monitors the driving environment 0 no automation the full-time performance by the human driver of all aspects of the dynamic driving task, even when enhanced by warning or intervention systems human driver human driver human driver n/a 1 drive assistance the driving mode-specific execution by a driver assistance system of either steering or acceleration/deceleration using information about the driving environment and with the expectation that the human driver performs all remaining aspects of the dynamic driving task human driver and system human driver human driver some driving modes 2 partial automation the driving mode-specific execution by one or more driver assistance systems of both steering and acceleration/deceleration using information about the driving environment and with the expectation that the human driver performs all remaining aspects of the dynamic driving task system human driver human driver some driving modes automated driving system monitors the driving environment 3 conditional automation the driving mode-specific performance by an automated driving system of all aspects of the dynamic driving task with the expectation that the human driver will respond appropriately to a request to intervene system system human driver some driving modes 4 high automation the driving mode-specific performance by an automated driving system of all aspects of the dynamic driving task, even if a human driver does not respond appropriately to a request to intervene system system system many driving modes 5 full automation the full-time performance by an automated driving system of all aspects of the dynamic driving task under all roadway and environmental conditions that can be managed by a human driver system system system all driving modes testing of automated driving systems ond!ej vaculín, michael gellrich, robert matawa, steffen witschass mecca 01 2020 page 9 without a driver. according to sae the development will be divided in several levels as indicated in table 1. in order to drive automatically, the vehicles must take responsibility from a human driver to its it systems and control algorithms. despite it is expected that driverless vehicles will be able to reduce significantly the number of accidents and fatalities, some sources expect even 90% or more, the initial stages of ad implementation will be accompanied by increase of accidents due to heterogeneous traffic of driverless and human driven vehicles and the insufficient maturity of ad systems [2]. currently the regulatory bodies and consumer organizations define for some vehicle categories couple of physical proving ground tests to assess the functionality of adas. however, the testing procedures based on physical testing seem to be insufficient to cover the all possible cases and thus to evaluate the effectiveness and safety. to cover the vast number of possible scenarios, simulation methods are the only feasible way [3]. however, the physical tests will be still needed for verification and validation of these simulation models and set-ups. the proper standardization and regulatory basis is important for all stakeholders. since current regulations and inspection specifications are not sufficient or even not existing, several committees and project groups such as german project pegasus are developing new international regulations and standards. to be able to implement complicated scenarios on a proving ground, new testing approaches must be developed and implemented, in which traffic simulation vehicles (tsv) and soft crash targets (sct) together with other entities define repeatable environment for testing of so-called vehicle under test (vut). such tasks are being solved within couple of projects and in an iso level in iso/tc 22/sc 33/wg 16 (active safety test equipment). 2. type approval of assistance systems as usual, the development of standards and regulations is slower than the development of the technology itself. the adas functions are implicitly addressed by the un ece regulations 13 and 79 with annexes on electronic systems. however, current regulation 79 explicitly defines the requirements for systems up to automatic parking, i.e. with low velocities. further development of regulation 79 is in progress. the vehicles of categories m2, m3, n2 and n3, i.e. trucks and buses with some exceptions are legislatively controlled by the commission regulation (eu) no. 351/2012 and 347/2012 to be equipped with the regulation 130 defines the approval tests for lane departure warning systems for vehicles categories n2, m2, n3, m3, i.e. trucks and buses. the test set-up is shown in figure 1. figure 1: test set-up according to un ece r 130 obrázek 1: test setup dle p!edpisu ehk osn 130 the regulation 131 defines the timing and type of warning as well as automatic braking maneuver based on tests with a stationary and moving target, which represents a passenger car of category m1, class aa saloon. the initial velocity is defined to 80 km/h. the aeb system should at first warn the driver and if he does not react then to automatically brake the vehicle. the warning timings are different for various categories of vehicles, warning time for n2 is shorter than for m3. further testing is focused on identification of failures and finally the driving in the gap between 2 parking vehicles, which are 4.5 meters side to side from each other as indicated in figure 2. figure 2: test set-up according to un ece r 131 obrázek 2: test setup dle p!edpisu ehk osn 131 testing of automated driving systems ond!ej vaculín, michael gellrich, robert matawa, steffen witschass mecca 01 2020 page 10 ldw and aeb functions since november 2015 [4, 5]. for aeb the deadline depends on the braking system and suspension. on the un ece level the regulations 130 and 131 exist, which define the technical requirements and testing procedures. figure 3: scenario traffic jam tail end obrázek 3: scéná! konec kolony figure 4: scenario lane change obrázek 4: scéná! zm#na jízdního pruhu two soft crash targets (scts) were installed on the proving ground as indicated in figure 5. sct 1 was a balloon car from the euroncap target for testing adas functions and sct 2 was a model of a motorcyclist. sct 2 tsv sct 1 figure 5: soft crash targets obrázek 5: m#kké cíle testing of automated driving systems ond!ej vaculín, michael gellrich, robert matawa, steffen witschass mecca 01 2020 page 11 3. consumer testing currently the consumer organizations are focused on advanced emergency braking (aeb) and lane departure warning (ldw). consumer organization tests under the new car assessment program (ncap) [6], serves for the testing of aeb and ldw in passenger cars. currently about nine different ncap consumer organizations around the world exist, however not each has the aeb tests in its portfolio. the different ncap test procedures demonstrate the heterogeneity of approaches in different countries and regions. while for example the us ncap is based on tests drivers, the euro ncap uses driving and pedal robots along with accurate measurements of vehicle position. the advantages of the european approach are obvious: the higher accuracy in the position and higher repeatability the lower number of necessary tests to be performed. euro ncap currently tests aeb systems in three areas: aeb city, aeb inter-urban and aeb pedestrian. despite the complete set of velocities, this method considers only single, limited representative scenarios without considering the driver’s behavior. this can be sufficient for consumer review to ensure comparability of different vehicles. however, for the vehicle safety and future type approval this is not enough, because realistic scenarios and driver and environmental influences are not included. 4. entities involved in testing to be able to generate the testing scenarios for both virtual and physical testing the possible set-ups should have a common basis. the presented structure has been developed in the project pegasus. the so-called generic approach for proving ground tests [7] summarizes the participants of the tests and defines the following entities [8, 9]: 1. test object 2. basic route 3. guidance infrastructure 4. temporary adjustments 5. stationary objects 6. mobile objects 7. environment the scenarios were performed in couple of runs in order to assess the repeatability and accuracy. the results achieved are presented in figures 6 and 7. the first graph presents the velocity profile of the test; the second graph shows the lateral deviation. the results indicate that further development of the vehicle dynamic controllers is necessary in order to achieve the trajectory deviation better than +/0.1 m. figure 6: measured data – traffic jam tail end obrázek 6: m#!ení – konec kolony testing of automated driving systems ond!ej vaculín, michael gellrich, robert matawa, steffen witschass mecca 01 2020 page 12 the testing scenario is then defined by a combination of different entities. in order to implement the generic procedure of the scenarios on the proving a control center must implement all the tasks. the entire system should complete measurement equipment to perform tests of highly automated functions. two types of scenarios are recognized: (i) time invariant and (ii) time variant. the time invariant test is synchronized by a traffic simulation vehicle. in the time variant case the test is synchronized by the vehicle under tests. the time variant case means that the tvs and sct trajectories must be modified dynamically. very important feature of the control center is the wireless communication with low latency to all testing entities. all moving entities such as tsv, sct and vut must be equipped with a precise localization based e.g. on real time kinematic (rtk) satellite navigation together with an inertial platform. since the trajectory of tsvs should be controlled, the vehicle must be actuated. either it is possible to use external actuators such as steering and pedal robots of the internal actuators, which are already available in the vehicle. the second solution is of advantage because no additional devices must be installed in the vehicle. the current implementation uses direct control of internal vehicle actuators for steering and throttle and indirect control of deceleration by a braking robot. the system is in development and in the next version, it is expected that also the braking function will be actuated directly without installation of a braking robot. 5. proving ground tests the first proving ground test has been performed in order to verify the implementation with selected test cases in real conditions. two scenarios have been selected: 1. traffic jam tail end 2. lane change traffic jam tail end (figure 3) is defined in the following steps: a) scts in lanes 1 and 3 with v = 0 km/h represent the tail end of a traffic jam. b) tsv, followed by vut with ~2 s distance, drives with ~80 km/h in lane 2. c) tsv decelerates ~123 m in front of scts with ~2 m/s( and stops beside the scts. lane change (figure 4) is defined in the following steps: a) scts in lanes 1 and 3 with v = 0 km/h represent the tail end of a traffic jam. figure 7: measured data – lane change obrázek 7: m#!ení – zm#na jízdního pruhu testing of automated driving systems ond!ej vaculín, michael gellrich, robert matawa, steffen witschass mecca 01 2020 page 13 b) tsv, followed by vut with ~2 s distance, drives with ~80 km/h in lane 2. c) tsv changes lane into lane 1 behind the scts and stops. vut accelerates in lane 2. 6. conclusion the proving ground testing will be a necessary part of the prove of effectiveness of the future automated driving functions. the complexity of the task requires to combine physical and virtual testing methods. the objective of the proving ground testing equipment is to deliver accurate and repeatable testing environment for the automated driving systems. the paper presented a generic approach and an example of its implementation into the real environment together with some preliminary results based on predefined time invariant scenarios. the results indicate that further development of the trajectory controllers must be performed in order to achieve the acceptable motion of the traffic simulation vehicle. such complex systems as automated driving shall always be considered not only in terms of their effectiveness, but also functional safety and it security issues are essential for the system overall rating. the system is in development and the next generation will include full direct control of the vehicle using vehicle actuators as well as time variant capability. furthermore, it is intended to integrate more traffic simulation vehicles together with moving platforms with soft crash targets for more complex scenarios. acknowledgements the author would like to acknowledge the support of project pegasus by german federal ministry of economic affairs and energy. references [1] sae j3016 (2016). taxonomy and definitions for terms related to driving automation systems for on-road motor vehicles, 2016-09-30. [2] sivak, m., schoettle, b. (2015). road safety with self-driving vehicles: general limitations and road sharing with conventional vehicles, university of michigan, transportation research institute, report no. umtri-2015-2. [3] vaculín, o., wech, l., steininger, u., lewerenz, p., prokop, p. (2016). virtuelle prüfungen als ergänzung von realen prüfungen für die typgenehmigung von fahrerassistenzsystemen. in: kompaß, k. (ed.). aktive sicherheit und automatisiertes fahren methodenentwicklung im expertendialog, hdt fachbuch band 144, essen, pp 76 – 87, isbn 3816933653. [4] commission regulation (eu) no. 351/2012: type-approval requirements for the installation of lane departure warning systems in motor vehicles, 2012. [5] commission regulation (eu) no. 347/2012: type-approval requirements for certain categories of motor vehicles with regard to advanced emergency braking systems, 2012. [6] p. seiniger (2016). ncap testing of safety related driver assistance systems. in: safetyupdate 2016, aschaffenburg, 2016. [7] ponn, t., vaculín, o., gimm, k., knake-langhorst, s., joganatham, r., schuldt, f., diermeyer, f., abdellatif, h. (2017). generischer ansatz für prüfgeländetests von hochautomatisierten fahrzeugen in `8. tagung fahrerassistenz‘, münchen. [8] bagschik, g., menzel, t., maurer, m. (2018). ontology based scene creation for the development of automated vehicles, https://arxiv.org/abs/1704.01006v4, 19 jan 2018. [9] schuldt, f. (2017). ein beitrag für den methodischen test von automatisierten fahrfunktionen mit hilfe von virtuellen umgebungen. universitätsbibliothek braunschweig, https:// doi.org/10.24355/dbbs.084-201704241210. experimental electric vehicle ešus gen2 josef břoušek, martin bukvic, pavel jandura mecca 02 2016 page 07 10.1515/mecdc-2016-0007 experimental electric vehicle ešus gen2 josef břoušek, martin bukvic, pavel jandura 1. introduction in 2011, the institute of mechatronics and computer engineering established ties with the department for vehicles and engines, both part of technical university of liberec, with the aim of expanding the competencies of both entities in the field of electric mobility. in the same year, a project was drafted to develop a light experimental bev category vehicle. this vehicle now serves as an open platform for educational purposes and the testing of existing and currently developed components designed for electric vehicles. these include, in particular, the design and implementation of an electric powertrain and the design of the traction battery and its management coupled with the other on-board electronics. 2. conception of the vehicle conceptually, it is a four-wheeled two-seat vehicle of the roadster type chassis with a solid frame and front wheel drive (fwd) see fig. 1. the frame design is mixed. it is a combination of a steel weldment and an assembly bolted from extruded aluminum profiles [1]. the wheelbase is 2462 mm. wheel track of both axles is identical at 1435 mm due to the specific use of a pair of front axles from the skoda fabia with mcpherson suspension. this solution opens up the possibility of future installation of a system for steering the rear axle. in the current version, the control of the rear axle is mechanically locked. vehicle height is 1300 mm and its length is 3350 mm. curb weight of the vehicle incl. traction battery is 850 kg. josef břoušek, martin bukvic, pavel jandura technical university of liberec, studentská 2, cz 461 17 liberec, czech republic, department of vehicles and engines, mechanical engineering faculty; institute for nanomaterials, advanced technologies and innovation e-mail: josef.brousek@tul.cz shrnutí v úvodu článku je popsán vznik a koncepce experimentálního elektromobilu. následuje popis použitých mechanických a elektrických komponent v kombinaci s konstrukčními řešeními dílčích celků jako je např. pohonné ústrojí vozidla nebo trakční baterie vozidla. volba použitých komponent a konstrukčních řešení je zde zhodnocena vzhledem k současným trendům ve vývoji elektromobilů. článek obsahuje i simulace dynamiky vozidla pro vybrané elektromotory se kterými se počítalo pro zástavbu do vozidla. klíčová slova: elektromobilita, hnací ústrojí, trakční elektromotor, převodovka, lithiové akumulátory abstract in the introduction to the article, the conception and development of an experimental electric vehicle is described. it is followed by a description of the used mechanical and electrical components in combination with the design solutions of sub-units, such as the vehicle powertrain and traction battery. the choice of components and design solutions is evaluated here with regard to the current trends in the development of battery electric vehicles. key words: electric mobilit y, powertrain, traction electric motor, transmission, lithium batteries experimental electric vehicle ešus gen2 figure 1: experimental electric vehicle ešus gen2. obrázek 1: experimentální elektromobil ešus gen2. experimental electric vehicle ešus gen2 josef břoušek, martin bukvic, pavel jandura mecca 02 2016 page 08 in the space between the axles, the perimeter steel frame forms a shaft designed for installation of the battery box with traction battery and the bms. this concept can dedicate most space for the traction battery while preserving the spatial comfort of the cabin and luggage compartment. its main drawback is the necessity of a higher seating position for the crew due to the minimum design height of the battery. this ranges from about 100 mm with tesla model s/x vehicles up to about 160 mm with the bmw i3 vehicle. for the ešus gen2 experimental vehicle, the construction height of the battery is 84 mm. 3. prototype of the dual motor drive system powertrain the main requirement of any powertrain concept is to achieve the maximum efficiency under all operating conditions. however, with the most common powertrain concept (one motor with sst) this requirement is hard to achieve in particular when there is high demand for vehicle driving dynamics or a wide range of driving speeds. this leads to the situation where one high power motor works at a fraction of its nominal power for the most of its operational time. this imposes high demands on the motor design in terms of its overall efficiency. there are several powertrain configurations [2][3] that due to more or less complicated technical solutions, offer significant improvement in this area of interest. one of these is a powertrain configuration known as the dual motor drive system (dmds). the main idea of operation is based on the joint control of torque of both powertrain motors primary and assistant. the dmds control algorithm can engage just the primary motor, which in most cases is designed for maximum effectiveness at low loads when the assistant motor is freewheeling. the assistant motor is automatically engaged by the control algorithm only under specified conditions and can thus be optimized for heavy load operation or better efficiency at high driving speed. the dmds therefore optimizes the efficiency of the powertrain for most operating conditions. one of technology advantages of dmds as opposed to powertrains with multi-speed transmission (mst) [4], [5], [6], is the seamless torque distribution to the wheels, which is problematic even with dual clutch transmission. also, the ability to achieve a better weight distribution of the vehicle mass and the cooling efficiency of individual components while preserving the compact design should be considered. several versions of the dmds concept can be implemented, but the most promising characteristics of dmds are offered in awd configuration using a combination of two sets of electric motors with its own singe-speed transmission (sst), installed at both axles. then, the ssts can also utilize different gear ratios. this particular dmds configuration is used by tesla powertrains [7]. they use two different asynchronous motors (acim) with the same gear ratio of i = 9.7 in both ssts. the only fundamental requirement for an assistance motor is that it must generate the smallest possible losses in its magnetic circuit when freewheeling. from this perspective, the acim type seems to be the best suited. in this mode of operation its relatively narrow band of high efficiency is not a great deficiency when compared with pmsm. based on the above characteristics, it can be said that dmds and its latest modification with three motors (two motors with electronic differential for torque vectoring on the rear axle, one motor with sst on the front axle) currently ranks among the most promising concepts of powertrains for bev. we have decided to verify the real world characteristics of dmds in the second generation of the experimental electric vehicle. our prototype of dmds anticipates the use of two electric motors mounted on both sides of a common shaft of one sst in fwd configuration. the main reasons for this particular design is to test the common behavior of two motors on the same shaft in the joint torque control. another important reason was the significant production cost of our sst design. however, the principle of operation remains the same. 3.1. requirements for driving dynamics the dmds device type provides an improvement in the overall efficiency in comparison with the powertrain with sst, primarily assuming a requirement for higher driving dynamics of the vehicle. for this reason, the powertrain of the gen2 vehicle was designed to achieve an acceleration of 0-100 km.h-1 in under 10 s. this value may be still considered as a borderline for vehicles with better driving dynamics. the maximum speed of the designed powertrain is 100 km.h-1. this value has been chosen to enable real world testing of the vehicle acceleration rate. the gen2 vehicle platform was never intended for use on the road, so the maximum speed and vehicle behavior at higher speeds was not a subject of interest. to meet this requirement, due to the design curb weight of 850 kg, it is necessary to have a peak mechanical output of the powertrain of over 70 kw. 3.2. the choice of electric traction motors to optimize the dmds concept for maximum efficiency it is necessary to differentiate the performance of both motors, usually in a ratio of 1:2 up to 1:3. the main machine should be able to operate continuously while driving over the entire range of constant speeds while exhibiting an efficiency of over 80%. for an up-to-date bev m1 category with a curb weight of 1500 kg, this corresponds to a permanent performance of 25-30 kw. for the gen2 vehicle, the requirement for permanent performance was calculated to a value of 10 kw with the ability experimental electric vehicle ešus gen2 josef břoušek, martin bukvic, pavel jandura mecca 02 2016 page 09 of short term overload to 20 kw. thus, the assistance motor must have a peak power of min. 50 kw. as the main motor we decided on the me 1302 type, liquid-cooled af-pmsm from motenergy, inc. as an assistance motor it was originally proposed to use the acim principle, ac-34 type from hpevs. however, during development we were forced to change the type of assistant motor. this change during development was due primarily to the limited budget allocated for this project. we used a custom modified version of an rf-pmsm motor originally developed by the zero motorcycles company, type 75-7. an important benefit was the availability of configuration files for sevcon gen4 series foc controllers which we decided to use. the main drawback of using this kind of “low-cost” motor is that in most cases there are no detailed technical data and efficiency maps available. however, this is not a crucial issue for verifying the fundamental characteristics of the dmds concept. 3.3. single-speed transmission design from the parameters of traction motors for the dmds device are derived the basic requirements for the parameters of the sst. designed maximum input torque is 200 nm and maximum operating speed is 8000 rpm. the overall gear ratio ic < 9 for the maximum vehicle speed of 100 km.h-1. due to the vehicle concept, it was decided to design the sst prototype in the form of a diploma thesis. for this design, components from the mq 200 02t manual six-speed mst were taken. the input shaft was designed and manufactured for the aforementioned connection of both electric motors. the adjustment of the standard input shaft also included installation of the parking pawl wheel. the countershaft was also modified from a standard one, by shortening and adjusting the diameters. the differential was left as a standard one, but because of the shortening of the resultant depth of the sst, it is rotated by 180° compared to its original location in the mq 200. the resulting gear is formed by tooth wheels of the second gear and differential constant gear with a gear number of ic = 8.9. the proposed sst allows service exchangeable gears in the range of second, third and fourth gear from the mq 200 02t. on both sides of the input shaft, joints are designed with tight springs for connecting the electric motors by means of fixed couplings. figure 2: from the left: motenergy me 1302, hpevs ac-34, zero motorcycles zf 75-7. obrázek 2: zleva: motenergy me 1302, hpevs ac-34, zero motorcycles zf 75-7. table 1: main parameters of dmds electric traction motors. tabulka 1: hlavní parametry trakčních motorů pro dmds. motor parameter unit motenergy me1302 hpevs ac-34 zero motorcycles zf 75-7 motor type [-] af-pmsm acim rf-pmsm peak torque [n.m] 50 144 144 cont. torque [n.m] 12 12 45 peak power [kw] 17 55 50 cont. power [kw] 4 4 17 max. speed [rpm] 8000 8000 6000* max. efficiency [-] 0.92 0.88 0.92 weight [kg] 15.9 38.5 17 * the lower max. speed of the zf 75-7 motor means it is necessary to use a third gear of the mq200 02t transmission to reach the speed of 100 km.h-1 figure 3: model of internal layout of the dmds transmission. obrázek 3: model vnitřního uspořádání dmds převodovky. figure 4: the final model of the dmds powertrain. obrázek 4: výsledný model hnacího ústrojí dmds. experimental electric vehicle ešus gen2 josef břoušek, martin bukvic, pavel jandura mecca 02 2016 page 10 the sst housing is made from aluminum alloy. since it is a prototype, manufacturing using chip machining on a cnc milling machine was chosen. the shapes of the sst housing were then subjected to this technology. the housing was designed with regard to low weight and sufficient stiffness of the construction. given the requirement for mutual alignment, the lid (cover) and the housing are secured with respect to one another with precise pins. material for manufacture of the prototype housing is en aw 7021 [alzn5.5mg1.5]. this material exhibits low internal stress, excellent dimensional stability, strength and also very good machinability. for oil filling and draining, there are formed two holes with plugs with threads on the sst. the weight of the housing including flanges for connecting electric motors is 8 kg. the complete sst including fillings weighs 22 kg. the parking pawl system prevents starting (drive away) of the vehicle, even when handbrake is unloaded. the base plate of the pawl (latch) is designed for manufacture by milling on a cnc machine from the same material as the sst housing. the pawl is mechanically operated by a bowden cable in the gen2 vehicle, which is based on the original vw group dsg transmission selector lever. the parking pawl is produced from 11 523 non-alloyed steel. other parts are taken from the vw group dq series transmission. 3.4. connecting the electric motors to the transmission and fitting the powertrain to the vehicle both types of electric motor have a standard nema c-face flange and a grooved output shaft. to connect them to the sst housing, flanges from the same material as the housing were designed. steel couplings are used for connection to the sst driving shaft. the dmds is positioned in the vehicle in front of the front axle. here it is hung behind the sst housing, both on an extruded profile, which is resiliently mounted in silent blocks, and furthermore it is flexibly clamped in the axle housing of the front axle. 4. description of the traction battery box design and the bms the battery box was designed as an aluminum welding with two reinforcing bars. the box is inserted into a shaft formed by a peripheral steel frame which is bolted to the lower rim of the box. this solution could be further developed in the form of an automatic exchange system for the battery box. requirements for traction batteries on current m1 category bevs are mostly met using li-ion cell technologies with nca-c(si) and nmc -c(si) chemical structures. in addition to the chemical structure, the format of the cell and its size also significantly affects its specific energy density. the small cylindrical format 18650 cells exhibit the highest specific energy density in the last decade. cells in other formats, whether prismatic, cylindrical or pouch embodiment, exhibit significantly worse specific energy density. modules of the gen2 traction battery are designed for saft vl 41 m cylindrical cells of the nca-c type. these large format (144 wh) cells were preferred to the small ones (~12 wh) of figure 5: parking pawl mechanism. obrázek 5: mechanismus parkovací západky. figure 6: detail of the dmds installation in the vehicle. obrázek 6: detail instalace dmds ve voze. experimental electric vehicle ešus gen2 josef břoušek, martin bukvic, pavel jandura mecca 02 2016 page 11 the 18650 format, mainly due to easier installation. for the next generation of traction battery, we already take into account a transition to the 18650 format or the newly introduced 20700 and 21700 formats. the designed battery box enables the setting up of modules with cells in two basic versions. the first one enables installation of 11 battery modules with an energy of 18.8 kwh, but without active thermal management. the second one uses thermal management for peak load of the 6c / 960a battery. then the box is set up with 10 modules with an energy of only 17.2 kwh. each module consists of 12 cells in the 3s4p wiring, see fig. 8. cells are positioned between two faces from flame retardant plastic. cell terminals are interconnected flat cu busbars with a cross-section of 70 mm2 and then covered with a plastic lid. one 10 k thermistor is attached to each four cells. their outlets together with the wires for sensing the cell voltage are connected to a common connector for connecting the module with the bms. thermal management was designed using the properties of the pcm material [8] to instantly transform heat from the cells to a change of its phase. this principle is extended to a system of distribution plates (sheets) that facilitate the rapid transfer of heat from the pcm to the exchanger in the battery box base. thus, it is hybrid management. in the traction battery prototype, this system has not been set up yet. the electronic bms system of the vehicle comes from ewert energy systems, inc. it is a centralized system with a main unit. balancing cell current is 100 ma. 5. charging system of the vehicle the charging system of the gen2 vehicle is implemented using three one phase on-board chargers, each with an output (power) of 2.3 kw. if there is a three-phase socket, it can be charged with a power up to 7 kw and the vehicle can thus be fully recharged in 3 hours. the vehicle is equipped with the european standardized charging plug according to iec 62196, also known as “mennekes”. the bms allows charging of the traction battery by recuperative braking. 6. conclusion at the beginning, given the considerable complexity of the issues as a whole, we have chosen a dmds with the same type of electric motors, namely with the me 1302 type. currently, there is an ongoing optimization of the setting of the inverters for master-slave operation of both motors on a common shaft to achieve the maximum possible parameters declared by the manufacturers. this optimization is evaluated by means of measurements on a chassis dynamometer at this time, see fig. 9. after the successful optimization of the master-slave operation we are planning to implement the fundamental parts of the dmds control algorithm, still with the me 1302 motors. in the future after evaluating the real-world characteristic we would like to implement an advanced dmds control algorithm with two different motors. figure 7: functional sample of the gen2 vehicle traction battery. obrázek 7: funkční vzorek trakční baterie vozu gen2. figure 8: model of disassembled module of gen2 traction battery. obrázek 8: model rozloženého modulu trakční baterie gen2. experimental electric vehicle ešus gen2 josef břoušek, martin bukvic, pavel jandura mecca 02 2016 page 12 acknowledgements this publication was written at the technical university of liberec as part of the project 21127 with the support of the specific university research grant, as provided by the ministry of education, youth and sports of the czech republic in the year 2016. the results of this project lo1201 were obtained through the financial support of the ministry of education, youth and sports in the framework of the targeted support of the “national programme for sustainability i” and the opr&di project centre for nanomaterials, advanced technologies and innovation cz.1.05/2.1.00/01.0005. list of abbreviations acim alternating current induction motor af axial flux electric machine bev battery electric vehicle bms battery management system dct dual clutch transmission dmds dual motor drive system li–ion lithium – ion technology mst multi – speed transmission nca nickel cobalt aluminum nedc new european driving cycle nmc nickel manganese cobalt pcm phase change material pmsm permanent magnet synchronous machine rf radial flux electric machine sst single – speed transmission awd all wheel drive references [1] jandura, p., bukvic, m.: lightweight battery electric vehicle for educational purposes. in: applied mechanics and materials vol. 390 (2013) pp. 281-285. icmae 2013, moscow. [2] ehsani, m., gao y., emadi, a. configurations of evs in: modern electric, hybrid electric, and fuel cell vehicles: fundamentals, theory, and design. 2nd ed. boca raton: crc press, c2010, xxii, 534 p. power electronics and applications series. isbn 14-200-5398-1. [3] felden, m., butterling, p., jeck, p., eckstein, l., hameyer, k. electric vehicle drive trains: from the specification sheet to the drive-train concept. in: proceedings of 14th international power electronics and motion control conference epepemc 2010. doi: 10.1109/epepemc.2010.5606531. [4] tang, y. tesla motors, inc.”dual motor drive and control system for an electric vehicle”. u.s. patent 20100222953. [5] ren, q., crolla, d.a., morris, a. effect of transmission design on electric vehicle (ev) performance. in: 2009 ieee vehicle power and propulsion conference. ieee, 2009, pp. 1260-1265. doi: 10.1109/vppc.2009.5289707. [6] viotto, f. a novel seamless 2-speed transmission system for electric vehicles: principles and simulation results. in: electronic systems for vehicle propulsion symposium. troy (detroit), mi, 8-9 november 2011. [7] holdstock, t., sorniotti, a., everitt m., fracchia m., bologna, s., bertolotto, s. energy consumption analysis of a novel four-speed dual motor drivetrain for electric vehicles. in: 2012 ieee vehicle power and propulsion conference. ieee, 2012, pp. 295-300. doi: 10.1109/ vppc.2012.6422721. [8] allcell technologies, llc. pcc thermal management material. chicago, usa, 2014. figure 9: experimental vehicle ešus gen2 on a chassis dynamometer. obrázek 9: experimentální elektromobil ešus gen2 na válcové brzdě. overview and trends in automotive gearboxes of standard powertrains gabriela achtenová mecca 02 2016 page 13 10.1515/mecdc-2016-0008 overview and trends in automotive gearboxes of standard powertrains gabriela achtenová 1. introduction in the first years of the 21st century, a remarkable increase of different transmission solutions occurred in serially produced cars. obviously, most of the ideas were invented in the last two decades of the 20th century, but as can be clearly seen from figure 1, the realisation and market introduction did not begin until the start of the 21st century. the reasons why after 60 years of slow evolution such a relatively brief period of intensive transmission research occurred seems to lie in the technological developments in combination with global economic and political situation: • growth of the new domain of mechatronics became possible thanks to the fast progress of electronics and microelectronics in the last decades of the 20th century. mechatronics are critical to the improvement of control and actuation of transmissions, in terms of acceptable shift comfort of automated transmissions for the passenger car driver. • during the observed last 20 years the internal combustion engine (ice) remained the main energy source. for the shortand medium-term future a revolution in the power unit is not likely to occur. in last years, many new ideas and different powertrain solutions are proposed based on hybrid powertrains or pure electric drives. the amount of these vehicles will grow, however, very much depending on the change of existing infrastructure, and on the willingness of customers to accept new types of powertrains. • the revolutionary growth of diversity of proposed powertrains can be further explained in the limits of crude oil and political instability in some areas of its deposits, which have lead developments of ice away from achieving more power to efficiency improvements. the transmission efficiency, the gearbox spread, and the number of gears are getting more important for the evaluation of the driveline. • because of the emergence of intercontinental automotive concerns which use one vehicle platform for different car brands and types (the trend started mainly because of the economic recession at the end of 20th century) the power-weight ratio of vehicles has become basically uniform for all continents (e.g. in the 1960’ies the power-weight ratio of us cars was gabriela achtenová czech technical university in prague, technická 4, cz-166 07, prague 6, czech republic, e-mail: gabriela.achtenova@fs.cvut.cz shrnutí článek shrnuje výsledek statistických dat čerpaných zejména z katalogu revue automobile z let 1995, 2000, 2005, 2012, 2015. shromážděná data dávají přehled o vývoji a trendech technických parametrů převodovek osobních vozidel. pouze „klasická“ hnací ústrojí, kde zdrojem energie je spalovací motor jsou zahrnuta do této studie. hybridizace nebo elektrifikace vozidel na počátku této statistiky neexistovala nebo jen ve zcela výjimečných případech. klíčová slova: převodovky osobních automobilů, hnací ústrojí se spalovacím motorem, statistické údaje abstract in this article we present an overview and summarize trends in automotive gearboxes of standard powertrains. the majority of data used in the statistics are obtained from catalogue de la revue automobile published in years 1995, 2000, 2005, 2012 and 2015. observed statistical data gives overview about trends in technical parameter of automotive transmissions. only “standard powertrains”, where the only energy source is the internal combustion engines are taken into account. the hybridization or electrification of powertrains was not an issue on the beginning of the study. keywords: passenger car gearboxes, powertrains with internal combustion engine, statistical data overview and trends in automotive gearboxes of standard powertrains overview and trends in automotive gearboxes of standard powertrains gabriela achtenová mecca 02 2016 page 14 twice that of european passenger vehicles). engines are downsized and transmission efficiency now plays an important role in car performance and fuel consumption. the whole drive-line has become subject of efficiency increase. • to stabilise environmental changes caused by emissions of noxious gases the governments worldwide introduced emission limits. the tightest limits are imposed in europe. • mobility has strongly increased and is now often considered a necessity. the need to manage the huge increase of transport could lead in the future to traffic supervisors, which may even intervene in the vehicle driveline, e.g. to change the vehicle speed according to instantaneous conditions like jams, accidents, weather, etc. fully automatic driveline control then becomes a necessity, which may lead to complete replacement of manual transmissions by automatic controlled ones. • mastering of previously known principle of dual clutch transmission to the level that it could be used in serially produced cars make a huge competitor to standard automatic transmission. • mastering of computer synthesis of stepped planetary gearboxes kept the position of automatic transmissions on the market. the evolution of the passenger car transmission market in the last 20 years is shown in the following graphs. the car parameters were taken from [1], [2], [3], [4] and [5] corresponding to the years 1995, 2000, 2005, 2012 and 2015. the parameters of more than 700 passenger car types in every chosen year were processed and statistically evaluated. the involved vehicles are all passenger car types. terrain vehicles, suvs, vans and cabrios were excluded. from the data we derive an overview of number of different transmission types corresponding to the number of different brands and models. it is important to note that the total volume of produced gear-boxes is not taken into consideration, but only the number of different types (thus, luxury models produced in low amount such as by mclaren or ferrari count as much as mass produced models). most of the studies published relies on the market share or on the number of produced units. these statistics are based on technical data, and on amount of vehicle types in which concerned transmissions are used. the overview concerning production figures up to 2004 can be found in for example [8]. we differentiate the transmissions into the following groups: m = mechanical driver shifted transmission; a = automatic transmission (generally transmissions which consists from planetary gearsets and hydrodynamic torque converter. important point is that gearshift is powershift); amt = automated different transmission systems in the vehicles in last 20 years 0 10 20 30 40 50 60 70 80 90 100 1995 2000 2005 2012 2015 p er ce nt ag e [% ] years cvt m6 m5 m4 a8 a7 a6 a5 a4 amt7 amt6 m7 a9 a3 amt5 cvt m6 m5 m4 a8 a7 a6 a5 a4 amt7 amt6 m7 a9 a3 amt5 figure 1: evolution of the amount of transmission types in last 20 years. obrázek 1: vývoj nasazení různých typů převodovek za posledních 20 let. overview and trends in automotive gearboxes of standard powertrains gabriela achtenová mecca 02 2016 page 15 transmission (in this group belong the classical automated transmissions with single automated clutch, but also the dual clutch transmissions. the decisive point is that driver has two pedal vehicle with a gearbox where the gearshift occurs with interruption of torque flow); cvt = continuously variable transmission of any existing type. for models where more engine variants are offered, the least powerful and the most powerful version of both petrol and diesel engines were taken. as can be seen in figure 1, between the years 1995 and 2000 the choice of transmissions remained the same: manual transmissions (mt) having 6, 5 and 4-speeds, automatic transmissions (at) with 5, 4 and 3-speeds and continuously variable transmissions (cvt). from the year 2000 till 2005 the offer increased with 6 and 7-speed automatic transmissions, automated mechanical transmissions (amt) dual clutch or the gearboxes with shifting with interruption of torque flow having 7, 6 or 5-speeds. in the most recent years the offer even increased more. the successful introduction of dual transmission on the market, together with mastering of synthesis of planetary sets “woke up” the segment of automatic transmissions. the variants with 7, 8 and 9-speeds were introduced on the market. the amount of the speeds of automatic transmissions is not final, as can be seen for example in this year’s introduced 10-speed at from ford. 2. engine parameters to be able to fully understand the development in the transmissions, we have to briefly look on the changes of engine parameters during the years. in the years 1995, 2005 and 2015 we observed also the curb weight of vehicles, wherefrom the specific power was calculated. the amount of specific power 110 100 90 80 70 60 50 40 100 80 60 40 20 0 1995 2005 2015 years kw/t (p) kw/t (d) 1995 2005 2015 p er ce n ta ge [ % ] years petrol diesel sp ec ifi c p o w er [ kw /t ] figure 2: changes of mean specific power of petrol (p) and diesel (d) engines of passenger cars during last two decades. obrázek 2: změny průměrné hodnoty měrného výkonu u zážehových (p) a vznětových (d) motorů osobních vozidel. representation of engines in vehicles 110 100 90 80 70 60 50 40 100 80 60 40 20 0 1995 2005 2015 years kw/t (p) kw/t (d) 1995 2005 2015 p er ce n ta ge [ % ] years petrol diesel sp ec ifi c p o w er [ kw /t ] figure 3: representation of usage of petrol and diesel engines in passenger vehicle models in last two decades. obrázek 3: poměr použití zážehových a vznětových motorů v modelech osobních vozidel v posledních 20 letech. mean engine toque related to different transmission types 0 50 100 150 200 250 300 350 1995 2000 2005 2012 2015 a4 a7 a8 a5 amt6 amt7 a3 m4 m6 m5 a9 a6 amt5 cvt m7 50 100 150 200 250 300 350 400 450 500 550 600 1995 2000 2005 2012 2015 e ng in e to rq ue [n m ] years m6 a5 a4 m5 cvt a3 m4 amt7 a9 a8 amt6 m7 a6 amt5 2 3 4 5 6 7 8 9 1995 2000 2005 2012 2015 g ea rb ox s pr ea d [] years amt6 m5 amt7 a6 m4 a4 a7 amt5 m7 a3 m6 a9 a5 cvt a8 a7 figure 4: mean value of transmitted torque by different transmission types during last two decades. obrázek 4: střední hodnota přenášeného točivého momentu jednotlivými druhy převodného ústrojí za posledních 20 let. range of torque for different transmission types in year 2015 m om en t [ n m ] m om en t [ n m ] range of torque for different transmission types in year 2015 12 10 8 6 4 2 0 1400 1200 1000 800 600 400 200 0 900 800 700 600 500 400 300 200 100 0 s pr ea d [1 ] !"#$%&'(&)*+%",&-#&)%+-"../&*+',01%,&2+"#)3-))-'#)&-#&4567& figure 5: torque range for different transmission types in 2015. obrázek 5: rozsah točivého momentu různých převodných ústrojí v roce 2015. overview and trends in automotive gearboxes of standard powertrains gabriela achtenová mecca 02 2016 page 16 observed vehicles has increased. in the year 1995 we treated in the statistics about 750 models, whilst in the year 2015 the number of relevant models has increased to 1350. the graphs on figures 2 and 3 show the outcomes concerning the percentage of the representation of diesel and petrol engine in different models (again no reference to number of produced pieces). further we determined the evolution of specific power during last 20 years for diesel and petrol engines. wherefrom we can clearly see, that the mean of specific power of diesel engines was constantly growing, although the graph in last decade has smaller progression factor. petrol engines at the end of last century kept the mean specific power constant. in last decade, we can observe important growth of specific power. from figure 3 we can observe the increase of usage of diesel engine. more precise the number of serially produced models equipped with diesel engine doubled the amount used in the year 1995. 3. transmission parameters the next interesting trend concerns the relationship between mean value of transmitted torque and the transmission type during the years (figure 4). the curves of 6-speed manual transmission have a downward trend, which means that from the class of luxury powerful cars the six speed transmissions move to the range of medium passenger car class. the upward curve of cvt shows the increasing development of the frictional transmission. the upward trend of 4 and 5-speed automatic gearboxes is interrupted in 2000, when automatic and automated gearboxes with higher number of speeds were introduced on the market. in all cases it is necessary to treat the values in newcomers, or values of almost obsolete models very carefully. for example, the 3-speed automatic transmission is in last decade used only in zil 4104. therefore, we cannot really speak about mean values, since it concerns only one type and one engine. the newcomer transmissions like 8 and 9-speed automatic transmissions are in the early stage of their usage limited to upper class vehicles only. as example we can cite the a9 (9-speed automatic transmission). this gearbox was in 2015 used only in following type of vehicles: chrysler 200, jeep renegade, land rover models and mercedes e-class. we can observe a strong increase of torque for amt7; this can be explained by two facts. the usage of amt7 is still relatively limited, so any vehicle with very high or very low torque can influence the result. in the year 2015 the 7-speed dual clutch transmission was used in bugatti veyron. its 850 nm influences the shape of the mean torque of this transmission. gearbox spread evolution 0 50 100 150 200 250 300 350 1995 2000 2005 2012 2015 a4 a7 a8 a5 amt6 amt7 a3 m4 m6 m5 a9 a6 amt5 cvt m7 50 100 150 200 250 300 350 400 450 500 550 600 1995 2000 2005 2012 2015 e ng in e to rq ue [n m ] years m6 a5 a4 m5 cvt a3 m4 amt7 a9 a8 amt6 m7 a6 amt5 2 3 4 5 6 7 8 9 1995 2000 2005 2012 2015 g ea rb ox s pr ea d [] years amt6 m5 amt7 a6 m4 a4 a7 amt5 m7 a3 m6 a9 a5 cvt a8 a7 figure 6: evolution of gearbox spread in different transmission types. obrázek 6: vývoj rozsahu jednotlivých druhů převodovek. range of spread in serially produced transmission in 2015 m om en t [ n m ] m om en t [ n m ] range of torque for different transmission types in year 2015 12 10 8 6 4 2 0 1400 1200 1000 800 600 400 200 0 900 800 700 600 500 400 300 200 100 0 s pr ea d [1 ] !"#$%&'(&)*+%",&-#&)%+-"../&*+',01%,&2+"#)3-))-'#)&-#&4567& figure 7: the range of spread of all type of transmissions for passenger cars produced in 2015. obrázek 7: rozpětí rozsahu všech typů převodovek sériově vyráběných v roce 2015 v osobních vozidlech. mean value of gearbox spread related with number of speeds y = 0,1002x3 1,7664x2 + 10,715x 16,93 10 9 8 7 6 5 4 3 2 1 0 2 3 4 5 6 7 8 9 10 11 g ea rb ox s pr ea d [] number of speeds [-] mean value of gearbox spread related with number of speeds cvt figure 8: relation of gearbox spread on number of speeds. obrázek 8: závislost rozsahu převodovky na počtu rychlostních stupňů. overview and trends in automotive gearboxes of standard powertrains gabriela achtenová mecca 02 2016 page 17 how big the range of torques of different transmission types can be is shown in figure 5. this figure is related to year 2015 only. in this graph are also clearly separated the amt transmissions with single clutch and double clutch transmissions. the torque introduced in figure 4 is just averaged value. an important parameter for any gearbox is its spread. in figure 6 we can observe the evolution. in this case we have to be even more careful about values for newcomer transmissions. the 8 and 9-speed automatic transmissions exist (or in model year 2015 existed) only in one or maximally two combinations of gear ratios. the spread for different transmission types can be very tight, something which is depicted clearly in figure 7. in this figure we can observe the range of spread of different transmission types used in the year 2015. the narrower field of the range the less variants of the gearbox exists. the interest of more speed transmissions is to obtain high transmission spread, which will allow better adherence to the traction hyperbola, and to better use the sweet point of internal combustion engine. figure 8 shows the relation between the mean spread and the number of speeds. the values were taken from the year 2015. all types of gearbox with the same number of speeds were averaged. for the stepped transmissions we can very roughly say, that the spread of transmission is approximately equal the number of speeds (just forward speeds counted). as in the year 2015 were not yet introduced the 10-speed gearboxes, we kept this column to show the averaged spread of all cvt systems in 2015. 4. conclusion in this paper we presented an overview and summarized trends in automotive gearboxes of standard powertrains, based on data mainly taken from catalogue de la revue automobile published in years 1995, 2000, 2005, 2012 and 2015. observed statistical data gives overview about trends in technical parameter of automotive transmissions. in 1995 existed on the market of serial produced vehicles 3 types of transmissions: mechanical, automatic and cvt’s. mechanical ones were available in 4-, 5and 6-speed variants, automatic planetary power shifted gearboxes existed in 3-, 4and 5-speed variants. totally were on the market 7 transmission variants. if we will group together the automated single and double clutch transmissions, then the amount of proposed transmission variants in 2015 just doubled the amount of 20 years ago. in the year 2015 the customers could choose from 3to 9-speed automatic transmissions, 5to 7-speed mechanical manually shifted gearboxes, 5to 7-speed automated transmissions, and cvt’s. if we will separate the automated single clutch gearboxes and double clutch transmissions, then we can count till 17 different gearbox variants on the market. during the years completely disappeared the 4-speed manually gearboxes. the 3-speed automatic gearbox is offered in one last vehicle type. the huge diversity on the market is in last period further enlarged by introduction of hybrid or electric vehicles, which are not included in this statistics. list of abbreviations m mechanical driver shifted gearbox amt automated transmission (single or double clutch) amtsc automated single clutch transmission amtdc double clutch transmission a automatic powershift transmission cvt continuously variable transmission acknowledgements this research has been realized using the support of the ministry of education, youth and sports program npu i (lo), project lo1311: ’development of centre of vehicles for sustainable mobility’. the support is gratefully acknowledged. references [1] katalog der automobil revue. hallwag ag, bern, isbn 3-444-10444-8, 1995 [2] katalog der automobil revue. hallwag ag, bern, isbn 3-444-105896-x, 2000 [3] katalog der automobil revue. büchler grafino ag, bern, isbn 3-905 386-05-4, 2005 [4] katalog der automobil revue, isbn 978-3613307186, 2012 [5] katalog der automobil revue. motorbuch verlag, isbn 978-3-613-30792-6, 2015 [6] sytný m., přehled a trendy ve vývoji převodovek osobních automobilů, bp čvut v praze, 2013 [7] kotrč j., přehled a trendy ve vývoji převodovek osobních automobile, bp čvut v praze, 2016 [8] naunheimer h., bertsche b., ryborz j., novak w., automotive transmissions, springer verlag, isbn 978-3-642-16213-8, 2011 tool for the synthesis of mechanisms of new engines based on dasy david richtr mecca 02 2017 page 1 10.1515/mecdc ‑2017 ‑0005 tool for the synthesis of mechanisms of new engines based on dasy david richtr 1. introduction and research the creation of the model of the single ‑cylinder parametric model was based on a four ‑cylinder engine. parameters of the different parts were available for this engine from cad models. data such as valve acceleration curves, actual speed and the forces acting on the rocker arm were available from experiments. the entire parametric model was divided into sub ‑models which were subjected to calibration according to this available data. a conventional approach to the simulation of the dynamics of the mechanism consists of modeling individual subsystems separately and subsequently using the results of its marginal conditions for another sub ‑model. it is advisable to approach the analysis of the individual interactions between individual subsystems holistically. it is possible to use commercial or university software. the commercial software includes, for example, gt ‑suite, a ricardo software suite (valvedyn, wave, engdyn…), or simpack. university software includes, for example, mbsim of the munich technical university. individual solutions are offered by modeling of a system of 1d/2d/3d bodies using an approach where the bodies can be solid or flexible. the finite element method is used to address the deformations of each body. depending on the complexity of the model and the required results, it is important to pick a suitable approach with respect to the time ‑intensity of the calculations. the advantage of modeling of individual subsystems separately is a greater number of parameters which describe the real model in greater david richtr ctu in prague, faculty of mechanical engineering, technická 4, 166 07, praha 6. tel.: +420728462851, e ‑mail: richtrd@gmail.com shrnutí článek se zabývá prezentací nástroje pro syntézu mechanismů motoru založený na dasy a jeho využití při návrhu parametrů experimentálního jednoválcového motoru. nástroj obsahuje parametrický model motoru založený na dasy. model umožní simulovat termodynamiku motoru a jeho mechanismy. skládá ze submodelů, které řeší termodynamiku, kinematiku a dynamiku rozvodového mechanismu, jeho řemenový pohon a hydraulický okruh natáčení vačkových hřídelí. metodik syntézy mechanismů bylo využito pro nalezení hodnot kalibračních parametrů. následně byly parametry submodelů validovány experimentálními daty a jejich hodnoty jsou obsaženy v dasy. ze submodelů byl sestaven model experimentálního jednoválce, který ověřuje jeho konstrukci, umožňuje optimalizovat jeho parametry a předpovídat jeho chování v různých simulovaných stavech. klíčová slova: variabilní ventilový rozvod, vačka, ventil, vačková hřídel, hydraulický přesuvník vačkové hřídele, simulace, experimentální zážehový motor, dynamika, výpočet, gt ‑suite abstract the article presents a tool for the synthesis of engine mechanisms based on dasy and the use thereof for designing the parameters of an experimental single ‑cylinder engine. the tool includes a parametric engine model based on dasy. the model will make it possible to simulate the engine thermodynamics and its mechanisms. it consists of sub ‑models which deal with the thermodynamics, kinematics and dynamics of the valve timing mechanism, its belt drive, and hydraulic circuit for camshaft adjustment. the methodologies of synthesis of mechanisms were used to determine the values of the calibration parameters. the parameters of the sub ‑models were subsequently validated by experimental data, and the values thereof are included in dasy. the sub ‑models were used to assemble the model of an experimental single ‑cylinder engine which validates the design thereof, makes it possible to optimize its parameters and predict its behavior in different simulated conditions. key words: variable valve train, cam, valve, camshaft, hydraulic cam phaser, experimental si engine, simulation, dynamics, calculation, gt ‑suite tool for the synthesis of mechanisms of new engines based on dasy tool for the synthesis of mechanisms of new engines based on dasy david richtr mecca 02 2017 page 2 detail and contribute to greater capability of calibration of the model with a relatively low time ‑intensity of the calculation. synthesis of the individual mechanisms therefore increases the number of parameters which are used for sufficient description of the entire mechanism, and thus the calculation demands. it is necessary to optimize the number of parameters, such as to achieve a reasonable calculation time and describe all important dynamic phenomena. out of the freely available sources, we can mention – as an example of holistic approach to the synthesis of mechanisms in [1]. the software used for calibration of the parameters of the individual sub ‑models was dasy as a multi ‑parametric solver that uses a genetic algorithm. 2. description of the sub ‑models the creation of the parametric engine model involved division of the entire model into sub ‑models. the parameters of these sub‑ ‑models were calibrated according to the available measurement data; see chapter 3. 2.1 thermodynamic sub ‑model the thermodynamic sub ‑model makes it possible to simulate the thermodynamics of the engine such as, for example, a model of the si combustion, heat transfer to the cylinder walls, fluid dynamics in the pipes. the sub ‑model can be used for determination of the performance characteristics of the engine, specific fuel consumption, and other parameters. an important capability of the thermodynamic model is determination of the optimal timing of the intake and exhaust valves to maximize the torque and minimize consumption, which should ensure reduction of the emissions in the exhaust gases. the determination of the optimal timing must be considered with regard to the design limits of the engine, respecting for example the collision of the piston and the valves. 2.2 model of the intake and exhaust valve dynamics one of the more sophisticated sub ‑models for calibration is the model of the intake and exhaust valve dynamics. their models are identical and only differ by the cam profiles used and input parameters of the individual elements. the specific type of the valve ‑operating mechanism used in the model is dohc. for the single ‑cylinder engine model it includes two intake valves and two exhaust valves. for calibration and acceleration of the calculation time, the sub ‑model was simplified to include one separate valve in order to find the values of the calibration parameters. the model is described by a total of 37 parameters with which it was calibrated. the calibration parameters are divided into two parts. the first part is physical, input parameters of the elements such as stiffness of the individual parts (valve, rocker arm…) which were determined using the fem. these parameters remain constant with the changing rotation speed. the second group is parameters of the contact points (figure 3) which are generally used for mathematic transmission of information between the individual elements and the value of which is difficult to determine. it is assumed that they can change with the change of the actual rotation speed. the reason is that some of these elements ensure convergence of the numerical solution. for example, the ramp function of stiffness simulates the flexibility upon contact of two bodies and deals with the step change of stiffness of the contact which would cause the complications in the numerical solution. the model includes an active predictive tribological model dealing with the elastohydrodynamic contact between the individual elements. 2.3 model of a timing belt with hydraulic cam phaser the model includes a toothed belt pulley with hydraulic cam phaser on the intake and exhaust side, a toothed belt pulley on the crankshaft, idler and tensioner, and a toothed belt. the gt‑ ‑ise environment models a toothed belt as a system of flexible beam elements and rigid bodies in the form of teeth. the beams are considered loaded with axial and shear stress and bending moment. the entire system is discretized using the principle of the finite element method. the number of teeth represents the number of the finite elements which are connected in nodes. in physical terms, the belt consists of a rubber body and steel cord. it is the steel cord that increases the overall stiffness of the belt and reduces the amplitude of inherent oscillation. based on the density of the composition of the rubber and the steel cord, the exhaust camphaser submodel intake camphaser submodel intake valve submodel exhaust valve submodel timing belt submodel thermodynmic submodel figure 1: schematic single ‑engine model in gt ‑ise. obrázek 1: schematický model parametrického jednoválcového motoru. tool for the synthesis of mechanisms of new engines based on dasy david richtr mecca 02 2017 page 3 weight and the moment of inertia of one element are estimated for the model. more accurate values of these parameters were determined based on calibration the results of which are provided in chapter 3.2. the parameters of the hydraulic cam phaser and the other inlet pipes and volumes were measured out from the available cad data. for the cam phaser were important moments of inertia of the stator and rotor, number and volume of the advance and retard chambers and the maximum angle of the phase change and the size of the effective area of the rotor blades. measurement data was not available for the hydraulic part, and therefore the results of the hydraulic model only server as prediction. the model of a drive of timing mechanism with cam phasers is shown on figure 4. 3. calibration and validation of the sub ‑models the calibration of individual sub ‑models was performed according to the available measurement data, at multiple rotation speed points. this approach ensures that a broader interval of dynamic phenomena is covered. the calibration and validation of the sub ‑models was performed using the dasy software in the case of the intake and exhaust valve dynamics and the thermodynamic sub ‑model. this software uses a genetic algorithm which is based on the principle of evolution biology and uses processes such as crossbreeding, figure 2: single ‑cylinder engine thermodynamic model with intake and exhaust system. obrázek 2: termodynamický model jednoválcového motoru. figure 3: model of single ‑valve mechanism. obrázek 3: model sacího ventilu. kinematic model from vt ‑design input rpm map contact points tool for the synthesis of mechanisms of new engines based on dasy david richtr mecca 02 2017 page 4 mutation, natural selection or hereditability. the advantage of this software is that it solves optimization tasks with many variable parameters and looks for the optimal solution according to the predefined criteria. gt ‑suite includes a program called gt ‑post which is used for displaying the simulation results. the results are divided into two types. the first type is display of the calculated values of magnitudes such as continuous function depending on time or angle in one or more operation cycles. the other type is display of the value of the magnitude as a single integral value in the form of average, maximum, minimum, or cumulative value integrated over a cycle. an example is effective mean pressure, average torque, average consumption, etc. this form of result is called rlt. 3.1 optimization of the thermodynamic model optimization of the valve timing is based on the rlt ‑type results. the optimization was performed in order to determine the maximum torque along with the minimum specific consumption. the results file of the gt ‑post program exports output rlt magnitudes of the specific consumption and torque into a text file. this file, together with the model from gt ‑ise, is uploaded to the dasy environment where independent and dependent parameters are chosen. the independent parameters are defined as input values, i.e., starts of valve lift. in addition, an interval is defined in which the input variables should change in order to prevent collision of the piston and valves. the dependent parameters are output magnitudes, i.e., values of the specific consumption and torque. a sample of the parameter settings together with a simple flowchart is shown on figure 5. the output is a set of results from which the compromise between the maximum torque and minimum consumption must be selected manually. in addition, it is necessary to respect figure 4: model of timing belt with pulleys and hydraulic cam phaser obrázek 4: model řemenového rozvodu a hydraulického camphaseru figure 5: setting the known and unknown parameters in dasy obrázek 5: nastavení známých a neznámých parametrů v dasy exhaust side timing belt mechanism input parametrs output parametrs intake side tool for the synthesis of mechanisms of new engines based on dasy david richtr mecca 02 2017 page 5 the rotation speed of the engine for which the optimization was performed. the optimal timing determined for the version used in this model, i.e., single ‑cylinder, unsupercharged engine with external formation of the mixture, is shown in table 1. the optimization was performed for maximum engine load. 3.2 calibration of the dynamics of the intake and exhaust valve calibration of the dynamic characteristics of the valve train mechanism was also performed using the dasy software. the process and evaluation of the calibration is identical as in the case of [3]. for the evaluation of the objective function, the genetic algorithm searched for the minimum value of the sum of the squares of the deviations between the objective function and the current curve from the simulation at the reference points. the deviations were observed on the valve acceleration curve in the time and frequency domain. the measured curve was decomposed by fourier transform into 64 harmonics where 15 reference points were determined (see [3]). 3.3 calibration of the timing belt transmission curves of actual rotation speed from the measurement and from the simulation results were compared in the toothed belt mechanism. as stated above, the material properties of the belt were used as parameters for calibration. the available data from the measurement, however, was for a four ‑cylinder engine, not for the single ‑cylinder engine under review. therefore, an auxiliary, purely mechanical model of four‑ ‑cylinder engine was built. this model was composed of the timing mechanism and intake and exhaust camshaft where the data from chapter 2.2 was used as the values of the valve mechanism parameters. this model was used only for more accurate determination of the toothed belt parameters. the basic material properties and the nominal pretensioning of the belt were determined by an estimate, and the more accurate value thereof was determined by calibration. the identical process was used as in the calibration of valve acceleration. in this case, however, there was sufficient decomposition into 32 harmonics using fourier transform of the actual rotation speed of the camshafts and only 6 reference points because the curve is periodical. the diagrammatic model from the dasy environment is shown below. the model includes the input parameters in the form of the material properties of the belt and the pretensioning thereof. the output is the reference points on the decomposed curve of the actual rotation speed. the best match was achieved at 2000 rpm. the parameters corresponding to this curve were used in the other rpm points. the value of the nominal pretensioning of the toothed belt was based on simulation of 253 n. according to the available table 1: results of valve timing optimization tabulka 1: výsledky hodnot optimálního časování ventilů rpm io before tdc [ca] eo before bdc [ca] 1000 17 29 2000 16 37.5 3000 14 42 4000 13 28 5000 10 25 6500 2 24 figure 6: comparison of simulation and measured data for intake valve acceleration obrázek 6: srovnání simulace a měření zrychlení sacího ventilu figure 8: comparison of the intake camshaft rpm from simulation and from measurement obrázek 8: porovnání průběhu okamžitých otáček na sací vačkové hřídeli ze simulace a měření figure 7: flowchart for calibration of the rotation speeds of camshafts in dasy figure 7: dasy set for camshaft rpms tool for the synthesis of mechanisms of new engines based on dasy david richtr mecca 02 2017 page 6 information, this value ranges between 305÷380 n in a real four ‑cylinder engine. this can be considered sufficiently accurate approximation to reality, to which also the below ‑pictured curve of the actual rotation speed corresponds. 4. reference results of the predictive model connection of the sub ‑models resulted in a predictive model of a single ‑cylinder engine which was used for calculations supporting the design of the parameters and design of a real engine. the parameters obtained from the auxiliary calibration sub ‑models were put in this predictive model for each rotation speed point. they are parameters of the toothed belt, the intake and exhaust valves. the predictive model of a virtual single ‑cylinder engine can be used also for prediction of the behavior of a real engine in different conditions which cannot yet be performed on a real engine as it is still under development. this can prevent conditions in which the timing elements would be damaged. a synthesis of the thermodynamic and mechanical model can be used to predict the load upon the timing system parts. the mechanical model provides the thermodynamic model with information on the lift curves and, on the other hand, receives information on the curve of the pressure in the channels, in the cylinder, and temperature gradients, which includes these influences on the calculation of the dynamics of mechanisms. the following three sub ‑chapters include the reference results of the single ‑cylinder engine. this data has not yet been validated experimentally. 4.1 determination of the maximum rotation speed the determination of the maximum rotation speed (rpm) of the timing mechanism is based on the monitoring of the valve lift curve and dynamic influences. the limit condition is one where the masses of the timing mechanism are accelerated and the valve spring is excited with a frequency approximating its natural frequency. at this moment the spring loses its pre‑ ‑tensioning and ability to close the valve in accordance with the defined cam profile. the valve seating velocity is also higher than the pre ‑scribed velocity, and valve separation occurs. this condition is undesirable because it increases the load and wear and tear of the entire mechanism. one of the possible methods to determine the limit rotation speed is monitoring and comparing the kinematic and dynamic lift curve of the valve. in the optimal scenario, the dynamic lift curve is lower than or equal to the kinematic curve due to the flexibility and stiffness of the different parts. to determine the valve separation from the seat, the valve separation element was used. it is element, which compares difference between dynamic and kinematic valve lift. the positive value of valve separation (exceeding zero value) represents the separation of the valve from the seat. based on the analysis of this curve, the maximum operating rotation speed of the valve train was determined. the chart below shows the curve of valve separation at the rotation speed limit where no separation occurs yet. after having exceeded this value, separation occurs after valve seating (the critical zone is depicted in red). it is the first identifiable condition where stroke occurs in the valve seat. the valve train, however, can be operated further up to higher speed because the limit value of valve separation is determined by the design limits of the mechanism. for example it means the maximum possible gap between valve and valve seat after valve bounce defined by designers. valve seating velocity gradient increases with the increasing rotation speed, which is also associated with excitation of the valve spring. as i have stated above, due to the loss of pretensioning of the valve spring by the excitation with natural frequency the valve separation is not absorbed by the spring. this results in increased stress on the entire valve train. figure 9: valve separation dependence on relative camshaft rpm obrázek 9: průběh odskoku ventilu od sedla v závislosti na otáčkách vačkové hřídele figure 10: valve lift curves and the impact on the actual rotation speed of the camshaft obrázek 10: průběh zdvihových křivek ventilů a vliv na průběh okamžitých otáček vačkové hřídele tool for the synthesis of mechanisms of new engines based on dasy david richtr mecca 02 2017 page 7 4.2 actual rotation speed curve the actual rotation speed curve periodically oscillates around the mean value of relative rotation speed of the camshaft. the action of the exhaust cam on the valve overcomes the pre ‑tensioning of the valve spring and reduces the actual rotation speed. upon closure of the valve, the pre ‑tensioning in the spring increases the rotation speed. the same principle operates in the intake valves. after they have been closed, the actual rotation speed stabilizes around the mean value, which is manifested by decrease of the amplitude thereof. a partial test was performed because of the impact of the oscillation of the actual rotation speed in the region of closing of the valves, whether more significant deviations occur. no greater oscillation of the belt occurs, according to figure 10, in the deviation of the amplitude of the actual rotation speed from the value of mean rotation speed in the region outside of the valve lift. it means the sufficient value of pretensioning of the toothed belt, which can be used to predict good adjustment thereof. 4.3 interruption of the supply of pressure oil one of the possible conditions in which a single ‑cylinder engine can be found is a condition of certain failure. for example, in an experimental test, the oil circuit may be interrupted and the pressure jumps to a lower value. the mechanism includes a hydraulic cam phaser which is operated by pressure oil. upon the loss of oil pressure, the valve timing may change, leading to a collision of the piston and valve in the event that the cam phaser rotor is not locked by a pin. therefore in the design of the mechanism, it is necessary to take this risk into account and set the range of the cam phaser and valve timing such that a collision of the piston and valve can never occur. decrease in oil pressure in the cam phaser chambers adds a degree of rotor freedom of the system between the stator and blades of the rotor of the cam phaser. the chart below shows the curve of the phase change of the cam phaser in the event of a step change of the oil pressure. the added degree of freedom of the mechanism between the pulley and camshaft causes a phase change due to the momentum transmitted through the pulley and the angular momentum of the system. decreasing angular speed due to valve springs can cause overturning of the rotor blades against the stator between its walls. this will result in chaotic actual rotation speed of the pulley or, more precisely the camshaft. the type of failure where the rotor oscillates against the stator due to the sudden drop of oil pressure and, at the same time, the pin locking does not occur is very unlikely. but if it happens, it will have impact on the entire mechanism. according to figure 11, there is an apparent oscillation of the phase change of the cam phaser after oil pressure loss in a very short time interval. one of the effects of this cause is the form of the resulting lift curve in comparison with the kinematic curve. this difference is shown on the picture below. the separation of dynamic from kinematic lift means greater valve acceleration than the one for which the mechanism is designed. in the first lift curve we can observe greater separation, which is also associated with the impact of the rocker roller all the way to the base of the cam. the spring does not manage to absorb the impact of the valve, and an additional valve separation occurs. therefore, only from mechanical point of view a short ‑term interruption of oil supply is not dangerous because increased stress of the individual parts, such as valves, valve seats etc., only occurs locally. but on the other hand, total oil pressure interruption is dangerous for whole engine, if engine does not stop as soon as possible. with this phenomenon is connected secondary problem, which is the deviation of the lift curve from the required curve. see figure 12. 5. conclusion the article presented the application of a tool for synthesis of engine mechanisms based on dasy. the application includes creation of a computer parametric model of variable valve train with toothed belt, and a thermodynamic model of a single ‑cylinder engine in the environment of the gt ‑suite software. dasy software with genetic algorithm was used figure 11: dependence of cam phaser phase angle on oil pressure obrázek 11: závislost fázové změny camphaseru na tlaku oleje figure 12: impact of oil pressure loss on valve lift curve obrázek 12: vliv poklesu tlaku oleje na zdvihovou křivku ventilu tool for the synthesis of mechanisms of new engines based on dasy david richtr mecca 02 2017 page 8 for calibration and optimization of the model. the optimal approach seems to be looking for the objective function of the continuous function such as valve acceleration or actual rotation speed curve using a set of reference points and evaluation using the method of minimum value of the sum of the squares of the deviations. calibration of individual models according to the data measured is more time ‑intensive also after having used certain simplifications, but a connection thereof leads to the resulting model with a relatively accurate predictability. the holistic approach to the mechanical part of the model seems beneficial in terms of examination of the mutual interactions between the mechanism members. with respect to the uniqueness of the prototype of the experimental engine, the computer model is a useful tool because it makes it possible to simulate conditions which cannot be performed on a test engine because it is still under development. some design modifications can be made, if applicable. last but not least, the simulation can prevent conditions where damage could occur to the engine, a fact that has been verified also by several predictive simulations. acknowledgements this work was supported by: • technological agency, czech republic, programme centre of competence, project #te01020020 josef božek competence centre for automotive industry. • the ministry of education, youth and sports program npu i (lo), project # lo1311 development of vehicle centre of sustainable mobility. list of notations and abbreviations dasy design assistance system b_d_c belt damping coefficient b_e_a belt axial stiffness b_e_i belt bending stiffness b_s_m belt sectional mass b_s_m_i belt sectional moment of inertia b_s_s belt shearing stiffness bsfc break specific fuel consumption dohc double over head camshaft eo exhaust valve open io intake valve open rpm revolution per minute tq torque si spark ignition references [1] fischer, thomas a benjamin schaal. holistic design of a cam phaser [online]. in: 2015, s. 28 [cit. 2017 ‑03 ‑19]. available from: https://www.gtisoft.com/wp ‑content/ uploads/2015/11/holistic_design_of_a_cam_phaser.pdf [2] gt ‑ise help, gt ‑suite version 2016, gamma technologies inc., 2015 [3] tichánek, radek. dasy based tool for the design of ice mechanisms. journal of middle european construction and design of cars. 2015 ‑01 ‑1, 13(3), doi: 10.1515/mecdc ‑2015 ‑0013. issn 1804 ‑9338. [4] richtr, david. výpočet dynamiky variabilního ventilového rozvodu [calculation of the variable valve train dynamics]. praha, 2017. thesis (by ing.). czech technical university in prague. faculty of mechanical engineering, department of automotive, combustion engine and railway engineering. supervisor: radek tichánek. https://www.gtisoft.com/wp-content/uploads/2015/11/holistic_design_of_a_cam_phaser.pdf https://www.gtisoft.com/wp-content/uploads/2015/11/holistic_design_of_a_cam_phaser.pdf _goback mecca 02 2017 page 49 study of the effects of ethanol as an additive with a blend of poultry litter biodiesel and alumina nanoparticles on a diesel engine ramesha d k, nishad rajmalwar, t sreeharsha varma, mrithyunajaya swamy k m 10.1515/mecdc ‑2017 ‑0008 study of the effects of ethanol as an additive with a blend of poultry litter biodiesel and alumina nanoparticles on a diesel engine ramesha d k, nishad rajmalwar, t sreeharsha varma, mrithyunajaya swamy k m ramesha d k, nishad ra jmalwar, t sreeharsha varma department of mechanical engineering, university visvesvaraya college of engineering, bangalore university, bangalore, karnataka, india ‑560001, dkramesha@bub.ernet.in mrithyuna jaya swamy k m department of mechanical engineering, vemana institute of technology, visvesvaraya technological university, bangalore, karnataka, india abstract with the increasing population and rise in industrialization, the demand for petroleum reserves is increasing almost daily. this is causing depletion of the non ‑renewable energy resources. this work aims to find an alternative fuel for diesel engines. the use of poultry litter oil biodiesel obtained from poultry industry waste, which is a non ‑edible source for biodiesel, is very encouraging as an alternative fuel for diesel engines. the aim of this study is to observe and maximize the performance of poultry litter oil biodiesel by adding alumina nanoparticles and ethanol. the biodiesel is prepared with acid and the base catalysed transesterification of poultry litter oil with methanol using concentrated sulphuric acid and potassium hydroxide as catalysts. the experimentation is carried out on a ci engine with three different blends – b20 biodiesel blend, b20 biodiesel blend with 30 mg/l alumina nanoparticles, and b20 biodiesel blend with 30 mg/l alumina nanoparticles and 15 ml/l ethanol. the performance, combustion and emission characteristics of all three blends are compared with neat diesel. the results of the experiment show that ethanol as an additive improves the combustion and performance characteristics. it increases the brake thermal efficiency and peak cylinder pressure. it also reduces co and ubhc emissions and there is a marginal increase in nox emissions as compared to neat diesel. key words: diesel engine; poultry litter oil methyl ester; biodiesel; alumina nanoparticles; transesterification; ethanol; performance; combustion; emission. shrnutí s rostoucím počtem obyvatel a nárůstem industrializace se den za dnem zvyšuje poptávka po ropných rezervách. to způsobuje vyčerpávání neobnovitelných zdrojů energie. tato práce si klade za cíl nalézt alternativní palivo pro dieselové motory. použití bionafty získané z oleje z použité podestýlky z chovů drůbeže, která představuje nekonzumovatelný zdroj pro výrobu bionafty jako alternativní palivo pro dieselové motory, je velmi slibné. cílem této studie je pozorovat a maximalizovat výkon bionafty z oleje z použité drůbeží podestýlky přidáním nanočástic oxidu hlinitého a etanolu. bionafta je připravována kyselinou a zásadou katalyzovanou transesterifikací oleje z použité drůbeží podestýlky a metanolem, kde jsou jako katalyzátory použity koncentrovaná kyselina sírová resp. draselný louh. experimentace se provádí na vznětovém motoru s třemi různými druhy směsi – směs bionafty b20, směs bionafty b20 s 30 mg/l nanočástic oxidu hlinitého a směs bionafty b20 s 30 mg/l nanočástic oxidu hlinitého a 15 ml/l etanolu. parametry výkonu, spalování a emisí všech tří směsí jsou srovnávány dieselovým palivem (naftou) bez přísad. výsledky experimentu ukazují, že etanol jako aditivum zlepšuje parametry spalování a výkonu. zvyšuje brzdnou tepelnou účinnost a maximální tlak ve válci. dále snižuje emise co a nespálených uhlovodíků, přičemž je zde marginální zvýšení emisí nox oproti naftě bez přísad. klíčová slova: dieselový motor; met ylester oleje z použité podestýlky drůbeže; biodiesel (bionafta); nanočástice oxidu hlinitého; transesterifikace; etanol; výkon; spalování; emise. study of the effects of ethanol as an additive with a blend of poultry litter biodiesel and alumina nanoparticles on a diesel engine mailto:dkramesha@bub.ernet.in mecca 02 2017 page 50 study of the effects of ethanol as an additive with a blend of poultry litter biodiesel and alumina nanoparticles on a diesel engine ramesha d k, nishad rajmalwar, t sreeharsha varma, mrithyunajaya swamy k m 1. introduction conventional fossil fuels cause environmental pollution and with demand for them ever increasing, they are being depleted at a fast pace. this situation necessitates paying greater attention to alternative fuels from natural resources, such as biodiesel and ethanol ‑biodiesel blends. both biodiesel and ethanol can be synthesized from feedstock, which is a renewable resource. the carbon in the biodiesel comes from the co2 present in the air, so the co2 engine emissions when running on biodiesel overall add much less to global warming compared to fossil fuels. efforts have been made to replace petroleum ‑based fuels with as much biofuel as possible because biodiesel by itself cannot be entirely used as a fuel [13] (xiaoyan shi et al. 2006). biodiesel can be produced using the process of transesterification of vegetable/ animal oil or fat with a short ‑chain alcohol like methanol or ethanol. the reaction gives mono ‑alkyl esters which can be used as biodiesel. neat oil cannot be used as a fuel mainly due to its high viscosity (28 ‑40mm²/s), which leads to deposition of carbon particles in the injector in a ci engine. this causes poorer atomization of fuel particles into the combustion chamber [2] (darunde dhiraj s. et al. 2012). since neat vegetable/animal oil or fat cannot be used as a fuel, transesterification is carried out to reduce the viscosity. transesterification is the reaction between a triglyceride molecule (found in vegetable oil or animal fat) and excess alcohol in the presence of a catalyst, such as koh, naoh etc., to give methyl esters and glycerin as a by ‑product [11] (sri harsha tirumala et al. 2012). the process occurs in several reversible steps where the triglyceride is converted to diglyceride, which is further converted to monoglyceride. these monoglycerides are then converted to esters and glycerol. the esters can be separated from glycerol using a separating funnel due to their density difference. in our experiment, the ester is called poultry litter oil methyl ester [3] (dr. sadhik b. j. et al. 2012). at present, diesel fuel additives are used to lower the particulate emissions and enhance fuel characteristics such as oxidation rate. additives also help to reduce emissions. one such additive are nanoparticles, which are pre ‑dissolved in the fuel and help increase the efficiency of the fuel and completion of the combustion process to reduce emissions of various harmful gases and particulate matter [8] (nithin samuel et al. 2015). with aluminium oxide nanoparticles as an additive, an increase in brake thermal efficiency and a reduction in emissions were observed. also, to increase the overall performance, combustion and emission characteristics of the engine, nanoparticles are the most suitable additive [9] (s.p. venkatesan et al. 2015). to further improve the performance of the engine, the potential use of biodiesel with an ethanol blend was investigated. ethanol improves the flow property of the fuel and helps ensure better atomization. it enhances the oxygen content of the fuel to help reduce emissions. the potential of poultry litter biodiesel with a blend of ethanol as a renewable energy resource is presented in this paper. 2. transesterification 2.1 esterification setup the oil used for biodiesel production was non ‑edible raw poultry litter oil. production was carried out using a laboratory setup. the setup consisted of beakers, flasks, a thermometer and a magnetic stirrer with temperature control and adjustable stirring speed. the properties of diesel fuel and plome are listed according to astm standards in table 4. the acid value of raw oil had been calculated using a standard titrimetric method as per european standard en14104. a conical flask was used as a laboratory scale reactor to carry out the transesterification process. the magnetic stirrer consisted of a heating coil with adjustable temperature. the flask was kept on the stirrer and the mixture was heated. the temperature for the reaction was maintained at 50 ‑60°c and the mixture was stirred at constant speed at all times. the esterification process was carried out in two steps since the oil viscosity was high. 2.2.1 acid catalysed transesterification acid transesterification was carried out by pouring 1 litre of raw poultry oil into the conical flask and heating it to a temperature of 50°c. once the oil reached this constant temperature, 500 ml of methanol was added and stirred for a few minutes. 10 ml of concentrated sulphuric acid was added to the mixture. this final mixture was maintained at a temperature of 50°c and stirred for 45 minutes at atmospheric pressure. the flask was removed from the stirrer and the mixture was allowed to settle. two layers separate out and were visible to the naked eye. the layers were separated using a separating funnel. the top layer consisted of excess methanol, sulphuric acid and light impurities, which were removed. the lower layer was poured into a different flask for the next step of experimentation. 2.2.2 base catalysed transesterification the final product from the first experimental setup of the acid catalysed process was used for alkaline esterification. the product was again heated to a temperature of 50°c in the flask. meanwhile, 0.24 g of koh was added to 100 ml of methanol in a beaker and thoroughly dissolved. this mixture was poured into the flask and heated at 50°c for 45 minutes. once the heating was complete, the mixture was allowed to cool down. again, layer separation was noticeable. this time the lower layer consisted of glycerol and impurities, which were discarded. the top layer mecca 02 2017 page 51 study of the effects of ethanol as an additive with a blend of poultry litter biodiesel and alumina nanoparticles on a diesel engine ramesha d k, nishad rajmalwar, t sreeharsha varma, mrithyunajaya swamy k m was the methyl ester, which was separated using the separating funnel. this ester contained some impurities and was therefore water washed. hot distilled water, 10% by volume, was sprayed over the surface of the ester and gently stirred. the water carried impurities and settled down at the bottom of the flask. the top layer (yellow colour) was the biodiesel which was separated and collected. 2.2.3 preparation of blend b20plome was prepared by mixing 20% by volume biodiesel with 80% by volume diesel in a beaker and stirring it for 15 minutes at constant room temperature. b20plome30a was prepared by adding 30 mg of alumina nanoparticles to 1 litre of b20plome biodiesel blend. b20plome30a15e was prepared by adding 15 ml/l of pure ethanol to the b20plome30a blend. 2.2.4 addition of alumina nanoparticles the nanoparticles were added to b20plome biodiesel fuel with the help of an ultrasonicator at a frequency of 24 khz. the process was carried out for 30 minutes. the mass fraction of the nanoparticles was 30 mg/l. it was weighed using an electronic weighing machine with readability of 1 mg. the ultrasonication technique disperses the nanoparticles in a base fluid, which in this case was the biodiesel fuel. it is the best suited technique since it prevents the aggregation of nanoparticles by agitating the particles using pulsating ultrasonic frequencies. the alumina nanoparticle specification is shown in table 1. figure 2 shows the morphology of alumina nanoparticles. surfactants were added to lower the surface tension between the liquid fuel and solid nanoparticles in order to stabilize the nanoparticles. 2.2.5 addition of ethanol ethanol was added with a composition of 15 ml of ethanol per litre of b20plome30a biodiesel fuel. the mixing process was carried out by constant stirring on the magnetic stirrer for 30 minutes without any heating, maintaining the mixture at room temperature. this final mixture is designated b20plome30a15e. 3. engine test the engine test was conducted on a single cylinder four‑ ‑stroke diesel engine with injection timing of 23 degrees btdc, injection pressure of 180, 17.5:1 compression ratio and a speed figure 2: transmission electron microscope image of alumina nanoparticle obrázek 2: obrázek elektronového mikroskopu hliníkových nanočástic figure 1: mechanism of the transesterification process obrázek 1: mechanismus procesu transesterifikace table 1: fuel properties tabulka 1: vlastnosti paliv sl. no. property astm method limits (b100) units diesel plome 1 colour ‑ ‑ ‑ orange pale yellow 2 density d941 ‑ kg/m³ 850 737 3 kinematic viscosity, 40°c d445 1.9 ‑6 mm²/s 2.5 5.48 4 calorific value d2015 ‑ kj/kg 42000 29000 5 fire point d93 ‑ °c 56 178 6 flash point d93 130 min. °c 50 154 7 cetane index d613 47 min. ‑ 55 61 mecca 02 2017 page 52 study of the effects of ethanol as an additive with a blend of poultry litter biodiesel and alumina nanoparticles on a diesel engine ramesha d k, nishad rajmalwar, t sreeharsha varma, mrithyunajaya swamy k m of 1500 rpm. the engine was initially hand cranked with a pure diesel supply to bring it to a steady state. the engine was coupled to an eddy current dynamometer that allowed varying of the engine load from no ‑load to full load. the engine test rig was computerized and both the engine and dynamometer were interfaced to a control panel in a computer. the computer had ‘engine analysis software’ which recorded test parameters such as temperature, air flow rate, fuel flow rate, load etc. it also plotted the engine performance characteristics such as brake thermal efficiency, heat release rate etc. the load was varied in four steps from no ‑load to full load. the engine was run with b20plome, b20plome30a and b20plom30a15e whilst keeping all the above conditions constant. the performance, combustion and emissions tests were carried out. an orotech exhaust gas analyzer, as specified in table 2, was used for exhaust gas analysis. the avl437c smoke meter, as specified in table 3, was used for recording smoke opacity. 3.1 uncertaint y analysis the uncertainties of the parameters are calculated by sequential perturbation. the average uncertainties of measured and calculated parameters are air flow rate (1.1%), liquid fuel flow rate (0.1%), gas flow rate (2%), engine load (0.1%), engine speed (1.3%), cylinder pressure (0.8%), temperature (1.0%) and lcv of liquid fuel (1.0%). based on these, the calculated accuracy of the performance and combustion studies of the engine is found to be within ±4.6%. however, the accuracy of the emission study is found to be ±4.6%. the maximum values of coefficient of variance (cov) of the performance parameters, viz., bte and bsfc are 3 and 4% respectively. whereas, the combustion emission parameters, namely peak cylinder pressure, ignition delay, co, hc and nox, are shown to have covs of 5, 4, 2, 2 and 6% respectively. 4. results and discussion 4.1 performance characteristics 4.1.1 brake thermal efficiency figure 3 shows the variation of bte with load. the bte of all the blends increased as load increases. the maximum load on the engine was 30 nm of torque and the brake mean effective pressure at maximum load was 4 bar. the b20plome blend showed an increase in bte due to better combustion. this is due to the oxygen content within the methyl ester. the addition of nanoparticles (b20plome30a) further improved bte because of the enhanced surface area to volume ratio, which leads to more fuel reacting with air causing rapid evaporation and combustion. b20plome30a15e blend showed a further increase in the combustion efficiency due to additional oxygen content from table 2: specification of alumina nanoparticles tabulka 2: vlastnosti hliníkových nanočástic properties specification chemical name gamma aluminium oxide (alumina, al2o3) nanopowder, gamma phase, 99.9% average particle size 20–50 nm appearance white melting point 2045 °c boiling point 2980 °c density 3.9 g/cm³ table 3: specifications of the orotech exhaust gas analyser tabulka 3: specifikace analyzátoru výfukových plynů orotech measurement parameters range resolution carbon monoxide (co) 0–10% vol. 0.001% vol. hydrocarbon (hc) 0–9999% ppm vol. 1.0 ppm vol. oxides of nitrogen (nox) 0–5000 ppm vol. 1.0 ppm vol. table 4: specification of the avl437c smoke meter tabulka 4: specifikace kouřoměru avl437c measurement parameters range resolution opacity 0–99.9% 0.1% linearity ±0.1 m ‑1 repeatability ±0.1 m ‑1 response time ‑ physical < 0.4 seconds response time ‑ electrical < 1 millisecond warm up time at atm. conditions < 7 minutes engine rpm 400–9990 rpm 10 rpm engine oil temperature 0 ‑150°c 1°c operating temperature 5°c to 50°c smoke measuring cell length 215mm (430mm folded length) mecca 02 2017 page 53 study of the effects of ethanol as an additive with a blend of poultry litter biodiesel and alumina nanoparticles on a diesel engine ramesha d k, nishad rajmalwar, t sreeharsha varma, mrithyunajaya swamy k m figure 3: variation of bte with load obrázek 3: změna tepelné účinnosti v závislosti na zátěži figure 4: variation of cylinder pressure with crank angle obrázek 4: změna tlaku ve válci v závislosti na natočení klikového hřídele figure 7:variation of co with load obrázek 7: změna emisí co v závislosti na zátěži figure 8: variation of ubhc with load obrázek 8: změna ubhc v závislosti na zátěži figure 5: variation of hrr with crank angle obrázek 5: změna hrr v závislosti na poloze klikového hřídele figure 6: variation of nox with load obrázek 6: změna emisí nox v závislosti na zátěži mecca 02 2017 page 54 study of the effects of ethanol as an additive with a blend of poultry litter biodiesel and alumina nanoparticles on a diesel engine ramesha d k, nishad rajmalwar, t sreeharsha varma, mrithyunajaya swamy k m ethanol. ethanol also decreased the density and viscosity of the fuel, which improved atomization. 4.2 combustion characteristics 4.2.1 peak cylinder pressure the variation of peak pressure displayed by the different fuels for various crank angles is shown in figure 4. at full load, the peak pressure of b20plome was higher than that of diesel for all loads. this can be attributed to the longer ignition delay and higher oxygen content in the case of b20plome. at full load, b20plome30a showed higher peak pressure than pure diesel due to higher ignition delay and more complete combustion because of the improved surface area volume ratio. for b20plome30a15e, the combustion pressure increased due to better mixing of air and fuel, which resulted in better combustion, and the addition of ethanol results in a lower cetane number of the blend and hence longer ignition delay [6] (krzysztof gorski et al. 2011). 4.2.2 heat release rate figure 5 shows the variation of hrr for various crank angles. b20plome displays a marginal increase in hrr when compared to diesel. at full load, hrr was slightly greater than diesel due to more oxygen molecules being present in b20plome than in diesel. b20plome30a shows a marginal increase in hrr compared to diesel because of better combustion, improved atomization and rapid evaporation. the hrr of b20plome30a was slightly lower than b20plome because the addition of nanoparticles causes advancement in combustion. b20plome30a15e showed higher hrr than b20plome30a because the longer ignition delay due to addition of ethanol causes rapid combustion in the premixed phase and results in an increase of hrr [12] (v. arul mozhiselvan et al. 2009). 4.3 emission characteristics 4.3.1 oxides of nitrogen figure 6 shows the variation of nox for various loads. atmospheric nitrogen is stable at normal temperature and pressure, and exists as a diatomic molecule. however, inside the engine cylinder, where it is subjected to high temperature and pressure, it reacts with oxygen to form various oxides. these are designated nox. nox formation is a strongly time and temperature dependent phenomena. nox emissions increased with increasing load for all fuels because as load increases, the temperature of the combustion chamber and rate at which temperature rises in the cylinder also increases. the hrr was high in the case of b20plome as a result of the temperature inside cylinder increasing rapidly, thereby increasing nox emissions when compared to diesel. the nox emissions of b20plome30a appear to decrease marginally compared to that of diesel, which was because the catalytic behaviour of nanoparticles promotes the reaction in the forward direction and form final products with the least thermal break down of the hydrocarbon compounds. the b20plome30a15e blend showed a marginal increase in nox emissions when compared to diesel. this can be attributed to the higher heat release rate of the b20plome30a15e blend. 4.3.2 carbon monoxide emissions figure 7 shows the variation of co emissions for various loads. co emissions decreased at part load and again increased at full load conditions for all fuels. the b20plome blend showed a decrease in co emissions when compared to diesel. this can be attributed to the higher oxygen content in the methyl esters. the catalytic behaviour of nanoparticles, improved ignition characteristics of alumina nanoparticles and the shortening of ignition delay further decreased the co emissions of the b20plome30a blend when compared to the b20plome blend. the higher oxygen content of the b20plome30a15e blend further promoted the oxidation of co to co2 and decreased co emissions when compared to the b20plome blend [5] (k. ramarao et al. 2015). 4.3.3 unburnt hydrocarbons (ubhc) figure 8 shows the variation of ubhc emissions for various loads. the ubhc emissions for all fuels increased with increasing load. ubhc emissions for all blends are lower than for diesel. at full load, b20plome, b20plome30a and b20plome30a15e showed respectively a 21.2%, 37.5% and 30.3% reduction in ubhc emissions when compared to diesel. the b20plome blend is comprised of animal fat oil methyl esters, i.e., it contains hydrocarbon chains whose one end of the chain is oxygenated. the presence of oxygen in biodiesel promotes combustion that leads to lowering the hydrocarbon emissions [10] (senthil kumar et al. 2001). the b20plome30a blend showed a further decrease in ubhc emissions, which can be attributed to the catalytic behaviour of alumina nanoparticles. the alumina nanoparticles were responsible for shortening the ignition delay and hence further reduced ubhc emissions [14] (yetter r. et al. 2009). at lower loads the b20plome30a15e blend displayed a decrease in ubhc emissions when compared to b20plome30a. however, at loads above 50% an increase in ubhc emissions was observed when compared to b20plome30a. this is because of the lower combustion temperature caused by the higher latent heat of vaporisation of ethanol [4] (hwanam kim et al. 2010). 4.3.4 smoke opacit y figure 9 shows the variation of smoke opacity with load. it was observed that the smoke opacity of exhaust gases increases with load for all fuels. smoke emission is closely related to the ignition delay, volatility and fuel oxygen content. the extended ignition mecca 02 2017 page 55 study of the effects of ethanol as an additive with a blend of poultry litter biodiesel and alumina nanoparticles on a diesel engine ramesha d k, nishad rajmalwar, t sreeharsha varma, mrithyunajaya swamy k m delay and high volatility can improve the fuel ‑air mixing process, and the oxygen in fuel can reduce the formation of soot precursors and enhance soot oxidation [15] (zunquing zheng et al. 2016). due to the higher viscosity of b20plome and b20plome30a, the volatility and air ‑fuel mixing of these blends was poor. also, since the molecules of b20plome and b20plome30a were heavier, they lead to an increase in smoke opacity of exhaust gases when compared to diesel [1] (baluswamy t et al. 2007). it can be observed that the smoke opacity of b20plome30a15e was marginally higher than that of diesel and lower than that of b20plome and b20plome30a. this is because adding ethanol to the blend increased the oxygen content and volatility and reduced soot precursor concentration [7] (m. mofijur et al. 2015). 5. conclusion the engine tests were conducted with b20plome, b20plome30a and b20plome30a15e from no load to full load conditions and the corresponding performance, combustion and emission characteristics were studied in comparison with diesel. the following results were observed – upon transesterification of poultry litter oil, it was observed that there was a reduction in kinematic viscosity and density whereas the calorific value was observed to increase. all the three blends showed increased bte when compared to diesel. b20plome30a15e showed a 10.7% increase in bte when compared to diesel. the highest cylinder pressure was recorded for b20plome30a15e. the addition of ethanol increases the volatility and oxygen content, which promotes combustion and as a result a further reduction in co emissions and smoke opacity were observed when compared to b20plome and b20plome30a. the addition of ethanol increases the ignition delay period, and as a result b20plome30a15e shows maximum peak cylinder pressure and hence the nox emissions of b20plome30a15e were marginally higher than that of b20plome30a. at 50% load, the ubhc emissions of b20plome30a15e were marginally higher than that of b20plome30a; this is due to higher latent heat of vaporisation of ethanol, which reduces the combustion temperature. this proves that poultry litter oil biodiesel with alumina nanoparticles and ethanol as an additive can be used as a renewable and environmentally friendly fuel, minimising the use of mineral diesel. also, poultry litter oil can be utilized as a fuel through this waste management technique. list of notations and abbreviations ci compression ignition btdc before top dead centre bp brake power bte brake thermal efficiency hrr heat release rate co carbon monoxide nox oxides of nitrogen ubhc unburnt hydrocarbons o2 oxygen ppm parts per million astm american society for testing and materials plome poultry litter oil methyl ester b20 20% biodiesel + 80% diesel b20plome 20% poultry litter methyl ester + 80% diesel b20plome30a 20% poultry litter methyl ester + 80% diesel + 30mg/l al2o3 b20plome30a15e 20% poultry litter methyl ester + 80% diesel + 30mg/l al2o3 + 15 ml ethanol/l references [1] baluswamy t, marappan r, performance evaluation of direct injection diesel engine with blends of thevetiaperuviana seed oil and diesel, journal for scientific and industrial research, vol 66, december 2007, 1035 ‑1040 [2] darunde dhiraj s., prof. deshmukh mangesh m., biodiesel production from animal fats and its impact on the diesel engine with ethanol ‑diesel blends: a review, ijetae, vol 2, issue 10, october 2012, issn 2250 ‑2459 [3] dr. sadhik b. j., anand, r. b. effects of nanoparticle additive in the water diesel emulsion fuel on the performance, emission and combustion characteristics of a diesel engine, journal of vehicle design, vol 59, issue 2/3, 164 ‑181, 2012 [4] hwanam kim, byungchul choi, the effect of biodiesel and bioethanol blended diesel fuel on nanoparticles and exhaust emissions from crdi diesel engine, renewable energy, 2010, vol 35, issue 1, 157 ‑163 figure 9: variation of smoke opacity with load obrázek 9: změna kouřivosti v závislosti na zátěži mecca 02 2017 page 56 study of the effects of ethanol as an additive with a blend of poultry litter biodiesel and alumina nanoparticles on a diesel engine ramesha d k, nishad rajmalwar, t sreeharsha varma, mrithyunajaya swamy k m [5] k. ramarao, c. j. rao , d. sreeramulu, the experimental investigation on performance and emission characteristics of a single cylinder diesel engine using nano additives in diesel and biodiesel, indian journal of science and technology, vol 8, issue 29, november 2015 [6] krzysztof gorski, ruslands smigins, impact of ether/ ethanol and biodiesel blends on combustion process of compression ignition engine, engineering for rural development, jelgava, 26, 2011. [7] m. mofijur, m.g. rasul, j. hyde, recent developments on internal combustion engine performance and emissions fuelled with biodiesel ‑diesel ‑ethanol blends, procedia engineering, vol 105, 2015, 658–664 [8] nithin samuel, muhammed shefeek k, performance and emission characteristics of a c.i. engine with cerium oxide nanoparticles as additive to diesel, ijsr, vol 4, issue 7, july 2015, issn (online): 2319 ‑7064 [9] s.p. venkatesan, kadiresh pn, influence of aluminum oxide nanoparticle additive on performance and exhaust emissions of diesel engine, ijaer, vol 10, issue 3, jan 2015, 5741 ‑5749 [10] senthil kumar, ramesh a and nagalingam b, experimental investigation on jatropha oil ‑methanol duel fuel engine, sae technical paper, vol 0153, issue 01, 2001 [11] sri harsha tirumala, a.v.rohit, siva krishna.m, sudiptasaha, synthesis of neem biodiesel, ijaet, vol 3, issue 1, january ‑march, 2012, 316 ‑318, e ‑issn 0976 ‑3945 [12] v. arul mozhiselvan, r. b. anand and m. udayakumar, effects of cerium oxide nanoparticle addition in diesel and diesel ‑biodiesel ‑ethanol blends on the performance and emission characteristics of a ci engine, arpn journal of engineering and applied sciences, vol 4, issue 7, september 2009, issn 1819 ‑6608 [13] xiaoyan shi, xiaobing pang, yujing mu, hong he, shijin shuai, jianxin wang, hu chen, rulong li, emission reduction potential of using ethanol–biodiesel–diesel fuel blend on a heavy ‑duty diesel engine, atmospheric environment, vol 40 issue 14, may 2006, 2567–2574 [14] yetter r. a., grant a r, steven f s, metal particle combustion and nanotechnology, proceedings of the combustion institute 2009, vol 32, issue 2, 1819 ‑1838 [15] zunquing zheng, xiaofeng wang, xiaofan zhong, bin hu, haifeng liu, mingfa yao, experimental study on the combustion and emission fuelling biodiesel/n ‑butanol, biodiesel/ethanol, and biodiesel/2,5 ‑dimethylfuran on a diesel engine, elsevier energy, vol 115, issue 1, november 2016, 539–549 http://www.indjst.org/index.php/indjst/search/authors/view?firstname=k.&middlename=&lastname=ramarao&affiliation=department%20of%20mechanical%20engineering,%20aitam%20engineering%20college,%20tekkali%20-%20532201,%20andhra%20pradesh&country=in http://www.indjst.org/index.php/indjst/search/authors/view?firstname=c.%20j.&middlename=&lastname=rao&affiliation=department%20of%20mechanical%20engineering,%20aitam%20engineering%20college,%20tekkali%20-%20532201,%20andhra%20pradesh&country=in http://www.indjst.org/index.php/indjst/search/authors/view?firstname=d.&middlename=&lastname=sreeramulu&affiliation=department%20of%20mechanical%20engineering,%20aitam%20engineering%20college,%20tekkali%20-%20532201,%20andhra%20pradesh&country=in _goback mecca_20-01_v10_web autonomous vehicles and european data protection law eva fialová mecca 01 2020 page 1 10.14311/mecdc.2020.01.01 autonomous vehicles and european data protection law eva fialová autonomous vehicles and european data protection law eva fialová institute of state and law of the czech academy of sciences, národní 18, praha 1, tel.: 723 981 144, email: eva.fialova@ilaw.cas.cz abstract autonomous vehicles process a huge amount of data about the driver, or rather passengers of the vehicle, as well as about other persons (pedestrians and passengers of other vehicles). this is why the autonomous vehicles raise questions about the protection of personal data. in 2018 a new european data protection legislation came into force. the general data protection regulation places new obligations on controllers of personal data and provides new rights to data subjects, which will relate to operations of autonomous vehicles and their infrastructure. the providers thereof will have to implement the principles of data protection legislation into their systems. in this context the personal data is not just data concerning the identity of the driver, a passenger or other persons, but any information relating to an identified or identifiable natural person who can be identified, directly or indirectly, in particular by reference to an identifier such as a name, an identification number, location data, or even due to a peculiar behaviour in the vehicle. the paper will focus on the new legal regulation in relation to the operation of autonomous vehicles. key words: autonomous vehicles, data protection, gdpr, privacy shrnutí autonomní vozidla zpracovávají velké mno!ství údaj" o #idi$i vozidla, resp. cestujících ve vozidle, jako! i o dal%ích osobách (spolucestujících, chodcích a pasa!érech v jin&ch vozidlech). to je d"vod, pro$ provoz autonomních vozidel vyvolává #adu otázek t&kajících se ochrany osobních údaj". v roce 2018 nabyla ú$innosti nová evropská právní úprava regulující tuto oblast. obecné na#ízení o ochran' osobních údaj" p#iná%í nové povinnosti správc"m osobních údaj", jako! i nová práva subjekt"m údaj", která se budou t&kat provozu autonomních vozidel a infrastruktury. v&robci a poskytovatelé slu!eb budou muset do sv&ch systém" implementovat legislativu o ochran' osobních údaj". osobními údaji nejsou pouze údaje t&kající se toto!nosti #idi$e, cestujících nebo jin&ch osob, ale ve%keré informace vztahujících se k identifikované nebo identifikovatelné fyzické osob', kterou lze p#ímo nebo nep#ímo identifikovat, zejména odkazem na identifikátor, jako je nap#. název, identifika$ní $íslo, lokaliza$ní údaje, nebo t#eba i kv"li osobitému chování ve vozidle. tento $lánek se zam'#uje na novou právní úpravu ve vztahu k provozu autonomních vozidel. klí!ová slova: autonomní vozidla, gdpr, ochrana úda j", soukromí 1. introduction the operation of autonomous vehicles results in a huge amount of personal data being processed about drivers, or in the case of fully autonomous vehicles, about users (for the sake of simplicity the term driver is used for the driver as well as for the user of a fully autonomous vehicle). the processed data may also relate to third persons, e.g. fellow-passengers, pedestrians and drivers and passengers of other (autonomous) vehicles, in other words, the cameras, sonars and radars collects huge amount of data about their interior and exterior [1]. the legal framework for the protection of personal data was harmonized in the european union on the basis of directive 95/46/ec on the protection of individuals with regard to the processing of personal data and on the free movement of such data. since the directive has been transposed in national legal systems and the level of protection of personal data differed across the european union, the protection of personal data is nowadays governed by the regulation (eu) 2016/679 on the protection of individuals with regard to the processing of personal data and on the free movement of such data (hereinafter referred to as “the regulation” or “gdpr”). the regulation is directly effective in all member states of the european union. this means that in contrast to the directive 95/46/ec the regulation does not have to be transposed into the national laws because of its direct effect. this paper will focus on the new data protection regulation and its application with respect to autonomous vehicles. p#ijato k publikaci v roce 2018 autonomous vehicles and european data protection law eva fialová mecca 01 2020 page 2 2. protection of personal data in the operation of autonomous vehicles according to art. 4 par. 1 gdpr, personal data is any information about an identified or identifiable natural person (a data subject). an identifiable person is a person who can be identified directly or indirectly, in particular by reference to an identifier such as name, identification number, location data, network identifier or one or more specific physical, physiological, genetic, psychological, economic, or social identifiers of a natural person. according to the court of justice of the european union, a person is identifiable if the controller has means reasonably likely be used in order to identify the data subject, even with the assistance of other persons [2]. the personal data is, therefore, any information that can be related to the driver of an autonomous vehicle, to passengers, and to drivers or passengers of other vehicles with which the autonomous vehicle comes into contact. such personal data could, for example, be the posture of the driver, his/her way of handling the vehicle, or his/her location or regular daily route from which a home and work address may be deduced. personal data may be processed only if the controller has a legal basis to perform such processing as enumerated in art. 6 gdpr. in the case of autonomous vehicles, the contract between the controller and the data subject will provide legal grounds for processing of the driver’s data. according to the european data protection board the aforementioned legal ground “will not cover processing which is useful but not objectively necessary for performing the contractual service or for taking relevant precontractual steps at the request of the data subject.“ [3]. if this is not the case, the controller will have to process the data under some other legal ground. another legal ground for processing may be the fulfilment of a legal obligation of the controller. for example, a law might prescribe to the controller’s obligation to process defined categories of data for specific purposes, e.g. insurance purposes, taxation, etc. beside that the controller is allowed to process the personal data when such processing is necessary to protect the vital interests of the data subject or of another natural person. for instance, in the case of an accident, the vehicle might evaluate some personal data essential for the saving of lives and transmit them to the controller for further processing in addition to data that are already programmed to be processed in such cases and are therefore processed under other legal grounds. other data may be processed if the processing is necessary for the purposes of the legitimate interests pursued by the controller or by a third party. as an example of such data could serve the data, which are indispensable for an examination of an accident and the determination of liability (provided that those data will not be processed for the fulfilment of the legal obligation). these interests can be overridden by the interests or fundamental rights and freedoms of the data subject (e.g. a right to privacy or interest in the protection of property). personal data may be also processed when the data subject has given consent to the processing of such data. consent means a freely given, specific, informed and unambiguous manifestation of the data subject’s wishes by which the data subject gives a declaration or other apparent confirmation of his/her consent to processing of personal data relating to him/her (art. 4 par. 11 gdpr).such consent to processing will be typical for the driver's personal data that cannot be processed in accordance with the aforementioned legal grounds. consent will also be typical for personal data necessary for providing additional services. the controller has to prove that the consent of the data subject has been given. the consent of the owner the vehicle could be attached to a contract of purchase. the controller may ask the driver for the consent during the operation of the vehicle. in the case of other vehicle’s user, the controller will have to find a solution for the granting of consent and demonstration thereof. there is a subtype of personal data that requires stricter protection, the “special categories” of personal data (art. 9 gdpr), and sensitive data according to the previous legislation. those data relate in particular to a racial or ethnic origin, religious or philosophical beliefs, sexual orientation and health. also sensitive according to the regulation are biometric data for the purpose of uniquely identifying a person, for example, the identification of the driver or passenger. the processing of such data is forbidden unless the controller disposes with a legal ground pursuant art. 9 gdpr. 3. obligations of the controller a controller is a person who determines the purposes and means of the processing of personal data (art. 4 par. 7 gdpr). in relation to the operation of the autonomous vehicles, the data controller may be a manufacturer, a lessor (the owner of a fleet), or an operator of telecommunication or traffic infrastructure. in interconnected vehicles and infrastructure, it will be difficult to determine who are the controller and the processor of data. besides the interconnected vehicles the autonomous ones might also be “self-contained”. this means all the data will rest in the vehicle itself [4]. the interconnected autonomous vehicles and communication between vehicle and infrastructure is under research in this field now [5]. autonomous vehicles and european data protection law eva fialová mecca 01 2020 page 3 the controller may also be a driver of the vehicle that processes the personal data of third persons and this processing falls within the scope of the regulation, such as the processing of personal data wholly or partly automatically. the driver may. for instance, be able to download data collected by cameras and sensors, to store them or to process them in any other way defined by art. 4 par. 2 gdpr. in such case, the driver has all the obligations of a data controller laid down by the regulation. the controller may engage a processor who processes the personal data for the controller on the basis of a written contract, e.g. a provider of cloud computing services or other storage services for data processed during the operation of the autonomous vehicles. nevertheless, it shall always be the controller who is responsible for personal data processing. the controller must adhere to the data protection principles enumerated in art. 5 gdpr in order to be compliant with the regulation. personal data must be processed lawfully, fairly and in a transparent manner. the controller has to have legitimate purposes for the processing. the personal data must not be processed in a manner that is incompatible with the given purposes. however, further processing for scientific or historical research purposes or statistical purposes are not considered to be incompatible with the initial purposes. the controller must stick to the data minimisation principle. this principle means that the controller can only process data relevant to the given purpose and are limited in scope to what is necessary for that purpose. it is likely that the controller will manage to defend the processing of personal data relating to vehicle operation and its further use in the development of the autonomous vehicles, even in case that the personal data cannot be anonymized. the processed data have to be accurate and must not be stored longer that is necessary for the purpose. after the retention period, the data cannot be further processed. one of the pivotal obligations of the controller and the processor is to ensure the integrity and confidentiality of the personal data. pursuant to art. 32 gdpr the controller has to implement appropriate technical and organisational measures to ensure a level of security appropriate to the risk in relation to the rights and freedoms of natural persons. these risks include not just the threat to the right to privacy and data protection. the potentially infringing information may be the location where the vehicle is parked overnight, what is the usual route of the vehicle, etc. based on the data, a detailed profile of the driver and his/her financial status, habits and preferences can be made [6]. the controller has to also assess the risk in relation to other rights, for instance the right not to be discriminated against in the case of profiling of a data subject. by selecting appropriate measures the controller will have to take into account the state of the art, the costs of implementation and the nature, scope, context and purposes of processing as well as the risk level in terms of likelihood and severity for the above-mentioned rights and freedoms. these measures include pseudonymisation and encryption, the ability to ensure confidentiality, integrity, availability and resilience of processing systems and services, the ability to restore the availability and access to personal data in a timely manner in the event of a physical or technical incident, and the implementation of a process for regularly testing, assessing and evaluating the effectiveness of technical and organisational measures for ensuring the security of the processing. it can be assumed that companies and authorities engaged in the operation of autonomous vehicles will process a huge amount of personal data on numerous data subjects, their identifiers, daily habits and routines, profiles, connection with other persons etc. the right to privacy, data protection and other rights of those data subjects may be infringed by a breach of the integrity of the system and data leakage and loss. a controller that processes the personal data collected during the operation of autonomous vehicles will thus have to adopt strict measures to ensure the data security. a data breach may cause an intrusion into the private and family life of a user, his or her information selfdetermination or in some cases it might even affect his/her her personal safety in case that the information about the regular locations and habits has been compromised. assuming the probability that a personal data breach will result in a risk to the rights and freedoms of natural persons, the controller must without undue delay and, where feasible, within 72 hours of having become aware of it, notify the the supervisory authority (art. 33 gdpr). another obligation of some controllers is to carry out a data protection impact assessment pursuant to art 35 gdpr. where a type of processing, especially one using new technologies, and taking into account the nature, scope, context and purposes of the processing, is likely to result in a high risk to the rights and freedoms of natural persons, the controller will, prior to the processing, carry out an assessment of the impact of the envisaged processing operations on the protection of personal data. a data protection impact assessment is in particular required in the case of a systematic and extensive evaluation of personal aspects relating to natural persons based on automated processing, including profiling or a systematic monitoring of a publicly accessible area on a large scale. it can be assumed that the controllers processing the personal data in connection with the operation of autonomous vehicles autonomous vehicles and european data protection law eva fialová mecca 01 2020 page 4 will be obliged to carry out a personal data impact assessment before commencing processing. the reason for the obligation is the above-mentioned character of personal data processing during the operation of the autonomous vehicles. moreover, the controllers will certainly systematically and extensively evaluate the personal data for safety or commercial reasons. autonomous vehicles will also incorporate new technologies, or the current technologies will be used differently, so the risk to the rights and freedoms of data subjects is difficult to estimate at present. this fact represents an additional reason for a data protection impact assessment carried out by the operator prior to processing. the controller in the case of personal data processing relating to the operation of the autonomous vehicle will have to designate a data protection officer (art. 37 gdpr). the data protection officer has to be designated when the core activities of the controller consist of processing operations which, by virtue of their nature, their scope and/or their purposes, require regular and systematic monitoring of data subjects on a large scale. since the operation of autonomous vehicles represents the processing of a huge amount of personal data on a large scale as well as regular and systematic monitoring, there is no doubt about the obligation of the controller to appoint a data protection officer. 4. data protection by design and by default according to the data minimisation principle, the controller processing personal data in connection with the operation of autonomous vehicle must take steps not to process more data than is necessary for the purpose for which the data are processed. in addition, art. 25 of the regulation obliges the controller to take all possible steps to guarantee data protection by design and by default. this means that appropriate technical and organisational measures have to be implemented so that the data protection principles are safeguarded in order to meet the requirements of the regulation, i.e. to protect the rights of data subjects and to ensure the security of the data processing. when implementing data protection by design (sometimes also called privacy by design) the controller has to consider the data protection principles already at the stage of product or system development. according to its originator ann cavoukian privacy by design means “embedding privacy into information technologies, business practices, and networked infrastructures, as a core functionality, right from the outset – means building in privacy right up front – intentionally, with forethought. pbd may thus be defined as an engineering and strategic management approach that commits to selectively and sustainably minimize information systems’ privacy risks through technical and governance controls.” [7]. autonomous vehicles have to be technically designed in a way compliant with the principles of personal data protection. data protection by default (or privacy by default) means that the manufacturer or designer applies the most stringent privacy settings which can only be subsequently changed only by the data subject. for cavoukian privacy by default is one element of the privacy by design approach [8]. the data subject can later opt-in for a less stringent data protection setting. however, the opt-in should not be irreversible. german verband der automobilindustrie (vda) supports the active involvement of the consumer in data processing options. “the members of the vda are striving to enable customers to determine themselves the processing and use of personal data through various options. the members of the vda will enable these options through contractual provisions, consents or technical features in the framework of optional features and choices that are given, through which the customer can activate or deactivate services, unless the processing is regulated by law.” [9]. data protection by design and the option for the user to change the privacy settings is advocated by the data protection and privacy commissioners in their resolution on data protection in automated and connected vehicles [10]. in the event of violation of the obligation, the supervisory authority may impose severe fines. the amount of the fine will depend in particular on the nature, severity and duration of the infringement. the supervisory authority will take into account the nature, extent or purpose of the processing, as well as the number of data subjects concerned and the extent of the damage caused to them. the imposed fine may be up to ! 20 million or 4 % of total worldwide annual turnover. 5. rights of the data subject the regulation strengthens the rights of data subjects. data subjects are the driver of the autonomous vehicle, a passenger or a third person outside the vehicle whose personal data are automatically processed during the operation of the vehicle. a data subject, whether it is a driver, a passenger or persons whose personal data are processed in connection with the operation of an autonomous vehicle, has the following rights under the regulation: 1. the right to information (art. 13 and 14 gdpr) 2. the right of access (art. 15 gdpr) 3. the right to rectification (art. 16 gdpr) 4. the right toerasure sometimes called the right to be forgotten (art. 17 gdpr) 5. right to restriction of data processing (art. 18 gdpr) autonomous vehicles and european data protection law eva fialová mecca 01 2020 page 5 6. the right to data portability (art. 20 gdpr) 7. the right to object (art. 21 gdpr) 8. the right not to be subject to a decision based solely on automated processing, including profiling, which produces legal or similar effects concerning the data subject (art. 22 gdpr). the right to data portability is the right to transfer the data between the controllers. this right can only be exercised when the data are processed on the basis of consent or a contract and the processing is carried out by automated means. this right may be applied in the case of changing the operator of an autonomous vehicle if the data subject is interested in transferring the personal data collected during the operation of the autonomous vehicle to another operator. the data subject cannot claim the right to erasure when his/her data are processed on the basis of a legal obligation of the data controller. the right to erasure is not absolute. if the processing of the personal data is required by a law which enshrines the obligation of processing of certain data collected in connection with the operation of the autonomous vehicles, the data subject cannot claim the right to erasure of his/her personal data. profiling of the personal data is allowed in accordance with the regulations. pursuant to art. 4 par. 4 gdpr profiling is any form of automated processing of personal data involving the use of data to evaluate certain personal aspects related to a physical person, such as driving or reactions of the vehicle user or his or her habits for the marketing purposes. the right not to be subject to automated processing may be typically applied in the assessment of insurance risk. profiling must not result in an automated decision. the right not to be subject to an automated decision will not apply if the automated processing is necessary for a performance of a contract or the automated decision-making is permitted by law or when this type of processing is based on the explicit consent of the data subject. 6. autonomous vehicles and eprivacy the processing of personal data in the field of electronic communications is regulated in the european law by directive 2002/58/ec concerning the processing of personal data and the protection of privacy in the electronic communications sector (directive on privacy and electronic communications). this directive applies to the processing of personal data in connection with the provision of publicly available electronic communications services or public communications networks. at present, the legal framework for the protection of personal data in the electronic communications sector is being revised. the european commission proposed a regulation on privacy and electronic communications (the “eprivacy regulation”), which will, along with the gdpr, be directly effective in all member states of the european union as well as the gdpr. even though it is only at the draft stage and and the final wording is not yet set down [11], the eprivacy regulation will probably apply to the transmission of communication between machines. the recital 12 of the eprivacy regulation mentions explicitly that the regulation shall apply to machineto-machine (m2m) communication. it is questionable what kind of m2m communication can be considered as an electronic communication service, the area regulated by the eprivacy regulation [12]. to assess whether the eprivacy regulation will enshrine the communication between autonomous vehicles and the vehicles and the infrastructure, a definition of the electronic communication service has to be taken into consideration. the definition of this service refers to the european electronic communications code (directive (eu) 2018/1972 establishing the european electronic communications code). pursuant to the art. 2 of the european electronic communications code the electronic communications service encompasses, besides other things, services consisting wholly or mainly in the conveyance of signals such as transmission services used for the provision of machine-to-machine services. it is not clear whether the m2m communication of the autonomous vehicles and to what extant can be consider as the electronic communication service [13]. the clarification thereof is significant since the data processing in case of the provision of the service will be conditioned by compliance with the rules of the eprivacy regulation. pursuant to the draft of the eprivacy regulation, service provider may provide the service primarily with the user’s consent unless he will process the data under other legal grounds which are nevertheless limited in number. 7. conclusion the operation of autonomous vehicles will involve the processing of a huge amount of data. the gdpr will apply to the processing of personal data collected, transmitted, disclosed, used or profiled in connection with the operation of the vehicles. the manufacturers, the lessors and other personal data controllers will have to be compliant with the new legislation when they will process the personal data of the driver, passenger or third persons. in comparison with directive 95/46/ec, the regulation will set down new obligations of the controller, in particular, to appoint a data protection officer, to notify the supervisory authority of a data breach, to carry out a data protection impact assessment and to implement the privacy by design and by autonomous vehicles and european data protection law eva fialová mecca 01 2020 page 6 default into their products and processes. on the other hand, the regulation provides the data subject with some new rights (the right to data portability, the right not to be subject to an automated decision and an enhanced right to data erasure). the rights of the data subject are aimed at ensuring greater transparency and control for the data subject over his/her personal data. however problematic issues may arise in practice, e.g. the finding of the appropriate legal ground of processing, a manner of obtaining the consent of data subject or appropriate data breach safeguards. a question whether the communication among vehicles and between the vehicles and the infrastructure will fall under the eprivacy regulation and if so, to what extent, still remains unclear. acknowledgements the paper was supported by the technology agency of the czech rebublic under grant no. tl02000085 civil liability for damage caused by operation of autonomous vehicles. references [1] collingwood, l. (2017). privacy implications and liability issues of autonomous vehicles. information and communications technology law, vol. 26, no. 1, p. 35. [2] judgement of the court of justice of the european union no. case c582/14 (patrik breyer v.bundesrepublik deutschland). [3] european data protection board. guidelines 2/2019 on the processing of personal data under article 6(1)(b) gdpr in the context of the provision of online services to data subjects (version for public consultation). p. 7. available at: guidelines 2/2019 on the processing of personal data under article 6(1)(b) gdpr in the context of the provision of online services to data subjects [4] glancy, d. j. (2012). privacy in autonomous vehicles. santa clara law review, vol. 52, no. 4, p. 1176. [5] friedrich, b. (2015) verkehrliche wirkung autonomer fahrzeuge, in: maurer, m. et al. autonomes fahren, berlin, hedelberg: springer verlag. 349. [6] collingwood, l. (2017). p. 36. [7] cavoukian, a. (2012). operationalizing privacy by design: a guide to implementing strong privacy practices, p. 8. available at: http://www.privacybydesign.ca/content/ uploads/2013/01/operationalizing-pbd-guide.pdf [8] ibid. [9] verband der automobilindustr (2014). data protection principles for connected vehicles, p. 3. available at: https://www.vda.de/de/themen/innovation-und-technik/ vernetzung/datenschutz-prinzipien-fuer-vernetzte-fahrzeug [10] 39th international conference of data protection and privacy commissioners (2017). resolution on data protection in automated and connected vehicles. available at: https://www.uoou.cz/assets/file.ashx?id_ org=200144&id_dokumenty=27212 [11] see eprivacy tracker. available at: https://www.eprivacy. law/e-privacy-chronology [12] storms, s. (2018), quo vadis, eprivacy? confidentiality of machine-to-machine communications. available at: https://www.law.kuleuven.be/citip/blog/quo-vadis-eprivacyconfidentiality-of-machine-to-machine-communications/ [13] european automotive and telecom alliance (2018). data protection & privacy. available at: https://www.acea. be/uploads/news_documents/eata_regulatory_briefing_ paper-data_protection_eprivacy.pdf implication of cycle‑to‑cycle variability in si engines karel páv mecca 01 2018 page 10 10.1515/mecdc‑2018‑0002 implication of cycle‑to‑cycle variability in si engines karel páv 1. introduction the cycle‑to‑cycle combustion variability is a well‑known phenomenon among engineers dealing with engine development. the dispersion in combustion process is generally caused by three factors: the variation in turbulent gas motion in a cylinder during combustion; the variation in the amounts of fuel, air, and burned gas present in a given cylinder during each cycle; variations in mixture composition within the cylinder near the spark plug – due to variations in mixing between air, fuel, recirculated exhaust gas and residual gas [3]. the strongest impact on resulting cycle‑to‑cycle combustion variability has the onset of the combustion process (flame kernel development) which is particularly essential in case of standard si engines. the pre‑flame period is negatively affected by non‑homogeneous mixture in vicinity of the spark plug and too weak or too intensive charge movement [1], [4], [9]. the further flame propagation is strongly influenced by the combustion chamber topology and the in‑cylinder turbulence intensity, while the most dominant factor in terms of cycle‑ to‑cycle variation is the turbulence intensity which varies substantially among individual cycles [10]. various measures of the cycle‑to‑cycle combustion variability are widely used. they can be defined in terms of variations in the cylinder pressure between different cycles or in terms of variations in the parameters of the burning process. the most used quantities of pressure‑related parameters are the maximum cylinder pressure, the crank angle at which this maximum pressure occurs, the maximum rate of pressure rise and the indicated mean effective pressure (imep). the burn‑ rate‑related parameters are the maximum heat‑release rate or mass burning rate, the crank angle at 50% of mass burned karel páv technická univerzita v liberci, katedra vozidel a motorů, studentská 2, liberec 461 17, czech republic email: karel.pav@tul.cz abstract the paper deals with utilization of an adaptive combustion model in order to simulate cycle‑to‑cycle combustion variability of si engines. the used empirical adaptive combustion model consists of two parts: the first part for ignition delay prediction and the second part for in‑cylinder combustion process description. there is proved mutual independence of these two phases and shown their characteristics in terms of cycle‑to‑cycle variability. the practical utilization of the cycle‑to‑cycle variability simulation is demonstrated by computational analysis of various variability levels at different engine operational points in order to assess its impact on engine fuel consumption. the calculation results are generalized for si gasoline engines independent of both engine load and combustion rate as well. key words: si engine, cycle-to-cycle variabilit y, adaptive combustion model, spark timing, ignition delay, variabilit y factor, fuel consumption. shrnutí tento příspěvek se zabývá použitím adaptivního modelu hoření za účelem simulace mezicyklové variability hoření ve válci zážehového spalovacího motoru. použitý numerický adaptivní model hoření sestává ze dvou částí: první část pro predikci průtahu zážehu a druhá část pro popis vlastního spalovacího procesu ve válci motoru. je zde ukázána vzájemná nezávislost těchto dvou částí a jejich vlastnosti s ohledem na mezicyklovou variabilitu. praktické využití simulace mezicyklové variability je demonstrováno na výpočtové analýze různých úrovní variability v různých pracovních bodech motoru s cílem ohodnotit dopad mezicyklové variability na spotřebu paliva. výsledky výpočtů jsou zobecněny pro zážehové benzínové motory a lze je využít nezávisle jak na zatížení motoru, tak i na rychlosti hoření. klíčová slova: zážehový motor, mezicyklová variabilita, adaptivní model hoření, předstih zážehu, průtah zážehu, faktor variabilit y, spotřeba paliva. implication of cycle-to-cycle variability in si engines implication of cycle‑to‑cycle variability in si engines karel páv mecca 01 2018 page 11 fraction, the flame development angle and the rapid burning angle [3]. the indicated mean effective pressure is very sensitive to measurement accuracy, especially when non water‑cooled sensors with high cyclic temperature drift are used [7]. the main task of this paper is to investigate cycle‑to‑cycle variability in terms of combustion process differences, i.e. without turbulence and other effects on changes in mass of charge trapped in the cylinder. the investigation of cylinder‑to‑cylinder variation sakes is also not a scope of this paper. therefore, the most convenient measure for the cycle‑to‑cycle variability assessment is the standard deviation (sdev) in crank angle at 50% of mass burned fraction mbf50% which reflects the phasing of combustion process and is nearly independent of charging variations ( ) 1 )( 2 = σ n mbf50%mbf50% mbf50%sdev (1) coefficient of variation (cov) can be used as an alternative measure of the maximum cylinder pressure pmax in form: ( ) 1 100 )( 2 = σ n pmaxpmax pmax pmaxcov (2) the frequently applied limit value for smooth engine run is cov(pmax) < 15%. however, this parameter has to be used carefully, especially when the spark timing is not set to its optimum. typical values of coefficient of variation of maximum cylinder pressure and standard deviation in crank angle at 50% of mass burned fraction at optimum ignition timing are shown in figure 1. all displayed engine operational points in these maps are used for further computational analysis of the potential for a fuel consumption reduction in this paper. at very low engine load at imep < 1 bar (not displayed in figure 1) the cycle‑to‑cycle variability is usually increasing due to lower compression pressure and temperature and higher content of residual gas in the cylinder. the relationship between two above mentioned measures in figure 2 is shown. the correlation between these two quantities is for maximum brake torque (mbt) spark timing very close. engine im e p [b ar ] 0 2 4 6 8 10 12 engine speed [1/min] 0 1000 2000 3000 4000 5000 6000 10.09.2 9.79.78.0 9.39.2 7.6 8.77.3 8.28.17.3 7.46.5 6.6 7.67.26.8 cov(pmax) [%] im e p [b ar ] 0 2 4 6 8 10 12 engine speed [1/min] 0 1000 2000 3000 4000 5000 6000 3.22.7 3.12.92.0 3.02.7 2.4 2.91.8 2.72.52.1 2.21.6 2.0 2.42.32.0 sdev(mbf50%) [°ca] figure 1: typical values of coefficient of variation of maximum cylinder pressure and standard deviation in crank angle at 50% of mass burned fraction. an example for naturally aspirated four‑cylinder si gasoline engine of swept volume 1.6 dm3. red colored points mark the engine operational points where a deeper computational analysis has been carried out. obrázek 1: typické hodnoty variačního koeficientu maximálního tlaku a směrodatné odchylky úhlu natočení klikového hřídele při 50% vyhoření náplně válce. příklad pro nepřeplňovaný čtyřválcový zážehový benzínový motor o zdvihovém objemu 1,6 dm3. červené body označují režimy motoru, při kterých byla provedena detailnější výpočtová analýza. s d e v (m b f 50 % ) [° c a ] 0 2 4 6 8 10 12 cov(pmax) [%] 0 5 10 15 20 limit sdev(mbf50%) < 5°ca limit cov(pmax) < 15% e n gi n e id le very late combustion area figure 2: relationship between coefficient of variation of maximum cylinder pressure and standard deviation in crank angle at 50% of mass burned fraction. obrázek 2: vzájemná korelace mezi variačním koeficientem maximálního tlaku a směrodatnou odchylkou úhlu natočení klikového hřídele při 50% vyhoření náplně válce. implication of cycle‑to‑cycle variability in si engines karel páv mecca 01 2018 page 12 operational points with exceptional spark timing lie outside this region, typically engine idle, as has been mentioned above. 2. description of adaptive combustion model for the simulation of different conditions during combustion process the empirical adaptive combustion model has been developed [4]. this model offers very simple implementation of variability control because it consists of two independent parts. the first part predicts the ignition delay djign which is defined as a crank angle difference between spark ignition and very first sign of the heat release, as graphically shown in figure 3. the second part is the flame propagation process. these two parts have been proven as an independent processes [5]. the crank angle duration of the ignition delay is mathematically given by improved empirical formula originally coming from [4], [5]. the investigation of more si engines allowed to achieved new form ( )[ ] ( ) ]11,k,bar,1/min,1, 1, ca,[ 1 8.02.0105 5 , 222.07.04 , ° + -λ+× × × =φδ -str mixignignvignignign x tpnaa (3) the formula improvement consists in change of multiplier and single exponents based on regression analysis of extended experiments. besides calibration factor aign there is also multiplier aign,v which is used for generation of the cycle‑to‑cycle variability. the ignition delay depends on the engine speed n, in‑cylinder pressure pign and mean in‑cylinder temperature tign at the moment of the spark ignition. relative air/fuel ratio in unburned mixture lmix is given by relative air/fuel ratio l and by residual mass fraction xr in the cylinder 1 1 1 1 ≤λ=λ >λ λ -λ +λ=λ mix r rmix x x a a (4) mass fraction of stoichiometric residual gases xr,st is given by formula 1 1 1 1 , , ≤λ= >λ λ+ + = rstr st st rstr xx l l xx a a (5) where lst denotes stoichiometric wet air/fuel ratio. the main combustion phase is described by the change of mass fraction of burned gas xb during combustion. improved empirical formula covering wider range of si engines has form ( )[ ] ( ) ( ) ]ca 1, 1, 1, ,m k,bar,1/min,1, 1, ca,[1/ 183.08.0 1015 3 5.2 0 1.14.4 , 4.42 5.1 4.03.05.05 , °° φ-φ--λ× × × = φ -mixstrmix c vbb b xx v v tpnaa d dx ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ (6) where p, t and v denotes instantaneous in‑cylinder pressure, mean in‑cylinder temperature and cylinder volume respectively. vc is the compression volume at piston top dead center (tdc) and xmix is the instantaneous unburned mixture mass fraction in the cylinder. the multiplier ab,v which extends the calibration factor ab is used for the cycle‑to‑cycle variability simulation. the meaning of the angles j and j0 follows from figure 3. the change of the mass of burned fuel mfuel is then φλ+ = φ d dx l m d dm b st cfuel 1 (7) where mc is the total cylinder mass. 2.1 determination of calibration and variabilit y factors for the determination of calibration and variability factors, it is necessary to evaluate sufficient volume of measured data – at least the sequence of 200 cycles. indicated pressure traces have to undergo thermodynamic analysis in terms of getting mean in‑ cylinder temperature and normalized burn rate rb which is crucial parameter. the determination of the single cycle‑based factor for the ignition delay comes from rearrangement of equation (3) r b [1 /° c a ] 0 0.01 0.02 0.03 0.04 0.05 0.06 ϕ [°ca] -50 -40 -30 -20 -10 tdc 10 20 30 40 50 60 70 ignition delay δϕign ϕign ϕ0 figure 3: normalized burn rate rb, definition of the ignition delay djign. obrázek 3: jednotková rychlost hoření rb, definice průtahu zážehu djign. implication of cycle‑to‑cycle variability in si engines karel páv mecca 01 2018 page 13 � �� �� ������������� ���������� ������������ ��� ������� ���� �� ��λ�� φδ � �� (8) � �� �� ������������� ���������� ������������ ��� ������� ���� �� ��λ�� φδ � �� where djign is the measured ignition delay for each single cycle. the product aign aign,v consists of the main calibration factor aign which is constant for the sequence of all cycles and of the variability factor aign,v which deviates from value 1 in the current cycle ( ) ( )vignign vignign vign vignignign aa aa a aaa , , , , median median = = (9) a similar procedure has to be done for the main combustion phase. for the determination of the single cycle‑based factor ab  ab,v used in equation (6), the most important region at the rate of burning curve (see figure 3) is the vicinity of its maximum. therefore, this factor can be determined based on measured in‑ cylinder conditions at 50% of mass burned fraction. thus, from equation (6) can be derived similarly to the previous case, the calibration factor ab is constant over the sequence of all cycles and variability factor ab,v deviates from value 1 according to the current cycle ( ) ( ) ( ) ( )vbb vbb vbb vbb vb vbbvbbb aa aa aa aa a aaaaa , , , , , ,, medianmode medianmode == == ˙ ˙ (11) here, the mode function should be used for an accurate evaluation because of asymmetrical frequency distribution of the factor ab ab,v. the mode of a set of data values is the value that appears most often. since the mode determination can cause some difficulties, the median has been used instead for an approximation. typical distribution of both mentioned variability factors is shown in figure 4. it is obvious that factors aign,v and ab,v are mutually almost independent, although a cross‑ correlation between ignition delay and combustion rate can be observed [8], [11]. while the frequency distribution of aign,v is quite symmetrical and corresponds to normal distribution, the distribution of ab,v is asymmetrically outspread to its higher values. a decision whether a distribution is symmetrical or not is possible by means of the adjusted fisher‑pearson standardized moment coefficient also called skewness [2]. the magnitude of skewness describes how symmetrical a distribution is about its mean. a positive value indicates a leaning to the right of mean and a negative value indicates a leaning to the left. the skewness is defined as ( )( )σ -= 3 )(21 )( xsdev xx nn n xskew ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ (12) from the thermodynamic analysis of a measured in‑cylinder pressure can be observed that quantities like indicated mean effective pressure, maximum heat‑release rate, maximum cylinder pressure or the crank angle at 50% of mass burned fraction follow almost normal distribution because their skewness for 200 cycles is within the 90 percent range ±0.28 [2]. sequences of calculated variability factors according to equations (9) and (11) with both measured and by means of simulation restored chosen quantities are depicted in figure 5. a b, v [] 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 aign,v [-] 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 f re qu en cy o f a ig n, v [% ] 0 20 40 60 frequency of ab,v [%] 0 10 20 30 figure 4: typical distribution of variability factors for ignition delay aign,v and main combustion phase ab,v over 870 successive cycles. traces of the normal distribution, dashed line represents a range where the normal distribution doesn’t coincide with measurement. obrázek 4: typické rozdělení faktorů pro variabilitu průtahu zážehu aign,v a variabilitu vlastního procesu hoření ab,v během 870 po sobě následujících pracovních cyklů. křivky reprezentující normální rozdělení, čárkovaná čára představuje oblast, kdy se normální rozdělení neshoduje s měřením. ( )[ ] ( ) ( ) ( ) 5.201.11.04.4,4.42 5.1 4.03.05.05 %50, , %50 %50 %50%50 5,01183.08.01015 φ-φ---λ-× = -rstrmix c b vbb xx v v tpn r aa ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ (10) implication of cycle‑to‑cycle variability in si engines karel páv mecca 01 2018 page 14 for purely simulation purposes, some artificial patterns of variability factors are desirable. as the distribution of the variability factor for ignition delay aign,v is symmetrical, one can write it in symbolic form σ+ σ-= 1,vigna (13) where s represents a random positive number, which deviates from zero and follows normal distribution with its median in 0. due to the asymmetrical frequency distribution of the main combustion variability factor ab,v the more detail analysis had to be carried out in computational tool [6] assuming calculation with the median in equation (11). in order to achieve almost normal frequency distribution of the maximum cylinder pressure and other above‑mentioned quantities the variation of the combustion variability factor has to follow relation σσ + σ-= 1, 1vba (14) where s represents a random positive number, which deviates from zero and follows normal distribution with its median in 0, s value in equation (14) is independent of that used in equation (13). note that the number of values lower and higher than 1 is equal, thereby the frequency distribution of the function (14) doesn’t exactly coincide with the distribution in figure 4 but the use of this relation for simulation purposes is quite sufficient. 2.2 magnitude of variabilit y factors as a measure of the cycle‑to‑cycle variability level can be considered the standard deviation in variability factors aign,v and ab,v whose sequence centric values correspond to the median of value 1, see equations (9) and (11). this approach allows separate assessment of preflame and main combustion phase. the calculation for ignition delay is simple but the standard deviation in combustion variability factor ab,v has to be evaluated for values lower or equal to 1 only due to its asymmetrical distribution ( ) ( ) 1 1 1 )( 1 1 )( , 2 , , 2 , , ≤ a = = σ σ vb vb vb vign vign a n a asdev n a asdev (15) cycle [-] 0 20 40 60 80 100 120 140 160 180 200 a ig n, v [] 0.0 0.5 1.0 1.5 2.0 skew(aign,v) = 0.10 δ ϕ ig n [° c a ] 0 5 10 15 20 25 measurement skew(δϕign) = 0.12 skew(δϕign) = 0.11 simulation cycle [-] 0 20 40 60 80 100 120 140 160 180 200 p m a x [b ar ] 15 20 25 30 35 40 skew(pmax) = -0.21 skew(pmax) = -0.28 a b, v [] 0.0 0.5 1.0 1.5 2.0 skew(ab,v) = 0.96 m b f 50 % [° c a ] -10 -5 0 5 10 15 skew(mbf50%) = 0.24 skew(mbf50%) = 0.19 cycle [-] 0 20 40 60 80 100 120 140 160 180 200 a ig n, v [] 0.0 0.5 1.0 1.5 2.0 skew(aign,v) = 0.10 δ ϕ ig n [° c a ] 0 5 10 15 20 25 measurement skew(δϕign) = 0.12 skew(δϕign) = 0.11 simulation cycle [-] 0 20 40 60 80 100 120 140 160 180 200 p m a x [b ar ] 15 20 25 30 35 40 skew(pmax) = -0.21 skew(pmax) = -0.28 a b, v [] 0.0 0.5 1.0 1.5 2.0 skew(ab,v) = 0.96 m b f 50 % [° c a ] -10 -5 0 5 10 15 skew(mbf50%) = 0.24 skew(mbf50%) = 0.19 figure 5: sequence of measured and simulated ignition delay for 200 successive cycles, used variability factors for ignition delay aign,v and main combustion phase ab,v , values of maximum cylinder pressure and crank angle at 50% of mass burned fraction. engine speed 3000 min‑1, imep = 5 bar. obrázek 5: sekvence naměřených a simulovaných průtahů zážehu pro 200 po sobě následujících cyklů, použité hodnoty faktorů pro variabilitu průtahu zážehu aign,v a variabilitu vlastního procesu hoření ab,v , maximální spalovací tlaky a úhel natočení klikového hřídele při 50% vyhoření náplně válce. otáčky motoru 3000 min‑1, imep = 5 bar. s d e v (a v) [] 0 0.1 0.2 0.3 0.4 ignition angle ϕign [°ca] -60 -50 -40 -30 -20 -10 0 sdev(ab,v) sdev(aign,v) figure 6: typical values of standard deviation in variability factors aign,v and ab,v as a function of ignition angle, bands of occurrence. obrázek 6: typické hodnoty směrodatných odchylek faktorů pro variabilitu průtahu zážehu aign,v a variabilitu vlastního procesu hoření ab,v v závislosti na předstihu zážehu, pásma výskytu. implication of cycle‑to‑cycle variability in si engines karel páv mecca 01 2018 page 15 typical values of standard deviation in variability factors as a function of ignition angle which has been found as a strong influencing parameter are shown in figure 6. other parameters like an engine speed, mean indicated pressure, combustion duration, etc. don’t show so close correlation. in general, advancing the spark increases the magnitude of ignition delay and also its standard deviation. the shortest ignition delay can be observed at ignition angles around tdc when both in‑ cylinder pressure and temperature reach the highest values – see the relation in equation (3). the variability factor aign,v induces relative changes in ignition delay, therefore sdev(aign,v) is increasing with decreasing of mean value of the ignition delay itself. if the ignition delay is close to zero the changes in the variability factor aign,v have no impact on the cycle‑to‑cycle variability level at all. 3. simulation of cycle-to-cycle variability the practical use of the cycle‑to‑cycle variability simulation is demonstrated on investigation of fuel saving potential by variability level reduction. the reference conditions have been given by cycle‑to‑cycle variability levels of the si gasoline engine from figure 1. all measured engine operational points have undergone thermodynamic analysis in order to get calibration and variability factors using equations (8) – (11). the calibration factors and sequences of variability factors have been then used for fuel consumption calculation at optimum ignition timing for all engine operational points. this calculation has been carried out in modified calculation software [6] for 200 successive cycles. afterwards, the variability level had been suppressed to zero (aign,v = 1, ab,v = 1) and calculated hypothetical fuel consumption at optimum ignition timing was compared with previous results. the outcome of this computational analysis is presented in figure 7. displayed values represent fuel consumption increase due to the cycle‑to‑cycle variability levels related to figure 1. one can see the maximum fuel consumption saving of magnitude 0.49%. however, this value is not even entirely achievable in practice due to the ultimate minimum variability level. 3.1 generalization of results the main goal of the results generalization was to assess a wide range of engine operational points including different combustion processes. a detailed simulation analysis has been carried out at four engine operational points – red colored points in figure 1. in order to evaluate entire scale of combustion rates it was necessary to generate artificial sequences of the variability factors of different variability levels as an input for the calculation. the standard deviations in variability factors calculated according to (15) have been chosen in range of á0, 0.4ñ with step 0.1. thereby, the calculation input was formed by the grid of 5x5 variability factor patterns. the artificial generation of the variability factors with respect of relations (13) and (14) has been done in labview 2010 environment by using function discrete random. additionally, in order to consider the influence im e p [b ar ] 0 2 4 6 8 10 12 engine speed [1/min] 0 1000 2000 3000 4000 5000 6000 100.49100.30 100.44100.33100.17 100.38100.30 100.23 100.29100.13 100.28100.27100.20 100.22100.13 100.20 100.20100.19100.17 fuel consumption [%] figure 7: calculated fuel consumption increase due to the cycle‑to‑cycle variability levels related to figure 1. obrázek 7: vypočtené navýšení spotřeby paliva vlivem mezicyklové variability dané parametry dle obrázku 1. f ue l c on su m pt io n [% ] 100 101 102 103 104 105 106 sdev(mbf50%) [°ca] 0 2 4 6 8 10 12 slow combustion intermediate combustion fast combustion figure 8: fuel consumption as a function of standard deviation in crank angle at 50% of mass burned fraction, calculation results for red colored engine operational points from figure 1 considering different combustion rates at optimum spark timing. obrázek 8: spotřeba paliva v závislosti na směrodatné odchylce úhlu natočení klikového hřídele při 50% vyhoření náplně válce, výsledky výpočtů pro červeně označené body v obrázku 1 s uvažováním různých rychlostí hoření při optimálním předstihu zážehu. implication of cycle‑to‑cycle variability in si engines karel páv mecca 01 2018 page 16 of different combustion rates the calculation was carried out for three different calibration factors ab = 0.5, 1 and 2 which represent slow, intermediate and fast combustion respectively. the calibration factor for ignition delay was invariable aign = 1. the simulation of 75 events at each of four engine operational points was performed in modified calculation software [6] for 200 successive cycles. the calculation results are summarized in graphical form in figure 8. the relative fuel consumption 100% is assigned to uniform combustion without any cycle‑to‑cycle variability implication. from the practical point of view it doesn’t matter how the resulting variability level has been achieved – by variation of the ignition delay or of the main combustion phase. therefore, the impact of the cycle‑to‑cycle variability on fuel consumption can be simply expressed as a function of standard deviation in crank angle at 50% of mass burned fraction which is easy detectable parameter. one can see that the influence of the combustion rate is marginal. assuming optimum spark timing and usual values of sdev(mbf50%) = 3°ca a theoretical potential for fuel consumption improvement in terms of cycle‑ to‑cycle variability reduction can be estimated to 0.4% only. this value corresponds to the results in figure 7. above mentioned marginal influence of the combustion rate can be explained by following computational analysis at four red colored engine operational points depicted in figure 1. the engine fuel consumption in steady state mode was calculated with various spark timing for three different combustion rates. the results after recalculation to relative change of the crank angle at 50% of mass burned fraction are shown in figure 9. the minimum fuel consumption corresponds to maximum brake torque spark timing (mbt), as expected. a leaning of the angle mbf50% either to lower or higher values leads to fuel consumption increase almost independent of the engine load or combustion rate magnitude like that in figure 8. therefore, the chart in figure 8 can be considered as generally valid for si gasoline engines with optimum spark timing. if the ignition timing is far from its optimum, the cycle‑to‑cycle variability level doesn’t influence engine fuel consumption so much, because the relationship between relative change of the angle mbf50% and fuel consumption is nearly linear as shown in figure 9. the location of the mean value of the angle mbf50% affects the fuel consumption almost an order of magnitude greater than a cycle‑ to‑cycle variability. if a knocking is considered the situation is more complex. under knocking conditions, the spark advance has to be retarded, i.e. the angle mbf50% is shifted from mbt point to higher values, which leads to significantly higher fuel consumption. since the knock event is related to stochastic nature of combustion the reduction of cycle‑to‑cycle variability suppresses a knock occurrence and thus allows advancing combustion [8]. 4. conclusion the cycle‑to‑cycle variability is often discussed topic related to overall engine efficiency and thereby a subject for optimization. the simulation of the cycle‑to‑cycle variability is possible by using empirical adaptive combustion model extended by variability factors. individual patterns of variability factors for ignition delay and main combustion phase, which are independent of each other, can be either measured or artificially generated according to required variability level. this approach leads to very good agreement with real engine behavior. although it is technically possible to reduce cycle‑to‑cycle variability the carried‑out sensitivity analysis without knock limitation at optimum spark timing shows that achievable engine fuel consumption reduction is up to 0.4% only. on the other hand, with an increasing variability the engine efficiency deterioration is more progressive, thus should be avoided. the right spark timing regarding the mean value of the crank angle at 50% of mass burned fraction has much stronger effect on engine fuel consumption than a cycle‑to‑cycle variability. f ue l c on su m pt io n [% ] 100 105 110 115 120 125 relative change of mbf50% [°ca] -15 -10 -5 0 5 10 15 20 25 slow combustion intermediate combustion fast combustion mbt figure 9: fuel consumption as a function of relative change of crank angle at 50% of mass burned fraction. obrázek 9: spotřeba paliva v závislosti na relativní změně úhlu natočení klikového hřídele při 50% vyhoření náplně válce. implication of cycle‑to‑cycle variability in si engines karel páv mecca 01 2018 page 17 references [1] beroun s., páv k. 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(2013). a computational study on the impact of cycle‑to‑cycle combustion fluctuations on fuel consumption and knock in steady‑state and drivecycle operation, sae technical paper 2013‑24‑0030, doi:10.4271/2013‑24‑0030 [9] schneider a., hettinger a., schünemann e. (2016). optical investigations of flame kernel formation in an si engine with diluted mixture, in: 12th international symposium on combustion diagnostics, baden‑baden, pp. 61‑79, isbn 978‑3‑9816971‑2‑4 [10] tatschl r., bogensperger m., pavlovic z., priesching p., schuemie h., vitek o., macek, j. (2013). les simulation of flame propagation in a direct‑ injection si‑engine to identify the causes of cycle‑to‑cycle combustion variations, sae technical paper 2013‑01‑1084, doi:10.4271/2013‑01‑1084 [11] vitek o., macek j., poetsch c., tatschl r. (2013). modeling cycle‑to‑cycle variations in 0‑d/1‑d simulation by means of combustion model parameter perturbations based on statistics of cycle‑resolved data, sae technical paper 2013‑01‑1314, doi:10.4271/2013‑01‑1314 ole_link5 ole_link6 ole_link4 ole_link1 ole_link11 ole_link12 ole_link7 ole_link8 _ref503366894 _ref502929276 _ref502929278 _ref505352558 _ref503367918 _ref503082741 _ref503112326 _ref503111897 _ref503111924 _ref503368086 _ref503368097 _ref503368213 _ref503363584 _ref503367501 _ref503368504 _ref503123797 _ref503947492 _ref503532965 _ref503123776 _ref503800139 _ref503972064 _ref503947157 turbocharging of high performance compressed natural gas si engine for light duty vehicle marcel škarohlíd, jiří vávra implication of cycle-to-cycle variability in si engines karel páv identification of cycle-to-cycle variability sources in si ice based on cfd modeling oldřich vítek, vít doleček, zbyněk syrovátka, jan macek physical 1d model of a high-pressure ratio centrifugal compressor for turbochargers jan macek mecca_21-01_web critical shifting window in switchable rocker finger follower petr kohout, jan kindermann mecca 01 2021 page 1 10.14311/mecdc.2021.01.01 critical shifting window in switchable rocker finger follower petr kohout, jan kindermann critical shifting window in switchable rocker finger follower petr kohout eaton european innovation center, bo!ivojova 2380, 252 63 roztoky, email: petrkohout@eaton.com jan kindermann eaton european innovation center, bo!ivojova 2380, 252 63 roztoky, email: jankindermann@eaton.com abstract a valvetrain including switchable rocker fi nger follower is capable of discrete switching between two modes (two cam profi les). the exact moment when switching occurs is called crossover point and this paper reviews the factors that cause the shift of the crossover point from its nominal design position. the range where crossover point can shift is called critical shifting window and its size and factors infl uencing it will be adressed. key words: cam, cam profile, cam design, switchable roller finger follower, tolerances, stack up, shifting window, cae shrnutí ventilov" rozvod s p!epínateln"m vahadlem s rolnami je schopen p!epínat mezi dv#ma re$imy (p!epínání mezi dv#ma va%kov"mi profi ly). okam$ik, kdy dojde k p!epnutí mezi jednotliv"mi va%kami, se naz"vá bod p!echodu. v tomto p!ísp#vku budou uvedeny jednotlivé faktory, které zp&sobují posun bodu p!echodu z jeho jmenovité návrhové pozice. cel" rozsah kam se m&$e bod p!echodu posunout je ozna%ován jako okno bodu p!echodu a v p!ísp#vku bude probráno jak jednotlivé faktory ovliv'ují jeho velikost. klí!ová slova: va!ka, profil va!ky, návrh va!ky, p"epínatelné vahadlo s rolnami, tolerance, toleran!ní anal#za, okno p"echodu, cae 1. introduction valvetrain mechanism between camshaft and a valve itself allows to transform camshaft rotational movement to the intake and exhaust valve translational movement. the conventional and simplest valvetrain operation allows the fresh air or air -fuel mixture to enter the cylinder during the intake stroke when intake valves are open, participate on combustion and let the combustion products leave the cylinder during exhaust stroke when exhaust valves are open. but as demands on engines increase and fulfilling prescribed emission limits is more and more challenging new technologies and innovation are being used. the valvetrain is no exception and variable valve timing (vvt) and variable valve lift (vvl) are used in vehicles nowadays. cam phaser is the most common way for vvt implementation. it allows to shift the entire valve lift within the specified range of an engine cycle and it appears in two versions – discrete and continuous timing switching. switching between different cams is used for the vvl realization. the axial camshaft shifting or switching the cam that controls the valve using advanced finger followers or rocker arms is used by oems. combination of vvt and vvl is commonly called as variable valve actuation (vva). different vva systems used by oems are usually called by their marketing name such as vtec, vanos, multiair, mivec etc. camless valvetrains are the most variable solution but they are used mainly in experimental and research engines so far [1]. more on the topic of vva can be found in the following publications – [2], [3], [4]. the switchable roller finger follower (srff) is one of the ways how to implement discrete variable valve lift. [5] that means it allows to switch between two different valve lifts. the crossover point is the moment when switch is realized, thus the moment when the valve changes cam lobe which prescribes its lift. the principle of srff will be explained followed by the thorough description of the critical shifting window, how it is created and influence of the specific factors on the window size. critical shifting window in switchable rocker finger follower petr kohout, jan kindermann mecca 01 2021 page 2 2. switchable roller finger follower valvetrain the conventional valvetrain system with a standard roller fi nger follower shown in figure 1 is often referred to as type ii valvetrain. it consists of a camshaft that acts on a roller fi nger follower through its roller. the roller fi nger follower is in contact with pivot on one side and valve stem on the other side. improvement of such a system by replacing the roller fi nger follower by its switchable version (figure 2) enables to switch between two different lifts on one valve. it allows to switch for example between normal mode and miller cycle on the intake side. the same thing could be applied to the exhaust side where normal exhaust valve lift can be supplemented by small extra lift during the intake stroke, which allows to get some of the exhaust gases entering back to the cylinder and this is often referred to as internal exhaust gas recirculation (iegr). srff can be used for cylinder deactivation or other advanced valve actuation strategies. inside the srff there is a latch pin (figure 3) and depending on its position the finger follower responds to the inner roller. when the pin is not latched the inner roller of srff makes so called lost motion. on the other hand, when the pin is latched the entire srff and thus also the valve reacts on the movement of the inner roller. to be able to perform two different lifts with srff valvetrain system a camshaft must have 3 cam lobes per srff (figure 4). two outer cam lobes are identical and act on outer rollers of the srff, figure 1: type ii valvetrain obrázek 1: ventilov" rozvod typ ii figure 2: switchable rocker fi nger follower (sfrr) obrázek 2: p!epínatelné vahadlo figure 3: srff section obrázek 3: (ez vahadlem figure 4: srff cam lobes obrázek 4: va%ky pro p!epínatelné vahadlo critical shifting window in switchable rocker finger follower petr kohout, jan kindermann mecca 01 2021 page 3 the inner cam lobe acts on inner roller which is connected to the inner arm and can either perform a lost motion or transmit the cam lift into the valve lift. function of srff valvetrain when the pin is not latched is as follows. on the base circle the outer cam lobes are in contact with outer roller (no lash is present because a hydraulic lash adjuster is often used). the lash between the inner cam lobe and the inner roller is present and is called mechanical lash at cam (mlc). as the camshaft rotates the valve lift is influenced only by outer cam lobes. during the camshaft rotation there is a moment when inner cam lobe gets in contact with inner roller and as mlc gets closed the impact on inner roller appears. the lift is not transferred from the inner cam lobe to the valve as pin is not latched and inner arm makes lost motion. when pin is latched the situation in the beginning is similar. outer rollers are in contact with cam lobes, mlc is present and there is also lash between latch pin shelf and inner arm mating surface which is called mechanical lash at latching pin (mll). during the camshaft rotation the mlc is closed first, then the inner arm starts to move and mll is closed. at this moment the valve lift is no more controlled by the outer lobe profiles and starts to be controlled by the inner lobe profile instead. this moment is considered as the crossover point. very similar conditions and phenomena as during crossover point happen when mlc is closed so further in the article it will be adressed as a crossover point 1 (cp1) and the actual crossover point when mll is closed as crossover point 2 (cp2). as the lift of the inner cam lobe decreases back to the base circle, the mll is opened first and outer cam lobes get in contact with outer rollers and valve is again controlled by the them. further as the inner cam lobe lift goes back to base circle the mlc is opened. 3. approach gt -suite is a cae toolset widely used in industry especially in the automotive as it has many useful features for simulation of the specific parts of the vehicles and engines. it is capable of 1-d flow simulation, kinematics, mbd etc.. two parts of this complex software package were used in order to examine influence of various factors on width of critical shifting window. the gt -ise where libraries for valvetrain and multibody dynamics were used and vtdesign where cam profiles were designed, and kinematics of the system was examined. in general, when designing cam profile, it is important to control cam velocity and acceleration. too high velocity during opening and closing ramps results in excessive impacts in the system which result in increased wear or higher failure probability. acceleration is controlled in order to avoid contact separation in the valvetrain. a separation could happen when inertia forces are higher than force generated by a valve spring. acceleration has a direct influence on manufacturability as with the high acceleration the concave radius of curvature of the cam decreases. if cam concave radius is smaller than the grinding tool, it will be impossible to grind some areas on the profile. specific limit values are usually set by internal company guidelines and are often treated as business secret. more about process of developing the cam profile can be found in [6]. the mbd model of the single valve mechanism including srff was built in gt -ise in such a way that position of various components in the valvetrain can be quickly and easily changed which allows to implement manufacturing tolerances and wear of the specific parts in the system. vtdesign was used to design cam lobe profiles which are then input in the mbd model. initially the simulation was performed with all the nominal dimensions and baseline cam profiles thus perfectly fulfilling the moment when cp1 and cp2 were intended to happen based on the specific requirements on the function of the valvetrain and engine. furthermore, the position of the components was changed in order to simulate influence and sensitivity of moment cp1 and cp2 on manufacturing tolerances and other aspects that will be discussed later in appropriate chapters followed by the interpretation of the results and conclusion. the main motivation for keeping critical shifting window small is because only in this area the crossover point can happen thus only here the velocity difference needs to be controlled. if the csw is too wide the velocity difference needs to be kept sufficiently small for a long time period and that results in restrictions for cam design of inner and outer cam lobe profile. figure 5: mechanical lashes in the srff obrázek 5: v&le v p!epínatelném vahadle critical shifting window in switchable rocker finger follower petr kohout, jan kindermann mecca 01 2021 page 4 4. baseline the mbd simulation using all the nominal dimensions was performed in order to set the nominal position of the cp1 and cp2. the critical shifting window will be created around those values as different factors will be changed in the following chapters. it is also important to set up the initial position of every simulation and derived angular positions of contacts during the cp. every simulation performed has the same layout as specified in figure 6. from the point of view, the valve is on the left and pivot on the right, the camshaft rotates counterclockwise and all the cam lobe first points (first point that is higher than cam base circle) lies on the global negative y axis. as the simulation time goes forward the camshaft rotates and angles !, ", # can be observed as in figure 7. ! is the angle between negative y axis and the cam lobe first point and gives us the information about the timing. it tells when the cp happens. " is the angle between first cam lobe point and the contact point between outer cam and roller. it gives us the information about where on outer cam profile does the cp happen. # is very similar to " but it goes from the first point of the cam lobe to the contact of inner cam and roller. all three angles will be used in description of the critical shifting windows. big deviation in ! signs that the function of the inner profi le lift can cause not desired infl uence on the engine cycle as the prescribed cp can happen too early or too late. angles " and # gives us the information where is the contact point on the cam when the cp happens. it is important as it gives us the information about the impact that appears in the system during cp. in order to realize cp, the velocity on the inner cam lobe has to be higher than on outer cam lobe so the lashes will get closed. but the velocity difference has to be limited so the strong impacts will not damage and wear the components and cause the system failure. relative velocity difference is calculated as described in equation (1) and (2). 𝑣𝑣!"##@%&'�=�𝑣𝑣"(()*(𝛾𝛾%&')�−�𝑣𝑣+,-)*(𝛽𝛽%&') 𝑣𝑣!"##@%&.�=�𝑣𝑣"(()*(𝛾𝛾%&.)�−�𝑣𝑣+,-)*(𝛽𝛽%&.) (1) 𝑣𝑣!"##@%&'�=�𝑣𝑣"(()*(𝛾𝛾%&')�−�𝑣𝑣+,-)*(𝛽𝛽%&') 𝑣𝑣!"##@%&.�=�𝑣𝑣"(()*(𝛾𝛾%&.)�−�𝑣𝑣+,-)*(𝛽𝛽%&.) (2) baseline design angles !, ", # are in the table 1 and relative velocity difference intable 2. cp1 happens when camshaft rotates 87,8° from the initial position and rollers are in contact at 91,3° of outer cam lobe and 91,1° of inner camlobe. cp2 design moment is at 101,9° rotation after initial state. outer cam lobe is in contact with roller at 102,7° of its profile and inner cam lobe at 101,9° of its profile. critical shifting window will be created around those nominal values. same cam lobe profiles will be used if not mentioned otherwise. figure 6: simulation initial state obrázek 6: po%áte%ní stav simulací figure 7: crossover point angles defi nition obrázek 7: defi nice úhl& pro bod p!echodu table 1: nominal crossover points tabulka 1: nominální p!echodové body baseline cp1 baseline cp2 ! [deg] " [deg] # [deg] ! [deg] " [deg] # [deg] 87,8 91,3 91,1 101,9 102,7 101,9 table 2: baseline relative velocity difference during crossover point tabulka 2: v"chozí relativní rozdíl rychlostí na va%kách v p!echodov"ch bodech baseline cp1 vel. difference [mm/deg] baseline cp2 vel. difference [mm/deg] 0,0075 0,0075 critical shifting window in switchable rocker finger follower petr kohout, jan kindermann mecca 01 2021 page 5 5. srff tolerance factors in an ideal case every product going from the same production line would be identical. but in practice even if material goes through same prescribed set of operations there is always some deviation in dimensions or material properties thus the final products have some level of variation. but that does not necessarily mean that the function is affected. setting the tolerances for manufacturing processes limits the deviation in final products in a way that desired function is assured. but setting the tolerance limits has its other side as well. the tighter are the deviation limits the more accurate thus more costly steps and processes must be utilized. it is always extremely important to find a compromise between the price and tolerance levels. all the component variations are taken in account in so called stack -up analysis to see if the desired function is assured. the stack -up analysis is not the object of interest in this article thus it will not be described in detail what is the cause of position change. only the stack-up analysis results of parts that affects the critical shifting window will be used. some of the cases that are discussed are artificially created but it helps to distinguish what is the real factor that moves a crossover point. it can be observed for example in first case where x position of outer rollers is changed. in real scenario the resulting change in position of outer roller would be caused by changed position of the outer roller axis and as this axis is in contact with bushing of the inner roller it would naturally change the initial position of inner roller and size of mlc. for sake of clarity and simplicity let’s consider cases where only one specific position is changed and rest stays in its nominal position. 5.1 outer rollers position infl uence of roller position tolerance was examined in 9 cases prescribed as in figure 8– 1 nominal position and then 8 positions of the outer roller axis on the circle with radius of 0.03 mm. results are in table 3 and it can be seen that values for ! (the angle describing the timing) go from 84,5° to 91° for cp1 and from 99° to 105,1° for cp2. if it is considered that 1° of cam angle rotation corresponds to 2° of crank angle (ca) rotation the shift of the cp1 in engine cycle can be shown. cp1 can happen 6,6° ca before or 6,4° ca after the designed moment and anywhere in between. cp2 can happen 5,8° ca before or 6,4° ca after the designed moment and anywhere in between. in the next chapters the result description will not be as detailed as here, but only table with results and critical shifting window expressed by the range of ! will be mentioned. 5.2 inner roller position the same strategy as in the previous chapter was used and 9 cases were simulated including nominal position and 8 axis offset positions on a circle around the nominal position (figure 9). figure 8: examined outer rolers axis positions obrázek 8: zkoumané pozice osy vn#j)ích rolen figure 9: examined inner rolers axis positions obrázek 9: zkoumané pozice osy vnit!ních rolen table 3: results for different outer rollers position tabulka 3: v"sledky pro r&zné pozice vn#j)ích rolen outer roller position tolerance cp1 cp2 x tol [mm] y tol [mm] ! [deg] " [deg] # [deg] ! [deg] " [deg] # [deg] 0 0 87,8 91,3 91,1 101,9 102,7 101,9 -0,03 0 86,4 90,4 90,0 100,4 101,5 100,6 -0,02121 0,02121 88,8 92,1 91,8 102,9 103,7 102,8 0 0,03 90,8 93,6 93,3 105,1 106,0 105,0 0,02121 0,02121 91,0 93,8 93,5 105,1 105,9 105,0 0,03 0 89,3 92,4 91,2 103,4 104,1 103,2 0,02121 -0,02121 86,7 90,3 90,2 100,9 101,8 101,1 0 -0,03 84,7 88,7 88,6 99,2 100,4 99,7 -0,02121 -0,02121 84,5 88,6 88,5 99,0 100,2 99,5 critical shifting window in switchable rocker finger follower petr kohout, jan kindermann mecca 01 2021 page 6 critical shifting window infl uenced only by the inner roller position goes from 84,5° to 91° in terms of ! for cp1 and from 99° to 105,1° for cp2. 5.3 latch -pin shelf tolerance when referring to the latch -pin shelf tolerance, the position of surface compared to nominal position as shown in figure 10 is meant. as this dimension is not anyhow involved during the cp1 its infl uence only on cp2 will be examined. the critical shifting window for cp2 in term of ! can go from 100° to 104,1° due to the latch -pin shelf tolerance. 6. cam lobe tolerances the same as for srff is valid for the cam lobe profi les. the tolerances that are taken in account here are cam profi le tolerance, wear and cam profi le angular tolerance. profi le tolerance is easy to understand as it means that the designed cam profi le can be either higher or lower by the specifi ed value. wear is captured by adding higher value to the negative side of the profi le tolerance so the actual cam profi le can be lower than the nominal partially because of manufacturing and partially due to wear over the time. cam angular tolerance means that the cam lobe profi le can be shifted relatively to the other cam lobe. in the baseline case, both cam lobes have their fi rst profi le point in the direction of negative y direction but in reality, the profi les can be shifted to each other due to angular position tolerance 6.1 outer cam lobe profile tolerance four cases were tested including again the nominal dimension, then two cases for ±0,03 caused by the manufacturing and then case -0,06 where the half of the value is caused by the manufacturing and half by the wear of the cam lobe. thus the tested cases and critical shifting window are not symmetrical. each case results are table 6. critical shifting window infl uenced only by outer cam profi le tolerance and wear goes from 80,3° to 91° in terms of ! for cp1 and from 96,4° to 105,0° for cp2. 6.2 inner cam lobe profile tolerance the same cases as in previous chapter were tested for the inner cam lobe tolerances. results are in the table 7. critical shifting window infl uenced only by inner cam profi le tolerance and wear goes from 84,5° to 91° in terms of ! for cp1 and from 99,3° to 105,1° for cp2. the trend is here opposite to the figure 10: latch -pin shelf tolerance obrázek 10: tolerance obrobení plochy p!epínacího %epu table 5: reults for latch -pin shelf tolerance tabulka 5: v"sledky pro tolerance plochy p!epínacího %epu pin tolerance cp2 [mm] ! [deg] " [deg] # [deg] 0 101,9 102,7 101,9 -0,03 100,0 101,0 100,3 -0,02 100,5 101,5 100,7 -0,01 101,2 102,1 101,3 0,01 102,6 103,4 102,5 0,02 103,4 104,1 103,2 0,03 104,1 104,9 103,9 table 6: results for outer cam profi le tolerance and wear tabulka 6: v"sledky pro profi lovou toleranci a opot!ebení vn#j)ích va%ek outer cam profi le tolerance cp1 cp2 [mm] ! [deg] " [deg] # [deg] ! [deg] " [deg] # [deg] 0 87,8 91,3 91,1 101,9 102,7 101,9 -0,06 80,3 85,2 85,2 96,4 98,0 97,5 -0,03 84,5 88,6 88,5 99,0 100,2 99,5 0,03 91,0 93,8 93,5 105,0 105,9 105,0 table 4: results for different inner rollers position tabulka 4: v"sledky pro r&zné pozice vnit!ních rolen inner roller position tolerance cp1 cp2 x tol [mm] y tol [mm] ! [deg] " [deg] # [deg] ! [deg] " [deg] # [deg] 0 0 87,8 91,3 91,1 101,9 102,7 101,9 -0,03 0 89,3 92,5 92,2 103,4 104,1 103,3 -0,02121 0,02121 86,6 90,3 90,2 101,0 101,9 101,1 0 0,03 84,7 88,8 88,7 99,2 100,4 99,7 0,02121 0,02121 84,5 88,6 88,5 99,0 100,2 99,5 0,03 0 86,4 90,1 89,9 100,5 101,5 100,6 0,02121 -0,02121 88,8 92,1 91,8 102,9 103,7 102,7 0 -0,03 90,7 93,6 93,3 105,1 105,9 104,9 -0,02121 -0,02121 91,0 93,8 93,5 105,1 105,9 105,0 critical shifting window in switchable rocker finger follower petr kohout, jan kindermann mecca 01 2021 page 7 tolerances of outer cam lobe. the higher is the inner cam profi le the earlier happen both crossover points while at the outer cam lobe the higher is the profi le the later the crossover points occur. 6.3 outer cam lobe angular tolerance changing the relative angular position of the cams means shifting the profi le timing thus changing all the cam lobe characteristics including lift, velocity and other higher derivatives. it is important to check if the relative velocity difference during cp do not exceed the prescribed guideline limits so the impacts in the system are controlled. results for outer cam lobe angle are in table 8. critical shifting window infl uenced only by outer cam angular tolerance goes from 83,2° to 93,9° in terms of ! for cp1 and from 95,9° to 108,5° for cp2. 6.4 inner cam lobe angle position tolerance same cases as prescribed in previous chapter were tested for inner cam lobe angular tolerance. see the results in the table 9. critical shifting window infl uenced only by inner cam angular tolerance goes from 83,7° to 93,4° in terms of ! for cp1 and from 96,4° to 108,0° for cp2. it can be observed that the trends are similar as in cam lobe profi le tolerance – shifting outer cam lobe angular position clockwise (+0,5°) cause cps occur later on the other hand shifting the inner cam lobe same direction causes that cps occur earlier. 7. worst case scenario after the examination of each factor infl uence to the position of cps the overall impact of all should be added together and see how it can infl uence the moment of cp1 and cp2. in reality such a case is highly improbable and statistical approach should be applied so the tolerances are not set too strict only for highly improbable combinations. see the results in table 10. it can be observed that due to manufacturing tolerances set as prescribed in the previous chapters the cp1 can happen anytime from 63,8 ° to 110,5° and cp2 from 78,2° to 120° in terms of !. critical shifting window is 46.7° wide for cp1 and 42,1°wide for cp2. such a width of csw and level of uncertainty when does the cp happen might not be suffi cient for some applications so in the next chapter there will be ways how to infl uence the the width of csw. 8. critical shifting window adjustments there are two ways how to adjust the width of csw. first way is very obvious, and it consists of making tolerances tighter. for our case the tolerances were halved. it can be considered that for roller tolerances the more accurate machine was used to drill the holes in srff, and more precise turning was used for rollers. that would result in roller’s axis lying in circle of radius 0,015mm around its nominal position. same applies for cam tolerances, table 7: results for inner cam profi le tolerance and wear tabulka 7: v"sledky pro profi lovou toleranci a opot!ebení vnit!ní va%ky inner cam profi le tolerance cp1 cp2 [mm] ! [deg] " [deg] # [deg] ! [deg] " [deg] # [deg] 0 87,8 91,3 91,1 101,9 102,7 101,9 -0,06 93,9 96,1 95,6 108,5 110,9 110,0 -0,03 91,0 93,8 93,5 105,1 105,9 105,0 0,03 84,5 88,6 88,5 99,3 100,4 99,7 table 8: results for angular tolerance of outer cam lobes tabulka 8: v"sedky pro úhlovou toleranci vn#j)ích va%ek outer cam angular tolerance cp1 cp2 [deg] ! [deg] " [deg] # [deg] ! [deg] " [deg] # [deg] 0 87,8 91,3 91,1 101,9 102,7 101,9 -0,5 83,2 88,0 87,5 95,9 98,1 97,1 0,5 93,9 95,7 95,7 108,5 109,5 109,3 table 9: results for angular tolerance of inner cam lobe tabulka 9: v"sledky pro úhlovou toleranci vnit!ní va%ky inner cam angular tolerance cp1 cp2 [deg] ! [deg] " [deg] # [deg] ! [deg] " [deg] # [deg] 0 87,8 91,3 91,1 101,9 102,7 101,9 -0,5 93,4 95,7 95,7 108,0 109,5 109,3 0,5 83,7 88,0 87,5 96,4 98,1 97,1 table 10: worst case scenario results tabulka 10: v"sledky pro kombinaci nejhor)ích mo$n"ch tolerancí worst case superposition cp1 cp2 ! [deg] " [deg] # [deg] ! [deg] " [deg] # [deg] beginning of csw 63,8 72,0 71,6 78,2 83,9 83,1 end of csw 110,5 112,4 113,3 120,3 126,0 127,5 critical shifting window in switchable rocker finger follower petr kohout, jan kindermann mecca 01 2021 page 8 furthermore the better material in terms of wear would be used so the peak wear decreases to 0,015mm thus cam profi le tolerance would go from -0,03 mm to +0,015 mm around nominal value and cam angle tolerance ±0,25°. infl uence on csw is in table 11. the improvement is signifi cant and csw for cp1 goes from 75° to 101,2° and for cp2 from 89,3° to 114,7° in terms of !. then width of the csw is 26,2° for cp1 and 25,4° for cp2. another way how to make csw tighter is the adjustment of cam design and its velocity specifi cally. tolerance deviation is basically increasing or decreasing the initial size of the lashes (mlc, mll) compared to nominal, which has to be closed. the relative velocity difference tells us how quickly get those lashes closed around cp. adjusting cam design in a way that position of cp stays the same but relative velocity difference is higher will result in closing the lashes with their deviations faster and so decreasing the infl uence of tolerances on csw size. the new inner cam profi le was designed wither higher relative velocity difference (table 12) and its infl uence on csw size is in table 13. the results show the size of csw can be decreased by proper cam design as well. in this case increasing relative velocity difference for cp1 from 0,0075 mm/deg to 0,0103 mm/deg decreased the size of csw by 12,9° in terms of !. with velocity difference increase from 0,0075 mm/deg to 0,0132 mm/deg for cp2 the csw was decreased by 10,6° in terms of !. increasing relative velocity is not for free as well, since the higher the difference is the higher is the impact that appears in the system during cp. the advantage of making csw tighter has to be compared with disadvantage of possible higher wear or necessity of using better material. last case in this article will be the combination of two adjustments made above. the results for case where tolerances have the half size compared to the worst case and the relative velocity difference is as in table 12. critical shifting window is 16,2° wide for cp1 and 17,7° wide for cp2 in terms of !. 9. conclusion concept and principle of critical shifting window was explained and infl uence of various factors on its size was examined. detailed study of each factor was performed and based on results the following can be stated. the presence of critical shifting window is inevitable, and its size is prescribed by the manufacturing tolerances and design of a cam lobe profi le during cp. adjustments to the size of csw can be done either by making manufacturing process more accurate or by increasing the relative velocity difference at cam lobes during the cp. the disadvantage of more accurate manufacturing process is the higher cost. the information about the actual tolerance classes, tolerance -based assembly and the trade -off between cost and csw width is usually considered as a business secret and it is extremely diffi cult to reach to such information. it is important to compare the brought advantage for the increased cost. for example, if improving production process of the camshaft would table 11: results for worst case scenario with half tolerances tabulka 11: v"sledky pro kombinaci nejhor)ích mo$n"ch polovi%ních toleranci worst case with half tolerances cp1 cp2 ! [deg] " [deg] # [deg] ! [deg] " [deg] # [deg] beginning of csw 75,0 81,1 80,8 89,3 92,6 91,9 end of csw 101,2 101,9 101,5 114,7 119,2 119,8 table 14: results for half tolerances and higher relative velocity difference tabulka 14: v"sledky pro polovi%ní tolerance a vy))í relativní rychlost mezi va%kami worst case with tighter tolerance and higher velocity difference cp1 cp2 ! [deg] " [deg] # [deg] ! [deg] " [deg] # [deg] beginning of csw 79,9 85,1 84,8 92,5 95,1 94,4 end of csw 96,1 97,6 97,2 110,2 112,3 111,5table 11: results for worst case scenario with half tolerances tabulka 11: v"sledky pro kombinaci nejhor)ích mo$n"ch polovi%ních toleranci worst case with half tolerances cp1 cp2 ! [deg] " [deg] # [deg] ! [deg] " [deg] # [deg] beginning of csw 75,0 81,1 80,8 89,3 92,6 91,9 end of csw 101,2 101,9 101,5 114,7 119,2 119,8 table 12: higher relative velocity difference for new inner cam tabulka 12: vy))í relativní rozdíl rychlostí pro novou vnit!ní va%ku higher cp1 vel. difference [mm/deg] higher cp2 vel. difference [mm/deg] 0,0103 0,0132 table 13: results for new inner cam with higher relative velocity difference tabulka 13: v"sledky pro novou vnit!ní va%ku s vy))í relativní rychlostí higher cam velocity difference cp1 cp2 ! [deg] " [deg] # [deg] ! [deg] " [deg] # [deg] beginning of csw 68,5 75,9 75,7 84,7 89,2 88,6 end of csw 102,3 102,6 102,6 116,2 120,9 121,8 critical shifting window in switchable rocker finger follower petr kohout, jan kindermann mecca 01 2021 page 9 bring the same benefi t as improving the accuracy of rollers position but the cost is rapidly higher for the camshaft then focusing on srff manufacturing process is the way to go to. the increased relative velocity difference has also its disadvantage because the higher is the velocity difference the higher are the impacts in the system and higher wear can occur. the infl uence of the tolerances to a valve lift change and to the engine breathing was not the area of interest for this paper but as the values of tolerances are in hundredths of millimetres it is expected to have minor or almost no infl uence to the engine performance. references [1] kisabo a.b., ibrahim m. j., oluwafemi o. a., comparative analysis between cam and cam -less valve actuating for automotive system. international journal of systems engineering, vol. 1, no. 2, 2017, pp. 48 – 57. doi: 10.11648/j.ijse.20170102.12 [2] lou z., zhu g., review of advancement in variable valve actuation of internal combustion engines. applied science. 2020, 10(4), 1216, 2020, doi:10.3390/app10041216. [3] j. r., variable valvetrain system technology, sae international, 2006, isbn 978-0-7680-1685-7 [4] norton l.r., cam design and manufacturing handbook – 2nd edition reference book, industrial press inc., 2009, isbn-13: 978-0831133672 [5] radulescu, a., mccarthy jr, j., and brownell, s., development of a switching roller finger follower for cylinder deactivation in gasoline engine applications, sae technical paper 2013-01-0589, 2013, https://doi.org/10.4271/2013-01-0589. [6] kohout p. (2020) cam design for variable valve lift system with switchable roller fi nger follower, conference paper at 51st international scientifi c conference of czech and slovak university departments and institutions dealing with the research of internal combustion engines, “koka 20”, ctu in prague, czech republic, pp. 138 – 148. isbn 978-80-01-06744-4 [7] qianfan x., diesel engine system design – 1st edition, woodhead publishing, 2011, isbn-13: 978-1845697150 [8] nicholas m. p., takashi m., wonjoon ch., shape interrogation for computer aided design and manufacturing, https://web.mit.edu/hyperbook/ patrikalakis-maekawa-cho/node17.html [9] gt -suite v2019 user manual, gamma technologies, llc. symbols and acronyms ca crank angle cae computer aided engineering cp crossover point csw critical shifting window iegr internal exhaust gas recirculation mlc mechanical lash at cam mll mechanical lash at latching pin oem original equipment manufacturer srff switchable roller fi nger follower vva variable valve actuation vvl variable valve lift vvt variable valve timing 13 csw critical shifting window iegr internal exhaust gas recirculation mlc mechanical lash at cam mll mechanical lash at latching pin oem original equipment manufacturer srff switchable roller finger follower vva variable valve actuation vvl variable valve lift vvt variable valve timing 𝑣𝑣!"##@%&' relative velocity difference at cp1 𝑣𝑣!"##@%&( relative velocity difference at cp2 𝑣𝑣"))*+(𝛾𝛾%&') velocity on inner cam lobe at contact point during cp1 𝑣𝑣"))*+(𝛾𝛾%&() velocity on inner cam lobe at contact point during cp2 𝑣𝑣"))*+(𝛽𝛽%&') velocity on outer cam lobe at contact point during cp1 𝑣𝑣"))*+(𝛽𝛽%&() velocity on outer cam lobe at contact point during cp2 α rotation angle of camshaft from initial state β angle between cam profile first point and contact point at outer cam profile γ angle between cam profile first point and contact point at inner cam profile relative velocity difference at cp1 13 csw critical shifting window iegr internal exhaust gas recirculation mlc mechanical lash at cam mll mechanical lash at latching pin oem original equipment manufacturer srff switchable roller finger follower vva variable valve actuation vvl variable valve lift vvt variable valve timing 𝑣𝑣!"##@%&' relative velocity difference at cp1 𝑣𝑣!"##@%&( relative velocity difference at cp2 𝑣𝑣"))*+(𝛾𝛾%&') velocity on inner cam lobe at contact point during cp1 𝑣𝑣"))*+(𝛾𝛾%&() velocity on inner cam lobe at contact point during cp2 𝑣𝑣"))*+(𝛽𝛽%&') velocity on outer cam lobe at contact point during cp1 𝑣𝑣"))*+(𝛽𝛽%&() velocity on outer cam lobe at contact point during cp2 α rotation angle of camshaft from initial state β angle between cam profile first point and contact point at outer cam profile γ angle between cam profile first point and contact point at inner cam profile relative velocity difference at cp2 13 csw critical shifting window iegr internal exhaust gas recirculation mlc mechanical lash at cam mll mechanical lash at latching pin oem original equipment manufacturer srff switchable roller finger follower vva variable valve actuation vvl variable valve lift vvt variable valve timing 𝑣𝑣!"##@%&' relative velocity difference at cp1 𝑣𝑣!"##@%&( relative velocity difference at cp2 𝑣𝑣"))*+(𝛾𝛾%&') velocity on inner cam lobe at contact point during cp1 𝑣𝑣"))*+(𝛾𝛾%&() velocity on inner cam lobe at contact point during cp2 𝑣𝑣"))*+(𝛽𝛽%&') velocity on outer cam lobe at contact point during cp1 𝑣𝑣"))*+(𝛽𝛽%&() velocity on outer cam lobe at contact point during cp2 α rotation angle of camshaft from initial state β angle between cam profile first point and contact point at outer cam profile γ angle between cam profile first point and contact point at inner cam profile velocity on inner cam lobe at contact point during cp1 13 csw critical shifting window iegr internal exhaust gas recirculation mlc mechanical lash at cam mll mechanical lash at latching pin oem original equipment manufacturer srff switchable roller finger follower vva variable valve actuation vvl variable valve lift vvt variable valve timing 𝑣𝑣!"##@%&' relative velocity difference at cp1 𝑣𝑣!"##@%&( relative velocity difference at cp2 𝑣𝑣"))*+(𝛾𝛾%&') velocity on inner cam lobe at contact point during cp1 𝑣𝑣"))*+(𝛾𝛾%&() velocity on inner cam lobe at contact point during cp2 𝑣𝑣"))*+(𝛽𝛽%&') velocity on outer cam lobe at contact point during cp1 𝑣𝑣"))*+(𝛽𝛽%&() velocity on outer cam lobe at contact point during cp2 α rotation angle of camshaft from initial state β angle between cam profile first point and contact point at outer cam profile γ angle between cam profile first point and contact point at inner cam profile velocity on inner cam lobe at contact point during cp2 13 csw critical shifting window iegr internal exhaust gas recirculation mlc mechanical lash at cam mll mechanical lash at latching pin oem original equipment manufacturer srff switchable roller finger follower vva variable valve actuation vvl variable valve lift vvt variable valve timing 𝑣𝑣!"##@%&' relative velocity difference at cp1 𝑣𝑣!"##@%&( relative velocity difference at cp2 𝑣𝑣"))*+(𝛾𝛾%&') velocity on inner cam lobe at contact point during cp1 𝑣𝑣"))*+(𝛾𝛾%&() velocity on inner cam lobe at contact point during cp2 𝑣𝑣"))*+(𝛽𝛽%&') velocity on outer cam lobe at contact point during cp1 𝑣𝑣"))*+(𝛽𝛽%&() velocity on outer cam lobe at contact point during cp2 α rotation angle of camshaft from initial state β angle between cam profile first point and contact point at outer cam profile γ angle between cam profile first point and contact point at inner cam profile velocity on outer cam lobe at contact point during cp1 13 csw critical shifting window iegr internal exhaust gas recirculation mlc mechanical lash at cam mll mechanical lash at latching pin oem original equipment manufacturer srff switchable roller finger follower vva variable valve actuation vvl variable valve lift vvt variable valve timing 𝑣𝑣!"##@%&' relative velocity difference at cp1 𝑣𝑣!"##@%&( relative velocity difference at cp2 𝑣𝑣"))*+(𝛾𝛾%&') velocity on inner cam lobe at contact point during cp1 𝑣𝑣"))*+(𝛾𝛾%&() velocity on inner cam lobe at contact point during cp2 𝑣𝑣"))*+(𝛽𝛽%&') velocity on outer cam lobe at contact point during cp1 𝑣𝑣"))*+(𝛽𝛽%&() velocity on outer cam lobe at contact point during cp2 α rotation angle of camshaft from initial state β angle between cam profile first point and contact point at outer cam profile γ angle between cam profile first point and contact point at inner cam profile velocity on outer cam lobe at contact point during cp2 ! rotation angle of camshaft from initial state " angle between cam profi le fi rst point and contact point at outer cam profi le # angle between cam profi le fi rst point and contact point at inner cam profi le ideas for testing of planetary gear sets of automotive transmissions gabriela achtenová mecca 01 2017 page 15 10.1515/mecdc-2017-0004 ideas for testing of planetary gear sets of automotive transmissions gabriela achtenová 1. introduction the physical testing of gearboxes, despite the quick development of simulation methods, remains a very important part of the design process. the main target is to determine the functional properties like efficiency, noise, vibrations, and endurance. the paper will be focused on closed-loop test stand. big advantage of the closed-loop test stand is the possibility to build a cheap experimental device, which allows large range of experiments. apart from endurance tests (typical for such device thanks to low energy demands) it will also be possible to measure transmission error, non-uniform load distribution on planets, vibrations and other parameters. the idea to test gear wheels or whole gearboxes in a closed loop stand is generally attributed to prof. niemann [1]. the load is raised by elasticity forces when distorting the shafts with help of bracing flange and torque arm with weights. the load circulates in the whole test stand. the power from the motor is used only to compensate the losses in the stand. two identical gearwheels (gearboxes) are necessary. one is called tested gearbox, the other technological gearbox. the technological gearbox rotates the opposite sense of rotation. the load torque enters the technological gearbox via the output shaft. the opposite sense of rotation combined with opposite torque flow implies that in both gearboxes the same teeth flanks are loaded. for the gearwheels we can obtain two results from one endurance test. the technological gearbox is loaded with a torque diminished by efficiency of the previous parts of test stand. as mentioned in previous paragraph the idea of the closedloop testing is well-known for many years, and is widely used. universities [2], [3] and research companies dealing with research and development of gearwheels are equipped with such test stands. they are using in-house stands, or standard test machine manufactured by e.g. stramamps maschinenbau gmbh [4]. the disadvantage is that most of the stands are dedicated for gabriela achtenová czech technical university in prague, faculty of mechanical engineering, technická 4, prague 6, gabriela.achtenova@fs.cvut.cz abstract the article describes the concept of modular stand, where is possible to provide tests of gear pairs with fixed axes from mechanical automotive gearboxes, as well as tests of separate planetary sets from automatic gearboxes. special attention in the article will be paid to the variant dedicated for testing of planetary gear sets. this variant is particularly interesting because: 1) it is rarely described in the literature, and 2) this topology allows big simplification with respect to testing of standard gearwheels. in the planetary closed-loop stand it is possible to directly link two identical planetary sets. without any bracing flange or other connecting clutches, shafts or gear sets, just two planetary sets face-to-face will be assembled and connected to the electric motor. key words: closed-loop test stand, efficiency of planetary set, endurance tests shrnutí článek popisuje koncept modulárního zkušebního stanoviště, kde je možné testovat jak ozubené převody s pevnou osou, tak planetová soukolí. zvláštní pozornost bude v článku věnována právě zkoušení planetových převodů. tato varianta je zajímavá z několika důvodů: 1) je velmi málo popsána v literatuře, 2) uspořádání umožňuje velké zjednodušení v porovnání se stavem pro soukolí s pevnou osou. v zkušebním stavu planetových soukolí je možné napřímo spojit dvě identická soukolí. bez jakých koli přídavných spojek, hřídelů, nebo dalších převodů. máme pouze dvě propojená soukolí, které jsou přímo poháněny elektromotorem. klíčová slova: uzavřený zkušební stav, účinnost planetových převodů, životnostní zkoušky ideas for testing of planetary gear sets of automotive transmissions ideas for testing of planetary gear sets of automotive transmissions gabriela achtenová mecca 01 2017 page 16 spur gears only; the gearwheel axis distance is approximatively 90 mm, which is too much for automotive gearbox. the mechanism of closed-loop test stand can be simplified if planetary gearsets will be used. prof. šalamoun [5] introduced the idea of usage of closed loop test stand for testing of planetary gearboxes. the test stand was newly built in laboratories of czech technical university in prague. the concept, design and first results are presented in this paper. 2. closed loop stand for planetary gear sets there is a huge variety of composition of planetary sets. typically in automotive gearboxes the mostly used sets are with central wheels (one sun and one crown wheel) with a single simple planet. the gearboxes with positive base ratio (with two planets) or with ravigneaux set are relatively exceptional. therefore we decided to start the test stand with the mostly used set with negative base ratio. the parameters of the planetary sets are mentioned in table 1. to use the real gear sets from the automotive transmission we disassembled the sets from two identical automatic transmissions. the scheme of the stand can be seen in the following figure. different solutions for different types of gear sets are elaborated in [6]. to be able to test different types of planetary sets the casings and their bearing houses are designed slightly overdimensioned. the following chapter is dedicated to description of the realized test stand. there are two possibilities how to introduce the preload into the circuit: • preload of reactional member (in figure 1 it can be realized by preloading of one of the crown wheels. the torque can be changed any time. • distortion of shaft linking suns or spiders (in figure 1 for example coupling 10 could be exchanged by bracing flange, when mounted externally from sets). the torque can be changed in steady state only. with regard to the simplicity of the solution and with regard to the possibility of change the load any time we decided to use the first option of preload. 3. realised test stand the tested planetary sets are depicted in figure 2. the four speed gearbox, from which we took the pgs consisted of two nested planetary sets with common sun; therefore the sun gearwheel is wide. the gear of the sun is manufactured directly on the hollow shaft, which is on one extremity equipped with splines. the crown wheel is a thin ring, which will be later equipped with strain gauges for measurement of non-uniformity of planet loading. the crown wheel is rigidly connected to a splined flange and with respect to the sun is connected via ball bearing. the spider holds three uniformly distributed planets. the spider is welded part. between spider and sun is placed a ball bearing. for the connection of spider with the spider of the second planetary set are dedicated 6 dogs. every planetary set is enclosed in the circular casing, which is mounted on two ball bearings. the casing has to be mounted free in rotation, to give the possibility to measure the reactional force on the casings, i.e. the reactional force on the crown wheel. next reason is that the preload into the circuit is introduced via loading of one reactional element, i.e. via loading of one casing. the spiders are linked together via rigid hollow tube. the suns are connected together via the flexible coupling. to clearly distinguish between both sets, we will introduce the following notation: the pgs linked with the electric motor is called “a”, the pgs where the load is introduced is called “b”. in the sun gear of pgs a was pressed the shaft which is via bellow coupling connected to the electric motor. the electric motor rotates the whole stand and compensates for the losses. the electric motor is controlled by frequency converter; the parameters are stated in the following table. legend: 1 – electric motor, 2 – stiff bellow clutch with clamping hub, 3 – sun gear, 4 – spider, 5 – crown wheel, 6 – planetary set casing, 7 – planet, 8 – frame, 9 – strain gauges, 10 – ge-t coupling with flexible spider, 11 – sensor of reactional force, 12 – tube connecting spiders 4a and 4b, a – belonging to gearbox a, b – belonging to gearbox b figure 1: scheme of the new test stand for planetary gear sets obrázek 1: schéma nového stavu pro zkoušky planetových soukolí table 1: parameters of the tested planetary sets tabulka 1: parametry použitého planetového soukolí element sun planet ring wheel number of teeths 31 22 74 base ratio ir = -2,3871 ideas for testing of planetary gear sets of automotive transmissions gabriela achtenová mecca 01 2017 page 17 the section of the assembled closed-loop planetary stand is depicted in figure 3. figure 4 shows the visualization of assembled stand. from figure 4 can be clearly seen, that one planetary casing is mounted on the linear rail in axial direction of the pgs (to facilitate the final assembly), one planetary casing is mounted on the subframe, which can be transversally manipulated to achieve perfect alignment of both planetary sets. the final grinding of both frames of planetary sets was done at once, to ensure the alignment in vertical direction. the lubrication is proposed as churning, in the future pressure lubrication will be designed. every casing has oil inlet and outlet connection socket, as well the draining tap. for the tested pgs’s there is no sealing between sun and spider, so the oil can partly fill the tube (12) connecting the spiders. the preload is introduced via flange (9), which is screwed to the casing (2), sealed with o-rings. the flange is equipped with dogs, in which is introduced the counter dogs of load lever. the lever can be screwed to the flange (9), on the extremity of the preload lever are put the weights. the weights can be added or removed also during rotation of the stand, so the preload can be changed. the lever was designed as one side lever, only, so the change of loading torque is not possible – see figure 4. figure 2a: vizualisation of the cross section of the tested planetary gear set; [7]. obrázek 2a: vizualizace řezu planetovým soukolím; [7]. figure 2b: photo of the pgs; [7]. obrázek 2b: fotografie planetového soukolí; [7]. table 2: parameters of electric motor tabulka 2: parametry elektromotoru electric motor n max p max m nominal abb m3eb 100e6 6400 1/min 18 kw 43 n.m legend: 1 – casing of pgs “a” linked with electric motor 2 – casing of the pgs “b” 3 – housing of ball bearing with axial fixation 4 – housing of ball bearing 5 + 6 – ball bearings supporting casings 7 – cover of spider sealing 8 – cover ensuring the axial fixation of bearing (6) 9 – flange for loading of pgs casing (2) 10 – cover with input shaft sealing 11 – input shaft 12 – tube connecting spiders 13 – flexible coupling connecting the suns 14 – spider sealing 15 – input shaft sealing 16 – circlip. figure 3: section of assembled stand; [7]. the frames and sub-frames are not depicted. obrázek 3: řez sestaveným zkušebním stavem; [7]. rámy a pomocné rámy nejsou znázorněny. ideas for testing of planetary gear sets of automotive transmissions gabriela achtenová mecca 01 2017 page 18 the reactional force is sensed with help of full-bridge strain gauge sensor hbm u2a with capacity of 1 t. the sensors are capable to measure the tensile and pressure force. above the pgs bearings, on the casing are screwed the accelerometers ks77c 10. the information about speed of rotation is actually taken from the frequency converter. since all elements are connected via gearwheels, the speed of rotation of remaining elements can be easily calculated. the frame holding the electric motor is composed from several sub-frames. the sub-frame is mounted on linear rails to achieve easy movement horizontally in axial direction of electric motor. to facilitate the alignment with gearbox input shaft the sub-frame is equipped with positioning screw, which can tune the position in transversal direction. the smallest part of the sub-frame where the electric motor is screwed is mounted on four screws which ensure the position in vertical direction. as the stand is designed as modular – allowing the test of the fixed axes gearwheels as well as of the planetary sets, the easy and precise tuning of position of electric motor is important. for connection of electric motor with gearbox input shaft is used bellow coupling with clamping hubs. 4. powerflow in planetary closed loop test stand for planetary sets are in fact just two possibilities of the powerflow in the closed loop test stand, see figure 6. the sense of circulating power depends on: • the sense of the preload; • basic ratio of the pgs, and architecture of the tested pgs’s; • sense of rotation and torque of the electric motor. the determination of the magnitude of circulating power (torque) is more complex than in the case of closed-loop test stands for gearwheels (gearboxes) with fixed axes, where the preload is in fact the circulating torque; [8]. in case of planetary case a) power on sun1 is positive. case b) power on sun 2 is positive. figure 6: two possible senses of the circulating power in the closed-loop test stand. obrázek 6: dva možné toky výkonu v uzavřeném zkušebním stavu figure 4: visualization of the assembled test stand; [7]. obrázek 4: vizualizace sestaveného zkušebního stavu; [7]. figure 5:. photo of the assembled test stand obrázek 5: fotografie dokončeného zkušebního stanoviště. ideas for testing of planetary gear sets of automotive transmissions gabriela achtenová mecca 01 2017 page 19 case 1 case 2 the equations of torque equilibrium     naloss p pp   1- sunbo mm  sunao mm  mosuna mmm  mosunb mmm    aamorarb immmm    bbmorarb immmm     1 aamocrowna immm     1 bbmocrownb immm           abamo bbaamo bbrbcrownb imm iimm imm       1 1          babmo aabbmo aaracrowna imm iimm imm       1 1 mlossblossa ppp      mbabaaa ppp   11         mbamoamo ppppp   11         mbmoabmo ppppp   11                   1 1 1 1 ba om ba om mm pp       naloss p pp   1- sunbo mm  sunao mm  mosuna mmm  mosunb mmm    aamorarb immmm    bbmorarb immmm     1 aamocrowna immm     1 bbmocrownb immm           abamo bbaamo bbrbcrownb imm iimm imm       1 1          babmo aabbmo aaracrowna imm iimm imm       1 1 mlossblossa ppp      mbabaaa ppp   11         mbamoamo ppppp   11         mbmoabmo ppppp   11                   1 1 1 1 ba om ba om mm pp       naloss p pp   1- sunbo mm  sunao mm  mosuna mmm  mosunb mmm    aamorarb immmm    bbmorarb immmm     1 aamocrowna immm     1 bbmocrownb immm           abamo bbaamo bbrbcrownb imm iimm imm       1 1          babmo aabbmo aaracrowna imm iimm imm       1 1 mlossblossa ppp      mbabaaa ppp   11         mbamoamo ppppp   11         mbmoabmo ppppp   11                   1 1 1 1 ba om ba om mm pp       naloss p pp   1- sunbo mm  sunao mm  mosuna mmm  mosunb mmm    aamorarb immmm    bbmorarb immmm     1 aamocrowna immm     1 bbmocrownb immm           abamo bbaamo bbrbcrownb imm iimm imm       1 1          babmo aabbmo aaracrowna imm iimm imm       1 1 mlossblossa ppp      mbabaaa ppp   11         mbamoamo ppppp   11         mbmoabmo ppppp   11                   1 1 1 1 ba om ba om mm pp       naloss p pp   1- sunbo mm  sunao mm  mosuna mmm  mosunb mmm    aamorarb immmm    bbmorarb immmm     1 aamocrowna immm     1 bbmocrownb immm           abamo bbaamo bbrbcrownb imm iimm imm       1 1          babmo aabbmo aaracrowna imm iimm imm       1 1 mlossblossa ppp      mbabaaa ppp   11         mbamoamo ppppp   11         mbmoabmo ppppp   11                   1 1 1 1 ba om ba om mm pp       naloss p pp   1- sunbo mm  sunao mm  mosuna mmm  mosunb mmm    aamorarb immmm    bbmorarb immmm     1 aamocrowna immm     1 bbmocrownb immm           abamo bbaamo bbrbcrownb imm iimm imm       1 1          babmo aabbmo aaracrowna imm iimm imm       1 1 mlossblossa ppp      mbabaaa ppp   11         mbamoamo ppppp   11         mbmoabmo ppppp   11                   1 1 1 1 ba om ba om mm pp       naloss p pp   1- sunbo mm  sunao mm  mosuna mmm  mosunb mmm    aamorarb immmm    bbmorarb immmm     1 aamocrowna immm     1 bbmocrownb immm           abamo bbaamo bbrbcrownb imm iimm imm       1 1          babmo aabbmo aaracrowna imm iimm imm       1 1 mlossblossa ppp      mbabaaa ppp   11         mbamoamo ppppp   11         mbmoabmo ppppp   11                   1 1 1 1 ba om ba om mm pp       naloss p pp   1- sunbo mm  sunao mm  mosuna mmm  mosunb mmm    aamorarb immmm    bbmorarb immmm     1 aamocrowna immm     1 bbmocrownb immm           abamo bbaamo bbrbcrownb imm iimm imm       1 1          babmo aabbmo aaracrowna imm iimm imm       1 1 mlossblossa ppp      mbabaaa ppp   11         mbamoamo ppppp   11         mbmoabmo ppppp   11                   1 1 1 1 ba om ba om mm pp       naloss p pp   1- sunbo mm  sunao mm  mosuna mmm  mosunb mmm    aamorarb immmm    bbmorarb immmm     1 aamocrowna immm     1 bbmocrownb immm           abamo bbaamo bbrbcrownb imm iimm imm       1 1          babmo aabbmo aaracrowna imm iimm imm       1 1 mlossblossa ppp      mbabaaa ppp   11         mbamoamo ppppp   11         mbmoabmo ppppp   11                   1 1 1 1 ba om ba om mm pp       naloss p pp   1- sunbo mm  sunao mm  mosuna mmm  mosunb mmm    aamorarb immmm    bbmorarb immmm     1 aamocrowna immm     1 bbmocrownb immm           abamo bbaamo bbrbcrownb imm iimm imm       1 1          babmo aabbmo aaracrowna imm iimm imm       1 1 mlossblossa ppp      mbabaaa ppp   11         mbamoamo ppppp   11         mbmoabmo ppppp   11                   1 1 1 1 ba om ba om mm pp   the equations of equilibrium of lost powers     naloss p pp   1- sunbo mm  sunao mm  mosuna mmm  mosunb mmm    aamorarb immmm    bbmorarb immmm     1 aamocrowna immm     1 bbmocrownb immm           abamo bbaamo bbrbcrownb imm iimm imm       1 1          babmo aabbmo aaracrowna imm iimm imm       1 1 mlossblossa ppp      mbabaaa ppp   11         mbamoamo ppppp   11         mbmoabmo ppppp   11                   1 1 1 1 ba om ba om mm pp       naloss p pp   1- sunbo mm  sunao mm  mosuna mmm  mosunb mmm    aamorarb immmm    bbmorarb immmm     1 aamocrowna immm     1 bbmocrownb immm           abamo bbaamo bbrbcrownb imm iimm imm       1 1          babmo aabbmo aaracrowna imm iimm imm       1 1 mlossblossa ppp      mbabaaa ppp   11         mbamoamo ppppp   11         mbmoabmo ppppp   11                   1 1 1 1 ba om ba om mm pp       naloss p pp   1- sunbo mm  sunao mm  mosuna mmm  mosunb mmm    aamorarb immmm    bbmorarb immmm     1 aamocrowna immm     1 bbmocrownb immm           abamo bbaamo bbrbcrownb imm iimm imm       1 1          babmo aabbmo aaracrowna imm iimm imm       1 1 mlossblossa ppp      mbabaaa ppp   11         mbamoamo ppppp   11         mbmoabmo ppppp   11                   1 1 1 1 ba om ba om mm pp       naloss p pp   1- sunbo mm  sunao mm  mosuna mmm  mosunb mmm    aamorarb immmm    bbmorarb immmm     1 aamocrowna immm     1 bbmocrownb immm           abamo bbaamo bbrbcrownb imm iimm imm       1 1          babmo aabbmo aaracrowna imm iimm imm       1 1 mlossblossa ppp      mbabaaa ppp   11         mbamoamo ppppp   11         mbmoabmo ppppp   11                   1 1 1 1 ba om ba om mm pp   final equations taking into account the lost power (torque), efficiencies and circulating power (torque)     naloss p pp   1- sunbo mm  sunao mm  mosuna mmm  mosunb mmm    aamorarb immmm    bbmorarb immmm     1 aamocrowna immm     1 bbmocrownb immm           abamo bbaamo bbrbcrownb imm iimm imm       1 1          babmo aabbmo aaracrowna imm iimm imm       1 1 mlossblossa ppp      mbabaaa ppp   11         mbamoamo ppppp   11         mbmoabmo ppppp   11                   1 1 1 1 ba om ba om mm pp   ratios used in previous equations   3871,33871,21 1 ..1   ra crownasuna crowna rasuna iii   295,0 3871,21 1 1 1 1 . . .       ra crownasuna crowna rasuna crowna sunaraa i i ii   295,0 3871,21 1 1 1 1 . . .       rb crownbsunb crownb rbsunb crownb sunbrbb i i ii   3871,33871,21 1 ..   rb crownbsunb crownb rbsunbb iii 3871,23871,31 3871,3 0     rbsunbcrownb brb b preload mmm im i m   3871,33871,21 1 ..1   ra crownasuna crowna rasuna iii   295,0 3871,21 1 1 1 1 . . .       ra crownasuna crowna rasuna crowna sunaraa i i ii   295,0 3871,21 1 1 1 1 . . .       rb crownbsunb crownb rbsunb crownb sunbrbb i i ii   3871,33871,21 1 ..   rb crownbsunb crownb rbsunbb iii 3871,23871,31 3871,3 0     rbsunbcrownb brb b preload mmm im i m   3871,33871,21 1 ..1   ra crownasuna crowna rasuna iii   295,0 3871,21 1 1 1 1 . . .       ra crownasuna crowna rasuna crowna sunaraa i i ii   295,0 3871,21 1 1 1 1 . . .       rb crownbsunb crownb rbsunb crownb sunbrbb i i ii   3871,33871,21 1 ..   rb crownbsunb crownb rbsunbb iii 3871,23871,31 3871,3 0     rbsunbcrownb brb b preload mmm im i m   3871,33871,21 1 ..1   ra crownasuna crowna rasuna iii   295,0 3871,21 1 1 1 1 . . .       ra crownasuna crowna rasuna crowna sunaraa i i ii   295,0 3871,21 1 1 1 1 . . .       rb crownbsunb crownb rbsunb crownb sunbrbb i i ii   3871,33871,21 1 ..   rb crownbsunb crownb rbsunbb iii 3871,23871,31 3871,3 0     rbsunbcrownb brb b preload mmm im i m ideas for testing of planetary gear sets of automotive transmissions gabriela achtenová mecca 01 2017 page 20 sets the preload is moment exerted on the reactional element. firstly we will determine the powerflow and circulating power for both possible senses and then we will determine which case is relevant for our test stand. 4.1 powerflow and circulating power – general derivation to determine the magnitude of circulating power as well as the efficiency of planetary sets, we will write the equations of power and torque equilibrium. in the following table can be seen the magnitude of powers on different elements. the appropriate equations are derived for both cases. before we will determine the equations valid for actual example, we will recall the definition of the lost power of any mechanism. the lost power can be determined with help of power on the input shaft, or of the output shaft.     naloss p pp   1- sunbo mm  sunao mm  mosuna mmm  mosunb mmm    aamorarb immmm    bbmorarb immmm     1 aamocrowna immm     1 bbmocrownb immm           abamo bbaamo bbrbcrownb imm iimm imm       1 1          babmo aabbmo aaracrowna imm iimm imm       1 1 mlossblossa ppp      mbabaaa ppp   11         mbamoamo ppppp   11         mbmoabmo ppppp   11                   1 1 1 1 ba om ba om mm pp   (1)    naloss p pp   1- sunbo mm  sunao mm  mosuna mmm  mosunb mmm    aamorarb immmm    bbmorarb immmm     1 aamocrowna immm     1 bbmocrownb immm           abamo bbaamo bbrbcrownb imm iimm imm       1 1          babmo aabbmo aaracrowna imm iimm imm       1 1 mlossblossa ppp      mbabaaa ppp   11         mbamoamo ppppp   11         mbmoabmo ppppp   11                   1 1 1 1 ba om ba om mm pp   (2) we are measuring the total lost power, i.e. the power of electric motor, and the reactional moments, therefore it will be wise to carefully look on the equations of power and torque equilibrium. 4.2 powerflow in treated case to determine the powerflow and magnitude of circulating power in our example, we will first treat the rotational speed, torque and power as algebraic values. we assume that the positive rotational speed and positive torque correspond with the sense of rotation and sense of torque of the electric motor. in such case the power of electric motor is also positive. to determine the sense of circulating power, we have to first determine the sense of preload on the reactional element. we can simplify the calculation with neglecting the losses. we introduce the preload on pgs “b”. the preload is introduced in the same sense as is the rotation and torque of electric motor. from the following calculation can be seen that the positive reactional torque can be obtained in case 2 in table 3 only.   3871,33871,21 1 ..1   ra crownasuna crowna rasuna iii   295,0 3871,21 1 1 1 1 . . .       ra crownasuna crowna rasuna crowna sunaraa i i ii   295,0 3871,21 1 1 1 1 . . .       rb crownbsunb crownb rbsunb crownb sunbrbb i i ii   3871,33871,21 1 ..   rb crownbsunb crownb rbsunbb iii 3871,23871,31 3871,3 0     rbsunbcrownb brb b preload mmm im i m (3) from the equation (3) can be seen that the positive reactional torque can be obtained only in case 2 – see table 3. 5. measurement results the measurement stand was recently built. unfortunately the load cell on crown wheel “a” did not function well, so the results are from the reactional torque on crown wheel b only. it means we can not determine the efficiency of the pgs “a” and pgs “b” separately. for planetary gear sets with high efficiency, the difference of efficiency for power flow from sun to spider with fixed crown and of the efficiency for power flow from spider to sun with fixed crown, can be neglected. in our case we obtained relatively low efficiency, but the reason is mainly in the lubrication, i.e. in the churning losses. in the following figure can be seen the graphs from measured data. the measurements were done with different speed of rotation and different preload. the efficiency of pgs was calculated as well as the magnitude of circulating power and torque. the measurements were done with the oil temperature equal 35 c. figure 8: dependence between efficiency and speed of rotation with respect to different preload on pgs b obrázek 8: závislost účinnosti na změně otáček vstupního hřídele a měnící se zátěži. figures 9: dependence between efficiency and preload with respect to different rpm’s. obrázek 9: závislost účinnosti na předpětí při různých otáčkách vstupu. ideas for testing of planetary gear sets of automotive transmissions gabriela achtenová mecca 01 2017 page 21 from figure 8 can be seen, that the efficiency is strongly dependent on the transmitted load. for low transmitted torque the efficiency is very low, while in the proportion “load : no load” losses is low. it means the no load losses (i.e. the lubrication, sealing) play the majority. from the graphs can be clearly seen, that for precise measurement of influence of different design changes on efficiency of planetary sets, it will be necessary to change the lubrication system. on figure 9 we can observe slight decrease of efficiency with increase of speed of rotation. this influence can be again explained with splash lubrication. to get an idea how big is the circulating torque/power with respect to the preload, following table brings the overview of measured and calculated data. the chosen example shows the data for maximal loading torque. 6. conclusion in the previous chapter the first measurement results were presented. when changing the splash lubrication with the pressure lubrication we can in the future obtain more precise data of the efficiency of the pgs. in the future is planned to measure: • influence of different bearing types of planets on efficiency, magnitude of axial force acting on planets. • influence of radial clearance of planets and number of planets on efficiency. • non-uniformity of load distribution on planets. • endurance test. although not all results are presented in the paper, the concept of the test stand is approved. the test stand is cheap, simple, easy to manipulate, with big potential for future measurements. acknowledgement this research has been realized using the support of the ministry of education, youth and sports program npu i (lo), project # lo1311 development of vehicle centre of sustainable mobility. the support is gratefully acknowledged. list of symbols unknowns p power m torque n speed of rotation i ratio ς coefficient of losses η efficiency subscripts o circulation (power, torque) a input n output m electric motor 1 belonging to pgs 1 2 belonging to pgs 2 r spider references [1] lechner g., naunheimer h.: automotive transmissions, springer verlag, 1999, isbn 3-540-65903x [2] achtenova, g. and milacek, o., “innovative configuration of the closed-loop test stand,” sae technical paper 2015-01-1092, 2015, doi:10.4271/2015-01-1092. [3] radev s., einfluss von flankenkorrekturen auf das anregungsverhalten gerade – und schrägverzahnter stirnradpaarungen. doktorarbeit tu münchen. 2007. [4] http://www.strama-mps.de/produkte/pruefstaende/ standards/fzg-zahnrad-verspannungspruefstand/ [5] šalamoun č.: the closed loop stand for planetary gearbox testing, in: proc. of mechanismen und getriebe spanabhebender werkzeugmaschinen, 1961 (in german) [6] rok j.: design of planetary gear box for closed-loop test stand. diploma work dp2012-mv05. ctu in prague. 2012. (in czech) [7] kazda l.: proposal of the closed loop test stand. diploma work. ctu in prague. 2017. (in czech) [8] moravec v., havlík j., folta z., achtenová g.: analysis of power flow in closed loop stands for endurance tests of gears and transmissions, journal mecca 2/2004, issn 1214-0821 table 4: example of measured and calculated data. tabulka 4: ukázka naměřených a vypočtených dat. n [rpm] p_m [w] mk2 [n.m] m_m [n.m] efficiency mo [n.m] po [w] 3000 3104 99,9 10,2 0,891 39,9 12532 2500 2549 95,6 10,0 0,8916 37,6 9845 2000 2111 92,1 10,2 0,8838 36,1 7561 1500 1623 97,9 10,5 0,8881 38,453 6038 1000 1072 96,3 10,3 0,8874 37,8 3956 ole_link26 ole_link27 ole_link28 _ref312143099 _goback result_box _ref497901876 result_box2 result_box3 result_box4 result_box5 result_box6 result_box7 result_box8 result_box9 result_box10 result_box11 result_box12 result_box13 _ref498511156 _ref499718432 evaluation of experiments on a twin scroll turbocharger turbine for calibration of a complex 1-d model zdeněk žák, jan macek, petr hatschbach mecca 03 2016 page 11 10.1515/mecdc-2016-0010 evaluation of experiments on a twin scroll turbocharger turbine for calibration of a complex 1-d model zdeněk žák, jan macek, petr hatschbach 1. introduction the twin scroll design of radial centripetal turbines is suitable for combustion engines with a pulsation exhaust system. the low volume exhaust systems with pulsating flow are typical for highly boosted downsized internal combustion engines. the advantage of an engine equipped with a twin entry turbine is primarily in the better response during the load or speed transients. the goal of the research is to describe the turbine behaviour under on-engine conditions, i.e. under unsteady flow and unequal partial admission of the turbine wheel. the research has to begin on the steady flow turbocharger test bed. the contribution presents the specific turbocharger hot gas stand with separated turbine sections, the evaluation methods of the measured results and the mapless approach, which is capable to describe the twin entry turbine performance under an arbitrary level of an impeller admission without the standard steady flow maps. for the measurement of twin scroll turbocharger turbine under different admission levels, it was needful to develop a specific turbocharger test bed with separated turbine sections. the test bench was developed and properly tested in cooperation with the company čz a.s., turbo division. the developed test bed significantly extends the potential of the current test facility and also adds new features to the test bed. at the early stage of the development, it was useful to create the virtual model of the future test bench for twin scroll turbochargers in gt-suite. the main dimensions of the test bed, boundary conditions, diameters of measuring orifices and throttling orifices are based on simulation results of the virtual open loop test bed. the proper combination of turbine selected for experiments, different systems for loading it by a compressor, using, e.g., a larger compressor wheel, detailed specification and schedule of real experimental work were also assessed in gt-suite. it is possible to measure the whole family of the twin entry turbines produced by čz a.s. on the developed test bed. it allows turbine testing at different pressures and temperatures turbine upstream. it is possible to test a turbine under uniform admission (mass flow rates in sections are equal), different level of partial admission (via throttling in one turbine section) and in the extreme case with one section closed. the turbocharger turbine can be driven by air, hot gases or a mixture of the two for better temperature control. the fuel is natural gas. the mass flow rate via the test facility is limited to 0.5 kg/s and the maximum temperature at burner outlet can be 1000°c. zdeněk žák, jan macek, petr hatschbach czech technical university, vehicle centre of sustainable mobility, technická 4, 16607 praha 6 e-mail: zdenek.zak@fs.cvut.cz, jan.macek@fs.cvut.cz, petr.hatschbach@fs.cvut.cz abstract the goal of the contribution is to describe the process of measurement on a twin entry turbocharger turbine, and evaluation of obtained data. a specific feature of the twin entry turbine measurement is the separation of turbine sections. it is necessary to control different conditions in each section to achieve partial admission of the turbine impeller. the results are fundamental for the calibration process of a developed physical 1-d model of a radial turbine with twin scroll. key words: t win scroll turbine, turbocharger test bed, turbocharger energy balance, adiabatic compressor, blocked impeller, complex 1-d turbine model shrnutí cílem příspěvku je popsat proces měření a vyhodnocení získaných dat pro zjištění vlastností turbíny turbodmychadla se dvouvstupovou skříní. specifikem měření dvouvstupových turbín je nutnost oddělení sekcí. je nezbytné řídit rozdílné podmínky v sekcích pro dosažení parciálního ostřiku oběžného kola turbíny. získané výsledky tvoří základ pro kalibraci vyvinutého fyzikálního 1-d modelu radiální turbíny se dvouvstupovou skříní. klíčová slova: dvouvstupová turbína, testovací stav turbodmychadel, energetická bilance turbodmychadla, adiabatický kompresor, zastavené oběžné kolo turbíny, komplexní 1-d model turbíny evaluation of experiments on a twin scroll turbocharger turbine for calibration of a complex 1-d model evaluation of experiments on a twin scroll turbocharger turbine for calibration of a complex 1-d model zdeněk žák, jan macek, petr hatschbach mecca 03 2016 page 12 the performing of measurements on the twin scroll turbocharger turbine over a wide range of temperatures, rpm, mass flow rates, different levels of impeller admission and load is essential for further development of turbocharger models based on physics. the partial admission of a turbine wheel and pulsating operation are typical for the twin entry turbocharger turbine. the optimal firing interval between cylinders to increase the advantages of turbine pulsating flow is about 120 degrees, so the twin scroll turbine is suitable for six cylinder engines. the chosen 1-d simulation approach is suited to the preliminary development of the turbocharged internal combustion engine. due to description of the phenomena inside the turbocharger, the developed full 1-d unsteady turbine model is able to support the development of the detailed 3-d cfd model of a turbine. 2. experiments the turbocharger test bed designated for testing twin entry turbines allows measurement of mass flow rates (orifice measuring sections a, b, including backflow if it occurs), temperatures and static pressures located upstream (sections a, b) and downstream of the turbine, midstream pressure at turbine outlet (without the influence of tangential velocity component), turbocharger speed, pressures, temperatures and volume flow rate of oil, mass flow rate via compressor, temperatures and pressures compressor upstream/ downstream. see figure 1 and figure 2. the mentioned test facility enables measurement of the twin scroll turbocharger turbine performance under uniform admission (like a single scroll machine), partial admission of turbine wheel via throttling in one section and partial admission with closed section. it is also possible to measure back flow if it occurs, see figure 3. the important feature of the open loop test bed is the ability to test a turbine over a wide range of blade speed ratio (bsr). when the turbine is driven by cold air only, the turbine is unloaded and bsr increases. it is more difficult to overload the turbine, thus decrease the blade speed ratio. in all analyzed cases, a complicated lay-out with a turbine dynamometer has been excluded. the first method is to increase the temperature upstream of a turbine, the second is to load the turbine using a larger compressor wheel, and the third is the combination of both methods. the other option, increasing pressure at compressor inlet and closing the air loop in the compressor circuit, was not used due to complicated lay-out and high thrust force at turbocharger shaft. no method analyzed excludes side-effects, such as change of turbine reynolds number (blade and windage losses) or friction losses due to thrust bearing. the final decision was a combination of the current turbine wheel with a larger compressor wheel and an increase in the turbine upstream temperature to 800°c for the purposes of the current measurements. the standard temperature during turbocharger testing is around 600°c upstream of a turbine. the selected radial turbine with twin entry volute was measured under full and partial admission of an impeller, at different blade speed ratios and different pressure ratios. using a compressor as figure 1: measurement chain of the developed turbocharger test bed with open loop obrázek 1: měřicí řetězec vyvinutého testovacího stavu s otevřenou smyčkou figure 2: turbocharger test bed with separated sections of the turbine with twin entry volute obrázek 2: testovací stav s oddělenými sekcemi dvouvstupové turbíny figure 3: test bed capability and types of measurement: 1) uniform admission; 2) partial admission (throttling in one section); 3) closed section; 4) backflow obrázek 3: možnosti testovacího stavu a typy zkoušek: 1) stejnoměrný ostřik oběžného kola turbíny; 2) parciální ostřik (škrcení v jedné sekci); 3) jedna zavřená sekce; 4) zpětný tok evaluation of experiments on a twin scroll turbocharger turbine for calibration of a complex 1-d model zdeněk žák, jan macek, petr hatschbach mecca 03 2016 page 13 the loading machine, the compressor input power has to be measured accurately excluding the well-known influence of heat fluxes inside turbocharger casings (figure 4). for that purpose, the turbocharger energy balance has to be analyzed. 3. energy balance of a turbocharger with twin entry turbine the evaluation of turbine measurement with hot gas, which enables achievement of optimum blade speed ratio, is associated with some problems due to heat transfer inside the turbocharger components – figure 4. a turbine does not work under adiabatic conditions. therefore, the indirect evaluation of internal turbine power from the difference of inlet and outlet enthalpy is not accurate enough. moreover, the heat flux between turbine and compressor casings increases the compressor outlet temperature and also distorts the relation between compressor specific power and the enthalpy difference determined from these temperatures. assuming that the heat flux via turbocharger shaft and casings to a compressor impeller is negligible, the compressor power is independent of turbine temperatures, since the work transferring part performs almost adiabatically. to avoid heat transfer to the compressor stator, which would distort the determination of the enthalpy difference, turbine feeding by cold air was used for calibration of compressor power based on enthalpy difference. this operation mode was used for calibration of friction losses measured from oil enthalpy difference. during turbine hot tests, the compressor power was calculated from the calibrated dependence of compressor mass flow rate and speed, as explained below. the friction losses at the bearings can be determined during cold tests although it is not possible to obtain the bearings power losses directly from oil temperature difference, because the outlet oil temperature is increased by the heat flux via turbocharger shaft (1). 3. energy balance of a turbocharger with twin entry turbine figure 4: energy balance of a turbocharger with relevant energy fluxes obrázek 4: energetická bilance turbodmychadla s relevantními energetickými toky the evaluation of turbine measurement with hot gas, which enables achievement of optimum blade speed ratio, is associated with some problems due to heat transfer inside the turbocharger components – figure 4. a turbine does not work under adiabatic conditions. therefore, the indirect evaluation of internal turbine power from the difference of inlet and outlet enthalpy is not accurate enough. moreover, the heat flux between turbine and compressor casings increases the compressor outlet temperature and also distorts the relation between compressor specific power and the enthalpy difference determined from these temperatures. assuming that the heat flux via turbocharger shaft and casings to a compressor impeller is negligible, the compressor power is independent of turbine temperatures, since the work transferring part performs almost adiabatically. to avoid heat transfer to the compressor stator, which would distort the determination of the enthalpy difference, turbine feeding by cold air was used for calibration of compressor power based on enthalpy difference. this operation mode was used for calibration of friction losses measured from oil enthalpy difference. during turbine hot tests, the compressor power was calculated from the calibrated dependence of compressor mass flow rate and speed, as explained below. the friction losses at the bearings can be determined during cold tests although it is not possible to obtain the bearings power losses directly from oil temperature difference, because the outlet oil temperature is increased by the heat flux via turbocharger shaft (1). (1) the results are only correct when the heat transfer from the turbine side is insignificant, e.g. in the case of a turbine driven by cold air (the mean temperature of oil roughly equals the mean gas temperature at (1) the results are only correct when the heat transfer from the turbine side is insignificant, e.g. in the case of a turbine driven by cold air (the mean temperature of oil roughly equals the mean gas temperature at a turbine). the solution consists of the use of a specific regression formula, which is capable to determine the pure bearing losses (p bear) and the heat flux via shaft (q shaft) from the turbocharger speed, mean gas temperature at the turbine, mean oil temperature, and compressor and turbine inlet/outlet pressures [11]. the regression formula for the calculation of pure losses in bearings is stated in (2). (2) if the compressor map is measured with a turbine driven by hot gases as usual, the heat fluxes from the turbine side influence the state downstream of the compressor and the compressor efficiency is then underestimated. the turbine power has to be evaluated from the whole turbocharger energy balance. during the experimental work, it was necessary to measure both compressors under different conditions. since the heat flux through a shaft to a compressor and external heat flux from a compressor impeller are small at any turbine power, it is convenient to measure the compressor specific power input (i.e., enthalpy difference) when the turbine is driven by cold air only. the heat fluxes (q case, q shaft) from turbine to compressor housing are almost zero in the mentioned case, so the compressor is an almost adiabatic machine, figure 4. the enthalpy difference depends on compressor speed and mass flow rate only. it can be calculated from these parameters even for hot gas operation if the changes in shaft and compressor wheel heat fluxes are negligible. the compressor power may be represented by a regression formula based on euler`s theorem (3). (3) the radial velocity at compressor outlet is determined from the mass flow rate via the compressor and main dimensions of the compressor wheel (4). a turbine). the solution consists of the use of a specific regression formula, which is capable to determine the pure bearing losses (p bear) and the heat flux via shaft (q shaft) from the turbocharger speed, mean gas temperature at the turbine, mean oil temperature, and compressor and turbine inlet/outlet pressures [11]. the regression formula for the calculation of pure losses in bearings is stated in (2). (2) if the compressor map is measured with a turbine driven by hot gases as usual, the heat fluxes from the turbine side influence the state downstream of the compressor and the compressor efficiency is then underestimated. the turbine power has to be evaluated from the whole turbocharger energy balance. during the experimental work, it was necessary to measure both compressors under different conditions. since the heat flux through a shaft to a compressor and external heat flux from a compressor impeller are small at any turbine power, it is convenient to measure the compressor specific power input (i.e., enthalpy difference) when the turbine is driven by cold air only. the heat fluxes (q case, q shaft) from turbine to compressor housing are almost zero in the mentioned case, so the compressor is an almost adiabatic machine, figure 4. the enthalpy difference depends on compressor speed and mass flow rate only. it can be calculated from these parameters even for hot gas operation if the changes in shaft and compressor wheel heat fluxes are negligible. the compressor power may be represented by a regression formula based on euler`s theorem (3). (3) the radial velocity at compressor outlet is determined from the mass flow rate via the compressor and main dimensions of the compressor wheel (4). (4) the appropriate circumferential velocity is calculated using equation (5). (5) the regression coefficients in dependence on turbocharger speed, based on measurement of an almost adiabatic compressor, are used for the assessment of compressor power under any conditions. when the power of an adiabatic compressor and the pure losses in bearings are known, the isentropic (6) and overall turbine efficiency (7) can be determined. (6) (7) the calculation of further partial energy fluxes (figure 4) is not required for current purposes. the overall twin entry turbine parameters have to take into account the interactions between turbine (4) the appropriate circumferential velocity is calculated using equation (5). a turbine). the solution consists of the use of a specific regression formula, which is capable to determine the pure bearing losses (p bear) and the heat flux via shaft (q shaft) from the turbocharger speed, mean gas temperature at the turbine, mean oil temperature, and compressor and turbine inlet/outlet pressures [11]. the regression formula for the calculation of pure losses in bearings is stated in (2). (2) if the compressor map is measured with a turbine driven by hot gases as usual, the heat fluxes from the turbine side influence the state downstream of the compressor and the compressor efficiency is then underestimated. the turbine power has to be evaluated from the whole turbocharger energy balance. during the experimental work, it was necessary to measure both compressors under different conditions. since the heat flux through a shaft to a compressor and external heat flux from a compressor impeller are small at any turbine power, it is convenient to measure the compressor specific power input (i.e., enthalpy difference) when the turbine is driven by cold air only. the heat fluxes (q case, q shaft) from turbine to compressor housing are almost zero in the mentioned case, so the compressor is an almost adiabatic machine, figure 4. the enthalpy difference depends on compressor speed and mass flow rate only. it can be calculated from these parameters even for hot gas operation if the changes in shaft and compressor wheel heat fluxes are negligible. the compressor power may be represented by a regression formula based on euler`s theorem (3). (3) the radial velocity at compressor outlet is determined from the mass flow rate via the compressor and main dimensions of the compressor wheel (4). (4) the appropriate circumferential velocity is calculated using equation (5). (5) the regression coefficients in dependence on turbocharger speed, based on measurement of an almost adiabatic compressor, are used for the assessment of compressor power under any conditions. when the power of an adiabatic compressor and the pure losses in bearings are known, the isentropic (6) and overall turbine efficiency (7) can be determined. (6) (7) the calculation of further partial energy fluxes (figure 4) is not required for current purposes. the overall twin entry turbine parameters have to take into account the interactions between turbine (5)figure 4: energy balance of a turbocharger with relevant energy fluxes obrázek 4: energetická bilance turbodmychadla s relevantními energetickými toky evaluation of experiments on a twin scroll turbocharger turbine for calibration of a complex 1-d model zdeněk žák, jan macek, petr hatschbach mecca 03 2016 page 14 the regression coefficients in dependence on turbocharger speed, based on measurement of an almost adiabatic compressor, are used for the assessment of compressor power under any conditions. when the power of an adiabatic compressor and the pure losses in bearings are known, the isentropic (6) and overall turbine efficiency (7) can be determined. a turbine). the solution consists of the use of a specific regression formula, which is capable to determine the pure bearing losses (p bear) and the heat flux via shaft (q shaft) from the turbocharger speed, mean gas temperature at the turbine, mean oil temperature, and compressor and turbine inlet/outlet pressures [11]. the regression formula for the calculation of pure losses in bearings is stated in (2). (2) if the compressor map is measured with a turbine driven by hot gases as usual, the heat fluxes from the turbine side influence the state downstream of the compressor and the compressor efficiency is then underestimated. the turbine power has to be evaluated from the whole turbocharger energy balance. during the experimental work, it was necessary to measure both compressors under different conditions. since the heat flux through a shaft to a compressor and external heat flux from a compressor impeller are small at any turbine power, it is convenient to measure the compressor specific power input (i.e., enthalpy difference) when the turbine is driven by cold air only. the heat fluxes (q case, q shaft) from turbine to compressor housing are almost zero in the mentioned case, so the compressor is an almost adiabatic machine, figure 4. the enthalpy difference depends on compressor speed and mass flow rate only. it can be calculated from these parameters even for hot gas operation if the changes in shaft and compressor wheel heat fluxes are negligible. the compressor power may be represented by a regression formula based on euler`s theorem (3). (3) the radial velocity at compressor outlet is determined from the mass flow rate via the compressor and main dimensions of the compressor wheel (4). (4) the appropriate circumferential velocity is calculated using equation (5). (5) the regression coefficients in dependence on turbocharger speed, based on measurement of an almost adiabatic compressor, are used for the assessment of compressor power under any conditions. when the power of an adiabatic compressor and the pure losses in bearings are known, the isentropic (6) and overall turbine efficiency (7) can be determined. (6) (7) the calculation of further partial energy fluxes (figure 4) is not required for current purposes. the overall twin entry turbine parameters have to take into account the interactions between turbine (6) a turbine). the solution consists of the use of a specific regression formula, which is capable to determine the pure bearing losses (p bear) and the heat flux via shaft (q shaft) from the turbocharger speed, mean gas temperature at the turbine, mean oil temperature, and compressor and turbine inlet/outlet pressures [11]. the regression formula for the calculation of pure losses in bearings is stated in (2). (2) if the compressor map is measured with a turbine driven by hot gases as usual, the heat fluxes from the turbine side influence the state downstream of the compressor and the compressor efficiency is then underestimated. the turbine power has to be evaluated from the whole turbocharger energy balance. during the experimental work, it was necessary to measure both compressors under different conditions. since the heat flux through a shaft to a compressor and external heat flux from a compressor impeller are small at any turbine power, it is convenient to measure the compressor specific power input (i.e., enthalpy difference) when the turbine is driven by cold air only. the heat fluxes (q case, q shaft) from turbine to compressor housing are almost zero in the mentioned case, so the compressor is an almost adiabatic machine, figure 4. the enthalpy difference depends on compressor speed and mass flow rate only. it can be calculated from these parameters even for hot gas operation if the changes in shaft and compressor wheel heat fluxes are negligible. the compressor power may be represented by a regression formula based on euler`s theorem (3). (3) the radial velocity at compressor outlet is determined from the mass flow rate via the compressor and main dimensions of the compressor wheel (4). (4) the appropriate circumferential velocity is calculated using equation (5). (5) the regression coefficients in dependence on turbocharger speed, based on measurement of an almost adiabatic compressor, are used for the assessment of compressor power under any conditions. when the power of an adiabatic compressor and the pure losses in bearings are known, the isentropic (6) and overall turbine efficiency (7) can be determined. (6) (7) the calculation of further partial energy fluxes (figure 4) is not required for current purposes. the overall twin entry turbine parameters have to take into account the interactions between turbine (7) the calculation of further partial energy fluxes (figure 4) is not required for current purposes. the overall twin entry turbine parameters have to take into account the interactions between turbine sections a and b. the procedures are based on averaging according to the power of sections a and b, see (8). sections a and b. the procedures are based on averaging according to the power of sections a and b, see (8). ��� � � �� �� ���� � � ���� � ���� � � �� � ���� � (8) the definition of the fictitious isentropic velocity (9) is derived from the balance of isentropic powers a and b. ����� � � � ��� ���� �� ��� ���̅��������� �� � ��� ����� ��� � � �� ���̅��������� �� � ��� ����� ��� ��� (9) the overall pressure ratio (total static) of the twin entry turbine is calculated via the relation (10). �������� � �� � �� � ���� � ��� � ���� � ��� ���� ���������������� � �� ���� (10) the turbine blade speed ratio (11) is defined as a fraction of the circumferential velocity and fictitious isentropic velocity. ������ ����������������� (11) the level of admission of the turbine impeller is the quotient of the isentropic power in the appropriate turbine section and the total isentropic power (12). the admission level of section b is analogical to equation (12). ������ �� �� � ����� � �� � ����� � ��� � ����� � (12) the overall discharge coefficient of the twin entry turbine (13) is evaluated as a fraction of the mass flow rates sum to the reference mass flow rate via machine. �������� ���� ���� ��� ��� � �� ���� � ������ ������� ���������������� ���� (13) 4. evaluation of measured data (8) the definition of the fictitious isentropic velocity (9) is derived from the balance of isentropic powers a and b. (9) the overall pressure ratio (total – static) of the twin entry turbine is calculated via the relation (10). sections a and b. the procedures are based on averaging according to the power of sections a and b, see (8). ��� � � �� �� ���� � � ���� � ���� � � �� � ���� � (8) the definition of the fictitious isentropic velocity (9) is derived from the balance of isentropic powers a and b. ����� � � � ��� ���� �� ��� ���̅��������� �� � ��� ����� ��� � � �� ���̅��������� �� � ��� ����� ��� ��� (9) the overall pressure ratio (total static) of the twin entry turbine is calculated via the relation (10). �������� � �� � �� � ���� � ��� � ���� � ��� ���� ���������������� � �� ���� (10) the turbine blade speed ratio (11) is defined as a fraction of the circumferential velocity and fictitious isentropic velocity. ������ ����������������� (11) the level of admission of the turbine impeller is the quotient of the isentropic power in the appropriate turbine section and the total isentropic power (12). the admission level of section b is analogical to equation (12). ������ �� �� � ����� � �� � ����� � ��� � ����� � (12) the overall discharge coefficient of the twin entry turbine (13) is evaluated as a fraction of the mass flow rates sum to the reference mass flow rate via machine. �������� ���� ���� ��� ��� � �� ���� � ������ ������� ���������������� ���� (13) 4. evaluation of measured data (10) the turbine blade speed ratio (11) is defined as a fraction of the circumferential velocity and fictitious isentropic velocity. sections a and b. the procedures are based on averaging according to the power of sections a and b, see (8). ��� � � �� �� ���� � � ���� � ���� � � �� � ���� � (8) the definition of the fictitious isentropic velocity (9) is derived from the balance of isentropic powers a and b. ����� � � � ��� ���� �� ��� ���̅��������� �� � ��� ����� ��� � � �� ���̅��������� �� � ��� ����� ��� ��� (9) the overall pressure ratio (total static) of the twin entry turbine is calculated via the relation (10). �������� � �� � �� � ���� � ��� � ���� � ��� ���� ���������������� � �� ���� (10) the turbine blade speed ratio (11) is defined as a fraction of the circumferential velocity and fictitious isentropic velocity. ������ ����������������� (11) the level of admission of the turbine impeller is the quotient of the isentropic power in the appropriate turbine section and the total isentropic power (12). the admission level of section b is analogical to equation (12). ������ �� �� � ����� � �� � ����� � ��� � ����� � (12) the overall discharge coefficient of the twin entry turbine (13) is evaluated as a fraction of the mass flow rates sum to the reference mass flow rate via machine. �������� ���� ���� ��� ��� � �� ���� � ������ ������� ���������������� ���� (13) 4. evaluation of measured data (11) the level of admission of the turbine impeller is the quotient of the isentropic power in the appropriate turbine section and the total isentropic power (12). the admission level of section b is analogical to equation (12). sections a and b. the procedures are based on averaging according to the power of sections a and b, see (8). ��� � � �� �� ���� � � ���� � ���� � � �� � ���� � (8) the definition of the fictitious isentropic velocity (9) is derived from the balance of isentropic powers a and b. ����� � � � ��� ���� �� ��� ���̅��������� �� � ��� ����� ��� � � �� ���̅��������� �� � ��� ����� ��� ��� (9) the overall pressure ratio (total static) of the twin entry turbine is calculated via the relation (10). �������� � �� � �� � ���� � ��� � ���� � ��� ���� ���������������� � �� ���� (10) the turbine blade speed ratio (11) is defined as a fraction of the circumferential velocity and fictitious isentropic velocity. ������ ����������������� (11) the level of admission of the turbine impeller is the quotient of the isentropic power in the appropriate turbine section and the total isentropic power (12). the admission level of section b is analogical to equation (12). ������ �� �� � ����� � �� � ����� � ��� � ����� � (12) the overall discharge coefficient of the twin entry turbine (13) is evaluated as a fraction of the mass flow rates sum to the reference mass flow rate via machine. �������� ���� ���� ��� ��� � �� ���� � ������ ������� ���������������� ���� (13) 4. evaluation of measured data (12) the overall discharge coefficient of the twin entry turbine (13) is evaluated as a fraction of the mass flow rates sum to the reference mass flow rate via machine. sections a and b. the procedures are based on averaging according to the power of sections a and b, see (8). ��� � � �� �� ���� � � ���� � ���� � � �� � ���� � (8) the definition of the fictitious isentropic velocity (9) is derived from the balance of isentropic powers a and b. ����� � � � ��� ���� �� ��� ���̅��������� �� � ��� ����� ��� � � �� ���̅��������� �� � ��� ����� ��� ��� (9) the overall pressure ratio (total static) of the twin entry turbine is calculated via the relation (10). �������� � �� � �� � ���� � ��� � ���� � ��� ���� ���������������� � �� ���� (10) the turbine blade speed ratio (11) is defined as a fraction of the circumferential velocity and fictitious isentropic velocity. ������ ����������������� (11) the level of admission of the turbine impeller is the quotient of the isentropic power in the appropriate turbine section and the total isentropic power (12). the admission level of section b is analogical to equation (12). ������ �� �� � ����� � �� � ����� � ��� � ����� � (12) the overall discharge coefficient of the twin entry turbine (13) is evaluated as a fraction of the mass flow rates sum to the reference mass flow rate via machine. �������� ���� ���� ��� ��� � �� ���� � ������ ������� ���������������� ���� (13) 4. evaluation of measured data (13) 4. evaluation of measured data the developed regression formula (2) represents the experimental data very well – figure 5, almost avoiding the dependence of friction losses on turbine averaged temperature. the low power losses in bearings are caused by low load of bearings and the measurement during turbocharger warm-up in several cases. the results of the regression are the power losses in bearings. the heat flux via turbocharger shaft has to be evaluated from equation (1). the comparison of measured compressor power under different conditions is in figure 6. the measured compressor power, when the turbine is driven by exhaust gases, is influenced by the heat transfer from the turbine side. the impact of the heat transfer from turbine to compressor housing is significant especially at low turbocharger speed, where the compressor efficiency is underestimated considerably. the effect decreases with increasing compressor speed, figure 7. the measured compressor efficiency is almost equal to the result of the appropriate regression formula at high speeds. coefficients k1 – k4, used in the regression formula (3) for the calculation of the compressor power, in dependence on compressor speed are presented in figure 8. the efficiency of the compressor measured when the turbine is driven by exhaust gases compared to the results of the regression formula based on the euler`s theorem is shown in figure 9. the impact of the heat transfer from the turbine side is clearly visible. turbine efficiency in dependence on pressure ratio, mass flow rate and full or partial admission of an impeller is influenced by the turbine scroll dimensions, the turbine wheel and the interaction of flows impeller upstream, figure 10. the optima of isentropic efficiency figure 5: evaluated power losses in bearings and heat flux via turbocharger shaft vs. averaged total temperature (average of total temperatures at turbine inlet sections a, b and turbine outlet); power losses in bearings + heat flux via turbocharger shaft (blue); power losses in bearings only (red triangles); heat flux via turbocharger shaft (black) obrázek 5: vyhodnocené ztráty v ložiskách a tepelný tok hřídelí turbodmychadla v závislosti na průměrované celkové teplotě (průměr celkových teplot na vstupu do sekcí a, b a výstupu turbíny); ztráty v ložiskách + tepelný tok hřídelí turbodmychadla (modrá); samotné ztráty v ložiskách (červené trojúhelníky); tepelný tok hřídelí turbodmychadla (černá) evaluation of experiments on a twin scroll turbocharger turbine for calibration of a complex 1-d model zdeněk žák, jan macek, petr hatschbach mecca 03 2016 page 15 under full and partial admission of an impeller are surprisingly almost the same, but they are reached at different mass flow rates via the turbine. the maximum efficiency of a turbine with one completely closed section is lower and shifted to higher mass flow rates, see figure 10. when comparing isentropic efficiency in dependence on blade speed ratio – bsr (11) at the same pressure ratio, the isentropic turbine power increases faster, due to increasing mass flow rate via the turbine, than the compressor power. power losses in bearings are not so significant, so the isentropic efficiency of the turbine decreases (6), figure 10, figure 11 and figure 13. the influence of the mass flow rate via the turbine is dominant. the experimental results at low pressure ratio are in figure 11. the turbine efficiency is affected by the partial admission of the turbine wheel (throttling in one section), which causes turbine efficiency reduction. further decrease in the efficiency takes place in the extreme case, when one section of a turbine is closed. the evaluated discharge coefficient (13) of a turbine at almost constant pressure ratio decreases in cases of throttling in section and closed section, figure 12. the isentropic efficiency of a turbine under full and partial admission is almost equal at a pressure ratio of 2.2 in figure 13. efficiency under partial admission at high blade speed ratios is even higher than in the case of full admission. the trend is obvious from figure 10 – the trend of efficiency courses in dependence on mass flow rate via turbine under different conditions in sections. the reason was found earlier using simulations [12]. the turbine efficiency depends on fitting the impeller and nozzle sections geometry. if the impeller exducer part is overloaded at high pressure ratios by expanded gas of high mass flow rate and low density, it increases outlet kinetic energy loss. in such a case, partial admission may help at the same mean pressure ratio since the mass flow rate is reduced in the highly loaded part by reaching the sonic limit. the impact of momentum loss at the twin scroll exit may be fully compensated by better efficiency of figure 6: measured compressor power (standard compressor wheel); turbine driven by exhaust gases (blue); turbine driven by cold air (black dashed line); turbocharger speed 40 krpm obrázek 6: měřený výkon kompresoru (standardní kompresorové kolo); turbína hnaná výfukovými plyny (modrá); turbína hnaná studeným vzduchem (černá čárkovaná čára); otáčky turbodmychadla 40 krpm figure 7: measured compressor power (standard compressor wheel); turbine driven by exhaust gases (blue); turbine driven by cold air (black dashed line); turbocharger speed 80 krpm obrázek 7: měřený výkon kompresoru (standardní kompresorové kolo); turbína hnaná výfukovými plyny (modrá); turbína hnaná studeným vzduchem (černá čárkovaná čára); otáčky turbodmychadla 80 krpm figure 8: courses of regression coefficients k1 – k4 used in the formula for calculation of compressor power (standard compressor wheel) obrázek 8: průběhy regresních koeficientů k1 – k4 použité ve vztahu pro výpočet výkonu kompresoru (standardní kompresorové kolo) figure 9: comparison of measured compressor efficiency (turbine driven by exhaust gases) and efficiency of an adiabatic machine based on regression formula; standard compressor wheel; turbocharger speed 40 krpm obrázek 9: porovnání měřené účinnosti kompresoru (turbína hnána výfukovými plyny) a účinnost adiabatického stroje dle regresního vztahu; standardní kompresorové kolo; otáčky turbodmychadla 40 krpm evaluation of experiments on a twin scroll turbocharger turbine for calibration of a complex 1-d model zdeněk žák, jan macek, petr hatschbach mecca 03 2016 page 16 the exducer, which was the investigated case. therefore, the results presented in figure 10, figure 11 and figure 13 are consistent. the zero operating point with blocked turbine impeller (bsr = 0) for the effect of centrifugal force assessment is also shown in figure 13 and figure 14. the zero point is also useful during the development and testing of regression as described in the text below. after the evaluation of all measured data, it was necessary to prepare and adapt regression formulas for turbine isentropic efficiency and discharge coefficient over a wide range of blade speed ratios. the results of regressions are fundamental for the calibration process of a physical unsteady 1-d model of a twin scroll turbine. measurement smoothing by regression can be used with confidence inside the measured hypercube. regression formulas derived from [11] are properly fitted to the experimental data. the regression model is based on pressure ratio and blade speed ratio polynomials up to the third power and mixed interaction terms of both independent variables with products up to the second power. the comparison of turbine isentropic efficiency evaluated from experiments with the results of tailored regression is in figure 15. the presented example at constant pressure ratio and full admission shows that the obtained results are satisfactory. it was necessary to prepare different formulas for full admission and two different cases of partial admission (throttling in section and closed section). the relations for efficiency and discharge coefficient are also different, so six specific regression forms are prepared in total. the tailored regression forms for efficiency or discharge coefficient as a function of turbine pressure ratio and blade speed ratio are the basis for the calibration process of the 1-d turbine model. the discharge coefficients obtained from experiments are compared with the results of tailored regression in figure 16 (the same measured points as in figure 15). knowledge of the zero point, when the turbine wheel is blocked, is useful during the regression adaptation. extrapolation of measured data by regression is generally risky, although in the current case the results seem to be reasonable. zero efficiency at nonzero bsr or zero discharge coefficient point have to be checked using the physical model. before the full 1-d model is tested, the validity of extrapolation cannot be assessed. the detailed measurement, comprehensive data evaluation based on turbocharger energy balance and further data processing using the tailored specific regression formulas enable the development of the specific unsteady turbine 1-d model with calibration coefficients based on physics. 5. conclusion the specific turbocharger test bench for twin entry turbines was developed and properly tested during the project including the figure 11: comparison of turbine isentropic efficiency courses – overall turbine pr ab = 1.3; full admission of an impeller (blue); partial admission (red square) – level a = 0.87; closed section (green triangle) obrázek 11: srovnání průběhů izoentropické účinnosti turbíny při pr ab = 1.3; plný ostřik oběžného kola (modrá); parciální ostřik (červený čtverec) – level a = 0.87; zavřená sekce (zelený trojúhelník) figure 12: discharge coefficient of a turbine – overall turbine pr ab = 1.3; full admission of an impeller (blue); partial admission (red square) – level a = 0.87; closed section (green triangle) obrázek 12: hltnostní součinitel turbíny – pr ab = 1.3; plný ostřik oběžného kola (modrá); parciální ostřik (červený čtverec) – level a = 0.87; zavřená sekce (zelený trojúhelník) figure 10: isentropic efficiency of turbine under full admission of a turbine wheel (blue); partial admission – throttling in one section (red square) – level a = 0.87; closed section (green triangle) obrázek 10: izoentropická účinnost turbíny při plném ostřiku oběžného kola (modrá); parciální ostřik – škrcení v jedné sekci (červený čtverec) – level a = 0.87; jedna zavřená sekce (zelený trojúhelník) evaluation of experiments on a twin scroll turbocharger turbine for calibration of a complex 1-d model zdeněk žák, jan macek, petr hatschbach mecca 03 2016 page 17 data acquisition and evaluation of in-house software. the selected turbocharger was properly tested with emphasis on the twin entry turbine performance under full and partial admission of an impeller over a wide blade speed ratio range. the detailed analysis of the turbocharger energy balance was utilized for the evaluation of measured data. the optima of turbine isentropic efficiency under full and partial admission, the courses of turbine efficiency and discharge coefficient, valid adiabatic compressor power and efficiency under any conditions and pure losses in bearings are identified and calculated. the overall regression formulas of turbine efficiency and discharge coefficient were tailored and properly tested over a wide range of turbine loads. the obtained maps of two adiabatic compressors are the byproduct of the work. the map of the main compressor will be used during the simulation of the whole turbocharged diesel engine. the full 1-d approach extends the feasibility of modelling, not only by describing the interaction between combustion engine and turbocharger, but it also describes the phenomena inside a turbine. the physical approach respects conditions for mixing of flows inside a scroll, asymmetry of flow admission and turbine scroll design. the results obtained during the research work, briefly described in the paper, will contribute to the further development of turbocharger models and their predictive capability. the preliminary turbocharger design, i.e. main dimensions of divided symmetrical or asymmetrical scroll, turbine impeller and outlet have to be optimized using the developed unsteady 1-d figure 13: comparison of turbine isentropic efficiency courses – overall turbine pr ab = 2.2; full admission of an impeller (blue) (zero point – blocked turbine wheel); partial admission (red square) – level a = 0.87; closed section (green triangle) obrázek 13: srovnání průběhů izoentropické účinnosti turbíny při pr ab = 2.2; plný ostřik oběžného kola (modrá) (nulový bod – zastavený rotor turbíny); parciální ostřik (červený čtverec) – level a = 0.87; zavřená sekce (zelený trojúhelník) figure 14: discharge coefficient of a turbine – overall turbine pr ab = 2.2; full admission of an impeller (blue) (zero point – blocked turbine wheel); partial admission (red square) – level a = 0.87; closed section (green triangle) obrázek 14: hltnostní součinitel turbíny – pr ab = 2.2; plný ostřik oběžného kola (modrá) (nulový bod – zastavený rotor turbíny); parciální ostřik (červený čtverec) – level a = 0.87; zavřená sekce (zelený trojúhelník) figure 15: turbine isentropic efficiency, overall turbine pr ab = 2.2, full admission of a turbine wheel; experimental data (blue); results of regression (red dashed line) obrázek 15: izoentropická účinnost turbíny, pr ab = 2.2, plný ostřik oběžného kola; experimentální data (modrá); výsledky regresí (červená čárkovaná) figure 16: discharge coefficient of a turbine – overall turbine pr ab = 2.2, full admission of a turbine wheel; experimental data (blue); results of regression (black dotted line) obrázek 16: hltnostní součinitel turbíny při pr ab = 2.2, plný ostřik oběžného kola; experimentální data (modrá); výsledky regresí (černá tečkovaná) evaluation of experiments on a twin scroll turbocharger turbine for calibration of a complex 1-d model zdeněk žák, jan macek, petr hatschbach mecca 03 2016 page 18 model. the turbocharger has to be developed with the combustion engine simultaneously. the most frequent operating modes, fuel consumption and required dynamics have to be taken into account. the appropriate 3-d cfd analysis of compressor and turbine may begin after the priorities are identified with the 1-d simulation. acknowledgements this work was supported by: this research has been realized using the support of the ministry of education, youth and sports program npu i (lo), project lo1311: ’development of centre of vehicles for sustainable mobility’. zvoníček’s foundation, czech republic, project – development of a 1-d model of a radial turbocharger turbine supported by the financial donation of dr. thomas morel all the support is gratefully acknowledged. list of notations and abbreviations a, b, ab turbine sections a, b; overall turbine ab at_ref[m 2] reference flow area b2[m] compressor wheel width (outlet) bsr [1] blade speed ratio comp compressor cp [j kg  -1k-1] average specific heat cs [m s  -1] isentropic velocity d2[m] compressor wheel diameter (outlet) dref[m] reference diameter of turbine wheel h [j kg -1] enthalpy in inlet k1 – k4 regression coefficients levela[1] admission level – turbine section a m. [kg s -1] mass flow rate oil oil out outlet p [pa] pressure pbear [w] power losses in bearings pcomp_adi [w] compressor power adiabatic pturbine_ab_ise_t_s [w] isentropic turbine power total-static pr [1] pressure ratio total-static r [j kg-1k-1] gas constant ref reference q. case [w] heat flux between housings q. ecomp [w] heat flux from compressor housing q. eturb [w] heat flux from turbine scroll q. shaft [w] heat flux via turbocharger shaft rpm [rpm] turbocharger speed s static t [k] temperature t, tot total u2 circumferential velocity w2_r radial velocity (compressor wheel outlet) ηturbine_ise [1] isentropic turbine efficiency ηturbine_overall [1] overall turbine efficiency κ [1] average specific heat ratio µturb_ab [1] discharge coefficient ρ2 [kg m -3] density at compressor outlet ψ [1] flow function references [1] dixon s. l.: fluid mechanics, thermodynamics of turbomachinery. pergamon press london 1975 [2] zinner, k., supercharging of internal combustion engines. springer heidelberg 1978 [3] watson, n., janota, m.s., turbocharging the internal combustion engine. macmillan publishers, london 1982, isbn 0 333 24290 4 [4] brinkert n., sumser s., schulz a., weber s., fieweger k., and bauer h.-j. understanding the twin -scroll turbine-flow similarity. asme turbo expo, 49:2207–2218, 2011. [5] de bellis, v., bozza, f., schernus, c., and uhlmann, t., “advanced numerical and experimental techniques for the extension of a turbine mapping,” sae int. j. engines 6(3):2013, doi:10.4271/2013-24-0119. [6] fredriksson c. f., xuwen qiu, baines n. c., müller m., brinkert n. and gutmann c. meanline modeling of radial inflow turbine with twin-entry scroll. asme turbo expo 2012,doi:10.1115/gt2012-69018 [7] aymanns r.; scharf j.; uhlmann t.; pischinger s., turbocharger efficiencies in pulsating exhaust gas flow. mtz, vol. 07-08/2012. [8] lückmann d.; uhlmann t.; kindl h.; pischinger s., separation in double entry turbine housings at boosted gasoline engines. mtz, vol. 10/2013. [9] uhlmann t., et al. “development and matching of double entry turbines for the next generation of highly boosted gasoline engines.” 34th international vienna motor symposium. 2013. [10] capobianco, m., marelli, s., “transient performance of automotive turbochargers: test facility and preliminary experimental analysis,” sae technical paper 2005-24-066, 2005, doi:10.4271/2005-24-066. [11] macek, j., vitek, o., and zak, z., “calibration and results of a radial turbine 1-d model with distributed parameters,” sae technical paper 2011-01-1146, 2011, doi:10.4271/2011-01-1146. [12] macek, j., zak, z., vitek, o.: “physical model of a twinscroll turbine with unsteady flow,” sae technical paper 2015-01-1718, 2015, doi:10.4271/2015-01-1718. mecca_21-01_web range extender ice multi -parametric multi -objective optimization mikulá! adámek, rastislav toman mecca 01 2021 page 11 10.14311/mecdc.2021.01.02 range extender ice multi -parametric multi -objective optimization mikulá! adámek, rastislav toman mikulá! adámek ctu in prague, faculty of mechanical engineering; technická 4, praha 6, 166 07, czech republic; e -mail: mikulas.adamek@fs.cvut.cz rastislav toman ctu in prague, faculty of mechanical engineering; technická 4, praha 6, 166 07, czech republic; e -mail: rastislav.toman@fs.cvut.cz abstract range extended electric vehicles (reev) are still one of the suitable concepts for modern sustainable low emission vehicles. reev is equipped with a small and lightweight unit, comprised usually of an internal combustion engine with an electric generator, and has thus the technical potential to overcome the main limitations of a pure electric vehicle – range anxiety, overall driving range, heating, and air -conditioning demands – using smaller battery: saving money, and raw materials. even though several rex ice concepts were designed in past, most of the available studies lack more complex design and optimization approach, not exploiting the advantageous single point operation of these engines. resulting engine designs are usually rather conservative, not optimized for the best effi ciency. this paper presents a multi -parametric and multi -objective optimization approach, that is applied on a rex ice. our optimization toolchain combines a parametric gt -suite ice simulation model, modefrontier optimization software with various optimization strategies, and a parametric cad model, that fi rst provides some simulation model inputs, and second also serves for the fi nal designs’ feasibility check. the chosen ice concept is a 90 degrees v -twin engine, four -stroke, spark -ignition, naturally aspirated, port injected, ohv engine. the optimization goal is to fi nd the thermodynamic optima for three different design scenarios of our concept – three different engine displacements – addressing the compactness requirement of a rex ice. the optimization results show great fuel effi ciency potential by applying our optimization methodology, following the general trends in increasing ice effi ciency, and power for a naturally aspirated concept. key words: range extender, range extended electric vehicle, hybrid electric vehicle, battery electric vehicle, internal combustion engine, spark -ignition, thermodynamic optimization, genetic algorithm shrnutí elektrické vozidlo s prodlou!en"m dojezdem (reev) je pova!ováno za jednu z mo!ností, jak vyrobit cenov# dostupn" automobil s nízk"mi emisemi $kodlivin a skleníkov"ch plyn%. hlavní v"hoda tohoto konceptu spo&ívá v malé (lehké) baterii, která by m#la svojí kapacitou pokr"t v#t$inu !ivotního cyklu, men$í baterie té! sni!uje cenu vozidla. aby u!ivatel nebyl omezen krátk"m dojezdem, je pro v"jime&né p'ípady vozidlo vybaveno tzv. prodlu!ova&em dojezdu. v#t$inou se jedná o pístov" spalovací motor s generátorem, jeho! pomocí se nabíjí hlavní baterie. v"vojem takového systému se zab"vala 'ada v"robc%, v#t$ina návrh% se v$ak zakládala pouze na zku$enostech v"vojá'% a v"sledné motory nebyly optimalizovány pro jejich provozní podmínky. (lánek pojednává o návrhu spalovacího motoru pro prodlu!ova& dojezdu pomocí mnoho -kriteriální a mnoho -cílová optimalizace pln# parametrického termodynamického modelu, v kooperaci s cad modelem. cad model je pou!it jako zdroj vstup% pro termodynamick" model a sou&asn# ke kontrole realizovatelnosti v"sledk% optimalizace. navrhovan" motor je &ty'dob", atmosférick", dvouválec do v, s rozvodem ohv a nep'ím"m vst'ikem paliva. celkem jsou optimalizovány t'i varianty motoru, li$ící se zdvihov"m objemem. cílem je pokud mo!no naplnit po!adavek na kompaktnost v"sledného motoru. v"sledky odpovídají trend%m pro zvy$ování ú&innosti a v"konu spalovacích motor% a vykazují velk" potenciál pro sní!ení spot'eby paliva spalovacího motoru. klí"ová slova: prodlu#ova" dojezdu, elektrické vozidlo s prodlou#en$m dojezdem. range extender, elektrick$ automobil s prodlu#en$m dojezdem, elektromobil, spalovací motor, zá#ehov$ motor, termodynamická optimalizace, genetick$ algoritmus range extender ice multi -parametric multi -objective optimization range extender ice multi -parametric multi -objective optimization mikulá! adámek, rastislav toman mecca 01 2021 page 12 1. introduction range extended electric vehicles (reev) are one of the doctrines considered for modern low emission vehicles. main advantage of this concept comes from using the battery as small as possible, this way helping to save the rare and expensive materials used in batteries, still without causing the “range anxiety” to the user. to fully exploit this advantage and to be economically viable, the range extender (rex) used in reev, needs to focus on the price, overall mass, package dimensions, and nvh (noise vibration and harshness). the most common type of range extender (and the only one considered in this paper) is the internal combustion engine (ice). several companies have developed a rex ice to some extent, including oems like lotus, tata, mahle, and some others [1; 2; 3; 4; 5]. design concepts from table 1 suggest, that most of rex ices are designed primarily to fulfi l the already mentioned requirements. most of the companies try to keep the price as low as possible, which means sticking to traditional concepts of natural aspiration, indirect injection, and two valves per cylinder heads: the only major difference is avl with its rotary rex concept [5]. all the evaluated range extender engines operate at stoichiometric conditions, allowing for the use of three -way catalyst to fulfi ll the emission regulation. although most of the engine concepts were designed from scratch, tata being the only difference [3], all the designs are mostly based on engineering teams’ experience, and internal oem’s empirical tools, and correlations. literature indicates that the effi ciency is subject to other parameters (especially to price). this way, the entire system’s effi ciency will always be poor, due to the double tank -to -wheel energy conversion. nevertheless, the fuel consumption can be signifi cantly reduced (which is always a positive attribute) by the engine optimization for its specifi c operation, even with “the cheapest” possible setup. 1.1 description of the general idea our general idea is based on building a detailed fully parametric thermodynamic model of an ice, equipped with simulation sub -models with appropriate predictive capabilities, and then running a multi -parametric, multi -objective optimization. the optimization result is then checked for its feasibility, using a parametric cad model of the engine block. this not only provides a necessary engineering feedback, but also helps to capture some important trends, that can occur when changing the basic engine parameters automatically: in our study it is for instance the con -rod elongation when decreasing the bore/ stroke ratio rb/s leading to the crank -train enlargement. range extender engines are designed to provide a specifi c power output pe (generally enough for the vehicle to achieve the highway speed), usually around 30 kw. the engine is expected to provide this power output at wide -open throttle conditions and for most of its lifetime. this single operating point feature makes the rex engines well suitable for a multi-parametric thermodynamic optimization mentioned above, although the general method can be easily extended on more operating points, and therefore other ice concepts. 1.2 goals of the paper our department at czech technical university in prague (ctu) has gathered vast amount of experience on ice design optimization throughout several former projects [6; 7]. the main goal of this article is to describe an ice design and optimization method, that combines cae simulation tools with cad structural design. the cad model sets up the simulation input data, and subsequently checks the fi nal design for its feasibility. avl mahle tata lotus kspg avl engine confi guration i2 i2 i2 i3 v2 (90 deg) rotary (single) [-] valvetrain layout sohc sohc sohc sohc ohv [-] valves per cylinder 2 2 2 2 2 [-] ice displacement vd 0.570 0.900 0.624 1.193 0.799 0.254 [l] bore b 70.0 83.0 73.5 75.0 80.0 [mm] stroke s 74.0 83.0 73.5 90.0 79.5 [mm] bore/stroke ratio rb/s 0.946 1.000 1.000 0.833 1.006 [-] compression ratio rc 11 10 10.3 10 n/a [-] ice speed nice 5000 4000 5500 3500 4500 5000 [rpm] mean piston speed cs 12.333 11.065 n/a 10.500 11.925 [m/s] brake power pe 18 30 28 36.8 30 15 [kw] bsfc 250 250 n/a 241 n/a 260 [g/kwh] table 1: overview of range extender ice concepts tabulka 1: p'ehled uspo'ádání motor% pro range extender range extender ice multi -parametric multi -objective optimization mikulá! adámek, rastislav toman mecca 01 2021 page 13 the article is divided into six chapters, that cover all the important aspects of our method, starting with the engine concept selection (in chapter 2); followed by the introduction of the thermodynamic model with its predictive sub -models, and preliminary design analysis in chapter 3. chapter 4 then discusses the optimization setup, results, and design analyses. chapter 5 presents some potential future developments of our methodology, and fi nally, chapter 6 contains important conclusions from our study. 2. ice design concept choosing the right base concept is extremely important, since it has a strong direct infl uence on nvh, package, mass, and price. our concept selection consists of weighing the four criteria (the lower the score, the better) in table 2, for four ice concepts. price is the most important parameter (weight of 4), followed by the nvh, mass, and total package: input weighing data for the package, mass, and price were taken directly from a table prepared by mahle in [8]. the inline two -cylinder engine without balance shaft is a baseline concept; the other assessed two -cylinder designs are the i2 with balance shaft, v -twin engine (v2) with 90 degrees between the cylinder axes, and a two -cylinder with opposed pistons – boxer engine. the nvh data in table 2 are our gt -suite simulation results of each assessed crank -train confi guration. we obtained the simulation inputs from parametric cad model: each engine setup had equal bore, stroke, and conn -rod lengths. first, all variants were fi rst order statically balanced. the i2 engines were simulated for the three feasible ignition orders (0 – 360 degrees, 0 – 180 degrees, and 0 – 450 degrees), and the best one of these is the i2 baseline in the fi nal table 2 comparisons (thus achieving 100%). the nvh relative value then represents a fraction of imbalanced force between the tested concept and i2 baseline. to enable the averaging of unbalanced forces and unbalanced moments together, the moments are weighted by the estimated bearing spacing. finally, table 2 suggests, that v2 concept seems to be the most promising for rex ice, and it is therefore chosen for our subsequent studies. to sum -up our ice design concept: later chapters of this article will deal with the optimizations of four stroke, v2, naturally aspirated, spark ignition engine with port fuel injection, and two valves per cylinder (ohv). 3. thermodynamic model a fully parametric thermodynamic model of our fi nal design concept serves for the subsequent multi -parametric and multi-objective optimizations. the simulation model of the rex ice was built within the 0d/1d gt -suite simulation platform, which allows for the simulation of a whole engine thermodynamic cycle. the engine is a virtual one, with a special attention placed on the use of suitable sub -models with predictive abilities. a sub -model without a proper predictive ability could mislead the optimization and guide it to unrealistic results. 3.1 main engine geometry the main parameters of the thermodynamic model are the cylinder bore b, engine operating speed nice, and bore/stroke ratio rb/s. valve design parameters are linked to the cylinder bore diameter, using empirical formulas from [9]: • intake valve diameter dvin = 0.36b; maximum intake valve lift lvin = 0.3dvin; • exhaust valve dvex = 0.3b; maximum exhaust valve lift lvex = 0.3dvex. the 1d intake and exhaust air paths are also fully parametric, sized accordingly to the cylinder bore b, using generic fl ow coeffi cients. intake air path contains also an air fi lter, throttle, and intake manifold volume. exhaust path then contains a simplifi ed model of a catalyst brick, to get a realistic exhaust back -pressure. 3.2 friction sub -model friction model has a key infl uence on the resulting ice’s setup, mainly on the rb/s ratio, and ice operating speed. a simple chen -flynn model which was used in previous research studies showed major fl aws when used in a multi -parametric optimization due to its lack of predictive ability [7]. therefore, we applied ctu in -house friction model vyva!, created by macek et al. [10]. in fact, its implementation into gt -suite thermodynamic model as a sub -assembly. this friction sub -model has three main parts: pressure part, mechanic part, and friction part. pressure part consists of series of pipe objects, that simulate engine blow -by, and predict the pressure differences between the piston rings – essential for the piston ring and skirt friction forces calculation. second – mechanic part, consists of detailed mechanical model of crank -train, and determines all velocities, accelerations, and forces acting on each package mass price nvh weighted average parameter weight 1 2 4 3 --i2 without balance shaft 100 100 100 100 100 i2 with balance shaft 100 115 110 31.1 86.3 v2 with 90° angle 128 105 102 32.7 84.4 boxer 104 108 103 44.7 86.6 table 2: decision table for the ice concept selection tabulka 2: rozhodovací tabulka pro v"b#r konceptu motoru range extender ice multi -parametric multi -objective optimization mikulá! adámek, rastislav toman mecca 01 2021 page 14 crank -train member. the last – friction part, calculates friction powers, fmeps, and friction forces for each member of crank-train, and piston assembly (crank bearings, main bearings, piston pin, piston skirt, and piston rings), using results obtained from the respective mechanic and pressure parts. friction coeffi cients necessary for fi nding the friction forces are calculated using a simple model based on a mathematical description of stribeck curve, that expresses a friction coeffi cient’s dependence on load, speed, and oil viscosity. vyva! model also contains empiric relations for oil, and fuel pump losses. finally, the friction loss in valve train is calculated by bishop’s formula [9]. 3.3 combustion sub -model another key area in spark -ignition ice optimization is the simulation of si combustion. we decided to use predictive phenomenological combustion model called engcylcombsiturb (siturb) available in gt -suite. siturb model calculates a differential equation for entrained mass rate of unburned gas with its main equation 1, where "u are unburned mixture density, and af a fl ame area. sl and st then represent the laminar and turbulent fl ame speeds. piston rings), using results obtained from the respective mechanic and pressure parts. friction coefficients necessary for finding the friction forces are calculated using a simple model based on a mathematical description of stribeck curve, that expresses a friction coefficient’s dependence on load, speed, and oil viscosity. vyvaž model also contains empiric relations for oil, and fuel pump losses. finally, the friction loss in valve train is calculated by bishop’s formula [9]. 3.3. combustion sub-model another key area in spark-ignition ice optimization is the simulation of si combustion. we decided to use predictive phenomenological combustion model called engcylcombsiturb (siturb) available in gt-suite. siturb model calculates a differential equation for entrained mass rate of unburned gas with its main equation 1, where 𝜌𝜌2 are unburned mixture density, and 𝐴𝐴3 a flame area. 𝑆𝑆4 and 𝑆𝑆5 then represent the laminar and turbulent flame speeds. 𝑑𝑑𝑀𝑀𝑑𝑑𝑑𝑑 = 𝜌𝜌2𝐴𝐴3(𝑆𝑆4 + 𝑆𝑆5) (1) these two flame speed parameters – 𝑆𝑆4 and 𝑆𝑆5 – limit the flame kernel development: during the initial phases, when the kernel size is still small, the entrainment rate is limited by the laminar flame speed 𝑆𝑆4 (equation 2); equation 3 then accounts for the flame transition into a turbulent one, with 𝑢𝑢´ representing the mean fluctuating turbulent velocity, 𝑅𝑅3 the flame radius, and 𝐿𝐿6 the turbulent length scale. 𝑆𝑆4 = @𝐵𝐵7 + 𝐵𝐵8(𝜙𝜙 − 𝜙𝜙7)9c ∙ e 𝑇𝑇2 𝑇𝑇:g ; ∙ e 𝑝𝑝 𝑝𝑝:g < ∙ (1 − 2,06𝐷𝐷𝐷𝐷𝐷𝐷:.>>?0@) (2) 𝑆𝑆5 = 𝐶𝐶a𝑢𝑢´o1 − 1 1 + 𝐶𝐶bp𝑅𝑅3 9 𝐿𝐿69⁄ rs (3) siturb needs a priori information about the turbulent flow in combustion chamber (𝐿𝐿6 and 𝑢𝑢´ parameters from equation 3). the source of these quantities is another gt-suite’s sub-model – engcylflow (flow) – a k-k-ε kinetic energy cascade flow model, that predicts the in-cylinder charge motion and turbulence. more details on both siturb and flow models, their evolution, and calibration can be found in [11; 12; 13]. siturb uses five different calibration parameters, four from equations 2 and 3 (𝐷𝐷𝐷𝐷𝑀𝑀, 𝐶𝐶b, 𝐶𝐶a, and 𝐿𝐿6), and taylor length scale multiplier 𝐶𝐶c (present in the burnup rate equation 𝑑𝑑𝑀𝑀d 𝑑𝑑𝑑𝑑⁄ , as a multiplier for the taylor microscale of turbulence). flow then has its own set of four calibration parameters. so, in total we have nine calibration parameters. first, we performed a thorough sensitivity analysis on these nine total calibration parameters, comparing the combustion model (combination of siturb and flow) responses on ice geometry, ice operating conditions (load, speed, and cooled egr content). the sensitivity analysis showed that the burn durations vary in accordance with our general experience: however general burn rates are lower, and the overall sensitivity on operating conditions is higher (load, speed, cooled egr). after the sensitivity analysis we performed a calibration of the nine siturb and flow calibration parameters using an available set of measurement data with ice load/speed dependencies. the set of these nine calibrated parameters was then used in all our subsequent rex ice optimizations, discussed in next chapters. 3.4. in-cylinder heat transfer sub-model (1) these two fl ame speed parameters – sl and st – limit the fl ame kernel development: during the initial phases, when the kernel size is still small, the entrainment rate is limited by the laminar fl ame speed sl (equation 2); equation 3 then accounts for the fl ame transition into a turbulent one, with u´ representing the mean fl uctuating turbulent velocity, rf the fl ame radius, and lt the turbulent length scale. (2) piston rings), using results obtained from the respective mechanic and pressure parts. friction coefficients necessary for finding the friction forces are calculated using a simple model based on a mathematical description of stribeck curve, that expresses a friction coefficient’s dependence on load, speed, and oil viscosity. vyvaž model also contains empiric relations for oil, and fuel pump losses. finally, the friction loss in valve train is calculated by bishop’s formula [9]. 3.3. combustion sub-model another key area in spark-ignition ice optimization is the simulation of si combustion. we decided to use predictive phenomenological combustion model called engcylcombsiturb (siturb) available in gt-suite. siturb model calculates a differential equation for entrained mass rate of unburned gas with its main equation 1, where 𝜌𝜌2 are unburned mixture density, and 𝐴𝐴3 a flame area. 𝑆𝑆4 and 𝑆𝑆5 then represent the laminar and turbulent flame speeds. 𝑑𝑑𝑀𝑀𝑑𝑑𝑑𝑑 = 𝜌𝜌2𝐴𝐴3(𝑆𝑆4 + 𝑆𝑆5) (1) these two flame speed parameters – 𝑆𝑆4 and 𝑆𝑆5 – limit the flame kernel development: during the initial phases, when the kernel size is still small, the entrainment rate is limited by the laminar flame speed 𝑆𝑆4 (equation 2); equation 3 then accounts for the flame transition into a turbulent one, with 𝑢𝑢´ representing the mean fluctuating turbulent velocity, 𝑅𝑅3 the flame radius, and 𝐿𝐿6 the turbulent length scale. 𝑆𝑆4 = @𝐵𝐵7 + 𝐵𝐵8(𝜙𝜙 − 𝜙𝜙7)9c ∙ e 𝑇𝑇2 𝑇𝑇:g ; ∙ e 𝑝𝑝 𝑝𝑝:g < ∙ (1 − 2,06𝐷𝐷𝐷𝐷𝐷𝐷:.>>?0@) (2) 𝑆𝑆5 = 𝐶𝐶a𝑢𝑢´o1 − 1 1 + 𝐶𝐶bp𝑅𝑅3 9 𝐿𝐿69⁄ rs (3) siturb needs a priori information about the turbulent flow in combustion chamber (𝐿𝐿6 and 𝑢𝑢´ parameters from equation 3). the source of these quantities is another gt-suite’s sub-model – engcylflow (flow) – a k-k-ε kinetic energy cascade flow model, that predicts the in-cylinder charge motion and turbulence. more details on both siturb and flow models, their evolution, and calibration can be found in [11; 12; 13]. siturb uses five different calibration parameters, four from equations 2 and 3 (𝐷𝐷𝐷𝐷𝑀𝑀, 𝐶𝐶b, 𝐶𝐶a, and 𝐿𝐿6), and taylor length scale multiplier 𝐶𝐶c (present in the burnup rate equation 𝑑𝑑𝑀𝑀d 𝑑𝑑𝑑𝑑⁄ , as a multiplier for the taylor microscale of turbulence). flow then has its own set of four calibration parameters. so, in total we have nine calibration parameters. first, we performed a thorough sensitivity analysis on these nine total calibration parameters, comparing the combustion model (combination of siturb and flow) responses on ice geometry, ice operating conditions (load, speed, and cooled egr content). the sensitivity analysis showed that the burn durations vary in accordance with our general experience: however general burn rates are lower, and the overall sensitivity on operating conditions is higher (load, speed, cooled egr). after the sensitivity analysis we performed a calibration of the nine siturb and flow calibration parameters using an available set of measurement data with ice load/speed dependencies. the set of these nine calibrated parameters was then used in all our subsequent rex ice optimizations, discussed in next chapters. 3.4. in-cylinder heat transfer sub-model (3) siturb needs a priori information about the turbulent fl ow in combustion chamber (lt and u´ parameters from equation 3). the source of these quantities is another gt -suite’s sub -model – engcylflow (flow) – a k -k -# kinetic energy cascade fl ow model, that predicts the in -cylinder charge motion and turbulence. more details on both siturb and flow models, their evolution, and calibration can be found in [11; 12; 13]. siturb uses fi ve different calibration parameters, four from equations 2 and 3 (dem, ck, cs, and lt), and taylor length scale multiplier c$ (present in the burnup rate equation dmb/dt, as a multiplier for the taylor microscale of turbulence). flow then has its own set of four calibration parameters. so, in total we have nine calibration parameters. first, we performed a thorough sensitivity analysis on these nine total calibration parameters, comparing the combustion model (combination of siturb and flow) responses on ice geometry, ice operating conditions (load, speed, and cooled egr content). the sensitivity analysis showed that the burn durations vary in accordance with our general experience: however general burn rates are lower, and the overall sensitivity on operating conditions is higher (load, speed, cooled egr). after the sensitivity analysis we performed a calibration of the nine siturb and flow calibration parameters using an available set of measurement data with ice load/speed dependencies. the set of these nine calibrated parameters was then used in all our subsequent rex ice optimizations, discussed in next chapters. 3.4 in -cylinder heat transfer sub -model prediction of in -cylinder energy loss due to heat transfer is calculated with a combination of two models. first, structure and surface temperatures are obtained with a predictive fi nite element (fe) gt -suite sub -model engcyltwallsoln. fe model requires a simplifi ed geometry of all the surfaces, together with coolant and oil boundary conditions. the cylinder structure geometry is also parametric and linked to the engine main geometry. second, the heat transfer coeffi cient is determined using classical woschni correlation without swirl [14]. this approach was successfully used in some previous ctu research projects on ice multi -parametric optimization [6; 7]. 3.5 knock sub -model knock prediction is modeled using a basic gt -suite model engcylknock (knock), which is based on a standard calculation of knock induction time integral. knock model obtains the induction time using a kinetics -fit -gasoline correlation. this correlation predicts the induction time with combination of reduced iso -octane oxidation and reduced n -heptane oxidation mechanisms [15]. we did not calibrate the knock model, because of the time constraints. however, our previous sensitivity studies showed, that the uncalibrated model tends to stay on the safe side in its response to ice operating condition changes, and this we consider advantageous [16]. 3.6 structural design analysis there are two main reasons for the use of a parametric cad model of our v2 engine block: • cad model helps us prepare some of the simulation input data for the friction model vyva!, that requires detailed knowledge of crank -train masses, and con -rod compensating moment of inertia with its coordinates. range extender ice multi -parametric multi -objective optimization mikulá! adámek, rastislav toman mecca 01 2021 page 15 • subsequently, it serves for the fi nal structural design’s feasibility check – after running the multi -parametric optimizations. there are some relations, that can be established only with this parametric cad model, and which are important inputs for vyva! friction model – as we have already discussed. first of those relations is the relation between the piston assembly’s mass and cylinder bore; the second one is the relation between the con -rod’s length l and its geometry parameters; third one is the relation of con -rod ratio $ with bore/stroke ratio rb/s, and bore diameter b in equation 4 (n and c are functions of cylinder bore; $ = s/(2*l). one can assume, that a designer would try to minimize the package volume using a con -rod as short as possible, because this is a parameter that plays a major role in determining the crank -train’s size, and therefore the total engine’s package volume. rediction of in-cylinder energy loss due to heat transfer is calculated with a combination of two models. first, structure and surface temperatures are obtained with a predictive finite element (fe) gtsuite sub-model engcylt allsoln. fe model requires a simplified geometry of all the surfaces, together with coolant and oil boundary conditions. the cylinder structure geometry is also parametric and linked to the engine main geometry. second, the heat transfer coefficient is determined using classical woschni correlation without swirl [1 ]. this approach was successfully used in some previous ct research pro ects on ice multi-parametric optimization [ ; ]. 3. . noc sub-model nock prediction is modeled using a basic gt-suite model engcylkno k (kno k), which is based on a standard calculation of knock induction time integral. kno k model obtains the induction time using a k n -f a ol n correlation. this correlation predicts the induction time with combination of reduced iso-octane oxidation and reduced n-heptane oxidation mechanisms [1 ]. we did not calibrate the kno k model, because of the time constraints. owever, our previous sensitivity studies showed, that the uncalibrated model tends to stay on the safe side in its response to ice operating condition changes, and this we consider advantageous [1 ]. 3. . tructural desi n analysis there are two main reasons for the use of a parametric ca model of our 2 engine block: • ca model helps us prepare some of the simulation input data for the friction model vyvaž, that requires detailed knowledge of crank-train masses, and con-rod compensating moment of inertia with its coordinates. • subsequently, it serves for the final structural design’s feasibility check – after running the multi-parametric optimizations. there are some relations, that can be established only with this parametric ca model, and which are important inputs for vyvaž friction model – as we have already discussed. first of those relations is the relation between the piston assembly’s mass and cylinder bore; the second one is the relation between the con-rod’s length 𝐷𝐷 and its geometry parameters; third one is the relation of con-rod ratio with bore/stroke ratio 𝑅𝑅 , and bore diameter 𝐵𝐵 in equation ( and are functions of cylinder bore; = 𝑆𝑆 2𝐷𝐷⁄ ). ne can assume, that a designer would try to minimize the package volume using a con-rod as short as possible, because this is a parameter that plays a ma or role in determining the crank-train’s size, and therefore the total engine’s package volume. = − p 𝑅𝑅 − 0 r 0 0 29 9 + 1 ∙ 0 012 + + p𝑅𝑅 − 0 r ( ) figure 1 shows this relation in comparison with data acquired directly from the ca model (marked by re suffix in legend), for four different bore diameters 𝐵𝐵. ur correlation gives feasible results, and these are fed into vyvaž sub-model ensuring higher optimization accuracy and results’ feasibility. okomentoval(a): [a4]: “con-rod” or “connecting rod” okomentoval(a): [a5r4]: done – „con-rod“ used everywhere okomentoval(a): [a6]: („rel“ suffix in the legend) okomentoval(a): [a7r6]: done (4) figure 1 shows this relation in comparison with data acquired directly from the cad model (marked by “rel” suffi x in legend), for four different bore diameters b. our correlation gives feasible results, and these are fed into vyva! sub -model ensuring higher optimization accuracy and results’ feasibility. figure 2 with con -rod ratio $ dependence on rb/s ratio then shows, that for rb/s ratios under 0.5, the con -rod length grows rapidly (lower $ ratio means longer con -rod length). this figure also clarifi es how we chose the rb/s ratio lower/upper limits in table 3, that will be introduced in next chapter. 4. optimization scenarios a general expectation in an optimization aimed for the best effi ciency natural aspirated ice is, that it will lead to relatively large displacement. this is however in a strong disagreement with the basic rex requirement for a compact design package, and low overall mass. to test this expectation, we decided to optimize our rex ice model in three different scenarios, with the same pe target of 30 kw, at the best possible bsfc. the only difference between the scenarios is the engine displacement. in the fi rst scenario, called vmax , the optimizer is not limited by the cylinder displacement, only by the minimum/maximum cylinder bore diameter b and bore/stroke ratio rb/s. main point of this scenario is to test, whether the optimization will properly follow the expected trends in increasing the ice effi ciency. second scenario v05 concept uses a fi xed cylinder displacement of 0.5 l, hence the name. this engine’s total displacement is slightly larger than most rex ices analyzed in chapter 1, but it is probably the most common engine displacement in automotive industry. last scenario is v035, should represent the design’s compactness requirement. since total displacement of 0.7 l is rather small for 30 kw power output, we expect the optimized design to turn out as “sporty”. 4.1 optimization setup there are nine total parameters chosen for the optimizations, summed -up in table 3 (sa is the spark advance angle; the fi ring tdc represents the 0 deg ca in all angular parameters). the vmax scenario optimizes all of them; in the case v05 and v035 scenarios bore and stroke values are linked together because of the “locked volume”, and the optimizer varies only the rb/s ratio. figure 1: con-rod length dependence on engine stroke (values obtained with relation 4 are marked with “rel”) obrázek 1: délka ojnice v závislosti na zdvihu motoru („rel“ zna&í hodnoty získané pomocí vztahu 4) figure 2: con-rod ratio dependence on bore/stroke ratio rb/s obrázek 2: závislost ojni&ního pom#ru na pom#ru zdvihu a vrtání rb/s range extender ice multi -parametric multi -objective optimization mikulá! adámek, rastislav toman mecca 01 2021 page 16 parameters fivc and fevo multiply the width of the base valve lift curves, and by that control the inlet valve opening event or exhaust valve closing events respectively (note: unity values of fivc and fevo correspond to 210 deg ca from open to closed valve, at 1 mm lift). all the optimizations are run using modefrontier’s pilopt hybrid algorithm, that combines local and global search, and is recommended for multi -objective problems [17]. pilopt algorithm is then searching for the thermodynamic optima, trying to fulfi ll also the pe demand. each scenario optimization took about 10 000 design iterations. as we have already discussed in our introductory part, we use a fully parametric cad model of v2 engine block for the design feasibility check, since a thermodynamically optimal design is not necessarily also feasible from the structural design viewpoint. 4.2 optimization results since the optimization is multi -objective, optimal results are received in a pareto front, which is a set of optimal values, where achieving improvement in one of the objectives will worsen the other. in our case, designs with lower bsfc tend to be further away from the desired power output, and vice versa. the optimal designs were then selected from the pareto front using standard criterial function f (equation 5), where the weight coeffi cient for bsfc (%i1) is 0.9, and for brake power pe (%i2) it is 0.1. the fraction xi/xi, max in equation 5 represents a normalization of pareto front values, so that the two different objective functions xi can be combined into one equation; xi, max is the maximum value of the ith objective function in pareto set. arameter mm de c de c de c o er limit . 1 29 32 . . er limit 1 1. 1 -1 3 1.3 1.3 esolution .1 . .1 1 1 1 . . able 3 imits and resolutions of the optimization parameters abul a 3 rozsahy a rozli en optimalizovan ch parametr arameters and 0 multiply the width of the base valve lift curves, and by that control the inlet valve opening event or exhaust valve closing events respectively ( ote: unity values of and 0 correspond to 21 deg ca from open to closed valve, at 1 mm lift). all the optimizations are run using modefr tier’s l t hybrid algorithm, that combines local and global search, and is recommended for multi-ob ective problems [1 ]. l t algorithm is then searching for the thermodynamic optima, trying to fulfill also the demand. each scenario optimization took about 1 design iterations. as we have already discussed in our introductory part, we use a fully parametric ca model of 2 engine block for the design feasibility check, since a thermodynamically optimal design is not necessarily also feasible from the structural design viewpoint. 4. . timi ation results since the optimization is multi-ob ective, optimal results are received in a areto front, which is a set of optimal values, where achieving improvement in one of the ob ectives will worsen the other. in our case, designs with lower bsfc tend to be further away from the desired power output, and vice versa. the optimal designs were then selected from the areto front using standard criterial function (equation ), where the weight coefficient for bsfc ( ) is .9, and for brake power ( 9) it is .1. the fraction 7 in equation represents a normalization of areto front values, so that the two different ob ective functions can be combined into one equation; 7 is the maximum value of the ith ob ective function in areto set. = 7 b ( ) 4. . . erall results results of all three optimization scenarios are summarized in table and figure 3. while table contains the set of optimal (independent – labelled with ’) parameters, main thermodynamic outputs, and some dependent parameters; figure 3 then shows the comparison of valve lift curves for each scenario. max 05 035 99. 9 .1 . [mm] . 3 1. .9 [-] 21 32 [r m] 1 .2 12. 1 .1 [-] 22. 3 . 2 . [deg ca] 13 .3 . 9 . [mm] 2.11 1. . [ ] okomentoval(a): [a r ]: corrected okomentoval(a): [a ]: he su scri t in the su tion e should e „i“ (5) 4.2.1 overall results results of all three optimization scenarios are summarized in table 4 and figure 3. while table 4 contains the set of optimal (independent – labelled with ‘*’) parameters, main thermodynamic outputs, and some dependent parameters; figure 3 then shows the comparison of valve lift curves for each scenario. the vmax scenario engine turned out as the most effi cient, with the best bsfc value of 214 g/kwh. but it is also the largest of the three engines. the fi nal vmax volume is 2.1 l, with a long stroke rb/s of 0.735, leading to a mean piston speed of 9.70 m/s. large volume means that the engine was able to achieve demanded pe with only 2150 rpm – following the ice down -speeding trend. a look at the figure 3 shows, that the vmax engine uses inlet valve open for extremely short time, running in miller cycle. tendency to push towards miller cycle is well known. however, in comparison to similar previous optimizations [7], the optimizer was given bigger freedom in valve timing parameters, resulting in “stronger” miller cycle. the combination of large volume, low speed, and miller cycle leads to rather small bmep of 7.95 bar, and volumetric effi ciency of only 58.7 %. although such rex engine would hardly fulfi l package requirement, lower bmep engines tend to be robust and reliable, which might be useful for an ice operating at wot right after start -up. vmax concept also has relatively large compression ratio of 14.2. this can seem extreme, but in combination with spark advance of 22 deg ca btdc, and miller cycle especially, it is feasible. the v05 scenario achieves worse bsfc results compared to the vmax variant, with a short stroke rb/s ratio of 1.485, at higher operating speed 3200 rpm, but lower cs of 7.05 m/s. we have parameter b [mm] rb/s [-] rc [-] nice [rpm] sa [deg ca] ivo [deg ca] evc [deg ca] fivc [-] fevo [-] lower limit 60 0.5 6 1000 80 290 320 0.7 0.7 upper limit 100 1.5 15 7000 -10 380 450 1.3 1.3 resolution 0.1 0.005 0.1 50 1 1 1 0.004 0.004 table 3: limits and resolutions of the optimization parameters tabulka 3: rozsahy a rozli$ení optimalizovan"ch parametr% vmax v05 v035 b* 99.50 98.15 75.74 [mm] rb/s* 0.735 1.485 0.975 [-] nice* 2150 3200 4650 [rpm] rc* 14.2 12.7 14.1 [-] sa* 22.0 36.0 27.0 [deg ca] s* 135.37 66.09 77.68 [mm] vd 2.11 1.00 0.70 [l] cs 9.70 7.05 12.04 [m/s] bsfc 214.0 229.8 238.5 [g/kwh] bmep 7.95 11.25 11.07 [bar] &' 58.67 89.27 91.08 [%] &m 92.78 90.70 84.48 [%] table 4: results for all three optimization scenarios tabulka 4: v"slední hodnoty pro v$echny optimaliza&ní scéná'e range extender ice multi -parametric multi -objective optimization mikulá! adámek, rastislav toman mecca 01 2021 page 17 seen some similar behavior before e.g. in [7], but there it was caused probably by the simple chen -flynn friction model [9], that lacks the predictive abilities, and therefore preferred this short -stroke confi guration. in this case, however, we think it is because of achieving good volumetric effi ciency, due to the direct link between the bore size and inlet valves diameter. the fact that v05 engine achieves high bmep of 11.25 bar despite using some level of millerization supports our assumption. compression ratio is 12.7 which is lower than in the previous vmax scenario, due to the short stroke confi guration, that leads to the increased knock tendencies [1]. however, with such a short stroke, even this compression ratio might be technically challenging to achieve. the last v035 scenario was chosen with rather small volume for such power output; the engine bsfc, ice operating speed, and mean piston speed grow accordingly. the optimal rb/s ratio is also a bit surprising, since the engine is slightly long stroke. the reason for this is probably the tendency of vyva! friction model (according to its author) to overrate the piston skirt friction growing with engine bore. another parallel explanation is that bishop’s formula uses the ice operating speed and valve diameter to determine the valvetrain losses: since the valve diameter is linked directly to the engine bore, smaller bore actually leads to relatively high mechanical effi ciency of 84.5 %, despite high rpms and mean piston speed (4650 rpm, 12.04 m/s). yet, the small inlet valve area, pushes the optimizer to change the valve timing approach, compared to the fi rst two scenarios: v035 engine uses a later ivc angle compared to other scenarios. this way the engine achieves suffi cient cylinder fi lling, although with slight backfl ow just before ivc, reducing effective compression ratio thus improving knock robustness. 4.4.2 package comparison from the package standpoint, all three design scenarios were also compared using parametric cad model of v2 engine block, since comparing just their volume is not particularly accurate, because the engine size is strongly infl uenced by rb/s ratio, and con -rod length (figure 4, and table 5). table 5 also contains estimated masses of the main engine components. the vmax engine is by far the largest of the three – as expected. it is rather interesting, that the two other scenarios v05 and v035 are very similar from the package standpoint, though v035 is slightly shorter. according to our cad model, all designs are figure 3: valve lift curves of optimized engines obrázek 3: ventilové zdvihové k'ivky optimalizovan"ch motor% figure 4: engine block cad models (from left vmax, v05, v035) obrázek 4: cad modely blok% (zleva vmax, v05, v035) width [mm] height [mm] length [mm] block mass [kg] piston assembly mass [kg] con-rod mass [kg] con-rod length [mm] vmax 574.8 356.1 192.3 13,15 0,73 0,70 219,9 v05 401.2 231.8 186.6 6,58 0,71 0,54 126,7 v035 389.4 232.5 160.9 5,88 0,36 0,57 144,5 table 5: engine blocks’ dimensions and estimated components’ masses tabulka 5: rozm#ry blok% motor% a odhadnuté hmotnosti hlavních komponent range extender ice multi -parametric multi -objective optimization mikulá! adámek, rastislav toman mecca 01 2021 page 18 feasible; however, v05 variant is on the limit, and some of the design features would be a very tight fi t. 5. potential for future development of the optimization methodology the designs resulting from our optimizations are generally feasible and achieve high yet not unrealistic effi ciencies for ohv designs. despite these positive results, there is still some further potential in the development of our optimization methodology, especially from the viewpoint of the structural design, specifi cally in two areas. the fi rst area is referenced to the fact, that we do not scale the main and conn -rod bearing diameters with bore size. and these are important inputs for vyva! friction model. a change in the con -rod bearing diameter would also infl uence the relation developed for con -rod ratio calculation (equation 4). we have already prepared some possible corrections to this formula, but these will be applied together with the bearing size scaling. the second area is connected to the valve lift scaling. currently we use a scaling coeffi cient f( for the respective intake/exhaust lift vectors (equation 6, where l( is the valve lift and d( the valve diameter) based on heywood’s formula, fi rst introduced in chapter 3.1 on main engine geometry. i ure 4 engine block ca models (from left , , br e 4 ca modely blok (zleva , , ) the engine is by far the largest of the three – as expected. it is rather interesting, that the two other scenarios and are very similar from the package standpoint, though is slightly shorter. according to our ca model, all designs are feasible; however, variant is on the limit, and some of the design features would be a very tight fit. idth mm ei ht mm en th mm loc ass iston assembly ass con-rod ass con-rod en th mm max . 3 .1 192.3 13,1 , 3 , 219,9 05 1.2 231. 1 . , , 1 , 12 , 035 3 9. 232. 1 .9 , ,3 , 1 , able engine blocks’ dimensions and estimated components’ masses abul a rozm ry blok motor a odhadnut hmotnosti hlavn ch komponent . otential for future de elo ment of the o timi ation methodolo y the designs resulting from our optimizations are generally feasible and achieve high yet not unrealistic efficiencies for designs. espite these positive results, there is still some further potential in the development of our optimization methodology, especially from the viewpoint of the structural design, specifically in two areas. the first area is referenced to the fact, that we do not scale the main and conn-rod bearing diameters with bore size. and these are important inputs for vyvaž friction model. a change in the con-rod bearing diameter would also influence the relation developed for con-rod ratio calculation (equation ). we have already prepared some possible corrections to this formula, but these will be applied together with the bearing size scaling. the second area is connected to the valve lift scaling. currently we use a scaling coefficient for the respective intake/exhaust lift vectors (equation , where 𝐿𝐿 is the valve lift and 𝐷𝐷 the valve diameter) based on eywood’s formula, first introduced in chapter 3.1 on main engine geometry. 0 𝐿𝐿 𝐷𝐷 = = 0 𝐷𝐷 𝐿𝐿 ( ) this simple relation gives decent result from the thermodynamic perspective. further increase in the intake valve lift from the optimal value of the design has a small additional positive effect on bsfc, which is clear from figure . (6) this simple relation gives decent result from the thermodynamic perspective. further increase in the intake valve lift from the optimal value of the vmax design has a small additional positive effect on bsfc, which is clear from figure 5. in practice, the lift curve is usually limited by the valve train dynamics. valve acceleration is determined by the lift curve shape – this acceleration relation can be simplifi ed to just valve lift and engine speed. however, rex ice operates only in one primary operating point and it is not controlled by the driver: this means, that there is little chance of over -speeding the engine. the lift curves can be therefore designed exactly for this one operating point, even possibly saving some extra fuel. 6. conclusion our paper presents a multi -parametric, multi -objective design optimization methodology, that was tested on a case of three design scenarios for a four -stroke, v -twin, natural aspirated, spark -ignition rex ice, operating in a single point reev’s operation. we defi ned our rex engine concept, aiming at the best possible balance of achievable mass, package, overall design simplicity and therefore low cost, based on the literature research and using a design selection table. the other layouts that we considered were inline two -cylinder variants with or without balance shaft, and an opposed pistons engine – boxer. thermodynamic 0d/1d model was built within the gt -suite simulation environment, with a special emphasis on predictive ability of its sub -models. our paper briefl y discusses some of these sub -models: ctu in prague in -house built friction model, gt -suite’s phenomenological predictive si combustion model, knock model, and fi nally the in -cylinder heat transfer model. apart from the gt -suite simulation model, our methodology uses also a parametric cad model of the engine block. this cad model provides some important input data for the gt -suite sub-models to enhance the optimization accuracy, and it is also used for the optimization result structural design’s feasibility check. finally, the multi -parametric and multi -objective optimizations of three different design scenarios featuring different engine displacement with the same power output goal were carried out in a modefrontier optimization platform, using a hybrid algorithm pilopt. resulting rex ice designs are realistic, following the current trends of ice effi ciency increase (millerization and down -speeding) and power increase for natural aspirated engine. our future work will mainly focus on further enhancements of our optimization methodology, adding more details of the crank-train mechanism design into the simulation sub -models. future simulation studies will consider different engine layouts. acknowledgements this work was realized using support of: • technological agency, czech republic, programme national competence centres, project # tn01000026 josef bozek national center of competence for surface vehicles. figure 5: bsfc dependence on the inlet valve lift for vmax scenario obrázek 5: závislost m#rné spot'eby na zdvihu sacího ventilu pro scéná' vmax range extender ice multi -parametric multi -objective optimization mikulá! adámek, rastislav toman mecca 01 2021 page 19 • the grant agency of the czech technical university in prague, grant no. sgs19/104/ohk2/2t/12. this support is gratefully acknowledged. list of abbreviations btdc bottom top dead center cad computer aided design cae computer aided engineering ctu czech technical university in prague egr exhaust gas recirculation fe finite element i2 inline two -cylinder engine i3 inline three -cylinder engine ice internal combustion engine nvh noise vibration and harshness oem original equipment manufacturer ohv over head valve reev range extended electric vehicle rex range extender si spark ignition sohc single over head camshaft tdc top dead center v2 v -twin engine wot wide open throttle fmep friction mean effective pressure bmep brake mean effective pressure bsfc brake -specifi c fuel consumption ca crank angle list of symbols af flame area bm maximum laminar speed b) laminar speed roll -of value ck flame kernel growth multiplier cs turbulent fl ame speed multiplier c$ taylor length scale multiplier dvex exhaust valve diameter dvin intake valve diameter fv valve lift scaling coeffi cient lvex maximum exhaust valve lift lvin maximum intake valve lift lt turbulent length scale mb burnup mass me entrained mass pe ice brake power rb/s bore/stroke ratio rf flame radius sl laminar fl ame speed st turbulent fl ame speeds vd ice displacement xk,max pareto set’s maximum value of the objective function xk optimization objective function cs mean piston speed nice engine speed p0 reference pressure rc compression ratio %k criterial function weight coeffi cient &m mechanical effi ciency &v volumetric effi ciency "u density of unburned gas )m fuel/air equivalence ratio at maximum laminar fl ame speed b bore dem dilution exponent multiplier dil mass fraction of the residuals in the unburned zone f criterial function s stroke sa spark advance angle c con -rod ratio relation coeffi cient 1 n con -rod ratio relation coeffi cient 2 p pressure u´ mean fl uctuating turbulent velocity * pressure exponent $ con -rod ratio ) fuel/air equivalence ratio references [1] turner j, blake d, moore j, et al. (2010) the lotus range extender engine. sae international 2010-01-2208:34. https://doi.org/10.4271/2010-01-2208 [2] andert j, kohler e, niehues j, schurmann g (2012) kspg range extender: a new pathfinder to electromobility. mtz worldwide 2012:7. https://doi.org/10.1007/s38313-012-0170-1 [3] agarwal a, lewis a, akehurst s, et al. development of a low cost production automotive engine for range extender application for electric vehicles. sae international 2016-01-1055. https://doi.org/10.4271/2016-01-1055 [4] atzwanger m, hubmann c, schoeffmann w, et al. two -cylinder gasoline engine concept for highly integrated range extender and hybrid powertrain applications. sae international 2010-09-28. https://doi.org/10.4271/2010-32-0130 [5] fraidl gk, fisher r, hubmann c, et al. (2009) range extender module: enabler for electric mobility. atzautotechnology 2009:40 – 49. https://doi.org/10.1007/bf03247140 range extender ice multi -parametric multi -objective optimization mikulá! adámek, rastislav toman mecca 01 2021 page 20 [6] bogomolov s, dolecek v, macek j, et al. (2014) combining thermodynamics and design optimization for finding ice downsizing limits: 2014-04-01. sae international 2014. https://doi.org/10.4271/2014-01-1098 [7] toman r, brankov i (2018) multi-parametric and multiobjective thermodynamic optimization of a sparkignition range extender ice. sciendo 2018:459 – 466. https://doi.org/0.5604/01.3001.0012.4368 [8] bassett m, thatcher i, bisordi a, et al. design of a dedicated range extender engine. sae international 2011-01-0862. https://doi.org/10.4271/2011-01-0862 [9] heywood, john. internal combustion engine fundamentals. 1. new york: mcgraw-hill, 1988. isbn 978-0070286375. [10] macek j, fuente d, emrich m (2011) a simple physical model of ice mechanical losses. sae international 2011-01-0610. https://doi.org/10.4271/2011-01-0610 [11] mirzaeian m, millo f, rolando l (2016) assessment of the predictive capabilities of a combustion model for a modern downsized turbocharged si engine. sae international 2016-01-0557. https://doi.org/10.4271/2016-01-0557 [12] rastislav t, jan m (2017) evaluation of the predictive capabilities of a phenomenological combustion model for natural gas si engine. journal of middle european construction and design of cars: the journal of czech technical university 2017:37 – 48. https://doi.org/10.1515/mecdc20170007 [13] fogla n, bybee m, mirzaeian m, et al. (2017) development of a k-k-# phenomenological model to predict in-cylinder turbulence. sae international journal of engines 10:562 – 575. https://doi.org/10.4271/2017-01-0542 [14] woschni g (1967) a universally applicable equation for the instantaneous heat transfer coeffi cient in the internal combustion engine. sae international 670931. https://doi.org/10.4271/670931 [15] ra y, reitz r (2008) a reduced chemical kinetic model for ic engine combustion simulations with primary reference fuels. sciencedirect 2008:713 – 738. https://doi.org/10.1016/j.combustfl ame.2008.05.002 [16] adámek m (2020) optimalizace termodynamiky a konstrukce spalovacího motoru pro range extender. diplomová práce [17] modefrontier user guide: release 2018r3, 2018 ed.. esteco vehicle si engine with mpi of liquid state lpg stanislav beroun, pavel brabec, aleš dittrich mecca 01 2016 page 41 doi: 10.1515/mecdc-2016-0004 vehicle si engine with mpi of liquid state lpg stanislav beroun, pavel brabec, aleš dittrich 1. introduction vehicle producers are currently focused primarily on cng as an alternative gas fuel for si engine powered vehicles. however, some properties of lpg remain of interest with respect to use by private car owners. in addition, there has recently been growing interest in the use of lpg for dual fuel diesel-gas engines. the most widespread method of mixture formation for a naturally aspirated si engine running on lpg is the injection of lpg in its gaseous state into the intake air. such si engines have around 5 – 8% lower power in comparison with an engine running on petrol. the cause of this power drop is the reduction in the fresh mass of air as a consequence of the volume of gaseous fuel in the fresh mixture. fuel systems for injection of gaseous state lpg often have a big problem at low ambient temperatures (low lpg pressure inside the pressure tank), which complicates the engine running in wintertime. a promising solution for a naturally aspirated si vehicle engine running on lpg fuel is mixture formation by injection of lpg in its liquid state into the intake manifold. very intensive evaporation stanislav beroun, pavel brabec, aleš dittrich technical university of liberec, studentská 2, cz 461 17 liberec, czech republic; department of vehicles and engines, mechanical engineering faculty; institute for nanomaterials, advanced technologies and innovation email: stanislav.beroun@tul.cz shrnutí v úvodní části článku jsou připomenuty možné způsoby tvoření směsi lpg se vzduchem (vstřikování lpg v plynném nebo kapalném stavu) a jejich vliv na provozní vlastnosti zážehového motoru. další kapitola vysvětluje děje, které působí na průběh vstřikování lpg v kapalném stavu do nasávaného vzduchu v sacím potrubí motoru. pomocí zjednodušeného výpočtového modelu je ukázáno, že vstřikování lpg v kapalném stavu je principiálně spojeno s extrémně nízkými teplotami lpg na výtoku ze vstřikovací trysky a s rizikem tvoření námrazy na výtokové trysce a příp. i v sacím potrubí. v článku je ukázána konstrukční úprava koncové části vstřikovače lpg s potlačeným rizikem pro tvoření námrazy. výsledky experimentálního výzkumu na zkušebním zážehovém motoru s tvořením směsi vstřikováním lpg v kapalném stavu ukazují velmi kvalitní vlastnosti motoru. měření průběhu tlaku lpg v koncové části vstřikovače a měření teplot na výtokové trysce potvrzují výsledky provedených výpočtů. měření na zkušebním motoru doplňují vizualizace vstřikování lpg do sacího potrubí. v závěru článku je souhrn poznatků z výzkumu tvoření směsi vstřikováním lpg v kapalném stavu do sacího potrubí motoru. klíčová slova: zážehový motor, vstřikování lpg v kapalném stavu, výkon motoru, námraza v sacím potrubí abstract the first part of the article reviews the possible methods for lpg and air mixture forming (injection of gaseous or liquid state lpg) and their influence on the operating properties of an si engine. the next chapter explains the processes that take place when liquid state lpg is injected into the air flow of an internal combustion engine intake manifold. a simplified calculation is used to show that the injection of liquid state lpg is associated with extreme low temperature of the lpg injected into intake manifold and with ice formation on the outlet nozzle. the article sets out the design of an end part injector (epi) for liquid state lpg that reduces the risk of icing of the outlet nozzle. the results of experimental research indicate very good operational properties for a vehicle si engine with the combustion mixture formed by the injection of liquid state lpg into the engine intake manifold. the calculation results are confirmed by recording plots of lpg pressure inside the end part of injector (epi) and the temperature on the outlet nozzle (on) of the lpg injector. visual inspection of injection of liquid state lpg into the intake manifold clearly supports the performed measurements. the conclusions summarize the knowledge gained from the laboratory investigation of liquid state lpg injection into an engine intake manifold. key words: si engine, liquid state lpg injection, engine power, icing inside intake manifold vehicle si engine with mpi of liquid state lpg vehicle si engine with mpi of liquid state lpg stanislav beroun, pavel brabec, aleš dittrich mecca 01 2016 page 42 of injected liquid state lpg leads to a drop in the temperature of the fresh mixture and subsequently to increased filling efficiency of the engine. this means the engine power when running on lpg is in effect equivalent to, or even slightly better than that of the engine running on petrol. however, an effect of the very low lpg temperature on the lpg injector outlet nozzle (on) on intake manifold (the lpg temperature is between -30°c and -55°c) is to cause icing on the on of lpg injector from the humidity of atmospheric air. fragments of ice are imported into the engine cylinder and can lead to an irregular misfire of the mixture in the engine cylinder. an si engine with injection of liquid state lpg must therefore have a special design of epi to prevent icing. the fuel system for injection of liquid state lpg is less sensitive to poorly evaporating substances in lpg than lpg fuel systems using an evaporator and pressure regulator for lpg injection in the gaseous state. however, fuel systems for injection of liquid state lpg require a special fuel pump (generally inside the pressure tank) and lpg pressure regulator, needed for both lpg injection and continual lpg flow through the electromagnetic valve of the lpg injectors (to prevent formation of lpg steam bubbles inside electromagnetic valves) and the return flow of lpg to the pressure tank. mixture formation by injection of liquid state lpg can be considered a promising approach both for si engines and for dual diesel-gas engines. 2. injection of liquid state lpg into the engine intake manifold figure 1 shows the lay-out of the liquid state lpg injector. the lpg injector consists of the electromagnetic valve (ev) which supplies the lpg charge (synchronized with the suction of the individual engine cylinders) to the end part injector (epi) in the intake manifold of each cylinder (mpi concept). after outflow of the lpg to the epi, there is a significant lpg pressure drop in the epi and then very rapid vaporization. the heat energy needed for evaporation is taken from the thermal energy of the lpg feed into the epi and to a lesser extent heat for the lpg evaporation is ambient heat transferred into the epi. the wet lpg steam, which has a very low temperature due to the intensive evaporation of lpg in the epi, is then injected into the inlet air. using a simplified computational simulation of the process in the epi, the relationships between the inside volume geometry of the epi, state quantities of lpg inside the epi and the outflow of the wet lpg steam into the engine intake manifold were investigated [1]. a brief description of the computation procedure of the lpg process in the epi is given in the following paragraph. the lpg charge is fed from the ev to the epi in elementary quantities ∆mlpg/liq. within the entire volume of the channels vepi before the outlet nozzle (on), part of the lpg vaporizes and part remains in liquid state and thus a wet lpg steam arises in the epi. we can express the density of wet lpg steam in the volume vepi as the sum of the density of lpg saturated steam and the density of the dispersed lpg liquid droplets. power in comparison with an engine running on petrol. the cause of this power drop is the reduction in the fresh mass of air as a consequence of the volume of gaseous fuel in the fresh mixture. fuel systems for injection of gaseous state lpg often have a big problem at low ambient temperatures (low lpg pressure inside the pressure tank), which complicates the engine running in wintertime. a promising solution for a naturally aspirated si vehicle engine running on lpg fuel is mixture formation by injection of lpg in its liquid state into the intake manifold. very intensive evaporation of injected liquid state lpg leads to a drop in the temperature of the fresh mixture and subsequently to increased filling efficiency of the engine. this means the engine power when running on lpg is in effect equivalent to, or even slightly better than that of the engine running on petrol. however, an effect of the very low lpg temperature on the lpg injector outlet nozzle (on) on intake manifold (the lpg temperature is between -300c and -550c) is to cause icing on the on of lpg injector from the humidity of atmospheric air. fragments of ice are imported into the engine cylinder and can lead to an irregular misfire of the mixture in the engine cylinder. an si engine with injection of liquid state lpg must therefore have a special design of epi to prevent icing. the fuel system for injection of liquid state lpg is less sensitive to poorly evaporating substances in lpg than lpg fuel systems using an evaporator and pressure regulator for lpg injection in the gaseous state. however, fuel systems for injection of liquid state lpg require a special fuel pump (generally inside the pressure tank) and lpg pressure regulator, needed for both lpg injection and continual lpg flow through the electromagnetic valve of the lpg injectors (to prevent formation of lpg steam bubbles inside electromagnetic valves) and the return flow of lpg to the pressure tank. mixture formation by injection of liquid state lpg can be considered a promising approach both for si engines and for dual diesel-gas engines. 2. injection of liquid state lpg into the engine intake manifold. fig. 1 shows the lay-out of the liquid state lpg injector. the lpg injector consists of the electromagnetic valve (ev) which supplies the lpg charge (synchronized with the suction of the individual engine cylinders) to the end part injector (epi) in the intake manifold of each cylinder (mpi concept). after outflow of the lpg to the epi, there is a significant lpg pressure drop in the epi and then very rapid vaporization. the heat energy needed for evaporation is taken from the thermal energy of the lpg feed into the epi and to a lesser extent heat for the lpg evaporation is ambient heat transferred into the epi. the wet lpg steam, which has a very low temperature due to the intensive evaporation of lpg in the epi, is then injected into the inlet air. using a simplified computational simulation of the process in the epi, the relationships between the inside volume geometry of the epi, state quantities of lpg inside the epi and the outflow of the wet lpg steam into the engine intake manifold were investigated 1]. a brief description of the computation procedure of the lpg process in the epi is given in the following paragraph. the lpg charge is fed from the ev to the epi in elementary quantities mlpg/liq. within the entire volume of the channels vepi before the outlet nozzle (on), part of the lpg vaporizes and part remains in liquid state and thus a wet lpg steam arises in the epi. we can express the density of wet lpg steam in the volume vepi as the sum of the density of lpg saturated steam and the density of the dispersed lpg liquid droplets. epiliqlpgepigaslpgepilpg /////   . (1) the proportion of the vaporized lpg in vepi determines the thermal balance of the lpg state inside the epi. the density of lpg saturated steam (gaseous state) depends on the lpg pressure and temperature inside the epi (volume vepi): epilpglpg epilpg epigaslpg tr p / / //   (2)                            (1) the proportion of the vaporized lpg in vepi determines the thermal balance of the lpg state inside the epi. the density of lpg saturated steam (gaseous state) depends on the lpg pressure and temperature inside the epi (volume vepi): power in comparison with an engine running on petrol. the cause of this power drop is the reduction in the fresh mass of air as a consequence of the volume of gaseous fuel in the fresh mixture. fuel systems for injection of gaseous state lpg often have a big problem at low ambient temperatures (low lpg pressure inside the pressure tank), which complicates the engine running in wintertime. a promising solution for a naturally aspirated si vehicle engine running on lpg fuel is mixture formation by injection of lpg in its liquid state into the intake manifold. very intensive evaporation of injected liquid state lpg leads to a drop in the temperature of the fresh mixture and subsequently to increased filling efficiency of the engine. this means the engine power when running on lpg is in effect equivalent to, or even slightly better than that of the engine running on petrol. however, an effect of the very low lpg temperature on the lpg injector outlet nozzle (on) on intake manifold (the lpg temperature is between -300c and -550c) is to cause icing on the on of lpg injector from the humidity of atmospheric air. fragments of ice are imported into the engine cylinder and can lead to an irregular misfire of the mixture in the engine cylinder. an si engine with injection of liquid state lpg must therefore have a special design of epi to prevent icing. the fuel system for injection of liquid state lpg is less sensitive to poorly evaporating substances in lpg than lpg fuel systems using an evaporator and pressure regulator for lpg injection in the gaseous state. however, fuel systems for injection of liquid state lpg require a special fuel pump (generally inside the pressure tank) and lpg pressure regulator, needed for both lpg injection and continual lpg flow through the electromagnetic valve of the lpg injectors (to prevent formation of lpg steam bubbles inside electromagnetic valves) and the return flow of lpg to the pressure tank. mixture formation by injection of liquid state lpg can be considered a promising approach both for si engines and for dual diesel-gas engines. 2. injection of liquid state lpg into the engine intake manifold. fig. 1 shows the lay-out of the liquid state lpg injector. the lpg injector consists of the electromagnetic valve (ev) which supplies the lpg charge (synchronized with the suction of the individual engine cylinders) to the end part injector (epi) in the intake manifold of each cylinder (mpi concept). after outflow of the lpg to the epi, there is a significant lpg pressure drop in the epi and then very rapid vaporization. the heat energy needed for evaporation is taken from the thermal energy of the lpg feed into the epi and to a lesser extent heat for the lpg evaporation is ambient heat transferred into the epi. the wet lpg steam, which has a very low temperature due to the intensive evaporation of lpg in the epi, is then injected into the inlet air. using a simplified computational simulation of the process in the epi, the relationships between the inside volume geometry of the epi, state quantities of lpg inside the epi and the outflow of the wet lpg steam into the engine intake manifold were investigated 1]. a brief description of the computation procedure of the lpg process in the epi is given in the following paragraph. the lpg charge is fed from the ev to the epi in elementary quantities mlpg/liq. within the entire volume of the channels vepi before the outlet nozzle (on), part of the lpg vaporizes and part remains in liquid state and thus a wet lpg steam arises in the epi. we can express the density of wet lpg steam in the volume vepi as the sum of the density of lpg saturated steam and the density of the dispersed lpg liquid droplets. epiliqlpgepigaslpgepilpg /////   . (1) the proportion of the vaporized lpg in vepi determines the thermal balance of the lpg state inside the epi. the density of lpg saturated steam (gaseous state) depends on the lpg pressure and temperature inside the epi (volume vepi): epilpglpg epilpg epigaslpg tr p / / //   (2)                            (2)   for the expression of the proportion of vaporized lpg in the epi the following relationship for saturation of the wet lpg steam was used:                           liquidlpg epilpg evaporkx / /1   ,     ( 3/ /550 mkgliquidlpg  ). (3) the value of the evaporation correction factor kevapor is determined by calibration of the computational model using the measured traces of lpg pressure inside the epi. the thermal balance for the wet lpg steam in the epi (simplified, ignoring the effect of the specific thermal capacities of the gas and liquid phases on temperature) comprises the following: heat contained in the lpg (lpgliq + lpggas) at the start of each calculation step  (0.2 ms) in the epi.   heat contained in the liquid lpg fed into the epi in the quantity mlpg/liq at the start of each calculation step.   ambient heat which transfers to the lpg inside epi at each calculation step. heat needed for lpg evaporation in the given calculation step for the estimated saturation of wet lpg steam. the temperature of the wet lpg steam is determined from the thermal balance for lpg inside the epi. the pressure of wet lpg steam inside the epi is determined by computing the relationship between temperature and pressure for saturated lpg steam (the relationship between temperature and pressure of saturated lpg steam is shown in fig. 2 for an lpg composition of propane and butane 50/50). figure 1: injector for liquid lpg injection. heating element in the lower part of the epi is for heating the outlet nozzle only (precaution against icing on the on, heat transfer from the heating element to the main part of the epi is minimal). obrázek 1: schéma vstřikovače kapalného lpg. topný element v nejspodnější partii koncové části vstřikovače (epi) je pro ohřev výtokové trysky (on) jako opatření proti vzniku námrazy na on, prostup tepla do hlavní části epi je minimální. ev epi liquid lpg plpg (supply, 12 bar) piezoresistive pressure sensor wet lpg steam: vepi , (mlpg/gas+ mlpg/liq), xlpg/steam , plpg/epi , tlpg/epi intake manifold heating element pint/man air  outlet nozzle (on) son, µon thermocouple heat transfer from ambient figure 1: injector for liquid lpg injection. heating element in the lower part of the epi is for heating the outlet nozzle only (precaution against icing on the on, heat transfer from the heating element to the main part of the epi is minimal). obrázek 1: schéma vstřikovače kapalného lpg. topný element v nejspodnější partii koncové části vstřikovače (epi) je pro ohřev výtokové trysky (on) jako opatření proti vzniku námrazy na on, prostup tepla do hlavní části epi je minimální. for the expression of the proportion of vaporized lpg in the epi the following relationship for saturation of the wet lpg steam was used:   for the expression of the proportion of vaporized lpg in the epi the following relationship for saturation of the wet lpg steam was used:                           liquidlpg epilpg evaporkx / /1   ,     ( 3/ /550 mkgliquidlpg  ). (3) the value of the evaporation correction factor kevapor is determined by calibration of the computational model using the measured traces of lpg pressure inside the epi. the thermal balance for the wet lpg steam in the epi (simplified, ignoring the effect of the specific thermal capacities of the gas and liquid phases on temperature) comprises the following: heat contained in the lpg (lpgliq + lpggas) at the start of each calculation step  (0.2 ms) in the epi.   heat contained in the liquid lpg fed into the epi in the quantity mlpg/liq at the start of each calculation step.   ambient heat which transfers to the lpg inside epi at each calculation step. heat needed for lpg evaporation in the given calculation step for the estimated saturation of wet lpg steam. the temperature of the wet lpg steam is determined from the thermal balance for lpg inside the epi. the pressure of wet lpg steam inside the epi is determined by computing the relationship between temperature and pressure for saturated lpg steam (the relationship between temperature and pressure of saturated lpg steam is shown in fig. 2 for an lpg composition of propane and butane 50/50). figure 1: injector for liquid lpg injection. heating element in the lower part of the epi is for heating the outlet nozzle only (precaution against icing on the on, heat transfer from the heating element to the main part of the epi is minimal). obrázek 1: schéma vstřikovače kapalného lpg. topný element v nejspodnější partii koncové části vstřikovače (epi) je pro ohřev výtokové trysky (on) jako opatření proti vzniku námrazy na on, prostup tepla do hlavní části epi je minimální. ev epi liquid lpg plpg (supply, 12 bar) piezoresistive pressure sensor wet lpg steam: vepi , (mlpg/gas+ mlpg/liq), xlpg/steam , plpg/epi , tlpg/epi intake manifold heating element pint/man air  outlet nozzle (on) son, µon thermocouple heat transfer from ambient   for the expression of the proportion of vaporized lpg in the epi the following relationship for saturation of the wet lpg steam was used:                           liquidlpg epilpg evaporkx / /1   ,     ( 3/ /550 mkgliquidlpg  ). (3) the value of the evaporation correction factor kevapor is determined by calibration of the computational model using the measured traces of lpg pressure inside the epi. the thermal balance for the wet lpg steam in the epi (simplified, ignoring the effect of the specific thermal capacities of the gas and liquid phases on temperature) comprises the following: heat contained in the lpg (lpgliq + lpggas) at the start of each calculation step  (0.2 ms) in the epi.   heat contained in the liquid lpg fed into the epi in the quantity mlpg/liq at the start of each calculation step.   ambient heat which transfers to the lpg inside epi at each calculation step. heat needed for lpg evaporation in the given calculation step for the estimated saturation of wet lpg steam. the temperature of the wet lpg steam is determined from the thermal balance for lpg inside the epi. the pressure of wet lpg steam inside the epi is determined by computing the relationship between temperature and pressure for saturated lpg steam (the relationship between temperature and pressure of saturated lpg steam is shown in fig. 2 for an lpg composition of propane and butane 50/50). figure 1: injector for liquid lpg injection. heating element in the lower part of the epi is for heating the outlet nozzle only (precaution against icing on the on, heat transfer from the heating element to the main part of the epi is minimal). obrázek 1: schéma vstřikovače kapalného lpg. topný element v nejspodnější partii koncové části vstřikovače (epi) je pro ohřev výtokové trysky (on) jako opatření proti vzniku námrazy na on, prostup tepla do hlavní části epi je minimální. ev epi liquid lpg plpg (supply, 12 bar) piezoresistive pressure sensor wet lpg steam: vepi , (mlpg/gas+ mlpg/liq), xlpg/steam , plpg/epi , tlpg/epi intake manifold heating element pint/man air  outlet nozzle (on) son, µon thermocouple heat transfer from ambient (3) the value of the evaporation correction factor kevapor is determined by calibration of the computational model using the measured traces of lpg pressure inside the epi. the thermal balance for the wet lpg steam in the epi (simplified, ignoring the effect of the specific thermal capacities of the gas and liquid phases on temperature) comprises the following: • heat contained in the lpg (lpg liq + lpg gas ) at the start of each calculation step ∆τ (0.2 ms) in the epi. vehicle si engine with mpi of liquid state lpg stanislav beroun, pavel brabec, aleš dittrich mecca 01 2016 page 43 • heat contained in the liquid lpg fed into the epi in the quantity ∆mlpg/liq at the start of each calculation step. • ambient heat which transfers to the lpg inside epi at each calculation step. • heat needed for lpg evaporation in the given calculation step for the estimated saturation of wet lpg steam. • the temperature of the wet lpg steam is determined from the thermal balance for lpg inside the epi. the pressure of wet lpg steam inside the epi is determined by computing the relationship between temperature and pressure for saturated lpg steam (the relationship between temperature and pressure of saturated lpg steam is shown in figure 2 for an lpg composition of propane and butane 50/50). figure 2 clearly illustrates the problem associated with the injection of liquid lpg into the engine intake manifold. after outflow of the liquid lpg from the ev into volume vepi in the epi, the lpg pressure decreases rapidly from plpg/liq = ~ 12  bar to plpg/vepi = ~ 1  bar (according to operating conditions of an si engine the lpg pressure in the epi drops to the pressure in the intake manifold pint/man) and the lpg temperature drops to tlpg/vepi ≈ -30°c (or lower) at start of intensive lpg evaporation. • the outflow of the wet lpg steam into the intake manifold is treated as an outflow of a gas. only saturated steam has the properties of gas, the outflow of which carries lpg droplets. in the calculation, the elementary quantities carried in the liquid phase (droplets) are included using the proportion of vaporized lpg (quantity x for the saturation of wet steam) inside the epi. fig. 2 clearly illustrates the problem associated with the injection of liquid lpg into the engine intake manifold. after outflow of the liquid lpg from the ev into volume vepi in the epi, the lpg pressure decreases rapidly from plpg/liq  12 bar to barp epivlpg 1/  (according to operating conditions of an si engine the lpg pressure in the epi drops to the pressure in the intake manifold pint/man) and the lpg temperature drops to ct epivlpg 0 / 30 (or lower) at start of intensive lpg evaporation. 0 2 4 6 8 -40 -30 -20 -10 0 10 20 30 temperature [oc] p re ss u re [ b ar ]   figure 2: the pressure of saturated lpg steam as a function of temperature for the composition propane and butane 50/50 at lpg 2]. obrázek 2: závislost tlaku nasycených par lpg na teplotě pro obsah propanu a butanu v lpg 50/50 2]. the outflow of the wet lpg steam into the intake manifold is treated as an outflow of a gas. only saturated steam has the properties of gas, the outflow of which carries lpg droplets. in the calculation, the elementary quantities carried in the liquid phase (droplets) are included using the proportion of vaporized lpg (quantity x for the saturation of wet steam) inside the epi.   onlpggasonlpggasonononlpg wx sm /// 1       (4)  substitution of the relationships for the velocity and density of lpg gaseous state at the on (respecting subcritical and critical outflow) gives the following formula:                                            lpg lpg lpg epilpg manin epilpg manin epilpglpg epilpg lpg lpgon ononlpg p p p p tr p x s m 1 / / 2 / / / 2 / / 11 2   (5)     the calculation procedure repeats through the injection of the whole liquid lpg charge from the ev to the epi up the outflow of wet lpg steam into the intake manifold. the computational model conforms relatively well with the results of measured lpg pressure plots inside the epi for the value of the evaporation correction factor kevapor  0.8. fig. 3 shows the calculated plot of lpg pressure and temperature inside the epi and the measured plot of lpg pressure inside the epi. the lpg temperature plot inside the epi is the outcome of thermal balance; the plot of calculated pressure into epi corresponds to the relationship between temperature t and pressure p in fig. 2. note: the lpg pressure inside the epi was measured on the injector inserted into a model intake manifold connected to the suction of a diesel engine (the intake air pressure in the model intake manifold was practically constant, barp man 1/int  ): the diesel engine was used as a generator for the air (4) substitution of the relationships for the velocity and density of lpg gaseous state at the on (respecting subcritical and critical outflow) gives the following – see formula (5). • the calculation procedure repeats through the injection of the whole liquid lpg charge from the ev to the epi up the outflow of wet lpg steam into the intake manifold. the computational model conforms relatively well with the results of measured lpg pressure plots inside the epi for the value of the evaporation correction factor kevapor = ~ 0.8. figure 3 shows the calculated plot of lpg pressure and temperature inside the epi and the measured plot of lpg pressure inside the epi. the lpg temperature plot inside the epi is the outcome of thermal balance; the plot of calculated pressure into epi corresponds to the relationship between temperature t and pressure ρ in figure 2. note: the lpg pressure inside the epi was measured on the injector inserted into a model intake manifold connected to the suction of a diesel engine (the intake air pressure in the model intake manifold was practically constant, pint/man = ~ 1  bar): the diesel engine was used as a generator for the air flow in the model intake manifold and also ensured the smooth combustion of the combustible mixture from the model intake manifold. fig. 2 clearly illustrates the problem associated with the injection of liquid lpg into the engine intake manifold. after outflow of the liquid lpg from the ev into volume vepi in the epi, the lpg pressure decreases rapidly from plpg/liq  12 bar to barp epivlpg 1/  (according to operating conditions of an si engine the lpg pressure in the epi drops to the pressure in the intake manifold pint/man) and the lpg temperature drops to ct epivlpg 0 / 30 (or lower) at start of intensive lpg evaporation. 0 2 4 6 8 -40 -30 -20 -10 0 10 20 30 temperature [oc] pr es su re [b ar ]   figure 2: the pressure of saturated lpg steam as a function of temperature for the composition propane and butane 50/50 at lpg 2]. obrázek 2: závislost tlaku nasycených par lpg na teplotě pro obsah propanu a butanu v lpg 50/50 2]. the outflow of the wet lpg steam into the intake manifold is treated as an outflow of a gas. only saturated steam has the properties of gas, the outflow of which carries lpg droplets. in the calculation, the elementary quantities carried in the liquid phase (droplets) are included using the proportion of vaporized lpg (quantity x for the saturation of wet steam) inside the epi.   onlpggasonlpggasonononlpg wx sm /// 1       (4)  substitution of the relationships for the velocity and density of lpg gaseous state at the on (respecting subcritical and critical outflow) gives the following formula:                                            lpg lpg lpg epilpg manin epilpg manin epilpglpg epilpg lpg lpgon ononlpg p p p p tr p x s m 1 / / 2 / / / 2 / / 11 2   (5)     the calculation procedure repeats through the injection of the whole liquid lpg charge from the ev to the epi up the outflow of wet lpg steam into the intake manifold. the computational model conforms relatively well with the results of measured lpg pressure plots inside the epi for the value of the evaporation correction factor kevapor  0.8. fig. 3 shows the calculated plot of lpg pressure and temperature inside the epi and the measured plot of lpg pressure inside the epi. the lpg temperature plot inside the epi is the outcome of thermal balance; the plot of calculated pressure into epi corresponds to the relationship between temperature t and pressure p in fig. 2. note: the lpg pressure inside the epi was measured on the injector inserted into a model intake manifold connected to the suction of a diesel engine (the intake air pressure in the model intake manifold was practically constant, barp man 1/int  ): the diesel engine was used as a generator for the air figure 2: the pressure of saturated lpg steam as a function of temperature for the composition propane and butane 50/50 at lpg [2]. obrázek 2: závislost tlaku nasycených par lpg na teplotě pro obsah propanu a butanu v lpg 50/50 [2]. 0,5 1,0 1,5 2,0 2,5 0 30 60 90 120 150 180 210 [deg ca] pr es su re [b ar a b s] 245 250 255 260 265 te m pe ra tu re [k ] 3000rpm-8ms-calcul 3000rpm-8ms-measur temp-3000rpm-8ms-calcul figure 3: the calculated and measured plots of lpg pressure inside the epi illustrate acceptable correlation in describing the injection mechanism for liquid lpg (the differences at the initial phase of liquid lpg charging from ev to epi are likely caused by a transport delay between ev and vepi inside the epi). obrázek 3: vypočtený a změřený průběh tlaku lpg v epi dokumentuje přijatelnou správnost popisu mechanizmu vstřikování kapalného lpg (rozdíl v počáteční fázi dodávky výtoku lpg z ev do epi je zřejmě důsledkem dopravního zpoždění mezi ev a objemem vepi uvnitř epi). fig. 2 clearly illustrates the problem associated with the injection of liquid lpg into the engine intake manifold. after outflow of the liquid lpg from the ev into volume vepi in the epi, the lpg pressure decreases rapidly from plpg/liq  12 bar to barp epivlpg 1/  (according to operating conditions of an si engine the lpg pressure in the epi drops to the pressure in the intake manifold pint/man) and the lpg temperature drops to ct epivlpg 0 / 30 (or lower) at start of intensive lpg evaporation. 0 2 4 6 8 -40 -30 -20 -10 0 10 20 30 temperature [oc] pr es su re [b ar ]   figure 2: the pressure of saturated lpg steam as a function of temperature for the composition propane and butane 50/50 at lpg 2]. obrázek 2: závislost tlaku nasycených par lpg na teplotě pro obsah propanu a butanu v lpg 50/50 2]. the outflow of the wet lpg steam into the intake manifold is treated as an outflow of a gas. only saturated steam has the properties of gas, the outflow of which carries lpg droplets. in the calculation, the elementary quantities carried in the liquid phase (droplets) are included using the proportion of vaporized lpg (quantity x for the saturation of wet steam) inside the epi.   onlpggasonlpggasonononlpg wx sm /// 1       (4)  substitution of the relationships for the velocity and density of lpg gaseous state at the on (respecting subcritical and critical outflow) gives the following formula:                                            lpg lpg lpg epilpg manin epilpg manin epilpglpg epilpg lpg lpgon ononlpg p p p p tr p x s m 1 / / 2 / / / 2 / / 11 2   (5)     the calculation procedure repeats through the injection of the whole liquid lpg charge from the ev to the epi up the outflow of wet lpg steam into the intake manifold. the computational model conforms relatively well with the results of measured lpg pressure plots inside the epi for the value of the evaporation correction factor kevapor  0.8. fig. 3 shows the calculated plot of lpg pressure and temperature inside the epi and the measured plot of lpg pressure inside the epi. the lpg temperature plot inside the epi is the outcome of thermal balance; the plot of calculated pressure into epi corresponds to the relationship between temperature t and pressure p in fig. 2. note: the lpg pressure inside the epi was measured on the injector inserted into a model intake manifold connected to the suction of a diesel engine (the intake air pressure in the model intake manifold was practically constant, barp man 1/int  ): the diesel engine was used as a generator for the air (5) vehicle si engine with mpi of liquid state lpg stanislav beroun, pavel brabec, aleš dittrich mecca 01 2016 page 44 the model calculations were primarily for research, but the results were also used for epi design with heating of the outlet nozzle and subsequently for experimental research on an si engine. 3. experimental research on si engine with mpi of liquid state lpg experimental research was performed on a vehicle si engine type ea111.03e (three-cylinder engine with 1.2 dm3 total displacement). standard as well as an advanced measuring technique normally used for overall research of an si engine on a test bench (high pressure indication with on-line thermodynamic analysis, exhaust emissions, visual monitoring of liquid state lpg injection into the suction manifold). lpg injectors and epi with heating of outlet nozzle (own design of epi) were installed into the intake manifold. a vialle lpg fuel system was used for alternative engine running on petrol or lpg. figures 4 and 5 show the lay-out of the epi on intake manifold and detail of the epi design. the engine was set to run on lpg based on the original ecu setting for petrol fuel. the ignition timing for the engine running on lpg was the same as for petrol fuel (ba95). based on experience from previous research on a similar engine [3], in the higher-load regime the engine ea111.03e-lpg across all revolutions was set to a less rich mixture than the ecu would set as standard when running on ba95 (the start of fuel inject was almost identical for both lpg and ba95, in the ecu for lpg it was only possible to adjust to a limited extent using a correction period for opening the lpg injectors, thus the size of the injected lpg dose). when adjusting and taking readings from the engine, on-line diagnostics was performed using high-pressure indication. for all cylinders the pressure plots have very similar characteristic parameters both running on lpg and on ba95. the cases of knocking were of lower intensity for the engine running on lpg (in comparison to running on ba95), and the knocking was suppressed by the standard activity of the ecu (decreasing spark advance – checking by reading recorded data from ecu). the results of exhaust emission measurements on the engine ea111.03e-lpg running on both lpg and ba95 conform to the former emissions measurements on engine ea111.03d-lpg [3]. the differences in the results of recorded measurements are between running the ea111.03e-lpg engine on lpg or ba95, and they correspond to the somewhat different engine settings running on lpg and ba95. the graphs below show the important characteristics of the engine ea111.03e-lpg running on petrol and on lpg. figure 6 shows adjustment of mixture richness for engine ea111.03e-lpg running both on lpg and ba95 at full load and varying speeds. the lower enrichment for the engine running on lpg causes an increase in the exhaust gas temperature at higher engine speed (t_exh/bcat – temperature before catalyzer). this increased temperature is of no risk to the catalyzer. figure 7 shows that the power output of si engine ea111.03e-lpg with mixture formed by mpi liquid lpg is identical to or higher than that achieved by the engine running on petrol (the engine power on lpg is about 2% higher at mid operating speed). engine ea111.03e-lpg has a higher overall efficiency on lpg due to the less rich mixture used in comparison with petrol running. the higher total efficiency of the engine running on lpg and the somewhat lower carbon content in lpg (compared to the carbon content in petrol) contributes to a lower production of carbon dioxide co 2 (the content of co 2 in a dry sample of exhaust gas at full load across the speed range for the engine running on ba95 was in the range 13.2 – 10.4%, and for engine running on lpg in the range 12.9 – 9.2%). the research program on the ea111.03e-lpg engine is also focused on a detailed study of injection of liquid state lpg into epi with the heating of outlet nozzle using water from the engine cooling system the spray of injected lpg endoscope with recording optics and lighting directed towards the intake port in the cylinder head model of epi with the heating of on using flowing water water inlet water outlet plastic duralumin λ=150w/m.k. wet vapor lpg plastic λ=0.16w/m.k. liquid lpg figure 4: model of epi location on the engine intake manifold. the bottom part of epi with the on is designed to minimize cross-section contraction in the intake manifold. the on is heated by flowing water (from the engine cooling system) around the front surface of the on. obrázek 4: model umístění epi do sacího potrubí motoru. konstrukce spodní části epi s on zajišťuje minimální omezení průtočného průřezu v sacím potrubí motoru. ohřev on je proveden průtokem vody (z chladicího systému motoru) kolem čelní plochy on. vehicle si engine with mpi of liquid state lpg stanislav beroun, pavel brabec, aleš dittrich mecca 01 2016 page 45 the intake manifold. figures 8 and 9 show selected results from the measuring of temperature on the front surface of the on, and pressure plots of wet lpg steam inside the epi. figure 8 plots the temperature on the front surface of the on for varying loads of the ea111.03e-lpg engine at 3700 rpm. temperatures on surface of the on are in the range 65 – 75°c for the engine running on petrol. the temperature decreases on the front surface of the on when the engine runs on lpg. with heating of the on, the temperature on its front surface is 35°c at very low engine load, which drops to 5°c at full engine load. the heating of the on by flowing water around the front of the on has sufficient effect. without heating of the on, the temperature declines sharply on the front surface of the on to below freezing point when the engine is run on lpg. the seemingly illogical plot of temperature with respect to engine load is determined by the relationship between the evaporating pressure and evaporating temperature of lpg – see plots of measured lpg pressure in the epi in figure 9: at very low engine load, the pressure in the intake manifold is about figure 5: view of the intake manifold with the lpg injectors. input of liquid lpg is to ev (yellow "cup"). input pressure of liquid lpg is 5 bar higher than the pressure in the lpg tank (the lpg pump in the tank, for the laboratory conditions, increases the pressure to plpg/liq = ~ 12 bar). ev are fixed to epi on the engine intake manifold. obrázek 5: pohled na sací potrubí motoru se vstřikovači lpg. přívod kapalného lpg je do ev (žluté "kloboučky"). vstupní tlak lpg do ev je o 5 bar větší než tlak lpg v nádrži (čerpadlo lpg v nádrži zvyšuje v podmínkách zkušebny tlak lpg do ev na plpg/liq = ~ 12 bar). ev jsou upevněny do epi na sacím potrubí. 0,75 0,8 0,85 0,9 0,95 1 1,05 1500 2000 2500 3000 3500 4000 4500 5000 5500 [rpm] la m bd a [] 650 700 750 800 850 900 950 t_ ex h [0 c ] lambda-petrol lambda-lpg t_exh/bcat-petrol t_exh/bcat-lpg figure 6: the mixture richness and exhaust gas temperature (t_exh/bcat – temperature before catalyzer) of engine ea111.03e-lpg at full load running on lpg or ba95. obrázek 6: bohatost směsi a teplota výfukových plynů (t_exh/bcat – teplota před katalyzátorem) motoru ea111.03e-lpg v režimech vnější otáčkové charakteristiky při provozu na lpg nebo ba95 90 95 100 105 110 115 120 1500 2000 2500 3000 3500 4000 4500 5000 5500 [rpm] m t [n m ] 9 10 11 12 13 14 15 qt e [m j/ kw h] mt-petrol mt-lpg qte-petrol gte-lpg figure 7: the plots of torque moment and specific heat (energy) consumption of engine ea111.03e-lpg running on lpg or ba95. obrázek 7: průběhy točivého momentu a měrné spotřeby tepla motoru ea111.03e-lpg při provozu na lpg nebo ba95. -60 -40 -20 0 20 40 60 80 0 20 40 60 80 100 120 mt [nm] t_ o n l p g [ 0 c ] t_on(lpg-without heat) t_on(lpg-with heat) t_on(run on petrol) figure 8: plots show the temperature on the front surface of the on in relation to engine load (ea111.03e-lpg) at 3700 rpm. obrázek 8: průběhy teplot na čele výtokové trysky on v zatěžovací charakteristice motoru ea111.03e-lpg při 3700 1/min. 0 0,5 1 1,5 2 2,5 3 0 90 180 270 360 450 540 630 720 [deg ca] p [b ar ] 116 nm 80 nm 65 nm 50 nm 20 nm 15 nm 5 nm figure 9: plots of lpg pressure inside the epi in relation to engine load at 3700 rpm. the pressure decreases in the intake manifold under the effect of throttling back to decrease si engine power. obrázek 9: průběhy tlaku lpg v epi v režimech zatěžovací charakteristiky při otáčkách motoru 3700 1/min. tlak v sacím potrubí motoru se snižuje účinkem škrticí klapky při kvantitativní regulaci výkonu motoru. vehicle si engine with mpi of liquid state lpg stanislav beroun, pavel brabec, aleš dittrich mecca 01 2016 page 46 0.25 bar, which corresponds to an evaporating temperature of lpg of about -60°c (data according to [4]). figure 9 shows the recorded plots of lpg pressure inside the epi in relation to load at 3700 rpm. the pressure decreases in the intake manifold under the effect of throttling back to decrease si engine power. the pressure from intake manifold transfers immediately into volume vepi in the epi, and the low pressure lpg inside the epi significantly reduces the temperature of lpg evaporation inside volume vepi (i.e. the temperature of wet lpg steam flowing out from the on) and if the on is not heated, the temperature on the on front surface drops well below freezing point. the fluctuation of measured lpg pressure inside the epi at high engine load relates to the dynamic effects in the intake manifold. note 1: figure 9 presents recorded plots of lpg pressure inside the epi without heating of the on. lpg pressures inside the epi is somewhat higher when on heating is applied. for example: maximum lpg pressure inside the epi at full engine load is 2.35 bar without heating and 2.55 bar with heating of the on; at very low engine load the maximum pressure is 0.75 bar without heating and 1.75 bar with heating of the on. this is caused by change of thermal balance of lpg inside epi, because in the approx. 8mm long channel before the on (see injector arrangement in figure 1) part of the heat for warming the on also goes into the wet lpg steam, and this effect is greater in the case of small lpg injection charges. note 2: position 0 [deg ca] in the graphs is not tdc of the crankshaft; the pressure plots of lpg inside the epi are converted from the recording of pressure over time (the lpg injection start points are identical to the petrol ecu injection times). 4. visual inspection of liquid state lpg injection visual monitoring of the injection of liquid state lpg into the intake manifold was performed using an avl engine videoscope 513d. figures 10 to 13 show selected pictures from the plot of liquid lpg injection for both very low and full engine load at mid-range operational rpm. the endoscope with lighting was used. 5. conclusion the experience of the authors from the technical university of liberec on research of a vehicle engine for alternative running on lpg with mixture forming by mpi of liquid state lpg can be summarized in the following points: 1. heating of the end face of the on with minimizing of the heat transfer to wet lpg steam before the on is an effective method against of icing on the front on surface. icing on inside wall of inlet tube icing on the bottom of epi the epi without icing lpg spray lpg spray figure 10: view of the injector on, engine running on lpg (3700 rpm, 6 nm). the left picture is the liquid lpg injection without on heating, the right picture is the liquid lpg injection with on heating. when operating without on heating, icing occurs on the on and on the wall inside the plastic suction manifold near the injector. obrázek 10: pohled na on vstřikovače, provoz motoru na lpg (3700 1/ min, 6 nm). snímek vlevo je vstřik lpg bez ohřevu on, vpravo je vstřik lpg s ohřevem on. při provozu motoru bez ohřevu on vzniká námraza na čelní ploše on a na stěně plastového sacího potrubí v blízkosti vstřikovače lpg. lpg spray lpg spray figure 11: view of the intake port of cylinder head, engine running on lpg (3700 rpm, 6 nm). the left picture is the liquid lpg injection without on heating, the right picture is the liquid lpg injection with on heating. no icing occurs on the plastic wall inside the suction manifold near the cylinder head port at very low engine load when running on lpg. obrázek 11: pohled směrem k sacímu kanálu v hlavě válců, provoz motoru na lpg (3700 1/min, 6 nm). snímek vlevo je vstřik lpg bez ohřevu on, vpravo je vstřik lpg s ohřevem on. stěna plastového sacího potrubí v blízkosti vstřikovače lpg je při provozu motoru na lpg při nízkém zatížení bez námrazy. big icing on the bottom of epi the epi without icing lpg spray lpg spray figure 12: view of lpg injector on, engine running on lpg (3700 rpm, 116 nm – full load). the left picture is the liquid lpg injection without on heating, the right picture is the liquid lpg injection with on heating. large icing only forms around the on when running the engine on lpg without on heating. obrázek 12: pohled na on vstřikovače lpg, provoz motoru na lpg (3700 1/min, 116 nm). snímek vlevo je vstřik lpg bez ohřevu on, vpravo je vstřik lpg s ohřevem on. velká námraza na čelní ploše on a na stěně plastového sacího potrubí v blízkosti vstřikovače lpg vzniká pouze při provozu motoru bez ohřevu on. vehicle si engine with mpi of liquid state lpg stanislav beroun, pavel brabec, aleš dittrich mecca 01 2016 page 47 2. research of liquid state lpg injection into the intake manifold shows that dominant factor for trouble-free running of an engine on lpg is the suitable design of the epi inside the engine intake manifold. dimensions and insertion of bottom epi part into the intake manifold must minimize the cross-section contraction in the intake manifold (particularly for a naturally aspirated si engine). 3. the outflow of wet lpg steam must be directed to the central area of the flow system inside the intake manifold. impact of wet lpg steam on the inside wall of the intake manifold risks icing on the wall. the parameters of the liquid state lpg injection can be improved using an ev with a higher flow rate and shortened time of ev opening. the pressure and temperature of lpg inside the epi is thereby increased significantly, and both the speed of lpg spray outflow from the on and the range of compact wet steam spray are increased. this reduces the potency of impact of the wet steam spray on the inside wall of the plastic intake manifold, and ice formation is thus suppressed. acknowledgements this research has been realized using the support of technological agency, czech republic, programme of centers competence, project # te01020020 josef božek centre for automotive industry. this support is gratefully acknowledged. list of notations and abbreviations ba95 petrol fuel (octane number 95) ecu electronic control unit epi end part of injector ev electromagnetic valve lpg liquefied petroleum gas mpi multi point injection on outlet nozzle si spark ignition tdc top dead center kevapor correction factor of evaporation mlpg/gas/epi mass gaseous lpg inside epi mlpg/liq/epi mass liquid lpg inside epi pint/man air pressure inside intake manifold plpg/liq/ev lpg pressure inside ev plpg/epi lpg pressure inside epi qt specific heat consumptin ρlpg gas constant of lpg xlpg/steam/epi factor of wet steam lpg saturation inside epi son flow area of on tlpg/epi lpg temperature inside epi vepi  volume inside epi dmlpg/liq mass elementary quantities lpg from ev to epi dt time of calculation step klpg adiabatic exponent of gaseous lpg µon flow coefficient of on ρlpg/epi density of wet steam lpg inside epi ρlpg//gas/epi density of saturated steam lpg inside epi ρlpg/liq/epi density of droplets lpg disspersed inside epi ρlpg/liquid density of liquid lpg (ρlpg/liquid  = 550 kg/m 3) references [1] beroun, s., brabec, p., dittrich, a., dráb, o., nguyen, t., t.: computational modeling of the liquid lpg injection into the suction manifold of an si vehicle engine. applied mechanics and materials vol. 390 (2013) pp. 355 – 359. icmae 2013, moscow. [2] bruner, g., chmela, f., pachta-reyhofen, g.: flüssiggasbetrieb bei omnibusen. gräf & stift and man, wien. [3] mareš, j., beroun, s., blažek, j., holubec, r,: automotive engine with injection of the liquid lpg into the inlet manifold. journal of kones, powertrain and transport, vo.14, no.3 2007. [4] šesták, j., bukovský, j., houška, m.: tepelné pochody, transportní a termodynamická data. skripta čvut v praze, 2004. isbn 80-01-02934-4. lpg spray lpg spray icing on inside wall of inlet tube icing on inside wall of inlet tube figure 13: view of intake port of cylinder head, engine running on lpg (3700 rpm, 116 nm – full load). the left picture is the liquid lpg injection without on heating, the right picture is the liquid lpg injection with on heating. icing forms on the plastic wall inside the intake manifold near the port of cylinder head both without on heating and with on heating at full load with the engine running on lpg: the icing is somewhat lower with on heating. obrázek 13: pohled směrem k sacímu kanálu v hlavě válců, provoz motoru na lpg (3700 1/min, 116 nm-100% zatížení). snímek vlevo je vstřik lpg bez ohřevu on, vpravo je vstřik lpg s ohřevem on. na stěně plastového sacího potrubí v blízkosti sacího kanálu v hlavě válců se v režimu plného zatížení motoru tvoří námraza jak bez ohřevu on, tak s ohřevem on: při provozu s ohřevem on je ale námraza na plastovém potrubí v blízkosti sacího kanálu poněkud menší. mecca_20-02_web evaluation of plug-in parallel hev topologies using optimal control methods and vehicle dynamics simulation rastislav toman, jolana he!manová mecca 02 2020 page 21 evaluation of plug-in parallel hev topologies using optimal control methods and vehicle dynamics simulation rastislav toman, jolana he!manová 10.14311/mecdc.2020.02.03 rastislav toman ctu in prague, faculty of mechanical engineering; technická 4, praha 6, 166 07, czech republic; rastislav.toman@fs.cvut.cz jolana he!manová ctu in prague, faculty of mechanical engineering; technická 4, praha 6, 166 07, czech republic; jolana.hermanova@fs.cvut.cz abstract hybrid electric vehicle (hev) powertrains with parallel topologies are among the frequently used layouts, because of their easy applicability on an existing conventional powertrain, by the addition of hybrid modules with mild, full, or a plug-in capability. this paper investigates three of such parallel hev topologies: p2, p3, and p4; all in a plug-in variant, to find-out which one performs best. apart from the topology consideration, one of the other common questions or challenges in hev development is the ice concept selection. to address it, the paper combines the three hev topologies with three technologically different internal combustion engines, all with the same power outputs. then, all the powertrain and ice combinations are tested in homologation driving cycles and vehicle dynamics simulation test – different acceleration tests – giving a holistic methodology suitable for thorough hev topology evaluation, identifying all possible hybridization benefits. to find the maximum co2 potential, it is convenient to exclude the effect of the energy management control strategy on the co2 result in a charge sustaining driving cycle; therefore, to use some optimal control method. for this task, the paper compares the equivalent consumption minimization strategy, that realizes a pontryagin’s minimum principle against the dynamic programming optimal control method, which is based on bellman’s principle of optimality. both control methods are available as a part of gt-suite 0d/1d/3d multi-physics cae simulation software, that is used in our whole study. key words: hybrid electric vehicle, optimal control method, energy management strategy, dynamic programming, ecms, pontryagin’s minimum principle, parallel hybrid powertrain topology, plug-in hybrid, vehicle dynamics simulation, gt-suite shrnutí hybridní elektrická vozidla (hev) v paralelních topologiích pat!í mezi b"#ná uspo!ádání zejména díky snadné aplikovatelnosti ve stávajících pohonn$ch !et"zcích p!idáním hybridních modul%, a to v r%zn$ch úrovních hybridizace od mild, full a# po plug-in hev. tento &lánek se v"nuje t!em paralelním topologiím: p2, p3 a p4 v plug-in variant" s cílem jejich celkového porovnání. krom" v$b"ru topologie hybridního vozidla je také &astou otázkou v$b"r konceptu spalovacího motoru vhodného pro pou#ití v hybridním vozidle. abychom se na tuto otázku pokusili odpov"d"t, porovnáváme v této práci t!i topologie hybridních pohon% se t!emi technicky r%zn$mi spalovacími motory o stejném maximálním v$konu. v'echny varianty jsou simulovány v homologa&ních jízdních cyklech a dal'ích dynamick$ch testech, které by m"ly poskytnout ucelenou metodologii pro kompletní porovnání hybridních topologií a identifikovat mo#né p!ínosy hybridizace. p!i hledání maximální úspory co2 je vhodné omezit vliv !ídící strategie na v$sledné hodnoty co2 v „charge sustaining" módu pou#itím n"které z optimálních metod !ízení. proto tato práce porovnává ecms strategii, která je zalo#ena na pontryaginov" minimálním principu a metodu dynamického programování zalo#ené na bellmanov" principu optimality. ob" metody jsou dostupné jako sou&ást 0d/1d/3d multi-fyzikálního simula&ního softwaru gt-suite, kter$ je v celé studii vyu#íván. klí"ová slova: hybridní elektrické vozidlo, optimální strategie !ízení, !ízení energetick#ch tok$ ve vozidle, dynamické programování, ecms, pontryagin$v minimální princip, topologie paralelního hybridního hnacího ústrojí, plug-in hybrid, simulace dynamiky vozidla, gt-suite evaluation of plug-in parallel hev topologies using optimal control methods and vehicle dynamics simulation evaluation of plug-in parallel hev topologies using optimal control methods and vehicle dynamics simulation rastislav toman, jolana he!manová mecca 02 2020 page 22 1. introduction the current mandatory fleet-wide average emission target in eu – set to 95 grams of co2/km starting with 2020 "phase-in" period and following full application from 2021 [1] – pushes the automotive industry into the realm of powertrain electrification. a fleet-wide electrification, either by pure electric vehicles (ev), or by hybrid electric vehicles (hev), brings the obvious economic implications, especially the higher development and production costs. the us and eu oems try to address these economic implications mainly by adopting the plug-in hev powertrains (phev), combined with parallel topologies. the popularity of plug-ins from the side of oems is caused by two factors: first is, that the low average emission targets indirectly push for them; the second then, that a plug-in size battery allows for higher electrical power output and "fun-to-drive" factor of these vehicles. the parallel hev topologies then give a great variety of options – usually in a form of hybrid modules applied on a conventional powertrain (icev) – allowing for relatively small changes in already existing powertrains, and help this way to manage development costs (especially compared to a pure ev powertrain, or more "hevtailored" solutions) and reduce complexity at the oem. however, there are many technical challenges that need to be addressed in the early development stages of any new hev powertrain. these revolve mainly around the overall co2 emission reduction potential, of the chosen parallel topology, different internal combustion engine (ice) technology, or battery size, but also – when talking about the phev solutions – the performance gains in dynamic tasks. the one variable affecting the co2 performance of a studied hev powertrain and its components is the energy management control strategy. it is therefore ideal to exclude its effects on the overall co2 results, and ensure a globally optimal solution, when performing this type of study. gt-suite multi-physics cae simulation software already contains two built-in optimal control strategies: dynamic programming algorithm (dp), and equivalent consumption minimization strategy (ecms). dp algorithm solves the highly nonlinear hev system’s behavior, in a globally optimal manner. it is a numerical control method of solving a multi-stage decision-making optimal control problem ([2] or [3]), based on the bellman’s principle of optimality, requiring a priori information about the entire optimization horizon (in our case the entire driving cycle). although it is not applicable for real-time control for its high computation demand, it can serve as a very good benchmarking tool, exactly according to the needs of our paper. a more computationally efficient option for the energy management strategy is the ecms algorithm, that realizes the pontryagin’s minimum principle (pmp). although the ecms is also an "optimal control method", it is not intrinsically optimal as such [4], meaning it is only optimal locally in each time step, not globally during the whole driving cycle. keeping the terminology from [4], we could further distinguish between the ecms and pmp methods: nowadays, the term ecms is more often used for the online causal method, whereas the pmp term is reserved for the offline non-causal application. some implementations of dp were used to study the optimal hybridization level in two parallel hev topologies in [2], to instruct rule-based energy management strategies in [5, 6], to optimize the transmission’s shifting strategy in [7], or to study the optimal strategy for a series-parallel toyota prius powertrain in [8]. then, zeng et al. presented an ecms implementation as a casual suboptimal method performed online, by using several simplifying assumptions for the equivalence factor based on past and present driving in [9], or nüesch et al. in [10] extended the hamiltonian function with a pollutant emissions minimization. there are also some comparative studies of dp vs. pmp performance, one from yuan et al. [11]. finally, zeman et al. [12] present a broad hev topologies’ co2 comparative study combined with modular simulation models within the gt-suite simulation platform, using only heuristic control methods. our paper is divided into four main chapters, following this introductory chapter 1. chapter 2 shows the vehicle data and parameters, together with more details on hev topologies, and internal combustion engines (ice). chapter 3 then presents our benchmarking simulation methodology, different simulation models, and homologation calculations. chapter 4 is dedicated to the results; and finally, chapter 5 presents some overall conclusions. 1.1 goals of the paper the main objective of our study is to showcase and apply a full development and benchmarking methodology for hev vehicle powertrains. this main objective then specifies in two following goals: • first, to present a sensitivity on a parallel hev topology type, comparing p2, p3, and p4 variants; • second, to test for a synergy effect between the ice downsizing and powertrain hybridization, comparing three ice technologies with three different downsizing levels. the presented methodology consists of vehicle co2 homologation results (using wltp methodology), together with some dynamic tasks. these can be easily expanded with other user dynamic tasks, or driving cycles, together with future rde cycles, or any other real-life user scenarios – if requested. all our simulation tests are carried-out on a c-class vehicle, with the same plug-in size battery, and hence pure electric drive capability (ev mode). evaluation of plug-in parallel hev topologies using optimal control methods and vehicle dynamics simulation rastislav toman, jolana he!manová mecca 02 2020 page 23 the additional goals of our paper are: • to compare the two optimal control methods implemented in gt-suite; • to study the ecms co2 sensitivity on different heuristic criteria with our hev powertrains; • to study the hev powertrains’ performances in some dynamic tasks (different acceleration tests, and maximum vehicle speed). 2. vehicle data and parameters table 1: main vehicle parameters tabulka 1: hlavní parametry vozidla base vehicle mass 1240 [kg] frontal area 2.20 [m2] drag coefficient 0.31 [-] tire rolling resistance factor 0.009 [-] tire rolling radius 307 [mm] we have chosen a c-class vehicle with front-wheel drive (fwd) as a baseline for all the simulations in our study. table 1 summarizes its main vehicle parameters (base vehicle mass is without ice). this baseline vehicle is compared to the three parallel hev topologies (figure 1). the first two of the investigated hev topologies – p2 and p3 – are fwd, the p4 offers the awd (all-wheel drive) capability, although aspects such as climbing ability are not considered. p2 and p4 solutions are especially common nowadays, with p2 being probably cheaper and easier to integrate into an existing conventional powertrain (depending on the original vehicle that is hybridized). the additional masses are then in table 2: hev masses include high voltage battery mass of 110 kg, em mass of 35 kg, and estimated masses for transmission adjustments, and additional clutches (k0 clutch for p2; p4 clutch). high voltage battery is based on a samsung sdi lithium ion prismatic battery cells with capacity of 37 ah, and nominal voltage of 3.7 v. the battery system is then configured into 104s1p (104 cells in series, one in parallel), giving the total energy capacity of 14.8 kwh at nominal voltage of 400 v. table 2: additional masses of ice and hev components tabulka 2: dodate&né hmotnosti spalovacích motor% a hybridních komponent%. 2.0 na 130 [kg] 1.5 tc 120 [kg] 1.0 tc 110 [kg] p2 hev 165 [kg] p3 hev 150 [kg] p4 hev 190 [kg] the powertrain hybridization ratio (pice!/pem) is kept fixed: three ice concepts with power output of around 135 kw are combined with the same electric motor (em) of 54 kw (table 3). the bsfc and efficiency maps are displayed in figure 2. table 3: ice and em main parameters tabulka 3: hlavní parametry spalovacích motor% a elektromotoru. maximum torque [nm] maximum power [kw] speed limit [rpm] bsfc [g/kwh] efficiency [%] 2.0 na 227 137 6500 224.9 1.5 tc 245 135 6000 237.7 1.0 tc 245 135 6000 238.5 em 141 54 8000 92.9 the em presents a classical high torque – high efficiency synchronous traction machine with permanent magnets. it is downscaled from gkn’s commercial af130 traction motor with 130 kw, keeping the same efficiency map. three spark ignition, direct injection ice concepts represent different levels of ice downsizing: • naturally aspirated 2.0 l four cylinder (2.0 na); • turbocharged 1.5 l three cylinder (1.5 tc) with a bmep of 20.5 bar; • highly turbocharged 1.0 l three cylinder (1.0 tc) with a bmep of 31.0 bar. figure 1: parallel hev topologies components’ layout obrázek 1: uspo!ádání komponent% v paralelních hev topologiích evaluation of plug-in parallel hev topologies using optimal control methods and vehicle dynamics simulation rastislav toman, jolana he!manová mecca 02 2020 page 24 turbocharged concepts use a single-stage charging system with charge-air-cooler, lowered compression ratios (compared to 2.0 na), together with intake and exhaust variable valve timing (vvt); the 2.0 na concept uses vvt only on the intake side. the 2.0 na concept represents a state-of-the-art direct injection naturally aspirated engine, with the best bsfc from all concepts. a great advantage – in comparison to the turbocharged concepts – should be its relative simplicity, reliability, and therefore also cost. the 1.5 tc concept’s performance and technology represent a standard in current downsizing era. the 1.0 tc should be the best from the packaging and mass viewpoint. however, this is offset by higher price, and poorer low-end-torque performance. all three ice concepts are matched to a distinct six-speed transmission with progressive and sporty gear ratios (figure 3). the transmissions’ efficiencies are taken from a similar production transmission, the other driveline efficiencies are kept constant. p4 variant adds a single-speed transmission, again with constant efficiency, and total gear ratio of 6.2 (transmission gear ratio of 2.48 and differential gear ratio of 2.5), that allows for the em use below 150 km/h, then it is de-clutched. 3. simulation methodology there are two basic vehicle simulation methods in gt-suite: a kinematic method, and a dynamic method. our simulation methodology fully exploits these two different modelling options, together with the modularity of gt-suite simulation software package. the first one – backward kinematic – calculates the ice/em operating point from the imposed vehicle speed, and from the vehicle external loads (optionally imposing ice/em speed and load, then called a forward kinematic method). the second method – dynamic – performs the physical sequence of actions as in the real-life vehicle with a driver: driver operates the accelerator and brake pedals, and shifts gears; his commands are then interpreted in an ecu model, and sent to the plant models (ice, em, etc.), the same way as in a real vehicle, resulting in vehicle acceleration. figure 2: bsfc maps of ice concepts; em efficiency map obrázek 2: m"rná spot!eba koncept% spalovacích motor%; mapa ú&innosti elektromotoru evaluation of plug-in parallel hev topologies using optimal control methods and vehicle dynamics simulation rastislav toman, jolana he!manová mecca 02 2020 page 25 the next chapters from 3.1. to 3.5. give a comprehensive look on the use of the two vehicle simulation methods in our studies: 3.1. shows how we work with these different simulation models; then we discuss the two optimal control methods (in 3.2. and 3.3.) with some heuristic criteria (in 3.4.); and 3.5. finally shows the different simulation test, that serve either for benchmark studies, or for vehicle homologation results. 3.1. simulation models there are two models for each hev powertrain topology: a dynamic model (dyn), and a kinematic model (kin). both are built using interchangeable modules or sub-systems (e.g. ice model, em model, hv-battery model etc.) for each simulation method, with the same database containing the vehicle data and parameters from chapter 2. this combined approach of using modular models in combination with parameter database aids the general use and simulation work, together with simple possible replacement of some sub-system with a new one, that for instance accounts for more detailed physical behavior, or control logic. these changes can be then done easily and quickly for each hev powertrain model. kin models are used for the icev co2 results simulation and since the optimal control methods – that will be discussed in next chapters – are coupled with the kinematic method, also the "charge sustaining" (cs) co2 results. dyn models are then used for the e-range estimation and all other vehicle dynamics studies. driveline model in gt-suite is built by the combination with 1d inertias with either rigid or compliant connections. the vehicle data in our simulation models (kin and dyn) are then mostly map based. high voltage battery is simulated as a resistive electricalequivalent model with separate open-circuit voltage, and internal resistance maps for charge and discharge. then, combustion engines are simulated through map-based models with fuel consumption maps, and torque limits dependent on rotational speed. this map-based approach for the ice simulation does not capture well the dynamic effects in transient behavior, which is especially apparent for the turbocharged ice concepts at vehicle dynamics test. on the other hand, the map-based approach is very simple and giving fast simulation times, and its accuracy in the driving cycle simulation depends on ices relative power to the total vehicle loads (smaller ice leads to more demanding transient behavior). the problem with ice transients can be mitigated with additional torque rise limit maps (in [nm/s]), or by more detailed physical ice sub-system using either full 1d or simplified 1d fast-running model. however, these are not used in our study. 1000 2000 3000 4000 5000 6000 ic e s pe ed [r p m ] 1.0 tc transmission 60 [km/h] 3973 [rpm] 91 [km/h] 4212 [rpm] 129 [km/h] 4464 [rpm] 174 [km/h] 4732 [rpm] 221 [km/h] 5016 [rpm] 6000 [rpm] gear ratio 1 = 3.420 gear ratio 2 = 2.265 gear ratio 3 = 1.590 gear ratio 4 = 1.183 gear ratio 5 = 0.933 gear ratio 6 = 0.780 fd ratio = 3.400 1000 2000 3000 4000 5000 6000 ic e s pe ed [r p m ] 1.5 tc transmission 60 [km/h] 3978 [rpm] 91 [km/h] 4217 [rpm] 129 [km/h] 4470 [rpm] 173 [km/h] 4738 [rpm] 219 [km/h] 5022 [rpm] 6000 [rpm] gear ratio 1 = 3.530 gear ratio 2 = 2.340 gear ratio 3 = 1.645 gear ratio 4 = 1.225 gear ratio 5 = 0.968 gear ratio 6 = 0.810 fd ratio = 3.300 0 50 100 150 200 250 300 vehicle speed [km/h] 1000 2000 3000 4000 5000 6000 7000 ic e s pe ed [r p m ] 2.0 na transmission 60 [km/h] 4301 [rpm] 90 [km/h] 4559 [rpm] 129 [km/h] 4833 [rpm] 173 [km/h] 5123 [rpm] 220 [km/h] 5430 [rpm] 6500 [rpm] gear ratio 1 = 3.520 gear ratio 2 = 2.329 gear ratio 3 = 1.634 gear ratio 4 = 1.215 gear ratio 5 = 0.958 gear ratio 6 = 0.800 fd ratio = 3.600 figure 3: transmission layouts for all three ice concepts obrázek 3: pilové diagramy t!í pou#it$ch p!evodovek evaluation of plug-in parallel hev topologies using optimal control methods and vehicle dynamics simulation rastislav toman, jolana he!manová mecca 02 2020 page 26 the em model is also map-based with an efficiency map, and torque limits dependent on the rotational speed. thanks to the very fast ems transient response, the map-based approach is accurate enough. finally, also the transmission models are map-based (together with other gear ratios), with efficiencies that are taken from a similar production manual transmission, and maps dependent on input torque, rotational speed, and engaged gear. 3.2. dynamic programming control method in gt-suite bellman’s principle of optimality used in the dp control method states [13]: “an optimal policy has the property that whatever the initial state and initial decision are, the remaining decisions must constitute an optimal policy with regard to the state resulting from the "rst decision. a!complex multistage optimal problem can be divided into a! series of single-stage optimal problem. each single-stage optimal problem is solved by optimal solutions, and cost function is minimized according to a!sequence of decisions for each step.” dp algorithm implementation within gt-suite is described in more detail in [3], therefore, we will reproduce only some of the most important concepts here. the dp cost function j is defined by the equation 1, where: • gn (xn) represents the final cost, and additional terminal state penalty tn (xn) , that partially constrains the final state; • function lk (xk, uk(xk)) represents the cost of applying control #k(xk) at xk, according to the control problem’s hamiltonian function; problem can be divided into a series of single-stage optimal problem. each single-stage optimal problem is solved by optimal solutions, and cost function is minimized according to a sequence of decisions for each step.” dp algorithm implementation within gt-suite is described in more detail in [3], therefore, we will reproduce only some of the most important concepts here. the dp cost function 𝐽𝐽 is defined by the equation 1, where: • 𝑔𝑔%(𝑥𝑥%) represents the final cost, and additional terminal state penalty 𝑇𝑇%(𝑥𝑥%), that partially constrains the final state; • function 𝐿𝐿&*𝑥𝑥&, 𝑢𝑢&(𝑥𝑥&)represents the cost of applying control 𝜇𝜇&(𝑥𝑥&) at 𝑥𝑥&, according to the control problem’s hamiltonian function; • 𝐽𝐽'(𝑥𝑥() = 𝑔𝑔%(𝑥𝑥%) + 𝑇𝑇%(𝑥𝑥%) + 1 𝐿𝐿&*𝑥𝑥&, 𝑢𝑢&(𝑥𝑥&)+ 𝑝𝑝&(𝑥𝑥&) %)* &)( (1) 𝑇𝑇% is then defined in equation 2, with its terminal state penalty weight 𝛾𝛾, and terminal state penalty exponent 𝛽𝛽. penalty function 𝑝𝑝&(𝑥𝑥&) enforces the state constraints for 𝑘𝑘 = 0,1, … , 𝑁𝑁 − 1. equation 3 gives the definition of 𝑝𝑝&(𝑥𝑥&), with penalty function weight 𝜆𝜆, and penalty function exponent 𝛼𝛼. battery soc related units here are the soc limits 𝑆𝑆𝑆𝑆𝑆𝑆+,and 𝑆𝑆𝑆𝑆𝑆𝑆+./, target battery soc 𝑆𝑆𝑆𝑆𝑆𝑆0,1230, and the discretized soc points 𝑆𝑆𝑆𝑆𝑆𝑆21.4, that is used only in the equation 2. 𝑇𝑇% = 𝛾𝛾*𝑆𝑆𝑆𝑆𝑆𝑆21.4 − 𝑆𝑆𝑆𝑆𝑆𝑆0,12305 (2) 𝑝𝑝(𝑆𝑆𝑆𝑆𝑆𝑆) = 𝜆𝜆 a 𝑆𝑆𝑆𝑆𝑆𝑆(𝑡𝑡) − 𝑆𝑆𝑆𝑆𝑆𝑆0,1230 (𝑆𝑆𝑆𝑆𝑆𝑆+,− 𝑆𝑆𝑆𝑆𝑆𝑆+./) 2 d 6 (3) the optimal policy minimizes 𝐽𝐽'(𝑥𝑥() for all admissible policies – meaning control inputs (e.g. powertrain mode, electrical motor torque, transmission gear etc.), where 𝜋𝜋 is the set of all of them (equation 4). 𝐽𝐽∗(𝑥𝑥() = min-∈' 𝐽𝐽'(𝑥𝑥() (4) based on the principle of optimality, dp evaluates the optimal cost-to-go function 𝐽𝐽&*𝑥𝑥.– or optimal control trajectory – at every node in discretized grid points (𝑥𝑥&. is one of the state variables, at a node with time index 𝑘𝑘 and state index 𝑖𝑖), with soc being the state variable (dp implementation in gt-suite version v2020 uses only one state variable – soc). dp then proceeds backward in time, with equation 5 yielding the end cost calculation, and equation 6 the cost calculation for steps 𝑘𝑘 = 0,1, … , 𝑁𝑁 − 1. 𝐽𝐽%*𝑥𝑥.= 𝑔𝑔%*𝑥𝑥.+ 𝑇𝑇%*𝑥𝑥. (5) 𝐽𝐽&*𝑥𝑥.= min9!∈:! j𝐿𝐿&*𝑥𝑥., 𝑢𝑢&+ 𝑝𝑝&(𝑥𝑥&) … + 𝐽𝐽&;* k𝑓𝑓&*𝑥𝑥., 𝑢𝑢&-mn (6) the right-hand side of equation 6 is minimized at each state-time node, for each 𝑥𝑥&. leading to the optimal control policy. however, 𝐽𝐽&;*(𝑥𝑥) is only evaluated for discretized points; output function 𝑓𝑓&*𝑥𝑥., 𝑢𝑢& must be interpolated, since the state output is continuous in the state space, and so generally does not coincide with the state grid nodes. this introduces numerical errors and bounds the solution’s accuracy to the discretization of the state space, and control inputs. if the discretization resolution increases, also the dp’s accuracy increases. though, also the computation load is higher. outputs from equations 5 and 6 create the optimal control map, from which the algorithm derives the optimal control trajectory. (1) tn is then defined in equation 2, with its terminal state penalty weight $, and terminal state penalty exponent %. penalty function pk(xk) enforces the state constraints for k = 0, 1, ... , n-1. equation 3 gives the definition of pk(xk), with penalty function weight &, and penalty function exponent '. battery soc related units here are the soc limits socmax and socmin, target battery soc soctarget, and the discretized soc points socgrid, that is used only in the equation 2. problem can be divided into a series of single-stage optimal problem. each single-stage optimal problem is solved by optimal solutions, and cost function is minimized according to a sequence of decisions for each step.” dp algorithm implementation within gt-suite is described in more detail in [3], therefore, we will reproduce only some of the most important concepts here. the dp cost function 𝐽𝐽 is defined by the equation 1, where: • 𝑔𝑔%(𝑥𝑥%) represents the final cost, and additional terminal state penalty 𝑇𝑇%(𝑥𝑥%), that partially constrains the final state; • function 𝐿𝐿&*𝑥𝑥&, 𝑢𝑢&(𝑥𝑥&)represents the cost of applying control 𝜇𝜇&(𝑥𝑥&) at 𝑥𝑥&, according to the control problem’s hamiltonian function; • 𝐽𝐽'(𝑥𝑥() = 𝑔𝑔%(𝑥𝑥%) + 𝑇𝑇%(𝑥𝑥%) + 1 𝐿𝐿&*𝑥𝑥&, 𝑢𝑢&(𝑥𝑥&)+ 𝑝𝑝&(𝑥𝑥&) %)* &)( (1) 𝑇𝑇% is then defined in equation 2, with its terminal state penalty weight 𝛾𝛾, and terminal state penalty exponent 𝛽𝛽. penalty function 𝑝𝑝&(𝑥𝑥&) enforces the state constraints for 𝑘𝑘 = 0,1, … , 𝑁𝑁 − 1. equation 3 gives the definition of 𝑝𝑝&(𝑥𝑥&), with penalty function weight 𝜆𝜆, and penalty function exponent 𝛼𝛼. battery soc related units here are the soc limits 𝑆𝑆𝑆𝑆𝑆𝑆+,and 𝑆𝑆𝑆𝑆𝑆𝑆+./, target battery soc 𝑆𝑆𝑆𝑆𝑆𝑆0,1230, and the discretized soc points 𝑆𝑆𝑆𝑆𝑆𝑆21.4, that is used only in the equation 2. 𝑇𝑇% = 𝛾𝛾*𝑆𝑆𝑆𝑆𝑆𝑆21.4 − 𝑆𝑆𝑆𝑆𝑆𝑆0,12305 (2) 𝑝𝑝(𝑆𝑆𝑆𝑆𝑆𝑆) = 𝜆𝜆 a 𝑆𝑆𝑆𝑆𝑆𝑆(𝑡𝑡) − 𝑆𝑆𝑆𝑆𝑆𝑆0,1230 (𝑆𝑆𝑆𝑆𝑆𝑆+,− 𝑆𝑆𝑆𝑆𝑆𝑆+./) 2 d 6 (3) the optimal policy minimizes 𝐽𝐽'(𝑥𝑥() for all admissible policies – meaning control inputs (e.g. powertrain mode, electrical motor torque, transmission gear etc.), where 𝜋𝜋 is the set of all of them (equation 4). 𝐽𝐽∗(𝑥𝑥() = min-∈' 𝐽𝐽'(𝑥𝑥() (4) based on the principle of optimality, dp evaluates the optimal cost-to-go function 𝐽𝐽&*𝑥𝑥.– or optimal control trajectory – at every node in discretized grid points (𝑥𝑥&. is one of the state variables, at a node with time index 𝑘𝑘 and state index 𝑖𝑖), with soc being the state variable (dp implementation in gt-suite version v2020 uses only one state variable – soc). dp then proceeds backward in time, with equation 5 yielding the end cost calculation, and equation 6 the cost calculation for steps 𝑘𝑘 = 0,1, … , 𝑁𝑁 − 1. 𝐽𝐽%*𝑥𝑥.= 𝑔𝑔%*𝑥𝑥.+ 𝑇𝑇%*𝑥𝑥. (5) 𝐽𝐽&*𝑥𝑥.= min9!∈:! j𝐿𝐿&*𝑥𝑥., 𝑢𝑢&+ 𝑝𝑝&(𝑥𝑥&) … + 𝐽𝐽&;* k𝑓𝑓&*𝑥𝑥., 𝑢𝑢&-mn (6) the right-hand side of equation 6 is minimized at each state-time node, for each 𝑥𝑥&. leading to the optimal control policy. however, 𝐽𝐽&;*(𝑥𝑥) is only evaluated for discretized points; output function 𝑓𝑓&*𝑥𝑥., 𝑢𝑢& must be interpolated, since the state output is continuous in the state space, and so generally does not coincide with the state grid nodes. this introduces numerical errors and bounds the solution’s accuracy to the discretization of the state space, and control inputs. if the discretization resolution increases, also the dp’s accuracy increases. though, also the computation load is higher. outputs from equations 5 and 6 create the optimal control map, from which the algorithm derives the optimal control trajectory. (2) problem can be divided into a series of single-stage optimal problem. each single-stage optimal problem is solved by optimal solutions, and cost function is minimized according to a sequence of decisions for each step.” dp algorithm implementation within gt-suite is described in more detail in [3], therefore, we will reproduce only some of the most important concepts here. the dp cost function 𝐽𝐽 is defined by the equation 1, where: • 𝑔𝑔%(𝑥𝑥%) represents the final cost, and additional terminal state penalty 𝑇𝑇%(𝑥𝑥%), that partially constrains the final state; • function 𝐿𝐿&*𝑥𝑥&, 𝑢𝑢&(𝑥𝑥&)represents the cost of applying control 𝜇𝜇&(𝑥𝑥&) at 𝑥𝑥&, according to the control problem’s hamiltonian function; • 𝐽𝐽'(𝑥𝑥() = 𝑔𝑔%(𝑥𝑥%) + 𝑇𝑇%(𝑥𝑥%) + 1 𝐿𝐿&*𝑥𝑥&, 𝑢𝑢&(𝑥𝑥&)+ 𝑝𝑝&(𝑥𝑥&) %)* &)( (1) 𝑇𝑇% is then defined in equation 2, with its terminal state penalty weight 𝛾𝛾, and terminal state penalty exponent 𝛽𝛽. penalty function 𝑝𝑝&(𝑥𝑥&) enforces the state constraints for 𝑘𝑘 = 0,1, … , 𝑁𝑁 − 1. equation 3 gives the definition of 𝑝𝑝&(𝑥𝑥&), with penalty function weight 𝜆𝜆, and penalty function exponent 𝛼𝛼. battery soc related units here are the soc limits 𝑆𝑆𝑆𝑆𝑆𝑆+,and 𝑆𝑆𝑆𝑆𝑆𝑆+./, target battery soc 𝑆𝑆𝑆𝑆𝑆𝑆0,1230, and the discretized soc points 𝑆𝑆𝑆𝑆𝑆𝑆21.4, that is used only in the equation 2. 𝑇𝑇% = 𝛾𝛾*𝑆𝑆𝑆𝑆𝑆𝑆21.4 − 𝑆𝑆𝑆𝑆𝑆𝑆0,12305 (2) 𝑝𝑝(𝑆𝑆𝑆𝑆𝑆𝑆) = 𝜆𝜆 a 𝑆𝑆𝑆𝑆𝑆𝑆(𝑡𝑡) − 𝑆𝑆𝑆𝑆𝑆𝑆0,1230 (𝑆𝑆𝑆𝑆𝑆𝑆+,− 𝑆𝑆𝑆𝑆𝑆𝑆+./) 2 d 6 (3) the optimal policy minimizes 𝐽𝐽'(𝑥𝑥() for all admissible policies – meaning control inputs (e.g. powertrain mode, electrical motor torque, transmission gear etc.), where 𝜋𝜋 is the set of all of them (equation 4). 𝐽𝐽∗(𝑥𝑥() = min-∈' 𝐽𝐽'(𝑥𝑥() (4) based on the principle of optimality, dp evaluates the optimal cost-to-go function 𝐽𝐽&*𝑥𝑥.– or optimal control trajectory – at every node in discretized grid points (𝑥𝑥&. is one of the state variables, at a node with time index 𝑘𝑘 and state index 𝑖𝑖), with soc being the state variable (dp implementation in gt-suite version v2020 uses only one state variable – soc). dp then proceeds backward in time, with equation 5 yielding the end cost calculation, and equation 6 the cost calculation for steps 𝑘𝑘 = 0,1, … , 𝑁𝑁 − 1. 𝐽𝐽%*𝑥𝑥.= 𝑔𝑔%*𝑥𝑥.+ 𝑇𝑇%*𝑥𝑥. (5) 𝐽𝐽&*𝑥𝑥.= min9!∈:! j𝐿𝐿&*𝑥𝑥., 𝑢𝑢&+ 𝑝𝑝&(𝑥𝑥&) … + 𝐽𝐽&;* k𝑓𝑓&*𝑥𝑥., 𝑢𝑢&-mn (6) the right-hand side of equation 6 is minimized at each state-time node, for each 𝑥𝑥&. leading to the optimal control policy. however, 𝐽𝐽&;*(𝑥𝑥) is only evaluated for discretized points; output function 𝑓𝑓&*𝑥𝑥., 𝑢𝑢& must be interpolated, since the state output is continuous in the state space, and so generally does not coincide with the state grid nodes. this introduces numerical errors and bounds the solution’s accuracy to the discretization of the state space, and control inputs. if the discretization resolution increases, also the dp’s accuracy increases. though, also the computation load is higher. outputs from equations 5 and 6 create the optimal control map, from which the algorithm derives the optimal control trajectory. (3) the optimal policy minimizes j((x0) for all admissible policies – meaning control inputs (e.g. powertrain mode, electrical motor torque, transmission gear etc.), where ( is the set of all of them (equation 4). problem can be divided into a series of single-stage optimal problem. each single-stage optimal problem is solved by optimal solutions, and cost function is minimized according to a sequence of decisions for each step.” dp algorithm implementation within gt-suite is described in more detail in [3], therefore, we will reproduce only some of the most important concepts here. the dp cost function 𝐽𝐽 is defined by the equation 1, where: • 𝑔𝑔%(𝑥𝑥%) represents the final cost, and additional terminal state penalty 𝑇𝑇%(𝑥𝑥%), that partially constrains the final state; • function 𝐿𝐿&*𝑥𝑥&, 𝑢𝑢&(𝑥𝑥&)represents the cost of applying control 𝜇𝜇&(𝑥𝑥&) at 𝑥𝑥&, according to the control problem’s hamiltonian function; • 𝐽𝐽'(𝑥𝑥() = 𝑔𝑔%(𝑥𝑥%) + 𝑇𝑇%(𝑥𝑥%) + 1 𝐿𝐿&*𝑥𝑥&, 𝑢𝑢&(𝑥𝑥&)+ 𝑝𝑝&(𝑥𝑥&) %)* &)( (1) 𝑇𝑇% is then defined in equation 2, with its terminal state penalty weight 𝛾𝛾, and terminal state penalty exponent 𝛽𝛽. penalty function 𝑝𝑝&(𝑥𝑥&) enforces the state constraints for 𝑘𝑘 = 0,1, … , 𝑁𝑁 − 1. equation 3 gives the definition of 𝑝𝑝&(𝑥𝑥&), with penalty function weight 𝜆𝜆, and penalty function exponent 𝛼𝛼. battery soc related units here are the soc limits 𝑆𝑆𝑆𝑆𝑆𝑆+,and 𝑆𝑆𝑆𝑆𝑆𝑆+./, target battery soc 𝑆𝑆𝑆𝑆𝑆𝑆0,1230, and the discretized soc points 𝑆𝑆𝑆𝑆𝑆𝑆21.4, that is used only in the equation 2. 𝑇𝑇% = 𝛾𝛾*𝑆𝑆𝑆𝑆𝑆𝑆21.4 − 𝑆𝑆𝑆𝑆𝑆𝑆0,12305 (2) 𝑝𝑝(𝑆𝑆𝑆𝑆𝑆𝑆) = 𝜆𝜆 a 𝑆𝑆𝑆𝑆𝑆𝑆(𝑡𝑡) − 𝑆𝑆𝑆𝑆𝑆𝑆0,1230 (𝑆𝑆𝑆𝑆𝑆𝑆+,− 𝑆𝑆𝑆𝑆𝑆𝑆+./) 2 d 6 (3) the optimal policy minimizes 𝐽𝐽'(𝑥𝑥() for all admissible policies – meaning control inputs (e.g. powertrain mode, electrical motor torque, transmission gear etc.), where 𝜋𝜋 is the set of all of them (equation 4). 𝐽𝐽∗(𝑥𝑥() = min-∈' 𝐽𝐽'(𝑥𝑥() (4) based on the principle of optimality, dp evaluates the optimal cost-to-go function 𝐽𝐽&*𝑥𝑥.– or optimal control trajectory – at every node in discretized grid points (𝑥𝑥&. is one of the state variables, at a node with time index 𝑘𝑘 and state index 𝑖𝑖), with soc being the state variable (dp implementation in gt-suite version v2020 uses only one state variable – soc). dp then proceeds backward in time, with equation 5 yielding the end cost calculation, and equation 6 the cost calculation for steps 𝑘𝑘 = 0,1, … , 𝑁𝑁 − 1. 𝐽𝐽%*𝑥𝑥.= 𝑔𝑔%*𝑥𝑥.+ 𝑇𝑇%*𝑥𝑥. (5) 𝐽𝐽&*𝑥𝑥.= min9!∈:! j𝐿𝐿&*𝑥𝑥., 𝑢𝑢&+ 𝑝𝑝&(𝑥𝑥&) … + 𝐽𝐽&;* k𝑓𝑓&*𝑥𝑥., 𝑢𝑢&-mn (6) the right-hand side of equation 6 is minimized at each state-time node, for each 𝑥𝑥&. leading to the optimal control policy. however, 𝐽𝐽&;*(𝑥𝑥) is only evaluated for discretized points; output function 𝑓𝑓&*𝑥𝑥., 𝑢𝑢& must be interpolated, since the state output is continuous in the state space, and so generally does not coincide with the state grid nodes. this introduces numerical errors and bounds the solution’s accuracy to the discretization of the state space, and control inputs. if the discretization resolution increases, also the dp’s accuracy increases. though, also the computation load is higher. outputs from equations 5 and 6 create the optimal control map, from which the algorithm derives the optimal control trajectory. (4) based on the principle of optimality, dp evaluates the optimal cost-to-go function j((xi) – or optimal control trajectory – at every node in discretized grid points (xki is one of the state variables, at a node with time index k and state index i), with soc being the state variable (dp implementation in gt-suite version v2020 uses only one state variable – soc). dp then proceeds backward in time, with equation 5 yielding the end cost calculation, and equation 6 the cost calculation for steps k = 0, 1, ... , n-1. problem can be divided into a series of single-stage optimal problem. each single-stage optimal problem is solved by optimal solutions, and cost function is minimized according to a sequence of decisions for each step.” dp algorithm implementation within gt-suite is described in more detail in [3], therefore, we will reproduce only some of the most important concepts here. the dp cost function 𝐽𝐽 is defined by the equation 1, where: • 𝑔𝑔%(𝑥𝑥%) represents the final cost, and additional terminal state penalty 𝑇𝑇%(𝑥𝑥%), that partially constrains the final state; • function 𝐿𝐿&*𝑥𝑥&, 𝑢𝑢&(𝑥𝑥&)represents the cost of applying control 𝜇𝜇&(𝑥𝑥&) at 𝑥𝑥&, according to the control problem’s hamiltonian function; • 𝐽𝐽'(𝑥𝑥() = 𝑔𝑔%(𝑥𝑥%) + 𝑇𝑇%(𝑥𝑥%) + 1 𝐿𝐿&*𝑥𝑥&, 𝑢𝑢&(𝑥𝑥&)+ 𝑝𝑝&(𝑥𝑥&) %)* &)( (1) 𝑇𝑇% is then defined in equation 2, with its terminal state penalty weight 𝛾𝛾, and terminal state penalty exponent 𝛽𝛽. penalty function 𝑝𝑝&(𝑥𝑥&) enforces the state constraints for 𝑘𝑘 = 0,1, … , 𝑁𝑁 − 1. equation 3 gives the definition of 𝑝𝑝&(𝑥𝑥&), with penalty function weight 𝜆𝜆, and penalty function exponent 𝛼𝛼. battery soc related units here are the soc limits 𝑆𝑆𝑆𝑆𝑆𝑆+,and 𝑆𝑆𝑆𝑆𝑆𝑆+./, target battery soc 𝑆𝑆𝑆𝑆𝑆𝑆0,1230, and the discretized soc points 𝑆𝑆𝑆𝑆𝑆𝑆21.4, that is used only in the equation 2. 𝑇𝑇% = 𝛾𝛾*𝑆𝑆𝑆𝑆𝑆𝑆21.4 − 𝑆𝑆𝑆𝑆𝑆𝑆0,12305 (2) 𝑝𝑝(𝑆𝑆𝑆𝑆𝑆𝑆) = 𝜆𝜆 a 𝑆𝑆𝑆𝑆𝑆𝑆(𝑡𝑡) − 𝑆𝑆𝑆𝑆𝑆𝑆0,1230 (𝑆𝑆𝑆𝑆𝑆𝑆+,− 𝑆𝑆𝑆𝑆𝑆𝑆+./) 2 d 6 (3) the optimal policy minimizes 𝐽𝐽'(𝑥𝑥() for all admissible policies – meaning control inputs (e.g. powertrain mode, electrical motor torque, transmission gear etc.), where 𝜋𝜋 is the set of all of them (equation 4). 𝐽𝐽∗(𝑥𝑥() = min-∈' 𝐽𝐽'(𝑥𝑥() (4) based on the principle of optimality, dp evaluates the optimal cost-to-go function 𝐽𝐽&*𝑥𝑥.– or optimal control trajectory – at every node in discretized grid points (𝑥𝑥&. is one of the state variables, at a node with time index 𝑘𝑘 and state index 𝑖𝑖), with soc being the state variable (dp implementation in gt-suite version v2020 uses only one state variable – soc). dp then proceeds backward in time, with equation 5 yielding the end cost calculation, and equation 6 the cost calculation for steps 𝑘𝑘 = 0,1, … , 𝑁𝑁 − 1. 𝐽𝐽%*𝑥𝑥.= 𝑔𝑔%*𝑥𝑥.+ 𝑇𝑇%*𝑥𝑥. (5) 𝐽𝐽&*𝑥𝑥.= min9!∈:! j𝐿𝐿&*𝑥𝑥., 𝑢𝑢&+ 𝑝𝑝&(𝑥𝑥&) … + 𝐽𝐽&;* k𝑓𝑓&*𝑥𝑥., 𝑢𝑢&-mn (6) the right-hand side of equation 6 is minimized at each state-time node, for each 𝑥𝑥&. leading to the optimal control policy. however, 𝐽𝐽&;*(𝑥𝑥) is only evaluated for discretized points; output function 𝑓𝑓&*𝑥𝑥., 𝑢𝑢& must be interpolated, since the state output is continuous in the state space, and so generally does not coincide with the state grid nodes. this introduces numerical errors and bounds the solution’s accuracy to the discretization of the state space, and control inputs. if the discretization resolution increases, also the dp’s accuracy increases. though, also the computation load is higher. outputs from equations 5 and 6 create the optimal control map, from which the algorithm derives the optimal control trajectory. (5) problem can be divided into a series of single-stage optimal problem. each single-stage optimal problem is solved by optimal solutions, and cost function is minimized according to a sequence of decisions for each step.” dp algorithm implementation within gt-suite is described in more detail in [3], therefore, we will reproduce only some of the most important concepts here. the dp cost function 𝐽𝐽 is defined by the equation 1, where: • 𝑔𝑔%(𝑥𝑥%) represents the final cost, and additional terminal state penalty 𝑇𝑇%(𝑥𝑥%), that partially constrains the final state; • function 𝐿𝐿&*𝑥𝑥&, 𝑢𝑢&(𝑥𝑥&)represents the cost of applying control 𝜇𝜇&(𝑥𝑥&) at 𝑥𝑥&, according to the control problem’s hamiltonian function; • 𝐽𝐽'(𝑥𝑥() = 𝑔𝑔%(𝑥𝑥%) + 𝑇𝑇%(𝑥𝑥%) + 1 𝐿𝐿&*𝑥𝑥&, 𝑢𝑢&(𝑥𝑥&)+ 𝑝𝑝&(𝑥𝑥&) %)* &)( (1) 𝑇𝑇% is then defined in equation 2, with its terminal state penalty weight 𝛾𝛾, and terminal state penalty exponent 𝛽𝛽. penalty function 𝑝𝑝&(𝑥𝑥&) enforces the state constraints for 𝑘𝑘 = 0,1, … , 𝑁𝑁 − 1. equation 3 gives the definition of 𝑝𝑝&(𝑥𝑥&), with penalty function weight 𝜆𝜆, and penalty function exponent 𝛼𝛼. battery soc related units here are the soc limits 𝑆𝑆𝑆𝑆𝑆𝑆+,and 𝑆𝑆𝑆𝑆𝑆𝑆+./, target battery soc 𝑆𝑆𝑆𝑆𝑆𝑆0,1230, and the discretized soc points 𝑆𝑆𝑆𝑆𝑆𝑆21.4, that is used only in the equation 2. 𝑇𝑇% = 𝛾𝛾*𝑆𝑆𝑆𝑆𝑆𝑆21.4 − 𝑆𝑆𝑆𝑆𝑆𝑆0,12305 (2) 𝑝𝑝(𝑆𝑆𝑆𝑆𝑆𝑆) = 𝜆𝜆 a 𝑆𝑆𝑆𝑆𝑆𝑆(𝑡𝑡) − 𝑆𝑆𝑆𝑆𝑆𝑆0,1230 (𝑆𝑆𝑆𝑆𝑆𝑆+,− 𝑆𝑆𝑆𝑆𝑆𝑆+./) 2 d 6 (3) the optimal policy minimizes 𝐽𝐽'(𝑥𝑥() for all admissible policies – meaning control inputs (e.g. powertrain mode, electrical motor torque, transmission gear etc.), where 𝜋𝜋 is the set of all of them (equation 4). 𝐽𝐽∗(𝑥𝑥() = min-∈' 𝐽𝐽'(𝑥𝑥() (4) based on the principle of optimality, dp evaluates the optimal cost-to-go function 𝐽𝐽&*𝑥𝑥.– or optimal control trajectory – at every node in discretized grid points (𝑥𝑥&. is one of the state variables, at a node with time index 𝑘𝑘 and state index 𝑖𝑖), with soc being the state variable (dp implementation in gt-suite version v2020 uses only one state variable – soc). dp then proceeds backward in time, with equation 5 yielding the end cost calculation, and equation 6 the cost calculation for steps 𝑘𝑘 = 0,1, … , 𝑁𝑁 − 1. 𝐽𝐽%*𝑥𝑥.= 𝑔𝑔%*𝑥𝑥.+ 𝑇𝑇%*𝑥𝑥. (5) 𝐽𝐽&*𝑥𝑥.= min9!∈:! j𝐿𝐿&*𝑥𝑥., 𝑢𝑢&+ 𝑝𝑝&(𝑥𝑥&) … + 𝐽𝐽&;* k𝑓𝑓&*𝑥𝑥., 𝑢𝑢&-mn (6) the right-hand side of equation 6 is minimized at each state-time node, for each 𝑥𝑥&. leading to the optimal control policy. however, 𝐽𝐽&;*(𝑥𝑥) is only evaluated for discretized points; output function 𝑓𝑓&*𝑥𝑥., 𝑢𝑢& must be interpolated, since the state output is continuous in the state space, and so generally does not coincide with the state grid nodes. this introduces numerical errors and bounds the solution’s accuracy to the discretization of the state space, and control inputs. if the discretization resolution increases, also the dp’s accuracy increases. though, also the computation load is higher. outputs from equations 5 and 6 create the optimal control map, from which the algorithm derives the optimal control trajectory. (6) the right-hand side of equation 6 is minimized at each state-time node, for each xki leading to the optimal control policy. however, jk+1(x) is only evaluated for discretized points; output function fk(xi,uk) must be interpolated, since the state output is continuous in the state space, and so generally does not coincide with the state grid nodes. this introduces numerical errors and bounds the solution’s accuracy to the discretization of the state space, and control inputs. if the discretization resolution increases, also the dp’s accuracy increases. though, also the computation load is higher. outputs from equations 5 and 6 create the optimal control map, from which the algorithm derives the optimal control trajectory. a challenge for each new dp simulation problem is to understand the results’ sensitivity on state variable resolution and limits (min/max values); sensitivities on four penalty parameters from equations 2 (%, $) and 3 (', &); and sensitivity on control variables’ discretization. this process can be very time consuming, but necessary. 3.3. ecms control method in gt-suite the equivalent consumption in ecms refers in its basic form in equation 7, to converting the battery power pb to an equivalent fuel power by using a non-dimensional equivalence factor s, and adding it to an actual fuel power pf [4]. challenge for each new dp simulation problem is to understand the results’ sensitivity on state variable resolution and limits (min max values); sensitivities on four penalty parameters from equations 2 (𝛽𝛽, 𝛾𝛾) and 3 (𝛼𝛼, 𝜆𝜆); and sensitivity on control variables’ discretization. this process can be very time consuming, but necessary. 3.3. ecms control method in gt-suite the equivalent consumption in ec s refers in its basic form in equation , to converting the battery power to an equivalent fuel power by using a non-dimensional equivalence factor , and adding it to an actual fuel power [4]. (𝑡𝑡, , 𝑢𝑢) = (𝑡𝑡, 𝑢𝑢) + (𝑡𝑡) (𝑡𝑡, 𝑢𝑢) ( ) this equivalence factor depends on the driving cycle, and on battery initial final conditions; it represents the cost of recharging the battery power in future (by regenerative braking or ice charging). therefore, to set the equivalence factor accurately, the future conditions (e.g. the driving cycle) need to be known beforehand (either for the online or offline applications). ec s algorithm implementation in gt-suite calculates the equivalent fuel consumption using the equation , combining the equivalence factor , with a penalty function 𝑝𝑝. the equivalence factor can generally vary during the driving cycle, however in this implementation it is used as a constant. the penalty function 𝑝𝑝 (equation ) helps to keep the 𝑆𝑆𝑆𝑆𝑆𝑆 within the certain limits and thus reach the final 𝑆𝑆𝑆𝑆𝑆𝑆 state at the end of the simulated driving cycle, where the penalty function’s exponent 𝛼𝛼 changes it’s aggressiveness with 𝑆𝑆𝑆𝑆𝑆𝑆 value deviating from 𝑆𝑆𝑆𝑆𝑆𝑆0,1230. the user then controls the ec s by varying these two parameters: equivalence factor , and the penalty function exponent 𝛼𝛼 ( ote: the penalty function exponent 𝛼𝛼 is not related to the one used in dp and can generally have different integer values). to simulate a charge-sustaining (cs) cycle, the optimal value of the factor must be found for the chosen hybrid powertrain and its initial final conditions. 3 (𝑡𝑡) = (𝑡𝑡) + ,00(𝑡𝑡) 𝑝𝑝(𝑆𝑆𝑆𝑆𝑆𝑆) ( ) 𝑝𝑝(𝑆𝑆𝑆𝑆𝑆𝑆) = 1 − a 𝑆𝑆𝑆𝑆𝑆𝑆(𝑡𝑡) − 𝑆𝑆𝑆𝑆𝑆𝑆0,1230 (𝑆𝑆𝑆𝑆𝑆𝑆+,− 𝑆𝑆𝑆𝑆𝑆𝑆+./) 2 d 6 ( ) we could say, that based on the terminology mentioned in the introductory chapter from [4], this gtsuite’s implementation could be called a p p method, since it works offline, and in combination with iterative approach to find the equivalence factor . lso, the nature of this implementation – numerical minimization of the equivalent fuel consumption in each time step – should lead to an aggressive behavior and results close to dp control method – uan et al. [11] presented a difference only of 0.4 between the two methods. 3.4. additional heuristic conditions for optimal control methods when using either one of the optimal control algorithms above, it is suitable to have some additional options to guide the algorithm apart from the basic limits, such as battery or e power limits etc. these can represent real-life scenarios and limits, that cannot be imposed by the simple control limits: e.g. forced ice starts to account for heating of the catalytic converter, limiting conditions on the use of e mode to ensure more predictable powertrain mode switching behavior, or imposing the limit conditions on maximum allowable gear when optimizing the gear shifting strategy. this way the user can get some idea of an impact of these criteria or conditions on the global fc (fuel consumption) optima. in the case of ec s, this can further improve its results – and in some cases ensure method’s convergence to cs result, which is not guaranteed (as will be shown in a chapter 4.5). when we have a look on the w tc and cs simulation, the local ec s’s optimality leads to an almost continual battery charge roughly in the first half of the cycle, followed by discharge in during the second half (figure 4, (7) this equivalence factor s depends on the driving cycle, and on battery initial/final conditions; it represents the cost of recharging evaluation of plug-in parallel hev topologies using optimal control methods and vehicle dynamics simulation rastislav toman, jolana he!manová mecca 02 2020 page 27 the battery power in future (by regenerative braking or ice charging). therefore, to set the equivalence factor accurately, the future conditions (e.g. the driving cycle) need to be known beforehand (either for the online or offline applications). ecms algorithm implementation in gt-suite calculates the equivalent fuel consumption using the equation 8, combining the equivalence factor s, with a penalty function p. the equivalence factor s can generally vary during the driving cycle, however in this implementation it is used as a constant. the penalty function p (equation 9) helps to keep the soc within the certain limits and thus reach the final soc state at the end of the simulated driving cycle, where the penalty function’s exponent ' changes it’s "aggressiveness" with soc value deviating from soctarget. the user then controls the ecms by varying these two parameters: equivalence factor s, and the penalty function exponent ' (note: the penalty function exponent ' is not related to the one used in dp and can generally have different integer values). to simulate a "charge-sustaining" (cs) cycle, the "optimal" value of the s factor must be found for the chosen hybrid powertrain and its initial/final conditions. challenge for each new dp simulation problem is to understand the results’ sensitivity on state variable resolution and limits (min max values); sensitivities on four penalty parameters from equations 2 (𝛽𝛽, 𝛾𝛾) and 3 (𝛼𝛼, 𝜆𝜆); and sensitivity on control variables’ discretization. this process can be very time consuming, but necessary. 3.3. ecms control method in gt-suite the equivalent consumption in ec s refers in its basic form in equation , to converting the battery power to an equivalent fuel power by using a non-dimensional equivalence factor , and adding it to an actual fuel power [4]. (𝑡𝑡, , 𝑢𝑢) = (𝑡𝑡, 𝑢𝑢) + (𝑡𝑡) (𝑡𝑡, 𝑢𝑢) ( ) this equivalence factor depends on the driving cycle, and on battery initial final conditions; it represents the cost of recharging the battery power in future (by regenerative braking or ice charging). therefore, to set the equivalence factor accurately, the future conditions (e.g. the driving cycle) need to be known beforehand (either for the online or offline applications). ec s algorithm implementation in gt-suite calculates the equivalent fuel consumption using the equation , combining the equivalence factor , with a penalty function 𝑝𝑝. the equivalence factor can generally vary during the driving cycle, however in this implementation it is used as a constant. the penalty function 𝑝𝑝 (equation ) helps to keep the 𝑆𝑆𝑆𝑆𝑆𝑆 within the certain limits and thus reach the final 𝑆𝑆𝑆𝑆𝑆𝑆 state at the end of the simulated driving cycle, where the penalty function’s exponent 𝛼𝛼 changes it’s aggressiveness with 𝑆𝑆𝑆𝑆𝑆𝑆 value deviating from 𝑆𝑆𝑆𝑆𝑆𝑆0,1230. the user then controls the ec s by varying these two parameters: equivalence factor , and the penalty function exponent 𝛼𝛼 ( ote: the penalty function exponent 𝛼𝛼 is not related to the one used in dp and can generally have different integer values). to simulate a charge-sustaining (cs) cycle, the optimal value of the factor must be found for the chosen hybrid powertrain and its initial final conditions. 3 (𝑡𝑡) = (𝑡𝑡) + ,00(𝑡𝑡) 𝑝𝑝(𝑆𝑆𝑆𝑆𝑆𝑆) ( ) 𝑝𝑝(𝑆𝑆𝑆𝑆𝑆𝑆) = 1 − a 𝑆𝑆𝑆𝑆𝑆𝑆(𝑡𝑡) − 𝑆𝑆𝑆𝑆𝑆𝑆0,1230 (𝑆𝑆𝑆𝑆𝑆𝑆+,− 𝑆𝑆𝑆𝑆𝑆𝑆+./) 2 d 6 ( ) we could say, that based on the terminology mentioned in the introductory chapter from [4], this gtsuite’s implementation could be called a p p method, since it works offline, and in combination with iterative approach to find the equivalence factor . lso, the nature of this implementation – numerical minimization of the equivalent fuel consumption in each time step – should lead to an aggressive behavior and results close to dp control method – uan et al. [11] presented a difference only of 0.4 between the two methods. 3.4. additional heuristic conditions for optimal control methods when using either one of the optimal control algorithms above, it is suitable to have some additional options to guide the algorithm apart from the basic limits, such as battery or e power limits etc. these can represent real-life scenarios and limits, that cannot be imposed by the simple control limits: e.g. forced ice starts to account for heating of the catalytic converter, limiting conditions on the use of e mode to ensure more predictable powertrain mode switching behavior, or imposing the limit conditions on maximum allowable gear when optimizing the gear shifting strategy. this way the user can get some idea of an impact of these criteria or conditions on the global fc (fuel consumption) optima. in the case of ec s, this can further improve its results – and in some cases ensure method’s convergence to cs result, which is not guaranteed (as will be shown in a chapter 4.5). when we have a look on the w tc and cs simulation, the local ec s’s optimality leads to an almost continual battery charge roughly in the first half of the cycle, followed by discharge in during the second half (figure 4, (8) challenge for each new dp simulation problem is to understand the results’ sensitivity on state variable resolution and limits (min max values); sensitivities on four penalty parameters from equations 2 (𝛽𝛽, 𝛾𝛾) and 3 (𝛼𝛼, 𝜆𝜆); and sensitivity on control variables’ discretization. this process can be very time consuming, but necessary. 3.3. ecms control method in gt-suite the equivalent consumption in ec s refers in its basic form in equation , to converting the battery power to an equivalent fuel power by using a non-dimensional equivalence factor , and adding it to an actual fuel power [4]. (𝑡𝑡, , 𝑢𝑢) = (𝑡𝑡, 𝑢𝑢) + (𝑡𝑡) (𝑡𝑡, 𝑢𝑢) ( ) this equivalence factor depends on the driving cycle, and on battery initial final conditions; it represents the cost of recharging the battery power in future (by regenerative braking or ice charging). therefore, to set the equivalence factor accurately, the future conditions (e.g. the driving cycle) need to be known beforehand (either for the online or offline applications). ec s algorithm implementation in gt-suite calculates the equivalent fuel consumption using the equation , combining the equivalence factor , with a penalty function 𝑝𝑝. the equivalence factor can generally vary during the driving cycle, however in this implementation it is used as a constant. the penalty function 𝑝𝑝 (equation ) helps to keep the 𝑆𝑆𝑆𝑆𝑆𝑆 within the certain limits and thus reach the final 𝑆𝑆𝑆𝑆𝑆𝑆 state at the end of the simulated driving cycle, where the penalty function’s exponent 𝛼𝛼 changes it’s aggressiveness with 𝑆𝑆𝑆𝑆𝑆𝑆 value deviating from 𝑆𝑆𝑆𝑆𝑆𝑆0,1230. the user then controls the ec s by varying these two parameters: equivalence factor , and the penalty function exponent 𝛼𝛼 ( ote: the penalty function exponent 𝛼𝛼 is not related to the one used in dp and can generally have different integer values). to simulate a charge-sustaining (cs) cycle, the optimal value of the factor must be found for the chosen hybrid powertrain and its initial final conditions. 3 (𝑡𝑡) = (𝑡𝑡) + ,00(𝑡𝑡) 𝑝𝑝(𝑆𝑆𝑆𝑆𝑆𝑆) ( ) 𝑝𝑝(𝑆𝑆𝑆𝑆𝑆𝑆) = 1 − a 𝑆𝑆𝑆𝑆𝑆𝑆(𝑡𝑡) − 𝑆𝑆𝑆𝑆𝑆𝑆0,1230 (𝑆𝑆𝑆𝑆𝑆𝑆+,− 𝑆𝑆𝑆𝑆𝑆𝑆+./) 2 d 6 ( ) we could say, that based on the terminology mentioned in the introductory chapter from [4], this gtsuite’s implementation could be called a p p method, since it works offline, and in combination with iterative approach to find the equivalence factor . lso, the nature of this implementation – numerical minimization of the equivalent fuel consumption in each time step – should lead to an aggressive behavior and results close to dp control method – uan et al. [11] presented a difference only of 0.4 between the two methods. 3.4. additional heuristic conditions for optimal control methods when using either one of the optimal control algorithms above, it is suitable to have some additional options to guide the algorithm apart from the basic limits, such as battery or e power limits etc. these can represent real-life scenarios and limits, that cannot be imposed by the simple control limits: e.g. forced ice starts to account for heating of the catalytic converter, limiting conditions on the use of e mode to ensure more predictable powertrain mode switching behavior, or imposing the limit conditions on maximum allowable gear when optimizing the gear shifting strategy. this way the user can get some idea of an impact of these criteria or conditions on the global fc (fuel consumption) optima. in the case of ec s, this can further improve its results – and in some cases ensure method’s convergence to cs result, which is not guaranteed (as will be shown in a chapter 4.5). when we have a look on the w tc and cs simulation, the local ec s’s optimality leads to an almost continual battery charge roughly in the first half of the cycle, followed by discharge in during the second half (figure 4, (9) we could say, that based on the terminology mentioned in the introductory chapter from [4], this gt-suite’s implementation could be called a pmp method, since it works offline, and in combination with iterative approach to find the equivalence factor s. also, the nature of this implementation – numerical minimization of the equivalent fuel consumption in each time step – should lead to an "aggressive" behavior and results close to dp control method – yuan et al. [11] presented a difference only of 0.4% between the two methods. 3.4. additional heuristic conditions for optimal control methods when using either one of the optimal control algorithms above, it is suitable to have some additional options to "guide" the algorithm apart from the basic limits, such as battery or em power limits etc. these can represent real-life scenarios and limits, that cannot be imposed by the simple control limits: e.g. forced ice starts to account for heating of the catalytic converter, limiting conditions on the use of ev mode to ensure more predictable powertrain mode switching behavior, or imposing the limit conditions on maximum allowable gear when optimizing the gear shifting strategy. this way the user can get some idea of an impact of these criteria or conditions on the global fc (fuel consumption) optima. in the case of ecms, this can further improve its results – and in some cases ensure method’s convergence to cs result, which is not guaranteed (as will be shown in a chapter 4.5). when we have a look on the wltc and cs simulation, the local ecms’s optimality leads to an almost continual battery charge roughly in the first half of the cycle, followed by discharge during the second half (figure 4, blue line). this results in sub-optimal fuel consumption for the cs cycle and phev powertrain from the global point of view. 0 200 400 600 800 1000 1200 1400 1600 1800 time [s] 24 26 28 30 32 34 36 38 s o c [% ] 0 20 40 60 80 100 120 140 v eh ic le s pe ed [k m /h ] ecms: no ev lim ecms: ev lim = 77 km/h dp: no evlim vehicle speed figure 4: soc comparison of dp vs. ecms with evlim heuristic parameter turned on/off in cs wltc obrázek 4: porovnání pr%b"h% soc algoritm% dp a ecms s heuristick$m parametrem evlim zapnut$m/vypnut$m v „charge sustaining” módu jízdního cyklu wltc this specific problem can be mitigated by the additional heuristic criteria, that limits the maximum vehicle speed, when the electric motor can act as a "primary mover" (evlim). above this limit, the electric motor can only fulfill the load point shifting function. similar methods are listed in [4]. the addition of evlim changes the "charge sustaining equivalence factor s", and also affects the overall powertrain behavior: the battery discharges in the first phases of the cycle, and charges in the later phases, improving the overall fuel consumption (figure 4, green line). red line in figure 4 represents the soc obtained with the dp algorithm. 3.5. simulation t ypes and co2 homologation calculations since one of the goals of this paper is to give a comprehensive benchmarking study of the three hev topologies combined with three representatives of ice downsizing level, here we evaluation of plug-in parallel hev topologies using optimal control methods and vehicle dynamics simulation rastislav toman, jolana he!manová mecca 02 2020 page 28 enumerate all simulation types and calculations, whose results will be presented in the next result chapter: • first, there are two simulation tasks, that use kin models: icev co2 and cs co2 (the latter combined with the two optimal control strategies); • second, the all electric range (aer) simulations using dyn models; • third, homologation co2 can be calculated from aer and cs co2 results, using the utility factor (uf) according to the wltp homologation procedure – brief description follows; • fourth and final are the vehicle dynamics simulations using dyn models. co2 homologation procedure of hybrid vehicles (ovc-hevs – off-vehicle charging hybrid electric vehicles) according to wltp includes mainly cs, "charge depleting" (cd), and aer test [14]. the final combined wltp fuel consumption (fcwltp) is calculated from cs and cd consumptions, and uf corresponding to the aer, according the equation 10. blue line). this results in sub-optimal fuel consumption for the cs cycle and phe powertrain from the global point of view. figure 4: soc comparison of dp vs. ecms with 𝐸𝐸𝐸𝐸!"# heuristic parameter turned on/off in cs wltc obrázek 4: porovnání průběhů soc algoritmů dp a ecms s heuristickým parametrem 𝐸𝐸𝐸𝐸!"# zapnutým/vypnutým v „charge sustaining“ módu jízdního cyklu wltc this specific problem can be mitigated by the additional heuristic criteria, that limits the maximum vehicle speed, when the electric motor can act as a primary mover ( .+). bove this limit, the electric motor can only fulfill the load point shifting function. similar methods are listed in [4]. the addition of .+ changes the charge sustaining equivalence factor , and also affects the overall powertrain behavior: the battery discharges in the first phases of the cycle, and charges in the later phases, improving the overall fuel consumption (figure 4, green line). ed line in figure 4 represents the soc obtained with the dp algorithm. 3. . simulation t pes and c 2 homolo ation calculations since one of the goals of this paper is to give a comprehensive benchmarking study of the three he topologies combined with three representatives of ice downsizing level, here we enumerate all simulation types and calculations, whose results will be presented in the next result chapter: • first, there are two simulation tasks, that use i models: ice co2 and cs co2 (the latter combined with the two optimal control strategies); • second, the ll electric ange ( e ) simulations using d models; • third, homologation co2 can be calculated from e and cs co2 results, using the utility factor ( f) according to the w tp homologation procedure – brief description follows; • fourth and final are the vehicle dynamics simulations using d models. co2 homologation procedure of hybrid vehicles (o c-he s – offehicle charging hybrid electric ehicles) according to w tp includes mainly cs, charge depleting (cd), and e test [14]. the final combined w tp fuel consumption ( 𝑆𝑆 ) is calculated from cs and cd consumptions, and f corresponding to the e , according the equation 10. 𝑆𝑆 = 1 * 𝑆𝑆 & )* + 1 − 1 & )* 𝑆𝑆 (10) (10) the fractional utility factor ufj is determined by the equation 11 for a distance dj driven at the jth period of the wltc: ci is a set of coefficients determined by the wltp standard, and dn represents a normalized distance. the fractional utility factor is determined by the equation 11 for a distance driven at the j period of the w tc: 𝑆𝑆. is a set of coefficients determined by the w tp standard, and / represents a normalized distance. * = 1 − − 1 𝑆𝑆. / .& .)* − 1 * )* (11) the ll electric ange represents a distance driven from fully charged battery, until the w tc phase, when the engine first starts. 4. simulation results the w tp requires a cs, and e tests for co2 or fuel consumption evaluation. since the analyzed powertrains are all phe type, the cs driving cycle initial and target soc values are set to 30 , which would correspond to a usual phe battery use: when the battery is charged, the vehicle uses mostly e mode; then if the soc level is low (usually around 20-30 soc) it switches to he mode. during the entire cs test all three topologies can use the ice load-point-shifting ( ps) in he mode (in case of p4 it is through-the-road ), together with e mode. the optimal use of e to he mode switching, and ps is determined by the dp or ec s control algorithms, switching the ice off in the e mode. the e tests start at soc of 6 , the e test stops then at 35 . similarly, the vehicle dynamics tests start with full battery (he and e tests), disregarding any derating behavior of the electrical components. egarding the gear shifting strategy, all the sets of results, except for 4.3, use shifting strategy generated by the w tp. the sensitivity in 4.3 compares the w tp strategy with the dp-optimized shifting, only for the p2 topology. the combination of co2 homologation simulations and vehicle dynamics tasks presents a full development and benchmarking methodology for he powertrains comparison. the results show the sensitivities on a topology type and a synergy effect between the ice downsizing and powertrain hybridization. the vehicle dynamic tests results further show the importance of holistic approach to the optimization of these powertrains. 4. . ce sensiti it on ce technolo this first ice powertrain sensitivity on different ice concepts (table 4) reveals an anticipated fact, that the downsized engines provide better fuel economy in homologation driving cycles. higher ice downsizing levels achieve lower fuel consumption and co2 production. ice fc [l/100km] co2 [g/km] 2.0 na 6.115 13 .42 1.5 tc 5. 131. 2 1.0 tc 5.251 11 . 2 b e 4: uel consumption and co2 sensitivity on different ce concepts bu k 4: spot eba paliva a produkce co2 pro různ koncepty spalovacích motorů 4. . erall c c 2 results e topolo ies s. ce concepts table 5 shows the overall results of all three phe topologies, combined with the three ice concepts: cs mode and combined values, together with e , f, and co2 potential compared to respective ice concepts. the cs mode results were simulated using dp control method, with the soc resolution (𝑆𝑆𝑆𝑆𝑆𝑆21.4) of 1 (101 soc levels), with .+ parameter turned off. ice cs mode fc cs mode co2 aer [km] uf [-] combined fc combined co2 combined δco2 (11) the all electric range represents a distance driven from fully charged battery, until the wltc phase, when the engine first starts. 4. simulation results the wltp requires a cs, and aer tests for co2 or fuel consumption evaluation. since the analyzed powertrains are all phev type, the cs driving cycle initial and target soc values are set to 30 %, which would correspond to a usual phev battery use: when the battery is charged, the vehicle uses mostly ev mode; then if the soc level is low (usually around 20-30 % soc) it switches to hev mode. during the entire cs test all three topologies can use the ice load-point-shifting (lps) in hev mode (in case of p4 it is "through-the-road"), together with ev mode. the optimal use of ev to hev mode switching, and lps is determined by the dp or ecms control algorithms, switching the ice off in the ev mode. the aer tests start at soc of 96 %, the aer test stops then at 35 %. similarly, the vehicle dynamics tests start with full battery (hev and ev tests), disregarding any derating behavior of the electrical components. regarding the gear shifting strategy, all the sets of results, except for 4.3, use shifting strategy generated by the wltp. the sensitivity in 4.3 compares the wltp strategy with the "dp-optimized" shifting, only for the p2 topology. the combination of co2 homologation simulations and vehicle dynamics tasks presents a full development and benchmarking methodology for hev powertrains comparison. the results show the sensitivities on a topology type and a synergy effect between the ice downsizing and powertrain hybridization. the vehicle dynamic tests results further show the importance of holistic approach to the optimization of these powertrains. 4.1. icev sensitivit y on ice technology this first icev powertrain sensitivity on different ice concepts (table 4) reveals an anticipated fact, that the downsized engines provide better fuel economy in homologation driving cycles. higher ice downsizing levels achieve lower fuel consumption and co2 production. table 4: fuel consumption and co2 sensitivity on different ice concepts tabulka 4: spot!eba paliva a produkce co2 pro r%zné koncepty spalovacích motor% ice fc [l/100km] co2 [g/km] 2.0 na 6.115 139.42 1.5 tc 5.777 131.72 1.0 tc 5.251 119.72 4.2. overall fc/co2 results (hev topologies vs. ice concepts) table 5 shows the overall results of all three phev topologies, combined with the three ice concepts: cs mode and combined values, together with aer, uf, and (co2 potential compared to respective icev concepts. the cs mode results were simulated using dp control method, with the soc resolution (socgrid) of 1% (101 soc levels), with evlim parameter turned off. first main observation is that the p4 topology has the biggest overall homologation co2 potential ((co2 in the last column in table 5), followed by p2, and p3 topologies. the same applies for the aer values, that dictate the uf then used for the combined homologation fc/co2 calculation (equations 10 and 11, with cd mode gco2/km equal to zero). considering that the p3 and p4 topologies work in a very similar way, the aer potential and subsequent combined fc results are evaluation of plug-in parallel hev topologies using optimal control methods and vehicle dynamics simulation rastislav toman, jolana he!manová mecca 02 2020 page 29 much better for the p4. the difference comes mainly from the much more favorable total gear ratio for the p4, together with better efficiencies in ev mode. the comparison of em operating points in figure 5 indicates, that the em in p3 topologies spends a lot of time in low speed – high torque regions; the p4 gear ratio on the other hand allows for generally higher em operating speeds with better overall efficiencies. a natural expectation for the p2 topology is, that it would use the ability to shift gears also in ev mode to offset the transmission efficiency disadvantage (compared for instance to p3 or p4). however, for the case of overall results, the gear shifting strategy comes from wltp – generated based on ice performance, not ems – which proves to be problematic. it is once again in full display in figure 5 with em operating points, table 5: overall fuel consumption and co2 results (hev topologies vs. ice concepts) tabulka 5: celkové v$sledky spot!eb paliva a produkce co2 (topologie hev vs. koncepty spalovacích motor%) ice cs mode fc [l/100km] cs mode co2 [g/km] aer [km] uf [-] combined fc [l/100km] combined co2 [g/km] combined (co2 [g/km] p2w 2.0 na 4.446 101.37 62.5 0.777 0.989 22.56 -116.86 1.5 tc 4.618 105.29 62.2 0.777 1.028 23.43 -108.28 1.0 tc 4.438 101.19 62.3 0.777 0.988 22.52 -97.20 p3 2.0 na 4.273 97.42 56.1 0.753 1.058 24.11 -115.31 1.5 tc 4.506 102.74 53.6 0.734 1.198 27.32 -104.40 1.0 tc 4.378 99.82 55.0 0.753 1.084 24.70 -95.02 p4 2.0 na 4.213 96.06 66.4 0.777 0.938 21.38 -118.05 1.5 tc 4.364 99.50 66.7 0.777 0.971 22.14 -109.57 1.0 tc 4.293 97.88 66.9 0.777 0.955 21.78 -97.94 figure 5: em operating points in wltc, driven in ev mode obrázek 5: pracovní body elektromotoru v jízdním cyklu wltc, v elektrickém módu evaluation of plug-in parallel hev topologies using optimal control methods and vehicle dynamics simulation rastislav toman, jolana he!manová mecca 02 2020 page 30 where the em operating points for p2 are "compressed" to the low speed regions with lower efficiencies. figure 6 depicts the cs mode co2 values only, and gives us another interesting observation, that the best cs mode results are achieved with 2.0 na concept and not with the turbocharged concepts: there is no synergy effect between the powertrain hybridization and ice downsizing. the explanation lays in the bsfc maps: 2.0 na best value is 12.8/13.7 g/kwh better compared to 1.5 tc and 1.0 tc respectively. co2 value for 1.0 tc in icev powertrain is already very good, thus it’s hybridization cs mode potential in all phev topologies is the smallest. however, for 1.5 tc versus 1.0 tc comparison the downsizing effect is lowered by the effect of powertrain hybridization. from the vehicle homologation perspective, these cs mode sensitivities do not play any role. the only important result is the combined co2 values from the table 5, where the wltp calculation clearly prefers the aer before the cs mode. however, the cs mode results could be interesting from the point of view of the oems: cheaper, higher-displacement ices, hybridized in a clever way can bring some economic benefits. 4.3. p2 sensitivit y on gear shifting the overall results from the above chapter showed p2 fuel consumption using wltp generated gear shifting points. further gear shifting optimization using dp algorithm for the p2 topology in cs mode shows another co2 potential ("dp-optimized" in and figure 7) in comparison to the wltp shifting strategy. the 1.5 tc and 2.0 na concept achieve a very similar additional cs mode co2 improvement (both at ~10 gco2/km), and the 1.0 tc only ~5 gco2/km. we did not calculate the further co2 potential from the homologation perspective, because this requires also the aer simulation with optimized gear shifting strategy. however, the cs mode improvement indicates, that the aer results will also be improved, leading to even lower homologation co2 values. concluding this sensitivity, it is important to once again stress, that 2.0 na concept still proves having the highest hybridization potential. 4.4. dp vs. ecms control strategy sensitivit y this next sensitivity compares ecms and dp algorithms’ performance. figure 8 shows three of the nine total combinations icev p2 p3 p4 90 95 100 105 110 115 120 125 130 135 140 145 c o 2 [g /k m ] 139.4 101.4 97.4 96.1 131.7 105.3 102.7 99.5 119.7 101.2 99.8 97.9 2.0 na 1.5 tc 1.0 tc figure 6: overall cs mode co2 results (topologies vs. ice concepts) obrázek 6: celkové v$sledky produkce co2 v „charge sustaining“ módu (topologie hev vs. koncepty spalovacích motor%) wltp dp-optimized 85 90 95 100 105 110 c o 2 [g /k m ] 101.4 92.4 105.3 95 101.2 96.3 2.0 na 1.5 tc 1.0 tc figure 7: p2 topology co2 sensitivity on gear shifting obrázek 7: co2 citlivost topologie p2 na pr%b"h !azení ecms dp 101 soc levels dp 201 soc levels dp 1001 soc levels 96 98 100 102 104 106 108 c o 2 [g /k m ] 99.89 102.01 101.80 101.82 106.45 104.97 104.74 104.58 97.81 101.32 101.19 101.00 p2 & 1.0 tc p3 & 1.5 tc p4 & 2.0 na figure 8: control strategy co2 sensitivity in cs mode obrázek 8: co2 citlivost !ídících strategií v "charge sustaining" módu evaluation of plug-in parallel hev topologies using optimal control methods and vehicle dynamics simulation rastislav toman, jolana he!manová mecca 02 2020 page 31 of hev topology and ice concept. all the results use the same evlim parameter of 77 km/h. for the ecms results, we had to calibrate the equivalence factor s for each of the simulations – to reach the cs cycle; for the dp simulations we have tried different soc resolutions, starting with 1% of the soc span (defined by the socmax and socmin values), that divides the soc span to 101 soc levels. the 0.5% resolution uses 201 levels, and 0.1% 1001 levels. higher number of soc level leads to results closer to global optimum, but also the simulation times are longer: 0.1% resolution leads to approximately 10-times longer simulation than 1%. however, a look on figure 8 reveals, that the gt-suite’s ecms implementation performs better than dp implementation for two of the three topologies (results are consistent for all ice concepts). the only case when the dp is closer to a global optimum are the p3 topology results. differences of fc/co2 are in favor of ecms for the p2 (~2%), and p4 (~4%), and in favor of the dp (~1.5%) for the case of p3 topology. it is also important to note, that the procedure of finding the cs equivalence factor s requires an iterative process – usually 20-40 simulations. it takes approximately the same simulation time to reach the cs results with ecms, as to simulate one dp run with 1% soc resolution. the first reason for the rather unexpected result for the p2 and p4 topologies can be the way how the ecms and dp use their penalty functions: it is possible, that using the same formulation of penalty functions, or not using any at all, could resolve the difference. the second possible reason is the different sensitivities of both methods on control variables, that were set-up the same way in our simulations. however, from the user point of view, the simulations with dp algorithm may take more time, and not always reach the global optima "as advertised", but they may be more comfortable to work with, since they do not require the iterative process of table 6: acceleration results for 2.0 na concept and all hev topologies tabulka 6: akcelerace pro koncept spalovacího motoru 2.0 na a v'echny hev topologie mode topology 0-100 km/h [s] 60-80 km/h [s] 60-100 km/h [s] 80-120 km/h [s] gear 5 gear 6 gear 5 gear 6 gear 5 gear 6 hev p2 5.1 3.1 3.7 5.8 7.2 5.8 7.4 p3 6.3 3.0 3.2 5.6 6.3 5.6 6.5 p4 5.8 2.4 2.5 4.8 5.3 5.4 6.1 icev p2 8.2 5.7 7.0 10.9 14.1 10.7 14.5 p3 8.1 5.7 7.0 10.9 14.1 10.7 14.5 p4 8.3 5.8 7.1 11.1 14.4 10.9 14.8 ev p2 15.8 7.1 9.3 15.3 19.4 16.9 22.2 p3 32.2 6.9 6.8 14.0 14.0 15.4 15.4 p4 20.3 4.1 4.1 9.6 9.6 13.7 13.7 evlim 77km/h optimized ev lim no evlim 92 94 96 98 100 102 104 106 108 110 c o 2 [g /k m ] 106.64 101.16 101.55 106.45 104.10 104.20 99.93 98.2097.81 93.07 97.06 95.69 94.83 95.35 92.68 92.80 p3 & 2.0 na p3 & 1.5 tc p3 & 1.0 tc p4 & 2.0 na p4 & 1.5 tc p4 & 1.0 tc figure 9: ecms control strategy co2 sensitivity on heuristic parameter evlim in cs mode obrázek 9: co2 citlivost !ídící strategie ecms na heuristick$ parametr evlim v „charge sustaining” módu evaluation of plug-in parallel hev topologies using optimal control methods and vehicle dynamics simulation rastislav toman, jolana he!manová mecca 02 2020 page 32 equivalence factor s calibrations. the crucial fact is, that the results for both the ecms and dp gt-suite implementations are qualitatively the same (general behavior is the same with all ice concepts and hev topologies), although quantitatively there are some differences. 4.5. ecms sensitivit y on maximum vehicle speed in ev mode the last set of cs mode simulations is the ecms control method sensitivity on the evlim parameter. similarly, as for the penultimate sensitivity in chapter 4.4, we show only some of the results. the optimized evlim values generally achieve the best co2 results (figure 9). but, the sensitivity of all ice concept and hev topology combinations in cs mode vary: • p4 topology with 1.0 tc concept, and all the p2 combinations are not able to reach the cs mode in simulations with evlim parameter turned off (explanation in chapter 3.4); • 2.0 na concept – for all topologies – achieves the best results using evlim above 100 km/h; • p3 topology also achieves the best results using evlim above 100 km/h – for all ice concepts; • 1.0 tc concept uses relatively low evlim values in combination with p2 and p4 topologies; • p4 topology’s optimal evlim values decrease with increasing ice downsizing level; • the lowest sensitivity of all combinations is for p4 topology with 1.5 tc concept, where the co2 results change only around one gco2/km. finally, for some combinations, the evlim optimization can bring up to 5 gco2/km potential. 4.6. overall vehicle dynamics results we have prepared several vehicle dynamics scenarios to compare the different hybridization variants: acceleration of 0-100 km/h, 60-80 km/h, 60-100 km/h, and 80-120 km/h, and the maximum vehicle speed simulation. we have simulated all hev powertrain and ice concept combination; however, here we present only the hev mode icev mode ev mode 0 5 10 15 20 25 30 35 010 0 km /h a cc el er at io n [s ] 5.1 8.2 15.8 6.3 8.1 32.2 5.8 8.3 20.3 p2 p3 p4 figure 10: 0-100 km/h acceleration for 2.0 na concept and all hev topologies obrázek 10: zrychlení 0-100 km/h pro koncept motoru 2.0 na a v'echny hev topologie hev mode icev mode ev mode 0 40 80 120 160 200 240 280 v eh ic le s pe ed [k m /h ] 258 237.8 169.4 258 237.8 174.3 237.8 237.8 150 p2 p3 p4 figure 12: maximum vehicle speed for 2.0 na concept and all hev topologies in different driving modes obrázek 12: maximální rychlost vozidla pro koncept motoru 2.0 na a v'echny hev topologie a jízdní módy hev mode icev mode ev mode 0 2 4 6 8 10 12 14 16 18 20 80 -1 20 k m /h a cc el er at io n [s ] 5.8 10.7 16.9 5.6 10.7 15.4 5.4 10.9 13.7 p2 p3 p4 figure 11: 80-120 km/h acceleration for 2.0 na concept and all hev topologies, at 5th gear obrázek 11: zrychlení 80-120 km/h pro koncept motoru 2.0 na a v'echny hev topologie, na 5. p!evodov$ stupe) evaluation of plug-in parallel hev topologies using optimal control methods and vehicle dynamics simulation rastislav toman, jolana he!manová mecca 02 2020 page 33 2.0 na concept results, as the map-based approach does not capture well the dynamic effects of turbocharged ice concepts 1.0 tc, and 1.5 tc – as it was discussed in chapter 3.1. the p2, p3, and p4 topologies are compared in three different modes: hybrid (hev), conventional (icev), and pure electric (ev). 4.6.1 acceleration results the acceleration tests consist of 0-100 km/h acceleration, and then the tests of 60-80 km/h, 60-100 km/h, and 80-120 km/h accelerations at the 5th and 6th gear, for all driving modes (hev, icev, ev). the gear shifting strategy for 0-100 km/h acceleration considers the maximum ice or em speed. all acceleration results are listed in table 6, and shown in figures 10, and 11. the p2 topology achieves the best 0-100 km/h acceleration in combined hev mode, followed by the p4, and p3 topologies (figure 10). the case of ev acceleration shows the same order in topologies’ performance: the best result is achieved by the p2, followed by p4, and finally p3. the icev 0-100 km/h accelerations are the only accelerations, where the variation is very low: all achieve results around 8.2 seconds. the hev and ev results are strongly influenced by the gear ratios available for the em: the p2 topology can shift gears, whereas the p3, and p4 can only make use of single gear, which is more beneficial for p4. finally, the ev accelerations are logically also limited by the maximum em power. the rest of the table 6 contains the other accelerations at constant gear: sensitivities 60-80 km/h, 60-100 km/h, and 80-120 km/h, both on 5th gear, and 6th gear; all for 2.0 na engine concept. the 80-120 km/h scenario at 5th gear is shown in figure 11. also, these results are influenced mostly by the total gear ratios for different machines (ice, em): the p4 topology performs consistently as the best for both the hev and ev acceleration modes, and p2 as the worst; the icev accelerations show very little sensitivity, because the only differences are the drivetrain efficiencies, and vehicle masses. the biggest variation happens again in case of ev acceleration mode, as the topologies vary greatly in their final gear ratios. the 6th gear acceleration modes are qualitatively the same as on 5th gear. 4.6.2 maximum vehicle speed the final test is the vehicle maximum speed, which depends mainly on the maximum total powertrain power, available for different driving modes (figure 12). the combined hev maximum speed is transmission range limited and exceeds the vehicle speeds of 250 km/h for both the p2 and p3 topology. the p4 maximum hev speed is in this case the same as for icev driving mode, due to p4 electric motor speed limit, as the em is declutched above 150 km/h, and therefore not providing power. the icev maximum speeds are all around 238 km/h. finally, the maximum achievable ev speeds are all limited by the em maximum power of 54 kw, the p3 performing better then p2 topology. p4 maximum ev speed is also limited by abovementioned em speed limit, that is bound to the rear axle gear ratio design. 5. conclusions our paper presents a full development and benchmarking methodology for hev powertrains, that is built on gt-suite simulation software platform. the methodology consists of a combination of vehicle co2 homologation simulations (using wltp methodology), and some vehicle dynamics tasks (different accelerations test, and maximum vehicle speed test). we have prepared hev simulation models using two different simulation approaches: a backward-kinematic approach (kin models), and a dynamic approach (dyn models). our kin models are combined with gt-suite’s built-in optimal energy management control methods ecms and dynamic programming (dp). both kin and dyn models were then used for the co2 wltp homologation studies, obtaining charge sustaining (cs) co2, and all electric range (aer) results, together with the already mentioned additional vehicle dynamics results. the whole presented methodology was tested on three different hev topologies (p2, p3, and p4) in combination with three different ice concepts (2.0 na, 1.5 tc, and 1.0 tc), at the same hybridization level (with pice of 135 kw and pem of 54 kw), using a six-speed transmissions, for a c-class plug-in hev with a 14.8 kwh high voltage battery. all combinations show very good results compared to conventional powertrain, either in co2 homologation tests, or in vehicle dynamics tests: • icev comparison of the three ice concepts with different downsizing levels reveal a well-known fact, that downsized engines perform better in homologation driving cycles, such as wltc; • total co2 reduction potentials from icev to phev homologation co2 values are similar for all powertrains, ranging from -95 to -119 gco2/km; • the first part of the homologation are the aer tests, that show greater potentials for p4 and p2 hev variants, since these use the em in a more efficient manner, reaching aer values of ~66.7 km (p4), ~62.3 km (p2). however, the p3 also achieves high aer values of ~54.9 km; • the second part of the homologation are the cs tests, where the different hev powertrain combinations evaluation of plug-in parallel hev topologies using optimal control methods and vehicle dynamics simulation rastislav toman, jolana he!manová mecca 02 2020 page 34 reach co2 reduction potentials from -22 to -45 gco2/ km (using dp control method); • the p4 powertrains perform the best in the cs tests, together with the 2.0 na ice concept – on the other end of the results were the p2 topology, and the 1.5 tc concept; • the p2 topology cs results can be further improved by the gear shifting strategy optimization: bringing additional ~5-10 gco2/km improvement, beating the abovementioned p4 results; • the vehicle 0-100 km/h acceleration tests show the biggest performance benefit for p2 – that shifts gears also for the em – followed by the p4, and then p3; • the p4 topology then performs best at constant gear vehicle acceleration tests, followed by the p3, and p2. there are three main conclusions from the phev homologation and vehicle dynamics studies: 1. there is no synergy effect between the powertrain hybridization and ice downsizing, the trend seems to be rather opposite: 2.0 na concept is reaching the highest co2 reduction potentials; 2. it is valuable to optimize the hev topology having the ice concept in mind; however, the current phev homologation favors the aer, which may discourage developments in this area: the "simple" addition of a large enough battery (with aer of 50 km), reduces the homologation co2 by 90 gco2/km or more; 3. the vehicle dynamics tests further stress the importance of holistic hev powertrain optimization: especially the transmissions gear ratios, with the goal of getting the best also out of the em operation. apart from the overall homologation co2 and vehicle dynamics studies, we have also tested the performance of the gt-suite’s implementations of ecms and dp optimal control methods: • dp control method is generally more computationally demanding, but offers a user advantage of not having to calibrate for a correct equivalence factor to reach a cs cycle condition, as for the ecms method; • rather surprising result of the comparison of these two control methods in gt-suite is, that in some cases the ecms can reach values closer to the theoretical global optimum compared to dp method, which is "advertised" as the globally optimal control method; • however, both methods are consistent, providing qualitatively the same results, showing similar trends; • both methods are sensitive on their settings: in the case of dp it is the discretization of control inputs, and of state variable; ecms is sensitive on the equivalence factor; • additional heuristic parameters help ensure the cs convergence of ecms method and can further improve the co2 results. our further work will focus mainly on two areas: first is the amplification of the hev model database – adding more hev topologies; and second, embedding our simulation methodology into a multi-parametric and multi-objective hev powertrain optimization strategy. acknowledgements this work was realized using support of: • technological agency, czech republic, programme national competence centres, project # tn01000026 josef bozek national center of competence for surface vehicles. • the grant agency of the czech technical university in prague, grant no. sgs19/104/ohk2/2t/12. this support is gratefully acknowledged. list of notations and abbreviations aer all electric range awd all-wheel drive bsfc brake-specific fuel consumption cae computer aided engineering cd charge depleting co2 carbon dioxide cs charge sustaining dp dynamic programming dyn dynamic model ecms equivalent consumption minimization strategy ecu engine control unit em electric motor ev electric vehicle fc fuel consumption fwd front-wheel drive gt gamma technologies hev hybrid electric vehicle hv high voltage ice internal combustion engine icev internal combustion engine vehicle kin kinematic model lps load point shifting na naturally aspirated oem original equipment manufacturer ovc-hev off-vehicle charging hybrid electric vehicle phev plug-in hybrid electric vehicle pmp pontryagin’s minimum principle rde real driving emissions rpm revolutions per minute soc state of charge tc turbocharged uf utility factor evaluation of plug-in parallel hev topologies using optimal control methods and vehicle dynamics simulation rastislav toman, jolana he!manová mecca 02 2020 page 35 vvt variable valve timing wltc worldwide harmonized light-duty vehicles test cycle wltp worldwide harmonized light-duty vehicles test procedure references [1] reducing co2 emissions from passenger cars. european commission, online, cited: 2019-06-31, accessed from: https://ec.europa.eu/clima/policies/transport/vehicles/ cars_en [2] sundström, o., guzzella, l., soltic, p. (2008). optimal hybridization in two parallel hybrid electric vehicles using dynamic programming, ifac proceedings volumes, 41, 2: 4642-4647 [3] lodaya, d., zeman, j., okarmus, m., mohon, s., et al. (2020). optimization of fuel economy using optimal controls on regulatory and real-world driving cycles, sae int. j. advances & curr. prac. in mobility 2(3):1705-1716, 2020, doi:10.4271/2020-01-1007. [4] guzzela, l., sciaretta, a. vehicle propulsion systems: introduction to modelling and optimization, springer, 2013, isbn 978-3-642-35913-2 [5] biasini, r., onori, s., rizzoni, g. (2013). a near-optimal rule-based energy management strategy for medium duty hybrid truck, int. j. powertrains, vol. 2, nos. 2/3: 232-261 [6] zhou, h., xu, z., liu, l., liu, d., zhang, l. (2018). a rule-based energy management strategy based on dynamic programming for hydraulic hybrid vehicles, hindawi – mathematical problems in engineering, vol. 2018, doi:10.1155/2018/9492026 [7] shen, w., yu, h., hu, y., xi, j. (2016). optimization of shift schedule for hybrid electric vehicle with automated manual transmission, energies 2016, 9, 220, doi:10.3390/en9030220 [8] wang, r., lukic, s. (2012) dynamic programming technique in hybrid electric vehicle optimization, ieee xplore, doi: 10.1109/ievc.2012.6183284 [9] zeng, y., sheng, j., ming, l. (2018). adaptive real-time energy management strategy for plug-in hybrid electric vehicle based on simplified-ecms and a novel driving pattern recognition method, mathematical problems in engineering, p. 1-12, doi:10.1155/2018/5816861 [10] nüesch, t., cerofolini, a., mancini, g., cavina, n., onder, ch., guzzella, l. (2014). equivalent consumption minimization strategy for control of real driving nox emissions of a diesel hybrid electric vehicle, in: energies 2014, vol. 7, p. 3148-3178, doi:10.3390/en70532148 [11] yuan, z., teng, l., fengchun, s., peng, h. (2013). comparative study of dynamic programming and pontryagin’s minimum principle on energy management for a parallel hybrid electric vehicle, energies 2013, 6, 2305-2318, doi:10.3390/en6042305 [12] zeman, j., papadimitriou, i., watanabe, k., kubo, m., kumagai, t. (2012). modeling and optimization of plugin hybrid electric vehicle fuel economy, sae technical paper 2012-01-1018, doi:10.4271/2012-01-1018 [13] bellman, r. (1966). dynamic programming, science, vol. 153, no. 3731, pp. 34-37. [14] un global technical regulation no. 15: worldwide harmonized light vehicles test procedure (ece/ trans/180/add.15). united nations economic commission for europe, 2019-06-26, cited: 2020-11-01, accessed from: https://www.unece.org/fileadmin/dam/ trans/main/wp29/wp29wgs/wp29gen/wp29registry/ecetrans-180a15am5e.pdf mecca 02 2017 page 37 evaluation of the predictive capabilities of a phenomenological combustion model for natural gas si engine rastislav toman, jan macek 10.1515/mecdc ‑2017 ‑0007 evaluation of the predictive capabilities of a phenomenological combustion model for natural gas si engine rastislav toman, jan macek rastislav toman, jan macek ctu in prague, faculty of mechanical engineering; technická 4, praha 6, 166 07, czech republic e ‑mail: rastislav.toman@fs.cvut.cz, jan.macek@fs.cvut.cz abstract the current study evaluates the predictive capabilities of a new phenomenological combustion model, available as a part of the gt ‑suite software package. it is comprised of two main sub ‑models: 0d model of in ‑cylinder flow and turbulence, and turbulent si combustion model. the 0d in ‑cylinder flow model (engcylflow) uses a combined k ‑k ‑ε kinetic energy cascade approach to predict the evolution of the in ‑cylinder charge motion and turbulence, where k and k are the mean and turbulent kinetic energies, and ε is the turbulent dissipation rate. the subsequent turbulent combustion model (engcylcombsiturb) gives the in ‑cylinder burn rate; based on the calculation of flame speeds and flame kernel development. this phenomenological approach reduces significantly the overall computational effort compared to the 3d ‑cfd, thus allowing the computation of full engine operating map and the vehicle driving cycles. model was calibrated using a full map measurement from a turbocharged natural gas si engine, with swirl intake ports. sensitivity studies on different calibration methods, and laminar flame speed sub ‑models were conducted. validation process for both the calibration and sensitivity studies was concerning the in ‑cylinder pressure traces and burn rates for several engine operation points achieving good overall results. key words: predictive phenomenological model; internal combustion engine; spark ‑ignition; k ‑k ‑ε kinetic energy cascade; 0d in ‑cylinder flow model; turbulent si combustion model; natural gas engine; genetic algorithm; gt ‑suite shrnutí predkladaný článok hodnotí prediktívne schopnosti nového fenomenologického modelu horenia, ktorý je k dispozícii ako súčasť softvérového balíka gt ‑suite. skladá sa z dvoch hlavných sub ‑modelov: 0d modelu prúdenia a turbulencie vo valci a zážihového turbulentného modelu horenia. 0d model prúdenia a turbulencie vo valci (engcylflow) používa kombinovaný prístup k ‑k ‑ε kaskády kinetickej energie na predpoveď pohybu zmesi a turbulencie vo valci, kde k a k sú stredné a turbulentné kinetické energie a  ε je turbulentná rýchlosť disipácie. následný model turbulentného horenia (engcylcombsiturb) určuje rýchlosť horenia vo valci na základe výpočtu rýchlosti čela plameňa a vývoja jadra plameňa. tento fenomenologický prístup výrazne znižuje celkovú výpočtovú náročnosť v porovnaní s 3d ‑cfd, čo umožňuje výpočet úplnej charakteristiky spaľovacieho motora a jazdných cyklov vozidla. model bol kalibrovaný pomocou meraní úplnej charakteristiky preplňovaného zážihového motora na zemný plyn so swirlovými vstupnými kanálmi. boli vykonané štúdie citlivosti na rôzne kalibračné metódy a na rôzne sub ‑modely laminárnej rýchlosti čela plameňa. validačný proces pre kalibrácie a štúdie citlivosti sa týkal tlaku vo valci a rýchlostí horenia pre niekoľko pracovných bodov motora, dosahujúc dobré celkové výsledky. klíčová slova: predik tívny fenomenologický model; zážihový spaľovací motor; k ‑k ‑ε kaskáda kinetickej energie; 0d modelu prúdenia vo valci; turbulentný zážihový model horenia; motor na zemný plyn; genetický algoritmus; gt ‑suite evaluation of the predictive capabilities of a phenomenological combustion model for natural gas si engine mecca 02 2017 page 38 evaluation of the predictive capabilities of a phenomenological combustion model for natural gas si engine rastislav toman, jan macek 1. introduction current development of the internal combustion engines (ice) is focused on the overall efficiency improvement and emissions reduction. to fulfil these goals, downsizing of the ice presents one of the most valuable options. but the increasing boost levels also lead to an increase in the knock likelihood, requiring spark timing retardation or mixture enrichment. moreover, current engines use progressively also additional advanced control systems, such as advanced gas exchange systems, cylinder deactivation, or variable compression ‑ratio systems. with many iterations needed, accurate and robust modelling of the combustion process have become essential during the ice development process, with an emphasis on the overall simulation time of one engine operating cycle. a detailed 3d computational fluid dynamics (3d ‑cfd) analysis of the in ‑cylinder flows, charge motion and combustion leads to accurate prediction of burn rate (if set‑ ‑up properly), but with the obvious drawback of its high computational demands [1]. 3d ‑cfd is therefore used mostly for the analysis of separate engine operating points. empirical combustion models usually use an approximation of a measured burn rate. the most common empirical model is a vibe formula [2]. however, if the user wants to obtain correct burn rate values in changed ice operating conditions, reference burn rate pattern must be adjusted by additional formulas [3], [4]. in general, empirical models are simple and work well inside the calibrated region, but their extrapolation abilities are poor [5]. multi ‑zone models of combustion and heat transfer in si engines present a fast, accurate, stable and above all physical‑ ‑based solution. a general theory of zone models based on the laws on conservation is described in [6], with a comparison of lagrangian and eulerian approaches. recent paper of hvezda [7] presents a specific adaptive approach to the chemical transformation. multi ‑zone model of hvezda models in detail the flame velocities using a turbulent coefficient, and accounts for the real geometry of the combustion chamber. finally, phenomenological combustion models also respect the combustion chamber geometry and obtain a burn rate by the calculation of turbulent flame speed and instantaneous flame area [8]. these models need an information on in‑ ‑cylinder flow quantities as well. several 0d turbulence models aim to reproduce the complex 3d phenomena, mainly by k ‑ε approach [9], [10], [11] or k ‑k approach recently studied in [12] and [13]. both, the multi ‑zone and phenomenological models show very good extrapolation capabilities and low computational demands, allowing for the fast simulation of vehicle driving cycles. a combustion model evaluated in this study consists of two main sub ‑models: 0d in ‑cylinder flow model engcylflow (or flow) and turbulent combustion model engcylcombsiturb (or siturb). gamma technologies is currently developing both sub ‑models as a part of gt ‑suite software package [14]. the flow model combines the k ‑ε approach of morel et al. [9], [10] with the k ‑k into combined k ‑k ‑ε kinetic energy cascade model. fogla et al. [15] describes the current flow model, comparing with 3d ‑cfd and former model version, using two similar turbocharged gasoline ices, with tumble intake ports. the siturb model – originally developed by wahiduzzaman, morel and sheard [8] – uses a turbulent flame concept, directly linked to the in ‑cylinder flow and turbulence calculation. mirzaeian et al. [16] assessed the predictive capability of the current model version adding the equation system description. they also proposed a calibration method starting with doe calibration of the flow model against the 3d ‑cfd data and continuing with the siturb calibration using the genetic algorithms (ga) with the objective to match the burn rate against the measurement data (turbocharged gasoline ice with tumble intake port). more detail on the combustion model follows in section 2. 1.1 main goals the main objectives of this paper are: • first, to calibrate the current combustion model, obtaining a single set of optimal model parameters; • second, to test its predictive capabilities. already mentioned papers [15] and [16] evaluated the model capabilities on turbocharged gasoline engines, with tumble intake ports. this study uses a full engine map measurement set with egr variations and stoichiometric conditions of the ice fueled by natural gas, with swirl intake ports. the additional goals of the paper are following: • to summarize the main features of the predictive combustion model; • to compare different calibration approaches; • to test the sensitivities of the combustion model on the laminar flame speed. 2. predictive combustion model 2.1 in ‑cylinder flow model the main equation system of the flow model contains three differential equations (equations 1 ‑3) that govern the mean kinetic energy k=(1⁄2)u 2 (u is the mean velocity inside the cylinder), turbulent kinetic energy k=(3⁄2)u' 2 (u' is the mean fluctuating turbulent velocity inside the cylinder), and the mecca 02 2017 page 39 evaluation of the predictive capabilities of a phenomenological combustion model for natural gas si engine rastislav toman, jan macek turbulent dissipation rate ε. the model assumes homogeneous and isotropic turbulent field [15].  to summarize the main features of the predictive combustion model;  to compare different calibration approaches;  to test the sensitivities of the combustion model on the laminar flame speed. 2. predictive combustion model 2.1 in-cylinder flow model the main equation system of the flow model contains three differential equations (equations 1-3) that govern the mean kinetic energy � � �1 2⁄ ��� (� is the mean velocity inside the cylinder), turbulent kinetic energy � � �3 2⁄ ���� (�� is the mean fluctuating turbulent velocity inside the cylinder), and the turbulent dissipation rate ϵ. the model assumes homogeneous and isotropic turbulent field [15]. ����� �� � ����1 � ������� � ��� ��� � �� (1) ����� �� � ��������� � ��� ��� � �� � ������ � �� (2) ����� �� � ������ √� �� � ��� ��� � �� � ������ √� �� � 1.�2 ��� � (3) first right-hand side terms in all three equations represent the production of each flow quantity, with the inflow energy ���. parameter ��� indicates the fraction of inflow energy entering the cylinder directly as turbulence, although not generated by the kinetic energy cascade process. the second right-hand side term in the main equations, describes the energy out-flow through the valves, with the mass flow rate of the cylinder exit flow �� ���. production terms �� and �� (equations 4-5) model the production of the turbulent kinetic energy and a dissipation rate from the large scale mean flows via the kinetic energy cascade process; �� represents a turbulent viscosity, � a density and �� a rate of change of density inside the cylinder. the appendix of [15] describes the evolution of these terms. �� � ���� 2�� ��� � 23�� � �� �� � 2 3��� � �� �� � (4) �� � � � ��.�6���� �� ��� � 2�� ����� � 2.64 3 ��� � �� �� � � (5) the last right-hand side term in each of the three main equations is a sink term for its respective quantity. the terms with the quantity � model the production of turbulence by the decay of the tumble macro-vortex during the compression [15]. simple equation systems for the time rate change of the angular momentum �� ��⁄ model the rotational components of the flow – tumble and swirl – as a single macro-vortex undergoing stretching and compression during the engine intake and compression. swirl and tumble are produced by the incoming charge, accounting for the measured swirl and tumble coefficients, and reduced by the cylinder out-flow. equation systems for both rotational motions contain a proper decay functions. paper [15] does not discuss the swirl decay function, but provides further information on the tumble decay function. former flow model ([10], [11]) accounted for the squish motion (inside the swirl model) and injection event kinetic energy and so does the current flow model. however, the exact equation systems are not available in [15]. since the current flow model calculates the kinetic energy and the dissipation rate, the evolution of integral length scale �� over time is then obtained directly with the equation 6 (�� � �.�� is a standard k-ε model constant) [15]. �� � ��� �⁄ �� �⁄ � (6) (1)  to summarize the main features of the predictive combustion model;  to compare different calibration approaches;  to test the sensitivities of the combustion model on the laminar flame speed. 2. predictive combustion model 2.1 in-cylinder flow model the main equation system of the flow model contains three differential equations (equations 1-3) that govern the mean kinetic energy � � �1 2⁄ ��� (� is the mean velocity inside the cylinder), turbulent kinetic energy � � �3 2⁄ ���� (�� is the mean fluctuating turbulent velocity inside the cylinder), and the turbulent dissipation rate ϵ. the model assumes homogeneous and isotropic turbulent field [15]. ����� �� � ����1 � ������� � ��� ��� � �� (1) ����� �� � ��������� � ��� ��� � �� � ������ � �� (2) ����� �� � ������ √� �� � ��� ��� � �� � ������ √� �� � 1.�2 ��� � (3) first right-hand side terms in all three equations represent the production of each flow quantity, with the inflow energy ���. parameter ��� indicates the fraction of inflow energy entering the cylinder directly as turbulence, although not generated by the kinetic energy cascade process. the second right-hand side term in the main equations, describes the energy out-flow through the valves, with the mass flow rate of the cylinder exit flow �� ���. production terms �� and �� (equations 4-5) model the production of the turbulent kinetic energy and a dissipation rate from the large scale mean flows via the kinetic energy cascade process; �� represents a turbulent viscosity, � a density and �� a rate of change of density inside the cylinder. the appendix of [15] describes the evolution of these terms. �� � ���� 2�� ��� � 23�� � �� �� � 2 3��� � �� �� � (4) �� � � � ��.�6���� �� ��� � 2�� ����� � 2.64 3 ��� � �� �� � � (5) the last right-hand side term in each of the three main equations is a sink term for its respective quantity. the terms with the quantity � model the production of turbulence by the decay of the tumble macro-vortex during the compression [15]. simple equation systems for the time rate change of the angular momentum �� ��⁄ model the rotational components of the flow – tumble and swirl – as a single macro-vortex undergoing stretching and compression during the engine intake and compression. swirl and tumble are produced by the incoming charge, accounting for the measured swirl and tumble coefficients, and reduced by the cylinder out-flow. equation systems for both rotational motions contain a proper decay functions. paper [15] does not discuss the swirl decay function, but provides further information on the tumble decay function. former flow model ([10], [11]) accounted for the squish motion (inside the swirl model) and injection event kinetic energy and so does the current flow model. however, the exact equation systems are not available in [15]. since the current flow model calculates the kinetic energy and the dissipation rate, the evolution of integral length scale �� over time is then obtained directly with the equation 6 (�� � �.�� is a standard k-ε model constant) [15]. �� � ��� �⁄ �� �⁄ � (6) (2)  to summarize the main features of the predictive combustion model;  to compare different calibration approaches;  to test the sensitivities of the combustion model on the laminar flame speed. 2. predictive combustion model 2.1 in-cylinder flow model the main equation system of the flow model contains three differential equations (equations 1-3) that govern the mean kinetic energy � � �1 2⁄ ��� (� is the mean velocity inside the cylinder), turbulent kinetic energy � � �3 2⁄ ���� (�� is the mean fluctuating turbulent velocity inside the cylinder), and the turbulent dissipation rate ϵ. the model assumes homogeneous and isotropic turbulent field [15]. ����� �� � ����1 � ������� � ��� ��� � �� (1) ����� �� � ��������� � ��� ��� � �� � ������ � �� (2) ����� �� � ������ √� �� � ��� ��� � �� � ������ √� �� � 1.�2 ��� � (3) first right-hand side terms in all three equations represent the production of each flow quantity, with the inflow energy ���. parameter ��� indicates the fraction of inflow energy entering the cylinder directly as turbulence, although not generated by the kinetic energy cascade process. the second right-hand side term in the main equations, describes the energy out-flow through the valves, with the mass flow rate of the cylinder exit flow �� ���. production terms �� and �� (equations 4-5) model the production of the turbulent kinetic energy and a dissipation rate from the large scale mean flows via the kinetic energy cascade process; �� represents a turbulent viscosity, � a density and �� a rate of change of density inside the cylinder. the appendix of [15] describes the evolution of these terms. �� � ���� 2�� ��� � 23�� � �� �� � 2 3��� � �� �� � (4) �� � � � ��.�6���� �� ��� � 2�� ����� � 2.64 3 ��� � �� �� � � (5) the last right-hand side term in each of the three main equations is a sink term for its respective quantity. the terms with the quantity � model the production of turbulence by the decay of the tumble macro-vortex during the compression [15]. simple equation systems for the time rate change of the angular momentum �� ��⁄ model the rotational components of the flow – tumble and swirl – as a single macro-vortex undergoing stretching and compression during the engine intake and compression. swirl and tumble are produced by the incoming charge, accounting for the measured swirl and tumble coefficients, and reduced by the cylinder out-flow. equation systems for both rotational motions contain a proper decay functions. paper [15] does not discuss the swirl decay function, but provides further information on the tumble decay function. former flow model ([10], [11]) accounted for the squish motion (inside the swirl model) and injection event kinetic energy and so does the current flow model. however, the exact equation systems are not available in [15]. since the current flow model calculates the kinetic energy and the dissipation rate, the evolution of integral length scale �� over time is then obtained directly with the equation 6 (�� � �.�� is a standard k-ε model constant) [15]. �� � ��� �⁄ �� �⁄ � (6)  to summarize the main features of the predictive combustion model;  to compare different calibration approaches;  to test the sensitivities of the combustion model on the laminar flame speed. 2. predictive combustion model 2.1 in-cylinder flow model the main equation system of the flow model contains three differential equations (equations 1-3) that govern the mean kinetic energy � � �1 2⁄ ��� (� is the mean velocity inside the cylinder), turbulent kinetic energy � � �3 2⁄ ���� (�� is the mean fluctuating turbulent velocity inside the cylinder), and the turbulent dissipation rate ϵ. the model assumes homogeneous and isotropic turbulent field [15]. ����� �� � ����1 � ������� � ��� ��� � �� (1) ����� �� � ��������� � ��� ��� � �� � ������ � �� (2) ����� �� � ������ √� �� � ��� ��� � �� � ������ √� �� � 1.�2 ��� � (3) first right-hand side terms in all three equations represent the production of each flow quantity, with the inflow energy ���. parameter ��� indicates the fraction of inflow energy entering the cylinder directly as turbulence, although not generated by the kinetic energy cascade process. the second right-hand side term in the main equations, describes the energy out-flow through the valves, with the mass flow rate of the cylinder exit flow �� ���. production terms �� and �� (equations 4-5) model the production of the turbulent kinetic energy and a dissipation rate from the large scale mean flows via the kinetic energy cascade process; �� represents a turbulent viscosity, � a density and �� a rate of change of density inside the cylinder. the appendix of [15] describes the evolution of these terms. �� � ���� 2�� ��� � 23�� � �� �� � 2 3��� � �� �� � (4) �� � � � ��.�6���� �� ��� � 2�� ����� � 2.64 3 ��� � �� �� � � (5) the last right-hand side term in each of the three main equations is a sink term for its respective quantity. the terms with the quantity � model the production of turbulence by the decay of the tumble macro-vortex during the compression [15]. simple equation systems for the time rate change of the angular momentum �� ��⁄ model the rotational components of the flow – tumble and swirl – as a single macro-vortex undergoing stretching and compression during the engine intake and compression. swirl and tumble are produced by the incoming charge, accounting for the measured swirl and tumble coefficients, and reduced by the cylinder out-flow. equation systems for both rotational motions contain a proper decay functions. paper [15] does not discuss the swirl decay function, but provides further information on the tumble decay function. former flow model ([10], [11]) accounted for the squish motion (inside the swirl model) and injection event kinetic energy and so does the current flow model. however, the exact equation systems are not available in [15]. since the current flow model calculates the kinetic energy and the dissipation rate, the evolution of integral length scale �� over time is then obtained directly with the equation 6 (�� � �.�� is a standard k-ε model constant) [15]. �� � ��� �⁄ �� �⁄ � (6) (3) first right ‑hand side terms in all three equations represent the production of each flow quantity, with the inflow energy ein. parameter αin indicates the fraction of inflow energy entering the cylinder directly as turbulence, although not generated by the kinetic energy cascade process. the second right ‑hand side term in the main equations, describes the energy out ‑flow through the valves, with the mass flow rate of the cylinder exit flow m· out. production terms pk and pє (equations 4 ‑5) model the production of the turbulent kinetic energy and a dissipation rate from the large scale mean flows via the kinetic energy cascade process; υt represents a turbulent viscosity, ρ a density and ρ· a rate of change of density inside the cylinder. the appendix of [15] describes the evolution of these terms.  to summarize the main features of the predictive combustion model;  to compare different calibration approaches;  to test the sensitivities of the combustion model on the laminar flame speed. 2. predictive combustion model 2.1 in-cylinder flow model the main equation system of the flow model contains three differential equations (equations 1-3) that govern the mean kinetic energy � � �1 2⁄ ��� (� is the mean velocity inside the cylinder), turbulent kinetic energy � � �3 2⁄ ���� (�� is the mean fluctuating turbulent velocity inside the cylinder), and the turbulent dissipation rate ϵ. the model assumes homogeneous and isotropic turbulent field [15]. ����� �� � ����1 � ������� � ��� ��� � �� (1) ����� �� � ��������� � ��� ��� � �� � ������ � �� (2) ����� �� � ������ √� �� � ��� ��� � �� � ������ √� �� � 1.�2 ��� � (3) first right-hand side terms in all three equations represent the production of each flow quantity, with the inflow energy ���. parameter ��� indicates the fraction of inflow energy entering the cylinder directly as turbulence, although not generated by the kinetic energy cascade process. the second right-hand side term in the main equations, describes the energy out-flow through the valves, with the mass flow rate of the cylinder exit flow �� ���. production terms �� and �� (equations 4-5) model the production of the turbulent kinetic energy and a dissipation rate from the large scale mean flows via the kinetic energy cascade process; �� represents a turbulent viscosity, � a density and �� a rate of change of density inside the cylinder. the appendix of [15] describes the evolution of these terms. �� � ���� 2�� ��� � 23�� � �� �� � 2 3��� � �� �� � (4) �� � � � ��.�6���� �� ��� � 2�� ����� � 2.64 3 ��� � �� �� � � (5) the last right-hand side term in each of the three main equations is a sink term for its respective quantity. the terms with the quantity � model the production of turbulence by the decay of the tumble macro-vortex during the compression [15]. simple equation systems for the time rate change of the angular momentum �� ��⁄ model the rotational components of the flow – tumble and swirl – as a single macro-vortex undergoing stretching and compression during the engine intake and compression. swirl and tumble are produced by the incoming charge, accounting for the measured swirl and tumble coefficients, and reduced by the cylinder out-flow. equation systems for both rotational motions contain a proper decay functions. paper [15] does not discuss the swirl decay function, but provides further information on the tumble decay function. former flow model ([10], [11]) accounted for the squish motion (inside the swirl model) and injection event kinetic energy and so does the current flow model. however, the exact equation systems are not available in [15]. since the current flow model calculates the kinetic energy and the dissipation rate, the evolution of integral length scale �� over time is then obtained directly with the equation 6 (�� � �.�� is a standard k-ε model constant) [15]. �� � ��� �⁄ �� �⁄ � (6) (4)  to summarize the main features of the predictive combustion model;  to compare different calibration approaches;  to test the sensitivities of the combustion model on the laminar flame speed. 2. predictive combustion model 2.1 in-cylinder flow model the main equation system of the flow model contains three differential equations (equations 1-3) that govern the mean kinetic energy � � �1 2⁄ ��� (� is the mean velocity inside the cylinder), turbulent kinetic energy � � �3 2⁄ ���� (�� is the mean fluctuating turbulent velocity inside the cylinder), and the turbulent dissipation rate ϵ. the model assumes homogeneous and isotropic turbulent field [15]. ����� �� � ����1 � ������� � ��� ��� � �� (1) ����� �� � ��������� � ��� ��� � �� � ������ � �� (2) ����� �� � ������ √� �� � ��� ��� � �� � ������ √� �� � 1.�2 ��� � (3) first right-hand side terms in all three equations represent the production of each flow quantity, with the inflow energy ���. parameter ��� indicates the fraction of inflow energy entering the cylinder directly as turbulence, although not generated by the kinetic energy cascade process. the second right-hand side term in the main equations, describes the energy out-flow through the valves, with the mass flow rate of the cylinder exit flow �� ���. production terms �� and �� (equations 4-5) model the production of the turbulent kinetic energy and a dissipation rate from the large scale mean flows via the kinetic energy cascade process; �� represents a turbulent viscosity, � a density and �� a rate of change of density inside the cylinder. the appendix of [15] describes the evolution of these terms. �� � ���� 2�� ��� � 23�� � �� �� � 2 3��� � �� �� � (4) �� � � � ��.�6���� �� ��� � 2�� ����� � 2.64 3 ��� � �� �� � � (5) the last right-hand side term in each of the three main equations is a sink term for its respective quantity. the terms with the quantity � model the production of turbulence by the decay of the tumble macro-vortex during the compression [15]. simple equation systems for the time rate change of the angular momentum �� ��⁄ model the rotational components of the flow – tumble and swirl – as a single macro-vortex undergoing stretching and compression during the engine intake and compression. swirl and tumble are produced by the incoming charge, accounting for the measured swirl and tumble coefficients, and reduced by the cylinder out-flow. equation systems for both rotational motions contain a proper decay functions. paper [15] does not discuss the swirl decay function, but provides further information on the tumble decay function. former flow model ([10], [11]) accounted for the squish motion (inside the swirl model) and injection event kinetic energy and so does the current flow model. however, the exact equation systems are not available in [15]. since the current flow model calculates the kinetic energy and the dissipation rate, the evolution of integral length scale �� over time is then obtained directly with the equation 6 (�� � �.�� is a standard k-ε model constant) [15]. �� � ��� �⁄ �� �⁄ � (6) (5) the last right ‑hand side term in each of the three main equations is a sink term for its respective quantity. the terms with the quantity t model the production of turbulence by the decay of the tumble macro ‑vortex during the compression [15]. simple equation systems for the time rate change of the angular momentum dl/dt model the rotational components of the flow – tumble and swirl – as a single macro ‑vortex undergoing stretching and compression during the engine intake and compression. swirl and tumble are produced by the incoming charge, accounting for the measured swirl and tumble coefficients, and reduced by the cylinder out ‑flow. equation systems for both rotational motions contain a proper decay functions. paper [15] does not discuss the swirl decay function, but provides further information on the tumble decay function. former flow model ([10], [11]) accounted for the squish motion (inside the swirl model) and injection event kinetic energy and so does the current flow model. however, the exact equation systems are not available in [15]. since the current flow model calculates the kinetic energy and the dissipation rate, the evolution of integral length scale lt over time is then obtained directly with the equation 6 (cμ = 0.09 is a standard k ‑ε model constant) [15].  to summarize the main features of the predictive combustion model;  to compare different calibration approaches;  to test the sensitivities of the combustion model on the laminar flame speed. 2. predictive combustion model 2.1 in-cylinder flow model the main equation system of the flow model contains three differential equations (equations 1-3) that govern the mean kinetic energy � � �1 2⁄ ��� (� is the mean velocity inside the cylinder), turbulent kinetic energy � � �3 2⁄ ���� (�� is the mean fluctuating turbulent velocity inside the cylinder), and the turbulent dissipation rate ϵ. the model assumes homogeneous and isotropic turbulent field [15]. ����� �� � ����1 � ������� � ��� ��� � �� (1) ����� �� � ��������� � ��� ��� � �� � ������ � �� (2) ����� �� � ������ √� �� � ��� ��� � �� � ������ √� �� � 1.�2 ��� � (3) first right-hand side terms in all three equations represent the production of each flow quantity, with the inflow energy ���. parameter ��� indicates the fraction of inflow energy entering the cylinder directly as turbulence, although not generated by the kinetic energy cascade process. the second right-hand side term in the main equations, describes the energy out-flow through the valves, with the mass flow rate of the cylinder exit flow �� ���. production terms �� and �� (equations 4-5) model the production of the turbulent kinetic energy and a dissipation rate from the large scale mean flows via the kinetic energy cascade process; �� represents a turbulent viscosity, � a density and �� a rate of change of density inside the cylinder. the appendix of [15] describes the evolution of these terms. �� � ���� 2�� ��� � 23�� � �� �� � 2 3��� � �� �� � (4) �� � � � ��.�6���� �� ��� � 2�� ����� � 2.64 3 ��� � �� �� � � (5) the last right-hand side term in each of the three main equations is a sink term for its respective quantity. the terms with the quantity � model the production of turbulence by the decay of the tumble macro-vortex during the compression [15]. simple equation systems for the time rate change of the angular momentum �� ��⁄ model the rotational components of the flow – tumble and swirl – as a single macro-vortex undergoing stretching and compression during the engine intake and compression. swirl and tumble are produced by the incoming charge, accounting for the measured swirl and tumble coefficients, and reduced by the cylinder out-flow. equation systems for both rotational motions contain a proper decay functions. paper [15] does not discuss the swirl decay function, but provides further information on the tumble decay function. former flow model ([10], [11]) accounted for the squish motion (inside the swirl model) and injection event kinetic energy and so does the current flow model. however, the exact equation systems are not available in [15]. since the current flow model calculates the kinetic energy and the dissipation rate, the evolution of integral length scale �� over time is then obtained directly with the equation 6 (�� � �.�� is a standard k-ε model constant) [15]. �� � ��� �⁄ �� �⁄ � (6) (6) equations 1 ‑5 contain four calibration parameters that can be used to match the in ‑cylinder flow model with 3d ‑cfd results and to enhance the predictive abilities of the consecutive turbulent combustion model. these parameters are following: • intake term multiplier c1 multiplies the intake term cin = 0.18c1 and thus accounts for the actual flow velocities through the valves, since these are not equal to the isentropic values assumed by the ein; • production term multiplier c2 adjusts the magnitudes of the production terms (equations 4 ‑5) directly through the production term cβ with cβ = 0.38 c2; • geometrical length scale multiplier c3 adjust the magnitudes of the production terms indirectly, through the scaling of geometrical length scale lg = clen × min(s, 0.5b), with b being the cylinder bore, s the instantaneous piston stroke, and clen = 0.19c3; • tumble term multiplier ctumb controls the intensity of the tumble decay contribution to the production of turbulence. 2.2 turbulent combustion model turbulent combustion model siturb predicts the burn rate for the homogeneous charge, respecting the geometry of the combustion chamber, spark location and timing, mixture motion and fuel properties. the model simulates the development of the flame as a turbulent entrainment process followed by a burnup process in a region behind the flame front [8]. equations 1-5 contain four calibration parameters that can be used to match the in-cylinder flow model with 3d-cfd results and to enhance the predictive abilities of the consecutive turbulent combustion model. these parameters are following:  intake term multiplier �� multiplies the intake term ��� � ��1��� and thus accounts for the actual flow velocities through the valves, since these are not equal to the isentropic values assumed by the ���;  production term multiplier �� adjusts the magnitudes of the production terms (equations 4-5) directly through the production term �� with �� � ������;  geometrical length scale multiplier �� adjust the magnitudes of the production terms indirectly, through the scaling of geometrical length scale �� � ���� � �����������, with � being the cylinder bore, � the instantaneous piston stroke, and ���� � ��1���;  tumble term multiplier ����� controls the intensity of the tumble decay contribution to the production of turbulence. 2.2 turbulent combustion model turbulent combustion model siturb predicts the burn rate for the homogeneous charge, respecting the geometry of the combustion chamber, spark location and timing, mixture motion and fuel properties. the model simulates the development of the flame as a turbulent entrainment process followed by a burnup process in a region behind the flame front [8]. ��� �� � �� ∙ �� ∙ ��� � ��� (7) the entrainment mass rate of unburned gas ��� ��⁄ is determined by the equation 7; with the flame front area ��, laminar and turbulent flame speeds �� and �� and finally the unburned gas density ��. dedicated sub-model evaluates the instantaneous flame front area from the combustion chamber geometry assuming the flame front spherical in shape [8]. a model parameter ������ (initial spark size) determines the initial flame front size. for a typical spark plug, its value should be the same as the gap between the spark plug electrodes. however, the real spark size can slightly differ, especially with high-energy spark plugs. therefore, we use the ������ as a model tuning parameter also, in a reasonable range of sizes. �� � ��� � �� ∙ �� � ����� ∙ � �� ��� � ∙ � ���� � ∙ �1 � ���� ∙ �������∙���� (8) �� � �� ∙ �� ∙ �1 � 1 1 � �� ∙ ��� ���⁄ � (9) during the initial flame kernel development, when the size of the flame kernel is still small, the unburned gas entrainment rate is limited by the laminar flame speed �� (equation 8). then, the equation 9 accounts for the transition to the turbulent flame speed, with �� representing the mean fluctuating turbulent velocity, �� the flame radius and �� the turbulent length scale [16]. the rate of burnup ��� ��⁄ behind the flame front is proportional to the unburned mass behind the flame front, resulting in the rate equation 10 for the burned mass ��. ��� �� � �� � �� � (10) model assumes that the burnup phase takes place in the laminar flame speed and over the taylor microscale of turbulence �, with time constant � (equation 11). other assumption is that the turbulence is isotropic and therefore the taylor microscale of turbulence � can be obtained from the integral length scale �� (equations 12). � � ��� (11) � � �� ∙ ������ (12a) ��� � �� ∙ �� ∙ �� � (12b) (7) the entrainment mass rate of unburned gas dme /dt is determined by the equation 7; with the flame front area af, laminar and turbulent flame speeds sl and st and finally the unburned gas density ρu. dedicated sub ‑model evaluates the instantaneous flame front area from the combustion chamber geometry assuming mecca 02 2017 page 40 evaluation of the predictive capabilities of a phenomenological combustion model for natural gas si engine rastislav toman, jan macek the flame front spherical in shape [8]. a model parameter ssinit (initial spark size) determines the initial flame front size. for a typical spark plug, its value should be the same as the gap between the spark plug electrodes. however, the real spark size can slightly differ, especially with high ‑energy spark plugs. therefore, we use the ssinit as a model tuning parameter also, in a reasonable range of sizes. equations 1-5 contain four calibration parameters that can be used to match the in-cylinder flow model with 3d-cfd results and to enhance the predictive abilities of the consecutive turbulent combustion model. these parameters are following:  intake term multiplier �� multiplies the intake term ��� � ��1��� and thus accounts for the actual flow velocities through the valves, since these are not equal to the isentropic values assumed by the ���;  production term multiplier �� adjusts the magnitudes of the production terms (equations 4-5) directly through the production term �� with �� � ������;  geometrical length scale multiplier �� adjust the magnitudes of the production terms indirectly, through the scaling of geometrical length scale �� � ���� � �����������, with � being the cylinder bore, � the instantaneous piston stroke, and ���� � ��1���;  tumble term multiplier ����� controls the intensity of the tumble decay contribution to the production of turbulence. 2.2 turbulent combustion model turbulent combustion model siturb predicts the burn rate for the homogeneous charge, respecting the geometry of the combustion chamber, spark location and timing, mixture motion and fuel properties. the model simulates the development of the flame as a turbulent entrainment process followed by a burnup process in a region behind the flame front [8]. ��� �� � �� ∙ �� ∙ ��� � ��� (7) the entrainment mass rate of unburned gas ��� ��⁄ is determined by the equation 7; with the flame front area ��, laminar and turbulent flame speeds �� and �� and finally the unburned gas density ��. dedicated sub-model evaluates the instantaneous flame front area from the combustion chamber geometry assuming the flame front spherical in shape [8]. a model parameter ������ (initial spark size) determines the initial flame front size. for a typical spark plug, its value should be the same as the gap between the spark plug electrodes. however, the real spark size can slightly differ, especially with high-energy spark plugs. therefore, we use the ������ as a model tuning parameter also, in a reasonable range of sizes. �� � ��� � �� ∙ �� � ����� ∙ � �� ��� � ∙ � ���� � ∙ �1 � ���� ∙ �������∙���� (8) �� � �� ∙ �� ∙ �1 � 1 1 � �� ∙ ��� ���⁄ � (9) during the initial flame kernel development, when the size of the flame kernel is still small, the unburned gas entrainment rate is limited by the laminar flame speed �� (equation 8). then, the equation 9 accounts for the transition to the turbulent flame speed, with �� representing the mean fluctuating turbulent velocity, �� the flame radius and �� the turbulent length scale [16]. the rate of burnup ��� ��⁄ behind the flame front is proportional to the unburned mass behind the flame front, resulting in the rate equation 10 for the burned mass ��. ��� �� � �� � �� � (10) model assumes that the burnup phase takes place in the laminar flame speed and over the taylor microscale of turbulence �, with time constant � (equation 11). other assumption is that the turbulence is isotropic and therefore the taylor microscale of turbulence � can be obtained from the integral length scale �� (equations 12). � � ��� (11) � � �� ∙ ������ (12a) ��� � �� ∙ �� ∙ �� � (12b) (8) equations 1-5 contain four calibration parameters that can be used to match the in-cylinder flow model with 3d-cfd results and to enhance the predictive abilities of the consecutive turbulent combustion model. these parameters are following:  intake term multiplier �� multiplies the intake term ��� � ��1��� and thus accounts for the actual flow velocities through the valves, since these are not equal to the isentropic values assumed by the ���;  production term multiplier �� adjusts the magnitudes of the production terms (equations 4-5) directly through the production term �� with �� � ������;  geometrical length scale multiplier �� adjust the magnitudes of the production terms indirectly, through the scaling of geometrical length scale �� � ���� � �����������, with � being the cylinder bore, � the instantaneous piston stroke, and ���� � ��1���;  tumble term multiplier ����� controls the intensity of the tumble decay contribution to the production of turbulence. 2.2 turbulent combustion model turbulent combustion model siturb predicts the burn rate for the homogeneous charge, respecting the geometry of the combustion chamber, spark location and timing, mixture motion and fuel properties. the model simulates the development of the flame as a turbulent entrainment process followed by a burnup process in a region behind the flame front [8]. ��� �� � �� ∙ �� ∙ ��� � ��� (7) the entrainment mass rate of unburned gas ��� ��⁄ is determined by the equation 7; with the flame front area ��, laminar and turbulent flame speeds �� and �� and finally the unburned gas density ��. dedicated sub-model evaluates the instantaneous flame front area from the combustion chamber geometry assuming the flame front spherical in shape [8]. a model parameter ������ (initial spark size) determines the initial flame front size. for a typical spark plug, its value should be the same as the gap between the spark plug electrodes. however, the real spark size can slightly differ, especially with high-energy spark plugs. therefore, we use the ������ as a model tuning parameter also, in a reasonable range of sizes. �� � ��� � �� ∙ �� � ����� ∙ � �� ��� � ∙ � ���� � ∙ �1 � ���� ∙ �������∙���� (8) �� � �� ∙ �� ∙ �1 � 1 1 � �� ∙ ��� ���⁄ � (9) during the initial flame kernel development, when the size of the flame kernel is still small, the unburned gas entrainment rate is limited by the laminar flame speed �� (equation 8). then, the equation 9 accounts for the transition to the turbulent flame speed, with �� representing the mean fluctuating turbulent velocity, �� the flame radius and �� the turbulent length scale [16]. the rate of burnup ��� ��⁄ behind the flame front is proportional to the unburned mass behind the flame front, resulting in the rate equation 10 for the burned mass ��. ��� �� � �� � �� � (10) model assumes that the burnup phase takes place in the laminar flame speed and over the taylor microscale of turbulence �, with time constant � (equation 11). other assumption is that the turbulence is isotropic and therefore the taylor microscale of turbulence � can be obtained from the integral length scale �� (equations 12). � � ��� (11) � � �� ∙ ������ (12a) ��� � �� ∙ �� ∙ �� � (12b) equations 1-5 contain four calibration parameters that can be used to match the in-cylinder flow model with 3d-cfd results and to enhance the predictive abilities of the consecutive turbulent combustion model. these parameters are following:  intake term multiplier �� multiplies the intake term ��� � ��1��� and thus accounts for the actual flow velocities through the valves, since these are not equal to the isentropic values assumed by the ���;  production term multiplier �� adjusts the magnitudes of the production terms (equations 4-5) directly through the production term �� with �� � ������;  geometrical length scale multiplier �� adjust the magnitudes of the production terms indirectly, through the scaling of geometrical length scale �� � ���� � �����������, with � being the cylinder bore, � the instantaneous piston stroke, and ���� � ��1���;  tumble term multiplier ����� controls the intensity of the tumble decay contribution to the production of turbulence. 2.2 turbulent combustion model turbulent combustion model siturb predicts the burn rate for the homogeneous charge, respecting the geometry of the combustion chamber, spark location and timing, mixture motion and fuel properties. the model simulates the development of the flame as a turbulent entrainment process followed by a burnup process in a region behind the flame front [8]. ��� �� � �� ∙ �� ∙ ��� � ��� (7) the entrainment mass rate of unburned gas ��� ��⁄ is determined by the equation 7; with the flame front area ��, laminar and turbulent flame speeds �� and �� and finally the unburned gas density ��. dedicated sub-model evaluates the instantaneous flame front area from the combustion chamber geometry assuming the flame front spherical in shape [8]. a model parameter ������ (initial spark size) determines the initial flame front size. for a typical spark plug, its value should be the same as the gap between the spark plug electrodes. however, the real spark size can slightly differ, especially with high-energy spark plugs. therefore, we use the ������ as a model tuning parameter also, in a reasonable range of sizes. �� � ��� � �� ∙ �� � ����� ∙ � �� ��� � ∙ � ���� � ∙ �1 � ���� ∙ �������∙���� (8) �� � �� ∙ �� ∙ �1 � 1 1 � �� ∙ ��� ���⁄ � (9) during the initial flame kernel development, when the size of the flame kernel is still small, the unburned gas entrainment rate is limited by the laminar flame speed �� (equation 8). then, the equation 9 accounts for the transition to the turbulent flame speed, with �� representing the mean fluctuating turbulent velocity, �� the flame radius and �� the turbulent length scale [16]. the rate of burnup ��� ��⁄ behind the flame front is proportional to the unburned mass behind the flame front, resulting in the rate equation 10 for the burned mass ��. ��� �� � �� � �� � (10) model assumes that the burnup phase takes place in the laminar flame speed and over the taylor microscale of turbulence �, with time constant � (equation 11). other assumption is that the turbulence is isotropic and therefore the taylor microscale of turbulence � can be obtained from the integral length scale �� (equations 12). � � ��� (11) � � �� ∙ ������ (12a) ��� � �� ∙ �� ∙ �� � (12b) (9) during the initial flame kernel development, when the size of the flame kernel is still small, the unburned gas entrainment rate is limited by the laminar flame speed sl (equation 8). then, the equation 9 accounts for the transition to the turbulent flame speed, with u' representing the mean fluctuating turbulent velocity, rf the flame radius and lt the turbulent length scale [16]. the rate of burnup dmb /dt behind the flame front is proportional to the unburned mass behind the flame front, resulting in the rate equation 10 for the burned mass mb. equations 1-5 contain four calibration parameters that can be used to match the in-cylinder flow model with 3d-cfd results and to enhance the predictive abilities of the consecutive turbulent combustion model. these parameters are following:  intake term multiplier �� multiplies the intake term ��� � ��1��� and thus accounts for the actual flow velocities through the valves, since these are not equal to the isentropic values assumed by the ���;  production term multiplier �� adjusts the magnitudes of the production terms (equations 4-5) directly through the production term �� with �� � ������;  geometrical length scale multiplier �� adjust the magnitudes of the production terms indirectly, through the scaling of geometrical length scale �� � ���� � �����������, with � being the cylinder bore, � the instantaneous piston stroke, and ���� � ��1���;  tumble term multiplier ����� controls the intensity of the tumble decay contribution to the production of turbulence. 2.2 turbulent combustion model turbulent combustion model siturb predicts the burn rate for the homogeneous charge, respecting the geometry of the combustion chamber, spark location and timing, mixture motion and fuel properties. the model simulates the development of the flame as a turbulent entrainment process followed by a burnup process in a region behind the flame front [8]. ��� �� � �� ∙ �� ∙ ��� � ��� (7) the entrainment mass rate of unburned gas ��� ��⁄ is determined by the equation 7; with the flame front area ��, laminar and turbulent flame speeds �� and �� and finally the unburned gas density ��. dedicated sub-model evaluates the instantaneous flame front area from the combustion chamber geometry assuming the flame front spherical in shape [8]. a model parameter ������ (initial spark size) determines the initial flame front size. for a typical spark plug, its value should be the same as the gap between the spark plug electrodes. however, the real spark size can slightly differ, especially with high-energy spark plugs. therefore, we use the ������ as a model tuning parameter also, in a reasonable range of sizes. �� � ��� � �� ∙ �� � ����� ∙ � �� ��� � ∙ � ���� � ∙ �1 � ���� ∙ �������∙���� (8) �� � �� ∙ �� ∙ �1 � 1 1 � �� ∙ ��� ���⁄ � (9) during the initial flame kernel development, when the size of the flame kernel is still small, the unburned gas entrainment rate is limited by the laminar flame speed �� (equation 8). then, the equation 9 accounts for the transition to the turbulent flame speed, with �� representing the mean fluctuating turbulent velocity, �� the flame radius and �� the turbulent length scale [16]. the rate of burnup ��� ��⁄ behind the flame front is proportional to the unburned mass behind the flame front, resulting in the rate equation 10 for the burned mass ��. ��� �� � �� � �� � (10) model assumes that the burnup phase takes place in the laminar flame speed and over the taylor microscale of turbulence �, with time constant � (equation 11). other assumption is that the turbulence is isotropic and therefore the taylor microscale of turbulence � can be obtained from the integral length scale �� (equations 12). � � ��� (11) � � �� ∙ ������ (12a) ��� � �� ∙ �� ∙ �� � (12b) (10) model assumes that the burnup phase takes place in the laminar flame speed and over the taylor microscale of turbulence λ, with time constant τ (equation 11). other assumption is that the turbulence is isotropic and therefore the taylor microscale of turbulence λ can be obtained from the integral length scale lt (equations 12). equations 1-5 contain four calibration parameters that can be used to match the in-cylinder flow model with 3d-cfd results and to enhance the predictive abilities of the consecutive turbulent combustion model. these parameters are following:  intake term multiplier �� multiplies the intake term ��� � ��1��� and thus accounts for the actual flow velocities through the valves, since these are not equal to the isentropic values assumed by the ���;  production term multiplier �� adjusts the magnitudes of the production terms (equations 4-5) directly through the production term �� with �� � ������;  geometrical length scale multiplier �� adjust the magnitudes of the production terms indirectly, through the scaling of geometrical length scale �� � ���� � �����������, with � being the cylinder bore, � the instantaneous piston stroke, and ���� � ��1���;  tumble term multiplier ����� controls the intensity of the tumble decay contribution to the production of turbulence. 2.2 turbulent combustion model turbulent combustion model siturb predicts the burn rate for the homogeneous charge, respecting the geometry of the combustion chamber, spark location and timing, mixture motion and fuel properties. the model simulates the development of the flame as a turbulent entrainment process followed by a burnup process in a region behind the flame front [8]. ��� �� � �� ∙ �� ∙ ��� � ��� (7) the entrainment mass rate of unburned gas ��� ��⁄ is determined by the equation 7; with the flame front area ��, laminar and turbulent flame speeds �� and �� and finally the unburned gas density ��. dedicated sub-model evaluates the instantaneous flame front area from the combustion chamber geometry assuming the flame front spherical in shape [8]. a model parameter ������ (initial spark size) determines the initial flame front size. for a typical spark plug, its value should be the same as the gap between the spark plug electrodes. however, the real spark size can slightly differ, especially with high-energy spark plugs. therefore, we use the ������ as a model tuning parameter also, in a reasonable range of sizes. �� � ��� � �� ∙ �� � ����� ∙ � �� ��� � ∙ � ���� � ∙ �1 � ���� ∙ �������∙���� (8) �� � �� ∙ �� ∙ �1 � 1 1 � �� ∙ ��� ���⁄ � (9) during the initial flame kernel development, when the size of the flame kernel is still small, the unburned gas entrainment rate is limited by the laminar flame speed �� (equation 8). then, the equation 9 accounts for the transition to the turbulent flame speed, with �� representing the mean fluctuating turbulent velocity, �� the flame radius and �� the turbulent length scale [16]. the rate of burnup ��� ��⁄ behind the flame front is proportional to the unburned mass behind the flame front, resulting in the rate equation 10 for the burned mass ��. ��� �� � �� � �� � (10) model assumes that the burnup phase takes place in the laminar flame speed and over the taylor microscale of turbulence �, with time constant � (equation 11). other assumption is that the turbulence is isotropic and therefore the taylor microscale of turbulence � can be obtained from the integral length scale �� (equations 12). � � ��� (11) � � �� ∙ ������ (12a) ��� � �� ∙ �� ∙ �� � (12b) (11) equations 1-5 contain four calibration parameters that can be used to match the in-cylinder flow model with 3d-cfd results and to enhance the predictive abilities of the consecutive turbulent combustion model. these parameters are following:  intake term multiplier �� multiplies the intake term ��� � ��1��� and thus accounts for the actual flow velocities through the valves, since these are not equal to the isentropic values assumed by the ���;  production term multiplier �� adjusts the magnitudes of the production terms (equations 4-5) directly through the production term �� with �� � ������;  geometrical length scale multiplier �� adjust the magnitudes of the production terms indirectly, through the scaling of geometrical length scale �� � ���� � �����������, with � being the cylinder bore, � the instantaneous piston stroke, and ���� � ��1���;  tumble term multiplier ����� controls the intensity of the tumble decay contribution to the production of turbulence. 2.2 turbulent combustion model turbulent combustion model siturb predicts the burn rate for the homogeneous charge, respecting the geometry of the combustion chamber, spark location and timing, mixture motion and fuel properties. the model simulates the development of the flame as a turbulent entrainment process followed by a burnup process in a region behind the flame front [8]. ��� �� � �� ∙ �� ∙ ��� � ��� (7) the entrainment mass rate of unburned gas ��� ��⁄ is determined by the equation 7; with the flame front area ��, laminar and turbulent flame speeds �� and �� and finally the unburned gas density ��. dedicated sub-model evaluates the instantaneous flame front area from the combustion chamber geometry assuming the flame front spherical in shape [8]. a model parameter ������ (initial spark size) determines the initial flame front size. for a typical spark plug, its value should be the same as the gap between the spark plug electrodes. however, the real spark size can slightly differ, especially with high-energy spark plugs. therefore, we use the ������ as a model tuning parameter also, in a reasonable range of sizes. �� � ��� � �� ∙ �� � ����� ∙ � �� ��� � ∙ � ���� � ∙ �1 � ���� ∙ �������∙���� (8) �� � �� ∙ �� ∙ �1 � 1 1 � �� ∙ ��� ���⁄ � (9) during the initial flame kernel development, when the size of the flame kernel is still small, the unburned gas entrainment rate is limited by the laminar flame speed �� (equation 8). then, the equation 9 accounts for the transition to the turbulent flame speed, with �� representing the mean fluctuating turbulent velocity, �� the flame radius and �� the turbulent length scale [16]. the rate of burnup ��� ��⁄ behind the flame front is proportional to the unburned mass behind the flame front, resulting in the rate equation 10 for the burned mass ��. ��� �� � �� � �� � (10) model assumes that the burnup phase takes place in the laminar flame speed and over the taylor microscale of turbulence �, with time constant � (equation 11). other assumption is that the turbulence is isotropic and therefore the taylor microscale of turbulence � can be obtained from the integral length scale �� (equations 12). � � ��� (11) � � �� ∙ ������ (12a) ��� � �� ∙ �� ∙ �� � (12b) (12a) equations 1-5 contain four calibration parameters that can be used to match the in-cylinder flow model with 3d-cfd results and to enhance the predictive abilities of the consecutive turbulent combustion model. these parameters are following:  intake term multiplier �� multiplies the intake term ��� � ��1��� and thus accounts for the actual flow velocities through the valves, since these are not equal to the isentropic values assumed by the ���;  production term multiplier �� adjusts the magnitudes of the production terms (equations 4-5) directly through the production term �� with �� � ������;  geometrical length scale multiplier �� adjust the magnitudes of the production terms indirectly, through the scaling of geometrical length scale �� � ���� � �����������, with � being the cylinder bore, � the instantaneous piston stroke, and ���� � ��1���;  tumble term multiplier ����� controls the intensity of the tumble decay contribution to the production of turbulence. 2.2 turbulent combustion model turbulent combustion model siturb predicts the burn rate for the homogeneous charge, respecting the geometry of the combustion chamber, spark location and timing, mixture motion and fuel properties. the model simulates the development of the flame as a turbulent entrainment process followed by a burnup process in a region behind the flame front [8]. ��� �� � �� ∙ �� ∙ ��� � ��� (7) the entrainment mass rate of unburned gas ��� ��⁄ is determined by the equation 7; with the flame front area ��, laminar and turbulent flame speeds �� and �� and finally the unburned gas density ��. dedicated sub-model evaluates the instantaneous flame front area from the combustion chamber geometry assuming the flame front spherical in shape [8]. a model parameter ������ (initial spark size) determines the initial flame front size. for a typical spark plug, its value should be the same as the gap between the spark plug electrodes. however, the real spark size can slightly differ, especially with high-energy spark plugs. therefore, we use the ������ as a model tuning parameter also, in a reasonable range of sizes. �� � ��� � �� ∙ �� � ����� ∙ � �� ��� � ∙ � ���� � ∙ �1 � ���� ∙ �������∙���� (8) �� � �� ∙ �� ∙ �1 � 1 1 � �� ∙ ��� ���⁄ � (9) during the initial flame kernel development, when the size of the flame kernel is still small, the unburned gas entrainment rate is limited by the laminar flame speed �� (equation 8). then, the equation 9 accounts for the transition to the turbulent flame speed, with �� representing the mean fluctuating turbulent velocity, �� the flame radius and �� the turbulent length scale [16]. the rate of burnup ��� ��⁄ behind the flame front is proportional to the unburned mass behind the flame front, resulting in the rate equation 10 for the burned mass ��. ��� �� � �� � �� � (10) model assumes that the burnup phase takes place in the laminar flame speed and over the taylor microscale of turbulence �, with time constant � (equation 11). other assumption is that the turbulence is isotropic and therefore the taylor microscale of turbulence � can be obtained from the integral length scale �� (equations 12). � � ��� (11) � � �� ∙ ������ (12a) ��� � �� ∙ �� ∙ �� � (12b) (12b) parameters in the laminar flame speed equation 8 depend on the fuel type and its composition. since the composition of the natural gas differs, gt ‑suite offers two different parameter sets (summed ‑up in table 1): • first set slng1 from hernandez et al. [17]; • the second one slng2 by the work of lio, jiang, and cheng [18] there are five different calibration parameters in the siturb model that we use to match the measured burn rate. these parameters are following: • turbulent flame speed multiplier cs scales the turbulent flame speed st in equation 9; • flame kernel growth multiplier ck scales the flame front evolution from the initial laminar smooth surface to a distorted turbulent flame front (equation 9); • taylor length scale multiplier cλ scales the taylor microscale of turbulence λ in equation 12 • dilution exponent multiplier dem accounts for the dilution by the exhaust residuals and egr, affecting the laminar flame speed in the equation 8; • initial spark size ssinit parameter determines the size of the initial flame front. 3. experimental set ‑up and test matrix the set of experimental data used in this study originates from a steady state engine test bed measurements with a four‑ ‑cylinder turbocharged si engine rebuilt from a ci variant and fueled by natural gas. the usual average composition of the natural gas is 98.39 [%vol] ch4, 0.44 [%vol] c2h6, 0.26 [%vol] higher hydrocarbons and 0.84 [%vol] n2. table 2 summarizes the main geometrical parameters of the experimental engine. one of the necessary inputs for the flow model is the swirl (or tumble) characteristic of the experimental ice. such measurements were conducted in 2005 but only the swirl table 1: laminar flame speed sub ‑model parameters tabuľka 1: parametre sub ‑modelu pre výpočet laminárnej rýchlosti čela plameňa parameter description slng1 [17] slng2 [18] bm [m/s] maximum laminar speed 0.490 0.397 bϕ [m/s] laminar speed roll ‑of value – 0.590 – 1.649 ϕm [ ‑] fuel/air equivalence ratio at maximum laminar flame speed 1.390 1.061 α [ ‑] temperature exponent 0.68 × ϕ2 – 1.70 × ϕ + 3.18 5.75 × ϕ2 – 12.15 × ϕ + 7.98 β [ ‑] pressure exponent – 0.52 × ϕ2 + 1.18 × ϕ – 1.18 – 0.925 × ϕ2 + 2 × ϕ – 1.473 mecca 02 2017 page 41 evaluation of the predictive capabilities of a phenomenological combustion model for natural gas si engine rastislav toman, jan macek characteristic is available – shown in figure 1, where cswirl represents the swirl coefficient (definition from [14]), bs the swirl torque, and lυ/dυ a ratio of valve lift to its diameter. the experimental ice is equipped with a central mixer for metering and delivery of the gaseous fuel mixture downstream the compressor inlet. the fuel flow control is either manual or automatic by a closed loop lambda control. ice features also a cooled low ‑pressure egr system, with the egr rate adjusted by a servo driven butterfly valve. variable turbine geometry performs the boost pressure control and the conventional throttle, located downstream from the intercooler, controls the mixture inflow. high ‑energy ignition system ensures the sufficient spark energy, with the possibility of the spark discharge angle adjustment or closed ‑loop ca50 control. automated data acquisition system records the engine speed and torque, fuel flow, airflow, exhaust gas composition and average temperatures in the intake and exhaust manifolds. uncooled piezoelectric transducer installed in the glow plug hole of the first cylinder measures the in ‑cylinder pressure and two piezo resistive pressure transducers measure the intake and exhaust pressures to get a full three ‑pressure‑ ‑analysis (tpa). details on the experimental set ‑up can be found in [5] and [19]. we used a measurement set containing 83 steady state operation points, representing the full engine map with the stoichiometric mixture and egr ratio variations (bmep 4.75‑ ‑19.30 bar; 1200 ‑2600 rpm). figure 2 shows the reduced test matrix with model calibration points (in blue) and prediction points (in red). the size of a circle and the number indicate the egr content. most of the calibration points represent medium ice loads; low to medium speeds; egr rates 0 ‑5.6%. only three ice operating points contain high egr rate of 17% and high ice speeds. the prediction points then cover low load/high load parts of the map, generally with high egr rates (except two low load points @ 1800 rpm with 0% egr rate), to really test the predictive capabilities of the combustion model. 4. calibration procedure 4.1 basis tpa model a proper function of the basis thermodynamic model must be ensured to allow for the calibration of the predictive combustion model. therefore, we have calibrated the basis tpa model beforehand, correcting some model uncertainties and measurement errors, namely: effective compression ratio, convection multiplier of the heat transfer model [20], tdc positon error, intake and exhaust ports pressure shifts. figure 2: test matrix from the full map measurement set with stoichiometric mixture and egr ratio variation. obrázok 2: testovacia matica z merania úplnej charakteristiky so stechiometrickou zmesou a variáciou pomeru egr we used a measurement set containing 83 steady state operation points, representing the full engine map with the stoichiometric mixture and egr ratio variations (bmep 4.75-19.30 bar; 1200-2600 rpm). figure 2 shows the reduced test matrix with model calibration points (in green) and prediction points (in blue). the size of a circle and the number indicate the egr content. most of the calibration points represent medium ice loads; low to medium speeds; egr rates 0-5.6%. only three ice operating points contain high egr rate of 17% and high ice speeds. the prediction points then cover low load/high load parts of the map, generally with high egr rates (except two low load points @ 1800 rpm with 0% egr rate), to really test the predictive capabilities of the combustion model. 4. calibration procedure 4.1 basis tpa model a proper function of the basis thermodynamic model must be ensured to allow for the calibration of the predictive combustion model. therefore, we have calibrated the basis tpa model beforehand, correcting some model uncertainties and measurement errors, namely: effective compression ratio, convection multiplier of the heat transfer model [20], tdc positon error, intake and exhaust ports pressure shifts. �� � 1���� � ������ � |����� � ����| ���� ������ �� (13) the determination of the optimal set of calibrated parameters implies the formulation of the objective functions for the whole calibration. in the case of this calibration, these are derived from following model parameters:  absolute pressure difference �� between the measured and simulated in-cylinder pressures (equation 13);  �������������� evaluated from the gt-suite output parameter lhv multiplier. the fuel energy lhv multiplier represents a multiplier of total fuel energy. when its value differs from unity, it indicates, that the input energy in the simulation system is different from the energy needed to follow exactly the measurement in-cylinder pressure trace. then, �������������� � �������������� � 1�. �� � � �� � ��� �� ������ (14) both variables are calculated for each calibration engine operation point from the calibration set (figure 2). the average and maximum values from all calibrated operating points serve as the objective functions (leading to four objective functions �� in total). ga [21] then minimizes these objective functions. the result of a multi-parameter and multi-criterial optimization is a set of non-dominated optimal solutions on a so-called pareto frontier. a single optimal solution from the pareto set is obtained by a criterial function (equation 14), whose value is calculated for each pareto set solution. the fraction �� ������⁄ than represents a normalization, so that different objective functions �� can be combined into a single equation. ������ is a maximum value from all pareto set solutions, for the respective objective function �� and parameter �� is a criterial function weight factor. table 3 summarizes the objective functions �� and values of weight factors ��; table 4 the selected optimal settings for the basis tpa model. figure 3 displays a pareto frontier for this specific calibration (optimum point in red); figure 4 the values of �� and �������������� for each calibrated ice operating point. objective function �� weight factor �� average �� 0.35 maximum �� 0.15 (13) figure 1: intake port swirl characteristics of the experimental ices obrázok 1: swirlová charakteristika sacích kanálov experimentálneho spaľovacieho motora figure 2: test matrix from the full map measurement set with stoichiometric mixture and egr ratio variation. obrázok 2: testovacia matica z merania úplnej charakteristiky so stechiometrickou zmesou a variáciou pomeru egr table 2: basic experimental ice features tabuľka 2: základné charakteristiky experimentálneho spaľovacieho motora bore 102 [mm] stroke 120 [mm] compression ratio 12:1 number of cylinders 4 valves per cylinder 4 ivo/ivc 342/595 [°ca atdc] @ 0.1 mm lift evo/evc 123/377 [°ca atdc] @ 0.1 mm lift maximum torque 600 nm @ 1600 ‑1800 rpm maximum power 120 kw @ 2000 rpm mecca 02 2017 page 42 evaluation of the predictive capabilities of a phenomenological combustion model for natural gas si engine rastislav toman, jan macek the determination of the optimal set of calibrated parameters implies the formulation of the objective functions for the whole calibration. in the case of this calibration, these are derived from following model parameters: • absolute pressure difference ∆p between the measured and simulated in ‑cylinder pressures (equation 13); • ∆lhvmultiplier evaluated from the gt ‑suite output parameter lhvmultiplier. the fuel energy lhvmultiplier represents a multiplier of total fuel energy. when its value differs from unity, it indicates, that the input energy in the simulation system is different from the energy needed to follow exactly the measurement in ‑cylinder pressure trace. then, ∆lhvmultiplier = |lhvmultiplier – 1|. both variables are calculated for each engine operation point from the calibration set (figure 2). the average and maximum values from all calibration points serve as the objective functions (leading to four objective functions xk in total). ga [21] then minimizes these objective functions. figure 2: test matrix from the full map measurement set with stoichiometric mixture and egr ratio variation. obrázok 2: testovacia matica z merania úplnej charakteristiky so stechiometrickou zmesou a variáciou pomeru egr we used a measurement set containing 83 steady state operation points, representing the full engine map with the stoichiometric mixture and egr ratio variations (bmep 4.75-19.30 bar; 1200-2600 rpm). figure 2 shows the reduced test matrix with model calibration points (in green) and prediction points (in blue). the size of a circle and the number indicate the egr content. most of the calibration points represent medium ice loads; low to medium speeds; egr rates 0-5.6%. only three ice operating points contain high egr rate of 17% and high ice speeds. the prediction points then cover low load/high load parts of the map, generally with high egr rates (except two low load points @ 1800 rpm with 0% egr rate), to really test the predictive capabilities of the combustion model. 4. calibration procedure 4.1 basis tpa model a proper function of the basis thermodynamic model must be ensured to allow for the calibration of the predictive combustion model. therefore, we have calibrated the basis tpa model beforehand, correcting some model uncertainties and measurement errors, namely: effective compression ratio, convection multiplier of the heat transfer model [20], tdc positon error, intake and exhaust ports pressure shifts. �� � 1���� � ������ � |����� � ����| ���� ������ �� (13) the determination of the optimal set of calibrated parameters implies the formulation of the objective functions for the whole calibration. in the case of this calibration, these are derived from following model parameters:  absolute pressure difference �� between the measured and simulated in-cylinder pressures (equation 13);  �������������� evaluated from the gt-suite output parameter lhv multiplier. the fuel energy lhv multiplier represents a multiplier of total fuel energy. when its value differs from unity, it indicates, that the input energy in the simulation system is different from the energy needed to follow exactly the measurement in-cylinder pressure trace. then, �������������� � �������������� � 1�. �� � � �� � ��� �� ������ (14) both variables are calculated for each calibration engine operation point from the calibration set (figure 2). the average and maximum values from all calibrated operating points serve as the objective functions (leading to four objective functions �� in total). ga [21] then minimizes these objective functions. the result of a multi-parameter and multi-criterial optimization is a set of non-dominated optimal solutions on a so-called pareto frontier. a single optimal solution from the pareto set is obtained by a criterial function (equation 14), whose value is calculated for each pareto set solution. the fraction �� ������⁄ than represents a normalization, so that different objective functions �� can be combined into a single equation. ������ is a maximum value from all pareto set solutions, for the respective objective function �� and parameter �� is a criterial function weight factor. table 3 summarizes the objective functions �� and values of weight factors ��; table 4 the selected optimal settings for the basis tpa model. figure 3 displays a pareto frontier for this specific calibration (optimum point in red); figure 4 the values of �� and �������������� for each calibrated ice operating point. objective function �� weight factor �� average �� 0.35 maximum �� 0.15 (14) the result of a multi ‑parameter and multi ‑criterial optimization is a set of non ‑dominated optimal solutions on a so ‑called pareto frontier. a single optimal solution from the pareto set is obtained by a criterial function (equation 14), whose value is calculated for each pareto set solution. the fraction xk /xk,max than represents a normalization, so that different objective functions xk can be combined into a single equation. xk,max is a maximum value from all pareto set solutions, for the respective objective function xk and parameter αk is a criterial function weight factor. table 3 summarizes the objective functions xk and values of weight factors αk; table 4 the selected optimal settings for the basis tpa model. figure 3 displays a pareto frontier for this specific calibration (optimum point in red); figure 4 the values of ∆p and ∆lhvmultiplier for each calibrated ice operating point. table 3: objective functions and weight factors for the basis tpa model calibration tabuľka 3: objektívne funkcie a váhové faktory pre kalibráciu základného modelu tpa objective function xk weight factor αk average ∆p 0.35 maximum ∆p 0.15 average ∆lhvmultiplier 0.35 maximum ∆lhvmultiplier 0.15 table 4: selected optimal settings of the basis tpa model tabuľka 4: vybrané optimálne nastavenie základného modelu tpa full map set effective compression ratio 12.36:1 convection multiplier 1.33 tdc position error 0.1 [°ca] intake port pressure shift ‑0.021 [bar] exhaust port pressure shift 0.041 [bar] figure 3: pareto frontiers with the optimum point for the basis tpa model calibration. obrázok 3: pareto hranice s optimálnym bodom pre kalibráciu základného modelu tpa figure 4: values of ∆p and ∆lhvmultiplier errors for the full map calibration set and optimal settings of the basis tpa model. obrázok 4: hodnoty ∆p a ∆lhvmultiplier základného tpa modelu pre jednotlivé pracovné body experimentálneho spaľovacieho motora a vybrané optimálne nastavenie parametrov. mecca 02 2017 page 43 evaluation of the predictive capabilities of a phenomenological combustion model for natural gas si engine rastislav toman, jan macek 4.2 main calibration and predictions main calibration of the combustion model is conducted on the calibration part of the full map measurement set, combining in total nine flow and siturb parameters (sections 2.1 and 2.2) and using the slng1 parameters for the laminar flame speed sub ‑model. the objective functions for main calibration of the combustion model are derived from two output parameters: • absolute pressure difference ∆p between the measured and simulated in ‑cylinder pressures, but now for the siturb model (equation 13); • burn rate rms error (gt ‑suite output parameter). the ga then minimizes four objective functions xk: two averages and two maxima. regarding, the values of weight factors αk in the criterial function (equation 14), ∆lhvmultiplier is exchanged for burn rate rms error. after the calibration of the combustion model, additional prediction points are also simulated. it is worth noting, that the optimal set of model parameters is universal for the whole ice map, without any dependencies on variables such as ice speed or ice load. the same applies for the following optimized set for both sensitivity studies. 4.3 sensitivit y studies apart from the main calibration, we have conducted two different sensitivity studies: • sensitivity 1 on calibration inputs, where we calibrated only the siturb parameters, with flow parameters fixed at default values (def = 1); • sensitivity 2 on laminar flame speed sub ‑model, changing its settings to slng2. the calibration procedure, objective functions, and weight factors of the criterial function are the same for the sensitivity 1 and sensitivity 2 as for the main calibration. 5. results and discussion 5.1 main calibration after the main calibration of the flow and siturb models, we kept constant the optimized parameters (table 5, first column) and simulated both the 14 calibration operating points and additional 16 prediction points. table 6 than summarizes the average and maximum values (note: the average errors are evaluated from absolute values for the individual operating points). figure 5 shows the imep percentage error between the experimental and simulated values; figure 6 displays the ca50 error; figure 7 the 10% ‑90% burn duration (mfb10 ‑90) error; figure 8 maximum firing pressure error; figure 9 the error of maximum firing pressure ca position. table 5: optimal values of the calibration parameters for the combustion model (main calibration, sensitivity 1, sensitivity 2) tabuľka 5: výsledné optimálne hodnoty kalibračných parametrov pre model horenia (hlavná kalibrácia, citlivosť 1, citlivosť 2) parameter main calibration sensitivity 1 sensitivity 2 turbulent flame speed multiplier cs 1.060 0.370 1.600 flame kernel growth multiplier ck 9.040 4.210 0.080 taylor length scale multiplier cλ 7.510 2.650 8.970 dilution exponent multiplier dem 0.830 0.830 0.710 initial spark size ssinit 3.500 3.560 4.810 intake term multiplier c1 1.640 def = 1 0.010 production term multiplier c2 3.690 def = 1 0.946 geometrical length scale multiplier c3 0.070 def = 1 0.050 tumble term multiplier ctumb 0.300 def = 1 1.410 table 6: main calibration average and maximum errors (calibration/prediction points) tabuľka 6: priemerné a maximálne odchýlky hlavnej kalibrácie (kalibračné/predikčné body) parameter avg. error max. error imep 1.35/0.95 [%] 4.75/2.84 [%] ca50 0.44/0.45 [°ca] 1.28/0.68 [°ca] mfb10 ‑90 0.52/0.82 [°ca] 2.18/1.14 [°ca] mfb10 ‑75 1.17/2.17 [°ca] ‑2.46/0.53 [°ca] maximum pressure 1.20/2.46 [bar] 3.94/5.78 [bar] ca @ maximum pressure 0.42/0.54 [°ca] 1.10/1.10 [°ca] figure 5: imep percentage errors of the experimental versus simulation values, main calibration obrázok 5: percentuálna chyba imep, experiment verzus simulácia mecca 02 2017 page 44 evaluation of the predictive capabilities of a phenomenological combustion model for natural gas si engine rastislav toman, jan macek figure 8: maximum firing pressure errors of the experimental versus simulation values, main calibration obrázok 8: chyba maximálneho tlaku, experiment verzus simulácia, hlavná kalibrácia figure 9: maximum firing pressure crank angle position errors of the experimental versus simulation values, main calibration obrázok 9: chyba polohy maximálneho tlaku, experiment verzus simulácia, hlavná kalibrácia figure 6: ca50 errors of the experimental versus simulation values, main calibration obrázok 6: chyba ca50, experiment verzus simulácia, hlavná kalibrácia figure 7: burn duration 10% ‑90% errors of the experimental versus simulation values, main calibration obrázok 7: chyba dĺžky horenia 10 ‑90% zhoreného paliva, experiment verzus simulácia, hlavná kalibrácia mecca 02 2017 page 45 evaluation of the predictive capabilities of a phenomenological combustion model for natural gas si engine rastislav toman, jan macek both, calibration and prediction operating points show very good overall agreement, supported by the visual comparison of the burn rate and in ‑cylinder pressure traces (e.g. figure 10 and figure 11). figure 10 shows the burn rate and in ‑cylinder pressure comparison for the operating point 81 (prediction set) with the worst imep error (2.84%) and figure 11 for operating point 28 (calibration set). in conclusion, table 5 shows that values for some model parameters, such as ck, cλ, and c1 are quite high, on the other hand the value of c3 is low. this means, that although the agreement of the overall parameters (in ‑cylinder pressure, imep burn rate) is very good, a comparison with 3d ‑cfd is necessary. the value for the initial spark size ssinit is reasonable. 5.2 sensitivit y 1: calibration inputs the first sensitivity compares the main calibration to reduced calibration set, with flow model parameters fixed on default values (def = 1). ga was only optimizing the siturb values. optimal siturb parameters are summarized in the second column of table 5. it is important to note that the optimal values for both sets (main calibration and sensitivity 1) are comparable to each ‑other, with a possible trade ‑off effect between the siturb parameter cs (turbulent flame speed multiplier) and flow parameter c2 (production term multiplier). table 7 sums ‑up the average and maximum error values. the overall agreement is also very good, but compared to the main calibration results (table 6), both the average and maximum errors are higher. to illustrate the effects of the flow model parameters, figure 12 shows the difference between the turbulent kinetic energy and turbulent flame speeds. the flow model parameters in the main calibration actually dampen the in‑ ‑cylinder flow motion, which is compensated by the turbulent velocities. 5.3 sensitivit y 2: laminar flame speed model sensitivity 2 deals about the effect of the laminar flame speed model, which is set to slng2 values. the third column of table 5 shows the optimized values for both the flow and siturb sub ‑models. in this case, compared to the main calibration outputs, the differences are notable. table 8 summarizes the average and maximum error values. the average and maximum error values are higher than in the sensitivity 1. and especially those for mfb10 ‑75% show the effect of the different laminar flame speed models. figure 13 than depicts the burn rate and in ‑cylinder pressure comparison of experimental values, main calibration, and sensitivity 2. the selected low load operating point 41 is taken from the prediction set (achieves a low overall error in the main calibration). table 7: sensitivity 1 average and maximum errors (calibration/prediction points) tabuľka 7: priemerné a maximálne odchýlky citlivosti 1 (kalibračné/predikčné body) parameter avg. error max. error imep 1.15/1.08 [%] 5.62/2.71 [%] ca50 0.49/0.59 [°ca] ‑1.74/ ‑1.52 [°ca] mfb10 ‑90 0.79/1.03 [°ca] 2.50/ ‑1.72 [°ca] mfb10 ‑75 3.04/3.71 [°ca] ‑4.49/ ‑5.44 [°ca] maximum pressure 1.30/3.13 [bar] 4.49/6.96 [bar] ca @ maximum pressure 0.55/0.72 [°ca] ‑1.40/ ‑1.40 [°ca] figure 12: comparison between the experimental and simulation of turbulent kinetic energy and turbulent flame speed at prediction operating point 65 (2000 rpm, bmep 16.61 bar, 10.7% egr) obrázok 12: porovnanie experimentálneho a simulačného priebehu turbulentnej kinetickej energie a turbulentnej rýchlosti čela plameňa pre predikčný pracovný bod 65 (2000 rpm, bmep 16.61 bar, 10.7% egr) << figure 10: comparison between the experimental and simulation burn rate and in ‑cylinder pressure at 2600 rpm, bmep 12.98 bar, 17.3% egr (operating point 81 maximum imep error for the prediction set) obrázok 10: porovnanie experimentálneho a simulačného priebehu rýchlosti horenia a tlaku vo valci pri 2600 rpm, bmep 12.98 bar, 17.3% egr (pracovný bod 81 s maximálnou percentuálnou chybou imep, z predikčného setu) < figure 11: comparison between the experimental and simulation burn rate and in ‑cylinder pressure at 1600 rpm, bmep 15.59 bar, 2.3% egr (operating point 28, calibration set) obrázok 11: porovnanie experimentálneho a simulačného priebehu rýchlosti horenia a tlaku vo valci pri 1600 rpm, bmep 15.59 bar, 2.3% egr (pracovný bod 28, kalibračný set) mecca 02 2017 page 46 evaluation of the predictive capabilities of a phenomenological combustion model for natural gas si engine rastislav toman, jan macek 6. conclusion we have evaluated the predictive capabilities of a 0d phenomenological in ‑cylinder flow model, based on the k ‑k ‑ε kinetic energy cascade approach and coupled with a turbulent combustion model, using a turbocharged natural gas si engine. first, we did a detailed model calibration using ga and then added two model sensitivity studies: regarding the calibration procedure and the laminar flame speed sub ‑model. the main detailed model calibration shows that: • very good agreement with the experimental data can be achieved on the side of in ‑cylinder pressure traces and burn rate; • the combustion model is capable of prediction outside of its calibration range, achieving good results; • some of the calibration parameters in the optimal set are high, which has to be further studied (e.g. comparison with 3d ‑cfd) the results from the first sensitivity on the calibration inputs (calibrating only the turbulent combustion model; the flow model set to default values) only strengthen the conviction of the necessary comparison with 3d ‑cfd: • the available results from the flow model are different than those in the main calibration; • however, if the flow model is not included in the calibration, the combustion model still shows good agreement with the experimental data and prediction abilities. the second calibration – concerning the laminar flame speed model – shows the importance of a correct model values: • we have tested two different sets of laminar flame speed sub ‑model values and both showing differences; • the overall effect on the burn rate and in ‑cylinder pressure traces is greater than in the first sensitivity. in conclusion, our work shows the importance of the in ‑cylinder flow model verification with the 3d ‑cfd, and the importance of a correct laminar flame speed model, especially for the natural gas fueled ice. future development concerning the natural gas ice will focus on a comparison of the 0d phenomenological in ‑cylinder flow model with a 3d ‑cfd and further extension of the test matrix. the extended test matrix will include the air dilution and spark ‑timing sweeps. after the studies on the natural gas engine, the work will move to a gasoline si ice also. acknowledgements this work was supported by the grant agency of the czech technical university in prague, grant no. sgs16/213/ohk2/3t/12 list of abbreviations 0d/3d zero/three ‑dimensional bmep brake mean effective pressure ca crank angle cfd computational fluid dynamics doe design of experiments egr exhaust gas recirculation evc exhaust valve close evo exhaust valve open ga genetic algorithms ice internal combustion engine imep indicated mean effective pressure ivo intake valve open ivc intake valve close mfb mass fraction burned rms root mean square si spark ignition tdc top dead center tpa three ‑pressure ‑analysis table 8: sensitivity 2 average and maximum errors (calibration/prediction points) tabuľka 8: priemerné a maximálne odchýlky citlivosti 2 (kalibračné/predikčné body) parameter avg. error max. error imep 0.69/0.92 [%] ‑1.97/ ‑1.93 [%] ca50 0.67/0.68 [°ca] 2.60/1.93 [°ca] mfb10 ‑90 0.37/0.41 [°ca] 0.84/0.97 [°ca] mfb10 ‑75 2.10/3.03 [°ca] ‑5.71/ ‑5.38 [°ca] maximum pressure 1.48/2.08 [bar] ‑3.69/ ‑5.63 [bar] ca @ maximum pressure 0.64/0.92 [°ca] 1.50/1.90 [°ca] figure 13: comparison between the experimental and simulation burn rate and in ‑cylinder pressure at prediction operating point 41 (1800 rpm, bmep 8.62 bar, 0.0% egr) obrázok 13: porovnanie experimentálneho a simulačného priebehu rýchlosti horenia a tlaku vo valci pre predikčný pracovný bod 41 (1800 rpm, bmep 8.62 bar, 0.0% egr) mecca 02 2017 page 47 evaluation of the predictive capabilities of a phenomenological combustion model for natural gas si engine rastislav toman, jan macek list of symbols 𝐴𝑓 flame front area 𝐵 cylinder bore 𝐵 𝑚 maximum laminar speed 𝐵 𝜙 laminar speed roll ‑of value 𝐶1 intake term multiplier 𝐶2 production term multiplier 𝐶3 geometrical length scale multiplier 𝐶𝑖𝑛 intake term 𝐶𝐾 flame kernel growth multiplier 𝐶𝑆 turbulent flame speed multiplier 𝐶𝑆𝑤𝑖𝑟𝑙 intake port swirl coefficient 𝐶𝑡𝑢𝑚𝑏 tumble term multiplier 𝐶𝛽 production term 𝐶𝜆 taylor length scale multiplier 𝐶𝜇 k ‑ε model constant 𝐷𝐸𝑀 dilution exponent multiplier 𝐷𝑖𝑙 mass fraction of the residuals in the unburned zone 𝐸𝑖𝑛 intake energy 𝐹 criterial function 𝑘 turbulent kinetic energy 𝐾 mean kinetic energy 𝐿 angular momentum 𝐿𝑔 geometrical length scale 𝐿𝑡 integral length scale 𝑚 in ‑cylinder mass 𝑚· 𝑜𝑢𝑡 cylinder exit mass flow rate 𝑀𝑏 burned mass 𝑀𝑒 entrained mass 𝑝 pressure 𝑝0 reference pressure 𝑃𝑘 turbulence production term 𝑃𝜖 dissipation rate production term 𝑅𝑓 flame front radius 𝑅𝑒 reynolds number 𝑠 piston stroke 𝑆𝐿 laminar flame speed 𝑆𝑇 turbulent flame speed 𝑆𝑆𝑖𝑛𝑖𝑡 initial spark size 𝑇𝑢 temperature of unburned gas 𝑇0 reference temperature 𝑇 tumble contribution to turbulence 𝑢' mean fluctuating turbulent velocity 𝑈 mean velocity inside the cylinder 𝑋𝑘 objective function 𝛼 temperature exponent 𝛼𝑖𝑛 intake energy fraction converted directly into turbulence 𝛼𝑘 weight factor 𝛽 pressure exponent δ difference 𝜖 turbulent dissipation rate 𝜆 taylor microscale of turbulence 𝜈𝑇 turbulent viscosity 𝜌 density 𝜌· density rate of change 𝜌𝑢 density of unburned gas 𝜙 fuel/air equivalence ratio 𝜙𝑚 fuel/air equivalence ratio at maximum laminar flame speed references [1] vitek, o., macek, j., tatschl, r., pavlovic, y., priesching, p. 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[cd ‑rom], 2012 _goback physical 1d model of a high‑pressure ratio centrifugal compressor for turbochargers jan macek mecca 01 2018 page 33 10.1515/mecdc‑2018‑0004 physical 1d model of a high‑pressure ratio centrifugal compressor for turbochargers jan macek jan macek czech technical university in prague, center of vehicles for sustainable mobility, technická 4, 166 07 praha 6, czech republic email: jan.macek@fs.cvut.cz abstract the physical model of a centrifugal compressor aims at finding detailed information on values inside the machine, based on standard compressor map knowledge and basic geometry of a compressor. the model describes aerodynamics of flow from compressor inlet to outlet at a central streamline, if mass flow rate and impeller speed is known. the solution of basic conservation laws can yield unknown, cross‑section averaged temperatures, pressures and velocities along central streamline for compressible fluid and treats transonic operation, as well. after the description of general methods for solving compressible fluid flow and transformation of radial blade cascades to axial ones, the system of equations is completed with empiric knowledge of compressor blade cascades – forces and losses. howell theory is used for axial inducer and after conform transformation to radial blade diffuser cascade, as well. radial vanes of a rotor are transformed fixing the same length of a blade and flow areas and flow separation at inducer outlet is taken into account. specific procedure is developed for a vaneless diffuser with friction losses. non‑linear equations of gas dynamics have to be solved in numerical and iterative way with help of newton‑raphson solver. the model treats transonic flow features in both compressor inducer and diffuser. the validation of the model will be published in the second paper focused to this topic. the model can be used for quasi‑steady simulation in a 1d model, especially if compressor map extrapolation is required. the model predictions create virtual sensors for identification of directly unmeasurable quantities inside a compressor. it helps in better understanding in‑compressor processes. moreover, the model offers parameters for unsteady model, based on 1d modules for unsteady flow modelling. key words: centrifugal compressor, 1d simulation, physical model of compressor map, transonic performance, radial diffuser shrnutí fyzikální model odstředivého kompresoru je zaměřen na odhad stavů proudu uvnitř kompresoru na základě změřené charakteristiky a základních geometrických rozměrů stroje. model popisuje aerodynamiku proudu na střední proudnici od vstupu do záběrníku po výstup ze spirály pro známý hmotnostní průtok a otáčky rotoru. řešení základních zákonů zachování určuje neznámé střední teploty, tlaky a rychlosti podél střední proudnice pro stlačitelnou tekutinu a bere v úvahu i transsonické stavy proudu. v článku jsou popsány použité iterační metody řešení proudění stlačitelné tekutiny v radiálních mřížích s využitím jejich konformního zobrazení na axiální mříž. soustava základních rovnic pak může být doplněna o empirické poznatky o silách a ztrátách v axiálních mřížích, zejména pomocí howellovy teorie pro záběrník rotoru a po konformní transformaci i pro radiální mříž difusoru. radiální lopatky oběžného kola jsou transformovány na ekvivalentní difusor se stejnou délkou a poměrem průřezů, i s ohledem na separační bublinu na výstupu ze záběrníku. nová metoda je vyvinuta pro modelování bezlopatkového difusoru s třecími ztrátami. nelineární soustava rovnic dynamiky plynů je řešena iteracemi s použitím newton‑raphsonovy metody. model bere v úvahu transsonické poměry na vstupu do záběrníku a do bezlopatkového difusoru. validace modelu bude předmětem dalšího článku. model lze použít pro kvazi‑stacionární simulace kompresoru v 1d modelech motoru, zejména při nutnosti extrapolovat charakteristiku kompresoru. model vytváří virtuální senzory pro odhad stavů uvnitř kompresoru, které nejsou přímo měřitelné. pomáhá v pochopení vlivu dějů v kompresoru na jeho vlastnosti. model nabízí do budoucna i rozšíření při použití modulů s nestacionárním jednorozměrným průtokem pro modelování jednotlivých částí kompresoru. klíčová slova: odstředivý kompresor, 1d simulace, fyzikální model charakteristiky kompresoru, transsonický režim, radiální difuzor physical 1d model of a high-pressure ratio centrifugal compressor for turbochargers physical 1d model of a high‑pressure ratio centrifugal compressor for turbochargers jan macek mecca 01 2018 page 34 1. introduction and motivation the high‑pressure ratios of turbocharger compressors, needed for the current brake mean effective pressure levels, call for the better description and understanding of processes inside centrifugal compressors. even using 1d approach only, suitable for repeated optimization simulations, the model can yield interesting results, if it is based on physical description of processes. the paper aims at the 1d, quasi‑steady, central streamline model of a centrifugal compressor with axial‑radial flow, suitable for 1d engine models with unsteady conditions during the both transient load and speed of a car engine – general requirements being described already in [12] and [13]. the developed model of a centrifugal compressor describes the aerodynamics of flow from compressor inlet if mass flow rate and impeller speed is known. the basic idea of solution of basic conservation laws has been successfully tested for the case of centripetal radial‑axial turbine – [1] and [2]. there are already such models, e.g., [15] or [16]. the current model tries to treat better transonic phenomena and use the available knowledge from axial compressor cascades taking the real asymmetric incidence angle influence into account, better than old naca shock loss theory [4] for today’s shapes of inlet blade profile. the main goal is a development of the compressor physical model for compressible fluid flow at the reasonable level of simplification for compressor performance description. the developed model will be validated by fitting to known compressor maps aiming at extrapolation of maps and better prediction of surge and choke lines. the model validation testing will be done against measured maps. finding fitting (correction) coefficients by optimization methods is realized in a similar way, as it was done for the case of radial centripetal turbine, e.g. [1]. the solution of basic conservation laws can yield unknown temperatures, pressures and velocities along central streamline for compressible fluid and treats transonic operation, as well. after the description of general methods for solving compressible fluid flow and transformation of radial blade cascades to axial ones as done partially in [3], the system of equations is completed with empiric knowledge of compressor blade cascades losses. howell theory – [4] and [5], originally published in [7] and [8] is used for axial inducer and after transformation fixing the same length of a blade and flow areas to radial blade cascades, as well. non‑linear equations of gas dynamics have to be solved in numerical and iterative way with help of newton solver. the treatment of transonic flow features in both compressor inducer and diffuser is described then, based on gas dynamics as described in [14]. the general compressor parameters are finally evaluated from detailed cascade description, making advantage from the modular design of the model. the model yields information, which could be received from virtual sensors of values inside a compressor. it is suitable for the assessment of collaboration between stages in multi‑stage machines and two‑stage turbocharging. in the future, the model will be used for the elucidation of compressor design issues and the proposal of ways improving compressor design. the validation of the model will be published in the second paper focused to this topic. moreover, the model offers parameters for unsteady model, based on 1d modules for unsteady flow modelling, as done in [1], [2] or [16]. the paper is structured in the following manner: first, geometry of blades and flow are described, taking the later use of profile cascade theory for lift and drag forces into account. relations for combination of mass and energy conservation laws are solved for finding procedures to determine total, stagnation and static states for compressible fluid dynamics then. loss definitions for diffuser and nozzle flows are treated after it in the form of numerical procedures. generalized results of axial profile blade theory are applied for compressor simulations after it. specific attention is devoted to a vaneless diffuser with compressible fluid flow. transonic performance of inducer inlet and vaneless diffuser is analyzed then. finally, the basic compressor component description and their interaction is described. 1 c1 w1 u1 u2 β1 α2 β2 r’’1 r’1 r2 b2 2 4 2 1 3 4 3 w2 c2 figure 1: a compressor impeller (1‑2) and diffuser (2‑3 vaneless, 3‑4 bladed) with positive sense of flow and blade angles (in reality, outlet from impeller features negative vane angle). obrázek 1: oběžné kolo kompresoru (1‑2) a difusor (2‑3 bezlopatkový, 3‑4 lopatkový) s kladným směrem rychlostí a úhlů lopatek. u skutečných kompresorů je úhel výstupní části lopatek oběžného kola záporný. physical 1d model of a high‑pressure ratio centrifugal compressor for turbochargers jan macek mecca 01 2018 page 35 2. geometry of radial compressor flow the compressor performance will be described at fixed mass flow rate and impeller speed with known geometry – at any location defined by the radius r, axial width b, step of blades in cascade s, blade chord c and blade angle measured from radius αb or βb for a stator or impeller, respectively. the positive direction of angle is measured in sense of impeller rotation. general scheme of radially‑axial centrifugal compressor is plotted in figure 1. defining flow angles by α or β for a stator or impeller, respectively, the velocity triangles and splitting vectors into tangential or axial/ radial components yield, e.g., cos cos tan 2 2 2 r 2 r 2 2 2t 2 2t 2 2 r 2 w β w c c α c u w u w β        ( 1 )  brdd and <0  2 2;ref reft a b k b kd br d dx dx br br br    ( 2 ) (1) symbols with arrows respect by their signs the real direction (positive in the direction of rotation), without signs are always positive (absolute values of vectors). a radial blade cascade may be converted into the axial one using conform (angle conserving) transformation from radial‑tangential cylindrical coordinates into cartesian axial‑tangential coordinates, used usually for profile cascade. the transformation assumes constant density (or density compensated by the appropriate change of axial width b) and angular momentum conservation in a free vortex flow. then, the both radial and axial components of velocity in polar coordinates are variable, but the product of velocity component and radius is conserved. the transformation is based on the same radial and axial area and rescaling of dφ and d(br) by the same constant factor. if channel width b is constant, then the angles of flow are conserved (conform transformation) and, especially, the velocity angle from radial direction is constant. cos cos tan 2 2 2 r 2 r 2 2 2t 2 2t 2 2 r 2 w β w c c α c u w u w β        ( 1 )  brdd and <0  2 2;ref reft a b k b kd br d dx dx br br br    ( 2 ) (2)             2 , , 2 2 , , 2 cos ln 2 2 cos ; ; ln out a out a in in t out t in out in br k x x k c br k x x k z zs brs c br                            ( 3 )           , , ln cos ; cos ln ln in in t t in a a in out out in in r c r x x x x c br br br br                         ( 4 )       ,2 2 , 2 2 32, cos 2 1 cos 1 r a b a r b r r a a co r cent r b a m m w w w r zb b r r w y f m w f m r w y                         ( 5 ) (3) for basic directions in axial or tangential straight line in cartesian coordinates transformation yields for constant blade height radial straight line or the arc of a circle, respectively. general straight lines are transformed into logarithmic spirals. points of blade surface can be transformed using             2 , , 2 2 , , 2 cos ln 2 2 cos ; ; ln out a out a in in t out t in out in br k x x k c br k x x k z zs brs c br                            ( 3 )           , , ln cos ; cos ln ln in in t t in a a in out out in in r c r x x x x c br br br br                         ( 4 )       ,2 2 , 2 2 32, cos 2 1 cos 1 r a b a r b r r a a co r cent r b a m m w w w r zb b r r w y f m w f m r w y                         ( 5 ) (4) the variability of blade height can be taken into account by this transformation, but the angles of flow are not the same as in cartesian coordinates more. the influence of centrifugal force from flow curvature and its influence on boundary layer (bl) development cannot be taken fully into account, of course. the same is valid for impeller centrifugal force, if applicable. although the transformation has to be corrected by calibration coefficients, the qualitative validity of this approach was several times proven for radial turbines, as in [3]. in the case of compressor impeller, the angles from radial direction are small, sometimes even zero (radial vanes), but mostly backswept (figure 3). even in the case of radial vanes, the flow inside impeller channels is not equivalent to purely straight diffuser channel. lift force from flow direction change in an axial cascade is replaced in the case of radial flow by the lift force created by coriolis inertia force. instead of centrifugal force due to channel curvature in an axial cascade, coriolis force acts on the flow, if radial velocity component exists. coriolis force causes pressure distribution in tangential direction with increase of pressure in counter‑rotation direction (counter‑ clockwise in figure 3). this pressure distribution is followed by the flow separation at the suction side of a vane being ahead in the sense of rotation. it is reflected by the outlet velocity profile, called “jet and wake” with flow separation bubble behind the leading vane and with jet part of flow close to the pressure side of the following vane. the equivalence of the centrifugal force in a curved axial channel and coriolis force in an impeller channel can be used for the estimate of deviation angle and losses in an impeller. only one r1 r2 +ϕ βb,in <0 cp o xt xa βb,in + βb,out cc βb,out γ figure 2: conform transformation of general straight line from polar coordinates. obrázek 2: konformní zobrazení obecně položené přímky z polárních souřadnic. physical 1d model of a high‑pressure ratio centrifugal compressor for turbochargers jan macek mecca 01 2018 page 36 half of coriolis acceleration has to be used since the flow features (almost) zero angular speed due to the slip of flow relative to vanes. using the same flow‑bearing velocities for both equivalent cascades in radial (subscript r) and axial direction (a), respectively, the force acting on the element of flow with the mass of δm is             2 , , 2 2 , , 2 cos ln 2 2 cos ; ; ln out a out a in in t out t in out in br k x x k c br k x x k z zs brs c br                            ( 3 )           , , ln cos ; cos ln ln in in t t in a a in out out in in r c r x x x x c br br br br                         ( 4 )       ,2 2 , 2 2 32, cos 2 1 cos 1 r a b a r b r r a a co r cent r b a m m w w w r zb b r r w y f m w f m r w y                         ( 5 ) (5) where y is a axial blade centerline shape, described by function of axial coordinate and derived for finding local curvature. then, the differential equation for transformed axial blade cascade centerline can be found from its curvature using obvious 2 2 ,2 , 2 1 tan 1 1 cos 1 b a b a r y y y w           ( 6 ) 2 0 2 2 2 0, 0 2 0 2 2 2rel t c dh d dh w u u dh d d dh d dh          ( 7 ) e.g., for a rotating impeller it yields after integration 2 2 2 0, , 0, ,2 2 out out in p rel out p out p rel in w u u c t c t c t      ( 8 ) (6) which can be integrated for tan βb,a using euler’s substitution. the described transformations can help to some extent for the estimation of losses, based on old but yet worthwhile generalizations of axial diffuser blade cascades – e.g., howell [7], [8] and [5]. unlike estimation of incidence loss by old shock loss theory, it takes the real behavior of bl into account better. the boundary layer development in an impeller is influenced by relative vortex, moreover (see equation (33)), that is why correction by calibration coefficient is necessary. 3. total, stagnation and static states stodola equation for energy conservation yields, using velocities c in steady (absolute) coordinate system or w in relative (rotating) coordinate system with relative or absolute stagnation (0) states and total state (t): 2 2 ,2 , 2 1 tan 1 1 cos 1 b a b a r y y y w           ( 6 ) 2 0 2 2 2 0, 0 2 0 2 2 2rel t c dh d dh w u u dh d d dh d dh          ( 7 ) e.g., for a rotating impeller it yields after integration 2 2 2 0, , 0, ,2 2 out out in p rel out p out p rel in w u u c t c t c t      ( 8 ) (7) e.g., for a rotating impeller it yields after integration 2 2 ,2 , 2 1 tan 1 1 cos 1 b a b a r y y y w           ( 6 ) 2 0 2 2 2 0, 0 2 0 2 2 2rel t c dh d dh w u u dh d d dh d dh          ( 7 ) e.g., for a rotating impeller it yields after integration 2 2 2 0, , 0, ,2 2 out out in p rel out p out p rel in w u u c t c t c t      ( 8 ) (8) non‑linear equations of gas dynamics have to be solved in numerical and iterative way with help of newton solver, as follows. if static state and mass flow rate are known, finding total state is without any numerical problem. the velocity of flow can be found from static density for reversed relation. total temperature is 2 2 2 2t p p w u t t c c    ( 9 ) 1 0 0 t p p t         ( 10 ) 2 2 1 0 0 0 1 2 p tm t t c a t                  ( 11 )       2 2 1 1 2 2 1 0 0 1 0 2 2 1 1 1 1 0 0 0 0 1 1 1 0 2 1 1 1 1 1 0 i i ip p i i i i i i i i tm dy y t t y t t should be c a t dt dy m m t t t t dt c a r a ydy y t t t t dydt dt                                                                                     ( 12 )  * 2 20 1 2 1 1 1out in out in t rt u u r              ( 13 ) (9) total or stagnation pressure is defined by isentropic change. in the case of stagnation pressure, it yields 2 2 2 2t p p w u t t c c    ( 9 ) 1 0 0 t p p t         ( 10 ) 2 2 1 0 0 0 1 2 p tm t t c a t                  ( 11 )       2 2 1 1 2 2 1 0 0 1 0 2 2 1 1 1 1 0 0 0 0 1 1 1 0 2 1 1 1 1 1 0 i i ip p i i i i i i i i tm dy y t t y t t should be c a t dt dy m m t t t t dt c a r a ydy y t t t t dydt dt                                                                                     ( 12 )  * 2 20 1 2 1 1 1out in out in t rt u u r              ( 13 ) (10) the most complicated case often occurs in a compressor description. the system of equations (9) and (10) can be replaced together with mass flow rate equation by 2 2 2 2t p p w u t t c c    ( 9 ) 1 0 0 t p p t         ( 10 ) 2 2 1 0 0 0 1 2 p tm t t c a t                  ( 11 )       2 2 1 1 2 2 1 0 0 1 0 2 2 1 1 1 1 0 0 0 0 1 1 1 0 2 1 1 1 1 1 0 i i ip p i i i i i i i i tm dy y t t y t t should be c a t dt dy m m t t t t dt c a r a ydy y t t t t dydt dt                                                                                     ( 12 )  * 2 20 1 2 1 1 1out in out in t rt u u r              ( 13 ) (11) and solved using newton’s method for unknown static temperature 2 2 2 2t p p w u t t c c    ( 9 ) 1 0 0 t p p t         ( 10 ) 2 2 1 0 0 0 1 2 p tm t t c a t                  ( 11 )       2 2 1 1 2 2 1 0 0 1 0 2 2 1 1 1 1 0 0 0 0 1 1 1 0 2 1 1 1 1 1 0 i i ip p i i i i i i i i tm dy y t t y t t should be c a t dt dy m m t t t t dt c a r a ydy y t t t t dydt dt                                                                                     ( 12 )  * 2 20 1 2 1 1 1out in out in t rt u u r              ( 13 ) (12) derivative of function in denominator must not be zero, which yields temperature limit. this temperature is just a critical temperature. if iteration result is limited to temperature greater u2 w2 c2 βb,out figure 3: backswept impeller vans and impeller outlet velocity profile (jet and wake). obrázek 3: oběžné kolo s dozadu zahnutými lopatkami. rychlostní pole na výstupu z kanálu dle teorie proudu na přetlakové straně lopatky a úplavu na podtlakové straně. physical 1d model of a high‑pressure ratio centrifugal compressor for turbochargers jan macek mecca 01 2018 page 37 than this limit (and less than t0), it yields subsonic solutions. it can be used for supersonic case, as well, if started with temperature less than limit one. in the case of rotating channel, the similar procedure can be found. if critical state is reached, energy conservation yields between inlet and outlet 2 2 2 2t p p w u t t c c    ( 9 ) 1 0 0 t p p t         ( 10 ) 2 2 1 0 0 0 1 2 p tm t t c a t                  ( 11 )       2 2 1 1 2 2 1 0 0 1 0 2 2 1 1 1 1 0 0 0 0 1 1 1 0 2 1 1 1 1 1 0 i i ip p i i i i i i i i tm dy y t t y t t should be c a t dt dy m m t t t t dt c a r a ydy y t t t t dydt dt                                                                                     ( 12 )  * 2 20 1 2 1 1 1out in out in t rt u u r              ( 13 ) (13) if the equation (13) is applied to calculation of static temperature from total one, the influence of centrifugal force energy is zero. the relation is valid for any adiabatic case including irreversibility. if supersonic inlet occurs, the result has to be carefully assessed from the point of view of physical stability of such solution. e.g., in the case of inducer inlet, the solution for too high mass flow rate, which would lead to further acceleration of supersonic flow in the following diffuser blade cascade, is not probably real. the inducer is choked at inlet by shock wave perpendicular to flow direction in such a case and the assumed mass flow rate cannot be reached. the maximum mass flow rate has to be calculated in advance for the static temperature from equation (13). in 3d reality, the process of choking is much more complicated and increases incidence loss via the series of oblique shocks in blade channel inlet, but the choking mass flow rate is valid, if the inlet area is corrected to possible boundary layer separation caused by λ‑like shocks in boundary layer. the situation is more complicated if transonic flow velocity is caused by high speed of impeller. further examples follow below. 4. diffuser flow and losses the isentropic efficiency and loss coefficient of diffuser flow is defined according to figure 4 by the following relations 2 1s 2 2 1 1 2 1 1 2 2 z in in w h w w         ( 14 ) 2 2 2 2 0 0 0 1 0 0 1 2 2 1                                    out in out in in out p p in out in in in in t u u tm y t t c c a t t ( 15 ) (14) should resulting temperature or density be determined, the procedure described above has to be changed, taking losses of kinetic energy and potential energy centrifugal force field into account. then, it yields for compressor flow through a generally rotating diffuser cascade with known state at blade inlet in the static state at outlet out the basic relation for newtonian iteration, similar to 2 w22s losth 2 w21 2 w21s 2 1s 2 2 1 1 2 1 1 2 2 z in in w h w w         ( 14 ) 2 2 2 2 0 0 0 1 0 0 1 2 2 1                                       out in out in in out p p in out in in in in t u u tm y t t c c a t t t t ( 15 ) the derivative of y can be easily found in analytical way and applied to ( 12 ). the temperature has to be greater than critical one according to ( 13 ) for subsonic solution. generalization of axial blade cascade results geometry of axial profile cascade the angles of flow are measured from axial direction. the blade angles are b, the angles of flow in coordinate system of blade cascade (relative flow coordinates) are , the angles of (15) 2 w22s losth 2 w21 2 w21s 2 1s 2 2 1 1 2 1 1 2 2 z in in w h w w         ( 14 ) 2 2 2 2 0 0 0 1 0 0 1 2 2 1                                       out in out in in out p p in out in in in in t u u tm y t t c c a t t t t ( 15 ) the derivative of y can be easily found in analytical way and applied to ( 12 ). the temperature has to be greater than critical one according to ( 13 ) for subsonic solution. generalization of axial blade cascade results geometry of axial profile cascade the angles of flow are measured from axial direction. the blade angles are b, the angles of flow in coordinate system of blade cascade (relative flow coordinates) are , the angles of the derivative of y can be easily found in analytical way and applied to (12). the temperature has to be greater than critical one according to (13) for subsonic solution. 5. generalization of axial blade cascade results 5.1 geometry of axial profile cascade the angles of flow are measured from axial direction. the blade angles are βb, the angles of flow in coordinate system of blade cascade (relative flow coordinates) are β, the angles of flow in steady (absolute) coordinate system are α. the following relations are used for flow turn angle, incidence angle and outlet deviation angle 2 w22s losth 2 w21 2 w21s 2 1s 2 2 1 1 2 1 1 2 2 z in in w h w w         ( 14 ) 2 2 2 2 0 0 0 1 0 0 1 2 2 1                                       out in out in in out p p in out in in in in t u u tm y t t c c a t t t t ( 15 ) the derivative of y can be easily found in analytical way and applied to ( 12 ). the temperature has to be greater than critical one according to ( 13 ) for subsonic solution. generalization of axial blade cascade results geometry of axial profile cascade the angles of flow are measured from axial direction. the blade angles are b, the angles of flow in coordinate system of blade cascade (relative flow coordinates) are , the angles of figure 4: diffuser flow and definition of losses in t‑s diagram. obrázek 4: proudění difuzorem a definice ztrát v t‑s diagramu. physical 1d model of a high‑pressure ratio centrifugal compressor for turbochargers jan macek mecca 01 2018 page 38 , , in out in b in b out out                ( 16 ) 2 2 2 ; 2 mean mean rr r r s z     ( 17 ) (16) moreover, the airfoils are described by length of chord c, cascade step s, maximum distance of airfoil centerline from chord p angles of tangent to centerline measured from axial direction βb. 5.2 howell theory of compressor blade cascades the losses have to be added from profile loss of planar airfoil cascade (surface friction and wake losses), secondary losses caused by induced vortices and blade tip losses. profile loss coefficient is calculated from drag coefficient at central streamline, using mean diameter of axial blades (if relevant) and blade step , , in out in b in b out out                ( 16 ) 2 2 2 ; 2 mean mean rr r r s z     ( 17 ) (17) profile cascade features can be found using howell’s approach generalizing angle of flow turn and drag coefficient for profile cascades. the normalized angle of flow turn ε / ε* can be found from the empirical dependence of normalized angle of incidence (ι – ι*)/ε* in figure 5. drag coefficient cx depends on normalized step of cascade. all curves can be substituted by polynomial regressions. in the case of flow turn angle, it is amended additionally by exponential correction to separation of boundary layer */   ** /  7* * 0.95 13 0.4* *6 0 13* * * 1 1 i ia a a e                                                        ( 18 ) 2 , * * * , , , 2 0.23 500; ; 1 1 500 b out out b out b in b out p c s c                     ( 19 ) * * 1.55tan tan 1 1.5 in out ss c      ( 20 ) * * * * * *;in out           ( 21 )     2 * * * 2 2* * * * 1 1 tan tan 8 tan cos cos arctan 4 tan out out out out out out s s s                   ( 22 )  * * *, *; , , ;in b in out inf                    ( 23 ) (18) */   ** /  7* * 0.95 13 0.4* *6 0 13* * * 1 1 i ia a a e                                                        ( 18 ) 2 , * * * , , , 2 0.23 500; ; 1 1 500 b out out b out b in b out p c s c                     ( 19 ) * * 1.55tan tan 1 1.5 in out ss c      ( 20 ) * * * * * *;in out           ( 21 )     2 * * * 2 2* * * * 1 1 tan tan 8 tan cos cos arctan 4 tan out out out out out out s s s                   ( 22 )  * * *, *; , , ;in b in out inf                    ( 23 ) reference values can be found from reference deviation angle (constant’s rule, naca – [4]) */   ** /  7* * 0.95 13 0.4* *6 0 13* * * 1 1 i ia a a e                                                        ( 18 ) 2 , * * * , , , 2 0.23 500; ; 1 1 500 b out out b out b in b out p c s c                     ( 19 ) * * 1.55tan tan 1 1.5 in out ss c      ( 20 ) * * * * * *;in out           ( 21 )     2 * * * 2 2* * * * 1 1 tan tan 8 tan cos cos arctan 4 tan out out out out out out s s s                   ( 22 )  * * *, *; , , ;in b in out inf                    ( 23 ) (19) */   ** /  7* * 0.95 13 0.4* *6 0 13* * * 1 1 i ia a a e                                                        ( 18 ) 2 , * * * , , , 2 0.23 500; ; 1 1 500 b out out b out b in b out p c s c                     ( 19 ) * * 1.55tan tan 1 1.5 in out ss c      ( 20 ) * * * * * *;in out           ( 21 )     2 * * * 2 2* * * * 1 1 tan tan 8 tan cos cos arctan 4 tan out out out out out out s s s                   ( 22 )  * * *, *; , , ;in b in out inf                    ( 23 ) and howell’s relation */   ** /  7* * 0.95 13 0.4* *6 0 13* * * 1 1 i ia a a e                                                        ( 18 ) 2 , * * * , , , 2 0.23 500; ; 1 1 500 b out out b out b in b out p c s c                     ( 19 ) * * 1.55tan tan 1 1.5 in out ss c      ( 20 ) * * * * * *;in out           ( 21 )     2 * * * 2 2* * * * 1 1 tan tan 8 tan cos cos arctan 4 tan out out out out out out s s s                   ( 22 )  * * *, *; , , ;in b in out inf                    ( 23 ) (20) angles are bound by the following relations */   ** /  7* * 0.95 13 0.4* *6 0 13* * * 1 1 i ia a a e                                                        ( 18 ) 2 , * * * , , , 2 0.23 500; ; 1 1 500 b out out b out b in b out p c s c                     ( 19 ) * * 1.55tan tan 1 1.5 in out ss c      ( 20 ) * * * * * *;in out           ( 21 )     2 * * * 2 2* * * * 1 1 tan tan 8 tan cos cos arctan 4 tan out out out out out out s s s                   ( 22 )  * * *, *; , , ;in b in out inf                    ( 23 ) (21) which yields for reference flow turn angle a quadratic equation from (20) and (21) with the solution */   ** /  7* * 0.95 13 0.4* *6 0 13* * * 1 1 i ia a a e                                                        ( 18 ) 2 , * * * , , , 2 0.23 500; ; 1 1 500 b out out b out b in b out p c s c                     ( 19 ) * * 1.55tan tan 1 1.5 in out ss c      ( 20 ) * * * * * *;in out           ( 21 )     2 * * * 2 2* * * * 1 1 tan tan 8 tan cos cos arctan 4 tan out out out out out out s s s                   ( 22 )  * * *, *; , , ;in b in out inf                    ( 23 ) (22) 0.000 0.020 0.040 0.060 0.080 0.100 0.120 0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 -1.00 -0.80 -0.60 -0.40 -0.20 0.00 0.20 0.40 0.60 0.80 c x ep s/ ep s* (i-i*)/eps* eps/eps* eps reg c x05 c x05 reg c x10 c x10 reg c x15 c x15 reg 0.000 0.020 0.040 0.060 0.080 0.100 0.120 0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 -1.00 -0.80 -0.60 -0.40 -0.20 0.00 0.20 0.40 0.60 0.80 c x ep s/ ep s* (i-i*)/eps* eps/eps* eps reg c x05 c x05 reg c x10 c x10 reg c x15 c x15 reg figure 5: relative angle of flow turn eps normalized by reference angle eps* and profile drag coefficient c x for compressor blade cascade – [7]. drag coefficient for different relative steps s/c 0.5, 1. and 1.5, as mentioned in curve descriptions. dependences on the difference of angle of incidence ι and its reference value ι* normalized by reference flow turn angle eps*. comparison of published data and regression model. obrázek 5: poměrný úhel natočení proudu eps normovaný jmenovitým úhlem eps* a profilový součinitel odporu c x pro kompresorovou profilovou mříž – [7]. součinitel odporu pro různé poměrné rozteče s/c 0.5, 1. a 1.5. závislosti na poměrné odchylce úhlu náběhu ι od jmenovitého úhlu ι*. srovnání publikovaných dat a regresního modelu. physical 1d model of a high‑pressure ratio centrifugal compressor for turbochargers jan macek mecca 01 2018 page 39 reference values are calculated once for the whole compressor map prediction. radial cascades in a vaned diffuser are transformed to axial ones using (4). then using (18) 1.5. závislosti na poměrné odchylce úhlu náběhu i od jmenovitého úhlu i*. srovnání publikovaných dat a regresního modelu. the normalized angle of flow turn */ can be found from the empirical dependence of normalized angle of incidence   ** /  in figure 5. drag coefficient xc depends on normalized step of cascade. all curves can be substituted by polynomial regressions. in the case of flow turn angle, it is amended additionally by exponential correction to separation of boundary layer 7* * 0.95 13 0.4* *6 0 13* * * 1 1 i ia a a e                                                        ( 18 ) reference values can be found from reference deviation angle (constant’s rule, naca – [4]) 2 , * * * , , , 2 0.23 500; ; 1 1 500 b out out b out b in b out p c s c                     ( 19 ) and howell’s relation * * 1.55tan tan 1 1.5 in out ss c      ( 20 ) angles are bound by the following relations * * * * * *;in out           ( 21 ) which yields for reference flow turn angle a quadratic equation from ( 20 ) and ( 21 ) with the solution     2 * * * 2 2* * * * 1 1 tan tan 8 tan cos cos arctan 4 tan out out out out out out s s s                   ( 22 ) reference values are calculate once for the whole compressor map prediction. radial cascades in a vaned diffuser are transformed to axial ones using ( 4 ). then using ( 18 )  * * *, *; , , ;in b in out inf                         ( 23 ) and drag coefficient can be found. incidence angle influence is described in a better way than by naca shock loss theory referred to in [15]. forces in a blade cascade (23) 1.5. závislosti na poměrné odchylce úhlu náběhu i od jmenovitého úhlu i*. srovnání publikovaných dat a regresního modelu. the normalized angle of flow turn */ can be found from the empirical dependence of normalized angle of incidence   ** /  in figure 5. drag coefficient xc depends on normalized step of cascade. all curves can be substituted by polynomial regressions. in the case of flow turn angle, it is amended additionally by exponential correction to separation of boundary layer 7* * 0.95 13 0.4* *6 0 13* * * 1 1 i ia a a e                                                        ( 18 ) reference values can be found from reference deviation angle (constant’s rule, naca – [4]) 2 , * * * , , , 2 0.23 500; ; 1 1 500 b out out b out b in b out p c s c                     ( 19 ) and howell’s relation * * 1.55tan tan 1 1.5 in out ss c      ( 20 ) angles are bound by the following relations * * * * * *;in out           ( 21 ) which yields for reference flow turn angle a quadratic equation from ( 20 ) and ( 21 ) with the solution     2 * * * 2 2* * * * 1 1 tan tan 8 tan cos cos arctan 4 tan out out out out out out s s s                   ( 22 ) reference values are calculate once for the whole compressor map prediction. radial cascades in a vaned diffuser are transformed to axial ones using ( 4 ). then using ( 18 )  * * *, *; , , ;in b in out inf                         ( 23 ) and drag coefficient can be found. incidence angle influence is described in a better way than by naca shock loss theory referred to in [15]. forces in a blade cascade and drag coefficient can be found. incidence angle influence is described in a better way than by naca shock loss theory referred to in [15]. 5.3 forces in a blade cascade tangential t and axial a  forces in an axial compressor blade cascade, acting from fluid to airfoils can be found from lift and drag forces using mean angle of flow – [4] – with positive directions defined in figure 2 and for the case of compressor  sign cos sin ; cos sin sin cos ; sin cos m y m x m y m x m y m x m y m x m t f f t f f a f f a f f                   ( 24 ) tan tan arctan 2 in out m           ( 25 ) ____ ____ 2 2 2 2;2 cos 2 cos a a y y x x m m w wb b f c c f c c       ( 26 )   ____ 2 tan tan ;a in out out int b sw         ( 27 ) ____ 2 2 2 1 1 sin cos 2 cos cos in y m x m a in out s b a f f w                 ( 28 )  2, 2 2 2 1 tan cos 2 tan 2 tan tan cos cos cos cos cos x in p m in in in m m x in in m out cc s cc s                          ( 29 )   2 cos tan tan tan sign m y in in x m m s c c c           ( 30 )  ,sin sinsep out b outs k     ( 31 )  2r b m w r z t s b        ( 32 )  sign cos sin ; cos sin sin cos ; sin cos m y m x m y m x m y m x m y m x m t f f t f f a f f a f f                   ( 24 ) tan tan arctan 2 in out m           ( 25 ) ____ ____ 2 2 2 2;2 cos 2 cos a a y y x x m m w wb b f c c f c c       ( 26 )   ____ 2 tan tan ;a in out out int b sw         ( 27 ) ____ 2 2 2 1 1 sin cos 2 cos cos in y m x m a in out s b a f f w                 ( 28 )  2, 2 2 2 1 tan cos 2 tan 2 tan tan cos cos cos cos cos x in p m in in in m m x in in m out cc s cc s                          ( 29 )   2 cos tan tan tan sign m y in in x m m s c c c           ( 30 )  ,sin sinsep out b outs k     ( 31 )  2r b m w r z t s b        ( 32 ) (24) using  sign cos sin ; cos sin sin cos ; sin cos m y m x m y m x m y m x m y m x m t f f t f f a f f a f f                   ( 24 ) tan tan arctan 2 in out m           ( 25 ) ____ ____ 2 2 2 2;2 cos 2 cos a a y y x x m m w wb b f c c f c c       ( 26 )   ____ 2 tan tan ;a in out out int b sw         ( 27 ) ____ 2 2 2 1 1 sin cos 2 cos cos in y m x m a in out s b a f f w                 ( 28 )  2, 2 2 2 1 tan cos 2 tan 2 tan tan cos cos cos cos cos x in p m in in in m m x in in m out cc s cc s                          ( 29 )   2 cos tan tan tan sign m y in in x m m s c c c           ( 30 )  ,sin sinsep out b outs k     ( 31 )  2r b m w r z t s b        ( 32 ) (25) and well‑known definition with lift and drag coefficients, replacing velocity in infinity by its axial component and mean angle of flow  sign cos sin ; cos sin sin cos ; sin cos m y m x m y m x m y m x m y m x m t f f t f f a f f a f f                   ( 24 ) tan tan arctan 2 in out m           ( 25 ) ____ ____ 2 2 2 2;2 cos 2 cos a a y y x x m m w wb b f c c f c c       ( 26 )   ____ 2 tan tan ;a in out out int b sw         ( 27 ) ____ 2 2 2 1 1 sin cos 2 cos cos in y m x m a in out s b a f f w                 ( 28 )  2, 2 2 2 1 tan cos 2 tan 2 tan tan cos cos cos cos cos x in p m in in in m m x in in m out cc s cc s                          ( 29 )   2 cos tan tan tan sign m y in in x m m s c c c           ( 30 )  ,sin sinsep out b outs k     ( 31 )  2r b m w r z t s b        ( 32 ) (26) drag force acts on fluid against mean velocity, lift force is perpendicular to it according to the sign of velocity circulation. if results of momentum conservation are combined with energy conservation, tangential and axial forces are determined  sign cos sin ; cos sin sin cos ; sin cos m y m x m y m x m y m x m y m x m t f f t f f a f f a f f                   ( 24 ) tan tan arctan 2 in out m           ( 25 ) ____ ____ 2 2 2 2;2 cos 2 cos a a y y x x m m w wb b f c c f c c       ( 26 )   ____ 2 tan tan ;a in out out int b sw         ( 27 ) ____ 2 2 2 1 1 sin cos 2 cos cos in y m x m a in out s b a f f w                 ( 28 )  2, 2 2 2 1 tan cos 2 tan 2 tan tan cos cos cos cos cos x in p m in in in m m x in in m out cc s cc s                          ( 29 )   2 cos tan tan tan sign m y in in x m m s c c c           ( 30 )  ,sin sinsep out b outs k     ( 31 )  2r b m w r z t s b        ( 32 ) (27)  sign cos sin ; cos sin sin cos ; sin cos m y m x m y m x m y m x m y m x m t f f t f f a f f a f f                   ( 24 ) tan tan arctan 2 in out m           ( 25 ) ____ ____ 2 2 2 2;2 cos 2 cos a a y y x x m m w wb b f c c f c c       ( 26 )   ____ 2 tan tan ;a in out out int b sw         ( 27 ) ____ 2 2 2 1 1 sin cos 2 cos cos in y m x m a in out s b a f f w                 ( 28 )  2, 2 2 2 1 tan cos 2 tan 2 tan tan cos cos cos cos cos x in p m in in in m m x in in m out cc s cc s                          ( 29 )   2 cos tan tan tan sign m y in in x m m s c c c           ( 30 )  ,sin sinsep out b outs k     ( 31 )  2r b m w r z t s b        ( 32 ) (28)  sign cos sin ; cos sin sin cos ; sin cos m y m x m y m x m y m x m y m x m t f f t f f a f f a f f                   ( 24 ) tan tan arctan 2 in out m           ( 25 ) ____ ____ 2 2 2 2;2 cos 2 cos a a y y x x m m w wb b f c c f c c       ( 26 )   ____ 2 tan tan ;a in out out int b sw         ( 27 ) ____ 2 2 2 1 1 sin cos 2 cos cos in y m x m a in out s b a f f w                 ( 28 )  2, 2 2 2 1 tan cos 2 tan 2 tan tan cos cos cos cos cos x in p m in in in m m x in in m out cc s cc s                          ( 29 )   2 cos tan tan tan sign m y in in x m m s c c c           ( 30 )  ,sin sinsep out b outs k     ( 31 )  2r b m w r z t s b        ( 32 ) the procedure is prepared for howell cascade results, in which flow angle change ε and drag coefficient cx are generalized from experiments. combining relations above, it yields for loss coefficient  sign cos sin ; cos sin sin cos ; sin cos m y m x m y m x m y m x m y m x m t f f t f f a f f a f f                   ( 24 ) tan tan arctan 2 in out m           ( 25 ) ____ ____ 2 2 2 2;2 cos 2 cos a a y y x x m m w wb b f c c f c c       ( 26 )   ____ 2 tan tan ;a in out out int b sw         ( 27 ) ____ 2 2 2 1 1 sin cos 2 cos cos in y m x m a in out s b a f f w                 ( 28 )  2, 2 2 2 1 tan cos 2 tan 2 tan tan cos cos cos cos cos x in p m in in in m m x in in m out cc s cc s                          ( 29 )   2 cos tan tan tan sign m y in in x m m s c c c           ( 30 )  ,sin sinsep out b outs k     ( 31 )  2r b m w r z t s b        ( 32 ) (29)  sign cos sin ; cos sin sin cos ; sin cos m y m x m y m x m y m x m y m x m t f f t f f a f f a f f                   ( 24 ) tan tan arctan 2 in out m           ( 25 ) ____ ____ 2 2 2 2;2 cos 2 cos a a y y x x m m w wb b f c c f c c       ( 26 )   ____ 2 tan tan ;a in out out int b sw         ( 27 ) ____ 2 2 2 1 1 sin cos 2 cos cos in y m x m a in out s b a f f w                 ( 28 )  2, 2 2 2 1 tan cos 2 tan 2 tan tan cos cos cos cos cos x in p m in in in m m x in in m out cc s cc s                          ( 29 )   2 cos tan tan tan sign m y in in x m m s c c c           ( 30 )  ,sin sinsep out b outs k     ( 31 )  2r b m w r z t s b        ( 32 )  sign cos sin ; cos sin sin cos ; sin cos m y m x m y m x m y m x m y m x m t f f t f f a f f a f f                   ( 24 ) tan tan arctan 2 in out m           ( 25 ) ____ ____ 2 2 2 2;2 cos 2 cos a a y y x x m m w wb b f c c f c c       ( 26 )   ____ 2 tan tan ;a in out out int b sw         ( 27 ) ____ 2 2 2 1 1 sin cos 2 cos cos in y m x m a in out s b a f f w                 ( 28 )  2, 2 2 2 1 tan cos 2 tan 2 tan tan cos cos cos cos cos x in p m in in in m m x in in m out cc s cc s                          ( 29 )   2 cos tan tan tan sign m y in in x m m s c c c           ( 30 )  ,sin sinsep out b outs k     ( 31 )  2r b m w r z t s b        ( 32 ) and lift coefficient can be found from  sign cos sin ; cos sin sin cos ; sin cos m y m x m y m x m y m x m y m x m t f f t f f a f f a f f                   ( 24 ) tan tan arctan 2 in out m           ( 25 ) ____ ____ 2 2 2 2;2 cos 2 cos a a y y x x m m w wb b f c c f c c       ( 26 )   ____ 2 tan tan ;a in out out int b sw         ( 27 ) ____ 2 2 2 1 1 sin cos 2 cos cos in y m x m a in out s b a f f w                 ( 28 )  2, 2 2 2 1 tan cos 2 tan 2 tan tan cos cos cos cos cos x in p m in in in m m x in in m out cc s cc s                          ( 29 )   2 cos tan tan tan sign m y in in x m m s c c c           ( 30 )  ,sin sinsep out b outs k     ( 31 )  2r b m w r z t s b        ( 32 ) (30) 6. application of profile blade cascade theory to compressor components outlet angle from an inducer axial blade cascade can be used for estimation of local flow separation at the start of radial impeller part, using empirical chord length of separated bubble with additional calibration coefficient  sign cos sin ; cos sin sin cos ; sin cos m y m x m y m x m y m x m y m x m t f f t f f a f f a f f                   ( 24 ) tan tan arctan 2 in out m           ( 25 ) ____ ____ 2 2 2 2;2 cos 2 cos a a y y x x m m w wb b f c c f c c       ( 26 )   ____ 2 tan tan ;a in out out int b sw         ( 27 ) ____ 2 2 2 1 1 sin cos 2 cos cos in y m x m a in out s b a f f w                 ( 28 )  2, 2 2 2 1 tan cos 2 tan 2 tan tan cos cos cos cos cos x in p m in in in m m x in in m out cc s cc s                          ( 29 )   2 cos tan tan tan sign m y in in x m m s c c c           ( 30 )  ,sin sinsep out b outs k     ( 31 )  2r b m w r z t s b        ( 32 ) (31) the part of cascade step blocked by boundary layer separation is used as contraction coefficient in radial velocity component determination  sign cos sin ; cos sin sin cos ; sin cos m y m x m y m x m y m x m y m x m t f f t f f a f f a f f                   ( 24 ) tan tan arctan 2 in out m           ( 25 ) ____ ____ 2 2 2 2;2 cos 2 cos a a y y x x m m w wb b f c c f c c       ( 26 )   ____ 2 tan tan ;a in out out int b sw         ( 27 ) ____ 2 2 2 1 1 sin cos 2 cos cos in y m x m a in out s b a f f w                 ( 28 )  2, 2 2 2 1 tan cos 2 tan 2 tan tan cos cos cos cos cos x in p m in in in m m x in in m out cc s cc s                          ( 29 )   2 cos tan tan tan sign m y in in x m m s c c c           ( 30 )  ,sin sinsep out b outs k     ( 31 )  2r b m w r z t s b        ( 32 ) (32) outlet angle from impeller (often backswept) vanes has to be corrected to relative vortex in intervane channel, namely subtracting tangential relative velocity component – e.g., in [4] – with correction coefficient, which respects the inter‑vane channel area reduction due to vane wall thickness 2 2 2 2 2 2 2 cos cos 2 out out t s b out i s b out out out r u w k k z z          ( 33 ) ; ; tan ; tant tt t a a a a c w u w c w c w w       ( 34 ) 1 , 1 1 1, 2 2 2 2, 2 2, arctan cos tan arctan t in in b in a out s b out r b out out out r c u w u u k w z w             ( 35 )       2 2 ,, ; 2a r sep r bsep a b m m w w k r z t s bk r r zt r r                 ( 36 ) 22 , 3 0.025 cos0.04 coscos iny in s m out k cb b s s c c c               ( 37 )   5 2 0.2 5 2 2 ,2 2 re 2.10 2.10 re p s c wp s              ( 38 ) , , ,in in p in s in l      ( 39 ) (33) incidence angle has to be calculated according to upstream flow direction, e.g., from velocity triangles, 2 2 2 2 2 2 2 cos cos 2 out out t s b out i s b out out out r u w k k z z          ( 33 ) ; ; tan ; tant tt t a a a a c w u w c w c w w       ( 34 ) 1 , 1 1 1, 2 2 2 2, 2 2, arctan cos tan arctan t in in b in a out s b out r b out out out r c u w u u k w z w             ( 35 )       2 2 ,, ; 2a r sep r bsep a b m m w w k r z t s bk r r zt r r                 ( 36 ) 22 , 3 0.025 cos0.04 coscos iny in s m out k cb b s s c c c               ( 37 )   5 2 0.2 5 2 2 ,2 2 re 2.10 2.10 re p s c wp s              ( 38 ) , , ,in in p in s in l      ( 39 ) (34) which yields, e.g., for inducer inlet or impeller outlet 2 2 2 2 2 2 2 cos cos 2 out out t s b out i s b out out out r u w k k z z          ( 33 ) ; ; tan ; tant tt t a a a a c w u w c w c w w       ( 34 ) 1 , 1 1 1, 2 2 2 2, 2 2, arctan cos tan arctan t in in b in a out s b out r b out out out r c u w u u k w z w             ( 35 )       2 2 ,, ; 2a r sep r bsep a b m m w w k r z t s bk r r zt r r                 ( 36 ) 22 , 3 0.025 cos0.04 coscos iny in s m out k cb b s s c c c               ( 37 )   5 2 0.2 5 2 2 ,2 2 re 2.10 2.10 re p s c wp s              ( 38 ) , , ,in in p in s in l      ( 39 ) (35) physical 1d model of a high‑pressure ratio centrifugal compressor for turbochargers jan macek mecca 01 2018 page 40 with flow rate velocities 2 2 2 2 2 2 2 cos cos 2 out out t s b out i s b out out out r u w k k z z          ( 33 ) ; ; tan ; tant tt t a a a a c w u w c w c w w       ( 34 ) 1 , 1 1 1, 2 2 2 2, 2 2, arctan cos tan arctan t in in b in a out s b out r b out out out r c u w u u k w z w             ( 35 )       2 2 ,, ; 2a r sep r bsep a b m m w w k r z t s bk r r zt r r                 ( 36 ) 22 , 3 0.025 cos0.04 coscos iny in s m out k cb b s s c c c               ( 37 )   5 2 0.2 5 2 2 ,2 2 re 2.10 2.10 re p s c wp s              ( 38 ) , , ,in in p in s in l      ( 39 ) (36) 2 2 2 2 2 2 2 cos cos 2 out out t s b out i s b out out out r u w k k z z          ( 33 ) ; ; tan ; tant tt t a a a a c w u w c w c w w       ( 34 ) 1 , 1 1 1, 2 2 2 2, 2 2, arctan cos tan arctan t in in b in a out s b out r b out out out r c u w u u k w z w             ( 35 )       2 2 ,, ; 2a r sep r bsep a b m m w w k r z t s bk r r zt r r                 ( 36 ) 22 , 3 0.025 cos0.04 coscos iny in s m out k cb b s s c c c               ( 37 )   5 2 0.2 5 2 2 ,2 2 re 2.10 2.10 re p s c wp s              ( 38 ) , , ,in in p in s in l      ( 39 ) the profile drag coefficient is found from regression described together with equation (18) and recalculated to loss coefficient according to (29). secondary losses depend on lift coefficient square, using classic glauert results. secondary loss coefficient has to be added to the profile loss one – see [4], [9] and [6] – for blade length b and radial shroud clearance k including tip losses according to [9] 2 2 2 2 2 2 2 cos cos 2 out out t s b out i s b out out out r u w k k z z          ( 33 ) ; ; tan ; tant tt t a a a a c w u w c w c w w       ( 34 ) 1 , 1 1 1, 2 2 2 2, 2 2, arctan cos tan arctan t in in b in a out s b out r b out out out r c u w u u k w z w             ( 35 )       2 2 ,, ; 2a r sep r bsep a b m m w w k r z t s bk r r zt r r                 ( 36 ) 22 , 3 0.025 cos0.04 coscos iny in s m out k cb b s s c c c               ( 37 )   5 2 0.2 5 2 2 ,2 2 re 2.10 2.10 re p s c wp s              ( 38 ) , , ,in in p in s in l      ( 39 ) (37) if rec,w in<200 000 (it may occur at high‑pressure compressor stages stages), correction to re should be done before loss coefficients are summarized – [4] 2 2 2 2 2 2 2 cos cos 2 out out t s b out i s b out out out r u w k k z z          ( 33 ) ; ; tan ; tant tt t a a a a c w u w c w c w w       ( 34 ) 1 , 1 1 1, 2 2 2 2, 2 2, arctan cos tan arctan t in in b in a out s b out r b out out out r c u w u u k w z w             ( 35 )       2 2 ,, ; 2a r sep r bsep a b m m w w k r z t s bk r r zt r r                 ( 36 ) 22 , 3 0.025 cos0.04 coscos iny in s m out k cb b s s c c c               ( 37 )   5 2 0.2 5 2 2 ,2 2 re 2.10 2.10 re p s c wp s              ( 38 ) , , ,in in p in s in l      ( 39 ) (38) otherwise no correction is applied. then 2 2 2 2 2 2 2 cos cos 2 out out t s b out i s b out out out r u w k k z z          ( 33 ) ; ; tan ; tant tt t a a a a c w u w c w c w w       ( 34 ) 1 , 1 1 1, 2 2 2 2, 2 2, arctan cos tan arctan t in in b in a out s b out r b out out out r c u w u u k w z w             ( 35 )       2 2 ,, ; 2a r sep r bsep a b m m w w k r z t s bk r r zt r r                 ( 36 ) 22 , 3 0.025 cos0.04 coscos iny in s m out k cb b s s c c c               ( 37 )   5 2 0.2 5 2 2 ,2 2 re 2.10 2.10 re p s c wp s              ( 38 ) , , ,in in p in s in l      ( 39 ) (39) all estimations have to be corrected by mentioned calibration coefficients. 6.1 impeller inducer the relations for flow turn angle and loss coefficient can be directly applied to quasi‑axial inducer blades with correction coefficients taking into account the influence of stodola vortex and centrifugal force stabilization of bl in radial part of blades. 6.2 bladed diffuser howell theory [7] or [8] can be used after transformation from polar coordinates to cartesian ones. the procedure is described by eqs. (4) and (18) – (24). 6.3 vaneless diffuser the classic vaneless diffuser theory assumes free vortex (i.e., angular momentum conservation) for tangential velocity component and mass conservation with constant density for radial velocity component. if constant axial width b of vaneless diffuser (as plotted between positions 2 and 3 in figure 1) is assumed, well‑known logarithmic spiral streamline is achieved. both assumptions are too much idealized, since recent compressors achieve transonic flow at an impeller outlet, the compressibility of fluid and friction loss at side walls of a vaneless diffuser should be taken into account. velocity components in absolute space of inlet to a vaneless diffuser are 2 2 , 2 2 2 2 2 2 , , 2, 2, 2, cos tan 2 out t in s b out r b out out r in sep r in in out u c u k w z m c k r b          ( 40 )       2 2 2 2 , 2 , 2 0.2 2 , 2 2 2 2 , 2 , 2 0.2 2 ,2 2 , 2 2 re 2 2 re 2 1 ft t t t in r inf b cf t in r inf b ct in t dmdc c r c dr r dr dr m c c rk bdm dr m m c c rk br c r c r m r                       ( 41 ) 2 2 t tr r r c cdc dcdp dr c dr r dr dt r dr       ( 42 )  2 2 ; 2 1 tr r p t r t tr r r r r r t r p db d b r br dcdc dcm dtdr dr c c c dr dr dr drrb db b r c dcdc dc dcdrc c c c c dr rb p r p dr c t dr dr                                 ( 43 ) (40) angular momentum conservation yields for radius greater than the inlet radius of a vaneless diffuser, if turbulent friction at side walls is assumed 2 2 , 2 2 2 2 2 2 , , 2, 2, 2, cos tan 2 out t in s b out r b out out r in sep r in in out u c u k w z m c k r b          ( 40 )       2 2 2 2 , 2 , 2 0.2 2 , 2 2 2 2 , 2 , 2 0.2 2 ,2 2 , 2 2 re 2 2 re 2 1 ft t t t in r inf b cf t in r inf b ct in t dmdc c r c dr r dr dr m c c rk bdm dr m m c c rk br c r c r m r                       ( 41 ) 2 2 t tr r r c cdc dcdp dr c dr r dr dt r dr       ( 42 )  2 2 ; 2 1 tr r p t r t tr r r r r r t r p db d b r br dcdc dcm dtdr dr c c c dr dr dr drrb db b r c dcdc dc dcdrc c c c c dr rb p r p dr c t dr dr                                 ( 43 ) (41) a simplified assumption has been used for friction torque estimate, considering constant channel with b, angular momentum and mean constant density. centrifugal force, inertia force from change of radial velocity and pressure equilibrium yield in cylindrical coordinates 2 2 , 2 2 2 2 2 2 , , 2, 2, 2, cos tan 2 out t in s b out r b out out r in sep r in in out u c u k w z m c k r b          ( 40 )       2 2 2 2 , 2 , 2 0.2 2 , 2 2 2 2 , 2 , 2 0.2 2 ,2 2 , 2 2 re 2 2 re 2 1 ft t t t in r inf b cf t in r inf b ct in t dmdc c r c dr r dr dr m c c rk bdm dr m m c c rk br c r c r m r                       ( 41 ) 2 2 t tr r r c cdc dcdp dr c dr r dr dt r dr       ( 42 )  2 2 ; 2 1 tr r p t r t tr r r r r r t r p db d b r br dcdc dcm dtdr dr c c c dr dr dr drrb db b r c dcdc dc dcdrc c c c c dr rb p r p dr c t dr dr                                 ( 43 ) (42) mass and energy conservations for adiabatic case conservation yield 2 2 , 2 2 2 2 2 2 , , 2, 2, 2, cos tan 2 out t in s b out r b out out r in sep r in in out u c u k w z m c k r b          ( 40 )       2 2 2 2 , 2 , 2 0.2 2 , 2 2 2 2 , 2 , 2 0.2 2 ,2 2 , 2 2 re 2 2 re 2 1 ft t t t in r inf b cf t in r inf b ct in t dmdc c r c dr r dr dr m c c rk bdm dr m m c c rk br c r c r m r                       ( 41 ) 2 2 t tr r r c cdc dcdp dr c dr r dr dt r dr       ( 42 )  2 2 ; 2 1 tr r p t r t tr r r r r r t r p db d b r br dcdc dcm dtdr dr c c c dr dr dr drrb db b r c dcdc dc dcdrc c c c c dr rb p r p dr c t dr dr                                 ( 43 ) 2 2 , 2 2 2 2 2 2 , , 2, 2, 2, cos tan 2 out t in s b out r b out out r in sep r in in out u c u k w z m c k r b          ( 40 )       2 2 2 2 , 2 , 2 0.2 2 , 2 2 2 2 , 2 , 2 0.2 2 ,2 2 , 2 2 re 2 2 re 2 1 ft t t t in r inf b cf t in r inf b ct in t dmdc c r c dr r dr dr m c c rk bdm dr m m c c rk br c r c r m r                       ( 41 ) 2 2 t tr r r c cdc dcdp dr c dr r dr dt r dr       ( 42 )  2 2 ; 2 1 tr r p t r t tr r r r r r t r p db d b r br dcdc dcm dtdr dr c c c dr dr dr drrb db b r c dcdc dc dcdrc c c c c dr rb p r p dr c t dr dr                                 ( 43 ) (43) 2 2 , 2 2 2 2 2 2 , , 2, 2, 2, cos tan 2 out t in s b out r b out out r in sep r in in out u c u k w z m c k r b          ( 40 )       2 2 2 2 , 2 , 2 0.2 2 , 2 2 2 2 , 2 , 2 0.2 2 ,2 2 , 2 2 re 2 2 re 2 1 ft t t t in r inf b cf t in r inf b ct in t dmdc c r c dr r dr dr m c c rk bdm dr m m c c rk br c r c r m r                       ( 41 ) 2 2 t tr r r c cdc dcdp dr c dr r dr dt r dr       ( 42 )  2 2 ; 2 1 tr r p t r t tr r r r r r t r p db d b r br dcdc dcm dtdr dr c c c dr dr dr drrb db b r c dcdc dc dcdrc c c c c dr rb p r p dr c t dr dr                                 ( 43 ) which can be solved for radial component derivative numerically, if tangential component derivative is expressed by means of physical 1d model of a high‑pressure ratio centrifugal compressor for turbochargers jan macek mecca 01 2018 page 41 the equation (41). the vaneless diffuser has to be divided into several radial sectors for at least approximate integration of those differential equations. narrow circular strips should be used for higher mach numbers. if mach number less than 0,5, the sensitivity to density change is small. resulting radial velocity, pressure, density and tangential velocity at the outlet radius of a vaneless diffuser can be found without major issues, if the inlet flow is subsonic. 7. transonic performance the above deduced procedure can be applied for all blade cascades in a compressor if mach number is less than approximately 0.7. it is fulfilled for impeller except for inducer inlet, especially at high speeds, as mention in comments to the equation (13). even before inducer inlet choking is reached, the local relative velocity mach number, namely the blade tip mach number, can exceed transonic limit. combining velocity triangles, continuity equation         1 122 2 1, 1 2 2 2 , cosa in in insep a b in b sep a m m w w k rk r r zt r r r r zt r r k k r                        ( 44 ) 2 3 2 01 01 1 1 1 1 32 1 1 22 2 1 1 sin cos 1 1 cos 2 in in in in in k r p a m m u m                  ( 45 ) (44)         1 122 2 1, 1 2 2 2 , cosa in in insep a b in b sep a m m w w k rk r r zt r r r r zt r r k k r                        ( 44 ) 2 3 2 01 01 1 1 1 1 32 1 1 22 2 1 1 sin cos 1 1 cos 2 in in in in in k r p a m m u m                  ( 45 )         1 122 2 1, 1 2 2 2 , cosa in in insep a b in b sep a m m w w k rk r r zt r r r r zt r r k k r                        ( 44 ) 2 3 2 01 01 1 1 1 1 32 1 1 22 2 1 1 sin cos 1 1 cos 2 in in in in in k r p a m m u m                  ( 45 ) and energy conservation with definition of stagnation state and mach number, the following relation can be found for the blade tip mach number         1 122 2 1, 1 2 2 2 , cosa in in insep a b in b sep a m m w w k rk r r zt r r r r zt r r k k r                        ( 44 ) 2 3 2 01 01 1 1 1 1 32 1 1 22 2 1 1 sin cos 1 1 cos 2 in in in in in k r p a m m u m                  ( 45 ) (45) this equation can be applied for mean radius and angle of inducer flow to find the approximate limit of inducer choking, as well. according to measurements, the flow separation coefficient should be corrected. the choking limit may be set by a diffuser, as well, as described below. as a difference to inducer choking, the diffuser choking depends more on compressor speed. in the dependence of mass flow rates for mach number greater than 1, the loss coefficient of inducer axial blades should be reduced before critical mass flow rate for the whole blade height is reached – [5]. in the case of a vaneless diffuser, the subsonic assumption might not be the case of current high‑pressure compressors. the step‑ by‑step integration of density history from equation ( 43 ) can be simultaneously used with assessment of transonic flow issues downstream of an impeller. inlet flow to a vaneless diffuser is mostly supersonic in high‑ pressure compressors today. it is caused by the high blade speed of an impeller. the vaneless part is very important to decrease flow velocity in absolute space before the flow enters bladed diffuser, otherwise intensive shock waves with possible bl separation can occur. if shock wave occurs in the vaneless diffuser, it is an oblique shock of angle σ’ measured from direction of absolute flow velocity (90° would mean a transversal shock wave). due to rotational symmetry, the shock wave line must have circular shape and the angle measured from radial direction is 90°σ’. there are three possible cases for transonic flow then: • angle α of flow velocity from radial direction is greater than 90°σ’ (angle of flow deviation due to oblique shock is θ = 0 in figure 6 – [14] and [17])     2 2 2 2 2 1 sin arctan tan 1 sin r r m m                  ( 46 ) r r r c c m a rt   ( 47 ) 2 *2 2 0 2 2 1 1 2 r r r r r p cr c c a a t c                 ( 48 ) 2 2 1 2 11 ; 1 2 1 11 1 r r p m p m                    ( 49 ) (46) the normal component of velocity to the possible shock line is subsonic then and no oblique shock may occur. integration for subsonic radial velocity can be done together with flow deceleration due to tangential component reduction according to angular momentum conservation – equations (41), (42) and (43); this case is often present in today’s compressor designs. • angle α of flow velocity from radial direction less than 90° σ’ but greater than 90°σ’ for maximum deviation angle θ (figure 6). oblique shock with supersonic radial velocity component occurs for radial mach number figure 6: oblique shock: flow deviation angle ѳ and shock front angle σ’ measured from velocity direction in front of shock for different initial mach numbers (from [17]). obrázek 6: šikmá rázová vlna: úhel odklonu proudu ѳ a úhle rázové vlny σ’ měřený od směru rychlosti před rázem pro různá počáteční machova čísla (převzato ze [17]). physical 1d model of a high‑pressure ratio centrifugal compressor for turbochargers jan macek mecca 01 2018 page 42     2 2 2 2 2 1 sin arctan tan 1 sin r r m m                  ( 46 ) r r r c c m a rt   ( 47 ) 2 *2 2 0 2 2 1 1 2 r r r r r p cr c c a a t c                 ( 48 ) 2 2 1 2 11 ; 1 2 1 11 1 r r p m p m                    ( 49 ) (47)     2 2 2 2 2 1 sin arctan tan 1 sin r r m m                  ( 46 ) r r r c c m a rt   ( 47 ) 2 *2 2 0 2 2 1 1 2 r r r r r p cr c c a a t c                 ( 48 ) 2 2 1 2 11 ; 1 2 1 11 1 r r p m p m                    ( 49 ) (48)     2 2 2 2 2 1 sin arctan tan 1 sin r r m m                  ( 46 ) r r r c c m a rt   ( 47 ) 2 *2 2 0 2 2 1 1 2 r r r r r p cr c c a a t c                 ( 48 ) 2 2 1 2 11 ; 1 2 1 11 1 r r p m p m                    ( 49 ) (49) after the shock, subsonic flow equations (41), (42) and (43) can be used. • angle α of flow velocity from radial direction is less than 90°σ’ for maximum of θ, which is approx. 20° (figure 6). the branches of curves between maximum of flow deviation and lateral shock are unstable. the shock wave tends to be lateral to flow direction, which is impossible due to rotational symmetry in the case of vaneless diffuser. mass flow rate has to be reduced to achieve the mach number just for maximum of deviation angle. choking at a diffuser occurs in this case, which is impeller speed dependent unlike the choking at an inducer according to equation (45) applied to the mean radius of a blade. 8. compressor performance the overall picture of processes inside a compressor is plotted in h‑s diagram in figure 7, using energy conservation for rotating channel, definition of total and stagnation states and velocity triangles. the simulation procedure is based on known mass flow rate and speed of an impeller. static states are determined form conservation of total states (figure 7), mass conservation yielding velocities and loss coefficients, determining entropy increases. the pressure losses in yet not described parts (an inlet casing or outlet scroll) may be estimated using empirical loss coefficient for friction loss at walls and local losses with approximately constant velocity and density 2 0, 0, 0, 2 lossout lost out in in out pw h t t        ( 50 ) (50) which yields input for the following part of a compressor. velocity triangles and decomposition of velocities into axial/radial and tangential components are described by equations similar to (34) for impeller inlet and outlet. starting with known inlet total state, the static states are determined going from inlet by equations sets (12) and (15). flow angles are calculated from howell theory according to (23) with correction to relative vortex in an impeller – equation (29). flow area and radial velocity is corrected to local bl separation – equation (31). loss coefficients are found according to regression similar to (18) after recalculation form drag coefficient to profile loss coefficient (29) adding all partial losses to it in (39). if inlet and outlet velocities at an impeller are known, the power can be calculated from eulerian theorem and checked by stodola for the adiabatic case – see figure 7    ,int 2 2 1 1 02 0c t t pip m c u c u mc h h     ( 51 ) 3 2 2 20.000735windp d u m ( 52 ) (51) windage loss of an impeller can be estimated from windage power    ,int 2 2 1 1 02 0c t t pip m c u c u mc h h     ( 51 ) 3 2 2 20.000735windp d u m ( 52 ) (52) for β=6 ... 8. windage power is subtracted from the internal power. reduced mass flow rate, reduced speed and isentropic efficiency are calculated according to standard definitions. 9. conclusion – prospects and further work the presented physical model of a centrifugal compressor is suitable for compressor simulation in 1d codes if calibrated according to measured compressor maps. on one hand, it uses the basic generalization of experiments valid for axial blade cascades, although amended by certain adoption of radial cascades features, which has to be corrected by available experiments. on the other hand, it treats the transonic flow in the compressors of high‑ pressure ratio, which yields an opportunity to extrapolate the maps with certain reliability. it is important for choke limit especially. the extrapolation or prediction of surge limits, especially under influence of engine pulsating inlet flow, has not been tested yet. the dynamic surge limit is still certainly a big issue. the procedures for transonic flow prediction are stable and controllable from the h s 0 01 2so 5s 05s 2 2 1w 0p 01p 2 2 2c 2 2 2w 2 2 2u 1 1p 2p 02p 2 2 1u 00 hh st  sh0 dh ih 2relt1relt hh ,,  o lossh sh 04p02 2 2 1c 02rel 01rel 3 3p 22 2 5 2 4 cc  03 05 03p 4 04 5 05p 5p 2s 4p 2 2 3c 2 figure 7: h‑s diagram of a compressor. obrázek 7: h‑s diagram kompresoru. physical 1d model of a high‑pressure ratio centrifugal compressor for turbochargers jan macek mecca 01 2018 page 43 numerical point of view, which ensures reliable behavior during calibration done by optimization. in any case, the further development and validation of the model is inevitable. the results will be published soon in some of the next mecca items. the still remaining items of the further development will cover • compressor inlet duct loss including the optional use of pre‑swirl blades • leakages at shroud and hub sides influencing back‑flow to inducer blades and windage loss at hub side of an impeller • inducer flow inlet angle corrected to the backflow through a shroud clearance adding angular momentum to inlet flow • internal recirculation channel (irc) for surge limit modification • influence of relative stodola vortex to secondary vortices in inducer blades (amplification of asymmetry of counter‑ rotating secondary vortex couple) • scroll friction and flow separation losses • the impact of an outlet diffuser located downstream of a scroll • heat transfer in a compressor casing. acknowledgments this research has been realized using the support of technological agency, czech republic, program centre of competence, project #te01020020 josef božek competence centre for automotive industry and the ministry of education, youth and sports program npu i (lo), project # lo1311 development of vehicle centre of sustainable mobility. this support is gratefully acknowledged. references [1] macek, j., zak, z., and vitek, o., physical model of a twin‑scroll turbine with unsteady flow, sae technical paper 2015‑01‑1718, 2015, doi:10.4271/2015‑01‑1718. [2] macek j., vítek o., burič j. and doleček v.: comparison of lumped and unsteady 1‑d models for simulation of a radial turbine. sae int. j. engines vol.2(1) 173‑188, 2009, issn 1946‑396. sae paper 2009‑01‑0303 [3] sherstjuk, a. n., zaryankin, a.e., “radial‑axial turbines of small power” (in russian), mashinostroenie, moscow 1976 [4] dixon s. l. fluid mechanics, thermodynamics of turbomachinery, pergamon press, oxford 1975 [5] kousal. m., “stationary gas turbines” (in czech), sntl prague 1965 [6] vavra, m. h., aero‑thermodynamics and flow in turbomachines, j. wiley&sons, new york 1960 [7] howell, a. r., the present basis of axial flow compressor design: part 1 – cascade theory and performance, arc r&m 2095, 1942 [8] howell, a.r., fluid dynamics of axial compressors, proc. i. mech. e, 153 (1945), #12, pp. 441‑452 [9] dunham, j., came, p.: improvements to the ainley‑ mathieson method of turbine performance prediction. trans. asme, series a, vol. 92, 1970 [10] canova m et al., a scalable modelling approach for the simulation and design optimization of automotive turbochargers, sae technical paper 2015‑01‑1288 [11] vítek o, macek j and polášek m, new approach to turbocharger optimization using 1‑d simulation tools, sae paper 2006‑01‑0438, 2006 [12] watson n and janota ms (1982) turbocharging the internal combustion engine. macmillan publishers, london 1982, isbn 0 333 24290 4 [13] zinner k., aufladung von verbrennungsmotoren, springer 1975 [14] shapiro, a. h., the dynamics and thermodynamics of compressible fluid flow, the ronald press comp., new york 1953. [15] nakhjiri, m., pelz, p., matyschok, b., däubler, l. et al., physical modeling of automotive turbocharger compressor: analytical approach and validation, sae technical paper 2011‑01‑2214, 2011, https://doi. org/10.4271/2011‑01‑2214. [16] bozza, f., de bellis, v., marelli, s., and capobianco, m., 1d simulation and experimental analysis of a turbocharger compressor for automotive engines under unsteady flow conditions, sae int. j. engines 4(1):1365‑1384, 2011, https://doi.org/10.4271/2011‑01‑1147. [17] jerie, j., “theory of aircraft engines” (in czech), ctu in prague, 1985 symbols and subscripts a flow area [m2]; axial force component [n] a sound velocity [m.s‑1]; axial cartesian coordinate; regression coefficient b blade length perpendicular to axial or radial direction [m] c chord length [m]; specific thermal capacity [j.k‑1.kg‑1]; absolute velocity [m.s‑1] cx drag coefficient [1] cy lift coefficient [1] h specific enthalpy [j.kg‑1] k tuning coefficient [1] k tuning coefficient [1; radial shroud clearance [m] m mach number [1] m mass, mass flow rate (dotted)[kg, kg.s‑1] physical 1d model of a high‑pressure ratio centrifugal compressor for turbochargers jan macek mecca 01 2018 page 44 n speed [min‑1] p power [w] p pressure [pa]; position of maximum distance between airfoil centerline and chord [m] r radius [m] re reynolds number [1] r radius [m]; specific gas constant [j.k‑1.kg‑1] s cascade step [m] t temperature [k]; tangential force component [n] t tangential cartesian coordinate [m]; blade profile thickness [m] u circumferential blade speed [m.s‑1] w relative velocity [m.s‑1] x cartesian coordinate [m] y iteration variable z number of blades [1] α angle of absolute velocity of flow (from radial or axial direction in the sense of speed)[deg] β angle of relative velocity of flow (from radial or axial direction) [deg] βb angle of tangent to blade centerline γ angle of airfoil chord from axial or radial direction[deg] δ flow deviation outlet angle [deg] ε flow turn angle [deg] η isentropic efficiency [1] ι flow incidence angle [deg] λ coefficient of secondary losses [1] φ polar or cylindrical coordinate angle [deg] κ cp/cv ratio, isentropic exponent [1] π pressure ratio >1 [1] ρ density [kg.m3] σ angle of oblique shock wave measured from flow velocity direction[deg] θ profile centerline turn angle [deg]; flow deviation angle in oblique shock ζ loss coefficient [1] ω angular velocity [rad.s‑1] subscripts a axial b blade c compressor; cartesian i impeller m mean max maximum min minimum p polar p at constant pressure; profile loss r radial red reduced ref reference reg regression rel relative state s isentropic; flow separation; secondary (induced) loss sep flow separation t turbine tc turbocharger t total state; tangential v at constant volume x drag y lift 0 stagnation state in inlet out outlet z loss 1, 2, 3.. position in a compressor ‘ blade root (hub) “ blade tip (shroud) * reference, nominal; critical state of flow averaged → vector (if value is used, it has to feature appropriate sign acc. to axis direction) acronyms bl boundary layer bmep brake mean effective pressure cr centripetal radial ice internal combustion engine imep indicated mean effective pressure irc internal recirculation channel (anti‑surge measure for centrifugal compressors) mfr mass flow rate rpm revolutions per minute wot wide‑open throttle curve ole_link5 ole_link6 ole_link4 ole_link1 ole_link11 ole_link12 ole_link7 ole_link8 _ref503366894 _ref502929276 _ref502929278 _ref505352558 _ref503367918 _ref503082741 _ref503112326 _ref503111897 _ref503111924 _ref503368086 _ref503368097 _ref503368213 _ref503363584 _ref503367501 _ref503368504 _ref503123797 _ref503947492 _ref503532965 _ref503123776 _ref503800139 _ref503972064 _ref503947157 turbocharging of high performance compressed natural gas si engine for light duty vehicle marcel škarohlíd, jiří vávra implication of cycle-to-cycle variability in si engines karel páv identification of cycle-to-cycle variability sources in si ice based on cfd modeling oldřich vítek, vít doleček, zbyněk syrovátka, jan macek physical 1d model of a high-pressure ratio centrifugal compressor for turbochargers jan macek in-cylinder heat transfer modelling zdeněk žák, miloslav emrich, michal takáts, jan macek mecca 03 2016 page 2 10.1515/mecdc-2016-0009 in-cylinder heat transfer modelling zdeněk žák, miloslav emrich, michal takáts, jan macek 1. introduction the goal of the contribution is to describe the specific features of in-cylinder heat transfer modelling and the feasibility of improving the accuracy of resulting models. the capability of the standard heat transfer models in gt-suite is limited due to model calibration constrains. it is possible to increase the capability of the simulation tool using the user model linked to the main solver of commercially available software. modelling is therefore not restricted to standard tools and templates, but it is possible to develop software utilities with very specific features. the original correlation formulas are usually not accurate enough in the case of a specific combustion engine, so it is desirable to tune the coefficients of empirical formulas during the model calibration process. the presented in-house heat transfer model enables use of any correlation formula and the varying of all applied coefficients. the code is open and ready for further development. the correlation formulas currently available in the developed user model are briefly described below. the developed user model is able to cooperate with a standard cylinder wall temperature solver based on the finite element method (fem). 2. heat transfer modelling the very popular and frequently used formula “woschni gt” is an improved correlation based on the original woschni relation without swirl. the woschni gt is recommended by gamma zdeněk žák, miloslav emrich, michal takáts, jan macek czech technical university, vehicle centre of sustainable mobility, technická 4, 16607 praha 6 e-mail: zdenek.zak@fs.cvut.cz, miloslav.emrich@fs.cvut.cz, michal.takats@fs.cvut.cz, jan.macek@fs.cvut.cz abstract the goal of the paper is to discuss specific features of the in-cylinder heat transfer calculation based on widely used empirical formulas. the potential of in-house codes compared with commercially available software packages is presented. the principles of user models in the gt-suite environment are also explained. the results of calibrated models are briefly discussed. key words: heat transfer coefficient, gt-suite, user model, fortran, diesel, john deere, woschni, hohenberg, eichelberg, annand, sitkei, ramanaiah, taylor, toong shrnutí cílem příspěvku je poukázat na problematiku výpočtu tepla odvedeného z válce na základě často používaných empirických vztahů. dále je ukázán potenciál vlastních programů v porovnání s komerčně dostupným programovým vybavením. v článku jsou také osvětleny základy uživatelských modelů v prostředí gt-suite. stručné výsledky kalibrovaných modelů jsou uvedeny v závěru. klíčová slova: součinitel přestupu tepla, gt-suite, uživatelský model, fortran, diesel, john deere, woschni, hohenberg, eichelberg, annand, sitkei, ramanaiah, taylor, toong in-cylinder heat transfer modelling figure 1: heat transfer coefficients; woschni gt adapted (red dashed line); woschni adapted (black long dashed line); 900 rpm, full load, imep = 9.6 bar obrázek 1: součinitelé přestupu tepla; woschni gt upravený vztah (červená čárkovaná čára); woschni upravený vztah (černá dlouze čárkovaná čára); 900 rpm, plné zatížení motoru, imep = 9.6 bar in-cylinder heat transfer modelling zdeněk žák, miloslav emrich, michal takáts, jan macek mecca 03 2016 page 3 technologies as the first choice at the beginning of the calibration process of the internal combustion engine model. the heat transfer coefficients calculated via the woschni gt and woschni formulas are in figure 1. the user may influence the heat transfer coefficient course via two tuning parameters, i.e. a radiation and convection multiplier. the radiation multiplier is typically equal to one for diesel engines and zero for other engines. the radiation part of the total heat transfer rate, when the radiation multiplier equals one, is compared with the total heat transfer rates estimated by the woschni gt and woschni in figure 2. it is strongly recommended to hold only one value of the convection multiplier for the complete engine characteristic, but obtained results are quite unsatisfactory. the calibration of convection multiplier in relation to engine speed and load provides much better results. the achievement of the exact measured in-cylinder pressure course is, however, often impossible. woschni classic, woschni swirl, woschni – huber and hohenberg correlations are also available in the gt-suite environment. in the case of the user model, when the in-house developed code is used, the user is able to adapt the model and algorithm to very specific purposes. the problems may consist of the number of calibration parameters and elaborateness of the mentioned approach. the fundamental woschni’s correlation without swirl (1), (2) and (3) is described in detail in [2] and [3]. coefficients c1 and c2 in the relation of in-cylinder gas velocity depend on the engine cycle phase (2). the user of the developed in-house code may tune all calibration coefficients a1-a8 arbitrarily. figure 2: heat transfer rate; woschni gt adapted (red dashed line); woschni adapted (black long dashed line); radiation (blue dashed and dotted line); 900 rpm, full load, imep = 9.6 bar obrázek 2: tepelný tok chlazením; woschni gt upravený vztah (červená čárkovaná čára); woschni upravený vztah (černá dlouze čárkovaná čára); radiační složka (modrá čerchovaná čára); 900 rpm, plné zatížení motoru, imep = 9.6 bar it is strongly recommended to hold only one value of the convection multiplier for the complete engine characteristic, but obtained results are quite unsatisfactory. the calibration of convection multiplier in relation to engine speed and load provides much better results. the achievement of the exact measured in-cylinder pressure course is, however, often impossible. woschni classic, woschni swirl, woschni huber and hohenberg correlations are also available in the gt-suite environment. in the case of the user model, when the in-house developed code is used, the user is able to adapt the model and algorithm to very specific purposes. the problems may consist of the number of calibration parameters and elaborateness of the mentioned approach. the fundamental woschni's correlation without swirl (1), (2) and (3) is described in detail in [2] and [3]. coefficients c1 and c2 in the relation of in-cylinder gas velocity depend on the engine cycle phase (2). the user of the developed in-house code may tune all calibration coefficients a1-a8 arbitrarily. � � ������������� b���� p ��� t����� w ��� � �� b �� p �� t �� w �� (1) w � c� s� � c� �� �������� ���� �p � p�� � �� s� � �� �� ���� ���� ���� �p � p�� (2) p� � p��� ������ � � � p��� ������ � �� (3) gas exchange period: c� � ����� c� � �; compression period: c� � ����� c� � �; combustion and expansion period: c� � ����� c� � ���� ��� �� the effect of the swirl is included in the second woschni formula (4), (5), (6), (7) and (8). see [2], [4] and [5]. the intensity of the swirl is described by rotational speed of the paddle wheel (7) and (8) obtained by measurement on a flowbench. figure 2: heat transfer rate; woschni gt adapted (red dashed line); woschni adapted (black long dashed line); radiation (blue dashed and dotted line); 900 rpm, full load, imep = 9.6 bar obrázek 2: tepelný tok chlazením; woschni gt upravený vztah (červená čárkovaná čára); woschni upravený vztah (černá dlouze čárkovaná čára); radiační složka (modrá čerchovaná čára); 900 rpm, plné zatížení motoru, imep = 9.6 bar it is strongly recommended to hold only one value of the convection multiplier for the complete engine characteristic, but obtained results are quite unsatisfactory. the calibration of convection multiplier in relation to engine speed and load provides much better results. the achievement of the exact measured in-cylinder pressure course is, however, often impossible. woschni classic, woschni swirl, woschni huber and hohenberg correlations are also available in the gt-suite environment. in the case of the user model, when the in-house developed code is used, the user is able to adapt the model and algorithm to very specific purposes. the problems may consist of the number of calibration parameters and elaborateness of the mentioned approach. the fundamental woschni's correlation without swirl (1), (2) and (3) is described in detail in [2] and [3]. coefficients c1 and c2 in the relation of in-cylinder gas velocity depend on the engine cycle phase (2). the user of the developed in-house code may tune all calibration coefficients a1-a8 arbitrarily. � � ������������� b���� p ��� t����� w ��� � �� b �� p �� t �� w �� (1) w � c� s� � c� �� �������� ���� �p � p�� � �� s� � �� �� ���� ���� ���� �p � p�� (2) p� � p��� ������ � � � p��� ������ � �� (3) gas exchange period: c� � ����� c� � �; compression period: c� � ����� c� � �; combustion and expansion period: c� � ����� c� � ���� ��� �� the effect of the swirl is included in the second woschni formula (4), (5), (6), (7) and (8). see [2], [4] and [5]. the intensity of the swirl is described by rotational speed of the paddle wheel (7) and (8) obtained by measurement on a flowbench. (1) figure 2: heat transfer rate; woschni gt adapted (red dashed line); woschni adapted (black long dashed line); radiation (blue dashed and dotted line); 900 rpm, full load, imep = 9.6 bar obrázek 2: tepelný tok chlazením; woschni gt upravený vztah (červená čárkovaná čára); woschni upravený vztah (černá dlouze čárkovaná čára); radiační složka (modrá čerchovaná čára); 900 rpm, plné zatížení motoru, imep = 9.6 bar it is strongly recommended to hold only one value of the convection multiplier for the complete engine characteristic, but obtained results are quite unsatisfactory. the calibration of convection multiplier in relation to engine speed and load provides much better results. the achievement of the exact measured in-cylinder pressure course is, however, often impossible. woschni classic, woschni swirl, woschni huber and hohenberg correlations are also available in the gt-suite environment. in the case of the user model, when the in-house developed code is used, the user is able to adapt the model and algorithm to very specific purposes. the problems may consist of the number of calibration parameters and elaborateness of the mentioned approach. the fundamental woschni's correlation without swirl (1), (2) and (3) is described in detail in [2] and [3]. coefficients c1 and c2 in the relation of in-cylinder gas velocity depend on the engine cycle phase (2). the user of the developed in-house code may tune all calibration coefficients a1-a8 arbitrarily. � � ������������� b���� p ��� t����� w ��� � �� b �� p �� t �� w �� (1) w � c� s� � c� �� �������� ���� �p � p�� � �� s� � �� �� ���� ���� ���� �p � p�� (2) p� � p��� ������ � � � p��� ������ � �� (3) gas exchange period: c� � ����� c� � �; compression period: c� � ����� c� � �; combustion and expansion period: c� � ����� c� � ���� ��� �� the effect of the swirl is included in the second woschni formula (4), (5), (6), (7) and (8). see [2], [4] and [5]. the intensity of the swirl is described by rotational speed of the paddle wheel (7) and (8) obtained by measurement on a flowbench. figure 2: heat transfer rate; woschni gt adapted (red dashed line); woschni adapted (black long dashed line); radiation (blue dashed and dotted line); 900 rpm, full load, imep = 9.6 bar obrázek 2: tepelný tok chlazením; woschni gt upravený vztah (červená čárkovaná čára); woschni upravený vztah (černá dlouze čárkovaná čára); radiační složka (modrá čerchovaná čára); 900 rpm, plné zatížení motoru, imep = 9.6 bar it is strongly recommended to hold only one value of the convection multiplier for the complete engine characteristic, but obtained results are quite unsatisfactory. the calibration of convection multiplier in relation to engine speed and load provides much better results. the achievement of the exact measured in-cylinder pressure course is, however, often impossible. woschni classic, woschni swirl, woschni huber and hohenberg correlations are also available in the gt-suite environment. in the case of the user model, when the in-house developed code is used, the user is able to adapt the model and algorithm to very specific purposes. the problems may consist of the number of calibration parameters and elaborateness of the mentioned approach. the fundamental woschni's correlation without swirl (1), (2) and (3) is described in detail in [2] and [3]. coefficients c1 and c2 in the relation of in-cylinder gas velocity depend on the engine cycle phase (2). the user of the developed in-house code may tune all calibration coefficients a1-a8 arbitrarily. � � ������������� b���� p ��� t����� w ��� � �� b �� p �� t �� w �� (1) w � c� s� � c� �� �������� ���� �p � p�� � �� s� � �� �� ���� ���� ���� �p � p�� (2) p� � p��� ������ � � � p��� ������ � �� (3) gas exchange period: c� � ����� c� � �; compression period: c� � ����� c� � �; combustion and expansion period: c� � ����� c� � ���� ��� �� the effect of the swirl is included in the second woschni formula (4), (5), (6), (7) and (8). see [2], [4] and [5]. the intensity of the swirl is described by rotational speed of the paddle wheel (7) and (8) obtained by measurement on a flowbench. (2) figure 2: heat transfer rate; woschni gt adapted (red dashed line); woschni adapted (black long dashed line); radiation (blue dashed and dotted line); 900 rpm, full load, imep = 9.6 bar obrázek 2: tepelný tok chlazením; woschni gt upravený vztah (červená čárkovaná čára); woschni upravený vztah (černá dlouze čárkovaná čára); radiační složka (modrá čerchovaná čára); 900 rpm, plné zatížení motoru, imep = 9.6 bar it is strongly recommended to hold only one value of the convection multiplier for the complete engine characteristic, but obtained results are quite unsatisfactory. the calibration of convection multiplier in relation to engine speed and load provides much better results. the achievement of the exact measured in-cylinder pressure course is, however, often impossible. woschni classic, woschni swirl, woschni huber and hohenberg correlations are also available in the gt-suite environment. in the case of the user model, when the in-house developed code is used, the user is able to adapt the model and algorithm to very specific purposes. the problems may consist of the number of calibration parameters and elaborateness of the mentioned approach. the fundamental woschni's correlation without swirl (1), (2) and (3) is described in detail in [2] and [3]. coefficients c1 and c2 in the relation of in-cylinder gas velocity depend on the engine cycle phase (2). the user of the developed in-house code may tune all calibration coefficients a1-a8 arbitrarily. � � ������������� b���� p ��� t����� w ��� � �� b �� p �� t �� w �� (1) w � c� s� � c� �� �������� ���� �p � p�� � �� s� � �� �� ���� ���� ���� �p � p�� (2) p� � p��� ������ � � � p��� ������ � �� (3) gas exchange period: c� � ����� c� � �; compression period: c� � ����� c� � �; combustion and expansion period: c� � ����� c� � ���� ��� �� the effect of the swirl is included in the second woschni formula (4), (5), (6), (7) and (8). see [2], [4] and [5]. the intensity of the swirl is described by rotational speed of the paddle wheel (7) and (8) obtained by measurement on a flowbench. (3) gas exchange period: c 1 = 6.18; c 2 = 0; compression period: c 1 = 2.28; c 2 = 0; combustion and expansion period: c 1 = 2.28; c 2 = 3.24 · 10 -3 the effect of the swirl is included in the second woschni formula (4), (5), (6), (7) and (8). see [2], [4] and [5]. the intensity of the swirl is described by rotational speed of the paddle wheel (7) and (8) obtained by measurement on a flowbench. � � ������������� b���� p ��� t����� w ��� � a�� b ��� p ��� t ��� w ��� (4) w � c� s� � c� �� �������� ���� �p � p�� � c� s� � a�� �� ���� ���� ���� �p � p�� (5) p� � p��� ������ � ��� (6) gas exchange period: c� � ���� � ����� b π �� ��� � a�� � a�� b π a�� � �� (7) rest of cycle: c� � ���� � ����� b π �� ��� (8) gas exchange period: c� � �; compression period: c� � �; combustion and expansion period: c� � ���� ��� �� the relation developed by hohenberg stated in (9) and [8]: � � ����� v����� p ��� t���� �s� � ���� ��� � a�� v ��� p ��� t ��� �s� � a��� ��� (9) eichelbergs' correlation is an often used formula, partly due to its simplicity (10) and [7]. � � ����� � �� �� s� �� p ��� t ��� � a�� s� ��� p ��� t ��� (10) the effect of in-cylinder radiation on the heat transfer coefficient, which is significant for diesel engines, is described in annand's equation directly (11) and (12), see also [9] and [10]. the radiation multiplier is different for si and ci engines and also differs depending on engine cycle period. � � � ��� re� � � σ ���� ��� ��� �� � a�� ���� re��� � a�� σ ���� ��� ��� �� (11) re � � �� � � � � �� � ��� (12) � � ���� � ���� � � ��� combustion and expansion period: (ci engine: � � �����; si engine: � � �����); rest of cycle: � � � the influence of radiation is also described in the equation of sitkei ramanaiah (13), (14) and [11]. the mentioned correlation is determined primarily for diesel engines. � � ������� �� � �� � ��� ����� ���� �� ��� �� ����� � � σ �� �� ��� ��� �� (13) � � a�� ���� ����� ���� �� ��� ���� ����� � a�� σ �� �� ��� ��� �� (14) di direct injection (b = 0 0.03); piston chamber (b = 0.05 0.1); swirl (b = 0.15 0.25); prechamber (b = 0.25 0.35) the formula developed by taylor toong stated in (15), (16) and [12]: � � ���� ��� re���� � a�� ��� � re��� (15) re � � �� � � � � �� � ��� (16) several standard templates in gt-suite support the utilization of the model developed by a user. the basic user model template is defined as a part of a parent template with a particular setup. the code � � ������������� b���� p ��� t����� w ��� � a�� b ��� p ��� t ��� w ��� (4) w � c� s� � c� �� �������� ���� �p � p�� � c� s� � a�� �� ���� ���� ���� �p � p�� (5) p� � p��� ������ � ��� (6) gas exchange period: c� � ���� � ����� b π �� ��� � a�� � a�� b π a�� � �� (7) rest of cycle: c� � ���� � ����� b π �� ��� (8) gas exchange period: c� � �; compression period: c� � �; combustion and expansion period: c� � ���� ��� �� the relation developed by hohenberg stated in (9) and [8]: � � ����� v����� p ��� t���� �s� � ���� ��� � a�� v ��� p ��� t ��� �s� � a��� ��� (9) eichelbergs' correlation is an often used formula, partly due to its simplicity (10) and [7]. � � ����� � �� �� s� �� p ��� t ��� � a�� s� ��� p ��� t ��� (10) the effect of in-cylinder radiation on the heat transfer coefficient, which is significant for diesel engines, is described in annand's equation directly (11) and (12), see also [9] and [10]. the radiation multiplier is different for si and ci engines and also differs depending on engine cycle period. � � � ��� re� � � σ ���� ��� ��� �� � a�� ���� re��� � a�� σ ���� ��� ��� �� (11) re � � �� � � � � �� � ��� (12) � � ���� � ���� � � ��� combustion and expansion period: (ci engine: � � �����; si engine: � � �����); rest of cycle: � � � the influence of radiation is also described in the equation of sitkei ramanaiah (13), (14) and [11]. the mentioned correlation is determined primarily for diesel engines. � � ������� �� � �� � ��� ����� ���� �� ��� �� ����� � � σ �� �� ��� ��� �� (13) � � a�� ���� ����� ���� �� ��� ���� ����� � a�� σ �� �� ��� ��� �� (14) di direct injection (b = 0 0.03); piston chamber (b = 0.05 0.1); swirl (b = 0.15 0.25); prechamber (b = 0.25 0.35) the formula developed by taylor toong stated in (15), (16) and [12]: � � ���� ��� re���� � a�� ��� � re��� (15) re � � �� � � � � �� � ��� (16) several standard templates in gt-suite support the utilization of the model developed by a user. the basic user model template is defined as a part of a parent template with a particular setup. the code (4) � � ������������� b���� p ��� t����� w ��� � a�� b ��� p ��� t ��� w ��� (4) w � c� s� � c� �� �������� ���� �p � p�� � c� s� � a�� �� ���� ���� ���� �p � p�� (5) p� � p��� ������ � ��� (6) gas exchange period: c� � ���� � ����� b π �� ��� � a�� � a�� b π a�� � �� (7) rest of cycle: c� � ���� � ����� b π �� ��� (8) gas exchange period: c� � �; compression period: c� � �; combustion and expansion period: c� � ���� ��� �� the relation developed by hohenberg stated in (9) and [8]: � � ����� v����� p ��� t���� �s� � ���� ��� � a�� v ��� p ��� t ��� �s� � a��� ��� (9) eichelbergs' correlation is an often used formula, partly due to its simplicity (10) and [7]. � � ����� � �� �� s� �� p ��� t ��� � a�� s� ��� p ��� t ��� (10) the effect of in-cylinder radiation on the heat transfer coefficient, which is significant for diesel engines, is described in annand's equation directly (11) and (12), see also [9] and [10]. the radiation multiplier is different for si and ci engines and also differs depending on engine cycle period. � � � ��� re� � � σ ���� ��� ��� �� � a�� ���� re��� � a�� σ ���� ��� ��� �� (11) re � � �� � � � � �� � ��� (12) � � ���� � ���� � � ��� combustion and expansion period: (ci engine: � � �����; si engine: � � �����); rest of cycle: � � � the influence of radiation is also described in the equation of sitkei ramanaiah (13), (14) and [11]. the mentioned correlation is determined primarily for diesel engines. � � ������� �� � �� � ��� ����� ���� �� ��� �� ����� � � σ �� �� ��� ��� �� (13) � � a�� ���� ����� ���� �� ��� ���� ����� � a�� σ �� �� ��� ��� �� (14) di direct injection (b = 0 0.03); piston chamber (b = 0.05 0.1); swirl (b = 0.15 0.25); prechamber (b = 0.25 0.35) the formula developed by taylor toong stated in (15), (16) and [12]: � � ���� ��� re���� � a�� ��� � re��� (15) re � � �� � � � � �� � ��� (16) several standard templates in gt-suite support the utilization of the model developed by a user. the basic user model template is defined as a part of a parent template with a particular setup. the code � � ������������� b���� p ��� t����� w ��� � a�� b ��� p ��� t ��� w ��� (4) w � c� s� � c� �� �������� ���� �p � p�� � c� s� � a�� �� ���� ���� ���� �p � p�� (5) p� � p��� ������ � ��� (6) gas exchange period: c� � ���� � ����� b π �� ��� � a�� � a�� b π a�� � �� (7) rest of cycle: c� � ���� � ����� b π �� ��� (8) gas exchange period: c� � �; compression period: c� � �; combustion and expansion period: c� � ���� ��� �� the relation developed by hohenberg stated in (9) and [8]: � � ����� v����� p ��� t���� �s� � ���� ��� � a�� v ��� p ��� t ��� �s� � a��� ��� (9) eichelbergs' correlation is an often used formula, partly due to its simplicity (10) and [7]. � � ����� � �� �� s� �� p ��� t ��� � a�� s� ��� p ��� t ��� (10) the effect of in-cylinder radiation on the heat transfer coefficient, which is significant for diesel engines, is described in annand's equation directly (11) and (12), see also [9] and [10]. the radiation multiplier is different for si and ci engines and also differs depending on engine cycle period. � � � ��� re� � � σ ���� ��� ��� �� � a�� ���� re��� � a�� σ ���� ��� ��� �� (11) re � � �� � � � � �� � ��� (12) � � ���� � ���� � � ��� combustion and expansion period: (ci engine: � � �����; si engine: � � �����); rest of cycle: � � � the influence of radiation is also described in the equation of sitkei ramanaiah (13), (14) and [11]. the mentioned correlation is determined primarily for diesel engines. � � ������� �� � �� � ��� ����� ���� �� ��� �� ����� � � σ �� �� ��� ��� �� (13) � � a�� ���� ����� ���� �� ��� ���� ����� � a�� σ �� �� ��� ��� �� (14) di direct injection (b = 0 0.03); piston chamber (b = 0.05 0.1); swirl (b = 0.15 0.25); prechamber (b = 0.25 0.35) the formula developed by taylor toong stated in (15), (16) and [12]: � � ���� ��� re���� � a�� ��� � re��� (15) re � � �� � � � � �� � ��� (16) several standard templates in gt-suite support the utilization of the model developed by a user. the basic user model template is defined as a part of a parent template with a particular setup. the code (5)� � ������������� b���� p ��� t����� w ��� � a�� b ��� p ��� t ��� w ��� (4) w � c� s� � c� �� �������� ���� �p � p�� � c� s� � a�� �� ���� ���� ���� �p � p�� (5) p� � p��� ������ � ��� (6) gas exchange period: c� � ���� � ����� b π �� ��� � a�� � a�� b π a�� � �� (7) rest of cycle: c� � ���� � ����� b π �� ��� (8) gas exchange period: c� � �; compression period: c� � �; combustion and expansion period: c� � ���� ��� �� the relation developed by hohenberg stated in (9) and [8]: � � ����� v����� p ��� t���� �s� � ���� ��� � a�� v ��� p ��� t ��� �s� � a��� ��� (9) eichelbergs' correlation is an often used formula, partly due to its simplicity (10) and [7]. � � ����� � �� �� s� �� p ��� t ��� � a�� s� ��� p ��� t ��� (10) the effect of in-cylinder radiation on the heat transfer coefficient, which is significant for diesel engines, is described in annand's equation directly (11) and (12), see also [9] and [10]. the radiation multiplier is different for si and ci engines and also differs depending on engine cycle period. � � � ��� re� � � σ ���� ��� ��� �� � a�� ���� re��� � a�� σ ���� ��� ��� �� (11) re � � �� � � � � �� � ��� (12) � � ���� � ���� � � ��� combustion and expansion period: (ci engine: � � �����; si engine: � � �����); rest of cycle: � � � the influence of radiation is also described in the equation of sitkei ramanaiah (13), (14) and [11]. the mentioned correlation is determined primarily for diesel engines. � � ������� �� � �� � ��� ����� ���� �� ��� �� ����� � � σ �� �� ��� ��� �� (13) � � a�� ���� ����� ���� �� ��� ���� ����� � a�� σ �� �� ��� ��� �� (14) di direct injection (b = 0 0.03); piston chamber (b = 0.05 0.1); swirl (b = 0.15 0.25); prechamber (b = 0.25 0.35) the formula developed by taylor toong stated in (15), (16) and [12]: � � ���� ��� re���� � a�� ��� � re��� (15) re � � �� � � � � �� � ��� (16) several standard templates in gt-suite support the utilization of the model developed by a user. the basic user model template is defined as a part of a parent template with a particular setup. the code (6) gas exchange period: � � ������������� b���� p ��� t����� w ��� � a�� b ��� p ��� t ��� w ��� (4) w � c� s� � c� �� �������� ���� �p � p�� � c� s� � a�� �� ���� ���� ���� �p � p�� (5) p� � p��� ������ � ��� (6) gas exchange period: c� � ���� � ����� b π �� ��� � a�� � a�� b π a�� � �� (7) rest of cycle: c� � ���� � ����� b π �� ��� (8) gas exchange period: c� � �; compression period: c� � �; combustion and expansion period: c� � ���� ��� �� the relation developed by hohenberg stated in (9) and [8]: � � ����� v����� p ��� t���� �s� � ���� ��� � a�� v ��� p ��� t ��� �s� � a��� ��� (9) eichelbergs' correlation is an often used formula, partly due to its simplicity (10) and [7]. � � ����� � �� �� s� �� p ��� t ��� � a�� s� ��� p ��� t ��� (10) the effect of in-cylinder radiation on the heat transfer coefficient, which is significant for diesel engines, is described in annand's equation directly (11) and (12), see also [9] and [10]. the radiation multiplier is different for si and ci engines and also differs depending on engine cycle period. � � � ��� re� � � σ ���� ��� ��� �� � a�� ���� re��� � a�� σ ���� ��� ��� �� (11) re � � �� � � � � �� � ��� (12) � � ���� � ���� � � ��� combustion and expansion period: (ci engine: � � �����; si engine: � � �����); rest of cycle: � � � the influence of radiation is also described in the equation of sitkei ramanaiah (13), (14) and [11]. the mentioned correlation is determined primarily for diesel engines. � � ������� �� � �� � ��� ����� ���� �� ��� �� ����� � � σ �� �� ��� ��� �� (13) � � a�� ���� ����� ���� �� ��� ���� ����� � a�� σ �� �� ��� ��� �� (14) di direct injection (b = 0 0.03); piston chamber (b = 0.05 0.1); swirl (b = 0.15 0.25); prechamber (b = 0.25 0.35) the formula developed by taylor toong stated in (15), (16) and [12]: � � ���� ��� re���� � a�� ��� � re��� (15) re � � �� � � � � �� � ��� (16) several standard templates in gt-suite support the utilization of the model developed by a user. the basic user model template is defined as a part of a parent template with a particular setup. the code � � ������������� b���� p ��� t����� w ��� � a�� b ��� p ��� t ��� w ��� (4) w � c� s� � c� �� �������� ���� �p � p�� � c� s� � a�� �� ���� ���� ���� �p � p�� (5) p� � p��� ������ � ��� (6) gas exchange period: c� � ���� � ����� b π �� ��� � a�� � a�� b π a�� � �� (7) rest of cycle: c� � ���� � ����� b π �� ��� (8) gas exchange period: c� � �; compression period: c� � �; combustion and expansion period: c� � ���� ��� �� the relation developed by hohenberg stated in (9) and [8]: � � ����� v����� p ��� t���� �s� � ���� ��� � a�� v ��� p ��� t ��� �s� � a��� ��� (9) eichelbergs' correlation is an often used formula, partly due to its simplicity (10) and [7]. � � ����� � �� �� s� �� p ��� t ��� � a�� s� ��� p ��� t ��� (10) the effect of in-cylinder radiation on the heat transfer coefficient, which is significant for diesel engines, is described in annand's equation directly (11) and (12), see also [9] and [10]. the radiation multiplier is different for si and ci engines and also differs depending on engine cycle period. � � � ��� re� � � σ ���� ��� ��� �� � a�� ���� re��� � a�� σ ���� ��� ��� �� (11) re � � �� � � � � �� � ��� (12) � � ���� � ���� � � ��� combustion and expansion period: (ci engine: � � �����; si engine: � � �����); rest of cycle: � � � the influence of radiation is also described in the equation of sitkei ramanaiah (13), (14) and [11]. the mentioned correlation is determined primarily for diesel engines. � � ������� �� � �� � ��� ����� ���� �� ��� �� ����� � � σ �� �� ��� ��� �� (13) � � a�� ���� ����� ���� �� ��� ���� ����� � a�� σ �� �� ��� ��� �� (14) di direct injection (b = 0 0.03); piston chamber (b = 0.05 0.1); swirl (b = 0.15 0.25); prechamber (b = 0.25 0.35) the formula developed by taylor toong stated in (15), (16) and [12]: � � ���� ��� re���� � a�� ��� � re��� (15) re � � �� � � � � �� � ��� (16) several standard templates in gt-suite support the utilization of the model developed by a user. the basic user model template is defined as a part of a parent template with a particular setup. the code (7) rest of cycle: � � ������������� b���� p ��� t����� w ��� � a�� b ��� p ��� t ��� w ��� (4) w � c� s� � c� �� �������� ���� �p � p�� � c� s� � a�� �� ���� ���� ���� �p � p�� (5) p� � p��� ������ � ��� (6) gas exchange period: c� � ���� � ����� b π �� ��� � a�� � a�� b π a�� � �� (7) rest of cycle: c� � ���� � ����� b π �� ��� (8) gas exchange period: c� � �; compression period: c� � �; combustion and expansion period: c� � ���� ��� �� the relation developed by hohenberg stated in (9) and [8]: � � ����� v����� p ��� t���� �s� � ���� ��� � a�� v ��� p ��� t ��� �s� � a��� ��� (9) eichelbergs' correlation is an often used formula, partly due to its simplicity (10) and [7]. � � ����� � �� �� s� �� p ��� t ��� � a�� s� ��� p ��� t ��� (10) the effect of in-cylinder radiation on the heat transfer coefficient, which is significant for diesel engines, is described in annand's equation directly (11) and (12), see also [9] and [10]. the radiation multiplier is different for si and ci engines and also differs depending on engine cycle period. � � � ��� re� � � σ ���� ��� ��� �� � a�� ���� re��� � a�� σ ���� ��� ��� �� (11) re � � �� � � � � �� � ��� (12) � � ���� � ���� � � ��� combustion and expansion period: (ci engine: � � �����; si engine: � � �����); rest of cycle: � � � the influence of radiation is also described in the equation of sitkei ramanaiah (13), (14) and [11]. the mentioned correlation is determined primarily for diesel engines. � � ������� �� � �� � ��� ����� ���� �� ��� �� ����� � � σ �� �� ��� ��� �� (13) � � a�� ���� ����� ���� �� ��� ���� ����� � a�� σ �� �� ��� ��� �� (14) di direct injection (b = 0 0.03); piston chamber (b = 0.05 0.1); swirl (b = 0.15 0.25); prechamber (b = 0.25 0.35) the formula developed by taylor toong stated in (15), (16) and [12]: � � ���� ��� re���� � a�� ��� � re��� (15) re � � �� � � � � �� � ��� (16) several standard templates in gt-suite support the utilization of the model developed by a user. the basic user model template is defined as a part of a parent template with a particular setup. the code (8) gas exchange period: c 2 = 0; compression period: c 2 = 0; combustion and expansion period: c 2 = 3.24 · 10 -3 the relation developed by hohenberg stated in (9) and [8]: � � ������������� b���� p ��� t����� w ��� � a�� b ��� p ��� t ��� w ��� (4) w � c� s� � c� �� �������� ���� �p � p�� � c� s� � a�� �� ���� ���� ���� �p � p�� (5) p� � p��� ������ � ��� (6) gas exchange period: c� � ���� � ����� b π �� ��� � a�� � a�� b π a�� � �� (7) rest of cycle: c� � ���� � ����� b π �� ��� (8) gas exchange period: c� � �; compression period: c� � �; combustion and expansion period: c� � ���� ��� �� the relation developed by hohenberg stated in (9) and [8]: � � ����� v����� p ��� t���� �s� � ���� ��� � a�� v ��� p ��� t ��� �s� � a��� ��� (9) eichelbergs' correlation is an often used formula, partly due to its simplicity (10) and [7]. � � ����� � �� �� s� �� p ��� t ��� � a�� s� ��� p ��� t ��� (10) the effect of in-cylinder radiation on the heat transfer coefficient, which is significant for diesel engines, is described in annand's equation directly (11) and (12), see also [9] and [10]. the radiation multiplier is different for si and ci engines and also differs depending on engine cycle period. � � � ��� re� � � σ ���� ��� ��� �� � a�� ���� re��� � a�� σ ���� ��� ��� �� (11) re � � �� � � � � �� � ��� (12) � � ���� � ���� � � ��� combustion and expansion period: (ci engine: � � �����; si engine: � � �����); rest of cycle: � � � the influence of radiation is also described in the equation of sitkei ramanaiah (13), (14) and [11]. the mentioned correlation is determined primarily for diesel engines. � � ������� �� � �� � ��� ����� ���� �� ��� �� ����� � � σ �� �� ��� ��� �� (13) � � a�� ���� ����� ���� �� ��� ���� ����� � a�� σ �� �� ��� ��� �� (14) di direct injection (b = 0 0.03); piston chamber (b = 0.05 0.1); swirl (b = 0.15 0.25); prechamber (b = 0.25 0.35) the formula developed by taylor toong stated in (15), (16) and [12]: � � ���� ��� re���� � a�� ��� � re��� (15) re � � �� � � � � �� � ��� (16) several standard templates in gt-suite support the utilization of the model developed by a user. the basic user model template is defined as a part of a parent template with a particular setup. the code � � ������������� b���� p ��� t����� w ��� � a�� b ��� p ��� t ��� w ��� (4) w � c� s� � c� �� �������� ���� �p � p�� � c� s� � a�� �� ���� ���� ���� �p � p�� (5) p� � p��� ������ � ��� (6) gas exchange period: c� � ���� � ����� b π �� ��� � a�� � a�� b π a�� � �� (7) rest of cycle: c� � ���� � ����� b π �� ��� (8) gas exchange period: c� � �; compression period: c� � �; combustion and expansion period: c� � ���� ��� �� the relation developed by hohenberg stated in (9) and [8]: � � ����� v����� p ��� t���� �s� � ���� ��� � a�� v ��� p ��� t ��� �s� � a��� ��� (9) eichelbergs' correlation is an often used formula, partly due to its simplicity (10) and [7]. � � ����� � �� �� s� �� p ��� t ��� � a�� s� ��� p ��� t ��� (10) the effect of in-cylinder radiation on the heat transfer coefficient, which is significant for diesel engines, is described in annand's equation directly (11) and (12), see also [9] and [10]. the radiation multiplier is different for si and ci engines and also differs depending on engine cycle period. � � � ��� re� � � σ ���� ��� ��� �� � a�� ���� re��� � a�� σ ���� ��� ��� �� (11) re � � �� � � � � �� � ��� (12) � � ���� � ���� � � ��� combustion and expansion period: (ci engine: � � �����; si engine: � � �����); rest of cycle: � � � the influence of radiation is also described in the equation of sitkei ramanaiah (13), (14) and [11]. the mentioned correlation is determined primarily for diesel engines. � � ������� �� � �� � ��� ����� ���� �� ��� �� ����� � � σ �� �� ��� ��� �� (13) � � a�� ���� ����� ���� �� ��� ���� ����� � a�� σ �� �� ��� ��� �� (14) di direct injection (b = 0 0.03); piston chamber (b = 0.05 0.1); swirl (b = 0.15 0.25); prechamber (b = 0.25 0.35) the formula developed by taylor toong stated in (15), (16) and [12]: � � ���� ��� re���� � a�� ��� � re��� (15) re � � �� � � � � �� � ��� (16) several standard templates in gt-suite support the utilization of the model developed by a user. the basic user model template is defined as a part of a parent template with a particular setup. the code (9) eichelbergs’ correlation is an often used formula, partly due to its simplicity (10) and [7]. figure 2: heat transfer rate; woschni gt adapted (red dashed line); woschni adapted (black long dashed line); radiation (blue dashed and dotted line); 900 rpm, full load, imep = 9.6 bar obrázek 2: tepelný tok chlazením; woschni gt upravený vztah (červená čárkovaná čára); woschni upravený vztah (černá dlouze čárkovaná čára); radiační složka (modrá čerchovaná čára); 900 rpm, plné zatížení motoru, imep = 9.6 bar in-cylinder heat transfer modelling zdeněk žák, miloslav emrich, michal takáts, jan macek mecca 03 2016 page 4 � � ������������� b���� p ��� t����� w ��� � a�� b ��� p ��� t ��� w ��� (4) w � c� s� � c� �� �������� ���� �p � p�� � c� s� � a�� �� ���� ���� ���� �p � p�� (5) p� � p��� ������ � ��� (6) gas exchange period: c� � ���� � ����� b π �� ��� � a�� � a�� b π a�� � �� (7) rest of cycle: c� � ���� � ����� b π �� ��� (8) gas exchange period: c� � �; compression period: c� � �; combustion and expansion period: c� � ���� ��� �� the relation developed by hohenberg stated in (9) and [8]: � � ����� v����� p ��� t���� �s� � ���� ��� � a�� v ��� p ��� t ��� �s� � a��� ��� (9) eichelbergs' correlation is an often used formula, partly due to its simplicity (10) and [7]. � � ����� � �� �� s� �� p ��� t ��� � a�� s� ��� p ��� t ��� (10) the effect of in-cylinder radiation on the heat transfer coefficient, which is significant for diesel engines, is described in annand's equation directly (11) and (12), see also [9] and [10]. the radiation multiplier is different for si and ci engines and also differs depending on engine cycle period. � � � ��� re� � � σ ���� ��� ��� �� � a�� ���� re��� � a�� σ ���� ��� ��� �� (11) re � � �� � � � � �� � ��� (12) � � ���� � ���� � � ��� combustion and expansion period: (ci engine: � � �����; si engine: � � �����); rest of cycle: � � � the influence of radiation is also described in the equation of sitkei ramanaiah (13), (14) and [11]. the mentioned correlation is determined primarily for diesel engines. � � ������� �� � �� � ��� ����� ���� �� ��� �� ����� � � σ �� �� ��� ��� �� (13) � � a�� ���� ����� ���� �� ��� ���� ����� � a�� σ �� �� ��� ��� �� (14) di direct injection (b = 0 0.03); piston chamber (b = 0.05 0.1); swirl (b = 0.15 0.25); prechamber (b = 0.25 0.35) the formula developed by taylor toong stated in (15), (16) and [12]: � � ���� ��� re���� � a�� ��� � re��� (15) re � � �� � � � � �� � ��� (16) several standard templates in gt-suite support the utilization of the model developed by a user. the basic user model template is defined as a part of a parent template with a particular setup. the code � � ������������� b���� p ��� t����� w ��� � a�� b ��� p ��� t ��� w ��� (4) w � c� s� � c� �� �������� ���� �p � p�� � c� s� � a�� �� ���� ���� ���� �p � p�� (5) p� � p��� ������ � ��� (6) gas exchange period: c� � ���� � ����� b π �� ��� � a�� � a�� b π a�� � �� (7) rest of cycle: c� � ���� � ����� b π �� ��� (8) gas exchange period: c� � �; compression period: c� � �; combustion and expansion period: c� � ���� ��� �� the relation developed by hohenberg stated in (9) and [8]: � � ����� v����� p ��� t���� �s� � ���� ��� � a�� v ��� p ��� t ��� �s� � a��� ��� (9) eichelbergs' correlation is an often used formula, partly due to its simplicity (10) and [7]. � � ����� � �� �� s� �� p ��� t ��� � a�� s� ��� p ��� t ��� (10) the effect of in-cylinder radiation on the heat transfer coefficient, which is significant for diesel engines, is described in annand's equation directly (11) and (12), see also [9] and [10]. the radiation multiplier is different for si and ci engines and also differs depending on engine cycle period. � � � ��� re� � � σ ���� ��� ��� �� � a�� ���� re��� � a�� σ ���� ��� ��� �� (11) re � � �� � � � � �� � ��� (12) � � ���� � ���� � � ��� combustion and expansion period: (ci engine: � � �����; si engine: � � �����); rest of cycle: � � � the influence of radiation is also described in the equation of sitkei ramanaiah (13), (14) and [11]. the mentioned correlation is determined primarily for diesel engines. � � ������� �� � �� � ��� ����� ���� �� ��� �� ����� � � σ �� �� ��� ��� �� (13) � � a�� ���� ����� ���� �� ��� ���� ����� � a�� σ �� �� ��� ��� �� (14) di direct injection (b = 0 0.03); piston chamber (b = 0.05 0.1); swirl (b = 0.15 0.25); prechamber (b = 0.25 0.35) the formula developed by taylor toong stated in (15), (16) and [12]: � � ���� ��� re���� � a�� ��� � re��� (15) re � � �� � � � � �� � ��� (16) several standard templates in gt-suite support the utilization of the model developed by a user. the basic user model template is defined as a part of a parent template with a particular setup. the code (10) the effect of in-cylinder radiation on the heat transfer coefficient, which is significant for diesel engines, is described in annand’s equation directly (11) and (12), see also [9] and [10]. the radiation multiplier is different for si and ci engines and also differs depending on engine cycle period. � � ������������� b���� p ��� t����� w ��� � a�� b ��� p ��� t ��� w ��� (4) w � c� s� � c� �� �������� ���� �p � p�� � c� s� � a�� �� ���� ���� ���� �p � p�� (5) p� � p��� ������ � ��� (6) gas exchange period: c� � ���� � ����� b π �� ��� � a�� � a�� b π a�� � �� (7) rest of cycle: c� � ���� � ����� b π �� ��� (8) gas exchange period: c� � �; compression period: c� � �; combustion and expansion period: c� � ���� ��� �� the relation developed by hohenberg stated in (9) and [8]: � � ����� v����� p ��� t���� �s� � ���� ��� � a�� v ��� p ��� t ��� �s� � a��� ��� (9) eichelbergs' correlation is an often used formula, partly due to its simplicity (10) and [7]. � � ����� � �� �� s� �� p ��� t ��� � a�� s� ��� p ��� t ��� (10) the effect of in-cylinder radiation on the heat transfer coefficient, which is significant for diesel engines, is described in annand's equation directly (11) and (12), see also [9] and [10]. the radiation multiplier is different for si and ci engines and also differs depending on engine cycle period. � � � ��� re� � � σ ���� ��� ��� �� � a�� ���� re��� � a�� σ ���� ��� ��� �� (11) re � � �� � � � � �� � ��� (12) � � ���� � ���� � � ��� combustion and expansion period: (ci engine: � � �����; si engine: � � �����); rest of cycle: � � � the influence of radiation is also described in the equation of sitkei ramanaiah (13), (14) and [11]. the mentioned correlation is determined primarily for diesel engines. � � ������� �� � �� � ��� ����� ���� �� ��� �� ����� � � σ �� �� ��� ��� �� (13) � � a�� ���� ����� ���� �� ��� ���� ����� � a�� σ �� �� ��� ��� �� (14) di direct injection (b = 0 0.03); piston chamber (b = 0.05 0.1); swirl (b = 0.15 0.25); prechamber (b = 0.25 0.35) the formula developed by taylor toong stated in (15), (16) and [12]: � � ���� ��� re���� � a�� ��� � re��� (15) re � � �� � � � � �� � ��� (16) several standard templates in gt-suite support the utilization of the model developed by a user. the basic user model template is defined as a part of a parent template with a particular setup. the code � � ������������� b���� p ��� t����� w ��� � a�� b ��� p ��� t ��� w ��� (4) w � c� s� � c� �� �������� ���� �p � p�� � c� s� � a�� �� ���� ���� ���� �p � p�� (5) p� � p��� ������ � ��� (6) gas exchange period: c� � ���� � ����� b π �� ��� � a�� � a�� b π a�� � �� (7) rest of cycle: c� � ���� � ����� b π �� ��� (8) gas exchange period: c� � �; compression period: c� � �; combustion and expansion period: c� � ���� ��� �� the relation developed by hohenberg stated in (9) and [8]: � � ����� v����� p ��� t���� �s� � ���� ��� � a�� v ��� p ��� t ��� �s� � a��� ��� (9) eichelbergs' correlation is an often used formula, partly due to its simplicity (10) and [7]. � � ����� � �� �� s� �� p ��� t ��� � a�� s� ��� p ��� t ��� (10) the effect of in-cylinder radiation on the heat transfer coefficient, which is significant for diesel engines, is described in annand's equation directly (11) and (12), see also [9] and [10]. the radiation multiplier is different for si and ci engines and also differs depending on engine cycle period. � � � ��� re� � � σ ���� ��� ��� �� � a�� ���� re��� � a�� σ ���� ��� ��� �� (11) re � � �� � � � � �� � ��� (12) � � ���� � ���� � � ��� combustion and expansion period: (ci engine: � � �����; si engine: � � �����); rest of cycle: � � � the influence of radiation is also described in the equation of sitkei ramanaiah (13), (14) and [11]. the mentioned correlation is determined primarily for diesel engines. � � ������� �� � �� � ��� ����� ���� �� ��� �� ����� � � σ �� �� ��� ��� �� (13) � � a�� ���� ����� ���� �� ��� ���� ����� � a�� σ �� �� ��� ��� �� (14) di direct injection (b = 0 0.03); piston chamber (b = 0.05 0.1); swirl (b = 0.15 0.25); prechamber (b = 0.25 0.35) the formula developed by taylor toong stated in (15), (16) and [12]: � � ���� ��� re���� � a�� ��� � re��� (15) re � � �� � � � � �� � ��� (16) several standard templates in gt-suite support the utilization of the model developed by a user. the basic user model template is defined as a part of a parent template with a particular setup. the code (11) � � ������������� b���� p ��� t����� w ��� � a�� b ��� p ��� t ��� w ��� (4) w � c� s� � c� �� �������� ���� �p � p�� � c� s� � a�� �� ���� ���� ���� �p � p�� (5) p� � p��� ������ � ��� (6) gas exchange period: c� � ���� � ����� b π �� ��� � a�� � a�� b π a�� � �� (7) rest of cycle: c� � ���� � ����� b π �� ��� (8) gas exchange period: c� � �; compression period: c� � �; combustion and expansion period: c� � ���� ��� �� the relation developed by hohenberg stated in (9) and [8]: � � ����� v����� p ��� t���� �s� � ���� ��� � a�� v ��� p ��� t ��� �s� � a��� ��� (9) eichelbergs' correlation is an often used formula, partly due to its simplicity (10) and [7]. � � ����� � �� �� s� �� p ��� t ��� � a�� s� ��� p ��� t ��� (10) the effect of in-cylinder radiation on the heat transfer coefficient, which is significant for diesel engines, is described in annand's equation directly (11) and (12), see also [9] and [10]. the radiation multiplier is different for si and ci engines and also differs depending on engine cycle period. � � � ��� re� � � σ ���� ��� ��� �� � a�� ���� re��� � a�� σ ���� ��� ��� �� (11) re � � �� � � � � �� � ��� (12) � � ���� � ���� � � ��� combustion and expansion period: (ci engine: � � �����; si engine: � � �����); rest of cycle: � � � the influence of radiation is also described in the equation of sitkei ramanaiah (13), (14) and [11]. the mentioned correlation is determined primarily for diesel engines. � � ������� �� � �� � ��� ����� ���� �� ��� �� ����� � � σ �� �� ��� ��� �� (13) � � a�� ���� ����� ���� �� ��� ���� ����� � a�� σ �� �� ��� ��� �� (14) di direct injection (b = 0 0.03); piston chamber (b = 0.05 0.1); swirl (b = 0.15 0.25); prechamber (b = 0.25 0.35) the formula developed by taylor toong stated in (15), (16) and [12]: � � ���� ��� re���� � a�� ��� � re��� (15) re � � �� � � � � �� � ��� (16) several standard templates in gt-suite support the utilization of the model developed by a user. the basic user model template is defined as a part of a parent template with a particular setup. the code (12) combustion and expansion period: (ci engine: c = 0.576; si engine: c = 0.075); rest of cycle: c = 0 the influence of radiation is also described in the equation of sitkei – ramanaiah (13), (14) and [11]. the mentioned correlation is determined primarily for diesel engines. � � ������������� b���� p ��� t����� w ��� � a�� b ��� p ��� t ��� w ��� (4) w � c� s� � c� �� �������� ���� �p � p�� � c� s� � a�� �� ���� ���� ���� �p � p�� (5) p� � p��� ������ � ��� (6) gas exchange period: c� � ���� � ����� b π �� ��� � a�� � a�� b π a�� � �� (7) rest of cycle: c� � ���� � ����� b π �� ��� (8) gas exchange period: c� � �; compression period: c� � �; combustion and expansion period: c� � ���� ��� �� the relation developed by hohenberg stated in (9) and [8]: � � ����� v����� p ��� t���� �s� � ���� ��� � a�� v ��� p ��� t ��� �s� � a��� ��� (9) eichelbergs' correlation is an often used formula, partly due to its simplicity (10) and [7]. � � ����� � �� �� s� �� p ��� t ��� � a�� s� ��� p ��� t ��� (10) the effect of in-cylinder radiation on the heat transfer coefficient, which is significant for diesel engines, is described in annand's equation directly (11) and (12), see also [9] and [10]. the radiation multiplier is different for si and ci engines and also differs depending on engine cycle period. � � � ��� re� � � σ ���� ��� ��� �� � a�� ���� re��� � a�� σ ���� ��� ��� �� (11) re � � �� � � � � �� � ��� (12) � � ���� � ���� � � ��� combustion and expansion period: (ci engine: � � �����; si engine: � � �����); rest of cycle: � � � the influence of radiation is also described in the equation of sitkei ramanaiah (13), (14) and [11]. the mentioned correlation is determined primarily for diesel engines. � � ������� �� � �� � ��� ����� ���� �� ��� �� ����� � � σ �� �� ��� ��� �� (13) � � a�� ���� ����� ���� �� ��� ���� ����� � a�� σ �� �� ��� ��� �� (14) di direct injection (b = 0 0.03); piston chamber (b = 0.05 0.1); swirl (b = 0.15 0.25); prechamber (b = 0.25 0.35) the formula developed by taylor toong stated in (15), (16) and [12]: � � ���� ��� re���� � a�� ��� � re��� (15) re � � �� � � � � �� � ��� (16) several standard templates in gt-suite support the utilization of the model developed by a user. the basic user model template is defined as a part of a parent template with a particular setup. the code (13) � � ������������� b���� p ��� t����� w ��� � a�� b ��� p ��� t ��� w ��� (4) w � c� s� � c� �� �������� ���� �p � p�� � c� s� � a�� �� ���� ���� ���� �p � p�� (5) p� � p��� ������ � ��� (6) gas exchange period: c� � ���� � ����� b π �� ��� � a�� � a�� b π a�� � �� (7) rest of cycle: c� � ���� � ����� b π �� ��� (8) gas exchange period: c� � �; compression period: c� � �; combustion and expansion period: c� � ���� ��� �� the relation developed by hohenberg stated in (9) and [8]: � � ����� v����� p ��� t���� �s� � ���� ��� � a�� v ��� p ��� t ��� �s� � a��� ��� (9) eichelbergs' correlation is an often used formula, partly due to its simplicity (10) and [7]. � � ����� � �� �� s� �� p ��� t ��� � a�� s� ��� p ��� t ��� (10) the effect of in-cylinder radiation on the heat transfer coefficient, which is significant for diesel engines, is described in annand's equation directly (11) and (12), see also [9] and [10]. the radiation multiplier is different for si and ci engines and also differs depending on engine cycle period. � � � ��� re� � � σ ���� ��� ��� �� � a�� ���� re��� � a�� σ ���� ��� ��� �� (11) re � � �� � � � � �� � ��� (12) � � ���� � ���� � � ��� combustion and expansion period: (ci engine: � � �����; si engine: � � �����); rest of cycle: � � � the influence of radiation is also described in the equation of sitkei ramanaiah (13), (14) and [11]. the mentioned correlation is determined primarily for diesel engines. � � ������� �� � �� � ��� ����� ���� �� ��� �� ����� � � σ �� �� ��� ��� �� (13) � � a�� ���� ����� ���� �� ��� ���� ����� � a�� σ �� �� ��� ��� �� (14) di direct injection (b = 0 0.03); piston chamber (b = 0.05 0.1); swirl (b = 0.15 0.25); prechamber (b = 0.25 0.35) the formula developed by taylor toong stated in (15), (16) and [12]: � � ���� ��� re���� � a�� ��� � re��� (15) re � � �� � � � � �� � ��� (16) several standard templates in gt-suite support the utilization of the model developed by a user. the basic user model template is defined as a part of a parent template with a particular setup. the code (14) di direct injection (b = 0 0.03); piston chamber (b = 0.05 0.1); swirl (b = 0.15 0.25); prechamber (b = 0.25 0.35) the formula developed by taylor – toong stated in (15), (16) and [12]: � � ������������� b���� p ��� t����� w ��� � a�� b ��� p ��� t ��� w ��� (4) w � c� s� � c� �� �������� ���� �p � p�� � c� s� � a�� �� ���� ���� ���� �p � p�� (5) p� � p��� ������ � ��� (6) gas exchange period: c� � ���� � ����� b π �� ��� � a�� � a�� b π a�� � �� (7) rest of cycle: c� � ���� � ����� b π �� ��� (8) gas exchange period: c� � �; compression period: c� � �; combustion and expansion period: c� � ���� ��� �� the relation developed by hohenberg stated in (9) and [8]: � � ����� v����� p ��� t���� �s� � ���� ��� � a�� v ��� p ��� t ��� �s� � a��� ��� (9) eichelbergs' correlation is an often used formula, partly due to its simplicity (10) and [7]. � � ����� � �� �� s� �� p ��� t ��� � a�� s� ��� p ��� t ��� (10) the effect of in-cylinder radiation on the heat transfer coefficient, which is significant for diesel engines, is described in annand's equation directly (11) and (12), see also [9] and [10]. the radiation multiplier is different for si and ci engines and also differs depending on engine cycle period. � � � ��� re� � � σ ���� ��� ��� �� � a�� ���� re��� � a�� σ ���� ��� ��� �� (11) re � � �� � � � � �� � ��� (12) � � ���� � ���� � � ��� combustion and expansion period: (ci engine: � � �����; si engine: � � �����); rest of cycle: � � � the influence of radiation is also described in the equation of sitkei ramanaiah (13), (14) and [11]. the mentioned correlation is determined primarily for diesel engines. � � ������� �� � �� � ��� ����� ���� �� ��� �� ����� � � σ �� �� ��� ��� �� (13) � � a�� ���� ����� ���� �� ��� ���� ����� � a�� σ �� �� ��� ��� �� (14) di direct injection (b = 0 0.03); piston chamber (b = 0.05 0.1); swirl (b = 0.15 0.25); prechamber (b = 0.25 0.35) the formula developed by taylor toong stated in (15), (16) and [12]: � � ���� ��� re���� � a�� ��� � re��� (15) re � � �� � � � � �� � ��� (16) several standard templates in gt-suite support the utilization of the model developed by a user. the basic user model template is defined as a part of a parent template with a particular setup. the code (15) � � ������������� b���� p ��� t����� w ��� � a�� b ��� p ��� t ��� w ��� (4) w � c� s� � c� �� �������� ���� �p � p�� � c� s� � a�� �� ���� ���� ���� �p � p�� (5) p� � p��� ������ � ��� (6) gas exchange period: c� � ���� � ����� b π �� ��� � a�� � a�� b π a�� � �� (7) rest of cycle: c� � ���� � ����� b π �� ��� (8) gas exchange period: c� � �; compression period: c� � �; combustion and expansion period: c� � ���� ��� �� the relation developed by hohenberg stated in (9) and [8]: � � ����� v����� p ��� t���� �s� � ���� ��� � a�� v ��� p ��� t ��� �s� � a��� ��� (9) eichelbergs' correlation is an often used formula, partly due to its simplicity (10) and [7]. � � ����� � �� �� s� �� p ��� t ��� � a�� s� ��� p ��� t ��� (10) the effect of in-cylinder radiation on the heat transfer coefficient, which is significant for diesel engines, is described in annand's equation directly (11) and (12), see also [9] and [10]. the radiation multiplier is different for si and ci engines and also differs depending on engine cycle period. � � � ��� re� � � σ ���� ��� ��� �� � a�� ���� re��� � a�� σ ���� ��� ��� �� (11) re � � �� � � � � �� � ��� (12) � � ���� � ���� � � ��� combustion and expansion period: (ci engine: � � �����; si engine: � � �����); rest of cycle: � � � the influence of radiation is also described in the equation of sitkei ramanaiah (13), (14) and [11]. the mentioned correlation is determined primarily for diesel engines. � � ������� �� � �� � ��� ����� ���� �� ��� �� ����� � � σ �� �� ��� ��� �� (13) � � a�� ���� ����� ���� �� ��� ���� ����� � a�� σ �� �� ��� ��� �� (14) di direct injection (b = 0 0.03); piston chamber (b = 0.05 0.1); swirl (b = 0.15 0.25); prechamber (b = 0.25 0.35) the formula developed by taylor toong stated in (15), (16) and [12]: � � ���� ��� re���� � a�� ��� � re��� (15) re � � �� � � � � �� � ��� (16) several standard templates in gt-suite support the utilization of the model developed by a user. the basic user model template is defined as a part of a parent template with a particular setup. the code (16) several standard templates in gt-suite support the utilization of the model developed by a user. the basic user model template is defined as a part of a parent template with a particular setup. the code has to be developed in fortran or c++. it is also needful to create a subroutine, which is unavoidable for communication between utilities, user templates and communication boxes. the user model (fortran code) is able to communicate with the main model (e.g. internal combustion engine) via communication boxes. some variables are accessible directly via the main solver. gt-suite software allows utilization of several user models concurrently. the heat transfer correlations mentioned above are available in the current version of the developed user model linked to gt-suite. the actual engine cycle phase is described in the model by cycle flag, see figure 3. the course of the heat release fraction is updated from cycle to cycle and the end of combustion (engine cycle flag = 3) is defined by the user via selectable variable “heat release fraction” in the setup (e.g. 0.99 in figure 3). the described function is independent of actual heat release course or mixture composition (lean/rich). the engine cylinders in the model are entirely independent (e.g. geometry, valve timing of relevant cylinder, volumetric efficiency, heat release etc.). the user model automatically detects the number of cylinders, firing order, local crank angle of the cylinder, number of species, mass for each species in zone etc. the presented model can operate with one or two temperature zones based on the used combustion model. in the case of two zones, the model calculates heat transfer coefficients for burned and unburned zones concurrently. the model also cooperates with the finite element (fem) cylinder wall temperature solver including cylinder liner, piston, head, valves and valve guides. the fem wall temperature model has to be calibrated independently as usual. the coefficients in the correlation formula can vary in dependence on engine cycle phase, according to cycle flag, or figure 3: engine cycle flag (black) – 1) intake valve closing – combustion; 2) combustion; 3) end of combustion – exhaust valve opening; 4) exhaust valve opening – exhaust valve closing; 5) intake valve opening – intake valve closing; exhaust valve lift (red dashed line); intake valve lift (blue); heat release rate (green) obrázek 3: fáze oběhu (černá) – 1) zavření sacího ventilu – hoření; 2) hoření; 3) konec hoření – otevření výfukového ventilu; 4) otevření výfukového venitlu – zavření výfukového ventilu; 5) otevření sacího ventilu – zavření sacího ventilu; zdvih výfukového ventilu (červená čárkovaná čára); zdvih sacího ventilu (modrá); vývin tepla (zelená) in-cylinder heat transfer modelling zdeněk žák, miloslav emrich, michal takáts, jan macek mecca 03 2016 page 5 with respect to local crank angle of the cylinder, see examples in figure 4. the aim is to improve the accuracy of the empirical formula by tuning the applied coefficients for the specific case. the next step could be creation of new formula suitable for special purposes. it is no problem to extend the current inhouse code of the presented user model. 3. results the single cylinder model of the internal combustion engine was developed in the gt-suite environment for the simulation purposes. the model is suitable for the three pressure analysis of the experimental data. experimental data, measured on the experimental six cylinder diesel engine (table 1), were used in the model calibration process. the goal is to show the behaviour of the developed user model. the comparison of the results predicted by the model, which utilized the user model of the in-cylinder heat transfer, with the experiments is a side effect only. the indicated pressures at intake port inlet, in cylinder and at exhaust port outlet are required for the three pressure analysis. further inputs for the model are engine geometry, temperatures, brake torque, fuel flow etc. the temperatures of the engine parts are not available from the measurement. the discussion of the simulation results starts with the heat transfer coefficients predicted by the correlation formulas in original forms are shown in figure 5 and figure 6. the difference between formulas, thus the predicted heat transfer coefficients are clearly visible. the accuracy level of results obtained using the original equations is not sufficient for the current purposes. it is needful to derive a correlation tailored to the specific combustion engine. the aim of the calibration was to create a model capable of predicting engine parameters comparable to the experiments. for the achievement of the same in-cylinder pressure, thus the indicated mean effective pressure, it was necessary to adapt the heat transfer correlations. the main coefficient of each equation, used in the relevant simulation was tuned. the main coefficient is the multiplier of the whole equation (e.g. a1 in woschni formula, a11, a23 etc.). it is of course possible to change any introduced calibration coefficient. it is recommended to try several different classical formulas, choose one with the best tendency and then calibrate it in dependence on the engine speed and load. the approach has been tested during the comprehensive three pressure analyses in the gt-suite environment. figure 4: coefficient a6 (c1) as a variable in the user model setup (or linked to gt-s case setup) (orange dotted line); example of user defined arbitrary course of coefficient vs. crank angle (green dash-dot line); engine cycle flag (by user model code) obrázek 4: součinitel a6 (c1) jako proměnná v nastavení uživatelského modelu (lze případně svázat s nastavením výpočtu v gt-s) (oranžová čárkovaná čára); příklad uživatelsky definovaného libovolného průběhu součinitele v závislosti na úhlu klikové hřídele (zelená čerchovaná čára); fáze oběhu (generováno uživatelským modelem) figure 5: heat transfer coefficients – original correlation formulas; woschni original (black dashed line); woschni swirl original (green line); eichelberg original (blue dashed and dotted line); 1200 rpm, full load, imep = 13 bar obrázek 5: součinitelé přestupu tepla – korelace v originálním tvaru; woschni original (černá čárkovaná); woschni swirl original (zelená); eichelberg original (modrá čerchovaná); 1200 rpm, plné zatížení motoru, imep = 13 bar label john deere 6068 diesel type compression ignition fuel diesel oil cylinders 6 in-line bore [mm] 106.426 stroke [mm] 127 displacement [dm3] 6.779 table 1: parameters of the experimental combustion engine tabulka 1: parametry experimentálního spalovacího motoru in-cylinder heat transfer modelling zdeněk žák, miloslav emrich, michal takáts, jan macek mecca 03 2016 page 6 the comparison of heat transfer coefficient courses calculated via original or adapted formulas is shown in figure 7. figure 7 shows the three pressure analysis results of original (uncalibrated) and adapted (calibrated) heat transfer correlation equations. the differences are obvious and confirmed in the following pictures. the original and adapted main coefficients are presented in figure 8. the indicated mean effective pressure predicted by the simulations compared to experimental data is shown in figure 9. the engine model based on the original woschni and eichelberg formulas is not able to reproduce the measured values. the indicated efficiency of the experimental engine is presented in figure 10. the results of indicated efficiency are consistent with the indicated mean effective pressures in figure 9. the results calculated by the model with adapted heat transfer correlations formulas are comparable to the experimental data. the engine model with in-cylinder heat transfer user model tailored to the specific combustion engine also reproduces the maximum pressure in cylinder very well as presented in figure 11. the adapted eichelberg equation predicts higher values of the in-cylinder heat transfer at full engine load than the woschni adapted relation – figure 12. the calculated percentage of useful exhaust energy in figure 13 is consistent with the tendency of the presented heat transfer. the simulation of the whole combustion engine, not just the single cylinder model for the purposes of three pressure analysis, has to be performed to answer the question of which formula is better for the current combustion engine. the balance between the in-cylinder heat transfer and useful exhaust energy is important for the estimation of turbine power, i.e. the overall energy balance of the turbocharged internal combustion engine. the differences between the adapted figure 6: heat transfer coefficients – original correlation formulas; hohenberg original (grey dashed and dotted line); annand original (purple dashed line); sitkei – ramanaiah original (orange line); taylor – toong original (blue long dashed line); 1200 rpm, full load, imep = 13 bar obrázek 6: součinitelé přestupu tepla – korelace v originálním tvaru; hohenberg original (šedá čerchovaná); annand original (fialová čárkovaná); sitkei – ramanaiah original (oranžová); taylor – toong original (modrá dlouze čárkovaná); 1200 rpm, plné zatížení motoru, imep = 13 bar figure 7: heat transfer coefficients – original and adapted correlation formulas; woschni original (red dashed line); woschni adapted (black long dashed line); eichelberg original (blue dashed and dotted line); eichelberg adapted (pink dotted line); 1200 rpm, full load, imep = 13 bar obrázek 7: součinitelé přestupu tepla – korelace v originálním a upraveném tvaru; woschni original (červená čárkovaná); woschni upravený (černá dlouze čárkovaná); eichelberg original (modrá čerchovaná); eichelberg upravený (růžová tečkovaná); 1200 rpm, plné zatížení motoru, imep = 13 bar figure 8: main coefficients (a1 – woschni; a31 – eichelberg) – original and adapted; woschni original (red dashed line); woschni adapted (black long dashed line); eichelberg original (blue dashed and dotted line); eichelberg adapted (pink dotted line) obrázek 8: hlavní koeficienty (a1 – woschni; a31 – eichelberg) – originální a upravené; woschni original (červená čárkovaná); woschni upravený (černá dlouze čárkovaná); eichelberg original (modrá čerchovaná); eichelberg upravený (růžová tečkovaná) in-cylinder heat transfer modelling zdeněk žák, miloslav emrich, michal takáts, jan macek mecca 03 2016 page 7 formulas results show – at least – uncertainties in obtaining correct heat transfer figures. the results will be analyzed and published in the future. the important feature of the presented model is the interaction between the heat transfer model and the fem model of wall temperatures. the fem solver includes the cylinder liner, piston, head, valves and valve guides. the wall temperature model has to be calibrated independently, but the calibration options are limited [16]. the cylinder temperature zones modelled in gt-suite are drawn in figure 14. the temperatures of particular parts calculated by the fem solver are presented in following pictures. it has to be stressed that the engine part temperatures are not available from the experiments. the aim is to show the trends of the predicted zone temperatures. the cylinder wall temperatures are slightly higher in the case of the eichelberg adapted figure 9: indicated mean effective pressure – original and adapted correlation formulas; experiment (black); woschni original (red dashed line); woschni adapted (black long dashed line); eichelberg original (blue dashed and dotted line); eichelberg adapted (pink dotted line) obrázek 9: střední efektivní tlak – korelace v originálním a upraveném tvaru; experiment (černá); woschni original (červená čárkovaná); woschni upravený (černá dlouze čárkovaná); eichelberg original (modrá čerchovaná); eichelberg upravený (růžová tečkovaná) figure 10: indicated efficiency – original and adapted correlation formulas; experiment (black); woschni original (red dashed line); woschni adapted (black long dashed line); eichelberg original (blue dashed and dotted line); eichelberg adapted (pink dotted line) obrázek 10: indikovaná účinnost – korelace v originálním a upraveném tvaru; experiment (černá); woschni original (červená čárkovaná); woschni upravený (černá dlouze čárkovaná); eichelberg original (modrá čerchovaná); eichelberg upravený (růžová tečkovaná) figure 11: maximum in-cylinder pressure – original and adapted correlation formulas; experiment (black); woschni original (red dashed line); woschni adapted (black long dashed line); eichelberg original (blue dashed and dotted line); eichelberg adapted (pink dotted line) obrázek 11: maximální tlak ve válci – korelace v originálním a upraveném tvaru; experiment (černá); woschni original (červená čárkovaná); woschni upravený (černá dlouze čárkovaná); eichelberg original (modrá čerchovaná); eichelberg upravený (růžová tečkovaná) figure 12: in-cylinder heat transfer (1 cylinder) – original and adapted correlation formulas; woschni original (red dashed line); woschni adapted (black long dashed line); eichelberg original (blue dashed and dotted line); eichelberg adapted (pink dotted line) obrázek 12: odvod tepla chlazením (jeden válec) – korelace v originálním a upraveném tvaru; woschni original (červená čárkovaná); woschni upravený (černá dlouze čárkovaná); eichelberg original (modrá čerchovaná); eichelberg upravený (růžová tečkovaná) in-cylinder heat transfer modelling zdeněk žák, miloslav emrich, michal takáts, jan macek mecca 03 2016 page 8 formula compared to woschni – figure 15, figure 16 and figure 17. the differences are, nevertheless, within the range of measurement errors. the temperatures of the cylinder head (figure 18) and piston (figure 19) are slightly lower for the eichelberg adapted formula in comparison with the adapted woschni relation. finally, the brake specific fuel consumption calculated by the models compared to the experimental data is given in figure 20. 4. conclusion the frequently used empirical formulas are not usually accurate enough, and therefore the level of accuracy and the predictive capability of the whole engine model are not sufficient. it is necessary to adjust classical formula to a unique application in order to achieve the desired course of the in-cylinder heat transfer coefficient and consequently proper heat transfer rate. the user model enables the creation of in-house heat transfer correlations and calibration of all coefficients during the calibration process (three pressure analysis or measured cylinder pressure analysis in gt-suite). it is feasible to calibrate not only the amount of transferred heat, but also to tune the heat transfer coefficient course to achieve the required cylinder pressure. the presented user model increases the number of usable empirical formulas, the ability of the heat transfer model figure 13: percentage of useful exhaust energy – original and adapted correlation formulas; woschni original (red dashed line); woschni adapted (black long dashed line); eichelberg original (blue dashed and dotted line); eichelberg adapted (pink dotted line) obrázek 13: podíl využitelné energie výfukových plynů – korelace v originálním a upraveném tvaru; woschni original (červená čárkovaná); woschni upravený (černá dlouze čárkovaná); eichelberg original (modrá čerchovaná); eichelberg upravený (růžová tečkovaná) figure 14: cylinder temperature zones, see [16] obrázek 14: teplotní zóny válce, viz [16] figure 15: temperature of cylinder wall (zone 1) – original and adapted correlation formulas; woschni original (red dashed line); woschni adapted (black long dashed line); eichelberg original (blue dashed and dotted line); eichelberg adapted (pink dotted line) obrázek 15: teplota stěny válce (zóna 1) – korelace v originálním a upraveném tvaru; woschni original (červená čárkovaná); woschni upravený (černá dlouze čárkovaná); eichelberg original (modrá čerchovaná); eichelberg upravený (růžová tečkovaná) figure 16: temperature of cylinder wall (zone 2) – original and adapted correlation formulas; woschni original (red dashed line); woschni adapted (black long dashed line); eichelberg original (blue dashed and dotted line); eichelberg adapted (pink dotted line) obrázek 16: teplota stěny válce (zóna 2) – korelace v originálním a upraveném tvaru; woschni original (červená čárkovaná); woschni upravený (černá dlouze čárkovaná); eichelberg original (modrá čerchovaná); eichelberg upravený (růžová tečkovaná) in-cylinder heat transfer modelling zdeněk žák, miloslav emrich, michal takáts, jan macek mecca 03 2016 page 9 to achieve required values and the level of accuracy of the whole model of the internal combustion engine. the general structure of the user model is the same for every template in the gt-suite environment, which allows development of an in-house algorithm for specific purposes. the mentioned approach is generally demanding, time consuming and the number of calibration parameters also increases. the potential of extension codes consists of the solution of very specific problems which are not solvable using standard commercial software templates. the main benefit of in-house code in combination with commercial software rests in the ability to solve a special problem and utilize all coupled models and main solver capability for basic problems at the same time. figure 17: temperature of cylinder wall (zone 3) – original and adapted correlation formulas; woschni original (red dashed line); woschni adapted (black long dashed line); eichelberg original (blue dashed and dotted line); eichelberg adapted (pink dotted line) obrázek 17: teplota stěny válce (zóna 3) – korelace v originálním a upraveném tvaru; woschni original (červená čárkovaná); woschni upravený (černá dlouze čárkovaná); eichelberg original (modrá čerchovaná); eichelberg upravený (růžová tečkovaná) figure 18: cylinder head temperature – original and adapted correlation formulas; woschni original (red dashed line); woschni adapted (black long dashed line); eichelberg original (blue dashed and dotted line); eichelberg adapted (pink dotted line) obrázek 18: teplota hlavy válce – korelace v originálním a upraveném tvaru; woschni original (červená čárkovaná); woschni upravený (černá dlouze čárkovaná); eichelberg original (modrá čerchovaná); eichelberg upravený (růžová tečkovaná) figure 19: piston temperature – original and adapted correlation formulas; woschni original (red dashed line); woschni adapted (black long dashed line); eichelberg original (blue dashed and dotted line); eichelberg adapted (pink dotted line) obrázek 19: teplota pístu – korelace v originálním a upraveném tvaru; woschni original (červená čárkovaná); woschni upravený (černá dlouze čárkovaná); eichelberg original (modrá čerchovaná); eichelberg upravený (růžová tečkovaná) figure 20: brake specific fuel consumption – original and adapted correlation formulas; experiment (black); woschni original (red dashed line); woschni adapted (black long dashed line); eichelberg original (blue dashed and dotted line); eichelberg adapted (pink dotted line) obrázek 20: měrná spotřeba paliva – korelace v originálním a upraveném tvaru; experiment (černá); woschni original (červená čárkovaná); woschni upravený (černá dlouze čárkovaná); eichelberg original (modrá čerchovaná); eichelberg upravený (růžová tečkovaná) in-cylinder heat transfer modelling zdeněk žák, miloslav emrich, michal takáts, jan macek mecca 03 2016 page 10 acknowledgements this work was supported by: technological agency, czech republic, programme centres of competence, project #te01020020 josef božek competence centre for automotive industry. eu regional development fund in op r&d for innovations (op vavpi) and ministry of education, czech republic, project #cz.1.05/2.1.00/03.0125 acquisition of technology for centre of vehicles for sustainable mobility. all the support is gratefully acknowledged. list of notations and abbreviations a, b, c coefficients a [m2] instantaneous surface area (piston, head, liner) a 1-n coefficients b [m] cylinder bore c 1-n coefficients (woschni correlations) h [wm-2k-1] instantaneous heat transfer coefficient k g [wm-1k-1] thermal conductivity n p [s-1] rotational speed of the paddle wheel (swirl measurement) p [pa] instantaneous in-cylinder pressure p m [pa] instantaneous motored in-cylinder pressure re [1] reynolds number ref reference values (after intake valve closing) s p [ms-1] mean piston speed t [k] instantaneous averaged in-cylinder temperature t g [k] instantaneous averaged in-cylinder temperature t w [k] cylinder wall temperature v [m3] instantaneous cylinder volume (displaced + clearance) v d [m3] displaced (swept) cylinder volume – constant w [ms-1] instantaneous averaged in-cylinder gas velocity ε [1] flame emissivity κ [1] specific heat ratio μ [pa. s] dynamic viscosity ρ [kg m-3] instantaneous in-cylinder gas density σ = 5.67 · 10-8 [wm-2k-4] stefan boltzmann constant references [1] heywood, j. b.: internal combustion engine fundamentals. mcgraw-hill series in mechanical engineering, printed in usa. mcgraw-hill, 1988. isbn 0-07-028637-x. [2] woschni, g., a universally applicable equation for the instantaneous heat transfer coefficient in the internal combustion engine. sae paper 670931, 1967. [3] woschni, g., die berechnung der wanderverluste und der thermischen belastung der bauteile von dieselmotoren. mtz, 1970. 30: 491–499. [4] woschni, g., prediction of thermal loading of supercharged diesel engines. sae paper 790821, 1979. [5] woschni, g., fieger, j., determination of local heat transfer coefficients at the piston of a high speed diesel engine by evaluation of measured temperature distribution. sae paper 790834, 1979. [6] woschni, g., huber, k., the influence of soot deposits on combustion chamber walls on heat losses in diesel engines, sae paper 910297, 1991. [7] eichelberg, g. some new investigations on old combustion engine problems. engineering, 1939. 148: 463–464, 547–560. [8] hohenberg, g.f., advanced approaches for heat transfer calculations. sae paper 790825, 1979. [9] annand, w.j.d., heat transfer in the cylinders of reciprocating internal combustion engines. proc. i. mech. e., 1963. 177: 973–996. [10] annand, w.j.d., ma, t.h., instantaneous heat transfer rates to the cylinder head surface of a small compressionignition engine. proc. i. mech. e., 1970. 185: 976–987. [11] sitkei, g., ramanaiah, g.v., a rational approach for calculation of heat transfer in diesel engines. sae paper 720027, 1972. [12] taylor, c.f., toong, t.y., heat transfer in internal combustion engines, asme paper, 1957. 57-ht-17 [13] depcik, c., jacobs, t., hagena, j., assanis, d., instructional use of a single-zone, premixed charge, spark-ignition engine heat release simulation, 2006, international journal of mechanical engineering education 35(1): 1–31 [14] chang, j., guralp, o., filipi, z., assanis, d. et al., new heat transfer correlation for an hcci engine derived from measurements of instantaneous surface heat flux, sae technical paper 2004-01-2996, 2004. doi:10.4271/2004-01-2996. [15] hansen, a.c., a diagnostic quasi-dimensional model of heat transfer and combustion in compression-ignition engines, ph.d. thesis, university of natal, 1989. [16] gt-suite application manuals, version 7.3, gamma technologies inc., westmont, il. 2012. mecca_18-02_web_fortl physical model of si-engine process and gas exchange for real-time implementation in engine management system jan fo!tl, johannes beer, jens keller, jan macek, fredrik borchsenius mecca 02 2018 page 11 10.1515/mecdc-2018-0006 physical model of si-engine process and gas exchange for real-time implementation in engine management system jan fo!tl, johannes beer, jens keller, jan macek, fredrik borchsenius 1. why physical modeling instead of data driven models? for spark ignited engines, torque control is realized in the engine control unit (ecu) by managing the in-cylinder air mass, while keeping the air-fuel ratio stoichiometric in order to minimize exhaust emissions. future co2 emission legislation is causing a growing complexity of the engine’s gas exchange system. in other words, the number of actuators is increasing. from a modeling perspective, it follows that additional degrees of freedom have to be covered. in principle, there are two modeling methods: 1. data driven models and 2. physical models, relying on fundamental physical jan fo!tl, johannes beer, jens keller continental, siemensstraße 12, d-93055 regensburg e-mail: janfortlcz@gmail.com, johannes.beer@continental-corporation.com, jens.2.keller@continental-corporation.com jan macek czech technical university in prague / faculty of mechanical eng., center of vehicles for sustainable mobility, technická 4, 166 07 praha 6, e-mail: jan.macek@fs.cvut.cz fredrik borchsenius regensburg university of applied sciences, faculty of mechanical engineering, seybothstraße 2, d-93053 regensburg, e-mail: fredrik.borchsenius@oth-regensburg.de abstract this paper presents a physical, crank angle resolved model of spark ignited (si) engine process and gas exchange developed by continental ag for real-time engine management system. transient 1d flow in pipe systems is the most time-consuming part of the numerical solution. a so-called detailed model, including intake and exhaust pipe components, is defined and reduced to its fast-running version where pipes are neglected. experimental validation confirms that the detailed model captures transient effects and fulfills accuracy targets over the entire engine operation range, while the fast-running model requires additional empirical parameterization. both models, however, provide more detailed information on dynamic gas exchange process and the in-cylinder state for each individual engine cycle than today’s data driven models do (e.g., transient gas states and internal engine exhaust gas recirculation). finally, simplifications according to classical acoustic theory are proposed for pipe components to solve the conflict between accuracy and real-time capability. key words: engine model, gas exchange, 1d/0d, ecu, real-time shrnutí tento !lánek prezentuje fyzikální model !ty"dobého procesu a v#plachu zá$ehového spalovacího motoru. model byl vyvinut u continental ag pro ú!ely sériov#ch "ídících jednotek. nestacionární 1d proud%ní v potrubních systémech je !asov% nejnáro!n%j&í sou!ástí numerického "e&ení. proto je nejprve definován podrobn# model, zahrnující "e&ení sacích a v#fukov#ch potrubí, kter# je dále zjednodu&en na rychle fungující verzi se zanedbáním zákona zachování impulsu v potrubních systémech. experimentální ov%"ení potvrzuje, $e podrobn# model zachycuje p"echodové jevy a spl'uje cíle p"esnosti v celém rozsahu provozu motoru, zatímco zjednodu&en# model vy$aduje dal&í empirickou parametrizaci. oba modely v&ak poskytují podrobn%j&í informace o v#plachu a termodynamickém stavu ve válcích ne$ to !iní b%$né datov% orientované modely (nap". p"echodné stavy plynu, nebo vnit"ní recirkulace v#fukov#ch plyn( motoru). nakonec jsou navr$ena zjednodu&ení "e&ení proud%ní v potrubích podle klasické akustické teorie s cílem vy"e&ení rozporu mezi p"esností a schopností dosáhnout "e&ení v reálném !ase na daném hardwaru (ecu 240 mhz). klí"ová slova: model motoru, v#m$na nápln$ válce, 1d/0d, ecu, real-time physical model of si-engine process and gas exchange for real-time implementation in engine management system physical model of si-engine process and gas exchange for real-time implementation in engine management system jan fo!tl, johannes beer, jens keller, jan macek, fredrik borchsenius mecca 02 2018 page 12 laws and natural constants. the simplest example of data driven models are look-up tables, which are very efficient in view of cpu performance. however, the memory used is increasing exponentially with the number of model inputs. this resulted in the development of polynomial approximation models and neural networks (e.g. lmn, lolimot [1] [2] [3]) with an increased level of physical based description. these modeling methods are widely used in today’s ecus. nevertheless, they remain still being data driven models, and therefore, become ineffective when used on complex engine configurations in terms of memory and calibration effort. one way to overcome the limitation of data driven models is the use of physical models describing the engine and gas exchange processes based on the solution of differential equations during engine operation [4] [5] [6] [7]. this paper presents a crank angle resolved real-time engine and gas exchange model for a turbocharged spark ignited (si) engine developed by continental ag. chosen methodology can cover different engine configurations due to its modular structure. main model outputs are the in-cylinder air and residual gas mass fractions for each single combustion event in addition to the states of the gas exchange system such as the exhaust back pressure and the turbocharger rotational speed. the knowledge of the in-cylinder state for each single combustion event allows a more efficient and emission optimized process control of the engine. for example, the ignition angle set point can be precontrolled in a more accurate way based on the knowledge of the in-cylinder air mass. 2. the engine development platform the model development and experimental investigations are based on a commercial 1.8 liter, 4 cylinder, turbocharged si-engine. the relevant gas exchange actuators are: • throttle valve • boost pressure actuator (wastegate) at the turbocharger • continuous variable valve timing (cvvt) on intake and exhaust side • 2-stage variable exhaust valve lift (vvl) • 2-stage port flap in intake manifold recorded actuator positions define the later model inputs. the later model validation is based on the measured in-cylinder air mass in specified engine operating conditions. signals from above listed actuators are transformed into effective flow areas in related components. port flap actuator is considered mainly for its influence on flow resistance in air path. two stages of port flap are represented with two cross sectional areas at opened and closed port flap. influence on combustion heat release in cylinder is considered indirectly by precalibrated parameters for vibe combustion model (map-based approach dependent on operating point). intake (p2) and exhaust (p3) pressures are measured with piezoresistive absolute pressure sensors (type kistler 4050, kulite ewct-312) with a 1° crank angle resolution. in-cylinder pressure is measured with piezoelectric relative sensors (type kistler 6041a) also with a 1° crank angle resolution. thermocouples on both intake and exhaust side are used to measure gas temperature. the engine testing was done under steady state and transient operating conditions. 3. si-engine process and gas exchange model engine components, such as cylinders, valves, pipes or manifolds are defined separately by sets of ordinary differential equations (odes). this enables modular composition of the complete engine gas exchange system. the numerical realization requires a hardware capability to calculate floating point arithmetic. mathematical formulation of an explicit system of odes :m8=6c<:�hnhi:b �.=:�cjb:g>86a�g:6a>o6i>dc�g:fj>g:h�6�=6g9l6g:�86e67>a>in�id�86a8ja6i:�;ad6i>c<�ed>ci� 6g>i=b:i>8 �� (6i=:b6i>86a�;dgbja6i>dc�d;�6c�:mea>8>i�hnhi:b�d;�*� h� � q�=fode�t,q� , q=~q1,q2,…,qn���������������������������������������������������� ��� � >h�jh:9�id�8dbedjc9�i=:�h:ih�d;�*� h�;dg�:68=�8dbedc:ci�>cid�dc:�8dajbc�k:8idg�;dg�i=:�:ci>g:�:c<>c:� bd9:a �.=:�:fj6i>dch�6g:�g:hdak:9�>c�i>b:�7n�jh>c<�i=:�:mea>8>i��c9�dg9:g�,jc<: &jii6�>ci:<g6i>dc� b:i=d9 �.=:�bd9:a�jh:h�6�<ad76a�*� h�hdak:g�l>i=�6�8dchi6ci�>ci:<g6i>dc�i>b:�hi:e��5�;dg�6aa�bd9:a� 8dbedc:cih � �i�i=:�7:<>cc>c<��6�9:i6>a:9�bd9:a�l6h�9:;>c:9�id�;ja;>aa�688jg68n�i6g<:ih �.=>h�9:i6>a:9�bd9:a��>c8aj9>c<� :a:k:c� � � +>e:�� 8dbedc:cih�� >h� g:eg:h:ci:9� 7n� ���� *� h � .=:� e>e:� 8dbedc:ci� =6h� 9db>c6i>c<� >c;aj:c8:�dc��+/�ad69��h::�h:8i>dc�� �� �!dg�i=>h�g:6hdc��i=:�bd9:a�l6h�g:9j8:9�id�>ih�;6hi gjcc>c<� k:gh>dc��g:hjai>c<�>c����*� h � .=:� cjb7:g� d;� :fj6i>dch� c::9:9� ;dg� :68=� 8dbedc:ci� d;� i=:� � 8na>c9:g� :c<>c:� >h� 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6>g�� 7jgc:9� ;j:a� 6c9� jc7jgc:9� ;j:a� id� g:eg:h:ci� i=:� <6h� 8dbedh>i>dc ���h>b>a6g�6eegd68=�>h�jh:9�;dg�i=:�:c<>c:�8na>c9:g � .=:� ��� �na>c9:g�� >h�jh:9� ;dg� i=:�:c<>c:�8na>c9:g� >ih:a;��=dl:k:g��=6h�699>i>dc6aan�6� i>b: k6g>67a:� kdajb:�g:eg:h:ci:9�7n�6�add@ je�i67a: �!>< � �h=dlh�ejah6i>c<�b6hh�6c9�:c:g<n�;ajm:h��7:>c<�8dch>9:g:9� id�86a8ja6i:�9nc6b>8�:fj>a>7g>jb�>ch>9:�8na>c9:g �!daadl>c<�6g:�;djg�dg9>c6gn�9>;;:g:ci>6a�:fj6i>dch� �*� h��i=6i�>aajhig6i:�i=:�8=6c<:�d;�>ih�i=:gbd9nc6b>8�<6h�hi6i:�� � � � m� air=m� in,air-m� ex,air� � ������ � &�sgdb\[ w 0� ^b�sgdb\[ v 0� \h�sgdb\[ u 0� v^y\� � ������ � m� unburned=m� in,unburned-m� ex,unburned-m� vibe� ������ � u� =hin�m� in-hex�m� ex-pcyl�v� -q� vibe-q� wall� � ������ � � � �20>;.�����na>c9:g�b6hh�6c9�:c:g<n� ig6chedgi� !+;dc.4����#bdicdhict�6� :c:g<:i>8@h�egnid@�kqa8:b� (1) is used to compound the sets of odes for each component into one column vector for the entire engine model. the equations are resolved in time by using the explicit 2nd order runge-kutta integration method. the model uses a global odes solver with a constant integration time step for all model components. at the beginning, a detailed model was defined to fulfill accuracy targets. this detailed model, including eleven '1d-pipe' components, is represented by 238 odes. the pipe component has dominating influence on cpu load (see section 3.2). for this reason, the model was reduced to its fast-running version, resulting in 73 odes. the number of equations needed for each component of the 4-cylinder engine is summarized in following table: in the following, the single model components of tab. 1 are explained. table 1: overview of model components and solved differential equations tabulka 1: p"ehled sou!ástí modelu a "e&en#ch diferenciálních rovnic number of model components number of solved ordinary differential equations detailed(1d) )238 odes fast-running(0d) )73 odes 8 x 0d-volume 8 x 4 = 32 odes 8 x 4 = 32 odes 4 x 0d-cylinder 4 x 4 = 16 odes 4 x 4 = 16 odes 16 x orifice 16 x 1 = 16 odes 16 x 1 = 16 odes 1 x turbocharger 1 x 3 = 3 odes 1 x 3 = 3 odes …other 6 x 1 = 6 odes 6 x 1 = 6 odes 11 x 1d-pipe 33 elements x 5 = 165 odes … all removed physical model of si-engine process and gas exchange for real-time implementation in engine management system jan fo!tl, johannes beer, jens keller, jan macek, fredrik borchsenius mecca 02 2018 page 13 basic approach for the engine process is the classic fillingemptying method. the thermodynamic '0d-volume' is used mainly for manifolds. only mass and energy conservation are considered. the gas is divided into three specie components: air, burned fuel and unburned fuel to represent the gas composition. a similar approach is used for the engine cylinder. the '0d-cylinder' is used for the engine cylinder itself, however, has additionally a time-variable volume represented by a lookup table. fig. 1 shows pulsating mass and energy fluxes, being considered to calculate dynamic 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>6+.;� 8/� 68-.5� ,86987.7=<�� >6+.;�8/�<85?.-�8;-27*;b�-2//.;.7=2*5�.:>*=287<�� �.=*25.-����������������������������������k �� !��<� �*<=�;>77270��������������������������k� � !��<� ����m��� 0dajb:�� ���m��������*� h� ���m��������*� h� ����m��� �na>c9:g� ���m����� ��*� h� ���m����� ��*� h� ��m�*g>;>8:� ��m� ��� ��*� h� ��m� ��� ��*� h� �� �m�.jg7d8=6g<:g� �� �m�������*� h� �� �m�������*� h� �����_di=:g� ����m� �����*� h� ����m� �����*� h� �m� � +>e:� ���:a:b:cih�m����� ���*� h� �_�6aa�g:bdk:9� � $c�i=:�;daadl>c<��i=:�h>c<a:�bd9:a�8dbedc:cih�d;�.67 � �6g:�:mea6>c:9 � �6h>8�6eegd68=�;dg�i=:�:c<>c:�egd8:hh�>h�i=:�8a6hh>8�;>aa>c< :bein>c<�b:i=d9 �.=:�i=:gbd9nc6b>8���� 0dajb:��>h�jh:9�b6>can�;dg�b6c>;da9h �*can�b6hh�6c9�:c:g<n�8dch:gk6i>dc�6g:�8dch>9:g:9 �.=:�<6h�>h� 9>k>9:9� >cid� i=g::� he:8>:� 8dbedc:cih�� 6>g�� 7jgc:9� ;j:a� 6c9� jc7jgc:9� ;j:a� id� g:eg:h:ci� i=:� <6h� 8dbedh>i>dc ���h>b>a6g�6eegd68=�>h�jh:9�;dg�i=:�:c<>c:�8na>c9:g � .=:� ��� �na>c9:g�� >h�jh:9� ;dg� i=:�:c<>c:�8na>c9:g� >ih:a;��=dl:k:g��=6h�699>i>dc6aan�6� i>b: k6g>67a:� kdajb:�g:eg:h:ci:9�7n�6�add@ je�i67a: �!>< � �h=dlh�ejah6i>c<�b6hh�6c9�:c:g<n�;ajm:h��7:>c<�8dch>9:g:9� id�86a8ja6i:�9nc6b>8�:fj>a>7g>jb�>ch>9:�8na>c9:g �!daadl>c<�6g:�;djg�dg9>c6gn�9>;;:g:ci>6a�:fj6i>dch� �*� h��i=6i�>aajhig6i:�i=:�8=6c<:�d;�>ih�i=:gbd9nc6b>8�<6h�hi6i:�� � � � m� air=m� in,air-m� ex,air� � ������ � &�sgdb\[ w 0� ^b�sgdb\[ v 0� \h�sgdb\[ u 0� v^y\� � ������ � m� unburned=m� in,unburned-m� ex,unburned-m� vibe� ������ � u� =hin�m� in-hex�m� ex-pcyl�v� -q� vibe-q� wall� � ������ � � � �20>;.�����na>c9:g�b6hh�6c9�:c:g<n� ig6chedgi� !+;dc.4����#bdicdhict�6� :c:g<:i>8@h�egnid@�kqa8:b� (5) combustion mass transfer is calculated according to vibe's empirical model as described in literature [8-page 243]. this model assumes that all unburned fuel inside cylinder burns in one single reaction. burned mass fraction is defined as ratio of current burned fuel heat to total fuel energy �db7jhi>dc�b6hh�ig6ch;:g�0� v^y\� >h�86a8ja6i:9�688dg9>c<�id�0>7:�h�:be>g>86a�bd9:a�6h�9:h8g>7:9�>c� a>i:g6ijg:�4� e6<:����5 �.=>h�bd9:a�6hhjb:h�i=6i�6aa�jc7jgc:9�;j:a�>ch>9:�8na>c9:g�7jgch�>c�dc:�h>c<a:� g:68i>dc ��jgc:9�b6hh�;g68i>dc�>h�9:;>c:9�6h�g6i>d�d;�8jgg:ci�7jgc:9�;j:a�=:6i�id�idi6a�;j:a�:c:g<n� � x= qvibe��� qb,tot =1-e �c������-�bs ��bd �����m+1� � � � � ������ � 0>7:�e6g6b:i:gh�c= ln�0.001�=-6.908�6c9��w��6g:�6hhjb:9�id�7:�8dchi6ci�dk:g�:ci>g:�de:g6i>c<�g6c<:�� l=:g:6h�8g6c@�6c<a:�6i�7jgc�hi6gi��bs�°crk��6c9�7jgc�9jg6i>dc���bd�°crk��6g:�d7i6>c:9�;gdb�86a>7g6i:9� add@ je�i67a:��9:e:c9:ci�dc�de:g6i>c<�ed>ci �.=:h:�e6g6b:i:gh�l:g:�86a8ja6i:9�;gdb�:c<>c:�i:hi�7:c8=� 8na>c9:g�>c9>86i>dc�6h� � ��bd=ca50-ca10� � � � � ������ 9su w ��� v � `b�:�=� z m � �9st�� � � ������ � l=:g:�ca10, ca50�6c9� ����6g:�8g6c@�6c<a:�k6aj:h�6i�l=>8=� ����������6c9������d;�=:6i�>h�g:a:6h:9�� 86a8ja6i:9�;gdb�b:6hjg:9�>c 8na>c9:g�eg:hhjg: �#:6i�ig6ch;:g�>cid�8na>c9:g�l6aah�>h�86a8ja6i:9�l>i=�6� 1dh8=c>�6eegd68=�4� e6<:��� 5 �.=:gbd9nc6b>8�egde:gi>:h�d;�8db7jhi>dc�<6h:h�6g:�6eegdm>b6i:9�l>i=� 6�e>:8: l>h:�edancdb>6a�bd9:a�jh>c<�6�96i676h:�ej7a>h=:9�7n�"g>aa�4�5 � "6h�:m8=6c<:�68ij6idgh��>ca:i�6c9�:m=6jhi�k6ak:h��i=gdiia:��:i8 ��a>hi:9�>c�h:8i>dc���6g:�g:eg:h:ci:9�7n�i=:� �*g>;>8:��8dbedc:ci �-><c6a�>ceji�;gdb� �/�g:eg:h:cih�i=:�8gdhh h:8i>dc�6g:6�d;�:68=�;adl�g:hig>8i>dc � .=:��*g>;>8:��;adl�>h�86a8ja6i:9�688dg9>c<�id�-6>ci 0:c6ci�g:a6i>dc�;dg�8dbeg:hh>7a:�;adl�4 �5�jh>c<�i=:� jehig:6b�6c9�9dlchig:6b�eg:hhjg:�;gdb�c:><=7dg>c<�8dbedc:cih �$ci6@:�6c9�:m=6jhi:9�k6ak:�9>h8=6g<:� 8d:;;>8>:cih�l:g:�d7i6>c:9�;gdb�6>g�;adl�i:hi�7:c8=�b:6hjg:b:ci �� .=:� �.jg7d8=6g<:g��8dbedc:ci� >h� g:eg:h:ci:9�7n�6� add@ je� i67a: 76h:9�bd9:a � $i� >h�:mi:c9:9�7n�6� 9>;;:g:ci>6a�:fj6i>dc�;dg�gdi6i>dc6a�b6hh�id�8dch>9:g�9nc6b>8�>c:gi>6�:;;:8ih ��6i6�;dg�8dbeg:hhdg�6c9� ijg7>c:�6g:�d7i6>c:9�;gdb�6�ijg7d8=6g<:g�hi6i>dc6gn�=di <6h�i:hi�7:c8= �� !adl� >c� >ci6@:� 6c9� :m=6jhi� e>e:� hnhi:bh�� >c8aj9>c<� l6k:� egde6<6i>dc� 6c9� <6h� >c:gi>6� :;;:8ih�� >h� g:eg:h:ci:9�>c�i=:�� � +>e:��8dbedc:ci�7:>c<�9>h8g:i>o:9�>c�he68:�^m��:mea6>c:9�>c�h:8i>dc���>c�bdg:� 9:i6>a� � � ��� $���7027.�";8,.<<�*7-��*<��a,1*70.��8-.5�� .d�;ja;>aa�i=:�8dcigda�d7?:8i>k:h��:m68i�eg:9>8i>dc�d;�>c 8na>c9:g�6>g�b6hh�>h�d;�@:n�>bedgi6c8: �(:6hjg:9� >c 8na>c9:g�6>g�b6hh�l6h�86a8ja6i:9�;gdb�>c?:8i:9�;j:a�6c9�8jgg:ci�6>g ;j:a�g6i>d ��>g ;j:a�g6i>d�l6h� :hi>b6i:9�;gdb��g:iih8=c:>9:g�:fj6i>dc ��99>i>dc6aan��h86k:c<>c<�b6hh�>h�8dch>9:g:9�>c�9:e:c9:c8:�dc� b:6hjg:9��*��*��g6i>d� id�86a8ja6i:� >c 8na>c9:g� ig6ee:9�b6hh �.=>h� >h�9dc:�7n�6c�6hhjbei>dc� ;dg� ig6ee>c<�:;;>8>:c8n�76h:9�dc�g:<g:hh>dc�;>i�d;�96i6�;gdb�h>b>a6g�g:;:g:c8:�:c<>c:�4 �5��4 �5 �(d9:a� 688jg68n� >h� i=:c�:hi>b6i:9� >c�:k:gn�de:g6i>c<�ed>ci�6h� i=:�e:g8:ci6<: :ggdg�7:il::c�b:6hjg:9�6c9� h>bja6i:9�>c 8na>c9:g�6>g�b6hh �� � +:g8:ci6<: :ggdg����������pe�@n/imep�= mair�simulation�-mair(measurement) mair(measurement) x 100%� � ������ � *k:g6aa�688jg68n�d;�����b:6hjg:9�de:g6i>dc�ed>cih�>h�9:;>c:9�6h�i=:��,ddi�(:6c�-fj6g:� ggdg���� � �>g b6hh :ggdg���� � �(&)! w �;b � � '!^ <b ^@; � � � �� ���� �� �dbe6g>hdc�d;�i=:�;jaa�:c<>c:�de:g6i>c<�g6c<:�>c�hi:69n�hi6i:�:me:g>b:cih�l>i=�i=:�9:i6>a:9�bd9:a�g:hjaih� >c�6c�dk:g6aa�6>g b6hh :ggdg�d;�,(���� ��:gg��h::�!>< �� ':;i� �#><=:hi�bd9:a�9:k>6i>dch�d88jg�6i� adl�:c<>c:�ad69 �.=>h�>h�id�7:�:me:8i:9�9j:�id�i=:�;68i�i=6i�688jg68n�8g>i:g>jb�>h�6�g:a6i>k:�9:k>6i>dc�l>i=� 9:cdb>c6idg�&x^d��7:>c<�hb6aa:g�6i�adl�ad69h ��88jg68n�g:fj>g:b:ci���:gg�6aadlh����0/�9:k>6i>dc�6i� ;jaa�ad69�ed>cih�l>i=�&x^d w ����0/��7ji�6aadlh�dcan��0/�9:k>6i>dc�6i�adl:hi�ad69h�l>i=�b:6hjg:9� (6) vibe parameters c = ln(0.001) = -6.908 and m = 2 are assumed to be constant over entire operating range, whereas crank angle at burn start !bs[°crk] and burn duration "!bd[°crk] are obtained from calibrated look-up table, dependent on operating point. these parameters were calculated from engine test bench cylinder 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'orifice' component. signal input from ecu represents the cross-section area of each flow restriction. the 'orifice' flow is calculated according to saintvenant relation for compressible flow [10] using the upstream and downstream pressure from neighboring components. intake and exhausted valve discharge coefficients were obtained from air flow test bench measurement. the 'turbocharger' component is represented by a look-up tablebased model. it is extended by a differential equation for rotational mass to consider dynamic inertia effects. data for compressor and turbine are obtained from a turbocharger stationary hot-gas test bench. flow in intake and exhaust pipe systems, including wave propagation and gas inertia effects, is represented in the '1d-pipe' component being discretized in space *x (explained in section 4 in more detail). 3.1 si-engine process and gas exchange model to fulfill the control objectives, exact prediction of in-cylinder air mass is of key importance. measured in-cylinder air mass was calculated from injected fuel and current air-fuel ratio. air-fuel ratio was estimated from brettschneider equation. additionally, scavenging mass is considered in dependence on measured co/ co2 ratio to calculate in-cylinder trapped mass. this is done by an assumption for trapping efficiency based on regression fit of data from similar reference engine [13], [14]. model accuracy is then estimated in every operating point as the percentage-error between measured and simulated in-cylinder air mass. percentage-error: �db7jhi>dc�b6hh�ig6ch;:g�0� v^y\� >h�86a8ja6i:9�688dg9>c<�id�0>7:�h�:be>g>86a�bd9:a�6h�9:h8g>7:9�>c� a>i:g6ijg:�4� e6<:����5 �.=>h�bd9:a�6hhjb:h�i=6i�6aa�jc7jgc:9�;j:a�>ch>9:�8na>c9:g�7jgch�>c�dc:�h>c<a:� g:68i>dc ��jgc:9�b6hh�;g68i>dc�>h�9:;>c:9�6h�g6i>d�d;�8jgg:ci�7jgc:9�;j:a�=:6i�id�idi6a�;j:a�:c:g<n� � x= qvibe��� qb,tot =1-e �c������-�bs ��bd �����m+1� � � � � ������ � 0>7:�e6g6b:i:gh�c= 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��99>i>dc6aan��h86k:c<>c<�b6hh�>h�8dch>9:g:9�>c�9:e:c9:c8:�dc� b:6hjg:9��*��*��g6i>d� id�86a8ja6i:� >c 8na>c9:g� ig6ee:9�b6hh �.=>h� >h�9dc:�7n�6c�6hhjbei>dc� ;dg� ig6ee>c<�:;;>8>:c8n�76h:9�dc�g:<g:hh>dc�;>i�d;�96i6�;gdb�h>b>a6g�g:;:g:c8:�:c<>c:�4 �5��4 �5 �(d9:a� 688jg68n� >h� i=:c�:hi>b6i:9� >c�:k:gn�de:g6i>c<�ed>ci�6h� i=:�e:g8:ci6<: :ggdg�7:il::c�b:6hjg:9�6c9� h>bja6i:9�>c 8na>c9:g�6>g�b6hh �� � +:g8:ci6<: :ggdg����������pe�@n/imep�= mair�simulation�-mair(measurement) mair(measurement) x 100%� � ������ � *k:g6aa�688jg68n�d;�����b:6hjg:9�de:g6i>dc�ed>cih�>h�9:;>c:9�6h�i=:��,ddi�(:6c�-fj6g:� ggdg���� � �>g b6hh :ggdg���� � �(&)! w �;b � � '!^ <b ^@; � � � �� ���� �� �dbe6g>hdc�d;�i=:�;jaa�:c<>c:�de:g6i>c<�g6c<:�>c�hi:69n�hi6i:�:me:g>b:cih�l>i=�i=:�9:i6>a:9�bd9:a�g:hjaih� >c�6c�dk:g6aa�6>g b6hh :ggdg�d;�,(���� ��:gg��h::�!>< �� ':;i� �#><=:hi�bd9:a�9:k>6i>dch�d88jg�6i� adl�:c<>c:�ad69 �.=>h�>h�id�7:�:me:8i:9�9j:�id�i=:�;68i�i=6i�688jg68n�8g>i:g>jb�>h�6�g:a6i>k:�9:k>6i>dc�l>i=� 9:cdb>c6idg�&x^d��7:>c<�hb6aa:g�6i�adl�ad69h ��88jg68n�g:fj>g:b:ci���:gg�6aadlh����0/�9:k>6i>dc�6i� ;jaa�ad69�ed>cih�l>i=�&x^d w ����0/��7ji�6aadlh�dcan��0/�9:k>6i>dc�6i�adl:hi�ad69h�l>i=�b:6hjg:9� (10) physical model of si-engine process and gas exchange for real-time implementation in engine management system jan fo!tl, johannes beer, jens keller, jan macek, fredrik borchsenius mecca 02 2018 page 14 comparison of the full engine operating range in steady state experiments with the detailed model results in an overall airmass-error of rmse = 5.7%err (see fig. 2-left). highest model deviations occur at low engine load. this is to be expected due to the fact that accuracy criterium is a relative deviation with denominator mair, being smaller at low loads. accuracy requirement 5%err allows 45 mg deviation at full load points with mair, = 900 mg, but allows only 5 mg deviation at lowest loads with measured mair, = 100 mg. beside this, loads with imep < 2 bar have higher cycle to cycle deviation (covariance of standard deviation of imep is 5 % at imep < 2 bar, but it is only 1,5 % in other operating points). to improve accuracy at low loads, more complex model calibration would be required. for example, current model assumes that 100 % of fuel burns inside of cylinder. in reality, part of the fuel burns outside cylinder, which is characterized by combustion efficiency. emission based combustion efficiency of measured engine varies between 90 % and 98 %. this fact may explain part of the unexpected model deviations and should be considered in future. another source of deviations is the numerical discretization. while the numerical solver is time based, higher integration time steps become limiting for calculation of crank angle dependent engine process. integration time step of *t = 300 µm corresponds to 1.5 degree at 850 rpm, but the resolution at maximum engine speed of 6000 rpm becomes with 11 degree quite inaccurate. fig. 2-right shows the comparison of both detailed and fast-running models with the exhaust pressure sensor in a selected turbocharged operating point. intake (in) and exhaust (ex) valve opening areas, as well as the top dead center (tdc), are marked gray in fig. 2 -right. the amplitude of pressure pulsations p3 is very high in comparison to its mean value. both models provide qualitatively realistic exhaust pressure pulsations in comparison to measurements. this shows the potential of physical modeling, for example to improve the boost pressure control, when used instead of classical mean value models. the accuracy results are obtained with the use of a global model parameterization, valid for the entire engine operating range. geometrical engine parameters such as valve effective flow areas and discharge coefficients, heat transfer coefficients, etc. are not recalibrated. however, the fast -running model cannot provide correct boundary conditions for the cylinders without additional empirical parameterization. moreover, the exhaust valve mass flow in fast -running model was stabilized due to numeric issues. the stabilization is based on 1st order differential equation added to the saint -venant 'orifice' flow. this causes an unwanted time delay in exhaust pressure dynamics by the fast -running model (see figure 2, right). the air -mass -error of fast -running model is rmse=7.4%err. due to this problem, the fast -running model would require higher calibration effort to reach the accuracy objectives. the detailed model shows a better model accuracy than the fast-running model. besides the model accuracy, real -time capability is crucial. 3.2 evaluation of real -time capabilit y a multicore engine computational unit (ecu) with a clock frequency of 240mhz, capable of calculating floating point arithmetic, was used as a validation platform. figure 3 illustrates necessary conditions to fulfill the real -time capability: engine management system expects model results at the end of every ecu sample period. therefore, the processor (cpu) has to be able to finish model execution by the end of the ecu sample period. this is expressed by the definition of real -time factor rt as a ratio of the cpu time to the ecu sample period. necessary cpu time for one integration time step of the odes solver was estimated offline by analyzing each model component. figure 2: left: engine map of detailed model providing pe in every measured steady state operating point resulting in an air-mass-error of rmse = 5.7%err. right: exhaust pressure pulsations p3 of detailed model and fast-running model compared to kulite ewct-312 sensor obrázek 2: vlevo: mapa motoru v detailním modelu, zobrazující pe v ka$dém m%"eném stacionárním bod%. v#sledná odchylka v hmotnosti vzduchu rmse = 5.7%err. vpravo: tlakové pulzace p3 ve v#fuku, detailní model a fast-running model, porovnání s m%"ením senzorem kulite ewct-312 physical model of si-engine process and gas exchange for real-time implementation in engine management system jan fo!tl, johannes beer, jens keller, jan macek, fredrik borchsenius mecca 02 2018 page 15 the offline estimation is based on the sum of the mathematical operations involved (additions/subtractions, multiplications, divisions, etc.) in the code, and taking into account the integration time step size used. this offline estimation was validated by implementation of the fast -running model on the target hardware. the detailed model requires a small integration time step of !t = 30 "s to satisfy the courant -lewy -friedrichs ( .=:�9:i6>a:9�bd9:a�g:fj>g:h�6�hb6aa�>ci:<g6i>dc�i>b:�hi:e�d;� !g>:9g>8=h���"% w z��f�h �� ;68idg�d;�,.����� �->bja6i>dc�8dja9�7:�i:c�i>b:h�;6hi:g�l>i=�6�i>b:�hi:e� ) stability condition in the exhaust pipe. this results in a very high real -time factor of rt = 43. simulation could be ten times faster with a time step !t = 300 "s so as the real -time factor becomes rt = 4.3 (see fig. 4 -blue). however, the simulation is then unstable. neglecting spatial resolution by removing of all ‘1d -pipe’ components results in the fast -running model and enables a stable calculation with a relatively high time step !t = 300 "s. the calculation of fast -running model components results in a real -time factor of rt = 1.9 (see fig. 4 -red). fig. 4 shows the computational demand of components in both detailed and fast -running model (see also tab. 1) estimated with an assumption of the same time step. the dashed line represents the development target for the complete engine model. sum of all component rt factors results in the rt factor of the entire model. the eleven ‘1d -pipe’ components would alone be 2.5 times beyond real time capability. this makes the complex 1d flow approach (explained in section 4.1) of the so -called detailed model not feasible for the real time implementation on target hardware. 3.3 conflict bet ween accuracy and real -time capabilit y following graph illustrates results achieved and presented above in this paper: again, the dashed line represents the development target. target model accuracy is a cylinder air -mass -error rmse<5%err being less than five percent over the engine operating range. figure 3: real-time control timing on ecu obrázek 3: +asování v ecu v reálném !ase figure 5: air-mass-accuracy and real-time factor of the fast-running model versus the detailed model obrázek 5: p"esnost ur!ení pr(toku vzduchu a real-time faktoru pro fast running model a detailní model figure 4: processor load by calculation of upper: detailed model (237 odes, )rt = 4.3) with assumption of instable time step *t = 300 µs. lower: fast-running model (72 odes, )rt = 1.9) with a stable time step *t = 300 µs obrázek 5: zatí$ení procesoru v#po!tem horní: detailního modelu (237 odr, )rt = 4.3) s p"edpokladem nestabil. !asového kroku *t = 300 µs. dolní: fast-running model (72 odr, )rt = 1.9) se stabilním !asov#m krokem t = 300 µs. physical model of si-engine process and gas exchange for real-time implementation in engine management system jan fo!tl, johannes beer, jens keller, jan macek, fredrik borchsenius mecca 02 2018 page 16 under some assumptions, the fast -running model (73 odes) has already a potential to be real -time capable on future ecus, for example when the cpu clock frequency increases to ~350mhz as stated in [12]. but the air -mass -error is not satisfying yet. sufficient accuracy is achieved by modelling of an engine gas exchange system in more detail, but it causes a conflict with the real -time capability. cpu time increases with space resolution and with the number of needed odes. the detailed model with a sufficient accuracy of rmse = 5.7%err is stable only using a time step *t , 30 µs. this model would need 43 times more processor performance to be real -time capable. 4. optimization of the ‘1d -pipe’ component the objective is to find the simplest possible approach to allow the calculation of pressure wave propagation through space, especially with unstable momentum conservation. the accuracy issues are not considered primarily. 4.1 complex transient 1d flow in pipes the 1d flow in the detailed model is described by the complete set of three transport conservation laws for mass, momentum and energy. governing equations can be taken from pischinger [10 -page 30]. mass conservation is formulated for all three gas components: air, burned fuel and unburned fuel. empirical source terms for wall friction and heat transfer are considered. caloric properties of the gas mixture are assumed to be a function of temperature and air -fuel ratio. the single pipe component is assumed to have constant cross -sectional area. partial differential equations (pdes) are discretized in space by using 1st order upwind scheme on a 1d finite volume mesh leading in a set of ordinary differential equations (odes). this differential scheme is computationally very fast; however, it requires additional numerical stabilization. the use of explicit time integration methods (2nd order runge-kutta), especially in combination with long integration time steps, leads to numerical oscillations. numerical stabilization was formulated as a function of element gas velocities by using a simple spring -damper model. the complex pipe model provides quite detailed information on thermal transport effects, though its complexity does not enable real -time capability on a current ecu. 4.2 simplification to 1d linear acoustics the complex '1d -pipe' approach is changed as follows: • governing equations: all three conservation laws (nonlinear) # linearized acoustic equations • discretization scheme: upwind # riemann solver • caloric gas properties: variable # constant classical acoustic theory provides a reasonable compromise to consider basic pressure wave propagation while reducing the computational time [6] [7] [10 -page 33]. constant gas properties reduce the computational time further. change of the discretization scheme improves numerical stability. simplifications according 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.=:gbd9nc6b>8�<6h�egde:gi>:h�6g:�86a8ja6i:9�dcan�dc8:�6i�i=:�>c>i>6a�i>b:�hi:e�;dg�6�<>k:c�g:;:g:c8:� i:be:g6ijg: � .=:� h>bea>;>:9� ig6chedgi� :fj6i>dch� 86c� 7:� lg>ii:c� >c� b6ig>m� ;dgb� jh>c<� i=:� hi6i:� 2�� a>c:6g>o:9�;ajm�. w � � 2�6c9�6�hdjg8:�i:gb�4� � 2q u ��2�r w �� � � � � � �� ��� � ���16�q u { � 8��s< � 8�y � } � �� �r w z � �iokh|� � � � �� ���� � �iokh�� a el� w ?icr ih�jt � � � � � �� ���� � .=:�dcan�hi6i:�k6g>67a:h�6g:�eg:hhjg:�1�6c9�k:ad8>in�6 �.=:�hdjg8:�i:gb�8dch>9:gh�:be>g>86a�l6aa�;g>8i>dc � -daji>dc�>h�d7i6>c:9�7n�jh>c<�6�hd 86aa:9�,>:b6cc�hdak:g��l=>8=�86a8ja6i:h�i=:�b>99a:�;ajm�dc�i=:�8:aa� 7djc96gn��>� ����9:e:c9>c<�dc�a:;i��'�>��6c9�g><=i��,�>� ��c:><=7dg>c<�hi6i:h ��j:�id�i=:�a>c:6g>in�d;� b6ig>m����>i�>h�edhh>7a:�id�:hi>b6i:�dcan�i=:�b>99a:�hi6i:�dc�i=:�8:aa�7djc96g>:h �.=:c�i=:�b>99a:�;ajm�>h� :6h>an�<>k:c�7n�.̂>; < w � � 2^>; <� � �20>;.� ��.>b: he68:�9db6>c��jee:g�>c9:m��@��>h�jh:9�;dg�i>b:�6c9�i=:�adl:g�>c9:m��>��;dg�he68:�>i:g6i>dc� !+;dc.4� ��i6hdegdhidgdkq�d7a6hi��=dgct�>c9:m�b@`�d9edkt9q�j6hj��9dact�>c9:m�b>`�d9edkt9q�egdhidgdksbj�@gd@j� (13) the only state variables are pressure and velocity u. the source term considers empirical wall friction. solution is obtained by using a so -called riemann solver, which calculates the middle flux on the cell boundary „i+1/2” depending on left „l=i” and right „r=i+1” neighboring states. due to the linearity of matrix a, it is possible to estimate only the middle state on the cell boundaries. then the middle flux is easily given by fi+1/2 = a$% qi+1/2 equation for middle state can be taken from leveque [11 -page 57] fj6i>dc�;dg�b>99a:�hi6i:�86c�7:�i6@:c�;gdb�':0:fj:�4 e6<:���5� � z �k>; < k>; <| w ��� � � ��k u �k>;� u �s�s � � k v k>;� � k u k>;� u � �s�sy � ��k v �k>;� �� � � �� ���� � -i6i>8�eg:hhjg:�>h�6hhjb:9�id�7:�@cdlc��;dg�:m6bea:�;gdb�6�c:><=7dg>c<���� 0dajb:��8dbedc:ci��6i� i=:� a:;i�7djc96gn�8dc9>i>dc� �:>; < w �ac� � 6c9�k:ad8>in� �;dg�:m6bea:� ;gdb�6�c:><=7dg>c<� 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formulate locally different integration time step. wall friction !pfric is calculated as a function of reynolds number. 4.3 discussion and expected benefits both numerical methods used in the complex (section 4.1) and the simplified acoustic (see section 4.2) ‘1d -pipe’ component were tested for stability by defining discontinuous initial value problems (so called riemann problems) and compared to their exact analytical solution. the riemann solver used in the simplified pipe provides better stability with fewer grid points than the previously used upwind scheme. therefore, higher critical cfl number can be used. maximum potential of presented simplifications when applied on all pipe components in detailed model results in a real -time factor rt=2.2 (see fig 4.). expected accuracy benefit in intake manifold components upstream of a throttle valve, and downstream of a turbocharger, is a part of current investigations. the presented approach has to be extended by energy conservation (also linearized) and formulated for entire gas composition (e.g., air, burned fuel, unburned fuel) to be able to capture transport problems in the primary intake and exhaust runners directly connected to cylinders. 5. conclusion the engine process and gas exchange were described with the use of 238 odes in the detailed model, providing all necessary information for control purpose of the selected 1.8 l, 4 -cylinder si -engine. the model was simplified to its fast -running version but lacking the required model information. the model real -time factor of rt = 1.9 is close to real time capability on the serial ecu equipped with a microprocessor of 240mhz clock frequency. ongoing research activities to reduce numerical effort for the cpu time consuming 1d pipe components are discussed. the complex approach for calculating all three transport conservation laws was simplified by using assumptions from classical linear acoustic theory. calculating of momentum conservation causes significantly lower processor load and remains numerically stable even for large integration time steps. the newly developed model is capable of providing more information than state -of -the -art ecu models (such as internal engine exhaust gas recirculation, in -cylinder air mass, as well as transient gas states in the complete engine’s gas exchange system). because of physical air path modelling (based on natural laws and constants), the calibration effort and required memory space does not increase exponentially with engine complexity. if the future ecu processor performance is constantly increasing as it has in the last couple of years, (as stated for example in [12]) it makes the newly developed model interesting for implementation in next generation ecus. figure 6: time-space domain, upper index „k” is used for time and the lower index „i” for space iteration obrázek 6: +asoprostorová oblast, horní index „k“ odpovídá !asu, dolní index „i“ odpovídá prostorovému kroku physical 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