Acta Polytechnica https://doi.org/10.14311/AP.2022.62.0549 Acta Polytechnica 62(5):549–557, 2022 © 2022 The Author(s). Licensed under a CC-BY 4.0 licence Published by the Czech Technical University in Prague DETERMINATION OF FAN DESIGN PARAMETERS FOR LIGHT-SPORT AIRCRAFT Jan Klesa Czech Technical University, Faculty of Mechanical Engineering, Department of Aerospace Engineering, Karlovo náměstí 13, Prague 2, Czech Republic correspondence: jan.klesa@fs.cvut.cz Abstract. This paper is focused on the preliminary design of an electric fan for light-sport aircraft. Usage of electric motors brings some advantages compared to piston engines, especially small size and the independence of power on shaft RPM. A 1D compressible fluid flow model is used for the determination of the performace. The influence of various system parameters is analysed. Results for the case of the UL-39 ultralight aircraft are presented. Finally, input parameters for the fan design are determined according to this analysis. This can be then used as input data for the standard fan (axial compressor) design procedure. Keywords: Ducted fan, electric propulsion, axial compressor. 1. Introduction Electric propulsion for aircrafts became a research topic in the last years, which is motivated by the huge progress in low-weight electric power systems. Electric flight was already developed in the 1960s for radio con- trolled model aircraft, e.g., work of Fred Militky [1]. The progress in battery technology (from NiCd to lithium-based batteries), electric motors (from sim- ple DC brush motors with ferrite magnets, later neodymium magnets, and today brushless DC mo- tors) and control electronics led to the increase of model performance and size.This led to the possi- bility of building manned electrical aircrafts in the last decade, e.g., projects of Airbus, Pipistrel, Extra, Jihlavan, etc. Today, the technology is advanced enough to build a small fully-electric aircraft. The electric propulsion brings some advantages, especially possible drag re- duction due to the lower volume and cross-section of electric motors in comparison with turboprop and piston engines. This allows to decrease the nacelle size (for multiple engine aircraft) and better fuselage nose shape (for single engine aircraft). However, cool- ing the electric components requires relatively large cooling systems because of the low temperature differ- ence. The main disadvantage remains the source of the electric energy. Batteries are relatively heavy and have a low energy density as compared with aircraft fuel [1]. Another problem is the long time necessary for recharging the batteries between flights. Refuelling is usually much faster and does not require a high power electric line connection at the airport. Thus, some hybrid system using standard aircraft fuel (e.g., Jet-A1) or hydrogen is necessary for a long range/high endurance aircraft. In this case, electricity is made onboard by means of an electric generator powered by turboshaft engine or APU. In this case, energy can be stored in the high energy density medium, but the overall efficiency is lower due to the chain of neces- sary energy transformations. Both systems are under development for use in aviation, e.g., Honeywell [2] or Rolls-Royce [3]. A ducted fan is used on electric-powered "jet" air- craft, e.g., Airbus E-Fan. A ducted fan allows the transformation of the electric energy to the propul- sive thrust at high flight velocity, where a propeller is inefficient. It became a dynamic research area in the last years due to the efforts of building electric or hybrid-electric transport aircrafts. However, ducted fans or ducted propellers have a lower performance at low flight speeds for multiple reasons: • Higher outlet velocity which causes lower propulsive efficiency. • Higher losses in the propulsion system due to the friction at duct walls. • Higher fuselage (nacelle) drag. • Higher drag when flying with the engine off-regime. But there is also some motivation for fan-powered low-speed aircraft, which can have various advantages: • Safety, because rotating parts are covered by the duct, and so the risk of damage or injures can be lower than for a conventional propeller. • Possible noise reduction. • “Jet-feeling” - fan-powered aircraft can be used for low-cost training of jet pilots. The preliminary design and a comparison of a ducted fan with a propeller was presented in [4]. This paper is based on the experience with the long devel- opement of the UL-39 aircraft at the Department of Aerospace Engineering of the Czech Technical Uni- versity in Prague. A more general approach with a compressible fluid flow model is used, which means 549 https://doi.org/10.14311/AP.2022.62.0549 https://creativecommons.org/licenses/by/4.0/ https://www.cvut.cz/en Jan Klesa Acta Polytechnica ELECTRIC MOTOR−→v0 −→v3 1 2 3 Figure 1. Propulsion system scheme. Free atmosphere 0 Plane in front of the fan 1 Plane behind the fan 2 Nozzle exit 3 Table 1. Section definitions. that this approach can also be used for a much faster aircraft than the UL-39. The aircraft and also its propulsion system must fullfill legal requirements. For Czech ultalight aircraft, it is certification specification UL-2 [5] (requirements of the German certification specification LTF-UL are very similar [6]). This brings the requirement that the aircraft has to take-off on a given distance, this creates requirement for thrust at low speeds so that the acceleration is adequate. 2. Methods The simulation model is based on a modified approach from [4] based on experience from the developement and testing of the UL-39 aircraft. A compressible fluid model is used so that this method can be used for a faster aircraft than the ultralight cathegory. An approach to the fan design based on the compari- son of various configurations for the complete flight velocity envelope is used due to certification specifi- cation requirements, which are contradictory to the requirement of high cruise speed as shown later in this paper, and led to the necessary modification of the approach presented in [4]. An iterative method in MATLAB is used for the solution of the system of equations. The result of the method is the fan design point which can then be used for the fan design by standard procedures, see e.g. [7] and [8]. 2.1. Physical model The aim of the first step is to find parameters of the propulsion system in design conditions, which were determined according to the experience with the UL-39 aircraft testing and operation [9]. It is a 1D compressible fluid flow model. Input parameters used for the fan design phase can be found in Table 2. The fan has to be placed into the available space in the fuselage, which limits the maximal fan diameter and determines the length of the exhaust duct. Figure 1 and Table 1 explain the numbering of different planes in the propulsion system. Due to the complexity of the equations, a numeri- cal iterative approach is used for the solution. Input parameters are the fan diameter D1 and nozzle cross- section ratio A1/A3. The thrust curve, i.e. depen- dence of the thrust T on the flight velocity v0, is then determined for every combination of D1 and A1/A3. The fan hub-to-tip radius ratio is set to 0.5, i.e. the Engine power P 200 kW Flight velocity range v0 0–100 m s−1 Air density ρ 1.225 kg m3 Atmospheric pressure ps0 101 325 Pa Intake duct pressure loss coefficient ζ01 0.1 Fan efficiency ηf an 0.85 Outlet duct wall friction factor λ23 0.013 Outlet duct length L 1.5 m Air ratio of specific heats κ 1.4 Air specific gas constant r 287 J kg−1 K−1 Air specific heat at constant pressure cp 1004.5 J kg−1 K−1 Table 2. Input parameters for the propulsion system. blade length is half of the fan radius. Then the fan cross-section A1 can be determined according to A1 = 3 4 πD21 4 . (1) The total pressure in the free atmosphere in front of the aircraft is detemined by the standard formula from flight Mach number M0 by pt0 = ps0(1 + κ − 1 2 M 20 ) κ κ−1 , (2) where the flight Mach number M0 is M0 = v0 a0 (3) and the speed of sound in the atmosphere a0 is a0 = √ κrTs0. (4) The total temperature can be deremined in a similar way Tt0 = Ts0 ( 1 + κ − 1 2 M 20 ) . (5) The total pressure in the intake duct is computed by means of a loss coefficient ζ01 and the fan axial velocity v1 pt1 = pt0 − ζ01ρ1v 2 1 2 , (6) 550 vol. 62 no. 5/2022 Determination of fan design parameters for light-sport aircraft where ζ01 = 0.1 (based on CFD simulations from [10]). The total pressure recovery coefficient (see [11]) cannot be used in this case due to the low flight speed (data from literature sources are suitable for a faster air- craft). Heat exchange in the intake duct is neglected, thus the total temperature remains the same Tt1 = Tt0. (7) The static temperature in front of the fan is Ts1 = Tt1 − v21 2cp , (8) the speed of sound is then a1 = √ κrTs1, (9) and the Mach number M1 = v1 a1 . (10) The static pressure can then be calculated from the Mach number ps1 = pt1 ( 1 + κ − 1 2 M 21 )− κ κ−1 . (11) The density and the air mass flow are then com- puted according to ρ1 = ps1 rTs1 , (12) ṁ1 = ρ1v1A1. (13) It is assumed that the whole engine power P is used by the fan, i.e. the total temperature is increased in the following way Tt2 = Tt1 + P cpρ1A1v1 . (14) The total temperature for isentropic compression due to the fan is Tt2i = Tt1 + ηF anP cpρ1A1v1 . (15) Then, the total pressure becomes pt2 = pt1 ( Tt2i Tt1 ) κ κ−1 , (16) and the fan pressure ratio is Π12 = pt2 pt1 . (17) The stagnation density behind the fan is ρt2 = pt2 rTt2 . (18) The critical air density (for choked flow state) be- hind the fan is ρc2 = ρt2 ( κ + 1 2 )− 1 κ−1 , (19) and the corresponding critical velocity is vc2 = √ 2 (κ − 1) cpTt2 κ + 1 , (20) and then, the critical flow density is (ρv)c2 = vc2ρc2. (21) M2 is computed so that the mass flow through the duct remains constant. i.e. (ρv)1 = (ρv)2. The speed of sound behind the fan is a2 = vc2 √ κ + 1 2 ( 1 + κ − 1 2 M 22 )−1 . (22) Then, the flow velocity is calculated from the Mach number M2 v2 = M2a2, (23) and the air density becomes ρ2 = ρt2 ( 1 + κ − 1 2 M 22 )− 1 κ−1 . (24) The total pressure at the nozzle exit 3 is computed from the exhaust duct loss coefficient ζ23 pt3 = pt2 − ζ23 ρ2v 2 2 2 . (25) The value of the loss coefficient ζ23 is determined according to the information from [12]. The flow den- sity at the nozzle exit is computed from the condition of constant mass flow (ρv)3 = (ρv)2 A3 A1 . (26) The total temperature behind the fan remains con- stant Tt3 = Tt2. (27) The total air density at the nozzle exit is ρt3 = pt3 rTt3 . (28) The critical (choked) air density in the nozzle exit is ρc3 = ρt3 ( κ + 1 2 )− 1 κ−1 , (29) and the corresponding critical air velocity is vc3 = √ 2 (κ − 1) cpTt3 κ + 1 , (30) and the critical flow density is (ρv)c3 = ρc3vc3. (31) 551 Jan Klesa Acta Polytechnica Figure 2. Thrust over flight speed for different fan diameters D1, nozzle contraction ratio A1/A3 = 1. Figure 3. Thrust over flight speed for different nozzle contraction ratios A1/A3, fan diameter D1 = 0.66 m. The static temperature in the nozzle exit is Ts3 = Tt3 ( ps0 pt3 ) κ−1 κ , (32) the corresponding speed of sound is a3 = √ κrTs3, (33) and the flow velocity is v3 = M3a3. (34) The nozzle exit Mach number M3 is determined from the relation between static pressure ps3 and total pressure pt3 ps3 = pt3 ( 1 + κ − 1 2 M 23 )− κ κ−1 . (35) The thrust of the propulsion system is determined from the momentum conservation law T = ṁ (v3 − v0) , (36) where the air mass flow is ṁ = ρ1A1v1. (37) Finally, the propulsion efficiency is defined by the standard formula η = T v0 P . (38) An iterative algorithm has to be used for the com- putation . A value v1 = 50 m s−1 can be used as a guess for the first iteration. Fan RPM is determined from the flow coefficient ϕ = vax/u which is assumed to be 0.5 nm = 120v1 πD1 . (39) 3. Results Thrust cuves (i.e. dependence of the thrust on the flight velocity) for different fan diameters D1 and nozzle contraction ratios A1/A3 are presented in Fig- ures 2 and 3. An increase in fan diameter D1 (see Figure 2) causes a thrust increase for the given ve- locity range, however, this influence diminishes with increasing flight velocity as expected from the general theory of aerospace propulsion. The influence of noz- zle contraction ratios A1/A3 on thrust (see Figure 3) is similar. Lower A1/A3 leads to a higher thrust at a lower flight velocity, but reduces the flight perfor- mance at a higher velocity. The influence of the fan diameter D1 and nozzle contraction ratio A1/A3 on the efficiency is presented in Figures 4 and 5. The efficiency is relatively low in comparison with the stan- dard propeller due to the small fan cross-section area and also due to the viscous losses in the duct system. Another important parameter for the fan design is the axial velocity v1 presented in Figures 6 and 7. It is clearly visible that there is a strong dependence of the fan axial velocity v1 on constant electric motor power. Both parameters, i.e. fan diameter D1 and nozzle contraction ratio A1/A3, have a strong influence on v1. The dependence of the fan pressure ratio on the flight velocity and fan diameter is presented in Figure 8. The fan RPM for the same situation is presented in Figure 9 (the assumption of constant ϕ = vax/u = 0.5 is used). Based on the above-mentioned results, the depen- dencies of fan pressure ratio Π, thrust T , fan axial velocity v1 and fan RPM nm on the fan diameter D and nozzle contraction ratio A1/A3 for static case (i.e. v0 = 0 km h−1, take-off) and for maximum flight velocity (i.e. v0 = 300 km h−1), are presented in Fig- ures 10–17. Based on this and the fuselage geometry, a fan diameter of D1 = 0.66 m was selected. The ratio A1/A3 is determined from the relative thrust shown in Figure 18. The relative thrust is defined as the ratio T /Tref , where the reference value Tref is 552 vol. 62 no. 5/2022 Determination of fan design parameters for light-sport aircraft Figure 4. Efficiency of the propulsion system for different fan diameters D1, nozzle contraction ratio A1/A3 = 1. Figure 5. Efficiency of the propulsion system for dif- ferent nozzle contraction A1/A3, fan diameter D1 = 0.66 m. Figure 6. Fan axial velocity component over flight speed for different fan diamenters and A1/A3 = 1. Figure 7. Fan axial velocity component over flight speed for different nozzle contraction ratios A1/A3, fan diameter D1 = 0.66 m. Figure 8. Fan pressure ratio over flight speed for different fan diamenters and A1/A3 = 1. Figure 9. Fan RPM over flight speed for different fan diamenters and A1/A3 = 1. 553 Jan Klesa Acta Polytechnica Figure 10. Dependence of static thrust on fan diameter and nozzle contraction ratio A1/A3. The selected fan design point parameters are marked by red cross. Figure 11. Dependence of thrust at flight speed v0 = 300 km h−1 on fan diameter and nozzle contraction ratio A1/A3. The selected fan design point parameters are marked by red cross. Figure 12. Dependence of fan pressure ratio at flight speed v0 = 0 km h−1 on fan diameter and nozzle con- traction ratio A1/A3. The selected fan design point parameters are marked by red cross. Figure 13. Dependence of fan pressure ratio at flight speed v0 = 300 km h−1 on fan diameter and nozzle contraction ratio A1/A3. The selected fan design point parameters are marked by red cross. the maximum thrust for each velocity. The optimal value is the maximum of relative thrust mean value for flight velocity 0 km h−1 and 300 km h−1. This gives an optimal value of A1/A3 equal to 1.17. The re- sulting performance of the propulsion system is then determined for this case, see Figures 19 and 20. Also, the dependence of the fan design parameters on the flight velocity is computed, i.e. fan pressure ratio Π in Figure 21, fan axial velocity v0 in Figure 22 and fan RPM nm in Figure 23. 4. Discussion The presented results show that the high static thrust requirement is in conflict with the high cruise speed requirement (i.e. high thrust at high flight velocity) as expected from the general aircraft propulsion the- ory. This is clearly visible in Figure 18. The UL-39 light-sport aircraft is used as an example for this com- putation; the results for similar aircrafts are expected to be comparable. That is why the optimal system configuration is set by means of relative thrust. The outputs of this method are the fan design parameters presented in Table 3. 5. Conclusions The results of the propulsion system simulation for ducted fan aircraft are presented. A compressible fluid flow model is used so the described procedure can be used for a wider range of flight velocities in comparison with a simple, incompressible flow model (e.g. [4]). The procedure is described and results are presented for the example of the UL-39 aircraft. The requirements for the propulsion system are contradic- tory, i.e. short take-off distance and high maximal 554 vol. 62 no. 5/2022 Determination of fan design parameters for light-sport aircraft Figure 14. Dependence of fan axial velocity component at flight speed v0 = 0 km h−1 on fan diameter and nozzle contraction ratio A1/A3. The selected fan design point parameters are marked by red cross. Figure 15. Dependence of fan axial velocity component at flight speed v0 = 300 km h−1 on fan diameter and nozzle contraction ratio A1/A3. The selected fan design point parameters are marked by red cross. Figure 16. Dependence of fan RPM at flight speed v0 = 0 km h−1 on fan diameter and nozzle contraction ratio A1/A3. The selected fan design point are marked by red cross. Figure 17. Dependence of fan RPM at flight speed v0 = 300 km h−1 on fan diameter and nozzle contraction ratio A1/A3. The selected fan design point parameters are marked by red cross. Fan pressure ratio Π 1.062 Fan diameter D 660 mm Electric motor RPM 6340 Air axial velocity at fan vax 109.54 m s−1 Fan air mass flow ṁ 33.46 kg s−1 Expected thrust at 300 km h−1 T 1401.9 N Expected efficiency at 300 km h−1 η 0.584 Table 3. UL-39 fan design parameters for flight speed 300 km h−1 at sea level international standard atmosphere and electric motor power 200 kW. flight velocity. This leads to the necessity of a trade- off for chosing the optimal system configuration. The influence of various design parameters on the propul- sion performance is presented for the expected range of flight velocities. The proposed selection of the optimal variant is based on the maximum of mean relative thrust for the static case (i.e. flight velocity of 0 km h−1) and the expected high speed cruise (i.e. flight velocity of 300 km h−1). The presented proce- dure and the results can be used for a ducted fan design for an electric powered aircraft. List of symbols a Speed of sound [m s−1] A Cross-section area of a duct [m2] cp Specific heat at constant pressure [J kg−1 K−1] D1 Fan diameter [m] L Duct length [m] 555 Jan Klesa Acta Polytechnica Figure 18. Dependence of relative thrust on nozzle con- traction ratio A1/A3 at flight speed 0 and 300 km h−1. The selected nozzle contraction ratio A1/A3 = 1.17 is marked by dashed line. Figure 19. Thrust over flight speed for chosen fan parameters, i.e. D1 = 0.66 m and A1/A3 = 1.17. Figure 20. Propulsive efficiency over flight speed for chosen fan parameters, i.e. D1 = 0.66 m and A1/A3 = 1.17. Figure 21. Fan pressure ratio over flight speed for chosen fan parameters, i.e. D1 = 0.66 m and A1/A3 = 1.17. Figure 22. Fan axial velocity component over flight speed for chosen fan parameters, i.e. D1 = 0.66 m and A1/A3 = 1.17. Figure 23. Fan RPM over flight speed for chosen fan parameters, i.e. D1 = 0.66 m and A1/A3 = 1.17. 556 vol. 62 no. 5/2022 Determination of fan design parameters for light-sport aircraft ṁ Air mass flow [kg s−1] M Mach number nm Fan RPM [RPM] ps Static pressure [Pa] pt Total pressure [Pa] P Engine power [W] r Air specific gas constant [J kg−1 K−1] T Thrust [N] Tt Total temperature [K] Ts Static temperature [K] v Velocity [m s−1] η Efficiency ζ Pressure loss coefficient κ Ratio of specific heats λ Wall friction factor Π12 Fan Pressure ratio ρ Air density [kg m−3] (ρv) Flow density [kg m−2 s−1] (ρv)c Critical flow density [kg m−2 s−1] Acknowledgements This work was supported by Technology Agency of the Czech Republic, grant No. FV40263. References [1] M. Hepperle. Electric flight – Potential and limitations. Energy Efficient Technologies and Concepts of Operation (STO-MP-AVT-209), 2012. Accessed 2022-10-26, https://elib.dlr.de/78726/. [2] Electric & hybrid-electric propulsion, 2022. 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Lufttüchtigkeitsforderungen für aerodynamisch gesteuerte Ultraleichtflugzeuge LTF-UL vom 15.01.2019 und Änderung vom 28.02.2019 (NfL 2-459-19), 2019. Accessed 2022-10-26, https: //www.daec.de/fileadmin/user_upload/files/2019/ Luftsportgeraete_Buero/LTF/LTF-UL_2019.pdf. [7] N. A. Cumpsty. Compressor Aerodynamics. Krieger Publishing Company, 2nd edn., 2004. [8] R. O. Bullock, I. A. Johnsen. Aerodynamic Design of Axial Flow Compressors. NASA-SP-36. NASA Lewis Research Center, Cleveland, OH, 1965. [9] R. Theiner, J. Brabec. Experience with the design of ultralight airplane with unconventional powerplant. Proceedings of the Institution of Mechanical Engineers, Part G; Journal of Aerospace Engineering 232(14):2721–2733, 2018. https://doi.org/10.1177/0954410018774117. [10] J. Hejna. Intake Desing for Experimental Fan. Master’s thesis, Czech Technical University in Prague, 2021. Accessed 2022-10-26, http://hdl.handle.net/10467/96889. [11] S. Farokhi. Aircraft Propulsion. 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Akademie-Verlag, 5th edn., 1978. 557 https://elib.dlr.de/78726/ https://aerospace.honeywell.com/us/en/products-and-services/product/hardware-and-systems/electric-power/hybrid-electric-electric-propulsion https://aerospace.honeywell.com/us/en/products-and-services/product/hardware-and-systems/electric-power/hybrid-electric-electric-propulsion https://aerospace.honeywell.com/us/en/products-and-services/product/hardware-and-systems/electric-power/hybrid-electric-electric-propulsion https://aerospace.honeywell.com/us/en/products-and-services/product/hardware-and-systems/electric-power/hybrid-electric-electric-propulsion https://www.rolls-royce.com/media/press-releases/2022/22-06-2022-rr-advances-hybrid-electric-flight-with-new-technology.aspx https://www.rolls-royce.com/media/press-releases/2022/22-06-2022-rr-advances-hybrid-electric-flight-with-new-technology.aspx https://www.rolls-royce.com/media/press-releases/2022/22-06-2022-rr-advances-hybrid-electric-flight-with-new-technology.aspx https://doi.org/10.2514/6.1996-376 https://www.laacr.cz/SiteCollectionDocuments/predpisy/UL2%20%C4%8D%C3%A1st%20I_26.3.2019.pdf https://www.laacr.cz/SiteCollectionDocuments/predpisy/UL2%20%C4%8D%C3%A1st%20I_26.3.2019.pdf https://www.laacr.cz/SiteCollectionDocuments/predpisy/UL2%20%C4%8D%C3%A1st%20I_26.3.2019.pdf https://www.daec.de/fileadmin/user_upload/files/2019/Luftsportgeraete_Buero/LTF/LTF-UL_2019.pdf https://www.daec.de/fileadmin/user_upload/files/2019/Luftsportgeraete_Buero/LTF/LTF-UL_2019.pdf https://www.daec.de/fileadmin/user_upload/files/2019/Luftsportgeraete_Buero/LTF/LTF-UL_2019.pdf https://doi.org/10.1177/0954410018774117 http://hdl.handle.net/10467/96889 Acta Polytechnica 62(5):549–557, 2022 1 Introduction 2 Methods 2.1 Physical model 3 Results 4 Discussion 5 Conclusions List of symbols Acknowledgements References