Article AL-QADISIYAH JOURNAL FOR ENGINEERING SCIENCES 14 (2021) 109–116 Contents lists available at http://qu.edu.iq Al-Qadisiyah Journal for Engineering Sciences Journal homepage: http://qu.edu.iq/journaleng/index.php/JQES * Corresponding author. E-mail address: mech.post04@qu.edu.iq (Duaa Y.haran) https://doi.org/10.30772/qjes.v14i2.752 2411-7773/© 2021 University of Al-Qadisiyah. All rights reserved. This work is licensed under a Creative Commons Attribution 4.0 International License. Application of LES/PDF and RANS/PDF approaches for simulation of spray combustion Duaa Y. Haran a* and Ahmed A. Majhool a a Department of mechanical engineering, University of Al-Qadisiyah, Al-Qadisiyah, Iraq. A R T I C L E I N F O Article history: Received 14 April 2021 Received in revised form 6 June 2021 Accepted 13 June 2021 Keywords: Spray combustion Eulerian/Lagrangian Turbulence model Fluent A B S T R A C T This paper is addressing of a coupling Large-eddy simulation (LES) and RANS turbulence models with mixture fraction/probability density function as a combustion model. The two models have been implemented to simulate ethanol-air spray combustion. The gas phase is described with the Eulerian approach while the liquid phase is designed using a Lagrangian framework. The LES/PDF approach is obtained statistically. The sub-grid scale energy equation is used with the LES/PDF approach. The numerical results are validated with experimental data. Both LES/PDF and RANS/PDF approaches are compared with the experimental data. The LES/PDF approach shows a good agreement in predicting the average gas temperature compared with RANS/PDF approach. The LES/PDF shows a better prediction of both turbulence intensity profiles and the vortices which are generated in the turbulent flow in comparison with the RANS/PDF approach. © 2021 University of Al-Qadisiyah. All rights reserved. 1. Introduction Liquid fuels are widely used in industrial combustion systems like the internal combustion engine, liquid-fueled rockets, and gas turbine. It plays a significant role in our energy supply. Typically, liquid fuels are provided as a turbulent spray into the combustion chamber. The efficiency of combustion, stability, and pollutant formation depend heavily on the turbulent spray characteristics[1-6]. Therefore, attention must be paid to understand the mechanism of turbulent spray combustion and developing methods that would give a clearer picture of the behavior of such phenomena. Modelling and the numerical simulation are considered a challenging because it involves complex processing such as turbulence, phase change, heat transfer, and chemical reactions. In recent years, large- eddy simulation of liquid spray combustion has received a lot of attention. LES can provide more accurate statistical results and detailed dynamic flow and flame structures compared to Reynolds- averaged modelling (RANS). In the future, it is predicted that the LES turbulence model will become a widely used computational fluid dynamics method that will replace RANS modelling[7, 8]. There are many pieces of research in LES of the turbulent two-phases flow and the liquid spray combustion were reviewed by the current authors. Jones et al. [9] CFD simulation of swirl stabilized flames fueled by liquid kerosene were provided by large-eddy simulation (LES). There were two flames studied for which experimental data was available. Flame (A) was a stable flame, while flame (B) was unstable due to its lower air fuels ratio. The results of a combined LES/ PDF technique were applied to high swirl reacting spray flows and compared to empirical data. The formulation took into account sub-grid turbulence-spray-chemistry interactions, as well as the coupling between the gas and liquid phase. Dodoulas et al. [10] Three pre-mixed piloted turbulence CH4/air flames at different Reynolds numbers were subjected to Large-eddy simulation/Filtered Density Function model. In contrast to experimental data using the same closures used in non-premixed combustion with no changes to the combustion regime, the results showed strong agreement. The effect of heat release on the flow domain was http://qu.edu.iq/ mailto:mech.post04@qu.edu.iq https://doi.org/10.30772/qjes.v13i http://creativecommons.org/licenses/by/4.0/ 110 DUAA Y.HARAN AND AHMED ABED AL-KADHEM MAJHOOL /AL-QADISIYAH JOURNAL FOR ENGINEERING SCIENCES 14 (2021) 109–116 investigated and correctly captured. The results showed that pre-mixed combustion could be modeled using LES/PDF methods, at least under work conditions, and that approach could reliably capture spray conditions where combustion was not significant and large pockets of extinction emerged. Heye et al. [11] The experimental data of a pilot-established ethanol spray flame was analysed using the LES/ODF method. A Lagrangian Monti-Carlo model was used to solve the PDF equation. The droplet evaporation occurred way from the flame front, separation two processes. Owing to the high flow rate of the droplet-laden air, the front flame was unable to propagate. As compared to the others, there were significant differences in the conditions of the droplet inflow. Ukai et al. [12] A combined Large-Eddy Simulation (LES)/Conditional Moment Closure approach applied to model spray combustion. Additional source terms in the transport equation of CMC originating from fuel evaporation were modelled, and their effect on flame structure and global quantities including tentatively averaged temperature profile had been investigated. The laboratory spray jet flame prediction was generally good. The evaporation source term caused a flux in mixture fraction space, which shifted peak temperatures to higher mixture fraction regions. Jones et al. [13]In the GENERIC combustor, LES was used to simulate kerosene/air. The liquid phase was defined using the Eulerian method, which was fully coupled with the Lagrangian method. Reacting and non-reacting environments were simulated in two separate test cases. In terms of mean statistics and flame structure estimation, the flow field simulations were satisfactory. Ukai et al. [14] To model spray combustion, a hybrid Large- Eddy Simulation (LES)/Conditional Moment Closure method was used. The CMC method was coupled with a chemistry table that allowed for spatial and temporal variations of the tabulated chemical composition and provided a fair reliable estimation of the chemical source term of the LES/filtered reaction development variable. The numerical results were validated with experimental of two dilute acetone spray with pre- evaporation. An axial spray velocities and temperature predictions were noticeably enhanced, while RMS velocity showed reasonable agreement. Dodoulas et al. [15] For simulating a non-premixed flame with high extinction, a Large Eddy Simulation/PDF method was used. This method is effective in predicting the local flame extinction at different flame locations, and the major species predictions were found to be in good agreement with the practical data. The flame structure was analyzed by using chemical explosive modes. Due to the turbulence combustion model nature, the statistical data on the sub-grid flame structure can be obtainable. Sub-grid explosive models, for example. According to the results, sub-grid structures were only essential near the inlet nozzle in the current flame, and downstream extinction was controlled by Large-Scale interaction. Wang et al. [16] On the acetone flame structure, three combustion models (finite-rate chemistry model, flame-prolongation of intrinsic low dimensional manifold model, and flamelet-progress variable model) were applied to achieve large-eddy simulation (LES) of a turbulence spray structure. In comparison to experimental results, the use of a finite-rate chemistry model combined with a reduced chemical mechanism results in improved prediction of spray flame structure and heat release among the three models. Sacomano Filho et al. [17] In the form of a C2H5OH/air turbulence flame, a turbulence flame interaction and evaporative cooling effect were investigated in LES turbulence. The artificially thickened flame method (ATF) was combined with the mixture adaptive thickening extension technique to account for enthalpy variations. The Eulerian/Lagrangian system was used to track the droplets. The flamelet-generated manifold method has been tabulated by chemistry (FMG). Variations in enthalpy were integrated into the outcomes FGM database in a universal manner that was not limited to heat losses due to evaporative cooling effects. Aside from being novel, the proposed modelling strategy’s comprehensiveness allowed for a significant contribution to the understanding of turbulent spray combustion modeling’s most relevant phenomena. [17] As a result of the introduction of renewable aviation fuels, alternative methods and models are needed that can predict the combustor performance based on the fuel composition. In the sense of Eulerian/Lagrangian LES, a multi-component vaporization model was coupled with a direct. The burner which used in this work exhibited some of the existing features of aero-engine combustors like the reaction zone position and measured spray combustion were fine reproduced by LES turbulence model. The computational outcomes showed that the evaporation and mixing were the rate-controlling stages in the flame zone. Chemistry can be presumed to be significantly fast in this zone. However, other regions existed where the finite rate chemistry influence available. The approach of the finite rate chemistry demonstrated great potential in terms of pollution formation. Furthermore, the formation of benzene from one specific chemical form in the fuel suggested that to accurately predicted soot emissions, multi-component explanation of the liquid phase and the evaporation process was needed. Paulhiac et al. [18] A spray-swirled burner was subjected to LES/Discrete particle simulation. There are two types of validation: reacting and non-reacting. The velocity field of the two-phases finding was consistent in both cases as compared to experimental data. The LES grid fails to describe the non-premixed flame set near the droplets due to direct interaction between the spray and flame. Instead, the current model referred to pre-mixed combustion, which allowed for a percentage error on both the burning rate and combustor efficiency. It was necessary for using a single droplet combustion model which is appropriated to the LES/DPS framework. [18] Spray reactive flow is used in a variety of technological instruments. A sub-grid scale combustion model is studied. Two different flamelet methods were implemented which were consisting of spray flamelet and multi-regime gas flamelet models. The numerical evaluation was implemented in large- eddy simulations (LES) of a benchmark C2H5OH/air spray flame a partial pre-vaporization. An Eulerian/Lagrangian numerical framework was adopted. Outcomes showed that the spray flamelets developed from counterflow partially-premixed spray flames showed a better agreement with the experimental data. In the present work, Ansys Fluent is applied for simulating two-phase flow in 2D, free shear stress with a certain domain 360mm×460 Ge et al. [19]. Large Eddy Simulation (LES) and Reynolds averaged Navier-Stokes equations (RANS) turbulence model are amplemented to simulate the turbulent spray of C2H5OH/air spray. Both turbulence models are combined with a Probability Density Function (PDF) as a combustion model. Then used for investigating using various parameters in an attempt to find out which of approach is the best in giving results closer to the practical results and closer visualization of the practical reality. 2. Governing equations The main physical processes of down-draft evaporative cooling consist of turbulent flow, species mixing, mass, and heat transfer. Differential equations for each species, mass conservation, momentum conservation, and energy conservation must be solved. Also, the transport equations for the turbulence model should be solved. These equations are employed into three sets, continuous phase (Euler phase) equations used DUAA Y.HARAN AND AHMED ABED AL-KADHEM MAJHOOL /AL-QADISIYAH JOURNAL FOR ENGINEERING SCIENCES 14 (2021) 109–116 111 for solving the fluid flow and species transport, dispersed phase (liquid phase ) calculate the trajectory of the fuel droplets, and due to strong cooperation between two-phases, the coupled effect must be solved for the complex environment. All equations and constants used based on ANSYS Fluent theory Fluent et al. [20]. The general equations that are using for the solution identified as following: 2.1. Euler phase model FLUENT ANSYS solves gas-phase flow as well as analysis the differential equations of mass conservation, momentum conservation, energy conservation, and species. In the initial stages of the process, the model solves the gas-phase without including the interaction between two phases, when the liquid phase (disperse particle) trajectories are solved, and the source terms are added [20]. FLUENT solves gas-phase with consideration of the source terms in the numerical calculations. The conservation mass equation is 𝜕 𝜕𝑥𝑖 (𝜌𝑢𝑖 ) = 𝑆𝑚 ( 1 ) where ( 𝑢𝑖 ) is the air velocity component in Euler-phase (m/s), 𝑆𝑚 defined as an additional mass to gas-phase from liquid-phase (discrete phase) (𝑘𝑔/𝑚3𝑠 ). The transformation momentum due to the exchange can be expressed: 𝜌𝑢𝑖 𝜕𝑢𝑖 𝜕𝑥𝑗 = 𝜕 𝜕𝑥𝑗 [𝜇 ( 𝜕𝑢𝑖 𝜕𝑥𝑗 + 𝜕𝑢𝑗 𝜕𝑥𝑖 ) − 2 3 𝜇 ( 𝜕𝑢𝑗 𝜕𝑥𝑗 ) 𝛿𝑖𝑗 ] + 𝜌𝑔𝑖 − 𝜕𝑝 𝜕𝑥𝑖 + 𝐹𝑖 (2) When the species diffusion and the source due to the energy interchange between phases are included, the energy equation is identified in the following part (),where 𝑆𝑛 is the volumetric heat source (𝑘𝑔/𝑠 3𝑚), the heat transfer is calculating by using: 𝜌𝑢𝑖 𝜕𝑒 𝜕𝑥𝑖 = −P ∂u𝑖 ∂x𝑖 + Φ𝜐 + 𝜕 𝜕𝑥𝑖 (𝑘 𝜕𝑇 𝜕𝑥𝐼 ) + 𝜕 𝜕𝑥𝐼 (∑ ℎ𝑖 𝐽𝑖 𝑛 𝑖=1 ) + 𝑆𝑛 (3) where 𝜇 is the molecular viscosity ( 𝑘𝑔/𝑚2𝑠2 ), 𝐹𝑖 is the momentum source (𝑘𝑔/𝑚2𝑠2), 𝑔𝑖 is a gravity (𝑚/𝑠 2), P is the static pressure (pa), 𝑒 is the internal energy (𝐽/𝑘𝑔), 𝑇 is air temperature in (𝐾) , ℎ𝑖 is the species enthalpy, Φ𝜐 is the Rayleigh dissipation function (𝑘𝑔/𝑠3𝑚) , 𝑘 is the thermal conductivity (𝑊/𝑚𝑘 ), 𝐽𝑖 is the species (i) diffusion flux( 𝑘𝑔/ 𝑚2𝑠). The species conservation equations For predicting the local mass fraction of each phase, i.e., gas-phase of fuel and air, are: 𝜌𝑢𝑖 𝜕𝑚𝑖 𝜕𝑥𝑖 = −𝑃 𝜕𝐽𝑖 𝜕𝑥𝑖 +𝑆𝑚 (4) 𝐽𝑖= − 𝜌𝐷𝑖,𝑚 𝜕𝑚𝑖 𝜕𝑥𝑖 (5) where 𝑚𝑖 is the local mass fraction of specific phase (i) and 𝐷𝑖,𝑚 is the diffusion coefficient for a specific phase (i) in the mixture. 2.2. Liquid phase model The discrete droplets in the gas-phase are suggested to be spherical. At the starting of the solutions, the Lagrangian approach is used to calculate the trajectory of the particles (discrete phase) by integrating the force balance, while the gas-phase is recalculated and adjusted, it solves the liquid-phase in the following equations: 𝑑𝑈𝑝 𝑑𝑡 = 𝐹𝐷 (𝑢 − 𝑢𝑝) + 𝑔𝑥(𝜌𝑝−𝜌) 𝜌𝑝 + 𝜌 𝜌𝑝 𝑢𝑝 𝜕𝑢 𝜕𝑥𝑖 (6) 𝐹𝐷 = 18𝜇 𝜌𝑝𝑑𝑝 2 𝐶𝐷𝑅𝑒 24 (7) 𝑅𝑒 = 𝑑𝑝𝜌∣𝑢𝑝−𝑢∣ 𝜇 (8) 𝐶𝐷 = 𝑎1 + 𝑎2 𝑅𝑒 + 𝑎3 𝑅𝑒 2 (9) where 𝑢𝑝 is the droplets velocity (m/s), 𝐹𝑑(𝑢 − 𝑢𝑝 ) is the drag force per unit droplet mass (𝑚/𝑠2), (𝑔𝑥(𝜌𝑝−𝜌) 𝜌𝑝⁄ ) is the gravitational force on the droplet, the last term on the right hand of the equation represents the additional force due to the pressure gradient in the fuel, 𝑑𝑈𝑃 𝑑𝑡⁄ is the evaporation rate of the droplet, 𝑔𝑥 is the gravity (𝑚/𝑠 2), 𝐶𝐷 is the drag coefficient, 𝑑𝑝 is the diameter of the droplet (m), and 𝑎1, 𝑎2, and 𝑎3 are constants obtain by Morsi and Alexander [21]. The heat balance utilizes for computing the heat transfer between the gas-phase and liquid-phase. Radiant heat transfer is ignoring, is identified as: 𝑚𝑝𝑐𝑝 𝑑𝑇𝑝 𝑑𝑡 = ℎ𝑓𝑔 𝑑𝑚𝑝 𝑑𝑡 + ℎ𝑝𝐴𝑝(𝑇∞ − 𝑇𝑝) (10) where 𝐴𝑃 is the droplet surface area (𝑚 2), 𝑐𝑝 is the droplet heat capacity ( 𝐽/𝑘𝑔 𝑘 ), 𝑇𝑃 , 𝑇∞ are the temperature of the droplet and gas-phase respectively in (k), ℎ is the convective heat transfer coefficient (𝑊/𝑚2𝑘 ), ℎ𝑓𝑔 is the latent heat of evaporating of fuel (𝐽/𝑘𝑔). 2.3. Coupling phases An iterative method is implementing to solve two coupled phases(gas phase and discrete phase). When the computation of the particle stream is done, including the calculation of the gain or loss of mass, momentum, and heat by the particle trajectory, then these quantities are added into the gas-phase (continuous) calculation. The mass exchange between two phases is evaluated as the mass differences between all C.V using. 𝑆𝑚 = ∆𝑚𝑝�̇�𝑝,𝑜 𝑚𝑝,𝑜 (11) where 𝑆𝑚 is the mass exchange, ∆𝑚𝑝 is the change of the particle mass in each C.V, 𝑚𝑝 is the particles mass flow rate, 𝑚𝑝,𝑜 is the mass flow rate of the particle at the initial state. Then 𝑆𝑚 included in the mass conservation equation. In addition, the gas-phase is added as a source of mass in the species equation. The momentum transfer between two phases can be calculated as: 𝐹𝑖= ∑ ( 18𝜇 𝜌𝑝𝐷 2 𝑃 𝐶𝐷𝑅𝑒 24 (𝑢𝑝 − 𝑢) + 𝑔𝑥(𝜌𝑝−𝜌) 𝜌𝑝 + 𝜌 𝜌𝑝 𝑢𝑝 𝜕𝑢 𝜕𝑥𝑖 ) �̇�𝑝∆𝑡 (12) The vaporization rate of the droplets is controlled by the concentration of the vapour between the surface of the droplet and gas-phase. 𝑁𝑖=𝑘𝑐 (𝐶𝑖,𝑠 − 𝐶𝑖,∞) (13) 𝐾𝑐= 𝑆ℎ 𝐷𝑖,𝑚 𝑑𝑝 = (2+0.6𝑅𝑒 1 2⁄ 𝑆𝑐 1 3⁄ )𝐷𝑖,𝑚 𝑑𝑝 (14) 𝐶𝑖,∞ = 𝑋𝑖 𝑃 𝑅𝑇∞ (15) 𝐶𝑖,𝑠 = 𝑃𝑠𝑎𝑡(𝑇𝑝) 𝑅(𝑇𝑝 ) (16) where 𝑁𝑖 is the vapour molar flux (𝑘𝑔 𝑚𝑜𝑙𝑒/𝑚 2𝑠), 𝐾𝑐 is the coefficient of the mass transfer (𝑚/𝑠), 𝐶𝑖,𝑠 is the vapour concentration at the surface of 112 DUAA Y.HARAN AND AHMED ABED AL-KADHEM MAJHOOL /AL-QADISIYAH JOURNAL FOR ENGINEERING SCIENCES 14 (2021) 109–116 the droplet (𝑘𝑔 𝑚𝑜𝑙𝑒/𝑚3), 𝐶𝑖,∞ is the vapour concentration in gas-phase (𝑘𝑔 𝑚𝑜𝑙𝑒/𝑚3), 𝑃𝑠𝑎𝑡 is the vapor pressure at saturated state (pa), 𝑅 is the universal gas constant ( 𝐽 𝑘𝑔⁄ 𝑘 ), 𝑆ℎ is the Sherwood number, 𝑆𝑐 is Schmidt number, 𝑋𝑖 is the local bulk mole fraction of specific phase 𝑖 . Droplet evaporation is submited to law 2 in FLUENT, and the change of the droplet mass can be found: 𝑚𝑝(𝑡 + ∆𝑡) = 𝑚𝑝(𝑡) − 𝑁𝑖 𝐴𝑝𝑀𝑤,𝑖 ∆𝑡 (17) where 𝑀𝑤,𝑖 is the molecular weight of specific phase 𝑖 ( 𝑘𝑔 𝑘𝑔 𝑚𝑜𝑙𝑒 ), 𝑆ℎ is the volumetric source term, can be expressed as 𝑆ℎ = [ �̅�𝑝 𝑚𝑝,𝑜 𝑐𝑝 ∆𝑇𝑝 + ∆𝑚𝑝 𝑚𝑝,𝑜 (−ℎ𝑓𝑔 + ∫ 𝐶𝑝,𝑖 𝑇𝑝 𝑇𝑟𝑒𝑓 𝑑𝑡)] �̇�𝑝,𝑜 (18) where �̃�𝑝 is the droplet average mass in a control volume (𝑘𝑔) 2.3.1. Turbulence model The turbulence model is a mathematical model used to describe the turbulent flow which is commonly used in a realistic and engineering application .Turbulence models are used to represent turbulence by using simple equations . In this work standard k-𝜖 and large-eddy simulation are used representing the random and irregular flow. 2.3.1.1. Standard k-𝝐 model In the Standard model derivation ,flow assumes fully turbulent and ignores influence molecular viscosity .It is appropriate just for fully turbulent. For the turbulent kinetic energy ,𝑘 𝜕 𝜕𝑡 (𝜌𝑘) + 𝜕 𝜕𝑥𝑖 (𝜌𝑘𝑢𝑖 ) = 𝜕 𝜕𝑥𝑗 ⌈(𝜇 + 𝜇𝑡 𝜎𝑘 ) 𝜕𝑘 𝜕𝑥𝑗 ⌉ + 𝐺𝑘 + 𝐺𝑏 − 𝜌𝜖 − 𝑌𝑀 + 𝑆𝑘 (19) For turbulence dissipation rate 𝜖 𝜕 𝜕𝑡 (𝜌𝜖) + 𝜕 𝜕𝑥𝑖 (𝜌𝜖𝑢𝑖 ) = 𝜕 𝜕𝑥𝑗 [(𝜇 + 𝜇𝑡 𝜎𝜖 ) 𝜕𝜖 𝜕𝑥𝑗 ] + 𝐶1𝜖 𝜖 𝑘 (𝐺𝑘 + 𝐶3𝜖 𝐺𝑏 ) − 𝐶2𝜖 𝜌 𝜖2 𝑘 + 𝑆𝜖 (20) Where 𝜇𝑡 is the Turbulent viscosity modeling as : 𝜇𝑡=𝜌𝐶𝜇 𝑘 2 𝜖 (21) 𝐺𝑘 = −𝜌𝑢𝑖́ 𝑢�́� 𝜕𝑢𝑗 𝜕𝑥𝑖 (22) 𝐺𝑏 is the effect of buoyancy 𝐺𝑏 = 𝛽𝑔𝑖 𝜇𝑡 𝑃𝑟𝑡 𝜕𝑇 𝜕𝑥𝑖 (23) Where : The Dissemination rate is 𝑌𝑚 , the production of turbulent kinetic energy is 𝐺𝑘 , the Turbulent velocity is �́�, the thermal expansion coefficient is 𝛽, the turbulent Prandtl number is 𝑃𝑟𝑡 is ,at default = 0.85, the source term defined by used are 𝑆𝑘 ,𝑆𝜖 ,and the reverse active prandtle are 𝜎𝜖 ,𝜎𝑘 for 𝜖 , 𝑘 respectively. Constants model at default value are 𝐶1𝜖=1.44 ,𝐶2𝜖=1.92,𝐶𝜇=0.09 ,𝜎𝑘 =1 ,𝜎𝜖 =1.3 ,𝐶3𝜖=-0.33 2.3.1.2. Sub-grid scale model energy equation stress model A sub-grid scale equation energy stress model is expressed as 𝜏𝑖𝑗 = 2 3 𝜌𝐾𝑠𝑔𝑠𝛿𝑖𝑗 − 2𝐶𝑘 𝜌𝐾𝑠𝑔𝑠 1 2⁄ ∆𝑓𝑆𝑖𝑗̅̅̅̅ (24) 𝐾𝑠𝑔𝑠 is acquired by solving the transport equation 𝜌 𝜕�̅�𝑠𝑔𝑠 𝜕𝑡 + 𝜌 𝜕𝑢𝑗�̅�𝑠𝑔𝑠 𝜕𝑥𝑗 = −𝜏𝑖𝑗 𝜕𝑢𝑖 𝜕𝑥 − 𝐶𝜖 𝜌 𝐾3 2⁄ ∆𝑓 + 𝜕 𝜕𝑥𝑗 ( 𝜇𝑡 𝜎𝑘 𝜕𝐾𝑠𝑔𝑠 𝜕𝑥𝑗 ) (25) 𝐾𝑠𝑔𝑠 = 1 2 (𝑢𝑘 2̅̅ ̅ − �̅�𝑘 2 ) (26) 𝜇𝑡 = 𝐶𝑘 𝜌𝐾𝑠𝑔𝑠 1 2⁄ ∆𝑓 (27) ∆𝑓 = 𝑉1 3⁄ (28) Where the filter size is ∆𝑓, the sub-grid scale eddy viscosity is 𝜇𝑡. The mechanism of the reaction is implemented in one step, the ethanol- oxygen reaction is described chemically as 𝐶2𝐻5𝑂𝐻 + 3𝑂2 →2𝐶𝑂2 + 3𝐻2𝑂 For the radiative heat transfer, the P1 model is used −�̅�𝑟 = 𝑎𝐺 − 4𝑎𝜎�̅� 4 (29) where the Stefan-Boltzmann constant denotes by 𝜎 = 5.67 ∗ 10−8𝐽. 𝐾−1, the absorption coefficient is 𝑎 = 0.1𝑚−1 and the incident flux is 𝐺 which is processed from the equation of the radative transfer. when 𝑎 → 0 ,𝑞𝑟̅̅ ̅ → 0. 2.3.2. Combustion model In this research, the probability density function (pdf) was employed to evaluae some combustion properties. Obtained from the mixture fraction to provide the effect of the turbulence fluctuation on the quantities of the conserved scalar, two types of probability density function : a clippsed Gaussian and beta function. In the present research, a beta function commonly is used for simplicity and lower cost . Beta function mathematically identified : 𝑝(𝑓) = 𝑓𝜓−1(1−𝑓)Β−1 ∫ 𝑓𝜓−1 1 0 (1−𝑓)Β−1𝑑𝑓 (30) 𝑓 = 𝑧𝑖 −𝑧𝑖,𝑜𝑥 𝑧𝑖,𝑓𝑢𝑒𝑙−𝑧𝑖,𝑜𝑥 (31) explicit functions of (𝑓, 𝑔) mathematically described : 𝜓 = 𝑓 [ 𝑓(1−𝑓) 𝑔 − 1] (32) Β = (1 − 𝑓)𝜓 (33) Species concentration of each product temperature and enthalpy were obtained by weighting the amount of these quantities with depending (pdf ) on mixture fraction ,�̃�(𝑓) . 𝑓,g is calculated using finite difference method for each grid ,𝑄 may be expressed ,where �̌� is the Favre- averaging quantity DUAA Y.HARAN AND AHMED ABED AL-KADHEM MAJHOOL /AL-QADISIYAH JOURNAL FOR ENGINEERING SCIENCES 14 (2021) 109–116 113 �̃� = ∫ 𝑝 1 0 (𝑓)𝑄(𝑓)𝑑𝑓 (34) where a mixture fraction is 𝑓 , Mean mixture fraction of mass is 𝑓coefficients of beta pdf are 𝐵 , 𝜓 , the mass fraction for species element I is 𝑍𝑖, the mass fraction for the fuel stream inlet is 𝑍𝑖,𝑓𝑢𝑒𝑙, and the mass fraction for oxidizer stream inlet is 𝑍𝑖,𝑜𝑥. 3. Numerical method and condition The computational domain in the present work was a combustor 360× 460 mm shown in Fig. 1 in which a C2H5OH/air coaxial diffusion flame can be generated at a pressure of 2 MPa atm [19]. Combustor geometry is shown in Fig. 2. The optimal grid size of the cells is 83200×167304× 84105 and a quadrilateral refinement shape is implemented. The numerical conditions that were used are summarized in Table 1. As mentioned in the introductory part, the probability density function (PDF) is coupled with the Large Eddy Simulation (LES) and RANS turbulence model which is representing standard k-𝜖 turbulence model. For temporal term, the SIMPLE algorithm as a numerical procedure with a second- order implicit scheme is adopted. For momentum, the second-order upwind is used. For boundary conditions, the inlet velocity of the droplet and the injection angle are implemented according to the experiment[22]. Fig. 3. Shows the comparison between numerical simulation is using FLUENT ANSYS and the measurement. Figure 1. The computational domain. Figure 2. The spray combustor. Table 1. Numerical test conditions[𝟏𝟗] [23] parameters units Atomization pressure Mpa 2 Ethanol flow rate g/s 0.47 Spray angle Computationdomain Velocity of inlet air through co-flow The time step of LES/PDF ° 𝑚𝑚2 m/s s 45 450×360 0.32 1× 10−6 4. Results and Conclusion 4.1. Results The injection conditions of C2H5OH/air spray combustion are used for validation related to the measurement data taken [19]. The numerical simulation for the spray combustion using RANS and LES turbulence models. 114 DUAA Y.HARAN AND AHMED ABED AL-KADHEM MAJHOOL /AL-QADISIYAH JOURNAL FOR ENGINEERING SCIENCES 14 (2021) 109–116 Figure 3. Gas-phase temperature at different levels when x above the exit nozzle. Fig. 3 shows the gas-phase temperature profiles at different levels above the nozzle at 𝑥 = 6 mm, 𝑥 = 10 mm, 𝑥 = 20 mm, and 𝑥 = 25 mm. The measurement is expressed by symbols utilizing multi-line imaging NO- LIF [13]. The dash lines demonstrate the numerical results of (RANS) model which is representing the standard k-𝜖 turbulence model coupled with the PDF combustion model. The solid line indicates the numerical results of large eddy simulation (LES) coupled with the PDF method. The LES/PDF gives an extremely better agreement than RANS/PDF approach. The spray flame wings are predicted by the LES/PDF approach especially at 20 mm and 25 mm better than RANS/PDF approach. According to the outcomes of the experiments, the gradients of the temperature at the flame edge are very high. This phenomenon at section 6 mm is closely predicted by the LES/PDF approach, whereas shows a smoother accurately in various point of the experimental data although it predicts the gas-phase temperature at the tip edge of the nozzle is broader than the measurement data. It is important to improve the sub-grid scale combustion model for large-eddy simulation of two phases [16] while RANS/PDF in comparison with LES/PDF is succeeded in predicting the regions at the tip edge of the nozzle and then the accuracy of the numerical results decreases. In section 10 mm, the numerical results predicted by LES/PDF fail in comparison with RANS/PDF approach. Figure 4. Contours plot of simulated gas-phase temperature using RANS/PDF, another published work, and Spray flame photograph [19],[23]. Figure 5. Gas-phase temperature in comparison with another published work when x above nozzle at 6 mm [19],[23]. (a) (b) ( c ) Figure 6. Contours plot of simulated gas-phase temperature and Spray flame photograph [𝟏𝟗]. Fig. 4 demonstrates the gas phase contours of the numerical simulations that were performed by other authors in comparison with the numerical results of the present work. Difference in flame capturing is attributed to many causes such as mesh type, mesh size, numerical method procedure, approaches performance, and anticipating the missing conditions. Fig. 5 shows the static temperature profiles of the present work and other authors with the experimental data at x=6 mm above the nozzle. Fig. 6 shows a comparison of the reactions zone calculated by the experiment [14] as shown in (a), and the numerical simulation achieved using FLUENT ANSYS 19.2 in (b,c). DUAA Y.HARAN AND AHMED ABED AL-KADHEM MAJHOOL /AL-QADISIYAH JOURNAL FOR ENGINEERING SCIENCES 14 (2021) 109–116 115 RANS/PDF LES/PDF Figure 7. Contours plot of the gas-phase temperature at RANS turbulence model and LES. Fig. 7 shows the contours of gas-phase temperature profiles. The coherent structure appears on the right side with LES/PDF in which shows the eddy size and energy variation through the domain that can be explained to sub- grid scale energy equation model the ability in reinforces the prediction of the small eddies in addition to large eddies which predict by the type of mesh utilizing in comparison to RANS/PDF approach. Figure 8. Mean mixture fraction profiles of reaction zone along with the radial distance. Fig. 8 shows a rising in a mean mixture fraction that can be expressed due to the evaporation rate. Mixing is relatively higher and the amount of the injected fuel at the nozzle region is higher too in comparison to the oxidizer in this domain. LES/PDF approach shows an additional consumption in the fuel in comparison with RANS/PDF. Fig. 9 shows a gas temperature phase against the mean mixture fraction. There is a low distribution of mean mixture fraction (pdf) confront with the low temperature at the nozzle region and then demonstrate both static temperature and mean mixture fraction rise along with radial distance, especially in the reaction zones when the mixing is done between the ethanol stream and the oxidizer in which the burnt gas created in the upstream and blended with un burnt gas that is resulting in the generation of the high-temperature zone. In comparison, the gas temperature against pdf that is determined by using the LES/PDF approach is slightly higher than predicted by RANS/PDF approach. Figure 9. Comparison of predicted gas-phase temperature against mean mixture profiles along with the radial distance. Fig. 10 shows the turbulence intensity of gas-phase profiles. At the nozzle region, the turbulence intensity records a high percentage which may be expressed to the turbulence resulting from the hydrodynamic effect, the chemical interaction between two phases, liquid velocity, and the rate of evaporation, then it is eliminated with progressing away from the nozzle region. LES/PDF approach with sub-grid scale energy equation shows an additional fluctuation in the turbulence intensity profiles along with the radial distance of the domain which demonstrates the realistic prediction in comparison with the RANS/PDF approach. Figure 10. Comparison of predicted turbulence intensity profiles along with the radial distance. Fig. 11 shows the vortices profiles along with the radial distance. In the near and inlet shear stress of the fuel jet flow, the coherent structures are expected to demonstrate and then are concentrated to be large vortices and eventually are weakly in the downstream area that can be predicted by using the LES/PDF approach while RANS/PDF approach fails in demonstration these phenomena. 116 DUAA Y.HARAN AND AHMED ABED AL-KADHEM MAJHOOL /AL-QADISIYAH JOURNAL FOR ENGINEERING SCIENCES 14 (2021) 109–116 Figure 11. Comparison of predicted vortices profiles along with the radial distance. 4.2. Conclusions The turbulent spray flame of ethanol/air which is studied in this work using two approaches: Large-eddy simulation coupled with a probability density function (LES/PDF) approach and standard k-𝜖 turbulence model combined with a probability density function as a combustion model (RANS/PDF) approach. 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