Transported PDF Modeling of Compressible Turbulent Reactive Flows by using the Eulerian Monte Carlo Fields Method

Pant, Tejas; Jain, Utsav; Wang, Haifeng

doi:10.1016/j.jcp.2020.109899

Transported PDF Modeling of Compressible Turbulent Reactive Flows by using the Eulerian Monte Carlo Fields Method

Journal Article · Wed Oct 07 00:00:00 EDT 2020 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2020.109899· OSTI ID:1678684

Pant, Tejas ^[1]; Jain, Utsav ^[2]; ^[2]

Purdue Univ., West Lafayette, IN (United States); Purdue University
Purdue Univ., West Lafayette, IN (United States)

Although the transported probability density function (PDF) method has been developed for decades, its application has been mainly focused on the low-Mach number flow problems. This work extends the transported PDF method to compressible flow problems. The Eulerian Monte Carlo fields (EMCF) solution method is employed to solve the transported PDF equation for compressible flow problems. A pseudo stagnation enthalpy is introduced and its stochastic partial differential equation is derived to ensure total energy conservation numerically. A new mixing model called interaction by partial exchange with mean (IPEM) is introduced to expand the available choices of mixing models for the EMCF method. The consistency of the EMCF method is examined for solving the transported PDF equation. Numerical implementation details are discussed, such as the density coupling between the compressible flow solver and the EMCF solver, discretization schemes for the mixing terms and the stochastic terms. The implemented compressible flow solver coupled with the EMCF solver is verified and validated in a series of test cases with increasing level of complexity, ranging from a statistically one-dimensional turbulent mixing layer to a self-excited resonance model rocket combustor. It is observed that in general with the increase of compressibility, there is an increase in the sensitivity of the modeling results to the different models and algorithms. This makes it necessary to develop a thorough understanding of the model sensitivity in order to develop a robust and accurate simulation solver for highly compressible turbulent reactive flows. The thermo-acoustic instability inside the model rocket combustor case is captured reasonably, which demonstrates the overall capability of the developed compressible turbulent combustion solver based on the transported PDF method.

View Accepted Manuscript (DOE)

Research Organization:: Purdue Univ., West Lafayette, IN (United States)

Sponsoring Organization:: USDOE Office of Energy Efficiency and Renewable Energy (EERE), Transportation Office. Vehicle Technologies Office

Grant/Contract Number:: EE0008876

OSTI ID:: 1678684

Alternate ID(s):: OSTI ID: 1775915
OSTI ID: 23203559

Journal Information:: Journal of Computational Physics, Journal Name: Journal of Computational Physics Vol. 425; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

References (88)

An updated comprehensive kinetic model of hydrogen combustion Li, Juan; Zhao, Zhenwei; Kazakov, Andrei International Journal of Chemical Kinetics, Vol. 36, Issue 10 https://doi.org/10.1002/kin.20026	journal	January 2004
Particle Method for Turbulent Flows: Integration of Stochastic Model Equations Pope, S. B. Journal of Computational Physics, Vol. 117, Issue 2 https://doi.org/10.1006/jcph.1995.1070	journal	March 1995
Assessment of Numerical Accuracy of PDF/Monte Carlo Methods for Turbulent Reacting Flows Xu, J.; Pope, S. B. Journal of Computational Physics, Vol. 152, Issue 1 https://doi.org/10.1006/jcph.1999.6241	journal	June 1999
A Consistent Hybrid Finite-Volume/Particle Method for the PDF Equations of Turbulent Reactive Flows Muradoglu, Metin; Jenny, Patrick; Pope, Stephen B. Journal of Computational Physics, Vol. 154, Issue 2 https://doi.org/10.1006/jcph.1999.6316	journal	September 1999
A Hybrid Algorithm for the Joint PDF Equation of Turbulent Reactive Flows Jenny, P.; Pope, S. B.; Muradoglu, M. Journal of Computational Physics, Vol. 166, Issue 2 https://doi.org/10.1006/jcph.2000.6646	journal	January 2001
The Hybrid Method for the PDF Equations of Turbulent Reactive Flows: Consistency Conditions and Correction Algorithms Muradoglu, Metin; Pope, Stephen B.; Caughey, David A. Journal of Computational Physics, Vol. 172, Issue 2 https://doi.org/10.1006/jcph.2001.6861	journal	September 2001
Continuous Markov processes and stochastic equations Maruyama, Gisiro Rendiconti del Circolo Matematico di Palermo, Vol. 4, Issue 1 https://doi.org/10.1007/BF02846028	journal	January 1955
Numerical Study of n-Heptane Auto-ignition Using LES-PDF Methods Jones, W. P.; Navarro-Martinez, S. Flow, Turbulence and Combustion, Vol. 83, Issue 3 https://doi.org/10.1007/s10494-009-9228-9	journal	June 2009
Large Eddy Simulation of Premixed Turbulent Flames Using the Probability Density Function Approach Dodoulas, I. A.; Navarro-Martinez, S. Flow, Turbulence and Combustion, Vol. 90, Issue 3 https://doi.org/10.1007/s10494-013-9446-z	journal	February 2013
Flame Dynamics During Combustion Instability in a High-Pressure, Shear-Coaxial Injector Combustor Srinivasan, S.; Ranjan, R.; Menon, S. Flow, Turbulence and Combustion, Vol. 94, Issue 1 https://doi.org/10.1007/s10494-014-9569-x	journal	September 2014
Consistent Behavior of Eulerian Monte Carlo fields at Low Reynolds Numbers Valiño, Luis; Mustata, Radu; Letaief, Khaled Ben Flow, Turbulence and Combustion, Vol. 96, Issue 2 https://doi.org/10.1007/s10494-015-9687-0	journal	November 2015
LES/PDF Modeling of Turbulent Premixed Flames with Locally Enhanced Mixing by Reaction Wang, Haifeng; Pant, Tejas; Zhang, Pei Flow, Turbulence and Combustion, Vol. 100, Issue 1 https://doi.org/10.1007/s10494-017-9831-0	journal	July 2017
Large Eddy Simulation of Supersonic Combustion Using the Eulerian Stochastic Fields Method Almeida, Y. P.; Navarro-Martinez, S. Flow, Turbulence and Combustion, Vol. 103, Issue 4 https://doi.org/10.1007/s10494-019-00055-7	journal	September 2019
Approximate Riemann solvers, parameter vectors, and difference schemes Roe, P. L. Journal of Computational Physics, Vol. 43, Issue 2 https://doi.org/10.1016/0021-9991(81)90128-5	journal	October 1981
An approach to the autoignition of a turbulent mixture Dopazo, César; O'Brien, Edward E. Acta Astronautica, Vol. 1, Issue 9-10 https://doi.org/10.1016/0094-5765(74)90050-2	journal	September 1974
Laminar diffusion flamelet models in non-premixed turbulent combustion Peters, N. Progress in Energy and Combustion Science, Vol. 10, Issue 3 https://doi.org/10.1016/0360-1285(84)90114-X	journal	January 1984
PDF methods for turbulent reactive flows Pope, S. B. Progress in Energy and Combustion Science, Vol. 11, Issue 2 https://doi.org/10.1016/0360-1285(85)90002-4	journal	January 1985
Comparison of Eulerian and Lagrangian Monte Carlo PDF methods for turbulent diffusion flames Möbus, H.; Gerlinger, P.; Brüggemann, D. Combustion and Flame, Vol. 124, Issue 3 https://doi.org/10.1016/S0010-2180(00)00207-8	journal	February 2001
Scalar and joint scalar-velocity-frequency Monte Carlo PDF simulation of supersonic combustion Mobus, H. Combustion and Flame, Vol. 132, Issue 1-2 https://doi.org/10.1016/S0010-2180(02)00428-5	journal	January 2003
A mixing model for turbulent reactive flows based on Euclidean minimum spanning trees Subramaniam, S. Combustion and Flame, Vol. 115, Issue 4 https://doi.org/10.1016/S0010-2180(98)00023-6	journal	December 1998
Conditional moment closure for turbulent combustion Klimenko, A. Y.; Bilger, R. W. Progress in Energy and Combustion Science, Vol. 25, Issue 6 https://doi.org/10.1016/S0360-1285(99)00006-4	journal	December 1999
Examination of errors of table integration in flamelet/progress variable modeling of a turbulent non-premixed jet flame Pant, Tejas; Han, Chao; Wang, Haifeng Applied Mathematical Modelling, Vol. 72 https://doi.org/10.1016/j.apm.2019.03.016	journal	August 2019
Micromixing effects in a reacting plume by the Stochastic Fields method Garmory, A.; Richardson, E. S.; Mastorakos, E. Atmospheric Environment, Vol. 40, Issue 6 https://doi.org/10.1016/j.atmosenv.2005.11.002	journal	February 2006
Turbulent lifted flames in a vitiated coflow investigated using joint PDF calculations Cao, Renfeng Richard; Pope, Stephen B.; Masri, Assaad R. Combustion and Flame, Vol. 142, Issue 4 https://doi.org/10.1016/j.combustflame.2005.04.005	journal	September 2005
Lifted methane–air jet flames in a vitiated coflow Cabra, R.; Chen, J.; Dibble, R. Combustion and Flame, Vol. 143, Issue 4 https://doi.org/10.1016/j.combustflame.2005.08.019	journal	December 2005
A probability density function Eulerian Monte Carlo field method for large eddy simulations: Application to a turbulent piloted methane/air diffusion flame (Sandia D) Mustata, Radu; Valiño, Luis; Jiménez, Carmen Combustion and Flame, Vol. 145, Issue 1-2 https://doi.org/10.1016/j.combustflame.2005.12.002	journal	April 2006
Large eddy simulation of autoignition with a subgrid probability density function method Jones, W.; Navarromartinez, S. Combustion and Flame, Vol. 150, Issue 3 https://doi.org/10.1016/j.combustflame.2007.04.003	journal	August 2007
Flow field studies of a new series of turbulent premixed stratified flames Seffrin, F.; Fuest, F.; Geyer, D. Combustion and Flame, Vol. 157, Issue 2 https://doi.org/10.1016/j.combustflame.2009.09.001	journal	February 2010
Large Eddy Simulation of the Sandia Flame Series (D–F) using the Eulerian stochastic field method Jones, W. P.; Prasad, V. N. Combustion and Flame, Vol. 157, Issue 9 https://doi.org/10.1016/j.combustflame.2010.05.010	journal	September 2010
Experimental and numerical analysis of a lean premixed stratified burner using 1D Raman/Rayleigh scattering and large eddy simulation Kuenne, Guido; Seffrin, Florian; Fuest, Frederik Combustion and Flame, Vol. 159, Issue 8 https://doi.org/10.1016/j.combustflame.2012.02.010	journal	August 2012
LES of a turbulent premixed swirl burner using the Eulerian stochastic field method Jones, W. P.; Marquis, A. J.; Prasad, V. N. Combustion and Flame, Vol. 159, Issue 10 https://doi.org/10.1016/j.combustflame.2012.04.008	journal	October 2012
Large eddy simulation/probability density function simulations of bluff body stabilized flames Popov, Pavel P.; Pope, Stephen B. Combustion and Flame, Vol. 161, Issue 12 https://doi.org/10.1016/j.combustflame.2014.05.018	journal	December 2014
An investigation of turbulent premixed counterflow flames using large-eddy simulations and probability density function methods Tirunagari, Ranjith R.; Pope, Stephen B. Combustion and Flame, Vol. 166 https://doi.org/10.1016/j.combustflame.2016.01.024	journal	April 2016
LES combustion modeling using the Eulerian stochastic field method coupled with tabulated chemistry Avdić, Amer; Kuenne, Guido; di Mare, Francesca Combustion and Flame, Vol. 175 https://doi.org/10.1016/j.combustflame.2016.06.015	journal	January 2017
Effects of molecular transport in LES/PDF of piloted turbulent dimethyl ether/air jet flames You, Jiaping; Yang, Yue; Pope, Stephen B. Combustion and Flame, Vol. 176 https://doi.org/10.1016/j.combustflame.2016.11.007	journal	February 2017
Turbulent jet ignition assisted combustion in a rapid compression machine Validi, AbdoulAhad; Schock, Harold; Jaberi, Farhad Combustion and Flame, Vol. 186 https://doi.org/10.1016/j.combustflame.2017.07.032	journal	December 2017
Modelling of diesel spray flames under engine-like conditions using an accelerated Eulerian Stochastic Field method Pang, Kar Mun; Jangi, Mehdi; Bai, Xue-Song Combustion and Flame, Vol. 193 https://doi.org/10.1016/j.combustflame.2018.03.030	journal	July 2018
Impact of source terms on reliability of CFD algorithms Lian, Chenzhou; Xia, Guoping; Merkle, Charles L. Computers & Fluids, Vol. 39, Issue 10 https://doi.org/10.1016/j.compfluid.2010.06.021	journal	December 2010
An Eulerian stochastic field cavitation model coupled to a pressure based solver Chen, Boxiong; Oevermann, Michael Computers & Fluids, Vol. 162 https://doi.org/10.1016/j.compfluid.2017.12.002	journal	January 2018
Variance consistent mean shift particle model for treating differential molecular diffusion in transported PDF methods for turbulent reactive flows Zhang, Pei; Wang, Haifeng Computers & Fluids, Vol. 170 https://doi.org/10.1016/j.compfluid.2018.04.021	journal	July 2018
Large-Eddy Simulation of combustion instabilities in a variable-length combustor Garby, Romain; Selle, Laurent; Poinsot, Thierry Comptes Rendus Mécanique, Vol. 341, Issue 1-2 https://doi.org/10.1016/j.crme.2012.10.020	journal	January 2013
Large eddy simulation of a premixed propane turbulent bluff body flame using the Eulerian stochastic field method Jones, W. P.; Marquis, A. J.; Wang, F. Fuel, Vol. 140 https://doi.org/10.1016/j.fuel.2014.06.050	journal	January 2015
Large-eddy simulations of turbulent flows in internal combustion engines Banaeizadeh, A.; Afshari, A.; Schock, H. International Journal of Heat and Mass Transfer, Vol. 60 https://doi.org/10.1016/j.ijheatmasstransfer.2012.12.065	journal	May 2013
Large eddy simulation of hydrogen combustion in supersonic flows using an Eulerian stochastic fields method Gong, Cheng; Jangi, Mehdi; Bai, Xue-Song International Journal of Hydrogen Energy, Vol. 42, Issue 2 https://doi.org/10.1016/j.ijhydene.2016.09.017	journal	January 2017
Solution-limited time stepping to enhance reliability in CFD applications Lian, Chenzhou; Xia, Guoping; Merkle, Charles L. Journal of Computational Physics, Vol. 228, Issue 13 https://doi.org/10.1016/j.jcp.2009.03.040	journal	July 2009
A multivariate quadrature based moment method for LES based modeling of supersonic combustion Donde, Pratik; Koo, Heeseok; Raman, Venkat Journal of Computational Physics, Vol. 231, Issue 17 https://doi.org/10.1016/j.jcp.2012.04.031	journal	July 2012
Lagrangian transported MDF methods for compressible high speed flows Gerlinger, Peter Journal of Computational Physics, Vol. 339 https://doi.org/10.1016/j.jcp.2017.02.049	journal	June 2017
Progress in probability density function methods for turbulent reacting flows Haworth, D. C. Progress in Energy and Combustion Science, Vol. 36, Issue 2 https://doi.org/10.1016/j.pecs.2009.09.003	journal	April 2010
Advances and challenges in modeling high-speed turbulent combustion in propulsion systems Gonzalez-Juez, Esteban D.; Kerstein, Alan R.; Ranjan, R. Progress in Energy and Combustion Science, Vol. 60 https://doi.org/10.1016/j.pecs.2016.12.003	journal	May 2017
LES of scalar mixing in supersonic mixing layers Sankaran, V.; Menon, S. Proceedings of the Combustion Institute, Vol. 30, Issue 2 https://doi.org/10.1016/j.proci.2004.08.027	journal	January 2005
The effect of mixing models in PDF calculations of piloted jet flames Cao, Renfeng Richard; Wang, Haifeng; Pope, Stephen B. Proceedings of the Combustion Institute, Vol. 31, Issue 1 https://doi.org/10.1016/j.proci.2006.08.052	journal	January 2007
LES-pdf simulation of a spark ignited turbulent methane jet Jones, W. P.; Prasad, V. N. Proceedings of the Combustion Institute, Vol. 33, Issue 1 https://doi.org/10.1016/j.proci.2010.06.076	journal	January 2011
A quadrature-based LES/transported probability density function approach for modeling supersonic combustion Koo, Heeseok; Donde, Pratik; Raman, Venkat Proceedings of the Combustion Institute, Vol. 33, Issue 2 https://doi.org/10.1016/j.proci.2010.07.058	journal	January 2011
Large eddy simulation/probability density function modeling of a turbulent CH4/H2/N2 jet flame Wang, Haifeng; Pope, Stephen B. Proceedings of the Combustion Institute, Vol. 33, Issue 1 https://doi.org/10.1016/j.proci.2010.08.004	journal	January 2011
A novel transient turbulent jet flame for studying turbulent combustion Wang, Haifeng; Juddoo, Mrinal; Starner, Sten H. Proceedings of the Combustion Institute, Vol. 34, Issue 1 https://doi.org/10.1016/j.proci.2012.06.021	journal	January 2013
LES of a methanol spray flame with a stochastic sub-grid model Jones, W. P.; Marquis, A. J.; Noh, D. Proceedings of the Combustion Institute, Vol. 35, Issue 2 https://doi.org/10.1016/j.proci.2014.06.086	journal	January 2015
A unified view of pilot stabilized turbulent jet flames for model assessment across different combustion regimes Wang, Haifeng; Zhang, Pei Proceedings of the Combustion Institute, Vol. 36, Issue 2 https://doi.org/10.1016/j.proci.2016.06.008	journal	January 2017
Large-scale structure and entrainment in the supersonic mixing layer Clemens, N. T.; Mungal, M. G. Journal of Fluid Mechanics, Vol. 284 https://doi.org/10.1017/S0022112095000310	journal	February 1995
Linear eddy modeling of turbulent combustion McMurtry, P. A.; Menon, S.; Kerstein, A. R. Energy & Fuels, Vol. 7, Issue 6 https://doi.org/10.1021/ef00042a018	journal	November 1993
Coupling between hydrodynamics, acoustics, and heat release in a self-excited unstable combustor Harvazinski, Matthew E.; Huang, Cheng; Sankaran, Venkateswaran Physics of Fluids, Vol. 27, Issue 4 https://doi.org/10.1063/1.4916673	journal	April 2015
Consistency and convergence of Eulerian Monte Carlo field method for solving transported probability density function equation in turbulence modeling Wang, Haifeng; Zhang, Pei; Pant, Tejas Physics of Fluids, Vol. 30, Issue 11 https://doi.org/10.1063/1.5053098	journal	November 2018
Direct, high resolution, four‐dimensional measurements of the fine scale structure of Sc≫1 molecular mixing in turbulent flows Dahm, Werner J. A.; Southerland, Kenneth B.; Buch, Kenneth A. Physics of Fluids A: Fluid Dynamics, Vol. 3, Issue 5 https://doi.org/10.1063/1.858093	journal	May 1991
Direct numerical simulations of the turbulent mixing of a passive scalar Eswaran, V.; Pope, S. B. Physics of Fluids, Vol. 31, Issue 3 https://doi.org/10.1063/1.866832	journal	January 1988
Scalar measurements in compressible axisymmetric mixing layers Clemens, N. T.; Paul, P. H. Physics of Fluids, Vol. 7, Issue 5 https://doi.org/10.1063/1.868761	journal	May 1995
Application of PDF methods to compressible turbulent flows Delarue, B. J.; Pope, S. B. Physics of Fluids, Vol. 9, Issue 9 https://doi.org/10.1063/1.869382	journal	September 1997
Calculations of subsonic and supersonic turbulent reacting mixing layers using probability density function methods Delarue, B. J.; Pope, S. B. Physics of Fluids, Vol. 10, Issue 2 https://doi.org/10.1063/1.869536	journal	February 1998
A thickened flame model for large eddy simulations of turbulent premixed combustion Colin, O.; Ducros, F.; Veynante, D. Physics of Fluids, Vol. 12, Issue 7 https://doi.org/10.1063/1.870436	journal	July 2000
The Eddy Dissipation Turbulence Energy Cascade Model ErtesvÅG, Ivar S.; Magnussen, BjØRn F. Combustion Science and Technology, Vol. 159, Issue 1 https://doi.org/10.1080/00102200008935784	journal	October 2000
Modelling of Premixed Laminar Flames using Flamelet-Generated Manifolds Oijen, J. A. Van; Goey, L. P. H. De Combustion Science and Technology, Vol. 161, Issue 1 https://doi.org/10.1080/00102200008935814	journal	December 2000
Simplified Reaction Mechanisms for the Oxidation of Hydrocarbon Fuels in Flames Westbrook, Charles K.; Dryer, Frederick L. Combustion Science and Technology, Vol. 27, Issue 1-2 https://doi.org/10.1080/00102208108946970	journal	December 1981
Comparisons of Lagrangian and Eulerian PDF methods in simulations of non-premixed turbulent jet flames with moderate-to-strong turbulence-chemistry interactions Jaishree, J.; Haworth, D. C. Combustion Theory and Modelling, Vol. 16, Issue 3 https://doi.org/10.1080/13647830.2011.633349	journal	June 2012
Computational study of lean premixed turbulent flames using RANSPDF and LESPDF methods Rowinski, David H.; Pope, Stephen B. Combustion Theory and Modelling, Vol. 17, Issue 4 https://doi.org/10.1080/13647830.2013.789929	journal	August 2013
Effects of fuel cetane number on the structure of diesel spray combustion: An accelerated Eulerian stochastic fields method Jangi, Mehdi; Lucchini, Tommaso; Gong, Cheng Combustion Theory and Modelling, Vol. 19, Issue 5 https://doi.org/10.1080/13647830.2015.1057234	journal	July 2015
Diesel flame lift-off stabilization in the presence of laser-ignition: a numerical study Gong, Cheng; Jangi, Mehdi; Bai, Xue-Song Combustion Theory and Modelling, Vol. 19, Issue 6 https://doi.org/10.1080/13647830.2015.1077997	journal	September 2015
Stochastic Eulerian field method for radiative heat transfer in a propane oxygen-enhanced turbulent diffusion flame Nmira, Fatiha; Burot, Daria; Consalvi, Jean-Louis Combustion Theory and Modelling, Vol. 21, Issue 1 https://doi.org/10.1080/13647830.2016.1211740	journal	August 2016
Studies of the flow and turbulence fields in a turbulent pulsed jet flame using LES/PDF Zhang, Pei; Masri, Assaad R.; Wang, Haifeng Combustion Theory and Modelling, Vol. 21, Issue 5 https://doi.org/10.1080/13647830.2017.1312546	journal	April 2017
Eulerian transported probability density function sub-filter model for large-eddy simulations of turbulent combustion Raman, Venkatramanan; Pitsch, Heinz; Fox, Rodney O. Combustion Theory and Modelling, Vol. 10, Issue 3 https://doi.org/10.1080/13647830500460474	journal	June 2006
Lagrangian investigation of local extinction, re-ignition and auto-ignition in turbulent flames Wang, Haifeng; Pope, Stephen B. Combustion Theory and Modelling, Vol. 12, Issue 5 https://doi.org/10.1080/13647830802056137	journal	September 2008
Compressibility Effects on Turbulence Lele, Sanjiva K. Annual Review of Fluid Mechanics, Vol. 26, Issue 1 https://doi.org/10.1146/annurev.fl.26.010194.001235	journal	January 1994
Formulation of the k-w Turbulence Model Revisited Wilcox, David C. AIAA Journal, Vol. 46, Issue 11 https://doi.org/10.2514/1.36541	journal	November 2008
Approaches for Comparing Numerical Simulation of Combustion Instability and Flame Imaging Hardi, Justin S.; Zach Hallum, W.; Huang, Cheng Journal of Propulsion and Power, Vol. 32, Issue 2 https://doi.org/10.2514/1.B35780	journal	March 2016
Compressible Scalar Filtered Mass Density Function Model for High-Speed Turbulent Flows Banaeizadeh, Araz; Li, Zhaorui; Jaberi, Farhad A. AIAA Journal, Vol. 49, Issue 10 https://doi.org/10.2514/1.J050779	journal	October 2011
Probability density function approach for multidimensional turbulentflow calculations with application to in-cylinder flows in reciprocating engines Haworth, Daniel C.; El Tahry, Sherif H. AIAA Journal, Vol. 29, Issue 2 https://doi.org/10.2514/3.10566	journal	February 1991
Experimental study of compressible turbulent mixing layers Goebel, Steven G.; Dutton, J. Craig AIAA Journal, Vol. 29, Issue 4 https://doi.org/10.2514/3.10617	journal	April 1991
Probability density function approach for compressible turbulent reacting flows Hsu, A. T.; Tsai, Y. -L. P.; Raju, M. S. AIAA Journal, Vol. 32, Issue 7 https://doi.org/10.2514/3.12209	journal	July 1994
Influence of Chemical Kinetics and Unmixedness on Burning in Supersonic Hydrogen Flames Evans, John S.; Schexnayder, Charles J. AIAA Journal, Vol. 18, Issue 2 https://doi.org/10.2514/3.50747	journal	February 1980
Conditional sampling of velocity in a turbulent nonpremixed propane jet Schefer, R. W.; Hartmann, V.; Dibble, R. W. AIAA Journal, Vol. 25, Issue 10 https://doi.org/10.2514/3.9786	journal	October 1987
Stochastic fields method for sub-grid scale emission heterogeneity in mesoscale atmospheric dispersion models Cassiani, M.; Vinuesa, J. F.; Galmarini, S. Atmospheric Chemistry and Physics, Vol. 10, Issue 1 https://doi.org/10.5194/acp-10-267-2010	journal	January 2010

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