A new particle-like method for high-speed flows with chemical non-equilibrium

Guzzo, Fábio Rodrigues; Azevedo, João Luiz F.

doi:10.5028/jatm.2010.02011732

Abstract:

The present work is concerned with the numerical simulation of hypersonic blunt body flows with chemical non-equilibrium. New theoretical and numerical formulations for coupling the chemical reaction to the fluid dynamics are presented and validated. The fluid dynamics is defined for a stationary unstructured mesh and the chemical reaction process is defined for "finite quantities" moving through the stationary mesh. The fluid dynamics is modeled by the Euler equations and the chemical reaction rates by the Arrhenius law. Ideal gases are considered. The thermodynamical data are based on JANNAF tables and Burcat's database. The algorithm proposed by Liou, known as AUSM+, is implemented in a cell-centered based finite volume method and in an unstructured mesh context. Multidimensional limited MUSCL interpolation method is used to perform property reconstructions and to achieve second-order accuracy in space. The minmod limiter is used. The second order accuracy, five stage, Runge-Kutta time-stepping scheme is employed to perform the time march for the fluid dynamics. The numerical code VODE, which is part of the CHEMKIN-II package, is adopted to perform the time integration for the chemical reaction equations. The freestream reacting fluid is composed of H₂ and air at the stoichiometric ratio. The emphasis of the present paper is on the description of the new methodology for handling the coupling of chemical and fluid mechanic processes, and its validation by comparison with the standard time-splitting procedure. The configurations considered are the hypersonic flow over a wedge, in which the oblique detonation wave is induced by an oblique shock wave, and the hypersonic flow over a blunt body. Differences between the solutions obtained with each formulation are presented and discussed, including the effects of grid refinement in each case. The primary objective of such comparisons is the validation of the proposed methodology. Moreover, for the hypersonic flow over a blunt body, solutions obtained for two meshes are shown, compared and analyzed. The numerical solutions are also compared with experimental data.

Keywords:
Hypersonic flows; Numerical simulations; Chemical non-equilibrium; Supersonic combustion; CFD

Full text is available only in PDF.

REFERENCES

Ahuja, J.K., and Tiwari, S.N., 1994, "A Parametric Study of Shock-Induced Combustion in a Hydrogen-Air System", AIAA Paper Nº94-0674, 32nd Aerospace Science Meeting and Exhibit, Reno, NV.
Ahuja, J.K., Tiwari, S.N., and Singh, D.J., 1992, "Investigation of Hypersonic Shock-Induced Combustion in a Hydrogen-Air System", AIAA Paper Nº92-0339, 30th AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV.
Anon, 1970, "JANNAF: Thermochemical Tables", Dow Chemical Co., Midland, Michigan.
Azevedo, J.L.F., and Figueira da Silva, L.F., 1997, "The Development of an Unstructured Grid Solver for Reactive Compressible Flow Applications", AIAA Paper Nº97-3239, 33rd AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, Seattle, WA.
Azevedo, J.L.F., Figueira da Silva, L.F., and Strauss, D., 2010, "Order of Accuracy Study of Unstructured Grid Finite Volume Upwind Schemes," to appear in the Journal of the Brazilian Society of Mechanical Sciences and Engineering.
Azevedo, J.L.F., and Korzenowski, H. , 1998, "Comparison of Unstructured Grid Finite Volume Methods for Cold Gas Hypersonic Flow Simulations", AIAA Paper Nº98-2629, Proceedings of the 16th AIAA Applied Aerodynamics Conference, Albuquerque, NM, pp. 447-463.
Balakrishnan, G., and Williams, F.A., 1993, "Turbulent Combustion Regimes for Hypersonic Propulsion Employing Hydrogen-Air Diffusion Flames", Journal of Propulsion and Power, Vol. 10, N. 3, pp. 434-436.
Burcat, A., 1984, "Thermochemical Data for Combustion Calculations", Combustion Chemistry, W.C. Gardiner, Ed., Springer-Verlag, New York.
Byrne, G.D., and Dean, A.M., 1993, "The Numerical Solution of Some Kinetics Models with VODE and CHEMKIN II", Computers Chem., Vol. 17, N. 3, pp. 297-302.
Ess, P.R., and Allen, C.B., 2005, "Parallel Computation of Two-Dimensional Laminar Inert and Chemically Reactive Multi-Species Gas Flows", International Journal for Numerical Methods in Heat & Fluid Flow, Vol. 15, N. 3, pp. 228-256.
Figueira da Silva, L.F., Azevedo, J.L.F., and Korzenowsk, H., 1999, "On the Development of an Unstructured Grid Solver for Inert and Reactive High Speed Flow Simulations", Journal of the Brazilian Society of Mechanical Sciences and Engineering, Vol. 21, N. 4, pp. 564-579.
Figueira da Silva, L.F., Azevedo, J.L.F., and Korzenowski, H., 2000, "Unstructured Adaptive Grid Flow Simulations of Inert and Reactive Gas Mixture", Journal of Computational Physics, Vol. 160, N. 2, pp. 522-540.
Guzzo, F.R., 2003, "Analysis and Simulation of Hypersonic Flows in Chemical Non-Equilibrium Conditions", Graduation Project, Instituto Tecnológico de Aeronáutica, São José dos Campos, SP (in Portuguese, original title is "Análise e Simulação de Escoamentos Hipersônicos em Condição de Não Equilíbrio Químico").
Guzzo, F.R., 2006, "Analysis and Simulation of the Combustion Induced by Projectiles at Hypersonic Speeds" ,Master Thesis, Instituto Tecnológico de Aeronáutica, São José dos Campos, SP (in Portuguese, original title is "Análise e Simulação da Combustão Induzida por Projéteis em Velocidades Hipersônicas").
Guzzo, F.R. and Azevedo, J.L.F., 2006, "Mesh Topology Influence on Supersonic Blunt Body Flow Simulations", Proceedings of the 11th Brazilian Congress of Thermal Sciences and Engineering - ENCIT 2006, Paper CIT06-0474, Curitiba, PR.
Hirsch, C., 1988, Numerical Computational of Internal and External Flows, Vol. 2, Wiley, New York.
Kee, R.J., Rupley, F.M., and Miller, J.A., 1991, "CHEMKIN-II: A Fortran Chemical Kinetics Package for the Analysis of Gas Phase Chemical Kinetics", Sandia National Laboratories, Technical Rep. SAND86-8009B/UC-706.
Korzenowski, H., 1998, "Unstructured Grid Techniques for the Simulation of High Mach Number Flows", Ph.D. Thesis, Instituto Tecnológico de Aeronáutica, São José dos Campos, SP (in Portuguese, original title is "Técnicas em Malhas Não Estruturadas para Simulação de Escoamentos a Altos Números de Mach").
Lee, S., and Deiwert, G.S., 1989, "Calculation of Nonequilibrium Hydrogen-Air Reactions with Implicit Flux Vector Splitting Method", AIAA Paper Nº89-1700, 24th AIAA Thermophysics Conference, Buffalo, NY.
Lehr, H.F., 1972, "Experiments on Shock-Induced Combustion", Astronautica Acta, Vol. 17, N. 4 & 5, pp. 589-597.
Liou, M.S., 1994, "A Continuing Search for a Near-Perfect Numerical Flux Scheme. Part I: AUSM+", NASA TM-106524, NASA Lewis Research Center, Cleveland, OH.
Liou, M.S., 1996, "A Sequel to AUSM: AUSM+", Journal of Computation Physics, Vol. 129, N. 2, pp. 364-382.
Matsuo, A., and Fujiwara, T., 1991, "Numerical Simulation of Shock-Induced Combustion around an Axisymmetric Blunt Body", AIAA Paper Nº91-1414, 26th AIAA Thermophysics Conference, Honolulu, HI.
Matsuo, A., Fujii, K. and Fujiwara, T., 1995, "Flow Features of Shock-Induced Combustion Around Projectile Traveling at Hypervelocities", AIAA Journal, Vol. 33, N. 6, pp. 1056-1063.
Mavriplis, D.J., 1988, "Multigrid Solution of the Two-Dimensional Euler Equations on Unstructured Triangular Meshes", AIAA Journal, Vol. 26, N. 7, pp. 824-831.
Mavriplis, D.J., 1990, "Accurate Multigrid Solution of the Euler Equations on Unstructured and Adaptive Meshes", AIAA Journal, Vol. 28, N. 2, pp. 213-221.
Pimentel, C.A.R., 2000, "Numerical Study of the Transition Between a Wedge-Stabilized Oblique Shock Wave and an Oblique Detonation Wave", Ph.D. Thesis, Instituto Tecnológico de Aeronáutica, São José dos Campos, SP (in Portuguese, original title is "Estudo Numérico da Transição entre uma Onda de Choque Oblíqua Estabilizada por um Diedro e uma Onda de Detonação Oblíqua").
Pimentel, C.A.R., Azevedo, J.L.F., Figueira da Silva, L.F., and Deshaies, B., 2002, "Numerical Study of Wedge Supported Oblique Shock Wave-Oblique Detonation Wave Transitions", Journal of the Brazilian Society of Mechanical Sciences, Vol. 24, N. 3, pp. 149-157.
Sarma, G.S.R., 2000, "Physico-Chemical Modelling in Hypersonic Flow Simulation", Progress in Aerospace Science, Vol. 36, N. 3, pp. 281-349.
Singh, D.J., Ahuja, J.K., and Carpenter M.H., 1992, "Numerical Simulation of Shock-Induced Combustion/Detonation", Symposium on High-Performance Computing for Flight Vehicles, Washington, D.C.
Strang, G., 1968, "On the Construction and Comparison of Difference Schemes", SIAM J. Num. Anal., Vol. 5, pp. 506-517.
Sussman, A.M., and Wilson, G.J., 1991, "Computation of Chemically Reacting Flow Using a Logarithmic Form of the Species Conservation Equations", Proceedings of the 4th International Conference on Numerical Combustion, Tampa, FL, pp. 224-227.
van Leer, B., 1979, "Towards the Ultimate Conservative Difference Scheme. V. A Second-Order Sequel to Godunov's Method", Journal of Computational Physics, Vol. 32, N. 1, pp. 101-136.
Wilson, G.J., and MacCormack, R.W., 1990, "Modeling Supersonic Combustion Using a Fully-Implicit Numerical Method", AIAA Paper Nº90-2307, 26th AIAA/ASME/SAE/ASEE Joint Propulsion Conference, Orlando, FL.
Wilson, G.J., and MacCormack, R.W., 1992, "Modeling Supersonic Combustion Using a Fully-Implicit Numerical Method", AIAA Journal, Vol. 30, N. 4, pp. 1008-1015.
Wilson, G.J., and Sussman, M.A., 1993, "Computation of Unsteady Shock-Induced Combustion Using Logarithmic Species Conservation Equations", AIAA Journal, Vol. 31, N. 2, pp. 294-301.
Yungster, S., Eberhardt, S., and Bruckner, A.P., 1989, "Numerical Simulation of Shock-Induced Combustion Generated by High-Speed Projectiles in Detonable Gas Mixtures", AIAA Paper Nº89-0673, 27th Aerospace Sciences Meeting and Exhibit, Reno, NV.

Publication Dates

Publication in this collection
Jan-Apr 2010

History

Received
11 Sept 2009
Accepted
19 Dec 2009

This is an Open Access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

[1] Ahuja, J.K., and Tiwari, S.N., 1994, "A Parametric Study of Shock-Induced Combustion in a Hydrogen-Air System", AIAA Paper Nº94-0674, 32nd Aerospace Science Meeting and Exhibit, Reno, NV.

[2] Ahuja, J.K., Tiwari, S.N., and Singh, D.J., 1992, "Investigation of Hypersonic Shock-Induced Combustion in a Hydrogen-Air System", AIAA Paper Nº92-0339, 30th AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV.

[3] Anon, 1970, "JANNAF: Thermochemical Tables", Dow Chemical Co., Midland, Michigan.

[4] Azevedo, J.L.F., and Figueira da Silva, L.F., 1997, "The Development of an Unstructured Grid Solver for Reactive Compressible Flow Applications", AIAA Paper Nº97-3239, 33rd AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, Seattle, WA.

[5] Azevedo, J.L.F., Figueira da Silva, L.F., and Strauss, D., 2010, "Order of Accuracy Study of Unstructured Grid Finite Volume Upwind Schemes," to appear in the Journal of the Brazilian Society of Mechanical Sciences and Engineering.

[6] Azevedo, J.L.F., and Korzenowski, H. , 1998, "Comparison of Unstructured Grid Finite Volume Methods for Cold Gas Hypersonic Flow Simulations", AIAA Paper Nº98-2629, Proceedings of the 16th AIAA Applied Aerodynamics Conference, Albuquerque, NM, pp. 447-463.

[7] Balakrishnan, G., and Williams, F.A., 1993, "Turbulent Combustion Regimes for Hypersonic Propulsion Employing Hydrogen-Air Diffusion Flames", Journal of Propulsion and Power, Vol. 10, N. 3, pp. 434-436.

[8] Burcat, A., 1984, "Thermochemical Data for Combustion Calculations", Combustion Chemistry, W.C. Gardiner, Ed., Springer-Verlag, New York.

[9] Byrne, G.D., and Dean, A.M., 1993, "The Numerical Solution of Some Kinetics Models with VODE and CHEMKIN II", Computers Chem., Vol. 17, N. 3, pp. 297-302.

[10] Ess, P.R., and Allen, C.B., 2005, "Parallel Computation of Two-Dimensional Laminar Inert and Chemically Reactive Multi-Species Gas Flows", International Journal for Numerical Methods in Heat & Fluid Flow, Vol. 15, N. 3, pp. 228-256.

[11] Figueira da Silva, L.F., Azevedo, J.L.F., and Korzenowsk, H., 1999, "On the Development of an Unstructured Grid Solver for Inert and Reactive High Speed Flow Simulations", Journal of the Brazilian Society of Mechanical Sciences and Engineering, Vol. 21, N. 4, pp. 564-579.

[12] Figueira da Silva, L.F., Azevedo, J.L.F., and Korzenowski, H., 2000, "Unstructured Adaptive Grid Flow Simulations of Inert and Reactive Gas Mixture", Journal of Computational Physics, Vol. 160, N. 2, pp. 522-540.

[13] Guzzo, F.R., 2003, "Analysis and Simulation of Hypersonic Flows in Chemical Non-Equilibrium Conditions", Graduation Project, Instituto Tecnológico de Aeronáutica, São José dos Campos, SP (in Portuguese, original title is "Análise e Simulação de Escoamentos Hipersônicos em Condição de Não Equilíbrio Químico").

[14] Guzzo, F.R., 2006, "Analysis and Simulation of the Combustion Induced by Projectiles at Hypersonic Speeds" ,Master Thesis, Instituto Tecnológico de Aeronáutica, São José dos Campos, SP (in Portuguese, original title is "Análise e Simulação da Combustão Induzida por Projéteis em Velocidades Hipersônicas").

[15] Guzzo, F.R. and Azevedo, J.L.F., 2006, "Mesh Topology Influence on Supersonic Blunt Body Flow Simulations", Proceedings of the 11th Brazilian Congress of Thermal Sciences and Engineering - ENCIT 2006, Paper CIT06-0474, Curitiba, PR.

[16] Hirsch, C., 1988, Numerical Computational of Internal and External Flows, Vol. 2, Wiley, New York.

[17] Kee, R.J., Rupley, F.M., and Miller, J.A., 1991, "CHEMKIN-II: A Fortran Chemical Kinetics Package for the Analysis of Gas Phase Chemical Kinetics", Sandia National Laboratories, Technical Rep. SAND86-8009B/UC-706.

[18] Korzenowski, H., 1998, "Unstructured Grid Techniques for the Simulation of High Mach Number Flows", Ph.D. Thesis, Instituto Tecnológico de Aeronáutica, São José dos Campos, SP (in Portuguese, original title is "Técnicas em Malhas Não Estruturadas para Simulação de Escoamentos a Altos Números de Mach").

[19] Lee, S., and Deiwert, G.S., 1989, "Calculation of Nonequilibrium Hydrogen-Air Reactions with Implicit Flux Vector Splitting Method", AIAA Paper Nº89-1700, 24th AIAA Thermophysics Conference, Buffalo, NY.

[20] Lehr, H.F., 1972, "Experiments on Shock-Induced Combustion", Astronautica Acta, Vol. 17, N. 4 & 5, pp. 589-597.

[21] Liou, M.S., 1994, "A Continuing Search for a Near-Perfect Numerical Flux Scheme. Part I: AUSM+", NASA TM-106524, NASA Lewis Research Center, Cleveland, OH.

[22] Liou, M.S., 1996, "A Sequel to AUSM: AUSM+", Journal of Computation Physics, Vol. 129, N. 2, pp. 364-382.

[23] Matsuo, A., and Fujiwara, T., 1991, "Numerical Simulation of Shock-Induced Combustion around an Axisymmetric Blunt Body", AIAA Paper Nº91-1414, 26th AIAA Thermophysics Conference, Honolulu, HI.

[24] Matsuo, A., Fujii, K. and Fujiwara, T., 1995, "Flow Features of Shock-Induced Combustion Around Projectile Traveling at Hypervelocities", AIAA Journal, Vol. 33, N. 6, pp. 1056-1063.

[25] Mavriplis, D.J., 1988, "Multigrid Solution of the Two-Dimensional Euler Equations on Unstructured Triangular Meshes", AIAA Journal, Vol. 26, N. 7, pp. 824-831.

[26] Mavriplis, D.J., 1990, "Accurate Multigrid Solution of the Euler Equations on Unstructured and Adaptive Meshes", AIAA Journal, Vol. 28, N. 2, pp. 213-221.

[27] Pimentel, C.A.R., 2000, "Numerical Study of the Transition Between a Wedge-Stabilized Oblique Shock Wave and an Oblique Detonation Wave", Ph.D. Thesis, Instituto Tecnológico de Aeronáutica, São José dos Campos, SP (in Portuguese, original title is "Estudo Numérico da Transição entre uma Onda de Choque Oblíqua Estabilizada por um Diedro e uma Onda de Detonação Oblíqua").

[28] Pimentel, C.A.R., Azevedo, J.L.F., Figueira da Silva, L.F., and Deshaies, B., 2002, "Numerical Study of Wedge Supported Oblique Shock Wave-Oblique Detonation Wave Transitions", Journal of the Brazilian Society of Mechanical Sciences, Vol. 24, N. 3, pp. 149-157.

[29] Sarma, G.S.R., 2000, "Physico-Chemical Modelling in Hypersonic Flow Simulation", Progress in Aerospace Science, Vol. 36, N. 3, pp. 281-349.

[30] Singh, D.J., Ahuja, J.K., and Carpenter M.H., 1992, "Numerical Simulation of Shock-Induced Combustion/Detonation", Symposium on High-Performance Computing for Flight Vehicles, Washington, D.C.

[31] Strang, G., 1968, "On the Construction and Comparison of Difference Schemes", SIAM J. Num. Anal., Vol. 5, pp. 506-517.

[32] Sussman, A.M., and Wilson, G.J., 1991, "Computation of Chemically Reacting Flow Using a Logarithmic Form of the Species Conservation Equations", Proceedings of the 4th International Conference on Numerical Combustion, Tampa, FL, pp. 224-227.

[33] van Leer, B., 1979, "Towards the Ultimate Conservative Difference Scheme. V. A Second-Order Sequel to Godunov's Method", Journal of Computational Physics, Vol. 32, N. 1, pp. 101-136.

[34] Wilson, G.J., and MacCormack, R.W., 1990, "Modeling Supersonic Combustion Using a Fully-Implicit Numerical Method", AIAA Paper Nº90-2307, 26th AIAA/ASME/SAE/ASEE Joint Propulsion Conference, Orlando, FL.

[35] Wilson, G.J., and MacCormack, R.W., 1992, "Modeling Supersonic Combustion Using a Fully-Implicit Numerical Method", AIAA Journal, Vol. 30, N. 4, pp. 1008-1015.

[36] Wilson, G.J., and Sussman, M.A., 1993, "Computation of Unsteady Shock-Induced Combustion Using Logarithmic Species Conservation Equations", AIAA Journal, Vol. 31, N. 2, pp. 294-301.

[37] Yungster, S., Eberhardt, S., and Bruckner, A.P., 1989, "Numerical Simulation of Shock-Induced Combustion Generated by High-Speed Projectiles in Detonable Gas Mixtures", AIAA Paper Nº89-0673, 27th Aerospace Sciences Meeting and Exhibit, Reno, NV.

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