C. Figure, Monitoring points at different locations in the computational domain showing that the steady state solution has been achieved. i.e., presented here are the Temperature and velocity (Top, V 0 = 1120 m/s , Bottom, 1829.

]. A. Hertzberg, D. W. Bruckner, and . Bogdanoff, The ram accelerator: A new chemical method of achieving ultra-high velocities, 1986.

A. Hertzberg, A. Bruckner, D. Bogdanoff, and C. Knowlen, The ram accelerator and its applications-A new approach for reaching ultrahigh velocities, 16th International Symposium of Shock tubes and waves, pp.117-128, 1988.

A. Hertzberg, Thermodynamics of the ram accelerator, AIP Conference Proceedings, pp.2-11, 1990.
DOI : 10.1063/1.39414

C. Knowlen, A. Bruckner, D. Bogdanoff, and A. Hertzberg, Performance capabilities of the ram accelerator, AIAA paper, pp.87-2152, 1987.

A. Bruckner, C. Knowlen, K. Scott, and A. Hertzberg, High-velocity modes of the thermally choked ram accelerator, 24th Joint Propulsion Conference, 1988.
DOI : 10.2514/6.1988-2925

A. Hertzberg, A. Bruckner, and C. Knowlen, Experimental investigation of ram accelerator propulsion modes, Shock Waves, vol.26, issue.1, pp.17-25, 1991.
DOI : 10.1007/BF01414864

A. Hertzberg, E. Burnham, and J. Hinkey, Recent advances in ram accelerator technology. Combustion in High Speed Flows, pp.309-342, 1994.

C. Knowlen, A. Bruckner, and A. Hertzberg, Internal Ballistics of the Ram Accelerator, 13th International Symposium on Ballistics, pp.1-3, 1992.

C. Knowlen and A. P. Bruckner, Direct space launch using ram accelerator technology, AIP Conference Proceedings, p.583, 2001.
DOI : 10.1063/1.1357980

A. Kull, E. Burnham, C. Knowlen, A. Bruckner, and A. Hertzberg, Experimental studies of superdetonative ram accelerator modes, 25th Joint Propulsion Conference, 1996.
DOI : 10.2514/6.1989-2632

C. C. Knowlen, Theoretical and Experimental Investigation of the Thermodynamics of the Ram Accelerator in the Thermally Choked Mode, 1991.

G. Chew, C. Knowlen, E. Burnham, A. Hertzberg, and A. Bruckner, Experiments on Hypersonic Ramjet Propulsion Cycles up to M=8.5 Using a Ram Accelerator, 1991.

D. Brackett and D. W. Bogdanoff, Computational investigation of oblique detonation ramjet-in-tube concepts, Journal of Propulsion and Power, vol.5, issue.3, pp.276-281, 1989.

S. Yungster, S. Eberhardt, and A. Bruckner, Numerical simulation of shockinduced combustion generated by high-speed projectiles in detonable gas mixtures, pp.89-0673, 1989.

S. Yungster and A. Bruckner, Computational studies of a superdetonative ram accelerator mode, Journal of Propulsion and Power, vol.8, issue.2, pp.457-463, 1992.
DOI : 10.2514/3.23499

D. Bogdanoff, Ram accelerator direct space launch system - New concepts, Journal of Propulsion and Power, vol.8, issue.2, pp.481-490, 1992.
DOI : 10.2514/3.23502

A. Higgins, C. Knowlen, and A. Bruckner, An investigation of ram accelerator gas dynamic limits, 29th Joint Propulsion Conference and Exhibit, 1993.
DOI : 10.2514/6.1993-2181

A. Higgins, Comment on "Performance Limits for Projectile Flight in the Ram and External Propulsion Accelerators", Journal of Propulsion and Power, vol.15, issue.1, p.159, 1999.
DOI : 10.2514/2.5407

E. Burnham, A. Kull, C. Knowlen, A. Bruckner, and A. Hertzberg, Operation of the ram accelerator in the transdetonative velocity regime, 26th Joint Propulsion Conference, p.1990, 1990.
DOI : 10.2514/6.1990-1985

A. Bruckner, C. Knowlen, A. Hertzberg, and D. W. Bogdanoff, Operational characteristics of the thermally choked ram accelerator, Journal of Propulsion and Power, vol.7, issue.5, pp.828-836, 1991.
DOI : 10.2514/3.23398

A. Bruckner, E. Burnham, C. Knowlen, A. Hertzberg, and D. W. Bogdanoff, Initiation of combustion in the thermally choked ram accelerator, Shock waves; Proceedings of the 18th International Symposium, 1991.
DOI : 10.1007/978-3-642-77648-9_98

C. Knowlen, A. Higgins, A. Bruckner, and A. Hertzberg, In-Tube Photography of Ram Accelerator Projectiles, 19th International Symposium on Shock Waves, pp.189-194, 1993.
DOI : 10.1007/978-3-642-78829-1_30

C. Knowlen, A. Higgins, A. Bruckner, and W. Seattle, Aerothermodynamics of the ram accelerator, 33rd Aerospace Sciences Meeting and Exhibit, pp.95-0289, 1995.
DOI : 10.2514/6.1995-289

C. Knowlen, A. J. Higgins, A. Bruckner, and P. Bauer, Ram accelerator operation in the superdetonative velocity regime, 34th Aerospace Sciences Meeting and Exhibit, pp.96-0098, 1996.
DOI : 10.2514/6.1996-98

J. Elvander, C. Knowlen, and A. Bruckner, High velocity performance of the ram accelerator, 32nd Joint Propulsion Conference and Exhibit, pp.96-2675, 1996.
DOI : 10.2514/6.1996-2675

J. Elvander, C. Knowlen, and A. Bruckner, Recent results of high acceleration experiments in the University of Washington ram accelerator, 33rd Joint Propulsion Conference and Exhibit, pp.97-2650, 1997.
DOI : 10.2514/6.1997-2650

C. Bundy, C. Knowlen, and A. Bruckner, Elevated pressure experiments in a 38-mm bore ram accelerator, 34th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, pp.98-3144, 1998.
DOI : 10.2514/6.1998-3144

C. Bundy, C. Knowlen, and A. Bruckner, Ram accelerator operating characteristics at fill pressures greater than 10 MPa, 35th Joint Propulsion Conference and Exhibit, 1999.
DOI : 10.2514/6.1999-2261

C. Bundy, C. Knowlen, and A. Bruckner, Investigation of ram accelerator operation at fill pressures up to 20 MPa, 36th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, 2000.
DOI : 10.2514/6.2000-3231

C. Knowlen, C. Bundy, and A. Bruckner, Ram accelerator experiments leading to operation at fill pressures up to 20 MPa, 40th AIAA Aerospace Sciences Meeting & Exhibit, 2002.
DOI : 10.2514/6.2002-1015

C. Bundy, C. Knowlen, and A. Bruckner, Unsteady Effects on Ram Accelerator Operation at Elevated Fill Pressures, Journal of Propulsion and Power, vol.20, issue.5, pp.801-810, 2004.

C. Knowlen, A. J. Higgins, P. Harris, and A. P. Bruckner, Hypersonic Shock-Induced Combustion Propulsion, 47th AIAA Aerospace Sciences Meeting including The New Horizons Forum and Aerospace Exposition, 2009.
DOI : 10.2514/6.2009-715

M. Giraud, J. Legendre, G. Simon, and L. Catoire, Ram accelerator in 90 mm caliber. First results concerning the scale effect in the thermally choked propulsion mode, 13th International Symposium on Ballistics, 1992.

M. Giraud, J. Legendre, and G. Simon, Ram-accelerator in 90-mm-caliber or RAMAC 90: experimental results concerning the transdetonative combustion mode, 14th International Symposium on Ballistics, pp.95-104, 1993.

M. Giraud, J. Legendre, and G. Simon, Ram accelerator studies in 90 mm caliber, 43rd Meeting of the Aeroballistic Range Association

K. W. Naumann and A. P. Bruckner, Ram accelerator ballistic range concept for softly accelerating hypersonic free-flying models, Journal of Aircraft, vol.31, issue.6, pp.31-1310, 1994.
DOI : 10.2514/3.46652

F. Seiler, G. Patz, G. Smeets, and J. Srulijes, The 30-mm-Caliber Scram Accelerator RAMAC 30 of ISL, IUTAM Symposium on Combustion Supersonic Flows, pp.263-272, 1997.
DOI : 10.1007/978-94-011-5432-1_21

M. Giraud and H. Simon, Sabot for projectiles of RAM accelerators and projectiles equipped with such a sabot, In United States Patent, vol.394, issue.5, p.805, 1995.

M. Giraud, J. Legendre, and M. Henner, RAMAC in subdetonative propulsion mode: State of the ISL studies, pp.65-77
DOI : 10.1007/978-3-642-46876-6_5

J. Legendre, M. Giraud, and M. Henner, Ram-accelerator: A new hypervelocity launcher for ballistic studies, International Journal of Impact Engineering, vol.23, issue.1, pp.533-545, 1999.
DOI : 10.1016/S0734-743X(99)00102-5

J. Legendre and M. Giraud, Enhanced RAMAC performance in subdetonative propulsion mode with semi-combustible projectile, Le Journal de Physique IV, vol.10, issue.PR11, p.10, 2000.
DOI : 10.1051/jp4:20001103

J. Legendre, P. Bauer, and M. Giraud, Helium dilution for ram accelerator operation, Shock Waves, vol.11, issue.5, pp.361-367, 2002.
DOI : 10.1007/s001930100114

M. Henner, Initiation of reactive mixtures in a ram accelerator, 33rd Joint Propulsion Conference and Exhibit, 1998.
DOI : 10.2514/6.1997-3173

M. Henner, M. Giraud, J. Legendre, and C. Berner, Initiation of reactive mixtures in a ram accelerator, 33rd Joint Propulsion Conference and Exhibit, pp.97-3173, 1997.
DOI : 10.2514/6.1997-3173

M. Henner, ContributionàContributionà l'´ etude de l'´ effet d'´ echelle dans les mécanismes d'accélération par effet stato, 1998.

D. Kruczynski, Analysis of ram acceleration for high velocity applications, 27th Joint Propulsion Conference, 1991.
DOI : 10.2514/6.1991-2488

D. Kruczynski and M. J. Nusca, Experimental and computational investigation of scaling phenomena ina large caliber ram accelerator, 28th Joint Propulsion Conference and Exhibit, 1992.
DOI : 10.2514/6.1992-3245

D. Kruczynski, New experiments in a 120-mm ram accelerator at high pressures, 29th Joint Propulsion Conference and Exhibit, pp.93-2589, 1993.
DOI : 10.2514/6.1993-2589

D. Kruczynski, Experiments in a 120-mm Ram Accelerator, 14th International Symposium on Ballistics, pp.1993-9618156, 1993.

D. L. Kruczynski, F. Liberatore, and M. Kiwan, FLOW VISUALIZATION OF STEADY AND TRANSIENT COMBUSTION IN A 120-MM RAM ACCELERATOR, 30th Joint Propulsion Conference and Exhibit, 1994.
DOI : 10.2514/6.1994-3344

D. Kruczynski and F. Liberatore, Ram accelerator experiments with unique projectile geometries, 31st Joint Propulsion Conference and Exhibit, 1995.
DOI : 10.2514/6.1995-2490

D. Kruczynski and F. Liberatore, Experimental investigation of high pressure/performance ram accelerator operation, 32nd Joint Propulsion Conference and Exhibit, pp.96-2676, 1996.
DOI : 10.2514/6.1996-2676

D. L. Kruczynski, F. Liberatore, and M. J. Nusca, Experimental flow visualization for a large-scale ram accelerator, Journal of Propulsion and Power, vol.12, issue.1, pp.206-210, 1996.
DOI : 10.2514/3.24013

D. Kruczynski, High performance ram accelerator research, Ram Accelerators: Proceedings of the Third International Workshop on Ram Accelerators Sendai, Japan, pp.16-18, 1997.
DOI : 10.1007/978-3-642-46876-6_8

C. Knowlen and A. Bruckner, Hugoniot analysis of the ram accelerator. Shock waves, pp.617-622, 1991.

P. Bauer, C. Knowlen, and A. Bruckner, Real gas effects on the prediction of ram accelerator performance, Shock Waves, vol.8, issue.2, pp.113-118, 1998.
DOI : 10.1007/s001930050104

O. Brochet, H. N. Heuze, P. Presles, and C. Bauer, Equation of state for dense gases, Arch Comb, vol.5, pp.35-45, 1985.

P. Bauer and C. Knowlen, Compressibility effects of unreacted propellant on thermally choked ram accelerator performance, The European Physical Journal Applied Physics, vol.21, issue.3, pp.233-238, 2003.
DOI : 10.1051/epjap:2002119

P. Bauer, C. Knowlen, and A. Bruckner, One-dimensional modeling of ram accelerator at high acceleration rates in the subdetonative velocity regime, The European Physical Journal Applied Physics, vol.29, issue.3, pp.253-258, 2005.
DOI : 10.1051/epjap:2004225

P. Bauer, C. Knowlen, and A. Bruckner, Modeling Acceleration Effects on Ram Accelerator Thrust at High Pressure, Journal of Propulsion and Power, vol.21, issue.5, pp.955-958, 2005.
DOI : 10.2514/1.13473

S. Yungster and A. Bruckner, A numerical study of the ram accelerator concept in the superdetonative velocity range, 25th Joint Propulsion Conference, pp.89-2677, 1989.
DOI : 10.2514/6.1989-2677

S. Yungster, Numerical study of shock-wave/boundary-layer interactions in premixed combustible gases, AIAA Journal, vol.30, issue.10, pp.2379-2387, 1992.
DOI : 10.2514/3.11237

S. Yungster, Navier-Stokes simulation of the supersonic combustion flowfield in a ram accelerator, pp.91-1916, 1991.

S. Yungster and M. J. Rabinowitz, Computation of shock-induced combustion using a detailed methane-air mechanism, Journal of Propulsion and Power, vol.10, issue.5, pp.609-617, 1994.
DOI : 10.2514/3.23770

F. Liberatore, Ram Accelerator Performance Calculations Using a Modified Version of the NASA CET89 Equilibrium Chemistry Code, 1994.

S. Yungster and K. Radhakrishnan, Computational study of reacting flow establishment in expansion tube facilities, Shock Waves, vol.7, issue.6, pp.335-342, 1997.
DOI : 10.1007/s001930050088

M. J. Nusca, Numerical simulation of reacting flow in a thermally choked ram accelerator projectile launch system, 27th Joint Propulsion Conference, 1991.
DOI : 10.2514/6.1991-2490

M. J. Nusca, Numerical simulation of fluid dynamics with finite-rate and equilibrium combustion kinetics for the 120-mm ram accelerator, 29th Joint Propulsion Conference and Exhibit, 1993.
DOI : 10.2514/6.1993-2182

M. J. Nusca, Numerical Simulation of Gas Dynamics and Combustion for 120- mm Ram Accelerator, 14th International Symposium on Ballistics, pp.261-272

M. J. Nusca, Navier-Stokes Simulation of Fluid Dynamic and Combustion Phenomena in the RAM Accelerator, 28th JANNAF Combustion Meeting, CPIA publication

C. K. Westbrook and F. L. Dryer, Simplified Reaction Mechanisms for the Oxidation of Hydrocarbon Fuels in Flames, Combustion Science and Technology, vol.12, issue.1-2, pp.31-43, 1981.
DOI : 10.1080/00102208108946970

M. Nusca, Numerical simulation of ram accelerator performance including transient effects during initiation of combustion and sensitivity studies The 31 st JANNAF Combustion Subcommittee Meeting, Johns Hopkins Univ, 1994.

M. J. Nusca, Reacting flow simulation of transient, multi-stage ram accelerator operation and design studies, 31st Joint Propulsion Conference and Exhibit, 1995.
DOI : 10.2514/6.1995-2494

S. Yungster and K. Radhakrishnan, Computational study of flow establishment in hypersonic pulse facilities, 2nd International Workshop on Ram Accelerators, pp.17-20, 1995.

M. Soetrisno, S. Imlay, and D. Roberts, Numerical simulations of the superdetonative ram accelerator combusting flow field, 29th Joint Propulsion Conference and Exhibit, 1993.
DOI : 10.2514/6.1993-2185

M. Soetrisno and S. T. Imlay, Simulation of the flow field of a ram accelerator, 27th Joint Propulsion Conference
DOI : 10.2514/6.1991-1915

P. Bauer, M. Henner, and M. Giraud, Numerical investigation of the fin geometry of ram accelerator projectiles in subdetonative propulsion mode, The European Physical Journal Applied Physics, vol.23, issue.2
DOI : 10.1051/epjap:2003043

J. B. Hinkey-jr, A Experimental and Numerical Investigation of the Three- Dimensional Flow Field about a RAM Accelerator Projectile, 1994.

M. Henner, M. Giraud, J. Legendre, and C. Berner, CFD computations of steady and non-reactive flow around fin-guided ram projectiles, Ram Accelerators: Proceedings of the Third International Workshop on Ram Accelerators, p.325, 1997.
DOI : 10.1007/978-3-642-46876-6_32

P. Bauer, M. Henner, J. Legendre, and M. Giraud, Diameter effect in the initiation process of combustion in a ram accelerator in subdetonative mode, The European Physical Journal Applied Physics, vol.19, issue.3
DOI : 10.1051/epjap:2002065

C. Li, K. Kailasanath, E. Oran, J. Boris, and A. Landsberg, Numerical simulations of transient flows in ram accelerators, 29th Joint Propulsion Conference and Exhibit, 1993.
DOI : 10.2514/6.1993-1916

C. Li, K. Kailasanath, E. Oran, A. Landsberg, and J. Boris, Analysis of transient flows in thermally choked ram accelerators, 29th Joint Propulsion Conference and Exhibit, pp.93-2187, 1993.
DOI : 10.2514/6.1993-2187

S. Bhat, Computational Examination of Parameters Influencing Practicability of Ram Accelerator, Defence Science Journal, vol.54, issue.3, pp.259-270, 2004.
DOI : 10.14429/dsj.54.2039

K. W. Naumann, Heating and ablation of projectiles during acceleration in a ram accelerator tube, 29th Joint Propulsion Conference and Exhibit, 1993.
DOI : 10.2514/6.1993-2184

K. Sung, I. Jeung, F. Seiler, G. Patz, G. Smeets et al., Numerical Study on Effect of Projectile Shape Change by Ablation in RAMAC30, Proc. 21st ICDERS

E. L. Petersen, D. F. Davidson, and R. Hanson, Ignition delay times of ram accelerator mixtures, 32nd Joint Propulsion Conference and Exhibit, 1996.
DOI : 10.2514/6.1996-2681

M. J. Nusca and D. L. Kruczynski, Reacting flow simulation for the large scale ram accelerator, 30th Joint Propulsion Conference and Exhibit, pp.61-69, 1996.
DOI : 10.2514/6.1994-2963

M. J. Nusca, Investigation of ram accelerator flows for high pressure mixtures of various chemical compositions, 32nd Joint Propulsion Conference and Exhibit, pp.96-2946, 1996.
DOI : 10.2514/6.1996-2946

M. J. Nusca, Computational Simulation of the Ram Accelerator Using a Coupled CFD/Interior-Ballistics Approach, AIAA paper, pp.97-2653, 1997.

M. J. Nusca, Computational simulation of starting dynamics in a ram accelerator, 34th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, pp.98-3146, 1998.
DOI : 10.2514/6.1998-3146

C. Li and K. Kailasanath, Initiation Mechanism of Thermally Choked Combustion in Ram Accelerators, Journal of Propulsion and Power, vol.15, issue.1, 1999.
DOI : 10.2514/2.5404

S. Yungster, K. Radhakrishnan, and M. J. Rabinowitz, Reacting Flow Establishment in Ram Accelerators: A Numerical Study, Journal of Propulsion and Power, vol.14, issue.1, pp.10-17, 1998.
DOI : 10.2514/2.5259

J. Y. Choi, I. S. Jeung, and Y. Yoon, Numerical study of scram accelerator starting characteristics, pp.1029-1038, 1998.

J. Y. Choi, I. S. Jeung, and Y. Yoon, Unsteady simulation of model ram accelerator in expansion tube, 34th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, pp.98-3450, 1998.
DOI : 10.2514/6.1998-3450

J. Y. Choi, I. Jeung, and Y. Yoon, Scaling effect of the combustion induced by shock-wave boundary-layer interaction in premixed gas, Symposium International on Combustion, pp.2181-2188, 1998.
DOI : 10.1016/S0082-0784(98)80067-2

J. Y. Choi, I. S. Jeung, and Y. Yoon, Unsteady-State Simulation of Model Ram Accelerator in Expansion Tube, AIAA Journal, vol.37, issue.5, pp.537-543, 1999.
DOI : 10.2514/2.770

M. J. Nusca, Numerical Simulation of the Ram Accelerator Using a New Chemical Kinetics Mechanism, Journal of Propulsion and Power, vol.18, issue.1, pp.44-52, 2002.
DOI : 10.2514/2.5931

K. Takayama, P. Bauer, C. Knowlen, Y. Hamate, M. Giraud et al., Ram Accelerators : History, Principles, Performance and Applications, 55th Aeroballistic Range Association, 2004.
DOI : 10.1007/978-3-642-46876-6

O. Heuzé, Equations of state of detonation products: Influence of the repulsive intermolecular potential, Physical Review A, vol.34, issue.1, pp.428-432, 1986.
DOI : 10.1103/PhysRevA.34.428

P. Bauer, H. Presles, and M. Dunand, Detonation characteristics of gaseous methane-oxygen-nitrogen mixtures at extremely elevated initial pressures. Dynamics of detonations and explosions: Detonations, Astronautics and aeronautics, pp.56-62, 1991.

P. Bauer, J. Legendre, C. Knowlen, and A. Higgins, A review of detonation initiation techniques for insensitive dense methane-oxygen-nitrogen mixtures, The European Physical Journal Applied Physics, vol.2, issue.2
DOI : 10.1051/epjap:1998182

M. Champion and P. A. Libby, Turbulent Premixed Combustion in a Boundary Layer, Combustion Science and Technology, vol.4, issue.1, pp.267-291, 1984.
DOI : 10.1080/00102208408923776

R. Borghi and M. Champion, Modélisation et théorie des flammes. Editions Technip, 2000.

F. A. Williams, Combustion theory. Perseus Books, 1985.
URL : https://hal.archives-ouvertes.fr/hal-00014918

T. Poinsot and D. Veynante, Theoretical and numerical combustion, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00270731

T. Poinsot, T. Echekki, and M. G. Mungal, A Study of the Laminar Flame Tip and Implications for Premixed Turbulent Combustion, Combustion Science and Technology, vol.228, issue.1-3, pp.45-73, 1992.
DOI : 10.1016/0021-9991(82)90036-5

D. C. Wilcox, Turbulence modeling for CFD. DCW Industries, 1993.

F. Menter, Two-equation eddy-viscosity turbulence models for aerodynamic flows, pp.93-2906, 1993.

K. Bray, M. Champion, and P. A. Libby, Premixed Flames in Stagnating Turbulence Part II. The Mean Velocities and Pressure and the Damk??hler Number, Combustion and Flame, vol.112, issue.4, pp.635-653, 1998.
DOI : 10.1016/S0010-2180(97)00124-7

R. Gayed and D. Bradley, Criteria for turbulent propagation limits of premixed flames, Combustion and Flame, vol.62, issue.1, pp.61-68, 1985.
DOI : 10.1016/0010-2180(85)90093-8

R. Abdel-gayed, D. Bradley, and M. Lawes, Turbulent Burning Velocities: A General Correlation in Terms of Straining Rates, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.414, issue.1847, pp.389-413, 1987.
DOI : 10.1098/rspa.1987.0150

W. Jones and R. Lindstedt, Global reaction schemes for hydrocarbon combustion, Combustion and Flame, vol.73, issue.3, pp.233-249, 1988.
DOI : 10.1016/0010-2180(88)90021-1

D. Spalding, Thirteenth Symposium International on Combustion. The Combustion Institute, p.649, 1971.

H. Mason and D. Spalding, Prediction of reaction-rates in turbulent premixed boundary-layer flows, Combustion Institute, European Symposium, pp.601-606, 1973.

B. R. Magnussen, On the structure of turbulence and a generalized eddy dissipation concept for chemical reaction in turbulent flow, 19th Aerospace Sciences Meeting, 1981.
DOI : 10.2514/6.1981-42

B. Magnussen, The Eddy dissipation concept, XI Task Leaders Meeting- Energy Conservation in Combustion, IEA, 1989.

A. Gosman and P. Harvey, Computer Analysis of Fuel-Air Mixing and Combustion in an Axisymmetric D.I Diesel, SAE Technical Paper Series, pp.121-141, 1982.
DOI : 10.4271/820036

S. Pichon, G. Black, N. Chaumeix, M. Yahyaoui, J. Simmie et al., The combustion chemistry of a fuel tracer: Measured flame speeds and ignition delays and a detailed chemical kinetic model for the oxidation of acetone, Combustion and Flame, vol.156, issue.2, pp.494-504, 2009.
DOI : 10.1016/j.combustflame.2008.10.001

C. Varnavas and D. Assanis, Combustion Studies in a Diesel Engine Using a Multidimensional Engine Simulation, ASME, vol.91, issue.2, 1991.

L. Lebrere, F. Neveu, B. Dillies, and A. Ducamin, Direct injection Diesel engine simulation: A combined numerical and experimental approach from aerodynamics to combustion, 1997.

A. Harten, High Resolution Schemes for Hyperbolic Conservation Laws, Journal of Computational Physics, vol.135, issue.2, pp.260-278, 1997.
DOI : 10.1006/jcph.1997.5713

B. Van-leer, Upwind and High-Resolution Methods for Compressible Flow: From Donor Cell to Residual-Distribution Schemes, 16th AIAA Computational Fluid Dynamics Conference, pp.192-205, 2006.
DOI : 10.2514/6.2003-3559

B. Launder and D. Spalding, The numerical computation of turbulent flows Computer methods in applied mechanics and engineering, pp.269-289, 1990.

M. F. Modest, Radiative heat transfer, 2003.

M. P. Menguc and B. Webb, Radiative heat transfer. Coal science and technology, pp.375-431, 1993.
URL : https://hal.archives-ouvertes.fr/hal-01021893

R. Marshak, Note on the Spherical Harmonic Method As Applied to the Milne Problem for a Sphere, Physical Review, vol.71, issue.7, pp.443-446, 1947.
DOI : 10.1103/PhysRev.71.443

. Tromberg, Boundary conditions for the diffusion equation in radiative transfer, Journal of the Optical Society of America A, vol.11, issue.10, pp.2727-2741, 1994.

E. Petersen, D. Davidson, and R. Hanson, Ignition Delay Times of Ram Accelerator CH/O/Diluent Mixtures, Journal of Propulsion and Power, vol.15, issue.1, pp.82-91, 1999.
DOI : 10.2514/2.5394

M. J. Nusca, Numerical simulations of unsteady ram accelerator flow phenomena, Ram Accelerators: Proceedings of the Third International Workshop on Ram Accelerators Sendai, Japan, pp.16-18, 1997.
DOI : 10.1007/978-3-642-46876-6_30

R. S. Barlow, J. Chen, N. S. Smith, and R. W. Bilger, Nitric oxide formation in dilute hydrogen jet flames: isolation of the effects of radiation and turbulence-chemistry submodels, Combustion and Flame, vol.117, issue.1-2, pp.4-31
DOI : 10.1016/S0010-2180(98)00071-6

W. Grosshandler, RADCAL: A narrow-band model for radiation calculations in a combustion environment, NIST Technical Note, vol.1402, 1993.
DOI : 10.6028/NIST.TN.1402

A. Amaee and W. Byers, Review of Equastion of State of Fluids Valid to High Densities, 1992.

T. Bengherbia, Y. Yao, and P. Bauer, Computational Investigation of Transitional Viscous Flow over a Ram Accelerator Projectile in Sub-Detonative Propulsion Mode, 44th AIAA Aerospace Sciences Meeting and Exhibit, 2006.
DOI : 10.2514/6.2006-558

S. Li and F. Williams, Reaction Mechanisms for Methane Ignition, Journal of Engineering for Gas Turbines and Power, vol.124, issue.3, p.471, 2002.
DOI : 10.1115/1.1377871

P. L. Houston, Chemical kinetics and reaction dynamics, 2006.

J. Warnatz, U. Maas, and R. W. Dibble, Combustion: physical and chemical fundamentals, modeling and simulation, experiments, pollutant formation

H. K. Versteeg and W. Malalasekera, An introduction to computational fluid dynamics: the finite volume method, 2007.

F. El-mahallawy and S. E. Habik, Fundamentals and technology of combustion, 2002.

B. Magnussen, Modeling of NO x and soot formation by the Eddy Dissipation Concept, Int. Flame Research Foundation, 1st Topic Oriented Technical Meeting, pp.17-19, 1989.

D. Bradley, P. Gaskell, and X. J. Gu, Burning velocities, markstein lengths, and flame quenching for spherical methane-air flames: A computational study, Combustion and Flame, vol.104, issue.1-2, pp.176-198, 1996.
DOI : 10.1016/0010-2180(95)00115-8

J. Hinze, Turbulence, Journal of Applied Mechanics, vol.27, issue.3, 1975.
DOI : 10.1115/1.3644063

K. Bray, M. Champion, and P. A. Libby, Premixed flames in stagnating turbulence part IV: a new theory for the Reynolds stresses and Reynolds fluxes applied to impinging flows, Combustion and Flame, vol.120, issue.1-2, pp.1-18, 2000.
DOI : 10.1016/S0010-2180(99)00080-2

K. Bray, M. Champion, and P. A. Libby, Pre-mixed flames in stagnating turbulence, Combustion and Flame, vol.127, issue.1-2, pp.2023-2040, 2001.
DOI : 10.1016/S0010-2180(01)00304-2

P. Bailly, M. Champion, and D. Garreton, Counter-gradient diffusion in a confined turbulent premixed flame, Physics of Fluids, vol.9, issue.3, p.766, 1997.
DOI : 10.1063/1.869231