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Large-Eddy Simulations of the Mascotte Test Cases Operating at Supercritical Pressure

  • Thomas SchmittEmail author
Article

Abstract

Liquid rocket, Diesel or aircraft engines may operate in the transcritical regime. In such thermodynamic conditions, the classical phase change that occurs at subcritical pressure disappears and the mixing layer between the dense and cold jet and the outer gaseous stream is characterized by large variations of density and thermodynamic properties. Fluids show strong departure from a perfect gas behavior and a real-gas formulation is needed to model the fluid state. The extension of the unstructured AVBP solver, jointly developed by CERFACS and IFPEN, to handle high-pressure thermodynamics is presented in details. It is then validated on the experimental coaxial injectors studied with the Mascotte test rig from ONERA that operate in the transcritical range, namely the LOx/GH2 cases A60 and C60 and the LOx/GCH4 configuration G2. The flame pattern observed in experiments is properly recovered, hence validating the numerical strategy. Numerical results are then discussed focusing on the role of the momentum flux ratio on the development of transcritical flames.

Keywords

Large-Eddy Simulation Transcritical regime Turbulent combustion 

Notes

Acknowledgements

Support provided by ArianeGroup, the prime contractor of the Ariane launcher cryogenic propulsion system and CNES, the French National Space Agency, is gratefully acknowledged. The author also greatly acknowledge Robin Nez from EM2C, Bénédicte Cuenot and Gabriel Staffelbach from Cerfacs and Laurent Selle from IMFT for their contributions in the AVBP-RG project. This work was granted access to the HPC resources of IDRIS and CINES made available by GENCI (Grand Equipement National de Calcul Intensif) under the allocation A0042B06176. A part of this work was performed using HPC resources from the mesocentre computing center of Ecole CentraleSupélec and Ecole Normale Supérieure Paris-Saclay supported by CNRS and Région Ile-de-France.

Compliance with Ethical Standards

Conflict of interests

The author declares that he has no conflict of interest.

References

  1. 1.
    Poling, B.E., Prausnitz, J.M., O’Connel, J.P.: The Properties of Gases and Liquids, 5th edn. McGraw-Hill, New York (2001)Google Scholar
  2. 2.
    Oschwald, M., Smith, J.J., Branam, R., Hussong, J., Shick, A., Chehroudi, B., Talley, D.: Injection of fluids into supercritical environments. Combust. Sci. Technol. 178, 49 (2006)CrossRefGoogle Scholar
  3. 3.
    Segal, C., Polikhov, S.: Subcritical to supercritical mixing. Phys. Fluids 20, 052101 (2008)zbMATHCrossRefGoogle Scholar
  4. 4.
    Habiballah, M., Orain, M., Grisch, F., Vingert, L., Gicquel, P.: Experimental studies of high-pressure cryogenic flames on the Mascotte facility. Combust. Sci. Technol. 178(1), 101 (2006)CrossRefGoogle Scholar
  5. 5.
    Gaillard, P., Giovangigli, V., Matuszewski, L.: A diffuse interface Lox/hydrogen transcritical flame model. Combust. Theor. Model. 20(3), 486 (2016)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Matheis, J., Hickel, S.: Multi-component vapor-liquid equilibrium model for LES of high-pressure fuel injection and application to ECN Spray A. Int. J. Multiphase Flow 99, 294 (2018)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Traxinger, C., Zips, J., Pfitzner, M.: Single-phase instability in non-premixed flames under liquid rocket engine relevant conditions. J. Propuls. Power 35(4), 675 (2019)CrossRefGoogle Scholar
  8. 8.
    Candel, S., Juniper, M., Single, G., Scouflaire, P., Rolon, C.: Structure and dynamics of cryogenic flames at supercritical pressure. Combust. Sci. Technol. 178, 161 (2006)CrossRefGoogle Scholar
  9. 9.
    Bellan, J.: Theory, modeling and analysis of turbulent supercritical mixing. Combust. Sci. Technol. 178(1), 253 (2006)CrossRefGoogle Scholar
  10. 10.
    Oefelein, J.: Thermophysical characteristics of shear-coaxial LOX-H2 flames at supercritical pressure. Proc. Combust. Inst. 30(2), 2929 (2005)CrossRefGoogle Scholar
  11. 11.
    Pons, L., Darabiha, N., Candel, S.: Pressure effects on nonpremixed strained flames. Combustion and Flame 152(1-2), 218 (2008)CrossRefGoogle Scholar
  12. 12.
    Ribert, G., Zong, N., Yang, V., Pons, L., Darabiha, N., Candel, S.: Counterflow diffusion flames of general fluids: Oxygen/hydrogen mixtures. Combustion and Flame 154(3), 319 (2008)CrossRefGoogle Scholar
  13. 13.
    Giovangigli, V., Matuszewski, L., Dupoirieux, F.: Detailed modeling of planar transcritical H2–O2–N2 flames. Combust. Theor. Model. 15(2), 141 (2011)zbMATHCrossRefGoogle Scholar
  14. 14.
    Giovangigli, V., Matuszewski, L.: Numerical simulation of transcritical strained laminar flames. Combustion and Flame 159(9), 2829 (2012)CrossRefGoogle Scholar
  15. 15.
    Banuti, D.T., Ma, P.C., Hickey, J.P., Ihme, M.: Thermodynamic structure of supercritical LOX–GH2 diffusion flames. Combustion and Flame 196, 364 (2018)CrossRefGoogle Scholar
  16. 16.
    Bellan, J.: Supercritical (and subcritical) fluid behavior and modeling: drops, streams, shear and mixing layers, jets and sprays. Prog. Energy Combust. Sci. 26, 329 (2000)CrossRefGoogle Scholar
  17. 17.
    Selle, L., Okong’o, N., Bellan, J., Harstad, K.: Modelling of subgrid-scale phenomena in supercritical transitional mixing layers: an a priori study. J. Fluid Mech. 593, 57 (2007)zbMATHCrossRefGoogle Scholar
  18. 18.
    Taşkinoğlu, E., Bellan, J.: Subgrid-scale models and large-eddy simulation of oxygen stream disintegration and mixing with a hydrogen or helium stream at supercritical pressure. J. Fluid Mech. 679, 156 (2011)MathSciNetzbMATHCrossRefGoogle Scholar
  19. 19.
    Bellan, J.: Direct numerical simulation of a high-pressure turbulent reacting temporal mixing layer. Combustion and Flame 176, 245 (2017)CrossRefGoogle Scholar
  20. 20.
    Lapenna, P.E., Creta, F.: Mixing under transcritical conditions: an a-priori study using direct numerical simulation. J. Supercrit. Fluid. 128, 263 (2017)CrossRefGoogle Scholar
  21. 21.
    Demoulin, F., Zurbach, S., Mura, A.: High-pressure supercritical turbulent cryogenic injection and combustion: a single-phase flow modeling proposal. Journal of Propulsion and Power 25(2) (2009)CrossRefGoogle Scholar
  22. 22.
    Poschner, M., Pfitzner, M.: CFD-Simulation of the injection and combustion of LOX and H2 at supercritical pressures. In: Proceedings of the European Combustion Meeting 2009 (2010)Google Scholar
  23. 23.
    Zong, N., Yang, V.: Cryogenic fluid jets and mixing layers in transcritical and supercritical environments. Combust. Sci. Technol. 178(1), 193 (2006)MathSciNetCrossRefGoogle Scholar
  24. 24.
    Oefelein, J.: Mixing and combustion of cryogenic oxygen-hydrogen shear-coaxial jet flames at supercritical pressure. Combust. Sci. Technol. 178(1), 229 (2006)CrossRefGoogle Scholar
  25. 25.
    Masquelet, M., Menon, S., Jin, Y., Friedrich, R.: Simulation of unsteady combustion in a LOX-GH2 fueled rocket engine. Aerosp. Sci. Technol. 13(8), 466 (2009)CrossRefGoogle Scholar
  26. 26.
    Terashima, H., Kawai, S., Yamanishi, N.: High-resolution numerical method for supercritical flows with large density variations. AIAA Journal 49(12), 2658 (2011)CrossRefGoogle Scholar
  27. 27.
    Schmitt, T., Méry, Y., Boileau, M., Candel, S.: Large-eddy simulation of oxygen/methane flames under transcritical conditions. Proc. Combust. Inst. 33(1), 1383 (2011)CrossRefGoogle Scholar
  28. 28.
    Schmitt, T., Rodriguez, J., Leyva, I., Candel, S.: Experiments and numerical simulation of mixing under supercritical conditions. Phys. Fluids 24(5), 055104 (2012)CrossRefGoogle Scholar
  29. 29.
    Petit, X., Ribert, G., Lartigue, G., Domingo, P.: Large-eddy simulation of supercritical fluid injection. J. Supercrit. Fluid. 84, 61 (2013)CrossRefGoogle Scholar
  30. 30.
    Petit, X., Ribert, G., Domingo, P.: Framework for real-gas compressible reacting flows with tabulated thermochemistry. J. Supercrit. Fluid. 101, 1 (2015)CrossRefGoogle Scholar
  31. 31.
    Kawai, S., Terashima, H., Negishi, H.: A robust and accurate numerical method for transcritical turbulent flows at supercritical pressure with an arbitrary equation of state. J. Comput. Phys. 300, 116 (2015)MathSciNetzbMATHCrossRefGoogle Scholar
  32. 32.
    Matheis, J., Müller, H., Lenz, C., Pfitzner, M., Hickel, S.: Volume translation methods for real-gas computational fluid dynamics simulations. J. Supercrit. Fluid. 107, 422 (2016)CrossRefGoogle Scholar
  33. 33.
    Ma, P.C., Lv, Y., Ihme, M.: Numerical framework for transcritical real-fluid reacting flow simulations using the flamelet progress variable approach. J. Comput. Phys. 340, 330 (2017)MathSciNetzbMATHCrossRefGoogle Scholar
  34. 34.
    Ma, P.C., Banuti, D., Hickey, J.P., Ihme, M.: Detailed modeling of planar transcritical H2–O2–N2 flames. In: 55th AIAA Aerospace Sciences Meeting, p 0143 (2017)Google Scholar
  35. 35.
    Zong, N., Ribert, G., Yang, V.: A flamelet approach for modeling of liquid oxygen (LOx)/methane flames at supercritical pressures. AIAA Paper 946, 2008 (2008)Google Scholar
  36. 36.
    Lacaze, G., Oefelein, J.C.: A non-premixed combustion model based on flame structure analysis at supercritical pressures. Combustion and Flame 159(6), 2087 (2012)CrossRefGoogle Scholar
  37. 37.
    Zips, J., Müller, H., Pfitzner, M.: Efficient thermo-chemistry tabulation for non-premixed combustion at high-pressure conditions. Flow, Turbulence and Combustion 101(3), 821 (2018)CrossRefGoogle Scholar
  38. 38.
    Karni, S.: Multicomponent flow calculations by a consistent primitive algorithm. J. Comput. Phys. 112, 31 (1994)MathSciNetzbMATHCrossRefGoogle Scholar
  39. 39.
    Abgrall, R.: How to prevent pressure oscillations in multicomponent flow calculations: a quasi conservative approach. J. Comput. Phys. 125, 150 (1996)MathSciNetzbMATHCrossRefGoogle Scholar
  40. 40.
    Lacaze, G., Schmitt, T., Ruiz, A., Oefelein, J.: Comparison of energy-, pressure-and enthalpy-based approaches for modeling supercritical flows. Computers and Fluids 181, 35 (2019)MathSciNetzbMATHCrossRefGoogle Scholar
  41. 41.
    Meng, H., Yang, V.: A unified treatment of general fluid thermodynamics and its application to a preconditioning scheme. J. Comput. Phys. 189, 277 (2003)zbMATHCrossRefGoogle Scholar
  42. 42.
    Müller, H., Pfitzner, M., Matheis, J., Hickel, S.: Large-eddy simulation of coaxial LN2/GH2 injection at trans-and supercritical conditions. J. Propuls. Power 32(1), 46 (2015)CrossRefGoogle Scholar
  43. 43.
    Müller, H., Pfitzner, M.: Large-Eddy Simulation of transcritical LOx/CH4 Jet Flames. In: 6th European Conference for Aeronautics and Space Sciences (EUCASS), Krakau, Poland (2015)Google Scholar
  44. 44.
    Müller, H., Niedermeier, C.A., Matheis, J., Pfitzner, M., Hickel, S.: Large-eddy simulation of nitrogen injection at trans-and supercritical conditions. Phys. Fluids 28(1), 015102 (2016)CrossRefGoogle Scholar
  45. 45.
    Schmitt, T., Selle, L., Ruiz, A., Cuenot, B.: Large-eddy simulation of supercritical-pressure round jets. AIAA Journal 48(9) (2010)CrossRefGoogle Scholar
  46. 46.
    Pantano, C., Saurel, R., Schmitt, T.: An oscillation free shock-capturing method for compressible van der Waals supercritical fluid flows. J. Comput. Phys. 335, 780 (2017)MathSciNetzbMATHCrossRefGoogle Scholar
  47. 47.
    Zong, N., Yang, V.: Near-field flow and flame dynamics of LOX/methane shear-coaxial injector under supercritical conditions. Proc. Combust. Inst. 31(2), 2309 (2007)MathSciNetCrossRefGoogle Scholar
  48. 48.
    Ruiz, A.M., Lacaze, G., Oefelein, J.C., Mari, R., Cuenot, B., Selle, L., Poinsot, T.: Numerical benchmark for high-reynolds-number supercritical flows with large density gradients. AIAA J. 54(5), 1445 (2015)CrossRefGoogle Scholar
  49. 49.
    Laurent, C., Esclapez, L., Maestro, D., Staffelbach, G., Cuenot, B., Selle, L., Schmitt, T., Duchaine, F., Poinsot, T.: Flame–wall interaction effects on the flame root stabilization mechanisms of a doubly-transcritical LO 2/LCH 4 cryogenic flame. Proceedings of the combustion institute (2018)Google Scholar
  50. 50.
    Wang, X., Huo, H., Unnikrishnan, U., Yang, V.: A systematic approach to high-fidelity modeling and efficient simulation of supercritical fluid mixing and combustion. Combustion and Flame 195, 203 (2018)CrossRefGoogle Scholar
  51. 51.
    Schmitt, T., Selle, L., Cuenot, B., Poinsot, T.: Simulation des Grandes Echelles de la combustion turbulente à pression supercritique. Comptes Rendus Mé,canique 337(6-7), 528 (2009)CrossRefGoogle Scholar
  52. 52.
    Matsuyama, S., Shinjo, J., Ogawa, S., Mizobuchi, Y.: Large Eddy simulation of LOX/GH2 shear-coaxial jet flame at supercritical pressure. In: 48th AIAA Aerospace Sciences Meeting, Orlando, Florida (2010)Google Scholar
  53. 53.
    Hakim, L., Ruiz, A., Schmitt, T., Boileau, M., Staffelbach, G., Ducruix, S., Cuenot, B., Candel, S.: Large eddy simulations of multiple transcritical coaxial flames submitted to a high-frequency transverse acoustic modulation. Proc. Combust. Inst. 35(2), 1461 (2015)CrossRefGoogle Scholar
  54. 54.
    Hakim, L., Schmitt, T., Ducruix, S., Candel, S.: Dynamics of a transcritical coaxial flame under a high-frequency transverse acoustic forcing: Influence of the modulation frequency on the flame response. Combustion and Flame 162(10), 3482 (2015)CrossRefGoogle Scholar
  55. 55.
    Schmitt, T., Coussement, A., Ducruix, S., Candel, S.: Large Eddy Simulations of high amplitude self-sustained acoustic oscillations in a rocket engine coaxial injector in the transcritical regime. In: Proceedings of Space Propulsion (2016)Google Scholar
  56. 56.
    Schmitt, T., Staffelbach, G., Ducruix, S., Gröning, S., Hardi, J., Oschwald, M.: Large-Eddy Simulations of a sub-scale liquid rocket combustor: influence of fuel injection temperature on thermo-acoustic stability. In: 7th European Conference for Aeronautics and Aerospace Sciences (EUCASS) (2017)Google Scholar
  57. 57.
    Chehroudi, B., Talley, D.: Visual characteristics and initial growth rate of round cryogenic jets at subcritical and supercritical pressures. E. Coy, Phys. Fluids 14(2), 850 (2002)zbMATHCrossRefGoogle Scholar
  58. 58.
    Poinsot, T., Veynante, D.: Theoretical and Numerical Combustion, 2nd edn. R.T. Edwards, Philadelphia (2005)Google Scholar
  59. 59.
    Lee, L.L., Starling, K.E., Chung, T.H., Ajlan, M.: Generalized multiparameters corresponding state correlation for polyatomic, polar fluid transport properties. Industrial and Chemical Engineering Research 27, 671 (1988)CrossRefGoogle Scholar
  60. 60.
    Juanós, A. J., Sirignano, W.A.: Pressure effects on real-gas laminar counterflow. Combustion and Flame 181, 54 (2017)CrossRefGoogle Scholar
  61. 61.
    Nicoud, F., Ducros, F.: Subgrid-scale stress modelling based on the square of the velocity gradient. Flow, Turbulence and Combustion 62(3), 183 (1999). JXzbMATHCrossRefGoogle Scholar
  62. 62.
    Borghesi, G., Bellan, J.: A priori and a posteriori investigations for developing large eddy simulations of multi-species turbulent mixing under high-pressure conditions. Phys. Fluids 27(035117) (2015)CrossRefGoogle Scholar
  63. 63.
    Soave, G.: Equilibrium constants from a modified Redlich-Kwong equation of state. Chem. Eng. Sci. 27, 1197 (1977)CrossRefGoogle Scholar
  64. 64.
    Lemmon, E., McLinden, M., Friend, D.: NIST Chemistry WebBook, NIST Standard Reference Database Number 69 (National Institute of Standards and Technology, Gaithersburg MD, 20899, 2009), chap. Thermophysical Properties of Fluid SystemsGoogle Scholar
  65. 65.
    Mayer, W., Tamura, H.: Propellant injection in a liquid oxygen/gaseous hydrogen rocket engine. J. Propuls. Power 12(6), 1137 (1996)CrossRefGoogle Scholar
  66. 66.
    Ivancic, B., Mayer, W.: Time-and length scales of combustion in liquid rocket thrust chambers. J. Propuls. Power 18(2), 247 (2002)CrossRefGoogle Scholar
  67. 67.
    Ruiz, A., Cuenot, B., Selle, L., Poinsot, T.: The flame structure of a turbulent supercritical hydrogen/oxygen flow behind a splitter plate. In: 47th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, p 6121 (2011)Google Scholar
  68. 68.
    Mari, R., Cuenot, B., Duchaine, F., Selle, L.: Stabilization mechanisms of a supercritical hydrogen/oxygen flame. In: Proceedings of the Summer Program, p 439. Citeseer (2012)Google Scholar
  69. 69.
    Veynante, D., Vervisch, L.: Turbulent combustion modeling. Prog. Energy Combust. Sci. 28, 193 (2002)CrossRefGoogle Scholar
  70. 70.
    Domingo, P., Vervisch, L., Veynante, D.: Large-eddy simulation of a lifted methane jet flame in a vitiated coflow. Combustion and Flame 152(3), 415 (2008)CrossRefGoogle Scholar
  71. 71.
    Pera, C., Colin, O., Jay, S.: Development of a FPI detailed chemistry tabulation methodology for internal combustion engines. Oil & Gas Science and Technology-Revue de l’IFP 64(3), 243 (2009)CrossRefGoogle Scholar
  72. 72.
    Zong, N., Yang, V.: An efficient preconditioning scheme for real-fluid mixtures using primitive pressure–temperature variables. Proc. Combust. Inst. 31(2), 2309 (2007)MathSciNetzbMATHCrossRefGoogle Scholar
  73. 73.
    Huo, H., Yang, V.: Large-Eddy Simulation of Supercritical Combustion: Model Validation Against Gaseous H 2–O 2 Injector. J. Propuls. Power 33(5), 1272 (2017)CrossRefGoogle Scholar
  74. 74.
    Moureau, V., Lartigue, G., Sommerer, Y., Angelberger, C., Colin, O., Poinsot, T.: High-order methods for DNS and LES of compressible multi-component reacting flows on fixed and moving grids. J. Comput. Phys. 202(2), 710 (2005)MathSciNetzbMATHCrossRefGoogle Scholar
  75. 75.
    Schönfeld, T., Poinsot, T.: Influence of boundary conditions in LES of premixed combustion instabilities. In: Annual Research Briefs, pp 73–84. Center for Turbulence Research, NASA Ames/Stanford University (1999)Google Scholar
  76. 76.
    Colin, O., Rudgyard, M.: Development of high-order Taylor-Galerkin schemes for unsteady calculations. J. Comput. Phys. 162(2), 338 (2000)MathSciNetzbMATHCrossRefGoogle Scholar
  77. 77.
    Okong’o, N., Bellan, J.: Consistent boundary conditions for multicompoment real gas mixtures based on characteristic waves. J. Comput. Phys. 176, 330 (2002)zbMATHCrossRefGoogle Scholar
  78. 78.
    Mathew, J., Lechner, R., Foysi, H., Sesterhenn, J., Friedrich, R.: An explicit filtering method for large eddy simulation of compressible flows. Phys. Fluids 15(8), 2279 (2003)zbMATHCrossRefGoogle Scholar
  79. 79.
    Stolz, S., Adams, N.A.: An approximate deconvolution procedure for large-eddy simulation. Phys. Fluids 11(7), 1699 (1999)zbMATHCrossRefGoogle Scholar
  80. 80.
    Colin, O., Ducros, F., Veynante, D., Poinsot, T.: Simulations aux grandes échelles de la combustion turbulente prémélangée dans les statoréacteurs. Phys. Fluids 12(7), 1843 (2000)zbMATHCrossRefGoogle Scholar
  81. 81.
    Vingert, L., Habiballah, M., Vuillermoz, P., Zurbach, S.: MASCOTTE, a test facility for cryogenic combustion research at high pressure. In: 51st International Astronautical Congress, Rio De Janeiro, Brazil (2000)Google Scholar
  82. 82.
    Juniper, M.: Structure et stabilisation des flammes cryotechniques. Ph.D. thesis, Ecole Centrale de Paris (2001)Google Scholar
  83. 83.
    Singla, G., Scouflaire, P., Rolon, C., Candel, S.: Transcritical oxygen/transcritical or supercritical methane combustion. Proc. Combust. Inst. 30(2), 2921 (2005)CrossRefGoogle Scholar
  84. 84.
    Schmitt, P., Poinsot, T.J., Schuermans, B., Geigle, K.: Large-eddy simulation and experimental study of heat transfer, nitric oxide emissions and combustion instability in a swirled turbulent high pressure burner. J. Fluid Mech. 570, 17 (2007)zbMATHCrossRefGoogle Scholar
  85. 85.
    Jaegle, F., Cabrit, O., Mendez, S., Poinsot, T.: Implementation methods of wall functions in cell-vertex numerical solvers. Flow, turbulence and combustion 85 (2), 245 (2010)zbMATHCrossRefGoogle Scholar
  86. 86.
    Poinsot, T., Lele, S.: Boundary conditions for direct simulations of compressible viscous flows. J. Comput. Phys. 101(1), 104 (1992)MathSciNetzbMATHCrossRefGoogle Scholar
  87. 87.
    Kraichnan, R.: Diffusion by a random velocity field. Phys. Fluids 13, 22 (1970)zbMATHCrossRefGoogle Scholar
  88. 88.
    Smirnov, A., Shi, S., Celik, I.: Random flow generation technique for large eddy simulations and particle-dynamics modeling. Trans. ASME. Journal of Fluids Engineering 123, 359 (2001)CrossRefGoogle Scholar
  89. 89.
    Juniper, M., Tripathi, A., Scouflaire, P., Rolon, J., Candel, S.: Structure of cryogenic flames at elevated pressures. Proc. Combust. Inst. 28(1), 1103 (2000)CrossRefGoogle Scholar
  90. 90.
    Fiala, T., Sattelmayer, T.: A posteriori computation of OH* radiation from numerical simulations in rocket combustion chambers. In: 5th European Conference for Aeronautics and Space Sciences (EUCASS), Munich, July, pp 1–5 (2013)Google Scholar
  91. 91.
    Zong, N., Yang, V.: Cryogenic fluid dynamics of pressure swirl injectors at supercritical conditions. Phys. Fluids 20, 056103 (2008)zbMATHCrossRefGoogle Scholar
  92. 92.
    Urbano, A., Selle, L., Staffelbach, G., Cuenot, B., Schmitt, T., Ducruix, S., Candel, S.: Exploration of combustion instability triggering using large eddy simulation of a multiple injector liquid rocket engine. Combustion and Flame 169, 129 (2016)CrossRefGoogle Scholar
  93. 93.
    Castiglioni, G., Bellan, J.: On models for predicting thermodynamic regimes in high-pressure turbulent mixing and combustion of multispecies mixtures. J. Fluid Mech. 843, 536 (2018)MathSciNetCrossRefGoogle Scholar
  94. 94.
    Pelletier, M., Thomas, S., Ducruix, S.: Implementation of a diffuse interface method in a compressible multicomponent LES solver. In: ICLASS 2018 (2018)Google Scholar
  95. 95.
    Nayigizente, D., Thomas, S., Ducruix, S.: Unsteady simulations of liquid/gas interfaces using the Second Gradient theory. In: ICLASS 2018 (2018)Google Scholar

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Authors and Affiliations

  1. 1.Laboratoire EM2CCNRS, CentraleSupélec, Université Paris-SaclayGif-sur-Yvette cedexFrance

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