Turbulence Quantification in Supercritical Nitrogen Injection: An Analysis of Turbulence Models


In Liquid Rocket Engines, higher combustion efficiencies come at the cost of the propellants exceeding their critical point conditions and entering the supercritical domain. The term fluid is used because, under these conditions, there is no longer a clear distinction between a liquid and a gas phase. The non-conventional behavior  of thermophysical properties makes the modeling of supercritical fluid flows a most challenging task. In the present work, a RANS computational method following an incompressible but variable density approach is devised on which the performance of several turbulence models is compared in conjunction with a high accuracy multi-parameter equation of state. Also, a suitable methodology to describe transport properties accounting for dense fluid corrections is applied. The results are validated against experimental data, becoming clear that there is no trend between turbulence model complexity and the quality of the produced results. For several instances, one- and two- equation turbulence models produce similar and better results than those  of Large Eddy Simulation (LES). Finally, considerations about the applicability of the tested turbulence models in supercritical simulations are given based on the results and the structural nature of each model.

Keywords: Supercritial fluids, RANS turbulence modeling, Liquid rocket engines

[1] D. Haeseler, F. Haidinger, L. Brummer, J. Haberle and P. Luger, “Development and Testing Status of the Vinci Thrust Chamber,” in 48th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, 2012.

[2] D. Banuti, M. Raju, P. C. Ma, M. Ihme and J. Hickey, “Seven questions about supercritical fluids - towards a new fluid state diagram,” in 55th AIAA Aerospace Sciences Meeting, 2017.

[3] M. O. McLinden, E. W. Lemmon and M. L. Huber, “NIST Thermodynamic and Transport Properties REFPROP, Version 7.0,” NIST Standard Reference Database 23, 2002.

[4] E. W. Lemmon, I. H. Bell, M. L. Huber and M. O. McLinden, NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties-REFPROP, Version 10.0, National Institute of Standards and Technology, 2018.

[5] R. Span, E. W. Lemmon, R. T. Jacobsen, W. Wagner and A. Yokozeki, “A Reference Equation of State for the Thermodynamic Properties of Nitrogen for Temperatures from 63.151 to 1000 K and Pressures to 2200 MPa,” Journal of Physical and Chemical Reference Data, vol. 29, pp. 1361-1433, 11 2000.

[6] E. W. Lemmon and R. T. Jacobsen, “Viscosity and Thermal Conductivity Equations for Nitrogen, Oxygen, Argon, and Air,” International Journal of Thermophysics, vol. 25, pp. 21-69, 1 2004.

[7] F. Ries, P. Obando, I. Shevchuck, J. Janicka and A. Sadiki, “Numerical analysis of turbulent flow dynamics and heat transport in a round jet at supercritical conditions,” International Journal of Heat and Fluid Flow, vol. 66, pp. 172-184, 8 2017.

[8] T. S. Park, “LES and RANS simulations of cryogenic liquid nitrogen jets,” The Journal of Supercritical Fluids, vol. 72, pp. 232-247, 12 2012.

[9] T. Schmitt, L. Selle, B. Cuenot and T. Poinsot, “Large-Eddy Simulation of transcritical flows,” Comptes Rendus Mécanique, vol. 337, pp. 528-538, 6 2009.

[10] T. Schmitt, L. Selle, A. Ruiz and B. Cuenot, “Large-Eddy Simulation of Supercritical-Pressure Round Jets,” AIAA Journal, vol. 48, pp. 2133-2144, 9 2010.

[11] M. Jarczyk and M. Pfitzner, “Large Eddy Simulation of Supercritical Nitrogen Jets,” in 50th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, 2012.

[12] C. A. Niedermeier, M. Jarczyk, S. Hickel, N. Adams and M. Pfitzner, “Large-Eddy Simulation of Turbulent Trans- and Supercritical Mixing,” in 21st AIAA Computational Fluid Dynamics Conference, 2013.

[13] J. Hickey, P. C. Ma, M. Ihme and S. S. Thakur, “Large Eddy Simulation of Shear Coaxial Rocket Injector: Real Fluid Effects,” in 49th AIAA/ASME/SAE/ASEE Joint Propulsion Conference, 2013.

[14] X. Petit, G. Ribert, G. Lartigue and P. Domingo, “Large-eddy simulation of supercritical fluid injection,”The Journal of Supercritical Fluids, vol. 84, pp. 61- 73, 12 2013.

[15] H. Mueller, C. A. Niedermeier, M. Jarczyk, M. Pfitzner, S. Hickel and N. A. Adams, “Large-eddy simulation of trans- and supercritical injection,” in Progress in Propulsion Physics, 2016.

[16] S. Taghizadeh and D. Jarrahbashi, “Proper Orthogonal Decomposition Analysis of Turbulent Cryogenic Liquid Jet Injeciton Under Transcritical and Supercritical Conditions,” Atomization and Sprays, vol. 28, pp. 875-900, 2018.

[17] L. Magalhães, A. Silva and J. Barata, “Locally variable turbulent Prandtl number considerations on the modeling of Liquid Rocket Engines operating above the critical point,” ILASS–Europe 2019, 29th Conference on Liquid Atomization and Spray Systems, 2-4 September 2019, Paris, France, 2019.

[18] W. Mayer, J. Telaar, R. Branam, G. Schneider and J. Hussong, “Raman Measurements of Cryogenic Injection at Supercritical Pressure,” Heat and Mass Transfer, vol. 39, pp. 709-719, 7 2003.

[19] P. Spalart and S. Allmaras, “A one-equation turbulence model for aerodynamic flows,” in 30th Aerospace Sciences Meeting and Exhibit, 1992.

[20] B. E. Launder and D. B. Spalding, Lectures in mathematical models of turbulence, London, England: Academic Press, 1972.

[21] V. Yakhot, S. A. Orszag, S. Thangam, T. B. Gatski and C. G. Speziale, “Development of turbulence models for shear flows by a double expansion technique,” Physics of Fluids A: Fluid Dynamics, vol. 4, pp. 1510-1520, 7 1992.

[22] Z. Yang and T. H. Shih, “New time scale based k-epsilon model for near-wall turbulence,” AIAA Journal, vol. 31, pp. 1191-1198, 7 1993.

[23] D. C. Wilcox, Turbulence modelling for CFD, 2nd ed. ed., La Cãnada, Calif: DCW Industries, 1998.

[24] F. R. Menter, “Two-equation eddy-viscosity turbulence models for engineering applications,” AIAA Journal, vol. 32, pp. 1598-1605, 8 1994.

[25] B. P. Leonard, “A stable and accurate convective modelling procedure based on quadratic upstream interpolation,” Computer Methods in Applied Mechanics and Engineering, vol. 19, pp. 59-98, 6 1979.

[26] Ansys-Fluent, “ANSYS Fluent Theory Guide,” 2015.

[27] F. Ries, J. Janicka and A. Sadiki, “Thermal Transport and Entropy Production Mechanisms in a Turbulent Round Jet at Supercritical Thermodynamic Conditions,” Entropy, vol. 19, p. 404, 8 2017.

[28] D. C. Wilcox, Turbulence modeling for CFD, 3rd ed. ed., La Cãnada, Calif: DCW Industries, 2006.