Validation of RANS Turbulence Models

A. A. Chernova

Russian journal of nonlinear dynamics, Tome 18 (2022) no. 1, pp. 61-82.

Résumé

This paper addresses problems of mathematical modeling of heat exchange processes in the pre-nozzle volume of a solid propellant rocket engine with a charge with starlike crosssection and a recessed hinged nozzle. Methods of mathematical modeling are used to solve the quasi-stationary spatial conjugate problem of heat exchange. An analysis is made of the influence of RANS turbulence models on the flow structure in the flow channels of the engine and on the computed heat flow distributions over the surface of the recessed nozzle. Methods of mathematical modeling are used to solve the quasi-stationary spatial conjugate problem of heat exchange. Results of validation of RANS turbulence models are presented using well-known experimental data. A comparison of numerical and experimental distributions of the heat-transfer coefficient over the inlet surface of the recessed nozzle for the engine with a cylindrical channel charge is made for a primary choice of turbulence models providing a qualitative agreement between calculated and experimental data. By analyzing the results of numerical modeling of the conjugate problem of heat exchange in the combustion chamber of the solid propellant engine with a starlike channel, it is shown that the SST $k-\omega$ turbulence model provides local heat-transfer coefficient distributions that are particularly close to the experimental data.

Détail

Keywords: solid propellant rocket engine, recessed nozzle, mathematical modeling, conjugate heat exchange problem, RANS turbulence models
Mots-clés : heat-transfer coefficient.

Bibliographie

[1] Aliev, A. V., Mishchenkova, O. V., and Cherepov, I. V., “Nonstationary Intra-Chamber Processes in Solid-Propellant Controlled Propulsion System”, Vestn. MGTU. Ser. Mashinostr., 4(109) (2016), 24–39 (Russian)

[2] Bardina, J. E., Huang, P. G., and Coakley, T. J., Turbulence Modeling Validation, Testing, and Development, NASA Technical Memorandum 110 446, 1997, 100 pp. | Zbl

[3] Bendersky, B. Ya. and Teneev, V. A., “Spatial Subsonic Flows in Areas with Composite Geometry”, Matem. Mod., 13:8 (2001), 121–127 (Russian)

[4] Bendersky, B. Ya., Cherepov, I. V., and Il'yashenko, K. V., “The Study of Gas Dynamic Processes in Engine Management”, Vestn. MGTU. Ser. Mashinostr., 2004, no. S, 95–103 (Russian)

[5] Benderskiy, B. Ya. and Chernova, A. A., “Formation of Vortex Structures in Channels with Mass Injection and Their Interaction with Surfaces in Solid-Fuel Rocket Engines”, Thermophys. Aeromechanics, 22:2 (2015), 185–190 | DOI

[6] Benderskiy, B. Ya. and Chernova, A. A., “Features of Heat Transfer in a Pre-Nozzle Volume of a Solid-Propellant Rocket Motor with Charges of Complex Shapes”, Thermophys. Aeromechanics, 25:2 (2018), 265–272 | DOI

[7] Bendersky, B. Ya. and Chernova, A. A., “Investigation of Heat Transfer in the Combustion Chamber of a Solid-Propellant Rocket Motor within the Framework of the Homogeneous Gas Model”, Khimich. Fiz. Mezoskop., 23:4 (2021), 412–429 (Russian)

[8] Garbaruk, A. V., Current Approaches to Turbulence Modeling, SPbPU, St. Petersburg, 2016, 233 pp. (Russian)

[9] Garbaruk, A. V., Viscous Fluid Flows and Turbulence Models: Methods for Calculating Turbulent Flows, SPbPU, St. Petersburg, 2010, 127 pp. (Russian)

[10] Garbaruk, A., Strelets, M. Kh., and Shur, M. L., Turbulence Modeling in Complex Flow Calculations, SPbPU, St. Petersburg, 2012, 88 pp. (Russian)

[11] Isaev, S., Gritckevich, M., Leontiev, A., and Popov, I., “Abnormal Enhancement of Separated Turbulent Air Flow and Heat Transfer in Inclined Single-Row Oval-Trench Dimples at the Narrow Channel Wall”, Acta Astronaut., 163, part A (2019), 202–207 | DOI

[12] Isaev, A. I. and Skorobogatov, S. V., “Hydrodynamic Verification and Validation of Numerical Methods of the Flow Calculation in Combustion Chamber of a Gas Turbine Engine”, Trudy MAI, 2017, no. 97, 28 pp. (Russian)

[13] Jagadeesh, P. and Murali, K., “Application of Low-Re Turbulence Models for Flow Simulations Past Underwater Vehicle Hull Forms”, Int. J. Nav. Archit. Ocean Eng., 2:1 (2005), 41–54 | DOI

[14] Kolmogorov, A. N., “Equations of Turbulent Motion of an Incompressible Fluid”, Dokl. Akad. Nauk SSSR. Ser. Fiz., 6:1–2 (1942), 56–58 (Russian)

[15] Koroleva, M. R., Mishchenkova, O. V., Kelemen, M., and Chernova, A. A., “Theoretical Research of the Internal Gas Dynamics Processes of Measurements of Hot Air Curtain with Cross-Flow Fan”, MM Sci. J., 2020, 3966–3972 | DOI

[16] Koroleva, M. R., Mishenkova, O. V., Raeder, T., Tenenev, V. A., and Chernova, A. A., “Numerical Simulation of the Process of Activation of the Safety Valve”, Kompyuternye Issledovaniya i Modelirovanie, 10:4 (2018), 495–509

[17] Gas-Dynamic and Thermophysical Processes in Solid Propellant Rocket Engines, ed. A. S. Koroteev, Mashinostroenie, Moscow, 2004, 512 pp. (Russian)

[18] Kravchuk, M. O., Kudimov, N. F., and Safronov, A. V., “Turbulence Modeling Issues for Supersonic High-Temperature Jet Computation”, Trudy MAI, 2015, no. 82, 20 (Russian)

[19] Larina, E. V., Kryukov, I. A., and Ivanov, I. E., “Numerical Simulation of Axisymmetric Jets Using Differential Eddy Viscosity Models”, Trudy MAI, 2016, no. 91, 24 (Russian)

[20] Launder, B. E. and Spalding, D. B., Lectures in Mathematical Models of Turbulence, Acad. Press, London, 1972, 169 pp. | Zbl

[21] Internal Ballistics of Solid Propellant Rocket Engines, eds. A. M. Lipanov et al., Mashinostroenie, Moskow, 2007, 504 pp. (Russian)

[22] Lipanov, A. M., Bobryshev, V. P., Aliev, A. V., Spiridonov, F. F., and Lisitsa, V. D., Numerical Experiment in the Theory of Solid Propellant Rocet Engines, Nauka, Ekaterinburg, 1994, 301 pp. (Russian)

[23] Lipanov, A. M., Dadikina, S. Yu., Shumikhin, A. A., Koroleva, M. R., and Karpov, A. I., “Numerical Simulation Intra-Chamber of Unsteady Turbulent Flows Stimulate: Part 1”, Vestn. YuUrGU. Ser. Mat. Model. Progr., 12:1 (2019), 32–43 (Russian) | Zbl

[24] Menter, F. R., “Zonal Two Equation $\kappa - \omega$ Turbulence Models for Aerodynamic Flows”, Proc. of the 24th Fluid Dynamics Conf. (American Institute of Aeronautics and Astronautics, Orlando, FL, July 1993), 128–143

[25] Menter, F. R., “Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications”, AIAA J., 32:8 (1994), 1598–1605 | DOI

[26] Menter, F. R. and Esch, T., “Advanced Turbulence Modelling in CFX”, CFX Update, 2001, no. 20, 4–5

[27] Menter, F. R., Kuntz, M., and Langtry, R., “Ten Years of Industrial Experience with the SST Turbulence Model”, Turbulence, Heat and Mass Transfer: Proc. of the 4th Internat. Symp. on Turbulence, Heat and Mass Transfer (Antalya, Turkey, Oct 2003), eds. K. Hanjalić, Y. Nagano, M. J. Tummers, Begell House, Danbury, Conn., 2003, 625–632

[28] Grotjans, H. and Menter, F., “Wall Functions for General Application CFD Codes”, ECCOMAS'98: Proc. of the 4th European Computational Fluid Dynamics Conf., eds. K. D. Papailiou et al., Wiley, Chichester, 1998, 1112–1117

[29] Naplekov, I. S., “Computer Modeling for Solving the Problem of Gas Flow from a Nozzle Using Different Turbulence Models”, The 14th Korolev's Readings: The Internat. Young Scientists Conf. (Samara, Oct 2017), SGU, Samara, 2017, 209–210 (Russian)

[30] Orszag, S. A., Yakhot, V., Flannery, W. S., Boysan, F., Choudhury, D., Maruzewski, J., and Patel, B., “Renormalization Group Modeling and Turbulence Simulations”, Proc. of the Internat. Conf. on Near-Wall Turbulent Flows (Tempe, AZ, March 1993), eds. R. M. C. So, Ch. G. Speziale, B. E. Launder, Elsevier, Amsterdam, 1993, 1031–1046

[31] Raeder, T., Tenenev, V. A., Koroleva, M. R., and Mishchenkova, O. V., “Nonlinear Processes in Safety Systems for Substances with Parameters Close to a Critical State”, Russian J. Nonlinear Dyn., 17:1 (2021), 119–138 | MR | Zbl

[32] Raeder, T., Tenenev, V. A., and Chernova, A. A., “Incorporation of Fluid Compressibility into the Calculation of the Stationary Mode of Operation of a Hydraulic Device at High Fluid Pressures”, Russian J. Nonlinear Dyn., 17:2 (2021), 195–209 | MR | Zbl

[33] Trottenberg, U., Oosterlee, C. W., and Schüller, A., Multigrid, Acad. Press, New York, 2000 | MR

[34] Ferziger, J. H. and Perić, M., Computational Methods for Fluid Dynamics, 2nd rev. ed., Springer, Berlin, 1999, xiv+389 pp. | MR | Zbl

[35] Safronov, A. V., “Applicability of Turbulent Viscosity Model for the Calculation of Supersonic Jet Streams”, Fiz.-Khim. Kinetika Gaz. Dinam., 13:1 (2012), 9, 17 pp. (Russian)

[36] Sandhem, N. D. and Kleiser, L., “The Late Stages of Transition to Turbulence in Channel Flow”, J. Fluid Mech., 245 (1992), 319–348 | DOI

[37] Saveliev, S. K., Emelyanov, V. N., and Benderskiy, B. Ya., Experimental Methods of SRM Gas Dynamics Research, Nedra, St. Petersburg, 2007, 268 pp. (Russian)

[38] Shishkov, A. A., Panin, S. D., and Rumyantsev, V. V., Workflows in Solid Propellant Rocket Engines, Mashinostroenie, Moskow, 1989 (Russian)

[39] Spalart, P. R. and Allmaras, S. R., A One-Equation Turbulence Model for Aerodynamic Flows, Technical Report AIAA-92-0439, American Institute of Aeronautics and Astronautics, 1992, 22 pp.

[40] Starchenko, A. V., Nuterman, R. B., and Danilkin, E. A., Numerical Modeling of Turbulent Currents and Impurity Transport in Street Canyons, TGU, Tomsk, 2015, 252 pp. (Russian)

[41] Launder, B. E. and Spalding, D. B., “The Numerical Computation of Turbulent Flows”, Comput. Methods Appl. Mech. Eng., 3:2 (1974), 269–289 | DOI | Zbl

[42] Volkov, K. N. and Emelyanov, V. N., Mass-Driven Gas Flows in Channels and Ducts of Power Plants, Fizmatlit, Moscow, 2011, 464 pp. (Russian)

[43] Volkov, K. N. and Emelyanov, V. N., “Mathematical Models of Three-Dimensional Turbulent Flows in the Ducts with Fluid Injection”, Matem. Mod., 16:10 (2004), 41–63 (Russian) | Zbl

[44] Volkov, K. N. and Emelyanov, V. N., Large Eddies Simulation in Turbulent Flow Calculations, Fizmatlit, Moscow, 2011 (Russian)

[45] Volkov, K. N., Denisikhin, Emelyanov, V. N., and Teterina, I. V., “Numerical Simulation of Gas-Dynamics Processes in Thrust Vectorable Nozzle”, Fiz.-Khim. Kinetika Gaz. Dinam., 19:2 (2018), 24 pp.

[46] Wilcox, D. C., Turbulence Modeling for CFD, DCW Industries, La Canada, Calif., 1998, 536 pp.