Library Subscription: Guest
Begell Digital Portal Begell Digital Library eBooks Journals References & Proceedings Research Collections
International Journal of Fluid Mechanics Research
ESCI SJR: 0.206 SNIP: 0.446 CiteScore™: 0.5

ISSN Print: 2152-5102
ISSN Online: 2152-5110

Volume 47, 2020 Volume 46, 2019 Volume 45, 2018 Volume 44, 2017 Volume 43, 2016 Volume 42, 2015 Volume 41, 2014 Volume 40, 2013 Volume 39, 2012 Volume 38, 2011 Volume 37, 2010 Volume 36, 2009 Volume 35, 2008 Volume 34, 2007 Volume 33, 2006 Volume 32, 2005 Volume 31, 2004 Volume 30, 2003 Volume 29, 2002 Volume 28, 2001 Volume 27, 2000 Volume 26, 1999 Volume 25, 1998 Volume 24, 1997 Volume 23, 1996 Volume 22, 1995

International Journal of Fluid Mechanics Research

DOI: 10.1615/InterJFluidMechRes.2018025734
pages 565-578


Alexander M. Molchanov
Aerospace Heating Engineering Department,Moscow Aviation Institute (National Research University) "MAI", Volokolamskoe shosse, d. 4, 125993, Moscow, Russia
Dmitry S. Yanyshev
Aerospace Heating Engineering Department,Moscow Aviation Institute (National Research University) "MAI", Volokolamskoe shosse, d. 4, 125993, Moscow, Russia
Leonid V. Bykov
Aerospace Heating Engineering Department, Moscow Aviation Institute (National Research University) "MAI", Volokolamskoe shosse, d. 4, 125993, Moscow, Russia
Ivan M. Platonov
Aerospace Heating Engineering Department,Moscow Aviation Institute (National Research University) "MAI", Volokolamskoe shosse, d. 4, 125993, Moscow, Russia


A turbulence model for free-stream and wall-bounded high-speed compressible flows is presented. The core of the model is based on the assumption that the key role in turbulent mixing processes is played by velocity fluctuations normal to streamlines. Thus a separate partial differential equation is solved to model this parameter correctly. Effect of compressibility is handled via modeling the rapid part of pressure-strain correlation depending on turbulent Mach number. To model turbulence in the near-wall region, a blending technique is used (similar to the one introduced in Menter's SST model). The developed model is verified in free-stream and wall-bounded conditions. Comparison of the simulation with available experimental data showed a good agreement for the above problems.


  1. Bertsch, R., Rapidly Sheared Compressible Turbulence: Characterization of Different Pressure Regimes and Effect of Thermodynamic Fluctuations, MS, Texas A&M University, Texas, USA, 2010.

  2. Blaisdell, G.A., Mansour, N.N., and Reynolds, W.C., Compressibility Effects on the Growth and Structure of Homogeneous Turbulent Shear-Flow, J. FluidMech., vol. 256, pp. 443-485,1993.

  3. Durbin, P.A., Near-Wall Turbulence Closure Modeling without Damping Functions, Theor. Comput. Fluid Dyn., vol. 3, no. 1, pp. 1-13,1991.

  4. Dutton, J.C. and Addy, A.L., Fluid Dynamic Mechanisms and Interactions within Separated Flows, U.S. Army Research Office Research Grant DAAH04-93-G-0226, Department of Mechanical and Industrial Engineering, University of Illinois, Urbana-Champagne, Urbana, IL, 1998.

  5. Fernholz, H.H. and Finley, P. J., A Critical Compilation of Compressible Turbulent Boundary Layer Data, no. 223, Neuilly-sur-Seine, France: AGARD, 1977.

  6. Freund, J.B., Lele, S.K., and Moin, P., Compressibility Effects in a Turbulent Annular Mixing Layer, Part 1, Turbulence and Growth Rate, J. Fluid Mech, vol. 421, pp. 229-267,2000.

  7. Glebov, G.A. and Molchanov, A.M., Model of Turbulence for Supersonic Reacting Jets, Investigation of Heat Transfer in Flying Vehicles (Issledovanie Teploobmena v Letatelnykh Apparatakh), Moscow, Russia: Moscow Aviation Institute, pp. 6-11,1982.

  8. Goebel, S.G. and Dutton, J.C., Experimental Study of Compressible Turbulent Mixing Layers, AIAAJ., vol. 29, no. 4, pp. 538-546, 1991.

  9. Gomez, C.A. and Girimaji, S.S., Algebraic Reynolds Stress Model (ARSM) for Compressible Shear Flows, AIAA Paper 2011-3572, p. 14,2011.

  10. Hossain, M.S., Mathematische Modellierung von Turbulenten Auftriebstromungen, PhD, University of Karlsruhe, Karlsruhe, Germany, 1980.

  11. Huang, S. and Fu, S., Modelling of Pressure-Strain Correlation in Compressible Turbulent Flow, Acta Mech. Sin, vol. 24, pp. 37-43,2008.

  12. Jones, R.M., Advanced Turbulence Modeling for Industrial Flows, PhD, Louisiana State University, Louisiana, USA, 1996.

  13. Kalitzin, G., Gould, A.R.B., and Benton, J.J., Application of Two-Equation Turbulence Models in Aircraft Design, AIAA Paper 96-0327, p. 14,1994.

  14. Kline, S.J., Cantwell, B.J., and Lilley, G.M., Eds., 1980-1981 AFOSR-HTTM-Stanford Conference on Complex Turbulent Flows, Stanford, CA: Stanford University Press, 1981.

  15. Kollmann, W., Ed., Prediction Methods for Turbulent Flows, Washington, DC: Hemisphere Publishing Corporation, 1980.

  16. Kraev, V.M. and Yanyshev, D.S., Unsteady Turbulent Flows in Channels of Powerplants, Krasnoyarsk, Russia: Siberian State Aerospace University, 2014.

  17. Krasotkin, VS., Myshanov, A.I., Shalaev, S.P., Shirokov, N.N., and Yudelovich, M.Y., Investigation of Supersonic Isobaric Submerged Turbulent Jets, FluidDyn., vol. 23, no. 4, pp. 529-534,1988.

  18. Lau, J.C., Morris, P. J., and Fisher, M.J., Measurements in Subsonic and Supersonic Free Jets Using a Laser Velocimeter, J. Fluid Mech., vol. 63, no. 1, pp. 1-27,1979.

  19. Lavin, T.A., Reynolds and Favre-Averaged Rapid Distortion Theory for Compressible, Ideal-Gas Turbulence, MS, Texas A&M University, Texas, USA, 2007.

  20. Ljuboja, M. and Rodi, W., Calculation of Turbulent Wall Jets with an Algebric Reynolds Stress Model, J. Fluid Eng., vol. 102, pp. 350-356,1980.

  21. Manceau, R. and Hanjalic, K., Elliptic Blending Model: A New Near-Wall Reynolds-Stress Turbulence Closure, Phys. Fluids, vol. 14, no. 2, pp. 744-754,2002.

  22. Mathur, T. and Dutton, J.C., Base-Bleed Experiments with a Cylindrical Afterbody in Supersonic Flow, J. Spacecraft Rockets, vol. 33, no. 1,pp. 30-37,1996.

  23. Menter, F.R., Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications, AIAA J, vol. 32, no. 8, pp. 1598-1605,1994.

  24. Molchanov, A.M., A Calculation of Supersonic Non-Isobaric Jets with Compressibility Corrections in a Turbulence Model, Vestnik MAI, vol. 16, no. 1, pp. 38-48,2009.

  25. Molchanov, A.M. and Bykov, L.V., Three-Equation K-e-Vn Turbulence Model for High-Speed Flows, AIAA Paper 2013-3181, p. 30,2013.

  26. Pantano, C. and Sarkar, S., a Study of Compressibility Effects in the High Speed Turbulent Shear Layer Using Direct Simulation, J. Fluid Mech, vol. 451, pp. 329-371,2002.

  27. Papamoschou, D. and Roshko, A., The Compressible Turbulent Shear Layer: An Experimental Study, J. Fluid Mech., vol. 197, pp. 453-477,1988.

  28. Sarkar, S., The Stabilizing Effect of Compressibility in Turbulent Shear Flow, J. Fluid Mech., vol. 282, pp. 163-186,1995.

  29. Sarkar, S., Erlebacher, G., and Hussaini, M.Y., Compressible Homogeneous Shear: Simulation and Modeling, NASA Contractor Report 189611 92-6,ICASE, 1992.

  30. Sarkar, S., Erlebacher, G., Hussaini, M.Y., and Kreiss, H.O., The Analysis and Modeling of Dilatational Terms in Compressible Turbulence, U.S. Army Research Office Research Grant Report No. ICASE-89-79, NAS 1.26:181959, NASA-CR-181959, NASA Langley Research Center, 1989.

  31. Simone, A., Coleman, G., and Cambon, C., The Effect of Compressibility on Turbulent Shear Flow: A Rapid-Distortion-Theory and Direct Numerical-Simulation, J. Fluid Mech, vol. 330, pp. 307-338,1997.

  32. Vreman, A.W., Sandham, N.D., and Luo, K.H., Compressible Mixing Layer Growth Rate and Turbulence Characteristics, J. Fluid Mech, vol. 320, pp. 235-258,1996.

  33. Zeman, O., Dilatation Dissipation: The Concept and Application in Modeling Compressible Mixing Layer, Phys. Fluids A, vol. 2, pp. 178-188,1990.