Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-17T15:13:50.922Z Has data issue: false hasContentIssue false
  • English
  • Français

Turbulent energy flux generated by shock/homogeneous-turbulence interaction

Published online by Cambridge University Press:  28 April 2016

Russell Quadros ,
Krishnendu Sinha  and
Johan Larsson
Russell Quadros
Affiliation:
Department of Aerospace Engineering, Indian Institute of Technology Bombay, Mumbai 400076, India
Krishnendu Sinha*
Affiliation:
Department of Aerospace Engineering, Indian Institute of Technology Bombay, Mumbai 400076, India
Johan Larsson
Affiliation:
Department of Mechanical Engineering, University of Maryland, College Park, MD 20742, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

High-speed turbulent flows with shock waves are characterized by high localized surface heat transfer rates. Computational predictions are often inaccurate due to the limitations in modelling of the unclosed turbulent energy flux in the highly non-equilibrium regions of shock interaction. In this paper, we investigate the turbulent energy flux generated when homogeneous isotropic turbulence passes through a nominally normal shock wave. We use linear interaction analysis where the incoming turbulence is idealized as being composed of a collection of two-dimensional planar vorticity waves, and the shock wave is taken to be a discontinuity. The nature of the postshock turbulent energy flux is predicted to be strongly dependent on the angle of incidence of the incoming waves. The energy flux correlation is also decomposed into its vortical, entropy and acoustic contributions to understand its rapid non-monotonic variation behind the shock. Three-dimensional statistics, calculated by integrating two-dimensional results over a prescribed upstream energy spectrum, are compared with available data from direct numerical simulations. A detailed budget of the governing equation is also considered in order to gain insight into the underlying physics.

JFM classification

Turbulent Flows: Isotropic turbulence Compressible Flows: Shock waves
Type
Papers
Information
Journal of Fluid Mechanics , Volume 796 , 10 June 2016 , pp. 113 - 157
Check for updates
Copyright
© 2016 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bowersox, R. D. W. 2009 Extension of equilibrium turbulent heat flux models to high-speed shear flows. J. Fluid Mech. 633, 61–70.CrossRefGoogle Scholar
Brinckman, K. W., Calhoon, W. H. Jr & Dash, S. M. 2007 Scalar fluctuation modeling for high-speed aeropropulsive flows. AIAA J. 45 (5), 1036–1046.CrossRefGoogle Scholar
Cambon, C., Coleman, G. N. & Mansour, N. N. 1993 Rapid distortion analysis and direct simulation of compressible homogeneous turbulence at finite Mach number. J. Fluid Mech. 257, 641–665.CrossRefGoogle Scholar
Durbin, P. A. & Zeman, O. 1992 Rapid distortion theory for homogeneous compressed turbulence with application to modeling. J. Fluid Mech. 242, 349–370.CrossRefGoogle Scholar
Fabre, D., Jacquin, L. & Sesterhenn, J. 2001 Linear interaction of a cylindrical entropy spot with a shock. Phys. Fluids 13 (8), 2403–2422.Google Scholar
Goldberg, U. C., Palaniswamy, S., Batten, P. & Gupta, V. 2010 Variable turbulent Schmidt and Prandtl number modeling. Engng Appl. Comput. Fluid Mech. 4, 511–520.Google Scholar
Griffond, J. 2005 Linear interaction analysis applied to a mixture of two perfect gases. Phys. Fluids 17, 086101.CrossRefGoogle Scholar
Griffond, J., Soulard, O. & Souffland, D. 1993 Reynolds stress model fitted to match linear interaction analysis predictions. Phys. Scr. T142, 014059.Google Scholar
Hanifi, A. E., Alfredsson, P. H., Johansson, A. V. & Henningson, D. S. 1999 Transition, Turbulence and Combustion Modelling, ERCOFTAC Series.CrossRefGoogle Scholar
Jacquin, L., Cambon, C. & Blin, E. 1993 Turbulence amplification by a shock wave and rapid distortion theory. Phys. Fluids. A 5, 2539–2550.Google Scholar
Kovasznay, L. S. G. 1953 Turbulence in supersonic flow. J. Aeronaut. Sci. 20 (10), 657–674.Google Scholar
Larsson, J., Bermejo-Moreno, I. & Lele, S. K. 2013 Reynolds- and Mach number effects in canonical shock-turbulence interaction. J. Fluid Mech. 717, 293–321.CrossRefGoogle Scholar
Larsson, J. & Lele, S. K. 2009 Direct numerical simulation of canonical shock-turbulence interaction. Phys. Fluids 21, 126101.CrossRefGoogle Scholar
Lee, S., Lele, S. K. & Moin, P. 1993 Direct numerical simulation of isotropic turbulence interacting with a weak shock wave. J. Fluid Mech. 251, 533–562.Google Scholar
Lee, S., Lele, S. K. & Moin, P. 1997 Interaction of isotropic turbulence with shock waves: effect of shock strength. J. Fluid Mech. 340, 225–247.CrossRefGoogle Scholar
Mahesh, K., Lee, S., Lele, S. K. & Moin, P. 1995 The interaction of an isotropic field of acoustic waves with a shock wave. J. Fluid Mech. 300, 383–407.CrossRefGoogle Scholar
Mahesh, K., Lele, S. K. & Moin, P.1996 The interaction of a shock wave with a turbulent shear flow, Tech. Rep. 69. Thermosciences Division, Department of Mechanical Engineering, Stanford University, Stanford, CA.Google Scholar
Mahesh, K., Lele, S. K. & Moin, P. 1997 The influence of entropy fluctuations on the interaction of turbulence with a shock wave. J. Fluid Mech. 334, 353–379.Google Scholar
Menter, F. R. 1994 Two-equation eddy-viscosity turbulence models for engineering applications. AIAA J. 32 (8), 1598–1605.Google Scholar
Moore, F. K.1954 Unsteady oblique interaction of a shock wave with a plane disturbances, NACA Tech. Rep. 1165.Google Scholar
Morkovin, M. V. 1962 Effects of compressibility on turbulent flows. In Mécanique de la Turbulence (ed. Favre, A.), pp. 367–380. CNRS.Google Scholar
Pasha, A. A. & Sinha, K. 2008 Shock-unsteadiness model applied to oblique shock-wave/turbulent boundary-layer interaction. Intl J. Comput. Fluid Dyn. 22 (8), 569–582.Google Scholar
Pasha, A. A. & Sinha, K. 2012 Shock-unsteadiness model applied to hypersonic shock-wave/turbulent boundary-layer interactions. J. Propul. Power 28 (1), 46–60.CrossRefGoogle Scholar
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.CrossRefGoogle Scholar
Ribner, H. S.1953 Convection of a pattern of vorticity through a shock wave, NACA Tech. Rep. TN-2864.Google Scholar
Ribner, H. S.1954 Shock-turbulence interaction and the generation of noise, NACA Tech. Rep. 1233.Google Scholar
Ristorcelli, J. R. & Blaisdell, G. A. 1997 Consistent initial conditions for the DNS of compressible turbulence. Phys. Fluids 9 (1), 4–6.Google Scholar
Roy, C. J. & Blottner, F. G. 2001 Review and assessment of turbulence models for hypersonic flows. Prog. Aerosp. Sci. 42 (7), 469–530.CrossRefGoogle Scholar
Ryu, J. & Livescu, D. 2014 Turbulence structure behind the shock in canonical shock-vortical turbulence interaction. J. Fluid Mech. 756, R1.CrossRefGoogle Scholar
Schulein, E. 2006 Optical skin friction measurements in short-duration facilities. AIAA J. 44, 1732–1741.Google Scholar
Sinha, K. 2012 Evolution of enstrophy in shock/homogeneous turbulence interaction. J. Fluid Mech. 707, 74–110.Google Scholar
Sinha, K., Mahesh, K. & Candler, G. V. 2003 Modeling shock-unsteadiness in shock-turbulence interaction. Phys. Fluids 15, 2290–2297.CrossRefGoogle Scholar
Sinha, K., Mahesh, K. & Candler, G. V. 2005 Modeling the effect of shock unsteadiness in shock-wave/turbulent boundary-layer interactions. AIAA J. 43 (3), 586–594.Google Scholar
Sommer, T. P., So, R. M. C. & Zhang, H. S. 1993 Near-wall variable-Prandtl-number turbulence model for compressible flows. AIAA J. 31 (1), 27–35.Google Scholar
Thivet, F., Knight, D. D., Zheltovodov, A. A. & Maksimov, A. I. 2001 Importance of limiting the turbulent stresses to predict 3D shock-wave/boundary-layer interactions. In 23rd International Symposium on Shock Waves, Ft. Worth, TX, Paper No. 2761, p. 7.Google Scholar
Veera, V. K. & Sinha, K. 2009 Modelling the effect of upstream temperature fluctuations on shock/homogeneous turbulence interaction. Phys. Fluids 21, 025101.CrossRefGoogle Scholar
Wilcox, D. C. 2008 Formulation of the k–𝜔 turbulence model revisited. AIAA J. 46 (11), 2823–2838.Google Scholar
Wouchuk, J. G., de Lira, C. Huete Ruiz & Velikovich, A. L. 2009 Analytical linear theory for the interaction of a planar shock wave with an isotropic turbulent vorticity field. Phys. Rev. E 79, 066315.CrossRefGoogle ScholarPubMed
Xiao, X., Hassan, H. A., Edwards, J. R. & Gaffney, R. L. Jr. 2007 Role of turbulent Prandtl numbers on heat flux at hypersonic Mach numbers. AIAA J. 45 (4), 806–813.CrossRefGoogle Scholar