Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-19T11:45:51.210Z Has data issue: false hasContentIssue false
  • English
  • Français

Compressible turbulent channel flows: DNS results and modelling

Published online by Cambridge University Press:  26 April 2006

P. G. Huang ,
G. N. Coleman  and
P. Bradshaw
P. G. Huang
Affiliation:
MCAT, Inc. San Jose, CA 95127, USA
G. N. Coleman
Affiliation:
Mechanical, Aerospace, and Nuclear Engineering Department, Univ. of California, Los Angeles, CA 90024-1597, USA
P. Bradshaw
Affiliation:
Department of Mechanical Engineering, Stanford University, Stanford, CA 94305-3030, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

The present paper addresses some topical issues in modelling compressible turbulent shear flows. The work is based on direct numerical simulation (DNS) of two supersonic fully developed channel flows between very cold isothermal walls. Detailed decomposition and analysis of terms appearing in the mean momentum and energy equations are presented. The simulation results are used to provide insights into differences between conventional Reynolds and Favre averaging of the mean-flow and turbulent quantities. Study of the turbulence energy budget for the two cases shows that compressibility effects due to turbulent density and pressure fluctuations are insignificant. In particular, the dilatational dissipation and the mean product of the pressure and dilatation fluctuations are very small, contrary to the results of simulations for sheared homogeneous compressible turbulence and to recent proposals for models for general compressible turbulent flows. This provides a possible explanation of why the Van Driest density-weighted transformation (which ignores any true turbulent compressibility effects) is so successful in correlating compressible boundary-layer data. Finally, it is found that the DNS data do not support the strong Reynolds analogy. A more general representation of the analogy is analysed and shown to match the DNS data very well.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 305 , 25 December 1995 , pp. 185 - 218
Copyright
© 1995 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

Baz, A. M. EL & Launder B. E. 1993 Second-moment modelling of compressible mixing layers. In Engineerig Turbulence Modelling and Experiments (ed W. Rodi & F. Martelli). Elsevier.
Blaisdell, G. A., Mansour, N. N. & Reynolds, W. C. 1993 Compressibility effects on the growth and structure of homogeneous turbulent shear flow. J. Fluid Mech. 256. 443–485.Google Scholar
Bradshaw, P. & Perot, J. B. 1993 A note on turbulent energy dissipation im the viscous wall region. Phys. Fluids A 5, 3305–3306.Google Scholar
Cebeci, T. & Smith A. M. O. 1974 Analysis of Turbulent Boundary Layers Academic Press.
Coleman, G. N., Buell J. C., Kim, J. & Moser, R. D. 1993 Direct simulation of compresible wall-bounded turbulence. In 9th Turbulent Shear Flows Conference. Aug. 16–18, Kyoto, Japan.
Coleman, G. N., Kim, J. & Moser, R. D. 1993 A numerical study of turbulent supersonic isothermal-wall channael flow. J. Fluid Mech. 305, 159–183.Google Scholar
Dinavahi, S. P. G. & Pruett, C. D. 1993 Analysis of direct numerical simulation data of a Mach 4.5 transitional boundary layer flow. ASME Fluids Engineering Conference, June 21–24, Washington DC.
Favre, A. 1969 Statistical equations of turbulent gases. Problems of Hydrodynamics and Continuum Mechanics, pp. 231–266. Philadelphia: SIAM.
Fernholz, H. H. & Finley, P. J. 1980 A critical commentary on mean flow data for two dimensional compressible turbulent boundary layers. AGARD-AG-253.
Gaviglio, J. 1987 Reynolds analogies and experimental studies of heat transfer in the supersonic boundary layer. Intl J. Heat Mass Transfer 30, 911–926.Google Scholar
Huang, P. G. 1991 Comment on the present state and the future direction of second order closure models for compressible flows. Workshop on Engineering Turbulence Modeling NASA CP-10088.
Huang, P. G. 1995 Relations between viscous diffusion and dissipation of turbulent kinetic energy. Presented at the Tenth Symposium on Turbulent Shear Flows, Penn. State U., Aug. 14–16. pp. 2-79–2-84.
Huang, P. G., Bradshaw, P. & Coakley, T. J. 1993 Skin friction and velocity profile family for compressible turbulent boundary layers. AIAA J. 31, 1600–1604.Google Scholar
Huang, P. G., Bradshaw, P. & Coakley, T. J. 1994 Turbulent models for compressible boundary layers. AIAA J. 32 735 740.Google Scholar
Huang, P. G. & Coleman, G. N. 1994 Van Driest transformation and compressible wall-bounded flows. AIAA J. 32 2110–2113 (and Errata AIAA J. 33, 1756).Google Scholar
Kim, J. & Moin, P. 1989 Transport of passive scalars in a turbulent channel flow. In Turbulent Shear Flows 6 (ed. J. C. André et. al.). Springer.
Kim, J., Moin, P. & Moser, R. D. 1987 Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133–166.Google Scholar
Lele, S. K. 1994 Compressibility effects on turbulence. Ann. Rev. Fluid Mech. 26, 211–254.Google Scholar
Mansour, N. N., Kim, J. & Moin, P. 1988 Reynolds-stress and dissipation-rate budgets in a turbulent channel flow. J. Fluid Mech. 194, 15–44.Google Scholar
Morkovin, M. V. 1964 Effects of compressibility on turbulent flows. In Mechanique de la Turbulence (ed. A. Favre), pp. 367–380. Gordon and Breach.
Reynolds, O. 1895 On the dynamical theory of incompressible viscous fluids and the determination of the criterion. Phil. Truns. R. Soc. Lond. A 186, 123–164.Google Scholar
Ristorcelli, J. R. 1993 A representation for the turbulent mass flux contribution to Reynolds-stress and two-equation closures for compressible turbulence. ICASE Rep. 93-88.
Rubesin, M. W. 1990 Extra compressibility terms for Favre-averaged two-equation models of inhomogeneous turbulent flows. NASA CR-177556.
Sarkar, S. 1995 The stabilizing effect of compressibility in turbulent shear flow. J. Fluid Mech. 282, 163–186.Google Scholar
Sarkar, S., Erlebacher, G. & Hussaini, M. Y. 1992 Compressible homogeneous shear: simulation and modeling. In Turbulent Shear Flows 8 (ed. F. Durst et al.). Springer.
Sarkar, S., Erlebacher, G., Hussaini, M. Y. & Kreiss, H. O. 1989 The analysis and modeling of dilatational terms in compressible turbulence. J. Fluid Mech. 227, 473–493.Google Scholar
Spina, E. F., Smits, A. J. & Robinson, S. K. 1994 The physics of supersonic turbulent boundary layers. Ann. Rev. Fluid Mech. 26, 287–319.Google Scholar
Driest, E. R. Van 1951 Turbulent boundary layer in compressible fluids. J. Aero. Sci. 18 145-160 and 216.Google Scholar
Zeman, O. 1990 Dilatational dissipation: the concept and application in modeling compressible turbulence. Phys. Fluids A 2, 178–188.Google Scholar
Zeman, O. 1993 New model for super/hypersonic turbulent boundary layers. AIAA Paper 93–0897.Google Scholar