Journal of Fluid Mechanics

Compressible turbulent channel flows: DNS results and modelling

P. G.  Huang a1c1, G. N.  Coleman a2 and P.  Bradshaw a3
a1 MCAT, Inc. San Jose, CA 95127, USA
a2 Mechanical, Aerospace, and Nuclear Engineering Department, Univ. of California, Los Angeles, CA 90024-1597, USA
a3 Department of Mechanical Engineering, Stanford University, Stanford, CA 94305-3030, USA

Article author query
huang pg   [Google Scholar] 
coleman gn   [Google Scholar] 
bradshaw p   [Google Scholar] 


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.

(Published Online April 26 2006)
(Revised August 11 1995)
(Revised November 1 1994)

c1 Mailing address: mail stop 229-1, NASA Ames Research center, Moffett Field, CA 94035, USA.