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Rapid distortion analysis and direct simulation of compressible homogeneous turbulence at finite Mach number

Published online by Cambridge University Press:  26 April 2006

C. Cambon ,
G. N. Coleman  and
N. N. Mansour
C. Cambon
Affiliation:
Laboratoire de Mécanique des Fluides et d'Acoustique, URA CNRS no. 263, Ecole Centrale de Lyon, 69130 Ecully, France
G. N. Coleman
Affiliation:
Center for Turbulence Research, Stanford University, Stanford, CA 94305-3030, USA
N. N. Mansour
Affiliation:
NASA Ames Research Center, Moffett Field, CA 94035-1000, USA
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Abstract

The effect of rapid mean compression on compressible turbulence at a range of turbulent Mach numbers is investigated. Rapid distortion theory (RDT) and direct numerical simulation results for the case of axial (one-dimensional) compression are used to illustrate the existence of two distinct rapid compression regimes. These regimes – the nearly solenoidal and the ‘pressure-released’ – are defined by a single parameter involving the timescales of the mean distortion, the turbulence, and the speed of sound. A general RDT formulation is developed and is proposed as a means of improving turbulence models for compressible flows. In contrast to the well-documented observation that ‘compressibility’ (measured, for example, by the turbulent Mach number) is often associated with a decrease in the growth rate of turbulent kinetic energy, we find that under rapid distortion compressibility can produce an amplification of the kinetic energy growth rate. We also find that as the compressibility increases, the magnitude of the pressure–dilation correlation increases, in absolute terms, but its relative importance decreases compared to the magnitude of the kinetic energy production.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 257 , December 1993 , pp. 641 - 665
Copyright
© 1993 Cambridge University Press

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