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Toward second-moment closure modelling of compressible shear flows

Published online by Cambridge University Press:  23 September 2013

Carlos A. Gomez  and
Sharath S. Girimaji
Carlos A. Gomez
Affiliation:
Department of Aerospace Engineering, Texas A&M University, College Station, TX 77843-3141, USA
Sharath S. Girimaji*
Affiliation:
Department of Aerospace Engineering, Texas A&M University, College Station, TX 77843-3141, USA
*
†Email address for correspondence: girimaji@tamu.edu
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Abstract

Compressibility profoundly affects many aspects of turbulence in high-speed flows, most notably stability characteristics, anisotropy, kinetic–potential energy interchange and spectral cascade rate. We develop a unified framework for modelling pressure-related compressibility effects by characterizing the role and action of pressure in different speed regimes. Rapid distortion theory is used to examine the physical connection between the various compressibility effects leading to model form suggestions for pressure–strain correlation, pressure–dilatation and dissipation evolution equations. The closure coefficients are established using fixed-point analysis by requiring consistency between model and DNS asymptotic behaviour in compressible homogeneous shear flow. The closure models are employed to compute high-speed mixing layers and boundary layers. The self-similar mixing-layer profile, increased Reynolds stress anisotropy and diminished mixing-layer growth rates with increasing Mach number are all well captured. High-speed boundary-layer results are also adequately replicated even without the use of advanced thermal-flux models or low-Reynolds-number corrections.

JFM classification

Turbulent Flows: Compressible turbulence Turbulent Flows: Shear layer turbulence Turbulent Flows: Turbulence modelling
Type
Papers
Information
Journal of Fluid Mechanics , Volume 733 , 25 October 2013 , pp. 325 - 369
Copyright
©2013 Cambridge University Press 

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