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Homogenized Euler equation: a model for compressible velocity gradient dynamics

Published online by Cambridge University Press:  10 February 2009

S. SUMAN  and
S. S. GIRIMAJI
S. SUMAN*
Affiliation:
Department of Aerospace Engineering, Texas A&M University, College Station, TX 77843-3141, USAgirimaji@aero.tamu.edu
S. S. GIRIMAJI
Affiliation:
Department of Aerospace Engineering, Texas A&M University, College Station, TX 77843-3141, USAgirimaji@aero.tamu.edu
*
†Email address for correspondence: sawan@tamu.edu
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Abstract

Along the lines of the restricted Euler equation (REE) for incompressible flows, we develop homogenized Euler equation (HEE) for describing turbulent velocity gradient dynamics of an isentropic compressible calorically perfect gas. Starting from energy and state equations, an evolution equation for pressure Hessian is derived invoking uniform (homogeneous) velocity gradient assumption. Behaviour of principal strain rates, vorticity vector alignment and invariants of the normalized velocity gradient tensor is investigated conditioned on dilatation level. The HEE results agree very well with the known behaviour in the incompressible limit. Indeed, at zero dilatation HEE reproduces the incompressible anisotropic pressure Hessian behaviour very closely. When compared against compressible direct numerical simulation results, the HEE accurately captures the strain rate behaviour at different dilatation levels. The model also recovers the fixed point behaviour of pressure-released (high-Mach-number limit) Burgers turbulence.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 620 , 10 February 2009 , pp. 177 - 194
Copyright
Copyright © Cambridge University Press 2009

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