# Algebraic Reynolds stress and scalar flux modeling for compressible mixing layer

DOI: 10.1615/ICHMT.2012.ProcSevIntSympTurbHeatTransfPal.1250
pages 1214-1217

M. Karimi
Aerospace Engineering Department, Texas A&M University, College Station, TX 77843, USA; Max Planck Institute for Meteorology, Bundesstr. 53, 20146 Hamburg, Germany

Sharath S. Girimaji
Department of Aerospace Engineering, Texas A&M University, College Station, Texas, USA; Department of Ocean Engineering, Texas A&M University, College Station, Texas, USA

C. A. Gomez
Aerospace Engineering Department, Texas A&M University, College Station, TX 77843, USA

## Abstract

We describe the formulation of new algebraic closures for the passive scalar flux and Reynolds stresses for compressible flows. Analogous to algebraic Reynolds stress modeling, the weak-equilibrium assumption is invoked to formulate the algebraic approximation from the exact transport equations of the normalized scalar flux. We employ a pressure-scalar gradient correlation that is valid over a wide range of gradient Mach numbers, Mg and consistent with rapid distortion theory. The pressure-scalar gradient closure varies with Mg as follows: (i) the incompressible model is used at low Mg, (ii) the pressure effects are taken to be negligible compared to inertial term at very large Mg, and (iii) the action of pressure is taken to nullify the inertial effects at intermediate Mach numbers. The algebraic roots selection criteria and parameter constraints to ensure stable computations are discussed. Finally, preliminary tests for mixing layer flows are performed and the results indicate that the model performs adequately.

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