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Second-order modelling of a variable-density mixing layer

Published online by Cambridge University Press:  21 April 2006

Tsan-Hsing Shih ,
John L. Lumley  and
J. Janicka
Tsan-Hsing Shih
Affiliation:
Sibley School of Mechanical & Aerospace Engineering, Cornell University. Ithaca, NY 14853, USA
John L. Lumley
Affiliation:
Sibley School of Mechanical & Aerospace Engineering, Cornell University. Ithaca, NY 14853, USA
J. Janicka
Affiliation:
Institut fur Technische Thermodynamik, RWTH-Aachen, West Germany Present address: Krupp-Koppers GmbH, Moltkestrasse 27, D-41 Essen, West Germany.
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Abstract

A conventional (non-density-weighted) averaging method is used to study variable-density turbulent flows, in particular, a helium-nitrogen mixing layer. A careful order-of-magnitude analysis is carried out, first in relative density fluctuations, and then in the ratio of cross-stream to streamwise lengthscales. In this way it is shown that, to lowest order, in jets and shear layers, the turbulence is unafffected by the density fluctuations, and conventional models can be used. The non-uniform density distribution influences only the mean-continuity and mean-momentum equations. Calculations (using a new form for the scalar-dissipation equation based on relaxation to an equilibrium timescale ratio) show good agreement with experiment. Calculation with a less truncated system indicates that neglected terms have little effect. We use a modified Patankar-Spalding method that overcomes numerical stability difficulties.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 180 , July 1987 , pp. 93 - 116
Copyright
© 1987 Cambridge University Press

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