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Inviscid spatial stability of a compressible mixing layer. Part 3. Effect of thermodynamics

Published online by Cambridge University Press:  26 April 2006

T. L. Jackson
Affiliation:
Department of Mathematics and Statistics, Old Dominion University, Norfolk, VA 23529, USA
C. E. Grosch
Affiliation:
Department of Oceanography and Department of Computer Science, Old Dominion University, Norfolk, VA 23529, USA

Abstract

We report the results of a comprehensive comparative study of the inviscid spatial stability of a parallel compressible mixing layer using various models for the mean flow. The models are (i) the hyperbolic tangent profile for the mean speed and the Crocco relation for the mean temperature, with the Chapman viscosity–temperature relation and a Prandtl number of one; (ii) the Lock profile for the mean speed and the Crocco relation for the mean temperature, with the Chapman viscosity-temperature relation and a Prandtl number of one; and (iii) the similarity solution for the coupled velocity and temperature equations using the Sutherland viscosity–temperature relation and arbitrary but constant Prandtl number. The purpose of this study was to determine the sensitivity of the stability characteristics of the compressible mixing layer to the assumed thermodynamic properties of the fluid. It is shown that the qualitative features of the stability characteristics are quite similar for all models but that there are quantitative differences resulting from the difference in the thermodynamic models. In particular, we show that the stability characteristics are sensitive to the value of the Prandtl number and to a particular value of the temperature ratio across the mixing layer.

Type
Research Article
Copyright
© 1991 Cambridge University Press

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