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Three-dimensional simulations of large eddies in the compressible mixing layer

Published online by Cambridge University Press:  26 April 2006

N. D. Sandham  and
W. C. Reynolds
N. D. Sandham
Affiliation:
DLR, Institute for Theoretical Fluid Mechanics, Gottingen, Germany
W. C. Reynolds
Affiliation:
Stanford University, Stanford, CA 94305, USA and NASA Ames Research Center, Moffett Field, CA 94035, USA
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Abstract

The effect of Mach number on the evolution of instabilities in the compressible mixing layer is investigated. The full time-dependent compressible Navier–Stokes equations are solved numerically for a temporally evolving mixing layer using a mixed spectral and high-order finite difference method. The convective Mach number Mc (the ratio of the velocity difference to the sum of the free-stream sound speeds) is used as the compressibility parameter. Simulations with random initial conditions confirm the prediction of linear stability theory that at high Mach numbers (Mc > 0.6) oblique waves grow more rapidly than two-dimensional waves. Simulations are then presented of the nonlinear temporal evolution of the most rapidly amplified linear instability waves. A change in the developed large-scale structure is observed as the Mach number is increased, with vortical regions oriented in a more oblique manner at the higher Mach numbers. At convective Mach numbers above unity the two-dimensional instability is found to have little effect on the flow development, which is dominated by the oblique instability waves. The nonlinear structure which develops from a pair of equal and opposite oblique instability waves is found to resemble a pair of inclined A-vortices which are staggered in the streamwise direction. A fully nonlinear computation with a random initial condition shows the development of large-scale structure similar to the simulations with forcing. It is concluded that there are strong compressibility effects on the structure of the mixing layer and that highly three-dimensional structures develop from the primary inflexional instability of the flow at high Mach numbers.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 224 , March 1991 , pp. 133 - 158
Copyright
© 1991 Cambridge University Press

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