Sandham, N.D.
(1989)
A numerical investigation of the compressible mixing layer.
*Stanford University, Department of Mechanical Engineering, Doctoral Thesis*, 244pp.

## Abstract

The effect of Mach number on the plane muong layer has been investigated by means of linear stability theory and two- and three-dimensional direct numerical simulations of the compressible Navier-Stokes equations. The objective was to identify the effects of compressibility on a building-block fluid flow, with applications to supersonic mixing and combustion.

Results from linear stability theory show that the amplification rate is reduced as Mach number is increased. Above a convective Mach number of 0.6 it is found that three-dimensional waves are more amplified than two-dimensional waves and a simple relation is found to give the orientation of the most amplified waves. It is

also shown that the linear stability theory can be used to predict the mixing layer growth rate as a function of velocity ratio, density ratio and Mach number.

Two-dimensional simulations show a strong reduction in growth rate of the two-dimensional motion as Mach number is increased, with more elongated structures forming at high Mach numbers. Shock waves are observed in two-dimensional simulations above a convective Mach number of 0.7. The supersonic modes of instability, which are the only two-dimensional unstable modes at high Mach numbers, are shown to be radiating and vortical, but have very low growth rates.

Three-dimensional simulations with random initial conditions confirm the linear stability result that oblique waves become the most amplified waves at high Mach numbers, with no evidence for any other modes of instability. Simulations beginning with a two-dimensional wave and a pair of equal and opposite oblique waves show a change in the evolved large-scale structure as Mach number is increased. Above a convective Mach number of 0.6 the oblique modes have most of the energy in the developed structure, and above a convective Mach number of 1 the two-dimensional instability wave has little effect on flow structure. Similar organized structure was found in a simulation with random initial conditions. No shock waves were found in the three-dimensional simulations, even at convective Mach numbers above 1.

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