A numerical investigation of the compressible mixing layer
Abstract
The effect of Mach number on the plane mixing layer was investigated by means of linear stability theory and 2D and 3D 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 3D waves are more amplified than 2D 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. Threedimensional 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 2D 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 convection 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 2D instability wave has little effect on flow structure. Similar organized structure was found in s simulation with random initial conditions.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 September 1989
 Bibcode:
 1989STIN...9020343S
 Keywords:

 Combustion;
 Compressible Flow;
 Digital Simulation;
 Mach Number;
 Mixing Layers (Fluids);
 Turbulent Flow;
 Convection;
 Jet Mixing Flow;
 Linearity;
 Modular Ratios;
 NavierStokes Equation;
 Shock Waves;
 Supersonic Flow;
 Fluid Mechanics and Heat Transfer