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

Sandham, N.D. and Reynolds, W.C. (1991) Three-dimensional simulations of large eddies in the compressible mixing layer Journal of Fluid Mechanics, 224, pp. 133-158. (doi:10.1017/S0022112091001684).


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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

Item Type: Article
Digital Object Identifier (DOI): doi:10.1017/S0022112091001684
ISSNs: 0022-1120 (print)
ePrint ID: 72047
Date :
Date Event
Date Deposited: 18 Jan 2010
Last Modified: 18 Apr 2017 20:58
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