Previous investigations have demonstrated that a compressible reacting mixing layer can develop two instability modes in addition to the more common central mode that exists unaccompanied in incompressible nonreacting flows. These two additional modes are termed “outer” because of their association with the fast and slow free streams. Numerical simulations have shown that mixing layers dominated by outer modes have a lower global reaction rate in comparison to a flow structure governed by the central mode. Therefore, the presence of these modes has important consequences for applications in supersonic combustion. Results are presented from a parametric study of the compressible reacting mixing layer’s regime space using linear stability analysis. The focus of our work is to develop a better understanding for the combined effects of compressibility, heat release and the ratios of density, equivalence, and velocity on the instability characteristics of each mode and on the structure predicted to result in a turbulent reacting mixing layer.

The parabolized stability equations (PSE) are used to investigate issues of nonlinear flow development and mixing in compressible reacting shear layers, which are modelled with an infinitely fast-chemistry assumption. Particular emphasis is placed on investigating the change in flow structure that occurs when compressibility and heat release are added to the flow. These conditions allow the ‘outer’ instability modes – one associated with each of the fast and slow streams – to dominate over the ‘central’, Kelvin–Helmholtz mode that exists unaccompanied in incompressible non-reacting mixing layers. Analysis of scalar probability density functions in flows with dominant outer modes demonstrates the ineffective, one-sided nature of mixing that accompanies these flow structures. Colayer conditions, where two modes have equal growth rate and the mixing layer is formed by two sets of vortices, offer some opportunity for mixing enhancement. Their extent, however, is found to be limited in the mixing layer's parameter space. Extensive validation of the PSE technique also provides a unique perspective on central-mode vortex pairing, further supporting the view that pairing is primarily governed by instability growth rates; mutual induction appears to be a secondary process. This perspective sheds light on how linear stability theory is able to provide such an accurate prediction of experimentally observed, fully nonlinear flow phenomenon.

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The ability of the velocity ratio parameter λ=(U1−U2)/(U1+U2) to scale linear stability amplification rates for a compressible reacting and compressible variable-density mixing layer is reported. Extensions to the definition of λ to reflect the dominance of outer modes in the flow structure at significant levels of heat release and compressibility are proposed and their performance is evaluated.