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This paper investigates the linear stability of confined mixing layers with special emphasis on the effects of heat release and compressibility. The results show that reflection of supersonic disturbances by the walls makes the confined supersonic mixing layer more unstable than the unconfined free shear layer. Decreasing the distance between the walls makes the flow more unstable. However, subsonic disturbances are relatively unaffected by the walls. Heat release and Mach number hardly change the growth rates of supersonic disturbances. The most unstable supersonic disturbances are two-dimensional in rectangular channel flows, but three-dimensional in partially confined flows. Finally, the reactants are not strongly mixed by supersonic instabilities, which mainly disturb one side of the layer.

Linear instability of compressible reacting mixing layers is analyzed with emphasis on the effects of heat release and compressibility. Laminar solutions of the compressible boundary-layer equations are used as the base flows. The parameters of this study are the adiabatic flame temperature, the Mach number of the upper stream, frequency, wavenumber, and the direction of propagation of the disturbance wave. Stability characteristics of the flow are presented. Three groups of unstable modes are found when the Mach number and/or heat release are large. Finally, it is shown that the unstable modes are two-dimensional for large heat release even in highly compressible flow.

This work is aimed at understanding the stability of reacting mixing layers. Linear instability is analyzed for a wide variety of mixing layers to study the effects of the heat release. Analytic functions as well as laminar solutions of thin shear layer equations are used as the base flows. Both temporal and spatial developing layers are investigated. The laminar solutions are more consistent than the analytic functions. The stability properties are sensitive to the mean profiles. Including variable transport properties changes the mean profiles considerably. Chemical reaction during the instability is not very important; its primary effect is to change the laminar profiles. New modes are found in the outer part of the layer when the heat release is significant, and become dominant for large heat release. In general, heat release stabilizes the center mode but the outer mode is less affected.