The instability and acoustic wave modes of supersonic mixing layers inside a rectangular channel

Abstract

At high supersonic convective Mach numbers the familiar Kelvin-Helmholtz instability of a thin unconfined two-dimensional shear layer becomes neutrally stable. In this paper, it is shown that when the same shear layer is put inside a rectangular channel the coupling between the motion of the shear layer and the acoustic modes of the channel produces new two-dimensional instability waves. The instability mechanism of these waves is examined. Extensive numerical computation of the properties of these new instability waves has been carried out. Based on these results two classes of these waves are identified. Some of the important characteristic features of these waves are reported in this paper. In addition to the unstable waves, a thorough analysis of the normal modes of a supersonic shear layer inside a rectangular channel reveals that there are basically two other families of neutral acoustic waves. Examples of some of the prominent characteristics of these neutral acoustic waves are also provided in this paper. The new instability waves are the dominant instabilities of a confined mixing layer at high supersonic convective Mach number. As such they are very relevant to the supersonic mixing and combustion processes inside a ramjet engine combustion chamber.