An investigation of the inviscid spatial instability of compressible mixing layers

Citation

Zhuang, Mei (1990) An investigation of the inviscid spatial instability of compressible mixing layers. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/650s-9t96. https://resolver.caltech.edu/CaltechETD:etd-11132007-094001

Abstract

NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. The behavior of both unbounded and bounded compressible plane mixing layers with respect to two- and three-dimensional, spatially growing wave disturbances is investigated using linear stability analysis. The mixing layer is formed by two parallel streams with different gases and the flow is assumed to be inviscid and non-reacting. For unbounded mixing layers, the effects of the free stream Mach number, velocity ratio, temperature ratio, gas constant (molecular weight) ratio and the ratios of specific heats on the linear spatial instability characteristics of a mixing layer are determined. A nearly universal dependence of the normalized maximum amplification rate on the convective Mach number is found for two-dimensional spatially growing disturbances. The effects of the mean flow profiles on the instability behavior of the mixing layers are also studied. It is shown that decreasing the thickness of the total temperature profile relative to the mean velocity profile, or adding a wake component in the mean velocity profile can make the normalized amplification rate decrease slower as the convective Mach number increases for both subsonic and supersonic convective Mach numbers. For an unbounded mixing layer with subsonic convective Mach numbers, there is only one unstable mode propagating with a phase velocity [...] approximately equal to the isentropically estimated convective velocity of the large scale structures [...]. As the convective Mach number approaches or exceeds unity, there are always two unstable spatial modes. One is with a phase velocity [...] (slow mode and the other is with a phase velocity [...] (fast mode). For the low supersonic convective Mach numbers, the fast mode is more unstable than the slow mode when the heavy gas is on the low speed side and the slow mode is dominant when the heavy gas is on the high speed side. The effect of parallel flow guide walls on a spatially growing mixing layer is also investigated. It is shown that, in this case, if the convective Mach number exceeds a critical value of approximately unity, there are many supersonic unstable modes. The maximum amplification rates of mixing layers approach an asymptotic value and this maximum amplification rate increases to a maximum value and decreases again as the distance between the walls decreases. For a mixing layer inside parallel flow guide walls, the growth rate of three-dimensional modes is larger than the corresponding two-dimensional mode at high convective Mach numbers. But the growth rate of two-dimensional supersonic instability waves has a larger value than their three-dimensional counterparts for a mixing layer inside a rectangular duct (Tam & Hu [1988], [1989]). Contour plots of the pressure perturbation fields for both unbounded and bounded mixing layers indicate that there are waves propagating outward from the mixing layer along the Mach angle, and that the walls provide a feedback mechanism between the growing mixing layer and this compression/expansion wave system. The bounded mixing layers are more unstable than the corresponding free mixing layers for supersonic convective Mach numbers. The streaklines of the flow confirm that the spreading rate of the mixing layer is unusually small for supersonic disturbances.

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