On subsonic, supersonic and hypersonic inflectional-wave/vortex interaction

Abstract

An unstable inflection point developing in an oncoming two-dimensional boundary layer can give rise to nonlinear three-dimensional inflectional-wave/vortex interaction as described in recent papers by Hall and Smith [1], Brown et al. [2], and Smith et al. [3]. In the current study on the compressible range the flow is examined theoretically just downstream of the linear neutral position, in order to understand how the interaction may be initiated. The research addresses both moderately and strongly compressible regimes. In the latter regime the vorticity mode, the most dangerous one, is taken as the wave part, causing the hypersonic interaction to become concentrated in a thin temperature-adjustment layer lying at the outer edge of the boundary layer, just below the free stream. In both regimes, the result is a nonlinear integro-differential equation for the wave-pressure which implies four different types of downstream behaviour for the interaction -a far-downstream saturation, a finite-distance singularity, exponentially decaying waves (leaving pure vortex motion) or periodicity. In a principal finding of the study, the coefficients of the equation are worked out explicitly for hypersonic flow, and in particular for the case of unit Prandtl number and a Chapman fluid, where it is shown that for sufficiently high wall temperatures the wave angle of propagation must lie between 45 ° and 90 ° relative to the free-stream direction and also no periodic solutions may occur then. The theory applies also to wake flows and others. Connections with experimental findings are noted.