Theory of Laminar Viscous-Inviscid Interactions in Supersonic Flow

This investigation is concerned with those fluid-mechanical problems in which the pressure distribution is determined by the interaction between an external, supersonic inviscid flow and an inner, laminar viscous layer. The boundary-layer approximations are assumed to remain valid throughout the viscous region, and the integral or moment method of Lees and Reeves, extended to include flows with heat transfer; is used in the analysis. The general features of interacting flows are established, including the important distinctions between subcritical and supercritical viscous layers. The eigensolution representing self-induced boundary-layer flow along a semi-infinite flat plate is determined, and a consistent set of departure conditions is derived for determining solutions to interactions caused by external disturbances. Complete viscous-inviscid interactions are discussed in detail, with emphasis on methods of solution for both subcritical and supercritical flows. The method is also shown to be capable of predicting the laminar flow field in the near wake of blunt bodies. Results of the present theory are shown to be in good agreement with the measurements of Lewis for boundary-layer separation in adiabatic and non-adiabatic compression corners, and with the near-wake experiments of Dewey and McCarthy for adiabatic flow over a circular cylinder. Extensions of the method to flows with mass injection at the surface and to subsonic interactions are indicated.

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