The Blowhard Problem- Inviscid Flows with Surface Injection

A simple model is presented for the analysis of inviscid flow fields over slender bodies accompanied by high rates of surface mass transfer. This model assumes a thin, inviscid injectant layer, which is separated from the outer flow by a contact discontinuity. Inviscid boundary-layer equations are shown to be applicable within the injectant layer, and the pressure gradient is found by matching pressure and flow direction at the dividing streamline. Using stream-function variables, an Abel integral equation is derived, and the inverse problem of determining the injection distribution from the shape of the dividing streamline is solved analytically for supersonic and hypersonic flow over flat plates and cones.