Pressure distribution on a surface with large normal injection.

Abstract

The changes in forces acting on a body moving at high speed because of large normal injection are investigated. The injection velocity is assumed to be much smaller than the velocity of the body but much larger than the value allowed for the boundary-layer theory. Based on these two conditions, the flowfield is governed by the inviscid equations with a discontinuity in velocity along the streamline that separates the inner region of the injected fluid from the outer region of freestream, and the flowfield in the inner region is assumed to be incompressible. Using linearized supersonic theory for the outer region, analytic solutions for injection with constant stagnation pressure (pSj) along the surface of a wedge are obtained. The dividing streamline is inclined to the wedge surface at a small angle 0o continuing nearly straight over the portion of the wedge with injection, and thereafter turning parallel to the wedge surface. The deflection of the outer flow by the angle 00 raises the pressure from the downstream value pm to psj. The additional force and moment caused by injection are obtained with the leading term equivalent to the rise of pressure from pm to pSj over the portion of the surface with injection, and the correction term is of the order 0o.