Reverse flow and supersonic interference

Abstract

First, from a volumetric formulation of the momentum theorem of linearized theory, a general analytic proof is presented of the invariance of the drag of an arbitrary spatial distribution of horseshoe vortices and sources under reversal of the undisturbed flow. By consideration of the interference drag of two such singularity distributions, a reverse-flow relation for steady subsonic or supersonic flow is then obtained. This relation, a generalization of the Ursell-Ward theorem, may be applied to configurations with bodies whose surfaces are not quasi-cylindrical and whose surface pressures are quadratically related to the perturbation velocity.The relation is used to discuss several interfering two-body arrangements in supersonic flow. It is shown that, in certain cases, the drag and lift may be determined without knowledge of the interference flow field associated with the arbitrarily prescribed body geometry. The simplicity of the results permits the formulation of optimum problems. The invariance of the drag under flow reversal with unchanged geometry is also established.