Diffraction of Disturbances Around a Convex Right Corner With Applications in Acoustics and Wing-Body Interference

The problem of the diffraction of a small disturbance or an arbitrary pulse by a convex right-angled corner is reduced to two unsteady problems in half space. The matching of the boundary conditions of the solutions to these two problems leads to a nonhomogeneous integral equation for the pressure distribution along the boundary. The solution is obtained by the method of successive substitution. I t is shown that the series given by this procedure converges faster than the power series of one half. The convergence of the series is accelerated by regrouping the terms so that the solutions corresponding to any one of the ordinal numbers of substitution possesses the correct behavior at the boundary of the domain. When the given disturbance is a plane weak (acoustic) shock, the solution corresponding to the second substitution is already in good agreement with the linearized conical solution. For the other two nonconical fundamental problems considered in this paper, the series converges so rapidly that there is no necessity to go beyond the second substitution. By superposition of these fundamental solutions, the pressure distribution on a rectangular barrier after it is contacted by a weak shock is obtained. The problem of interference of a prismatic body of rectangular cross section with a planar wing in supersonic flight can be reduced to the problem presented in this paper and the one amenable to solution by Evvard's method. The pressure distribution is obtained for four different wing-body configurations. The value of the integral of the pressure distribution agrees with the value obtained directly by means of a certain integral relationship.