Second-order forces and pressure distributions on three-dimensional bodies by reverse-flow integral method

Abstract

The general second-order reverse-flow relation derived by Glarke has been applied to fusiform bodies and to combinations of fusiform bodies and quasi-cylindrical wings. It is first shown that the second-order drag of an isolated fusiform body can be expressed in terms of the firstorder forward and reverse flow over the body provided the angle of incidence is not too large. The innovation of a reverse flow which is not simply antiparallel to the forward-flow at infinity is introduced and then used to derive separate integral statements on the three rectangular components of the second-order velocity perturbation on the surface of an isolated fusiform body. Two of these integral statements are inverted to yield information on the second-order surface pressure distribution. The inversions effected are valid for unrestricted incidence. The uninclined body is covered as a special case. By considering the perturbation field of a wing-body combination as a sum of isolated body and wing fields and an interference field, the leading contribution of the interference field to the second-order drag is obtained from the reverse-flow relation. The result presumes that the second-order fields of the isolated body and wing are known in advance. The reverse flow due to a two-dimensional flat-plate wing is then used to achieve an integral for the leading second-order contribution to the lift on a wing-body combination. This integral is used to calculate the lift contribution on the conical wing-body configuration for cone half-angles dc of 5° and 10°. The numerical results are compared to those obtained by direct application of Van Dyke's second-order cone potential. The difference ranges from 4%, for [(M2 — 1)1/2 tanSc] = 0.2, to 16%, for [(M2 - 1) 1/2 tanSc] = 0.8.