A theoretical study of acoustic diffraction by a finite strip in uniform flow

Abstract

Concise and rigorous formulation and solution are derived by using on Wiener-Hopf technique and asymptotic integration for high frequency gust-airfoil interaction problem. Two single integral equations are constructed by decoupling manipulations and the complete solution in complex domain is obtained by series form of Kobayashi's generalized gamma function and also interpreted as (i) semi-infinite leading edge scattering term, (ii) trailingedge correction term and (iii) interaction term between leading and trailing edges, respectively. The inverse Fourier transform of the first two terms are evaluated exactly and the third term is evaluated by an asymptotic evaluation using saddle point method along the steepest descent path in complex plane adequate for high frequency or transonic Mach number. This solution has no restriction of observer's position due to singularities for some specific observation angles which appear in solutions based on geometrical theory of diffraction. And it is more efficient and easier to increase the accuracy of solution than Amiet's or Martinez&Widnall's obtained by using edge separation technique based on the idea of Schwarzscfaild who solved successive semi-infinite problems. Explicit solution in physical domain is visualized by the contour plot and directivity pattern of far field acoustics with the consideration of the effect of fluid convection. This fundamental mathematical work is also expected to be available for a benchmark problem for computational aeroacoustics.