Transonic flow past thin wings

Abstract

This paper is devoted to a discussion of steady inviscid transonic flow past thin wings, with subsonic free-stream Mach number M∞ < 1, by the integral equation method. The integral equation formulation is developed for a thin unsymmetric wing at small incidence. A simple approximate analytical solution is presented for shock-free supercritical flow past a thin symmetric wing at zero incidence. The direct iteration scheme of Niyogi and Chakraborty is then extended to the three-dimensional zero incidence case, which may be used to obtain more accurate solutions for shockfree flows as well as for flows with shocks. The question of the existence and the uniqueness of a solution has been studied by means of the Banach contraction mapping principle in the spaceL 2 (E3), which establishes the condition of convergence of the direct iteration scheme. Simultaneously it provides us with an error estimate for the solution.