An Inverse Design Method for Wings Using Integral Equations and Its Recent Progress

Abstract

An inverse design method using integral equations is explicated. Two other recently developed design methods are introduced. They are the extension of the first method. The formulation of an inverse problem used in each design method is also discussed for three major design categories. Each method designs a wing section shape which realizes the prescribed target pressure distribution by iterating a residual-correction loop which consists of a flow simulation and an inverse problem. It starts with the initial guess of current wing shape. The residual, defined as the difference between the target and simulated current pressure distributions, is compensated by solving the inverse problem. The inverse problem determines the section geometry of the wing. Each of three inverse problems here are formulated to be an integral equation system by mathematically converting the partial differential equations which govern the flowfield. The first inverse problem is for transonic wing design. The second one is for supersonic and the third one is for design of multiple wing systems. Emphasis is put on the discussion of the formulation. Works on wing design using the method with the first inverse problem are cited. Design problems by the second and third ones are also presented.