An inverse method with regularity condition for transonic airfoil design

Summary It is known from Lighthill's exact solution of the incompressible inverse problem that in the inverse design problem the surface pressure distribution and the free stream speed cannot both be prescribed independently. This implies the existence of a constraint (regularity condition) on the prescribed pressure distribution. The same constraint exists at compressible speeds. In this paper, an inverse design method for transonic airfoil is presented. In the method, the target pressure distribution contains a free parameter that is adjusted during the computation to satisfy the regularity condition derived in this paper. A few design results are presented here in order to demonstrate the capability of the method.