Inverse Method with Geometry Constraints for Transonic Airfoil Design

摘要

An engineering method for the design of airfoils having a prescribed pressure distribution in subsonic or transonic flow is described. The method is based on an iterative procedure of residual-correction type. In each iteration step, the difference between a current and a target pressure distribution (residual) is determined by a fast (multigrid) finite volume full-potential code. Corrections to the geometry driving the pressure residual to zero are determined by a global, inverse, thin airfoil theory based method for the subsonic part of the flow field, and by a local, inverse wavy-wall theory based formula for the supersonic part of the flow field. The determination of the geometry correction is formulated as a minimization problem, in that pressure distribution and geometry requirements may be balanced in a weighted least squares sense. The capabilities of the method are illustrated by examples of airfoil designs.