Inverse method with geometric constraints for transonic aerofoil design

An engineering method for the design of aerofoils 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 (multi‐grid) finite‐volume full‐potential code. Corrections to the geometry driving the pressure residual to zero are determined by a global, inverse, thin‐aerofoil theory based method for the subsonic part of the flow field, and by means of a local, inverse, wavy‐wall theory based formula for the supersonic part of the flow field. The determination of the geometry correction has been formulated as a minimization problem in the sense that pressure distribution and geometry requirements may be balanced in a weighted least squares sense. The method is described briefly, including the basic mathematical/physical formulation and the main computational aspects. The capabilities of the method are illustrated by means of examples of aerofoil designs.