A new numerical method for solving inverse aerodynamic shape design problem of airfoils in a linear periodic cascade using a fully-viscous compressible flow model has been developed. The general inverse problem refers to the problem in which the pressure distributions on suction and pressure surfaces of the airfoil are given, but the corresponding airfoil shape is unknown. The calculations are performed directly in the physical plane by Navier-Stokes equations employing nonorthogonal curvilinear H-type grid and nonorthogonal velocity components. In this article, the MacCormack's explicit time-marching algorithm with Baldwin-Lomax turbulence model are adopted as the basic flow solver. In order to satisfy the specified surface pressure distribution, the blade surface points move regularly with integration time steps until zero surface normal velocity is reached. Comparison of numerical and experimental results indicates that the method is very effective.
