A coordinate system for a viscous transonic cascade analysis

Abstract A coordinate system suitable for the numerical computation of viscous transonic cascade flows is constructed. The system consists of coordinate loops surrounding the airfoil and radial coordinate lines normal to the airfoil surface. The outermost loop is constructed so that the cascade periodicity conditions can be applied without interpolation between grid points. The coordinates are orthogonal on the airfoil surface but gradually become nonorthogonal away from the airfoil. The coordinate distribution of mesh points is simple and direct; this is a useful property for the resolution of large solution gradients. In addition to the above, the coordinates are generated from discrete input data, little restriction is placed on airfoil camber or spacing, and the entire analysis is easily extended to three dimensions. Moreover, the method of coordinate generation can be readily applied to a wide variety of other problems.

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