Numerical treatment of parabolic three dimensional cascade flow. Flow modeling and computational experiments

A method of solution for three dimensional cascade flow is illustrated. The flow is assumed laminar and incompressible. The governing equations consist of three equations of motion, an energy equation, and a continuity equation. The addition of the energy equation results in easier and numerically more stable handling by the proposed method of solution, and allows for eventual computation of compressible flows. As the calculation of reverse flow is not included, the governing equations are parabolized in the downstream direction. The downstream pressure gradient is iteratively corrected by permanent control of the overall mass flow. The choice of a nonorthogonal, curvilinear coordinate system makes it possible to accommodate different cascade contours.