A numerical method for solving the three–dimensional aerothermodynamic design problem with some type of the Mach number distributions on the blade surfaces is presented. In the usual aerothermodynamic design of a turbomachinery the three–dimensional coordinates of the blade is attained through the stacking of the cascade profiles and may not ensure the desired velocity distribution. To avoid this problem the present method will give new coordinates of the blade according to the required Mach number distribution. The method is based on the pseudostream function formulation and the treatment of the boundary conditions in the design problem is given. The numerical results show that the method is simple and useful in design.

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