Inverse methods able to work in the transonic regime have for a long time been the weak part in the inverse method universe, albeit most of current gas turbines work in this regime. The present iterative inverse method is based on a Finite Volume time-marching scheme that is able to accurately compute the flowfield inside turbomachinery passages. In our design method we prescribe the acrodynamic load and blade thickness. Imposition of these variables precludes any existence and uniqueness problems and enables us to incorporate information regarding thermal and mechanical stresses in the first design stages. The method herein presented starts with an analysis of the flow in an initial geometry that is afterward adjusted by a modification in camber line. A new time-lagged formulation for the camber line generator will be presented. In order to design in three-dimensions a flexible stacking line generator will be introduced, as a mean to independently control sweep and lean for the blades. The results presented illustrate how an annular turbine cascade can be re-designed, with the present method, for better blade performance.

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