Three-Dimensional Inverse Method for Turbomachinery Blading Design

An iterative procedure for three-dimensional blade design is presented, in which the three-dimensional blade shape is modified using a physical algorithm, based on the transpiration model. The transpiration flux is computed by means of a modified Euler solver, in which the target pressure distribution is imposed along the blade surfaces. Only a small number of modifications is needed to obtain the final geometry. The method is based on a high-resolution three-dimensional Euler solver. An upwind biased evaluation of the advective fluxes allows for a very low numerical entropy generation, and sharp shock capturing. Non-reflecting boundary conditions are applied along the inlet/outlet boundaries. The capabilities of the method are illustrated by redesigning a transonic compressor rotor blade, to achieve, for the same mass flow and outlet flow angle, a shock-free deceleration along the suction side. The second example concerns the design of a low aspect ratio turbine blade, with a positive compound lean to reduce the intensity of the passage vortices. The final blade is designed for an optimized pressure distribution, taking into account the forces resulting from the blade lean angle.