An adjoint-based shape optimization approach for supersonic turbine cascade is proposed. The algorithm is based on a discrete adjoint method, state-of-the-art parametrization techniques (NURBS) and a preconditioned steepest descent optimizer to search the optimal point. The potential of the optimization approach is verified on two different design problems. Initially the design methodology is applied to the re-design of an existing supersonic turbine cascade operating at nominal conditions, with the aim of obtaining a more uniform flow at blade outlet section. Then, an original extension of the algorithm for treating off-design conditions is envisaged. The method combines a standard multi-point optimization technique with an uncertainty quantification algorithm to assess the design points and the weights of the multi-point problem. The capability of the novel approach in providing robust designs is finally investigated by maximizing the performances of the same baseline configuration working under a relatively wide range of operating conditions. In both tests remarkable outcomes are achieved in terms of improvement of blade performances and computational efficiency.

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