Abstract: Geometric deviation is a principal source of aerodynamic uncertainty for turbomachinery blades. The aero-dynamic shape optimization considering uncertainty effects of geometric design parameters, also named Robust Aerodynamic Design Optimization (RADO), is suggested to improve both the mean aerodynamic performance and aerodynamic robustness. The basic principles and implementations of RADO are firstly introduced, followed by the evaluation of statistic mean and variance of aerodynamic performance changes by using the sensitivity-based uncertainty quantification method, from which the gradients of RADO cost function to the design parameters can be calculated. Then the study of RADO on a transonic turbine cascade, HS1A, considering the uncertainty of geometric design parameters is performed to reduce the mean total pressure loss and the corresponding variance. The optimization results compared with those of Deterministic Aerodynamic Design Optimization (DADO) demonstrate the effectiveness and superiority of RADO in improving the aerodynamic robustness. Finally, the statistical flow solutions of the original, DADO and RADO cascades are compared and presented to illustrate the mechanisms of reducing the sensitivity of total pressure loss through aerodynamic shape optimization by RADO.

Key words: aerodynamic design optimization, robust, uncertainty, adjoint method, cascades