A robust shape optimization procedure based on a multi-objective genetic algorithm coupled to a non-intrusive uncertainty quantification analysis was applied to a transonic inviscid flow of a dense gas over a plane turbine cascade. The goal was to simultaneously improve the mean turbine performance and the system stability under fluctuating thermodynamic inlet conditions. Despite an elevated computational cost, the optimization procedure was capable of generating a Pareto front of turbine geometries which improved the mean isentropic turbine efficiency μ(ηs) over the baseline profile, while limiting the solution variability in terms of the coefficient of variation of the power output CV(P2D). In addition to demonstrating an excellent parallel scalability over 1600 processors, the robust optimization revealed that variability of CV(P2D) depends more on the variation of inlet conditions than turbine geometry. A posteriori stochastic analyses on selected optimized turbine geometries allowed an investigation of flow behavior variability, as well as propositions for the improved selection of robust optimization cost criteria in future simulations.

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