Performance of Adjoint-Optimized Contoured Endwalls for Multiple Off-Design Purge Flow Rates in Axial Turbines

Abstract Endwall contouring in gas turbines has become a critical area of research aimed at improving aerodynamic efficiency and reducing secondary flow losses. As modern gas turbine designs push the boundaries of performance, secondary flows — generated by pressure gradients between rotor and stator components and wall-bounded viscous effects — contribute significantly to overall efficiency losses. By optimizing the endwall geometry, particularly through non-axisymmetric contouring, it is possible to mitigate these detrimental flows and enhance turbine performance. In this paper, an adjoint-based optimization approach is utilized within commercially available software to aerodynamically optimize the blade endwall of a cooled high-pressure turbine through targeted contouring. A series of computational fluid dynamics (CFD) simulations has been conducted on a full turbine stage in a high-pressure production engine to assess the effects of these optimizations when the turbine is operating at a different condition than that used for optimization. Particular emphasis is placed on the performance of the endwall optimization at off-design rim seal purge conditions. Comparisons between an array of optimized endwalls and the baseline geometry are made, providing insight into how endwall contouring decreases aerodynamic loss across the purge rate range tested. A maximum efficiency improvement of 0.58% was achieved, and it was found that all contours optimized for a given purge condition improved efficiency across all purge conditions, with contours optimized for higher purge conditions decreasing the sensitivity of efficiency with purge flow rate. This was true for contours tested at each of their converged optimums, and when held at equal optimization passes.