Aerodynamic Optimization of Transonic High-Pressure Turbine Vanes with Non-Axisymmetric Endwalls for Rotating Detonation Engines

For coupling a transonic high-pressure turbine vane with a rotating detonation combustor, several integration approaches have been considered. Endwall diffusion in the vane row can facilitate coupling by enabling a higher turbine inlet Mach number operating range. Nonetheless, the introduction of diffusive axisymmetric endwalls may promote flow separation and enlarged secondary flows, leading to an overall reduction in turbine stage efficiency. To address this, the present study introduces a shape optimization framework based on computational fluid dynamics for designing diffusive non-axisymmetric endwalls in a transonic vane downstream of a rotating detonation combustor. The reference geometry is a transonic vane with diffusive axisymmetric endwalls, previously analyzed in numerical studies. Both hub and shroud endwalls are parameterized using 20 design variables, and a random sampling approach generates 1000 distinct geometrical configurations. Each design undergoes geometry generation, meshing, and steady Reynolds-Averaged Navier-Stokes computation under transonic conditions using a three-dimensional commercial solver. Aerodynamic performances are assessed, and a genetic aggregation method is employed to construct a response surface. A gradient-based optimization algorithm identifies the optimal non-axisymmetric endwall configuration, which is then simulated. Comparative analysis shows that the optimized non-axisymmetric endwall significantly mitigates hub and shroud vortex effects, enhancing aerodynamic efficiency and supporting integration within turbine systems equipped with rotating detonation combustors.