Machine learning tools represent a key methodology for the shape optimization of complex geometries in the turbomachinery field. One of the current challenges is to redesign High-Pressure Turbine (HPT) stages to couple them with innovative combustion technologies. In fact, recent developments in the gas turbine field have led to the introduction of pioneering solutions such as Rotating Detonation Combustors (RDCs) aimed at improving the overall efficiency of the thermodynamic cycle at low overall pressure ratios. In this study, a HPT vane equipped with diffusive endwalls is optimized to allow for ingesting a high-subsonic flow ($Ma=0.6$) delivered by a RDC. The main purpose of this paper is to investigate the prediction ability of machine learning tools in case of multiple input parameters and different objective functions. Moreover, the model predictions are used to identify the optimal solutions in terms of vane efficiency and operating conditions. A new solution that combines optimal vane efficiency with target values for both the exit flow angle and the inlet Mach number is also presented. The impact of the newly designed geometrical features on the development of secondary flows is analyzed through numerical simulations. The optimized geometry achieved strong mitigation of the intensity of the secondary flows induced by the main flow separation from the diffusive endwalls. As a consequence, the overall vane aerodynamic efficiency increased with respect to the baseline design.

The use of film cooling is crucial to avoid high metal temperatures in gas turbine applications, thus ensuring a high lifetime for vanes and blades. The complex turbulent mixing process between the coolant and the main flow requires an accurate numerical prediction to correctly estimate the impact of ejection conditions on the cooling performance. Recent developments in numerical models aim at using hybrid approaches that combine high precision with low computational cost. This paper is focused on the numerical simulation of a cylindrical film cooling hole that operates at a unitary blowing ratio, with a hot gas Mach number of ${\mathit{Ma}}_m$ = 0.6, while the coolant is characterized by plenum conditions (${\mathit{Ma}}_c$ = 0). The adopted numerical approach is the Stress-Blended Eddy Simulation model (SBES), which is a blend between a Reynolds-Averaged Navier–Stokes approach and a modeled Large Eddy Simulation based on the local flow and mesh characteristics. The purpose of this paper is to investigate the ability of the hybrid model to capture the complex mixing between the coolant and the main flow. The cooling performance of the hole is quantified through the film cooling effectiveness, the Net Heat Flux Reduction (NHFR), and the discharge coefficient $C_D$ calculation. Numerical results are compared both with the experimental data obtained by the University of Karlsruhe during the EU-funded TATEF2 project and with a Scale Adaptive Simulation (SAS) run on the same computational grid. The use of ${\lambda }_2$ profiles extracted from the flow field allows for isolating the main vortical structures such as horseshoe vortices, counter-rotating vortex pairs (e.g., kidney vortices), Kelvin–Helmholtz instabilities, and hairpin vortices. Eventually, the contribution of the unsteady phenomena occurring at the hole exit section is quantified through Proper Orthogonal Decomposition (POD) and Spectral Proper Orthogonal Decomposition methods (SPOD).