Cost-effective multi-fidelity strategy for the optimization of high-Reynolds number turbine flows guided by LES

A cost-effective multi-objective shape optimization strategy is proposed for high-Reynolds number flows involving complex phenomena such as boundary layer transition, shock-wave interactions, and turbulent wakes. These processes are poorly captured by Reynolds-Averaged Navier--Stokes (RANS) models, necessitating higher-fidelity approaches like Large Eddy Simulation (LES). However, LES is computationally prohibitive at high Reynolds numbers, making its direct use in optimization impractical. To address this, we introduce a low-dimensional design space representation using Singular Value Decomposition (SVD) and construct a multi-fidelity co-Kriging (MFK) surrogate model combining wall-resolved LES (WRLES) and RANS. Adaptive infill criteria are employed to strategically enrich the surrogate model within a limited computational budget (fewer than 10 LES samples). The methodology is applied to optimize a supersonic turbine vane for Organic Rankine Cycles (ORC), operating at Reynolds numbers of $\sim 10^6$. While RANS-LES correlation weakens near the optimal region, the MFK model outperforms single-fidelity Kriging (SFK) trained on the same LES data, effectively leveraging both abundant low-fidelity and scarce high-fidelity data. RANS accurately predicts global objective function trends but fails to resolve key flow features, whereas the MFK model captures fine-detail geometry trends from LES. Loss analysis reveals that LES is essential for identifying performance-detrimental mechanisms, while RANS-only optimization yields sub-optimal designs.