Gaussian Process Regression-Based Optimization of Fan-Shaped Film Cooling Holes on Concave Walls

In this study, a Gaussian Process Regression (GPR) surrogate model coupled with a Bayesian optimization algorithm was employed for the single-objective design optimization of fan-shaped film cooling holes on a concave wall. Fan-shaped holes, commonly used in gas turbines and aerospace applications, flare toward the exit to form a protective cooling film over hot surfaces, enhancing thermal protection compared to cylindrical holes. An initial hole configuration was used to improve adiabatic cooling efficiency. Design variables included the hole injection angle, forward expansion angle, lateral expansion angle, and aperture ratio, while the objective function was the average adiabatic cooling efficiency of the concave wall surface. Optimization was performed at two representative blowing ratios, M = 1.0 and M = 1.5, using the GPR-based surrogate model to accelerate exploration, with the Bayesian algorithm identifying optimal configurations. Results indicate that the optimized fan-shaped holes increased cooling efficiency by 15.2% and 12.3% at low and high blowing ratios, respectively. Analysis of flow and thermal fields further revealed how the optimized geometry influenced coolant distribution and heat transfer, providing insight into the mechanisms driving the improved cooling performance.