Efficient Global Optimization of a laidback fan-shaped cooling hole using Large-Eddy Simulation

In the film cooling technique, cold fluid exiting from holes on the surface of the turbine creates a protective film which prevents the ruin of the solid material composing the blades. It is now known that the hole geometry is a key element of this approach and determines the adiabatic film cooling effectiveness. The design of optimal holes which can operate at conditions of high-pressure turbines is, however, a challenge for which several research groups and industrial companies have invested in intensive numerical and experimental campaigns. In the present study, a Large-Eddy Simulation based approach is adopted and demonstrated to be able to optimize the shape of a fan-shaped hole on a flat plate configuration in engine-representative conditions in static conditions, i.e. without rotation. The obtained results target high-pressure vanes and further studies are mandatory to investigate the effect of rotation for the application to turbine blades. This work is purely numerical as no experimental campaign has been done for such hot conditions. Nonetheless, the numerical setup used has been validated in a previously published studies. To do so, four main geometrical parameters defining such a cooling hole shape, namely the depth of the expanded section, the hole inclination angle and the forward as well as the lateral expansion angles are selected as design variables. The Bayesian based Efficient Global Optimization method along with the Expected Improvement as the acquisition function are used to find the maximum surface averaged film cooling effectiveness as the objective function. After nine database enrichment iterations needed to reduce the overall model error, an optimal shape for a given operating condition defined by the blowing and density ratios is obtained. Based on the response surface analysis, the effects of the design parameters on the adiabatic film cooling effectiveness are investigated. Finally, deeper analysis of the flow physics for four shapes is proposed to apprehend the role of the geometrical parameters on the fluid dynamics and on the adiabatic film cooling effectiveness.