Large eddy simulation in optimization of fan-shaped cooling holes using modal subdivision design variables

In advanced gas turbine engines, fan-shaped cooling holes are widely employed to protect turbine components from the high-temperature mainstream flow. The geometric characteristics of these holes are critical in determining the film-cooling effectiveness. Therefore, identifying an optimal hole configuration is essential to enhance thermal protection and overall cooling performance. In this study, a large eddy simulation (LES) approach was conducted to investigate the influences of surface geometry modifications on the film-cooling effectiveness and turbulent flow structures for a 7-7-7 laidback fan-shaped cooling hole (7-degree expansion angle in each direction). The cooling hole was located on a flat plate with a 30-degree injection angle, operating at a constant density and blowing ratio of 1.5. A novel modal shape parameterization technique was introduced to systematically modify the hole surface geometry, providing a compact physic-based representation of complex shape variations. Eight designed cases were generated using Latin Hypercube sampling (LHS) based on two shape parameters: mode number and mode amplitude. The area-averaged film-cooling effectiveness on the flat plate was selected as the objective function. A genetic aggregation method was adopted to construct a response surface model using the LES data. Subsequently, a multi-objective genetic algorithm (MOGA) was used to identify the optimal surface geometry. The results indicated a substantial improvement in cooling effectiveness across all modified configurations compared to the reference case. The optimized design demonstrated reduced internal turbulent fluctuations within the cooling hole and diminished flow disturbances in the interaction region with the mainstream, resulting in a 22% improvement in cooling performance-from 0.2028 to 0.2475-compared to the reference configuration.