Large Eddy Simulation in the Optimization of Laidback Fan-Shaped Hole Geometry to Enhance Film-Cooling Performance

Abstract

Large eddy simulation (LES) was applied to optimize the geometry configuration of a laidback fan-shaped hole in order to maximize overall averaged film-cooling performance. The cooling hole is located on a flat plate surface with a 30-degree injection angle with respect to the main flow stream at a constant film density ratio of 2, and a blowing ratio of 2. The computational results achieved by our method were validated by previously gathered experimental data in terms of laterally and time-averaged film-cooling effectiveness. Three geometric parameters, the metering length, forward expansion angle, and lateral expansion angle of the fan-shaped hole were selected as design variables. Thirteen different design cases were selected using the Box-Behnken approach and were numerically modeled. The response surface methodology (RSM) was used to maximize the overall averaged film-cooling effectiveness as an objective function. The film-cooling performance of the numerically optimized cooling hole is significantly improved by 49.55% compared to that of the reference cooling hole. It is confirmed that the numerically optimized cooling hole found using the LES method is in a good agreement with the experimentally optimized cooling hole in terms of optimal shape configuration. In addition, the overall averaged film-cooling effectiveness found by both approaches was very similar. This study demonstrates that the LES approach combined with the RSM optimization algorithm is an effective method for the optimization of laidback fan-shaped cooling holes.