Large Eddy simulation in optimizing trench configuration to improve cooling effectiveness of a laidback fan-shaped hole

In modern gas turbines, a thermal barrier coating (TBC) is used to protect the components of the turbine from the hot flow coming from the combustor, which results in the cooling holes on the blade surfaces being embedded in a 2D trench slot. In this study, large eddy simulations (LES) were carried out to investigate the effects of trench geometry on the film-cooling effectiveness of a shaped cooling hole. The shaped cooling hole is located on a flat surface with an injection angle of 30 degrees, and the blowing and density ratios are fixed at 1.5. Thirteen different designed cases were sampled using Box-Behnken method based on three different geometry parameters of the trench slot, trench height and upstream and downstream trench lengths. A genetic aggregation algorithm was applied to achieve the optimal trench configuration that maximizes the overall cooling effectiveness. The film-cooling performance computed by the LES method was validated for a reference case without a trench and three different trenched cases with the experiments using the PSP (pressure sensitive paint) technique. The cooling effectiveness of the trench cavity and flat plate was found to be significantly enhanced in cases of trenches with relatively greater trench height and less downstream trench length. The optimal trench configuration demonstrated less turbulent fluctuations in the mixing region, and the overall area-averaged adiabatic film-cooling effectiveness was improved by 23% in comparison with a reference hole without a trench.