Large eddy simulation on effects of trench geometry on film cooling effectiveness through fan-shaped holes

Modern gas turbines require the use of external film-cooling techniques to effectively cool the turbine blades, which are heated by hot combustion gases. Large eddy simulation (LES) is conducted to numerically evaluate the influences of trench configurations on film-cooling effectiveness and flow-field behavior of a shaped hole. The cooling hole was a laidback fan-shaped hole with a 17.5-degree forward expansion angle located on a flat plate surface with a 30-degree injection angle at a constant blowing ratio of 2.0 and a constant density ratio of 1.5. The computed film-cooling effectiveness was validated with that obtained in the experimental data for the reference case at two blowing ratios. Two geometrical parameters of the trench height and width were selected as design variables, and overall area-averaged film-cooling effectiveness was considered as an objective function. The Latin Hypercube sampling (LHS) method was applied to generate the designed cases and two different optimization algorithms, the response surface methodology (RSM) and the Kriging method, were employed to maximize the objective function. The computational LES results revealed that trenched cases with a larger trench height and a relatively smaller trench width improved cooling performance. The optimal trench configurations based on the RSM and Kriging method, demonstrated improvements in cooling performance by 27% and 25%, respectively, compared to the reference case without a trench slot. The transient analysis also showed that the flow unsteadiness and velocity disturbances near the trench exit at the mixing region were weakened for the cooling holes with the optimal trench cases.