Comparative study on the adiabatic film cooling performances with elliptical or super-elliptical holes of various length-to-width ratios

In this study, the effects of elliptical and super-elliptical film holes on the adiabatic film cooling effectiveness under a density ratio of 2 and blowing ratios 0.5 and 1 are studied. Five different cases are designed by considering various length-to-width ratios and the baseline is the model with cylindrical film hole. The DES with the Realizable k-ε model is adopted for the five cases to investigate the cooling performance and clarify the film cooling mechanisms for all considered cases. The results show that with the increase of the blowing ratio, the vertical mixing between the hot gas and cooling jet becomes stronger due to the higher jet momentum and the promoted normal penetration into the mainstream. Therefore, the laterally averaged film cooling effectiveness for all cases is decreased at the higher blowing ratio. This phenomenon is most obvious for the baseline along the whole mainstream direction, while this phenomenon only becomes obvious near the hole region for the elliptical and super-elliptical models with the higher length-to-width ratio. Besides, it is found that the cases with the higher length-to-width ratio result in a better laterally averaged cooling performance compared with those with the lower length-to-width ratio at each blowing ratio. In addition, under the same length-to-width ratio, the elliptical model and super-elliptical model present similar film cooling performances. The model possessing a better cooling performance depends on the blowing ratio and the actual position along the streamwise direction.