Direct numerical simulation of film cooling with a fan-shaped hole under low Reynolds number conditions

Shaped film cooling holes have several features that can greatly improve film cooling effectiveness, and it has been studied and utilized in gas turbine engines for decades. Few studies, however, have reported the effects of low mainstream Reynolds number on shaped film cooling holes. In this study, the effects of mainstream Reynolds number on film cooling with a fan shaped hole are studied by utilizing direct numerical simulation (DNS). In addition, the compressibility and the viscosity of the working fluid are simultaneously considered, and the non-reflecting and absorbing boundary conditions are adopted at the exit of the main channel. The methods of the Roe scheme, preconditioning, and dual time stepping are employed together to solve the governing equations of a low-speed compressible flow problem. This study considers the mainstream Reynolds numbers of Re_D = 480 and 3200 with 0% and 5% turbulence intensity in the mainstream. Results reveal that the coolant jet penetrates into the mainstream with a mainstream Reynolds number of 480. However, at the higher Reynolds number, the coolant jet develops along the wall and results in better film cooling effectiveness. In addition, special attention is paid to the structures of the vortices developed from the crossflow. Hairpin vortices become smaller at higher mainstream Reynolds numbers. On the contrary, horseshoe vortices appear when the mainstream Reynolds number is increased. A detailed comparison of the vortices is presented in this study.