Numerical and experimental investigation of film cooling effectiveness distribution predictions that considers the effects of the turbulent Schmidt number

Film cooling is a critical protective cooling technique that is used in gas turbine engines. However, predicting the film cooling effectiveness can be quite challenging due to the complex mixing processes involved. As a result, simulations commonly require experimental validation or modification of their numerical methods. In this study, predictions of film cooling effectiveness distributions were enhanced by an examination of the impact of the turbulent Schmidt number, Sc_t, on the coolant-covered areas. An existing turbulent viscosity modification method, the MIX model, was utilized to obtain more accurate flow field representations. The definition, physical implications, and role of the turbulent Schmidt number in numerical simulations, along with the principles of the pressure-sensitive paint measurement method, which was used to characterize the film cooling effectiveness, were explored. Both numerical simulations and experimental validation were employed. The study results revealed that small-scale turbulent eddies, which were averaged in the RANS method according to the Sc_t, critically influenced the mixing between the coolant and the mainstream, thereby impacting the cooling effectiveness. It was also revealed that as Sc_t decreased, the cooling effectiveness diminished in the streamwise direction but increased in the spanwise and vertical directions, regardless of the momentum ratio value. An Sc_t value of 0.3 was found to be more suitable than the commonly used value of 0.7, particularly for a low momentum ratio of 0.43. When Sc_t=0.3, the error in the area-averaged cooling effectiveness was 10 %, while it was 51 % when Sc_t=0.7. Additionally, an Sc_t value of 0.3 produced better overall cooling effectiveness distributions. Consequently, an Sc_t value of 0.3 is recommended for most low-speed and incompressible-flow simulation conditions.