Theoretical model for two-dimensional film cooling effectiveness distribution prediction

Abstract

Film cooling is commonly categorized as a jet in crossflow phenomenon. Due to its fully three-dimensional flow field, characteristically two-dimensional (2-D) cooling effectiveness distributions are observed on the target wall. A theoretical method for 2-D film cooling effectiveness distribution predictions is developed by modeling the diffusion and convective transportation in the lateral direction. The effective diffusion coefficient is introduced to quantify the combined effects of the turbulent and laminar expansion. The convection effect, mainly the vortex entrainment, is quantified based on the analytical Oseen vortex. The intensity, scale, and location of the kidney vortex are modeled, respectively. The 2-D model in the current study can well satisfy the demand both academically and industrially. The time consumption of a 2-D effectiveness distribution calculation is on the magnitude of 1 ×10−2 s. The prediction error is within 8% if given especially correlated model coefficients, or within 14% otherwise.