Film cooling effectiveness in single row of holes: First moment closure modeling

The present article focuses on the evaluation of a first-moment closure model applicable to film cooling flow and heat transfer computations. The present first-moment closure model consists of a higher level of turbulent heat flux modeling in which two additional transport equations for temperature variance kθ and its dissipation rate εθ are considered. It not only employs a time scale that is characteristic of the turbulent momentum field, but also an additional time scale devoted to the turbulent thermal field. The low Reynolds number k — ε turbulence model is combined with a two-equation kθ — εθ  heat flux model to simulate the flow and heat transfer in a three-dimensional single row of cylindrical holes film cooling application. Comparisons with available experimental data show that the two-equation heat flux model improves the over-predictions of center-line film cooling effectiveness caused by the standard simple eddy diffusivity (SED) model with a fixed value of turbulent Prandtl number. This is due to the enhancement of turbulent heat flux components in the first-moment closure simulations. Also, the span wise distributions of effectiveness are computed with more accuracy due to better predictions of coolant jet spreading. However, the limitations of first-moment closure due to its isotropic approach should be taken into consideration.