On Predicting the Turbulent Prandtl Number in Film Cooling Flow

Numerical simulation of turbulent flow and heat transfer in film cooling from a cylindrical hole in three-dimensional case is considered. For this purpose, turbulent heat flux term of energy equation is usually modeled by simple eddy diffusivity model with constant turbulent Prandtl number, while experimental and numerical researches show that the prescribed constant value of turbulent Prandtl number is far from reality. In the present study, second moment closure (SMC) models with wall-reflection term is applied for modeling the turbulent flow and heat transfer in film cooling flow. Comparison between the numerical and experimental results show that the explicit algebraic second moment closure models have more ability to better prediction of temperature field in film cooling. In addition, turbulent Prandtl number distribution for film cooling has been investigated. The range of this parameter for the desired geometry has been identified from 0.1 to 0.95 in the near of injection hole to far from it respectively. Finally, in order to enhance the capability of simple eddy diffusivity model in simulating film cooling heat transfer, the value of 0.7 has been proposed for turbulent Prandtl number instead of the common value of 0.85.