Generalization of machine-learned turbulent heat flux models applied to film cooling flows

Abstract

The design of film cooling systems relies heavily on Reynolds-Averaged Navier-Stokes (RANS) simulations, which solve for mean quantities and model all turbulent scales. Most turbulent heat flux models, which are based on isotropic diffusion with a fixed turbulent Prandtl number (Pr t ), fail to accurately predict heat transfer in film cooling flows. In the present work, machine learning models are trained to predict a non-uniform Pr t field, using various datasets as training sets. The ability of these models to generalize beyond the flows on which they were trained is explored. Furthermore, visualization techniques are employed to compare distinct datasets and to help explain the cross-validation results. NOMENCLATUREθ Dimensionless temperature u i Velocity component in the i-th direction D Hole diameter in film cooling flows BR Blowing ratio in a jet in crossflow configuration d Distance to the nearest wall k Turbulent kinetic energy ε Turbulent dissipation rate ν t Eddy viscosity calculated by realizable k − ε model [m 2 /s] α t Turbulent diffusivity [m 2 /s] Pr t Turbulent Prandtl number ν t /α t V (i) Volume of the i-th computational cell