Analysis of k-[epsilon] Budgets for film cooling using direct numerical simulation

Results of a direct numerical simulation of a film cooling jet are used to evaluate the terms in the standard k-[epsilon] turbulence model From the direct numerical simulation data all terms and correlations appearing in the exact k-[epsilon] equations are reconstructed and compared with the models for these terms used in the standard k-[epsilon] turbulence model. Unlike a channel flow, the turbulent diffusion terms that contain fluctuations of pressure are found to be significant and to have a different distribution from the turbulent diffusion terms involving only velocity fluctuations. Using an eddy viscosity derived from minimizing the error in representing the direct numerical simulation data by the Boussinesq gradient approximation, it is shown that the Boussinesq gradient approximation as used in the standard k-[epsilon] turbulence model is a reasonable model for the various terms in the exact k-[epsilon] equations. However, the expression for the eddy viscosity of the standard k-[epsilon] turbulence model ([C.sub.[mu]]([k.sup.2]/[epsilon])Re) is shown to be greatly in error. Using the direct numerical simulation data, two new damping functions are presented that greatly reduce the error in the eddy viscosity in the standard k-[epsilon] turbulence model. DOI: 10.2514/1.50597