On the judicious use of the k-ε model, wall functions and adaptivity

Abstract This paper shows that accurate predictions of skin friction and Stanton number for a flat plate boundary layer can be achieved with the k – e model of turbulence with wall functions, provided the computational model (turbulence model, geometry, boundary conditions, etc.) is properly defined and that the simulation is grid converged. Emphasis is put on good CFD practices such as verification and validation. Verification allows to obtain numerical predictions with controlled accuracy. Validation of the computational model is thus performed on solid grounds. Predictions of the local skin friction coefficient on the plate were obtained for Reynolds numbers of 2×10 5 and 2×10 6 . In the case Re =2×10 5 , the effects of inlet boundary turbulence Reynolds number, geometry of the plate and type of wall functions are assessed. It is found that an inlet turbulence Reynolds number equal to 10% of the Reynolds number yields realistic results. Significant improvements are achieved if the plate thickness is included in the computational model. Two-velocity scale wall functions prove to be superior to the more popular one-velocity scale wall functions. For the case Re =2×10 6 , predictions of the local skin friction coefficient ( C f ( x )) and the local heat transfer coefficient ( St ( x )) are in good agreement with correlations.