REASSESSMENT OF THE SCALE-DETERMINING EQUATION FOR ADVANCED TURBULENCE MODELS

A comprehensive and critical review of closure approximations for two-equation turbulence models has been made. Particular attention has focused on the scale-determining equation in an attempt to find the optimum choice of dependent variable and closure approximations. Using a combination of singular perturbation methods and numerical computations, this paper demonstrates that: (1) conventional κ-Ε and κ-ω+2$/ formulations generally are inaccurate for boundary layers in adverse pressure gradient; (2) using 'wall functions' tends to mask the shortcomings of such models; and (3) a more suitable choice of dependent variables exists that is much more accurate for adverse pressure gradient. Based on the analysis, a two-equation turbulence model is postulated that is shown to be quite accurate for attached boundary layers in adverse pressure gradient, compressible boundary layers, and free shear flows.