Reassessment of the scale-determining equation for advanced turbulence models

TLDR

The study seeks to identify the optimal dependent variable and closure approximations for the scale‑determining equation, leading to a new two‑equation turbulence model accurate for attached boundary layers, compressible flows, and free shear flows. The proposed model eliminates viscous damping of closure coefficients and wall functions, allowing integration through the viscous sublayer and employing surface boundary conditions that enable accurate predictions over rough surfaces and with surface mass addition. The review shows that conventional A:−ε and A>ε formulations are generally inaccurate for adverse pressure‑gradient boundary layers, that using functions can mask these deficiencies, and that a more suitable dependent variable yields substantially improved accuracy.

Abstract

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 A:-e and A>w formulations generally are inaccurate for boundary layers in adverse pressure gradient; 2) using 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. With no viscous damping of the model's closure coefficients and without the aid of wall functions, the model equations can be integrated through the viscous sublayer. Surface boundary conditions are presented that permit accurate predictions for flow over rough surfaces and for flows with surface mass addition.