Critical Examination of Two-Equation Turbulence Closure Models for Boundary Layers

Abstract

An objective three-part comparison of the Jones-Launder, Ng-Spalding, Saffman-Wilcox, and Wilcox-Traci two-equation turbulence models has been conducted. First, a term-by-term algebraic comparison demonstrated that the forms of the model equations appear very similar for the four models. However, the comparison also indicated that the Saffman-Wilcox and Wilcox-Traci dissipation-rate formulations admit straightforward integration through the viscous sublayer, whereas integration through the viscous sublayer is a more difficult issue with the Jones-Launder dissipation-function and the Ng-Spalding length-scale formulations. Next, numerical computations were conducted in which the models were applied to four equilibrium boundary-layer flows including adverse, zero, and favorable pressure gradients. The models were tested using the same numerics, boundary conditions, and starting profiles. Overall, the Ng-Spalding and Wilcox-Traci models yielded results in closest agreement with experimental data. Most importantly, these two models are as accurate as mixing length for equilibrium boundary layers. Computations of zero pressure gradient flow over a convex wall composed the final part of the comparison. With rationally devised streamline curvature modifications, the Jones-Launder, Ng-Spalding, and Wilcox-Traci models yielded excellent agreement with experimental data for the flow considered.