Critical Evaluation and Development of One-Equation Near-Wall Turbulence Models

Abstract

A systematic evaluation of one-equation near-wall turbulence models is completed and a new model is developed. The study includes five one-equation near- wall models and one two-equation model such that the performance of the one-equation models can be viewed in context of the performance of this more widely used class of models.

It is found that the majority of one-equation near-wall models do not reproduce the variation of the Reynolds shear stress near the wall, do not reproduce the dissipation at the wall, and do not predict the dissipation well in the region near the wall for a boundary layer flow. The new model is found to provide improved performance for the boundary layer and a wavy-wall channel. Specifically, it is found that the new model predicts the turbulent kinetic energy and dissipation in closer agreement with direct numerical simulation data than existing one-equation models for the boundary layer and provides improved predictions of the shear stress distribution for the wavy-wall channel.

It is found that the one-equation near-wall models generally predict the shear stress distribution for the wavy-wall channel with greater accuracy than the two-equation model. In addition, it is shown that computations using the one-equation models are less sensitive to wall spacing than those using the two-equation model. This suggests that one-equation near-wall models, and in particular the new model, are ideal for engineering computations of practical flows where computational expense may be a significant factor entering into the choice of turbulence model.