Improved two-equation k-omega turbulence models for aerodynamic flows

TLDR

The paper introduces two new variants of the k‑omega turbulence model. The authors develop a Baseline (BSL) model that matches Wilcox’s k‑omega near the wall but blends to a high‑Reynolds‑number k‑ε formulation at the boundary‑layer edge, and a Shear‑Stress Transport (SST) variant that adds transport of the principal shear stress via a Bradshaw‑based eddy‑viscosity, testing both on numerous flow fields. Both models yield results comparable to the original k‑omega yet are free‑stream independent, with the SST variant showing excellent agreement with experimental data for adverse pressure gradient boundary‑layer flows.

Abstract

Two new versions of the k-omega two-equation turbulence model will be presented. The new Baseline (BSL) model is designed to give results similar to those of the original k-omega model of Wilcox, but without its strong dependency on arbitrary freestream values. The BSL model is identical to the Wilcox model in the inner 50 percent of the boundary-layer but changes gradually to the high Reynolds number Jones-Launder k-epsilon model (in a k-omega formulation) towards the boundary-layer edge. The new model is also virtually identical to the Jones-Lauder model for free shear layers. The second version of the model is called Shear-Stress Transport (SST) model. It is based on the BSL model, but has the additional ability to account for the transport of the principal shear stress in adverse pressure gradient boundary-layers. The model is based on Bradshaw's assumption that the principal shear stress is proportional to the turbulent kinetic energy, which is introduced into the definition of the eddy-viscosity. Both models are tested for a large number of different flowfields. The results of the BSL model are similar to those of the original k-omega model, but without the undesirable freestream dependency. The predictions of the SST model are also independent of the freestream values and show excellent agreement with experimental data for adverse pressure gradient boundary-layer flows.