Turbulence Modelling of Unsteady Turbulent Flows Using the Stress Strain Lag Model

Abstract

This paper reports the application of a recently developed turbulence modelling scheme known as the Cas model. This model was specifically developed to capture the effects of stress-strain misalignment observed in turbulent flows with mean unsteadiness. Earlier work has reported the approach applied within a linear k-e modelling framework, and some initial testing of it within the k-ω SST model of Menter (AIAA J 32:1598–1605, 1994). The resulting k-e-Cas and SST-Cas models have been shown to result in some of the advantages of a full Reynolds Stress transport Model (RSM), whilst retaining the computational efficiency and stability benefits of a eddy viscosity model (EVM). Here, the development of the the high-Reynolds-number version of the Cas model is outlined, with some example applications to steady and unsteady homogeneous shear flows. The SST-Cas form of the model is then applied to further, more challenging cases of 2-D flow around a NACA0012 aerofoil beyond stall and the 3-D flow around a circular cylinder in a square duct, both being flows which exhibit large, unsteady, separated flow regions. The predictions returned by a range of other common turbulence modelling schemes are included for comparison and the SST-Cas scheme is shown to return generally good results, comparable in some respects to those obtainable from far more complex schemes, for only moderate computing resource requirements.