A Stress-Strain Lag Eddy Viscosity Model for Unsteady Mean Flow

Abstract

This chapter proposes a new eddy viscosity model to include stress-strain lag effects in the modeling of unsteady mean flows. Many everyday turbulent flows are inherently unsteady, both industrial and natural. These flows can be a result of imposed fluctuating boundary conditions or geometry induced oscillations, or a combination of both. The presence of such unsteadiness in a flow significantly alters the behavior of important parameters, such as the Reynolds stresses, turbulent kinetic energy, and dissipation rate. In this chapter, a transport equation for the lag parameter, hereby denoted Cas is derived from a full Reynolds Stress Model (RSM), to be solved in conjunction with a standard two equation low Reynolds number Eddy Viscosity Model (EVM). The performance of the new k-c-. Cas model is compared to the flow in a channel driven by a pressure gradient oscillating around a nonzero mean. Results are compared with large eddy simulations (LES) of the same flow, and the addition of the lag parameter equation is shown to give improved results when compared to the standard EVM. © 2005 Elsevier B.V. All rights reserved.