A stress–strain lag Eddy viscosity model for unsteady mean flow

A new Eddy viscosity model is proposed to include stress–strain lag effects in the modelling of unsteady mean flows. 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 Eddy viscosity model (EVM). The performance of the new k–ε–Cas model is assessed by applying it to the flow in a homogeneous irrotational cyclic strain; a channel flow driven by a pressure gradient oscillating around a non-zero mean, and a NACA0012 profile in deep stall. For the oscillating channel, results are compared with recent 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 outside the near wall region.