Statistical characteristics of unsteady reynolds-averaged navier-stokes simulations

The statistical characteristics of unsteady Reynolds-averaged Navier-Stokes (RANS) turbulence models, utilizing the eddy-viscosity concept, are investigated. Detailed assessment is made to the original Launder-Spalding k-ε model as well as a nonlinear modification utilizing multiple scales from both turbulent variables and the local mean strain rate. The purpose of the study is to shed light on the issues of unsteady RANS computations, not to recommend a "good" model. The models are tested for flow past a square cylinder, employing progressively refined resolutions. The comparison between the length scale imposed by the turbulence model and the length scale of the spatial resolution helps understand the fidelity of the simulations. If the eddy viscosity is low, the flow field can be numerically underresolved in RANS computations, and consequently the solutions exhibit noticeable sensitivity to numerics such as discretization schemes and grid distribution. Under such situations, in practical computations, grid-independent solutions will be difficult to attain with conventional numerical schemes used in RANS simulations. It is demonstrated that in order to appreciate the statistical behavior of a turbulence model, both time-averaged and time-dependent results need be examined.