Filter-based unsteady RANS computations

The Reynolds-averaged Navier-Stokes (RANS) approach has been popular for engineering turbulent flow computations. The most widely used ones, such as the k-ε two-equation model, have well-recognized deficiencies when treating time dependent flow fields. To identify ways to improve the predictive capability of the current RANS-based engineering turbulence closures, conditional averaging is adopted for the Navier-Stokes equation, and one more parameter, based on the filter size, is introduced into the k-ε model. The sub-filter stresses are constructed directly by using the filter size and the conventional turbulence closure. The filter is decoupled from the grid, making it possible to obtain grid independent solutions with a fixed filter scale. The model is assessed in transient, planar turbulent wake flow simulations over a square cylinder utilizing progressively refined grid. In comparison to the standard k-ε model, overall, the filter-based model is shown to improve the predictive capability considerably.