Filter-Based Unsteady RANS Computations for Single-Phase and Cavitating Flows

The widely used Reynolds-Averaged Navier-Stokes (RANS) approach, such as the k-ε two-equation model, has been found to over-predict the eddy viscosity and can dampen out the time dependent fluid dynamics in both single- and two-phase flows. To improve the predictive capability of this type of engineering turbulence closures, a consistent method is offered to bridge the gap between DNS, LES and RANS models. Based on the filter size, conditional averaging is adopted for the Navier-Stokes equation to introduce one more parameter into the definition of the eddy viscosity. Both time-dependent single-phase and cavitating flows are simulated by a pressure-based method and finite volume approach in the framework of the Favre-averaged equations coupled with the new turbulence model. The impact of the filter-based concept, including the filter size and grid dependencies, is investigated using the standard k-ε model and with the available experimental information.