Design and Validation of a Scale-Adaptive Filtering Technique for LRN Turbulence Modeling of Unsteady Flow

An adaptive low-pass filtering procedure for the modeled turbulent length and time scales is derived and applied to Wilcox’ original low reynolds number $k-ω$ turbulence model. It is shown that the method is suitable for complex industrial unsteady flows in cases where full large eddy simulations (LESs) are unfeasible. During the simulation, the modeled length and time scales are compared to what can potentially be resolved by the computational grid and time step. If the modeled scales are larger than the resolvable scales, the resolvable scales will replace the modeled scales in the formulation of the eddy viscosity. The filtered $k-ω$ model is implemented in an in-house computational fluid dynamics (CFD) code, and numerical simulations have been made of strongly swirling flow through a sudden expansion. The new model surpasses the original model in predicting unsteady effects and producing accurate time-averaged results. It is shown to be superior to the wall-adpating local eddy-viscosity (WALE) model on the computational grids considered here, since the turbulence may not be sufficiently resolved for an accurate LES. Because of the adaptive formulation, the filtered $k-ω$ model has the potential to be successfully used in any engineering case where an LES is unfeasible and a Reynolds (ensemble) averaged Navier–Stokes simulation is insufficient.