A Hybrid-Filter Approach to Turbulence Simulation

Abstract

Germano (Theor Comput Fluid Dyn 17:225–331, 2004) proposed a hybrid-filter approach, which additively combines an LES-like filter operator (F) and a RANS-like statistical operator (E) using a blending function k: H = kF + (1 − k)E. Using turbulent channel flow as an example, we first conducted a priori tests in order to gain some insights into this hybrid-filter approach, and then performed full simulations to further assess the approach in actual simulations. For a priori tests, two separate simulations, RANS (E) and LES (F), were performed using the same grid in order to construct a hybrid-filtered field (H). It was shown that the extra terms arising out of the hybrid-filtered Navier–Stokes (HFNS) equations provided additional energy transfer from the RANS region to the LES region, thus alleviating the need for the ad hoc forcing term that has been used by some investigators. The complexity of the governing equations necessitated several modifications in order to render it suitable for a full numerical simulation. Despite some issues associated with the numerical implementation, good results were obtained for the mean velocity and skin friction coefficient. The mean velocity profile did not have an overshoot in the logarithmic region for most blending functions, confirming that proper energy transfer from the RANS to the LES region was a key to successful hybrid models. It is shown that Germano’s hybrid-filter approach is a viable and mathematically more appealing approach to simulate high Reynolds number turbulent flows.