Analysis of filtered Navier-Stokes equation for hybrid RANS/LES simulation

Hybrid Reynolds-averaged Navier-Stokes/large eddy simulation (RANS/LES) is expected to accurately predict wall-bounded turbulent flows at high Reynolds numbers. It is known that extra terms due to the noncommutivity between the hybrid filter and the spatial derivative appear in the hybrid-filtered equations. In this paper the filtered Navier-Stokes equation is investigated using direct numerical simulation data of turbulent channel flow. In particular, the transport equations for the resolved and modeled energies are evaluated to examine the contribution of the extra terms. The RANS and LES regions are located by setting the width of the hybrid filter varying from the grid spacing to the channel half width. In the first case the RANS region is located near the wall for wall modeling in LES. In the second case the RANS and LES regions are located upstream and downstream, respectively. The extra terms in the Navier-Stokes and continuity equations show fairly large values in the RANS/LES interface region in both cases. The extra terms for the convection and the turbulent diffusion represent the energy transfer from the modeled part to the resolved part. This energy transfer suggests that conventional hybrid simulations neglecting the extra terms may underpredict velocity fluctuations in the interface region, causing an insufficient momentum transport and velocity mismatch in channel flow. These results show that the effect of the extra terms should be taken into account in the filtered Navier-Stokes equation as well as in the turbulent-energy equation in hybrid simulations. (C) 2011 American Institute of Physics. [doi:10.1063/1.3549933]