Zonal PANS: evaluation of different treatments of the RANS–LES interface

Abstract

ABSTRACTThe partially Reynolds-averaged Navier–Stokes (PANS) model can be used to simulate turbulent flows either as RANS, large eddy simulation (LES) or DNS. Its main parameter is fk whose physical meaning is the ratio of the modelled to the total turbulent kinetic energy. In RANS fk = 1, in DNS fk = 0 and in LES fk takes values between 0 and 1. Three different ways of prescribing fk are evaluated for decaying grid turbulence and fully developed channel flow: fk = 0.4, fk = k3/2tot/ϵ and, from its definition, fk = k/ktot where ktot is the sum of the modelled, k, and resolved, kres, turbulent kinetic energy. It is found that the fk = 0.4 gives the best results. In Girimaji and Wallin, a method was proposed to include the effect of the gradient of fk. This approach is used at RANS– LES interface in the present study. Four different interface models are evaluated in fully developed channel flow and embedded LES of channel flow: in both cases, PANS is used as a zonal model with fk = 1 in the unsteady RANS (URANS) region and fk = 0.4 in the LES region. In fully developed channel flow, the RANS– LES interface is parallel to the wall (horizontal) and in embedded LES, it is parallel to the inlet (vertical). The importance of the location of the horizontal interface in fully developed channel flow is also investigated. It is found that the location – and the choice of the treatment at the interface – may be critical at low Reynolds number or if the interface is placed too close to the wall. The reason is that the modelled turbulent shear stress at the interface is large and hence the relative strength of the resolved turbulence is small. In RANS, the turbulent viscosity – and consequently also the modelled Reynolds shear stress – is only weakly dependent on Reynolds number. It is found in the present work that it also applies in the URANS region.