An active hybrid Reynolds-averaged Navier–Stokes/large eddy simulation approach for gray area mitigation

Abstract

During the transition from the RANS (Reynolds-Averaged Navier–Stokes) mode to the LES (Large Eddy Simulation) mode, i.e., in the so-called gray area, continuous hybrid RANS/LES approaches suffer from the well-known problem of excessively slow generation of resolved structures. Indeed, when the mesh is refined in the direction of the flow, the model is designed to reduce the modeled energy, but there is no mechanism to transfer the equivalent amount of energy into the resolved motion. Hence, the total turbulent energy and turbulent stresses are underestimated, which strongly affects the prediction of the mean flow. This also constitutes a violation of the conservation of mechanical energy, which can only be corrected by an active approach, i.e., an approach that allows the injection of resolved energy. The aim of this work is to develop such an active approach based on the introduction of a fluctuating volume force into the resolved momentum equation, similar to the anisotropic linear forcing (ALF) method proposed previously. The major difference with ALF is that the new method does not require target statistics obtained by a RANS computation but is based on a simple analysis of the rate of energy transfer related to variations in resolution, enabling the forcing to be extended to continuous hybrid RANS/LES. The application of the new method to the cases of a channel with or without periodic constriction shows a drastic improvement over the case without forcing. Although the method is applied herein to a particular hybrid RANS/LES approach (HTLES, hybrid temporal LES), it can easily be extended to any other approach, as long as a parameter identifies variations in resolution, and thus offers vast application prospects.