Applications of An Eddy-Viscosity Eliminator Based on Sigmoid Functions in Reynolds-Averaged Navier-Stokes Simulations of Sloshing Flow

Reynolds-averaged Navier-Stokes (RANS) turbulence modeling can lead to the excessive turbulence level around the interface in two-phase flow, which causes the unphysical motion of the interface in sloshing simulation. In order to avoid the unphysical motion of the interface, a novel eddy-viscosity eliminator based on sigmoid functions is designed to reduce the excessive turbulence level, and the eddy-viscosity eliminator based on polynomials is extracted from the cavitation simulations. Surface elevations by combining the eddy-viscosity eliminators and classical two-equation closure models are compared with the experiments, the ones by using the adaptive asymptotic model (AAM) and the ones by using the modified two-equation closure models. The root-mean-squared error (RMSE) is introduced to quantify the accuracies of surface elevations and the forces. The relation between the turbulence level in the transition layer and RMSEs of surface elevations is studied. Besides, the parametric analysis of the eddy-viscosity eliminators is carried out. The studies suggest that (1) the excessive turbulence level in the transition layer around the interface has a significant influence on the accuracies of surface elevations and the forces; (2) the eddy-viscosity eliminators can effectively reduce the excessive turbulence level in the transition layer to avoid the unphysical motion of the interface; (3) the k − ω SST model combined with the eddy-viscosity eliminators is appropriate for predicting surface elevations and forces in RANS simulations of sloshing flow.