Volume of Fluid simulation of air–water co-current and Counter-current flow with variable density turbulence formulation

Abstract

Co-current and counter-current air–water flows are studied by Volume of Fluid (VOF) simulation, with emphasis on turbulence modelling near the interface. The relevance of constant density (ρ-con) and variable density (ρ-var) formulations of the turbulence transport equations in two classical two-equation turbulence models, k−ϵ RNG and k−ω SST models, is discussed. The Reynolds Stress Tensor (RST) model approach is also investigated and literature results with the two-fluid model are included for comparison. Our results with VOF show that the widely used constant density formulation underestimates the turbulence dissipation without capturing the turbulence jump across the interface, which also affects the interface liquid height, the velocity profiles of both phases and the pressure drop along the domain. In contrast, the variable density formulation significantly improves the results by increasing the turbulence dissipation at the interface. Although the best solutions have been obtained using the RST model, the ρ-var and k−ϵ RNG gave quite good agreement with experimental data. Despite the narrowness of the domains, three-dimensional simulations have been in better agreement than the two-dimensional ones. Both the VOF results obtained with either the RST and the ρ-var turbulence formulations were found to be superior to those reported with the TF model using damping corrections specifically calibrated for the tests. This study demonstrates that VOF simulation combined with ρ-var two equations turbulence models is a suitable method for modelling large-scale interface segregated flows.