Reynolds-averaged modeling of turbulence damping near a large-scale interface in two-phase flow

Abstract

The two-fluid Euler-Euler model can be used for the description of co-existing stratified and dispersed multiphase flow within one flow domain. For realistic engineering applications, turbulence is often modeled in the Reynolds-averaged Navier-Stokes (RANS) framework where closure of the Reynolds stresses is mostly achieved using the turbulent viscosity formulation. It is a well-known problem that at large-scale interfaces between two phases such turbulence modeling breaks down as turbulent viscosity in the vicinity of an interface is over-predicted. To address this issue, we adopt the Egorov approach (Egorov et al., 2014) which locally damps turbulence near the interface. This model is based upon the idea that at a large-scale interface the lighter phase may see the heavier phase much like a solid wall, suggesting a wall-like treatment of turbulent dissipation at the interface. The implementation of the model inside a two-phase formulation of the k–ω model is discussed, and shown to give good predictions of interfacial turbulence in co-current stratified two-phase flow. The Egorov approach is extended to the k–ε model, which may be relevant for a large array of engineering applications in which the k–ε model is more effective than the k-ω model. It is shown that the non-dimensional Egorov approach coefficient is grid dependent. We introduce a new formulation of the interfacial damping term in the two-fluid Euler-Euler model which gives more consistent results for different computational grids in comparison to the original formulation of the Egorov approach. This feature, as well as its straightforward implementation in both the k–ω and k–ε models, make the new model useful to a large array of multiphase engineering problems in which interfacial turbulence damping is relevant.