A new approach to include surface tension in the subgrid eddy viscosity for the two-phase LES

Abstract

Turbulent two-phase flows feature different mechanisms for production and dissipation of turbulent kinetic energy compared to the single-phase flows. However, this difference is usually neglected in developing eddy viscosity-based subgrid scale (SGS) models for the two-phase large eddy simulation (LES). In this study, a new approach is presented for the two-phase LES to include the surface tension, which is a production mechanism for the kinetic energy in the small scale motions, into the subgrid eddy viscosity model. We follow the Favre-filtered governing equations of interfacial flows based on the volume of fluid (VOF) approach and derive the transport equation for the turbulent kinetic energy to include the effect of surface tension. The original contribution of this study is to propose a new form for the eddy viscosity based on the mixing length assumption which includes an additional production mechanism of turbulent kinetic energy stemming from the interfacial work i.e. surface tension. The proposed model for eddy viscosity is employed to close all the SGS terms. The model performance is evaluated by means of the a-priori filtering of the fine grid simulation of phase inversion problem. To test the generality of the model at different physical conditions, two different density ratios were considered for the fine grid simulation. The results highlight a significant improvement of the eddy viscosity-based SGS models in prediction of the turbulent kinetic energy for the small unresolved scales particularly for the regions of low shear. Furthermore, the model appears to perform more accurately in the case of low density ratios. This study provides a proper perspective for future SGS models in the context of large eddy simulation of two-phase flows.