A Sub-grid Scale Energy Dissipation Rate Model for Large-eddy Spray Simulations

Abstract: In high Reynolds number turbulent flows, energy dissipation refers to the process of energy transfer from kinetic energy to internal energy due to molecular viscosity. In large eddy simulation (LES) with one-equation turbulence models, the energy dissipation process is modeled by a rate term in the transport equation of the subgrid-scale (SGS) kinetic energy. Despite its important role in maintaining a proper energy balance between the resolved and SGS scales, modeling of the energy dissipation rate has received scarce attention. In this paper, a SGS model belonging to the dynamic structure family is developed based on findings from direct numerical simulation (DNS) studies of decaying isotropic turbulence. The model utilizes a Leonard-type term, a SGS viscosity, and a characteristic scaling term to predict the energy dissipation rate in LES. A posteriori tests of the model have been carried out under direct-injection gasoline and diesel engine-like conditions. Spray characteristics such as penetration rates and mixture fractions have been examined. It is found that the current SGS model accurately predicts vapor-phase penetrations across different mesh resolutions under both gasoline and diesel spray conditions, due to its correct scaling of SGS energy dissipation rate with the SGS kinetic energy and LES fitter width. In contrast, the classic model that is widely used in the literature predicts a scaling of energy dissipation rate upon mesh resolution, exhibiting a noticeable mesh dependence.