Subgrid-scale modelling of surface tension within interface tracking-based Large Eddy and Interface Simulation of 3D interfacial flows

Abstract

This paper introduces a novel modelling procedure for unresolved surface tension in interface tracking-based Large Eddy and Interface Simulation (LEIS) of interfacial flows. The approach involves modelling of the subgrid-scale (SGS) surface tension appearing in the filtered momentum equation, and explicitly the dominant SGS curvature part of that term. The procedure for modelling the SGS curvature is based on the analysis of variations in curvature resulting from using different filter widths, as well from using alternative discretization-based and direct-filtering techniques for generating coarse-filter curvature estimates. Unresolved surface tension modelling can act to smooth spatial curvature variations and dampen parasitic modes, and can alternatively restore interface wrinkling when super-grid scale resolution underpredicts local curvature. The paper outlines the principles involved in identifying local regions of unresolved surface tension, and in constructing a model that is robust across the range of interface topologies. The current implementation is based on the height-function curvature discretization scheme in Volume-of-Fluid (VOF) interfacial flow simulations.The procedure represents a SGS model in the true sense of the term – it is not a discretization scheme. The model should be used for Large Interface Simulation (LIS) of laminar interfacial flow modelling, too, complementing discretization schemes employed for resolved surface tension. Understandably the contribution of the model diminishes with mesh resolution as laminar flow does not continually introduce filter-scale interfacial deformations. The model may be more useful though for LEIS of turbulent interfacial flows, supporting discretization schemes for better capturing interface wrinkling, atomization and large bubble breakup.