Modelling and A-Posteriori Assessment of Closure Models for Sub-Grid Surface Tension Considering a Rising Gas Bubble

Correctly predicting the behaviour gas-liquid multiphase flows with numerical simulation tools is a highly complex task, especially when considering industrial scales. The most challenging task in that regard might be the large range of length scales of turbulent as well as of interfacial structures. Based on the two-fluid model, a hybrid methodology is developed with the goal to adaptively combine Euler-Euler and Volume-of-Fluid (VOF) simulation methods for statistical and scale-resolving representation of gas-liquid interfaces, respectively (Meller et al., 2021). With that approach, inevitably situations arise, where interfacial dynamics need to be predicted with VOF in combination with a particularly coarse grid resolution.
Low-pass filtering of the underlying two-fluid equations in this context reveals an unclosed sub-grid surface tension term, besides the convective and other unclosed terms (Meller et al., 2022). This contribution expresses the interfacial forces due to surface tension, which are not captured on a comparatively coarse computational grid. Different functional and structural closure models for that unclosed term are assessed in an a-posteriori fashion in case of a gas bubble rising in stagnant liquid. This contributes to an improved predictive power of the numerical model regarding large-scale interface and turbulent dynamics, even with low spatial resolution.