Spatiotemporal evolutions of forces and vortices of flow past ellipsoidal bubbles: Direct numerical simulation based on a Cartesian grid scheme

Abstract

An in-depth investigation of two fixed non-spherical bubbles is an indispensable step toward revealing fundamental mechanisms in complex bubbly flows, where direct numerical simulation (DNS) is one of the most promising approaches to conduct such a task. However, accurately modeling force distribution and efficiently generating satisfactory mesh around a non-spherical bubble pair are challenging to current DNS methods. In this study, an effective non-body-fitted gas-liquid interface tracking scheme based on the Cartesian grid was developed to conduct three-dimensional DNS of two fixed ellipsoidal bubbles with frozen shape in an incompressible Newtonian fluid. The grid-independent analysis and analytical validation prove that our developed non-body-fitted gas-liquid interface tracking scheme is able to accurately retrieve all force components exerted on a bubble with less mesh generation and computational efforts than body-fitted counterparts. Using this non-body-fitted gas-liquid interface tracking scheme, spatiotemporal evolutions of forces and vortices around the two fixed ellipsoidal bubbles were directly simulated under various values of Reynolds numbers, separation distances, and the bubble's ellipsoidicity. The analysis of drag force shows that the overall drag behaviors of ellipsoidal bubbles are quite similar to those of spherical bubbles though larger ellipsoidicity produces a higher drag coefficient. However, the sign of lift forces, i.e., either the two bubbles attract or repel each other, is highly dependent on ellipsoidicity. For the bubble pair with moderate ellipsoidicity, attractive force dominates at moderate-to-high Reynold numbers, while the two bubbles tend to repel at low Reynolds numbers. For the bubble pair with high ellipsoidicity, the two bubbles repel each other at all values of Reynolds numbers and separation distances. Characteristics of vortex developments, which are the reason behind these ellipsoidicity-dependent force behaviors, are presented and discussed. This study highlights the importance of the bubble's shape in the interactions and associated vortex between two adjacent fixed ellipsoidal bubbles.