Modeling and Simulation of Multiple Bubble Entrainment and Interactions With a Traveling Vortex Ring

Bubble interactions with vortical structures are important to better understand the mechanisms of bubble induced boundary layer drag reduction and chemical mixing. Traditionally, many studies of disperse bubble or particle-laden flows have utilized an Euler-Lagrange two-way coupling approach, wherein the dispersed phase is assumed subgrid and its dynamics is modeled. In this work, results on full three-dimensional simulation of traveling vortex ring together with a few microbubbles are presented utilizing a volumetric coupling approach, wherein the displaced mass due to the presence of the bubbles is accounted for by using mixture theory based conservation laws in an Euler-Lagrange formulation. It is shown that the volumetric coupling approach is necessary to reproduce the experimental observations of Sridhar & Katz, JFM (1999). Experimental work by S&K on bubble entrainment into a traveling vortex ring has shown that the settling location of the bubble relative to the vortex core can be well predicted based on the ratio of the buoyancy force to the hydrodynamic pressure gradient. Additionally, the experimental results find that even at low volume fractions, bubble injection can significantly affect the structure of the vortex core. The two-way coupling model, wherein the fluid displacement due to bubble motion is neglected, of bubble-laden flows is unable to capture these effects on the vortical structure.