Volume Displacement Effects in Bubble-laden Flows

When a few bubbles are entrained in a traveling vortex ring, it has been shown that even at extremely low volume loadings, their presence can significantly affect the structure of the vortex core (Sridhar {\&} Katz 1999). A typical Euler-Lagrange point-particle model with two-way coupling for this dilute system, wherein the bubbles are assumed subgrid and momentum point-sources are used to model their effect on the flow, is shown to be unable to accurately capture the experimental trends of bubble settling location and vortex distortion for a range of bubble parameters and vortex strengths. The bubbles experience a significant amount of drag, lift, added mass, pressure, and gravity forces. However, these forces are in balance of each other, as the bubbles reach a mean settling location away from the vortex core. Accounting for fluid volume displacement due to bubble motion, using a model termed as volumetric coupling, experimental trends on vortex distortion and bubble settling location are well captured. The fluid displacement effects are studied by introducing a notion of a volumetric coupling force, the net force on the fluid due to volumetric coupling, which is found to be dominant even at the low volume loadings investigated here.