When a few bubbles are entrained in a travelling 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, J. Fluid Mech., vol. 397, 1999, pp. 171–202). 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 capture accurately the experimental trends of bubble settling location, bubble escape and vortex distortion for a range of bubble parameters and vortex strengths. The bubbles experience significant amounts of drag, lift, added mass, pressure and gravity forces. However, these forces are in balance with each other as the bubbles reach a mean settling location away from the vortex core. The reaction force on the fluid due to the net summation of these forces alone is thus very small and is unable to affect the vortex core. By accounting for fluid volume displacement due to bubble motion, experimental trends on vortex distortion and bubble settling location are captured accurately. The fluid displacement effects are studied by computing various contributions to an effective volume displacement force and are found to be important even at low volume loadings. As the bubble size and hence bubble Reynolds number increase, the bubbles settle further away from the vortex centre and have strong potential for vortex distortion. The net volume displacement force depends on the radial pressure force, the radial settling location of the bubble, as well as the vortex Reynolds number. The resultant of the volume displacement force is found to be roughly at $4{5}^{\circ } $ with the vortex travel direction, resulting in wakes directed towards the vortex centre. Finally, a simple modification to the standard point-particle two-way coupling approach is developed wherein the interphase reaction source terms are consistently altered to account for the fluid displacement effects and reactions due to bubble accelerations.

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.