Volume displacement effects during bubble entrainment in a travelling vortex ring

Abstract

AbstractWhen 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.