Modeling bubble-vortex interactions Modeling and simulation of multiple bubble entrainment and interactions with two dimensional vortical flows

1 Modeling bubble-vortex interactions Simulations of bubble entrainment and interactions with two dimensional vorti-cal flows are preformed using a Discrete Element Model (DEM). In this Eulerian-Lagrangian approach, solution to the carrier phase is obtained using direct numerical simulation whereas motion of subgrid bubbles is modeled using Lagrangian tracking. The volumetric displacement of the fluid by the finite size of the bubbles is modeled along with interphase momentum-exchange for a realistic coupling of the bubbles to the carrier phase. In order to assess the importance of this volumetric coupling effect even at low overall volume loading, simulations of few microbubbles entrained in a traveling vortex tube is studied in detail. The test case resembles the experiments conducted by Sridhar & Katz [JFM, 1999] on bubble-entrainment in vortex-rings. It is shown that under some conditions, the entrainment of eight small bubbles, 1, 100µm or less in diameter, result in significant levels of vortex distortion when modeled using the volumetric coupling effect. Neglecting these effects; however, does not result in any vortex distortion due to entrained bubbles. The non-dimensionalized vortex-strength versus bubble settling locations are compared with experimental data to show collapse of the data along the trends observed in experiments only when the volumetric effects are modeled. Qualitative and quantitative assessments of this distortion observed with volumetric coupling are made using three methods; bubble induced vortex asymmetry, relative change in the decay of angular momentum, and relative change in the peak vorticity. It is found that in all cases the volumetric effects result in a relative increase of the vortex decay rate. The concept of a relative reaction force, defined as the ratio of net bubble to fluid reaction to the local driving force of the vortex, is introduced to analyze this effect. It is shown that the global increases in vortex decay rate are directly proportional to the magnitude of this highly local relative reaction force. Model a) 2 Modeling bubble-vortex interactions