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

Abstract

Simulations of bubble entrainment and interactions with two dimensional vortical flows are preformed using a discrete element model. 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 a small number of microbubbles entrained in a traveling vortex tube are studied in detail. The test case resembles the experiments conducted by Sridhar and Katz ͓JFM, 1999͔ on bubble entrainment in vortex rings. It is shown that under some conditions, the entrainment of eight small bubbles, 1100 m 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 nondimensionalized 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.

Particle based modelling and simulation of natural sand dynamics in the wave bottom boundary layer

“…The two systems of equations for the particles (equations (2.1)-(2.3)) and fluid (equations (2.20)-(2.21)) are coupled and solved in a structured Cartesian grid framework using a finite volume discretization and a pressure based second-order fractional time-stepping scheme based on the work of Finn et al (2011 and Cihonski et al (2013). Extensive validation of the method for dilute Natural sand dynamics in the wave bottom boundary layer bubble-and particle-laden flows has been reported in these works.…”

Volume displacement effects during bubble entrainment in a travelling vortex ring

“…(a) The previous work (Finn et al 2011) was a two-dimensional study and the present work is a full three-dimensional study. Although this in itself is a significant difference in the actual problem setting, this work also focuses on several new aspects of the bubble-vortex ring interactions and helps explore fundamental physics of this interaction by using two-phase flow modelling.…”

“…1.3. Problem description A travelling vortex ring, shown in figure 3(a), is generated through an inlet velocity pulse (Sridhar & Katz 1999;Finn et al 2011). This pulse forms a shear layer, which rolls up into a vortex ring that is convected downstream.…”

“…sum close to zero in each direction. The force balance on the bubbles at a radial settling location from the core, shown in figure 3(c), indicates a balance of the pressure (F p ), added mass (F am ), lift (F ), drag (F d ) and gravity forces (F g ), respectively (Sridhar & Katz 1999;Finn et al 2011;Rastello et al 2011). For the cases studied in the present work, the angle (θ s ) at which the bubbles settle is typically small (θ s → 0) and, under such a situation, the gravity and buoyancy forces are approximately balanced by the drag force, whereas the radial settling location (r s ) is then obtained from an approximate balance of the lift, the added mass and the dynamic pressure-gradient forces, respectively.…”

Bubble–bubble interaction effects on dynamics of multiple bubbles in a vortical flow field

“…Some other researchers focused on the bubble-vortex interactions rather than BBI. Finn et al 19 developed a discrete element model to simulate the bubble entrainment and interactions with two-dimensional vortical flows. It was found that the existence of the bubble resulted in the distortion of the vortex.…”