Study of collisions between particles and unloaded bubbles with point-particle model embedded in the direct numerical simulation of turbulent flows

Abstract

Simulations of a particle-bubble collision system composed of monosized spherical solid particles and air bubbles in a quiescent liquid and homogeneous isotropic turbulence have been performed using the pseudo-spectral method for the fluid flow and Lagrangian tracking for particles and bubbles. Particle-bubble collisions in a quiescent liquid were first simulated and compared to the existing theoretical models of particle-bubble collisions. Both numerical results and theoretical models indicate that decreasing bubble size and increasing particle size can increase the particle-bubble collision efficiency. A DNS model for studying the effect of turbulence on the collisions between particles and unloaded bubbles was then developed. A nonuniform time-dependent stochastic forcing scheme was implemented to maintain turbulence intensity at targeted levels. A statistical analysis of a group of particles and bubbles in the forced turbulent flow was performed to probe the mechanism of particle-bubble collision in a turbulent flow. A simplifying assumption (motivated purely by computational limitations) has been made that bubbles and particles can be randomly relocated during the simulation, unlike what happens in reality, but the size of the effect that this simplifying assumption will have on our results is unknown. Reductions in particle-bubble collisions due to preferential concentrations of particles and bubbles in different flow regions were not found. Comparing respectively the contributions of radial relative velocity and radial distribution function to the collision kernel, the contribution of radial distribution function could be neglected because the radial relative velocity increases by about 1900% (from 1.55 cm/s to 28.87 cm/s) while the radial distribution function decreases by only 33% (from 1.33 to 1.00). Collisions between particles and bubbles increased with turbulent dissipation rate primarily due to the fact that radial relative velocities between particles and bubbles increased with the flow dissipation rate.