Effect of the History Force on the Translational Motion of Bubbles and Particles in Cellular Flow

Abstract

Effect of a history force, that has been often neglected in one-way coupling simulatios, is numerically investigated on a translational motion of bubbles and particles in a cellular flow. The simulation method is developed to take into account the Basset history force. A fully developed particle distribution and a mean velocity are examined for various dimensionless parameters : density ratio “ρ*”, Stokes number “St” and drift velocity in a quiescent fluid “W*”. As reported in our previous study without the history force (Sugiyama et al., 2003), similar results are obtained under some conditions, i.e., (1) for the heavier particle or the bubble with the large drift velocity (W*> 0 (1)), the bifurcation does not occur, (2) for bubbles (ρ*=0) with small W*, they accumulate and are trapped in the center of the vortex. Quantitatively, the particle distribution and the mean velocity are strongly affected by the history force when the drag and inertia forces are comparable (St = O (1)). Especially, for the heavier particle (ρ*>1) with small W*, the preferential concentration of the particle with the history force term in its equation is stronger than that without the history force.