DYNAMICS OF CONCENTRATION AND VORTICITY MODIFICATION IN A CELLULAR-FLOW LADEN WITH SOLID HEAVY-PARTICLES

The processes of the accumulation of solid heavy particles settling un der gravity and modification of the carrier flow are studied analytica lly and numerically. The dilute limit is considered when the effects o f particle-particle interactions are neglected. The flow Reynolds numb er is assumed to be large enough to disregard effects related to the v iscous dissipation. Particles with a small Stokes (St) number are cons idered, when approximate solution for the particulate velocity in the form of a series in St can be derived. Analytical solutions are obtain ed for initially uniform distribution of particles in a cellular flow (formed by a lattice of two-dimensional vortices with different circul ations) describing dynamics of the particulate concentration and corre sponding modification of the fluid flow. Two different regimes of larg e and moderate flow Froude number (Fr) are considered. Solutions obtai ned show that in the first case (Fr much greater than 1), when the gra vitational settling of the particles is insignificant, the concentrati on of particles drops at the centers and grows at the periphery of the vortices, so that sheets of the increased concentration are formed in the vicinity of the flow separatrices. Due to the coupling between th e particulate and fluid dynamics, the flow vorticity is reduced at the cells centers. The flow gradients grow due to the drag forces between the two phases and sheets of increased vorticity are generated in the vicinity of the concentration sheets. In the case Fr similar to 1 the concentration sheets correspond to the particle settling paths. Vorti city is effectively generated in the vicinity of these paths, where th e drag force based on the local slip velocity is enhanced by the settl ing. As a result, vortex centers are shifted toward the settling paths , so that the whole symmetry of the flow is changed by the coupling. R esults of direct numerical simulations performed for St similar to 1 s how a good agreement with analytical solutions. It is observed also th at the average value of particle settling velocity may exceed that in the still fluid (similar to the earlier result obtained by Maxey [Phil os. Trans. R. Sec. London Ser. A 333, 289 (1990)] under assumption tha t the influence of the particulate on the carrier flow remains negligi ble). (C) 1995 American Institute of Physics.