Accumulation of heavy particles in N-vortex flow on a disk

Abstract

The motion of heavy particles in potential vortex flows on the unit disk is investigated theoretically and numerically. Configurations with one vortex and with two vortices are considered. In both cases, each vortex follows a regular path on the disk. In the one-vortex case, it is shown that small, heavy particles may accumulate in elliptic regions of the flow, counter-rotating with respect to the vortex. When the particle Stokes number exceeds a threshold depending on the vortex configuration, all particles are expelled from the circular domain. A stability criterion for particle accumulation is derived analytically and verified by numerical results. In the two-vortex case, heavy particles are shown to accumulate in elliptic islands of regular motion. Again, this result is explained by a stability analysis. The results may be useful in the design of gas-particle separators containing a helical vortex filament.

Numerical simulation of the accumulation of heavy particles in a circular bounded vortex flow

“…Note that the particle-particle collisions are also taken into account for the one-way coupling case. In contrast to the point-particle results obtained by IJzermans and Hagmeijer (2006), the present results are obtained for finite size particles that may collide with others frequently due to the high particle concentration…”

“…Implementation details of IBM are described in references (Lima E Silva et al 2003;Mittal and Iaccarino 2005;Peskin 2002;Taira and Colonius 2007;Uhlmann 2005).  is given by (IJzermans and Hagmeijer 2006):…”

“…The motion of small heavy particles (like droplets, impurities and dust) in gas flows plays an important role in both the cloud formation in the earth's atmosphere and many industrial applications, such as steam turbines, gas-particle separators and combustion engines. Thus, it has gathered much attention from both the theoretical and numerical point of views in the past two decades (Balachandar and Eaton 2010;Gañán-Calvo and Lasheras 1991;Ijzermans 2007;Ijzermans and Hagmeijer 2006;Provenzale 1999;Sánchez and Moreno-López 2005;Tio et al 1993a;Tio et al 1993b). A salient feature of such suspensions is the appearance of strong heterogeneities in the spatial distribution of particles, often dubbed preferential accumulation.…”

Effect of drag models on the accumulation of heavy particles in a circular bounded vortex flow

“…The motion of small heavy particles (like dust, impurities and droplets) in gas flows has important implications in many natural phenomena and industrial processes and has gathered much attention both from a theoretical and a numerical point of view in the past two decades [1][2][3]. A salient feature of such suspensions is the appearance of strong inhomogeneities in the spatial distribution of particles, often dubbed preferential accumulation.…”

“…The circular bounded vortex flow considered is characterized by an eccentrically placed point vortex in a closed circular domain and directly relevant to industrial gas-particle or gas-condensate separator. IJzermans and Hagmeijer [3] explored the accumulation of heavy particles in bounded potential vortex flows but their results are based on oneway coupling. In this paper, the inter-phase coupling, and inter-particle or particle-wall collisions are all taken into account.…”