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Dispersion of heavy particles in an isolated pancake-like vortex Goater, Aurelie

Abstract

The objective of the present study is to characterize the dispersion of small, spherical particles (mainly heavy particles) in a quasi two-dimensional axisymmetric pancake-like vortex. The velocity field for a pancake vortex is substituted into the Maxey-Riley (1983) equation, and the resulting equations of motion are solved numerically, in non-dimensional form, for a given set of parameters. The particles' characteristics that are of primary importance are their density and their diameter. In general, the particles considered are denser than the surrounding fluid. Therefore they move away from the vortex centre with time. The Stokes number, a function of the particle diameter and density, measures the sensitiveness of the particle to the surrounding velocity field. The lateral dispersion of the particles is examined for different values of the Stokes number, ranging from 10"' to 10. The analysis is first conducted in the 2D horizontal plane of the vortex. By looking at the dynamics of individual particles, it is shown that particles of the same size and density cannot accumulate in the core of the vortex, but they can do so in the outer region of the vortex, increasing the possibility of flocculation. In addition, if the Stokes number is large enough, particles initially located in the central region of the vortex are able to overtake particles initially located further from the vortex centre. The analysis of the concentration profiles in the horizontal plane of the vortex, when the flow is initially seeded with a homogeneous distribution of particles of the same size and density, shows that accumulation of particles takes the form of a concentration wave that grows and travels away from the vortex centre. The larger the Stokes number is, the faster the particles are ejected, but optimal accumulation occurs for intermediate values of the Stokes number (St ~ 1). Also, for large Stokes numbers (St ~ 10), overtaking is observed. It occurs at very early times and substantially modifies the dispersion process, causing a second peak of concentration to appear. Just before the second peak of concentration detaches itself from the first one, a very high local concentration is observed, because the catch-up phenomenon adds up to the local accumulation of particles. Further calculations show that overtaking is associated with a very high probability of collision between the particles, so that, in reality, flocculation is expected to play an important role for large Stokes numbers. The analysis is extended to the settling of heavy particles through the vortex. A 3D study shows that the second peak of concentration observed in the case of large Stokes numbers (Sr ~ 10) will not occur unless the vortex thickness is large enough.

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