Romuald Verjus | Searcharxiv

arXiv2016

Chaotic sedimentation of particle pairs in a vertical channel at low Reynolds number: multiple states and routes to chaos

The sedimentation of a pair of rigid circular particles in a two-dimensional vertical channel containing a Newtonian fluid is investigated numerically, for terminal particle Reynolds numbers ranging from 1 to 10, and for a confinement ratio equal to 4. While it is widely admitted that sufficiently inertial pairs should sediment by performing a regular DKT oscillation (Drafting-Kissing-Tumbling), the present analysis shows in contrast that a chaotic regime can also exist for such particles, leading to a much slower sedimentation velocity. It consists of a nearly horizontal pair, corresponding to a maximum effective blockage ratio, and performing a quasiperiodic transition to chaos under increasing the particle weight. For less inertial regimes, the classical oblique doublet structure and its complex behavior (multiple stable states and hysteresis, period-doubling cascade and chaotic attractor) are recovered, in agreement with previous work [Aidun & Ding, Physics of Fluids 15(6), 2003]. As a consequence of these various behaviors, the link between the terminal Reynolds number and the non-dimensional driving force is complex: it contains several branches displaying hysteresis as well as various bifurcations. For the range of Reynolds number considered here, a global bifurcation diagram is given.

physics.flu-dyn↗

arXiv2016

Critical Stokes number for the capture of inertial particles by recirculation cells in 2D quasi-steady flows

Inertial particles are often observed to be trapped, temporarily or permanently, by recirculation cells which are ubiquitous in natural or industrial flows. In the limit of small particle inertia, determining the conditions of trapping is a challenging task, as it requires a large number of numerical simulations or experiments to test various particle sizes or densities. Here, we investigate this phenomenon analytically and numerically in the case of heavy particles (e.g. aerosols) at low Reynolds number, to derive a trapping criterion that can be used both in analytical and numerical velocity fields. The resulting criterion allows to predict the characteristics of trapped particles as soon as single-phase simulations of the flow are performed. Our analysis is valid for two-dimensional particle-laden flows in the vertical plane, in the limit where the particle inertia, the free-fall terminal velocity, and the flow unsteadiness can be treated as perturbations. The weak unsteadiness of the flow generally induces a chaotic tangle near heteroclinic or homoclinic cycles if any, leading to the apparent diffusion of fluid elements through the boundary of the cell. The critical particle Stokes number Stc below which aerosols also enter and exit the cell in a complex manner has been derived analytically, in terms of the flow characteristics. It involves the non-dimensional curvature-weighted integral of the squared velocity of the steady fluid flow along the dividing streamline of the recirculation cell. When the flow is unsteady and St > Stc, a regular motion takes place due to gravity and centrifugal effects, like in the steady case. Particles driven towards the interior of the cell are trapped permanently. In contrast, when the flow is unsteady and St < Stc, particles wander in a chaotic manner in the vicinity of the border of the cell, and can escape the cell.

physics.flu-dyn↗