Three-dimensional sedimentation patterns of two interacting disks in a viscous fluid

The sedimentation of two spherical solid objects in a viscous fluid has been extensively investigated and well understood. However, a pair of flat disks (in three dimensions) settling in the fluid shows more complex hydrodynamic behaviors. The present work aims to improve understanding of this phenomenon by performing Direct Numerical Simulations (DNS) and physical experiments. The present results show that the sedimentation processes are significantly influenced by disk shape, characterized by a dimensionless moment of inertia I*, and Reynolds number of the leading disk Re. For the flatter disks with smaller I*, steady falling with enduring contact transits to periodic swinging with intermittent contacts as Re increases. The disks with larger I* tend to fall in a Drafting-Kissing-Tumbling (DKT) mode at low Re and to remain separated at high Re. Based on I* and Re, a phase diagram is created to classify the two-disk falling into ten distinctive patterns. The planar motion or three-dimensional motion of the disks is determined primarily by Re. Turbulent disturbance flows at a high Re contribute to the chaotic three-dimensional rotation of the disks. The chance for the two disks to contact is increased when I* and Re are reduced.Comment: 51 pages, 28 figure

Numerical study of the particle sedimentation in a viscous fluid using a coupled DEM-IB-CLBM approach

At low terminal Reynolds numbers Re = 2 - 10, there are multiple asymmetrical principal movement states for the sedimentation of a pair of particles in a channel filled with a viscous fluid. The main emphasis of this work is to investigate the formation process of these states and the effect of the natural rotation on the process when particles are released symmetrically. The flow field around each particle is fully resolved with an Immersed Boundary Method (IBM) coupled with the Cascaded Lattice Boltzmann Method (CLBM). An improved algorithm is developed to couple IBM with CLBM which can fully exploit the Graphic Processing Unit (GPU) for parallelisation. The collision between particles is handled with the Discrete Element Model (DEM). The approach is validated considering the sedimentation of a single particle released asymmetrically and also the Drafting-Kissing-Tumbling (DKT) problem of two particles. The trajectories of particles corresponding to different principal movement states are determined for the sedimentation of a pair of particles released symmetrically in a long narrow channel. By analysing the trajectories, it is found that particles go through two distinct symmetry breaking phenomena, a sudden lateral migration that leads to asymmetrical movement centres, and (or) a divergent oscillation that leads to a zero phase lag between the fundamental frequencies of oscillating particles. Since particle's lateral movement and natural rotation display a strong coherence of nearly 1.0 over a transitional oscillatory period, the trajectories of particles without rotational degree-of-freedom are then considered to determine the impacts of natural rotation on the principal movement states. It is shown that the lateral migration can still take place even after removing the rotational degree-of-freedom. However, the divergent oscillation disappears, which makes particles move in a steady oblique or horizontal structure and leads to a smaller terminal Reynolds number