Direct Simulation of Initial Value Problems for the Motion of Solid Bodies in a Newtonian Fluid Part 1. Sedimentation

J. Feng, H. H. Hu and D. D. Joseph

*J. Fluid Mech*. **261**, 95-134
(1994)

**Abstract** This paper reports the result of direct
simulations of fluid-particle motions in two dimensions. We solve the initial
value problem for the sedimentation of circular and elliptical particles
in a vertical channel. The fluid motion is computed from the Navier-Stokes
equations for moderate Reynolds numbers in the hundreds. The particles are
moved according to the equations of motion of a rigid body under the action
of gravity and hydrodynamic forces arising from the motion of the fluid.
The solutions are as exact as our finite element calculations will allow.
As the Reynolds number is increased to 600, a circular particle can be said
to experience five different regimes of motion: steady motion with and without
overshoot and weak, strong and irregular oscillations. An elliptic particle
always turns its long axis perpendicular to the fall, and drifts to the
center-line of the channel during sedimentation. Steady drift, damped oscillation
and periodic oscillation of the particle are observed for different ranges
of the Reynolds number. For two particles which interact while settling,
a steady staggered structure, a periodic wake-action regime and an active
drafting-kissing-tumbling scenario are realized at increasing Reynolds numbers.
The non-linear effects of particle-fluid, particle-wall and inter-particle
interactions are analyzed, and the mechanisms controlling the simulated flows
are shown to be lubrication, turning couples on long bodies, steady and unsteady
wakes and wake interactions. The results are compared to experimental and
theoretical results previously published.