Direct simulation of initial value problems for the motion of solid bodies in a Newtonian fluid Part 1. Sedimentation

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 turn its long axis perpendicular to the fall, and drifts to the centreline 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 nonlinear effects of particle-fluid, particle-wall and interparticle interactions are analysed, 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. 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 turn its long axis perpendicular to the fall, and drifts to the centreline 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 nonlinear effects of particle-fluid, particle-wall and interparticle interactions are analysed, and the mechanisms controlling the simulated flows are shown to be lubrication, turning couples on long bodies, s...

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

“…It has been systematically compared to existing results from the literature: fixed or oscillating cylinder [12,13,18,21] ; unique cylindrical particle sedimenting in a vertical channel with either axial or asymmetric initial position [21,24] ; pairs of particles interacting in a vertical channel [8,21,24].…”

The motion of an axisymmetric body falling in a tube at moderate Reynolds numbers

“…Feng, Hu & Joseph (1994) investigated numerically the sedimentation of particles of spherical and elliptical cross-section in two dimensions. For Reynolds numbers Rec lower than 60 for S = 0.25, they observed that the spherical particle displays a rectilinear or weakly oscillatory motion with a mean position corresponding to the channel centreline.…”

Direct simulation of the sedimentation of elliptic particles in Oldroyd-B fluids

“…This means that the effects of inertia and viscoelasticity are to be found only in the reaction pressure evaluated on the body. Hu, Joseph and Crochet (1992), Feng, Hu and Joseph (1994) and Huang, Feng and Joseph (1994) have shown that an ellipse sedimenting in a Newtonian fluid turns broadside-on but at high Reynolds numbers vortex shedding will make it oscillate.…”