DIRECT SIMULATION OF INITIAL-VALUE PROBLEMS FOR THE MOTION OF SOLID BODIES IN A NEWTONIAN FLUID .1. SEDIMENTATION

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 chann el. The fluid motion is computed from the Navier-Stokes equations for moderate Reynolds numbers in the hundreds. The particles are moved acc ording 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 all ow. As the Reynolds number is increased to 600, a circular particle ca n be said to experience five different regimes of motion: steady motio n with and without overshoot and weak, strong and irregular oscillatio ns. An elliptic particle always turn its long axis perpendicular to th e fall, and drifts to the centreline of the channel during sedimentati on. Steady drift, damped oscillation and periodic oscillation of the p article are observed for different ranges of the Reynolds number. For two particles which interact while settling, a steady staggered struct ure, a periodic wake-action regime and an active drafting-kissing-tumb ling scenario are realized at increasing Reynolds numbers. The nonline ar effects of particle-fluid, particle-wall and interparticle interact ions are analysed, and the mechanisms controlling the simulated flows are shown to be lubrication, turning couples on long bodies, steady an d unsteady wakes and wake interactions. The results are compared to ex perimental and theoretical results previously published.