Simulations of an ellipsoid settling in a cylindrical tube

The motion of an ellipsoid settling in an infinite cylindrical tube, under the influence of gravity, has been simulated numerically using an arbitrary Lagrangian Eulerian based finite element scheme. Previously such a scheme has been developed for the case of spheres. The use of quaternions and modified meshing and particle motion update techniques has been used here to study the behaviour of non-spherical particles. The motion of ellipsoids, released at the center of a long tube, and oriented at various initial angles has been observed to be dependent on both the Stokes number and the Reynolds number measuring the partcile and fluid inertia respectively. For the case of Stokes' flow, the motion is seen to follow an oscillatory motion wherein the body moves from side to side and rotates near the walls. This motion is seen to vary with both the Stokes' number as well as the initial orientation with no stable equilibrium configuration. For the case of moderate Reynolds number, the particles eventually are seen to ``settle" in an equilibrium configuration where they experience no torque and move purely in the direction of the external body force. The position of this equilibrium as well as the orientation of the body are seen to be functions of the Reynolds number.