The transient motion of a solid sphere between parallel walls

Abstract

This thesis describes an investigation of the velocity field in a fluid around a solid sphere undergoing transient motion parallel to, and midway between, two plane walls. Particle Image Velocimetry (PIV) was used to measure the velocity at many discrete locations in a plane that was perpendicular to the walls and included the centre of the sphere. The transient motion was achieved by releasing the sphere from rest and allowing it to accelerate to terminal velocity. To avoid complex wake structures, the terminal Reynolds number was kept below 200. Using solutions of glycerol and water, two different fluids were tested. The first fluid was 100%wt glycerol, giving a terminal Reynolds number of 0.6 which represents creeping flow. The second solution was 80%wt glycerol yielding a terminal Reynolds number of 72. For each of these fluids, three wall spacings were examined giving wall spacing to sphere diameter ratios of h/d = 1.2, 1.5 and 6.0. Velocity field measurements were obtained at five locations along the transient in each case. Using Y to denote the distance the sphere has fallen from rest, velocity fields were obtained at Y/d = 0.105, 0.262, 0.524, 1.05, and 3.15. It was observed that the proximity of the walls tends to retard the motion of the sphere. A simple empirical correlation was fit to the observed sphere velocities in each case. A wall correction factor was used on the quasi-steady drag term in order to make the predicted unbounded terminal velocity match the observed terminal velocity when the walls had an effect. While it has been previously established that the velocity of a sphere is retarded by the proximity of walls, the current research examined the link between the motion of the sphere and the dynamics of the fluid that surrounds it. By examining the velocity profile between the surface of the sphere at the equator and the wall, it was noticed that the shear stresses acting on the sphere increase throughout the transient, and also increase as the wall spacing decreases. This is due to the walls blocking the diffusion of vorticity away from the sphere as it accelerates leading to higher shear stresses. In an unbounded fluid, the falling sphere will drag fluid along with it, and further from the sphere, fluid will move upward to compensate. It was found that there is a critical wall spacing that will completely prevent this recirculation in the gap between the sphere and the wall. In the 80%wt glycerol case, this critical wall spacing is between h/d = 1.2 and 1.5, and in the 100%wt glycerol case the critical wall spacing is between h/d = 1.5 and 6.0.