Experiments On Rolling Sphere Submerged In An Incompressible Fluid

Abstract

Experiments are done using a smooth solid rigid homogeneous acrylic sphere rolling on an inclined plane which is submerged in water. The motivation for these experiments comes from a need to understand a class of solid-fluid interaction problems that include sediment transport, movement of gravel on ocean floor and river bed due to water currents. Experiments are performed in a glass water tank 15 cm wide by 14 cm deep by 61 cm long which can be tilted to desired angle. The sphere is released from rest on the inclined false bottom of the tank in quiescent water. Our experimental study has twofold aim: (1)to study the boundary layer separation, the three-dimensional eddying motion in the wake and the near-wake structure and(2) to establish hydrodynamic force coefficients by analyzing kinematical data of the sphere motion from start to till it attains terminal velocity. Experiments are carried out at moderate Reynolds number Rearound1500. Previous studies on the first problem exist in the literature for Reup to 350. Previous studies on the second problem do not clearly define the added-mass coefficient and the influence of the water tank side-walls on the drag coefficient. In the first study, the characterization of the wake is done using flow visualization methods (fluoresce in dye visualization and particle streak visualization) and Particle Image Velocimetry (PIV). Laser light sheet obtained from an argon ion continuous laser beam is taken in different orientations to illuminate the fluoresce in dye or 14 m silver-coated hollow glass spheres. These experiments show that the wake behind the rolling sphere up to 1.6 diameters (or 1.6D) downstream is confined within height 1.2Dand width1.2D. At about 1.8Ddownstream, the wake sways alternately on either side of the equatorial plane, moving in lateral-vertical direction and moving out of the confining region; this gives zigzag appearance to the wake. Also in these experiments, we observe that the flow separations from the surface of the rolling sphere show three separation zones. The eddies shed from the primary separation surface on the upper hemisphere are symmetrical about the equatorial plane with Strouhal number St=1.0. The primary separation is affected by the symmetrical secondary separations on the rear surface in the piggyback region — it is the region near the upper rear surface of the sphere behind the transverse equatorial plane and below the primary separation surface. The lower eddies below the primary separation zone are shed alternately on either side of the equatorial plane with shedding frequency St=0.5. Our experiments show that there is a viscous blockage of width 0.4Dat the crevice near the point of contact. On either side of the viscous blockage at the crevice, we see weak symmetric eddies. Based on our experimental observations, we proceed to build a simple physical model of the separated flow on the surface of the rolling sphere. In the second study, the motion of the sphere is photographed and paired data of the displacement and time is obtained for the sphere motion from the start of motion till terminal velocity is reached at about 4.5 sphere diameters from the point of release of the sphere. Equation of motion of the sphere is solved numerically treating added-mass coefficient Ca and drag coefficient Cd as parameters. Experimental data is fitted on these solutions and the best fit gives the values of the force coefficients. Theoretical value of Ca equal to 0.621 is confirmed experimentally. Value of Cd is found to be 1.23 at Re=990 and it is 1.06 at Re= 1900. Side-wall effects become important for ratio of diameter of sphere to width of tank greaterthan0.20.