MSc project: Hydrodynamic interactions between spheres rolling down a plate in a viscous fluid

MSc student: Lyckle Drost

Project supervisors: Dr. ir. W.-P. Breugem, Dr. ir. C. Poelma and P.S. Costa MSc

Project start: January 2014

Project description:

In every river some sediment such as sand, mud and gravel is transported along with the turbulent flow. The sediment load or volume fraction in the river depends on the balance between sedimentation (bed formation) and resuspension (bed erosion) processes. Two distinct sediment transport regions can be distinguished in the flow: 1) the suspended-load region away from the river bed and 2) the mobile-bed region near the river bed. In the latter region the particles are rolling, sliding and saltating (hopping) along the bed. The dynamics of the sediment-water mixture in this region is strongly influenced by particle-particle and particle-bed collisions as well as hydrodynamic interactions between particles (e.g., wake and lubrication effects).

The goal of the present MSc project is to gain understanding of the dynamics of interacting particles in the mobile-bed region. To simplify the problem, only the interaction of two rolling solid spheres will be considered. The influence of sediment volume concentration, the bed morphology and turbulence of the external flow will not be studied. Experiments will be performed on two solid spheres, which are initially placed behind each other at some distance and then start to roll down an inclined plate. An optical technique will be used to track the position of the spheres in time. Preliminary numerical simulations have shown that the rear particle may move faster due to shielding by the wake of the front particle ("drafting"). This results in a short moment of contact between the spheres (“kissing”), after which the rear particle overtakes the front particle and moves away from it (“tumbling”). This drafting-kissing-tumbling phenomenon is believed to play an important role in sedimentation processes. The physics of this phenomenon is more complex in the present case due to rolling friction and confinement of the flow and particle motion by the plate.

During the first part of the project, the oblique impact of a particle with a plane wall will be considered. From this the rotational coefficient of restitution and the coefficient of sliding friction of the particle can be determined. The results will be compared with available experimental data from literature. In the second part of the project, experiments will be performed on a single sphere rolling down an inclined plate; results will again be compared with literature. Finally, in the third part of the project, the hydrodynamic interaction between two spheres rolling down an inclined plate will be studied. If possible within the time frame of this project, numerical simulations will be performed on the same flow with a fully-resolved flow solver.