Investigation of the Dynamics of Steady Granular Flow in a Rotating Drum by Lagrangian Coherent Structure Evolution

This thesis studies the Lagrangian coherent structures (LCS) for a dry or a fully immersed steady granular flow in a rotating drum by systematic experiments to complement the information based on Eulerian description. In this thesis, LCS is located by the Finite-Time Lyapunov Exponent (FTLE) field. We drove the drum at various constant speeds (w = 0.135~0.4654rad/s) so that the Froude numbers are 6.28*10^-4~7.5*10^-3 giving flows in the rolling regime. The granulate motion was monitored by high speed digital camera and we developed a method of index similarity to locate particle centers exploiting the fact that identical spheres poly possess similar surface texture. The same sphere was paired in two consecutive images by the method of the nearest neighbor to achieve particle traking velocimetry (PTV) to obtain its instantaneous velocity. A mean Eulerian velocity field was then interpolated and averaged from these particle velocities.The obtained velocity field was employed to advect virtual particles in time so their trajectories can be used to compute FTLE and the corresponding LCS. Higher FTLE value was measured in the flowing layer due to the faster bulk motion therein. In contrast, the value in the packed bed in solid body rotation remained a nearly constant small value. It took about 5-7 rotation cycles to extract LCS structure and LCS for the immersed bulk seemed more smeared out since the lubricated particles could move more easily and hence randomly than dry ones. In addition, attracting LCS (aLCS) was found to intersect with repelling LCS (rLCS) and aLCS was observed to encompass rLCS for the dry flow but the opposite was found for the immersed flow. We also tried to calculate FTLE using real particle trajectories and virtual trajectories as advected by a theoretical model. Dynamically similar results were found. Lastly, the long-time virtual particle trajectories merged onto a limit cycle suggesting longitudinal velocity component in the current thin drum flows and such three dimensional flow was confirmed by simple visualization experiments.