Erosion boundary effects due to fill fraction variation : a study of quasi 2D tumblers of granular systems
Spitulnik, Adam N.
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Simulations of granular flow assume a consistent flowing layer profile observed in circular tumblers that were half full. While the constant shear rate model predicts mixing kinematics adequately, the model has not been empirically tested in systems where the erosion from the solid body has velocity components along the dynamic angle of repose. This thesis explores experiments that analyze the relationship be- tween tumbler fill fraction and the kinematics of the erosion boundary transition into the flowing layer. Tumblers greater than 50% full have inertial velocity along the angle of repose; fill conditions less than 50% enter with velocity opposite the free surface angle. Results confirm that flowing layer chord length alone properly scales flowing layer depth only when fill fraction is near 50%; otherwise fill fraction must be considered. This is due to the streamwise velocity of particles at the erosion boundary affecting the energy balance of the system. In addition the asymmetric velocity profile derived from the non-dimensional momentum equation is confirmed for non half full systems. Lastly, linear and exponential shear models are explored and shown to be qualitatively similar; variation is only exhibited at extreme fill and positions.