Cotinuum simulation method of dense granular flows and experimental evidence of a flow stress boundary condition

• Main Authors: Cheng-Chuan Lin, 林正釧
• Other Authors: 楊馥菱
• Format: Others
• Language: en_US
• Published: 2017
• Online Access: http://ndltd.ncl.edu.tw/handle/j2a825

博士 === 國立臺灣大學 === 機械工程學研究所 === 106 === A generic continuum rheology model for dense granular material has been widely investigated but its success in practical applications is still far from satisfactory due to unsettled issues in the rheology model and the flow boundary condition. The resulting governing equations are often nonlinear and require numerical solutions but a feasible continuum solver is not available until very recently [59]. The main difficulty results from the dual nature of a granular material that it possess yield strength as a solid in quasi-static state but transits to flow as a non-Newtonian fluid in agitated state. Hence, the first part of this thesis sets out to fill the gaps by developing a continuum solver (finite volume method with pressure implicit of splitting operator scheme) for a recently proposed local μ(I) rheology model in which we further incorporate non-local effect on transport mechanism for the very first time in literature. In particular, we propose a regularization scheme to handle the tricky viscoplastic behavior of μ(I) rheology so that new flow phenomenon can be predicted over a wider range of bulk Forde number in the configurations. The unique features include a non-Bagnold velocity profile in shallow surface flows on mild slope and the non-linear velocity profile in simple shear cell flows. The other half of the thesis studies how to assign the bulk wall friction coefficient for a Coulomb-type stress assignment in both laboratory experiments and discrete element (DE) simulations. Using finite mass avalanche as the benchmark problem, a promoted degree of grain rotation relative to translation, characterized by a non-dimensional rotation index Ω , has been identified as a reduction mechanism in DE simulated avalanche events [103]. In search of experimental evidence, we develop a novel image processing algorithm to measure angular velocity vector of individual sphere from the high-speed digital images at the flow boundary. The measured angular velocities are employed in a friction degradation model for μw/f with f being pure sliding friction coefficient between grains and flow boundary, which is further compared to the other literature model in terms of granular temperature T [5]. To correlate the two models, we discover a linear relation between the measured angular speed ω and T for the first time in the literature which links a bulk continuum property to particle-level dynamics. Furthermore, we conducted dimension analysis to further reveal a monotonic decay of the rotation index Ω with √(T/(p/ρ)) where p and ρ are confining pressure and grain intrinsic density. The finding shall shed light on how the microscopic mechanism for friction degradation correlates to bulk continuum properties. More importantly, it provides an explicit relation to solve the closure problem in continuum flow modeling when a flow-dependent boundary condition model is desired.