A Modified Kinetic Theory Model for Studying Collisional Granular Flows
Kinetic theory (KT) has been successfully used to model rapid granular flows in which particle interactions are frictionless and near elastic, predicting results that agree well with the simulation results of the event-driven Hard Sphere (HS) model or the more sophisticated soft-sphere Discrete Element Method (DEM). However, the existing KT models become less accurate when particle interactions are frictional and inelastic or when the granular flows are in dense regimes with high particle-particle collision frequencies. This dissertation contains three essays and it aims to extend the applicability of KT to a wider range of granular flow regimes without compromising its accuracy. For granular flows of frictional and inelastic particle-particle collisions, an impact velocity dependent restitution coefficient as well as the particle surface friction have been incorporated into the modified KT model, as detailed in Essay 1. For granular flows that move away from the rapid flow regime, the particle stiffness has been included in the new KT model as an input parameter to account for the non-dissipative elastic potential energy in particle-particle collisions. Two different approaches of incorporating particle stiffness into the KT, namely the cut-off time approach and the elastic deformation approach, have been developed in Essay II and Essay III, respectively.
Our results show that both the velocity-dependent restitution coefficient and the particle surface friction are important in predicting the free cooling process of granular flows with inelastic collision and surface frictions; the modified KT model that integrates these two factors is able to improve the simulation results and led to a better agreement with the experimental results. As for the granular shear flows, by including particle stiffness in the KT model the present modification extends the applicability to the transition regime between elastic regime and inertial regime. Utilizing the modified KT model, the rheological crossover has been explained and the regime boundaries that separate the inertial regime and the elastic regime have been quantitatively determined, showing a good agreement with the previous regime map that is based on the DEM simulation results.