Granular Materials At Meso Scale PDF Download

Explosively dispersed granular materials frequently exhibit macroscale coherent particle clustering and jetting structures. The underlying mechanism is of significant interest to study instability and mixing in high-speed gas-solid flows but remains unclear, primarily attributed to the complex mesoscale multiphase interactions involved in the dispersal process. In order to advance the understanding of particle clustering and jetting instabilities, this thesis establishes a numerical framework for solving interface-resolved gas-solid flows with non-deforming bodies that are able to move, contact, and collide. The developed framework is implemented to create a computational solver and then verified using a variety of gas-solid flow problems at different geometric scales. Employing the developed framework and solver, this thesis further studies the particle clustering and jetting instabilities in explosively dispersed granular materials. A Cartesian, 3D, high-resolution, parallelized, gas-solid flow solver is created with the capability of tackling shocked flow conditions, irregular and moving geometries, and multibody collisions. The underlying numerical framework integrates operator splitting for partitioned fluid-solid interaction in the time domain, 2nd/3rd order strong stability-preserving Runge--Kutta methods and 3rd/5th order weighted essentially nonoscillatory schemes for high-resolution tempo-spatial discretization, the front-tracking method for evolving phase interfaces, a new field function developed for facilitating the solution of complex and dynamic fluid-solid systems on Cartesian grids, a new collision model developed for deterministic multibody contact and collision with parameterized coefficients of restitution and friction, and a new immersed boundary method developed for treating arbitrarily irregular and moving boundaries. The developed framework and solver are able to accurately, efficiently, and robustly solve coupled fluid-fluid, fluid-solid, and solid-solid interactions with flow conditions ranging from subsonic to hypersonic states. Employing the developed framework and solver, direct simulations that capture interface-resolved multiphase interactions and deterministic mesoscale granular dynamics are conducted to investigate particle clustering and jetting instabilities. A random sampling algorithm is employed to generate stochastic payload morphologies with randomly distributed particle positions and sizes. Through solving and analyzing cases that cover a set of stochastic payloads, burster states, and coefficients of restitution, a valid statistical dissipative property of the framework in solving explosively dispersed granular materials with respect to Gurney velocity is demonstrated. The predicted surface expansion velocities can extend the time range of the velocity scaling law with regard to Gurney energy in the Gurney theory from the steady-state termination phase to the unsteady evolution phase. When considering the mean surface expansion velocities, the maximum error of the unsteady velocity scaling law is about $0.792\%$ among the investigated Gurney energies. In addition, a dissipation analysis of the current discrete modeling of granular payloads suggests that incorporating the effects of porosity can enhance the prediction of Gurney velocity for explosively dispersed granular payloads. On the basis of direct simulations, an explanation for particle clustering and jetting instabilities is proposed to increase the understanding of established experimental observations in the literature. Results suggest that the development of internal sliding and colliding lines in the shock-compacted granular payload can be critical to the subsequent fracture pattern of the payload. Particle clusters manifested through payload fracture are then maintained by local pressure gradient between surrounding and interstitial flows as well as by dissipative inter-grain collisions. The existence of stable clusters introduce a more non-equilibrium momentum distribution in the overall payload, exhibiting as a form of clustering instability. Under the current assumptions of non-deformable grains, the mesoscale granular dynamics largely depends on the payload morphology as a result of packing methods. Different payload morphologies can develop varied sliding and colliding lines, which lead to a corresponding pattern for payload fracturing and particle clustering. With the rapid development of high-performance computing technology, future direct simulations on stochastic payloads with significantly increased domain sizes, number of particles, and solution times are expected to lead to a better understanding of the flow instability in explosively dispersed granular payloads. It is suggested that statistics collected from a large number of mesoscale computations based on random payload morphologies can potentially evolve into a macroscopic theory of multiphase flow instability for particle clustering and jetting phenomena widely observed in many areas involving dense gas-solid flows.