### Can cellular automata based models accurately simulate granular material flow?

**Wheel, MA; Edmans, B ***(Strathclyde)*

Thursday 08 January 2009, 14:50-15:15

Seminar Room 1, Newton Institute

#### Abstract

Cellular automata (CA) based methods have been suggested as an alternative to continuum and discrete element models for predicting the flow of granular materials. These methods divide the flow field into cells, each of which can display a finite number of states. The current state of each cell is a function of its state and those of its neighbours at the previous timestep. This function is governed by update rules that definte the interactions that can occur between particles moving around a lattice connecting adjacent cell centres. The rules themselves can incorporate mass and momentum conservation albeit in a simple, discrete manner. CA methods offer significant potential in simulating the behaviour of systems with very large numbers of degrees of freedom: they are well suited to parallel processing, rule sets are easy to implement in a software environment and numerical stability is ensured by the local conservation attribute. While a number of potentially suitable CA methods for simulating granular flows have been described in the literature, insufficient quantitative data have, as yet, been reported to validate their predictive capabilities across a range of flow conditions. To remedy this three previously reported CA methods were implemented within a MATLAB based environment. These methods were the viscous model of Peng and Ohta, which can be regarded as a variant of the lattice gas model previously used in modelling hydrodynamic phenomena, the lattice grain model of Gutt and Haff, which is similar to the first model but incorporates continuous rather than discrete particle velocities, and the hopper flow model of Kozicki and Tejchman, which incorporates void filling update rules that are mass but not momentum conserving and is therefore non synchronus. Each of the models was used to simulate the emptying of a two dimensional hopper across a range of flow conditions. Experiments were also performed to observe the flow of glass beads in a similar hopper when emptying. Flow conditions were varied by altering the wall angle of the funnel section constituting the lower part of the hopper. The experiments revealed that as the wall angle increased (with respect to the vertical axis of the hopper) the particle flow rate at the exit reduced. However, the lattice grain model predicted that the flow rate was insensitive to the changing wall angle while results provided by the hopper flow model indicate that the flow rate will increase with wall angle. Nevertheless, the overall forms of flow fields predicted by the latter two models show sufficient similarity with the experiments to encourage more detailed assessment of the suitability of CA methods in simulating granular flows.

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