Monte Carlo calculation of the flow of granular materials

Citation

Kawasaki, Kazunori (1986) Monte Carlo calculation of the flow of granular materials. Engineer's thesis, California Institute of Technology. doi:10.7907/6b67-x610. https://resolver.caltech.edu/CaltechETD:etd-11092007-110816

Abstract

The flow of granular materials has been investigated theoretically using the Direct Simulation Monte Carlo (DSMC) method for rarefied gas flows implemented on the Caltech concurrent 64-node Cosmic Cube computer. A fundamental understanding of the behavior of a heavily loaded gas under conditions for which collisions among the solid particles suspended in the gas are frequent is very important for a variety of problems, e.g., grain explosions and the performance of metallized solid-propellant rockets. At one extreme of particulate flow (granular material flow), the effect of the interstitial fluid is negligible. In particular, the numerical method has been applied to the problem of sedimentation and channel flow.

Bird's method has been applied to granular material flows by using a hard, rough-sphere particle model and introducing restitution and slip coefficients for particle-particle and particle-boundary collisions, respectively. In the DSMC method, physical space is divided into many cells, each containing several simulated particles. The distance between particles is much greater than the particle diameter. Using the concurrent computer, cells are assigned singly or in groups to individual processors (nodes). Calculations of particle-particle collisions are carried out locally by each node and information is communicated between adjacent nodes. Using the concurrent computer has enabled powerful computational ability to be brought to bear on the DSMC calculation.

For a gas sedimentation calculation simulating the gravitational collapse of a uniform atmosphere, significant thermal and wave effects are observed. For flow in a channel at Mach number 2.76 and Reynolds number 32.6, differences are observed between the behavior of granular material flow and gas flow. For both cases significant "slip" at the wall is observed. For the flow of granular material, the boundary layer is thin and the velocity reduction near the wall is small.

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