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Research Papers: Coatings & Solid Lubricants

The Inclusion of Friction in Lattice-Based Cellular Automata Modeling of Granular Flows

[+] Author and Article Information
Martin C. Marinack, C. Fred Higgs

Mechanical Engineering Department,  Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA 15213-3890

J. Tribol 133(3), 031302 (Jul 25, 2011) (13 pages) doi:10.1115/1.4004103 History: Received October 08, 2010; Revised April 01, 2011; Published July 25, 2011; Online July 25, 2011

Granular flows continue to be a complex problem in nature and industrial sectors where solid particles exhibit solid, liquid, and gaseous behavior, in a manner which is often unpredictable locally or globally. In tribology, they have also been proposed as lubricants because of their liquid-like behavior in sliding contacts and due to their ability to carry loads and accommodate surface velocities. The present work attempts to model a granular Couette flow using a lattice-based cellular automata computational modeling approach. Cellular automata (CA) is a modeling platform for obtaining fast first-order approximations of the properties of many physical systems. The CA framework has the flexibility to employ rule-based mathematics, first-principle physics, or both to rapidly model physical processes, such as granular flows. The model developed in this work incorporates dissipative effects due to friction between particles and between particles and boundaries, in addition to the derivative effects of friction, namely particle spin. This new model also includes a rigorous and physically relevant treatment of boundary–particle interactions. The current work compares this new friction and spin inclusive CA model and the author’s previous frictionless CA model against experimental results for an annular shear cell. The effects of granular collision properties were also examined through parametric studies on particle–particle coefficient of restitution (COR) and coefficient of friction (COF), which is a unique and added capability of the friction inclusive model.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 3

Snapshot of CA animation of the GSC at t = 0

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Figure 4

Particle movement on the CA lattice. (a) At time step = 1, the particle has an x-velocity of 0.4 “grid spaces per time step” and an offset of 0.0, yielding an intended movement of 0.4 grid spaces. (b) The particle remains stationary since its intended movement is less than 0.5 grid spaces and only updates its offset to 0.4. (c) During the second time step, the particle’s intended motion is updated to 0.8 grid spaces, obtained from the sum of the x-velocity and x-offset of the particle. (d) Since the intended motion is greater than 0.5, the particle moves 1 grid space to the right. The particle’s offset is now updated to −0.2.

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Figure 5

Two particles preparing to participate in a particle–particle collision event

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Figure 1

Top view of the granular shear cell. Gravity acts into the page.

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Figure 2

Granule interaction neighborhood

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Figure 6

A particle preparing to participate in a (a) completely exterior and (b) completely interior collision event with the inner wheel

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Figure 7

Annular gap of the simulated GSC divided into radial bins

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Figure 8

GSC regime snapshot. During a given trial, the granular flow may exist as entirely kinetic, entirely contact, or as a “transitional flow” A “transitional” flow is a combination of the two, as seen in this image, which contains approximately 1600 granules inside the annular gap. The kinetic regime is sparsely populated with short high-speed collisions, while the contact regime displays dense particle packing and enduring contacts. In all the experiments and modeling done in this work, the flow inside the annular gap is much more dilute (only 200 particles) and remains entirely kinetic (across the entire width of the gap).

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Figure 9

Local flow parameters versus radial location, comparison between CA models and experimental results: (a) normalized tangential velocity, (b) solid fraction ratio, and (c) normalized granular temperature

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Figure 10

Local flow parameters versus radial location as a function of particle–particle coefficient of restitution: (a) normalized tangential velocity, (b) solid fraction ratio, and (c) normalized granular temperature

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Figure 11

Average steady-state kinetic energy (Eq. 25; t  > 10 s) versus particle–particle coefficient of restitution

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Figure 12

Local flow parameters versus radial location as a function of particle–particle coefficient of friction: (a) normalized tangential velocity, (b) solid fraction ratio, and (c) normalized granular temperature

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Figure 13

Average steady-state kinetic energy (Eq. 25; t  > 10 s) versus particle–particle coefficient of friction values

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