Localized Structures in Vertically Vibrated Granular Materials

[+] Author and Article Information
Piroz Zamankhan1

Laboratory of Computational Fluid and BioFluid Dynamics, Lappeenranta University of Technology, Lappeenranta, Finland and Department of Mechanical Engineering, Shahrekord University, P.O. Box 115, Shahrekord, Iranqpz002000@yahoo.com

Jun Huang

Laboratory of Computational Fluid and BioFluid Dynamics, Lappeenranta University of Technology, Lappeenranta, Finland


Corresponding author.

J. Fluids Eng 129(2), 236-244 (Aug 15, 2006) (9 pages) doi:10.1115/1.2409358 History: Received December 15, 2005; Revised August 15, 2006

Granular materials exhibit unusual kinds of behavior, including pattern formations during the shaking of the granular materials; the characteristics of these various patterns are not well understood. Vertically shaken granular materials undergo a transition to convective motion that can result in the formation of bubbles. A detailed overview is presented of collective processes in gas-particle flows that are useful for developing a simplified model for molecular dynamic type simulations of dense gas-particle flows. The governing equations of the gas phase are solved using large eddy simulation technique. The particle motion is predicted by a Lagrangian method. Particles are assumed to behave as viscoelastic solids during interactions with their neighboring particles. Interparticle normal and tangential contact forces are calculated using a generalized Hertzian model. The other forces that are taken into account are gravitational and drag force resulting from velocity difference with the surrounding gas. A simulation of gas-particle flow is performed for predicting the flow dynamics of dense mixtures of gas and particles in a vertical, pentagonal, prism shaped, cylindrical container. The base wall of the container is subjected to sinusoidal oscillation in the vertical direction that spans to the bottom of the container. The model predicts the formation of oscillon type structures on the free surface. In addition, the incomplete structures are observed. Interpretations are proposed for the formation of the structures, which highlights the role played by the surrounding gas in dynamics of the shaken particles.

Copyright © 2007 by American Society of Mechanical Engineers
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Figure 1

(a) Initial configuration of spherical particles in a vibrofluidized granular matter device. Also shown, is the typical instantaneous velocity vector field of particles located at the base of the container. (b) Top view of the initial configuration of spherical particles. All the sizes are normalized using particle diameter as a characteristic length. (c) Instantaneous configuration of particles located adjacent to the base of the container. To obtain a better visualization, the displacements of particles are rescaled. (d) Schematic of the container. The sidewalls of the container are neither moving nor deforming. The air flow in the container is resolved using 4×104 tetrahedral cells, nonuniformly distributed in the grid, where only one-seventh of the computational cells are used in N⩽30.

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Figure 2

Variations of the normalized coefficient of diffusivity of particles, D*=D∕D0, with Γ. Note that, Γ, measures the acceleration of the container base relative to gravity. Here, D0 is the coefficient of diffusivity at Γ=1.3. Also shown is the fitting expressed as D*∝e−a0∕(Γ−Γc) with a0=0.3 as a solid line.

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Figure 3

(a) Instantaneous configuration of glass particles in a typical perfect, descending structure. This structure was observed on the free surface of glass particles at Γ≈10. Here, gravity is directed in the negative z-direction. (b) Configuration of the glass particles in (a) after 1∕2fs. (c) Configuration of the glass particles in (b) after roughly 1∕fs. To obtain better visualizations, approximate shapes are presented as insets in (a), (b), and (c). (d) A typical localized ascending structure. (e) Particles within chains in (d) are highlighted. (f) The most recent contacts between the chains and single particles marked by arrows. Note that dissipations at the scale of large chains keep the structure localized. (g) Particle displacements due to chains-single particle contacts.

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Figure 4

(a) Probability density of the normalized collision time, τ*, for a sample data taken after 0.2s of vibrations at Γ≈10. The data highlights the presence of a number of structures with long collision times. These may include active chains, whose sample is illustrated in Fig. 3. The straight line indicates the power law (τ*)−5.2. (b) Probability density of the particle normalized velocity, Vp*=Vp∕σg, for the ascending and descending particle in the sample used in (a). The histogram illustrates a bimodal distribution.

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Figure 5

(a) An instantaneous configuration of glass particles in a vibrated, pentagonal, prism-shaped container at in the device at Γ=10 after t=0.2s and Γ=10. Four localized structures are shown, one of which is perfect. Imperfect structures can be seen on the left side of the container. An imperfect structure consists of a number of single particles as well as thread-like chains flying over the free surface. The formation of imperfect structures may be linked to bubble burst out as they approach the free surface. (b) Computed instantaneous air velocity field around an ascending structure on two cutting yz-planes and xz-planes perpendicular to the free surface. To obtain a better visualization, the particles are also added in (b). (c) The cavities deep inside of the granular bed located near the sidewalls. Inset: Computed instantaneous air velocity field on a cutting xz-plane in the wall region. Some signatures of weak recirculation bubbles can be observed in the inset. Note that both in (b) and (c) computed velocity vectors have been interpolated onto uniform meshes.

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Figure 6

(a) An instantaneous configuration of glass particles in the vibrodevice at Γ≈8 taken after t=2s of shaking. Here, only a limited number of particles are shown. (b) Two instantaneous realizations in a slice as highlighted with yellow in (a), each separated by t≈0.2s.

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Figure 7

(a) A snapshot of the free surface of glass particles in the vertical vibrated pentagonal prism at Γ≈10 at t=0.4s. (b) A different view of the free surface. Note that peaks and depressions can be observed. (c) and (d) Computed instantaneous velocity field on a cutting xy-plane located at N=35, above the location of the initial free surface (see Fig. 2). Computed velocity vectors have been interpolated onto a uniform mesh. To obtain a better visualization, the particles are also added in (c) and (d).



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