Macroscopic behavior of vibrating beds of smooth inelastic spheres

Abstract

Three-dimensional granular dynamics simulations are carried out to investigate macroscopic behavior of granular materials subjected to vibrations. Particles, idealized as smooth inelastic, uniform spheres, are gravitationally loaded into a rectangular periodic cell having an open top and plane floor. Vibrations to the bed are subsequently imposed through the sinusoidally oscillated floor. Significant differences in the character of the bed are found, depending on the strength of the applied floor accelerations Γ=aω2, even if the boundary input energy is fixed. At high acceleration values, a dense upper region is supported on a fluidized low-density region near the floor. The temperature is maximum at the floor and monotonically attenuates upward, while the solids fraction profile peaks at some intermediate depth. When lower accelerations are applied, the granular temperature no longer decreases monotonically from the bottom to the top and the solids fraction depth profile bulges at approximately three diameters from the floor. The surface of the bed appears chaotic and fluidized, where a low solids fraction and high temperature occurs. The bed height, which remains almost constant below 1.2g, undergoes a pronounced expansion when 1.2g≤Γ≤2.0g, and subsequently flattens out at Γ≂2.8g. Computed granular temperature and solids fraction depth profiles are in good agreement with recent kinetic theory predictions when the acceleration is large enough, while bed expansion at lower accelerations is quantitatively consistent with existing experimental data.

Simulations of dense granular gases without gravity with impact-velocity-dependent restitution coefficient

“…Far enough from the piston, the density decreases exponentially with altitude. A dense upper region supported on a fluidized low- density region near the vibrating piston is also reported experimentally [3], numerically [33] and predicted theoretically [34]. Without gravity, the spatial-dependence of the energy is examined in Fig.…”

Time dependence and density inversion in simulations of vertically oscillated granular layers

“…Density inversion, in which a low-density region near the bottom of a granular layer supports a higher-density region above it, has proven to be significant for the study of granular hydrodynamics. This phenomenon has been identified in vertically shaken layers [7,9,[15][16][17] as well as in layers flowing parallel to a surface, such as in gravity-driven flow down an incline [18,19].…”

“…Density inversion, in which a low-density region near the bottom of a granular layer supports a higher-density region above it, has proven to be significant for the study of granular hydrodynamics. This phenomenon has been identified in vertically shaken layers [7,9,[15][16][17] as well as in layers flowing parallel to a surface, such as in gravity-driven flow down an incline [18,19].In their seminal investigation [7], Lan and Rosato studied density inversion in vertically vibrated granular media. A layer of grains with depth H and uniform diameter σ atop a plate that oscillates sinusoidally with frequency f and amplitude A will leave the plate at some time in the oscillation cycle if the maximum acceleration of the plate a max = A (2πf ) 2 exceeds the acceleration of gravity g. The oscillating plate can be characterized by the dimensionless parameters Γ = a max /g and f * = f H/g.…”

“…Similar time dependence at low acceleration is found in conjunction with shocks [21], patterns [22], and compaction [23] of granular beds. Lan and Rosato found that their continuum model could not accurately describe these density profiles [7] in this regime.Since that time, several studies have focused mainly on the high-Γ, steady-state regime, providing significant evidence that steady-state hydrodynamic solutions can accurately model this regime [15][16][17]. A further study investigated the transition from a time-independent Leidenfrost state (in which a high-density crystalline cluster is supported by a low-density, fast-moving granular gas) to a convection state using linear stability analysis of time-dependent continuum equations [9].…”

“…We show that continuum simulations yield results consistent with molecular dynamics results in both regimes. 05.65.+b,47.57.Gc Although experimental [1,2] and computational [3][4][5][6][7] evidence demonstrate the potential for hydrodynamic models to describe important aspects of granular flow, a general set of governing equations for granular media is not yet recognized [8,9]. Several proposed rapid granular flow models use binary, inelastic hard-sphere collision operators in kinetic theory to derive equations of motion for the continuum fields: number density n, velocity u, and granular temperature T [10-12].…”