Boundary conditions for high-shear grain flows

Hui, K. L.; Haff, P. K.; Ungar, J. E.; Jackson, R.

doi:10.1017/s0022112084002883

Cited by 158 publications

(90 citation statements)

References 10 publications

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“…We will show that a boundary condition for moving walls can also be derived from the similar condition of energy conservation. As noted in [36], there are two energy flows near a boundary. One is the thermal conduction, and the other is the energy transfer by collisions between the particles and the boundary.…”

Section: Boundary Conditionmentioning

confidence: 91%

Scaling behavior of granular particles in a vibrating box

Lee

1995

Physica A: Statistical Mechanics and its Applications

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Using numerical and analytic methods, we study the behavior of granular particles contained in a vibrating box. We measure, by molecular dynamics (MD) simulation, several quantities which characterize the system. These quantities-the density and the granular temperature fields, and the vertical expansion-obey scaling in the variable x = Af . Here, A and f are the amplitude and the frequency of the vibration. The behavior of these quantities is qualitatively different for small and large values of x. We also study the system using NavierStokes type equations developed by Haff. We develop a boundary condition for moving boundaries, and solve for the density and the temperature fields of the steady state in the quasi-incompressible limit, where the average separation between the particles is much smaller than the average diameter of the particles. The fields obtained from Haff's equations show the same scaling as those from the simulations. The origin of the scaling can be easily understood. The behavior of the fields from the theory is consistent with the simulation data for small x, but they deviate significantly for large x. We argue that the deviation is due to the breakdown of the quasi-incompressibility condition for large x.

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Section: Boundary Conditionmentioning

confidence: 91%

Scaling behavior of granular particles in a vibrating box

Lee

1995

Physica A: Statistical Mechanics and its Applications

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“…The discretized governing equations were solved by the finite volume method employing the Semiimplicit Method for the Pressure-Linked Equations (SIMPLE) algorithm that was developed by Patankar and Spalding [4] for multiphase flow using the Partial Elimination Algorithm (PEA). Several research groups [10,11,[23][24][25][26][33][34][35][36] have used extensions of the SIMPLE method, which appears to be the method of choice in commercial CFD codes [7,[9][10][11]. In this study, the second-order discretization schemes at time step of 0.001 s with 10 −3 convergence criterion were used in numerical procedure.…”

Section: Model Solutionmentioning

confidence: 99%

CFD Modeling and Simulation of Hydrodynamics in a Fluidized Bed Dryer with Experimental Validation

Hamzehei

2011

ISRN Mechanical Engineering

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Gas-solid fluidized bed dryers are used in a wide range of industrial applications. With applying computational fluid dynamic (CFD) techniques, hydrodynamics of a two-dimensional nonreactive gas-solid fluidized bed dryer was investigated. A multifluid Eulerian model incorporating the kinetic theory for solid particles was applied to simulate the unsteady state behavior of this dryer and momentum exchange coefficients were calculated by using the Syamlal-O'Brien drag functions. A suitable numerical method that employed finite volume method was used to discretize the equations. Simulation results also indicated that small bubbles were produced at the bottom of the bed. These bubbles collided with each other as they moved upwards forming larger bubbles. Also, solid particles diameter and superficial gas velocity effect on hydrodynamics were studied. Simulation results were compared with the experimental data in order to validate the CFD model. Pressure drops and bed expansion ratio as well as the qualitative gas-solid flow patterns predicted by the simulations were in good agreement with experimental measurements at superficial gas velocities higher than the minimum fluidization velocity. Furthermore, this comparison showed that the model can predict hydrodynamic behavior of gas solid fluidized bed reasonably well.

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“…However, due to slippage near the moving plate the relation between the plate speed and the shear stress is complicated. We do not address the issue of boundary conditions here as it is a subject of a separate study (see for example [32]). Here we simply use the values which are obtained in numerical simulations (the last column in Table I), as parameters in our theoretical model.…”

Section: Surface-driven Shear Granular Flow Under Gravitymentioning

confidence: 99%

Partially fluidized shear granular flows: Continuum theory and molecular dynamics simulations

2003

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The continuum theory of partially fluidized shear granular flows is tested and calibrated using two dimensional soft particle molecular dynamics simulations. The theory is based on the relaxational dynamics of the order parameter that describes the transition between static and flowing regimes of granular material. We define the order parameter as a fraction of static contacts among all contacts between particles. We also propose and verify by direct simulations the constitutive relation based on the splitting of the shear stress tensor into a"fluid part" proportional to the strain rate tensor, and a remaining "solid part". The ratio of these two parts is a function of the order parameter. The rheology of the fluid component agrees well with the kinetic theory of granular fluids even in the dense regime. Based on the hysteretic bifurcation diagram for a thin shear granular layer obtained in simulations, we construct the "free energy" for the order parameter. The theory calibrated using numerical experiments with the thin granular layer is applied to the surface-driven stationary two dimensional granular flows in a thick granular layer under gravity.

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Boundary conditions for high-shear grain flows

Cited by 158 publications

References 10 publications

Scaling behavior of granular particles in a vibrating box

Scaling behavior of granular particles in a vibrating box

CFD Modeling and Simulation of Hydrodynamics in a Fluidized Bed Dryer with Experimental Validation

Partially fluidized shear granular flows: Continuum theory and molecular dynamics simulations

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