A continuum constitutive model for cohesionless granular flows

Daniel, Richard C.; Poloski, Adam P.; Sáez, A. Eduardo

doi:10.1016/j.ces.2006.11.035

Cited by 19 publications

(8 citation statements)

References 17 publications

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“…2. The assumptions (34) are based on the observations that at an equilibrium state no production appear. Substituting (34) 1;2 respectively into (7) and (8) leads to the results that (8) is automatically satisfied, and (7) reduces to r Á Cj E ¼ 0.…”

Section: Equilibrium Constitutive Modelsmentioning

confidence: 99%

“…the revised Goodman-Cowin model), in which the second time derivative of m is used, is more appropriate to take into account the microstructural effects of the short-term instantaneous inelastic collision (rapid flow) [9]. Theoretical models to slow and dense laminar flows [9,12,[21][22][23], and for rapid laminar flows [9,[15][16][17][18][19][20][24][25][26][27][28][29][30][31][32][33][34] have been developed. Of particular interest are the extensions of the Wilmánski and revised Goodman-Cowin models for slow and rapid turbulent flows, respectively, in which the distributions of the turbulent kinetic energy and turbulent dissipation are found to be similar to those of Newtonian fluids in turbulent boundary layer flows [35][36][37].…”

Section: Introductionmentioning

confidence: 99%

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Rapid dry granular flows down an incline: a constitutive theory with an independent kinematic internal length

Fang

2015

Meccanica

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Rapid, isothermal, gravity-driven dry granular flows with incompressible solid grains down an incline are investigated by the thermodynamically consistent constitutive model. To this end, the revised Goodman-Cowin theory is applied for the time evolution of the volume fraction, in which a kinematic internal length is introduced. The Müller-Liu entropy principle is carried out to derive the equilibrium constitutive models, with their dynamic responses postulated in the context of a quasi-static theory. Numerical simulations show that both the volume fraction and velocity increase from the minimum values on the plane toward the maximum values on the free surface with an ''exponential-like'' tendency, while the internal length increases in a logarithmic manner. With the equilibrated stress system in the revised Goodman-Cowin theory, the kinematic internal length is recognized as a characteristic length of the long-term enduring frictional contact and sliding between the grains (a characteristic length of the inelastic network among the grains).

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Section: Equilibrium Constitutive Modelsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Rapid dry granular flows down an incline: a constitutive theory with an independent kinematic internal length

Fang

2015

Meccanica

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“…While these findings were not taken into account in purely laminar formulations, e.g. [10][11][12][13][14][15][16][17][18][19][20][21][22], they were not accounted for in the limiting turbulent formulations, e.g. [23][24][25][26].…”

Section: Introductionmentioning

confidence: 96%

Influence of Velocity Slip on Turbulent Features of a Drygranular Dense Flow

Fang

2015

J. mech.

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A zero-order turbulence closure model of a dry granular dense flow is proposed, with the boundary considered an energy source and sink of the turbulent kinetic energy of the grains. Muller-Liu entropy principle is carried out to derive the equilibrium closure relations, with their dynamic responses postulated from the experimental calibrations. A gravity-driven flow with incompressible grains down an inclined moving plane is studied to investigate the influence of velocity slip near solid boundary on the turbulent features of the flow. While the calculated mean porosity and velocity correspond to the experimental outcomes, increasing velocity slip on the boundary tends to enhance the turbulent dissipation nearby. The distribution of the turbulent dissipation shows a similarity with that of conventional Newtonian fluids in turbulent boundary layer flows. Boundary as an energy sink is more apparent in the zero-order model.

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“…Their interpretation [31] is based upon an extension of the plane shearing models by DaCruz et al [32] and Jop et al [33]. Their resembles earlier models by Tardos et al [25] and Soller et al [28] in many respects, because it involves surface integrals over b) The cylinder of rotation for estimating the torque is the vane diameter augmented by a particle diameter, D + d, and the immersion depth augmented by a particle radius, z + d/2.…”

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confidence: 99%

Rheology of evolving bidisperse granular media

Soller

Cook

Koehler³

2011

Phys. Rev. E

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We investigate mixing of a bidisperse distributions of spherical particles for slowly rotating vanes by pouring smaller beads, diameter d1, onto a monodisperse bed composed of larger beads, diameter d0, and monitoring the torque and lift forces. If the mixing beads are too small, d1/d0 < 0.05, the drag and lift are unaltered. Otherwise smaller beads displace larger beads from the shearing region, and if present in sufficient quantity both the drag and lift diminish to values of a monodisperse bed composed entirely of the smaller beads. We observe reductions in the torque up to 70%. The rate at which smaller beads leave the shearing region decreases as their size relative to the larger beads increases, and for d1/d0 > 0.155 the smaller beads remain inside the shearing region.

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A continuum constitutive model for cohesionless granular flows

Cited by 19 publications

References 17 publications

Rapid dry granular flows down an incline: a constitutive theory with an independent kinematic internal length

Rapid dry granular flows down an incline: a constitutive theory with an independent kinematic internal length

Influence of Velocity Slip on Turbulent Features of a Drygranular Dense Flow

Rheology of evolving bidisperse granular media

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