Kinetic theory for granular flow of dense, slightly inelastic, slightly rough spheres

Lun, C. K. K.

doi:10.1017/s0022112091000599

Cited by 280 publications

(270 citation statements)

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“…The model is originally developed for dry granular flow and consists of smooth, slightly inelastic, spherical particles (Jenkins and Savage, 1983;Lun and Savage, 1987;Lun, 1991). Here, we adopt the model suggested by Ding and Gidaspow (1990), which takes into account the fluid phase.…”

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confidence: 99%

SedFoam-2.0: a 3-D two-phase flow numerical model for sediment transport

et al. 2017

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Abstract. In this paper, a three-dimensional two-phase flow solver, SedFoam-2.0, is presented for sediment transport applications. The solver is extended from twoPhaseEulerFoam available in the 2.1.0 release of the open-source CFD (computational fluid dynamics) toolbox OpenFOAM. In this approach the sediment phase is modeled as a continuum, and constitutive laws have to be prescribed for the sediment stresses. In the proposed solver, two different intergranular stress models are implemented: the kinetic theory of granular flows and the dense granular flow rheology µ(I ). For the fluid stress, laminar or turbulent flow regimes can be simulated and three different turbulence models are available for sediment transport: a simple mixing length model (one-dimensional configuration only), a k − ε, and a k − ω model. The numerical implementation is demonstrated on four test cases: sedimentation of suspended particles, laminar bed load, sheet flow, and scour at an apron. These test cases illustrate the capabilities of SedFoam-2.0 to deal with complex turbulent sediment transport problems with different combinations of intergranular stress and turbulence models.

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Section: Keyword Name Keyword Valuementioning

confidence: 99%

SedFoam-2.0: a 3-D two-phase flow numerical model for sediment transport

et al. 2017

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“…In our model the collisions are instantaneous and binary; they conserve momentum and dissipate energy. Particles are assumed to be frictionless; particle friction can be incorporated into kinetic theories [25,26], and was included in the simulations of oscillated granular media, [9,10,4], but introduces complications that we wish to avoid for this study.…”

Section: Driven Granular Media Simulationsmentioning

confidence: 99%

Transport coefficients for granular media from molecular dynamics simulations

et al. 1999

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Under many conditions, macroscopic grains flow like a fluid; kinetic theory predicts continuum equations of motion for this granular fluid. In order to test the theory, we perform event driven molecular simulations of a two-dimensional gas of inelastic hard disks, driven by contact with a heat bath. Even for strong dissipation, high densities, and small numbers of particles, we find that continuum theory describes the system well. With a bath that heats the gas homogeneously, strong velocity correlations produce a slightly smaller energy loss due to inelastic collisions than that predicted by kinetic theory. With an inhomogeneous heat bath, thermal or velocity gradients are induced. Determination of the resulting fluxes allows calculation of the thermal conductivity and shear viscosity, which are compared to the predictions of granular kinetic theory, and which can be used in continuum modeling of granular flows. The shear viscosity is close to the prediction of kinetic theory, while the thermal conductivity can be overestimated by a factor of 2; in each case, transport is lowered with increasing inelasticity.

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“…Previous attempts have been restricted to nearly elastic collisions (α 1) and either nearly smooth particles (β −1) [17,20,21] or nearly perfectly rough particles (β 1) [17,24]. The goal of this paper is to uncover the whole range of values of the two coefficients of restitution α and β and derive explicit expressions for the NSF transport coefficients of a dilute granular gas beyond the above limiting situations.…”

Section: Introductionmentioning

confidence: 99%

Transport coefficients of a granular gas of inelastic rough hard spheres

Kremer¹,

Santos

Garzó

2014

Phys. Rev. E

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The Boltzmann equation for inelastic and rough hard spheres is considered as a model of a dilute granular gas. In this model, the collisions are characterized by constant coefficients of normal and tangential restitution and hence the translational and rotational degrees of freedom are coupled. A normal solution to the Boltzmann equation is obtained by means of the Chapman-Enskog method for states near the homogeneous cooling state. The analysis is carried out to first order in the spatial gradients of the number density, the flow velocity, and the granular temperature. The constitutive equations for the momentum and heat fluxes and for the cooling rate are derived, and the associated transport coefficients are expressed in terms of the solutions of linear integral equations. For practical purposes, a first Sonine approximation is used to obtain explicit expressions of the transport coefficients as nonlinear functions of both coefficients of restitution and the moment of inertia. Known results for purely smooth inelastic spheres and perfectly elastic and rough spheres are recovered in the appropriate limits.

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Kinetic theory for granular flow of dense, slightly inelastic, slightly rough spheres

Cited by 280 publications

References 26 publications

SedFoam-2.0: a 3-D two-phase flow numerical model for sediment transport

SedFoam-2.0: a 3-D two-phase flow numerical model for sediment transport

Transport coefficients for granular media from molecular dynamics simulations

Transport coefficients of a granular gas of inelastic rough hard spheres

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