Homogeneous cooling state of a low-density granular flow

Brey, J. Javier; Ruiz‐Montero, M. J.; Cubero, David

doi:10.1103/physreve.54.3664

Cited by 196 publications

(213 citation statements)

References 22 publications

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“…The deviations from the Gaussian moments exhibit a weak dependence on e, first becoming more sub-Gaussian as e decreases from unity but then becoming superGaussian for e near zero. The behavior near e = 1 is consistent with the known results for the homogeneous cooling state of a granular flow [8]. Nevertheless, the sixth-order central moment with e = 0 is considerably smaller than the corresponding central moment for Case 5 with e = 0.9 in the main text, indicating that the presence of a mean temperature gradient has a much stronger effect on the non-Gaussian behavior than does the restitution coefficient.…”

Section: B Kinetic Models For Granular Flowsupporting

confidence: 79%

“…In the elastic limit (ω =1), setting ζ =1 [7,8] in Eq. (2.4) recovers the Bhatnagar-GrossKrook (BGK) collision model [3].…”

Section: Moment Methods For the Boltzmann Kinetic Equationmentioning

confidence: 99%

“…To illustrate how significant is the non-Gaussian behavior, we present results for selected standardized central moments for Case 5 (e =0.9). In the homogeneous case (see Appendix C and [8]) the odd-order moments are null. In Fig.…”

Section: Non-gaussian Moments Due To Inelastic Collisionsmentioning

confidence: 99%

“…It is well known [8] that in the homogeneous cooling state the velocity moments of a granular flow show small deviations from the Gaussian values for e < 1. In comparison, for the system studied in this work, the inelastic collisions generate moments that are much farther from the Gaussian values due to the presence of the mean temperature gradients.…”

Section: Non-gaussian Moments Due To Inelastic Collisionsmentioning

confidence: 99%

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A Quadrature-Based Kinetic Model for Dilute Non-Isothermal Granular Flows

Passalacqua

Galvin²,

Vedula

et al. 2011

Commun. comput. phys.

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A moment method with closures based on Gaussian quadrature formulas is proposed to solve the Boltzmann kinetic equation with a hard-sphere collision kernel for mono-dispersed particles. Different orders of accuracy in terms of the moments of the velocity distribution function are considered, accounting for moments up to seventh order. Quadrature-based closures for four different models for inelastic collisionthe Bhatnagar-GrossKrook, ES-BGK, the Maxwell model for hard-sphere collisions, and the full Boltzmann hard-sphere collision integral-are derived and compared. The approach is validated studying a dilute non-isothermal granular flow of inelastic particles between two stationary Maxwellian walls. Results obtained from the kinetic models are compared with the predictions of molecular dynamics (MD) simulations of a nearly equivalent system with finite-size particles. The influence of the number of quadrature nodes used to approximate the velocity distribution function on the accuracy of the predictions is assessed. Results for constitutive quantities such as the stress tensor and the heat flux are provided, and show the capability of the quadrature-based approach to predict them in agreement with the MD simulations under dilute conditions. Abstract. A moment method with closures based on Gaussian quadrature formulas is proposed to solve the Boltzmann kinetic equation with a hard-sphere collision kernel for mono-dispersed particles. Different orders of accuracy in terms of the moments of the velocity distribution function are considered, accounting for moments up to seventh order. Quadrature-based closures for four different models for inelastic collisionthe Bhatnagar-Gross-Krook, ES-BGK, the Maxwell model for hard-sphere collisions, and the full Boltzmann hard-sphere collision integral-are derived and compared. The approach is validated studying a dilute non-isothermal granular flow of inelastic particles between two stationary Maxwellian walls. Results obtained from the kinetic models are compared with the predictions of molecular dynamics (MD) simulations of a nearly equivalent system with finite-size particles. The influence of the number of quadrature nodes used to approximate the velocity distribution function on the accuracy of the predictions is assessed. Results for constitutive quantities such as the stress tensor and the heat flux are provided, and show the capability of the quadrature-based approach to predict them in agreement with the MD simulations under dilute conditions. Disciplines Aerospace Engineering | Biological Engineering | Chemical Engineering | Mechanical Engineering Comments This article is from Communication in Computational Physics

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Section: B Kinetic Models For Granular Flowsupporting

confidence: 79%

“…In the elastic limit (ω =1), setting ζ =1 [7,8] in Eq. (2.4) recovers the Bhatnagar-GrossKrook (BGK) collision model [3].…”

Section: Moment Methods For the Boltzmann Kinetic Equationmentioning

confidence: 99%

Section: Non-gaussian Moments Due To Inelastic Collisionsmentioning

confidence: 99%

Section: Non-gaussian Moments Due To Inelastic Collisionsmentioning

confidence: 99%

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A Quadrature-Based Kinetic Model for Dilute Non-Isothermal Granular Flows

Passalacqua

Galvin²,

Vedula

et al. 2011

Commun. comput. phys.

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“…Overpopulated tails were first found theoretically by studying scaling or similarity solutions of the nonlinear EnskogBoltzmann equation for the IHS fluid, both in freely evolving IHS systems without energy input [4], as well as in driven or fluidized systems [4][5][6], and confirmed afterwards by Monte Carlo simulations of the Boltzmann equation [7,8], and by laboratory experiments [1]. Overpopulated tails in free IHS fluids [9] and driven ones [10] have also been studied by molecular dynamics simulations of inelastic hard spheres.…”

Section: Introductionmentioning

confidence: 99%

Untitled

Ernst

Brito

2002

Journal of Statistical Physics

106

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This paper deals with solutions of the nonlinear Boltzmann equation for spatially uniform freely cooling inelastic Maxwell models for large times and for large velocities, and the nonuniform convergence to these limits. We demonstrate how the velocity distribution approaches in the scaling limit to a similarity solution with a power law tail for general classes of initial conditions and derive a transcendental equation from which the exponents in the tails can be calculated. Moreover on the basis of the available analytic and numerical results for inelastic hard spheres and inelastic Maxwell models we formulate a conjecture on the approach of the velocity distribution function to a scaling form.

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Using the discrete element method to develop collisional dissipation rate models that incorporate particle shape

2017

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Discrete Element Method simulations of Homogeneous Cooling Systems (HCS) are used to develop a collisional dissipation rate model for non-spherical particle systems that can be incorporated in a two-fluid multiphase flow framework. Two types of frictionless, elongated particle models are compared in the HCS simulations: glued-sphere and true cylinder. Simulation results show that the ratio of translational to rotational granular temperatures is equal to one for the true cylindrical particles with particle aspect ratios (AR) greater than one and glued-sphere particles with AR >1.5, while the temperature ratio is less than one for glued-sphere particles with 1 < AR <1.5. The total collisional dissipation rate, which is associated with both translational and rotational granular temperature change rates, increases linearly with the particle aspect ratio. Thus, a collisional dissipation rate model for the elongated cylinders is developed by a simple modification of the existing spherical particle model.The error bar and extended black dotted lines represent the standard deviation of the measurements from 10 simulations with 100 particles. (Glued-sphere particles, AR 5 4, and a s 5 0.2).

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Homogeneous cooling state of a low-density granular flow

Cited by 196 publications

References 22 publications

A Quadrature-Based Kinetic Model for Dilute Non-Isothermal Granular Flows

A Quadrature-Based Kinetic Model for Dilute Non-Isothermal Granular Flows

Untitled

Using the discrete element method to develop collisional dissipation rate models that incorporate particle shape

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