On the role of the Knudsen layer in rapid granular flows

Galvin, Janine E.; Hrenya, Christine M.; Wildman, Ricky D.

doi:10.1017/s0022112007006489

Cited by 33 publications

(50 citation statements)

References 40 publications

(102 reference statements)

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“…The system under examination in this work, investigated previously using MD simulations [23], is constituted by a quiescent granular flow made of spherical, frictionless and inelastic particles between two stationary walls of constant set temperatures T C and T H , with T C T H , as schematically represented in Fig. 1.…”

Section: Description Of the System And Simulation Conditionsmentioning

confidence: 99%

“…A Maxwellian distribution is adopted for the initial velocity distribution function. Results provided by QMOM are reported once the numerical solution reached steady state and compared to the MD simulations described elsewhere [23]. The significant parameters of the simulation are the wall temperatures T C and T H , the average particle volume fraction α, and the restitution coefficient e for collisions between particles.…”

Section: Description Of the System And Simulation Conditionsmentioning

confidence: 99%

“…The significant parameters of the simulation are the wall temperatures T C and T H , the average particle volume fraction α, and the restitution coefficient e for collisions between particles. The characteristic length of the system is L = 1, and L/d p = 35 in all the MD simulations [23]. Different conditions were examined as reported in Table 1, where the average Knudsen number is defined as Kn = d p /(6αL).…”

Section: Description Of the System And Simulation Conditionsmentioning

confidence: 99%

“…In order to judge the magnitude of the finite-particle effects in the MD simulations with L/d p = 35, for some of the statistics we will present MD results for the kinetic and collisional-flux parts separately. The latter are computed as described in [23]. For the QMOM calculations, only the kinetic parts of the velocity statistics are included in the collision models.…”

Section: Description Of the System And Simulation Conditionsmentioning

confidence: 99%

“…For the system under consideration the off-diagonal components should be null for all times, and this is confirmed by the simulations. For finite-size particles (e.g., the MD simulations), the stress tensor contains an additional term due to the collisional fluxes [22,23], not present in the QMOM calculations, which scales like Tα 2 s . Thus, we can anticipate that Eq.…”

Section: Description Of the System And Simulation Conditionsmentioning

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: Description Of the System And Simulation Conditionsmentioning

confidence: 99%

Section: Description Of the System And Simulation Conditionsmentioning

confidence: 99%

Section: Description Of the System And Simulation Conditionsmentioning

confidence: 99%

Section: Description Of the System And Simulation Conditionsmentioning

confidence: 99%

Section: Description Of the System And Simulation Conditionsmentioning

confidence: 99%

See 3 more Smart Citations

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

Passalacqua

Galvin²,

Vedula

et al. 2011

Commun. comput. phys.

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Dynamic multiscale method for gas‐solid flow via spatiotemporal coupling of two‐fluid model and discrete particle model

Chen

Wang

2017

AIChE Journal

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Various computational fluid dynamics methods have been developed to study the hydrodynamics of gas‐solid flows, however, none of those methods is suitable for all the problems encountered due to the inherent multiscale characteristics of gas‐solid flows. Both discrete particle model (DPM) and two‐fluid model (TFM) have been widely used to study gas‐solid flows, DPM is accurate but computationally expensive, whereas TFM is computationally efficient but its deficiency is the lack of reliable constitutive relationships in many situations. Here, we propose a hybrid multiscale method (HMM) or dynamic multiscale method to make full use of the advantages of both DPM and TFM, which is an extension of our previous publication from rapid granular flow (Chen et al., Powder Technol. 2016;304:177–185) to gas‐solid two‐phase flow. TFM is used in the regions where it is valid and DPM is used in the regions where continuum description fails, they are coupled via dynamical exchange of parameters in the overlap regions. Simulations of gas‐solid channel flow and fluidized bed demonstrate the feasibility of the proposed HMM. The Knudsen number distributions are also reported and analyzed to explain the differences. © 2017 American Institute of Chemical Engineers AIChE J, 63: 3681–3691, 2017

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Particle tracking velocimetry study of the nonequilibrium characteristics of a fluidized bed

2023

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The nonequilibrium characteristic of fluidization is closely related to the mesoscale structures. To help uncover this relationship, we performed a particle‐level experiment in a bubbling fluidized bed making particle tracking velocimetry (PTV) measurements. We found a large Knudsen number not only in bubbles or over bubble interfaces, but also in the dense emulsion where various banded structures exist, indicating a pervasive violation of the local equilibrium. Analysis of these banded structures identified stretching, compression, or shearing between particles. Non‐Gaussian velocity distributions were found throughout the bed, including in the dense emulsion with a small Knudsen number. In future work, we expect that the nonequilibrium characteristic will act as a local criterion for the assessment of various models of bubbling fluidized beds.

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On the role of the Knudsen layer in rapid granular flows

Cited by 33 publications

References 40 publications

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

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

Dynamic multiscale method for gas‐solid flow via spatiotemporal coupling of two‐fluid model and discrete particle model

Particle tracking velocimetry study of the nonequilibrium characteristics of a fluidized bed

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