Investigation of the particle–particle drag in a dense binary fluidized bed

Chao, Zhongxi; Wang, Yuefa; Jakobsen, Jana P.; Fernandino, María; Jakobsen, Hugo A.

doi:10.1016/j.powtec.2012.03.013

Cited by 57 publications

(32 citation statements)

References 33 publications

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“…12, there is only a moderate difference between the two particle-particle drag models in the case of normal inlet geometry (the conclusion of tangential inlet geometry is the same). This is in accordance with the previous studies on CFB risers [62]. For keeping the concept consistency with the choice of binary KTGF of Chao et al [37], its corresponding particle-particle drag coefficient model will be used in the optimized model.…”

Section: The Effect Of Kinetic Theory Of Granular Flowsupporting

confidence: 72%

Evaluation of multifluid model for heat transfer behavior of binary gas–solid flow in a downer reactor

et al. 2015

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Section: The Effect Of Kinetic Theory Of Granular Flowsupporting

confidence: 72%

Evaluation of multifluid model for heat transfer behavior of binary gas–solid flow in a downer reactor

et al. 2015

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“…A few examples (among many others) of an incorrect or incomplete formulation can be found in Ahmadi & Ma (1990), Simonin, Deutsch & Minier (1993), He & Simonin (1993), Simonin (1996), Peirano & Leckner (1998), Cheng et al (1999), Benavides, & van Wachem (2008), Chao et al (2011Chao et al ( , 2012, Jiang & Zhang (2012), and Rao et al (2012). Interestingly, Hrenya & Sinclair (1997) give the correct expression for the PA granular temperature R. O.…”

Section: Introductionmentioning

confidence: 99%

On multiphase turbulence models for collisional fluid–particle flows

Fox¹

2014

J. Fluid Mech.

181

215

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Starting from a kinetic theory (KT) model for monodisperse granular flow, the exact Reynolds-averaged (RA) equations are derived for the particle phase in a collisional fluid-particle flow. The corresponding equations for a constant-density fluid phase are derived from a model that includes drag and buoyancy coupling with the particle phase. The fully coupled macroscale/hydrodynamic model, rigorously derived from a kinetic equation for the particles, is written in terms of the particle-phase volume fraction, the particle-phase velocity and the granular temperature (or total granular energy). As derived from the hydrodynamic model, the RA turbulence model solves for the RA particle-phase volume fraction, the phase-averaged (PA) particle-phase velocity, the PA granular temperature and the PA turbulent kinetic energy of the particle phase. Thus, unlike in most previous derivations of macroscale turbulence models for moderately dense granular flows, a clear distinction is made between the PA granular temperature Θ p , which appears in the KT constitutive relations, and the particle-phase turbulent kinetic energy k p , which appears in the turbulent transport coefficients. The exact RA equations contain unclosed terms due to nonlinearities in the hydrodynamic model and we briefly discuss the available closures for these terms. Finally, we demonstrate by comparing model predictions with direct numerical simulation results that even for non-collisional fluid-particle flows it is necessary to provide separate models for Θ p and k p in order to correctly account for the effect of the particle Stokes number and mass loading.

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“…Among these properties are the basic conservation laws 16 which can be deduced invoking the principle of homogeneity of time and space for closed systems that do not interact with any external forces.…”

Section: Lagrangian Mechanicsmentioning

confidence: 99%

“…In a similar manner Laurent et al [88] derived the governing conservation equations for poly-dispersed dense sprays of evaporating liquid droplets. Lathouwers and Bellan [83][84][85][86][87] and Chao et al [16,17] proposed a similar model for poly-dispersed gas-solid multicomponent reactive processes in fluidized beds. The main challenge in formulating these equations is related to the definition of the collision operator.…”

Section: Governing Equations For Polydispersed Multiphase Systemsmentioning

confidence: 99%

Elementary Kinetic Theory of Gases

Jakobsen

2014

Chemical Reactor Modeling

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It is convenient to introduce the notion of collisional invariants (or summational invariants) (e.g., [55], p. 460; [90], p. 150). The validity of (2.211) is commonly justified by the following arguments: Due to the symmetry properties of the collision term expression, interchanging variables gives the following equalities:These symmetry properties can be combined to give the following relationship:The linearity of the J operator allows the latter result to be manipulated as:In conclusion, a function ψ(c) is a summation invariant if:

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Investigation of the particle–particle drag in a dense binary fluidized bed

Cited by 57 publications

References 33 publications

Evaluation of multifluid model for heat transfer behavior of binary gas–solid flow in a downer reactor

Evaluation of multifluid model for heat transfer behavior of binary gas–solid flow in a downer reactor

On multiphase turbulence models for collisional fluid–particle flows

Elementary Kinetic Theory of Gases

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