Derivation and validation of a binary multi-fluid Eulerian model for fluidized beds

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

doi:10.1016/j.ces.2011.04.027

Cited by 70 publications

(46 citation statements)

References 24 publications

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“…The particle collision characteristics are defined based on the restitution coefficient, and the wall boundary conditions are defined in at least three ways, which are the traditional no-slip boundary conditions and two partial slip conditions [9,10]. The effects of these parameters on the simulation results have been studied by some researchers.…”

Section: Introductionmentioning

confidence: 99%

An Investigation of the Restitution Coefficient Impact on Simulating Sand-Char Mixing in a Bubbling Fluidized Bed

Zhao¹,

Eri²,

Wang³

2017

Energies

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Abstract:In the present work, the effect of the restitution coefficient on the numerical results for a binary mixture system of sand particles and char particles in a bubbling fluidized bed with a huge difference between the particles in terms of density and volume fraction has been studied based on two-fluid model along with the kinetic theory of granular flow. Results show that the effect of restitution coefficient on the flow characteristics varies in different regions of the bed, which is more evident for the top region of the bed. The restitution coefficient can be categorized into two classes. The restitution coefficients of 0.7 and 0.8 can be included into one class, whereas the restitution coefficient of 0.9 and 0.95 can be included into another class. Moreover, four vortices can be found in the time-averaged flow pattern distribution, which is very different from the result obtained for the binary system with the similar values between particles in density and volume fraction.

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Section: Introductionmentioning

confidence: 99%

An Investigation of the Restitution Coefficient Impact on Simulating Sand-Char Mixing in a Bubbling Fluidized Bed

Zhao¹,

Eri²,

Wang³

2017

Energies

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“…The final rms values are then the square root of timeaverage square differences. As discussed elsewhere, 53 the rms values found in this manner are expected to be much larger than those found using the granular temperature.…”

Section: ■ Numerical Simulationsmentioning

confidence: 89%

“…The lower value of Kn at the wall is justified by the higher particle concentration in that region of the system, which leads to higher values of the collision frequency, making the flow locally dominated by collisions. It is worth noting that if a hydrodynamic model, 41,42,53 derived with the hypothesis of small particle Knudsen number (continuum regime, Kn < 0.01), were used to perform the simulations, the adoption of partial slip boundary conditions 68 would have been necessary to describe the behavior of the particle flow in the zone adjacent to the walls, where Kn ≈ 0.1. However, the hydrodynamic model may deviate from the correct behavior in the center of the riser, where higher values of the particle Knudsen number are present.…”

Section: ■ Results and Discussionmentioning

confidence: 99%

“…A description of the full Boltzmann−Enskog integral for denser flows can be found elsewhere. 32 It is worth noticing that the quadrature-based moment closure for the collision integral described above includes all the terms in the polydisperse kinetic theory discussed in Chao et al 53 In particular, the term corresponding to the f luid dynamic velocity dif ference is accounted for exactly in eq 25, up to the accuracy of the quadrature approximation.…”

Section: Industrial and Engineering Chemistry Researchmentioning

confidence: 99%

“…A riser flow used previously in experiments, 22 Euler−Lagrange 30 or Euler−Euler 53 simulations, was used here for testing our simulation code for bidisperse gas-particle flows. The original system has an internal diameter of 0.032 m and is 1.0 m tall.…”

Section: ■ Numerical Simulationsmentioning

confidence: 99%

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Simulation of Mono- and Bidisperse Gas-Particle Flow in a Riser with a Third-Order Quadrature-Based Moment Method

Passalacqua¹,

Fox²

2012

Ind. Eng. Chem. Res.

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Gas-particle flows can be described by a kinetic equation for the particle phase coupled with the Navier−Stokes equations for the fluid phase through a momentum exchange term. The direct solution of the kinetic equation is prohibitive for most applications due to the high dimensionality of the space of independent variables. A viable alternative is represented by moment methods, where moments of the velocity distribution function are transported in space and time. In this work, a fully coupled third-order, quadrature-based moment method is applied to the simulation of mono-and bidisperse gas-particle flows in the riser of a circulating fluidized bed. Gaussian quadrature formulas are used to model the unclosed terms in the moment transport equations. A Bhatnagar−Gross−Krook (BGK) collision model is used in the monodisperse case, while the full Boltzmann integral is adopted in the bidisperse case. The predicted values of mean local phase velocities, rms velocities, and particle volume fractions are compared with the Euler−Lagrange simulations and experimental data from the literature. The local values of the time-average Stokes, Mach, and Knudsen numbers predicted by the simulation are reported and analyzed to justify the adoption of high-order moment methods as opposed to models based on hydrodynamic closures. ABSTRACT: Gas-particle flows can be described by a kinetic equation for the particle phase coupled with the Navier−Stokes equations for the fluid phase through a momentum exchange term. The direct solution of the kinetic equation is prohibitive for most applications due to the high dimensionality of the space of independent variables. A viable alternative is represented by moment methods, where moments of the velocity distribution function are transported in space and time. In this work, a fully coupled third-order, quadrature-based moment method is applied to the simulation of mono-and bidisperse gas-particle flows in the riser of a circulating fluidized bed. Gaussian quadrature formulas are used to model the unclosed terms in the moment transport equations. A Bhatnagar−Gross−Krook (BGK) collision model is used in the monodisperse case, while the full Boltzmann integral is adopted in the bidisperse case. The predicted values of mean local phase velocities, rms velocities, and particle volume fractions are compared with the Euler−Lagrange simulations and experimental data from the literature. The local values of the time-average Stokes, Mach, and Knudsen numbers predicted by the simulation are reported and analyzed to justify the adoption of high-order moment methods as opposed to models based on hydrodynamic closures. Disciplines Biological Engineering | Chemical Engineering Comments

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Numerical evaluation of a one‐dimensional two‐fluid model applied to gas–solid cold‐flows in fluidised beds

2013

Self Cite

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Computational demanding two‐ and three‐dimensional two‐fluid models are frequently adopted simulating gas–solid flows in fluidised beds. Reduced computational cost is favourable for efficient numerical studies of technologies such as the novel chemical looping combustion (CLC), chemical looping reforming (CLR), and sorption‐enhanced steam methane reforming (SE‐SMR) processes. In this study, we elucidate the potential of a one‐dimensional two‐fluid model to describe gas–solid cold‐flows in fluidised beds. The validity of the numerical simulation results of the bubbling beds and risers have been compared to experimental data in the literature. Moreover, sensitivity analyses on drag closure laws and operation condition have been performed and a number of model solution techniques and algorithms are studied. In addition, simulation results of the one‐dimensional model are compared to results of a two‐dimensional model. For particular sets of operating conditions and flow characteristics, the one‐dimensional model compares fairly well to the simulation results of the two‐dimensional model and to experimental data. Under other operating conditions, large quantitative deviations can be observed. However, the one‐dimensional model is assumed to be sufficently accurate for particular reactor process optimisation and design evaluations.

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Derivation and validation of a binary multi-fluid Eulerian model for fluidized beds

Cited by 70 publications

References 24 publications

An Investigation of the Restitution Coefficient Impact on Simulating Sand-Char Mixing in a Bubbling Fluidized Bed

An Investigation of the Restitution Coefficient Impact on Simulating Sand-Char Mixing in a Bubbling Fluidized Bed

Simulation of Mono- and Bidisperse Gas-Particle Flow in a Riser with a Third-Order Quadrature-Based Moment Method

Numerical evaluation of a one‐dimensional two‐fluid model applied to gas–solid cold‐flows in fluidised beds

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