A fully coupled quadrature-based moment method for dilute to moderately dilute fluid–particle flows

Passalacqua, Alberto; Fox, Rodney O.; Garg, Rahul; Subramaniam, Shankar

doi:10.1016/j.ces.2009.09.002

Cited by 71 publications

(86 citation statements)

References 29 publications

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“…The model presented above has been implemented in the CFD code MFIX 57,58 as described in detail elsewhere, 31 and is validated here against the experimental measurements in a gasparticle flow riser with monodisperse 29 and bidisperse particles. 22 Here, we briefly describe the solution procedure and the simulation setup for the mono-and bidisperse cases.…”

Section: ■ Numerical Simulationsmentioning

confidence: 99%

“…Using the moment definition, transport equations for the moments of f i can be found from eq 4, leading to (10) where A i γ and C ij γ are, respectively, the moments of order γ of the acceleration term and of the collision term. It is worth noticing that the coupling between each particle type and the fluid phase is achieved by means of the acceleration term, 31 while the momentum exchange between particles is described by the collision term. As a consequence, the set of equations constituted by the Navier−Stokes equations for the fluid and the moment transport equations for each particle type accounts for the full coupling among the phases, without any need to specify a drag correlation for particle−particle interactions between particle types.…”

Section: ■ Model Descriptionmentioning

confidence: 99%

“…Boundary conditions for the moment transport equations are specified in terms of the quadrature approximation, as shown elsewhere. 31,35 For example, a specular reflective condition at the walls is defined as …”

Section: Industrial and Engineering Chemistry Researchmentioning

confidence: 99%

“…The general procedure for the numerical solution of the moment transport equations and their coupling with the fluid phase is described in detail elsewhere. 31 The fluid-phase equations are solved with an iterative procedure based on the SIMPLE algorithm 59,60 and coupled with the QMOM equations using the partial elimination algorithm. 61 The second-order scheme with a Superbee limiter was used to discretize the fluid-phase equations.…”

Section: ■ Numerical Simulationsmentioning

confidence: 99%

“…We perform numerical simulations of both systems using a thirdorder quadrature-based moment method coupled with a fluid solver. 31 Results are compared to experimental data and to Euler−Lagrange simulations. 29,30 Flow statistics of the particle phase are computed, and dimensionless parameters such as the particle-phase Mach, Knudsen, and Stokes numbers are examined in order to justify the adoption of high-order moment methods.…”

Section: ■ Introductionmentioning

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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Section: ■ Numerical Simulationsmentioning

confidence: 99%

Section: ■ Model Descriptionmentioning

confidence: 99%

Section: Industrial and Engineering Chemistry Researchmentioning

confidence: 99%

Section: ■ Numerical Simulationsmentioning

confidence: 99%

Section: ■ Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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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Modeling the thermochemical degradation of biomass inside a fast pyrolysis fluidized bed reactor

Bruchmüller

Wachem

et al. 2011

AIChE Journal

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A fast pyrolysis process in a bubbling fluidized bed has been modeled, thoroughly reproduced and scrutinized with the help of a combined Eulerian/Lagrangian simulation method. The 3-D model is compared to experimental results from a 100 g/h bubbling fluidized bed pyrolyzer including such variables as particle composition at the outlet and gas/vapor/water yields as a function of fluidization conditions, biomass moisture concentrations, and bed temperatures. Multiprocessor simulations on a high-end computer have been carried out to enable the tracking of each of the 0.8 million individual discrete sand and biomass particles, making it possible to look at accurate and detailed multiscale information (i.e., any desired particle property, trajectory, particle interaction) over the entire particle life time. The overall thermochemical degradation process of biomass is influenced by local flow and particle properties and, therefore, accurate and detailed modeling reveals unprecedented insight into such complex processes. It has been found, that the superficial fluidization velocity is important while the particle moisture content is less significant for the final bio-oil yield

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A second‐order moment method applied to gas–solid risers

et al. 2012

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Second‐order moment method of particles is proposed on the basis of the kinetic theory of granular flow. Closure equations for the third‐order velocity moments are presented to account for the increase of the probability of collisions of particles on the basis of the elementary kinetic theory and order of magnitude analysis. The boundary conditions for the set of equations describing flow of particles are proposed with the consideration of the momentum exchange by collisions between the wall and the particles. The distributions of velocity, concentration and moments of particles are predicted. Simulated results are compared with experimental data measured by Tartan and Gidaspow and Bhusarapu et al. in risers, and Tsuji et al. in a vertical pipe. The effects of the closure equations for the third‐order velocity moments and the fluid‐particle velocity correlation tensor on flow behavior of particles are analyzed. © 2012 American Institute of Chemical Engineers AIChE J, 2012

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A fully coupled quadrature-based moment method for dilute to moderately dilute fluid–particle flows

Cited by 71 publications

References 29 publications

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

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

Modeling the thermochemical degradation of biomass inside a fast pyrolysis fluidized bed reactor

A second‐order moment method applied to gas–solid risers

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