Gas‐particle flow in a vertical pipe with particle‐particle interactions

Sinclair, JL; Jackson, R.

doi:10.1002/aic.690350908

Cited by 605 publications

(415 citation statements)

References 14 publications

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“…The functions ξ ε ( ), θ ε ( ) and f 1 ε ( ) obtained from collision theory of gas-solid suspensions can be expressed as (Sinclair and Jackson [1989]). …”

Section: Phase Arrangement and Stability Of Annular Flowsmentioning

confidence: 99%

Stability of annular flow and slugging

Joseph

Bannwart

Liu

1996

International Journal of Multiphase Flow

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In this work we propose an effective viscosity criterion for the stabilization of annular gas-liquid and liquid-particle flows and an inertial mechanism which drives waves into slugs in slugging gas-liquid flows. Annular flow is stable when the fluid having the higher effective viscosity occupies the core region and the lower viscosity fluid is the annulus. The eddy viscosity criterion is shown to be very consistent with published work on annular flow transitions in horizontal and vertical gas-liquid flows. It also applies to a variety of liquid-solid and gas-solid flows. In the second part of the paper we propose a mechanism for explaining the growth of initially small waves and initiation of slugs in gas-liquid flow.

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“…The functions ξ ε ( ), θ ε ( ) and f 1 ε ( ) obtained from collision theory of gas-solid suspensions can be expressed as (Sinclair and Jackson [1989]). …”

Section: Phase Arrangement and Stability Of Annular Flowsmentioning

confidence: 99%

Stability of annular flow and slugging

Joseph

Bannwart

Liu

1996

International Journal of Multiphase Flow

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“…It was applied to steady, developed riser flow in a pioneering paper by Sinclair and Jackson (1989) using the Johnson and Jackson (1987) boundary conditions. Developed flow requires the solids pressure to be constant.…”

Section: A Solids Viscosity and Kinetic Theory Modelsmentioning

confidence: 99%

Computational and Experimental Modeling of Three-Phase Slurry-Bubble Column Reactor

Gamwo¹,

Gidaspow²

1999

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Considerable progress has been achieved in understanding three-phase reactors from the point of view of kinetic theory. In a paper in press for publication in Chemical Engineering Science we have obtained a complete numerical solution of bubble column reactors.In view of the complexity of the simulation a better understanding of the processes using simplified analytical solutions is required. Such analytical solutions are presented in the attached paper, Large Scale Oscillations or Gravity Waves in Risers and Bubbling Beds. This paper presents analytical solutions for bubbling frequencies and standing wave flow patterns. The flow patterns in operating slurry bubble column reactors are not optimum. They involve upflow in the center and downflow at the walls. It may be possible to control flow patterns by proper redistribution of heat exchangers in slurry bubble column reactors.We also believe that the catalyst size in operating slurry bubble column reactors is not optimum. To obtain an optimum size we are following up on the observation of George Cody of Exxon who reported a maximum granular temperature (random particle kinetic energy) for a particle size of 90 microns. The attached paper, Turbulence of Particles in a CFB and Slurry Bubble Columns Using Kinetic Theory, supports George Cody's observations. However, our explanation for the existence of the maximum in granular temperature differs from that proposed by George Cody. Further computer simulations and experiments involving measurements of granular temperature are needed to obtain a sound theoretical explanation for the possible existence of an optimum catalyst size.iii ObjectiveThe overall objective of this research is to develop predictive hydrodynamic models for gasliquid-solid catalyst reactors using momentum balances for each phase. The unique feature of our approach is the modeling of turbulence of the catalyst particles using kinetic theory.This project is a collaborative effort between the University of Akron, Illinois Institute of Technology and two industries: UOP and Energy International.The tasks involve the development of transient two and three dimensional computer codes for Fischer-Tropsch synthesis in slurry bubble column reactors, optimization, comparison to data, and measurement of input parameters, such as the catalyst viscosity and effective restitution coefficients. Heat and mass transfer rates will be measured in the IIT two-story riser by injection of liquid nitrogen into an air-catalyst stream. Accomplishment to DateOur paper describing the basic approach using kinetic theory to predict the turbulence of catalyst particles in a slurry bubble column reactor, based mainly on the work accomplished in a previous UCR grant, has been accepted for publication in a refereed journal .The simulation predicted the existence of multiple vortices in the LaPorte Air Products methanol reactor.In view of the complexity of the simulation a better understanding of the processes using simplified analytical solutions is required. Such analyt...

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“…By adopting an appropriate drag correlation, 4 one can properly predict flow regimes typical of CFB risers. 5,6 If all the interactions between the phases are accounted for and correlated to the averaged and fluctuating components of the phase velocity fields, 7,8 a hydrodynamic model is able to properly predict the behavior of gas−solid flow in a riser. A stationary hydrodynamic model 7 is able to predict the particle phase stresses through the kinetic theory of granular flow as a function of the particle fluctuating energy (granular energy).…”

Section: ■ Introductionmentioning

confidence: 99%

“…5,6 If all the interactions between the phases are accounted for and correlated to the averaged and fluctuating components of the phase velocity fields, 7,8 a hydrodynamic model is able to properly predict the behavior of gas−solid flow in a riser. A stationary hydrodynamic model 7 is able to predict the particle phase stresses through the kinetic theory of granular flow as a function of the particle fluctuating energy (granular energy). A modified model 9 has been proposed and validated against experimental data, 10 showing a high sensitivity to the value of the restitution coefficient, whose reduction may lead to a wrong prediction of the particle segregation patterns inside the duct.…”

Section: ■ Introductionmentioning

confidence: 99%

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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Gas‐particle flow in a vertical pipe with particle‐particle interactions

Cited by 605 publications

References 14 publications

Stability of annular flow and slugging

Stability of annular flow and slugging

Computational and Experimental Modeling of Three-Phase Slurry-Bubble Column Reactor

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

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