Computational models for polydisperse particulate and multiphase systems

Computational models for polydisperse particulate and multiphase systems /

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Providing a clear description of the theory of polydisperse multiphase flows, with emphasis on the mesoscale modelling approach and its relationship with microscale and macroscale models, this all-inclusive introduction is ideal whether you are working in industry or academia. Theory is linked to pr...

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Bibliographic Details
Main Authors: Marchisio, Daniele L. (Author), Fox, Rodney O., 1959- (Author)
Format: Electronic eBook
Language:English
Published: Cambridge : Cambridge University Press, 2013.
Series:Cambridge series in chemical engineering.
Subjects:
Multiphase flow > Mathematical models.
Chemical reactions > Mathematical models.
Transport theory.
Dispersion > Mathematical models.
Online Access:Full text (Emerson users only)
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Table of Contents:
  • Cover
  • Contents
  • Preface
  • Notation
  • 1 Introduction
  • 1.1 Disperse multiphase flows
  • 1.2 Two example systems
  • 1.2.1 The population-balance equation for fine particles
  • 1.2.2 The kinetic equation for gas
  • particle flow
  • 1.3 The mesoscale modeling approach
  • 1.3.1 Relation to microscale models
  • 1.3.2 Number-density functions
  • 1.3.3 The kinetic equation for the disperse phase
  • 1.3.4 Closure at the mesoscale level
  • 1.3.5 Relation to macroscale models
  • 1.4 Closure methods for moment-transport equations
  • 1.4.1 Hydrodynamic models
  • 1.4.2 Moment methods
  • 1.5 A road map to Chapters 2
  • 8
  • 2 Mesoscale description of polydisperse systems
  • 2.1 Number-density functions (NDF)
  • 2.1.1 Length-based NDF
  • 2.1.2 Volume-based NDF
  • 2.1.3 Mass-based NDF
  • 2.1.4 Velocity-based NDF
  • 2.2 The NDF transport equation
  • 2.2.1 The population-balance equation (PBE)
  • 2.2.2 The generalized population-balance equation (GPBE)
  • 2.2.3 The closure problem
  • 2.3 Moment-transport equations
  • 2.3.1 Moment-transport equations for a PBE
  • 2.3.2 Moment-transport equations for a GPBE
  • 2.4 Flow regimes for the PBE
  • 2.4.1 Laminar PBE
  • 2.4.2 Turbulent PBE
  • 2.5 The moment-closure problem
  • 3 Quadrature-based moment methods
  • 3.1 Univariate distributions
  • 3.1.1 Gaussian quadrature
  • 3.1.2 The product
  • difference (PD) algorithm
  • 3.1.3 The Wheeler algorithm
  • 3.1.4 Consistency of a moment set
  • 3.2 Multivariate distributions
  • 3.2.1 Brute-force QMOM
  • 3.2.2 Tensor-product QMOM
  • 3.2.3 Conditional QMOM
  • 3.3 The extended quadrature method of moments (EQMOM)
  • 3.3.1 Relationship to orthogonal polynomials
  • 3.3.2 Univariate EQMOM
  • 3.3.3 Evaluation of integrals with the EQMOM
  • 3.3.4 Multivariate EQMOM
  • 3.4 The direct quadrature method of moments (DQMOM)
  • 4 The generalized population-balance equation.
  • 4.1 Particle-based definition of the NDF
  • 4.1.1 Definition of the NDF for granular systems
  • 4.1.2 NDF estimation methods
  • 4.1.3 Definition of the NDF for fluid
  • particle systems
  • 4.2 From the multi-particle
  • fluid joint PDF to the GPBE
  • 4.2.1 The transport equation for the multi-particle joint PDF
  • 4.2.2 The transport equation for the single-particle joint PDF
  • 4.2.3 The transport equation for the NDF
  • 4.2.4 The closure problem
  • 4.3 Moment-transport equations
  • 4.3.1 A few words about phase-space integration
  • 4.3.2 Disperse-phase number transport
  • 4.3.3 Disperse-phase volume transport
  • 4.3.4 Fluid-phase volume transport
  • 4.3.5 Disperse-phase mass transport
  • 4.3.6 Fluid-phase mass transport
  • 4.3.7 Disperse-phase momentum transport
  • 4.3.8 Fluid-phase momentum transport
  • 4.3.9 Higher-order moment transport
  • 4.4 Moment closures for the GPBE
  • 5 Mesoscale models for physical and chemical processes
  • 5.1 An overview of mesoscale modeling
  • 5.1.1 Mesoscale models in the GPBE
  • 5.1.2 Formulation of mesoscale models
  • 5.1.3 Relation to macroscale models
  • 5.2 Phase-space advection: mass and heat transfer
  • 5.2.1 Mesoscale variables for particle size
  • 5.2.2 Size change for crystalline and amorphous particles
  • 5.2.3 Non-isothermal systems
  • 5.2.4 Mass transfer to gas bubbles
  • 5.2.5 Heat/mass transfer to liquid droplets
  • 5.2.6 Momentum change due to mass transfer
  • 5.3 Phase-space advection: momentum transfer
  • 5.3.1 Buoyancy and drag forces
  • 5.3.2 Virtual-mass and lift forces
  • 5.3.3 Boussinesq
  • Basset, Brownian, and thermophoretic forces
  • 5.3.4 Final expressions for the mesoscale acceleration models
  • 5.4 Real-space advection
  • 5.4.1 The pseudo-homogeneous or dusty-gas model
  • 5.4.2 The equilibrium or algebraic Eulerian model
  • 5.4.3 The Eulerian two-fluid model.
  • 5.4.4 Guidelines for real-space advection
  • 5.5 Diffusion processes
  • 5.5.1 Phase-space diffusion
  • 5.5.2 Physical-space diffusion
  • 5.5.3 Mixed phase- and physical-space diffusion
  • 5.6 Zeroth-order point processes
  • 5.6.1 Formation of the disperse phase
  • 5.6.2 Nucleation of crystals from solution
  • 5.6.3 Nucleation of vapor bubbles in a boiling liquid
  • 5.7 First-order point processes
  • 5.7.1 Particle filtration and deposition
  • 5.7.2 Particle breakage
  • 5.8 Second-order point processes
  • 5.8.1 Derivation of the source term
  • 5.8.2 Source terms for aggregation and coalescence
  • 5.8.3 Aggregation kernels for fine particles
  • 5.8.4 Coalescence kernels for droplets and bubbles
  • 6 Hard-sphere collision models
  • 6.1 Monodisperse hard-sphere collisions
  • 6.1.1 The Boltzmann collision model
  • 6.1.2 The collision term for arbitrary moments
  • 6.1.3 Collision angles and the transformation matrix
  • 6.1.4 Integrals over collision angles
  • 6.1.5 The collision term for integer moments
  • 6.2 Polydisperse hard-sphere collisions
  • 6.2.1 Collision terms for arbitrary moments
  • 6.2.2 The third integral over collision angles
  • 6.2.3 Collision terms for integer moments
  • 6.3 Kinetic models
  • 6.3.1 Monodisperse particles
  • 6.3.2 Polydisperse particles
  • 6.4 Moment-transport equations
  • 6.4.1 Monodisperse particles
  • 6.4.2 Polydisperse particles
  • 6.5 Application of quadrature to collision terms
  • 6.5.1 Flux terms
  • 6.5.2 Source terms
  • 7 Solution methods for homogeneous systems
  • 7.1 Overview of methods
  • 7.2 Class and sectional methods
  • 7.2.1 Univariate PBE
  • 7.2.2 Bivariate and multivariate PBE
  • 7.2.3 Collisional KE
  • 7.3 The method of moments
  • 7.3.1 Univariate PBE
  • 7.3.2 Bivariate and multivariate PBE
  • 7.3.3 Collisional KE
  • 7.4 Quadrature-based moment methods
  • 7.4.1 Univariate PBE.
  • 7.4.2 Bivariate and multivariate PBE
  • 7.4.3 Collisional KE
  • 7.5 Monte Carlo methods
  • 7.6 Example homogeneous PBE
  • 7.6.1 A few words on the spatially homogeneous PBE
  • 7.6.2 Comparison between the QMOM and the DQMOM
  • 7.6.3 Comparison between the CQMOM and Monte Carlo
  • 8 Moment methods for inhomogeneous systems
  • 8.1 Overview of spatial modeling issues
  • 8.1.1 Realizability
  • 8.1.2 Particle trajectory crossing
  • 8.1.3 Coupling between active and passive internal coordinates
  • 8.1.4 The QMOM versus the DQMOM
  • 8.2 Kinetics-based finite-volume methods
  • 8.2.1 Application to PBE
  • 8.2.2 Application to KE
  • 8.2.3 Application to GPBE
  • 8.3 Inhomogeneous PBE
  • 8.3.1 Moment-transport equations
  • 8.3.2 Standard finite-volume schemes for moments
  • 8.3.3 Realizable finite-volume schemes for moments
  • 8.3.4 Example results for an inhomogeneous PBE
  • 8.4 Inhomogeneous KE
  • 8.4.1 The moment-transport equation
  • 8.4.2 Operator splitting for moment equations
  • 8.4.3 A realizable finite-volume scheme for bivariatevelocity moments
  • 8.4.4 Example results for an inhomogeneous KE
  • 8.5 Inhomogeneous GPBE
  • 8.5.1 Classes of GPBE
  • 8.5.2 Spatial transport with known scalar-dependent velocity
  • 8.5.3 Example results with known scalar-dependent velocity
  • 8.5.4 Spatial transport with scalar-conditioned velocity
  • 8.5.5 Example results with scalar-conditioned velocity
  • 8.5.6 Spatial transport of the velocity-scalar NDF
  • 8.6 Concluding remarks
  • Appendix A Moment-inversion algorithms
  • A.1 Univariate quadrature
  • A.1.1 The PD algorithm
  • A.1.2 The adaptive Wheeler algorithm
  • A.2 Moment-correction algorithms
  • A.2.1 The correction algorithm of McGraw
  • A.2.2 The correction algorithm of Wright
  • A.3 Multivariate quadrature
  • A.3.1 Brute-force QMOM
  • A.3.2 Tensor-product QMOM
  • A.3.3 The CQMOM
  • A.4 The EQMOM.
  • A.4.1 Beta EQMOM
  • A.4.2 Gamma EQMOM
  • A.4.3 Gaussian EQMOM
  • Appendix B Kinetics-based finite-volume methods
  • B.1 Spatial dependence of GPBE
  • B.2 Realizable FVM
  • B.3 Advection
  • B.4 Free transport
  • B.5 Mixed advection
  • B.6 Diffusion
  • Appendix C Moment methods with hyperbolic equations
  • C.1 A model kinetic equation
  • C.2 Analytical solution for segregated initial conditions
  • C.2.1 Segregating solution
  • C.2.2 Mixing solution
  • C.3 Moments and the quadrature approximation
  • C.3.1 Moments of segregating solution
  • C.3.2 Moments of mixing solution
  • C.4 Application of QBMM
  • C.4.1 The moment-transport equation
  • C.4.2 Transport equations for weights and abscissas
  • Appendix D The direct quadrature method of moments fully conservative
  • D.1 Inhomogeneous PBE
  • D.2 Standard DQMOM
  • D.3 DQMOM-FC
  • D.4 Time integration
  • References
  • Index.

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