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Author Marchisio, Daniele L
Title Computational Models for Polydisperse Particulate and Multiphase Systems
Imprint New York : Cambridge University Press, 2013
©2013
book jacket
Descript 1 online resource (548 pages)
text txt rdacontent
computer c rdamedia
online resource cr rdacarrier
Series Cambridge Series in Chemical Engineering
Cambridge Series in Chemical Engineering
Note 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
All-inclusive introduction to polydisperse multiphase flows linking theory to practice through numerous real-world examples and MATLAB scripts for key algorithms
Description based on publisher supplied metadata and other sources
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2020. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries
Link Print version: Marchisio, Daniele L. Computational Models for Polydisperse Particulate and Multiphase Systems New York : Cambridge University Press,c2013 9780521858489
Subject Multiphase flow -- Mathematical models.;Chemical reactions -- Mathematical models.;Transport theory.;Dispersion -- Mathematical models
Electronic books
Alt Author Fox, Rodney O
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