Gidaspow Multiphase Flow and Fluidization

Continuum and Kinetic Theory Descriptions
1. Auflage 2012
ISBN: 978-0-08-051226-6
Verlag: Elsevier Science & Techn.
Format: EPUB
Kopierschutz: 6 - ePub Watermark

E-Book, Englisch, 467 Seiten

Useful as a reference for engineers in industry and as an advanced level text for graduate engineering students, Multiphase Flow and Fluidization takes the reader beyond the theoretical to demonstrate how multiphase flow equations can be used to provide applied, practical, predictive solutions to industrial fluidization problems. Written to help advance progress in the emerging science of multiphase flow, this book begins with the development of the conservation laws and moves on through kinetic theory, clarifying many physical concepts (such as particulate viscosity and solids pressure) and introducing the new dependent variable--the volume fraction of the dispersed phase. Exercises at the end of each chapterare provided for further study and lead into applications not covered in the text itself. - Treats fluidization as a branch of transport phenomena - Demonstrates how to do transient, multidimensional simulation of multiphase processes - The first book to apply kinetic theory to flow of particulates - Is the only book to discuss numerical stability of multiphase equations and whether or not such equations are well-posed - Explains the origin of bubbles and the concept of critical granular flow - Presents clearly written exercises at the end of each chapter to facilitate understanding and further study

Autoren/Hrsg.

Gidaspow, Dimitri

Inhaltsverzeichnis

1;Front Cover;1
2;Multiphase Flow and Fluidization: Continuum and Kinetic Theory Descriptions;4
3;Copyright Page;5
4;Table of Contents;6
5;Preface;10
6;Nomenclature;14
7;Chapter 1. Transport Equations;22
7.1;1.1 Basic Approach;22
7.2;1.2 Mass Balances;23
7.3;1.3 Momentum Balances;24
7.4;1.4 Energy Balances;28
7.5;1.5 Entropy Balance;31
7.6;1.6 Mixture Equations;32
7.7;1.7 Multicomponent Multiphase Flow;41
8;Chapter 2. One-Dimensional Steady Gas-Solid Flow;52
8.1;2.1 One-Dimensional, Steady Mixture Momentum Balance;52
8.2;2.2 One-Dimensional, Steady Gas Momentum Balance: Pressure Drop in Both Phases — Model A;54
8.3;2.3 Fluid Particle Drag;56
8.4;2.4 Buoyancy;58
8.5;2.5 Drag for Models B and C;60
8.6;2.6 Entrance Length in Pneumatic Transport;61
8.7;2.7 Pressure Drop;66
8.8;2.8 Pressure Drop Correlation in a Dilute Lift Line;72
9;Chapter 3. Drift Flux;82
9.1;3.1 Introduction;82
9.2;3.2 Hold-Up in Homogeneous and Slip Flow;82
9.3;3.3 Single Particle Analysis;83
9.4;3.4 Ergun Equation Prediction;84
9.5;3.5 Two Regimes in a Bubble Column;87
9.6;3.6 Other Applications;89
10;Chapter 4. Critical Granular Flow;94
10.1;4.1 One-Dimensional Granular Flow Momentum Balance;94
10.2;4.2 One-Dimensional Statics: Jannssen Equation;96
10.3;4.3 Incompressible, Frictionless Flow and Discharge;98
10.4;4.4 Thermodynamics of Powders: Compressibility;100
10.5;4.5 Critical Flow Theory for Granular Materials;103
10.6;4.6 Example of Critical Granular Flow;107
10.7;4.7 "Sound Speed" from Kinetic Theory;109
11;Chapter 5. The Fluidized State;118
11.1;5.1 Introduction: Fluidization Regimes;118
11.2;5.2 Minimum Fluidization Velocity;119
11.3;5.3 Geldart's Classification of Powders;125
11.4;5.4 Kinetic Energy Dissipation Analysis;127
12;Chapter 6. On the Origin of Bubbles;136
12.1;6.1 Introduction;136
12.2;6.2 Void Propagation in Incompressible Fluids;137
12.3;6.3 Shocks and Dispersion with No Solids Stress;140
12.4;6.4 Bubbling Criterion for Small Particles;142
13;Chapter 7. Inviscid Multiphase Flows: Bubbling Beds;150
13.1;7.1 Basic Equations;150
13.2;7.2 Compressible Granular Flow;152
13.3;7.3 Well-Posedness of Two-Phase Models;155
13.4;7.4 Homogeneous Flow and Pressure Propagation;160
13.5;7.5 Solids Vorticity and Void Propagation;162
13.6;7.6 Davidson Bubble Model;167
13.7;7.7 Computer Fluidization Models;170
13.8;7.8 Comparison of Computations to Observations;175
14;Chapter 8. Viscous Flow and Circulating Fluidized Beds;218
14.1;8.1 Introduction;218
14.2;8.2 Multiphase Navier-Stokes Equation Model;219
14.3;8.3 Dimensional Analysis: Scale Factors;222
14.4;8.4 CFB or Riser Flow: Experimental;228
14.5;8.5 Need for Clusters in One-D Modeling;235
14.6;8.6 Computation of Cluster Flow;237
14.7;8.7 Computation of Core-Annular Regime;245
14.8;8.8 Radial Profiles and Turbulence;249
15;Chapter 9. Kinetic Theory Approach;260
15.1;9.1 Introduction;260
15.2;9.2 Maxwellian Distribution for Particles;261
15.3;9.3 Properties of the Maxwellian State;263
15.4;9.4 Dynamics of an Encounter between Two Particles;265
15.5;9.5 The Frequency of Collisions;268
15.6;9.6 Mean Free Path;273
15.7;9.7 Elementary Treatment of Transport Coefficients;274
15.8;9.8 Boltzmann Integral-Differential Equation;277
15.9;9.9 Maxwell's Transport Equation;280
15.10;9.10 Conservation Laws with No Collisions;282
15.11;9.11 Second Approximation to the Frequency Distribution;284
15.12;9.12 Integral Equation Solver Strategy;293
15.13;9.13 Viscous Kinetic Stress Tensor;295
15.14;9.14 Dense Transport Theorem;297
15.15;9.15 Particulate Momentum Equation;300
15.16;9.16 Fluctuating Kinetic Energy Equation;302
15.17;9.17 Viscosity-Collisional Momentum Transfer;305
15.18;9.18 Granular Conductivity;311
16;Chapter 10. Applications of Kinetic Theory;318
16.1;10.1 Granular Shear Flow;318
16.2;10.2 Flow down a Chute;328
16.3;10.3 Bubbling Bed: Flow Patterns;332
16.4;10.4 Liquid-Solid Fluidization;339
16.5;10.5 Circulating Fluidized Bed Loop Simulation;345
16.6;10.6 Maximum Solids Circulation in a CFB;351
17;Chapter 11. Kinetic Theory of Granular Mixtures;358
17.1;11.1 Empirical Input: Restitution Coefficients;358
17.2;11.2 Boltzmann Equations for a Mixture;360
17.3;11.3 Dense Transport Theorem;360
17.4;11.4 Granular Temperatures and Applications;362
17.5;11.5 Particle-to-Particle Drag;364
17.6;11.6 Summary;366
18;Chapter 12. Sedimentation and Consolidation;376
18.1;12.1 Conservation of Particles;376
18.2;12.2 Settling in a Sedimentation Column: Introduction;378
18.3;12.3 Free Settling;381
18.4;12.4 Compression Settling;387
18.5;12.5 Consolidation: Relation to Osmotic Pressure;391
18.6;12.6 Electrokinetic Phenomenon: Zeta Potential;397
18.7;12.7 Effect of Zeta Potential on Sedimentation;400
19;Appendices: Formulation of Continuum Problems: Introduction;412
19.1;Appendix A: Overall (Macroscopic Balances);414
19.2;Appendix B: Eulerian Approach: One-D Energy Balance;426
19.3;Appendix C: Leibniz Formula and Relation to Transport;432
19.4;Appendix D: Lagrangian Approach: One-D Conservation of Species and Population Balance;434
19.5;Appendix E: Reynolds Transport Theorem;444
20;Appendices: The Methods of Characteristics: Introduction;450
20.1;Appendix F: First Order Partial Differential Equation;452
20.2;Appendix G: Solution of a Hyperbolic System of First Order Partial Differential Equations;462
21;Index;478

Leseproben

NOMENCLATURE

Surface area, m2

Constant related to phase pressure

? Constant, used to evaluate conductivity

a Area

A Constant vector, Chapman and Cowling’s (1961) notation

Cross-sectional area

Volumetric compressibility, 1/

Constant related to phase viscosity

µ Constant, used to evaluate viscosity

B Constant vector, Chapman and Cowling’s (1961) notation

Mobilities, related to Onsager friction coefficients

C Peculiar particle velocity = c - v

C Propagation velocity in Chapter 6

Drag coefficient

Critical or sonic velocity

Granular specific heat

s Specific heat at a constant stress

c Instantaneous particle velocity

c12 Relative velocity = c1 – c2

Diameter

Dielectric constant

Diffusion coefficient or consolidation coefficient

Dissipation of energy, J/s

Orifice diameter

Tube diameter

Diameter of particle

Electric field strength

Electrophoretic mobility

e Restitution coefficient

Void ratio

Unit shearing stress in the plane

Flux

f External force per unit mass acting on the particle

f Force acting on phase

?i Force per unit mass acting on phase

Frequency distribution function of particle velocities

Gas wall friction factor

(0) Maxwellian distribution function

(2) Pair distribution function

Particle-particle modulus (?Ps/?es) = (?s/?es), N/m2

G Center of mass velocity, Eq. (9.31)

Acceleration due to gravity

Radial distribution function

g Gravitational acceleration

~ Buoyancy group, (?s – ?)/?

Height of interface

Initial slurry height

¯ Dimensionless height of interface

Enthalpy of phase per unit mass, J/kg

in Enthalpy of phase at non-equilibrium

h Volumetric heat transfer coefficient, kW/m3

Current

I(A) Integral of A, Chapman and Cowling’s (1961) notation

I(B) Integral of B, Chapman and Cowling’s (1961) notation

I Unit matrix or unit tensor

J Bracket integral, Chapman and Cowling’s (1961) notation

Mass flux

Maximum solids flux

Drift flux of gas e(vg-v¯)

K Effective friction coefficient defined by Eq. (4.11)

k Thermal conductivity, J/sec-2-K

Permeability

Cohesive force per unit area

Boltzmann constant

k Unit vector along the line from center of particle 1 to 2

Length

Mean free path

Molecular weight

Molecular weight of species , kg/mol

Mass of particle

Mass of phase , kg

'i Mass of rate of production of phase , kg/m3 total-s

'is Specific rate of production of phase , kg/m3“i”-s

'k Rate of phase production, kg/s-m3

Source like contribution defined by Eq. (9.192)

12 Number of binary collisions per unit time per unit volume

Number of particles per unit volume

Number of particles of type per unit volume

n Normal, outward drawn

Pressure

Collisional pressure like contribution defined by Eq. (9.193)

Pressure of phase

Pressure of phase , Pa

p Particle stress or pressure tensor

P Collisional stress tensor

P Kinetic stress tensor

P Momentum supply or phase interaction, N/m3

Quantity like mass, momentum or energy

Volumetric flow rate of phase

Heat input into phase , J

Charge, electrical

Net rate of heat outflow out of phase i, kW/m3

q Conduction like flux vector of fluctuation energy

R Ideal gas law constant, J/mol-K

Re Reynolds number

Radius of particle or radial coordinate

Bubble radius

Rate of reaction of component , mol/m3-s

r Position vector

r Center of mass position vector

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