ISBN-10:
1848216173
ISBN-13:
9781848216174
Pub. Date:
12/09/2013
Publisher:
Wiley
Turbulent Multiphase Flows with Heat and Mass Transfer / Edition 1

Turbulent Multiphase Flows with Heat and Mass Transfer / Edition 1

by Roland Borghi, Fabien Anselmet
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Product Details

ISBN-13: 9781848216174
Publisher: Wiley
Publication date: 12/09/2013
Series: ISTE Series
Pages: 480
Product dimensions: 6.30(w) x 9.10(h) x 1.30(d)

About the Author

Roland Borghi is Professor Emeritus at Ecole Centrale Marseille, France.

Fabien Anselmet is Professor at Ecole Centrale Marseille, France.

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Table of Contents

Acknowledgments xi

Introduction xiii

PART 1. APPROACH AND GENERAL EQUATIONS 1

Chapter 1. Towards a Unified Description of Multiphase Flows3

1.1. Continuous approach and kinetic approach 3

1.2. Eulerian–Lagrangian and Eulerianformulations 7

Chapter 2. Instant Equations for a Piecewise ContinuousMedium 9

2.1. Integral and differential forms of balanceequations 10

2.2. Phase mass balance equations in a piecewise continuousmedium 13

2.3. Momentum balances 17

2.4. Energy balances 21

2.5. Position and interface area balance equations 23

2.6. Extension for a fluid phase that is a mixture 25

2.7. Completing the description of the medium 27

Chapter 3. Description of a “Mean MultiphaseMedium” 29

3.1. The need for a mean description 29

3.2. How are mean values defined? 31

3.2.1. Temporal average 31

3.2.2. Volumetric average 32

3.2.3. Statistical average 34

3.2.4. Filtered average 35

3.3. Which average to choose, according to their advantages anddisadvantages? 37

Chapter 4. Equations for the Mean Continuous Medium39

4.1. Global balance equations for the mean medium 39

4.1.1. Total mass 39

4.1.2. Total momentum 40

4.1.3. Total energy 41

4.2. Balance equations for the phases of a meanmedium 42

4.2.1. Phase mass 43

4.2.2. Phase momentum 44

4.2.3. Energies of each phase 47

4.2.4. Phase volume 49

4.3. Complete representation of the mean medium 49

4.3.1. Global representation 50

4.3.2. Multifluid representation 51

4.4. Mean equations of state 55

4.5. Extensions 58

4.5.1. Extension when a fluid phase is a mixture 58

4.5.2. Extension for dispersed media 59

4.6. Boundary conditions 61

PART 2. MODELING: A SINGLE APPROACH ADAPTABLE TO MULTIPLEAPPLICATIONS 67

Chapter 5. The Modeling of InterphaseExchanges 69

5.1. General methodology 69

5.2. Interface between phases and its mean area per unit ofvolume 71

5.2.1. Case of a suspension of liquid or solidparticles 71

5.2.2. Case of a medium containing parcels of variable shapesand sizes 72

5.2.3. Case of a suspension of particles of constant and knownsizes 74

5.3. Forces of contact and friction between phases 75

5.3.1. Pressure forces on spherical particles in a non-viscousflow 76

5.3.2. Friction on solid particles in steady flow 80

5.3.3. Slightly curved liquid–gas interfaces 87

5.3.4. Drops or bubbles 93

5.4. Heat transfers at the surface of a particle, without massexchange 96

5.5. Heat and mass transfers during boiling 99

5.5.1. Slightly curved liquid–gas interfaces 99

5.5.2. Bubbles 105

5.6. Mass and heat exchanges by vaporization 107

5.6.1. Mass transfer by evaporation at a flatinterface 107

5.6.2. Evaporation of a drop 113

5.6.3. Combustion of a drop 117

Chapter 6. Modeling Turbulent DispersionFluxes 119

6.1. Global modeling 119

6.1.1. General information 119

6.1.2. Kinetic energy of the “globalfluctuations” 123

6.1.3. Modeling the kinetic energy of thefluctuations 128

6.1.4. Length scales for fluctuations and time scale for thedissipation of kinetic energy of fluctuations 132

6.1.5. Further studies on the dispersion flux of aphase 137

6.2. “Multifluid” modeling 147

6.2.1. The kinetic energy of the fluctuations in each phase149

6.2.2. Modeling the balance equations of the kinetic energies ofturbulence 152

6.2.3. The modeling of time or spatial scales 158

6.2.4. Modeling of the Reynolds tensor for everyphase 162

Chapter 7. Modeling the Mean Gas–Liquid Interface Areaper Unit Volume 165

7.1. Introduction 165

7.2. Initial equation for the mean interface area per unitvolume 166

7.3. Model of the mean interface area during the“atomization” of a liquid jet 168

7.4. Effects of vaporization on the interface area 172

Chapter 8. “Large Eddy Simulation” StyleModels 175

8.1. Introduction 175

8.2. Filtered equations and the nature of the models to beprovided 177

8.3. Classic LES modeling for SGS additional fluxes 181

8.3.1. Reminder of LES in single-phase, constant densityturbulent flows 181

8.3.2. Toward an extension for multiphase flows 183

8.4. Subgrid modeling of the interface area per unitvolume 185

8.5. Partially Integrated Turbulence Modeling 188

Chapter 9. Contribution of Thermodynamics of IrreversibleProcesses 191

9.1. Global two-phase medium models 192

9.1.1. Entropy of a mean two-phase medium using the Prandtlmodel 194

9.1.2. Entropy for the k–ε model, in a medium with avariable density 200

9.2. Contribution of thermodynamics to multifluidmodels 206

Chapter 10. Experimental Methods 213

10.1. Introduction 213

10.2. Intrusive methods 214

10.2.1. Pitot tubes 215

10.2.2. Hot films 216

10.2.3. Optical needle probes (single probes, bi-probes andquadri-probes) 219

10.2.4. Wire networks 223

10.3. Non-intrusive methods 224

10.3.1. Particle image velocimetry (PIV) 225

10.3.2. Droplet tracking velocimetry 230

10.3.3. Laser Doppler anemometry (LDA) 234

10.3.4. Phase Doppler anemometry (PDA) 237

10.3.5. Ultrasonic Doppler Anemometry 241

10.3.6. Densimetry by attenuation of gamma, X-ray or neutronradiation 243

10.4. Advanced optical methods 245

10.4.1. Laser induced fluorescence 245

10.4.2. Interferometric methods (digital inline holography,Fourier interferometric imaging, ILIDS/IPI, rainbow) 252

Chapter 11. Some Experimental Results Pertaining toMultiphase Flow Properties that Are Still LittleUnderstood 265

11.1. Atomization/fragmentation of liquid jets 265

11.2. Isolated bubbles, bubbles in swarm and their effects oncarrier fluid 274

11.3. Boiling crisis 285

PART 3. FROM FLUIDIZED BEDS TO GRANULAR MEDIA 297

Chapter 12. Fluidized Beds 299

12.1. Introduction 299

12.1.1. Classification of different fluidizationregimes 299

12.1.2. Minimum fluidization and bubblingvelocities 304

12.2. Complete models for the dynamics of fluidizedbeds 306

12.2.1. Bubbling fluidization regime 307

12.2.2. Turbulent fluidization regime 315

12.3. Global models for chemical conversion in fluidizedbeds 321

12.3.1. Bubbling regime fluidizations 321

12.3.2. Fast fluidization regime 324

12.3.3. Turbulent fluidization regime 325

12.4. Global models for heat transfers in fluidizedbeds 328

12.4.1. Bubbling fluidization regime 328

12.4.2. Fast fluidization regimes – circulatingbeds 331

12.5. Conclusion 334

Chapter 13. Generalizations for GranularMedia 335

13.1. Introduction 335

13.2. Balance equations for mean granular media 336

13.3. Necessary closure approximations 342

13.4. Some already proposed methods 345

Chapter 14. Modeling of Cauchy Tensor of SlidingContacts 349

14.1. Hypotheses and basic equations 349

14.2. Unclosed balance equation for Cauchy tensor of slidingcontact 351

14.3. Closure approximations for irreversible terms 358

Chapter 15. Modeling the Kinetic Cauchy StressTensor 363

15.1. Prandtl–Bagnold modeling 364

15.2. K-lt or “turbulent granular gas” modeling366

15.3. Toward a general model for all regimes 371

15.4. Boundary conditions at walls 373

PART 4. STUDYING FLUCTUATIONS AND PROBABILITYDENSITIES 377

Chapter 16. Fluctuations of the Gas Phase in ReactiveTwo-Phase Media 379

16.1. Specificities of reactive two-phase media 379

16.2. Probability density of composition fluctuations of the gasphase 380

16.2.1. Instant basic equations of the gas medium 382

16.2.2. PDF equation 385

16.3. Modeling the terms due to exchanges betweenphases 390

16.3.1. Total mass exchange 390

16.3.2. Mass exchange for species 392

16.3.3. Heat exchange 393

16.4. Modeling micromixing and turbulent dispersion 395

16.4.1. The “micromixing” term in PDFequations 395

16.4.2. Turbulent diffusion terms in PDF equations 396

16.5. Practical use of PDF equations 397

Chapter 17. Temperature Fluctuations in CondensedPhases 399

17.1. Problems 399

17.2. Instantaneous equation for the temperature of the liquidphase 401

17.3. Equation for the PDF of the temperature of theliquid 403

17.4. Closure of the equation of the temperaturePDF 405

Chapter 18. Study of the PDF for Velocity Fluctuations andSizes of Parcels 409

18.1. Phase velocity PDF equation 410

18.2. Modeling the exchanges between phases and the internalinteractions 415

18.2.1. Terms of exchanges between phases 415

18.2.2. Internal dissipation and production of fluctuations418

18.3. Practical calculation of PDF 419

18.4. The study of the sizes of the dispersed phaseparcels 420

18.5. Eulerian–Lagrangian simulation of dispersedmedia 423

18.5.1. Lagrangian equations of the parcels 423

18.5.2. Stochastic simulations 426

Bibliography 431

Index 443

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