Numerous industrial systems or natural environments involve
multiphase flows with heat and mass transfer. The authors of this
book present the physical modeling of these flows, in a unified
way, which can include various physical aspects and several levels
of complexity.

Thermal engineering and nuclear reactors; the extraction and
transport of petroleum products; diesel and rocket engines;
chemical engineering reactors and fluidized beds; smoke or aerosol
dispersion; landslides and avalanches & #8722; the modeling of
multiphase flows with heat and mass transfer for all these
situations can be developed following a common methodology. This
book is devoted to the description of the mathematical bases of how
to incorporate adequate physical ingredients in agreement with
known experimental facts and how to make the model evolve according
to the required complexity.

Contents

Part 1. Approach and General Equations

1. Towards a Unified Description of Multiphase Flows.

2. Instant Equations for a Piecewise Continuous Medium.

3. Description of a "Mean Multiphase Medium".

4. Equations for the Mean Continuous Medium.

Part 2. Modeling: A Single Approach Adaptable to Multiple
Applications

5. The Modeling of Interphase Exchanges.

6. Modeling Turbulent Dispersion Fluxes.

7. Modeling the Mean Gas-Liquid Interface Area per Unit
Volume.

8. "Large Eddy Simulation" Style Models.

9. Contribution of Thermodynamics of Irreversible Processes.

10. Experimental Methods.

11. Some Experimental Results Pertaining to Multiphase Flow
Properties that Are Still Little Understood.

Part 3. From Fluidized Beds to Granular Media

12. Fluidized Beds.

13. Generalizations for Granular Media.

14. Modeling of Cauchy Tensor of Sliding Contacts.

15. Modeling the Kinetic Cauchy Stress Tensor.

Part 4. Studying Fluctuations and Probability Densities

16. Fluctuations of the Gas Phase in Reactive Two-Phase
Media.

17. Temperature Fluctuations in Condensed Phases.

18. Study of the PDF for Velocity Fluctuations and Sizes of
Parcels.

About the Authors

Roland Borghi is Professor Emeritus at Ecole Centrale Marseille
in France and works as a consultant in the space, petrol and
automobile sectors. His research activities cover fluid mechanics,
combustion and flames, and multi-phase and granular flows. He was a
member of the CNRS scientific committee and a laureate of the
French Academy of Science.

Fabien Anselmet is Professor at Ecole Centrale Marseille in France.
His research activities focus on the turbulence of fluids and its
varied applications in industry and in fields linked to the
environment.
With a unified, didactic style, this text presents tangible models
of multiphase flows with heat and mass transfer with attention to
various levels of complexities. It addresses thermal engineering
and nuclear reactors, extraction and transport of petroleum
products, diesel engines and rocket engines, chemical engineering
reactors and fluidized beds, smoke or aerosol dispersion, and
landslides and avalanches. Engineers, researchers, and scientists
will appreciate the discussions of modeling principles, flows and
granular media, and fluctuations around averages.

Fabien Anselmet is Professor at Ecole Centrale Marseille, France.

Zusammenfassung
Numerous industrial systems or natural environments involve multiphase flows with heat and mass transfer. The authors of this book present the physical modeling of these flows, in a unified way, which can include various physical aspects and several levels of complexity.
Thermal engineering and nuclear reactors; the extraction and transport of petroleum products; diesel and rocket engines; chemical engineering reactors and fluidized beds; smoke or aerosol dispersion; landslides and avalanches the modeling of multiphase flows with heat and mass transfer for all these situations can be developed following a common methodology. This book is devoted to the description of the mathematical bases of how to incorporate adequate physical ingredients in agreement with known experimental facts and how to make the model evolve according to the required complexity.

Contents

Part 1. Approach and General Equations
1. Towards a Unified Description of Multiphase Flows.
2. Instant Equations for a Piecewise Continuous Medium.
3. Description of a Mean Multiphase Medium.
4. Equations for the Mean Continuous Medium.
Part 2. Modeling: A Single Approach Adaptable to Multiple Applications
5. The Modeling of Interphase Exchanges.
6. Modeling Turbulent Dispersion Fluxes.
7. Modeling the Mean GasLiquid Interface Area per Unit Volume.
8. Large Eddy Simulation Style Models.
9. Contribution of Thermodynamics of Irreversible Processes.
10. Experimental Methods.
11. Some Experimental Results Pertaining to Multiphase Flow Properties that Are Still Little Understood.
Part 3. From Fluidized Beds to Granular Media
12. Fluidized Beds.
13. Generalizations for Granular Media.
14. Modeling of Cauchy Tensor of Sliding Contacts.
15. Modeling the Kinetic Cauchy Stress Tensor.
Part 4. Studying Fluctuations and Probability Densities
16. Fluctuations of the Gas Phase in Reactive Two-Phase Media.
17. Temperature Fluctuations in Condensed Phases.
18. Study of the PDF for Velocity Fluctuations and Sizes of Parcels.

About the Authors

Roland Borghi is Professor Emeritus at Ecole Centrale Marseille in France and works as a consultant in the space, petrol and automobile sectors. His research activities cover fluid mechanics, combustion and flames, and multi-phase and granular flows. He was a member of the CNRS scientific committee and a laureate of the French Academy of Science.
Fabien Anselmet is Professor at Ecole Centrale Marseille in France. His research activities focus on the turbulence of fluids and its varied applications in industry and in fields linked to the environment.

Acknowledgments xi

Introduction xiii

Part 1. Approach and General Equations 1

Chapter 1. Towards a Unified Description of Multiphase Flows 3

1.1. Continuous approach and kinetic approach 3

1.2. EulerianLagrangian and Eulerian formulations 7

Chapter 2. Instant Equations for a Piecewise Continuous Medium 9

2.1. Integral and differential forms of balance equations 10

2.2. Phase mass balance equations in a piecewise continuous medium 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 Multiphase Medium 29

3.1. The need for a mean description 29

3.2. How are mean values defined? 31

3.…