DESCRIPTION
The book aims at providing to master and PhD students the basic knowledge in fluid mechanics for chemical engineers. Applications to mixing and reaction and to mechanical separation processes are addressed.
The first part of the book presents the principles of fluid mechanics used by chemical engineers, with a focus on global theorems for describing the behavior of hydraulic systems. The second part deals with turbulence and its application for stirring, mixing and chemical reaction. The third part addresses mechanical separation processes by considering the dynamics of particles in a flow and the processes of filtration, fluidization and centrifugation. The mechanics of granular media is finally discussed.
Mathieu Mory, Université de Pau et des pays de l'Adour, France.
Preface xiii
PART I. ELEMENTS IN FLUID MECHANICS 1
Chapter 1. Local Equations of Fluid Mechanics 3
1.1. Forces, stress tensor, and pressure 4
1.2. Navier–Stokes equations in Cartesian coordinates 6
1.3. The plane Poiseuille flow 10
1.4. Navier–Stokes equations in cylindrical coordinates: Poiseuille flow in a circular cylindrical pipe 13
1.5. Plane Couette flow 17
1.6. The boundary layer concept 19
1.7. Solutions of Navier–Stokes equations where a gravity field is present, hydrostatic pressure 22
1.8. Buoyancy force 25
1.9. Some conclusions on the solutions of Navier–Stokes equations 26
Chapter 2. Global Theorems of Fluid Mechanics 29
2.1. Euler equations in an intrinsic coordinate system 30
2.2. Bernoulli’s theorem 31
2.3. Pressure variation in a direction normal to a streamline 33
2.4. Momentum theorem 36
2.5. Evaluating friction for a steady-state flow in a straight pipe 38
2.6. Pressure drop in a sudden expansion (Borda calculation) 40
2.7. Using the momentum theorem in the presence of gravity 43
2.8. Kinetic energy balance and dissipation 43
2.9. Application exercises 47
Exercise 2.I: Force exerted on a bend 47
Exercise 2.II: Emptying a tank 48
Exercise 2.III: Pressure drop in a sudden expansion and heating 48
Exercise 2.IV: Streaming flow on an inclined plane 49
Exercise 2.V: Impact of a jet on a sloping plate 50
Exercise 2.VI: Operation of a hydro-ejector 51
Exercise 2.VII: Bypass flow 53
Chapter 3. Dimensional Analysis 55
3.1. Principle of dimensional analysis, Vaschy–Buckingham theorem 56
3.2. Dimensional study of Navier–Stokes equations 61
3.3. Similarity theory 63
3.4. An application example: fall velocity of a spherical particle in a viscous fluid at rest 65
3.5. Application exercises 69
Exercise 3.I: Time of residence and chemical reaction in a stirred reactor 69
Exercise 3.II: Boundary layer on an oscillating plate 69
Exercise 3.III: Head capacity curve of a centrifugal pump 70
Chapter 4. Steady-State Hydraulic Circuits 73
4.1. Operating point of a hydraulic circuit 73
4.2. Steady-state flows in straight pipes: regular head loss 78
4.3. Turbulence in a pipe and velocity profile of the flow 81
4.4. Singular head losses 83
4.5. Notions on cavitation 87
4.6. Application exercises 88
Exercise 4.I: Regular head loss measurement and flow rate in a pipe 88
Exercise 4.II: Head loss and cavitation in a hydraulic circuit 89
Exercise 4.III: Ventilation of a road tunnel 91
Exercise 4.IV: Sizing a network of heating pipes 92
Exercise 4.V: Head, flow rate, and output of a hydroelectric power plant 93
4.7. Bibliography 93
Chapter 5. Pumps 95
5.1. Centrifugal pumps 96
5.2. Classification of turbo pumps and axial pumps 105
5.3. Positive displacement pumps 106
Chapter 6. Transient Flows in Hydraulic Circuits: Water Hammers 111
6.1. Sound propagation in a rigid pipe 111
6.2. Over-pressures associated with a water hammer: characteristic time of a hydraulic circuit 115
6.3. Linear elasticity of a solid body: sound propagation in an elastic pipe 118
6.4. Water hammer prevention devices 120
Exercise 121
Chapter 7. Notions of Rheometry 123
7.1. Rheology 123
7.2. Strain, strain rate, solids and fluids 126
7.3. A rheology experiment: behavior of a material subjected to shear 129
7.4. The circular cylindrical rheometer (or Couette rheometer) 132
7.5. Application exercises 136
Exercise 7.I: Rheometry and flow of a Bingham fluid in a pipe 136
Exercise 7.II: Cone/plate rheometer 137
PART II. MIXING AND CHEMICAL REACTIONS 139
Chapter 8. Large Scales in Turbulence: Turbulent Diffusion – Dispersion 141
8.1. Introduction 141
8.2. Concept of average in the turbulent sense, steady turbulence, and homogeneous turbulence 142
8.3. Average velocity and RMS turbulent velocity 145
8.4. Length scale of turbulence: integral scale 146
8.5. Turbulent flux of a scalar quantity: averaged diffusion equation 151
8.6. Modeling turbulent fluxes using the mixing length model 153
8.7. Turbulent dispersion 157
8.8. The k-ε model 159
8.9. Appendix: solution of a diffusion equation in cylindrical coordinates 163
8.10. Application exercises 165
Exercise 8.I: Dispersion of fluid streaks introduced into a pipe by a network of capillary tubes 165
Exercise 8.II: Grid turbulence and k-ε modeling 167
Chapter 9. Hydrodynamics and Residence Time Distribution – Stirring 171
9.1. Turbulence and residence time distribution 172
9.2. Stirring 178
9.3. Appendix: interfaces and the notion of surface tension 185
Chapter 10. Micromixing and Macromixing 193
10.1. Introduction 193
10.2. Characterization of the mixture: segregation index 195
10.3. The dynamics of mixing 198
10.4. Homogenization of a scalar field by molecular diffusion: micromixing 201
10.5. Diffusion and chemical reactions 202
10.6. Macromixing, micromixing, and chemical reactions 204
10.7. Experimental demonstration of the micromixing process 205
Chapter 11. Small Scales in Turbulence 209
11.1. Notion of signal processing, expansion of a time signal into Fourier series 210
11.2. Turbulent energy spectrum 213
11.3. Kolmogorov’s theory 214
11.4. The Kolmogorov scale 218
11.5. Application to macromixing, micromixing and chemical reaction 221
11.6. Application exercises 222
Exercise 11.I: Mixing in a continuous stirred tank reactor 222
Exercise 11.II: Mixing and combustion 223
Exercise 11.III: Laminar and turbulent diffusion flames 225
Chapter 12. Micromixing Models 229
12.1. Introduction 229
12.2. CD model 233
2.3. Model of interaction by exchange with the mean 245
12.4. Conclusion 250
12.5. Application exercise 251
Exercise 12.I: Implementation of the IEM model for a slow or fast chemical reaction 251
PART III. MECHANICAL SEPARATION 253
Chapter 13. Physical Description of a Particulate Medium Dispersed Within a Fluid 255
13.1. Introduction 255
13.2. Solid particles 257
13.3 Fluid particles 270
13.4. Mass balance of a mechanical separation process 273
Chapter 14. Flows in Porous Media 277
14.1. Consolidated porous media; non-consolidated porous media, and geometrical characterization 278
14.2. Darcy’s law 280
14.3. Examples of application of Darcy’s law 282
14.4. Modeling Darcy’s law through an analogy with the flow inside a network of capillary tubes 289
14.5. Modeling permeability, Kozeny-Carman formula 291
14.6. Ergun’s relation 293
14.7. Draining by pressing 293
14.8. The reverse osmosis process 298
14.9. Energetics of membrane separation 301
14.10. Application exercises 301
Exercise: Study of a seawater desalination process 301
Chapter 15. Particles Within the Gravity Field 305
15.1. Settling of a rigid particle in a fluid at rest 306
15.2. Settling of a set of solid particles in a fluid at rest 309
15.3. Settling or rising of a fluid particle in a fluid at rest 312
15.4. Particles being held in suspension by Brownian motion 315
15.5. Particles being held in suspension by turbulence 319
15.6. Fluidized beds 321
15.7. Application exercises 329
Exercise 15.I: Distribution of particles in suspension and grain size sorting resulting from settling 329
Exercise 15.II: Fluidization of a bimodal distribution of particles 330
Chapter 16. Movement of a Solid Particle in a Fluid Flow 331
16.1. Notations and hypotheses 332
16.2. The Basset, Boussinesq, Oseen, and Tchen equation 333
16.3. Movement of a particle subjected to gravity in a fluid at rest 336
16.4. Movement of a particle in a steady, unidirectional shear flow 339
16.5. Lift force applied to a particle by a unidirectional flow 341
16.6. Centrifugation of a particle in a rotating flow 350
16.7. Applications to the transport of a particle in a turbulent flow or in a laminar flow 355
Chapter 17. Centrifugal Separation 359
17.1 Rotating flows, circulation, and velocity curl 360
17.2. Some examples of rotating flows 364
17.3. The principle of centrifugal separation 377
17.4. Centrifuge decanters 381
17.5. Centrifugal separators 385
17.6. Centrifugal filtration 388
17.7. Hydrocyclones 391
17.8. Energetics of centrifugal separation 396
17.9. Application exercise 397
Exercise 17.I: Grain size sorting in a hydrocyclone 397
Chapter 18. Notions on Granular Materials 401
18.1. Static friction: Coulomb’s law of friction 402
18.2. Non-cohesive granular materials: Angle of repose, angle of internal friction 403
18.3. Microscopic approach to a granular material 405
18.4. Macroscopic modeling of the equilibrium of a granular material in a silo 407
18.5. Flow of a granular material: example of an hourglass 413
Physical Properties of Common Fluids 417
Index 419
PART I. ELEMENTS IN FLUID MECHANICS 1
Chapter 1. Local Equations of Fluid Mechanics 3
1.1. Forces, stress tensor, and pressure 4
1.2. Navier–Stokes equations in Cartesian coordinates 6
1.3. The plane Poiseuille flow 10
1.4. Navier–Stokes equations in cylindrical coordinates: Poiseuille flow in a circular cylindrical pipe 13
1.5. Plane Couette flow 17
1.6. The boundary layer concept 19
1.7. Solutions of Navier–Stokes equations where a gravity field is present, hydrostatic pressure 22
1.8. Buoyancy force 25
1.9. Some conclusions on the solutions of Navier–Stokes equations 26
Chapter 2. Global Theorems of Fluid Mechanics 29
2.1. Euler equations in an intrinsic coordinate system 30
2.2. Bernoulli’s theorem 31
2.3. Pressure variation in a direction normal to a streamline 33
2.4. Momentum theorem 36
2.5. Evaluating friction for a steady-state flow in a straight pipe 38
2.6. Pressure drop in a sudden expansion (Borda calculation) 40
2.7. Using the momentum theorem in the presence of gravity 43
2.8. Kinetic energy balance and dissipation 43
2.9. Application exercises 47
Exercise 2.I: Force exerted on a bend 47
Exercise 2.II: Emptying a tank 48
Exercise 2.III: Pressure drop in a sudden expansion and heating 48
Exercise 2.IV: Streaming flow on an inclined plane 49
Exercise 2.V: Impact of a jet on a sloping plate 50
Exercise 2.VI: Operation of a hydro-ejector 51
Exercise 2.VII: Bypass flow 53
Chapter 3. Dimensional Analysis 55
3.1. Principle of dimensional analysis, Vaschy–Buckingham theorem 56
3.2. Dimensional study of Navier–Stokes equations 61
3.3. Similarity theory 63
3.4. An application example: fall velocity of a spherical particle in a viscous fluid at rest 65
3.5. Application exercises 69
Exercise 3.I: Time of residence and chemical reaction in a stirred reactor 69
Exercise 3.II: Boundary layer on an oscillating plate 69
Exercise 3.III: Head capacity curve of a centrifugal pump 70
Chapter 4. Steady-State Hydraulic Circuits 73
4.1. Operating point of a hydraulic circuit 73
4.2. Steady-state flows in straight pipes: regular head loss 78
4.3. Turbulence in a pipe and velocity profile of the flow 81
4.4. Singular head losses 83
4.5. Notions on cavitation 87
4.6. Application exercises 88
Exercise 4.I: Regular head loss measurement and flow rate in a pipe 88
Exercise 4.II: Head loss and cavitation in a hydraulic circuit 89
Exercise 4.III: Ventilation of a road tunnel 91
Exercise 4.IV: Sizing a network of heating pipes 92
Exercise 4.V: Head, flow rate, and output of a hydroelectric power plant 93
4.7. Bibliography 93
Chapter 5. Pumps 95
5.1. Centrifugal pumps 96
5.2. Classification of turbo pumps and axial pumps 105
5.3. Positive displacement pumps 106
Chapter 6. Transient Flows in Hydraulic Circuits: Water Hammers 111
6.1. Sound propagation in a rigid pipe 111
6.2. Over-pressures associated with a water hammer: characteristic time of a hydraulic circuit 115
6.3. Linear elasticity of a solid body: sound propagation in an elastic pipe 118
6.4. Water hammer prevention devices 120
Exercise 121
Chapter 7. Notions of Rheometry 123
7.1. Rheology 123
7.2. Strain, strain rate, solids and fluids 126
7.3. A rheology experiment: behavior of a material subjected to shear 129
7.4. The circular cylindrical rheometer (or Couette rheometer) 132
7.5. Application exercises 136
Exercise 7.I: Rheometry and flow of a Bingham fluid in a pipe 136
Exercise 7.II: Cone/plate rheometer 137
PART II. MIXING AND CHEMICAL REACTIONS 139
Chapter 8. Large Scales in Turbulence: Turbulent Diffusion – Dispersion 141
8.1. Introduction 141
8.2. Concept of average in the turbulent sense, steady turbulence, and homogeneous turbulence 142
8.3. Average velocity and RMS turbulent velocity 145
8.4. Length scale of turbulence: integral scale 146
8.5. Turbulent flux of a scalar quantity: averaged diffusion equation 151
8.6. Modeling turbulent fluxes using the mixing length model 153
8.7. Turbulent dispersion 157
8.8. The k-ε model 159
8.9. Appendix: solution of a diffusion equation in cylindrical coordinates 163
8.10. Application exercises 165
Exercise 8.I: Dispersion of fluid streaks introduced into a pipe by a network of capillary tubes 165
Exercise 8.II: Grid turbulence and k-ε modeling 167
Chapter 9. Hydrodynamics and Residence Time Distribution – Stirring 171
9.1. Turbulence and residence time distribution 172
9.2. Stirring 178
9.3. Appendix: interfaces and the notion of surface tension 185
Chapter 10. Micromixing and Macromixing 193
10.1. Introduction 193
10.2. Characterization of the mixture: segregation index 195
10.3. The dynamics of mixing 198
10.4. Homogenization of a scalar field by molecular diffusion: micromixing 201
10.5. Diffusion and chemical reactions 202
10.6. Macromixing, micromixing, and chemical reactions 204
10.7. Experimental demonstration of the micromixing process 205
Chapter 11. Small Scales in Turbulence 209
11.1. Notion of signal processing, expansion of a time signal into Fourier series 210
11.2. Turbulent energy spectrum 213
11.3. Kolmogorov’s theory 214
11.4. The Kolmogorov scale 218
11.5. Application to macromixing, micromixing and chemical reaction 221
11.6. Application exercises 222
Exercise 11.I: Mixing in a continuous stirred tank reactor 222
Exercise 11.II: Mixing and combustion 223
Exercise 11.III: Laminar and turbulent diffusion flames 225
Chapter 12. Micromixing Models 229
12.1. Introduction 229
12.2. CD model 233
2.3. Model of interaction by exchange with the mean 245
12.4. Conclusion 250
12.5. Application exercise 251
Exercise 12.I: Implementation of the IEM model for a slow or fast chemical reaction 251
PART III. MECHANICAL SEPARATION 253
Chapter 13. Physical Description of a Particulate Medium Dispersed Within a Fluid 255
13.1. Introduction 255
13.2. Solid particles 257
13.3 Fluid particles 270
13.4. Mass balance of a mechanical separation process 273
Chapter 14. Flows in Porous Media 277
14.1. Consolidated porous media; non-consolidated porous media, and geometrical characterization 278
14.2. Darcy’s law 280
14.3. Examples of application of Darcy’s law 282
14.4. Modeling Darcy’s law through an analogy with the flow inside a network of capillary tubes 289
14.5. Modeling permeability, Kozeny-Carman formula 291
14.6. Ergun’s relation 293
14.7. Draining by pressing 293
14.8. The reverse osmosis process 298
14.9. Energetics of membrane separation 301
14.10. Application exercises 301
Exercise: Study of a seawater desalination process 301
Chapter 15. Particles Within the Gravity Field 305
15.1. Settling of a rigid particle in a fluid at rest 306
15.2. Settling of a set of solid particles in a fluid at rest 309
15.3. Settling or rising of a fluid particle in a fluid at rest 312
15.4. Particles being held in suspension by Brownian motion 315
15.5. Particles being held in suspension by turbulence 319
15.6. Fluidized beds 321
15.7. Application exercises 329
Exercise 15.I: Distribution of particles in suspension and grain size sorting resulting from settling 329
Exercise 15.II: Fluidization of a bimodal distribution of particles 330
Chapter 16. Movement of a Solid Particle in a Fluid Flow 331
16.1. Notations and hypotheses 332
16.2. The Basset, Boussinesq, Oseen, and Tchen equation 333
16.3. Movement of a particle subjected to gravity in a fluid at rest 336
16.4. Movement of a particle in a steady, unidirectional shear flow 339
16.5. Lift force applied to a particle by a unidirectional flow 341
16.6. Centrifugation of a particle in a rotating flow 350
16.7. Applications to the transport of a particle in a turbulent flow or in a laminar flow 355
Chapter 17. Centrifugal Separation 359
17.1 Rotating flows, circulation, and velocity curl 360
17.2. Some examples of rotating flows 364
17.3. The principle of centrifugal separation 377
17.4. Centrifuge decanters 381
17.5. Centrifugal separators 385
17.6. Centrifugal filtration 388
17.7. Hydrocyclones 391
17.8. Energetics of centrifugal separation 396
17.9. Application exercise 397
Exercise 17.I: Grain size sorting in a hydrocyclone 397
Chapter 18. Notions on Granular Materials 401
18.1. Static friction: Coulomb’s law of friction 402
18.2. Non-cohesive granular materials: Angle of repose, angle of internal friction 403
18.3. Microscopic approach to a granular material 405
18.4. Macroscopic modeling of the equilibrium of a granular material in a silo 407
18.5. Flow of a granular material: example of an hourglass 413
Physical Properties of Common Fluids 417
Index 419
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