Fluid Mechanics for Chemical Engineering

Mathieu Mory, Université de Pau et des pays de l'Adour, France.

• Preface xiiiPART I. ELEMENTS IN FLUID MECHANICS 1Chapter 1. Local Equations of Fluid Mechanics 31.1. Forces, stress tensor, and pressure 41.2. Navier–Stokes equations in Cartesian coordinates 61.3. The plane Poiseuille flow 101.4. Navier–Stokes equations in cylindrical coordinates: Poiseuille flow in a circular cylindrical pipe 131.5. Plane Couette flow 171.6. The boundary layer concept 191.7. Solutions of Navier–Stokes equations where a gravity field is present, hydrostatic pressure 221.8. Buoyancy force 251.9. Some conclusions on the solutions of Navier–Stokes equations 26Chapter 2. Global Theorems of Fluid Mechanics 292.1. Euler equations in an intrinsic coordinate system 302.2. Bernoulli’s theorem 312.3. Pressure variation in a direction normal to a streamline 332.4. Momentum theorem 362.5. Evaluating friction for a steady-state flow in a straight pipe 382.6. Pressure drop in a sudden expansion (Borda calculation) 402.7. Using the momentum theorem in the presence of gravity 432.8. Kinetic energy balance and dissipation 432.9. Application exercises 47Exercise 2.I: Force exerted on a bend 47Exercise 2.II: Emptying a tank 48Exercise 2.III: Pressure drop in a sudden expansion and heating 48Exercise 2.IV: Streaming flow on an inclined plane 49Exercise 2.V: Impact of a jet on a sloping plate 50Exercise 2.VI: Operation of a hydro-ejector 51Exercise 2.VII: Bypass flow 53Chapter 3. Dimensional Analysis 553.1. Principle of dimensional analysis, Vaschy–Buckingham theorem 563.2. Dimensional study of Navier–Stokes equations 613.3. Similarity theory 633.4. An application example: fall velocity of a spherical particle in a viscous fluid at rest 653.5. Application exercises 69Exercise 3.I: Time of residence and chemical reaction in a stirred reactor 69Exercise 3.II: Boundary layer on an oscillating plate 69Exercise 3.III: Head capacity curve of a centrifugal pump 70Chapter 4. Steady-State Hydraulic Circuits 734.1. Operating point of a hydraulic circuit 734.2. Steady-state flows in straight pipes: regular head loss 784.3. Turbulence in a pipe and velocity profile of the flow 814.4. Singular head losses 834.5. Notions on cavitation 874.6. Application exercises 88Exercise 4.I: Regular head loss measurement and flow rate in a pipe 88Exercise 4.II: Head loss and cavitation in a hydraulic circuit 89Exercise 4.III: Ventilation of a road tunnel 91Exercise 4.IV: Sizing a network of heating pipes 92Exercise 4.V: Head, flow rate, and output of a hydroelectric power plant 934.7. Bibliography 93Chapter 5. Pumps 955.1. Centrifugal pumps 965.2. Classification of turbo pumps and axial pumps 1055.3. Positive displacement pumps 106Chapter 6. Transient Flows in Hydraulic Circuits: Water Hammers 1116.1. Sound propagation in a rigid pipe 1116.2. Over-pressures associated with a water hammer: characteristic time of a hydraulic circuit 1156.3. Linear elasticity of a solid body: sound propagation in an elastic pipe 1186.4. Water hammer prevention devices 120Exercise 121Chapter 7. Notions of Rheometry 1237.1. Rheology 1237.2. Strain, strain rate, solids and fluids 1267.3. A rheology experiment: behavior of a material subjected to shear 1297.4. The circular cylindrical rheometer (or Couette rheometer) 1327.5. Application exercises 136Exercise 7.I: Rheometry and flow of a Bingham fluid in a pipe 136Exercise 7.II: Cone/plate rheometer 137PART II. MIXING AND CHEMICAL REACTIONS 139Chapter 8. Large Scales in Turbulence: Turbulent Diffusion – Dispersion 1418.1. Introduction 1418.2. Concept of average in the turbulent sense, steady turbulence, and homogeneous turbulence 1428.3. Average velocity and RMS turbulent velocity 1458.4. Length scale of turbulence: integral scale 1468.5. Turbulent flux of a scalar quantity: averaged diffusion equation 1518.6. Modeling turbulent fluxes using the mixing length model 1538.7. Turbulent dispersion 1578.8. The k-ε model 1598.9. Appendix: solution of a diffusion equation in cylindrical coordinates 1638.10. Application exercises 165Exercise 8.I: Dispersion of fluid streaks introduced into a pipe by a network of capillary tubes 165Exercise 8.II: Grid turbulence and k-ε modeling 167Chapter 9. Hydrodynamics and Residence Time Distribution – Stirring 1719.1. Turbulence and residence time distribution 1729.2. Stirring 1789.3. Appendix: interfaces and the notion of surface tension 185Chapter 10. Micromixing and Macromixing 19310.1. Introduction 19310.2. Characterization of the mixture: segregation index 19510.3. The dynamics of mixing 19810.4. Homogenization of a scalar field by molecular diffusion: micromixing 20110.5. Diffusion and chemical reactions 20210.6. Macromixing, micromixing, and chemical reactions 20410.7. Experimental demonstration of the micromixing process 205Chapter 11. Small Scales in Turbulence 20911.1. Notion of signal processing, expansion of a time signal into Fourier series 21011.2. Turbulent energy spectrum 21311.3. Kolmogorov’s theory 21411.4. The Kolmogorov scale 21811.5. Application to macromixing, micromixing and chemical reaction 22111.6. Application exercises 222Exercise 11.I: Mixing in a continuous stirred tank reactor 222Exercise 11.II: Mixing and combustion 223Exercise 11.III: Laminar and turbulent diffusion flames 225Chapter 12. Micromixing Models 22912.1. Introduction 22912.2. CD model 23312.3. Model of interaction by exchange with the mean 24512.4. Conclusion 25012.5. Application exercise 251Exercise 12.I: Implementation of the IEM model for a slow or fast chemical reaction 251PART III. MECHANICAL SEPARATION 253Chapter 13. Physical Description of a Particulate Medium Dispersed Within a Fluid 25513.1. Introduction 25513.2. Solid particles 25713.3 Fluid particles 27013.4. Mass balance of a mechanical separation process 273Chapter 14. Flows in Porous Media 27714.1. Consolidated porous media; non-consolidated porous media, and geometrical characterization 27814.2. Darcy’s law 28014.3. Examples of application of Darcy’s law 28214.4. Modeling Darcy’s law through an analogy with the flow inside a network of capillary tubes 28914.5. Modeling permeability, Kozeny-Carman formula 29114.6. Ergun’s relation 29314.7. Draining by pressing 29314.8. The reverse osmosis process 29814.9. Energetics of membrane separation 30114.10. Application exercises 301Exercise: Study of a seawater desalination process 301Chapter 15. Particles Within the Gravity Field 30515.1. Settling of a rigid particle in a fluid at rest 30615.2. Settling of a set of solid particles in a fluid at rest 30915.3. Settling or rising of a fluid particle in a fluid at rest 31215.4. Particles being held in suspension by Brownian motion 31515.5. Particles being held in suspension by turbulence 31915.6. Fluidized beds 32115.7. Application exercises 329Exercise 15.I: Distribution of particles in suspension and grain size sorting resulting from settling 329Exercise 15.II: Fluidization of a bimodal distribution of particles 330Chapter 16. Movement of a Solid Particle in a Fluid Flow 33116.1. Notations and hypotheses 33216.2. The Basset, Boussinesq, Oseen, and Tchen equation 33316.3. Movement of a particle subjected to gravity in a fluid at rest 33616.4. Movement of a particle in a steady, unidirectional shear flow 33916.5. Lift force applied to a particle by a unidirectional flow 34116.6. Centrifugation of a particle in a rotating flow 35016.7. Applications to the transport of a particle in a turbulent flow or in a laminar flow 355Chapter 17. Centrifugal Separation 35917.1 Rotating flows, circulation, and velocity curl 36017.2. Some examples of rotating flows 36417.3. The principle of centrifugal separation 37717.4. Centrifuge decanters 38117.5. Centrifugal separators 38517.6. Centrifugal filtration 38817.7. Hydrocyclones 39117.8. Energetics of centrifugal separation 39617.9. Application exercise 397Exercise 17.I: Grain size sorting in a hydrocyclone 397Chapter 18. Notions on Granular Materials 40118.1. Static friction: Coulomb’s law of friction 40218.2. Non-cohesive granular materials: Angle of repose, angle of internal friction 40318.3. Microscopic approach to a granular material 40518.4. Macroscopic modeling of the equilibrium of a granular material in a silo 40718.5. Flow of a granular material: example of an hourglass 413Physical Properties of Common Fluids 417Index 419

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