Fluid Mechanics for Chemical Engineering

<p>Preface xiii</p>
<p>PART I. ELEMENTS IN FLUID MECHANICS 1</p>
<p>Chapter 1. Local Equations of Fluid Mechanics 3</p>
<p>1.1. Forces, stress tensor, and pressure 4</p>
<p>1.2. Navier Stokes equations in Cartesian coordinates 6</p>
<p>1.3. The plane Poiseuille flow 10</p>
<p>1.4. Navier Stokes equations in cylindrical coordinates: Poiseuille flow in a circular cylindrical pipe 13</p>
<p>1.5. Plane Couette flow 17</p>
<p>1.6. The boundary layer concept 19</p>
<p>1.7. Solutions of Navier Stokes equations where a gravity field is present, hydrostatic pressure 22</p>
<p>1.8. Buoyancy force 25</p>
<p>1.9. Some conclusions on the solutions of Navier Stokes equations 26</p>
<p>Chapter 2. Global Theorems of Fluid Mechanics 29</p>
<p>2.1. Euler equations in an intrinsic coordinate system 30</p>
<p>2.2. Bernoulli s theorem 31</p>
<p>2.3. Pressure variation in a direction normal to a streamline 33</p>
<p>2.4. Momentum theorem 36</p>
<p>2.5. Evaluating friction for a steady–state flow in a straight pipe 38</p>
<p>2.6. Pressure drop in a sudden expansion (Borda calculation) 40</p>
<p>2.7. Using the momentum theorem in the presence of gravity 43</p>
<p>2.8. Kinetic energy balance and dissipation 43</p>
<p>2.9. Application exercises 47</p>
<p>Exercise 2.I: Force exerted on a bend 47</p>
<p>Exercise 2.II: Emptying a tank 48</p>
<p>Exercise 2.III: Pressure drop in a sudden expansion and heating 48</p>
<p>Exercise 2.IV: Streaming flow on an inclined plane 49</p>
<p>Exercise 2.V: Impact of a jet on a sloping plate 50</p>
<p>Exercise 2.VI: Operation of a hydro–ejector 51</p>
<p>Exercise 2.VII: Bypass flow 53</p>
<p>Chapter 3. Dimensional Analysis 55</p>
<p>3.1. Principle of dimensional analysis, Vaschy Buckingham theorem 56</p>
<p>3.2. Dimensional study of Navier Stokes equations 61</p>
<p>3.3. Similarity theory 63</p>
<p>3.4. An application example: fall velocity of a spherical particle in a viscous fluid at rest 65</p>
<p>3.5. Application exercises 69</p>
<p>Exercise 3.I: Time of residence and chemical reaction in a stirred reactor 69</p>
<p>Exercise 3.II: Boundary layer on an oscillating plate 69</p>
<p>Exercise 3.III: Head capacity curve of a centrifugal pump 70</p>
<p>Chapter 4. Steady–State Hydraulic Circuits 73</p>
<p>4.1. Operating point of a hydraulic circuit 73</p>
<p>4.2. Steady–state flows in straight pipes: regular head loss 78</p>
<p>4.3. Turbulence in a pipe and velocity profile of the flow 81</p>
<p>4.4. Singular head losses 83</p>
<p>4.5. Notions on cavitation 87</p>
<p>4.6. Application exercises 88</p>
<p>Exercise 4.I: Regular head loss measurement and flow rate in a pipe 88</p>
<p>Exercise 4.II: Head loss and cavitation in a hydraulic circuit 89</p>
<p>Exercise 4.III: Ventilation of a road tunnel 91</p>
<p>Exercise 4.IV: Sizing a network of heating pipes 92</p>
<p>Exercise 4.V: Head, flow rate, and output of a hydroelectric power plant 93</p>
<p>4.7. Bibliography 93</p>
<p>Chapter 5. Pumps 95</p>
<p>5.1. Centrifugal pumps 96</p>
<p>5.2. Classification of turbo pumps and axial pumps 105</p>
<p>5.3. Positive displacement pumps 106</p>
<p>Chapter 6. Transient Flows in Hydraulic Circuits: Water Hammers 111</p>
<p>6.1. Sound propagation in a rigid pipe 111</p>
<p>6.2. Over–pressures associated with a water hammer: characteristic time of a hydraulic circuit 115</p>
<p>6.3. Linear elasticity of a solid body: sound propagation in an elastic pipe 118</p>
<p>6.4. Water hammer prevention devices 120</p>
<p>Exercise 121</p>
<p>Chapter 7. Notions of Rheometry 123</p>
<p>7.1. Rheology 123</p>
<p>7.2. Strain, strain rate, solids and fluids 126</p>
<p>7.3. A rheology experiment: behavior of a material subjected to shear 129</p>
<p>7.4. The circular cylindrical rheometer (or Couette rheometer) 132</p>
<p>7.5. Application exercises 136</p>
<p>Exercise 7.I: Rheometry and flow of a Bingham fluid in a pipe 136</p>
<p>Exercise 7.II: Cone/plate rheometer 137</p>
<p>PART II. MIXING AND CHEMICAL REACTIONS 139</p>
<p>Chapter 8. Large Scales in Turbulence: Turbulent Diffusion Dispersion 141</p>
<p>8.1. Introduction 141</p>
<p>8.2. Concept of average in the turbulent sense, steady turbulence, and homogeneous turbulence 142</p>
<p>8.3. Average velocity and RMS turbulent velocity 145</p>
<p>8.4. Length scale of turbulence: integral scale 146</p>
<p>8.5. Turbulent flux of a scalar quantity: averaged diffusion equation 151</p>
<p>8.6. Modeling turbulent fluxes using the mixing length model 153</p>
<p>8.7. Turbulent dispersion 157</p>
<p>8.8. The k– model 159</p>
<p>8.9. Appendix: solution of a diffusion equation in cylindrical coordinates 163</p>
<p>8.10. Application exercises 165</p>
<p>Exercise 8.I: Dispersion of fluid streaks introduced into a pipe by a network of capillary tubes 165</p>
<p>Exercise 8.II: Grid turbulence and k– modeling 167</p>
<p>Chapter 9. Hydrodynamics and Residence Time Distribution Stirring 171</p>
<p>9.1. Turbulence and residence time distribution 172</p>
<p>9.2. Stirring 178</p>
<p>9.3. Appendix: interfaces and the notion of surface tension 185</p>
<p>Chapter 10. Micromixing and Macromixing 193</p>
<p>10.1. Introduction 193</p>
<p>10.2. Characterization of the mixture: segregation index 195</p>
<p>10.3. The dynamics of mixing 198</p>
<p>10.4. Homogenization of a scalar field by molecular diffusion: micromixing 201</p>
<p>10.5. Diffusion and chemical reactions 202</p>
<p>10.6. Macromixing, micromixing, and chemical reactions 204</p>
<p>10.7. Experimental demonstration of the micromixing process 205</p>
<p>Chapter 11. Small Scales in Turbulence 209</p>
<p>11.1. Notion of signal processing, expansion of a time signal into Fourier series 210</p>
<p>11.2. Turbulent energy spectrum 213</p>
<p>11.3. Kolmogorov s theory 214</p>
<p>11.4. The Kolmogorov scale 218</p>
<p>11.5. Application to macromixing, micromixing and chemical reaction 221</p>
<p>11.6. Application exercises 222</p>
<p>Exercise 11.I: Mixing in a continuous stirred tank reactor 222</p>
<p>Exercise 11.II: Mixing and combustion 223</p>
<p>Exercise 11.III: Laminar and turbulent diffusion flames 225</p>
<p>Chapter 12. Micromixing Models 229</p>
<p>12.1. Introduction 229</p>
<p>12.2. CD model 233</p>
<p>12.3. Model of interaction by exchange with the mean 245</p>
<p>12.4. Conclusion 250</p>
<p>12.5. Application exercise 251</p>
<p>Exercise 12.I: Implementation of the IEM model for a slow or fast chemical reaction 251</p>
<p>PART III. MECHANICAL SEPARATION 253</p>
<p>Chapter 13. Physical Description of a Particulate Medium Dispersed Within a Fluid 255</p>
<p>13.1. Introduction 255</p>
<p>13.2. Solid particles 257</p>
<p>13.3 Fluid particles 270</p>
<p>13.4. Mass balance of a mechanical separation process 273</p>
<p>Chapter 14. Flows in Porous Media 277</p>
<p>14.1. Consolidated porous media; non–consolidated porous media, and geometrical characterization 278</p>
<p>14.2. Darcy s law 280</p>
<p>14.3. Examples of application of Darcy s law 282</p>
<p>14.4. Modeling Darcy s law through an analogy with the flow inside a network of capillary tubes 289</p>
<p>14.5. Modeling permeability, Kozeny–Carman formula 291</p>
<p>14.6. Ergun s relation 293</p>
<p>14.7. Draining by pressing 293</p>
<p>14.8. The reverse osmosis process 298</p>
<p>14.9. Energetics of membrane separation 301</p>
<p>14.10. Application exercises 301</p>
<p>Exercise: Study of a seawater desalination process 301</p>
<p>Chapter 15. Particles Within the Gravity Field 305</p>
<p>15.1. Settling of a rigid particle in a fluid at rest 306</p>
<p>15.2. Settling of a set of solid particles in a fluid at rest 309</p>
<p>15.3. Settling or rising of a fluid particle in a fluid at rest 312</p>
<p>15.4. Particles being held in suspension by Brownian motion 315</p>
<p>15.5. Particles being held in suspension by turbulence 319</p>
<p>15.6. Fluidized beds 321</p>
<p>15.7. Application exercises 329</p>
<p>Exercise 15.I: Distribution of particles in suspension and grain size sorting resulting from settling 329</p>
<p>Exercise 15.II: Fluidization of a bimodal distribution of particles 330</p>
<p>Chapter 16. Movement of a Solid Particle in a Fluid Flow 331</p>
<p>16.1. Notations and hypotheses 332</p>
<p>16.2. The Basset, Boussinesq, Oseen, and Tchen equation 333</p>
<p>16.3. Movement of a particle subjected to gravity in a fluid at rest 336</p>
<p>16.4. Movement of a particle in a steady, unidirectional shear flow 339</p>
<p>16.5. Lift force applied to a particle by a unidirectional flow 341</p>
<p>16.6. Centrifugation of a particle in a rotating flow 350</p>
<p>16.7. Applications to the transport of a particle in a turbulent flow or in a laminar flow 355</p>
<p>Chapter 17. Centrifugal Separation 359</p>
<p>17.1 Rotating flows, circulation, and velocity curl 360</p>
<p>17.2. Some examples of rotating flows 364</p>
<p>17.3. The principle of centrifugal separation 377</p>
<p>17.4. Centrifuge decanters 381</p>
<p>17.5. Centrifugal separators 385</p>
<p>17.6. Centrifugal filtration 388</p>
<p>17.7. Hydrocyclones 391</p>
<p>17.8. Energetics of centrifugal separation 396</p>
<p>17.9. Application exercise 397</p>
<p>Exercise 17.I: Grain size sorting in a hydrocyclone 397</p>
<p>Chapter 18. Notions on Granular Materials 401</p>
<p>18.1. Static friction: Coulomb s law of friction 402</p>
<p>18.2. Non–cohesive granular materials: Angle of repose, angle of internal friction 403</p>
<p>18.3. Microscopic approach to a granular material 405</p>
<p>18.4. Macroscopic modeling of the equilibrium of a granular material in a silo 407</p>
<p>18.5. Flow of a granular material: example of an hourglass 413</p>
<p>Physical Properties of Common Fluids 417</p>
<p>Index 419</p>