Flows and Chemical Reactions in Homogeneous Mixtures

Roger Prud’homme has been Emeritus Research Director at CNRS, in France, since 2004. His most recent research topics have included flames (premixed flame modeling and their behavior in microgravity), two phase flows (droplet combustion with condensation of the products, sound propagation in suspensions, vortex, chock wave structure) and the modeling of fluid interfaces. He has published 5 books, 7 contributions to volumes and 50 publications in international journals.

• Symbols ixPreface xxiiiChapter 1. Flows in Nozzles 11.1. Sound propagation in the presence of chemical reactions 11.1.1. Thermodynamic considerations 21.1.2. Sound propagation in a mono-reactive medium 71.1.3. Sound propagation in a multi-reactive medium 121.2. Relaxed flows in nozzles 261.2.1. Calculation of a continuous flow with a recombination-dissociation reaction in a de Laval nozzle 271.2.2. Asymptotic study of the transonic zone of a continuous monodimensional flow in a de Laval nozzle 311.3. Flows in thermal and chemical non-equilibrium 351.3.1. Balance equations and closure relations in the presence of thermal and chemical non-equilibria 351.3.2. Application 371.4. Conclusion about flows in nozzles 45Chapter 2. Chemical Reactors 472.1. Ideal reactors, real reactors, balance equations 482.1.1. Ideal chemical reactors 482.1.2. Balance equations for chemical reactors 502.2. Perfectly mixed homogeneous chemical reactors 552.2.1. Equations for a perfectly stirred homogeneous chemical reactor 552.2.2. Steady regimes in perfectly stirred homogeneous chemical reactors 592.2.3. Stability of operating points in the perfectly stirred homogeneous chemical reactor 612.3. Tubular reactor 672.3.1. Plug flow reactor 682.3.2. Reactor with axial mixing 702.3.3. Reactor with radial mixing 732.4. Residence time distribution 742.4.1. Balance equations 742.4.2. Perfectly stirred homogeneous reactors in a steady regime 762.4.3. Plug flow reactors 762.4.4. Poiseuille flow 762.4.5. Real reactors 78Chapter 3. Laminar and Turbulent Flames 793.1. Laminar premixed combustion 793.1.1. Rankine-Hugoniot theory 803.1.2. Velocity and structure of the plane adiabatic laminar and steady premixed flame 873.1.3. Other examples of a steady laminar premixed flame 913.2. Laminar non-premixed combustion 953.2.1. Burke–Schumann problem 953.2.2. Other examples of diffusion flames 983.3. Turbulent combustion 1043.3.1. Averaged balance equation for turbulent combustion 1053.3.2. Premixed turbulent combustion regimes 1073.3.3. Non-premixed turbulent combustion regimes 1103.3.4. Models of turbulent combustion 1123.3.5. LESs in combustion 1193.3.6. Triple flames 121APPENDICES 125Appendix 1. Dimensionless Numbers, Similarity 127A1.1. Fundamentals of dimensional analysis: groups 128A1.1.1. Basic considerations 128A1.1.2. Vaschy–Buckingham theorem (1890) or Π theorem 129A1.1.3. Practical advantage to dimensional analysis 130A1.1.4. Example of application: head loss in a cylindrical pipe 130A1.2. Similarity  132A1.2.1. Definition 132A1.2.2. Application: condition of similarity in a soft balloon placed in a current of air with a given velocity  133A1.3. Analytical searching for solutions to a heat transfer problem (self-similar solution) 135A1.4. Some dimensionless numbers 137Appendix 2. Thermodynamic Functions 141A2.1. General points 141A2.2. Translational motion 142A2.3. Internal motions 143A2.3.1. Monatomic species 143A2.3.2. Diatomic species 145A.2.3.3. Linear polyatomic species 146A2.3.4. Nonlinear polyatomic species 147Appendix 3. Concepts of Turbulence 149A3.1. Experimental demonstration 151A3.1.1. Reynolds’ experiment 151A3.1.2. Viscous flow over a smooth plane plate 152A3.1.3. Effect of roughness of the plate 153A3.1.4. Effect of turbulence on chemical reactivity 153A3.2. Apparition and damping of turbulence 154A3.2.1. Instability between two superposed fluids 154A3.2.2. Instability of a fluid between two rotating cylinders 158A3.2.3. Instability of a premixed flame 165A3.2.4. Damping of turbulence 169A3.3. Classic turbulence (RANS model) 170A3.3.1. Turbulent transfer and chemical kinetics coefficients 170A3.3.2. Remarks about averages and scales 176A3.3.3. models (closure for transfer terms) 178A3.3.4. Spectral analysis and Kolmogorov’s theory 181A3.4. Ideas about large eddy simulation 185A3.4.1. Filtering 187A3.4.2. Filtered balance equations for a non-reactive incompressible fluid 189A3.4.3. Closure relations for the filtered balance equations 190A3.5. Conclusion 193Appendix 4. Thermodynamic functions for a mixture in disequilibrium 195A4.1. Thermodynamics 195A4.2. Chemistry 197A4.3. Vibration 197Appendix 5. Notion of bifurcation 199Appendix 6. Confined flame 201Appendix 7. Limits of Validity of the First-order Expansions for Diffusion Flames 203A7.1. Burke–Schumann flame 203A7.2. Juxtaposed oxidizer/fuel flows from rectangular burners 204Bibliography 207Index 219