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Flows and Chemical Reactions in Homogeneous Mixtures

Flows and Chemical Reactions in Homogeneous Mixtures

Roger Prud'homme

ISBN: 978-1-118-83265-3

Oct 2013, Wiley-ISTE

223 pages


Flows with chemical reactions can occur in various fields such as combustion, process engineering, aeronautics, the atmospheric environment and aquatics.
The examples of application chosen in this book mainly concern homogeneous reactive mixtures that can occur in propellers within the fields of process engineering and combustion:
– propagation of sound and monodimensional flows in nozzles, which may include disequilibria of the internal modes of the energy of molecules;
– ideal chemical reactors, stabilization of their steady operation points in the homogeneous case of a perfect mixture and classical instruments of experimental and theoretical analysis such as population balances, and the distribution of residence and passage times;
– laminar and turbulent flames, separating those which are premixed from those which are not and which do not exhibit the same mechanisms, but which also occur in the case of triple flames.
Flows and Chemical Reactions in Homogeneous Mixtures provides information on dimensional analysis, statistical thermodynamics with coupling between internal modes and chemical reactions, the apparition and damping of fluid turbulence as well as its statistical processing, bifurcations, flames in a confined medium and diffusion.


1. Flows in Nozzles.
2. Chemical Reactors.
3. Laminar and Turbulent Flames.
Appendix 1. Dimensionless Numbers, Similarity.
Appendix 2. Thermodynamic Functions.
Appendix 3. Concepts of Turbulence.
Appendix 4. Thermodynamic functions for a mixture in disequilibrium.
Appendix 5. Notion of bifurcation.
Appendix 6. Confined flame.
Appendix 7. Limits of Validity of the First-order Expansions for Diffusion Flames.

About the Authors

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 ix

Preface xxiii

Chapter 1. Flows in Nozzles 1

1.1. Sound propagation in the presence of chemical reactions 1

1.1.1. Thermodynamic considerations 2

1.1.2. Sound propagation in a mono-reactive medium 7

1.1.3. Sound propagation in a multi-reactive medium 12

1.2. Relaxed flows in nozzles 26

1.2.1. Calculation of a continuous flow with a recombination-dissociation reaction in a de Laval nozzle 27

1.2.2. Asymptotic study of the transonic zone of a continuous monodimensional flow in a de Laval nozzle 31

1.3. Flows in thermal and chemical non-equilibrium 35

1.3.1. Balance equations and closure relations in the presence of thermal and chemical non-equilibria 35

1.3.2. Application 37

1.4. Conclusion about flows in nozzles 45

Chapter 2. Chemical Reactors 47

2.1. Ideal reactors, real reactors, balance equations 48

2.1.1. Ideal chemical reactors 48

2.1.2. Balance equations for chemical reactors 50

2.2. Perfectly mixed homogeneous chemical reactors 55

2.2.1. Equations for a perfectly stirred homogeneous chemical reactor 55

2.2.2. Steady regimes in perfectly stirred homogeneous chemical reactors 59

2.2.3. Stability of operating points in the perfectly stirred homogeneous chemical reactor 61

2.3. Tubular reactor 67

2.3.1. Plug flow reactor 68

2.3.2. Reactor with axial mixing 70

2.3.3. Reactor with radial mixing 73

2.4. Residence time distribution 74

2.4.1. Balance equations 74

2.4.2. Perfectly stirred homogeneous reactors in a steady regime 76

2.4.3. Plug flow reactors 76

2.4.4. Poiseuille flow 76

2.4.5. Real reactors 78

Chapter 3. Laminar and Turbulent Flames 79

3.1. Laminar premixed combustion 79

3.1.1. Rankine-Hugoniot theory 80

3.1.2. Velocity and structure of the plane adiabatic laminar and steady premixed flame 87

3.1.3. Other examples of a steady laminar premixed flame 91

3.2. Laminar non-premixed combustion 95

3.2.1. Burke–Schumann problem 95

3.2.2. Other examples of diffusion flames 98

3.3. Turbulent combustion 104

3.3.1. Averaged balance equation for turbulent combustion 105

3.3.2. Premixed turbulent combustion regimes 107

3.3.3. Non-premixed turbulent combustion regimes 110

3.3.4. Models of turbulent combustion 112

3.3.5. LESs in combustion 119

3.3.6. Triple flames 121


Appendix 1. Dimensionless Numbers, Similarity 127

A1.1. Fundamentals of dimensional analysis: groups 128

A1.1.1. Basic considerations 128

A1.1.2. Vaschy–Buckingham theorem (1890) or Π theorem 129

A1.1.3. Practical advantage to dimensional analysis 130

A1.1.4. Example of application: head loss in a cylindrical pipe 130

A1.2. Similarity  132

A1.2.1. Definition 132

A1.2.2. Application: condition of similarity in a soft balloon placed in a current of air with a given velocity  133

A1.3. Analytical searching for solutions to a heat transfer problem (self-similar solution) 135

A1.4. Some dimensionless numbers 137

Appendix 2. Thermodynamic Functions 141

A2.1. General points 141

A2.2. Translational motion 142

A2.3. Internal motions 143

A2.3.1. Monatomic species 143

A2.3.2. Diatomic species 145

A.2.3.3. Linear polyatomic species 146

A2.3.4. Nonlinear polyatomic species 147

Appendix 3. Concepts of Turbulence 149

A3.1. Experimental demonstration 151

A3.1.1. Reynolds’ experiment 151

A3.1.2. Viscous flow over a smooth plane plate 152

A3.1.3. Effect of roughness of the plate 153

A3.1.4. Effect of turbulence on chemical reactivity 153

A3.2. Apparition and damping of turbulence 154

A3.2.1. Instability between two superposed fluids 154

A3.2.2. Instability of a fluid between two rotating cylinders 158

A3.2.3. Instability of a premixed flame 165

A3.2.4. Damping of turbulence 169

A3.3. Classic turbulence (RANS model) 170

A3.3.1. Turbulent transfer and chemical kinetics coefficients 170

A3.3.2. Remarks about averages and scales 176

A3.3.3. models (closure for transfer terms) 178

A3.3.4. Spectral analysis and Kolmogorov’s theory 181

A3.4. Ideas about large eddy simulation 185

A3.4.1. Filtering 187

A3.4.2. Filtered balance equations for a non-reactive incompressible fluid 189

A3.4.3. Closure relations for the filtered balance equations 190

A3.5. Conclusion 193

Appendix 4. Thermodynamic functions for a mixture in disequilibrium 195

A4.1. Thermodynamics 195

A4.2. Chemistry 197

A4.3. Vibration 197

Appendix 5. Notion of bifurcation 199

Appendix 6. Confined flame 201

Appendix 7. Limits of Validity of the First-order Expansions for Diffusion Flames 203

A7.1. Burke–Schumann flame 203

A7.2. Juxtaposed oxidizer/fuel flows from rectangular burners 204

Bibliography 207

Index 219