Roger Prud'Homme

Flows and Chemical Reactions (eBook, PDF)

• Format: PDF

Produktbeschreibung

The aim of this book is to relate fluid flows to chemical reactions. It focuses on the establishment of consistent systems of equations with their boundary conditions and interfaces, which allow us to model and deal with complex situations. Chapter 1 is devoted to simple fluids, i.e. to a single chemical constituent. The basic principles of incompressible and compressible fluid mechanics, are presented in the most concise and educational manner possible, for perfect or dissipative fluids. Chapter 2 relates to the flows of fluid mixtures in the presence of chemical reactions. Chapter 3 is concerned with interfaces and lines. Interfaces have been the subject of numerous publications and books for nearly half a century. Lines and curvilinear media are less known Several appendices on mathematical notation, thermodynamics and mechanics methods are grouped together in Chapter 4. This summary presentation of the basic equations of simple fluids, with exercises and their solutions, as well as those of chemically reacting flows, and interfaces and lines will be very useful for graduate students, engineers, teachers and scientific researchers in many domains of science and industry who wish to investigate problems of reactive flows. Portions of the text may be used in courses or seminars on fluid mechanics.

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Produktdetails

• Verlag: John Wiley & Sons
• Seitenzahl: 352
• Erscheinungstermin: 9. Januar 2013
• Englisch
• ISBN-13: 9781118587935
• Artikelnr.: 38256082

Autorenporträt

Roger Prud'homme is Emeritus Research Director at Dalembert Institute, UPMC/CNRS UMR, Paris, France.

Inhaltsangabe

Preface xiii List of the Main Symbols xv Chapter 1. Simple Fluids 1 1.1.
Introduction 1 1.2. Key elements in deformation theory - Lagrangian
coordinates and Eulerian coordinates 2 1.2.1. Strain rates 2 1.2.2.
Lagrangian coordinates and Eulerian coordinates 7 1.2.3. Trajectories,
stream lines, emission lines 8 1.3. Key elements in thermodynamics
Reversibility, irreversible processes: viscosity, heat conduction 9 1.3.1.
Thermodynamic variables, definition of a system, exchanges, differential
manifold of equilibrium states, transformation 9 1.3.2. Laws of
thermodynamics 11 1.3.3. Properties of simple fluids at equilibrium. 14
1.4. Balance equations in fluid mechanics. Application to incompressible
and compressible perfect fluids and viscous fluids 18 1.4.1. Mass balance
18 1.4.2. Concept of a particle in a continuous medium: local state 19
1.4.3. Balance for the property F 20 1.4.4. Application to volume, to
momentum and to energy 22 1.4.5. Entropy balance and the expression of the
rate of production of entropy 23 1.4.6. Balance laws for discontinuity 25
vi Flows and Chemical Reactions 1.4.7. Application to incompressible
perfect fluids 26 1.4.8. Application to dissipative fluids 31 1.5. Examples
of problems with 2D and 3D incompressible perfect fluids 32 1.5.1. Planar
2D irrotational flows: description in the complex plane of steady flows 32
1.5.2. 3D irrotational flows of incompressible perfect fluids: source,
sink, doublet 36 1.5.3. Rotational flows of incompressible perfect fluids
41 1.6. Examples of problems with a compressible perfect fluid: shockwave,
flow in a nozzle, and characteristics theory 44 1.6.1. General theorems 44
1.6.2. Propagation of sound in an ideal gas 44 1.6.3. Discontinuities 46
1.6.4. Unsteady characteristics 47 1.6.5. Steady normal shockwave: Hugoniot
and Prandtl relations 48 1.6.6. Flow in a de Laval nozzle 49 1.6.7. Simple
wave 53 1.7. Examples of problems with viscous fluids 56 1.7.1. General
equations 56 1.7.2. Incompressible viscous fluid 57 1.7.3. Flow of a
compressible dissipative fluid: structure of a shockwave 61 1.8. Exercises
64 1.8.1. Exercises in kinematics (section 1.2) 64 1.8.2. Exercises in
thermodynamics (section 1.3). 67 1.8.3. Exercises for the balance equations
in fluid mechanics (section 1.4) 68 1.8.4. Examples of problems with 2D and
3D incompressible perfect fluids (section 1.5) 70 1.8.5. Examples of
problems with a compressible perfect fluid (section 1.6) 74 1.8.6. Examples
of problems with viscous fluids (section 1.7) 77 1.9. Solutions to the
exercises 79 1.9.1. Solutions to the exercises in kinematics. 79 1.9.2.
Solutions to the Exercises in thermodynamics 83 1.9.3. Solutions to the
exercises for the balance of equations in fluid mechanics 88 1.9.4.
Solutions to the examples of problems with 2D and 3D incompressible perfect
fluids 89 Table of Contents vii 1.9.5. Solutions to the examples of
problems with a compressible perfect fluid 93 1.9.6. Solutions to the
examples of problems with viscous fluids 95 Chapter 2. Reactive Mixtures
101 2.1. Introduction 101 2.2. Equations of state 103 2.2.1. Definition of
the variables of state of a mixture 103 2.2.2. Thermodynamic properties of
mixtures 108 2.2.3. Reactive mixture 118 2.2.4. Other issues relating to
the thermodynamics of mixtures 123 2.3. Balance equations of flows of
reactive mixtures 124 2.3.1. Balance of mass of the species j and overall
balance of mass 124 2.3.2. General balance equation of a property F. 127
2.3.3. Momentum balance 129 2.3.4. Energy balance 129 2.3.5. Balance
relations in a discrete system. 132 2.3.6. Entropy balance in a continuum
137 2.3.7. Balance equations at discontinuities in continuous media 140
2.4. Phenomena of transfer and chemical kinetics 142 2.4.1. Introduction
142 2.4.2. Presentation of the transfer coefficients by linear TIP 143
2.4.3. Other presentations of the transfer coefficients 147 2.4.4. Elements
of chemical kinetics 152 2.5. Couplings 155 2.5.1. Heat transfer and
diffusion 155 2.5.2. Shvab-Zeldovich approximation 158 Chapter 3.
Interfaces and Lines 163 3.1. Introduction 163 3.1.1. Interfaces 163 3.1.2.
Lines 165 3.2. Interfacial phenomena 166 3.2.1. General aspects 166 3.2.2.
General form of an interfacial balance law 168 3.2.3. Constitutive laws for
interfaces whose variables directly satisfy the classical equations in
thermostatics and in 2D-TIP 173 3.2.4. Constitutive laws for interfaces
deduced from classical thermostatics and 3D-TIP. Stretched flame example
177 3.2.5. Interfaces manifesting resistance to folding 179 viii Flows and
Chemical Reactions 3.2.6. Numerical modeling 179 3.2.7. Interfaces and the
second gradient theory. 182 3.2.8. Boundary conditions of the interfaces
185 3.2.9. Conclusion 185 3.3. Solid and fluid curvilinear media: pipes,
fluid lines and filaments 186 3.3.1. General aspects 186 3.3.2.
Establishing the balance equations in a curvilinear medium. 188 3.3.3.
Simplified theories 209 3.3.4. Triple line and second gradient theory 216
3.3.5. Conclusion 220 3.4. Exercises 222 3.4.1. Exercises regarding solid
curvilinear media 222 3.4.2. Exercises regarding fluid curvilinear media
222 3.5. Solutions to the exercises 223 3.5.1. Solutions to exercises
regarding solid curvilinear media. 223 3.5.2. Solutions to the exercises
regarding fluid curvilinear media 225 APPENDICES 229 Appendix 1. Tensors,
Curvilinear Coordinates, Geometry and Kinematics of Interfaces and Lines
231 A1.1. Tensor notations 231 A1.1.1. Tensors and operations on tensors
231 A1.2. Orthogonal curvilinear coordinates. 234 A1.2.1. General aspects
234 A1.2.2. Curl of a vector field 236 A1.2.3. Divergence of a vector field
237 A1.2.4. Gradient of a scalar 238 A1.2.5. Laplacian of a scalar 238
A1.2.6. Differentiation in a curvilinear basis 238 A1.2.7. Divergence of a
second order tensor 239 A1.2.8. Gradient of a vector 239 A1.2.9.
Cylindrical coordinates and spherical coordinates 240 A1.3. Interfacial
layers 242 A1.3.1. Prevailing directions of an interfacial medium 242
A1.3.2. Operators of projection for interfaces 244 A1.3.3. Surface
gradients of a scalar field 245 A1.3.4. Curvature vector of a curve 245
A1.3.5. Normal and tangential divergences of a vector field 246 A1.3.6.
Extension of surface per unit length 246 A1.3.7. Average normal curvature
of a surface 247 A1.3.8. Breakdown of the divergence of a vector field 248
A1.3.9. Breakdown of the Laplacian of a scalar field 249 A1.3.10. Breakdown
of the divergence of a second order tensor 249 A1.3.11. Projection
operators with the intrinsic definition of a surface 252 A1.3.12.
Comparison between the two descriptions 253 A1.4. Curvilinear zones 254
A1.4.1. Presentation 254 A1.4.2. Geometry of the orthogonal curvilinear
coordinates 256 A1.4.3. Projection operators and their consequences 257
A1.5. Kinematics in orthogonal curvilinear coordinates 260 A1.5.1.
Kinematics of interfacial layers 260 A1.5.2. Kinematics of curvilinear
zones 266 A1.5.3. Description of the center line 269 Appendix 2. Additional
Aspects of Thermostatics 277 A2.1. Laws of state for real fluids with a
single constituent 277 A2.1.1. Diagram of state for a pure fluid 277
A2.1.2. Approximate method to determine the thermodynamic functions 278
A2.1.3. Van der Waals fluid 279 A2.1.4. Other laws for dense gases and
liquids 279 A2.2. Mixtures of real fluids 280 A2.2.1. Mixture laws for a
real mixture 280 A2.2.2. Expression of the free energy of a real mixture
281 Appendix 3. Tables for Calculating Flows of Ideal Gas ?× ?1.4 283
A3.1. Calculating the parameters in continuous steady flow (section
1.6.6.2) 286 A3.2. Formulae for steady normal shockwaves 288 Appendix 4.
Extended Irreversible Thermodynamics. 289 A4.1. Heat balance equations in a
non-deformable medium in EIT 290 A4.2. Application to a 1D case of heat
transfer 293 A4.3. Application to heat transfer with the evaporation of a
droplet 296 A4.3.1. Reminders about evaporating droplets 296 A4.3.2.
Evaporating droplet with EIT. 300 A4.4. Application to thermal shock 302
A4.4.1. Presentation of the problem and solution using CIT 302 x Flows and
Chemical Reactions A4.4.2. Thermal shock and EIT 303 A4.4.3. Application of
the second order approximation into two examples of thermal shock 305 A4.5.
Outline of EIT 307 A4.6. Applications and perspectives of EIT 310 Appendix
5. Rational Thermodynamics 313 A5.1. Introduction 313 A5.2. Fundamental
hypotheses and axioms 314 A5.2.1. Basic hypotheses 314 A5.2.2. Basic axioms
316 A5.3. Constitutive laws 318 A5.4. Case of the reactive mixture 320
A5.4.1. Principle of material frame indifference 320 A5.4.2. Constitutive
laws for a reactive mixture 321 A5.5. Critical remarks 324 Appendix 6.
Torsors and Distributors in Solid Mechanics 325 A6.1. Introduction 325
A6.1.1. Torsor 325 A6.1.2. Distributor 325 A6.1.3. Power 326 A6.2.
Derivatives of torsors and distributors which depend on a single position
parameter 326 A6.2.1. Derivative of the velocity distributor 327 A6.2.2.
Derivative of the tensor of forces 328 A6.3. Derivatives of torsors and
distributors dependent on two positional parameters 328 A6.3.1. Expression
of the velocity distributor 329 A6.3.2. Derivative of the velocity
distributor 329 Appendix 7. Virtual Powers in a Medium with a Single
Constituent 331 A7.1. Introduction 331 A7.2. Virtual powers of a system of
n material points 332 A7.3. Virtual power law 333 A7.4. The rigid body and
systems of rigid bodies 333 A7.4.1. The rigid body 333 A7.4.2. System of
rigid bodies, concept of a link 334 A7.5. 3D deformable continuous medium
335 A7.5.1. First gradient theory 335 A7.5.2. A 3D case of perfect internal
linkage: the incompressible perfect fluid 337 A7.5.3. Second gradient
theory 337 A7.6. 1D continuous deformable medium 338 A7.6.1. First gradient
theory 338 A7.6.2. A 1D case of perfect internal linkage: perfectly
flexible and inextensible wires 340 A7.7. 2D deformable continuous medium
340 Bibliography 343 Index 355