Flows and Chemical Reactions E-Book

Roger Prud'homme

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Seitenzahl: 331

Veröffentlichungsjahr: 2013

Beschreibung

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.

Leseprobe

Table of Contents

Preface

List of the Main Symbols

Chapter 1: Simple Fluids

1.1. Introduction

1.2. Key elements in deformation theory – Lagrangian coordinates and Eulerian coordinates

1.3. Key elements in thermodynamics. Reversibility, irreversible processes: viscosity, heat conduction

1.4. Balance equations in fluid mechanics. Application to incompressible and compressible perfect fluids and viscous fluids

1.5. Examples of problems with 2D and 3D incompressible perfect fluids

1.6. Examples of problems with a compressible perfect fluid: shockwave, flow in a nozzle, and characteristics theory

1.7. Examples of problems with viscous fluids

1.8. Exercises

1.9. Solutions to the exercises

Chapter 2: Reactive Mixtures

2.1. Introduction

2.2. Equations of state

2.3. Balance equations of flows of reactive mixtures

2.4. Phenomena of transfer and chemical kinetics

2.5. Couplings

Chapter 3: Interfaces and Lines

3.1. Introduction

3.2. Interfacial phenomena

3.3. Solid and fluid curvilinear media: pipes, fluid lines and filaments

3.4. Exercises

3.5. Solutions to the exercises

APPENDICES

Appendix 1: Tensors, Curvilinear Coordinates, Geometryand Kinematics of Interfaces and Lines

A1.1. Tensor notations

A1.2. Orthogonal curvilinear coordinates

A1.3. Interfacial layers

A1.4. Curvilinear zones

A1.5. Kinematics in orthogonal curvilinear coordinates

Appendix 2: Additional Aspects of Thermostatics

A2.1. Laws of state for real fluids with a single constituent

A2.2. Mixtures of real fluids

Appendix 3: Tables for Calculating Flows of Ideal Gas (=1 .4)

A3.1. Calculating the parameters in continuous steady flow (section 1.6.6.2)

A3.2. Formulae for steady normal shockwaves

Appendix 4: Extended Irreversible Thermodynamics

A4.1. Heat balance equations in a non-deformable medium in EIT

A4.2. Application to a 1D case of heat transfer

A4.3. Application to heat transfer with the evaporation of a droplet

A4.4. Application to thermal shock

A4.5. Outline of EIT

A4.6. Applications and perspectives of EIT

Appendix 5: Rational Thermodynamics

A5.1. Introduction

A5.2. Fundamental hypotheses and axioms

A5.3. Constitutive laws

A5.4. Case of the reactive mixture

A5.5. Critical remarks

Appendix 6: Torsors and Distributors in Solid Mechanics

A6.1. Introduction

A6.2. Derivatives of torsors and distributors which depend on a single position parameter

A6.3. Derivatives of torsors and distributors dependent on two positional parameters

Appendix 7: Virtual Powers in a Medium with a Single Constituent

A7.1. Introduction

A7.2. Virtual powers of a system of n material points

A7.3. Virtual power law

A7.4. The rigid body and systems of rigid bodies

A7.5. 3D deformable continuous medium

A7.6. 1D continuous deformable medium

A7.7. 2D deformable continuous medium

Bibliography

Index

First published 2012 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc.

Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address:

ISTE LtdJohn Wiley & Sons, Inc.27-37 St George’s Road111 River StreetLondon SW19 4EUHoboken, NJ 07030UKUSAwww.iste.co.ukwww.wiley.com

© ISTE Ltd 2012

The rights of Roger Prud’homme to be identified as the author of this work have been asserted by him in accordance with the Copyright, Designs and Patents Act 1988.

Library of Congress Cataloging-in-Publication Data

Prud'homme, Roger.

Flows and chemical reactions / Roger Prud'homme.

p. cm.

Includes bibliographical references and index.

ISBN 978-1-84821-425-5

1.Chemical reactions. 2. Fluid mechanics. I. Title.

QD501.P8285 2012

541'.39--dc23

2012025722

British Library Cataloguing-in-Publication Data

A CIP record for this book is available from the British Library ISBN: 978-1-84821-425-5

Preface

Over the past several decades, numerous publications have been devoted to the subject of flows with chemical reactions. Having initially aroused the interest of combustion specialists, their behaviors have been of direct concern for scientists in the fields of process engineering, astronautics, the atmospheric and aquatic environment, and many others.

The interactions between fluid flow, heat exchange and chemical reactions are such that in numerous applications it is impossible to deal with these aspects separately.

Indeed, it is very difficult to consider, for example, combustion in a rocket engine as the superimposition of a non-reactive fluid flow, determined first, with the chemical reactions and heat exchanges to be added. The same is true in many other fields which involve highly energetic reactions in a fluid medium which is usually compressible and dilatable.

These considerations linked to applications have given birth to a new scientific discipline – Aerothermochemistry – which is primarily concerned with establishing coherent systems of equations, with their boundary and interface conditions, which enable us to model and deal with complex situations involving multiple parameters.

This book, entitled Flows and Chemical Reactions, is divided into three chapters and seven appendices, which aim to present the equations of homogeneous laminar flows, interfaces and lines.

Chapter 1 is devoted to simple fluids – that is fluids with only one chemical component. The aim is to give a concise and academic presentation of the essential principles of fluid mechanics for incompressible and compressible, non-dissipative or dissipative fluids. This chapter’s contents formed the basis for a Masters-level module taught three times at the University of Lomé between 2004 and 2011. It offers a great many exercises and their solutions.

Chapter 2 relates to the flow of fluid mixtures in the presence of chemical reactions. This chapter has been the object of numerous teaching sessions in the DEA (Masters) in the Physics of Liquids and in the Ecoles d’Ingénieurs (specialized engineering schools – Ecole des Mines, Ecole Polytechnique).

Chapter 3 is concerned with interfaces and lines. Interfaces have been discussed in numerous books and other publications over the past fifty years.

Less is known about lines, or curvilinear media. A few basic exercises are offered, along with their solutions.

The Appendices are comprised of Appendix 1 to Appendix 7; each of which contains additional information from the fields of mathematics, thermodynamics and mechanics.

Our goal in writing this book is to provide students with a reference tool in the field of fluid mechanics, which strays somewhat from the beaten track in terms of content or form. However, this book is also aimed at researchers, lecturer/researchers, and at industrial engineers in sectors concerned with reactive fluid flows.

Part of this work is made up of texts which hitherto were only available in course notes or internal reports at ONERA (French Aerospace Lab) or CNRS (National Center for Scientific Research). These texts have been reorganized and often rethought and enriched. Other elements have been reworked from the author’s recent publications. Finally, other parts result from the study of a body of literature on the subject of flows and chemical reactions.

Roger PRUD’HOMME

August 2012

List of the Main Symbols

Latin characters

a, bvan der Waals coefficientsa jactivity of the species jAchemical affinityadiabatic transformation; power of the acceleration forcechemical elementB, C, C'virial coefficientsBjkvirial coefficients of a mixturecspeed of sound; molecular velocityCtotal number of moles per unit volumeCffriction coefficientCjmolar concentration per unit volumeCp, Cvspecific heat at constant pressure or constant volume respectively, (cp, cv for the unit of mass)Crcrispation numberdmolecular diameter; or distance; or differentialDdiffusion coefficientstrain rate tensorDTthermal diffusion coefficientorthonormal basis vectorEinternal energy (e per unit mass)state of equilibriumEaactivation energychemical speciesforce acting on each unit massforce acting on the unitary mass of the species jFHelmholtz free energy (f for the unit of mass); general force; any extensive value (f for the unit of mass)forceGGibbs free enthalpy (g for the unit of mass)acceleration due to gravity (of modulus g); or shear-force vector of a shellgjchemical potential per unit mass of the species j in a mixtureHenthalpy (h per unit mass)unit tensorJgeneralized fluxtotal mass fluxflux of the species jdiffusion flux of the species jkBoltzmann’s constant; volume viscosity; wave numberKkinetic energy (k per unit mass); compressibility; number of chemical reactions in a mixture; or wave numberk(T)specific reaction rateKa, KC, Kpequilibrium constants for the activities, the concentrations and the partial pressures, respectivelyllatent heat per unit mass; or mean free pathLlength; molar latent heat; number of chemical elements in a mixture or phenomenological coefficientLeLewis numbermtotal massbending moment of a shellMmolecular massmean molar massmoment of a beam ( torque, bending moment)bending stress tensor of a shellmjmass of the species jmolar mass of the species junit mass flow ratentotal number of moles; or coordinate normal to an interface at the mesoscopic scalenjnumber of moles of the species jNnumber of species; number of molecules per unit volume; or coordinate normal to an interfaceunitary normal to an interfacepthermodynamic pressuresurface density of forces acting on a shellpressure tensormechanical powerpower of the internal and external forces respectivelyPrPrandtl numberqparameter; or heat fluxheat flux vectorheat flux vector due to the temperature gradientQquantity of heatorthogonal tensormolar enthalpy of formation of the species per unit mass)rperfect gas constant per unit mass; radius; or calorific power received per unit volumeRuniversal molar gas constant; radius; or number of independent species in a mixtureRrchemical reactionSentropy (s per unit mass); or Arrhenius exponentS, SsurfaceScSchmidt numberttimeTabsolute temperaturelineic density of forces at the edge of a shelllineic density of forces on a beam ( normal force, shear force)u, v, wvelocity components in Cartesian coordinates (vr, vθ, vz in cylindrical coordinates)u, vcoefficients in the equation of state for real gasesreference velocityvelocity vector; barycentric velocity vector in a composite fluidvelocity vector of the species jVvelocity; force; or potentialvector; mixed velocity of interface or line volumeVmanifold of equilibrium in thermodynamic spaceVisurface viscosity numberrate of diffusion of the species velocity of a surface (normal component w or , tangential component )Wworklocal velocity vector of a discontinuity; velocity vector of a fictitious motionrate of production of the quantity Fx, y, zCartesian coordinates (X, Y, Z in a relative frame)position vectorXj, Yjmolar and mass fraction of the species j respectively

Greek symbols

heat exchange coefficient; dilatation coefficientreduced concentrationnumber of atoms l in the molecule jreduced temperatureinfinitesimal differenceΔdifference; or Laplaciansmall dimensionless parametervelocity potentiallinear density of the torquessurface density of the torquespartial molar quantity associated with the quantity quantity of mixture associated with isentropic coefficient cp/cvvolume viscosity; or reduced coordinateelements of reduction of the 1D strain rate torsorthermal diffusivity ; or mean curvature of a surfacecoefficient of thermal conductivity; or scale factorcoefficient of head loss; or heat transfer coefficientcoefficient of shear viscosity; or Gibbs free energy per molemolar chemical potential of a species j in a mixturekinematic viscosity frequency of collisionalgebraic stoichiometric coefficient stoichiometric coefficient of the direct reaction, or its inverse respectivelynormal mean pressureviscous pressure tensortemperature; or angular coordinatevolume per unit mass (inverse of the density)density (volumic mass)partial densitysurface tensionsurface tension tensor; or membrane stress tensorΣsurface; area of a surfacestress tensortemperature derivative of the surface tensioncharacteristic timespeed of rotation; or pulsation of an oscillating waverotation vectorspeed of rotationrotation rate tensorprogress variable per unit mass; reduced coordinate; or correlation lengthstream functionprogress variable per unit volume; or reduced variablerate of production of a chemical reaction

Subscripts, superscripts and other symbols

ainterface; relative to the quantities per unit area of the interfacecconcentrationCcritical pointchemchemicalDdirect; dissociation; or diffusiveeequilibrium flow; externalffixed composition (frozen flow); or flameG, ggasi, jthe speciesiinternal; or irreversiblelline; relative to the extensive curvilinear quantitieslliquidLline; relative to the specific or intensive curvilinear quantitiesmof mixture; or of massmechmechanicalpat constant pressure; solid phaserchemical reaction; referenceRreverse; or recombinationssteady state; or surfaceSsurface; relative to the specific or intensive interfacial quantitiesTtemperature; or at constant temperatureTsecond-order tensor; transpose of a tensor°deviator from a tensorththermalVvapor//parallel to a surfacenormal to a surfaceSscalarVvectorial0standard reference value•pure simple substance·per unit time; or for a rate of production–thermodynamic value per mole; or average quantity;′disturbance in relation to an average valueS(  )symmetrical part of a matrix or a tensor~transpose of tensor; transpose of matrixinfinitesimal reversible transformation^pre-exponential factorstandard thermodynamic function×vector producttensor product.scalar product (singly-contracted tensor product):dyadic product (doubly-contracted tensor product)^exterior product*sonic conditions; or reference state; or virtualnabla (gradient operator)jump of a quantity across an interface{  }kinetic torsor[  ]torsor (or distributor)d/dtmaterial derivative equal to partial time derivativedw/dtmaterial derivative associated with the velocity equal to

Chapter 1

Simple Fluids

1.1. Introduction

This first chapter is devoted to fluids with a single chemical component – that is, it may be considered an introduction to conventional fluid mechanics. However, this chapter alone cannot take the place of the numerous detailed works which deal with all, or part, of this topic.

The first two sections (1.2 and 1.3), are given over to the fundamental notions – deformation theory, Lagrangian and Eulerian coordinates, and the laws of thermodynamics – meaning that in section 1.4, we have the necessary groundwork in place to lay out the fundamental equations of fluid mechanics.

The last three sections are dedicated to the applications and solutions of the fundamental equations. Sections 1.5 and 1.6 relate to perfect1 fluids, i.e. fluids in a state of reversible evolution in the thermodynamic sense: incompressible perfect fluids in section 1.5, and compressible perfect fluids in section 1.6. In section 1.7, we shall turn to fluids in irreversible evolution, which exhibit viscosity and heat conduction, limiting our discussion to linearized irreversible phenomena.

Each section is illustrated with examples which not only enable the reader to familiarize themselves with the notions and theorems under discussion, but which also set out some solution methods which are conventional in fluid mechanics.