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A guide to the theoretical underpinnings and practical applications of chemically reacting flow

Chemically Reacting Flow: Theory, Modeling, and Simulation, Second Edition combines fundamental concepts in fluid mechanics and physical chemistry while helping students and professionals to develop the analytical and simulation skills needed to solve real-world engineering problems. The authors clearly explain the theoretical and computational building blocks enabling readers to extend the approaches described to related or entirely new applications. New to this Second Edition are substantially revised and reorganized coverage of topics treated in the first edition. New material in the book includes two important areas of active research: reactive porous-media flows and electrochemical kinetics. These topics create bridges between traditional fluid-flow simulation approaches and transport within porous-media electrochemical systems.

The first half of the book is devoted to multicomponent fluid-mechanical fundamentals. In the second half the authors provide the necessary fundamental background needed to couple reaction chemistry into complex reacting-flow models. Coverage of such topics is presented in self-contained chapters, allowing a great deal of flexibility in course curriculum design.

•       Features new chapters on reactive porous-media flow, electrochemistry, chemical thermodynamics, transport properties, and solving differential equations in MATLAB

•       Provides the theoretical underpinnings and practical applications of chemically reacting flow

•       Emphasizes fundamentals, allowing the analyst to understand fundamental theory underlying reacting-flow simulations

•       Helps readers to acquire greater facility in the derivation and solution of conservation equations in new or unusual circumstances

•       Reorganized to facilitate use as a class text and now including a solutions manual for academic adopters

Computer simulation of reactive systems is highly efficient and cost-effective in the development, enhancement, and optimization of chemical processes. Chemically Reacting Flow: Theory, Modeling, and Simulation, Second Edition helps prepare graduate students in mechanical or chemical engineering, as well as research professionals in those fields take utmost advantage of that powerful capability.

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CHEMICALLY REACTING FLOW

Theory, Modeling, and Simulation

Second Edition

Robert J. Kee

Colorado School of Mines

Michael E. Coltrin

Sandia National Laboratories

Peter Glarborg

Technical University of Denmark

Huayang Zhu

Colorado School of Mines

This edition first published 2018 © 2018 by John Wiley & Sons, Inc

All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, except as permitted by law. Advice on how to obtain permission to reuse material from this title is available at http://www.wiley.com/go/permissions.

The right of Robert J. Kee, Michael E. Coltrin, Peter Glarborg, Huayang Zhu to be identified as the authors of this work has been asserted in accordance with law.

Registered OfficeJohn Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, USA

Editorial Office111 River Street, Hoboken, NJ 07030, USA

For details of our global editorial offices, customer services, and more information about Wiley products visit us at www.wiley.com.

Wiley also publishes its books in a variety of electronic formats and by print-on-demand. Some content that appears in standard print versions of this book may not be available in other formats.

Limit of Liability/Disclaimer of WarrantyIn view of ongoing research, equipment modifications, changes in governmental regulations, and the constant flow of information relating to the use of experimental reagents, equipment, and devices, the reader is urged to review and evaluate the information provided in the package insert or instructions for each chemical, piece of equipment, reagent, or device for, among other things, any changes in the instructions or indication of usage and for added warnings and precautions. While the publisher and authors have used their best efforts in preparing this work, they make no representations or warranties with respect to the accuracy or completeness of the contents of this work and specifically disclaim all warranties, including without limitation any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives, written sales materials or promotional statements for this work. The fact that an organization, website, or product is referred to in this work as a citation and/or potential source of further information does not mean that the publisher and authors endorse the information or services the organization, website, or product may provide or recommendations it may make. This work is sold with the understanding that the publisher is not engaged in rendering professional services. The advice and strategies contained herein may not be suitable for your situation. You should consult with a specialist where appropriate. Further, readers should be aware that websites listed in this work may have changed or disappeared between when this work was written and when it is read. Neither the publisher nor authors shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages.

Library of Congress Cataloging-in-Publication Data

Names: Kee, R. J., author. | Coltrin, Michael Elliott, 1953- author. | Glarborg, Peter, author. | Zhu, Huayang, author. Title: Chemically reacting flow : theory, modeling, and simulation / Robert J. Kee, Michael E. Coltrin, Peter Glarborg,  Huayang Zhu. Description: Second edition. | Hoboken, NJ : John Wiley & Sons, 2017. | Includes index. | Identifiers: LCCN 2017011676 (print) | LCCN 2017018820 (ebook) | ISBN 9781119186281 (pdf) | ISBN 9781119186298  (epub) | ISBN 9781119184874 (cloth) Subjects: LCSH: Transport theory. | Fluid dynamics. | Thermodynamics. Classification: LCC TP156.T7 (ebook) | LCC TP156.T7 K44 2017 (print) | DDC 660/.299–dc23 LC record available at https://lccn.loc.gov/2017011676

Cover Design and Images: Courtesy of Robert and Judy Kee

 

 

 

 

 

 

We dedicate this book to aclose friend and highlyvalued colleague, Prof.David G. Goodwin(1957-2012) of Caltech.

CONTENTS

PREFACE

ACKNOWLEDGMENTS

NOMENCLATURE

Greek Symbols

CHAPTER 1 INTRODUCTION

1.1 Foregoing Texts

1.2 Objectives and Approach

1.3 What is a Fluid?

1.4 Chemically Reacting Fluid Flow

1.5 Physical Chemistry

1.6 Illustrative Examples

References

CHAPTER 2 FLUID PROPERTIES

2.1 Equations of State

2.2 Thermodynamics

2.3 Transport Properties

References

CHAPTER 3 FLUID KINEMATICS

3.1 Path to Conservation Equations

3.2 System and Control Volume

3.3 Stress and Strain Rate

3.4 Fluid Strain Rate

3.5 Vorticity

3.6 Dilatation

3.7 Stress Tensor

3.8 Stokes Postulates

3.9 Transformation from Principal Coordinates

3.10 Stokes Hypothesis

3.11 Summary

Notes

CHAPTER 4 CONSERVATION EQUATIONS

4.1 Mass Continuity

4.2 Navier-Stokes Equations

4.3 Species Diffusion

4.4 Species Conservation

4.5 Conservation of Energy

4.6 Mechanical Energy

4.7 Thermal Energy

4.8 Ideal Gas and Incompressible Fluid

4.9 Conservation Equation Summary

4.10 Pressure Filtering

4.11 Helmholtz Decomposition

4.12 Potential Flow

4.13 Vorticity Transport

4.14 Mathematical Characteristics

4.15. Summary

References

CHAPTER 5 PARALLEL FLOWS

5.1 Nondimensionalization

5.2 Couette and Poiseuille Flows

5.3 Hagen–Poiseuille Flow in a Circular Duct

5.4 Ducts of Noncircular Cross Section

5.5 Hydrodynamic Entry Length

5.6 Transient Flow in a Duct

5.7 Richardson Annular Overshoot

5.8 Stokes Problems

5.9 Rotating Shaft in Infinite Media

5.10 Graetz Problem

References

CHAPTER 6 SIMILARITY AND LOCAL SIMILARITY

6.1 Jeffery–Hamel Flow

6.2 Planar Wedge Channel

6.3 Radial-Flow Reactors

6.4 Spherical Flow between Inclined Disks

6.5 Radial Flow between Parallel Disks

6.6 Flow between Plates with Wall Injection

References

CHAPTER 7 STAGNATION FLOWS

7.1 Similarity in Axisymmetric Stagnation Flow

7.2 Generalized Steady Axisymmetric Stagnation Flow

7.3 Semi-Infinite Domain

7.4 Finite-Gap Stagnation Flow

7.5 Finite-Gap Numerical Solution

7.6 Rotating Disk

7.7 Rotating Disk in a Finite Gap

7.8 Unified View of Axisymmetric Stagnation Flow

7.9 Planar Stagnation Flows

7.10 Opposed Flow

7.11 Tubular Flows

7.12 Stagnation-Flow Chemical Vapor Deposition

7.13 Boundary-Layer Bypass

References

CHAPTER 8 BOUNDARY-LAYER CHANNEL FLOW

8.1 Scaling Arguments for Boundary Layers

8.2 General Setting Boundary-Layer Equations

8.3 Boundary Conditions

8.4 Computational Solution

8.5 Introduction to the Method of Lines

8.6 Method-of-Lines Boundary-Layer Algorithm

8.7 Von Mises Transformation

8.8 Von Mises Formulation as DAEs

8.9 Hydrodynamic Entry Length

8.10 Physical and von Mises Coordinates

8.11 General von Mises Boundary Layer

8.12 Limitations

8.13 Chemically Reacting Channel Flow

References

CHAPTER 9 LOW-DIMENSIONAL REACTORS

9.1 Batch Reactors (Homogeneous Mass-Action Kinetics)

9.2 Plug-Flow Reactor

9.3 Plug Flow with Porous Walls

9.4 Plug Flow with Variable Area and Surface Chemistry

9.5 Perfectly Stirred Reactors

9.6 Transient Stirred Reactors

9.7 Stagnation-Flow Catalytic Reactor

Notes

References

CHAPTER 10 THERMOCHEMICAL PROPERTIES

10.1 Kinetic Theory of Gases

10.2 Molecular Energy Levels

10.3 Partition Function

10.4 Statistical Thermodynamics

10.5 Example Calculations

References

CHAPTER 11 MOLECULAR TRANSPORT

11.1 Introduction to Transport Coefficients

11.2 Molecular Interactions

11.3 Kinetic Gas Theory of Transport Properties

11.4 Rigorous Theory of Transport Properties

11.5 Evaluation of Transport Coefficients

11.6 Momentum and Energy Fluxes

11.7 Species Fluxes

11.8 Diffusive Transport Example

Notes

References

CHAPTER 12 MASS-ACTION KINETICS

12.1 Gibbs Free Energy

12.2 Equilibrium Constant

12.3 Mass-Action Kinetics

12.4 Pressure-Dependent Unimolecular Reactions

12.5 Bimolecular Chemical Activation Reactions

Notes

References

CHAPTER 13 REACTION RATE THEORIES

13.1 Molecular Collisions

13.2 Collision Theory Reaction Rate Expression

13.3 Transition-State Theory

13.4 Unimolecular Reactions

13.5 Bimolecular Chemical Activation Reactions

References

CHAPTER 14 REACTION MECHANISMS

14.1 Models for Chemistry

14.2 Characteristics of Complex Reactions

14.3 Mechanism Development

14.4 Combustion Chemistry

Notes

References

CHAPTER 15 LAMINAR FLAMES

15.1 Premixed Flat Flame

15.2 Premixed Flame Structure

15.3 Methane-Air Premixed Flame

15.4 Stagnation Flames

15.5 Opposed-Flow Diffusion Flames

15.6 Premixed Counterflow Flames

15.7 Arc-Length Continuation

Note

References

CHAPTER 16 HETEROGENEOUS CHEMISTRY

16.1 Taxonomy

16.2 Surface Species Naming Conventions

16.3 Concentrations within Phases

16.4 Surface Reaction Rate Expressions

16.5 Thermodynamic Considerations

16.6 General Surface Kinetics Formalism

16.7 Surface-Coverage Modification of the Rate Expression

16.8 Sticking Coefficients

16.9 Flux-Matching Conditions at a Surface

16.10 Surface Species Governing Equations

16.11 Developing Surface Reaction Mechanisms

16.12 Example Reaction Mechanism

Notes

References

CHAPTER 17 REACTIVE POROUS MEDIA

17.1 Introduction

17.2 Pore Characterization

17.3 Multicomponent Transport

17.4 Mass Conservation Equations

17.5 Energy Conservation Equations

17.6 Tubular Packed-Bed Reactor

17.7 Reconstructed Microstructures

17.8 Intra-Particle Pore Diffusion

References

CHAPTER 18 ELECTROCHEMISTRY

18.1 Electrochemical Reactions

18.2 Electrochemical Potentials

18.3 Electrochemical Thermodynamics and Reversible Potentials

18.4 Electrochemical Kinetics

18.5 Electronic and Ionic Species Transport

18.6 Modeling Electrochemical Unit Cells

18.7 Principles of Composite SOFC Electrodes

18.8 SOFC Button-Cell Example

18.9 Chemistry and Model Development

References

APPENDIX A VECTOR AND TENSOR OPERATIONS

A.1 Vector Algebra

A.2 Unit Vector Algebra

A.3 Unit Vector Derivatives

A.4 Scalar Product

A.5 Vector Product

A.6 Vector Differentiation

A.7 Gradient

A.8 Gradient of a Vector

A.9 Curl of a Vector

A.10 Divergence of a Vector

A.11 Divergence of a Tensor

A.12 Laplacian

A.13 Laplacian of a Vector

A.14 Vector Derivative Identities

A.15 Gauss Divergence Theorem

A.16 Substantial Derivative

A.16.1 Substantial Derivative of a Vector

A.17 Symmetric Tensors

A.18 Stress Tensor and Stress Vector

A.19 Direction Cosines

A.20 Coordinate Transformations

A.21 Principal Axes

A.22 Tensor Invariants

A.23 Matrix Diagonalization

APPENDIX B NAVIER–STOKES EQUATIONS

B.1 General Vector Form

B.2 Stress Components

B.3 Cartesian Navier–Stokes Equations

B.4 Cartesian Navier–Stokes, Constant Viscosity

B.5 Cylindrical Navier–Stokes Equations

B.6 Cylindrical Navier–Stokes, Constant Viscosity

B.7 Spherical Navier–Stokes Equations

B.8 Spherical Navier–Stokes, Constant viscosity

B.9 Orthogonal Curvilinear Navier–Stokes

APPENDIX C EXAMPLE IN GENERAL CURVILINEAR COORDINATES

C.1 Governing Equations

APPENDIX D SMALL PARAMETER EXPANSION

APPENDIX E BOUNDARY-LAYER ASYMPTOTIC BEHAVIOR

E.1 Boundary-Layer Approximation

E.2 A Prototype for Boundary-Layer Behavior

APPENDIX F COMPUTATIONAL ALGORITHMS

F.1 Differential Equations from Chemical Kinetics

F.2 Stiff Model Problem

F.3 Solution Methods

F.4 Differential-Algebraic Equations

F.5 Solution of Nonlinear Algebraic Equations

F.6 Continuation Procedures

F.7 Transient Sensitivity Analysis

F.8 Transient Ignition Example

References

APPENDIX G MATLAB EXAMPLES

G.1 Steady-State Couette–Poiseuille Flow

G.2 Steady Semi-Infinite Stagnation Flow

G.3 Steady Finite-Gap Stagnation Flow

G.4 Transient Stokes Problem

G.5 Graetz Problem

G.6 Channel Boundary Layer Entrance

G.7 Rectangular Channel Friction Factor

INDEX

EULA

List of Tables

Chapter 2

Table 2.1

Chapter 7

Table 7.1

Table 7.2

Chapter 10

Table 10.1

Chapter 11

Table 11.1

Table 11.2

Chapter 12

Table 12.1

Chapter 14

Table 14.1

Table 14.2

Chapter 16

Table 16.1

Chapter 17

Table 17.1

Chapter 18

Table 18.1

Guide

Cover

Table of Contents

Preface

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