Fluid Mechanics for Chemical Engineering E-Book

Mathieu Mory

• Herausgeber: John Wiley & Sons
• Kategorie: Fachliteratur
• Sprache: Englisch

Seitenzahl: 597

Veröffentlichungsjahr: 2013

Beschreibung

The book aims at providing to master and PhD students the basic knowledge in fluid mechanics for chemical engineers. Applications to mixing and reaction and to mechanical separation processes are addressed. The first part of the book presents the principles of fluid mechanics used by chemical engineers, with a focus on global theorems for describing the behavior of hydraulic systems. The second part deals with turbulence and its application for stirring, mixing and chemical reaction. The third part addresses mechanical separation processes by considering the dynamics of particles in a flow and the processes of filtration, fluidization and centrifugation. The mechanics of granular media is finally discussed.

Leseprobe

Table of Contents

Preface

Part I: Elements in Fluid Mechanics

Chapter 1: Local Equations of Fluid Mechanics

1.1. Forces, stress tensor, and pressure

1.2. Navier–Stokes equations in Cartesian coordinates

1.3. The plane Poiseuille flow

1.4. Navier–Stokes equations in cylindrical coordinates: Poiseuille flow in a circular cylindrical pipe

1.5. Plane Couette flow

1.6. The boundary layer concept

1.7. Solutions of Navier–Stokes equations where a gravity field is present, hydrostatic pressure

1.8. Buoyancy force

1.9. Some conclusions on the solutions of Navier–Stokes equations

Chapter 2: Global Theorems of Fluid Mechanics

2.1. Euler equations in an intrinsic coordinate system

2.2. Bernoulli’s theorem

2.3. Pressure variation in a direction normal to a streamline

2.4. Momentum theorem

2.5. Evaluating friction for a steady-state flow in a straight pipe

2.6. Pressure drop in a sudden expansion (Borda calculation)

2.7. Using the momentum theorem in the presence of gravity

2.8. Kinetic energy balance and dissipation

2.9. Application exercises

Chapter 3: Dimensional Analysis

3.1. Principle of dimensional analysis, Vaschy–Buckingham theorem

3.2. Dimensional study of Navier–Stokes equations

3.3. Similarity theory

3.4. An application example: fall velocity of a spherical particle in a viscous fluid at rest

3.5. Application exercises

Chapter 4: Steady–State Hydraulic Circuits

4.1. Operating point of a hydraulic circuit

4.2. Steady-state flows in straight pipes: regular head loss

4.3. Turbulence in a pipe and velocity profile of the flow

4.4. Singular head losses

4.5. Notions on cavitation

4.6. Application exercises

4.7. Bibliography

Chapter 5: Pumps

5.1. Centrifugal pumps

5.2. Classification of turbo pumps and axial pumps

5.3. Positive displacement pumps

Chapter 6: Transient Flows in Hydraulic Circuits: Water Hammers

6.1. Sound propagation in a rigid pipe

6.2. Over-pressures associated with a water hammer: characteristic time of a hydraulic circuit

6.3. Linear elasticity of a solid body: sound propagation in an elastic pipe

6.4. Water hammer prevention devices

Chapter 7: Notions of Rheometry

7.1. Rheology

7.2. Strain, strain rate, solids and fluids

7.3. A rheology experiment: behavior of a material subjected to shear

7.4. The circular cylindrical rheometer (or Couette rheometer)

7.5. Application exercises

Part II: Mixing and Chemical Reactions

Chapter 8: Large Scales in Turbulence: Turbulent Diffusion – Dispersion

8.1. Introduction

8.2. Concept of average in the turbulent sense, steady turbulence, and homogeneous turbulence

8.3. Average velocity and RMS turbulent velocity

8.4. Length scale of turbulence: integral scale.

8.5. Turbulent flux of a scalar quantity: averaged diffusion equation

8.6. Modeling turbulent fluxes using the mixing length model

8.7. Turbulent dispersion

8.8. The k-ε model

8.9. Appendix: solution of a diffusion equation in cylindrical coordinates

8.10. Application exercises

Chapter 9: Hydrodynamics and Residence Time Distribution – Stirring

9.1. Turbulence and residence time distribution

9.2. Stirring

9.3. Appendix: interfaces and the notion of surface tension

Chapter 10: Micromixing and Macromixing

10.1. Introduction

10.2. Characterization of the mixture: segregation index

10.3. The dynamics of mixing

10.4. Homogenization of a scalar field by molecular diffusion: micromixing

10.5. Diffusion and chemical reactions

10.6. Macromixing, micromixing, and chemical reactions

10.7. Experimental demonstration of the micromixing process

Chapter 11: Small Scales in Turbulence

11.1. Notion of signal processing, expansion of a time signal into Fourier series

11.2. Turbulent energy spectrum.

11.3. Kolmogorov’s theory

11.4. The Kolmogorov scale.

11.5. Application to macromixing, micromixing and chemical reaction

11.6. Application exercises

Chapter 12: Micromixing Models

12.1. Introduction

12.2. CD model.

12.3. Model of interaction by exchange with the mean

12.4. Conclusion

12.5. Application exercise

Part III: Mechanical Separation

Chapter 13: Physical Description of a Particulate Medium Dispersed Within a Fluid

13.1. Introduction

13.2. Solid particles

13.3 Fluid particles

13.4. Mass balance of a mechanical separation process

Chapter 14: Flows in Porous Media

14.1. Consolidated porous media; non-consolidated porous media, and geometrical characterization

14.2. Darcy’s law

14.3. Examples of application of Darcy’s law

14.4. Modeling Darcy’s law through an analogy with the flow inside a network of capillary tubes

14.5. Modeling permeability, Kozeny-Carman formula

14.6. Ergun’s relation

14.7. Draining by pressing

14.8. The reverse osmosis process

14.9. Energetics of membrane separation

14.10. Application exercises

Chapter 15: Particles Within the Gravity Field

15.1. Settling of a rigid particle in a fluid at rest

15.2. Settling of a set of solid particles in a fluid at rest

15.3. Settling or rising of a fluid particle in a fluid at rest

15.4. Particles being held in suspension by Brownian motion

15.5. Particles being held in suspension by turbulence

15.6. Fluidized beds

15.7. Application exercises

Chapter 16: Movement of a Solid Particle in a Fluid Flow

16.1. Notations and hypotheses

16.2. The Basset, Boussinesq, Oseen, and Tchen equation

16.3. Movement of a particle subjected to gravity in a fluid at rest

16.4. Movement of a particle in a steady, unidirectional shear flow

16.5. Lift force applied to a particle by a unidirectional flow

16.6. Centrifugation of a particle in a rotating flow

16.7. Applications to the transport of a particle in a turbulent flow or in a laminar flow

Chapter 17: Centrifugal Separation

17.1 Rotating flows, circulation, and velocity curl

17.2. Some examples of rotating flows

17.3. The principle of centrifugal separation

17.4. Centrifuge decanters

17.5. Centrifugal separators

17.6. Centrifugal filtration

17.7. Hydrocyclones

17.8. Energetics of centrifugal separation.

17.9. Application exercise

Chapter 18: Notions on Granular Materials

18.1. Static friction: Coulomb’s law of friction

18.2. Non-cohesive granular materials: Angle of repose, angle of internal friction

18.3. Microscopic approach to a granular material

18.4. Macroscopic modeling of the equilibrium of a granular material in a silo

18.5. Flow of a granular material: example of an hourglass

Physical Properties of Common Fluids

Index

First published 2011 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 Ltd27-37 St George’s RoadLondon SW19 4EUUKJohn Wiley & Sons, Inc.111 River StreetHoboken, NJ 07030USAwww.iste.co.ukwww.wiley.com

© ISTE Ltd 2011

The rights of Mathieu Mory 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

Mory, Mathieu.

Fluid mechanics for chemical engineering / Mathieu Mory.

p. cm.

Includes bibliographical references and index.

ISBN 978-1-84821-281-7 (hardback)

1. Chemical processes. 2. Fluid dynamics. I. Title.

TP155.7. M673 2011

660’.29--dc22

2010048940

British Library Cataloguing-in-Publication Data

A CIP record for this book is available from the British Library

ISBN 978-1-84821-281-7

Preface

This book is mainly about fluid mechanics, but it is first intended to MSc and professionals who need to make use of fluid mechanics skills for applications pertaining to chemical and process engineering. This objective explains the presentation of fluid mechanics as given in this book. The foundations of the discipline are generally not set out, but the book endeavours to help students and professionals to use the tools of fluid mechanics in a pertinent way, while attempting to point out the key ideas associated with the concepts encountered.

As an example, the ability to use Navier-Stokes equations appropriately is more important, to most practitioners, than the ability to prove them. It is of course very interesting to have reflected upon that proof at some point, but this can be found in other books, and this is not the intended objective of this book. Besides, I will be very happy if this book can prove useful for specialists in fluid mechanics, giving them the opportunity to discover important applications of fluid mechanics in the field of chemical engineering.

The book is divided into three parts.

The first part is about the basics of fluid mechanics. Emphasis is on general theorems that constitute the tools used in the first instance by engineers. Chapter 2 forms the main foundation of that part, which then branches into short chapters tackling the key notions implemented by a specialist in process engineering (hydraulic circuits, pumps, rheometry, etc.). The concepts of dimensional analysis are also emphasized (Chapter 3).

The second part deals with mixing phenomena associated with turbulence. In that part, notions relating to turbulence are first presented. The problems associated with dispersion and mixing in connection with chemical reactions are then considered. The key notion, from a fundamental standpoint, regards the interrelation between the phenomena of turbulence and that of molecular diffusion, the latter being the actual cause for mixing that allows a chemical reaction to occur. Toward the end of this part, elementary models for the simulation of reacting flows are also presented.

The third part presents the tools of fluid mechanics used in mechanical fluid/solid and fluid/fluid separation processes. Process unit operations considered include filtration, fluidization, and centrifugal separation. I have also tried to provide, in that part, means for understanding more complex approaches regarding the modeling of a solid particle’s dynamics within a fluid flow (Chapter 16) and a presentation of the physics of a granular material, which will often be of interest to specialists in process engineering.

Although the whole treatment might not seem very ambitious, my goal was primarily to specify the elementary notions in fields related to fluid mechanics, in order to facilitate access to other, more specialized books.

This book draws its material chiefly from the courses I have been teaching for about 10 years at the École Nationale Supérieure en Génie des Technologies Industrielles, an engineering curriculum at the University of Pau and the Adour Region (UPPA) in the chemical and process engineering specialization. For the sake of consistency, I have endeavored to expand the coverage of the subject matter by complementing certain parts of my lectures. As this is an adaptation of a book previously published in French, and of course drawn from material originally taught to French students, there were of course issues regarding the references. I am fully aware that some of the literature in French will not be available to non-French speakers, and I apologise for this, but it would have been unfair not to keep these citations, as they were significant sources for writing the book. Wherever possible English substitutions to the French references have been provided, and where not, additional English textbooks have been suggested as a complement to the reading of the book.

I wish to thank the UPPA for giving me an opportunity to lecture in these topics. I am thankful to my colleagues S. Alexandrova, A. Saboni, and D. Graebling, from the UPPA, for their insightful discussions that proved invaluable to me while writing this book. Beyond this, their friendship has been a tremendous support for me throughout this critical work.

I have also used my experience in research and education while writing the various chapters of this book.

It is important to me to mention first my first teaching experiences, when I joined a team in Grenoble, teaching fluid mechanics at the École Nationale des Travaux Publics de l’Etat. The course taught by C. Le Provost, who was then in charge, emphasized the use and understanding of tools rather than the proof of their validity. I have tried to emphasize and retain that approach as far as possible in this book. Later, I was lucky to receive an invaluable educational tutoring from R. Moreau, M. Favre-Marinet, and A. Temperville, at the École Nationale Supérieure d’Hydraulique et de Mécanique de Grenoble and at Joseph Fourier University.

This book also includes the legacy of the one year I spent (1988–1989) on secondment to the Centre d’Etudes et de Recherche de Grenoble (ALSTHOM group)1, when I learnt a great deal alongside specialists in industrial hydraulics. My thanks to P. Chantrel, who was my supervisor and also to the whole team in this regard.

My thesis supervisor, E. Hopfinger, might not recognize much of himself in this book. Yet, I received my training, first and foremost, from him during my PhD years. He was instrumental in expanding my knowledge base. More importantly, by making himself available to me, he enabled me to get acquainted with the way he saw and tackled fluid mechanics. Those years were undoubtedly the richest and the most momentous in my professional life. I wish to express to him my recognition and my gratitude.

Lastly, I thank the experts who agreed to read this book and took time to offer very useful reviews in order to improve it and rectify errors. Jean-Luc Achard monitored the whole enterprise and I thank him for that, although I often cursed him during the editing stage for obvious reasons! Nevertheless, he has remained a true friend since 1982.

Mathieu MoryJanuary 2011

1 Now a subsidiary of the Environne’Tech company (http://cerg-fluides.com/_)

Part I

Elements in Fluid Mechanics

Chapter 1

Local Equations of Fluid Mechanics

In this chapter, to begin with, we recall the Navier–Stokes equations that govern the flow of a Newtonian fluid. These equations explain the behavior of common fluids such as water or air. For a given force field and boundary conditions, the solution of Navier–Stokes equations controls both the flow velocity and pressure at any point and at any time in the domain under consideration. The Navier–Stokes equations are the most commonly used equations in fluid mechanics; they provide the knowledge of the flow of Newtonian fluids at the local level.

The solutions to Navier–Stokes equations are typically very difficult to arrive at. This fact is attested to by the extraordinary development of numerical computation in fluid mechanics. Only a few exact analytical solutions are known for Navier– Stokes equations. We present in this chapter some laminar flow solutions whose interpretation per se is essential in this regard. We then introduce the boundary layer concept. We conclude the chapter with a discussion on the uniqueness of solutions to Navier–Stokes equations, with special reference to the phenomenon of turbulence.

This being the introductory chapter, we have not included a prolonged discussion on continuum mechanics. The derivation of Navier–Stokes equations is available in other continuum mechanics or fluid mechanics books.1 We have consciously avoided concentrating on the derivational aspects of Navier–Stokes equations as we are convinced that it is far more important to understand the meaning of the different terms of these equations and to hence interpret the way they are applied in the study of fluid mechanics in general. In addition, we limit ourselves to introducing the only classical concept from continuum mechanics to be used in this book, namely, the ability to calculate the force acting through a surface passing through a point that lies inside a continuum, using the stress tensor. Hence, Chapter 1 partly serves as a collection of formulae, while proper physical principles are discussed in the remainder of this book. The reader might wish to read this chapter without pondering on it for long, and then may refer to it later, if necessary, for it may be insightful in such a case.

1.1. Forces, stress tensor, and pressure

Consider a domain, V, containing a fluid. The fluid’s flow is controlled by various forces acting on it. The laws of mechanics help us to distinguish two types of forces:

– Body forces, which are exerted at every point in a domain. Weight is the most common body force.

– Forces that are transferred from one particle to another, at the boundary of and within the domain. These forces are expressed using the stress tensor. This is where the continuum concept intervenes.

The force at a point M in the continuum is associated with surface element ds whose orientation is given by the unit normal vector (Figure 1.1). The force , which is proportional to the surface ds, varies when the orientation of the surface changes. It is determined at the point M using the stress tensor [Σ], which is a symmetric,2 3 × 3 matrix:

[1.1]

Figure 1.1.Forcesandexerted at a point M through two surface elements ds1and ds2, whose orientations are given by normalsand. Both ds1and ds2are elements of closed surfaces S1(solid line) and S2(dashed line), respectively, surrounding volumes V1and V2

The force through the surface element ds whose normal is is written as:

[1.2]

The force applied to a closed surface S surrounding an arbitrary volume V in the continuum (Figure 1.1) can be derived using the surface integral:

[1.3]

The concept of the stress tensor is inseparable from the mechanical principle of action and reaction. The normal vector is oriented toward the exterior of the domain on which the force is applied. The direction of the force is reversed if one considers the force exerted by the domain V on the exterior. . The force is exerted by the external environment through the surface of separation.