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Computational Flow Modeling for Chemical Reactor Engineering 1st Edition Vivek V. Ranade (Eds.) Computational Flow Modeling for Chemical Reactor Engineering 1st Edition Vivek V. Ranade (Eds.) Computational Flow Modeling for Chemical Reactor Engineering 1st Edition Vivek V. Ranade (Eds.)

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Computational Flow Modeling for Chemical Reactor Engineering 1st Edition Vivek V. Ranade (Eds.)
Computational Flow Modeling for Chemical Reactor Engineering 1st Edition Vivek V. Ranade (Eds.) Digital Instant Download Author(s): Vivek V. Ranade (Eds.) ISBN(s): 9780125769600, 0125769601 Edition: 1st File Details: PDF, 6.62 MB Year: 2002 Language: english
COMPUTATIONAL FLOW MODELING FOR CHEMICAL REACTOR ENGINEERING
Process Systems Engineering Series A series edited by George Stephanopoulos and John Perkins Volume 1 Mathematical Modeling Rutherford Aris Volume 2 Data Processing and Reconciliation for Chemical Process Operations Jos´ anchez e A Romagnoli & Mabel Cristina S´ Volume 3 Linear Algebra and Linear Operators in Engineering Ted H Davis & Kendall T Thomson Volume 4 Process Modelling and Model Analysis Katalin Hangos & Ian Cameron Volume 5 Computational Flow Modeling for Chemical Reactor Engineering Vivek V Ranade
COMPUTATIONAL FLOW MODELING FOR CHEMICAL REACTOR ENGINEERING Vivek V. Ranade Industrial Flow Modeling Group Chemical Engineering Division National Chemical Laboratory Pune 411008, India San Diego San Francisco New York Boston London Sydney Tokyo
This book is printed on acid-free paper. Copyright © 2002 by ACADEMIC PRESS All Rights Reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without the prior permission in writing from the publisher. The appearance of the code at the bottom of the first page of a chapter in this book indicates the Publisher’s consent that copies of the chapter may be made for personal or internal use of specific clients. This consent is given on the condition, however, that the copier pay the stated per copy fee through the Copyright Clearance Center, Inc. (222 Rosewood Drive, Danvers, Massachusetts 01923), for copying beyond that permitted by Sections 107 or 108 of the U.S. Copyright Law. This consent does not extend to other kinds of copying, such as copying for general distribution, for advertising or promotional purposes, for creating new collective works, or for resale. Copy fees for pre-2002 chapters are as shown on the title pages. If no fee code appears on the title page, the copy fee is the same as for current chapters. ISSN# /2002 $35.00. Explicit permission from Academic Press is not required to reproduce a maximum of two figures or tables from an Academic Press chapter in another scientific or research publication provided that the material has not been credited to another source and that full credit to the Academic Press chapter is given. Academic Press A Harcourt Science and Technology Company 525 B Street, Suite 1900, San Diego, California 92101-4495, USA http://www.academicpress.com Academic Press Harcourt Place, 32 Jamestown Road, London NW1 7BY, UK http://www.academicpress.com ISBN 0-12-576960-1 Library of Congress Catalog Number: 2001090198 A catalogue record of this book is available from the British Library Typeset by Newgen Imaging Systems (P) Ltd., Chennai, India Printed and bound in Great Britain by Bookcraft, Bath, UK 02 03 04 05 06 07 BC 9 8 7 6 5 4 3 2 1
To Nanda & Vishakha
Computational Flow Modeling for Chemical Reactor Engineering 1st Edition Vivek V. Ranade (Eds.)
CONTENTS PREFACE xi I INTRODUCTION 1 Reactor Engineering and Flow Modeling 1.1. Chemical Reactor Engineering (CRE) 7 1.2. Computational Flow Modeling (CFM) 19 1.3. CFM for CRE 25 References 30 II COMPUTATIONAL FLOW MODELING 2 Mathematical Modeling of Flow Processes 2.1. Basic Governing Equations 35 2.2. Auxiliary Equations 44 2.3. Boundary Conditions 45 vii
3 viii CONTENTS 2.4. Discussion 52 2.5. Summary 54 References 54 Turbulent Flow Processes 3.1. Introduction 57 3.2. Turbulence: Physical Picture 58 3.3. Modeling Approaches 62 3.4. Turbulence Models Based on RANS 68 3.5. Summary 81 References 82 4 Multiphase Flow Processes 4.1. Introduction 85 4.2. Modeling Dispersed Multiphase Flows 90 4.3. Other Types of Multiphase Flows 112 4.4. Summary 114 References 115 Appendix 4.1. Time Scales for Dispersed Multiphase Flows 118 Appendix 4.2. Correlations for Drag Coefficient 119 Appendix 4.3. Interphase Heat and Mass Transfer Correlations 121 5 Reactive Flow Processes 5.1. Introduction 123 5.2 Turbulent Reactive Mixing 124 5.3. Modeling Approaches 131 5.4. RANS-based Models of Reactive Flow Processes 134 5.5. Multiphase Reactive Flow Processes 144 5.6. Summary 147 References 147 6 Numerical Solution of Model Equations 6.1. Introduction 151 6.2. Finite Volume Method 153 6.3. Finite Volume Method for Calculation of Flow Field 165 6.4. Finite Volume Method for Unsteady Flows 173 6.5. Application of Finite Volume Method 175 6.6. Summary 185 References 188
ix 7 CONTENTS Numerical Solution of Complex Flow Models 7.1. Simulation of Turbulent Flows 191 7.2. Simulation of Multiphase Flows 197 7.3. Simulation of Reactive Flows 216 7.4. Special Topics 219 7.5. Summary 225 References 226 8 Computational Tools for Simulating Flow Processes 8.1. Mapping a Computational Flow Model on a Computer 229 8.2. Pre-processors 232 8.3. Solvers 236 8.4. Post-processors 238 8.5. Summary 240 References 240 III CFM FOR CRE 9 Flow Modeling for Reactor Engineering 9.1. Reactor Engineering Methodology 244 9.2. Example 1: Suspension Polymerization Reactor 247 9.3. Example 2: OXY Reactor for EDC 254 9.4. Example 3: Bubble Column Reactor 264 9.5. Example 4: FCC Regenerator 271 9.6. Summary 281 References 281 IV APPLICATIONS 10 Stirred Reactors 10.1. Engineering of Stirred Reactors 286 10.2. CFD-based Modeling of Stirred Reactors 290 10.3. Computational Snapshot Approach 292 10.4. Application to Reactor Engineering 318 10.5. Summary 323 References 323
x CONTENTS 11 Bubble Column Reactors 11.1. Engineering of Bubble Column Reactors 328 11.2. CFD-based Modeling of Bubble Column Reactors 332 11.3. Application to Reactor Engineering 355 11.4. Summary 360 References 361 Appendix 11.1. Multigroup Model to Simulate Bubble Size Distribution 363 12 Fluidized Bed Reactors 12.1. Engineering Fluidized Bed Reactors 368 12.2. CFD Modeling of Gas–Solid Reactors 376 12.3. Applications to Reactor Engineering 394 12.4. Summary 400 References 400 13 Fixed Bed and Other Types of Reactors 13.1. Fixed Bed Reactors 403 13.2. Trickle Bed Reactors/Packed Column Reactors 415 13.3. Other Reactors 419 13.4. Summary 421 References 422 V EPILOGUE 14 Epilogue NOTATION 433 AUTHOR INDEX 439 SUBJECT INDEX 445 Colour plate section between pages 210–211
PREFACE Industrial Flow Modeling Group, iFMg at National Chemical Laboratory undertakes contract research and consultancy projects in the general area of reactor engineering. We use computational flow modeling to carry out these industrial projects. Compu­ tational flow modeling is a powerful tool for the design and analysis of industrial flow processes. Though it is routinely used as a design tool in aerospace engineering, chemical engineers have started exploiting the power of computational flow model­ ing only recently. Considering the central role played by reactors in chemical process industries, there is tremendous potential for applying computational flow-modeling tools to improve reactor engineering. Through interactions with practicing engineers from industry, it has been real­ ized that there is insufficient help available to harness state of the art computational flow modeling tools for complex, industrial reactor engineering applications. Many reactor engineers either consider that the flow complexities of industrial reactors are impossible to simulate, or expect miracles from off-the-shelf, commercial flow mod­ eling tools. These two diverse views arise because of inadequate interactions between the flow modeling and industrial reactor engineering communities. It is essential to clearly understand the role of flow modeling in reactor engineering. It is necessary to relate the individual aspects of reactor engineering and computational flow mod­ eling in a coherent and consistent way to realize the potential of computational flow modeling for reactor engineering research and practice. To assist practicing engi­ neers in these aspects, workshops on ‘computational flow modeling for chemical process industries’ were started at the National Chemical Laboratory. The enthusi­ astic response to these workshops has encouraged me to write this book, which is xi
xii PREFACE an expanded and formalized presentation of workshop notes. I have tried to provide sufficient information to understand and to define the specific role of computational flow modeling for reactor engineering applications, to select appropriate tools and to apply these tools to link reactor hardware to reactor performance. The intended audience of the book is practicing chemical engineers working in industry as well as chemical engineering scientists and research students working in the area of reactor engineering. Some prior background in reactor engineering and numerical techniques is assumed. The information in the book is organized to facilitate the central task of reac­ tor engineer, that is, relating reactor hardware to reactor performance. Several steps to achieve such a task are discussed to clearly define the role of flow modeling in the overall reactor engineering activity. The necessity of using a hierarchy of mod­ eling tools and establishing a clear relationship between the objectives of reactor engineering and the computational flow model is emphasized with the help of exam­ ples. The overall methodology of achieving the objectives of reactor engineering via computational flow modeling is discussed. Desirable characteristics and key issues in selecting appropriate computational fluid dynamics (CFD) codes are briefly dis­ cussed. A number of examples and case studies covering the four major reactor types used in chemical industries, namely, stirred reactors, bubble column reactors, flu­ idized bed reactors and fixed bed reactors are included. In view of the wide range of reactor types, however, it is impossible to cover all the reactor types and flows relevant to these reactor types. Emphasis on certain topics and the selection of examples is biased and is directly related to my own research and consulting experience. Some topics, like radiative heat transfer, laminar reactive flows are completely omitted. I have, however, made an attempt to evolve general guidelines, which will be useful for solving practical reactor engineering problems. Some comments on future trends in computational flow modeling and its use by the chemical engineering community are also included. The material included in this book may be used in several ways and at various stages of flow modeling projects. It may be used as a basic resource for making appro­ priate decisions about investment in the application of CFD to reactor engineering. It may be used as a study material for an in-house course to facilitate the apprecia­ tion and application of computational flow modeling for reactor engineering. It may be used as a companion book while solving practical reactor engineering problems. I hope that this book will encourage chemical engineers to exploit the potential of computational flow modeling and will eventually lead to better reactor engineering. This book is essentially the outcome of my last fifteen years of association with this subject. I have received a great deal of help from numerous persons over these years in formulating and revising my views on both computational flow modeling and chemical reactor engineering. I am particularly indebted to my teacher and mentor, Professor J.B. Joshi, who has been one of the leading practitioners of process fluid dynamics for three decades. There are not adequate words to express his contributions to this book. I was fortunate to have an opportunity to work with Dr R.V. Chaudhari and Dr R.A. Mashelkar at the National Chemical Laboratory. Both of them always extended their full support and encouragement in my every endeavor. Without their support, it would not have been possible to develop our industrial flow modeling activity, on which this book is based. I would like to acknowledge the support pro­ vided by Professor H.E.A. van den Akker of Delft University of Technology and by
PREFACE xiii Professors G.F. Versteeg and J.A.M. Kuipers of University of Twente, The Nether­ lands. My brief stay at Professor van den Akker’s laboratory at Delft introduced me to different commercial CFD solvers and expanded my horizons. The idea of this book was formalized during my second visit to The Netherlands at University of Twente. I would also like to thank Dr Bharatan Patel of Fluent Inc. and Mr Paresh Patel of Fluent India for their support. I am grateful to my associates and collaborators with whom I worked on different industrial projects. In particular, I owe much to Professor J.R. Bourne, Mr Vaibhav Deshpande, Ms S.M.S. Dommeti and Mr Yatin Tayalia. My students, especially Kapil Girotra, Ashwin Sunthankar, Ranjit Utikar, Aravind Rammohan, Sachin Muthian, Avinash Khopkar, Prashant Gunjal, Vivek Buwa and Shishir Sable have contributed to this book in different ways. This includes technical contributions either in a direct or indirect way, helping me to collect the required information and reading the draft manuscript. My father, Mr V.B. Ranade also has painstakingly read the entire manuscript and suggested several ways to enhance the clarity of presenta­ tion. The manuscript was improved wherever their suggestions were incorporated. Any remaining errors or shortcomings are, needless to say, the responsibility of the author. Finally, I wish to thank my wife, Nanda, for her patience, understanding and enthusiastic support, which carried me through this long and arduous writing process. Vivek V. Ranade December 2000 Pune
Computational Flow Modeling for Chemical Reactor Engineering 1st Edition Vivek V. Ranade (Eds.)
PART I INTRODUCTION
Computational Flow Modeling for Chemical Reactor Engineering 1st Edition Vivek V. Ranade (Eds.)
1 REACTOR ENGINEERING AND FLOW MODELING All industrial chemical processes are designed to transform cheap raw materials to high value products (usually via chemical reactions). A ‘reactor’, in which such chem­ ical transformations take place, has to carry out several functions such as bringing reactants into intimate contact (to allow chemical reactions to occur), providing an appropriate environment (temperature and concentration fields, catalysts) for an ade­ quate time and allowing for the removal of products. Chemical reactor engineering includes all the activities necessary to evolve the best possible hardware and operating protocol of the reactor to carry out the desired transformation of raw materials (or reactants) to value added products. A reactor engineer has to ensure that the reactor hardware and operating protocol satisfy various process demands without compro­ mising safety, the environment and economics. To realize this, the reactor engineer has to establish a relationship between reactor hardware and operating protocols and various performance issues (Fig. 1.1). Successful reactor engineering requires expertise from various fields including thermodynamics, chemistry, catalysis, reaction engineering, fluid dynamics, mixing and heat and mass transfer. The reactor engineer has to interact with chemists to understand the basic chemistry and peculiarities of the catalyst. Based on such an understanding and proposed performance targets, the reactor engineer has to abstract the information relevant to identifying the characteristics of the desired fluid dynamics of the reactor. The reactor engineer then has to conceive suitable reactor hardware and operating protocols to realize this desired fluid dynamics in practice. Thus, fluid 3
4 CHAPTER 1 REACTOR ENGINEERING AND FLOW MODELING 4A=?J�H 2AHB�H�=�?A +��LAHIE�� �FAH=E�EJO 2H�@K?J GK=�EJO +�IJI -�LEH���A�J=� E�F=?J 5=BAJO IA�E�=J?D� ?��JE�K�KI 4A=?J�H �FAH=JE�C @EIJHEKJ�HI IDKJ�@�M� FH�J�?��I IA�A?JELEJO 5J=E�EJO 4A=?J�H0=H@M=HA �FAH=JE�C2H�J�?��I ��@A �B �FAH=JE��� =J?D� ?��BECKH=JE��� IE�A ID=FA� BAA@ ANEJ �����AI ?��@EJE��I�B��M H=JA�FHAIIKHA� JA�FAH=JKHA�B��M HACE�A�46, 4A=?J�H E�JAH�=�I =BB�AI� DA=J JH=�IBAH ?�E�I� 5J=HJ�KF FIGURE 1.1 Chemical reactor engineering. dynamicsplaysapivotalroleinestablishingtherelationshipbetweenreactorhardware and reactor performance. To establish the relationship between reactor hardware and reactor performance, it is necessary to use a variety of different tools/models. Creative application of the best possible tools is required to evolve the best possible hardware configura­ tion and operating protocol for the reactor under consideration. Various tools for modeling chemical kinetics and reactions are already well developed and routinely used in practice. This activity constitutes the major part of conventional chemical reaction engineering. Several excellent textbooks discussing these tools are available (for example, Aris, 1965; Levenspiel, 1972; Westerterp et al., 1984; Naumann, 1987). Most models falling in this category make use of drastic simplifications when treating the reactor fluid dynamics. Indeed, sophisticated models and theories are available to predict the interaction between chemistry and transport processes such as mixing, heat and mass transfer. However, these models rarely attempt to rigorously relate transport properties with the reactor hardware and operating protocol. For a specific chemistry/catalyst, the reactor performance is a complex function of the underlying transport processes. These transport processes are, in turn, governed by the underlying fluid dynamics, and therefore by a variety of design and operating parameters of the process equipment. In conventional reaction engi­ neering, experimental and semi-theoretical methods (like cold flow simulations or tracer studies) are used to relate fluid dynamics and mixing with reactor hardware and operating parameters. The information obtainable from these methods is usu­ ally described in an overall/global parametric form. This practice conceals detailed local information about turbulence and mixing, which may ultimately determine reactor performance. This approach essentially relies on prior experience and trial and error methods to evolve suitable reactor hardware. These tools, therefore, are increasingly perceived as being expensive and time consuming ways of developing better reactor technologies. It is necessary to adapt and develop better techniques and tools to relate reactor hardware with fluid dynamics and resultant transport processes.
5 CHAPTER 1 REACTOR ENGINEERING AND FLOW MODELING Over the years, aerospace engineers, who are most concerned with the task of establishing the relationship between the hardware and resulting fluid dynamics, have developed and routinely use computational fluid dynamics. Computational fluid dynamics (CFD) is a body of knowledge and techniques used to solve mathematical models of fluid dynamics on digital computers. In recent years, chemical engineers have realized that, although establishing a relationship between reactor hardware and fluid dynamics is less central (compared to aerospace engineers) to their role, it is no less important. With the development of high performance computers and advances in numerical techniques and algorithms, chemical engineers have started exploiting the power of computational fluid dynamics tools. Considering the cen­ tral role of reactors in chemical process industries, there is tremendous potential for applying these tools for better reactor engineering. If applied properly, computa­ tional flow modeling (CFM) may reduce development time, leading to reduced time to market, shorter payback time and better cash flow. It is, however, necessary to adapt CFD techniques and to develop a computational flow modeling approach to apply them to chemical reactor engineering. This book is written with the inten­ tion of assisting practicing engineers and researchers to develop such an approach. Individual aspects of chemical reactor engineering and computational flow modeling (CFM) are discussed and related in a coherent way to convey and clarify the potential of computational flow modeling for reactor engineering research and practice. The emphasis is not on providing a complete review but is on equipping the reader with adequate information and tips to undertake a complex flow-modeling project. The focus is on modeling fluid flows and developing tractable reactor engineering mod­ els. Numerical issues are dealt with in adequate detail to provide appreciation of the important aspects and to guide the development and incorporation of new models into available solvers. Readers interested in developing their own complete solvers may refer to specialized books on CFD (for example, Ferziger and Peric, 1995; Patankar, 1980). The information in this book is organized to facilitate the central task of a reactor engineer, that is, relating reactor hardware to reactor performance. This chapter pro­ vides a brief introduction to the contents to be covered in detail in subsequent chapters. Here, the roles of flow modeling and computational flow modeling are discussed in the context of reactor engineering. Various aspects of chemical reaction and reactor engineering are discussed in Section 1.1 to clearly define the role of flow modeling in overall activity. Computational flow modeling, its advantages and limitations are discussed in Section 1.2. Introduction to the use of CFM for reactor engineering is given in Section 1.3. This chapter, as a whole, will be used to appreciate and identify the potential of CFM for reactor engineering. The theoretical and numerical basis of computational flow modeling (CFM) is described in detail in Part II. The three major tasks involved in CFD, namely, mathe­ matical modeling of fluid flows, numerical solution of model equations and computer implementation of numerical techniques are discussed. The discussion on mathe­ matical modeling of fluid flows has been divided into four chapters (2 to 5). Basic governing equations (of mass, momentum and energy), ways of analysis and possible simplifications of these equations are discussed in Chapter 2. Formulation of different boundary conditions (inlet, outlet, walls, periodic/cyclic and so on) is also discussed. Most of the discussion is restricted to the modeling of Newtonian fluids (fluids exhibit­ ing the linear dependence between strain rate and stress). In most cases, industrial
6 CHAPTER 1 REACTOR ENGINEERING AND FLOW MODELING reactors are operated under a turbulent flow regime. Introduction to turbulence and various approaches (direct numerical simulations or DNS, large eddy simulations or LES and Reynolds averaged Navier–Stokes equations or RANS simulations) to modeling turbulent flows are discussed in Chapter 3. Turbulence models based on the RANS approach are discussed in more detail, with special consideration to reactor engineering applications. For several industrial applications, multiphase reactors are used, which involves contacting more than one phase. Various approaches to mod­ eling such multiphase flows are discussed in Chapter 4 with special emphasis on dispersed multiphase flows. The interactions between chemical reactions and fluid dynamics are discussed in Chapter 5. Model equations governing flow processes relevant to reactor engineering appli­ cations are quite often complex, non-linear and coupled. More often than not, analytical solutions are not possible and numerical methods are required to obtain a solution to the model equations. The numerical methods relevant to solving model equations are discussed in Chapters 6 and 7. Chapter 6 covers use of the finite volume method to solve generic flow models. Various aspects of the finite volume method such as discretization schemes, grid arrangements, implementation of boundary con­ ditions and algorithms for handling pressure–velocity coupling are discussed in detail. Applications of these methods to solve turbulent flows, multiphase flows and reac­ tive flows are discussed in Chapter 7. Guidelines for making appropriate selection of the available techniques based on the objective at hand are discussed. Practical ways of estimating errors in numerical solutions of model equations are discussed. The methodology and the desired qualities of computational tools required to implement these numerical methods on a digital computer to solve model equations are discussed in Chapter 8. PartIIIofthebookdiscussestheoverallmethodologyofusingcomputationalflow modeling for reactor engineering. The necessity of using a hierarchy of modeling tools and establishing a clear relationship between the objectives of reactor engineering and the computational flow model is illustrated with the help of examples. The importance of a physical understanding of the system for facilitating rational simplification of the problem, formulation of appropriate boundary conditions and identification of key issues is emphasized. The information discussed in Part I and Part II is used to evolve a systematic methodology for linking reactor hardware with reactor performance. The methodology is illustrated with the help of some practical examples. Details of the application of computational flow modeling to different types of reactors are discussed in Part IV. A separate chapter is devoted to three major reactor types used in chemical industries, namely, stirred reactors, bubble column reactors and fluidized bed reactors. Applications to fixed bed reactors and other miscella­ neous reactor types are briefly discussed in Chapter 13. Recent work on modeling the complex fluid dynamics in these reactors is critically reviewed. The modeling approaches and the flow results obtained therefrom are evaluated from the point of view of their application to reactor engineering. Limitations of the current state of knowledge in describing the complex underlying physics of some of the flows relevant to reactor engineering are discussed. Despite such limitations, suggestions are made for making the best use of these computational flow models for reactor engineering applications. The Epilogue recapitulates the lessons learnt from our experience of apply­ ing computational flow modeling while addressing practical reactor engineering
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THROUGH THE MILL If I can compose my way to success Then some time I’ll compose the rest, It will be of my childhood days Building mud houses for different plays. Oh! I was bad and mischievous, too, And always looking for something to do, And when I found nothing I surely was sad, To be good very long would make me mad. Though I longed to go to school, But I was poor and fate overruled, Then my mother, whom I love so dear, Passed away at the end of the year. Then I fought this old, rough world, For I had lost my valued pearl. And now she sleeps beneath the sod; It brought me deep sorrow though it’s the will of God. Just think of my mother, she guides me yet, And keeps me away from those sinful nets. All through life, from place to place, She ne’er let alcohol enter my taste. And I’ve ne’er lived a day I want to live o’er, Unless it was school days which I could love more, Now I’ll thank God and that sweet little her, My life’s been rough, but never a blur.
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BECKER’S JEALOUSY
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TRUELET Each day there is sunshine, Each day there are showers, Means some day in May Day We’ll be picking wild flowers.
INCH BY INCH I’m yet in the path A jogging along, That’s leading to the righteous Away from the wrong. We have not time To talk evil of others, For losing enemies To gain heavenly brothers. Oh, Lord! May the day be long In which you have power To sound the heavenly gong. We know this means Our last day, Bless us and save us In that land far away.
THE PLACE WHERE LITTLE MARY LIVES
Down a beautiful country road The roses in bloom and their perfume strewed, Oh! the joy it brought to my heart, ’Twas so tender, so sweet, I couldn ne’er depart From that place where little Mary lives. Oh! that spot beside the hill Where nature and beauty can always build, Tells a story it really seems And will always be life’s sweetest dream Of that place where little Mary lives. When she plucked and gave to me A beautiful rose in a manner so free, The heavenly breezes begin to blow And the tenderness through my heart did flow For that place where little Mary lives. That was a day of God’s decree, And oh! no scenes could sweeter be, They soothed my heart and eased my pain, May the bright sunshine ne’er turn to rain, Down where little Mary lives. But summer is soon to fade away, Followed by a cold winter day. The howling winds in the month of December, But that dear little rose I’ll always remember That come from the place where little Mary lives. Now I see the blustery snow And it’s changed the scenes where I used to go, It’s all over white Though the stars are shining bright, How sad be that place where little Mary lives. At times I think and really sigh To think of those roses that are sleeping nearby
To think of those roses that are sleeping nearby. But they will return To my heart that yearns, And for that place and its beauty Where little Mary lives.
A QUESTION Why are great men’s lives Thrown into the mist? One’s who aim at the sky, Are found at the bottom of the list.
MR. FINK
I met a man The other day On a Chicago train. By the way His face was strange And very old, And holds a sad story Yet to be told. He says, my boy, We’ll have a drink. I said, no I thank you, Mr. Fink. Then he gave a real deep sigh, Like a child about to cry. In a moment he raised and said, Then he stroked his old bald head, Patting me on my shoulder then. He faded his wrinkles into a grin, Now my lad, as I sit and think, May you never be like Mr. Fink. My younger days had I refused, Now I’d stand in different shoes; I could throw this blanket off of me And this deadly sorrow that you see Then with a nod he solemnly winked, Try and remember Mr. Fink. With a trembling he then relates Of his mighty love that’s turned to hate, He called a name that was once his wife. This was the pride that wrecked his life, Saying once I was rich, but now I beg. She’s the cause, a wretched old hag, Then there was love with a broken link
Mournfully told by Mr. Fink.
GRAY HEADS Two gray heads bowed in tears, Above hung memories of wasted years, For once they were young with the blessings of health. They sought not happiness, righteousness nor wealth, But now they jog along to end of life’s rope, The end is not far, just o’er the slope. Their lives must be studied With their heads bloomed gray To direct souls Along life’s sweeter way. ’Twill teach you their sorrow Each day ’twill bring The joy that’s in our lives ’Twill loudly ring. But if heads are hard And holds within The things you crave Be worldly sins We’ll go down to a joyless end, Leaving sorrow to have its sway, We’ll be like those two I saw the other day.
HER SOLEMN THOUGHTS Oh! cruel, cruel fate is mine, Why am I tortured with life so unkind. Cruel as the grave, it means peace for me, For there only, my sorrow, will e’er let me be. Peace or happiness, I truly know not, And gone art the sunshine that lightened my darkened spots The little birds for me do not sing so sweet And the roses have withered from the warm summer’s heat. —Mrs. Perry H. McGee
YOUR EYES AND MY EYES Your eyes so beautiful tells a tale And o’er me holds the bill of sale. With each glance they tenderly bring A little love song for my heart to sing. They hold the warmth around my soul With love, kind love, too sweet to be told. Were my eyes allowed to tell How my poor heart beats by spells. For your love it really craves, Why send it down to its grave? Time take away my haunted years And your love, sweet love, that’s caused me tears. Let your eyes shine for me real true, Then I’ll explain more love for you. The world then would cease my sorrow. This brings a brighter day to-morrow, Then forever we’d live in sweet loveland With love, much love, I’d hold your hand. By your eyes I traced your love, Being guided by the Savior above; I saw a weakening along the way That I could strengthen would it pay, But those things are hard to mend When two has love that doesn’t blend. Be careful in your daily walks, Because from some source or other there’s always a watching eye.
NATURAL BORN COLORED MAN Sam Jackson was goin’ with a real yallow gal, the one that he called his own-side pal, But he found she would deceive, she told a friend by the name of Stark. She could love Sam if he wasn’t so dark; This made a discord down town, Cause Sam was standing near, and seemed to overhear and just then he spoke right up and said: Chorus I’m a natural born gen-u-wine colored man, you don’t have to look twice to see who I am, You look at me once and your thoughts will end, cause I got that puro-de colored skin. It’s the kind of skin that the sun don’t tan, this makes me the king of the sunny land, So you go your way but bear in mind I’m what you call the puro-de gen-u- wine. Now all high yellows to Sam is in vain, he never lets them bother his brain, And all through his life he’ll letum alone, he knows that his skin’s a bit shady, So he will avoid every yellow lady, he’s got a club of his own. Where all brown skins can meet and have a musical treat For every night Sam kindly sings.
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Computational Flow Modeling for Chemical Reactor Engineering 1st Edition Vivek V. Ranade (Eds.)

  • 1. Computational Flow Modeling for Chemical Reactor Engineering 1st Edition Vivek V. Ranade (Eds.) pdf download https://ebookfinal.com/download/computational-flow-modeling-for- chemical-reactor-engineering-1st-edition-vivek-v-ranade-eds/ Explore and download more ebooks or textbooks at ebookfinal.com
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  • 5. Computational Flow Modeling for Chemical Reactor Engineering 1st Edition Vivek V. Ranade (Eds.) Digital Instant Download Author(s): Vivek V. Ranade (Eds.) ISBN(s): 9780125769600, 0125769601 Edition: 1st File Details: PDF, 6.62 MB Year: 2002 Language: english
  • 7. Process Systems Engineering Series A series edited by George Stephanopoulos and John Perkins Volume 1 Mathematical Modeling Rutherford Aris Volume 2 Data Processing and Reconciliation for Chemical Process Operations Jos´ anchez e A Romagnoli & Mabel Cristina S´ Volume 3 Linear Algebra and Linear Operators in Engineering Ted H Davis & Kendall T Thomson Volume 4 Process Modelling and Model Analysis Katalin Hangos & Ian Cameron Volume 5 Computational Flow Modeling for Chemical Reactor Engineering Vivek V Ranade
  • 8. COMPUTATIONAL FLOW MODELING FOR CHEMICAL REACTOR ENGINEERING Vivek V. Ranade Industrial Flow Modeling Group Chemical Engineering Division National Chemical Laboratory Pune 411008, India San Diego San Francisco New York Boston London Sydney Tokyo
  • 9. This book is printed on acid-free paper. Copyright © 2002 by ACADEMIC PRESS All Rights Reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without the prior permission in writing from the publisher. The appearance of the code at the bottom of the first page of a chapter in this book indicates the Publisher’s consent that copies of the chapter may be made for personal or internal use of specific clients. This consent is given on the condition, however, that the copier pay the stated per copy fee through the Copyright Clearance Center, Inc. (222 Rosewood Drive, Danvers, Massachusetts 01923), for copying beyond that permitted by Sections 107 or 108 of the U.S. Copyright Law. This consent does not extend to other kinds of copying, such as copying for general distribution, for advertising or promotional purposes, for creating new collective works, or for resale. Copy fees for pre-2002 chapters are as shown on the title pages. If no fee code appears on the title page, the copy fee is the same as for current chapters. ISSN# /2002 $35.00. Explicit permission from Academic Press is not required to reproduce a maximum of two figures or tables from an Academic Press chapter in another scientific or research publication provided that the material has not been credited to another source and that full credit to the Academic Press chapter is given. Academic Press A Harcourt Science and Technology Company 525 B Street, Suite 1900, San Diego, California 92101-4495, USA http://www.academicpress.com Academic Press Harcourt Place, 32 Jamestown Road, London NW1 7BY, UK http://www.academicpress.com ISBN 0-12-576960-1 Library of Congress Catalog Number: 2001090198 A catalogue record of this book is available from the British Library Typeset by Newgen Imaging Systems (P) Ltd., Chennai, India Printed and bound in Great Britain by Bookcraft, Bath, UK 02 03 04 05 06 07 BC 9 8 7 6 5 4 3 2 1
  • 10. To Nanda & Vishakha
  • 12. CONTENTS PREFACE xi I INTRODUCTION 1 Reactor Engineering and Flow Modeling 1.1. Chemical Reactor Engineering (CRE) 7 1.2. Computational Flow Modeling (CFM) 19 1.3. CFM for CRE 25 References 30 II COMPUTATIONAL FLOW MODELING 2 Mathematical Modeling of Flow Processes 2.1. Basic Governing Equations 35 2.2. Auxiliary Equations 44 2.3. Boundary Conditions 45 vii
  • 13. 3 viii CONTENTS 2.4. Discussion 52 2.5. Summary 54 References 54 Turbulent Flow Processes 3.1. Introduction 57 3.2. Turbulence: Physical Picture 58 3.3. Modeling Approaches 62 3.4. Turbulence Models Based on RANS 68 3.5. Summary 81 References 82 4 Multiphase Flow Processes 4.1. Introduction 85 4.2. Modeling Dispersed Multiphase Flows 90 4.3. Other Types of Multiphase Flows 112 4.4. Summary 114 References 115 Appendix 4.1. Time Scales for Dispersed Multiphase Flows 118 Appendix 4.2. Correlations for Drag Coefficient 119 Appendix 4.3. Interphase Heat and Mass Transfer Correlations 121 5 Reactive Flow Processes 5.1. Introduction 123 5.2 Turbulent Reactive Mixing 124 5.3. Modeling Approaches 131 5.4. RANS-based Models of Reactive Flow Processes 134 5.5. Multiphase Reactive Flow Processes 144 5.6. Summary 147 References 147 6 Numerical Solution of Model Equations 6.1. Introduction 151 6.2. Finite Volume Method 153 6.3. Finite Volume Method for Calculation of Flow Field 165 6.4. Finite Volume Method for Unsteady Flows 173 6.5. Application of Finite Volume Method 175 6.6. Summary 185 References 188
  • 14. ix 7 CONTENTS Numerical Solution of Complex Flow Models 7.1. Simulation of Turbulent Flows 191 7.2. Simulation of Multiphase Flows 197 7.3. Simulation of Reactive Flows 216 7.4. Special Topics 219 7.5. Summary 225 References 226 8 Computational Tools for Simulating Flow Processes 8.1. Mapping a Computational Flow Model on a Computer 229 8.2. Pre-processors 232 8.3. Solvers 236 8.4. Post-processors 238 8.5. Summary 240 References 240 III CFM FOR CRE 9 Flow Modeling for Reactor Engineering 9.1. Reactor Engineering Methodology 244 9.2. Example 1: Suspension Polymerization Reactor 247 9.3. Example 2: OXY Reactor for EDC 254 9.4. Example 3: Bubble Column Reactor 264 9.5. Example 4: FCC Regenerator 271 9.6. Summary 281 References 281 IV APPLICATIONS 10 Stirred Reactors 10.1. Engineering of Stirred Reactors 286 10.2. CFD-based Modeling of Stirred Reactors 290 10.3. Computational Snapshot Approach 292 10.4. Application to Reactor Engineering 318 10.5. Summary 323 References 323
  • 15. x CONTENTS 11 Bubble Column Reactors 11.1. Engineering of Bubble Column Reactors 328 11.2. CFD-based Modeling of Bubble Column Reactors 332 11.3. Application to Reactor Engineering 355 11.4. Summary 360 References 361 Appendix 11.1. Multigroup Model to Simulate Bubble Size Distribution 363 12 Fluidized Bed Reactors 12.1. Engineering Fluidized Bed Reactors 368 12.2. CFD Modeling of Gas–Solid Reactors 376 12.3. Applications to Reactor Engineering 394 12.4. Summary 400 References 400 13 Fixed Bed and Other Types of Reactors 13.1. Fixed Bed Reactors 403 13.2. Trickle Bed Reactors/Packed Column Reactors 415 13.3. Other Reactors 419 13.4. Summary 421 References 422 V EPILOGUE 14 Epilogue NOTATION 433 AUTHOR INDEX 439 SUBJECT INDEX 445 Colour plate section between pages 210–211
  • 16. PREFACE Industrial Flow Modeling Group, iFMg at National Chemical Laboratory undertakes contract research and consultancy projects in the general area of reactor engineering. We use computational flow modeling to carry out these industrial projects. Compu­ tational flow modeling is a powerful tool for the design and analysis of industrial flow processes. Though it is routinely used as a design tool in aerospace engineering, chemical engineers have started exploiting the power of computational flow model­ ing only recently. Considering the central role played by reactors in chemical process industries, there is tremendous potential for applying computational flow-modeling tools to improve reactor engineering. Through interactions with practicing engineers from industry, it has been real­ ized that there is insufficient help available to harness state of the art computational flow modeling tools for complex, industrial reactor engineering applications. Many reactor engineers either consider that the flow complexities of industrial reactors are impossible to simulate, or expect miracles from off-the-shelf, commercial flow mod­ eling tools. These two diverse views arise because of inadequate interactions between the flow modeling and industrial reactor engineering communities. It is essential to clearly understand the role of flow modeling in reactor engineering. It is necessary to relate the individual aspects of reactor engineering and computational flow mod­ eling in a coherent and consistent way to realize the potential of computational flow modeling for reactor engineering research and practice. To assist practicing engi­ neers in these aspects, workshops on ‘computational flow modeling for chemical process industries’ were started at the National Chemical Laboratory. The enthusi­ astic response to these workshops has encouraged me to write this book, which is xi
  • 17. xii PREFACE an expanded and formalized presentation of workshop notes. I have tried to provide sufficient information to understand and to define the specific role of computational flow modeling for reactor engineering applications, to select appropriate tools and to apply these tools to link reactor hardware to reactor performance. The intended audience of the book is practicing chemical engineers working in industry as well as chemical engineering scientists and research students working in the area of reactor engineering. Some prior background in reactor engineering and numerical techniques is assumed. The information in the book is organized to facilitate the central task of reac­ tor engineer, that is, relating reactor hardware to reactor performance. Several steps to achieve such a task are discussed to clearly define the role of flow modeling in the overall reactor engineering activity. The necessity of using a hierarchy of mod­ eling tools and establishing a clear relationship between the objectives of reactor engineering and the computational flow model is emphasized with the help of exam­ ples. The overall methodology of achieving the objectives of reactor engineering via computational flow modeling is discussed. Desirable characteristics and key issues in selecting appropriate computational fluid dynamics (CFD) codes are briefly dis­ cussed. A number of examples and case studies covering the four major reactor types used in chemical industries, namely, stirred reactors, bubble column reactors, flu­ idized bed reactors and fixed bed reactors are included. In view of the wide range of reactor types, however, it is impossible to cover all the reactor types and flows relevant to these reactor types. Emphasis on certain topics and the selection of examples is biased and is directly related to my own research and consulting experience. Some topics, like radiative heat transfer, laminar reactive flows are completely omitted. I have, however, made an attempt to evolve general guidelines, which will be useful for solving practical reactor engineering problems. Some comments on future trends in computational flow modeling and its use by the chemical engineering community are also included. The material included in this book may be used in several ways and at various stages of flow modeling projects. It may be used as a basic resource for making appro­ priate decisions about investment in the application of CFD to reactor engineering. It may be used as a study material for an in-house course to facilitate the apprecia­ tion and application of computational flow modeling for reactor engineering. It may be used as a companion book while solving practical reactor engineering problems. I hope that this book will encourage chemical engineers to exploit the potential of computational flow modeling and will eventually lead to better reactor engineering. This book is essentially the outcome of my last fifteen years of association with this subject. I have received a great deal of help from numerous persons over these years in formulating and revising my views on both computational flow modeling and chemical reactor engineering. I am particularly indebted to my teacher and mentor, Professor J.B. Joshi, who has been one of the leading practitioners of process fluid dynamics for three decades. There are not adequate words to express his contributions to this book. I was fortunate to have an opportunity to work with Dr R.V. Chaudhari and Dr R.A. Mashelkar at the National Chemical Laboratory. Both of them always extended their full support and encouragement in my every endeavor. Without their support, it would not have been possible to develop our industrial flow modeling activity, on which this book is based. I would like to acknowledge the support pro­ vided by Professor H.E.A. van den Akker of Delft University of Technology and by
  • 18. PREFACE xiii Professors G.F. Versteeg and J.A.M. Kuipers of University of Twente, The Nether­ lands. My brief stay at Professor van den Akker’s laboratory at Delft introduced me to different commercial CFD solvers and expanded my horizons. The idea of this book was formalized during my second visit to The Netherlands at University of Twente. I would also like to thank Dr Bharatan Patel of Fluent Inc. and Mr Paresh Patel of Fluent India for their support. I am grateful to my associates and collaborators with whom I worked on different industrial projects. In particular, I owe much to Professor J.R. Bourne, Mr Vaibhav Deshpande, Ms S.M.S. Dommeti and Mr Yatin Tayalia. My students, especially Kapil Girotra, Ashwin Sunthankar, Ranjit Utikar, Aravind Rammohan, Sachin Muthian, Avinash Khopkar, Prashant Gunjal, Vivek Buwa and Shishir Sable have contributed to this book in different ways. This includes technical contributions either in a direct or indirect way, helping me to collect the required information and reading the draft manuscript. My father, Mr V.B. Ranade also has painstakingly read the entire manuscript and suggested several ways to enhance the clarity of presenta­ tion. The manuscript was improved wherever their suggestions were incorporated. Any remaining errors or shortcomings are, needless to say, the responsibility of the author. Finally, I wish to thank my wife, Nanda, for her patience, understanding and enthusiastic support, which carried me through this long and arduous writing process. Vivek V. Ranade December 2000 Pune
  • 22. 1 REACTOR ENGINEERING AND FLOW MODELING All industrial chemical processes are designed to transform cheap raw materials to high value products (usually via chemical reactions). A ‘reactor’, in which such chem­ ical transformations take place, has to carry out several functions such as bringing reactants into intimate contact (to allow chemical reactions to occur), providing an appropriate environment (temperature and concentration fields, catalysts) for an ade­ quate time and allowing for the removal of products. Chemical reactor engineering includes all the activities necessary to evolve the best possible hardware and operating protocol of the reactor to carry out the desired transformation of raw materials (or reactants) to value added products. A reactor engineer has to ensure that the reactor hardware and operating protocol satisfy various process demands without compro­ mising safety, the environment and economics. To realize this, the reactor engineer has to establish a relationship between reactor hardware and operating protocols and various performance issues (Fig. 1.1). Successful reactor engineering requires expertise from various fields including thermodynamics, chemistry, catalysis, reaction engineering, fluid dynamics, mixing and heat and mass transfer. The reactor engineer has to interact with chemists to understand the basic chemistry and peculiarities of the catalyst. Based on such an understanding and proposed performance targets, the reactor engineer has to abstract the information relevant to identifying the characteristics of the desired fluid dynamics of the reactor. The reactor engineer then has to conceive suitable reactor hardware and operating protocols to realize this desired fluid dynamics in practice. Thus, fluid 3
  • 23. 4 CHAPTER 1 REACTOR ENGINEERING AND FLOW MODELING 4A=?J�H 2AHB�H�=�?A +��LAHIE�� �FAH=E�EJO 2H�@K?J GK=�EJO +�IJI -�LEH���A�J=� E�F=?J 5=BAJO IA�E�=J?D� ?��JE�K�KI 4A=?J�H �FAH=JE�C @EIJHEKJ�HI IDKJ�@�M� FH�J�?��I IA�A?JELEJO 5J=E�EJO 4A=?J�H0=H@M=HA �FAH=JE�C2H�J�?��I ��@A �B �FAH=JE��� =J?D� ?��BECKH=JE��� IE�A ID=FA� BAA@ ANEJ �����AI ?��@EJE��I�B��M H=JA�FHAIIKHA� JA�FAH=JKHA�B��M HACE�A�46, 4A=?J�H E�JAH�=�I =BB�AI� DA=J JH=�IBAH ?�E�I� 5J=HJ�KF FIGURE 1.1 Chemical reactor engineering. dynamicsplaysapivotalroleinestablishingtherelationshipbetweenreactorhardware and reactor performance. To establish the relationship between reactor hardware and reactor performance, it is necessary to use a variety of different tools/models. Creative application of the best possible tools is required to evolve the best possible hardware configura­ tion and operating protocol for the reactor under consideration. Various tools for modeling chemical kinetics and reactions are already well developed and routinely used in practice. This activity constitutes the major part of conventional chemical reaction engineering. Several excellent textbooks discussing these tools are available (for example, Aris, 1965; Levenspiel, 1972; Westerterp et al., 1984; Naumann, 1987). Most models falling in this category make use of drastic simplifications when treating the reactor fluid dynamics. Indeed, sophisticated models and theories are available to predict the interaction between chemistry and transport processes such as mixing, heat and mass transfer. However, these models rarely attempt to rigorously relate transport properties with the reactor hardware and operating protocol. For a specific chemistry/catalyst, the reactor performance is a complex function of the underlying transport processes. These transport processes are, in turn, governed by the underlying fluid dynamics, and therefore by a variety of design and operating parameters of the process equipment. In conventional reaction engi­ neering, experimental and semi-theoretical methods (like cold flow simulations or tracer studies) are used to relate fluid dynamics and mixing with reactor hardware and operating parameters. The information obtainable from these methods is usu­ ally described in an overall/global parametric form. This practice conceals detailed local information about turbulence and mixing, which may ultimately determine reactor performance. This approach essentially relies on prior experience and trial and error methods to evolve suitable reactor hardware. These tools, therefore, are increasingly perceived as being expensive and time consuming ways of developing better reactor technologies. It is necessary to adapt and develop better techniques and tools to relate reactor hardware with fluid dynamics and resultant transport processes.
  • 24. 5 CHAPTER 1 REACTOR ENGINEERING AND FLOW MODELING Over the years, aerospace engineers, who are most concerned with the task of establishing the relationship between the hardware and resulting fluid dynamics, have developed and routinely use computational fluid dynamics. Computational fluid dynamics (CFD) is a body of knowledge and techniques used to solve mathematical models of fluid dynamics on digital computers. In recent years, chemical engineers have realized that, although establishing a relationship between reactor hardware and fluid dynamics is less central (compared to aerospace engineers) to their role, it is no less important. With the development of high performance computers and advances in numerical techniques and algorithms, chemical engineers have started exploiting the power of computational fluid dynamics tools. Considering the cen­ tral role of reactors in chemical process industries, there is tremendous potential for applying these tools for better reactor engineering. If applied properly, computa­ tional flow modeling (CFM) may reduce development time, leading to reduced time to market, shorter payback time and better cash flow. It is, however, necessary to adapt CFD techniques and to develop a computational flow modeling approach to apply them to chemical reactor engineering. This book is written with the inten­ tion of assisting practicing engineers and researchers to develop such an approach. Individual aspects of chemical reactor engineering and computational flow modeling (CFM) are discussed and related in a coherent way to convey and clarify the potential of computational flow modeling for reactor engineering research and practice. The emphasis is not on providing a complete review but is on equipping the reader with adequate information and tips to undertake a complex flow-modeling project. The focus is on modeling fluid flows and developing tractable reactor engineering mod­ els. Numerical issues are dealt with in adequate detail to provide appreciation of the important aspects and to guide the development and incorporation of new models into available solvers. Readers interested in developing their own complete solvers may refer to specialized books on CFD (for example, Ferziger and Peric, 1995; Patankar, 1980). The information in this book is organized to facilitate the central task of a reactor engineer, that is, relating reactor hardware to reactor performance. This chapter pro­ vides a brief introduction to the contents to be covered in detail in subsequent chapters. Here, the roles of flow modeling and computational flow modeling are discussed in the context of reactor engineering. Various aspects of chemical reaction and reactor engineering are discussed in Section 1.1 to clearly define the role of flow modeling in overall activity. Computational flow modeling, its advantages and limitations are discussed in Section 1.2. Introduction to the use of CFM for reactor engineering is given in Section 1.3. This chapter, as a whole, will be used to appreciate and identify the potential of CFM for reactor engineering. The theoretical and numerical basis of computational flow modeling (CFM) is described in detail in Part II. The three major tasks involved in CFD, namely, mathe­ matical modeling of fluid flows, numerical solution of model equations and computer implementation of numerical techniques are discussed. The discussion on mathe­ matical modeling of fluid flows has been divided into four chapters (2 to 5). Basic governing equations (of mass, momentum and energy), ways of analysis and possible simplifications of these equations are discussed in Chapter 2. Formulation of different boundary conditions (inlet, outlet, walls, periodic/cyclic and so on) is also discussed. Most of the discussion is restricted to the modeling of Newtonian fluids (fluids exhibit­ ing the linear dependence between strain rate and stress). In most cases, industrial
  • 25. 6 CHAPTER 1 REACTOR ENGINEERING AND FLOW MODELING reactors are operated under a turbulent flow regime. Introduction to turbulence and various approaches (direct numerical simulations or DNS, large eddy simulations or LES and Reynolds averaged Navier–Stokes equations or RANS simulations) to modeling turbulent flows are discussed in Chapter 3. Turbulence models based on the RANS approach are discussed in more detail, with special consideration to reactor engineering applications. For several industrial applications, multiphase reactors are used, which involves contacting more than one phase. Various approaches to mod­ eling such multiphase flows are discussed in Chapter 4 with special emphasis on dispersed multiphase flows. The interactions between chemical reactions and fluid dynamics are discussed in Chapter 5. Model equations governing flow processes relevant to reactor engineering appli­ cations are quite often complex, non-linear and coupled. More often than not, analytical solutions are not possible and numerical methods are required to obtain a solution to the model equations. The numerical methods relevant to solving model equations are discussed in Chapters 6 and 7. Chapter 6 covers use of the finite volume method to solve generic flow models. Various aspects of the finite volume method such as discretization schemes, grid arrangements, implementation of boundary con­ ditions and algorithms for handling pressure–velocity coupling are discussed in detail. Applications of these methods to solve turbulent flows, multiphase flows and reac­ tive flows are discussed in Chapter 7. Guidelines for making appropriate selection of the available techniques based on the objective at hand are discussed. Practical ways of estimating errors in numerical solutions of model equations are discussed. The methodology and the desired qualities of computational tools required to implement these numerical methods on a digital computer to solve model equations are discussed in Chapter 8. PartIIIofthebookdiscussestheoverallmethodologyofusingcomputationalflow modeling for reactor engineering. The necessity of using a hierarchy of modeling tools and establishing a clear relationship between the objectives of reactor engineering and the computational flow model is illustrated with the help of examples. The importance of a physical understanding of the system for facilitating rational simplification of the problem, formulation of appropriate boundary conditions and identification of key issues is emphasized. The information discussed in Part I and Part II is used to evolve a systematic methodology for linking reactor hardware with reactor performance. The methodology is illustrated with the help of some practical examples. Details of the application of computational flow modeling to different types of reactors are discussed in Part IV. A separate chapter is devoted to three major reactor types used in chemical industries, namely, stirred reactors, bubble column reactors and fluidized bed reactors. Applications to fixed bed reactors and other miscella­ neous reactor types are briefly discussed in Chapter 13. Recent work on modeling the complex fluid dynamics in these reactors is critically reviewed. The modeling approaches and the flow results obtained therefrom are evaluated from the point of view of their application to reactor engineering. Limitations of the current state of knowledge in describing the complex underlying physics of some of the flows relevant to reactor engineering are discussed. Despite such limitations, suggestions are made for making the best use of these computational flow models for reactor engineering applications. The Epilogue recapitulates the lessons learnt from our experience of apply­ ing computational flow modeling while addressing practical reactor engineering
  • 26. Discovering Diverse Content Through Random Scribd Documents
  • 27. Gee, Gee, Yo better quit dat pestern me. Woe, tell I unkiber dis corn, A raskul like yo shud nebber ben bon, When de sun comes out yo am looken fo de cool An’ dat’s de powful acten uv a lazy mule. Den dah’s de minet I gits de bridle Yo eyes am shut yo mine goes idle. Did yo had no risens or go to school—no. Ah, dat’s de rezen yo’s a lazy mule. Now maybe tumorh I’ll drove yo tu town, And what I means yo gwine tu sweep de groun, Yo won’t drug along acten a fool, Yo’ll git up an muv, lazy mule. Yo ets a wagon loder con an’ a bale o hay, Den yo leans er ginst de fence when yo goes tu bray, I recken som time you’ll ax fo a stool So you kin set doun yo lazy mule. Den tu I recken I’ll trade yo off, Yo lon nekhog, yo ets de hay out de loft, Now yo kin git mad but I got er nu rule, Yo good for nothen lazy mule. And when I goes tu mak dis deal, Yo run around de barn an’ kick up yo heal, Stah rit sid dat ole marh Brule Den de man won’t no he’s giten sich a lazy mule. Ah, an when he gits yo you’ll cease tu balk, Fo he am goter a chalklin yo has tu walk, From dat dah on yo’ll be a liven tool Dat I’ll en yo actens uv er lazy mule. An mah de dah come when yo cease tu breve
  • 28. An mah de dah come when yo cease tu breve Den yo’ll flot wid de angles fru de trees, An de buzzards will fite one mo duel An I’ll sah dah gones de essene uv dat lazy mule.
  • 29. THROUGH THE MILL If I can compose my way to success Then some time I’ll compose the rest, It will be of my childhood days Building mud houses for different plays. Oh! I was bad and mischievous, too, And always looking for something to do, And when I found nothing I surely was sad, To be good very long would make me mad. Though I longed to go to school, But I was poor and fate overruled, Then my mother, whom I love so dear, Passed away at the end of the year. Then I fought this old, rough world, For I had lost my valued pearl. And now she sleeps beneath the sod; It brought me deep sorrow though it’s the will of God. Just think of my mother, she guides me yet, And keeps me away from those sinful nets. All through life, from place to place, She ne’er let alcohol enter my taste. And I’ve ne’er lived a day I want to live o’er, Unless it was school days which I could love more, Now I’ll thank God and that sweet little her, My life’s been rough, but never a blur.
  • 30. A heart without love And nowhere to build, The mind wanders far, Leaving the soul to chill.
  • 31. A DROOPING ROSE She’ll always be Sweet like the breath you give In trying to console me. I hope you’re not leaving, ’Twould break my heart to think, I love you better than all the rest, For your petals are all over pink. Cheer up! little rose, With your petals looking mad, My sweet heart is dying, That’s why I’m looking sad. Oh! there is your companions And they are blooming all gay, But I wonder if you know My love is to pass away, But forever in my memory.
  • 33. Lody, Lody, chile am yo heard de nues, Ole Ruby Gee go dem late stile shoes (no!) Yo noes dem kin wid de heel so high, An all de men’s jist looks when she goes by, Course she ain’t as swell as she thinks she am, ef all ports am true. She oder member, dat I noder, when she worned a boot an a shoe. Mursey me, I kin seed her now in church a gazen aroun Tryen to make eber body seer, so de nues, kin spread de town. But um goner taut alls in de quar jist how to act renoun An when Ole Ruby Gee comes in church we kin gider one pison frown. Oh! but I loves dat uman jist like I loves a snake, An I ain’t fogot how tonny she acted don at Ras Johnson’s wake. Eber time dey passed de coffee she’d tuck it an kinder linger, An put on de mostest airs, posen her little finger. Dar she sit an sip, an saped, An droped de hol cup in her lap. Mursey me, I laughed, tell my sides almos buss, Den we had one awful fuss, But bleave me, chile, I helt my groun, Ef things did look powful dark aroun. An ef it hadn’t ben fo waken uv de dead Dah ben one awful pullen uv de heads. Yo nows fo a minit I acted refine, But after dat she got a piece uv my mine. Den eber body look all eck mased, Sam Thomptson whispered to drunken Hays, What yo spose dey am fusen about. Well sur we broke up dat wake, widout a dout, Den all along de streets on our wah home ’twas a site befo de king, We was a gibberen an a gabberen, an bof un us sushed When dat troll-bell ring. Den we was quiet where de siety folks lived An we hardly drewed our breff, But when we’s out uv dat part uv toun I nocked her rite an lef.
  • 34. TRUELET Each day there is sunshine, Each day there are showers, Means some day in May Day We’ll be picking wild flowers.
  • 35. INCH BY INCH I’m yet in the path A jogging along, That’s leading to the righteous Away from the wrong. We have not time To talk evil of others, For losing enemies To gain heavenly brothers. Oh, Lord! May the day be long In which you have power To sound the heavenly gong. We know this means Our last day, Bless us and save us In that land far away.
  • 36. THE PLACE WHERE LITTLE MARY LIVES
  • 37. Down a beautiful country road The roses in bloom and their perfume strewed, Oh! the joy it brought to my heart, ’Twas so tender, so sweet, I couldn ne’er depart From that place where little Mary lives. Oh! that spot beside the hill Where nature and beauty can always build, Tells a story it really seems And will always be life’s sweetest dream Of that place where little Mary lives. When she plucked and gave to me A beautiful rose in a manner so free, The heavenly breezes begin to blow And the tenderness through my heart did flow For that place where little Mary lives. That was a day of God’s decree, And oh! no scenes could sweeter be, They soothed my heart and eased my pain, May the bright sunshine ne’er turn to rain, Down where little Mary lives. But summer is soon to fade away, Followed by a cold winter day. The howling winds in the month of December, But that dear little rose I’ll always remember That come from the place where little Mary lives. Now I see the blustery snow And it’s changed the scenes where I used to go, It’s all over white Though the stars are shining bright, How sad be that place where little Mary lives. At times I think and really sigh To think of those roses that are sleeping nearby
  • 38. To think of those roses that are sleeping nearby. But they will return To my heart that yearns, And for that place and its beauty Where little Mary lives.
  • 39. A QUESTION Why are great men’s lives Thrown into the mist? One’s who aim at the sky, Are found at the bottom of the list.
  • 41. I met a man The other day On a Chicago train. By the way His face was strange And very old, And holds a sad story Yet to be told. He says, my boy, We’ll have a drink. I said, no I thank you, Mr. Fink. Then he gave a real deep sigh, Like a child about to cry. In a moment he raised and said, Then he stroked his old bald head, Patting me on my shoulder then. He faded his wrinkles into a grin, Now my lad, as I sit and think, May you never be like Mr. Fink. My younger days had I refused, Now I’d stand in different shoes; I could throw this blanket off of me And this deadly sorrow that you see Then with a nod he solemnly winked, Try and remember Mr. Fink. With a trembling he then relates Of his mighty love that’s turned to hate, He called a name that was once his wife. This was the pride that wrecked his life, Saying once I was rich, but now I beg. She’s the cause, a wretched old hag, Then there was love with a broken link
  • 42. Mournfully told by Mr. Fink.
  • 43. GRAY HEADS Two gray heads bowed in tears, Above hung memories of wasted years, For once they were young with the blessings of health. They sought not happiness, righteousness nor wealth, But now they jog along to end of life’s rope, The end is not far, just o’er the slope. Their lives must be studied With their heads bloomed gray To direct souls Along life’s sweeter way. ’Twill teach you their sorrow Each day ’twill bring The joy that’s in our lives ’Twill loudly ring. But if heads are hard And holds within The things you crave Be worldly sins We’ll go down to a joyless end, Leaving sorrow to have its sway, We’ll be like those two I saw the other day.
  • 44. HER SOLEMN THOUGHTS Oh! cruel, cruel fate is mine, Why am I tortured with life so unkind. Cruel as the grave, it means peace for me, For there only, my sorrow, will e’er let me be. Peace or happiness, I truly know not, And gone art the sunshine that lightened my darkened spots The little birds for me do not sing so sweet And the roses have withered from the warm summer’s heat. —Mrs. Perry H. McGee
  • 45. YOUR EYES AND MY EYES Your eyes so beautiful tells a tale And o’er me holds the bill of sale. With each glance they tenderly bring A little love song for my heart to sing. They hold the warmth around my soul With love, kind love, too sweet to be told. Were my eyes allowed to tell How my poor heart beats by spells. For your love it really craves, Why send it down to its grave? Time take away my haunted years And your love, sweet love, that’s caused me tears. Let your eyes shine for me real true, Then I’ll explain more love for you. The world then would cease my sorrow. This brings a brighter day to-morrow, Then forever we’d live in sweet loveland With love, much love, I’d hold your hand. By your eyes I traced your love, Being guided by the Savior above; I saw a weakening along the way That I could strengthen would it pay, But those things are hard to mend When two has love that doesn’t blend. Be careful in your daily walks, Because from some source or other there’s always a watching eye.
  • 46. NATURAL BORN COLORED MAN Sam Jackson was goin’ with a real yallow gal, the one that he called his own-side pal, But he found she would deceive, she told a friend by the name of Stark. She could love Sam if he wasn’t so dark; This made a discord down town, Cause Sam was standing near, and seemed to overhear and just then he spoke right up and said: Chorus I’m a natural born gen-u-wine colored man, you don’t have to look twice to see who I am, You look at me once and your thoughts will end, cause I got that puro-de colored skin. It’s the kind of skin that the sun don’t tan, this makes me the king of the sunny land, So you go your way but bear in mind I’m what you call the puro-de gen-u- wine. Now all high yellows to Sam is in vain, he never lets them bother his brain, And all through his life he’ll letum alone, he knows that his skin’s a bit shady, So he will avoid every yellow lady, he’s got a club of his own. Where all brown skins can meet and have a musical treat For every night Sam kindly sings.
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