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The primary objective in any engineering design process has to be the elimination of uncertainties. In thermal design of heat exchangers there are presently many stages in which assumptions in mathematical solution of the design problem are being made. Accumulation ofthese assumptions (e.g. use of mean values) may introduce variations in design as large as the uncertainties introduced in heattransfer and flowfriction correlations. The designer needs to understand where these inaccuracies may arise, and strive to climinate as many sources of error as possible by choosing design configurations that avoid such problems at source.
Advances in Thermal Design of Heat Exchangers A Numerical Approach: Direct-sizing, step-wise rating, and transients Eric M Smith John Wiley & Sons, Ltd Professional Advances in Thermal Design of Heat Exchangers: A Numerical Approach: Direct-sizing, step-wise rating, and transients Eric M Smith Copyright 2005 John Wiley & Sons, Ltd ISBN: 0-470-01616-7 Advances in Thermal Design of Heat Exchangers Related Titles Combined Power and Process - An Exergy Approach F J Barclay 86058 129 Optical Methods and Data Processing in Heat and Fluid Flow Edited by C Created, J Cosgrove, and J M Buick 86058 281 Axial-Flow Compessors A Strategy for Aerodynamic Design and Analysis R H Aungier 86058 422 Advances in Thermal Design of Heat Exchangers A Numerical Approach: Direct-sizing, step-wise rating, and transients Eric M Smith John Wiley & Sons, Ltd Professional Copyright © 2005 Eric M Smith Published by John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ, England Telephone (+44) 1243 779777 Email (for orders and customer service enquiries): cs-books@wiley.co.uk Visit our Home Page on www.wiley.com 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, scanning or otherwise, except under the terms of the Copyright, Designs and Patents Act 1988 or under the terms of a licence issued by the Copyright Licensing Agency Ltd, 90 Tottenham Court Road, London WIT 4LP, UK, without the permission in writing of the Publisher Requests to the Publisher should be addressed to the Permissions Department, John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ, England, or emailed to permreq@wiley.co.uk, or faxed to (+44) 1243 770620 This publication is designed to provide accurate and authoritative information in regard to the subject matter covered It is sold on the understanding that the Publisher is not engaged in rendering professional services If professional advice or other expert assistance is required, the services of a competent professional should be sought Other Wiley Editorial Offices John Wiley & Sons Inc., I l l River Street, Hoboken, NJ 07030, USA Jossey-Bass, 989 Market Street, San Francisco, CA 94103-1741, USA Wiley-VCH Verlag GmbH, Boschstr 12, D-69469 Weinheim, Germany John Wiley & Sons Australia Ltd, 33 Park Road, Milton, Queensland 4064, Australia John Wiley & Sons (Asia) Pte Ltd, Clementi Loop #02-01, Jin Xing Distripark, Singapore 129809 John Wiley & Sons Canada Ltd, 22 Worcester Road, Etobicoke, Ontario, Canada M9W 1L1 Wiley also publishes its books in a variety of electronic formats Some content that appears in print may not be available in electronic books British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library ISBN 1-86058-461-6 Typeset by Techset Composition Limited, Salisbury, Wiltshire Printed and bound in Great Britain by Antony Rowe, Ltd, Chippenham, Wiltshire This book is printed on acid-free paper responsibly manufactured from sustainable forestry in which at least two trees are planted for each one used for paper production This volume is dedicated to Dorothy my wife for her unfailing kindness and understanding, and to my three sons for their consistent support 'If you can build hotter or colder than anyone else, If you can build higher or faster than anyone else, If you can build deeper or stronger than anyone else, If Then, in principle, you can solve all the other problems in between.' (Attributed to Sir Monty Finniston, FRS) Contents Preface xxiii Chapter 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 1.10 1.11 Classification Class definition Exclusions and extensions Helical-tube, multi-start coil Plate-fin exchangers RODbaffle Helically twisted flattened tube Spirally wire-wrapped Bayonet tube Wire-woven heat exchangers Porous matrix heat exchangers Some possible applications 1 7 9 10 Chapter 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.10 Fundamentals Simple temperature distributions Log mean temperature difference LMTD-Ntu rating problem LMTD-Ntu sizing problem Link between Ntu values and LMTD The 'theta' methods Effectiveness and number of transfer units e-Ntu rating problem e-Ntu sizing problem Comparison of LMTD-Ntu and e-Ntu approaches Sizing when Q is not specified Optimum temperature profiles in contraflow Optimum pressure losses in contraflow Compactness and performance Required values of Ntu in cryogenics To dig deeper Dimensionless groups 19 19 21 23 25 26 26 27 31 32 35 40 42 42 45 47 Steady-State Temperature Profiles Linear temperature profiles in contraflow General cases of contraflow and parallel flow 59 59 61 2.11 2.12 2.13 2.14 2.15 2.16 2.17 Chapter 3.1 3.2 33 34 viii Contents 3.3 3.4 3.5 3.6 3.7 3.8 3.9 3.10 3.11 3.12 3.13 Condensation and evaporation Longitudinal conduction in contraflow Mean temperature difference in unmixed crossflow Extension to two-pass unmixed crossflow Involute-curved plate-fin exchangers Longitudinal conduction in one-pass unmixed crossflow Determined and undetermined crossflow Possible optimization criteria Cautionary remark about core pressure loss Mean temperature difference in complex arrangements Exergy destruction 66 67 74 79 82 83 90 92 92 93 94 Chapter 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 4.10 4.11 4.12 4.13 4.14 4.15 4.16 4.17 4.18 Direct-Sizing of Plate-Fin Exchangers Exchanger lay-up Plate-fin surface geometries Flow-friction and heat-transfer correlations Rating and direct-sizing design software Direct-sizing of an unmixed crossflow exchanger Concept of direct-sizing in contraflow Direct-sizing of a contraflow exchanger Best of rectangular and triangular ducts Best small, plain rectangular duct Fine-tuning of ROSF surfaces Overview of surface performance Headers and flow distribution Multi-stream design (cryogenics) Buffer zone or leakage plate 'sandwich' Consistency in design methods Geometry of rectangular offset strip fins Compact fin surfaces generally Conclusions 99 99 101 103 103 106 110 113 120 125 127 127 130 130 130 132 133 138 138 Chapter 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 5.10 5.11 Direct-Sizing of Helical-Tube Exchangers Design framework Consistent geometry Simplified geometry Thermal design Completion of the design Thermal design results for t/d = 1.346 Fine tuning Design for curved tubes Discussion Part-load operation with by-pass control Conclusions 143 143 145 151 153 159 162 163 168 172 174 174 Contents ix Chapter 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 6.10 Direct-Sizing of Bayonet-Tube Exchangers Isothermal shell-side conditions Evaporation Condensation Design illustration Non-isothermal shell-side conditions Special explicit case Explicit solution General numerical solutions Pressure loss Conclusions 177 177 178 189 190 191 194 196 199 201 204 Chapter 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 7.10 7.11 7.12 7.13 7.14 7.15 7.16 7.17 Direct-Sizing of RODbaffle Exchangers Design framework Configuration of the RODbaffle exchanger Approach to direct-sizing Flow areas Characteristic dimensions Design correlations Reynolds numbers Heat transfer Pressure loss tube-side Pressure loss shell-side Direct-sizing Tube-bundle diameter Practical design Generalized correlations Recommendations Other shell-and-tube designs Conclusions 207 207 208 208 209 209 210 211 211 213 214 215 217 217 220 222 222 224 Chapter Exergy Loss and Pressure Loss 229 Exergy loss Objective Historical development Exergy change for any flow process Exergy loss for any heat exchangers Contraflow exchangers Dependence of exergy loss number on absolute temperature level Performance of cryogenic plant Allowing for leakage Commercial considerations Conclusions 229 229 230 231 233 234 8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.8 8.9 8.10 236 238 240 242 242 Notation Symbol Parameter 499 Units Greek symbols a blade angle, preferred notation for gas turbines y isentropic index, (CP/CV) 17 efficiency angle Subscripts e, n, o,p fg s 0, 1, 2, equilibrium, normal, ortho-, para- (forms of hydrogen) saturation field minimum isentropic dead state stations in radial turbine analysis Embellishments ~ mean value Chapter 12 Heat transfer and flow friction in two-phase flow Symbol Parameter a A B c C d E,F,H f Fl G f m m n P numerical constant area for flow numerical constant numerical constant numerical parameter depending on flow condition tube diameter parameters in Friedel's correlation friction factor heat flux acceleration due to gravity mass velocity length numerical constant mass flowrate numerical constant absolute pressure (bar x 105) heat flowrate temperature overall heat-transfer coefficient dryness fraction ratio defined in text q T U X X2 Units m2 m W or J/s m/s2 kg/(m2 s) m kg/s N/m2 W or J/s K J/(m2 s K) 500 Advances in Thermal Design of Heat Exchangers Symbol Parameter Greek symbols heat-transfer coefficient a length increment M pressure loss AP absolute viscosity i? density P surface tension a two-phase flow multiplier 4> Subscripts crit f fg g Units J/(m2 s K ) m N/m2 kg/(m s) kg/m3 N/m critical liquid saturation vapour two-phase Appendix A Transient equations with longitudinal conduction and wall thermal storage Symbol A C e e f I L m M P r rhyd R S t T u V Parameter wall cross-section for longitudinal conduction specific heat at constant pressure specific internal energy strain rate friction factor unit matrix length mass rate of flow mass of exchanger solid wall, (Mw = p^A^L) absolute pressure (bar x 105) heat flow rate radiation hydraulic radius gas constant reference surface area time temperature velocity total volume of exchanger solid wall Units m J/(kg K) J/kg m kg/s kg N/m2 J/(m2 s) J/(m3 s) m J/(kgK) m2 s K m/s m3 Notation Symbol Parameter 501 Units dissipation terms distance K/s m J/(m2 s K) kg/(m s) m2/s