Advances in Thermal Design of Heat Exchangers A Numerical Approach: Direct-sizing, step-wise rating, and transients Eric M Smith Professional John Wiley & Sons, Ltd 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 Optical Methods and Data Processing in Heat and Fluid Flow Axial-Flow Compessors - A Strategy for Aerodynamic Design and Analysis F J Barclay 1 86058 129 3 Edited by C Created, 1 86058 281 8 J Cosgrove, and J M Buick R H Aungier 1 86058 422 5 Advances in Thermal Design of Heat Exchangers A Numerical Approach: Direct-sizing, step-wise rating, and transients Eric M Smith Professional John Wiley & Sons, Ltd 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., Ill 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, 2 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 Chapter 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 1.10 1.11 Chapter 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.10 2.11 2.12 2.13 2.14 2.15 2.16 2.17 Chapter 3 3.1 3.2 Preface 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 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 Steady-State Temperature Profiles Linear temperature profiles in contraflow General cases of contraflow and parallel flow xxiii 1 1 1 3 5 6 7 7 8 9 9 10 19 19 21 23 25 26 26 27 31 32 33 34 35 40 42 42 45 47 59 59 61 viii Contents 3.3 Condensation and evaporation 66 3.4 Longitudinal conduction in contraflow 67 3.5 Mean temperature difference in unmixed crossflow 74 3.6 Extension to two-pass unmixed crossflow 79 3.7 Involute-curved plate-fin exchangers 82 3.8 Longitudinal conduction in one-pass unmixed crossflow 83 3.9 Determined and undetermined crossflow 90 3.10 Possible optimization criteria 92 3.11 Cautionary remark about core pressure loss 92 3.12 Mean temperature difference in complex arrangements 93 3.13 Exergy destruction 94 Chapter 4 Direct-Sizing of Plate-Fin Exchangers 99 4.1 Exchanger lay-up 99 4.2 Plate-fin surface geometries 101 4.3 Flow-friction and heat-transfer correlations 103 4.4 Rating and direct-sizing design software 103 4.5 Direct-sizing of an unmixed crossflow exchanger 106 4.6 Concept of direct-sizing in contraflow 110 4.7 Direct-sizing of a contraflow exchanger 113 4.8 Best of rectangular and triangular ducts 120 4.9 Best small, plain rectangular duct 125 4.10 Fine-tuning of ROSF surfaces 127 4.11 Overview of surface performance 127 4.12 Headers and flow distribution 130 4.13 Multi-stream design (cryogenics) 130 4.14 Buffer zone or leakage plate 'sandwich' 130 4.15 Consistency in design methods 132 4.16 Geometry of rectangular offset strip 4.17 Compact fin surfaces generally 138 4.18 Conclusions 138 Chapter 5 Direct-Sizing of Helical-Tube Exchangers 143 5.1 Design framework 143 5.2 Consistent geometry 145 5.3 Simplified geometry 151 5.4 Thermal design 153 5.5 Completion of the design 159 5.6 Thermal design results for t/d = 1.346 162 5.7 Fine tuning 163 5.8 Design for curved tubes 168 5.9 Discussion 172 5.10 Part-load operation with by-pass control 174 5.11 Conclusions 174 fins 133 Contents ix Chapter 6 Direct-Sizing of Bayonet-Tube Exchangers 6.1 Isothermal shell-side conditions 6.2 Evaporation 6.3 Condensation 6.4 Design illustration 6.5 Non-isothermal shell-side conditions 6.6 Special explicit case 6.7 Explicit solution 6.8 General numerical solutions 6.9 Pressure loss 6.10 Conclusions Chapter 7 Direct-Sizing of RODbaffle Exchangers 7.1 Design framework 7.2 Configuration of the RODbaffle exchanger 7.3 Approach to direct-sizing 7.4 Flow areas 7.5 Characteristic dimensions 7.6 Design correlations 7.7 Reynolds numbers 7.8 Heat transfer 7.9 Pressure loss tube-side 7.10 Pressure loss shell-side 7.11 Direct-sizing 7.12 Tube-bundle diameter 7.13 Practical design 7.14 Generalized correlations 7.15 Recommendations 7.16 Other shell-and-tube designs 7.17 Conclusions Chapter 8 Exergy Loss and Pressure Loss Exergy loss 8.1 Objective 8.2 Historical development 8.3 Exergy change for any flow process 8.4 Exergy loss for any heat exchangers 8.5 Contraflow exchangers 8.6 Dependence of exergy loss number on absolute temperature level 8.7 Performance of cryogenic plant 8.8 Allowing for leakage 8.9 Commercial considerations 8.10 Conclusions 177 177 178 189 190 191 194 196 199 201 204 207 207 208 208 209 209 210 211 211 213 214 215 217 217 220 222 222 224 229 229 229 230 231 233 234 236 238 240 242 242 [...]... through optimization, to the study of transients Most automotive heat exchangers operate in crossflow, and have a relatively small flow length on the air-side They may be constructed of tubes inserted in corrugated plate-fins, or made up from welded channels with corrugated fins The Advances in Thermal Design of Heat Exchangers: A Numerical Approach: Direct-sizing, step-wise rating, and transients Eric... 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 of these assumptions (e.g use of mean values) may introduce variations in design as large as the uncertainties introduced in heat- transfer and flowfriction correlations The designer needs... differential equations As the Mach number in heat exchangers is normally less than (Ma = 0.1) it becomes practicable to separate the problem into solution of mass flowrate and temperature-field disturbances A full numerical study of transients in a two-stream contraflow exchanger involves preparation of interpolating cubic spline-fits for both heat- transfer and flow-friction data against Reynolds number, and. .. teaching and research to post-graduate level in Mechanical Engineering at the University of Newcastle upon Tyne Dr Smith has published with IMechE, ASME, and ASTM, and has presented papers at international and national level He has represented the UK at a Nato AGARD Special Technical Meeting in Washington DC, and was retained as an expert witness by Norton Rose of London on behalf of shipbuilders Harland... Direct-sizing of plate-fin exchangers Direct-sizing of helical-tube exchangers Direct-sizing of bayonet-tube exchangers Direct-sizing of RODbaffle exchangers Exergy loss and pressure loss Transients in heat exchangers Single-blow test methods Heat exchangers in cryogenic plant Heat transfer and flow friction in two-phase flow Transient equations with longitudinal conduction and wall thermal storage Creep... Depending on geometry and availability of appropriate heat- transfer and flowfriction correlations, thermal design can be approached in the same way as for plate-fin exchangers Lamella heat exchangers Flat tube ducts are fitted inside a tubular shell, leaving equal spacing for shell-side flow between the flat tube ducts The geometry offers a very flexible surface arrangement, with good means for header... 0-470-01616-7 2 Advances in Thermal Design of Heat Exchangers small air flow length rather marks them out as a special design case and the subject deserves separate attention It is not covered in this text Segmentally baffled shell -and- tube designs Segmentally baffled and disc -and- doughnut baffled shell -and- tube designs are not specifically included because the exchanger core may not have sufficiently regular flow... in assessing the performance of heat exchangers and should be used in combination xxiv Preface The present treatment shows that: • The LMTD-Ntu approach is fully explicit in finding terminal temperatures in contraflow and parallel flow, and contains expressions for 'energy' and 'rate' processes ( iteration cannot be avoided when only inlet temperatures and LMTD are known and outlet temperatures are... original spline-fitting algorithm since used extensively over many years Special thanks to my close colleagues Tom Frost and Attila Fogarasy in the Department of Mechanical Engineering, University of Newcastle upon Tyne, whose patience and talents were outstanding, both professionally and personally Particularly so when Tom took the leadership with an inexperienced partner in rock climbing and hilarious... considers asymmetrically corrugated plates Inlet and return headering for plate -and- frame designs, and the same arrangement for plate-fin designs, may add a phase shift to the outlet transient response following an inlet disturbance Effects of this headering arrangement have been considered by Das & Roetzel (1995) Faster response is obtained with U-type headering than with Z-type headering, and the choice of . Advances in Thermal Design of Heat Exchangers A Numerical Approach: Direct-sizing, step-wise rating, and transients Eric M Smith Professional John Wiley & Sons, Ltd Advances in. 0-470-01616-7 Advances in Thermal Design of Heat Exchangers Related Titles Combined Power and Process - An Exergy Approach Optical Methods and Data Processing in Heat and Fluid Flow Axial-Flow . 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