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. Smith Copyright 2005 John Wiley & Sons, Ltd. ISBN: 0-470-01616-7 Advances in Thermal Design of Heat Exchangers Related Titles Combined Power and F J Barclay 1 86058 129 3 Process - An Exergy Approach Optical Methods and Data Edited by C Created, 1 86058 281 8 Processing in Heat and J Cosgrove, and J M Buick Fluid Flow Axial-Flow Compessors - R H Aungier 1 86058 422 5 A Strategy for Aerodynamic Design and Analysis 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.uk Visit our Home Page on www.com All Rights Reserved.
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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 Classification 1 1.2 Exclusions and extensions 1 1.3 Helical-tube, multi-start coil 3 1.4 Plate-fin exchangers 5 1.6 Helically twisted flattened tube 7 1.7 Spirally wire-wrapped 7 1.9 Wire-woven heat exchangers 9 1.10 Porous matrix heat exchangers 9 1.11 Some possible applications 10 Chapter 2 Fundamentals 19 2.1 Simple temperature distributions 19 2.2 Log mean temperature difference 21 2.3 LMTD-Ntu rating problem 23 2.4 LMTD-Ntu sizing problem 25 2.5 Link between Ntu values and LMTD 26 2.6 The 'theta' methods 26 2.7 Effectiveness and number of transfer units 27 2.8 e-Ntu rating problem 31 2.9 e-Ntu sizing problem 32 2.10 Comparison of LMTD-Ntu and e-Ntu approaches 33 2.11 Sizing when Q is not specified 34 2.12 Optimum temperature profiles in contraflow 35 2.13 Optimum pressure losses in contraflow 40 2.14 Compactness and performance 42 2.15 Required values of Ntu in cryogenics 42 2.16 To dig deeper 45 2.17 Dimensionless groups 47 Chapter 3 Steady-State Temperature Profiles 59 3.1 Linear temperature profiles in contraflow 59 3.2 General cases of contraflow and parallel flow 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 fins 133 4.17 Compact fin surfaces generally 138 4.18 Conclusions 138 Chapter 5 Direct-Sizing of Helical-Tube Exchangers 143 5.5 Completion of the design 159 5.6 Thermal design results for t/d = 1.8 Design for curved tubes 168 5.10 Part-load operation with by-pass control 174 5.11 Conclusions 174 Contents ix Chapter 6 Direct-Sizing of Bayonet-Tube Exchangers 177 6.1 Isothermal shell-side conditions 177 6.5 Non-isothermal shell-side conditions 191 6.6 Special explicit case 194 6.8 General numerical solutions 199 6.10 Conclusions 204 Chapter 7 Direct-Sizing of RODbaffle Exchangers 207 7.2 Configuration of the RODbaffle exchanger 208 7.3 Approach to direct-sizing 208 7.9 Pressure loss tube-side 213 7.10 Pressure loss shell-side 214 7.12 Tube-bundle diameter 217 7.16 Other shell-and-tube designs 222 7.17 Conclusions 224 Chapter 8 Exergy Loss and Pressure Loss 229 Exergy loss 229 8.3 Exergy change for any flow process 231 8.4 Exergy loss for any heat exchangers 233 8.6 Dependence of exergy loss number on absolute temperature level 236 8.7 Performance of cryogenic plant 238 8.8 Allowing for leakage 240 8.10 Conclusions 242 x Contents Pressure loss 243 8.11 Control of flow distribution 243 8.13 Minimizing effects of flow maldistribution 250 8.14 Embedded heat exchangers 251 8.15 Pumping power 253 Chapter 9 Transients in Heat Exchangers 257 9.1 Review of solution methods - contraflow 257 9.2 Contraflow with finite differences 259 9.4 Engineering applications - contraflow 266 9.5 Review of solution methods - crossflow 267 9.6 Engineering applications - crossflow 268 Chapter 10 Single-Blow Test Methods 275 10.1 Features of the test method 275 10.2 Choice of theoretical model 276 10.3 Analytical and physical assumptions 277 10.5 Relative accuracy of outlet response curves in experimentation 284 10.6 Conclusions on test methods 287 10.8 Solution by finite differences 289 10.9 Regenerators 290 Chapter 11 Heat Exchangers in Cryogenic Plant 297 11.2 Liquefaction concepts and components 298 11.3 Liquefaction of nitrogen 307 11.4 Hydrogen liquefaction plant 313 11.5 Preliminary direct-sizing of multi-stream heat exchangers 314 11.6 Step-wise rating of multi-stream heat exchangers 317 11.7 Future commercial applications 321 11.8 Conclusions 322 Chapter 12 Heat Transfer and Flow Friction in Two-Phase Flow 325 12.1 With and without phase change 325 12.2 Two-phase flow regimes 326 12.3 Two-phase pressure loss 327 Contents xi 12.4 Two-phase heat-transfer correlations 331 12.5 Two-phase design of a double-tube exchanger 333 12.7 Aspects of air conditioning 340 12.8 Rate processes 343 Appendix A Transient Equations with Longitudinal Conduction and Wall Thermal Storage 349 A.
1 Mass flow and temperature transients in contraflow 349 A.2 Summarized development of transient equations for contraflow 352 A.3 Computational approach 355 Appendix B Algorithms And Schematic Source Listings 361 B.I Algorithms for mean temperature distribution in one-pass unmixed crossflow 361 B.2 Schematic source listing for direct-sizing of compact one-pass crossflow exchanger 364 B.3 Schematic source listing for direct-sizing of compact contraflow exchanger 365 B.4 Parameters for rectangular offset strip fins 366 B.5 Longitudinal conduction in contraflow 370 B.6 Spline-fitting of data 375 B.7 Extrapolation of data 376 B.8 Finite-difference solution schemes for transients 377 Supplement to Appendix B - Transient Algorithms 383 Appendix C Optimization of Rectangular Offset Strip, Plate-Fin Surfaces 405 C.I Fine-tuning of rectangular offset strip fins 405 C.4 Manglik & Bergles correlations 409 Appendix D Performance Data for RODbaffle Exchangers 411 D.I Further heat-transfer and flow-friction data 411 D.2 Baffle-ring by-pass 414 Appendix E Proving the Single-Blow Test Method - Theory and Experimentation 419 E.I Analytical approach using Laplace transforms 419 xii Contents E.2 Numerical evaluation of Laplace outlet response 420 E.3 Experimental test equipment 423 Appendix F Most Efficient Temperature Difference in Contraflow 425 F. 1 Calculus of variations 425 F.2 Optimum temperature profiles 426 Appendix G Physical Properties of Materials and Fluids 429 G.I Sources of data 429 G.3 Solids 431 Appendix H Source Books on Heat Exchangers 433 H.I Texts in chronological order 433 H.2 Exchanger types not already covered 439 H.3 Fouling - some recent literature 442 Appendix I Creep Life of Thick Tubes 443 1.3 Early work on thick tubes 445 1.4 Equivalence of stress systems 446 1.5 Fail-safe and safe-life 447 1.6 Constitutive equations for creep 447 1.7 Clarke's creep curves 449 1.8 Further and recent developments 451 1.9 Acknowledgements 451 Appendix J Compact Surface Selection for Sizing Optimization 455 J. 1 Acceptable flow velocities 455 J.2 Overview of surface performance 455 J.5 Possible surface geometries 467 Appendix K Continuum Equations 469 K.I Laws of continuum mechanics 469 K.2 Coupled continuum theory 473 K.3 De-coupling the balance of energy equation 474 Appendix L Suggested Further Research 477 L.I Sinusoidal-lenticular surfaces 477 L.2 Steady-state crossflow 478 Contents xiii L.4 Transients in contraflow 479 Appendix M Conversion Factors 483 Notation 487 Commentary 487 Chapter 2 Fundamentals 488 Chapter 3 Steady-state temperature profiles 489 Chapter 4 Direct-sizing of plate-fin exchangers 490 Chapter 5 Direct-sizing of helical-tube exchangers 491 Chapter 6 Direct-sizing of bayonet-tube exchangers 493 Chapter 7 Direct-sizing of RODbaffle exchangers 494 Chapter 8 Exergy loss and pressure loss 495 Chapter 9 Transients in heat exchangers 496 Chapter 10 Single-blow test methods 497 Chapter 11 Heat exchangers in cryogenic plant 498 Chapter 12 Heat transfer and flow friction in two-phase flow 499 Appendix A Transient equations with longitudinal conduction and wall thermal storage 500 Appendix I Creep life of thick tubes 501 Index 503 XIV THERMAL DESIGN ROADMAP (outline guide for contraflow) DIRECT-SIZING (minimum input data required) INPUT DATA contraflow Qduty OPTIMAL TEMPERATURE DISTRIBUTION Grassman & Kopp exergy constraint -—- — const. Ntu VALUES {find Th2 Tci} LMTD-nT approach approach EXCHANGER TYPE Plate-fin Helical-tube RODbaffle MEAN PHYSICAL PROPERTIES specific heats absolute viscosities thermal conductivities XV APPLY LMTD Qduty UxS = LMTD COMPACT PLATE-FIN GEOMETRIES heat-transfer correlations flow-friction correlations FIXED GEOMETRIES VARIABLE GEOMETRIES K&L correlations 1 ( M&B correlations L&S correlations | =spline-fits=>- I (ROSF variable) range of validity J [ range of validity DIRECT-SIZING block heat exchanger equivalent plate with half-height surfaces optimal pressure loss exergy constraint but preferably design with Ma < 0.1 FOR RANGE OF Re VALUES FOR SIDE-1 GENERATE heat-transfer curve pressure-loss curve, Side-1 pressure-loss curve, Side-2 FIXED GEOMETRIES VARIABLE GEOMETRIES coincidence of coincidence of Ap curves unlikely Ap curves possible XVI NEAR-OPTIMUM EXCHANGER estimated cross-section and length LONGITUDINAL CONDUCTION (reduced performance in most exchangers) STEADY-STATE TEMPERATURE PROFILES three simultaneous partial differential equations ( hot fluid.
balance of energy } solid wall. balance of energy \ cold fluid.
