Boiling Research and Advances 978-0-08-101010-5

Table of contents :
Front Cover......Page 1
Boiling......Page 4
Copyright Page......Page 5
Contents......Page 6
List of Contributors......Page 26
Biographies......Page 30
Preface......Page 42
The Phase Change Research Committee......Page 44
Contributors......Page 45
1 Outline of Boiling Phenomena and Heat Transfer Characteristics......Page 48
1.1 Pool Boiling......Page 49
1.2 Flow Boiling......Page 51
1.3 Other Aspects......Page 55
References......Page 57
2 Nucleate Boiling......Page 60
2.1.1 Introduction......Page 62
2.1.2.2 Signal Conditioning......Page 64
2.1.2.3 Sensor Design for Pool Nucleate Boiling......Page 65
2.1.2.4 Sensor Calibration......Page 66
2.1.2.6 Calculation of Local Heat Flux......Page 67
2.1.2.7 Calculation of Wall Heat Transfer and Latent Heat in Bubble......Page 68
2.1.3.1 Bubble Growth Characteristics......Page 69
2.1.3.2 Phenomenological Model of Isolated Bubble Pool Boiling......Page 70
2.1.3.3 Fundamental Heat Transfer Phenomena Observed from Local Wall Temperature and Heat Flux......Page 71
2.1.3.4 Microlayer Thickness......Page 73
2.1.3.5 Characteristics of Wall Heat Transfer and Bubble Growth......Page 75
2.1.3.6 Effect of Wall Superheat on Boiling Heat Transfer......Page 78
2.1.4 Conclusion......Page 80
References......Page 82
2.2.1 Introduction......Page 83
2.2.2.1 Experimental Apparatus and Method......Page 84
2.2.2.2 Initial Distribution of Microlayer Thickness......Page 88
2.2.3 Measurement of Microlayer Structure by Laser Interferometric Method......Page 89
2.2.4 Basic Characteristics and Correlations Concerning the Microlayer in Nucleate Pool Boiling......Page 91
2.2.5 Numerical Simulation on the Heat Transfer Plate During Boiling......Page 94
2.2.5.1 Heat Transfer Characteristics of the Microlayer in an Evaporation System......Page 95
2.2.5.2 Contribution of Microlayer Evaporation......Page 96
2.2.6 Numerical Simulation on the Two-Phase Vapor–Liquid Flow During Boiling......Page 98
2.2.6.1 Variation in Microlayer Radius and Bubble Volume......Page 99
2.2.6.2 Temperature Distribution of Liquid in the Vicinity of the Bubble Interface......Page 101
2.2.6.3 Heat Transfer Characteristics of Microlayer Evaporation......Page 102
2.2.6.4 Contribution of Microlayer Evaporation......Page 104
2.2.7 Conclusion......Page 105
References......Page 106
2.3.1 Introduction......Page 107
2.3.2.1.1 Effect of surface wetting on boiling heat transfer characteristics in mini-/micro-gaps......Page 110
2.3.2.1.2 Mechanisms and characteristics of boiling heat transfer in the narrow-gap mini-/microchannel on a wettable surface......Page 111
2.3.2.1.3 Experimental apparatus and method......Page 113
2.3.2.2.1 Effect of heat flux, distance from bubble inception site, bubble forefront velocity and gap size on the initial m.........Page 115
2.3.2.2.2 Distribution of initial microlayer thickness......Page 117
2.3.2.3.2 Analysis and discussion of the heat transfer characteristics......Page 118
2.3.3.1 Measurement of Microlayer Thickness for Various Test Liquids......Page 120
2.3.3.2.1 Formulation of the problem and the model geometry and initial and boundary conditions......Page 122
2.3.3.2.2 Comparison between simulation and measurement results for HFE7200......Page 127
2.3.3.2.3 Study of effect of physical properties......Page 128
2.3.3.3 Dimension Analysis and Correlation......Page 130
2.3.4 Conclusion......Page 132
Nomenclature......Page 133
References......Page 134
2.4.1 Introduction......Page 135
2.4.2.1 Method......Page 136
2.4.2.2 Results......Page 140
2.4.3.1 Method......Page 144
2.4.3.2 Results......Page 147
2.4.4 Conclusion......Page 148
References......Page 149
2.5.1.1 Phase Equilibrium Diagram......Page 150
2.5.1.2 Boiling Incipience......Page 151
2.5.1.3 Bubble Growth Rate......Page 152
2.5.1.4 Bubble Departure......Page 154
2.5.2.1 Predicting Method and Correlations......Page 155
2.5.2.2 Existing Topics for Mixture Boiling......Page 160
2.5.3 Experimental Investigation of the Marangoni Effect......Page 161
2.5.4.2 Existing Research......Page 167
2.5.4.3 Phase Equilibrium......Page 168
2.5.4.4 Experimental Results......Page 170
2.5.5 Conclusions......Page 173
Nomenclature......Page 174
Subscripts......Page 175
References......Page 176
2.6.2.1 Overview......Page 178
2.6.2.2 Heat Transfer Models......Page 180
2.6.2.3 Models for Void Fraction Evolution and Phase Change Rates......Page 182
2.6.3 Bubble Dynamics in Subcooled Flow Boiling......Page 183
2.6.4 Conclusion......Page 187
Subscripts......Page 188
References......Page 189
3 CHF—Transition Boiling......Page 192
3.1.2 Previously Proposed CHF Mechanisms for Pool Boiling......Page 196
3.1.3.1 Characteristics of CHF in Subcooled Pool Boiling......Page 197
3.1.3.3 The Liquid–Vapor Structure Beneath Vapor Masses......Page 199
3.1.3.4.1 The detection of surface dry-out by conductance probe......Page 202
3.1.3.5 The Mechanism of CHF and the Cause of the Increase in CHF in Subcooled Boiling......Page 205
3.1.4 CHF in Saturated Boiling on Inclined Surfaces......Page 207
3.1.5 CHF in Saturated Boiling of Binary Aqueous Solutions......Page 210
3.1.6 CHF in Boiling of Water on a Heating Surface Coated with Nanoparticles......Page 214
Nomenclature......Page 218
References......Page 219
3.2.1 Introduction......Page 220
3.2.2.1 Basic Ideas of the Microlayer......Page 222
3.2.2.2 Description of Heat Transfer in Fully Developed Nucleate Boiling......Page 223
3.2.2.3 Microlayer Thickness and Dry-Out Radius Beneath an Individual Bubble......Page 226
3.2.2.4 Bubble Dynamics During the Final Growth Period......Page 227
3.2.3 Results and Discussion......Page 228
Greek Symbols......Page 231
References......Page 232
3.3.1 Introduction......Page 234
3.3.2.1 Total Reflection Technique......Page 235
3.3.2.2 Liquid–Solid Contact Patterns......Page 236
3.3.2.3 Contact-Line-Length Density......Page 239
3.3.3.1 Quasi-Two-Dimensional Boiling System......Page 244
3.3.3.2 Nucleate Boiling Curve and CHF in Quasi-Two-Dimensional Space......Page 245
3.3.3.3 Bubble Structures......Page 246
3.3.4.1 Experimental Setup and Conditions......Page 250
3.3.4.3 Liquid–Solid Contact Situations While Liquid Spray Cooling......Page 251
3.3.4.4 Liquid–Solid Contact Situations with Liquid Jet Impingement......Page 253
Nomenclature......Page 257
References......Page 258
3.4.1 Introduction......Page 259
3.4.2.1 Effect of Micropores and Vapor Escape Channels on the CHF......Page 261
3.4.2.2 Effects of the Heights in HPPs δh on the CHF......Page 262
3.4.2.3 The CHF Model Based on Capillary Limit......Page 264
3.4.2.4 Optimization in Geometry of HPP......Page 265
3.4.2.5 Effect of Heater Size on the CHF Enhancement......Page 266
3.4.3.1 Two-Layer Structured HPP......Page 267
3.4.3.2 Combination of HPP, Nanoparticle-Coated Surface, and Honeycomb Solid Structures (HSSs) in Pure Water......Page 268
3.4.3.3 Combination of HPP and Nanofluid......Page 270
Nomenclature......Page 272
References......Page 273
3.5.1 Introduction......Page 274
3.5.2.1 Available CHF Data Correlations......Page 276
3.5.2.2 Recent Experimental Study and Results......Page 278
3.5.2.3 Discussions and Remaining Problems......Page 281
3.5.3.2 CHF on Chips with Modified Surfaces......Page 283
3.5.4 CHF Data Correlation on Heaters of Various Shapes and Configurations......Page 285
3.5.5 Parameters and Factors Affecting CHF......Page 286
References......Page 288
3.6.2.1 Heating with Steam......Page 290
3.6.3 Automatic Temperature Control......Page 293
3.6.4.1 In the Case of Steady Boiling......Page 295
3.6.5 Conclusion......Page 298
Nomenclature......Page 299
References......Page 300
3.7.1 Introduction......Page 301
3.7.2.1 Experimental Apparatus......Page 302
3.7.2.2 Experimental Procedure......Page 303
3.7.2.4 Experimental Uncertainty......Page 304
3.7.3.1 Heat-Transfer Characteristics: Boiling Curve......Page 305
3.7.3.2 Liquid–Solid Contact Fraction: Correlation......Page 306
3.7.3.3 Void Fraction Near Heating Surface......Page 307
3.7.4.1 First Model......Page 309
3.7.4.2 Present Model......Page 310
3.7.4.3.1 Correlation model......Page 312
3.7.4.4 Application to Core Cooling......Page 313
3.7.5 Conclusion......Page 315
References......Page 317
3.8.1 Introduction......Page 318
3.8.2 Criterion for the Judgement of Flow Pattern Development......Page 320
3.8.3.1 Introduction......Page 323
3.8.3.2 Liu–Nariai Model......Page 327
3.8.3.2.1 Vapor clot velocity uB and vapor clot length LB......Page 328
3.8.3.2.2.1 Calculation of the thickness of vapor clot DB......Page 330
3.8.3.2.2.3 Calculation of initial thickness of the liquid sublayer δ0......Page 331
3.8.3.2.3 Dealing with low L/D conditions......Page 332
3.8.3.3 Validation of the Proposed CHF Model......Page 333
3.8.4.1 CHF Triggering Mechanism and Prediction......Page 335
3.8.4.2 Validation of the Proposed Model......Page 336
3.8.5 Conclusion......Page 339
Nomenclature......Page 340
Subscripts......Page 341
References......Page 342
3.9.1 Introduction......Page 344
3.9.2 The Definition of Flow Instability......Page 345
3.9.3 The Historical Background......Page 346
3.9.4 Simple Model—Quasi-Steady Assumption......Page 348
3.9.5 Estimation by Lumped-Parameter Model—Dumping Effect of Two-Phase......Page 352
3.9.6 Dry-out Under Natural Circulation Loop—Flow Oscillation Caused by the System......Page 355
3.9.7 More Detailed Discussion of Boiling Phenomena under Oscillatory Flow Conditions......Page 358
3.9.8 Conclusion......Page 360
Subscripts......Page 361
References......Page 362
3.10.1 Introduction......Page 363
3.10.2 Minimum Wetting Rate......Page 364
3.10.2.1 Analytical Model of MWR......Page 365
3.10.2.2 Measurement of MWR, Contact Angle, and Wave Characteristics......Page 366
3.10.2.3 Results......Page 367
3.10.2.4 Effect of Waves on MWR......Page 373
3.10.3 CHF of Film Flow......Page 375
3.10.4 CHF of Mini-Channel......Page 380
3.10.5 Characteristics of Falling Film Flow......Page 384
3.10.5.1 Wave Profile......Page 385
3.10.5.2 Film Thickness......Page 386
3.10.5.3 Wave Velocity......Page 391
3.10.5.4 Wavelength......Page 392
3.10.5.5 Development of Correlations of Wave Properties......Page 393
3.10.6 Conclusion......Page 397
Nomenclature......Page 398
References......Page 399
3.11.2.1 Design-CHF Correlation for an LWR Fuel Assembly......Page 401
3.11.2.2 CHF Prediction Using a Film Dry-Out Model for a Vertical Tube......Page 402
3.11.2.3 Analysis of Critical Power Prediction for BWR Fuel Assembly......Page 406
3.11.2.4 Enhancement of Heat-Removal Limit......Page 409
3.11.2.5 Post-BT Criteria......Page 412
Greek Symbols......Page 413
References......Page 414
4 Minimum Heat Flux—Film Boiling......Page 416
Nomenclature......Page 417
4.1.1 Introduction......Page 418
4.1.2 Experimental Apparatus and Procedure......Page 419
4.1.3.1 Behavior of wetting and temperature at wetting......Page 421
4.1.3.2 Wetting area and contact angle......Page 424
4.1.3.3 Estimation of contact angle......Page 425
4.1.4 Conclusions......Page 426
Further Reading......Page 427
4.2.1 Introduction......Page 428
4.2.2.2 Experimental procedures......Page 429
4.2.3.1 Characteristics of single-phase liquid flow......Page 431
4.2.3.3 Dependence on distance......Page 432
4.2.3.4 Dependence on bulk-liquid velocity and liquid subcooling......Page 433
4.2.3.5 Critical condition and correlation of dimensionless numbers......Page 434
4.2.4 Mechanism of Transition......Page 435
4.2.5 Conclusions......Page 436
Subscripts......Page 437
4.3.1 Introduction......Page 438
4.3.2 Inverse Analysis Technique in Transient Heat Transfer......Page 439
4.3.3 Experimental Study on Quenching of a Hot Block With Liquid Jet or Spray......Page 441
4.3.4 Visual and Acoustic Observations of Quenching Phenomenon......Page 443
4.3.5 Change in Surface Temperature and Surface Heat Flux Distributions Evaluated With 2D Inverse Heat Conduction Analysis......Page 445
4.3.6 Characteristics of Cooling and Boiling Curves During Quenching......Page 447
4.3.7 Wetting and Quenching Temperatures......Page 448
4.3.8 Characteristics of Maximum Heat Flux During Quenching......Page 451
4.3.9 Conclusions......Page 453
Subscripts......Page 455
References......Page 456
5 Numerical Simulation......Page 458
5.1.1 Introduction......Page 459
5.1.2.2 Mesoscopic Approach......Page 460
5.1.2.3 Macroscopic Approach......Page 461
5.1.3 Governing Equations Based on MARS......Page 462
5.1.4 Non-Empirical Boiling and Condensation Model......Page 463
5.1.5 Comparison of Numerical Results to Visualization Results......Page 464
5.1.6 Bubble Departure Behavior......Page 466
5.1.7 Effects of Wettability on Departure Behavior......Page 468
5.1.8 Bubble Condensation Behaviors......Page 469
5.1.9 Conclusion......Page 471
Subscripts......Page 472
References......Page 473
5.2.2.1 Governing Equations......Page 476
5.2.2.2 Interface Tracking Method......Page 477
5.2.3.1 Two-Phase Flow Fluid Mixing Test......Page 480
Subscripts......Page 488
References......Page 489
6 Topics on Boiling: From Fundamentals to Applications......Page 490
6.1.1 Introduction......Page 495
6.1.2.1 Useful Functions and Relations Between State Variables......Page 496
6.1.3 Equation of State......Page 500
6.1.4.1 GCEOS VTPR......Page 501
6.1.4.2 GCEOS VGTPR......Page 507
6.1.5 Conclusion......Page 511
Nomenclature......Page 512
Subscripts......Page 513
References......Page 514
6.2.1 Introduction......Page 515
6.2.2 Interfacial Transport Across the Liquid–Vapor Interface......Page 516
6.2.3 Condensation Coefficient Based on Molecular Dynamic Simulation......Page 517
6.2.3.2 Microscopic Condensation Coefficient: Molecular Translational Energy Dependence......Page 518
6.2.3.3 Boundary Condition Based on the Microscopic Condensation Coefficient......Page 522
6.2.3.4 Nonequilibrium Microscopic Boundary Condition at the Liquid–Vapor Interface......Page 523
6.2.4 Condensation Coefficient Based on the Transition State Theory......Page 525
Nomenclature......Page 530
Subscripts......Page 531
References......Page 532
6.3.1 Introduction......Page 534
6.3.2.1 Theory......Page 535
6.3.2.2 Movement of the Triple-Phase Contact Line......Page 539
6.3.2.3 Molecular Dynamics Simulation......Page 540
6.3.2.4 Multiscale Simulation......Page 542
6.3.3 Microscopic Investigation of Nucleation of Boiling Bubbles......Page 544
6.3.4 Boiling Heat Transfer Enhancement by Micro-/Nano-Hybrid Structures......Page 547
Greek Symbols......Page 548
References......Page 549
6.4.1 Introduction......Page 551
6.4.2 Fundamental Characteristics of Transient Boiling and Overview of the Studies......Page 552
6.4.3 Direct Transition to Film Boiling......Page 556
6.4.4 Relevance of Nucleation Phenomena to Direct Transition......Page 557
6.4.6 Modeling of Boiling Front Propagation......Page 559
6.4.7 On the Mechanism of Transition to Film Boiling in Direct Transition......Page 561
6.4.8 Conclusion......Page 562
Subscripts......Page 563
References......Page 564
6.5.1 Introduction......Page 566
6.5.2 Dynamic Neutron Radiography......Page 568
6.5.3.1 Adiabatic Air–Water Two-Phase Flow......Page 569
6.5.3.2 Boiling Heat Transfer in a Round Tube......Page 570
6.5.3.3 Gas/Liquid–Metal Two-Phase Flow......Page 571
6.5.3.4 Direct Contact Evaporation of a Water Droplet in a Heated Liquid-Metal Pool......Page 574
References......Page 575
6.6.1 Introduction......Page 577
6.6.2.1 Subcooled Flow Boiling in a Millimeter-Sized Rectangular Channel: Hydraulic Diameter=7.3–8.2mm......Page 584
6.6.2.2 Subcooled Flow Boiling in a Mini-Channel [17]: Hydraulic Diameter=0.7–1.3mm......Page 586
6.6.3.1 Bubble Behaviors on the Heating Surface and Pressure Fluctuation......Page 588
6.6.3.2 Instability of the Vapor Bubble Interface in a Subcooled Liquid......Page 590
6.6.4 Summary......Page 593
References......Page 594
6.7.1 Introduction......Page 595
6.7.2 Surface Temperature Measurement......Page 597
6.7.3 Microscale Heaters......Page 598
6.7.4 Artificial Cavities and Nucleation Control......Page 599
6.7.5.1 Objectives: Specifying the Occurrence Conditions of Microbubble Emission Boiling......Page 600
6.7.5.3 Temperature Trend and Bubbling Behavior......Page 601
6.7.5.4 Bubbling Pattern Map......Page 604
References......Page 606
6.8.1 Introduction......Page 609
6.8.2.1 Experiment for On-Plate Boiling......Page 610
6.8.2.2 Results for On-Plate Boiling......Page 611
6.8.3.1 Experiment for On-Wire Boiling......Page 613
6.8.3.2 Results for On-Wire Boiling......Page 614
6.8.4.1 Experiment for Vapor Injection......Page 621
6.8.4.2 Results for Vapor Injection......Page 622
6.8.5 Summary......Page 627
References......Page 628
6.9.1 Introduction......Page 629
6.9.2 Boiling Heat Transfer Characteristics on the Thermal Spray Coating......Page 631
6.9.3 Pool Boiling on Thermal Spray Coatings Under Microgravity......Page 635
6.9.4 Conclusion......Page 638
References......Page 639
6.10.1 Introduction......Page 640
6.10.2 General Knowledge about Boiling Heat Transfer Enhancement Utilizing Porous Layers......Page 641
6.10.3 Nucleate Boiling Heat Transfer Enhancement by Unique Porous Media......Page 647
6.10.4 Boiling Heat Transfer Enhancement with Functional Porous Media......Page 650
6.10.5 Conclusion......Page 654
References......Page 655
6.11.1 Overview of Wettability Effects in Boiling and Evaporation......Page 657
6.11.2 Boiling Enhancement by Mixed-Wettability Surfaces......Page 660
6.11.3 Peculiar Boiling Behaviors on Superhydrophobic Surfaces and the Effect of Dissolved Air......Page 662
References......Page 666
6.12.1 Introduction......Page 667
6.12.2.1 Surface Tension of Self-Rewetting Fluids......Page 668
6.12.2.2 Nano-Self-Rewetting Fluids......Page 670
6.12.2.3 Ternary Mixtures and Self-Rewetting Brines......Page 671
6.12.3.1 Fundamental Behavior at the Liquid–Vapor Interface......Page 672
6.12.3.2 Pool Boiling and Other Boiling Heat Transfer......Page 674
6.12.3.3 Heat Pipes......Page 676
6.12.3.4 Space Experiments with Self-Rewetting Fluids (SELENE)......Page 677
References......Page 682
6.13.1.1 Introduction......Page 684
6.13.1.2.1 Automotive transformation-induced plasticity (TRIP) steel......Page 685
6.13.1.2.2 Steel plates......Page 687
6.13.2 Water Cooling Systems in the Steel Industry......Page 690
6.13.3.1 Issues of Heat Transfer Control Technology Concerning Boiling Heat Transfer in Steel Processes......Page 694
6.13.3.2.1 Numerical calculation of flow on a moving plate during laminar cooling......Page 696
6.13.3.2.2 Heat transfer characteristics of laminar cooling......Page 698
6.13.3.2.4 Temperature analysis of moving hot steel strip......Page 701
6.13.3.3.1 Effect of heat-transfer surface movement......Page 702
6.13.3.3.2 Effect of heat-transfer surface residual water height......Page 703
6.13.3.3.3 Research on high water flow density region......Page 710
6.13.3.3.4 Research on spray flow patterns......Page 711
References......Page 713
6.14.1 Introduction......Page 716
6.14.2 Model of Behavior of Spray on a Hot Surface......Page 718
6.14.3 Parametric Effects on Spray-Cooling Heat Transfer Characteristics......Page 719
6.14.3.2 Effect of Cooling Surface Wettability......Page 720
6.14.3.4 Effect of Porosity of Cooling Surface Layer......Page 722
6.14.3.5 Effect of Unsteady-State of Cooling Surface......Page 723
6.14.3.7 Effect of Coolant-Related Parameters......Page 725
6.14.4 Cooling Instability Phenomenon......Page 727
References......Page 728
6.15.1 Introduction......Page 729
6.15.2 Elementary Process of Vapor Explosion......Page 730
6.15.3 Theory of Vapor Explosion......Page 731
6.15.3.1 Thermal Detonation Model......Page 732
6.15.3.2 Spontaneous Nucleation Model......Page 733
6.15.4.1.1 Experimental apparatus......Page 736
6.15.4.1.2 Experimental results......Page 737
6.15.4.2.1 Experimental apparatus......Page 741
6.15.4.2.2 Experimental results......Page 743
Subscripts......Page 750
References......Page 751
6.16.1 Introduction......Page 753
6.16.2.2 Solution Droplet Impingement onto Molten Alloy Pool......Page 754
6.16.2.3 Solid Sphere Quenching into Solution Pool......Page 757
6.16.3.1 Visual Observation and Phenomena Classification......Page 758
6.16.3.2 Interfacial Mixing Structure......Page 760
6.16.3.3 Effect of Surface Property......Page 763
6.16.3.4 Effect of Material Property......Page 766
6.16.3.6 Effect of Thermal Capacity......Page 767
6.16.3.7 Controlling Additive to Promote and Suppress Vapor Explosion......Page 768
6.16.4 Vapor Film Stability Analysis......Page 774
6.16.5 Conclusions......Page 776
References......Page 777
6.17.1 Introduction......Page 779
6.17.2.1 Flow Regime......Page 780
6.17.2.2 Heat Transfer in Annular Flow Regime......Page 781
6.17.3 Flow Boiling in a Horizontal Internally Spirally Grooved Tube......Page 784
6.17.3.1 Flow Regime for Discussion of Heat Transfer Characteristics......Page 785
6.17.3.2 Heat Transfer Coefficients......Page 786
6.17.4 Concluding Remarks......Page 788
Subscripts......Page 789
References......Page 790
6.18.1 Introduction......Page 792
6.18.2 Fluid Information......Page 793
6.18.3.1 Experimental Set-Up......Page 794
6.18.3.2 Test Conditions and Procedure......Page 795
6.18.3.3 Data Reduction and Measurement Uncertainty......Page 796
6.18.4.1 Hysteresis of Nucleate Boiling Inception, Departure from Single-Phase Natural Convection......Page 797
6.18.4.2 Comparative Assessment on Fully Developed Nucleate Boiling HTC for Low-GWP Refrigerants......Page 798
6.18.4.3 Comparison for Correlations with “Estimated Transport Properties”......Page 800
Greek Symbols......Page 803
References......Page 804
6.19.1 Introduction......Page 806
6.19.2 A Brief Review of Previously Conducted Research......Page 807
6.19.3 Experimental Set-up for Gravity-Feed of Liquid Nitrogen......Page 809
6.19.4 Gravity-Feed Reflooding......Page 810
6.19.5 Simplified Modeling of Dynamics of Gravity Reflooding......Page 815
6.19.6 Constant-Feed Reflooding Experiment with Water......Page 817
6.19.7 Simplified Lumped-Parameter Modeling......Page 820
6.19.8 Conclusion......Page 822
Subscripts......Page 823
References......Page 824
Index......Page 826
Back Cover......Page 849

Citation preview

Boiling

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Boiling Research and Advances

Edited by

Yasuo Koizumi Japan Atomic Energy Agency, Japan

Masahiro Shoji The University of Tokyo, Japan

Masanori Monde Saga University, Japan

Yasuyuki Takata Kyushu University, Japan

Niro Nagai University of Fukui, Japan

Elsevier Radarweg 29, PO Box 211, 1000 AE Amsterdam, Netherlands The Boulevard, Langford Lane, Kidlington, Oxford OX5 1GB, United Kingdom 50 Hampshire Street, 5th Floor, Cambridge, MA 02139, United States Copyright r 2017 Elsevier Ltd. 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 permission in writing from the publisher. Details on how to seek permission, further information about the Publisher’s permissions policies and our arrangements with organizations such as the Copyright Clearance Center and the Copyright Licensing Agency, can be found at our website: www.elsevier.com/permissions. This book and the individual contributions contained in it are protected under copyright by the Publisher (other than as may be noted herein). Notices Knowledge and best practice in this field are constantly changing. As new research and experience broaden our understanding, changes in research methods, professional practices, or medical treatment may become necessary. Practitioners and researchers must always rely on their own experience and knowledge in evaluating and using any information, methods, compounds, or experiments described herein. In using such information or methods they should be mindful of their own safety and the safety of others, including parties for whom they have a professional responsibility. To the fullest extent of the law, neither the Publisher nor the authors, contributors, or editors, assume any liability for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions, or ideas contained in the material herein. British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library Library of Congress Cataloging-in-Publication Data A catalog record for this book is available from the Library of Congress ISBN: 978-0-08-101010-5

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Contents List of Contributors ........................................................................................................................... xxv Biographies ....................................................................................................................................... xxix Preface ................................................................................................................................................. xli

CHAPTER 1 Outline of Boiling Phenomena and Heat Transfer Characteristics ..... 1 Yasuo Koizumi 1.1 Pool Boiling................................................................................................................ 2 Masanori Monde 1.2 Flow Boiling............................................................................................................... 4 Yasuo Koizumi 1.3 Other Aspects ............................................................................................................. 8 Yasuyuki Takata References................................................................................................................. 10

CHAPTER 2 Nucleate Boiling ................................................................................. 13 2.1 MEMS Sensor Technology and the Mechanism of Isolated Bubble Nucleate Boiling....................................................................................................... 15 Tomohide Yabuki and Osamu Nakabeppu 2.1.1 Introduction .................................................................................................... 15 2.1.2 MEMS Sensor Technology in Boiling Research .......................................... 17 2.1.2.1 Sensor Type and Performance ......................................................... 17 2.1.2.2 Signal Conditioning ......................................................................... 17 2.1.2.3 Sensor Design for Pool Nucleate Boiling ....................................... 18 2.1.2.4 Sensor Calibration............................................................................ 19 2.1.2.5 Experimental System and Conditions ............................................. 20 2.1.2.6 Calculation of Local Heat Flux ....................................................... 20 2.1.2.7 Calculation of Wall Heat Transfer and Latent Heat in Bubble...... 21 2.1.3 Heat Transfer Mechanisms Revealed by MEMS Thermal Measurement .... 22 2.1.3.1 Bubble Growth Characteristics........................................................ 22 2.1.3.2 Phenomenological Model of Isolated Bubble Pool Boiling ..................................................................................... 23 2.1.3.3 Fundamental Heat Transfer Phenomena Observed from Local Wall Temperature and Heat Flux.......................................... 24 2.1.3.4 Microlayer Thickness....................................................................... 26 2.1.3.5 Characteristics of Wall Heat Transfer and Bubble Growth............ 28

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2.1.3.6 Effect of Wall Superheat on Boiling Heat Transfer ....................... 31 2.1.3.7 Continuous Bubble Boiling ............................................................. 33 2.1.4 Conclusion...................................................................................................... 33 References...................................................................................................... 35 2.2 Measurement of the Microlayer during Nucleate Boiling and its Heat Transfer Mechanism................................................................................................. 36 Yoshio Utaka and Zhihao Chen 2.2.1 Introduction .................................................................................................... 36 2.2.2 Measurement of Microlayer Structure by Laser Extinction Method............ 37 2.2.2.1 Experimental Apparatus and Method .............................................. 37 2.2.2.2 Initial Distribution of Microlayer Thickness................................... 41 2.2.3 Measurement of Microlayer Structure by Laser Interferometric Method ........................................................................................................... 42 2.2.4 Basic Characteristics and Correlations Concerning the Microlayer in Nucleate Pool Boiling................................................................................ 44 2.2.5 Numerical Simulation on the Heat Transfer Plate during Boiling ............... 47 2.2.5.1 Heat Transfer Characteristics of the Microlayer in an Evaporation System ......................................................................... 48 2.2.5.2 Contribution of Microlayer Evaporation ......................................... 49 2.2.6 Numerical Simulation on the Two-Phase Vapor
Liquid Flow during Boiling............................................................................................................ 51 2.2.6.1 Variation in Microlayer Radius and Bubble Volume ..................... 52 2.2.6.2 Temperature Distribution of Liquid in the Vicinity of the Bubble Interface............................................................................... 54 2.2.6.3 Heat Transfer Characteristics of Microlayer Evaporation .............. 55 2.2.6.4 Contribution of Microlayer Evaporation ......................................... 57 2.2.7 Conclusion...................................................................................................... 58 Nomenclature................................................................................................. 59 Greek Symbols............................................................................................... 59 Subscripts....................................................................................................... 59 References...................................................................................................... 59 2.3 Configuration of the Microlayer and Characteristics of Heat Transfer in a Narrow-Gap Mini-/Microchannel Boiling System........................................... 60 Yoshio Utaka 2.3.1 Introduction .................................................................................................... 60 2.3.2 Mechanisms and Characteristics of Boiling Heat Transfer in the Narrow-Gap Mini-/Microchannels ................................................................ 63 2.3.2.1 General Features of Boiling Phenomena in Narrow-Gap Mini-/Microchannels........................................................................ 63 2.3.2.2 Configuration of the Microlayer in a Narrow-Gap Mini-/Microchannel Boiling System ............................................... 68

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2.3.2.3 Consideration of Heat Transfer Characteristics on the Basis of Configuration of the Microlayer ................................................. 71 2.3.3 Characteristics of a Microlayer for Various Liquids and a Correlation of Microlayer Thickness in a Narrow-Gap Mini-/Micro-Boiling System ......................................................................... 73 2.3.3.1 Measurement of Microlayer Thickness for Various Test Liquids ... 73 2.3.3.2 Numerical Simulation of the Bubble Growth Process in the Microchannel ......................................................................... 75 2.3.3.3 Dimension Analysis and Correlation............................................... 83 2.3.4 Conclusion...................................................................................................... 85 Nomenclature................................................................................................. 86 Greek Symbols............................................................................................... 87 Nondimensional Numbers ............................................................................. 87 References...................................................................................................... 87 2.4 Surface Tension of High-Carbon Alcohol Aqueous Solutions: Its Dependence on Temperature and Concentration and Application to Flow Boiling in Minichannels ............................................................................................................ 88 Naoki Ono 2.4.1 Introduction .................................................................................................... 88 2.4.2 Surface Tension Measurements of High-Carbon Alcohol Aqueous Solutions ........................................................................... 89 2.4.2.1 Method ............................................................................................. 89 2.4.2.2 Results .............................................................................................. 93 2.4.2.3 Discussion ........................................................................................ 97 2.4.3 Effect of High-Carbon Alcohol Aqueous Solutions on the Critical Heat Flux Condition in Boiling with Impinging Flow in a Minichannel..... 97 2.4.3.1 Method ............................................................................................. 97 2.4.3.2 Results ............................................................................................ 100 2.4.3.3 Discussion ...................................................................................... 101 2.4.4 Conclusion.................................................................................................... 101 Acknowledgments ....................................................................................... 102 Nomenclature............................................................................................... 102 Greek Symbols............................................................................................. 102 References.................................................................................................... 102 2.5 Nucleate Boiling of Mixtures ................................................................................ 103 Haruhiko Ohta 2.5.1 Mixture Effects on Elementary Processes of Nucleate Boiling ................. 103 2.5.1.1 Phase Equilibrium Diagram........................................................... 103 2.5.1.2 Boiling Incipience .......................................................................... 104 2.5.1.3 Bubble Growth Rate ...................................................................... 105 2.5.1.4 Bubble Departure ........................................................................... 107

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2.5.2 Heat Transfer Coefficient ............................................................................ 108 2.5.2.1 Predicting Method and Correlations.............................................. 108 2.5.2.2 Existing Topics for Mixture Boiling ............................................. 113 2.5.3 Experimental Investigation of the Marangoni Effect.................................. 114 2.5.4 Superior Heat Transfer Characteristics of Immiscible Mixtures ................ 120 2.5.4.1 Objectives to use Immiscible Mixtures ......................................... 120 2.5.4.2 Existing Research........................................................................... 120 2.5.4.3 Phase Equilibrium .......................................................................... 121 2.5.4.4 Experimental Results ..................................................................... 123 2.5.5 Conclusions .................................................................................................. 126 Nomenclature............................................................................................... 127 Greek Symbols............................................................................................. 128 Subscripts..................................................................................................... 128 References.................................................................................................... 129 2.6 Bubble Dynamics in Subcooled Flow Boiling ...................................................... 131 Tomio Okawa 2.6.1 Introduction .................................................................................................. 131 2.6.2 Review of the Subcooled Flow Boiling Models ......................................... 131 2.6.2.1 Overview ........................................................................................ 131 2.6.2.2 Heat Transfer Models .................................................................... 133 2.6.2.3 Models for Void Fraction Evolution and Phase Change Rates .... 135 2.6.3 Bubble Dynamics in Subcooled Flow Boiling............................................ 136 2.6.4 Conclusion.................................................................................................... 140 Nomenclature............................................................................................... 141 Greek Symbols............................................................................................. 141 Subscripts..................................................................................................... 141 References.................................................................................................... 142

CHAPTER 3 CHF—Transition Boiling ................................................................... 145 3.1 Critical Heat Flux and Near-Wall Boiling Behaviors in Pool Boiling................. 149 Hiroto Sakashita 3.1.1 Introduction .................................................................................................. 149 3.1.2 Previously Proposed CHF Mechanisms for Pool Boiling........................... 149 3.1.3 CHF in Subcooled Pool Boiling on Upward Surfaces................................ 150 3.1.3.1 Characteristics of CHF in Subcooled Pool Boiling ...................... 150 3.1.3.2 Experimental Apparatus for Measuring Liquid
Vapor Behaviors........................................................................................ 152 3.1.3.3 The Liquid
Vapor Structure Beneath Vapor Masses .................. 152 3.1.3.4 Behavior of Surface Dry-Out ........................................................ 155 3.1.3.5 The Mechanism of CHF and the Cause of the Increase in CHF in Subcooled Boiling ........................................................ 158

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3.1.4 CHF in Saturated Boiling on Inclined Surfaces.......................................... 160 3.1.5 CHF in Saturated Boiling of Binary Aqueous Solutions............................ 163 3.1.6 CHF in Boiling of Water on a Heating Surface Coated with Nanoparticles................................................................................................ 167 3.1.7 Conclusion.................................................................................................... 171 Nomenclature............................................................................................... 171 References.................................................................................................... 172 3.2 Microlayer Modeling for Critical Heat Flux in Saturated Pool Boiling............... 173 Takaharu Tsuruta 3.2.1 Introduction .................................................................................................. 173 3.2.2 Microlayer Model for Fully Developed Nucleate Boiling and CHF.......... 175 3.2.2.1 Basic Ideas of the Microlayer........................................................ 175 3.2.2.2 Description of Heat Transfer in Fully Developed Nucleate Boiling.......................................................... 176 3.2.2.3 Microlayer Thickness and Dry-Out Radius Beneath an Individual Bubble...................................................................... 179 3.2.2.4 Bubble Dynamics During the Final Growth Period...................... 180 3.2.3 Results and Discussion ................................................................................ 181 3.2.4 Conclusion.................................................................................................... 184 Nomenclature............................................................................................... 184 Greek Symbols............................................................................................. 184 Subscripts..................................................................................................... 185 References.................................................................................................... 185 3.3 Heat-Transfer Modeling Based on Visual Observation of Liquid
Solid Contact Situations and Contact Line Length......................................................... 187 Niro Nagai 3.3.1 Introduction .................................................................................................. 187 3.3.2 Observation of Liquid
Solid Contact Pattern and Concept of Contact-Line-Length Density ...................................................................... 188 3.3.2.1 Total Reflection Technique ........................................................... 188 3.3.2.2 Liquid
Solid Contact Patterns...................................................... 189 3.3.2.3 Contact-Line-Length Density ........................................................ 192 3.3.3 Observation of Cross-Sectional Structure of Boiling.................................. 197 3.3.3.1 Quasi-Two-Dimensional Boiling System...................................... 197 3.3.3.2 Nucleate Boiling Curve and CHF in Quasi-Two-Dimensional Space ..................................................... 198 3.3.3.3 Bubble Structures........................................................................... 199 3.3.4 Observation of Liquid
Solid Contact Situations During Cooling by Liquid Jet or Spraying ............................................................................ 203 3.3.4.1 Experimental Setup and Conditions .............................................. 203 3.3.4.2 Leidenfrost Temperature and Limit of Liquid Superheat of the Test Liquid .......................................................................... 204

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3.3.4.3 Liquid
Solid Contact Situations While Liquid Spray Cooling..................................................................... 204 3.3.4.4 Liquid
Solid Contact Situations with Liquid Jet Impingement .................................................................................. 206 3.3.5 Conclusion.................................................................................................... 210 Nomenclature............................................................................................... 210 Greek Symbols............................................................................................. 211 References.................................................................................................... 211 3.4 Critical Heat Flux Enhancement in Saturated Pool Boiling ................................. 212 Shoji Mori 3.4.1 Introduction .................................................................................................. 212 3.4.2 Fundamental Effects of HPP on the CHF Enhancement ............................ 214 3.4.2.1 Effect of Micropores and Vapor Escape Channels on the CHF..................................................................................... 214 3.4.2.2 Effects of the Heights in HPPs δ h on the CHF............................. 215 3.4.2.3 The CHF Model Based on Capillary Limit................................... 217 3.4.2.4 Optimization in Geometry of HPP ................................................ 218 3.4.2.5 Effect of Heater Size on the CHF Enhancement .......................... 219 3.4.3 Further CHF Enhancement Techniques by HPP......................................... 220 3.4.3.1 Two-Layer Structured HPP ........................................................... 220 3.4.3.2 Combination of HPP, Nanoparticle-Coated Surface, and Honeycomb Solid Structures (HSSs) in Pure Water..................... 221 3.4.3.3 Combination of HPP and Nanofluid ............................................. 223 3.4.4 Conclusion.................................................................................................... 225 Nomenclature............................................................................................... 225 References.................................................................................................... 226 3.5 Dependence of Critical Heat Flux on Heater Size ................................................ 227 Masahiro Shoji 3.5.1 Introduction .................................................................................................. 227 3.5.2 CHF on Wires and Cylinders ...................................................................... 229 3.5.2.1 Available CHF Data Correlations.................................................. 229 3.5.2.2 Recent Experimental Study and Results ....................................... 231 3.5.2.3 Discussions and Remaining Problems........................................... 234 3.5.3 CHF on Plates .............................................................................................. 236 3.5.3.1 CHF on a Plain Surface ................................................................. 236 3.5.3.2 CHF on Chips with Modified Surfaces ......................................... 236 3.5.4 CHF Data Correlation on Heaters of Various Shapes and Configurations .......................................................................... 238 3.5.5 Parameters and Factors Affecting CHF....................................................... 239 3.5.6 Summary and Concluding Remarks ............................................................ 241 References.................................................................................................... 241

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3.6 Stability of Transition Boiling ............................................................................... 243 Yoshihiko Haramura 3.6.1 Introduction .................................................................................................. 243 3.6.2 Attempt to Attain Steady Transition Boiling by Low-Resistance Heat Exchange ............................................................................................. 243 3.6.2.1 Heating with Steam........................................................................ 243 3.6.2.2 Heating with Convective Cooling/Heating ................................... 246 3.6.2.3 Temperature Stabilization by Conduction to the Surroundings for a Small Surface ........................................... 246 3.6.3 Automatic Temperature Control.................................................................. 246 3.6.4 Temperature Uniformity Across the Surface .............................................. 248 3.6.4.1 In the Case of Steady Boiling........................................................ 248 3.6.4.2 In the Case of Transient Boiling ................................................... 251 3.6.5 Conclusion.................................................................................................... 251 Nomenclature............................................................................................... 252 References.................................................................................................... 253 3.7 Derivations of Correlation and Liquid
Solid Contact Model of Transition Boiling Heat Transfer ...................................................................... 254 Hiroyasu Ohtake 3.7.1 Introduction .................................................................................................. 254 3.7.2 Experimental Apparatus and Procedure ...................................................... 255 3.7.2.1 Experimental Apparatus................................................................. 255 3.7.2.2 Experimental Procedure................................................................. 256 3.7.2.3 Stable Conditions for Steady Transition Boiling............................................................................................ 257 3.7.2.4 Experimental Uncertainty .............................................................. 257 3.7.3 Experimental Results and Discussion.......................................................... 258 3.7.3.1 Heat-Transfer Characteristics: Boiling Curve ............................... 258 3.7.3.2 Liquid
Solid Contact Fraction: Correlation................................. 259 3.7.3.3 Void Fraction Near Heating Surface ............................................. 260 3.7.4 Modeling and Discussion............................................................................. 262 3.7.4.1 First Model ..................................................................................... 262 3.7.4.2 Present Model ................................................................................ 263 3.7.4.3 Application to Rewetting ............................................................... 265 3.7.4.4 Application to Core Cooling.......................................................... 266 3.7.5 Conclusion.................................................................................................... 268 Nomenclature............................................................................................... 270 Subscripts..................................................................................................... 270 References.................................................................................................... 270

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3.8 Critical Heat Flux in Subcooled Flow Boiling...................................................... 271 Wei Liu 3.8.1 Introduction .................................................................................................. 271 3.8.2 Criterion for the Judgement of Flow Pattern Development........................ 273 3.8.3 CHF Prediction for the Subcooled Flow Boiling of the Conventional Flow Pattern................................................................ 276 3.8.3.1 Introduction .................................................................................... 276 3.8.3.2 Liu
Nariai Model ......................................................................... 280 3.8.3.3 Validation of the Proposed CHF Model........................................ 286 3.8.4 CHF Prediction for the Subcooled Flow Boiling of the Homogeneous-Nucleation-Governed Flow Pattern..................................... 288 3.8.4.1 CHF Triggering Mechanism and Prediction ................................. 288 3.8.4.2 Validation of the Proposed Model................................................. 289 3.8.5 Conclusion.................................................................................................... 292 Nomenclature............................................................................................... 293 Greek Symbols............................................................................................. 294 Subscripts..................................................................................................... 294 References.................................................................................................... 295 3.9 Convective Boiling Under Unstable Flow Conditions.......................................... 297 Hisashi Umekawa 3.9.1 Introduction .................................................................................................. 297 3.9.2 The Definition of Flow Instability............................................................... 298 3.9.3 The Historical Background.......................................................................... 299 3.9.4 Simple Model—Quasi-Steady Assumption................................................. 301 3.9.5 Estimation by Lumped-Parameter Model—Dumping Effect of Two-Phase ............................................................................................... 305 3.9.6 Dry-Out Under Natural Circulation Loop—Flow Oscillation Caused by the System.................................................................................. 308 3.9.7 More Detailed Discussion of Boiling Phenomena under Oscillatory Flow Conditions ........................................................................ 311 3.9.8 Conclusion.................................................................................................... 313 Nomenclature............................................................................................... 314 Greek Symbols............................................................................................. 314 Subscripts..................................................................................................... 314 References.................................................................................................... 315 3.10 Film Flow on a Wall and Critical Heat Flux ........................................................ 316 Yasuo Koizumi 3.10.1 Introduction ................................................................................................ 316 3.10.2 Minimum Wetting Rate ............................................................................. 317 3.10.2.1 Analytical Model of MWR........................................................ 318 3.10.2.2 Measurement of MWR, Contact Angle, and Wave Characteristics ............................................................................ 319

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3.10.2.3 Results ........................................................................................ 320 3.10.2.4 Effect of Waves on MWR ......................................................... 326 3.10.3 CHF of Film Flow ..................................................................................... 328 3.10.4 CHF of Mini-Channel ................................................................................ 333 3.10.5 Characteristics of Falling Film Flow......................................................... 337 3.10.5.1 Wave Profile .............................................................................. 338 3.10.5.2 Film Thickness........................................................................... 339 3.10.5.3 Wave Velocity ........................................................................... 344 3.10.5.4 Wavelength ................................................................................ 345 3.10.5.5 Development of Correlations of Wave Properties .................... 346 3.10.6 Conclusion.................................................................................................. 350 Nomenclature............................................................................................. 351 Greek Symbols........................................................................................... 352 Subscripts................................................................................................... 352 References.................................................................................................. 352 3.11 Boiling Transition and CHF for the Fuel Rod of a Light Water Reactor............................................................................................ 354 Shinichi Morooka 3.11.1 Introduction ................................................................................................ 354 3.11.2 Prediction of the Heat-Removal Limit ...................................................... 354 3.11.2.1 Design-CHF Correlation for an LWR Fuel Assembly.............. 354 3.11.2.2 CHF Prediction Using a Film Dry-Out Model for a Vertical Tube ............................................................................. 355 3.11.2.3 Analysis of Critical Power Prediction for BWR Fuel Assembly .................................................................................... 359 3.11.2.4 Enhancement of Heat-Removal Limit....................................... 362 3.11.2.5 Post-BT Criteria ......................................................................... 365 3.11.3 Conclusion.................................................................................................. 366 Nomenclature............................................................................................. 366 Greek Symbols........................................................................................... 366 Subscripts................................................................................................... 367 References.................................................................................................. 367

CHAPTER 4 Minimum Heat Flux—Film Boiling ................................................... 369 4.1 The Behavior of the Wetted Area and the Contact Angle Right After Liquid
Wall Contact in Saturated and Subcooled Pool Boiling ......................... 370 Hiroyasu Ohtake Nomenclature.......................................................................................................... 370 Greek Symbols........................................................................................................ 371 Suffixes ................................................................................................................... 371

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4.1.1 Introduction .................................................................................................. 371 4.1.2 Experimental Apparatus and Procedure ...................................................... 372 4.1.3 Experimental Results and Discussion.......................................................... 374 4.1.3.1 Behavior of Wetting and Temperature at Wetting........................ 374 4.1.3.2 Wetting Area and Contact Angle .................................................. 377 4.1.3.3 Estimation of Contact Angle ......................................................... 378 4.1.4 Conclusions .................................................................................................. 379 References.................................................................................................... 380 Further Reading ........................................................................................... 380 4.2 Study on Forced-Convection Film-Boiling Heat Transfer (Heat Transfer Characteristics in the High
Reynolds-Number Region and the Critical Condition)............................................................................................................... 381 Hiroyasu Ohtake 4.2.1 Introduction .................................................................................................. 381 4.2.2 Experimental Apparatus and Procedures..................................................... 382 4.2.2.1 Experimental Apparatus................................................................. 382 4.2.2.2 Experimental Procedures ............................................................... 382 4.2.3 Experimental Results and Discussion.......................................................... 384 4.2.3.1 Characteristics of Single-Phase Liquid Flow ................................ 384 4.2.3.2 Boiling Curve (Dependence on Wall Superheat).......................... 385 4.2.3.3 Dependence on Distance................................................................ 385 4.2.3.4 Dependence on Bulk-Liquid Velocity and Liquid Subcooling .... 386 4.2.3.5 Critical Condition and Correlation of Dimensionless Numbers ... 387 4.2.4 Mechanism of Transition ............................................................................. 388 4.2.5 Conclusions .................................................................................................. 389 Nomenclature............................................................................................... 390 Greek Symbols............................................................................................. 390 Subscripts..................................................................................................... 390 References.................................................................................................... 391 4.3 Transient Transition-Boiling Heat Transfer in Quenching with Liquid Impinging Jet or Spray........................................................................................... 391 Yuichi Mitutake 4.3.1 Introduction .................................................................................................. 391 4.3.2 Inverse Analysis Technique in Transient Heat Transfer............................. 392 4.3.3 Experimental Study on Quenching of a Hot Block with Liquid Jet or Spray .............................................................................. 394 4.3.4 Visual and Acoustic Observations of Quenching Phenomenon ................. 396 4.3.5 Change in Surface Temperature and Surface Heat Flux Distributions Evaluated with 2D Inverse Heat Conduction Analysis............................... 398 4.3.6 Characteristics of Cooling and Boiling Curves During Quenching .................................................................................................... 400

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4.3.7 Wetting and Quenching Temperatures ........................................................ 401 4.3.8 Characteristics of Maximum Heat Flux During Quenching ....................... 404 4.3.9 Conclusions .................................................................................................. 406 Nomenclature............................................................................................... 408 Greek Symbols............................................................................................. 408 Superscripts.................................................................................................. 408 Subscripts..................................................................................................... 408 References.................................................................................................... 409

CHAPTER 5 Numerical Simulation ....................................................................... 411 5.1 Direct Numerical Simulation Studies on Boiling Phenomena.............................. 412 Tomoaki Kunugi 5.1.1 Introduction .................................................................................................. 412 5.1.2 Direct Numerical Simulation Studies on Boiling ....................................... 413 5.1.2.1 Microscopic Approach................................................................... 413 5.1.2.2 Mesoscopic Approach.................................................................... 413 5.1.2.3 Macroscopic Approach .................................................................. 414 5.1.3 Governing Equations Based on MARS....................................................... 415 5.1.4 Non-Empirical Boiling and Condensation Model....................................... 416 5.1.5 Comparison of Numerical Results to Visualization Results....................... 417 5.1.6 Bubble Departure Behavior ......................................................................... 419 5.1.7 Effects of Wettability on Departure Behavior ............................................ 421 5.1.8 Bubble Condensation Behaviors.................................................................. 422 5.1.9 Conclusion.................................................................................................... 424 Nomenclature..................................................................................................... 425 Greek Symbols................................................................................................... 425 Subscripts........................................................................................................... 425 References.......................................................................................................... 426 5.2 Numerical Simulation of Liquid
Gas Two-Phase Flow ...................................... 429 Taku Nagatake and Hiroyuki Yoshida 5.2.1 Introduction .................................................................................................. 429 5.2.2 Numerical Simulation Method of TPFIT .................................................... 429 5.2.2.1 Governing Equations...................................................................... 429 5.2.2.2 Interface Tracking Method ............................................................ 430 5.2.3 Numerical Simulation and Results with TPFIT .......................................... 433 5.2.3.1 Two-Phase Flow Fluid Mixing Test.............................................. 433 5.2.4 Conclusion.................................................................................................... 441 Nomenclature............................................................................................... 441 Subscripts..................................................................................................... 441 References.................................................................................................... 442

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CHAPTER 6 Topics on Boiling: From Fundamentals to Applications.................. 443 6.1 Estimation of Phase Equilibria .............................................................................. 448 Tomohiko Yamaguchi 6.1.1 Introduction .................................................................................................. 448 6.1.2 Thermodynamics for Phase Equilibria in Multicomponent Systems ......... 449 6.1.2.1 Useful Functions and Relations Between State Variables............ 449 6.1.2.2 Criteria for Vapor
Liquid Equilibrium in Multicomponent Systems........................................................................................... 453 6.1.3 Equation of State.......................................................................................... 453 6.1.4 Group Contribution Equation of State (GCEOS)........................................ 454 6.1.4.1 GCEOS VTPR ............................................................................... 454 6.1.4.2 GCEOS VGTPR............................................................................. 460 6.1.5 Conclusion.................................................................................................... 464 Nomenclature............................................................................................... 465 Greek Symbols............................................................................................. 466 Superscripts.................................................................................................. 466 Subscripts..................................................................................................... 466 References.................................................................................................... 467 6.2 Molecular Dynamic Research on the Condensation Coefficient .......................... 468 Gyoko Nagayama and Takaharu Tsuruta 6.2.1 Introduction .................................................................................................. 468 6.2.2 Interfacial Transport Across the Liquid
Vapor Interface.......................... 469 6.2.3 Condensation Coefficient Based on Molecular Dynamic Simulation ........ 470 6.2.3.1 Temperature Dependence of the Macroscopic Condensation Coefficient...................................................................................... 471 6.2.3.2 Microscopic Condensation Coefficient: Molecular Translational Energy Dependence ................................................. 471 6.2.3.3 Boundary Condition Based on the Microscopic Condensation Coefficient............................................................... 475 6.2.3.4 Nonequilibrium Microscopic Boundary Condition at the Liquid
Vapor Interface................................................................. 476 6.2.4 Condensation Coefficient based on the Transition State Theory ............... 478 6.2.5 Conclusion.................................................................................................... 483 Nomenclature............................................................................................... 483 Greek Symbols............................................................................................. 484 Subscripts..................................................................................................... 484 References.................................................................................................... 485 6.3 Micro-/Nanoscale Phenomena Related with Boiling ............................................ 487 Yuyan Jiang and Shigeo Maruyama 6.3.1 Introduction .................................................................................................. 487

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6.3.2 Microscopic Representation of Solid
Liquid
Vapor Interfaces .............. 488 6.3.2.1 Theory ............................................................................................ 488 6.3.2.2 Movement of the Triple-Phase Contact Line ................................ 492 6.3.2.3 Molecular Dynamics Simulation ................................................... 493 6.3.2.4 Multiscale Simulation .................................................................... 495 6.3.3 Microscopic Investigation of Nucleation of Boiling Bubbles .................... 497 6.3.4 Boiling Heat Transfer Enhancement by Micro-/Nano-Hybrid Structures.. 500 6.3.5 Conclusion.................................................................................................... 501 Nomenclature............................................................................................... 501 Greek Symbols............................................................................................. 501 Subscripts..................................................................................................... 502 References.................................................................................................... 502 6.4 Transient Boiling Under Rapid Heating Conditions ............................................. 504 Kunito Okuyama 6.4.1 Introduction .................................................................................................. 504 6.4.2 Fundamental Characteristics of Transient Boiling and Overview of the Studies ............................................................................................... 505 6.4.3 Direct Transition to Film Boiling................................................................ 509 6.4.4 Relevance of Nucleation Phenomena to Direct Transition......................... 510 6.4.5 Boiling Front Propagation ........................................................................... 512 6.4.6 Modeling of Boiling Front Propagation ...................................................... 512 6.4.7 On the Mechanism of Transition to Film Boiling in Direct Transition ..... 514 6.4.8 Conclusion.................................................................................................... 515 Nomenclature............................................................................................... 516 Greek Symbols............................................................................................. 516 Superscripts.................................................................................................. 516 Subscripts..................................................................................................... 516 References.................................................................................................... 517 6.5 Measurement by Neutron Radiography ................................................................. 519 Yasushi Saito 6.5.1 Introduction .................................................................................................. 519 6.5.2 Dynamic Neutron Radiography ................................................................... 521 6.5.3 Application of Neutron Radiography to Two-Phase Flow ......................... 522 6.5.3.1 Adiabatic Air
Water Two-Phase Flow ........................................ 522 6.5.3.2 Boiling Heat Transfer in a Round Tube........................................ 523 6.5.3.3 Gas/Liquid
Metal Two-Phase Flow............................................. 524 6.5.3.4 Direct Contact Evaporation of a Water Droplet in a Heated Liquid-Metal Pool ...................................................... 527 6.5.4 Summary ...................................................................................................... 528 References.................................................................................................... 528

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6.6 Topics of Boiling Heat Transfer: Microbubble Emission Boiling Observed in Highly Subcooled Boiling.................................................... 530 Koichi Suzuki 6.6.1 Introduction .................................................................................................. 530 6.6.2 Subcooled Flow Boiling of Water with Microbubble Emission in a Horizontal Rectangular Channel.................................................................. 537 6.6.2.1 Subcooled Flow Boiling in a Millimeter-Sized Rectangular Channel: Hydraulic Diameter 5 7.3
8.2 mm............................... 537 6.6.2.2 Subcooled Flow Boiling in Mini-Channel: Hydraulic Diameter 5 0.7
1.3 mm................................................................ 539 6.6.2.3 Terminal Stage of MEB................................................................. 541 6.6.3 Solid
Liquid Contact on Heating Surface in MEB ................................... 541 6.6.3.1 Bubble Behaviors on the Heating Surface and Pressure Fluctuation...................................................................................... 541 6.6.3.2 Instability of the Vapor Bubble Interface in a Subcooled Liquid ............................................................................................. 543 6.6.4 Summary ...................................................................................................... 546 References.................................................................................................... 547 6.7 MEMS Technology for Fundamental Research of Microbubble Emission Boiling.......................................................................... 548 Manabu Tange 6.7.1 Introduction .................................................................................................. 548 6.7.2 Surface Temperature Measurement ............................................................. 550 6.7.3 Microscale Heaters....................................................................................... 551 6.7.4 Artificial Cavities and Nucleation Control.................................................. 552 6.7.5 Surface Temperature Measurement with Nucleation Control .................... 553 6.7.5.1 Objectives: Specifying the Occurrence Conditions of Microbubble Emission Boiling...................................................... 553 6.7.5.2 Experimental System and Procedure............................................. 554 6.7.5.3 Temperature Trend and Bubbling Behavior.................................. 554 6.7.5.4 Bubbling Pattern Map .................................................................... 557 6.7.6 Conclusion.................................................................................................... 559 References.................................................................................................... 559 6.8 Vapor Bubble Behaviors in Condensation ............................................................ 562 Ichiro Ueno, Tomohiro Osawa, Yasusuke Hattori, Takahito Saiki, Jun Ando, Kazuna Horiuchi and Yusuke Koiwa 6.8.1 Introduction .................................................................................................. 562 6.8.2 Microbubble Emission Boiling.................................................................... 563 6.8.2.1 Experiment for On-Plate Boiling................................................... 563 6.8.2.2 Results for On-Plate Boiling.......................................................... 564 6.8.3 Boiling on Thin Wire................................................................................... 566

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6.10

6.11

6.12

xix

6.8.3.1 Experiment for On-Wire Boiling................................................... 566 6.8.3.2 Results for On-Wire Boiling.......................................................... 567 6.8.4 Vapor Injection to Subcooled Pool ............................................................. 574 6.8.4.1 Experiment for Vapor Injection..................................................... 574 6.8.4.2 Results for Vapor Injection............................................................ 575 6.8.5 Summary ...................................................................................................... 580 Acknowledgments ....................................................................................... 581 References.................................................................................................... 581 Heat Transfer Enhancement and the Effect of Gravity in Boiling Phenomena ............................................................................................................. 582 Hitoshi Asano 6.9.1 Introduction .................................................................................................. 582 6.9.2 Boiling Heat Transfer Characteristics on the Thermal Spray Coating....... 584 6.9.3 Pool Boiling on Thermal Spray Coatings Under Microgravity.................. 588 6.9.4 Conclusion.................................................................................................... 591 Nomenclature............................................................................................... 592 Greek Symbol .............................................................................................. 592 References.................................................................................................... 592 Boiling on Porous Media ....................................................................................... 593 Kazuhisa Yuki 6.10.1 Introduction ................................................................................................ 593 6.10.2 General Knowledge About Boiling Heat Transfer Enhancement Utilizing Porous Layers ............................................................................. 594 6.10.3 Nucleate Boiling Heat Transfer Enhancement by Unique Porous Media.......................................................................................................... 600 6.10.4 Boiling Heat Transfer Enhancement with Functional Porous Media....... 603 6.10.5 Conclusion.................................................................................................. 607 References.................................................................................................. 608 Effect of Surface Wettability on Boiling and Evaporation................................... 610 Yasuyuki Takata 6.11.1 Overview of Wettability Effects in Boiling and Evaporation .................. 610 6.11.2 Boiling Enhancement by Mixed-Wettability Surfaces ............................. 613 6.11.3 Peculiar Boiling Behaviors on Superhydrophobic Surfaces and the Effect of Dissolved Air................................................................. 615 References.................................................................................................. 619 Self-Rewetting Fluids............................................................................................. 620 Yoshiyuki Abe and Raffaele Savino 6.12.1 Introduction ................................................................................................ 620 6.12.2 Surface Tension and Related Properties.................................................... 621 6.12.2.1 Surface Tension of Self-Rewetting Fluids ................................ 621 6.12.2.2 Nano-Self-Rewetting Fluids ...................................................... 623 6.12.2.3 Ternary Mixtures and Self-Rewetting Brines ........................... 624

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6.12.3 Heat Transfer with Self-Rewetting Fluids................................................. 625 6.12.3.1 Fundamental Behavior at the Liquid
Vapor Interface ............ 625 6.12.3.2 Pool Boiling and Other Boiling Heat Transfer ......................... 627 6.12.3.3 Heat Pipes .................................................................................. 629 6.12.3.4 Space Experiments with Self-Rewetting Fluids (SELENE) ....................................................................... 630 6.12.4 Conclusion.................................................................................................. 635 References.................................................................................................. 635 6.13 Boiling in the Steel Industry (Research Content of Hot Rolling Mill ROT Cooling Research Group, Iron and Steel Institute of Japan) ....................... 637 Yoshihiro Serizawa 6.13.1 The Importance of Boiling Cooling in the Steel Industry ........................ 637 6.13.1.1 Introduction ................................................................................ 637 6.13.1.2 Overview of Steel Property Control .......................................... 638 6.13.2 Water Cooling Systems in the Steel Industry ........................................... 643 6.13.3 Boiling Cooling Research Initiatives of Hot Rolling Mill, ROT Cooling Research Group (Iron and Steel Institute of Japan).................... 647 6.13.3.1 Issues of Heat Transfer Control Technology Concerning Boiling Heat Transfer in Steel Processes .................................. 647 6.13.3.2 Activities of Hot Rolling Mill ROT Cooling Model Building Research Group, Iron and Steel Institute of Japan ................... 649 6.13.3.3 Research on Boiling Heat Transfer in the Steel Process .......... 655 6.13.4 Conclusion.................................................................................................. 666 References.................................................................................................. 666 6.14 Spray Cooling Characteristics in the Steel Industry ............................................. 669 Hidetoshi Ohkubo 6.14.1 Introduction ................................................................................................ 669 6.14.2 Model of Behavior of Spray on a Hot Surface ......................................... 671 6.14.3 Parametric Effects on Spray-Cooling Heat Transfer Characteristics ............................................................................................ 672 6.14.3.1 Effect of Roughness of the Cooling Surface............................. 673 6.14.3.2 Effect of Cooling Surface Wettability....................................... 673 6.14.3.3 Effect of Thermal-Insulation Layer Covering a Cooling Surface.......................................................................... 675 6.14.3.4 Effect of Porosity of Cooling Surface Layer ............................ 675 6.14.3.5 Effect of Unsteady-State of Cooling Surface............................ 676 6.14.3.6 Effect of Heat-Transfer Surface Orientation ............................. 678 6.14.3.7 Effect of Coolant-Related Parameters ....................................... 678 6.14.4 Cooling Instability Phenomenon ............................................................... 680 6.14.5 Summary .................................................................................................... 681 References.................................................................................................. 681

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6.15 Vapor Explosion Between High-Temperature Molten Liquid Droplet and Water Pool....................................................................................................... 682 Yutaka Abe and Shinpei Saitho 6.15.1 Introduction ................................................................................................ 682 6.15.2 Elementary Process of Vapor Explosion................................................... 683 6.15.3 Theory of Vapor Explosion ....................................................................... 684 6.15.3.1 Thermal Detonation Model........................................................ 685 6.15.3.2 Spontaneous Nucleation Model ................................................. 686 6.15.4 Experiments................................................................................................ 689 6.15.4.1 Experiment without External Trigger........................................ 689 6.15.4.2 Experiment with External Trigger............................................. 694 6.15.5 Conclusion.................................................................................................. 703 Nomenclature............................................................................................. 703 Greek Symbols........................................................................................... 703 Subscripts................................................................................................... 703 References.................................................................................................. 703 6.16 Vapor Explosion..................................................................................................... 706 Masahiro Furuya 6.16.1 Introduction ................................................................................................ 706 6.16.2 Experimental Facility................................................................................. 707 6.16.2.2 Solution Droplet Impingement Onto Molten Alloy Pool .................................................................................. 707 6.16.2.3 Solid Sphere Quenching Into Solution Pool ............................. 710 6.16.3 Experimental Results and Discussions ...................................................... 711 6.16.3.1 Visual Observation and Phenomena Classification .................. 711 6.16.3.2 Interfacial Mixing Structure ...................................................... 713 6.16.3.3 Effect of Surface Property ......................................................... 716 6.16.3.4 Effect of Material Property........................................................ 719 6.16.3.5 Effect of System Pressure.......................................................... 720 6.16.3.6 Effect of Thermal Capacity ....................................................... 720 6.16.3.7 Controlling Additive to Promote and Suppress Vapor Explosion.................................................................................... 721 6.16.3.8 Effect of Dissolved Gas ............................................................. 727 6.16.4 Vapor Film Stability Analysis ................................................................... 727 6.16.5 Conclusions ................................................................................................ 729 Acknowledgments ..................................................................................... 730 References.................................................................................................. 730 6.17 Flow Boiling in Pipes of Refrigerants ................................................................... 732 Satoru Momoki 6.17.1 Introduction ................................................................................................ 732 6.17.2 Flow Boiling in a Smooth Tube of Fluorocarbon Refrigerants................ 733

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6.17.2.1 Flow Regime .............................................................................. 733 6.17.2.2 Heat Transfer in Annular Flow Regime.................................... 734 6.17.3 Flow Boiling in a Horizontal Internally Spirally Grooved Tube ............................................................................................ 737 6.17.3.1 Flow Regime for Discussion of Heat Transfer Characteristics ............................................................................ 738 6.17.3.2 Heat Transfer Coefficients......................................................... 739 6.17.4 Concluding Remarks.................................................................................. 741 Nomenclature............................................................................................. 742 Greek Symbols........................................................................................... 742 Subscripts................................................................................................... 742 References.................................................................................................. 743 6.18 Pool Boiling of Low-Global-Warming-Potential Refrigerants ............................. 745 Chieko Kondou and Shigeru Koyama 6.18.1 Introduction ................................................................................................ 745 6.18.2 Fluid Information ....................................................................................... 746 6.18.3 Experiment ................................................................................................. 747 6.18.3.1 Experimental Set-Up.................................................................. 747 6.18.3.2 Test Conditions and Procedure.................................................. 748 6.18.3.3 Data Reduction and Measurement Uncertainty ........................ 749 6.18.4 Assessment of Heat Transfer Data ............................................................ 750 6.18.4.1 Hysteresis of Nucleate Boiling Inception, Departure from Single-Phase Natural Convection .............................................. 750 6.18.4.2 Comparative Assessment on Fully Developed Nucleate Boiling HTC for Low-GWP Refrigerants ................................. 751 6.18.4.3 Comparison for Correlations with “Estimated Transport Properties”.................................................................................. 753 6.18.5 Conclusion.................................................................................................. 756 Nomenclature............................................................................................. 756 Greek Symbols........................................................................................... 756 Subscripts................................................................................................... 757 References.................................................................................................. 757 6.19 Gravity-Feed Re-Flooding: A Fundamental Feature of the Cooling Process of High-Temperature Tube Wall and Scaling Parameter...................................... 759 Mamoru Ozawa 6.19.1 Introduction ................................................................................................ 759 6.19.2 A Brief Review of Previously Conducted Research................................. 760 6.19.3 Experimental Set-Up for Gravity-Feed of Liquid Nitrogen ..................... 762 6.19.4 Gravity-Feed Reflooding ........................................................................... 763 6.19.5 Simplified Modeling of Dynamics of Gravity Reflooding ....................... 768 6.19.6 Constant-Feed Reflooding Experiment with Water .................................. 770

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6.19.7 Simplified Lumped-Parameter Modeling .................................................. 773 6.19.8 Conclusion.................................................................................................. 775 Nomenclature..................................................................................................... 776 Greek Symbols................................................................................................... 776 Subscripts........................................................................................................... 776 References.......................................................................................................... 777 Index .................................................................................................................................................. 779

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List of Contributors Yoshiyuki Abe Japan Science and Technology Agency, Tokyo, Japan Yutaka Abe University of Tsukuba, Tsukuba, Japan Jun Ando Tokyo University of Science, Chiba, Japan Hitoshi Asano Kobe University, Kobe, Japan Zhihao Chen Tianjin University, Tianjin, China Masahiro Furuya Central Research Institute of Electric Power Industry, Japan Yoshihiko Haramura Kanagawa University, Yokohama, Japan Yasusuke Hattori Tokyo University of Science, Chiba, Japan Kazuna Horiuchi Tokyo University of Science, Chiba, Japan Yuyan Jiang Chinese Academy of Sciences, Beijing, People’s Republic of China; University of Chinese Academy of Sciences, Beijing, People’s Republic of China Yusuke Koiwa Tokyo University of Science, Chiba, Japan Yasuo Koizumi Japan Atomic Energy Agency, Tokai, Japan Chieko Kondou Nagasaki University, Nagasaki, Japan Shigeru Koyama Kyushu University, Fukuoka, Japan Tomoaki Kunugi Kyoto University, Kyoto, Japan Wei Liu Kyushu University, Fukuoka, Japan Shigeo Maruyama The University of Tokyo, Tokyo, Japan; National Institute of Advanced Industrial Science and Technology, Tokyo, Japan

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List of Contributors

Yuichi Mitutake Saga University, Saga, Japan Satoru Momoki Nagasaki University, Nagasaki, Japan Masanori Monde Saga University, Saga, Japan Shoji Mori Yokohama National University, Yokohama, Japan Shinichi Morooka Waseda University, Tokyo, Japan Niro Nagai University of Fukui, Fukui, Japan Taku Nagatake Japan Atomic Energy Agency, Tokai, Japan Gyoko Nagayama Kyushu Institute of Technology, Kitakyushu, Japan Osamu Nakabeppu Meiji University, Tokyo, Japan Hidetoshi Ohkubo Tamagawa University, Tokyo, Japan Haruhiko Ohta Kyushu University, Fukuoka, Japan Hiroyasu Ohtake Kogakuin University, Tokyo, Japan Tomio Okawa The University of Electro-Communications, Tokyo, Japan Kunito Okuyama Yokohama National University, Yokohama, Japan Naoki Ono Shibaura Institute of Technology, Tokyo, Japan Tomohiro Osawa Tokyo University of Science, Chiba, Japan Mamoru Ozawa Kansai University, Osaka, Japan Takahito Saiki Tokyo University of Science, Chiba, Japan Shinpei Saitho University of Tsukuba, Tsukuba, Japan

List of Contributors

Yasushi Saito Kyoto University, Osaka, Japan Hiroto Sakashita Hokkaido University, Sapporo, Japan Raffaele Savino University of Naples Federico II, Napoli, Italy Yoshihiro Serizawa Nippon Steel & Sumitomo Metal Corp., Tokyo, Japan Masahiro Shoji University of Tokyo, Tokyo, Japan Koichi Suzuki Tokyo University of Science, Japan Yasuyuki Takata Kyushu University, Fukuoka, Japan Manabu Tange Shibaura Institute of Technology, Japan Takaharu Tsuruta Kyushu Institute of Technology, Kitakyushu, Japan Ichiro Ueno Tokyo University of Science, Chiba, Japan Hisashi Umekawa Kansai University, Suita, Japan Yoshio Utaka Tianjin University, Tianjin, China; Tamagawa University, Tokyo, Japan Tomohide Yabuki Kyushu Institute of Technology, Kitakyushu, Japan Tomohiko Yamaguchi Nagasaki University, Nagasaki, Japan Hiroyuki Yoshida Japan Atomic Energy Agency, Tokai, Japan Kazuhisa Yuki Tokyo University of Science, Yamaguchi, Japan

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Biographies Yutaka Abe is an Executive Officer and the Provost of the Faculty of Engineering, Information and Systems at the University of Tsukuba. He is a former chair of the Department of Engineering Mechanics and Energy and a former Dean of the College of Engineering Systems, University of Tsukuba. He is a fellow of the Japanese Society of Mechanical Engineers (JSME) and chairman of the Power and Energy System division of JSME. He was the conference chair of ICONE-21 held in China, 2013. He had research careers in Japan Atomic Energy Research Institute, Los Alamos National Laboratory in the United States, Yamagata University in Japan, and the University of Toronto in Canada, before he moved to the University of Tsukuba. His areas of expertise are the transport phenomena in two-phase flow, ultra-high-speed phase-change phenomena such as vapor explosion, explosive wave propagation of ultra-high viscous fluid simulating volcanic explosion, molten material jet break-up behavior in coolants, hydrodynamics of supersonic steam injectors, and developmental study of microchannel heat exchangers. He has over 130 refereed journal articles and 204 refereed international conference papers. Yoshiyuki Abe is at present a senior research analyst at JST. He received PhD from Keio University in 1981, and worked at Electrotechnical Laboratory (ETL) and National Institute of Advanced Industrial Science and Technology (AIST: reorganized institute of ETL in 2001) from 1981 to 2014. Since 2014 he has been working at JST. His major research topics included thermophysical properties, high gravity materials processing, thermal storage, boiling heat transfer and heat pipe. Jun Ando received his master degree (Master of Engineering) from the Tokyo University of Science, and was graduated from the Division of Mechanical Engineering, Graduate School of Science and Technology in March 2016. Hitoshi Asano is an associate professor of the Department of Mechanical Engineering at Kobe University, Japan. He graduated from Kobe University in 1990. He started research on two-phase flow dynamics as a research associate of Kobe University after 3.5 years working in Daikin Industries, Ltd. He obtained the degree of Dr Eng. from Kobe University in 2000, and was promoted to associate professor in 2001. From 2001 to 2002 he visited the laboratory of Prof. MuellerSteinhagen in Stuttgart University as a research fellow of the Alexander von Humboldt Foundation, and started the investigation into boiling heat transfer enhancement by thermal spraying. Currently, he is studying the effect of surface structures on boiling heat transfer including ONB, DNB, and dryout. His interests are also focused on thermofluid dynamics in compact heat exchangers for HVAC systems, gas
liquid two-phase flows in power systems, especially the effect of surface tension and gravity on gas
liquid two-phase flows in small-diameter tubes. He is a co-investigator of the JAXA (The Japan Aerospace Exploration Agency) project on two-phase flow experiments on board the international space station.

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Zhihao Chen has been an associate professor in Tianjin University from June 2015. Before that he was an assistant professor in the Faculty of Engineering, Yokohama National University after receiving his PhD degree from same University in 2011. His research interest is phase-change heat transfer, especially in boiling and condensation. His studies focused on the high-accuracy measurement of microlayer structure and its contribution to boiling heat transfer, and the spontaneous movement of condensate drop during Marangoni condensation of binary vapor. Masahiro Furuya is a deputy associate vice president and sector leader at Nuclear Technology Research Laboratory, Central Research Institute of Electric Power Industry (CRIEPI). He worked for CRIEPI since 1993 to date. He became a visiting professor at Tokyo Institute of Technology since 1995. He received his PhD from Delft University of Technology in the Netherlands in 2006. He received his PhD from M. Science and Engineering at the Graduate School of Tokyo Institute of Technology in 1993. His research concerns the field of heat transfer with phase change (boiling, condensation, melting, and solidification), material processing, and electro-chemistry. He is recognized in the Who’s Who in the World of Marquis for his work in science field. Yoshihiko Haramura is a professor in the Department of Mechanical Engineering of Kanagawa University. He received PhD degree from the University of Tokyo in 1984. He started his research career at Kanagawa University as a lecturer. He visited the laboratory of John H. Lienhard in the University of Houston from 1989 to 1990. He was promoted to professor in 1995. His research is focused on the area of pool boiling, especially on critical heat flux and transition boiling. He is also interested in heat transfer in Stirling engines and engines themselves. Yasusuke Hattori received his master degree (Master of Engineering) from Tokyo University of Science, and was graduated from the Division of Mechanical Engineering, Graduate School of Science and Technology in Mar. 2010. Kazuna Horiuchi received her master degree (Master of Engineering) from the Tokyo University of Science, and was graduated from Division of Mechanical Engineering, Graduate School of Science and Technology in March 2017. Yuyan Jiang is a professor in the Institute of Engineering Thermophysics (IET), Chinese Academy of Sciences (CAS). He received a B.E. degree from Xi’an Jiaotong University (1996), an M.E. degree from Tsinghua University (1999,) and a PhD from the University of Tokyo (2002). He has been a postdoctoral researcher in IIS, the University of Tokyo, a senior research fellow in AdvanceSoft Inc. and a visiting researcher in Toyota Central R&D Labs Inc. He has also been working with CD-Adapco as a senior software engineer. He was chosen by the 1000-Youth Talents Project of China and joined IET in 2013. Dr. Jiang’s research interests include the boiling heat transfer computations of two-phase flows with phase change. He is one of the major developers of the general-purpose CFD code, FrontFlow/Red. He has published more than 50 peer-reviewed journal papers and has 20 disclosed patents. In their latest study, he and his co-workers invented surfaces with deformable microstructures made of shape memory alloys for the enhancement and smart control of boiling.

Biographies

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Yusuke Koiwa received his master degree (Master of Engineering) from the Tokyo University of Science, and was graduated from the Division of Mechanical Engineering, Graduate School of Science and Technology in March 2017. Yasuo Koizumi has been an invited researcher of the Japan Atomic Energy Agency for the last 2 years. He received his PhD degree from the University of Tokyo in 1977. He started his research career at the Japan Atomic Energy Research Institute in 1977 as a research engineer for nuclear reactor safety. He stayed at the Idaho National Engineering Laboratory from 1981 through 1983. He moved to the Department of Mechanical Engineering of Kogakuin University in 1989. Then, he moved to the Department of Functional Machinery and Mechanics of Shinshu University in 2008. He retired as professor in 2014 and he has been in his present position since then. His research is focused in the areas of pool and flow boiling, critical heat flux, condensation heat transfer, and two-phase flow. He is also interested in heat transfer and fluid flow on the microscale. Since his research field is closely related to energy systems, he has great interest in thermal and nuclear power stations and energy supply in society. Chieko Kondou is an associate professor at the Division of System Science in Nagasaki University. She worked as an engineer on air conditioners and commercial refrigeration systems in Hitachi Appliances Inc. for 7 years and received her PhD from Kyushu University in 2008. She worked as a visiting scholar under the supervision of Prof. Hrnjak at the University of Illinois at Urbana-Champaign from 2009 to 2011. During that period, they investigated condensation flow in the presence of superheated vapor at pressures just below the critical point. She started her academic career at Prof. Koyama’s laboratory in Kyushu University in 2011. Her research interest is the development of heat pump systems using environmentally benign refrigerants for air conditioning, industrial heating, and refrigeration applications. Shigeru Koyama has been a professor at Kyushu University. He received his PhD degree from Kyushu University in 1980. He worked as a research engineer at Instrument Research Laboratory in Showa Denko Ltd. for 2 years. In 1982, he started his academic career at Kyushu University as an associate professor at the Research Institute of Industrial Science. In 1995, he was promoted to a professor of the Institute of Advanced Material Study in Kyushu University. He has been working as a professor at the Faculty of Engineering Sciences in Kyushu University since 2006. He has also been working as a WPI professor at the International Institute for Carbon-Neutral Energy since 2010. He has been involved in clarifying the heat and mass transfer mechanisms in condensation, evaporation, and adsorption. Tomoaki Kunugi graduated and received an MS degree from Keio University. He received PhD from the University of Tokyo. He worked at Japan Atomic Energy Research Institute from 1979 to 1997, and he moved to Tokai University in 1998 and moved again to Kyoto University in 1999. He became a full professor of Kyoto University in 2007. He is an international authority in computational multiphase flow and heat transfer technology and is a specialist in nuclear reactor thermal-hydraulics, safety technology, and fusion nuclear technology. He was the first to develop the automatic liquid-crystal thermometry and found the leakage heat flow inside the heat transfer

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plate by using the numerical simulation coupled with the measured surface temperature via this liquid-crystal thermometry. He has been developing several CFD codes including RANS, LES, and DNS for single-phase flows and DNS for multiphase flows including phase change phenomena. He found the turbulence structure of turbulent free-surface flows with deformed interfaces. He also invented a new heat transfer enhancement augmentation by a nano- and microscale porous layer formed on the surface without the pressure drop increase. In this decade, he focused on the understanding of the heat transfer mechanisms of both pool and flow boiling phenomena via a computational fluid dynamics for multiphase flows compared to the ultra-high time-spatial resolution experimental data which are taken by himself. He has published over 300 archival publications, including monographs and textbooks, journal papers, and contributions at international conferences. Wei Liu is a principal researcher at the Development Group for Thermal-Hydraulics Technology, Nuclear Science and Engineering Center, Japan Atomic Energy Agency (JAEA). She received her bachelor degree in engineering from Shanghai Jiao Tong University, China, in 1992, and her PhD in engineering from the University of Tsukuba, Japan, in 2000. Her research interests include thermal hydraulics in light water reactors and fundamental researches such as CHF, boiling, and twophase flow. Shigeo Maruyama is a distinguished professor in the Department of Mechanical Engineering at the University of Tokyo. Dr. Maruyama has been the President of the Fullerenes, Nanotubes and Graphene Research Society since 2011 and has a cross-appointment Fellowship at the National Institute of Advanced Industrial Science and Technology (AIST). He was previously a visiting professor at Ecole Centrale Paris. His major research areas are carbon nanotubes and fullerenes and molecular heat transfer. Yuichi Mitutake graduated from Saga University in 1989. He started his research career at the Heavy Apparatus Engineering Laboratory of Toshiba Corporation in 1989 as an engineer in the field of thermo-hydrodynamic analysis in thermal and nuclear power plant components. He moved to the Department of Mechanical Engineering of Saga University as a research associate in 1995. Then, he has been in the present position from 2014. He received PhD from Saga University in 2003. His research field focuses on critical heat flux during pool and external flow boilings, transient transition boiling heat transfer during liquid column jet or spray jet impinging on hot surface, measurement technique of transient heat transfer with inverse heat conduction analysis, and development of hydrogen storage system with metal hydride alloy. Recently his focus is on fundamental quenching and wetting phenomena in material production processes. Masanori Monde is Vice President at Saga University. He has received his PhD from the University of Tokyo, Department of Mechanical Engineering. In 1976, he has served as a lecturer in the Department of Mechanical Engineering, Saga University. In 1989, he joined as a professor in the Department of Mechanical Engineering, Saga University. In 2014, he is an Emeritus Professor at Saga University.

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Satoru Momoki has been a professor at the Graduate School of Engineering, Nagasaki University since 2012. He started his research career at the Department of Mechanical Systems Engineering at Nagasaki University in 1992 as a lecturer in 1992. He became an associate professor in 1994. From 1995 to 1996, he had been a visiting scholar the Department of Mechanical Engineering, University of Minnesota, Minneapolis. His research focuses on the areas of film boiling and flow boiling. Shinichi Morooka is Professor of Cooperative Major of Nuclear Energy at Waseda University. He graduated from the Department of Mechanical Engineering at Waseda University in 1977. He received Dr. Eng. degree from Waseda University in 1980. His research field includes thermalhydraulics of nuclear power plant. He has worked at Toshiba Corporation in thermal-hydraulics R&D Center of nuclear power plants for about 30 years. He has a great deal of experience in developing components for actual nuclear power plants. He came back to Waseda University as a professor in 2010. Now, he optimizes the heat transfer performance for Light Water Reactor components using Computed Fluid Dynamics code and experimental technologies. Target Components are Nuclear Fuel, Separator system, Steam Generator, so on. He constructs flow mechanism, develops our own simulation code based on flow mechanisms, and predicts the heat transfer performance of fuel assembly. Shoji Mori received his PhD from Kyushu University in 2003. He joined the Department of Chemical Engineering at Yokohama National University as a research associate in 2004. He became an associate professor in 2007. From 2009 to 2011, he studied cryopreservation and thermal therapies at Bioheat and Mass Transfer Laboratory, Department of Mechanical Engineering, University of Minnesota, Minneapolis, as a visiting professor (Prof. John C. Bischof). His research interests are currently focusing on novel thermal systems using porous materials and bio-transport phenomena. Niro Nagai has been a professor in the Field of Mechanical Engineering at the University of Fukui since 2013. He received his PhD degree from the University of Tokyo in 1996. He started his research career at Fukui University in 1993 as a research associate for heat transfer engineering, especially boiling heat transfer. He stayed at the University of California Berkeley from 2000 to 2001. He continued working at the Field of Mechanical Engineering of University of Fukui from 1993 until now. His research is focused in the areas of pool and flow boiling, liquid
solid contact situations in high heat flux boiling and near MHF point. He is also interested in utilization of shallow geothermal energy, hydrogen production by water electrolysis, and application of heat pipe. Taku Nagatake received PhD degree from Kyoto University, Japan, in 2010. He joined Japan Atomic Energy Agency and started his research. Now he is a research engineer of Development Group of Thermal-Hydraulics Technology. His main subject is development of numerical simulation method for melting behavior and thermal-hydraulic behavior in a spent fuel pool at a severe accident condition.

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Gyoko Nagayama received her PhD degree from Kyushu Institute of Technology in 2001. She was a postdoctoral fellow in the Hong Kong University of Science and Technology (2001
2002), an assistant professor in Tokuyama College of Technology (2003
2005), a visiting associate professor in the University of British Columbia (2011). She has been an associate professor in the Department of Mechanical Engineering, Kyushu Institute of Technology since 2005. Having been engaged in the research of engineering thermophysics, presently, she focuses on nano/microscale interfacial transport phenomena at the liquid
vapor interface, solid
liquid
vapor triple phase interface and its application in micro fuel cell and micro heat pipe. Osamu Nakabeppu is a professor in the Department of Mechanical Engineering, School of Science and Engineering, Meiji University, Kawasaki, Japan. He received his M. Eng, and D. Eng. degrees from Tokyo Institute of Technology (Tokyo Tech.). He was engaged at Tokyo Tech. (1990-), the University of Tokyo (1996-), Tokyo Tech. (1998-) and Meiji University (2006-). His research concerns the field of microthermal engineering including Scanning Thermal Microscopy, Nano-calorimetry, Boiling Heat Transfer Mechanism with MEMS, Heat Flux Sensor for Internal Combustion Engine, etc. Hiroyasu OHTAKE has been a professor in the Department of Mechanical Engineering at Kogakuin University. He received PhD degree from the University of Tokyo in 1992. His research focuses on the areas of pool and flow boiling, critical heat flux, condensation, and two-phase flow. He is also interested in heat transfer and fluid flow in micro-nano scale. Haruhiko Ohta is a professor at the Department of Aeronautics and Astronautics at Kyushu University. In 1981, he became a lecturer in the Department of Mechanical Engineering at Kyushu University and received the degree of Dr Eng. from Kyushu University. He became an associate professor of the same department in 1983. He moved to the Department of Aeronautics and Astronautics, Kyushu University in 1999 as a professor. From 2003 to 2005, he also worked as a program officer in MEXT/JST. He is currently working as a principal investigator of the ISS experiment by JAXA to be scheduled in 2017 on the flow boiling/two-phase flow collaborating with the International Topical Team directed by ESA. He is currently interested in the development of high-performance cooling systems for semiconductors by the application of boiling heat transfer to immiscible mixtures. Hidetoshi Ohkubo started his research career at the Institute of Industrial Science at the University of Tokyo in 1982 as a research associate. He received PhD from the University of Tokyo in 1993. He moved to the Department of Mechanical Engineering of Tamagawa University in 1995 as an associate professor. Then, he has been in the present position from 2004. His research focuses on the areas of boiling, frosting, and thermal storage. Tomio Okawa started his research career at the Central Research Institute of the Electric Power Industry in 1990 and earned a doctor of engineering degree from the Tokyo Institute of Technology in 1995 after receiving bachelor’s and master’s degrees from Tokyo Institute of Technology. Then, he moved to the Department of Mechanical Engineering at Osaka University in 1999, and to his present position (University of Electro-Communications) in 2011. His main research areas are multiphase flow and heat transfer with phase change. His research topics include numerical stability of

Biographies

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two-phase flow numerical simulation, Lagrangian simulation of bubbly flow, droplet deposition and entrainment in annular flow, liquid film dryout in annular flow, mechanistic modeling of subcooled flow boiling, high-heat-flux heat removal, boiling heat transfer of nanofluids and drop impact phenomena. Kunito Okuyama has been a professor in Department of Chemical Engineering Science at Yokohama National University for the last 14 years. He received a PhD degree from Tokyo Institute of Technology in 1985. He started his research career at Japan Atomic Energy Research Institute in 1985 as a research engineer for the research and development of a high-temperature gas-cooled reactor for hydrogen production. He moved to Department of Material Science and Chemical Engineering of Yokohama National University in 1988, and he has been in the present position since 2003. Within the period, he stayed temporarily at University of Pennsylvania as a visiting faculty from 1992 through 1993. His research is focused on the transient boiling near the limit of liquid superheat, micro-actuators using rapid boiling as in the ink jet printers, the utilization of the ink jet technology for novel processes. He is also interested in the passive processes using liquid
vapor phase change phenomena caused in porous materials, particularly the rapid generation of highly superheated steam and the hydrogen production using catalytic reactions, and microheat pipes using the self-excited oscillation induced by an unique structure. His researches are closely related to the cooling of the high-density energy dissipating systems, and the effective use of energy and the development of novel functional processes utilizing phase-change phenomena in microsystems. Naoki Ono received the B.S., M.S. and D.Eng. degrees in mechanical engineering from the University of Tokyo in 1985, 1987, and 1998, respectively. From 1987 to 2002, he was with Mitsubishi Materials Corp., Japan, and from 2003 to 2005, he was with SUMCO Corp., Japan, as a research engineer. In those companies his research topic was heat and mass transfer analysis of the crystal growth process of semiconductor silicon including Marangoni effect. In 2005, he joined the faculty of the department of engineering science and mechanics, Shibaura Institute of Technology, Tokyo, Japan, as an associate professor. He has been a professor since 2010. His current research is in heat and mass transfer in mini-/microchannels, surface tension effects and boiling in mini-/ microsystems, micromixing, and cooling technology in practical thermal systems. Tomohiro Osawa received his master degree (Master of Engineering) from the Tokyo University of Science, and was graduated from the Division of Mechanical Engineering, Graduate School of Science and Technology in March 2014. Mamoru Ozawa has been a professor at Kansai University for more than two decades. He received a Doctoral degree from Osaka University in 1977, then he started his research career at the Mechanical Engineering Department, Osaka University, mainly in the field of two-phase flow dynamics including flow instabilities in boiling channels. He moved to Kobe University. Then he further moved to Kansai University. During the period of December 1979 to January 1981, he was a research fellow of the Alexander von Humboldt Foundation, West Germany, and worked at the Institute of Thermal Process Engineering, the University of Karlsruhe (present Karlsruhe Institute of Technology). Kansai University founded a new faculty, Societal Safety Science, in 2010. Since

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then he has served as Vice Dean and then Dean of the Faculty. His research activity has extended in a variety of fields, e.g., boiling heat transfer, critical heat flux, two-phase flow dynamics, fluidized bed, natural convection. At present he is focusing his interest on the historical development of boiler technology. Takahito Saiki received his master degree (Master of Engineering) from the Tokyo University of Science, and was graduated from the Division of Mechanical Engineering, Graduate School of Science and Technology in March 2014. Shimpei Saito is a PhD student at the University of Tsukuba and is also a research fellow of the Japan Society for the Promotion of Science (JSPS). He received his B.E. and M.E. degrees in Mechanical Engineering from the University of Tsukuba in 2014 and 2016, respectively. His research interest includes two-phase flow dynamics, high-speed phase change, and mesoscale simulation of transport phenomena. Yasushi Saito has been a professor at the Research Reactor Institute, Kyoto University since 2013. He received his PhD degree from the Department of Chemical Engineering, Kyoto University in 1998. He started his research career at the Research Reactor Institute, Kyoto University in 1996 as a research associate in the heat transport laboratory. He stayed at the University of Karlsruhe (TH) (KIT at present) from 2006 to 2008 as a visiting research fellow supported by the Alexander von Humboldt Foundation. His research is focused on the areas of the boiling heat transfer and liquidmetal flows. He is also interested in the development and application of neutron imaging techniques, mainly for thermal hydraulic research. Hiroto Sakashita received PhD degree in 1998 from Hokkaido University, Japan. He started his research career in 1981 as a research assistant at the Department of Nuclear Engineering, Hokkaido University. He is currently an associate professor at the Division of Energy and Environmental Systems at Hokkaido University. His current research interest is in the areas of boiling heat transfer, especially the mechanism of critical heat flux, critical heat flux enhancement using binary mixtures and nanofluids, and boiling behaviors at high pressures. He is also interested in the thermalhydraulic problems of nuclear engineering. Raffaele Savino received a PhD in Aerospace Engineering from Naples University in 1993 and, since 1995, he has been working at the same University as a researcher, until 2000, as an associate professor, and as a full professor since 2016. He has also been Professor of Aerodynamics at the Italian Air Force Academy, since 2000, and research associate at the Institute of Science and Technology for Ceramics of the National Research Council (CNR). His memberships include the International Academy of Astronautics (IAA), the International Astronautical Federation (IAF) and the American Institute of Aeronautics and Astronautics (AIAA). He has been scientific coordinator of several international research programs, in collaboration with aerospace industries, research centers and space agencies, and investigator in microgravity experiments performed onboard airplanes in parabolic flights, sounding rockets and orbital platforms. He has authored more than 220 publications in the fields of Fluid Dynamics, Microgravity and Space Experimentation, Physics of Fluids, Hypersonic Aerodynamics, Heat Transfer, and Rocket Propulsion.

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Yoshihiro Serizawa has been a senior researcher at Nippon Steel & Sumitomo Metal Corporation for 13 years. He received a PhD degree from Tamagawa University in 2015. He started his research career at Nagoya factory of Nippon Steel & Sumitomo Metal Corporation in 1986 as a research engineer for heat transfer in iron and steel making processes. He stayed there from 1986 through 1997. He moved to the present workplace in 1997 and he has been in the present discipline since then. His research is focused on the areas of pool and flow boiling, minimum heat flux. He is also interested in heat transfer in the steel making process. He also has an interest in thermal conduction between solid objects, gas jet heat transfer. Masahiro Shoji received his PhD from the University of Tokyo (UT) in 1971.He started his career at UT in 1971 and has been engaged in research and education for over 30 years. He retired form UT in 2004 and moved to AIST (Advanced Institute of Science and Technology) as the invited researcher. In 2006, he started to work at Kanagawa University (UK) as the professor and the dean of the Faculty of Engineering. He retired from UK in 2014. His main research field is phase change heat transfer and he has interests in wide problems of thermal and fluid phenomena such as surface tension driven phenomena, nonlinear chaotic phenomena and others. Koichi Suzuki is a professor of the Department of Mechanical Engineering at Tokyo University of Science. He graduated from the department of applied physics at Tokyo University of Science in 1967. He had been engaged in research on combustion technology of gaseous fuels and boiling heat transfer at Department of Mechanical Engineering of Tokyo University of Science since 1967. He received Dr. Eng. degree from Tokyo University of Science in 1989. He stayed at Professor Ping Cheng’s Laboratory of Shanghai Jiao Tong University as a visiting professor in 2008. He moved to Tokyo University of Science-Yamaguchi in 2010 and continued research on boiling heat transfer. He served as a Dean of Engineering in 2015. Then, he came back to Tokyo University of Science as a professor in 2016. He was given a Professor-Emeritus from Tokyo University of Science-Yamaguchi in 2016. His research is focused in the area of the pool boiling, the flow boiling, the critical heat flux and the boiling heat transfer in microgravity. Especially, the microbubble emission boiling, MEB, generated in highly subcooled boiling, is main research task for the future advanced cooling technology. Yasuyuki Takata is a professor of thermofluid physics in the Department of Mechanical Engineering and a Lead Principal Investigator of the Thermal Science and Engineering Research Division at the International Institute for Carbon-Neutral Energy Research (WPI-I2CNER), Kyushu University, Japan. His research area covers phase change heat transfer, micro JT cooler, micro heat transfer devices, and thermophysical properties of hydrogen, as well as a database of thermophysical properties of fluids. He received The JSTP Award for Outstanding Achievement in 1995, The JSTP Best Paper Award in 2010 from the Japan Society of Thermophysical Properties, Heat Transfer Society Award for Scientific Contribution in 2002 from the Heat Transfer Society of Japan, and JSME Thermal Engineering Achievement Award in 2010 from the Thermal Engineering Division of the Japan Society of Mechanical Engineers. He is a fellow and he also served as executive board director of the Japan Society of Mechanical Engineers (JSME), executive board director of international affairs of the Heat Transfer Society of Japan (HTSJ) and the President elect of the Japan Society of Thermophysical Properties (JSTP).

xxxviii Biographies

Manabu Tange has been an associate professor in the Department of Mechanical Engineering of Shibaura Institute of Technology. He received his PhD degree from the University of Tokyo in 2008. He started his research career at Advanced Industrial Science and Technology in 2008 as a research engineer for heat and mass transfer of metal hydride vessels. After engagement as assistant professor of the University of Tokyo in 2009, he moved to the Department of Mechanical Engineering of Shibaura Institute of Technology in 2010. His research interest is microscale thermo-fluid phenomena including boiling heat transfer and Marangoni convection. He also engages in study on flow visualization and image processing of microscale thermo-fluid phenomena. Takaharu Tsuruta received a PhD degree from the University of Tokyo in 1989. He started his research career at the Japan Atomic Energy Research Institute in 1981 as a research engineer for nuclear reactor safety. He moved to the Department of Mechanical Engineering of Kyushu Institute of Technology in 1984. He stayed at the University of Illinois at Urbana-Champaign from 1991 through 1992. He has been in his present position from 1999. His research is focused on the phase change phenomena including pool boiling, critical heat flux, condensation and molecular transportation at the liquid
vapor interface. He is also interested in drying and freezing preservation of biomaterials. Ichiro Ueno received PhD from the University of Tokyo for a thesis entitled “Thermal-Fluid Phenomena Induced by Nanosecond-Pulsed Laser Heating of Materials in Water” under the supervision by Prof. Masahiro Shoji in the Department of Mechanical Engineering, School of Engineering in March 1999. He had also served as JSPS Research Fellowships for Young Scientists (DC1). He had served as a research associate at the Department of Mechanical Engineering, Faculty Science & Technology, Tokyo University of Science from April 1999 to March 2004. He then had served as an assistant professor since April 2004 till March 2009, as an associate professor since April 2009 till March 2015, and then as a professor since April 2015. He has been supervising Interfacial Thermo-Fluid Dynamics Lab at the same affiliation since April 2004. He also has served as Director of International Research Division of Interfacial Thermo-Fluid Dynamics, Research Institute for Science & Technology (RIST), Tokyo University of Science since April 2012. He served as a co-investigator (CI) for Fluid Physics Experiment on the Japanese Experimental Module “Kibo” aboard the ISS since 2000. He has also served as a CI for Japan-Europe Research Experiment on Marangoni Instability (JEREMI); planning to carry out an on-orbit experiments on the “Kibo” aboard the ISS. His current research areas are wetting/dewetting phenomena, surface-tension-driven convection, gas/vapor bubble, evaporating droplet, and interaction between particles and free surface. Hisashi Umekawa has been a professor of Kansai University since 2009. He received his PhD degree from Kansai University in 1998, and also received a Master’s degree from Kansai University in 1988. He started his career at Daikin industries, Ltd in 1988, and then moved to the Department of Mechanical Engineering of Kansai University in 1991. He stayed at the Institute for Nuclear and Energy Technologies (IKET) in Research Center of Karsruhe (FZK) from 1999 through 2000, supported by the Alexander von Humboldt Research Fellowship. His research is focused in the areas of flow boiling, critical heat flux, and two-phase flow. Since his research field is closely related to energy systems, he has great interest in thermal and nuclear power stations and energy supply in society.

Biographies

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Yoshio Utaka is a professor at the School of Mechanical Engineering, Tianjin University, Tianjin, China, and Visiting Professor at the Faculty of Engineering, Tamagawa University, Tokyo and Graduate school of Engineering, Kanto Gakuin University, Yokohama, Japan. He is a Professor Emeritus of Yokohama National University (YNU). He received his M.Eng. and D.Eng. degrees from the University of Tokyo. He was engaged at the Tokyo Institute of Technology (1978-), National Defense Academy (1992-) and YNU (1994
2015). His research concerns the field of heat transfer with phase change (condensation, boiling, solidification, and melting) and heat and mass transfer for performance improvement of PEFC. He has been the head of the department, the regent and the president’s aid at YNU. He is a former president of the Heat Transfer Society of Japan and an honorary member of JSME. Tomohide Yabuki received his PhD degree from Meiji University in 2014. He started his research carrier in the Department of Mechanical and Control Engineering at Kyushu Institute of Technology in 2014 as an associate professor. Currently, He is an associate professor at Kyushu Institute of Technology. He was a JSPS research fellow from 2011 to 2014, and a visiting scholar at the University of California, Berkeley from 2015 to 2016. His current interests include heat transfer mechanisms of boiling heat transfer, the high-resolution thermal measurement with a MEMS sensor, and nonlinear thermal devices. Tomohiko Yamaguchi got a contract as a research associate at the Department of Mechanical Systems Engineering, Nagasaki University in 1996. He is working at Nagasaki University as an associate professor from 2001. He is a member of PROPATH (PROgram PAckage for THermophysical properties of fluids) group and developing PROPATH from 1994. The work by PROPATH group was awarded “Outstanding Achievement Award of the JSTP” from Japan Society of Thermophysical Properties in 1995. Funded by KITEC in 2002 he had worked with Professor J. Gmehling and Dr. J. Rarey at Universita¨t Oldenburg, Germany, as for the topics of the prediction and measurement of thermophysical properties of fluids. The numerical simulation of solid–gas or liquid
gas two-phase flow is another main topic of his research. In 2012, he worked with Professor Y. Yan at the University of Nottingham in UK as a visiting researcher for 13 months, funded by JSPS in order to study the LBM for the two-phase flow in heat pipes and the MRI measurement of the water delivery in plants. Hiroyuki Yoshida received his PhD from Kyushu University, Japan, in 1994. He is a group leader of the Development Group of Thermal-Hydraulics Technology in the Japan Atomic Energy Agency. And he is also an adjunct professor of the University of Tsukuba. His current interests are nuclear engineering, thermal-hydraulic phenomena in sever accident, and development of multiphase flow simulation method. Kazuhisa Yuki received a PhD degree from Kyushu University in 1998. He started his research career at Tohoku University in 1998 as an assistant professor in Nuclear Engineering department. He had moved to the Department of Mechanical Engineering at Tokyo University of Science, Yamaguchi in 2009. He has been in his present position from 2015. His research is focused on High heat flux removal utilizing porous media, microbubble emission boiling, heat transfer enhancement, flow visualization etc.

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Preface Boiling has a long history—since the appearance of mankind on the Earth. Boiling has been used as a method to cook foods. A kettle filled with water is put on a gas flame—it is quite routine. The temperature of the gas flame is approximately 2000 K and the melting point of the kettle made of aluminum is approximately 930 K. Why does the kettle not melt? We never pay attention to this fact when we boil water. We instinctively know that boiling has quite a high capability to take heat away. Thus, we throw water over a hot object to cool it down rapidly. Boiling is widely utilized in industry, since it is the best way to cool a hot body and to retrieve heat from a heat source effectively. For example, boiling is one of the key technologies in thermal power plants, nuclear reactors, and steel manufacturing. The modern research on boiling was initiated by Professor Nukiyama (1934). He presented the boiling curve, which is the basis of boiling research. Since then, numerous experimental and theoretical researches have been performed. Boiling has been a main topic in lectures and in laboratories in departments of engineering at universities around the world. Japan was involved in extreme technological deployment in the period from 1950 to 1960, with the introduction of advanced thermal power plants and nuclear reactors. As a result, research on boiling evolved and was advanced by many researchers combined with the research history from Professor Nukiyama. The boiling research was expanded to understand pool boiling, film boiling, burn-out, and so on. So many products were developed to enhance the understanding of boiling. Even so, scientists were quite sure that unknowns still existed in boiling research. The Japan Society of Mechanical Engineers established the survey and research committee on boiling heat transfer in 1961 to survey and catalog the knowledge obtained so far and to extract the mechanism of boiling heat transfer for the better understanding of boiling. The committee published Boiling Heat Transfer in 1965 as the fruit of their activities. Research results achieved since Nukiyama were included in the book. A great deal of references were reviewed. The book consisted of fundamentals such as bubble behavior, boiling theory and modeling, pool boiling burn-out, forced flow boiling burn-out, flow boiling, transition boiling, film boiling, and peculiar-type boiling. Because of its rich content, it was the bible for boiling researchers for a long period of time in Japan. As time went by, thermal power plants made remarkable advancements, and many nuclear reactors were introduced in Japan. The continuing perseverance into the development of boiling research was of course of great help in these advancements. New and more advanced achievements had been developed since the publication of Boiling Heat Transfer in 1965. Then, the Japan Society of Mechanical Engineers established a committee to gather and document new findings on boiling and cooling of high-temperature heat transfer surfaces. The committee updated Boiling Heat Transfer by including a large number of paper reviews that had been presented up to that point and launched Boiling Heat Transfer and Cooling in 1998, two decades after Boiling Heat Transfer. The new volume was composed of chapters of introduction, fundamentals, and application. The fundamentals chapter included sections on nucleate boiling, critical heat flux, transition boiling, minimum heat flux point, film boiling, and transient boiling. The application chapter had sections on quenching, amorphous and cooling by boiling, spray and jet cooling, cryogen, electric device cooling by boiling, boiling transition, critical heat flux of a nuclear fuel assembly, cooling

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Preface

during reflooding of uncovered nuclear fuel assembly, debris bed cooling, steam explosion, augmentation and control of boiling heat transfer, boiling of peculiar fluid, and characteristics of boiling heat transfer surfaces and their cleaning. Since the new volume covered quite a vast area of topics it seemed to be the most complete textbook and reference book on boiling. Because of the importance of boiling, research on the subject has been continuously carried out by many researchers in Japan. Research results have accumulated. As a result of the advancing technology in electronics, instrumentation, high-speed video cameras, and computers, boiling research has become more advanced, more detailed, and more profound. In the meantime, researchers in Japan agreed that, although the fundamental textbooks and reference books had been covered in the previously mentioned two books, recent research advancements should be collected and compiled into one volume to leave for future scientists and to provide new researchers coming into boiling research field with a book for consultation and guidance. There are a large number of boiling researchers in Japan, thus it is the duty of Japanese boiling researchers to provide such a volume. The Thermal Engineering Division of the Japan Society of Mechanical Engineers established the Phase Change Research Committee (PCRS) in 2007 to meet that need. Forty-eight boiling researchers are gathered in the PCRS. The principal policies for the planned book that were established by the committee through discussions are: • • •

•

•

The former two books are sufficient as textbooks and as reference books for the fundamentals of boiling. The new volume should specialize in recent advancements made in the last 20 years. Providing details of the advancements in each area should take precedence over the relationships between sections. Details of advancements in technology regarding experiments and insight into their fundamentals, and also areas of interest for new incoming researchers should be included. Since Japan is one of major regions for boiling research in the world, the new volume should be published in English although the former volumes were published in Japanese, in order to share valuable research achievements accumulated over the years to the rest of the world. The contributor for each section should be the researcher who actually worked on the subject in that section.

Boiling research is still advancing. The most current research has been compiled for this volume. However, the present volume does not include all findings on boiling research since this task was performed by a limited number of committee members. We sincerely hope that this volume will help to further advance boiling research. Finally, this volume is the product of the devoted work of committee members and contributors, and our heartfelt thanks are extended to them. Yasuo Koizumi, Niro Nagai, and Hiroyasu Ohtake The Phase Change Research Committee, Thermal Engineering Division, The Japan Society of Mechanical Engineers

May 31, 2016

Preface

THE PHASE CHANGE RESEARCH COMMITTEE Chair: Koizumi, Yasuo Secretary: Nagai, Niro Ohtake, Hiroyasu

Japan Atomic Energy Agency/Shinshu University University of Fukui Kogakuin University

Members: Abe, Yutaka Adachi, Akio Arima, Hirofumi Asano, Hitoshi Furuya, Masahiro Haramura, Yoshihiko Inada, Shigeaki Itoh, Kazuhiro Kaminaga, Fumito Kamoshida, Shunji Koshituka, Seiichi Koyama, Shigeru Kunugi, Tomoaki Liu, Wei Matsumura, Kunihito Mishima, Kaichiro Mitutake, Yuichi Momoki, Satoru Monde, Masanori Mori, Mishitsugu Mori, Shoji Morooka, Shinichi Nishio, Shigefumi Ohta, Haruhiko Okawa, Tomio Okuyama, Kunito Ono, Naoki Ohsawa, Akihiro Ozawa, Mamoru Saito, Yasushi Sakashita, Hiroto Shikazono, Naoki Shoji, Masahiro Suzuki, Koichi Takata, Yasuyuki Takushima, Akira Tange, Manabu

University of Tsukuba Fuji Electric Advanced Technology Company Limited Saga University Kobe University Central Research Institute of Electric Power Industry Kanagawa University Inada Teion Plasma Laboratory University of Hyogo Ibaraki University Shibaura Institute of Technology The University of Tokyo Kyushu University Kyoto University Kyushu University Ibaraki University Institute of Nuclear Safety System Incorporated Saga University Nagasaki University Saga University Hokkaido University Yokohama National University Waseda University The University of Tokyo Kyusyu University The University of Electro Communications Yokohama National University Shibaura Institute of Technology Komatsu Limited Kansai University Kyoto University Hokkaido University The University of Tokyo The University of Tokyo Tokyo University of Science Kyushu University Samsung Electronics Co., Ltd Shibaura Institute of Technology

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Preface

Tsuruta, Takaharu Ueno, Ichiro Umekawa, Hisashi Utaka, Yoshio Yamaguchi, Tomohiko Yatsuzuka, Shinichi Yoshida, Hiroyuki Yuki, Kazuhisa

Kyushu Institute of Technology Tokyo University of Science Kansai University Tianjin University/Tamagawa University Nagasaki University Denso Corporation Japan Atomic Energy Agency Tokyo University of Science

Observer: Ikeno, Tutomu

Nuclear Fuel Industries Limited

CONTRIBUTORS Name Abe, Yoshiyuki Abe, Yutaka Asano, Hitoshi Chen, Zhihao Furuya, Masahiro Haramura, Yoshihiko Jiang, Yuyan Koizumi, Yasuo Kondou, Chieko Koyama, Shigeru Kunugi, Tomoaki Liu, Wei Maruyama, Shigeo Mitutake, Yuichi Momoki, Satoru Monde, Masanori Mori, Shoji Morooka, Shinichi Nagai, Niro Nagatake, Taku Nagayama, Gyoko Nakabeppu, Osamu Ohkubo, Hidetoshi Ohta, Haruhiko Ohtake, Hiroyasu Okawa, Tomio Okuyama, Kunito

Japan Science and Technology Agency University of Tsukuba Kobe University Tianjin University Central Research Institute of Electric Power Industry Kanagawa University Institute of Engineering Thermodynamics, Chinese Academy of Sciences Japan Atomic Energy Agency Nagasaki University Kyushu University Kyoto University Kyushu University The University of Tokyo/Advanced Industrial Science and Technology Saga University Nagasaki University Saga University Yokohama National University Waseda University University of Fukui Japan Atomic Energy Agency Kyushu Institute of Technology Meiji University Tamagawa University Kyusyu University Kogakuin University The University of Electro Communications Yokohama National University

Contributed sections 6.12 6.15 6.9 2.2 6.16 3.6 6.3 1.2, 3.10 6.18 6.18 5.1 3.8 6.3 4.3 6.17 1.1 3.4 3.11 3.3 5.2 6.2 2.1 6.14 2.5 3.7, 4.1, 4.2 2.6 6.4

Preface

Ono, Naoki Ozawa, Mamoru Shinpei, Saitho Saito, Yasushi Sakashita, Hiroto Savino, Raffaele Serizawa, Yoshihiro Shoji, Masahiro Suzuki, Koichi Takata, Yasuyuki Tange, Manabu Tsuruta, Takaharu Ueno, Ichiro Umekawa, Hisashi Utaka, Yoshio Yabuki, Tomohide Yamaguchi, Tomohiko Yoshida, Hiroyuki Yuki, Kazuhisa

Shibaura Institute of Technology Kansai University University of Tsukuba Kyoto University Hokkaido University University of Naples Federico II Nippon Steel & Sumitomo Metal Corporation The University of Tokyo Tokyo University of Science Kyushu University Shibaura Institute of Technology Kyushu Institute of Technology Tokyo University of Science Kansai University Tianjin University/Tamagawa University Kyushu Institute of Technology Nagasaki University Japan Atomic Energy Agency Tokyo University of Science

2.4 6.19 6.15 6.5 3.1 6.12 6.13 3.5 6.6 1.3, 6.11 6.7 3.2, 6.2 6.8 3.9 2.2, 2.3 2.1 6.1 5.2 6.10

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CHAPTER

OUTLINE OF BOILING PHENOMENA AND HEAT TRANSFER CHARACTERISTICS

1 Yasuo Koizumi

Japan Atomic Energy Agency, Tokai, Japan

CHAPTER OUTLINE 1.1 Pool Boiling......................................................................................................................................2 1.2 Flow Boiling .....................................................................................................................................4 1.3 Other Aspects ...................................................................................................................................8

The objective of this book is to gather together research works completed over the last 20 years, covering the progress of boiling research in Japan after the Japan Society of Mechanical Engineers (JSME) published Boiling Heat Transfer [1] and Boiling Heat Transfer and Cooling [2]. Anyone taking this book in his/her hand is assumed to have some experience or a basic knowledge of boiling heat transfer. Thus, the contents of this book are mainly focused on research results, not on such fundamentals as are found in general text books. This book includes the following five chapters: Chapter 2, Nucleate Boiling; Chapter 3, CHF—Transition Boiling; Chapter 4, MHF— Film Boiling; Chapter 5, Numerical Simulation; and Chapter 6, Topics on Boiling: From Fundamentals to Application. Each chapter is composed of several sections, and was written by experts in that particular research area. Reviewing boiling phenomena before moving into the main body of this book, this chapter covers the fundamental outlines of pool nucleate boiling and flow boiling. Since the publication of the two former volumes, new thinking that boiling is considered to be a basic science that can be studied by numerical simulation or from the aspect of microscopic physics has come to the fore. This new trend is also briefly overviewed in a later section in this chapter. Readers wishing to study the fundamentals of boiling heat transfer should consult the two formerly published books on the subject.

Boiling. DOI: http://dx.doi.org/10.1016/B978-0-08-101010-5.00001-4 Copyright © 2017 Elsevier Ltd. All rights reserved.

1

2

CHAPTER 1 OUTLINE OF BOILING PHENOMENA

1.1

POOL BOILING

Masanori Monde Saga University, Saga, Japan

When a liquid in a vessel is heated on a submerged solid surface by a heat source, such as an electric heater, a vapor on the heated surface is generated at a temperature higher than the liquid saturation temperature. This process of vapor production, called pool boiling, is commonly encountered in daily life and in industrial applications. The relationship between wall superheat, ΔTsat, and wall heat flux, q, during pool boiling for saturated liquid was first identified by Nukiyama [1] as shown in Fig. 1.1.1. Fig. 1.1.1 qualitatively shows the boiling curve, illustrating the relationship between wall superheat and wall heat flux as the heat flux is increased. The onset of nucleate boiling (ONB), critical

FIGURE 1.1.1 Typical pool boiling curve for water at one atmosphere. CHF, critical heat flux; MHF, minimum heat flux; ONB, onset of nucleate boiling.

POOL BOILING

3

heat flux (CHF), and minimum heat flux (MHF) are very important points in the characterization of boiling behavior. At a heat flux below the ONB point, no bubbles appear on the surface and the heat transfer is dominant in natural convection. The ONB point is strongly influenced, for example, by surface roughness and wettability. Therefore, the line between the ONB and CHF points shifts depending on the ONB point. An improvement in boiling heat transfer can be manipulated by artificially controlling the surface conditions by shifting this line toward the left hand side. Boiling heat transfer between the ONB and CHF points can be characterized as two stages: the first is a low-heat-flux region, called isolated bubble boiling where the discrete bubbles are randomly released from many activated cavities; and the second, a high-heat-flux region where the bubbles merge with each other into a large vapor mass, called fully developed nucleate boiling. The heat transfer in the second stage is better than that in the first stage. The heat transfer is controlled by a very thin layer being adhesive on the surface. This layer is hardly influenced by bulk liquid flow and surface conditions such that the boiling heat transfer becomes independent of the surroundings. Many different types of empirical correlations predicting heat transfer coefficient in pool boiling have been proposed for any liquid and a wide range of pressures, which are omitted here since the details will be included in the following chapter. The relationship between ΔTsat and q can be summarized for most nucleate boiling as m qBCΔTsat

(1.1.1)

The C and m in Eq. (1.1.1) are constant values, depending on the liquid thermal properties and surface conditions. Thus, a qualitative understanding of pool boiling has become clear, however a complete understanding still remains to be described. The upper limit of pool boiling is called the CHF or the maximum heat flux, which is of great importance in industrial applications, as well as from a scientific point of view. Many empirical correlations and theoretical equations based on a different idea for the mechanism of CHF may converge into the Kutateladze correlation (1.1.2) for a saturated liquid on a large horizontal surface, which was derived for various liquids and a wide range of pressures from the dimensional analysis. qco =ðρv hfg Þ p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 5 K 5 ð0:13 2 0:19Þ 4 σgðρl 2 ρv Þ

(1.1.2)

For a fine heated wire and vertical heater and also for subcooled liquids, a modified correlation has been proposed based on Eq. (1.1.2). If the wall heat flux is loaded beyond the CHF point, the nucleate boiling cannot transport the loaded heat from the heated surface into the liquid in a stable manner. As a result, the stable nucleate boiling is ruptured resulting in another stage, called either transition boiling or film boiling. In the case of a constant heat flux heater such as an electrical heater, most of the loaded heat flux may be stored in the heater, by which the temperature of the heater is rapidly increased until another stable point on film boiling. In the most cases, the heater would melt. In the case of a controlled heat flux heater, the transition boiling can be artificially realized. In most cases, however, after post-CHF the surface condition quickly passes the transition boiling region and reaches the stable film boiling stage. Therefore, the stable transition boiling is hardly realized, because at any point on the surface, conditions may oscillate between film and nucleate boiling.

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CHAPTER 1 OUTLINE OF BOILING PHENOMENA

Film boiling can be reached at relatively higher temperatures where the surface cannot be wetted and is completely covered by a vapor blanket. The lower limit of heat flux at which the stable film boiling can be sustained, is described as the MHF or sometimes as the Leidenfrost point (LFP). The heat transfer coefficient for the film boiling will be discussed later.

1.2

FLOW BOILING

Yasuo Koizumi Japan Atomic Energy Agency, Tokai, Japan

As liquid flows in a heated channel, the temperature of the liquid reaches saturation temperature. Then, boiling is initiated in the channel. As the flow moves downstream, the vapor volume increases and eventually the channel is completely filled with vapor. This consecutive phase change phenomenon in the heated channel is called flow boiling. The progress of the sub-cooled flow boiling in a uniformly heated pipe with a heat flux q is qualitatively illustrated in Fig. 1.2.1. Boiling is initiated at some location. When the progress of the flow boiling is considered, an axial position of the pipe is sometimes expressed with the thermodynamic equilibrium quality xe for convenience instead of the axial length z. When liquid with the enthalpy hin flows into the pipe of inner diameter D at the mass flow rate G, the thermodynamic equilibrium quality xe at z from the inlet of the pipe is xe 5

hin 1 ðπDqz=GÞ 2 hls : hfg

(1.2.1)

Here, hfg and hls are the latent heat and the saturated liquid enthalpy of the fluid, respectively. The bulk fluid is subcooled, saturated and superheated when xe , 0.0, 0.0 # xe # 1.0 and xe . 1.0, respectively. Even if xe , 0.0, i.e., the liquid in the bulk flow is still subcooled, boiling starts on the pipe wall since the temperature of the wall and also the temperature of the liquid near the wall locally become higher than the saturation temperature. This boiling initiation and this boiling state are called incipient boiling and subcooled boiling, respectively. Then, bubbles start to leave from the wall. This is called net vapor generation initiation. As the flow moves further downstream, the liquid in the bulk flow reaches the saturation condition; xe 5 0.0. After xe . 0.0, the boiling state is called saturation boiling. The flow state is initially bubbly flow and then turns to slug/churn flow as net vapor volume increases with an increase in xe. Heat transfer at the wall is principally governed by nucleate boiling.

FLOW BOILING

Inlet

Tf, TW

Outlet

Vapor Temperature

Wall Temperature

Bulk Fluid Temperature

Liquid Center Temperature

h

5

Heat Transfer Coefficient

α

Void Fraction

1

0

1

xe z

Vapor Single-Phase

Liquid Single-Phase

Bubbly Flow Liquid SinglePhase Flow

Slug/Churn Flow

Dispersed Flow

Vapor SinglePhase Flow

Post Dry-out

Forced Convection

Dry-out Nucleate Boling and Forced Convection Saturated Boiling

Forced Convection

Annular/Annular Dispersed Flow

Subcooled Boiling

Forced Convection -Evaporation

FIGURE 1.2.1 Flow and heat transfer progress of flow boiling in heated pipe.

6

CHAPTER 1 OUTLINE OF BOILING PHENOMENA

Since the specific volume of vapor is considerably larger than that of liquid, a small amount of phase change from liquid to vapor results in producing a large amount of vapor volume. The void fraction α, that is the ratio of vapor volume to total volume of vapor and liquid which flow through that cross-section, increases rapidly right after the initiation of boiling as shown in Fig. 1.2.1. Then, the center portion of the pipe is mainly occupied with vapor, and liquid flows on the pipe wall as a film. Liquid also usually flows as entrained droplets in the vapor flow. This flow state is called annular flow or annular dispersed flow. The film thickness in this flow state is usually so thin that heat from the wall is transferred from the wall to the film surface through heat conduction and convection in the film and is released by evaporation on the film surface. This boilingsuppressed heat transfer state is called forced convection evaporation. In some cases, such as when the heat flux is very high or when the flow rate is very high, bubble nucleation occurs on the wall in the film. This state is called forced convection boiling and evaporation. As the flow goes downstream further, a dry area comes out in the wall and eventually spreads out entirely. After the film flow vanishes and the wide dry area appears, the wall temperature goes up sharply. This flow state transition is called dry-out. After this point, the flow state is called dispersed flow where vapor flows in the pipe with entrained droplets. Although xe , 1.0 and droplets exist in the vapor flow, heat transfer at the wall is mainly undertaken by the vapor flow, so the heat transfer coefficient becomes low and the vapor is superheated. The thermal non-equilibrium condition where superheated vapor and droplets coexist emerges. The entrained droplets gradually evaporate in the superheated vapor to disappear and the flow turns to vapor single-phase flow. The state after the appearance of dry-out until the transition to the vapor single-phase flow is called the post-dry-out region. The typical variations of the heat transfer coefficient and the wall temperature along the pipe under flow boiling are included in Fig. 1.2.1. Heat transfer until incipient boiling is single-phase flow heat transfer of liquid. Thus, the heat transfer coefficient is almost constant along the pipe. The wall temperature gradually increases following an increase in the liquid temperature because of being heated. After boiling starts, the heat transfer coefficient begins to increase. Wall temperature increase slows down, and then becomes almost constant after saturated boiling initiation. The heat transfer coefficient also keeps an almost constant value after the initiation of saturated boiling although it has a slight increasing tendency. This situation continues until the transition from nucleate boiling to forced convection evaporation heat transfer. After the heat transfer state turns to forced convection evaporation, heat transfer coefficient gradually increases again because of film thickness thinning with an increase in xe. Thus, wall temperature decreases slightly with xe. After the occurrence of dry-out, there is a large increase in the wall temperature since the heat transfer coefficient decreases greatly. Heat transfer at the wall is mainly undertaken by vapor single-phase flow even if impinging droplets to the wall take some heat away from the wall. Evaporation of droplets mainly takes place in superheated vapor flow. Thus vapor temperature is determined by the balance between the heat transfer from the wall to the vapor and heat transfer from the superheated vapor to the droplets. The vapor flow rate increases due to the evaporation of droplets in superheated vapor and on the wall. So, whether vapor temperature increases or decreases with xe is determined by relations among heat transfer from the wall to vapor, heat transfer from the wall to the droplets and heat transfer from superheated vapor to the droplets, i.e., the

FLOW BOILING

7

evaporation of droplets in vapor flow. The droplets continue to exist in superheated vapor and finally disappear long after xe . 1.0. Finally vapor temperature asymptotically reaches thermodynamic equilibrium superheated-vapor temperature. Wall temperature is determined by single-phase vapor forced-convection heat transfer and increases following vapor temperature increase with xe. A sharp increase in the wall temperature due to the occurrence of dry-out which is shown in Fig. 1.2.1 is practically important since there is a possibility that in some cases the sharp temperature increase may lead to melting of a pipe wall. Heat transfer coefficient transient with xe during flow boiling is principally affected by a wall heat flux as shown in Fig. 1.2.2. As the wall heat flux is increased, the heat transfer coefficient transient progress with xe changes from (a) through (d). Boiling tends to occur at a more upstream position with an increase in the heat flux. The heat transfer coefficient during nucleate boiling becomes higher, the nucleate boiling duration period

h

(d) (a)

(c) (b)

0

1.0 xe

FIGURE 1.2.2 Variation of heat transfer coefficient in flow boiling.

8

CHAPTER 1 OUTLINE OF BOILING PHENOMENA

becomes longer, and the forced convection evaporation duration period becomes shorter as the heat flux increases. In the cases (c) and (d), the heat transfer coefficient during the nucleate boiling period is quite high. However, since xe is quite low, the wall is covered with vapor and the center bulk fluid is still liquid. This situation is similar to film boiling in pool boiling. In an extreme case, the pipe wall is physically burnt out because of wall temperature excursion. Thus, the sudden drop in the heat transfer coefficient is usually called departure from nucleate boiling (DNB) or burn-out as in pool boiling. The occurrence of the dry-out, DNB and the burn-out is referred to as the critical heat flux (CHF) condition.

REFERENCES [1] JSME, Boiling Heat Transfer, JSME, Tokyo, 1965. [2] JSME, Boiling Heat Transfer and Cooling, Japan Industrial Publishing Co., Ltd, Tokyo, 1989.

1.3

OTHER ASPECTS

Yasuyuki Takata Kyushu University, Fukuoka, Japan

Physical understanding of boiling phenomena needs absolutely exhaustive parametric studies on conceivable factors that may influence the boiling characteristics. These factors are inherent in fluids and solids. The factors in fluids are the thermophysical properties of the liquid and vapor phases such as density, specific heat capacity, viscosity, thermal conductivity of liquid and vapor, latent heat of vaporization, and surface tension. These factors are a function of temperature and pressure of the fluid and, therefore, liquid temperature (degree of subcooling) and wall temperature (degree of superheating) are the major factors. In addition to these, body forces such as gravity and electrostatic force influence the boiling characteristics too. For instance, boiling nature greatly depends on the orientation and magnitude of gravity [1]. Factors of heat transfer surfaces are thermophysical properties of solids such as specific heat capacity, thermal conductivity and density as well as the geometric structures like surface roughness. Wettability of the surface is one of the important factors. It is an interaction between liquids and solids. The degree of wettability is usually measured as a static contact angle that is defined as the angle between the solid and the tangent line of the liquid surface at the triple phases contact point. In general, a hydrophilic surface needs higher superheating for ONB and has lower heat transfer performance in the boiling region. However, the hydrophilic surface has higher CHF than a

OTHER ASPECTS

9

normal copper surface. On the contrary, a hydrophobic surface has higher heat transfer coefficient in nucleate boiling but has very low CHF. Since the contact angle is determined by the force balance among three interfacial tensions, the effect is not always the same if the contact angles are the same. For instance, water containing surfactant shows very low contact angle, which is similar to a hydrophilic surface. However, the surfactant decreases the surface tension of water and, therefore, the surface superheating at ONB becomes lower and the heat transfer in nucleate boiling is enhanced. This example indicates that the wettability effects cannot be determined by the contact angle alone. In order to understand mechanistically the effects of conceivable factors in boiling systems, a numerical simulation is a powerful tool. In recent years, a rapid improvement in computation speed and memory sizes has brought a drastic advancement in numerical simulation of boiling phenomena as a useful method for the understanding of boiling fundamentals [2]. There is, however, no allpowerful numerical method that can simulate perfectly the boiling phenomena. The reason for this difficulty is due to the multiscale in the boiling phenomena and the free-moving boundary between liquid and vapor. In the final analysis the phase change at the liquid
vapor interface occurs on the molecular scale but, on the other hand, the bubble departures from the heat transfer surface are of the order of millimeters. One attempt to understand liquid
vapor phase change on the molecular scale is to make use of a molecular dynamic (MD) simulation. The MD simulation has been a success in the qualitative understanding of the phenomena. A number of studies have been reported on evaporation/condensation from/to a thin liquid film [3
5]. Recently, Cannon et al. have been examining the effects of surface wettability and dissolved air on the nucleation of boiling bubbles [5]. Their MD simulations have revealed that bubble nucleation is more likely to occur on the hydrophobic surface than on the hydrophilic surface when both hydrophilic and hydrophobic surfaces coexist. They also found that the superheating of ONB decreases when non-condensable gases are dissolved into the boiling liquid. These phenomena are exactly what we often observe in the experiments. The MD simulation, however, cannot explain the phenomena quantitatively. We cannot predict a nucleation of bubble that grows from a microscale cavity. When we simulate a periodic bubble nucleation, we must use an artificial model of a bubble nucleus with a finite size at periodic intervals. There are a number of remaining issues to be solved and the current status is far from a seamless numerical method for a complete boiling simulation. On the other hand, numerical methods for the continuum moving free boundary problem have succeeded to some extent and, therefore, are applied to simulate boiling phenomena quantitatively. A typical popular method may be a volume of fluid (VOF) method developed by Hirt et al. [6] in the 1980s. As described in detail in Section 5.1, the VOF method uses a function F ranging from 0 to 1 that represents the fraction of fluid contained in the control volume. The transport equation for F is solved to track the liquid
vapor interface of the next time-step. @F 1 uUrF 5 0 @t

(1.3.1)

F is also used to calculate the curvature of the interface to take the surface tension force into account in momentum equations. This method can be extended to phase change problems and Takata et al. [7] applied the VOF to solve a single bubble growth and detachment of helium pool boiling. It is very difficult to handle evaporation and/or condensation for a fluid with a large density ratio between liquid and vapor. For instance, the density ratio of water vapor to liquid at

10

CHAPTER 1 OUTLINE OF BOILING PHENOMENA

atmospheric pressure is about 1600. Even if a very small amount of liquid water evaporates the expansion of vapor phase volume is considerably large. Eventually a large truncation error occurs in the computation of the transport equation for the F function and mass conservation is not assured. In the case of helium, the density ratio between liquid and vapor is about 7.4 at atmospheric pressure and there is no serious truncation error. Water at higher pressure may be much easier than water at lower pressure. In addition to the VOF method, there are a variety of numerical methods for free boundary problems such as a level set [8
12], Multi-interfaces Advection and Reconstruction Solver (MARS) [13], phase-field [14], Lattice Boltzmann (LB) [15
24], etc. The details of the MARS method are given in Section 5.1. In recent years, many researchers have used the LB method to simulate a single bubble departure from the heated surface. Their computation results agree well with the Fritz correlation for bubble size at departure. Most of them are twodimensional using coaxial coordinate systems, but some [18] are three-dimensional (3D). The 3D simulations will increase with the progress of computation power in memory and operation speed in the very near future. For more detail on the numerical simulation in pool boiling, see Section 5.1 in this book or review papers by Dhir et al. [2] and Kunugi [25].

REFERENCES [1] H. Ohta, Microgravity heat transfer in flow boiling, Adv. Heat Transfer 37 (2003) 1
76. [2] V.K. Dhir, G.R. Warrier, E. Aktinol, Numerical simulation of pool boiling: a review, J. Heat Transfer 135 (6) (2013) 061502
061502-17. [3] G. Nagayama, M. Kawagoe, A. Tokunaga, T. Tsuruta, On the evaporation rate of ultra-thin liquid film at the nanostructured surface: a molecular dynamics study, Int. J. Thermal Sci. 49 (2010) 59
66. [4] H.R. Seyf, Y. Zhang, Molecular dynamics simulation of normal and explosive boiling on nanostructured surface, J. Heat Transfer 135 (2013)121503-1 [5] J. Cannon, J. Shiomi, Molecular dynamics simulation study of how surface characteristics effect water
surface interaction during heating, 11th International Conference on Nanoschannels, Microchannels and Minichannels (ICNMM), Sapporo, Japan, 2013. [6] C.W. Hirt, B.D. Nichols, Volume of fluid (VOF) method for the dynamics of free boundaries, J. Computat. Phys. Vol. 39 (1981) 201
225. [7] Y. Takata, et al., Numerical analysis of single bubble departure from a heated surface, Proceedings of the 11th International Heat Transfer Conference, vol. 4, 1998, pp. 355
360. [8] V.K. Dhir, Numerical simulations of pool-boiling heat transfer, AIChE J. 47 (4) (2001) 813
834. [9] G. Son, N. Ramanujapu, V.K. Dhir, Numerical simulation of bubble merger process on a single nucleation site during pool nucleate boiling, J. Heat Transfer 124 (2002) 51
62. [10] A. Mukherjee, V.K. Dhir, Study of lateral merger of vapor bubbles during nucleate pool boiling, J. Heat Transfer 126 (2004) 1023
1039. [11] A. Mukherjee, S.G. Kandlikar, Numerical study of single bubbles with dynamic contact angle during nucleate pool boiling, Int. J. Heat Mass Transfer 50 (2007) 127
138. [12] J. Wu, V.K. Dhir, Numerical simulations of the dynamics and heat transfer associated with a single bubble in subcooled pool boiling, J. Heat Transfer 132 (11) (2010) 111501
111501-15. [13] T. Kunugi, MARS for multiphase calculation, Computat. Fluid Dynamics J. 9 (2001) 563
571. [14] M. Fukuta, Y. Yamamoto, Development of boiling heat transfer analysis method, Proceedings of the ASME 2014 4th Joint US-European Fluids Engineering Division Summer Meeting and 11th

REFERENCES

[15] [16] [17] [18] [19] [20] [21]

[22] [23] [24] [25]

11

International Conference on Nanochannels, Microchannels, and Minichannels, FEDSM2014, FEDSM2014-21679, August 3
7, 2014. Z. Dong, W. Li, Y. Song, A numerical investigation of bubble growth on and departure from a superheated wall by lattice Boltzmann method, Int. J. Heat Mass Transfer 53 (2010) 4908
4916. S. Gong, P. Cheng, A lattice Boltzmann method for simulation of liquid
vapor phase-change heat transfer, Int. J. Heat Mass Transfer 55 (2012) 4923
4927. S. Gong, P. Cheng, Lattice Boltzmann simulation of periodic bubble nucleation, growth and departure from a heated surface in pool boiling, Int. J. Heat Mass Transfer 64 (2013) 122
132. T. Sun, W. Li, Three-dimensional numerical simulation of nucleate boiling bubble by lattice Boltzmann method, Computers Fluids 88 (2013) 400
409. T. Sun, W. Li, S. Yang, Numerical simulation of bubble growth and departure during flow boiling period by lattice Boltzmann method, Int. J. Heat Fluid Flow 44 (2013) 120
129. E. Sattari, M.A. Delavar, E. Fattahi, K. Sedighi, Numerical investigation the effects of working parameters on nucleate pool boiling, Int. Commun. Heat Mass Transfer 59 (2014) 106
113. A. Begmohammadi, M. Farhadzadeh, M.H. Rahimian, Simulation of pool boiling and periodic bubble release at high density ratio using lattice Boltzmann method, Int. Commun. Heat Mass Transfer 61 (2015) 78
87. Q. Li, Q.J. Kang, M.M. Francois, Y.L. He, K.H. Luo, Lattice Boltzmann modeling of boiling heat transfer: the boiling curve and the effects of wettability, Int. J. Heat Mass Transfer 85 (2015) 787
796. S. Gong, P. Cheng, Numerical simulation of pool boiling heat transfer on smooth surfaces with mixed wettability by lattice Boltzmann method, Int. J. Heat Mass Transfer 80 (2015) 206
216. S. Gong, P. Cheng, Lattice Boltzmann simulations for surface wettability effects in saturated pool boiling heat transfer, Int. J. Heat Mass Transfer 85 (2015) 635
646. T. Kunugi, Brief review of latest direct numerical simulation on pool and film boiling, Nucl. Eng. Technol. 44 (8) (2012) 847
854.

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CHAPTER

NUCLEATE BOILING

2

CHAPTER OUTLINE 2.1 MEMS Sensor Technology and the Mechanism of Isolated Bubble Nucleate Boiling ........................... 15 2.1.1 Introduction ............................................................................................................... 15 2.1.2 MEMS Sensor Technology in Boiling Research .............................................................. 17 2.1.2.1 Sensor Type and Performance ................................................................................17 2.1.2.2 Signal Conditioning .................................................................................................17 2.1.2.3 Sensor Design for Pool Nucleate Boiling..................................................................18 2.1.2.4 Sensor Calibration ..................................................................................................19 2.1.2.5 Experimental System and Conditions.......................................................................20 2.1.2.6 Calculation of Local Heat Flux.................................................................................20 2.1.2.7 Calculation of Wall Heat Transfer and Latent Heat in Bubble....................................21 2.1.3 Heat Transfer Mechanisms Revealed by MEMS Thermal Measurement ............................ 22 2.1.3.1 Bubble Growth Characteristics ................................................................................22 2.1.3.2 Phenomenological Model of Isolated Bubble Pool Boiling ........................................23 2.1.3.3 Fundamental Heat Transfer Phenomena Observed from Local Wall Temperature and Heat Flux ....................................................................................24 2.1.3.4 Microlayer Thickness..............................................................................................26 2.1.3.5 Characteristics of Wall Heat Transfer and Bubble Growth.........................................28 2.1.3.6 Effect of Wall Superheat on Boiling Heat Transfer ....................................................31 2.1.3.7 Continuous Bubble Boiling......................................................................................33 2.1.4 Conclusion ............................................................................................................. 33 2.2 Measurement of the Microlayer during Nucleate Boiling and its Heat Transfer Mechanism................. 36 2.2.1 Introduction ............................................................................................................... 36 2.2.2 Measurement of Microlayer Structure by Laser Extinction Method................................... 37 2.2.2.1 Experimental Apparatus and Method ......................................................................37 2.2.2.2 Initial Distribution of Microlayer Thickness...............................................................41 2.2.3 Measurement of Microlayer Structure by Laser Interferometric Method............................ 42 2.2.4 Basic Characteristics and Correlations Concerning the Microlayer in Nucleate Pool Boiling.............................................................................................. 44 2.2.5 Numerical Simulation on the Heat Transfer Plate during Boiling ..................................... 47 2.2.5.1 Heat Transfer Characteristics of the Microlayer in an Evaporation System.................48 2.2.5.2 Contribution of Microlayer Evaporation ....................................................................49 2.2.6 Numerical Simulation on the Two-Phase Vapor
Liquid Flow during Boiling ..................... 51 2.2.6.1 Variation in Microlayer Radius and Bubble Volume..................................................52 2.2.6.2 Temperature Distribution of Liquid in the Vicinity of the Bubble Interface .................54 2.2.6.3 Heat Transfer Characteristics of Microlayer Evaporation ...........................................55 Boiling. DOI: http://dx.doi.org/10.1016/B978-0-08-101010-5.00002-6 Copyright © 2017 Elsevier Ltd. All rights reserved.

13

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CHAPTER 2 NUCLEATE BOILING

2.2.6.4 Contribution of Microlayer Evaporation ....................................................................57 2.2.7 Conclusion ............................................................................................................. 58 2.3 Configuration of the Microlayer and Characteristics of Heat Transfer in a Narrow-Gap Mini-/Microchannel Boiling System................................................................................................. 60 2.3.1 Introduction ............................................................................................................... 60 2.3.2 Mechanisms and Characteristics of Boiling Heat Transfer in the Narrow-Gap Mini-/Microchannels ................................................................................................... 63 2.3.2.1 General Features of Boiling Phenomena in Narrow-Gap Mini-/Microchannels...........63 2.3.2.2 Configuration of the Microlayer in a Narrow-Gap Mini-/Microchannel Boiling System .......................................................................................................68 2.3.2.3 Consideration of Heat Transfer Characteristics on the Basis of Configuration of the Microlayer ........................................................................................................71 2.3.3 Characteristics of a Microlayer for Various Liquids and a Correlation of Microlayer Thickness in a Narrow-Gap Mini-/Micro-Boiling System.................................................. 73 2.3.3.1 Measurement of Microlayer Thickness for Various Test Liquids ................................73 2.3.3.2 Numerical Simulation of the Bubble Growth Process in the Microchannel ................75 2.3.3.3 Dimension Analysis and Correlation ........................................................................83 2.3.4 Conclusion................................................................................................................. 85 2.4 Surface Tension of High-Carbon Alcohol Aqueous Solutions: Its Dependence on Temperature and Concentration and Application to Flow Boiling in Minichannels ........................................................ 88 2.4.1 Introduction ............................................................................................................... 88 2.4.2 Surface Tension Measurements of High-Carbon Alcohol Aqueous Solutions ..................... 89 2.4.2.1 Method ..................................................................................................................89 2.4.2.2 Results...................................................................................................................93 2.4.2.3 Discussion .............................................................................................................97 2.4.3 Effect of High-Carbon Alcohol Aqueous Solutions on the Critical Heat Flux Condition in Boiling with Impinging Flow in a Minichannel ........................................................... 97 2.4.3.1 Method ..................................................................................................................97 2.4.3.2 Results.................................................................................................................100 2.4.3.3 Discussion ...........................................................................................................101 2.4.4 Conclusion............................................................................................................... 101 2.5 Nucleate Boiling of Mixtures......................................................................................................... 103 2.5.1 Mixture Effects on Elementary Processes of Nucleate Boiling ....................................... 103 2.5.1.1 Phase Equilibrium Diagram...................................................................................103 2.5.1.2 Boiling Incipience.................................................................................................104 2.5.1.3 Bubble Growth Rate .............................................................................................105 2.5.1.4 Bubble Departure.................................................................................................107 2.5.2 Heat Transfer Coefficient........................................................................................... 108 2.5.2.1 Predicting Method and Correlations ......................................................................108 2.5.2.2 Existing Topics for Mixture Boiling .........................................................................113 2.5.3 Experimental Investigation of the Marangoni Effect ..................................................... 114 2.5.4 Superior Heat Transfer Characteristics of Immiscible Mixtures...................................... 120 2.5.4.1 Objectives to Use Immiscible Mixtures ..................................................................120 2.5.4.2 Existing Research .................................................................................................120 2.5.4.3 Phase Equilibrium ................................................................................................121 2.5.4.4 Experimental Results ............................................................................................123

2.1.1 INTRODUCTION

15

2.5.5 Conclusions ............................................................................................................. 126 2.6 Bubble Dynamics in Subcooled Flow Boiling .................................................................................. 131 2.6.1 Introduction ............................................................................................................. 131 2.6.2 Review of the Subcooled Flow Boiling Models ............................................................. 131 2.6.2.1 Overview ..............................................................................................................131 2.6.2.2 Heat Transfer Models ...........................................................................................133 2.6.2.3 Models for Void Fraction Evolution and Phase Change Rates .................................135 2.6.3 Bubble Dynamics in Subcooled Flow Boiling............................................................... 136 2.6.4 Conclusion............................................................................................................... 140

This chapter deals with topics on nucleate boiling in aspects of heat transfer mechanisms based on both recently developed measurement techniques and new ideas from each authors’ research in recent decades. The first three sections report on nucleate boiling heat transfer mechanisms in microscopic view revealed through well-arranged developments of measurement techniques. Section 2.1 demonstrates nucleate boiling heat transfer mechanisms for the isolated bubble region based on measurement results obtained by MEMS sensor for local surface temperature. Sections 2.2 and 2.3 report on measurement results of microlayer thickness in pool boiling or narrow-gap mini-/microchannel boiling systems, which are considered to play important roles in nucleate boiling heat transfer, through laser extinction and laser interferometric methods. The following three sections cover other aspects of nucleate boiling mechanisms. Section 2.4 reports on the effects of temperature and concentration on surface tension of high-carbon alcohol aqueous solutions, which leads to applications of flow boiling in minichannels. Section 2.5 covers mixture boiling, particularly focusing on superior heat transfer characteristics when immiscible mixtures are used as coolants under specified conditions. The last section (Section 2.6) discusses subcooled nucleate flow boiling from viewpoints of bubble dynamics such as bubble size and trajectory after departure from the nucleation site.

MEMS SENSOR TECHNOLOGY AND THE MECHANISM OF ISOLATED BUBBLE NUCLEATE BOILING

2.1

Tomohide Yabuki1 and Osamu Nakabeppu2 1

Kyushu Institute of Technology, Kitakyushu, Japan 2Meiji University, Tokyo, Japan

2.1.1 INTRODUCTION Microelectromechanical systems (MEMS) sensors open a way for better understanding of the mechanisms involved in boiling heat transfer. Here we introduce the use of MEMS sensor

16

CHAPTER 2 NUCLEATE BOILING

technology for boiling research and illustrate the heat transfer mechanisms present in isolated bubble nucleate boiling of water based on our research [1,2]. In the 1960s, Moore and Mesler [3] and Cooper and Lloyd [4] introduced high-resolution thermometers as a powerful tool to explore boiling heat transfer mechanisms. They demonstrated the presence of the thin liquid film below a nucleate boiling bubble called the microlayer, through the measurement of the local wall temperature below the single bubbles using tiny temperature sensors. Recent development of high-resolution measurement techniques such as the MEMS sensor [1,2,5
7] and the high-speed infrared (IR) camera [8
12] permits more precise measurement of the fundamental heat transfer phenomena in the boiling heat transfer which conventional diagnostics cannot grasp, such as evaporation and dry-out of the microlayer [4], threephase contact line heat transfer [13], and the rewetting heat transfer [5
7]. The highly resolved measurement result is considered useful not only for exploring heat transfer mechanisms but also for the verification of numerical simulations of the boiling heat transfer. Studies on mechanisms in the single bubble nucleate boiling using the high-resolution diagnostics are well reviewed by Kim [14]. In most microscale studies on the boiling heat transfer mechanisms using the MEMS sensor and the high-speed IR camera, the heat transfer is quantified through the transient heat conduction calculation using the measured temperature. Thus, the boundary condition at the surface is required to be appropriately constructed from the measured surface temperatures. The high-speed IR camera has an advantage of being able to measure a two-dimensional surface temperature distribution, and therefore the measurement result is easily converted to the surface boundary condition. The MEMS sensor is superior in temporal resolution but is inferior in number of the measurement points (sensors) with respect to the IR camera. Thus, in studies with MEMS sensors, the construction of the surface boundary condition requires devising the sensor arrangement. In our study, we set a target to elucidate the heat transfer mechanisms in isolated bubble boiling, where the bubble has high symmetry and the two-dimensional axisymmetric coordinate system is applicable in the heat transfer analysis using local temperatures measured with temperature sensors arranged discretely in a straight line. Water was selected as the boiling liquid in this study since there are few microscale experimental data for it and it has many applications as a refrigerant in heat exchangers. The outline of the authors’ boiling study with the MEMS sensor is as follows. First, local temperature variation on a heated wall beneath a boiling bubble nucleated by a triggering device under a controlled condition and timing is measured by introducing thin-film temperature sensors placed in a straight line around the triggering device. Then, local heat flux distribution at the wall surface is derived through the axisymmetric transient heat conduction simulation in the heating wall using the measured surface temperatures as a boundary condition. In addition, the latent heat stored in the bubble is measured from high-speed video images of the bubble. From the data for wall heat transfer and bubble growth, we investigate boiling characteristics, such as evaporation and formation characteristics of microlayer, and the contribution of microlayer evaporation to bubble growth.

2.1.2 MEMS SENSOR TECHNOLOGY IN BOILING RESEARCH

17

2.1.2 MEMS SENSOR TECHNOLOGY IN BOILING RESEARCH 2.1.2.1 SENSOR TYPE AND PERFORMANCE In the case of a MEMS sensor fabricated on a substrate, a thin-film thermocouple (TC) and a resistance temperature detector (RTD) can usually be used to measure the temperatures at the substrate surface. The two types of sensors have different characteristics and merits, thus it is important to use them to complement each other. The TC measures the temperature difference between a sensing junction and a reference junction. Calibration of the TC is an important process to obtain an accurate result and requires a special design of the sensor, because both sensing and reference junctions are located on the same substrate. The spatial resolution is limited to the size of the sensing junction, which can be as small as 10 μm based on laboratory-grade microfabrication. A DC amplifier and a low-pass filter are usually employed to condition a raw TC signal. On the other hand, the RTD can measure absolute temperature from electrical resistance. To calibrate it, the temperature coefficient of resistance is measured during a slow temperature scan inside a box including the RTD. A sensing area of the RTD tends to be larger than that of the TC to obtain a practicable resistance of the 100-Ω level. In addition, the RTD requires four electrodes to measure the accurate resistance. Therefore the RTD occupies a wider area on the substrate and is inferior in spatial resolution compared with the TC. The authors’ thin-film sensor on a silicon substrate with silicon oxide layers has a response time of 10 μs. The temperature resolution is about 0.05 K, based on a noise level of 1.5 μV for the TC sensors. The heat flux resolution converted from the surface temperature data through the transient heat conduction simulation was 28 kW/m2. These values are enough to observe the heat transfer mechanisms of single bubble boiling. Although the MEMS sensor has a high spatial and temporal resolution, a thin-film sensor fixed on a substrate usually requires a phenomenon of interest to occur on the sensor. In boiling studies using a MEMS sensor, the thin-film sensor requires a boiling bubble to grow on the sensor. Thus, the authors’ group developed a unique device called an electrolysis trigger for generating a bubble at a controlled position and time on the MEMS sensor. The electrolysis trigger comprising two Ni electrodes can supply a tiny hydrogen bubble as a bubble nucleus with electrolysis of water by a Gaussian voltage pulse. Typically, 20 pJ of thermal energy is supplied by the voltage pulse of 8 V amplitude and 2 ms width, which is much smaller than the latent heat of the boiling bubble of 1 mm diameter [1].

2.1.2.2 SIGNAL CONDITIONING The thermoelectric voltage of a micro-volt range output by the thin-film TC on the MEMS sensor includes a relatively large electrical noise because of its higher electric resistance than ordinary wire-type TCs. Thus the TC signal should be amplified and passed through a low-pass filter. We used a homemade circuit including an instrumentation amplifier (e.g., AD620) of 1000-fold gain and a low-pass filter of 12.5 kHz cut-off frequency to record the TC signal by the A/D board at a sampling frequency of 50 kHz.

18

CHAPTER 2 NUCLEATE BOILING

FIGURE 2.1.1 MEMS sensor for boiling research: (A) topside, (B) backside, (C) arrangement of TCs, RTDs, and electrolysis trigger, (D) magnified photograph of center part on topside, and (E) sensing junction of TC and electrolysis trigger [2].

The RTD is usually driven by a bridge circuit, but the nonlinearity of the output voltage against a resistance change cannot be ignored for large temperature changes of over 10 K. We employed a constant current circuit using a voltage reference IC (e.g., LM385-ADJ) and measured voltage drop across the RTD. The resistance of the RTD can be calculated from the voltage drop and the driving current.

2.1.2.3 SENSOR DESIGN FOR POOL NUCLEATE BOILING Fig. 2.1.1 shows photographs of the MEMS sensor fabricated using the photolithography technique for the patterning of the sensor design and magnetron sputtering for film deposition. The substrate is a 180-μm-thick silicon wafer with a size of 32 mm 3 32 mm. It has a thermally grown SiO2 insulation layer of 2-μm thickness on both sides. The silicon has metal level high thermal conductivity of 116 W/m2K at 100 C. The sensor has the electrolysis trigger at the center, 11 Ni
Cr thin-film TCs, and 2 Ni four-wire RTDs (called RTDS). Copper leads are connected to the pads placed in a margin of the substrate using a silver paste. The wired pads act as reference junctions of the TCs. Therefore the TCs indicate the temperature difference between the sensing junctions in the central region and the reference junctions. The temperature variations at the reference junctions during a fast boiling event are negligible, and therefore the

2.1.2 MEMS SENSOR TECHNOLOGY IN BOILING RESEARCH

19

signals of the TCs correspond to the temperature variations at sensing junctions. The RTDS was used for measuring the wall superheat as an experimental parameter. The distances of the temperature sensors from the electrolysis trigger range from 50 to 2500 μm as shown in Fig. 2.1.1C. The sensor sizes of the TC and the RTDS corresponding to those spatial resolutions are 20 μm 3 40 μm and 63 μm 3 205 μm, respectively. The two RTDSs were used in both the experiment and the calibration of the TCs. In addition, another two RTDs of two-wire type located in the margin of the substrate (called RTDR) were used in the calibration process of the TCs to measure the reference junction temperature. Two chromium thin-film heaters of 8 mm 3 8 mm were sputtered on the backside. In the final fabrication process of each surface, a B1-μm-thick silicon dioxide layer was sputtered for electric insulation except at the trigger point. The static contact angle between a water droplet and the sputtered SiO2 surface is between 10 and 15 degrees, when measured just after a wash treatment with ethanol, acetone, and water.

2.1.2.4 SENSOR CALIBRATION First, the temperature coefficients of the RTDS and RTDR were calibrated by setting the sensor in a small aluminum box with a stirrer placed on a hotplate. After the air temperature in the box reached 120 C by the heating of the hotplate, the relationships between the resistances of the RTDs and air temperature were collected during the cooling process. The thermoelectric power α of the TCs was then calibrated as shown in Fig. 2.1.2. The backside heater generates temperature differences between the sensing and reference junctions of the TCs. The thermoelectric power was calibrated by measuring the sensing junction temperature Ts by the RTDS at 600 μm, the reference one Tr by the RTDR, and the electromotive force VTC of the TCs at 400 and 800 μm nearest to the RTDS. The resultant thermoelectric power was 28.4
29.7 μV/K, which is about 70% of the standard Ni
Cr TC. The thin-film TC made by the microfabrication process often shows a disagreement in the thermoelectric power with the bulk TC, thus the calibration process is essential and the design enabling the calibration process is important for the accurate measurement. An average sensitivity of the two TCs 29.1 μV/K was used for the temperature conversion of the signals from all the TCs because it is known empirically that the TCs simultaneously fabricated have almost the same sensitivity.

FIGURE 2.1.2 Calibration method of thermoelectric power of thermocouple [2].

20

CHAPTER 2 NUCLEATE BOILING

FIGURE 2.1.3 Schematic of the experimental apparatus.

2.1.2.5 EXPERIMENTAL SYSTEM AND CONDITIONS Fig. 2.1.3 shows a schematic of the experimental system, which can synchronize the bubble generation using the electrolysis trigger and recording of the bubble behavior and temperature signals by an electric pulse from a function generator. The TC and RTD signals were collected at 50 kHz, and the bubble behavior was captured with a high-speed camera at 4000 frames per second (fps). The test chamber made by bonding the MEMS sensor and an optical glass cell has an inner crosssectional area of 10 mm 3 10 mm. The boiling liquid is distilled water. The liquid was heated to the saturation temperature by a wire heater wound on the glass cell and a temperature control unit, and then the heating of the backside heater was started. The wall superheat was controlled by changing the heating rate of the backside heater. The experimental data were collected at a wall superheat ranging from about 8 K to 15 K under saturation conditions. The range of the base heat flux q_b was 30
39 kW/m2, which corresponded to the isolated bubble region in the general boiling curve for the boiling of water on a horizontal copper surface [15]. The resultant maximum bubble radius was 1.2
3.3 mm.

2.1.2.6 CALCULATION OF LOCAL HEAT FLUX The local wall temperature under an isolated bubble is first measured using the experimental setup shown above. Then, the wall heat transfer is calculated by a transient heat conduction simulation using the measured wall temperature as a boundary condition. The cylindrical coordinate system (r 3 z) was applied in the simulation since the data was axially symmetric. Temperature distributions were constructed using the temperatures measured with the sensors on the left and right sides across the electrolysis trigger. The symmetry of the temperature distribution under the isolated bubble was confirmed from the temperatures measured by the sensors on the right and left sides. The transient boundary condition data at the surface (z 5 0) was developed by

2.1.2 MEMS SENSOR TECHNOLOGY IN BOILING RESEARCH

21

FIGURE 2.1.4 Calculated temperature variation distribution and local heat flux from heated surface.

the spatial interpolation of the measurement data, in which the local wall temperatures measured on the left side were transferred to the right side. The calculation domain had dimensions 5 mm (r) 3 185 μm (z) and consisted of the silicon substrate and the SiO2 insulation layers on the both surfaces. The isothermal condition and adiabatic condition were applied on the other boundaries at r 5 5 mm and z 5 185 μm, respectively. The time-step is 20 μs corresponding to the measurement period of the wall temperature, and the mesh size adjacent to the surface (z 5 0) is B0.5 μm in the z direction. This heat transfer analysis calculated the temperature distribution variation from just before bubble nucleation in the heating wall ΔT ðr; z; tÞ, and thus the local wall heat flux variation Δq_ðr; tÞ was calculated using the gradient of the calculated temperature variation in the z direction at z 5 0. The initial temperature variation ΔT ðr; z; tÞ was uniformly set at zero. The actual heat flux q_ðr; tÞ was calculated by summing the variation Δq_ðr; tÞ and the base heat flux q_b . Fig. 2.1.4 shows the calculated temperature distribution in the heating wall and the local heat flux from the surface at 3.5 ms after bubble nucleation. The heat flux distribution clearly indicates that the dry-out of the surface occurred at r , 200 μm and the microlayer strongly evaporated outside the dry-patch. The maximum evaporative heat flux of the microlayer exceeded 1 MW/m2. As described later, the microlayer, dry-out, and the rewetting can be well understood from the measured local wall temperature and the calculated local heat flux.

2.1.2.7 CALCULATION OF WALL HEAT TRANSFER AND LATENT HEAT IN BUBBLE The wall heat flow Q_ w was calculated by spatially integrating the local heat flux q_ within the maximum bubble radius Rmax, and the wall heat Qw was calculated by temporally integrating the wall heat flow Q_ w over the elapsed time. The latent heat in the bubble Qb was calculated using the bubble volume Vb extracted from the bubble image. Here, ρv and hlv denote the density of the vapor and the latent heat of vaporization, respectively. Q_ w ðr; tÞ 5 2π

ð Rmax

_ tÞdr r qðr;

(2.1.1)

0

Qw ðtÞ 5

ðt

0

Q_ w ðtÞdt

(2.1.2)

22

CHAPTER 2 NUCLEATE BOILING

Qb ðtÞ 5 ρv hlv Vb ðtÞ

(2.1.3)

We also calculated a microlayer heat flow Q_ ml and a microlayer heat Qml to evaluate the contribution of microlayer evaporation to wall heat transfer and bubble growth. The microlayer heat flow Q_ ml is derived by integrating the local heat flux within the apparent contact radius Rc (microlayer formation radius), and the microlayer heat Qml is derived by integrating the microlayer heat flow within the elapsed time from the nucleation, as shown in Eqs (2.1.4) and (2.1.5), respectively. The apparent contact radius corresponding to the radius of the bubble base was extracted from the bubble image. As a result, the Qml is almost the same as Qw. This indicates that the microlayer evaporation plays the most important role in the wall heat transfer beneath the isolated bubble boiling of water. Q_ ml ðtÞ 5

ð Rc ðtÞ

qðr; _ tÞdA 5 2π

0

Qml ðtÞ 5

ðt

ð Rc ðtÞ

r qðr; _ tÞdr

(2.1.4)

0

Q_ ml ðtÞdt

(2.1.5)

0

2.1.3 HEAT TRANSFER MECHANISMS REVEALED BY MEMS THERMAL MEASUREMENT 2.1.3.1 BUBBLE GROWTH CHARACTERISTICS The equivalent bubble radius Req 5 (3Vb/4π)1/3 for all wall superheat conditions in our experiment was plotted against time in Fig. 2.1.5. The bubble volume Vb was calculated by extracting a bubble contour from the high-speed video. Bubble growths calculated with the model of Mikic et al. [16] for the maximum and minimum wall superheats are also shown. The experimental result showed

FIGURE 2.1.5 Bubble growth in isolated pool boiling of water (ΔTsat 5 8
15 K, Rmax 5 1.2
3.6 mm) [2].

2.1.3 HEAT TRANSFER MECHANISMS

23

that the bubble radius is proportional to t0.6 until 3
5 ms after nucleation begins, and then is proportional to t0.1. The growth in the early to middle stages agrees with the model of Mikic et al., considering the liquid inertia and thermal diffusion in the semi-infinite superheated liquid around the bubble. The slowdown of the growth in the middle to final stages reflects the consumption of the enthalpy in the superheated liquid around the bubble with finite thickness. The largest bubble generated at the highest wall superheat condition shows the same growth trend as other smaller bubbles. This means that the bubbles grew without significant influence from the side walls of the test chamber.

2.1.3.2 PHENOMENOLOGICAL MODEL OF ISOLATED BUBBLE POOL BOILING Since a study by Cooper and Lloyd [4], the mechanisms of the bubble growth in pool boiling has been understood by the phenomenological model, in which the bubble is grown by evaporation of the superheated liquid surrounding the bubble and also the microlayer beneath the bubble. Fig. 2.1.6 shows a schematic of the heat transfer phenomena during a bubble cycle. After bubble nucleation, the growing bubble pushes away the surrounding liquid. In this bubble growth process, a small amount of liquid is left on the heated wall, forming a thin liquid film called the microlayer (Fig. 2.1.6A). The microlayer evaporates vigorously because of its low thermal resistance in the thickness direction. Then, dry-out occurs and the dry-patch spreads from the center by the complete evaporation of the microlayer (Fig. 2.1.6B). After that, in the bubble departure process, the contact area shrinks as the bubble extends longitudinally as shown in Fig. 2.1.6C. In this process, the dryout area is rewetted by the liquid flowing towards the bubble’s foot. After the bubble departs, the bubble moves upward with accompanying flow, and the liquid is gathered from the periphery to the nucleation site (Fig. 2.1.6D). A similar bubble cycle was captured experimentally. As shown in Fig. 2.1.7, the bubble rapidly grows in a horizontally long oval
spherical shape at an early stage, and then the contact area shrinks as the growth rate decreases and the center of gravity moves upward. Finally, the bubble departs from the wall and rises in the liquid.

FIGURE 2.1.6 Fundamental heat transfer phenomena under an isolated boiling bubble.

24

CHAPTER 2 NUCLEATE BOILING

FIGURE 2.1.7 Typical isolated boiling bubble in the test chamber.

FIGURE 2.1.8 Bubble behavior and local wall temperature under the isolated bubble (ΔTsat 5 10.8 K, Dmax 5 4.4 mm) [2].

2.1.3.3 FUNDAMENTAL HEAT TRANSFER PHENOMENA OBSERVED FROM LOCAL WALL TEMPERATURE AND HEAT FLUX From the local wall temperature measured by the MEMS sensor, we can precisely observe the fundamental heat transfer phenomena under a bubble included in the scenario of the bubble growth model (Fig. 2.1.6). From the wall heat transfer calculated from the measured temperature, we can quantitatively discuss the mechanisms of the wall heat transfer and the bubble growth. It is historically meaningful that the features of the fundamental phenomena in the isolated bubble boiling were clearly demonstrated using the MEMS measurement technique. Fig. 2.1.8 shows the measured local wall temperature and the captured bubble images for ΔTsat 5 10.8 K. The maximum bubble diameter Dmax was 4.4 mm. The evaporation and dry-out of

2.1.3 HEAT TRANSFER MECHANISMS

25

the microlayer and the rewetting of the dry-patch can be observed in the measured temperature, and the timings of those heat transfer phenomena are indicated in the figure. Just after the bubble nucleation, the temperature near the center suddenly drops and then turns to increase after a negative peak. The sudden drop corresponds to the formation of the microlayer and its vigorous evaporation with a very high heat transfer coefficient. The minimum point shows the onset of the dry-out with almost zero heat transfer coefficient. The similar temperature variation travels from the center toward outside, which indicates the spreading of the microlayer and drypatch in the radial direction from the center. In particular, the temperature re-decreased even in the dry-out state at 50 and 100 μm. This is due to the transient heat conduction in the wall from the dried inside area to the outer microlayer evaporation area. After the minimum point, the bubble enters the departure process. Here, the contact area shrinks as the bubble extends longitudinally, and the dry-out area is rewetted by the liquid flowing from the outside of the bubble foot. Small negative peaks traveling from outside to inside in the temperature recovering process show the momentary heat transfer enhancement by the rewetting. At 1000 μm, where the microlayer was formed but not dried out, the temperature starts to increase after the passage of the advancing apparent contact line in the bubble departure process. After the bubble departure, the temperature slowly recovers to the level before the nucleation. The convection caused by the rising bubble does not look having a significant effect on wall heat transfer. Fig. 2.1.9 shows spatial distributions of the wall temperature measured under a different wall superheat. In this case, the bubble departed at 22.5 ms. The temperatures measured on the right and left sides of the trigger were plotted in this figure, and are shifted with a negative offset at each time. At 0.1 ms from the bubble nucleation, the surface temperature at r , 200 μm was decreased by the formation and evaporation of the microlayer. At 1 ms, the microlayer expanded to 1000 μm, and the wall surface at r , 200 μm was already dried out. The dry-out region expanded to rB400 μm at 3 ms. The minimum temperature point advancing outward with time until 15 ms corresponds to the intensive evaporation near the threephase contact line of the microlayer. After the bubble departure, the temperature of the wall surface slowly returned to the level before the nucleation. The temperature recovery took about 1 s in this case. The progress of the heat transfer phenomena included in the model (Fig. 2.1.6) was successfully confirmed from the temperature distribution obtained by the high-resolution measurement with the MEMS sensor. Additionally, the symmetry of the heat transfer phenomena was confirmed from this smooth temperature distribution. This is the basis of what we can apply the axisymmetric cylindrical coordinate system in the heat transfer analysis. Fig. 2.1.10 shows the spatiotemporal distributions of the measured local wall temperature and the local heat flux calculated by the transient heat conduction analysis. The bubble radius and the apparent contact radius are also shown in both color maps. The wall temperature decrease advances outward with the expansion of the microlayer formation area. High heat flux over 1 MW/m2 comparable to the normal critical heat flux (CHF) of water pool boiling can be observed within the apparent contact area corresponding to the microlayer formation area. Since the formed microlayer becomes thinner towards the bubble center, the maximum heat flux increases with decreasing distance from the nucleation site. The maximum heat flux was 2.8 MW/m2 for this data. The velocity of the vapor generated from the microlayer surface at the

26

CHAPTER 2 NUCLEATE BOILING

FIGURE 2.1.9 Radial wall temperature distribution beneath the bubble (ΔTsat 5 14.5 K, Dmax 5 6 mm). The axial symmetry is confirmed by the smooth distribution of the measured temperature on the left and right sides.

maximum heat flux is calculated as B2 m/s. This means there is fast vapor flow inside the bubble with a diameter of the millimeter order. The maximum heat flux was found to increase linearly with increasing wall superheat: e.g., it reached 3.9 MW/m2 at the maximum wall superheat in our study of 15.3 K. The dry-patch with almost zero heat transfer appeared from 1 ms at the bubble center and expanded to 600 μm. Although the temperature outside the apparent contact area decreased, the heat transfer enhancement cannot be seen in the heat flux distribution. This means that the temperature decrease observed outside the contact area was induced not by the wall
liquid heat transfer but by the transient heat conduction inside the wall between the microlayer formation area and the outside of the microlayer.

2.1.3.4 MICROLAYER THICKNESS Information about the microlayer thickness is important for exploring the heat transfer mechanisms and constructing the mechanistic model of nucleate boiling heat transfer. Here, the microlayer thickness at the moment of the formation at an arbitrary radial position, r, which is called initial

2.1.3 HEAT TRANSFER MECHANISMS

27

FIGURE 2.1.10 Spatiotemporal distributions of surface temperature (left) and local heat flux (right) (ΔTsat 5 10.8 K, Dmax 5 4.4 mm) [2].

microlayer thickness, was calculated using the local heat flux. Considering the 1D heat transfer in the thickness direction, the energy balance between the heat transferred from the surface, sensible heat initially stored in the thin liquid film and evaporative latent heat needed for complete evaporation of the microlayer is given by ð tme

_ tÞdt 1 δ0 ðrÞρl cl ΔTðrÞ 5 δ0 ðrÞρl hlv qðr;

(2.1.6)

0

where tme is the microlayer evaporation duration, ρl is the liquid density, cl is the specific heat of the liquid, ΔT is the average superheat in the microlayer, hlv is the latent heat of evaporation, and δ0 is the initial microlayer thickness. The sensible heat in the microlayer which is the second term on the left-hand side is negligible, and so the initial microlayer thickness can be expressed by Eq. (2.1.7). δ0 ðrÞ 5

ð tme

_ tÞdt=ρl hlv qðr;

(2.1.7)

0

Fig. 2.1.11 shows the calculated spatial distribution of the initial microlayer thickness. Since the microlayer evaporation duration can be extracted from the local wall temperature data, the initial thickness was calculated only at the sensor positions. The initial microlayer thickness increases

28

CHAPTER 2 NUCLEATE BOILING

FIGURE 2.1.11 Spatial distribution of initial microlayer thickness.

with increasing the distance from the bubble nucleation site. Fig. 2.1.11 also shows the correlation equation of Utaka et al. [17] obtained by an optical measurement method called the laser extinction method. Our results show good agreement with the correlation equation by Utaka et al. This supports the validity of our result. An interesting tendency is observed in the relation between thickness and wall superheat. The bubble growth rate and the formation velocity of the microlayer increase with increasing wall superheat, and the microlayer thickness increases at higher wall superheat. This trend opposes the boundary layer model of the microlayer formation process proposed by Cooper and Lloyd [4]. Unfortunately the relationship between the thickness and the hydrodynamic parameters (e.g., formation velocity, physical properties of liquid) remains unclear. The investigation of the hydrodynamic mechanisms of the microlayer formation will be an important task in future work. At present, we propose an approximate profile of the initial microlayer thickness expressed by Eq. (2.1.8) as a function of the distance r [mm]: δ0 5 4:66r 0:69 ðμmÞ

(2.1.8)

2.1.3.5 CHARACTERISTICS OF WALL HEAT TRANSFER AND BUBBLE GROWTH In this section, we will discuss the contributions of heat transfer phenomena to bubble growth or overall wall heat transfer in the isolated bubble boiling of water. Figs. 2.1.12 and 2.1.13 show the measured wall temperature and the result of heat transfer evaluation for low and high wall superheat conditions in our experiment, respectively. In Fig. 2.1.12 for the low wall superheat, the wall heat transfer Q_ w was increased by microlayer evaporation, and reached a maximum of B1.2 W. Then the dry-out of the microlayer resulted in the decrease of the wall heat transfer to the level before the nucleation by 6 ms when the bubble growth was almost stopped. The increase in wall heat transfer due to the rewetting at 13
15 ms

2.1.3 HEAT TRANSFER MECHANISMS

29

FIGURE 2.1.12 Local temperature and wall heat flow at relatively low wall superheat (ΔTsat 5 8.1 K, Dmax 5 2.8 mm) [2].

was much smaller than that due to the microlayer evaporation. The wall heat Qw steeply increased during the microlayer evaporation, and then the increase rate became small due to spread of the dry-patch. Comparing Qw with Qb, both increased in a similar manner from the nucleation to the departure, and the ratio Qw/Qb is about 50%. In Fig. 2.1.13 for the high wall superheat, the qualitative behaviors of the wall heat transfer and the bubble growth are similar to the behaviors for the low wall superheat, though the bubble growth time became longer. The microlayer evaporation caused a significant increase in wall heat transfer, and the bubble growth rate dQb/dt is small in the bubble departure process. The time evolutions of Qw and Qb are analogous and the ratio Qw/Qb is about 50% as with the case at the low wall superheat.

30

CHAPTER 2 NUCLEATE BOILING

FIGURE 2.1.13 Local temperature and wall heat flow at relatively high wall superheat (ΔTsat 5 15.3 K, Dmax 5 7.2 mm) [2].

Moreover, any remarkable heat transfer increase was not observed after the bubble departures in the authors’ experiment. The forced convection induced by the rising bubble (Rohsenow’s model [18]) and the transient heat conduction within the liquid layer flowing to the heated surface after the bubble departure (Han and Griffith’s model [19]) have negligible effect on the wall heat transfer, at least in our experimental system. Fig. 2.1.14 shows the temperature field of the liquid phase around an isolated boiling bubble (details of the experimental method are described in Ref. [20]). Although we can obviously see the wake of the superheated liquid below the departed bubble, the heat transfer enhancement effect of the convection and the transient heat conduction was not detected in our experiment. Demiray and Kim [5] pointed out from a boiling experiment of FC72 that the rewetting phenomenon produced a larger heat transfer than the microlayer evaporation in contrast to our result. The modified Jacob number Ja 5 cl ΔTsat =hlv is helpful [14] in predicting which is important: the sensible heat transfer (rewetting heat transfer and convective heat transfer) or the latent heat transfer (microlayer

2.1.3 HEAT TRANSFER MECHANISMS

31

FIGURE 2.1.14 Temperature field of liquid phase around an isolated bubble in saturated boiling visualized by laser interferometry.

evaporation). The Ja 5 0.34 in the case of Demiray and Kim, whereas Ja 5 0.014
0.028 in our case. Because of the relatively small Ja, the latent heat transfer with the microlayer evaporation is dominant in the wall heat transfer in the case of the isolated bubble pool boiling of water. To summarize, by the use of the MEMS sensor, the spatiotemporal distributions of the temperature and the surface heat flux from the nucleation through the growth and departure to the rising of the bubble were quantitatively evaluated, and the scenario of the heat transfer from the wall surface to the bubble was understood in detail. Microlayer evaporation was indicated to be the dominant heat transfer mechanism of the wall heat transfer in the isolated bubble boiling of water.

2.1.3.6 EFFECT OF WALL SUPERHEAT ON BOILING HEAT TRANSFER The experiment was conducted at a wall superheat of 8
15 K as described above. Some values, as indices featuring the isolated bubble boiling of water, were summarized against wall superheat. Fig. 2.1.15 shows the maximum equivalent bubble radius Req,max, maximum radii of the microlayer region Rml and dry-out region Rdry-out, and the time until bubble departure tdp. The maximum radii of the microlayer region Rml and dry-out region Rdry-out were read from the local wall temperature data, and their error bars show the uncertainty resulting from the discrete location of the temperature sensors. Since wall superheat is the driving force to evaporate the microlayer, Req,max and Rdry-out increase with increasing wall superheat. The increase of the bubble size Req,max results in an increase of the microlayer radius Rml. Also, a larger bubble generated at a higher wall superheat takes a longer time to depart from the wall. Fig. 2.1.16 shows the microlayer evaporation heat Qml, the latent heat in the bubble Qb, and the contribution of microlayer evaporation to bubble growth Qml/Qb plotted against wall superheat. The microlayer evaporation heat Qml and the latent heat Qml increased with an exponent of power 4.3 and of power 4.1 to wall superheat, respectively, as shown in Eqs (2.1.9) and (2.1.10). Although both values indicate nonlinearity with wall superheat, the contribution of the microlayer evaporation to the bubble growth is around the averaged value of 44% and is almost constant with wall superheat. This finding also indicates that the remaining 56% of the latent heat was supplied by the evaporation of the superheated liquid layer surrounding the bubble.

32

CHAPTER 2 NUCLEATE BOILING

FIGURE 2.1.15 Characteristic parameters of the isolated bubble pool boiling of water against wall superheat (time until bubble departure tdp, maximum bubble radius Rmax, radius of microlayer region Rml, and radius of microlayer region Rdry-out).

FIGURE 2.1.16 Contribution of microlayer evaporation to bubble growth.

Consistency of correlation equations displayed in Fig. 2.1.15 and Eq. (2.1.9) was examined below by estimating the volume of the evaporated microlayer Vml ~ Qml . From the radius of microlayer region RmlBΔTsat1.8 in Fig. 2.1.15 and the profile of the microlayer δ0Br0.69 in Eq. (2.1.8), the microlayer thickness averaged within the formation area δ can be expressed as

2.1.4 CONCLUSION

33

δBΔTsat1.24. The possible minimum volume of the evaporated microlayer Vml,min would be proportional to ΔTsat3.16 from the relation Vml,minBRdry-out2 3 δ, whereas the possible maximum volume of the evaporated microlayer Vml,max would be proportional to ΔTsat4.84 from the relation Vml,maxBRml2 3 δ. The exponent of ΔTsat in Eq. (2.1.9) lies between 3.16 (a conservative estimate) and 4.84 (a liberal estimate), and thus the consistency of the correlations in Fig. 2.1.15 and Fig. 2.1.9 was confirmed. Therefore, the correlation equations in Figs. 2.1.15 and 2.1.16 are considered useful for evaluating numerical simulation results or other experimental studies. 4:3 Qml 5 7:2 3 1024 ΔTsat ðmJÞ 23

Qb 5 2:7 3 10

4:1 ΔTsat

ðmJÞ

(2.1.9) (2.1.10)

2.1.3.7 CONTINUOUS BUBBLE BOILING Although this work mostly collected data for the isolated bubble boiling, we also obtained some data for continuous bubble boiling. Fig. 2.1.17 shows the data for a case of four continuous bubble generations. The heat transfer evaluation was performed to first three bubbles because the symmetry of the temperature distribution was lost for the fourth bubble generated just after the departure of the third bubble. The maximum bubble diameter and the wall superheat sequentially decreased with bubble generations because the enthalpy in the wall and the superheated liquid layer was consumed by a departed preceding bubble. The tendency of the temperature variation and the heat transfer for the second and third bubbles are similar with those for the perfectly isolated first bubble; the temperature steeply dropped and the microlayer evaporation heat flow largely increased during the microlayer evaporation. Comparing the microlayer heat Qml and the latent heat Qb in the bubble at the bubble departure, the contributions of the microlayer evaporation Qml/Qb for the three bubbles were 51%, 36%, and 52%, respectively. Though an increase in contribution of the superheated liquid layer evaporation (Qb 2 Qml)/Qb could be expected from the visualization result shown in Fig. 2.1.14, where the superheated liquid was accumulated near the nucleation site by departure and rising of a previous bubble, there was not a significant difference in Qml/Qb between the isolated first bubble and the later bubbles.

2.1.4 CONCLUSION The availability of the MEMS thermal measurement technique for studying the isolated bubble nucleate pool boiling of water was described. The physical mechanisms of the boiling phenomena were investigated in detail through the local wall temperature measurement, the high-speed recording of bubble behavior, and the quantitative evaluation of the local wall heat transfer using the MEMS sensor, a high-speed video camera and the transient heat conduction simulation. The obtained findings are as follows:

34

CHAPTER 2 NUCLEATE BOILING

FIGURE 2.1.17 Measured wall temperature (upper) and contribution of microlayer evaporation to bubble growth (bottom) in continuous bubble generation boiling (1st bubble: ΔTsat 5 14.5 K,，Dmax 5 6 mm, 2nd bubble: ΔTsat 5 12 K,， Dmax 5 5.7 mm,，3rd bubble: ΔTsat 5 11.9 K,，Dmax 5 3.7 mm).

•

•

•

•

The developed MEMS sensor has a unique trigger device for bubble nucleation, called an electrolysis trigger. These micro-temperature sensors have a spatial resolution of at minimum 20 μm 3 40 μm and a time response of B10 μs. The fundamental heat transfer phenomena below the isolated boiling bubble, including evaporation and dry-out of the microlayer and the rewetting phenomenon of the dry-patch, were precisely observed through the local wall temperature measurement using the MEMS sensor. The evaporative local heat flux of the microlayer is over 1 MW/m2, which is comparable with the CHF in the general saturated pool boiling of water. The spatial distribution of the initial microlayer thickness was calculated from the local wall heat flux distribution. The microlayer evaporation plays the dominant role, and the rewetting in the bubble departure process and the forced convection induced by the rising bubble play the minor role in the wall heat transfer.

REFERENCES

•

35

The isolated bubble is grown by the evaporation of both the microlayer and the superheated liquid layer around it in the early to middle stages of the bubble growth process. The contribution of the microlayer evaporation to the bubble growth is on average about 50%, and this percentage does not vary much against the wall superheat. The remaining heat can be supplied from the superheated liquid layer.

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CHAPTER 2 NUCLEATE BOILING

[17] Y. Utaka, Y. Kashiwabara, M. Ozaki, Microlayer structure in nucleate boiling of water and ethanol at atmospheric pressure, Int. J. Heat Mass Transfer 57 (2013) 222
230. [18] W.M. Rohsenow, A method of correlating heat-transfer data for surface boiling of liquids, Trans. ASME 74 (1951) 969
976. [19] C.Y. Han, P. Griffith, The mechanism of heat transfer in nucleate pool boiling—Part II, The heat fluxtemperature difference relation, Int. J. Heat Mass Transfer 8 (1965) 905
914. [20] T. Yabuki, T. Hamaguchi, O. Nakabeppu, Interferometric measurement of the liquid-phase temperature field around an isolated boiling bubble, J. Thermal Sci. Technol. 7 (3) (2012) 463
474.

2.2

MEASUREMENT OF THE MICROLAYER DURING NUCLEATE BOILING AND ITS HEAT TRANSFER MECHANISM

Yoshio Utaka1,2 and Zhihao Chen1 1

Tianjin University, Tianjin, China 2Tamagawa University, Tokyo, Japan

2.2.1 INTRODUCTION Nucleate boiling is widely used in industry due to its good heat transfer characteristics. However, some physicochemical aspects of the heat transfer mechanism of nucleate boiling, including bubble nucleation, bubble growth, bubble behavior, phase changes at the liquid
vapor interface and more complex phenomena, remain unknown. The heat transfer mechanisms of nucleate boiling have been classified into two categories: convective heat transfer and latent heat transfer. The convective heat transfer mechanism is based on diffusion of the thermal boundary layer by bubble motion and sensible heat transport, whereas the latent heat transfer mechanism involves sensible heat stored in the superheated liquid layer being converted into vapor and evaporation of the microlayer that forms between a growing bubble and the heat transfer surface. Although the heat transfer mechanism of nucleate boiling has been investigated in terms of these proposed mechanisms, there has not been sufficient quantitative understanding. The heat transfer characteristics of microlayer evaporation, in which a large amount of heat transport results from latent heat of evaporation, is especially important. Therefore, clarification of the microlayer structure and heat transfer characteristics is fundamental to understanding the boiling process. The existence and distribution of the microlayer was confirmed by utilizing several different methods in recent experimental studies. For example, the unsteady temperature measurement of heat transfer plate [1
3] and the optical measurement including laser interferometry [4
9] and laser extinction [10
13]. Moore and Mesler [1] first experimentally demonstrated the formation of

2.2.2 MEASUREMENT BY LASER EXTINCTION METHOD

37

a microlayer formed under boiling water bubbles. Cooper and Lloyd [2] measured the microlayer for various organic liquids. Yabuki and Nakabeppu [3] performed high precision measurements of water using microelectromechanical system (MEMS) sensors. The optical measurement technique enables direct measurement of the microlayer thickness. In early studies of using the interferometric method, Sharp [4] confirmed the presence of a microlayer and measured its thickness for water, and Jawurek [5] confirmed that of ethanol, by adopting mercury arc lamps as light sources. Furthermore, Voutsinos and Judd [6] measured the microlayer thickness in dichloromethane using a laser light source. Koffman and Plesset [7] measured microlayer thickness distributions for subcooled water and ethanol with high-speed photography. Gao et al. [8] and Haginiwa and Utaka [9] recently adopted a similar interferometric method and measured the microlayer thickness for water and ethanol. Moreover, Utaka and his coworkers [10
13] were advanced to determine the distribution of initial microlayer thickness for water and ethanol using the laser extinction method and analyze the microlayer behavior by the recorded images with a high-speed camera.

2.2.2 MEASUREMENT OF MICROLAYER STRUCTURE BY LASER EXTINCTION METHOD 2.2.2.1 EXPERIMENTAL APPARATUS AND METHOD Figs. 2.2.1 and 2.2.2, respectively, show schematics of the experimental system and the pool boiling apparatus used in the present study. The pool boiling apparatus consists of a system for boiling water and ethanol at atmospheric pressure and a system for measuring the transmission ratio of laser light. As the heat transfer plate, a 2-mm-thick and 25-mm-diameter quartz plate that has a high transparency at the laser wavelength was attached to the bottom of the boiling chamber. The single cavity of the small scratch of around 0.25 mm in diameter for the nucleation site was given artificially on the quartz glass heat transfer plate. The test liquid in the boiling chamber was maintained at its saturation temperature by heating it with an electric heater. The rear of a cavity on the He-Ne laser

chopper optical fiber lens

N᧮

high speed camera pc

heated gas jet heat surface lens

N᧮ nitrogen tank

FIGURE 2.2.1 Experimental apparatus of the laser extinction method.

Pb-Se detecter

38

CHAPTER 2 NUCLEATE BOILING

optical fiber spring

position adjust screw

12

thin tube

2

262

215

137

high-speed camera heat transfer surface

gas jet heater

FIGURE 2.2.2 Details of the pool boiling apparatus.

heat transfer surface was heated by impinging a jet of hot nitrogen gas from a nozzle (inner diameter: 2 mm) at an angle of 60 to generate bubbles at a fixed point. A system for adjusting the position of the optical fiber was installed on top of the boiling container. The velocity of the nitrogen jet was approximately 180 m/s and its temperature was varied between 513 and 673 K to adjust the heat flux. The heat flux was determined by performing iterative calculations for the overall heat transfer system using the heating-side heat transfer coefficient obtained from the flow rate, the temperature of the nitrogen jet, and the boiling heat transfer coefficient obtained from the boiling characteristic curve. The laser light transmission ratio measurement system consists of a helium
neon laser (wavelength: 3.39 μm) and a Pb
Se detector. Fig. 2.2.3 depicts the principle of the laser extinction method used to measure the microlayer thickness without contact. The intensity of the laser light is attenuated by scattering and adsorption in the microlayer formed under the bubble on the heat transfer surface. The intensity ratio of transmitted light to incident light (I/I0) is measured. Laser light from an oscillator was concentrated and directed through a 94-μm-diameter optical fiber (with 140-μm-diameter clad and 250-μm-diameter buffer) that has a high transmission for infrared light. The reference transmitted light intensity, I0, was determined by detecting the intensity after passing through air and a dry heat transfer plate. The microlayer thickness was then be determined by applying Lambert’s law: e2Aδ 5

I ; I0

(2.2.1)

where δ is the microlayer thickness, A is the extinction coefficient (55.42 3 104 for water and 1.22 3 105 for ethanol). The behavior of boiling bubble was simultaneously observed from the laser signal using two high-speed digital cameras (maximum frame rate: 5000 fps) oriented in orthogonal

2.2.2 MEASUREMENT BY LASER EXTINCTION METHOD

39

FIGURE 2.2.3 Principle of the laser extinction method.

He-Ne laser optical fiber

nitorogeen stainless steel pipe

stainless steel wire water

bubble

caviity heat transfer surface

microlayer detector

FIGURE 2.2.4 Schematic diagram of the method for measurement of microlayer thickness.

directions in the plane of the heat transfer surface. This data was used to determine the distances from the optical fiber to the incipient bubble points. During the measurements, the bulk liquid must be removed from the laser path in the liquid pool and the optical fiber. Since the optical fiber is made of fluorinated glass, it must be prevented from becoming wetted. Therefore, a thin (diameter 0.4 mm) stainless-steel tube was used to cover the optical fiber and confine the nitrogen flow in the apparatus, as shown in Fig. 2.2.4. In this system, the optical fiber is installed inside the thin stainless-steel tube and is positioned near the point of bubble generation. The gas blown through this tube coalesces with the vapor bubble to remove the effect of the bulk liquid. Furthermore, to prevent a thin liquid film forming between the nitrogen gas bubbles and the vapor bubbles, several fine (diameter 70 μm) wires were attached to the tip of the stainless-steel tube. Fig. 2.2.5A shows a typical example of the temporal variation of the microlayer thickness from bubble inception (t 5 0 ms) to when it leaves the field of view for water. Fig. 2.2.5B shows

40

CHAPTER 2 NUCLEATE BOILING

FIGURE 2.2.5 Variation of microlayer thickness and aspect of bubble growth for water: (A) microlayer thickness; (B) aspect of bubble growth.

corresponding images of the bubble for h 5 3.3 mm, r 5 0.39 mm, and q 5 50 kW/m2. The measurement data is intermittent due to chopping of the laser beam. It is not possible to measure the microlayer thickness in the early stages of bubble formation because bulk liquid exists between the bubbles of the vapor and nitrogen so that most of the laser light is absorbed or scattered by the bulk liquid. After a short period of time, the bulk liquid disappears with the growth of the bubble and the laser light is partially extinguished by the microlayer, so that the microlayer thickness can be measured when the vapor bubble reaches the thin stainless-steel tube containing the optical fiber. The initial microlayer was approximately 1.5 μm thick and its thickness decreased with time due to evaporation. The film thickness became zero at approximately t 5 20 ms and a dry region appeared. Fig. 2.2.6A and B shows examples of initial microlayer thickness determined from the measurement data for water in Fig. 2.2.5. All the data are used in Fig. 2.2.6A. On the other hand, Fig. 2.2.6B shows an example of a calculation in which the first half of the data was omitted; the time period without data was intentionally enlarged to compare with the results in Fig. 2.2.6A. In order to obtain the initial microlayer thickness, one-dimensional and two-dimensional numerical calculations on the heat conduction of heat transfer plate with the heat flux of microlayer evaporation as the boundary condition, the variation of microlayer thickness in the calculation that is coincident with the measuring results was shown in the figures. Moreover, the linear and quadratic curves obtained by least-squares fitting are shown in both figures. As Fig. 2.2.6A shows, the

2.2.2 MEASUREMENT BY LASER EXTINCTION METHOD

41

FIGURE 2.2.6 Comparison among different methods in determining initial microlayer thickness for water: (A) using all measured data; (B) using reduced measured data.

one-dimensional and two-dimensional numerical calculations and the quadratic curve obtained by least-squares fitting give similar values for the initial microlayer thickness. This is because the period without data is shortened. In contrast, two least-squares fittings give quite different values from the other two numerical calculation methods for the case shown in Fig. 2.2.6B due to the longer period without measurement data. However, the one-dimensional and two-dimensional calculations give similar variations in the microlayer thickness to those shown in Fig. 2.2.6A. Therefore, one-dimensional calculations were performed to calculate the initial microlayer thickness because of their simplicity.

2.2.2.2 INITIAL DISTRIBUTION OF MICROLAYER THICKNESS The major results of the initial microlayer thickness obtained by the laser extinction method [12] were summarized in Figs. 2.2.7 and 2.2.8 for water and ethanol, respectively. The results obtained by other measuring methods were also shown for comparison. The results clarified that the initial microlayer thickness, δ0, increased linearly with the distance from the bubble inception site. The relation between the distance from the bubble inception site and the microlayer thickness are

CHAPTER 2 NUCLEATE BOILING

Initial microlayer thickness δ0 µm

42

10 8

Water

6 Utaka et al. (laser extinction) Haginiwa–Utaka (laser interferometry) Koffman–Plesset Yabuki–Nakabeppu

4 2

0 1 2 3 Distance from incipient bubble site r mm

FIGURE 2.2.7

Initial microlayer thickness δ0 µm

Variation of initial microlayer thickness as a function of distance from the incipient bubble site for water. 15 Ethanol 10

5

Utaka et al. (laser extinction) Haginiwa–Utaka (laser interferometry) Koffman–Plesset Gao et al.

0 0 1 2 Distance from incipient bubble site r mm

FIGURE 2.2.8 Variation of initial microlayer thickness as a function of distance from the incipient bubble site for ethanol.

expressed by Eqs (2.2.2) and (2.2.3) for water and ethanol, respectively. Besides, the experimental results obtained by different measuring methods were consistent with each other. δ0 5 4:46 3 1023 Ur 23

δ0 5 10:2 3 10 Ur

(2.2.2) (2.2.3)

2.2.3 MEASUREMENT OF MICROLAYER STRUCTURE BY LASER INTERFEROMETRIC METHOD The microlayer structure of water and ethanol were also measured using the laser interferometric method [9]. The experimental apparatus was shown in Fig. 2.2.9. The microlayer thickness was measured based on the distribution of the interference fringes. A sample image of the interference fringes was shown in Fig. 2.2.10. Every interference fringe represents the microlayer in the same

2.2.3 MEASUREMENT BY LASER INTERFEROMETRIC METHOD

Boiling cell High speed camera Heater Beam collimator Gas jet heater

laser

Half mirror

Microscope Nitrogen tank

PC

High speed camera

FIGURE 2.2.9 Experimental apparatus of the laser interferometric method.

Liquid

δ

Bubble

Microlayer thickness

Glass Im

In

(A)

0.5mm (B)

FIGURE 2.2.10 Sample image of laser interferometry for water.

43

44

CHAPTER 2 NUCLEATE BOILING

thickness. The thickness difference between two neighbor bright/dark interference fringes is λ/2n, the fringe at the outside represents the larger thickness since it was known that the microlayer thickness increases with the distance from the bubble inception site. Therefore, the microlayer thickness was determined based on the following equations by counting the order of the interference fringes: Microlayer thickness at the position of bright fringes: δ 5 mλ=2n; m 5 0; 1; 2; . . .

(2.2.4)

Microlayer thickness at the position of dark fringes: δ 5 ðm 1 1=2Þλ=2n; m 5 0; 1; 2; . . .

(2.2.5)

where δ is the microlayer thickness, m is the order of light or dark fringes from the center, λ is the wavelength of laser, and n is the refractive index of liquid. The major results of the initial distribution of the microlayer thickness for water and ethanol obtained by the laser interferometric method were also summarized in Figs. 2.2.7 and 2.2.8 for comparison. It was shown that the results obtained by the laser interferometric method were in good agreement with the other measuring methods. The linear relationship (Eqs 2.2.2 and 2.2.3) obtained by the laser extinction method was adopted in the numerical simulation in Sections 2.2.5 and 2.2.6.

2.2.4 BASIC CHARACTERISTICS AND CORRELATIONS CONCERNING THE MICROLAYER IN NUCLEATE POOL BOILING A schematic diagram of the variation in growth for the vapor bubble and microlayer is shown in Fig. 2.2.11, which also defines the dominant physical parameters. A vapor bubble is generated, r

RMmax

r

RBd

HBd

RBmax

0

bubble inception

microlayer appearance at r

maximum microlayer radius

commencement of microlayer decrease

disappearance of microlayer at r

tMmax tMd tBd tg

ΔtMe

FIGURE 2.2.11 Definition of times relating to size of microlayer and bubble growth.

bubble departure

tB

2.2.4 BASIC CHARACTERISTICS AND CORRELATIONS

45

Radius of microlayer RM mm

grows, and departs at the inception site, while a microlayer with a radius that increases on the heat transfer surface is formed. The vapor bubble subsequently departs from the surface due to the forces of buoyancy and flow inertia. During the departure process, the radius of the microlayer decreases, the heat transfer surface becomes covered with bulk liquid, and the area of the microlayer disappears. The bubble cycle, in which the superheat of the heating surface recovers during the waiting period and a vapor bubble forms, is then repeated. Although the velocity of bubble growth was different, the qualitative trend in the variation of microlayer radius RM from vapor generation to bubble departure was analogous. Here, the elapsed time from bubble inception is denoted as tB and tMmax is the elapsed time before the appearance of the maximum radius of the microlayer. The elapsed time before completion of bubble departure, the period until the formation of microlayer at r, and the duration of the microlayer at r are tBd, tg and ΔTMe, respectively. The measured characteristic quantities determining the features of nucleate boiling were measured during the experiments [13] and are discussed next. Fig. 2.2.12 shows the variation in growth rate of microlayer radii RM, which indicates the growth area of the microlayer for water and ethanol as a function of the time elapsed from bubble formation tB. Only a slight dependence on heat flux was observed, whereas the duration of the microlayer increased with the microlayer radius. The size of the microlayer increased abruptly during the interval of 5
10 ms and reached a maximum, after which it diminished and disappeared during the bubble departure process. After the maximum was reached, the rate of decrease in the microlayer radius was gradual compared to the rate of radius increase. It was shown that the qualitative trends in the variation of the microlayer radii from bubble formation to departure are similar both for water and ethanol. Therefore, it is possible to obtain systematic correlations among the physical factors concerning bubble and microlayer variation by normalization of the microlayer radius and the bubble growth time. Fig. 2.2.13 shows the results where the variations in microlayer radii RM and tB, from bubble formation to departure were normalized using RMmax and tBd, respectively. The nondimensional bubble growth curves show uniform variation and confirm that the q kW/m2 water ethanol 50 76 105 103 143

5 4 3 2 1 0

0.01 Time tB s

FIGURE 2.2.12 Variation of microlayer radius on heat transfer surface.

0.02

0.03

46

CHAPTER 2 NUCLEATE BOILING

q kW/m2 water ethanol 50 76 105 103 143

1

RM / RM max

0.8 0.6 0.4 0.2 0

0.2

0.4 0.6 tB / tBd

0.8

1

FIGURE 2.2.13

Duration of microlayer ΔtMes

Variation of dimensionless microlayer radius over dimensionless time.

q kW/m2 water ethanol 0.02

50 76 103

105 143

0.01

0 1 2 Distance from bubble inception site r mm

FIGURE 2.2.14 Variation of microlayer duration as a function of distance from the incipient bubble site.

microlayer radii for water and ethanol grow in a similar manner. Thus, a better correlation was obtained by normalization. The duration of the microlayer ΔtMe, with respect to the distance r is shown in Fig. 2.2.14. The duration of the microlayer is widely variable, even at the same distance, and a fixed relation is not easily determined, but the trends of change for water and ethanol are similar. The value of ΔtMe decreases with increase in r. The relation between the local position and duration of the microlayer shown in Fig. 2.2.14 was converted to a nondimensional form using RMmax and tBd, as shown in Fig. 2.2.15. The cohesiveness of the data is promoted by normalization and indicates that water and ethanol have almost equal relations. The relation for both materials in bulk can be expressed as ΔtMe r 5 20:662 3 1 0:941: RMmax tBd

(2.2.6)

2.2.5 NUMERICAL SIMULATION ON THE HEAT TRANSFER PLATE

47

q kW/m2 water ethanol 1

50 76 103

ΔtMe / tBd

0.8

105 143 all

0.6 0.4 0.2 0

0.2

0.4 0.6 r/RMmax

0.8

1

FIGURE 2.2.15 Variation of dimensionless microlayer duration as a function of dimensionless position.

2

q kW/m water ethanol 50 76 103

1

105 143

δ0 / δmax

0.8 0.6 0.4 0.2 0

0.2

0.4 0.6 r/RMmax

0.8

1

FIGURE 2.2.16 Relationship between dimensionless microlayer thickness and dimensionless position.

The relations between the initial microlayer thickness and the local position (Figs. 2.2.7 and 2.2.8) were normalized similarly using δmax and RMmax with respect to the heat flux q, as shown in Fig. 2.2.16. It can be confirmed that there is no dependency on q in this experimental range.

2.2.5 NUMERICAL SIMULATION ON THE HEAT TRANSFER PLATE DURING BOILING So far, the existence of a microlayer was experimentally confirmed and its structure was also measured for water and ethanol. Since both evaporation from the microlayer and the superheated

48

CHAPTER 2 NUCLEATE BOILING

liquid layer are closely related to the bubble growth in saturated nucleate boiling, it is necessary to quantitatively evaluate both the evaporation from the microlayer and that from the superheated liquid layer to elucidate the mechanism of nucleate boiling.

2.2.5.1 HEAT TRANSFER CHARACTERISTICS OF THE MICROLAYER IN AN EVAPORATION SYSTEM

Vapor volume from microlayer VML mm3

Utaka and his coworkers [13] conducted 2D numerical simulations on the transient heat conduction of a heat transfer plate during boiling, with the heat flux of microlayer evaporation and heating as the boundary conditions on the two surfaces of the heat transfer plate. In accordance with the experiments, quartz glass was adopted as the material for the heat transfer plate in the simulations. The heat flux of microlayer evaporation is calculated based on the surface superheat and the microlayer thickness, with the initial values of ΔTi (surface superheat at bubble inception) and δ0 (initial microlayer thickness) measured from the experiments, respectively. The growth of microlayer was considered by adopting the experimentally summarized correlations in Section 2.2.4. Besides, the results after the periodic steady state of temperature variation was achieved were adopted for analysis. Fig. 2.2.17 gives a comparison between the calculation results of microlayer evaporation under a heat flux of 103 kW/m2, as used in the experiment, and under the assumption of 50 kW/m2. The effect of heat flux on the vapor volume generated from the microlayer was not significantly large and the difference was less than 10% when the heat flux was increased twofold. Therefore, the heat consumed by microlayer evaporation is mainly dependent on the unsteady release of stored heat in the heating plate before bubble generation, i.e., it is dependent upon the unsteady temperature change of the heating plate rather than heat flux given at the plate bottom. The variation of temperature distribution on the heat transfer surface (z 5 0) and at the thermal penetration depth δh (z 5 0.67 mm) in the heating plate are shown in Fig. 2.2.18A and B, under the

2

300

q kW/m 103 50

2D calculation

200

100

0

RMmax =4.5 mm Δ Ti =22 K

10 Time tB ms

FIGURE 2.2.17 Volume of vapor from the microlayer as a function of time.

20

180

z = 0 mm 160 140

RMmax =4.5 mm q =103 kW/m2 ΔTi =22 K

120 100 0

tB ms 0 7.0 13.0 20.0 28.0 48.0

1 2 3 4 5 Distance from the center x mm

Temperature of heat transfer surface TºC

Temperature of heat transfer surface TºC

2.2.5 NUMERICAL SIMULATION ON THE HEAT TRANSFER PLATE

200 180

z = 0.67 mm RMmax =4.5 mm q =103 kW/m2 ΔTi =22 K

160 140 0

(A) z = 0 mm

49

tB ms 0 10.0 20.0 30.0 48.0

1 2 3 4 5 Distance from the center x mm

(B) z = 0.67 mm

FIGURE 2.2.18 Variation of distribution of heat transfer surface temperature under a periodic steady state for water.

condition of heat flux of 103 kW/m2. Since the bubble cycle was approximately 48 ms, the thermal penetration depth δh was determined from Eq. (2.2.7) to be 0.67 mm, where αw is thermal diffusivity of water. δh 5

pffiffiffiffiffiffiffiffiffiffiffiffiffi 12αW t

(2.2.7)

It is confirmed from Fig. 2.2.18A that the temperature of the heating surface decreased with microlayer evaporation and was a minimum at tB 5 13 ms, and then recovered after bubble departure. And there was no significant temperature variation at the position of thermal penetration depth, as shown in Fig. 2.2.18B. Thus, it is confirmed that the enthalpy stored in the heating plate within the distance from the heating surface to the thermal penetration depth during the interval of bubble suspension was consumed by microlayer evaporation through unsteady thermal conduction. Therefore, the heat flux of heating that applied on the bottom of the heating plate had little effect on the microlayer evaporation rate and mainly determined the length of a bubble cycle as a timeaveraged heat supply.

2.2.5.2 CONTRIBUTION OF MICROLAYER EVAPORATION The contribution of microlayer evaporation to the total amount of evaporation (bubble volume) during the bubble growth process were also quantitatively evaluated [13]. In 2D numerical simulations on the heat conduction of the heat transfer plate (quartz glass), the amount of microlayer evaporation was calculated based on the experimentally measured value of initial microlayer thickness and bubble inception temperature, and it was compared to the bubble volume that was obtained based on the recorded image of bubble. The relations between the ratio of VML/VB (VML 5 vapor volume from microlayer evaporation, VB 5 vapor volume of the entire bubble) at

50

CHAPTER 2 NUCLEATE BOILING

1 Water

VML / V B

0.8

2

0.6

RMmaxmm 2.0–2.5 2.5–3.0 3.0–3.5 3.5–4.0 4.0–

0.4 0.2 0

q kW/m 50 76 103

10 20 30 40 50 Superheat at bubble inception Δ Ti K (A) 1 Ethanol

VML / V B

0.8 0.6 q kW/m2 105 143 RMmaxmm 2.0–2.5 2.5–3.0

0.4 0.2 0

10 20 30 40 50 Superheat at bubble inception Δ Ti K

(B)

FIGURE 2.2.19 Contribution of evaporation from the microlayer as a function of surface superheat at bubble inception: (A) water; (B) ethanol.

the bubble detachment and the superheat of the heating surface at bubble inception are shown in Fig. 2.2.19A and B for water and ethanol. The results for both water and ethanol are similar. The ratios of VML/VB were 20
70% in the range of ΔTi 5 6
39 K, and the ratio of VML/VB increased linearly with the increase of surface superheat. VML/VB had little dependency on RMmax. The relationship between VML/VB and the surface superheat at bubble inception are expressed by leastsquares fitting in Eqs (2.2.8) and (2.2.9) for water and ethanol, respectively. VML =VB 5 1:89 3 1022 3 ΔTi 22

VML =VB 5 1:76 3 10

3 ΔTi

(2.2.8) (2.2.9)

Thus, the occupation ratios of vapor volume from microlayer evaporation to the vapor of the entire bubble for water and ethanol resemble each other. The evaporations from the microlayer and from the superheated bulk liquid supply vapor into the bubble, and both phenomena are dominated mainly by heat conduction in the liquid layer. Hence, the appearance of similar values for water and ethanol could be understood. The surface superheat at bubble inception varies widely under similar heating conditions as seen in Fig. 2.2.19, because there is little necessarily fixed relationship between the heat flux of heating, surface superheat, and the temperature of superheated bulk liquid, due to the essential effects of other possible factors in boiling phenomena, such as the bubble inception conditions due to surface heterogeneity and so forth.

2.2.6 NUMERICAL SIMULATION

51

2.2.6 NUMERICAL SIMULATION ON THE TWO-PHASE VAPOR
LIQUID FLOW DURING BOILING In addition to the 2D simulation on the heat transfer plate, the process of bubble growth and twophase vapor
liquid flow induced by the growth of a single bubble during nucleate boiling was also simulated using the Volume of Fluid (VOF) method [14]. The calculation domain is a 2D axisymmetric domain including fluid and solid regions that has a radius of 6 mm, 10 mm height for the fluid region and 2 mm for the solid region, as shown in Fig. 2.2.20. Quartz glass is set as the solid region material, in accordance with the experimental apparatus, while water (vapor and liquid) is set as the fluid region material. The physical properties of vapor and liquid at the saturation state under atmospheric pressure were adopted in the numerical calculations. Instead of using the experimentally measured volume of the boiling bubble as in Section 2.2.5, the numerically calculated bubble volume that was determined based on the evaporation both from the microlayer and the surrounding superheated liquid layer was adopted for calculating the contribution of microlayer evaporation, whereas the microlayer evaporation on a quartz glass heat transfer plate was calculated using the same method as mentioned above [13]. Since the microlayer between a growing bubble and the heat transfer surface is extremely thin compared with the bubble size, it is difficult to simulate the microlayer region in the calculation for the macroscopic bubble using the VOF method, so that special handling is necessary for simulation of the microlayer. Therefore, a special model is proposed where the evaporation from the microlayer and superheated liquid layer are computed separately. The microlayer was ignored in the volume fraction of fluid calculation, while vapor generation from the microlayer and the corresponding variation in momentum and heat were computed and applied to the source terms of the respective governing equations. Specifically, a hypothetical microlayer, as shown in Fig. 2.2.21, was applied and arranged to the calculation cells adjacent to the heat transfer surface that are full of vapor, and the experimentally measured distribution of initial microlayer thickness (Eq. 2.2.2) [12] was adopted. The heat flux of microlayer evaporation was determined based on 1D heat conduction of the microlayer and the interfacial evaporation heat transfer coefficient. 6 mm

10 mm

Fluid

z O

FIGURE 2.2.20 Calculation domain.

Heat transfer plate

r

2 mm

Bubble

52

CHAPTER 2 NUCLEATE BOILING

Vapor

Bulk liquid

δ ML(r,t)

Microlayer

Heat transfer plate z O

Tw

r

FIGURE 2.2.21 Schematic diagram of the vapor
liquid interface for a microlayer.

Microlayer radius RM mm

Vapor volume mm3

500 400 300 200 100

Exp. Cal.

0

q kW/m2 ΔTi K 76 76 103 103

3

10 19 24 26

2 1 0 0

10 20 Time tB ms

30

FIGURE 2.2.22 Variation in microlayer radius and vapor volume as a function of bubble time.

2.2.6.1 VARIATION IN MICROLAYER RADIUS AND BUBBLE VOLUME The experimental and numerical results for the variations in microlayer radius and bubble volume are shown in Fig. 2.2.22 for four different conditions of heat flux and surface superheat at bubble inception ΔTi. The results obtained during the experiments using the laser extinction method were adopted for comparison. For all the results given in Fig. 2.2.22, the microlayer radius increased sharply during the early stage of bubble growth, then decreased gradually after reaching maximum values. For three groups of results out of four (except for q 5 76 W/m2 and ΔTi 5 10 K), the experimental and numerical results for the maximum value of the microlayer radius were approximately coincident. Although the variations in both the simulated and experimental microlayer radius

2.2.6 NUMERICAL SIMULATION

53

showed a similar trend, delayed growth appeared in the numerical simulation. Corresponding delays in the bubble volume growth were also revealed. The delay in bubble growth may be caused by the small difference in the initial temperature distribution of the liquid region between the simulation and the experiment, and the neglect of the drag force induced by the wake flow left by the previously detached bubble. For the condition of q 5 76 W/m2 and ΔTi 5 10 K, the calculation results for the microlayer radius and vapor volume indicate slower growth and a smaller maximum value than the experimental results. The possible reason for this is that ΔTi 5 10 K is different from the average value. Consequently, except for the condition that differed significantly from the average state, it could be concluded that similar tendencies were observed for the experimental and calculation results, although some quantitative differences remained. It was also confirmed that the growth and detachment process of boiling bubbles can generally be simulated using the calculation method proposed. The experimental images of boiling bubbles and the calculated bubble shapes during the bubble growth process shown in Fig. 2.2.23 (q 5 103 W/m2 and ΔTi 5 24 K) confirm that approximately similar bubble shapes can be achieved by numerical simulation in comparison with the experiments.

2 mm

2 mm

tB = 1.0 ms

2 mm

2 mm

tB = 5.1 ms

2 mm

tB = 14.8 ms

FIGURE 2.2.23 Comparison of experimental and calculated bubble shapes.

2 mm

54

CHAPTER 2 NUCLEATE BOILING

Liquid

Vapor

395.55

(A) tB=5.1 ms

Liquid

Vapor

398.21

(B) tB=10.2 ms

FIGURE 2.2.24 Isothermal diagrams of liquid in the vicinity of the bubble base: (A) tB 5 5.1 ms; (B) tB 5 10.2 ms.

2.2.6.2 TEMPERATURE DISTRIBUTION OF LIQUID IN THE VICINITY OF THE BUBBLE INTERFACE The evaporation at the vapor
liquid interface is closely related to the temperature distribution of the liquid in the vicinity of the interface during the bubble growth process. Therefore, the liquid temperature distribution in the vicinity of the bubble interface was investigated. Isothermal diagrams for the vicinity of the bubble base are shown in Fig. 2.2.24 for the conditions of q 5 103 W/m2 and ΔTi 5 24 K. It is confirmed that the liquid temperature approaches the saturation temperature when nearing the vapor
liquid interface and a temperature gradient is induced by the evaporation. The temperature gradient is larger when the position is closer to the heat transfer surface, because the liquid superheat is larger when closer to the heat transfer surface; a larger temperature gradient is thus induced by the more rapid evaporation. Moreover, the high-temperature liquid near the vapor
liquid interface moves farther from the heat transfer surface along the vapor
liquid interface with bubble growth. As a result, a high-temperature region is formed in the vicinity of the vapor
liquid interface near the bubble base.

2.2.6 NUMERICAL SIMULATION

55

2.2.6.3 HEAT TRANSFER CHARACTERISTICS OF MICROLAYER EVAPORATION

Microlayer thickness δ μm

The variations in the microlayer thickness distribution, the temperature of the heat transfer surface and the heat flux for microlayer evaporation under the condition of q 5 103 W/m2 and ΔTi 5 24 K are shown in Figs. 2.2.25
2.2.27, respectively. From Fig. 2.2.25, it is confirmed that the microlayer

15 tB ms 1.0 5.1 10.2 14.8 20.0

10 5 0 0

1

2 Radius r mm

3

4

FIGURE 2.2.25

Surface superheat ΔTsat K

Distributions of microlayer thickness as a function of radius for various bubble times.

30 20

tB ms 1.0 5.1 10.2 14.8 20.0

10 0 0

1

2 3 Radius r mm

4

FIGURE 2.2.26

Heat flux of evaporation q kW/m 2

Distributions of surface superheat as a function of radius for various bubble times.

tB ms 1.0 5.1 10.2 14.8 20.0

2000

1000

0 0

1

2

3

4

Radius r mm

FIGURE 2.2.27 Distributions of heat flux for microlayer evaporation as a function of radius for various bubble times.

56

CHAPTER 2 NUCLEATE BOILING

Amount of evaporation mm

3

grows and becomes thinner with time due to evaporation, and dry-out (thickness is zero) occurs initially at the center of the microlayer and then extends towards the outer region. Corresponding to the variation in microlayer thickness, the superheat of the heat transfer surface decreases rapidly with evaporation of the microlayer and then recovers after dry-out occurs, as shown in Fig. 2.2.26. The heat flux distribution for microlayer evaporation is shown in Fig. 2.2.27. As the microlayer radius increases, there is larger heat flux for microlayer evaporation in the outer margin of the microlayer, because the high-temperature heat transfer surface is continuously exposed with the increase in the microlayer radius; higher heat flux for evaporation is thus achieved in the newly exposed region of the microlayer. The higher heat flux region disappears after bubble detachment starts and the microlayer radius decreases, because the exposed high-temperature heat transfer surface is recovered by bulk liquid again. Furthermore, for the entire microlayer region, a higher heat flux of evaporation was achieved during the early stage of bubble growth, and the heat flux of evaporation for the entire microlayer region then decreases with time. For each stage of bubble ΔTi K 10 19

150 q=76 kW/m2 100 Total 50

From microlayer 0 0

10 Time tB ms

20

(A)

ΔTi K 10 19

0.8 2

q=76 kW/m VML/VB

0.6 0.4 0.2 0 0

10 Time tB ms

20

(B)

FIGURE 2.2.28 Characteristics of microlayer evaporation for q 5 76 kW/m2: (A) amount of evaporation from the microlayer and the total evaporation; (B) ratio of microlayer evaporation to the bubble volume.

2.2.6 NUMERICAL SIMULATION

57

growth shown in Fig. 2.2.27, an extremely narrow region with a sharp increase in heat flux can be observed in the inner region of the microlayer (the connection of the microlayer and dry-out regions). The reasons for the existence of the extremely small region are: (1) the rapid increase in heat flux with the decrease in microlayer thickness, especially for the extremely thin microlayer region, because the heat flux of the microlayer evaporation has an inverse relationship with the microlayer thickness; and (2) the heat supplied by heat conduction from the relatively hightemperature dry-out region.

2.2.6.4 CONTRIBUTION OF MICROLAYER EVAPORATION

Amount of evaporation mm3

The variations in microlayer evaporation and total evaporation during a bubble cycle from the bubble inception to detachment are shown in Figs. 2.2.28 and 2.2.29 for two heat flux conditions of q 5 76 and 103 kW/m2. Evaporation from the microlayer and the total amount of evaporation are

400

ΔTi K 24 26

q =103 kW/m2

300 200

Total

100 From microlayer 0 0

10 20 Time tB ms

30

(A)

0.8

VML/VB

0.6

ΔTi K 24 26

q =103 kW/m2

0.4 0.2 0 0

10 20 Time tB ms

30

(B)

FIGURE 2.2.29 Characteristics of microlayer evaporation for q 5 103 kW/m2: (A) amount of evaporation from the microlayer and the total evaporation; (B) ratio of microlayer evaporation to the bubble volume.

58

CHAPTER 2 NUCLEATE BOILING

1 Water

VML/V B

0.8 0.6 0.4 0.2 0

Exp. q kW/m2 RMmax mm 50 76 103 0.5–1.0 2.0–2.5 2.5–3.0 3.0–3.5 3.5–4.0 4.0-

Cal. 2 q kW/m 76 103

10 20 30 40 50 Superheat at bubble inception ΔTi K

FIGURE 2.2.30 Comparison of the contribution from microlayer evaporation with previous results.

presented as time integration values. Similar tendencies are observed for the variations in microlayer evaporation and the total evaporation under all calculation conditions. The ratio of microlayer evaporation to the total rate of evaporation of the bubble (VML/VB), which was calculated based on the time integration values of VML and VB, are also shown in Fig. 2.2.28B and Fig. 2.2.29B. Although a small change is evident, it could be concluded that the ratio of microlayer evaporation to the bubble volume remains almost constant during a bubble cycle. Fig. 2.2.30 shows the simulation results of the ratio of microlayer evaporation VML to the total amount of evaporation VB (bubble volume) during the period from bubble inception to detachment, the results in Fig. 2.2.19A based on the experimentally measured bubble volume were also shown for comparison. It can be concluded that the VML/VB ratios obtained by the two different methods are approximately coincident with each other. The proportion of evaporation from the microlayer to the bubble volume increased with the surface superheat at bubble inception ΔTi, the value was approximately 20%
70% as shown in Fig. 2.2.30. Consequently, it can be concluded that the evaporation from the microlayer makes a large contribution to the bubble growth in nucleate pool boiling.

2.2.7 CONCLUSION The microlayer structure was measured using the laser extinction method and laser interferometric method during nucleate pool boiling of water. The evaporation of the microlayer was analyzed by numerical simulation on the basis of experimentally measured microlayer structure. It has been shown that the initial microlayer thickness increases linearly with the distance from the bubble inception site, and the gradient of the line depends on the test fluids. Furthermore, the contribution of microlayer evaporation is approximately 40%.

REFERENCES

59

NOMENCLATURE A h I n q r RM RMmax t tB tMmax tBd tg ΔTi ΔTMe VML VB

extinction coefficient distance from heat transfer surface to optical fiber tip laser intensity at microlayer refractive index of liquid heat flux distance from origin at bubble inception site microlayer radius on heat transfer surface maximum microlayer radius time elapsed time from bubble inception elapsed time before the appearance of the maximum radius of the microlayer elapsed time from bubble inception to completion of bubble departure period until the formation of microlayer at r surface superheat temperature at bubble inception duration of the microlayer at r vapor volume from microlayer evaporation vapor volume of the entire bubble

GREEK SYMBOLS αW δ δh λ

thermal diffusivity of water microlayer thickness thermal penetration wavelength of laser

SUBSCRIPTS 0 initial max maximum

REFERENCES [1] F.D. Moore, R.B. Mesler, The measurement of rapid surface temperature fluctuations during nucleate boiling of water, AIChE J. 7 (4) (1961) 620
624. [2] M.G. Cooper, A.J.P. Lloyd, The microlayer in nucleate pool boiling, Int. J. Heat Mass Transfer 12 (1969) 895
913. [3] T. Yabuki, O. Nakabeppu, On heat transfer mechanism of nucleate boiling with MEMS sensors (3rd Report, evaluation of the approach method and heat transfer characteristics of isolated boiling bubble), Trans. Jpn. Soc. Mech. Eng. (Ser. B) 76 (771) (2010) 1932
1941. [4] R. Sharp, The nature of liquid film evaporation during nucleate boiling, NASA TN D-1997, Lewis Research Center, Cleveland, OH, 1964.

60

CHAPTER 2 NUCLEATE BOILING

[5] H.H. Jawurek, Simultaneous determination of microlayer geometry and bubble growth in nucleate boiling, Int. J. Heat Mass Transfer 12 (1969) 843
848. [6] C.M. Voutsinos, R.L. Judd, Laser interferometric investigation of the microlayer evaporation phenomenon, J. Heat Transfer 97 (1) (1975) 88
92. [7] L.D. Koffman, M.S. Plesset, Experimental observations of the microlayer in vapor bubble growth on a heated solid, J. Heat Transfer 105 (1983) 625
632. [8] M. Gao, L. Zhang, P. Cheng, X. Quan, An investigation of microlayer beneath nucleation bubble by laser interferometric method, Int. J. Heat Mass Transfer 57 (2012) 183
189. [9] A. Haginiwa, Y. Utaka, Measurement of microlayer structure in nucleate boiling at atmospheric pressure by laser interference method, Proceedings of 50th National heat transfer symposium of Japan, 2013, E221. [10] Y. Utaka, K. Nakamura, A. Sakurai, K. Itagaki, A. Sonoda, Configuration of microlayer in nucleate boiling, Trans. Jpn. Soc. Mech. Eng. (Ser. B) 74 (747) (2008) 2358
2364. [11] K. Nakamura, Y. Utaka, Heat transfer characteristics based on micro-layer configuration in nucleate boiling, Trans. Jpn. Soc. Mech. Eng. (Ser. B) 74 (748) (2008) 2560
2567. [12] Y. Utaka, Y. Kashiwabara, M. Ozaki, Microlayer structure in nucleate boiling of water and ethanol at atmospheric pressure, Int. J. Heat Mass Transfer 57 (2013) 222
230. [13] Y. Utaka, Y. Kashiwabara, M. Ozaki, Z. Chen, Heat transfer characteristics based on microlayer structure in nucleate pool boiling for water and ethanol, Int. J. Heat Mass Transfer 68 (2014) 479
488. [14] Z. Chen, Y. Utaka, On heat transfer and evaporation characteristics in the growth process of a bubble with microlayer structure during nucleate boiling, Int. J. Heat Mass Transfer 81 (2015) 750
759.

2.3

CONFIGURATION OF THE MICROLAYER AND CHARACTERISTICS OF HEAT TRANSFER IN A NARROW-GAP MINI-/MICROCHANNEL BOILING SYSTEM

Yoshio Utaka1,2 1

Tianjin University, Tianjin, China 2Tamagawa University, Tokyo, Japan

2.3.1 INTRODUCTION Boiling in mini-/microscale channels is becoming increasingly important in various applications because this technique is capable of removing large amounts of heat over small areas. Generally, the bulk liquid, superheated microlayer and the bubbles affect the heat transfer characteristics in

2.3.1 INTRODUCTION

61

Channel gap s

Bubble

Initial microlayer thickness δ0

Flat microlayer region Tip region

Liquid

Microchannel

FIGURE 2.3.1 Schematic of an elongated bubble in a microchannel.

complicated ways in the boiling process. Moreover, phase change heat transfer mechanisms and characteristics at the microscale are distinctly different from those at the macroscale. In microchannels, bubbles nucleate and quickly grow to the channel size such that elongated bubbles that are confined by the channel walls are formed, and these bubbles grow very quickly in length, with a dynamic tip as shown in Fig. 2.3.1. Therefore, the rate of evaporation at the microlayer between the plates and the bubbles plays an important role in determining the heat transfer rate. There have been many investigations on boiling in mini-/microchannels. For example, Kandlikar [1] studied the behavior of flow caused by a pressure drop between the inlet and outlet in a horizontal microchannel with a cross section of 1.0 3 1.0 mm. Wen et al. [2] studied the heat transfer coefficient of a vertical microchannel with a cross-section of 1.0 mm 3 2.0 mm, and a vertical pipe ranging in diameter from 0.8 to 1.7 mm. Thome et al. [3] and Dupont et al. [4] presented a three-zone flow boiling model formulated to describe evaporation of elongated bubbles in microchannels and was compared to experimental data on the basis of microlayer evaporation that was the principal form of heat transfer. For the boiling in narrow-gap mini-/microchannels, Katto and Yokoya [5] and Fujita et al. [6] reported that the evaporation characteristics in a mini-/microchannel with a reduced gap size formed by a flat heating surface are completely different from those of pool boiling. Thus, the transient evaporation of the microlayer underneath the elongated bubbles is considered to be a major heat transfer mechanism. As such, the microlayer formed by the movement of the vapor
liquid interface has been investigated theoretically and experimentally in numerous studies. Taylor [7] measured the amount of liquid remaining on the tube wall after an air bubble propagated through the glass tube filled with a glycerin
water solution. The thickness of the film deposited on the wall was demonstrated to increase with an increase in Capillary number (Ca 5 μLVL/σ), where σ, μL, and VL are the surface tension, viscosity, and velocity of the bubble forefront, respectively. Bretherton [8] theoretically derived a prediction method for the microlayer thickness based on a lubrication approximation for the limit of Re ,, 1 while neglecting gravitational forces and

62

CHAPTER 2 NUCLEATE BOILING

suggested that the liquid layer thickness could scale with the Capillary number. For the limit of slow flow, Aussillous and Quere [9] proposed a first-order analysis using scaling arguments. Based on their experimental results, a correlation of microlayer formation at the steady high-velocity region was proposed as a function of Ca. The mechanism of microlayer formation under steady, adiabatic conditions has nearly been clarified. Under a slow-motion limit of bubbles with negligible inertia, the microlayer thickness is determined by the balance between the viscous and capillary forces near the bubble tip; thus, the microlayer thickness (normalized by the tube radius or gap size) is only dependent on Ca. As the steady propagation speed of a bubble increases, the inertia effects cannot be neglected. The steady Navier
Stokes equation must be employed for taking into account the inertia term instead of the Stokes equation [10]. Aussillous and Quere [9] also investigated the inertia effect using low-viscosity liquids and found that above a threshold of Ca, the microlayer is thicker than the correlation derived from the Stokes equation. They analyzed the problem by scaling the steady Navier
Stokes equation and found that the nondimensional microlayer thickness could be correlated with Ca and Weber number We (5ρsVL2/σ), δ Ca2=3 B : r 1 1 Ca2=3 2 We

(2.3.1)

Using a laser focus displacement meter, Han and Shikazono [11] measured the thickness of a microlayer formed in adiabatic slug flow in microtubes. They confirmed that the liquid microlayer thickness is determined only by Ca at a small Ca. However, as Ca increases, the effect of inertia is not neglected. Based on the measurement results, a correlation was obtained as 8 > 0:67Ca2=3 > > > > 1 1 3:13Ca2=3 1 0:504Ca0:672 Re0:589 2 0:352We0:629 > > > > 0 12=3 > > > > 2 ðRe , 2000Þ < μ 1 δ A 106:0@ 5 ρσ Di Di > > ðRe . 2000Þ > > 0 1 0 10:672 0 10:629 > 2=3 > > > 2 2 2 > μ 1A μ 1A μ 1A > > 1 7330@ 2 5000@ > 1 1 497:0@ > ρσ Di ρσ Di ρσ Di :

(2.3.2)

With regard to microchannel boiling, bubbles quickly grow and elongate to the channel size; these grow nonlinearly in length owing to the rapid evaporation of the microlayer [12]. This requires the consideration of local acceleration. However, there are not sufficient published studies on microlayer formation under accelerated motion as shown in Fig. 2.3.8A. Moriyama and Inoue [13] reported that the microlayer thickness follows one of two trends as the interface traveling velocity increases. Two regimes for microlayer formation in their experimental study were identified according to whether the Bond number, (5ðρDi 2 =σÞfU 2 =ð2DÞg) is greater than 2 as in Eq. (2.3.3), 8 0:07Ca0:41 ðBo # 2Þ > > > < 2 30:84 δ sffiffiffiffiffiffiffiffiffi 5 ; 1 μL tg 5 s > > 0:104 ðBo . 2Þ > : s ρL

(2.3.3)

2.3.2 MECHANISMS AND CHARACTERISTICS

63

where s is the distance between the two parallel plates; D the distance from the bubble forefront to the inception site; tg the bubble growth time; and μL and ρL are the viscosity and density of the liquid, respectively. Han and Shikazono [14] assumed that under accelerated conditions, the bubble nose curvature is affected by the viscous boundary layer. Based on the measured results of the microlayer thickness under adiabatic conditions, a modification coefficient f 5 0:692Bo0:414 was obtained at Bo . 1. Then, a correlation for the data at Bo . 1 is proposed as δ 0:968Ca2=3 Bo20:414 5 : D 1 1 4:838Ca2=3 Bo20:414

(2.3.4)

Based on a review of the literature, an insufficient number of studies have examined the accelerated motion of bubbles confined in mini-/microchannels with respect to boiling when the bubble grows nonlinearly due to rapid evaporation of the microlayer.

2.3.2 MECHANISMS AND CHARACTERISTICS OF BOILING HEAT TRANSFER IN THE NARROW-GAP MINI-/MICROCHANNELS 2.3.2.1 GENERAL FEATURES OF BOILING PHENOMENA IN NARROW-GAP MINI-/MICROCHANNELS 2.3.2.1.1 Effect of surface wetting on boiling heat transfer characteristics in mini-/micro-gaps In the boiling process, the wettability of the heat transfer surface shows remarkable effects on the behaviors of bulk liquid, superheated microlayer and the bubbles in complicated ways. As a result, the wettability of the heat transfer surface shows remarkable effects on heat transfer in the mini-/ microchannel. Tasaki and Utaka [15] described observations of the aspects of vapor behavior and heat transfer measurements in the mini-/micro-gap boiling for water using the boiling section of narrow-gap mini-/microchannel experimental system shown in Section 2.3.2.1.3 (Fig. 2.3.5). The effects of the gap size (0.25, 0.5, 1.0 and 10.0 mm) on a copper heating plate of 102 mm length and 50 mm width and the wettability of the heating surface, which was changed from hydrophilic to hydrophobic, on the heat transfer characteristics were experimentally studied. Fig. 2.3.2A and B shows the two typical heat transfer characteristics for the gap sizes of 0.5 mm and 10.0 mm, respectively, on the surfaces of titanium oxide-coated, lapped/aged, lapped/fresh, and siliconecoated. It was confirmed that the wide range of surface wettability was realized from the static contact angles of water on their surfaces, as shown in Fig. 2.3.3A. The effects of surface wettability on the boiling curve were measured and it was elucidated that the higher wettability degrades the heat transfer for the 10.0-mm gap, which is close to the condition of pool boiling as shown in Fig. 2.3.2A. On the other hand, Fig. 2.3.2B shows that the higher wettability improves heat transfer for narrow-gap size of 0.5 mm. Therefore, the hydrophilic characteristics enhanced heat transfer in the microchannel with a gap size ranging from 0.25 to 1.0 mm because the aspects of boiling were quite different depending upon the surface wettability as shown in Fig. 2.3.3B. Thus, the effect of the wettability of the heating surface is thought to be the one of main factors dominating the behavior of the microlayer, and thereby eventually affects the heat transfer characteristics in the microchannel. Thus, the enhancement of heat transfer in the mini-/microchannel was

64

CHAPTER 2 NUCLEATE BOILING

Heat flux q kW/m2

1000 䕕 䕿 䕧 䕻

100

s mm Surface properties 10 flat, titanium oxide-coated 10 flat, lapped/aged 10 flat, lapped/fresh 10 flat, silicone-coated

10

Hydrophilic

1 0.1

1

Surface superheat Δ T K

10

100

(A) 1000

Heat flux q kW/m2

䕕 䕿 䕧 䕻

s mm Surface properties 0.5 flat, titanium oxide-coated 0.5 flat, lapped/aged 0.5 flat, lapped/fresh 0.5 flat, silicone-coated

100

10

Hydrophilic

1 0.1

1

10

100

Surface superheat Δ T K

(B)

FIGURE 2.3.2 Relationship between boiling curve and wettability: (A) 10.0-mm gap; (B) 0.5-mm gap (closed symbols indicate same heat flux level).

due to the formation and sustaining of a microlayer on the heating plate with a highly wettable surface.

2.3.2.1.2 Mechanisms and characteristics of boiling heat transfer in the narrow-gap mini-/microchannel on a wettable surface As shown in Section 2.3.2.1.1, the wettability of the heat transfer surface shows remarkable effects on the heat transfer characteristics in mini-/microchannels. It is thought to be the basis for studying the boiling characteristics for a wettable surface, since it is not easy to maintain the

2.3.2 MECHANISMS AND CHARACTERISTICS

65

FIGURE 2.3.3 Contact angles and aspect of boiling on the surface of different wettability: (A) static contact angles for each surface (flat); (B) boiling patterns for each surface type (0.5-mm gap; heat flux of 16 kW/m2).

nonwettable surface and the usual metal surfaces show the wettable nature. In the case of a restricted flow path such as a mini-/microchannel, the microlayer is formed on the wettable surface as a result of liquid remaining on the heating surface immediately after the bulk liquid is pushed away due to the bubble growth. Therefore, the enhancement of heat transfer is due to the formation and sustaining of a microlayer on the heating plate with a highly wettable surface, because of the high rate of evaporation at the microlayer.

66

CHAPTER 2 NUCLEATE BOILING

Heat Flux q kW/m2

1000

ss mm mm Region Region 10.0 10.0 0.25 0.25 Microlayer Micro-layer 1.0 1.0 0.15 0.15 dominant dominant 0.5 0.5 0.5 0.5 0.25 0.25 Dryout Dryout 0.15 0.15

100

10

1 0.1

1 10 Surface Superheat Δ T K

100

FIGURE 2.3.4 Effect of gap sizes on boiling curves on a titanium oxide-coated surface.

Two regions are seen for boiling or vaporization in the narrow-gap mini-/microchannels, namely a microlayer-dominant region and a dry-out region as shown in Fig. 2.3.4 [15]. The open and closed symbols denote the microlayer-dominant region and the dry-out region, respectively. Intermittent formation of the microlayer, due to the generation of a vapor bubble, is observed in the first region. In the other region, periodic forward and backward movements of the liquid at the entrance of the channel, and the appearance of dry-out at the exit are observed. The dotted line divides the two regions. Although for all cases of a gap size of less than 0.5 mm, the maximum heat flux occurs in the dry-out region, the microlayer-dominant region occupies approximately 70%
80% of the maximum heat flux. Hence, the microlayer-dominant region represents the principal form of heat transfer for mini-/microchannel boiling. For instance, in the region of relatively low superheat, a narrower gap size results in a higher heat transfer coefficient. However, with increasing superheat, the change tends to have an opposite trend. Therefore, clarification of the behavior of the microlayer is a very important factor in elucidating the mechanism and characteristics of boiling heat transfer in a mini-/microchannel vaporizer. The characteristics of the microlayer that forms in the mini-/microchannel generated during boiling were investigated by the application of high response and noncontact laser extinction method to measure the microlayer thickness, which was applied to the thickness measurement of thin liquid film in Marangoni condensation by Utaka and Nishikawa [16,17]. Furthermore, the mechanism and characteristics of heat transfer was quantitatively analyzed by investigating factors such as the position of the generated vapor bubble, velocity of the vapor forefront, the periods of microlayer dominance and liquid saturation in the boiling cycle, and so forth, on the basis of the heat transfer measurements, observations of the aspect of boiling and the configuration of the microlayer.

2.3.2.1.3 Experimental apparatus and method Fig. 2.3.5A shows the experimental apparatus consisting of a boiling section in the narrow-gap mini-/microchannel system, and a section for measuring the microlayer thickness by application of

2.3.2 MECHANISMS AND CHARACTERISTICS

(A)

67

PC

hot air passage high-speed camera quartz glass

condenser

microchannel lens chopper

filter lens He-Ne laser

Pb-Se controller detector fan heater

fan heater

heating tank

reservoir tank

heater

hot air orifice vapor

channel gap

(B)

K type thermocouple (0.25 mm in dia.) hot air

hot air passage quartz glass

15 water

82 115 137 166

10 10

microchannel

45 70 mm

FIGURE 2.3.5 Experimental apparatus for measuring microlayer thickness: (A) schematic of whole experimental system; (B) details of mini-/microchannel and heat transfer plate.

the laser extinction method [12,15]. The vapor generator is located between a laser emitter and a detector. The water supplied to the mini-/microchannel apparatus was boiled in a heating tank that was open to the atmosphere. Vapor generated from the mini-/micro-gap vapor generator and the heating tank flowed through a condenser and back to the water reservoir. Fig. 2.3.5B shows the details of the mini-/micro-gap test apparatus. Quartz glass with a high transparency for infrared light was mainly utilized for the test apparatus to enable more accurate measurements. Two quartz glass plates form the narrow-gap mini-/microchannel, which is filled with water as the test fluid. Passages for high-temperature air used as the heating fluid to heat the mini-/micro-gap were positioned at the back and front of the mini-/microchannel. The central part of the 82-mm-high passage,

68

CHAPTER 2 NUCLEATE BOILING

which essentially served as the heating area, was narrowed to enhance heating. The width of the passage was 45 mm. The heat flux into the mini-/micro-gap was controlled by varying the air temperature from 110 to 300 C. For the laser extinction method, a laser ray (3.39 μm wavelength) was launched from a He
Ne laser emitter through the mini-/micro-gap and focused to a diameter of 0.6 mm and was introduced to a Pb
Se detector. The microlayer thickness was determined using Lambert’s law, as given in Eq. (2.3.5), δ 5 2 ð1=AÞlnðI=I0 Þ

(2.3.5)

where I0 and I denote the light intensities at the detector when the mini-/microchannel is filled with steam and with a thin water layer and steam, respectively. δ and A are the microlayer thickness and extinction coefficient, respectively.

2.3.2.2 CONFIGURATION OF THE MICROLAYER IN A NARROW-GAP MINI-/MICROCHANNEL BOILING SYSTEM In Sections 2.3.2.2 and 2.3.2.3, the results concerning the configuration of the microlayer and characteristics of heat transfer in a narrow-gap mini-/microchannel boiling system performed by Utaka et al. [12] will be discussed.

2.3.2.2.1 Effect of heat flux, distance from bubble inception site, bubble forefront velocity and gap size on the initial microlayer thickness Attention was focused on the initial microlayer thickness δ0 that appears immediately after the passage of the bubble forefront. The effect of heat flux and the distance from the bubble inception site were examined as possible factors affecting the initial microlayer thickness for the gap sizes of 0.15, 0.3 and 0.5 mm for water. No distinction in the initial microlayer thickness was observed for different heat flux levels for all gap sizes, indicating that the formation of the microlayer is determined by the dynamic behavior of the liquid
vapor interface. Therefore, δ0 must be determined by the kinetic interface behavior in the process of bubble growth without being affected by evaporation of the microlayer, the microlayer thickness possibly varies due to the effects of bubble forefront velocity. The variation of δ0 in relation to the bubble forefront velocity is shown in Fig. 2.3.6 for different gap sizes. Although there are some other factors concerning δ0, which will be discussed later in Section 2.3.2.3, the gap size and bubble forefront velocity are considered as the major factors here for investigating the major heat transfer characteristic in mini-/micro-gap boiling. δ0 may depend on the effect of the two characteristic regions that are distinguished at a bubble forefront velocity of approximately 2 m/s under those experimental conditions for water. δ0 between 2 and 23 μm were measured in the linear-increase region and approximately 18 μm in the constant thickness region for a gap size of 0.3 mm. The initial microlayer thickness was strongly affected by the gap size, and decreased with decreasing gap size. In the constant thickness region, δ0 of 23, 18, and 9 μm were measured for gap sizes of 0.5, 0.3, and 0.15 mm, respectively. Also, the effect of the distance from the bubble formation site on δ0 for the gap size of 0.5 mm is shown in Fig. 2.3.7 for six different bubble forefront velocities. It was observed that δ0 was weakly dependent on the distance from the bubble inception site, similar tendencies were shown for the cases of 0.15- and 0.3-mm gap sizes.

2.3.2 MECHANISMS AND CHARACTERISTICS

69

Initial microlayer thickness δ0 µm

40 s mm 0.5 0.3 0.15

30

20

10

0

1

2

3

4

5

6

Local velocity of bubble forefront VL m/s FIGURE 2.3.6 Velocity of bubble forefront and initial microlayer thickness.

Microlayer thickness δ 0 μm

40

30

s=0.5 mm

VL m/s 0㹼Y0.4 0.4㹼0.8 0.8㹼1.2 1.2㹼1.6 1.6㹼2.0 2.0㹼

20

10

0 0

10

20

30

40

50

60

Distance from incipient bubble site D mm FIGURE 2.3.7 Effects of distance from bubble inception site and velocity of bubble forefront on initial microlayer thickness for s 5 0.5 mm.

70

CHAPTER 2 NUCLEATE BOILING

These characteristics suggest that, for smaller gap sizes, the heat flux is larger in the low heat flux domain and the critical heat flux is lower in the boiling curves. That is, in the microlayerdominant region, the vaporization rate is increased, and higher boiling heat transfer is possible due to the thinner microlayer. On the contrary, due to an increase in heat flux, the thinner liquid film disappears for a short time and a dry-out region appears.

2.3.2.2.2 Distribution of initial microlayer thickness Fig. 2.3.8B shows the distributions of δ0 on the heating surface, derived from the relation between the bubble forefront velocity and the distance from the bubble formation site as shown in Figs. 2.3.6 and 2.3.7 with the typical variations of bubble forefront velocity in relation to the distance D from the bubble inception site given in Fig. 2.3.8A. δ0 increases with increasing D, which corresponds to the tendency for the bubble forefront velocity to increase as shown in Fig. 2.3.6. The δ0 increases monotonically in the lower heat flux region in which the bubble forefront velocity is out of the region of constant microlayer thickness. On the other hand, as the heat flux increases,

Velocity of bubble forefront VL m/s

(A)

6 5

Initial microlayer thickness δ0 μm

s = 0.5 mm

4 3 2 1 0

(B)

q kW/m2 6.7 4.5 2.5

10 20 30 40 50 60 Distance from incipient bubble site D mm

70

40 q kW/m2

30

s = 0.5 m m

6.67 4.51 2.51

20 10

0

10 20 30 40 50 60 Distance from incipient bubble site D mm

FIGURE 2.3.8 Distribution of initial microlayer thickness for s 5 0.5 mm: (A) velocity of bubble forefront and distance from bubble inception site; (B) initial microlayer thickness and distance from bubble inception site.

2.3.2 MECHANISMS AND CHARACTERISTICS

71

a constant thickness appears in the region of larger D. The δ0 becomes constant at smaller D with increasing heat flux.

2.3.2.3 CONSIDERATION OF HEAT TRANSFER CHARACTERISTICS ON THE BASIS OF CONFIGURATION OF THE MICROLAYER 2.3.2.3.1 Characteristics of phenomena in microlayer-dominant region and method of analysis of heat transfer characteristics A microlayer-dominant region is the principal form of heat transfer in narrow-gap mini-/microchannel boiling. Therefore, the heat transfer characteristics are discussed using various characteristics of the microlayer thickness shown above and heat transfer measurement data and analysis of images taken for the microlayer-dominant region reported in Tasaki and Utaka [15]. The microlayer-dominant region consists of a liquid saturation period where the whole gap is filled with the liquid and a microlayer period where the vapor bubble is formed in the gap and a microlayer exists on the heat transfer surface. These two periods are repeated alternately. Furthermore, the microlayer period can be classified into two phases: an initial liquid microlayer that is formed on the surface by bubble generation and growth from the liquid saturation period, and a reformed liquid microlayer that is formed again by the movement of a liquid slug accompanying the dynamic and complicated bubble behaviors. To study the evaporation mechanism and heat transfer characteristics in the microlayer-dominant region, the mini-/microchannel boiling phenomenon is modeled with the assumption of constant heat flux and with the usage of the averaged values of factors such as the bubble-generation cycle, liquid saturation period, microlayer period, bubble inception site, and bubble growth rate. The liquid saturation period and the microlayer period were measured and the relationship between the average heat flux, and the average liquid saturation period tL and liquid microlayer period tM are shown in Fig. 2.3.9. The liquid saturation period becomes shorter and the microlayer period becomes longer with the increases in nondimensional position x , which is normalized by passage height, from the inlet and the heat flux. Since the microlayer period consists of both initial and reformed microlayers, it is necessary to determine the number of microlayers reformed by the movement of liquid slugs in a single liquid microlayer period. The number of initial microlayers formed by bubble growth NB, and the number of microlayers reformed by later liquid slug movement NR were determined from the images. Fig. 2.3.10 shows the ratio of NR/NB against heat flux. In the region of small heat flux, the number of reformed microlayers is very small. However, as the heat flux increases, the movement of the liquid slug becomes active and the frequency of microlayer reformation increases. At the upstream where nondimensional position x is small, microlayers are hardly reformed. However, as x increases, the frequency of reformed microlayers increases.

2.3.2.3.2 Analysis and discussion of the heat transfer characteristics To study the heat transfer characteristics where a liquid microlayer is formed, the variation of the liquid microlayer thickness and the degree of superheat in the bubble-generation cycle were determined. In the microlayer period, steady-state heat conduction through the microlayer, which is dependent on the wall temperature TW and the saturation temperature T0, causes liquid to evaporate at constant heat flux, so that the microlayer loses thickness δ from the initial microlayer thickness δ0. Immediately after vapor bubbles pass, the gap is filled with water at saturation temperature, and

CHAPTER 2 NUCLEATE BOILING

Microlayer dominant period tM ms

Liquid saturation period tL ms

72

800 s = 0.5 mm

x* = 0.8 x* = 0.5 x* = 0.2

600 400 200 0 600 400 200 0

0

5

10 15 20 25 Heat flux q kW/m2

30

35

FIGURE 2.3.9 Heat flux versus liquid saturation period and microlayer period.

4

s = 0.5 mm

x*= 0.8 x*= 0.5 x*= 0.2

NR / NB

3

2

1

0

0

5

10

15

20

Heat flux q kW/m

FIGURE 2.3.10 Relationship between average heat flux and NR/NB.

25 2

30

35

2.3.3 CHARACTERISTICS OF A MICROLAYER

73

is heated from the heating surface. The liquid moves comparatively slowly, so that only heat conduction is considered in the liquid. The analysis was performed for a 0.5-mm gap with five patterns of heat flux. As an example, Fig. 2.3.11A
C shows the transitions of the microlayer thickness, and the degree of surface superheat during a cycle of bubble generation at nondimensional position of x 5 0.20, 0.50, and 0.80, respectively. In the liquid saturation period, the degree of superheat increases over time. Once the microlayer is formed, the degree of superheat drastically decreases. As evaporation reduces the thickness of the microlayer, the degree of superheat is gradually decreased further. The microlayer period can be divided into several periods. Between the divided periods, there are also periods of several milliseconds in duration where the microlayer thickness increases due to the quick passage of a liquid slug. Different results are given for each x on the right and left in Fig. 2.3.11. This is because the value of the microlayer reformation ratio NR/NB does not generally become an integer. Fig. 2.3.12 shows the results of calculating the average superheat at each heat flux for the gap sizes of 0.5 and 0.25 mm, and comparing the calculated results with the experimentally obtained boiling curve in Ref. [15]. This confirms that an evaporation rate can be predicted using the microlayer thickness; that the microlayer-dominant region, the principal form of narrow-gap mini-/microchannel boiling, is determined by the liquid saturation period constituting a bubble-generation cycle, and a microlayer period where the microlayer evaporates. In addition, it was confirmed that the heat transfer was enhanced due to the microlayer evaporation and the low degree of superheat in the microlayer period, which occupied a comparatively long duration, indicates good heat transfer in the microlayer-dominant region.

2.3.3 CHARACTERISTICS OF A MICROLAYER FOR VARIOUS LIQUIDS AND A CORRELATION OF MICROLAYER THICKNESS IN A NARROW-GAP MINI-/MICRO-BOILING SYSTEM In this section, the general characteristics of initial microlayer thickness will be investigated and the correlation of it will be proposed [18].

2.3.3.1 MEASUREMENT OF MICROLAYER THICKNESS FOR VARIOUS TEST LIQUIDS The microlayer thickness for various test liquids with widely ranging physical properties were measured using the same experimental apparatus as the mini-/microchannel boiling system shown in Fig. 2.3.5. As indicated in section 2.3.2, attention was focused on the initial microlayer thickness δ0, which determines the basic characteristics of heat transfer in the microchannel. The variations of δ0 versus the bubble forefront velocity VL are shown in Fig. 2.3.13 for HFE7200, toluene, water, and ethanol at three different mini-/micro-gap sizes of 0.50, 0.30, and 0.15 mm. δ0 was strongly affected by the gap size and was increased with the increasing gap size. Moreover, the results for any of the four liquids showed a similar tendency for any gap size—that is, in low-velocity regions, the microlayer thickness increases with VL; however, as the VL increases, the thickness becomes almost constant or decreases slightly for sufficiently high VL similar to that shown in Fig. 2.3.6 for water. For the four kinds of liquids with a representative gap size, Fig. 2.3.14 shows the variations

Surface superheat ΔT K Microlayer thickness δ μm

(A) 30 x* = 0.2

x* = 0.2

20 10 0 8 6 4 2 0

100

200

300

0 Time t ms

100

200

300

Surface superheat ΔT K

Microlayer thickness δ μm

(B) 30

x* = 0.5

x* = 0.5 20

10

0 3 2 1

0

100

200

0

Time t ms

100

200

Microlayer thickness δ μm

30

Surface superheat ΔT K

(C)

3

20

10

x* = 0.8

x* = 0.8

0

2 1

0

100

200

300

0

100

200

300

Time t ms

FIGURE 2.3.11 Variations of microlayer thickness and surface superheat in a vapor bubble cycle for s 5 0.5 and q 5 31.8 kW/m2. (A) x 5 0.2; (B) x 5 0.5; (C) x 5 0.8.

2.3.3 CHARACTERISTICS OF A MICROLAYER

75

1000

Heat flux q kW/m2

s mm Exp. Cal.

0.5

0.25

100

10

1 0.5

1

Surface superheat ΔT K

5

FIGURE 2.3.12 Comparison between experiment and calculation in boiling curves.

of VL against δ0 with the distance from the bubble inception site D. It could be observed that in the region of high velocity, δ0 increased with increasing D, whereas in the region of low VL, the effect of D became weak or vanished. Because of the limited data on the microlayer thickness measurements during boiling in the microchannel, there are only a few cases that can be used to compare the independent data with various methods. Fig. 2.3.15 shows experimental data of δ0 for HFE7200 with the calculated thickness for R113 from Moriyama and Inoue [13] and Han and Shikazono [14] for FC40 (all three kinds of refrigerant liquids have largely similar physical properties, as shown in Table 2.3.1). Although the experimental conditions are not exactly the same, the microlayer thicknesses measured by Moriyama and Inoue [13] are significantly thinner compared with the other two measurements. Furthermore, Fig. 2.3.16 shows the measurements of water with a channel size of 0.5 mm in the present study and Han and Shikazono [14] for a circular tube. In the region of low velocity, the measurements obtained by the two different methods show good agreement; however, perhaps due to the different channel geometry and experimental conditions, the data at the region of high velocity are in slight disagreement. It could be confirmed that the methods used in those studies result in similar accuracy of the microlayer thickness measurements.

2.3.3.2 NUMERICAL SIMULATION OF THE BUBBLE GROWTH PROCESS IN THE MICROCHANNEL 2.3.3.2.1 Formulation of the problem and the model geometry and initial and boundary conditions The numerical simulation was performed to investigate the hydrodynamic characteristics of the bubble growth process in the microchannel within two parallel plates to provide deeper insight into

76

CHAPTER 2 NUCLEATE BOILING

s = 0.50 mm

50 40 30 20

Initial microlayer thickness δ0 μm

10 50 s = 0.30 mm 40

30

20

HFE7200 Toluene

10

Water Ethanol

0 s = 0.15mm

30

20

10

0

5 10 Local velocity of bubble forefront VL m/s

FIGURE 2.3.13 Microlayer thicknesses versus local bubble forefront velocity for water, toluene, and HFE7200.

2.3.3 CHARACTERISTICS OF A MICROLAYER

HFE7200 s = 0.3mm

40 30 20 10 0

Toluene s = 0.30mm

40 30

Initial microlayer thickness δ0 (µm)

20 10 0 40

Water s = 0.50mm

D mm : Distance from incipient bubble site

30 20 10

0 < D < 10 10 < D < 20

0 40

20 < D < 30 Ethanol

30 < D < 40

s = 0.15mm

40 < D < 50 50 < D < 60

30 20 10

0

2 4 6 8 Local velocity of bubble forefront VL m/s

FIGURE 2.3.14 Effect of distance from bubble inception site D.

10

77

78

CHAPTER 2 NUCLEATE BOILING

Fluid

Channel size mm R113 0.4 Moriyama and Inoue R113 0.2 FC40 0.5 Han and Shikazono HFE7200 0.5 Present HFE7200 0.3

Microlayer thickness δ0 (μm)

60

40

20

0

1 2 3 4 Local velocity of bubble forefront VL (m/s)

5

6

FIGURE 2.3.15 Comparison of initial microlayer thickness measured by different methods for refrigerants.

Table 2.3.1 Properties of the Test Fluids at Atmospheric Pressure and Saturation Point HFE7200 R113 FC40

ρ (kg/m3)

μ (μPa s)

σ (mN/m)

1307 1499 1849

330.0 515.7 326.7

9.4 14.8 16

the underlying physical mechanisms and thus foster understanding of the gas
liquid two-phase flow. It can also provide a unique velocity field, phase distribution, and microlayer with high spatial and temporal resolution, which is difficult to measure precisely. FLUENT (Release 12.1 2010) was used to simulate the growth process of a bubble in an initially static liquid in a microchannel within two parallel plates. The movement of the gas
liquid interface is tracked based on the Volume of Fluid (VOF) method. The geometric reconstruction scheme that is based on the piece linear interface calculation (PLIC) method is applied to reconstruct the bubble-free surface. The surface tension is approximated by the continuum surface force (CSF) model. The continuity equation and momentum equation are solved throughout the domain. The momentum equation is dependent on the volume fractions of all phases through the properties ρ and μ.

2.3.3 CHARACTERISTICS OF A MICROLAYER

79

Initial microlayer thickness δ0 (μm)

50

40

30

20

Channel size mm 0.5 0.5

10

0

Present Han and Shikazono

10 Local velocity of bubble forefront VL (m/s)

20

FIGURE 2.3.16 Comparison of microlayer thickness of water with channel size of 0.5 mm from the present study and the study by Han and Shikazono [14].

LB=1.5mm

pL=p0

Vout䠙a䞉t(m/s)

pG=p0

Gas

Liquid

Ly=0.3mm

Rb=0.14mm

y x x

Lx=30mm

FIGURE 2.3.17 Schematic representation of the geometry and boundary conditions used in the simulations.

A two-dimensional coordinate system assuming symmetry about the centerline of the microchannel was used because of the large aspect ratio of the cross-section of the microchannel. To investigate the effect of acceleration or distance from the bubble forefront interface to the bubble inception site, the calculation domain was determined to be 100s, where s is the microchannel gap size. Fig. 2.3.17 displays the calculation area and boundary conditions. The no-slip wall condition is applied. Using a user-defined function, the velocity normal to the outlet is specified as unsteady flow uout 5 aUt, where a is the acceleration of the bubble forefront movement, and t is the time of bubble growth. The inlet for liquid and gas is specified as a pressure-fixed boundary condition. Then, the process of elongated bubble growth is simulated under initial conditions of circular tip and constant microlayer thickness, and boundary conditions.

80

CHAPTER 2 NUCLEATE BOILING

2.3.3.2.2 Comparison between simulation and measurement results for HFE7200 After the confirmation of dependencies on grid size and initial microlayer thickness, the calculation was carried out. HFE7200 was adopted as a representative test fluid to investigate the outcome of each parametric effect of the physical properties. In the low-velocity region, the experimental results show that the initial microlayer thickness δ0 increases almost linearly with the bubble forefront velocity VL. This is because the velocity profile is similar to that of the steady internal flow. The viscous boundary layer is still not developed, and its thickness δV is much thicker than the thickness of the microlayer δ0—i.e., the viscous boundary layer has little effect on the development of the microlayer, as shown in Fig. 2.3.18A (δ0 =δV 5 0:26). In this region, the distance from the bubble inception site to the bubble forefront D (or acceleration a, according to the relationship a 5 VL2/2D by assuming that the acceleration is approximately constant) almost does not affect the build-up of the microlayer. The experimental results show that in the region of high velocity, the microlayer thickness increased with D, as shown in Fig. 2.3.14. This can be limited by the viscous boundary layer when it develops well in the bulk liquid in front of the bubble forefront and its thickness δV approaches δ0, as indicated by Moriyama and Inoue [13]. The velocity gradient increases near the wall, and the profile of the velocity for the core of the fluid nearly becomes a parallel flow instead of parabolic, as shown in Fig. 2.3.18B, and the ratio of δ0/δV increases. Fig. 2.3.19 shows the comparison between the simulations and measurements for different accelerations and velocities—almost good agreement is achieved, except the slope of the linearly increasing region is slightly smaller than

FIGURE 2.3.18 Velocity profile of liquid bulk in front of bubble forefront for HFE7200 of gap width of 0.3 mm: (A) a 5 60 m/s2, VL 5 0.74 m/s, and δ0/δV 5 0.26; (B) a 5 100 m/s2, VL 5 1.95 m/s, and δ0/δV 5 0.83.

Initial microlayer thickness δ0 (µm)

2.3.3 CHARACTERISTICS OF A MICROLAYER

40

HFE7200 s = 0.3mm

30 20

81

D mm Measurement Simulation 5 < D < 10 D=7.5 10 < D < 15 D=10 D=12.5 15 < D < 20 20 < D < 25 25 < D < 30 30 < D < 35 35 < D < 40

10

0

1 2 3 4 5 6 Local velocity of bubble forefront VL m/s

FIGURE 2.3.19 Comparison between simulation and measurement results for HFE7200 with s 5 0.3 for fixed distances from bubble inception site D.

1

δ0/δV

0.8 0.6

a m/s2 60 100 300 500 1000

0.4 0.2 0 0

1

2 VL (m/s)

3

4

FIGURE 2.3.20 Ratio of microlayer thickness to boundary layer thickness obtained by simulation results of HFE7200 for different accelerations and velocities.

that of the measurement. The ratio of δ0/δV obtained by the simulation results of HFE7200 for different accelerations and velocities is shown in Fig. 2.3.20 and shows an obvious increasing trend with the velocity in the low-velocity region, but the increasing trend weakens for the high-velocity region. Therefore, it is clear that the microlayer thickness formation is hardly affected by the viscous boundary layer in the low-velocity region but is limited by δV in the high-velocity region, as stated previously.

2.3.3.2.3 Study of effect of physical properties Fig. 2.3.21A
D shows the effects of the physical properties and the shape of the bubble tip. For microchannel boiling, the surface tension coefficient is a dominant parameter. This pushes out the

82

CHAPTER 2 NUCLEATE BOILING

Y (μm)

150

(A)

100 σ ρ μ VL a mN/m kg/m3 μPas m/s m/s2 9.4 1304 330.0 2.56 100 58.9 1304 330.0 2.53 100

50

Y (μm)

150 0

(B)

100 VL μ ρ σ μPas kg/m3 mN/m m/s 660.0 1304 9.4 2.13 2.14 330.0 1304 9.4

50

Y (μm)

150 0

a m/s2 100 100

(C)

100 ρ

50

kg/m3 1304 958

μ

VL a σ μPas mN/m m/s m/s2 330.0 9.4 0.91 100 330.0 9.4 0.92 100

0 Y (μm)

(D)

ρ

μ

σ

kg/m3 µPas mN/m 1304 330.0 9.4 330.0 9.4 998

–3

–2

VL a m/s m/s2 2.32 100 2.34 100

–1

0

X (mm)

FIGURE 2.3.21 Parametric effects of physical properties on microlayer formation: (A) effect of surface tension; (B) effect of viscosity; (C) effect of density for low velocity; and (D) effect of density at high-velocity region.

liquid in the microlayer by the inner pressure of the vapor bubble due to the very large curvature of the vapor
liquid interface at the bubble forefront. Two simulation results of the bubble nose shape for different surface tension coefficients are shown in Fig. 2.3.21A. The bubble forefront with relatively small surface tension is sharper than that with large surface tension; consequently, the thickness of the microlayer in the flat region for the bubble with a small surface tension is thicker than the one with a large surface tension. On the contrary, viscous force is favorable to the microlayer, and large viscosity increases the thickness, as shown in Fig. 2.3.21B. The shape of the bubble calculated with small viscosity is more blunt than the bubble with large viscosity because its weak viscous force cannot overcome the surface tension force (which acts to minimize the surface areas) and cannot remain as liquid as the one with large viscosity. Consequently, the thickness of the microlayer for the bubble with weak viscosity is relatively thin. It was stated in the introduction that for steady slow motion, the microlayer thickness is a function of the Capillary number, and the inertia force can almost be omitted. However, as the bubble movement velocity increased, the inertia force began to affect the formation of the microlayer and increase

2.3.3 CHARACTERISTICS OF A MICROLAYER

83

its thickness. The simulation results of the bubble forefront shape for two different densities at low velocity are shown in Fig. 2.3.21C. Because the forefront velocity is not high, the two bubble shapes close to each other—i.e., the thickness of the flat microlayer region—are almost the same, although the nose of the bubble with a large density is slightly elongated due to the inertial force. When the velocity increases, as shown in Fig. 2.3.21D, the effect of the inertia force becomes significant, and larger density increases the microlayer thickness, as mentioned previously.

2.3.3.3 DIMENSION ANALYSIS AND CORRELATION To create a correlation, dimension analysis was attempted. On the basis of the experiment, it was shown that the microlayer thickness can be expressed as δ0 Bf ðVL ; D; s; ρ; μ; σÞ:

(2.3.6)

The experimental and simulation results show that the initial microlayer thickness δ0 is proportional to viscosity and density and inversely proportional to surface tension. Therefore, the thickness can be expressed as δ0 B

μρ Mτ B 4 ; σ L

(2.3.7)

where M, L, and τ denote mass, length, and time, respectively. By introducing VL and s to which the microlayer thickness is also proportional, according to the experimental results, the right side of Eq. (2.3.7) can be nondimensionalized as ρμVL 3 s B1: σ2

(2.3.8)

Using the Buckingham Π theorem, we can also determine that the nondimensional microlayer thickness is qualitatively a function of Ca, We, and Bo, where Bo 5 ρas2 =σ is the Bond number that represents the ratio of the inertial force due to the acceleration to the surface tension force. We represents the ratio of the inertial force to the surface tension force. Here, according to the study of Moriyama and Inoue [13], as the velocity increases, the microlayer is limited by the viscous boundary layer. Therefore, perhaps it is reasonable to nondimensionalize the microlayer thickness with the viscous boundary layer thickness, and then the nondimensional relationship changes to become δ0 ρμVL 3 s B : σ2 δV

(2.3.9)

Here, although in the low-velocity region, formation of a thin liquid film is not considered to be strongly dependent on the boundary layer because of the accelerative growth of the elongated bubble during the microchannel boiling phenomenon, as mentioned previously, it is thought that the influence of the forces of inertia and acceleration in addition to viscosity and surface tension for thin liquid film thickness formation should be considered. The effects of acceleration, surface tension, and viscosity are included in the left side of Eq. (2.3.9). If the boundary layer thickness is transformed as δV 5 δVn 5 s

sffiffiffiffiffiffiffiffiffiffiffiffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi rffiffiffi DVL 2Dσ μVL 1 0:5 20:5 5 U 5 Ca Bo ρVL s2 2 ρVL 2 s2 2σ

(2.3.10)

84

CHAPTER 2 NUCLEATE BOILING

100

(A)

HFE7200

10–1

(δ0/s)Ca-0.50Bo0.50

=0.44(Ca·We)0.03

10–2

(δ0/s)Ca-0.50Bo0.50

=0.32(Ca·We)0.45

(δ0/s)Ca-0.50Bo0.50

10–3 100

(B)

Toluene

10–1 10–2 10–3 100 Water

HFE7200 Toluene Water Ethanol

s mm 0.15 0.3 0.5

(C)

10–1 10–2 10–3 100

(D)

Ethanol

10–1 10–2 10–3 –4 –3 –2 –1 0 10 10 10 10 10 101 102 103 104

Ca·We

FIGURE 2.3.22 Relation among nondimensional microlayer thickness and dominant nondimensional parameters (effect of test fluids): (A) HFE7200; (B) toluene; (C) water; and (D) ethanol.

Equation (2.3.9) is transformed into Eq. (2.3.11) using nondimensional numbers, pffiffiffi δ0 20:5 0:5 2 Ca Bo BCaUWe: s

(2.3.11)

All of the experimental data are plotted in Figs. 2.3.22 and 2.3.23, where the coordinate is the nondimensional group of Eq. (2.3.11). Fig. 2.3.22A
D shows the effect of the test fluid; each graph denotes each fluid brought to the front, respectively, because the symbols of the front fluid tend to overlap other data. In addition, Fig. 2.3.23A
C shows the effect of each gap size. It is shown that each fluid and each gap size correlated well without apparent discord as shown in Figs. 2.3.22 and 2.3.23, respectively. Eqs (2.3.12) and (2.3.13) are fitting equations for the experiment data with CaUWe , 0:1 and CaUWe . 10, respectively, plotted as solid lines in Figs. 2.3.22 and 2.3.23, and the area between the two regions is considered the transition region. Then, the continuous equation can be created by combining the two equations obtained from Figs. 2.3.22 and 2.3.23 as shown in Eq. (2.3.14), which is rewritten in a simpler form (dashed line in Figs. 2.3.22 and 2.3.23),

2.3.4 CONCLUSION

100

s = 0.15 mm

10–1

85

(A) (δ0/s)Ca-0.50Bo0.50 =0.44(Ca·We)0.03

10–2 (δ0/s)Ca-0.50Bo0.50 =0.32(Ca·We)0.45 (δ0/s)Ca-0.50Bo0.50

10–3 100 s = 0.30 mm

(B)

10–1 10–2

10–3 100 s = 0.50 mm

s mm 0.15 0.3 0.5

HFE7200 Toluene Water s mm Ethanol 0.15 0.3 0.5

(C) 10–1 10–2 10–3 10–4 10–3 10–2 10–1 100 101 102 103 104

Ca·We

FIGURE 2.3.23 Relation among nondimensional microlayer thickness and dominant nondimensional parameters (effect of gap size): (A) s 5 0.15 mm; (B) s 5 0.30 mm; and (C) s 5 0.50 mm.

δ0 20:50 0:50 Ca Bo 5 0:32ðCaUWeÞ0:45 ; s δ0 20:50 0:50 Ca Bo 5 0:44ðCaUWeÞ0:03 ; s

(2.3.12) (2.3.13)

and 21=3 δ0  5 ½0:32Ca0:95 We0:45 Bo20:5 23 1½0:44Ca0:53 We0:03 Bo20:5 23 : s

(2.3.14)

2.3.4 CONCLUSION Experiments were performed to directly measure the microlayer that forms on a heating surface by vapor growth during boiling in a mini-/microchannel formed by two parallel plates using the laser extinction method. The characteristics of microlayer formation and boiling heat transfer were investigated.

86

CHAPTER 2 NUCLEATE BOILING

1. The effect of surface wettability on boiling characteristic curves was studied. The higher wettability improves heat transfer characteristics due to the effective formation and sustainability of the thin liquid film on the heating surface. Boiling modes with wettable surfaces are classified into typically two regimes of expansion of a single bubble with a thin liquid film and dry-out of the greater part of the channel. 2. The initial microlayer thickness was mainly determined by the gap sizes and the velocity of the bubble forefront. In the low-velocity region, the velocity profile of the liquid in front of the bubble is parabolic; therefore, the development of the microlayer is not affected by the boundary layer. In the high-velocity region, the core flow of liquid became a parallel flow. Consequently, the viscous boundary layer limited the development of the microlayer. 3. The dominant heat transfer mechanisms as the microlayer evaporation and the prediction of the vaporization rate were confirmed based on the characteristics of the microlayer. 4. On the basis of the results of the experiment and simulation using dimension analysis, a uniform empirical correlation was proposed for the nondimensional microlayer thickness correlated well as a function of the Capillary number, Weber number, and Bond number.

NOMENCLATURE A a D Di g I I0 LB Lx, Ly NB NR P q Rb s t tL tM T T0 TW ΔT 5 TW 2 T0 U VL Vout x

extinction coefficient acceleration distance from incipient bubble site hydraulic diameter of the channel gravitational acceleration detected laser intensity with liquid
layer detected laser intensity without liquid
layer initial bubble length lengths of calculation domain number of times of initial microlayer appearance by bubble growth in a bubble period number of times of microlayer appearance by liquid slug in a bubble period pressure average heat flux initial bubble radius gap size time after formation of microlayer term filled with bulk liquid term with microlayer liquid temperature vapor saturation temperature temperature of heat transfer surface superheat of heat transfer surface bubble moving velocity local bubble forefront velocity outlet velocity nondimensional height of heat transfer surface

REFERENCES

87

GREEK SYMBOLS δ δ0 δV μ σ ρL ρV

microlayer thickness initial microlayer thickness viscous boundary layer thickness viscosity surface tension coefficient liquid density vapor density

NONDIMENSIONAL NUMBERS Ca capillary number 5 μLVL/σ We Weber number 5 ρsVL2/σ Bo Bond number 5 (ρDi2/σ){U2/(2D)} or ρas2/σ

REFERENCES [1] S.G. Kandlikar, Two-phase flow patterns, pressure drop and heat transfer during boiling in mini-channel and micro-channel flow passages of compact evaporators, Heat Transfer Eng. 23 (2002) 5
23. [2] D.S. Wen, Y. Yan, D.B.R. Kenning, Saturated flow boiling of water at atmospheric pressure in a 2 mm 3 1 mm vertical channel: time-averaged heat transfer coefficients and correlations, Proc. 8th UK National Heat Transfer Conference (2003). [3] J.R. Thome, V. Dupont, A.M. Jacobi, Heat transfer model for evaporation in microchannels. Part I: presentation of the model, Int. J. Heat Mass Transfer 47 (2004) 3375
3385. [4] V. Dupont, J.R. Thome, A.M. Jacobi, Heat transfer model for evaporation in microchannels. Part II: comparison with the database, Int. J. Heat Mass Transfer 47 (2004) 3387
3401. [5] Y. Katto, S. Yokoya, Experimental study of nucleate pool boiling in case of making interference plate approach to the heating surface, Proc. 3rd Int. Heat Transfer Conf. 3 (1966) 219. [6] Y. Fujita, H. Ohta, S. Uchida, Heat transfer in nucleate boiling within a vertical narrow space, JSME Int. J. II 31 (3) (1988) 513. [7] G.I. Taylor, Deposition of a viscous fluid on the wall of a tube, J. Fluid Mech. 10 (1961) 1161
1165. [8] F.P. Bretherton, The motion of long bubbles in tubes, J. Fluid Mech. 10 (1961) 166
188. [9] P. Aussillous, D. Quere, Quick deposition of a fluid on the wall of a tube, Phys. Fluids 12 (2000) 2367
2371. [10] Y.H. Zhang, Y. Utaka, Characteristics of microlayer formation and heat transfer in mini/microchannel boiling systems: a review, Front. Heat Mass Transfer 3 (1) (2012) 013003. [11] Y. Han, N. Shikazono, Measurement of the liquid film thickness in micro tube slug flow, Int. J. Heat Fluid Flow 30 (5) (2009) 842
853. [12] Y. Utaka, S. Okuda, Y. Tasaki, Configuration of the micro-layer and characteristics of heat transfer in a narrow gap mini/micro-channel boiling system, Int. J. Heat Mass Transfer 52 (2009) 2205
2214.

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[13] K. Moriyama, A. Inoue, Thickness of the liquid film formed by a growing bubble in a narrow gap between two horizontal plates, Trans. ASME J. Heat Transfer 118 (1996) 132
139. [14] Y. Han, N. Shikazono, The effect of bubble acceleration on the liquid film thickness in micro tubes, Int. J. Heat Fluid Flow 31 (2010) 630
639. [15] Y. Tasaki, Y. Utaka, Effects of surface properties and gap sizes on boiling heat transfer characteristics in a micro-channel vapor generator, J. Enhanced Heat Transfer 13 (3) (2006) 245
260. [16] Y. Utaka, T. Nishikawa, Measurement of condensate film thickness for solutal marangoni condensation applying laser extinction method, J. Enhanced Heat Transfer 10 (2) (2003) 119
129. [17] Y. Utaka, T. Nishikawa, An investigation of liquid film thickness during solutal Marangoni condensation using laser absorption method: absorption property and examination of measuring method, Heat Transfer Asian Res. 30 (8) (2003) 700
711. [18] Y.H. Zhang, Y. Utaka, Characteristics of a liquid microlayer formed by a confined vapor bubble in micro gap boiling between two parallel plates, Int. J. Heat Mass Transfer 84 (2015) 475
485.

2.4

SURFACE TENSION OF HIGH-CARBON ALCOHOL AQUEOUS SOLUTIONS: ITS DEPENDENCE ON TEMPERATURE AND CONCENTRATION AND APPLICATION TO FLOW BOILING IN MINICHANNELS

Naoki Ono Shibaura Institute of Technology, Tokyo, Japan

2.4.1 INTRODUCTION The temperature dependence of the surface tension of certain high-carbon alcohol aqueous solutions, such as those of butanol and pentanol, has peculiar characteristics. The surface tension of these solutions increases when their temperature is raised above a certain threshold, whereas the surface tension of normal fluids such as pure water monotonously decreases with increasing temperature. The author has referred to this characteristic reversal of the temperature dependence of the surface tension (namely, the reversal of the sign of @σ=@T with increasing temperature) as “nonlinearity” [1]. This peculiar characteristic of high-carbon alcohol aqueous solutions was discovered by Vochten et al. about 40 years ago, the publication of which is well known [2]. They established that alcohol compounds with four and more carbon atoms per molecule exhibit the described

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89

peculiarity. However, since the publication, very little additional information regarding surface tension values has been provided. It is very difficult to measure the surface tension of the interface between an alcohol aqueous solution and its vapor in equilibrium in chemical thermodynamic terms. However, the author has considered it meaningful to evaluate the surface tension of high-carbon alcohol aqueous solutions even for measurements performed at the interface between the solution and air [3]. Conversely, a number of applications of high-carbon alcohol aqueous solutions to practical boiling systems have been recently investigated [4
7]. In particular, for the cooling of small-scaled heat-emitting devices, like central processing units in personal computers and optical components such as lasers, the usage of high-carbon alcohol aqueous solutions is regarded as an important future application. This focus on small-scaled devices is because the surface tension and the peculiarities of the working fluid play a more significant role in mini- or microscale channels than in normal-scale channels. Simultaneously, several studies have also attempted to apply high-carbon alcohol aqueous solutions toward heat pipes and have obtained successful results [8]. This type of high-carbon aqueous solution has also been referred to as ‘self-rewetting fluid’ by Abe [5]. The merit of using this fluid is that the direction of the thermocapillary force in a liquid film of the solution on a heated surface acts in the same direction as the solutocapillary force. In the following sections, the author reports on two issues: (1) surface tension measurements of high-carbon alcohol aqueous solutions, and (2) the author’s basic findings concerning the effect of high-carbon alcohol aqueous solutions on the critical heat flux (CHF) in boiling with impinging flow in a minichannel.

2.4.2 SURFACE TENSION MEASUREMENTS OF HIGH-CARBON ALCOHOL AQUEOUS SOLUTIONS 2.4.2.1 METHOD Since Vochten et al. discovered the unusual temperature dependence of the surface tension of some high-carbon alcohol aqueous solutions, the behavior of these fluids has been of substantial interest to many researchers. However, the temperature dependence of the surface tension of these solutions has not been thoroughly measured and has been little publicized except for Vochten’s paper [2]. One reason for the lack of further studies is that it is somewhat difficult, technically, to reproduce Vochten’s data because the procedure requires careful handling and heating of the solution. Another reason is that the originally measured values of a given solution for a single particular concentration were normalized and plotted in such a manner that does not allow for simple and clear comparison with the data measured by other researchers. Moreover, in Vochten’s study, the concentration dependence was not well investigated. The present work reports on the results of the temperature and concentration dependence of several alcohol aqueous solutions determined by the maximum bubble pressure method. The maximum bubble pressure method was deemed a better choice as a measuring technique because changes in the alcohol concentration of the test fluid during heating was well constrained, and the results compared favorably with those of Wilhelmy’s method, which will be discussed later.

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Fig. 2.4.1 shows a schematic diagram of the measurement apparatus of the maximum bubble pressure method used in the measurements [3]. The principle of the measuring technique has been described in detail elsewhere [9]. A fine capillary tube was immersed in the test fluid, and air was forced into the tube from the rear end. Thus, a small semispherical bubble was generated at the tube end immersed in the fluid. This method utilizes the internal pressure at the instant when the bubble is detached from the capillary tube. Fig. 2.4.2 shows the pressure balance among atmospheric pressure p0, fluid static pressure, and the head difference in the manometer. When the end of a tube of inner radius R0 is located at a distance h1 below the fluid free surface and the curvature radius of the bubble is R, and the gravitational acceleration is g, the pressure inside the bubble p(R) can be expressed using Eq. (2.4.1) with the surface tension γ, because p(R) is equal to the pressure of the air between the bubble and the

FIGURE 2.4.1 Schematic of the measurement apparatus employed for maximum bubble pressure method [3].

FIGURE 2.4.2 Description of balance of static pressure in maximum bubble pressure method [3].

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91

manometer. The density of the air in the manometer is ignored because it is negligibly small compared to the density ρ of the fluid. pðRÞ 5 p0 1 ρgh1 1

2γ R

(2.4.1)

The third term on the right-hand side of Eq. (2.4.1) is the so-called Laplace pressure caused by surface tension. In contrast, using the manometer reading h2, the following equation can be obtained. pðRÞ 5 p0 1 ρgh2

(2.4.2)

Here, it is assumed that the density ρ of the fluid in the container is the same as that of the fluid in the U-shaped manometer. Combining Eqs (2.4.1) and (2.4.2), the expression for the surface tension γ can be deduced as follows. γ5

ρgðh2 2 h1 ÞR 2

(2.4.3)

Whenever static balance is achieved, Eq. (2.4.3) is satisfied. In the measurement, water drops were added into the manometer one by one from the tube edge in the air, then a pressure increment was imposed inside the manometer. As the pressure inside the manometer increased, the radius R of the bubble decreased from the initial near-flat shape of the gas
liquid interface, and its minimum value was achieved when the bubble radius became equal to the tube’s inner radius R0. Subsequently, the bubble radius again increased. However, in most cases, the bubble detached from the tube as soon as the radius increased, as was well confirmed by actual observations [3] (not specified in this article). When the bubble radius obtained a minimum, the Laplace pressure obtained a maximum. Thus, the surface tension can be deduced from Eq. (2.4.3) using the pressure balance at this instant. In this study, the following equation was used to obtain the surface tension. γ5

ρgðh2 2 h1 ÞR0 2

(2.4.4)

A 32-mm-long glass tube with an inner diameter of 0.20 mm and outer diameter of 0.68 mm was used as the capillary tube. The tube was a special product for biological science use with high precision in terms of its diameter. The precision of the diameter was within 0.01 mm. The tube was connected to a U-shaped manometer that measured the pressure of the inner air. By adding a small drop of pure water into the manometer with a spuit or a syringe filled with the fluid, the pressure of the inner air was raised, and the air was gradually pushed into the test liquid. At the instant when the bubble detached from the capillary tube, the maximum pressure was obtained using the head difference in the U-shaped manometer because the bubble radius at that instant was nearly equal to the tube inner radius. Regarding the addition of a drop of pure water into the manometer, pure water was used because of the simplicity and readiness in handling it and because of the fact that the lowconcentration alcohol aqueous solutions used in the experiments had nearly the same density as that of pure water. The test fluid was held in a glass container with an inner diameter of 60 mm, and the bottom of the container was heated by an electric heater. The glass container was covered with a holder and a lid, which were made of an insulating material. The capillary tube and thermocouple were attached to the lid and inserted into the test fluid. The lid prohibited the vapor from

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escaping the container. To maintain atmospheric pressure during the experiments, volume expansion of the gas phase inside the container was vented through the lid into a small vinyl balloon. The fluid temperature was slowly increased from room temperature at increments of 5 C. After confirming that the temperature was constant and steady, a temperature measurement was conducted. The method employed here is a static procedure using the maximum bubble pressure method. A dynamic procedure (for example, fluctuated interface method, etc.) also exists, and measuring equipment for the dynamic method is commercially available. It should be noted that the values measured in this experiment differ somewhat from an exact surface tension in the chemical thermodynamic sense. The exact surface tension should be at the free surface between the solution and its vapor phase in equilibrium. As shown in Fig. 2.4.1, the gas inside the capillary tube and manometer tube was air when the experiment began. The gas could certainly contain vapor from the heated solution; however, the partial pressure of the vapor phase was not controlled. Conversely, as was mentioned, the diameter of the bubble at the end of the capillary tube was as small as 0.20
0.68 mm. Thus, the surface area of the bubble was so small that solution evaporation through the bubble surface might have provided little change in the gas components. To obtain a more exact value of surface tension, the partial pressure equilibrium of the evaporated alcohol has to be achieved at the temperature of the solution. Therefore, the surface tension data obtained here is useful to the extent that it can be assumed that the surface tension between the solution and the gas phase in equilibrium in the chemical thermodynamic sense and the surface tension between the solution and the air are nearly equivalent. As an alternative, the well-known Wilhelmy’s method was also employed to obtain surface tension data, and the results obtained were compared with those obtained by the maximum bubble pressure method [3]. A pictorial description of the apparatus used for Wilhelmy’s method is given in Fig. 2.4.3. When the contact angle between the fluid and the platinum plate is unknown, the

FIGURE 2.4.3 Apparatus employed in Wilhelmy’s method.

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93

force due to surface tension is usually measured at the instant when the plate is detached from the liquid. As can be seen in Fig. 2.4.3, this method requires a hole in the liquid container to allow movement of the hanging wire. Therefore, the influence of solution evaporation cannot be eliminated, which forms a disadvantage of the method for measurements conducted at high temperatures. The test fluids used in this study were 1-butanol, 1-pentanol, and ethanol aqueous solutions as well as pure water. Moreover, pure 1-butanol and 1-pentanol were investigated for comparison. For the remainder of this article, 1-butanol and 1-pentanol are referred to as butanol and pentanol, respectively.

2.4.2.2 RESULTS Before presenting the data measured by the maximum bubble pressure method, some results of the method are compared to those of Wilhelmy’s method to validate the method employed and to identify its advantages in the present high-temperature experiments. In Fig. 2.4.4, the data for pure water obtained by Wilhelmy’s method (“Wilhelmy” in the figure) and the maximum bubble pressure method (“bubble” in the figure) are compared. The notations used in Fig. 2.4.4 are employed in all subsequent figures. In the case of pure water, pure water evaporation has no influence on the measured values even in Wilhelmy’s method because concentration is not a factor. In addition, the data publicized by the JSME (Japan Society of Mechanical Engineers) is also shown [10] in the figure. Note that figures similar to Figs. 2.4.4
2.4.8 can be found in the author’s previous work [3]; however, the symbols and arrangements are modified for the reader’s convenience in the present article.

FIGURE 2.4.4 Comparisons of surface tensions obtained from the maximum bubble pressure method and Wilhelmy’s method for pure water.

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FIGURE 2.4.5 Comparisons of surface tensions obtained from maximum bubble pressure method and Wilhelmy’s method for various alcohol aqueous solutions.

According to Fig. 2.4.4, the data measured by the maximum bubble pressure method agrees well with those obtained by Wilhelmy’s method for pure water. Moreover, deviations from the publicized JSME data were in the range 0.1
0.4 mN/m, which is reasonably small. The above comparisons confirm that the maximum bubble pressure method is sufficiently valid. Fig. 2.4.5 shows the measured data for representative alcohol concentrations of butanol, pentanol, and ethanol aqueous solutions by the maximum bubble pressure method and by Wilhelmy’s method. The peculiar behavior discussed, namely, the tendency for the surface tension to increase above a critical temperature as the temperature is increased, is observed for the butanol and pentanol aqueous solutions. The data obtained by the maximum bubble pressure method exhibits a smaller increase with increasing temperature. The observed difference between the results from the two methods is attributed to the elimination of escaping vapor in the maximum bubble pressure method. Fig. 2.4.5 indicates that the influence of escaping vapor on the alcohol concentration in Wilhelmy’s method was not negligible, and that the maximum bubble pressure method served in successfully preventing this problem. The author is of the view that more reliable results were obtained by the maximum bubble pressure method and that this method is suitable for alcohol solution surface tension measurements at high temperatures. Fig. 2.4.6 shows the measured results for butanol aqueous solutions of various concentrations. With increasing temperature, the surface tension of all butanol solutions decreased until approximately 60 C. Above 60 C, the surface tension began increasing with increasing temperature. At the higher concentrations of butanol, the absolute value of the surface tension was lower, whereas the magnitude of the increase above 60 C was larger. Fig. 2.4.6 also includes results for pure butanol, referred to simply as butanol. As expected, the surface tension of butanol monotonically decreased with increasing temperature. Fig. 2.4.7 shows the measured results for pentanol aqueous solutions

2.4.2 SURFACE TENSION MEASUREMENTS

FIGURE 2.4.6 Surface tensions of butanol aqueous solutions measured by maximum bubble pressure method.

FIGURE 2.4.7 Surface tensions of pentanol aqueous solutions measured by maximum bubble pressure method.

95

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FIGURE 2.4.8 Surface tensions of ethanol aqueous solutions measured by maximum bubble pressure method.

of various concentrations. The overall tendency is similar to that of butanol aqueous solutions, except that, with the pentanol solutions, the surface tension began increasing at temperatures above 55 C rather than 60 C, as was observed for butanol solutions. Fig. 2.4.8 shows the measured results for ethanol aqueous solutions of various concentrations. The surface tension for all concentrations tended to decrease monotonically with increasing temperature. However, surface tension remained constant or increased slightly above 75 C. The author is of the view that this could be because of the onset of boiling. Because the boiling points of the ethanol aqueous solutions of the concentrations studied are about 80 C, the ethanol concentration might have been decreased due to its evaporation with boiling at the high temperature. Concerning the observed error in the measured data, the validity of employing Eq. (2.4.4) is an important issue. Eq. (2.4.4) assumes that the test fluid and pure water densities in the manometer are equal, although the actual differences in the measurements could cause a small error in the determined surface tension. From an estimation of the actual density differences, the errors were 1.6% for the butanol 7.15 wt% solution and 0.4% for the pentanol 2.0 wt% solution, which can be regarded as small. Conversely, in the case of the ethanol solution, the error was 14.6% for the ethanol 55.0 wt% solution. Therefore, it should be noted that the measured surface tension values of the high-concentration ethanol solutions include some amount of error.

2.4.3 EFFECT OF HIGH-CARBON ALCOHOL AQUEOUS SOLUTIONS

97

2.4.2.3 DISCUSSION As shown in Fig. 2.4.5, the maximum bubble pressure method provided for a milder nonlinearity for the surface tension of butanol and pentanol aqueous solutions. This is attributed to the fact that the maximum bubble pressure method enclosed the test fluid and vapor, and the resulting errors caused by changes in the alcohol concentration due to species evaporation was minimized. This condition was different from that employed in Wilhelmy’s method. The solubility of butanol in pure water at room temperature is 7.15 wt%, whereas that of pentanol in pure water at room temperature is 2.0 wt%. The surface tension of pure water is very sensitive to the addition of these alcohols. At solubility concentrations, the surface tension of the aqueous solutions approached that of pure alcohols at low temperature, as shown in Figs. 2.4.6 and 2.4.7. The surface tension of pentanol solutions exhibited a stronger reversing tendency than that of butanol solutions, as indicated by comparing Figs. 2.4.6 and 2.4.7. In this sense, pentanol is a more efficient additive for obtaining an increasing surface tension with increasing temperature. This enhanced tendency was also suggested in Vochten’s original work [2]. However, as the number of carbon atoms in the alcohol molecule increases, the solubility in pure water drastically decreases. Therefore, it can be concluded that it will be technically difficult to prepare a mixture of pure water and alcohols consisting of a large number of carbon atoms in the molecular formula for use in a practical application. The solubility of pentanol in pure water at room temperature is only 2.0 wt%, and it would be difficult to maintain this small concentration in practical applications for an extended period of time. Butanol would be a better and more reasonable choice for applications from the viewpoint of property changes over time.

2.4.3 EFFECT OF HIGH-CARBON ALCOHOL AQUEOUS SOLUTIONS ON THE CRITICAL HEAT FLUX CONDITION IN BOILING WITH IMPINGING FLOW IN A MINICHANNEL 2.4.3.1 METHOD As previously mentioned, the direction of the thermocapillary force in a liquid film of a highcarbon alcohol aqueous solution on a heated surface acts in the same direction as the solutocapillary force. Conversely, in normal fluids, the directions of the two forces are opposite, and the resultant capillary flow for wetting a heated wall is weakened. Thus, a high-carbon alcohol aqueous solution can be expected to restrain dry-out, or CHF phenomena, in boiling heat transfer. In fact, high-carbon alcohol aqueous solutions are already applied to heat pipes [8]. The author performed a basic experiment involving boiling with impinging flow in a minichannel, and reports on the merits of these solutions in terms of their CHF. A description of the experimental apparatus and photos of the test section are shown in Figs. 2.4.9, 2.4.10, and 2.4.11. The working fluid in a tank was stirred by a hot stirrer and sent to a pressure tank by a chemical pump. The fluid was heated in the pressure tank with a stick heater and was set to a predetermined temperature using a belt heater and a thermoregulator. The fluid that passed the test section was cooled with a heat exchanger and was then returned to the tank.

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FIGURE 2.4.9 Experimental apparatus.

FIGURE 2.4.10 Test section (middle section) of apparatus shown in Fig. 2.4.9. PBI, polybenzimidazole.

2.4.3 EFFECT OF HIGH-CARBON ALCOHOL AQUEOUS SOLUTIONS

99

FIGURE 2.4.11 Heated surface and its rod.

The test section was composed of PEEK (polyetheretherketone) resin, which has a high insulating property, and PBI (polybenzimidazole) resin was used for the vicinity of the heating area subject to a very high temperature. The test section comprised three sections, where only the middle section is shown in Fig. 2.4.10. It had glass windows for the observation of boiling bubbles, which is not specified in this article. The flow channel was constructed in a T-junction shape, and the middle section was combined with the other two sections, one on each side, with rubber packing. The heated surface formed of a copper block 3 mm 3 10 mm was installed in the upper part of the channel center, and K-type thermocouples were attached at several locations in the vertical direction from the heated surface. In the experiment, after confirming that the temperature attained a steady state, the heat flux from the heated surface to the fluid was calculated by the measured temperature data, and its gradient was determined using Fourier’s law. The temperature at the heated surface was obtained by extrapolating from the measured temperature distribution. The experimental conditions and the test fluids used in the experiments are listed in Tables 2.4.1 and 2.4.2, respectively. In the experiments, aqueous solutions of some low-carbon alcohols, namely, ethanol and 2-propanol, were also investigated for fair comparison with those of high-carbon alcohols. Aqueous solutions of butanol and pentanol have been reported to have the effect of increasing the CHF in pool boiling [11,12].

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Table 2.4.1 Critical Heat Flux Experimental Conditions Volume flow rate Flow velocity Reynolds number Subcooling

40 mL/min 7.4 3 1022 m/s 780 20 K

Table 2.4.2 Test Fluids Used in Critical Heat Flux Experiments Test Fluid

Concentration (wt%)

Aqueous solution Aqueous solution Aqueous solution Aqueous solution Pure water

of 1-butanol of 1-pentanol of 2-propanol of ethanol

Heat flux [W/m2]

1.0E + 07

]

2

3.0 1.5 11.0 15.0


1-Pentanol aq. sol. (1.5 wt%) 1-Butanol aq. sol. (3 wt%) 2-propanol aq. sol. (11 wt%) Ethanol aq. sol. (15 wt%) Pure water Rohsenow (Pure water) Katto (Pure water) Zuber (Pure water)

1.0E + 06

1.0E + 05 1.0E + 00

1.0E + 01 Wall super heat [°C]

1.0E + 02

FIGURE 2.4.12 Boiling curves (critical heat flux of various fluids are encircled in gray).

2.4.3.2 RESULTS The obtained boiling curves are shown in Fig. 2.4.12. The symbols marked by the gray circles indicate the CHF of each fluid. In the figure, three well-known correlation lines are also depicted. These lines represent Rohsenow’s correlation for nucleate boiling of pure water [13], Zuber’s prediction of the CHF for pure water [14], and Katto’s prediction of forced-convection heat transfer in

2.4.4 CONCLUSION

101

laminar impinging flow for pure water [15]. These are well-established theories, and, therefore, the details are not discussed here. As shown in the figure, the CHF of 1-pentanol was the highest among the solutions evaluated, and the CHFs of the high-carbon alcohol aqueous solutions (1-pentanol and 1-butanol) were higher than those of the low-carbon alcohol aqueous solutions (2-propanol and ethanol) and pure water.

2.4.3.3 DISCUSSION It was found from the experiments that the 1-pentanol aqueous solution (1.5 wt%) provided the highest CHF value, which was approximately 2.6 times higher than that of pure water, whereas the CHF of the 1-butanol solution (3.0 wt%) was 2.2 times higher than that of pure water. These results indicate that the nonlinearity of the temperature dependence of the surface tension may have played a role in delaying the onset of dry-out and increasing of the CHF. In practical applications of highcarbon alcohol aqueous solutions, the small solubility of 1-pentanol at room temperature, which is only about 2 wt%, would cause difficulties in controlling the concentration during running time. Thus, 1-butanol could be a better selection from a practical viewpoint. Conversely, the 2-propanol aqueous solution (11 wt%) also provided a higher CHF than that of pure water. Except for the near-CHF region, 2-propanol and ethanol did not exhibit heat transfer deterioration in the lower wall superheat region relative to 1-pentanol and 1-butanol. 2-propanol and ethanol are categorized as low-carbon alcohols, and their aqueous solutions are not thought to demonstrate a nonlinear surface tension dependence on temperature. However, the author is of the view that their solutocapillary effect was sufficiently strong to enhance CHF under the present experimental conditions nearly as well as the combination of thermocapillary and solutocapillary effects of high-carbon alcohols. Determination of a detailed mechanism and a comprehensive interpretation of the above results require further study in the future.

2.4.4 CONCLUSION In this section, the results of surface tension measurements of high-carbon alcohol aqueous solutions and the author’s basic findings regarding the effect of high-carbon alcohol aqueous solutions on CHF in boiling with impinging flow in a minichannel are reported. These are summarized as follows. 1. To investigate the peculiar temperature dependence of the surface tension of butanol and other high-carbon alcohol aqueous solutions, measurements were performed by applying the maximum bubble pressure method in an enclosed container. The measured surface tension was a property of the interface between the solution and air, not the vapor phase in equilibrium. However, the measurement revealed the nonlinearity of the temperature dependence of the surface tension of high-carbon alcohol aqueous solutions and provided more reliable data than Wilhelmy’s method. The author believes that the data will be found useful for various purposes in the future. 2. In a T-junction rectangular minichannel (3 mm 3 3 mm), boiling with impinging flow on the heated surface was performed to investigate the effect of high-carbon alcohol aqueous solutions

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on the CHF condition. In the current experiments, 1-pentanol solution (1.5 wt%) provided the highest CHF of any other high or low-carbon alcohol aqueous solution. Although the precise mechanism is still unclear, the author is of the view that the nonlinear surface tension dependence on temperature would have played some role in delaying the onset of dry-out and increasing CHF value.

ACKNOWLEDGMENTS The author would like to thank Prof. M. Shoji, Associate Prof. M. Tange, and Dr Nishiguchi for their helpful suggestions and aid in the research. Appreciation must also be extended to T. Kaneko, T. Ueno, T. Ojiro, and H. Itoh for their assistance in the author’s laboratory with the experiments and measurements. This research was partially supported by the MEXT/JSPS, Grant-in-Aid for Scientific Research (C, No. 21560225).

NOMENCLATURE R R0 g h1 h2 p0 p(R)

radius of the bubble inner radius of the tube gravitational acceleration height of the tube in the liquid below the free surface height of the liquid in manometer reading atmospheric pressure pressure inside the bubble with radius R

GREEK SYMBOLS γ surface tension of the fluid ρ density of the fluid

REFERENCES [1] N. Ono, T. Yoshida, M. Shoji, F. Takemura, T.-H. Yen, Heat transfer and liquid motion of forced convective boiling in a mini-tube for aqueous solutions with nonlinear surface energy, Multiphase Sci. Technol. 19 (4) (2007) 225
240. [2] R. Vochten, G. Petre, Study of the heat of reversible adsorption at the air
solution interface II. Experimental determination of the heat of reversible adsorption of some alcohols, J. Colloid Interface Sci. 42 (2) (1973) 320
327. [3] N. Ono, T. Kaneko, S. Nishiguchi, M. Shoji, Measurement of temperature dependence of surface tension of alcohol aqueous solutions by maximum bubble pressure method, J. Thermal Sci. Technol. (JSME) 4 (2) (2009) 284
293.

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103

[4] K. Suzuki, Microbubble emission boiling of alcohol
water mixtures, IASME Trans. 2 (7) (2005) 1106
1111. [5] Y. Abe, Thermal management with self-rewetting fluids, Jpn. Soc. Microgravity Appl. 23 (2) (2006) 80
87. [6] Y. Abe, Self-rewetting fluids, Ann. N Y Acad. Sci. 1077 (2006) 650
667. [7] S. Nishiguchi, N. Ono, M. Shoji, Boiling heat transfer of butanol aqueous solution
augmentation of critical heat flux, J. ASTM Int. (2012) Paper IDJAI 103452-10, online journal. [8] Y. Abe, A flexible wickless heat pipes with self-rewetting fluids, Proc. 9th AIAA/ASME Joint Thermo Physics and Heat Transfer Conference, AIAA Paper No. 2006-3105, 2006. [9] A.W. Adamson, A.P. Gast, Physical Chemistry of Surfaces, Wiley-Interscience, 1997. [10] JSME Data book: Thermophysical properties of fluids, Japan Society of Mechanical Engineers, 1983 (in Japanese). [11] H. Sakashita, A. Ono, Y. Nakabayashi, Measurement of critical heat flux and liquid
vapor structure near the heating surface in pool boiling of 2-propanol/water mixtures, Int. J. Heat Mass Transfer 53 (7
8) (2010) 1554
1562. [12] Y. Fujita, Q. Bai, Critical heat flux of binary mixtures in pool boiling and its correlation in terms of Marangoni number, Int. J. Refrigeration 20 (8) (1997) 616
622. [13] W.M. Rohsenow, A method of correlating heat transfer data for surface boiling liquids, Trans. ASME 74 (1952) 969 1952. [14] N. Zuber, On the stability of boiling heat transfer, Trans. ASME Vol. 80 (1958) 711. [15] Y. Katto, JSME Data Book: Heat Transfer, 5th Edition, JSME, in Japanese, 2009, p. 33, its original work was in 1981.

2.5

NUCLEATE BOILING OF MIXTURES

Haruhiko Ohta Kyushu University, Fukuoka, Japan

2.5.1 MIXTURE EFFECTS ON ELEMENTARY PROCESSES OF NUCLEATE BOILING 2.5.1.1 PHASE EQUILIBRIUM DIAGRAM Fig. 2.5.1A shows an example of phase equilibrium for soluble mixtures at a constant pressure, where the mixture is composed of a more-volatile component and a less-volatile component, and suffixes 1 and 2 are given, respectively. The mixture is described usually as “component 1
component 2.” The abscissa is selected as either mole fraction X1 (liquid), Y1 (vapor) or weight

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FIGURE 2.5.1 Different shapes of phase equilibrium diagram and terminology: (A) without azeotropic point; (B) with azeotropic point.

fraction x1 (liquid), y1 (vapor) of the more-volatile component. A part of the mixture has an azeotropic concentration as shown in Fig. 2.5.1B, where the mixture behaves as a single component fluid with properties of the relevant concentration. For “nonazeotropic” (“zeoropic”) mixtures, or nonazeotropic concentrations of azeotropic mixtures, the concentration of liquid in the vicinity of the evaporating liquid
vapor interface is different from that of the bulk liquid due to the existence of mass transfer resistance. The preferential evaporation of more-volatile component 1 makes the concentration of vapor phase Y1b larger than that of bulk liquid X1b. The concentration of the more volatile component of liquid at the interfaces X1i becomes lower than X1b in the presence of mass diffusion resistance, resulting in the increase in interfacial temperature Ti from the equilibrium bulk temperature Tb. At higher heat flux, this trend is more pronounced, and the interfacial concentration of liquid approaches the minimum value X1i,min. For lower values less than X1i,min it is impossible to keep the mass conservation of individual components. The maximum value of interfacial temperature Tint,max is defined at X1i,min. Fig. 2.5.2 shows the distribution of temperature T and concentration X1 around a single bubble neglecting the pressure difference due to the curvature of the liquid
vapor interface. For a given surface temperature Tw, the substantial reduction of surface superheat from ΔT to the effective value ΔTeff is clear. From another point of view, the bulk liquid is subcooled as much as Δθ (5Ti 2 Tb).

2.5.1.2 BOILING INCIPIENCE The elementary processes for nucleate boiling of mixtures are summarized by Thome and Shock [1]. The same equation for a pure component can be applied to the required liquid superheat for the nucleation under the thermal equilibrium condition, but the gradient of the vapor pressure curve is given by the following equation [2]:

2.5.1 MIXTURE EFFECTS ON ELEMENTARY PROCESSES

105

FIGURE 2.5.2 Temperature and concentration distributions across a bubble surface.

2σ RðdP=dTÞsat       2  dP @P Pð Y1 2 X1 Þ @X1 @ g 5 1 dT sat @ T X1 Ro Tsat @ T P @X1 2 T;P ΔTsat 5

(2.5.1) (2.5.2)

where the terms on the right side can be approximately evaluated at X 5 X1b and T 5 Tb at a given pressure. Shock [3] showed the increase in (dP/dT)sat and the decrease in surface tension with increasing concentration of more-volatile components for ethanol
water and ethanol
benzene, which reduces the equilibrium superheat given by Eq. (2.5.1). The trend, however, is contradictory to the drastic increase of measured superheat at the boiling incipience for ethanol
water [4]. The contradiction is explained by the reduction of contact angle which makes the nuclei in cavities filled with liquid. Thome and Shakir [5] obtained almost constant activation superheat in the entire concentration range of N2
Ar, while the superheat takes a maximum for ethanol
water. In both mixtures, the calculated superheat decreases monotonously with increasing concentration of the more-volatile component.

2.5.1.3 BUBBLE GROWTH RATE Scriven [6] solved equations of momentum, energy, and mass transfer to obtain the bubble growth controlled by heat and mass diffusion. Van Stralen [7
10] discussed the bubble growth in uniformly superheated liquid based on the model by Plesset and Zwick [11]. When the evaporated more-volatile component is assumed to be supplied only by the diffusion across the boundary layer

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of thickness δM around a bubble as shown in Fig. 2.5.2 (using mass concentrations instead of mole concentrations), the mass balance for a unit interfacial area yields ρg ðy1i 2 x1i ÞðdR=dtÞ 5 ρ‘ Dð@x1 =@rÞr5R

(2.5.3)

2

where D is the diffusion coefficient for the liquid phase (m /s). The concentration gradient is evaluated approximately assuming linear concentration profile across the boundary layer thickness. ð@x=@rÞr5R Dðx1b 2 x1i Þ=δM

(2.5.4)

The transient boundary layer thicknesses for mass diffusion are evaluated along the same manner as heat diffusion. δM 5 ½ðπ=3ÞDt 1=2

(2.5.5)

The substitution of Eqs (2.5.4) and (2.5.5) into Eq. (2.5.3) gives the bubble growth rate. Taking account of the growing diffusion boundary layer with time similar to that of thermal boundary layer, the bubble growth rate derived from the mass balance is obtained. !  1=2 dR 3 ρ‘ 5 Gd D1=2 t21=2 dT π ρg

(2.5.6)

The parameter Gd is referred to as “vaporized mass diffusion fraction” defined as Gd  ðx1b 2 x1i Þ=ðy1i 2 x1i Þ

(2.5.7)

On the other hand, the bubble growth rate is obtained also from the energy balance, which is given by Plesset and Zwick [11] for a pure component.  1=2 dR 3 1=2 5 Ja κ‘ t21=2 dt π

(2.5.8)

Ja  ðρ‘ cp‘ =ρg hfg ÞΔT

(2.5.9)

where κ‘ is the thermal diffusivity of liquid (m /s), Ja is Jakob number (-), ΔT is the liquid superheat based on the temperature of bulk liquid Tb. For mixtures, ΔT is replaced by the effective superheat ΔTeff taking account of increment of interfacial temperature Δθ. 2

ΔTeff  ΔT 2 Δθ  1=2 ρ‘ cp‘ dR 3 1=2 5 ΔTeff κ‘ t21=2 dt π ρg hfg

(2.5.10) (2.5.11)

The bubble growth rate for mixtures is smaller than that of a pure component with the same properties. Equating both bubble growth rates Eqs. (2.5.6) and (2.5.11) from mass diffusion and heat diffusion, respectively, a key value Δθ can be evaluated.     Δθ hfg D 1=2 ΔT 5 21 cpl κ‘ Gd Δθ

(2.5.12)

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107

The term Δθ/Gd is regarded as the gradient of bubble point curve 2dT/dx1 multiplied by the concentration difference y1 2 x1 between vapor and liquid, which is evaluated graphically from a phase equilibrium diagram for small bulk concentrations x1b [12
15]. Δθ  2 x1b ðKb 2 1ÞðdT=dx1 Þx1 5x1b ; Kb 5 y1b =xb1 Gd

(2.5.13)

The reduction of growth rate for mixtures (“m”) compared to the hypothetical pure component (“p”) with the same properties is given using Eq. (2.5.12). C1;m ðdR=dTÞm ΔTeff ΔT 2 Δθ 1 5  5 5 C1;p ðdR=dTÞp ΔT ΔT 1 1 ðκ‘ =DÞ1=2 ðcp‘ =hfg ÞðΔθ=Gd Þ

(2.5.14)

The ratio is modified again by the substitution of Eq. (2.5.13). C1;m 1 5 1=2 C1;p 1 2 ðyb1 2 xb1 Þðκ‘ =DÞ ðcp‘ =hfg ÞðdT=dx1 Þx1 5x1b

(2.5.15)

The bubble radius for mixtures at the same instance is reduced by the same ratio.  R5

 12 1=2 C1;m Ja ðκ‘ tÞ1=2 π C1;p

(2.5.16)

Equation (2.5.16) without the term C1,m/C1,p is given by Plesset and Zwick [11]. Equation (2.5.15) is often referred to as Scriven number Sn. Van Stralen et al. [16] developed an improved model of diffusion-controlled bubble growth, where the evaporation from microlayer underneath a bubble is taken into account in addition to that from the superheated layer around a bubble.

2.5.1.4 BUBBLE DEPARTURE Fritz [17] gave a criterion of bubble departure by the failure of local interfacial force balance along the entire bubble surface during bubble growth. However, the bubble departure is often discussed simply by the comparison of upward and downward forces acting on a bubble to take dynamic forces into account, where the surface tension, drag and liquid inertia in the later stage act against the buoyancy. The reduction of bubble growth rate for mixtures decreases the adhesive forces except the surface tension, resulting in a smaller departure diameter. Thome [18] gives the ratio of mixture departure diameter Dd to that of ‘ideal’ single component Dd,I when the liquid inertia is dominant. Dd 5 Sn4=5 Dd; I

(2.5.17)

where Sn is the Scriven number defined by Eq. (2.5.15). For the bubble departure against the surface tension force   Dd σ sin γ 2 5 Sn Dd;I σI sin γ I

(2.5.18)

where γ is the contact angle. If the values for the hypothetical single component with the same properties as the relevant mixture are assumed to be referred to as “ideal” here, both equations become similar and are strongly dependent on Scriven number. The mixture departure diameter

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takes the minimum near the composition where |y1b 2 x1b| becomes the maximum by the nature of the Scriven number.

2.5.2 HEAT TRANSFER COEFFICIENT 2.5.2.1 PREDICTING METHOD AND CORRELATIONS The model of scraping thermal boundary layer [19], for example, is useful to predict a heat transfer rate reflecting the elementary process for nucleate boiling of mixtures. However, no coherent result including that for nucleation site density or bubble departure frequency was obtained except in the model for bubble growth rate described in Section 2.5.1.3. The use of semi-empirical methods for the evaluation of the heat transfer deterioration is unavoidable, and consists of three processes: (1) evaluation of reference value to define the degree of heat transfer deterioration, (2) evaluation of increased interfacial temperature around a bubble or on the surface of microlayer, and (3) establishment of heat transfer model to reflect the increased interfacial temperature to the heat transfer deterioration. To distinguish the effect of mass transfer resistance inherent in nonazeotropic mixtures on the heat transfer deterioration from the effect of properties, the reference heat transfer coefficient should be the value for a hypothetical single component liquid with the same properties as the mixture of relevant bulk concentration. However, it is quite difficult to obtain reference values with good accuracy. There is a possibility of using the existing correlation with linearly interpolated multiplier fitting the measured heat transfer coefficients for pure liquids or the mixture at an azeotropic concentration, provided that the correlation is developed from a reliable heat transfer model. Usually, a linear interpolation of surface superheats for a pure or an azeotropic mixture is used under a constant heat flux condition, resulting in a harmonic mean value of heat transfer coefficients. The value by such a linear interpolation using the mole or weight fractions of bulk liquid is often referred to as an “ideal” one with ambiguity. An example using mole fractions is as follows: ΔTI  X1 ΔT1 1 X2 ΔT2 5 X1 ΔT1 1 ð1 2 X1 Þ ΔT2

(2.5.19)

Stephan and Ko¨rner [20] derived the simplest correlation: α=αI 5 1=½1 1 A0 jY1 2 X1 jUð0:88 1 0:12P½barÞ

(2.5.20)

where A0 is an empirical constant given for an individual mixture. The correlation is the early one relating the deterioration to the difference between liquid and vapor concentrations. Some semitheoretical methods were proposed to evaluate the deterioration by the concept of effective surface superheat mentioned in Section 2.5.1.3. Calus and Leonidopulos [21] derived the correlation based on the analysis by Scriven [6]: α=αI 5 1=½1 2 ðy1 2 x1 Þðκ‘ =DÞ1=2 ðcp‘ =hfg ÞðdT=dx1 Þ  Sn

(2.5.21)

where the ideal heat transfer coefficient was evaluated based on Eq. (2.5.19) but using weight fraction. Jungnickel et al. [22] included the effect of heat flux for refrigerant mixtures, where larger deterioration was predicted at larger heat flux. α=α0l 5 1=½1 1 Ko jY1 2 X1 jUqð0:4810:1X1 Þ ðρg =ρ‘ Þ

(2.5.22)

2.5.2 HEAT TRANSFER COEFFICIENT

109

The empirical constant Ko was given as a function of saturation temperature difference between both pure components. αI0 was directly interpolated between the heat transfer coefficients of pure components. The density ratio, introduced instead of an explicit pressure term, gives larger heat transfer deterioration at higher pressure. Schlu¨nder [23] applied the film theory for evaluating the interfacial temperature and introduced the effect of heat flux theoretically. α=αI 5 1=½1 1 ðY1 2 X1 ÞðTsat;1 2 Tsat;2 ÞUðαI =qÞUf1 2 expð2 Bo ðq=ρ‘ β ‘ hfg ÞÞg

(2.5.23)

where both the mass transfer coefficient β ‘ and the mass flux q=ρ‘ hfg prescribe the thickness of the boundary layer implicitly. The term αI/q is identical to ΔTI in Eq. (2.5.19). In Eqs (2.5.20)
(2.5.23), all values can be evaluated approximately at bulk concentration and bulk temperature. Thome [24] simplified the relation from the concept of effective superheat (see Section 2.5.1.3, Fig. 2.5.2) α=αI 5 ΔTI =ΔT 5 1=ð1 1 Δθ=ΔTI Þ

(2.5.24)

α=αI D1=ð1 1 ΔTBP =ΔTI Þ

(2.5.25)

as where ΔTBP is defined in Fig. 2.5.1A. The correlation predicts the upper limit of possible deterioration. In Fig. 2.5.3, the deterioration rates of the heat transfer coefficient evaluated by Eqs (2.5.20),

FIGURE 2.5.3 Comparison between the rates of heat transfer deterioration calculated by existing correlations and experimental data at selected pressures [25]: (A) ethanol
water; (B) R11
R113.

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FIGURE 2.5.4 Phase equilibrium diagrams: (A) ethanol
water; (B) R11
R113.

(2.5.21), and (2.5.25) are compared with experimental data for ethanol
water and R11
R113. The phase equilibrium diagrams are shown in Fig. 2.5.4 for different two pressures. Ohta and Fujita [25] avoided the contradiction inherent in solving only the diffusion equation of the more-volatile component, where the less-volatile component diffuses implicitly from the interface to the liquid bulk, and applied Fick’s first law with bulk convection. N1 5 2C Dð@X1 =@zÞ 1 X1 ðN1 1 N2 Þ N2 5 2C Dð@X2 =@zÞ 1 X2 ðN1 1 N2 Þ

(2.5.26)

where C is molar concentration [kmol/m3], N is mole flux (kmol/m2s). The periodical twodimensional mass transfer in the liquid layer underneath a bubble is simplified into onedimensional steady mass transfer across the film. Then, N1 5 N1;i 5 const:; N2 5 N2;i 5 const:

(2.5.27)

where subscript “i” denotes the interface, i.e., surface of the thin liquid film. If the molar concentration C is approximated as a constant, the derivative of the first equation with respect to z, i.e., a coordinate from the film surface toward the heating surface, becomes 2CD

d2 X1 dX1  N1;i 1 N2;i 5 0 1 2 dz dz

(2.5.28)

2.5.2 HEAT TRANSFER COEFFICIENT

111

Boundary conditions are X1 5 X1,i at z 5 0, and X1 5 X1,b at z 5 δ0 , where δ0 is an extended film thickness taking account of the shortage of the more-volatile component even at the backside contacting the heating surface. The solution gives the liquid and vapor concentrations X1,i and Y1,i at the liquid
vapor interface in relation to the bulk concentration X1,b as a known value.   X1;i 2 Y1;i N1;i 1 N2;i 5 e; e 5 exp 2δ0 X1;b 2 Y1;i CD

(2.5.29)

The total mole flux N1,i 1 N2,i at the interface and the molar concentration C are obtained using properties evaluated at the bulk concentration. N1;i 1 N2;i 5 2 qi = Mhfg

(2.5.30)

C 5 ρl =M

(2.5.31)

where qi is heat flux at the surface of liquid film and M is molecular weight. The surface heat flux q is approximated by qi, i.e., qiDq. The exponential term of heat flux is similar to that involved in Schlu¨nder’s correlation (2.5.23). The value δ0 is evaluated by the operation of a multiplier η(η . 1) to the film thickness δ from Cooper and Lloyd’s correlation [26], where the bubble growth period is evaluated from Fritz and Ende’s correlation [27] using the bubble departure diameter Dd by Cole and Rohsenow [28]. pffiffiffi δ0 5 δη 5 0:2 πDd ðPr 0:5 =JaÞη; Ja 5 ðρ‘ cp‘ =ρg hfg ÞΔTideal

(2.5.32)

The excess temperature Δθ at the interface is evaluated by the gradients of boiling point and dew point curves on the phase equilibrium diagram. ΔθD

2 ðe 2 1Þð Y1;b 2 X1;b Þ ½1=ðdT=dX1 Þ 1 ðe 2 1Þ=ðdT=dY1 Þ

(2.5.33)

The gradients dT/dX1 and dT/dY1 are approximated by straight lines in Fig. 2.5.1A. dT=dX1 D 2 ΔTBP =ðX1;b 2 X1i;min Þ dT=dY1 D 2 ΔTBP =ðY1; b 2 X1;b Þ

(2.5.34)

The heat transfer deterioration is calculated by Eq. (2.5.24), where the excess temperature Δθ is evaluated from Eq. (2.5.33) using the value of e defined by Eq. (2.5.29). Predicted heat transfer coefficients α for η 5 2 are compared with the experimental data in Figs. 2.5.5 and 2.5.6 for ethanol
water and R11
R113, respectively. In Fig. 2.5.5A, the heat transfer coefficient is calculated separately in two ranges bounded by the azeotropic point. Figs. 2.5.5B and 2.5.6B show the effect of heat flux q on α at the concentration with observed maximum deterioration, where the broken line of αI is evaluated as harmonic mean values of coefficients for pure components weighted by mixture concentrations using a relation α ~ q0.8. The predicted values of heat transfer coefficients are represented by a solid line, which coincides well with the experimental data except the low heat flux where the contribution of free convection cannot be neglected. For a fixed value of η, the prediction reproduces well the effects of composition, pressure, and heat flux on the deteriorated heat transfer for both mixtures, as compared in Fig. 2.5.7 The prediction is not sensitive to the value of η, and the evaluated Δθ never exceeds ΔTBP defined in Fig. 2.5.1A.

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FIGURE 2.5.5 Effects of concentration, pressure, and heat flux for ethanol
water by a proposed method [25]: (A) effects of concentration and pressure at constant heat flux qo 5 105 W/m2; (B) effect of heat flux at different concentrations.

FIGURE 2.5.6 Effects of concentration, pressure and heat flux for R11
R113 by a proposed method [25]: (A) effects of concentration and pressure at constant heat flux qo 5 105 W/m2; (B) effect of heat flux at different concentrations.

2.5.2 HEAT TRANSFER COEFFICIENT

113

FIGURE 2.5.7 Comparison between measured heat transfer coefficients, aM, and calculated ones, aC, at different concentrations and pressures [25]: (A) ethanol
water; (B) R11
R113.

2.5.2.2 EXISTING TOPICS FOR MIXTURE BOILING Kern and Stephan [29,30] proposed a single bubble model to reproduce the heat transfer coefficient of mixtures taking account of the Marangoni effect, adhesion pressure between surface and liquid, and interfacial thermal resistance, in addition to the local variation of concentration. They indicated that the diffusive mass transfer and Marangoni effects had an almost insignificant influence on the heat and mass transfer. Conflicting trend of increase or decrease in critical heat flux (CHF) values was reported among experimental studies for different mixtures, heating surface geometries, and pressure levels. Hovestreijdt [31] speculated the significance of decreased bubble growth rate and Marangoni effect for CHF of mixtures, and McGillis and Carey [32] developed a correlation based on this idea. They evaluated the Marangoni effect as an additional liquid restoring force, and incorporated it into the hydrodynamic model by Zuber, where CHF values could be increased or decreased depending on the direction of the restoring force. They suggested that the Marangoni effect was a primary reason for the variation in CHF for mixtures. Fujita et al. [33] also considered the Marangoni effect to evaluate the increase in CHF of binary mixtures. They explained that the Marangoni flow replenished the thin liquid film, delayed the expansion of dry patches and the coalescence of departing bubbles, resulting in the increase in CHF. McEligot [34] regarded the increase in CHF as the result of increased effective subcooling corresponding to the rise in the interfacial temperature. The idea is reflected in the correlation proposed by Reddy and Lienhard [35]. The increase in effective subcooling was evaluated by Jakob number with the temperature difference between the vapor and bulk liquid, which was related to the bulk concentration difference between vapor and liquid on a phase equilibrium diagram.

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2.5.3 EXPERIMENTAL INVESTIGATION OF THE MARANGONI EFFECT In mixture boiling, the Marangoni effect is caused by the concentration gradient and/or the temperature gradient along the liquid
vapor interface. Vochten and Petre [36] showed the increase in surface tension with increasing temperature for alcohol aqueous solutions with large carbon numbers in the higher temperature range, as shown in Fig. 2.5.8A, where no information for concentrations was given. Abe [37] verified the increase of CHF in a heat pipe which contained “self-rewetting fluid” of 1-butanol aqueous solution. The change in surface tension for positive and negative mixtures is classified in Fig. 2.5.9, where the term “self-wetting” with the meaning similar to “self-rewetting” implies here that the surface tension increases towards the three-phase interline underneath bubbles. When the increment of surface tension is represented by the total differential form with respect to concentration and temperature, the contribution of the concentration gradient is generally larger than

FIGURE 2.5.8 Unusual behaviors in aqueous solution of high-carbon alcohol: (A) effect of temperature on surface tension of alcohol aqueous solutions [36]; (B) observed increase in CHF for an alcohol aqueous solution [38].

2.5.3 EXPERIMENTAL INVESTIGATION OF THE MARANGONI EFFECT

115

FIGURE 2.5.9 Effects of concentration and temperature increases on the change in surface tension along the evaporation interface.

that of the temperature gradient. The present author expected that the heat transfer could also be enhanced in addition to the increase in CHF, e.g., Fig. 2.5.8B by Van Stralen [38]. Detailed experiments especially at low alcohol concentrations of aqueous solutions were performed using a horizontal flat heating surface of 40 mm in diameter at 0.1 MPa [39]. Three mixtures of 1-propanol
water, 2-propanol
water and water
ethylene glycol were employed as shown in Fig. 2.5.10. The variation of surface tension is shown in Fig. 2.5.11A, where the surface tension significantly decreases with a small increase in alcohol concentration for 1-propanol
water and 2-propanol
water, which indicates that a large Marangoni effect is expected. In the definition of Marangoni number, Ma, a mass diffusion coefficient as a dominant parameter to suppress the Marangoni flow, instead of a thermal diffusivity, should be used. The variation in Ma is shown in Fig. 2.5.11B, where a sharp spike is observed at low alcohol concentration for two alcohol solutions. ð2 @σ=@x1 Þðy1 2 x1 ÞLa μ‘ D rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi σ La  gðρ‘ 2 ρg Þ

Ma 5

(2.5.35) (2.5.36)

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FIGURE 2.5.10 Phase equilibrium diagrams of three mixtures at 0.1 MPa for the confirmation of the Marangoni effect on the heat transfer using a flat plate heating surface: (A) 1-propanol
water; (B) 2-propanol
water; (C) water
ethylene glycol.

FIGURE 2.5.11 Variation of surface tension (A) and Marangoni number (B) with concentration.

Fig. 2.5.12 shows heat transfer coefficients at selected heat fluxes, where the predicted heat transfer coefficients by Stephan
Ko¨rner [20] and Thome [24] correlations are also shown. Fig. 2.5.13 is the enlarged one in the low concentration range. For 1-propanol
water and 2-propanol
water, the enhancement of heat transfer coefficients is observed at very low alcohol concentrations, while it is turned to the deterioration in the moderate concentration range. For water
ethylene glycol, however,

2.5.3 EXPERIMENTAL INVESTIGATION OF THE MARANGONI EFFECT

117

FIGURE 2.5.12 Heat transfer coefficients: (A) 1-propanol
water; (B) 2-propanol
water; (C) water
ethylene glycol.

FIGURE 2.5.13 Heat transfer enhancement observed at low concentrations of alcohol aqueous solutions: (A) 1-propanol
water; (B) 2-propanol
water; (C) water
ethylene glycol.

no heat transfer enhancement is observed, and the heat transfer coefficient gradually changes with the concentration. Generally, there are two conflicting trends of heat transfer deterioration due to mass diffusion resistance and of heat transfer enhancement due to the Marangoni effect. The correlations without the term of the Marangoni effect cannot reproduce the detailed trend at low concentrations. The following general form is proposed for the prediction of the heat transfer. α 1 1 C Ma 5 αI 11F

(2.5.37)

where C is a constant and 1 1 F is given with reference to the dominator of, e.g., Eq. (2.5.20) or Eq. (2.5.21). In Fig. 2.5.13, the prediction by Eq. (2.5.37) is included, where C 5 0.12 3 1028 is used for three alcohol aqueous solutions. An opposite effect of the Marangoni force on the heat transfer can be possible at concentrations larger than the azeotropic value. For most cases of mixtures, the influence of the term C Ma in the numerator of Eq. (2.5.37) is hidden by F in the denominator.

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The experimental results for CHF are shown in Fig. 2.5.14, where CHF values predicted by Zuber correlation using the same properties as mixtures are also shown. The measured CHF values are gradually decreased with increasing alcohol concentration as is predicted by the correlation except in the case of water
ethylene glycol. At low alcohol concentrations for 1-propanol
water, 2-propanol
water, CHF values has clearly the local minimum despite the peak in Marangoni number here. The decrease in CHF for a flat plate is obvious in the present results and also in, e.g., Bobrovich et al. [40] and Kutateladze et al. [41], while an increase in CHF for a wire or a thin tube was reported by Hovestreijdt [31], Fijita and Bai [33], and Reddy and Lienhard [35]. Fig. 2.5.15 shows the bubble structures (A) on a large flat plate and (B) on a wire. On the flat plate, a coalesced bubble has a compound structure, where many single bubbles (primary bubbles) exist in the macrolayer, and the heat transfer is dominated by the primary bubbles generated directly from the heating surface [42]. At high heat flux, the consumption of liquid in the macrolayer is accelerated after the supply of liquid by the detachment of a coalesced bubble. The consumption of the

FIGURE 2.5.14 Critical heat fluxes: (A) 1-propanol
water; (B) 2-propanol
water; (C) water
ethylene glycol.

FIGURE 2.5.15 Compound structure of nucleated bubbles at high heat flux: (A) flat plate; (B) wire.

2.5.3 EXPERIMENTAL INVESTIGATION OF THE MARANGONI EFFECT

119

macrolayer, however, does not occur at the same time in the entire base area of a coalesced bubble, and the generation and extension of local dry-out of macrolayer induces the CHF condition. The Marangoni force acting on the surface of the microlayer beneath primary bubbles enhances the liquid supply from the macrolayer as a liquid reservoir to the three-phase interlines, which promotes the local dry-out of the macrolayer and reduces CHF values as shown in Fig. 2.5.16A. For a thin

FIGURE 2.5.16 Marangoni effect on the behavior of liquid
vapor interfaces underneath a coalesced bubble: (A) with Marangoni flow; (B) without Marangoni flow.

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wire, on the other hand, bubble coalescence occurs at the top of wire and single bubbles continue to generate from the bottom as illustrated in Fig. 2.5.15B. The structure of coalesced bubble on the top surface of wire is expected to be similar to that on the flat plate, and the supply of liquid to the primary bubbles is disturbed by the existence of a coalesced bubble before its detachment. At the bottom surface, on the other hand, the liquid is supplied to the base of single bubbles directly from the bulk liquid. Both the Marangoni force acting on the surface of the microlayer of single bubbles and their periodical detachment due to the upward sliding along the wire surface enhance the liquid supply, preventing the extension of the dry area in the microlayer. Provided that the bottom part of the wire is cooled enough, temperature excursion does not occur. Just before CHF conditions, the entire wire surface, including the bottom part, is surrounded by coalesced bubbles.

2.5.4 SUPERIOR HEAT TRANSFER CHARACTERISTICS OF IMMISCIBLE MIXTURES 2.5.4.1 OBJECTIVES TO USE IMMISCIBLE MIXTURES Under the situation of increasing heat generation density from electronic devices, the practical application of boiling to realize high-performance cooling systems attracts much attention. The present author noticed the superior heat transfer characteristics shown below during nucleate boiling of immiscible mixtures even on a smooth surface without microstructures [43
45]: 1. Operation at pressure higher than atmospheric pressure keeping low liquid temperature and preventing the mixing of incondensable air. 2. Increase in CHF by self-sustained liquid subcooling of the less-volatile component resulted from the excessive compression by the higher partial vapor pressure of the more-volatile component. 3. Reduction in surface temperature during the free convection or nucleate boiling of the lessvolatile liquid by the generating vapor of the more-volatile component. 4. Reduction in surface temperature overshooting at the boiling incipience by selecting the combination of fluids and optimizing their quantities, which is an important requirement for, e.g., the cooling of automobile inverters with a large fluctuation of thermal load.

2.5.4.2 EXISTING RESEARCH There are many results on nucleate boiling of oil mixtures. Recently, Filipczak et al. [46] studied dilute emulsions, where the distribution of oil, water, and vapor was examined for different heat flux levels. Because of the larger contribution of free convection, the heat transfer coefficients for water
oil mixtures with high oil concentration were far smaller than those for pure water. Foaming was observed at the initial stage of nucleate boiling before the formation of emulsion. Roesle and Kulacki [47] investigated nucleate boiling of dilute emulsions, FC72/water and pentane/ water, on a horizontal wire. The concentrations of the more-volatile components FC72 and pentane dispersed in the continuous phase of water were varied at 0.2%
1.0% and 0.5%
2.0%, respectively. Depending on the level of heat flux, either boiling of the dispersed component or of the dispersed and continuous components was observed. The heat transfer was enhanced for the volume

2.5.4 IMMISCIBLE MIXTURES

121

fraction of the dispersed component larger than 1% owing to its boiling. Bulanov and Gasanov [48] tested four emulsions, n-pentane/glycerin, diethyl ether/water, R113/water and water/oil, where the more-volatile components were dispersed in the continuous less-volatile components. Compared with the pure liquids of the continuous phase, the reduction of surface superheat at the boiling incipience was reported. Conversely, the amount of research on immiscible mixtures which form stratified layers before heating is very limited [49
51]. The interpretation of data, however, was not given in detail except the classification of modes of heat transfer to individual layers of component liquids [50]. Gorenflo et al. [52] studied boiling of water/1-butanol on a horizontal tube. The mixture becomes soluble or partially soluble depending on its concentration, temperature, and pressure. Under the variation of concentration and pressure, they reported a small effect of solubility on the nucleate boiling heat transfer.

2.5.4.3 PHASE EQUILIBRIUM An example of phase equilibrium diagrams for FC72/Water at the total pressure of 0.1 MPa is shown in Fig. 2.5.17. The point where the two curves merge becomes the concentration of vapor phase. The dew point concentration represented by two different curves is calculated by the following equations [53].   hfg;1 1 1 2 Tsat;1 R1 T   hfg;2 1 1 2 lnð1 2 Y1 Þ 5 2 Tsat;2 R2 T lnY1 5 2

FIGURE 2.5.17 Phase equilibrium diagram of FC72/water mixture.

(2.5.38) (2.5.39)

122

CHAPTER 2 NUCLEATE BOILING

where Y1 is the mole fraction of more-volatile component in vapor on dew point curve (-), T is the dew point temperature (K), Tsat is the saturation temperature (K) for a total pressure P, hfg is the latent heat of vaporization (kJ/kg), and R is the gas constant (kJ/kg K). The equilibrium temperatures Tb of immiscible liquids at P 5 0.1 MPa are listed in Table 2.5.1 for five insoluble and partially soluble mixtures. As shown in Fig. 2.5.18, higher saturated vapor pressure of the morevolatile component compresses the less-volatile liquid resulting in higher subcooling than the subcooling of the more-volatile liquid compressed by the lower saturation pressure of the less-volatile

Table 2.5.1 Equilibrium Temperature and Subcooling of Component Liquids at 0.1 MPa

Classification of Immiscible Mixtures

1: More-Volatile Liquid with Higher Density

2: Less-Volatile Liquid with Lower Density

Insoluble

FC72 Novec649 Novec7200 FC72 FC72

Water Water Water n-Propanol i-Propanol

Partially soluble

Equilibrium Temperature

Subcooling of More-Volatile Liquid

Subcooling of Less-Volatile Liquid

Tb ( C)

ΔTsub,1 (K)

ΔTsub,2 (K)

51.6 45.9 66.4 51.7 48.7

4.3 3.3 12.0 4.2 7.2

48.4 54.1 33.6 45.6 33.6

FIGURE 2.5.18 Equilibrium state for immiscible mixture on vapor pressure curves (an example of FC72/water at 0.1 MPa).

2.5.4 IMMISCIBLE MIXTURES

123

component. The degree of subcooling ΔTsub for each component liquid is summarized in the table. The self-sustaining subcooling is imposed for both component liquids of immiscible mixtures even in a closed container without an additional loop for cooling of liquid or an accumulator.

2.5.4.4 EXPERIMENTAL RESULTS For a horizontal flat heating surface facing upwards, the combination of a thin layer of morevolatile liquid with higher density and a thick layer of less-volatile liquid with lower density before the start of heating gives superior heat transfer characteristics (1)
(4) described in Section 2.5.4.1. Another possibility is the combination of a thick layer of less-volatile liquid with higher density and a layer of more-volatile liquid with lower density, which have the advantages of (1) and (2). Both combinations are shown schematically in Fig. 2.5.19. The experiments were performed in the former case, where layer thickness H1 of the more-volatile liquid before heating was selected as one of experimental parameters keeping the total thickness H1 1 H2 constant at 100 mm. The diameter of the heating surface is 40 mm. The experiments are performed at the total pressure of 0.1 MPa. Nothing is changed from the pool boiling experiment of pure liquid, where the bulk liquid temperature is regulated by adjusting the cooling rate at the condenser located in the top of the cylindrical vessel. At low and moderate heat fluxes before the initiation of water boiling, the bulk liquid temperature is almost the same as the equilibrium temperature listed in Table 2.5.1, while it increases at high heat flux with the release of sensible heat of water bubbles surrounded by high subcooled liquid. Figure 2.5.20 shows the heat flux q versus temperature difference for insoluble mixtures, (A) FC72/water, (B) Novec649/water, and (C) Novec7200/water [44]. The data for pure more-volatile and pure less-volatile components at the same pressure is also included. In the abscissa, the temperature difference ΔTb between the heating surface and the bulk liquid temperature at the subcooled

FIGURE 2.5.19 Two possible combinations of liquid density and layer thickness for immiscible mixture valid for the improvement of heat transfer: (A) higher density of the more-volatile liquid; (b) lower density of the more volatile liquid.

124

CHAPTER 2 NUCLEATE BOILING

107

107 FC72/Water

Water FC72

P = 0.1 MPa

107 Novec649/Water P = 0.1 MPa

106 q W/m2

q W/m2 105

105

105

H1 = 0 mm H1 = 5 mm H1 = 10 mm H1 = 50 mm

104 0 10

101

102 ΔTsat , ΔTb K

(A)

Water Novec7200

Novec7200/Water P = 0.1 MPa

106

q W/m2

106

Water Novec649

H1 = 0 mm H1 = 5 mm H1 = 10 mm

103

104 0 10

101

102 ΔTsat , ΔTb K

(B)

H1 = 0 mm H1 = 5 mm H1 = 10 mm

103

104 0 10

101

102

103

ΔTsat , ΔTb K

(C)

FIGURE 2.5.20 Heat flux versus temperature difference: (A) FC72/water; (B) Novec649/water; (C) Novec7200/water.

state is used for the mixture, while the surface superheat ΔTsat is used for pure components at the saturation state under the same pressure. For FC72/water at H1 5 5 mm and 10 mm of FC72 layer, the phenomenon regarded as burnout is recognized by the small temperature jump at 2 3 105 W/m2. The crisis of heat transfer is recovered by the change of liquid from FC72 to water without catastrophic temperature excursion, followed by the stable heat transfer by natural convection of subcooled water. The present authors referred to the phenomenon as “intermediate (heat flux) burnout.” At higher heat flux, heat transfer due to nucleate boiling of water is dominated. For a large thickness H1 5 50 mm of FC72 layer, the curve almost coincides with that for pure FC72 at the saturation state because of its small subcooling. For H1 5 0 mm, FC72 is filled only around the cylindrical heating block without the layer on the heating surface before heating. By the disturbance at the liquid
liquid interface around the heating block imposed by the falling condensate droplets of FC72 and the natural circulation of liquid in the vessel, a portion of FC72 is carried on the heating surface. As a result, the curve becomes similar to those for H1 5 5 mm at high heat flux. The trends for Novec649/water and Novec7200/ water are similar to those for FC72/water, except that no distinct intermediate burnout is observed for Novec649/water at H1 5 5 mm and 10 mm. The curves shifted gradually from the morevolatile-dominated to the less-volatile-dominated region because of the enhanced physical mixing of water with Novec649. The variation in the transition of curves was discussed in the paper by Kita et al. [45]. The heat transfer performances for immiscible mixtures and pure components are compared by the relation of heat flux q versus surface temperature Tw in Fig. 2.5.21. For FC72/water, the surface temperature is clearly reduced from that for pure water at high heat flux. It is worthy of note that the heat transfer coefficients even in such a case are superficially deteriorated from those of pure components because of the mixtures subcooling at the equilibrium temperature. The substantial enhancement of heat transfer in both regions of natural convection and nucleate boiling of water is

2.5.4 IMMISCIBLE MIXTURES

107

107 Water FC72

FC72/Water P = 0.1 MPa

Water Novec649

Novec649/Water P = 0.1 MPa

106 2

q W/m2

q W/m2

106

105

105 H1 = 0 mm H1 = 5 mm H1 = 10 mm H1 = 50 mm

104

125

60

80

100

120 Tw°C

140

160

180

H1 = 0 mm H1 = 5 mm H1 = 10 mm

104

60

80

100

(A)

120 Tw°C

140

160

180

(B) 107 Novec7200/Water P = 0.1 MPa

Water Novec7200

q W/m

106

105 H1 = 0 mm H1 = 5 mm H1 = 10 mm

104

60

80

100

120 Tw°C

140

160

180

(C) FIGURE 2.5.21 Heat flux versus surface temperature: (A) FC72/water; (B) Novec649/water; (C) Novec7200/water.

caused by the mixing of FC72 vapor into liquid water, where the vapor of FC72 is not condensed in water at the equilibrium temperature. The reduction of surface temperature is caused by the enhanced agitation of liquid water by the generation of FC72 vapor before the initiation of water boiling and by the formation of a thin water film as illustrated in Fig. 2.5.22. The figure shows an example of liquid and vapor distribution after the initiation of water boiling. A similar reduction in the surface temperature is also observed for H1 5 0 mm and also in Novec649/water and Novec7200/water. Horizontal dotted lines in Figs. 2.5.20 and 2.5.21 represent the measured values of CHF accompanied by the catastrophic temperature excursion, where some lines are hidden because of almost the same values of CHF. Although the actual CHF values for immiscible mixtures are of utmost interest, these values were not yet measured owing to the limitation from the specification of the experimental setup employed. For FC72/water at H1 5 5 mm, the maximum value of the heat flux measured becomes 1.7 3 106 W/m2, i.e., at least 1.36 times higher than CHF of pure

126

CHAPTER 2 NUCLEATE BOILING

FIGURE 2.5.22 Liquid
vapor distribution for FC72/water immiscible mixture at moderate heat flux.

water under the same pressure. Recently, we measured heat flux up to 2.8 3 106 W/m2 for H1 5 0 mm using the same heating surface with a diameter of 40 mm, while the CHF predicted by the Ivey and Morris correlation [54] for self-sustaining subcooling ΔTsub 5 48.4 K of water shown in Table 2.5.1 becomes a value larger than 4 3 106 W/m2. The layer thickness H1 5 10 mm is too large to increase CHF because the thick layer of more-volatile liquid can become a barrier for the penetration of subcooled water into the heating surface during the intermediate heat flux burnout. In the case of partially soluble mixtures listed in Table 2.5.1, the heat transfer characteristics of insoluble mixtures mentioned above becomes weakened.

2.5.5 CONCLUSIONS Boiling of nonazeotropic mixtures has a long history and many theoretical and experimental approaches were performed. However, the deteriorated heat transfer cannot be avoided compared to the hypothetical pure liquids with the same properties as the mixture under the same pressure. As has been verified experimentally by the present author, the Marangoni effect could enhance the heat transfer coefficients. Unfortunately, the increment is very small even at the concentrations where the Marangoni effect is at the maximum. Substantial improvement of heat transfer cannot be expected for nonazeotropic mixtures provided that a new combination of liquids and their optimal composition for enhanced Marangoni force is not newly discovered. Using wire heaters, a large

NOMENCLATURE

127

increase in CHF was reported for, e.g., aqueous solution of alcohols, while no increase was also confirmed for a plate heater in the present study. Although the boiling phenomena of nonazeotropic mixtures provides the interest of investigations, it gives almost no advantage for the improvement of cooling performance except the use as antifreezing coolants or as working fluids alternative to the discontinued ones, and except its application to flow boiling to reduce the exergy loss due to the heat-exchange process. Conversely, the application of immiscible mixtures to the cooling system involves a large potential ability. For a flat heating surface, the drastic increase in CHF was confirmed only by the addition of small amount of immiscible component. Other advantages for cooling systems described in Section 2.5.4.1 are also true for immiscible mixtures, where one component can be antifreezing coolant widely used in automobiles. Further decreases in surface temperature or further increases in CHFs might be possible for surfaces with microstructures or with fine fins. Using immiscible mixtures, the improvement of heat transfer is also expected in the nucleate boiling region of flow boiling, provided that the ‘self-compression’ is possible near the heating surface by the introduction of a passive accumulator actuated by the mixture vapor. Various configurations of the heating surface assembly are expected for flow boiling systems utilizing the liquid inertia to distribute both liquids optimally around the tube wall or the heating surface in a duct. Further investigation is needed to verify the performance of immiscible mixtures in various boiling systems.

NOMENCLATURE Bo C cp D Dd Gd g hfg Ja Kb La M Ma N P Pr q qCHF R Ro Sn T

coefficient in Eq. (2.5.23) molar concentration, kmol/m3 heat capacity, J/kg K diffusion coefficient of liquid, m2/s bubble detachment diameter, m mass diffusion fraction,
Gibbs free energy or gravitational acceleration, J/kmol or m/s2 latent heat of vaporization, J/kg Jakob number,
equilibrium constant,
Laplace constant, m molecular weight, kg/kmol Marangoni number defined by Eq. (2.5.35),
mole flux, kmol/m2s pressure, N/m2 Prandtl number,
heat flux, W/m2 critical heat flux, W/m2 bubble radius or gas constant, m or J/kg K universal gas constant, J/kmol K Scriven number defined by Eq. (2.5.15) or Eq. (2.5.21),
temperature,  C or K

128

Tsat Tw t tG r X x Y y

CHAPTER 2 NUCLEATE BOILING

saturation temperature, K surface temperature,  C time, s bubble growth period, s radial distance, m mole fraction in liquid,
weight fraction in liquid,
mole fraction in vapor,
weight fraction in vapor,


GREEK SYMBOLS α β γ ΔT ΔTBP ΔTeff ΔTsat ΔTw Δθ δ δ0 κ μ ρ σ η

heat transfer coefficient, W/m2 K mass transfer coefficient, m/s bubble contact angle, deg liquid superheat or surface superheat based on the bulk state of liquid on boiling point curve, K temperature difference defined in Fig. 2.5.1.1A, K effective superheat of liquid or surface, K surface or liquid superheat, K temperature difference between surface and bulk liquid, K excess temperature at liquid
vapor interface, K film thickness underneath bubble, m extended film thickness, m thermal diffusivity, m2/s dynamic viscosity, Pa s density, kg/m3 surface tension, N/m multiplier taking account of the shortage of more volatile component in thin film underneath bubble (η . 1),


SUBSCRIPTS 0 1 2 b C g I i ‘ M m p sat T

constant value more volatile component less volatile component bulk or equilibrium state calculated vapor linearly interpolated value liquid
vapor interface liquid mass or measured mixture pure component saturated temperature

REFERENCES

129

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776. [44] S. Ohnishi, H. Ohta, N. Ohtani, Y. Fukuyama, H. Kobayashi, Boiling heat transfer by nucleate boiling of immiscible liquids, Interfacial Phenomena Heat Transfer 1 (1) (2013) 63
83. [45] S. Kita, S. Ohnishi, Y. Fukuyama, H. Ohta, Improvement of nucleate boiling heat transfer characteristics by using immiscible mixtures, Proc. 15th Int. Heat Transfer Conf., Kyoto, Japan, IHTC15-8941, 2014. [46] G. Filipczak, L. Troniewski, S. Witczak, Pool boiling of liquid
liquid multiphase systems, in: A. Ahsan (Ed.), Evaporation Condensation and Heat Transfer, INTECH, 2011, pp. 123
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2165. [48] N.V. Bulanov, B.M. Gasanov, Peculiarities of boiling of emulsions with a low-boiling disperse phase, High Temp. 44 (2) (2006) 267
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131

[51] G.D. Sump, J.W. Westwater, Boiling heat transfer from a tube to immiscible liquid
liquid mixtures, Int. J. Heat Mass Transfer 14 (1971) 767
779. [52] D. Gorenflo, F. Gremer, E. Danger, A. Luke, Pool boiling heat transfer to binary mixtures with miscibility gap: experimental results for a horizontal copper tube with 4.35 mm O.D, Exp. Thermal Fluid Sci. 25 (5) (2001) 243
254. [53] I. Prigogine, R. Defay, Chemical Thermodynamics, Longmans Green and Co, 1954. [54] H.J. Ivey, D.J. Morris, Critical heat flux and subcooled pool boiling in water at atmospheric pressure, Proc. Third Int. Heat Transfer Conf. 3 (1966) 129
142.

BUBBLE DYNAMICS IN SUBCOOLED FLOW BOILING

2.6 Tomio Okawa

The University of Electro-Communications, Tokyo, Japan

2.6.1 INTRODUCTION In subcooled flow boiling, wall heat transfer can be partitioned to multiple components associated with the forced convection and the nucleate boiling. In addition, evaporation and condensation occur simultaneously within the same channel cross-section as a consequence of thermal nonequilibrium. Thus, accurate evaluations of the wall temperature and void fraction in the subcooled boiling region in an evaporation tube are of considerable practical importance but are technically challenging issues [1
5]. In what follows, empirical and mechanistic subcooled flow boiling models developed so far are briefly reviewed. It is revealed that, particularly in mechanistic modeling of the subcooled flow boiling, sufficient understanding is indispensable for the bubble dynamics such as the bubble size and the trajectory after the departure from the nucleation site. Hence, some recent studies concerning the bubble dynamics in subcooled flow boiling and the related studies conducted by the present author are discussed.

2.6.2 REVIEW OF THE SUBCOOLED FLOW BOILING MODELS 2.6.2.1 OVERVIEW A schematic diagram of subcooled flow boiling is illustrated in Fig. 2.6.1. A subcooled liquid is injected from one end of a heated channel. For a certain distance from the inlet, the bulk liquid

132

CHAPTER 2 NUCLEATE BOILING

Single phase

Subcooled boiling

Partial boiling

Saturated boiling

Fully-developed boiling

Subcooled liquid

A (ONB)

B

C

D

(NVG)

FIGURE 2.6.1 Schematic diagram of subcooled flow boiling. NVG, net vapor generation; ONB, onset of nuclear boiling.

temperature Tl and the wall temperature Tw rise gradually but lower than the saturation temperature Tsat. Thus, no boiling takes place and the situation is single-phase liquid flow. At point A, Tl is still lower than Tsat but Tw exceeds Tsat sufficiently to permit formation of first bubbles at nucleation cavities on the heated surface. This phenomenon is identified as the onset of nucleate boiling (ONB). The subcooled boiling region hence begins at point A. The earlier models to predict the location of this point were developed by Hsu [6], Sato and Matsumura [7], and Davis and Anderson [8]; some more recent models are reviewed by Okawa [9]. At point D, Tl also reaches Tsat and the situation moves from subcooled boiling to saturated nucleate boiling. In consequence, the region between the points A and D is regarded as the subcooled boiling region. A distinct feature of the subcooled boiling region is the presence of thermal nonequilibrium: within a channel cross-section of this region, evaporation occurs in the high-temperature region near the heated wall whilst condensation may take place in the low-temperature region away from the wall. The subcooled boiling region can further be divided to several sub-regions from the standpoints of heat transfer and void fraction. At point A that is the start point of the subcooled boiling region, only a small number of nucleation sites are activated and the heat transfer from the heated wall to the fluid is mainly governed by single-phase forced convection. Main heat transfer mode changes gradually from the single-phase convection to the nucleate boiling with an increase in the distance from point A. The contribution of single-phase convection becomes eventually relatively negligible at point B which is located within the subcooled boiling region. Thus, the region between points A and B is identified as the partial boiling region and the region downstream of point B is the fully developed boiling region. It is also known that the void fraction is very low just downstream of point A and a rapid increase in the void fraction is incepted at point C. Thus, the void fraction between points A and C is neglected in many subcooled flow boiling models as

2.6.2 REVIEW OF THE SUBCOOLED FLOW BOILING MODELS

133

discussed later. Point C is therefore identified as the point of the net vapor generation (NVG) or the onset of significant void (OSV). In the subcooled flow boiling region, heat transfer performance is drastically enhanced in comparison with that in the single-phase region. Thus, it may be used for the heat removal from highpower-density systems such as the high-performance electronic devices and the diverters of nuclear fusion reactors. In addition, in the systems in which subcooled liquid is heated to produce steam (e.g., boilers, thermal power plants, and nuclear power plants), subcooled flow boiling is inevitably encountered and the void fraction in the subcooled boiling region may have significant influence on the inception of two-phase flow instability. In nuclear power plants, fuel burn-up is also affected by the void fraction in the subcooled boiling region. Accurate prediction of the wall temperature and the void fraction in the subcooled boiling region is of considerable importance from the engineering standpoint. In consequence, numerous studies have been conducted so far to develop reliable models for the heat transfer coefficient and the net vaporization rate in subcooled flow boiling since these parameters are of primary importance in evaluating the aforementioned macroscopic values. In what follows of this section, available subcooled flow boiling models are briefly reviewed to show that sufficient understanding of bubble dynamics is of crucial importance to develop a reliable subcooled flow boiling model.

2.6.2.2 HEAT TRANSFER MODELS The heat transfer models developed for subcooled flow boiling may be divided into the empirical and mechanistic models. The heat transfer mechanisms in the subcooled boiling region can be regarded as the combination of single-phase forced convection and nucleate boiling. The singlephase convection is dominant in the region close to point A in Fig. 2.6.1 whilst the nucleate boiling essentially governs the heat transfer in the region downstream of point B. Hence, in many empirical models, the total heat flux in the partial boiling region in the subcooled boiling region qSCB is expressed using that of single-phase convection qSPC and that of nucleate boiling qNB. One such method, proposed by Bergles and Rohsenow [10], is given by " qSCB 5 qSPC

 2 #1=2 qNB qNB;A 11 12 qSPC qNB

(2.6.1)

where qNB,A is the nucleate boiling heat flux evaluated at point A (point of ONB). One can confirm that q 5 qSPC at point A where qNB 5 qNB,A, and q approaches to qNB with an increase in the wall superheat ΔTW because qNB .. qSPC and qNB .. qNB,A at a high value of ΔTW. If an empirical interpolation method like Eq. (2.6.1) is used, the wall temperature in the partial boiling region can readily be calculated from the heat transfer correlations for the single-phase convection and nucleate boiling. Different interpolation methods have been developed so far by Kutateladze [11], Liu and Winterton [12], and Kandlikar [13]. For the fully developed boiling region, several empirical heat transfer correlations have also been developed by McAdams et al. [14], Jens and Lottes [15], Thom et al. [16] and Kandlikar [13], among others. Another approach to predict the wall temperature is the mechanistic modeling. One such model was developed by Kurul and Podowski [17], in which qSCB is expressed as the sum of the heat fluxes associated with the forced-convection qFC, evaporation qEV, and surface quenching qQ.

134

CHAPTER 2 NUCLEATE BOILING

qSCB 5 qFC 1 qEV 1 qQ

(2.6.2)

The concepts of qFC, qEV and qQ are delineated in Fig. 2.6.2. When a bubble is lifted off the wall, local liquid flow directing toward the wall is formed to fill the volume previously occupied by the bubble. The component qQ is the heat flux transferred by this surface quenching phenomenon. Each component in the above equation is expressed by qFC 5 ð1 2 AQ ÞhFC ðTW 2 Tl Þ

(2.6.3)

3 πdb;lift 6 2kl ðTW 2 Tl Þ qQ 5 AQ tw fb pffiffiffiffiffiffiffiffiffiffiffiffi παl tw

qEV 5 ρb Δhv Ns fb

(2.6.4) (2.6.5)

where AQ is the fractional area over which the heat transfer is governed by the above-described local liquid flow and expressed by AQ 5 KNs

2 πdb;lift 4

(2.6.6)

where K is the constant of the order of unity. From the above equations, one can see that the mechanistic models require appropriate correlations for various elementary processes such as the nucleation site density Ns, the bubble size at lift-off db,lift, the bubble release frequency fb, and the bubble waiting time tw, etc. It has been observed experimentally that bubbles may slide along the heated surface before being lifted off the wall [18
21]. Hence, in more recent mechanistic models such as those developed by Basu et al. [22,23], Cheung et al. [4], and Yeoh et al. [5], the quenching heat transfer is evaluated separately during the sliding and lift-off stages. This clearly indicates that the bubble trajectory after the departure from the nucleation site should also be understood sufficiently. The mechanistic models are considered advantageous in comparison with the empirical models particularly in complex situations such as in transient state and complex geometry. It may, however, be obvious that if appropriate correlations are not available for these elementary processes, the mechanistic models cannot be reliable.

Departing bubble Flow

Growing bubble Local liquid flow

Heated wall

qFC

qEV

qQ

Heat flux associated with nucleation

FIGURE 2.6.2 The concept of wall heat flux partitioning.

2.6.2 REVIEW OF THE SUBCOOLED FLOW BOILING MODELS

135

2.6.2.3 MODELS FOR VOID FRACTION EVOLUTION AND PHASE CHANGE RATES In the prediction of the void fraction evolution, although the bubble rise velocity relative to continuous liquid is also important, accurate evaluation of the phase change rates (evaporation rate ΓEV and condensation rate ΓCOND) is of primary importance since they determine the axial development of vapor quality. In the empirical heat transfer models, the total heat flux in the subcooled boiling region qSCB is known but the component associated with the evaporation qEV is unknown. To evaluate qEV, the pumping factor ε that is defined as the ratio of qQ to qEV (ε 5 qQ/qEV) is often used. If ε is introduced and qFC is evaluated using a single-phase heat transfer correlation, Eq. (2.6.2) is rewritten as qSCB 5 hFC ðTW 2 TL Þ 1 ð1 1 εÞqEV

(2.6.7)

One can see that qEV can be calculated from qSCB if the correlation for ε is available. Once qEV is determined, ΓEV is readily calculated by ΓEV 5

qEV AH Δhv V0

(2.6.8)

where V0 is the volume of interest and AH is the heated surface area within V0. In a simple method to estimate ε proposed by Lahey [24], it is supposed that liquid whose volume is the same as that of the bubbles produced on the heated surface is heated from the bulk liquid temperature Tl to the saturation temperature Tsat by qQ. Using this concept, qQ is evaluated by qQ 5 ρl cpl ðTsat 2 Tl ÞNs fb

3 πdb;lift 6

(2.6.9)

From Eqs (2.6.4) and (2.6.9), ε is calculated only from the macroscopic parameters by ε5

ρl cpl ΔTsub ρb Δhv

(2.6.10)

In the mechanistic models, ΓEV should be calculated from Eqs (2.6.4) and (2.6.8) for consistency with the heat transfer model. Another important model required in calculating ΓEV is that for the point of NVG (point C in Fig. 2.6.1). If bubbles stay at the nucleation sites of their origin, successive bubble generation is not permitted. The bubble departure from the nucleation site is hence necessary for the void fraction to increase rapidly. It should however be noted that the bubble departure is not sufficient to cause OSV. In fact, bubble departure is often observed experimentally even at the point of ONB [25,26]. The mechanisms to cause NVG or OSV have not been understood sufficiently [27]. Thus, empirical models such as those developed by Levy [28] and Saha and Zuber [29] are usually used to estimate the point of NVG in both the empirical and mechanistic subcooled flow boiling models, and ΓEV is supposed to be zero upstream of the point of NVG. In both the empirical and mechanistic models, ΓCOND is expressed by ΓCOND 5

hCOND ðTSAT 2 Tl;Ref Þai Δhv

(2.6.11)

where hCOND is the condensation heat transfer coefficient, ai is the interfacial area concentration, and Tl,Ref is the reference liquid temperature at the bubble position. The value of Tl,Ref is high if

136

CHAPTER 2 NUCLEATE BOILING

bubbles stay on the heated surface whilst it is low if they are propelled to the subcooled bulk liquid. Therefore, the bubble trajectory after the departure from the nucleation site should be understood to evaluate Tl,Ref correctly. However, since such information is not sufficient, Tl,Ref is often assumed to be equal to the bulk liquid temperature Tl. This may lead to overestimation of ΓCOND since a significant portion of bubbles may be present near the wall. Alternatively, Lahey [24] expressed ΓCOND as ΓCOND 5 H0 ρg αg ðTSAT 2 Tl Þ

(2.6.12)

where the dimensional constant H0 may be regarded as the empirical parameter to consider the bubble position within the channel cross-section.

2.6.3 BUBBLE DYNAMICS IN SUBCOOLED FLOW BOILING The review in the previous section shows that mechanistic subcooled flow boiling models require appropriate constitutive models for various processes including nucleation site density, bubble size, bubble release frequency, bubble trajectory, condensation heat transfer, etc. Although several mechanistic models have been developed [4,5,17,22,23], the processes encountered in subcooled flow boiling are extremely complex and sufficient understanding has not been achieved. Here, for further improvement of mechanistic subcooled flow boiling models, discussion is made focusing on the state-of-the-art knowledge of the bubble dynamics in subcooled flow boiling. Considering the importance in industrial applications, vertical upward flow is mainly discussed. The bubbles formed at the nucleation sites on a vertical heated surface in subcooled boiling region may (1) grow and collapse while remaining attached to the nucleation sites of their origin [30], (2) slide along the heated surface for a long distance [18,31], and (3) be lifted off the heated surface [21,25,32,33]. Bubbles may slide for several bubble diameters before being lifted off the surface. After lift-off, bubbles usually disappear quickly due to condensation but reattachment to the heated surface occurs in some experimental conditions [20,27]. Consecutive images of sliding bubble, lift-off bubble and reattaching bubble are displayed in Fig. 2.6.3A
C, respectively [20]. Obviously, the effect of bubble trajectory on void fraction is significant. For example, it can be seen that in Fig. 2.6.3, the bubble lifetime is much shorter for the lift-off bubble than for the sliding and reattaching bubbles. Ahmadi et al. [27] indicated that the bubble reattachment can trigger the NVG. In addition, it has been reported that sliding bubbles enhance the heat transfer significantly [18,34]. This implies that the heat transfer as well as void fraction depends strongly on the bubble trajectory after the departure from nucleation sites. One of the promising methods to predict the bubble trajectory is the force balance model originally developed by Klausner et al. [35] and later modified by several investigators [36
39]. The concept of the force balance model is schematically shown in Fig. 2.6.4. In this model, the force acting on the bubble growing on the heated surface is broken down into several components such as the surface tension force, quasi-steady and unsteady drag forces, buoyancy force, shear lift force, hydrodynamic pressure force, contact pressure force, etc., and the time variation of each component is evaluated using appropriate correlation; a model to estimate the time variation of bubble size is also necessary to evaluate the above-mentioned forces. It is supposed that the bubble starts to slide

2.6.3 BUBBLE DYNAMICS IN SUBCOOLED FLOW BOILING

FIGURE 2.6.3 Consecutive bubble images in subcooled flow boiling of water at low pressure (left: side view, right: bottom view) [20].

FIGURE 2.6.4 Schematic diagram of the force balance model [35].

137

138

CHAPTER 2 NUCLEATE BOILING

along the surface if the net force acting in the direction parallel to the heated surface becomes nonzero whilst it is lifted off the surface if the net force in the direction perpendicular to the heated surface becomes nonzero. It has been shown that the force balance model can predict the bubble size at the departure from nucleation site db,dep fairly well for an upward-facing heated surface in horizontal flow [35,36] and for a vertically heated surface in upward and downward flows [37], although predictive performance seems deteriorated for a downward-facing surface in horizontal flow [40]. For the bubble size at the lift-off from the heated surface, db,lift, good agreement with experimental data has been reported for an upward-facing heated surface in horizontal flow [36] and a vertical heated surface in downward flow [37]; however, comparison with experimental data of db,lift has not been conducted extensively for the vertical heated surface in upward flow. For example, Thorncroft and Klausner [37] indicated that the model does not predict lift-off to occur in vertical upward flow, which seems inconsistent with the experimental observation in Fig. 2.6.3B. In both the experiments of pool boiling [41] and vertical upward flow boiling [21], it has been reported that the bubble lift-off from a vertical heated surface is more likely to occur when the bubble grows fast immediately after the inception. This would be consistent with the fact the bubble lift-off is frequently observed in low-pressure water experiments [25,32,33] but not in experiments using high-pressure water and fluorinert [18,31]. One possible reason for the lift-off may be the unsteady drag force, or the growth force Fgrow that arises due to asymmetric bubble growth on the heated surface. Klausner et al. [35] expressed Fgrow by Fgrow 5 2 πρl a2



3 2 a_ 1 aa¨ 2

(2.6.13)

where a is the bubble radius. To calculate Fgrow from the above equation, a should be expressed as a function of time. In most studies, a is assumed proportional to the square root of time based on the theoretical analysis by Mikic et al. [42]. In this case, Fgrow is always negative; this implies that the growth force pushes the bubble against the wall. However, the bubble growth rate commonly retards in subcooled boiling due to condensation. Fig. 2.6.5 displays the time variation of bubble size on a vertical heated surface in subcooled pool boiling of water [41]; here, db1 and t1 are the 1.5 θ = 0º 0

0.5

db+ is proportional to t+

db+

1

0.5 TSUB = 5 K TSUB = 0 K

0 0

0.5 t+

1

FIGURE 2.6.5 Bubble growth curves on a vertical heated surface in subcooled pool boiling of water [41].

2.6.3 BUBBLE DYNAMICS IN SUBCOOLED FLOW BOILING

139

bubble diameter and the time from inception normalized by the values at lift-off (db1 5 1 and t1 5 1 at lift-off). It can be confirmed that although the bubble size is proportional to the square root of time within the short period after inception, the bubble growth retards gradually when t1 exceeds about 0.15. The bubble size is maximized at around t1 5 0.7 and it is already decreasing at the moment of lift-off. The reduction in bubble size prior to lift-off is also observed in flow boiling [21]. When the bubble size is maximized, a_ is zero while a¨ is negative. Equation (2.6.13) therefore suggests that the growth force initially pushes the bubble against the wall but it pulls the bubble from the wall in the later stage to promote the lift-off. In subcooled boiling, the bubble is often flattened along the heated surface immediately after inception and rounded gradually as can be seen in Fig. 2.6.3. Okawa et al. [20] pointed out that the local liquid flow induced by the change in bubble shape may assist the lift-off. Fig. 2.6.6 displays the process of bubble lift-off observed in subcooled flow boiling of water under low pressure [21]. Here, the same images are shaded and overlapped with the next images to highlight the timeevolution of bubble dimensions. It can be seen that the reduction of the bubble volume prior to the lift-off occurs at the side wall rather than at the top of the bubble. It appears that the condensation is most significant on the downside of the bubble. Based on this observation result, Ahmadi et al. [21] discussed that since local liquid flow directing toward the bubble base may cut out the connection between the bubble and the wall, the net condensation prior to the lift-off is also expected to contribute the bubble lift-off. Cao et al. [43] also discussed the importance of local liquid flow formed around the bubble and discussed that the Marangoni effect might be the main cause of the local liquid flow. The force balance model is a sophisticated tool for mechanistic prediction of the bubble trajectory, the bubble size at the departure from the nucleation site, and the bubble size at the lift-off from a heated surface. However, further experimental and analytical studies are needed to achieve accurate evaluation of each component of the force acting on a bubble. Because of the extreme complexity of the force acting on a bubble, Miyano et al. [44] tested an alternative approach to

FIGURE 2.6.6 Overlapped bubble images during the lift-off process (time interval is 0.67 ms) [21].

140

CHAPTER 2 NUCLEATE BOILING

FIGURE 2.6.7 Snapshots of subcooled flow boiling of water in a vertical rectangular channel (heat flux is increased from 161 to 760 kW/m2 from left to right) [45].

estimate db,lift. When the bubble size is maximized, the vaporization rate around the bubble should be equal to the condensation rate (net vaporization is zero). It may also be expected that db,lift is fairly proportional to the maximum bubble size reached prior to the lift-off (see Fig. 2.6.5). Hence, Miyano et al. [44] deduced a new correlation for db,lift from the balance of vaporization rate and condensation rate. Only limited success has been achieved so far, but predictive performance would be improved if the mechanisms of phase change around the bubble are understood in more detail. Another issue in the prediction of bubble size in subcooled flow boiling is the bubble size distribution. Fig. 2.6.7 shows the snapshots of subcooled flow boiling of water in a vertical rectangular channel at different wall heat fluxes; a transparent ITO film deposited on the glass wall was electrically heated to generate bubbles [45]. It was found that in this experiment, the size of the bubbles produced at the same nucleation site was fairly constant but the bubble size was significantly different between the different sites; the difference could be greater than one order of magnitude (the range of bubble size was approximately 0.2
2.5 mm in their experiments). It is considered that the correlation for the mean bubble size is not sufficient and that for the bubble size distribution is required in the mechanistic subcooled flow boiling models in the future.

2.6.4 CONCLUSION In this section, available subcooled flow boiling models were reviewed and the studies of bubble dynamics, which is a key phenomenon in mechanistic modeling of subcooled flow boiling, are discussed. It should, however, be noted that other parameters should also be understood sufficiently for mechanistic modeling of subcooled flow boiling. Most typical ones would be the bubble release frequency fb and the nucleation site density Ns. Commonly, fb decreases with an increase in the bubble size db [46,47]. Hence, fb should be different between the nucleation sites at which the bubbles of different size are produced. In addition, Kaiho et al. [48] carried out the detailed visualization of subcooled flow boiling to indicate that the relation between fb and db usually agreed with the available correlations fairly well but the value of fb was remarkably low at a nonnegligible number of nucleation sites. Such experimental information is expected to be taken into consideration in improved correlations for fb and Ns. Another phenomenon to be correctly modeled is the

SUBSCRIPTS

141

bubble interaction. The probability of bubble coalescence affects the interfacial area concentration and consequently the condensation rate and the void fraction. It has also been pointed out that sliding bubbles affect the time-averaged value and the temporal variation of local wall temperature [5,31,34]. Thus, the bubble generation at the nucleation sites located in the path of a sliding bubble may be enhanced or mitigated. The macroscopic parameters in subcooled flow boiling such as the wall temperature and the void fraction are determined as a consequence of many complicated elementary processes. Further fundamental studies are needed before completing mechanistic and reliable subcooled flow boiling models.

NOMENCLATURE A a ai cp db db,dep db,lift fb h k Ns q T tw V0

area bubble radius interfacial area concentration specific heat bubble diameter departure bubble diameter lift-off bubble diameter bubble release frequency heat transfer coefficient thermal conductivity nucleation site density heat flux temperature waiting time volume of interest

GREEK SYMBOLS α Δhv ΔTsub ε Γ ρ

thermal diffusivity or void fraction latent heat of vaporization liquid subcooling pumping factor phase change rate per unit volume density

SUBSCRIPTS b COND EV FC H

bubble condensation evaporation forced convection heated

142

l lift NB Q sat SCB SPC W

CHAPTER 2 NUCLEATE BOILING

liquid phase lift-off nucleate boiling quenching saturation subcooled boiling single-phase convection wall

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CHAPTER

CHF—TRANSITION BOILING

3

CHAPTER OUTLINE 3.1 Critical Heat Flux and Near-Wall Boiling Behaviors in Pool Boiling ............................................... 149 3.1.1 Introduction ........................................................................................................... 149 3.1.2 Previously Proposed CHF Mechanisms for Pool Boiling .............................................. 149 3.1.3 CHF in Subcooled Pool Boiling on Upward Surfaces .................................................. 150 3.1.3.1 Characteristics of CHF in Subcooled Pool Boiling ................................................150 3.1.3.2 Experimental Apparatus for Measuring Liquid
Vapor Behaviors ..........................152 3.1.3.3 The Liquid
Vapor Structure Beneath Vapor Masses............................................152 3.1.3.4 Behavior of Surface Dry-Out ...............................................................................155 3.1.3.5 The Mechanism of CHF and the Cause of the Increase in CHF in Subcooled Boiling...........................................................................................158 3.1.4 CHF in Saturated Boiling on Inclined Surfaces.......................................................... 160 3.1.5 CHF in Saturated Boiling of Binary Aqueous Solutions............................................... 163 3.1.6 CHF in Boiling of Water on a Heating Surface Coated with Nanoparticles .................... 167 3.1.7 Conclusion............................................................................................................. 171 3.2 Microlayer Modeling for Critical Heat Flux in Saturated Pool Boiling............................................. 173 3.2.1 Introduction ........................................................................................................... 173 3.2.2 Microlayer Model for Fully Developed Nucleate Boiling and CHF................................. 175 3.2.2.1 Basic Ideas of the Microlayer ..............................................................................175 3.2.2.2 Description of Heat Transfer in Fully Developed Nucleate Boiling .........................176 3.2.2.3 Microlayer Thickness and Dry-Out Radius Beneath an Individual Bubble.............179 3.2.2.4 Bubble Dynamics During the Final Growth Period ...............................................180 3.2.3 Results and Discussion ........................................................................................... 181 3.2.4 Conclusion............................................................................................................. 184 3.3 Heat-Transfer Modeling Based on Visual Observation of Liquid
Solid Contact Situations and Contact Line Length ............................................................................................................. 187 3.3.1 Introduction ........................................................................................................... 187 3.3.2 Observation of Liquid
Solid Contact Pattern and Concept of Contact-Line-Length Density .................................................................................................................. 188 3.3.2.1 Total Reflection Technique ..................................................................................188 3.3.2.2 Liquid
Solid Contact Patterns ............................................................................189 3.3.2.3 Contact-line-Length Density ................................................................................192 3.3.3 Observation of Cross-Sectional Structure of Boiling ................................................... 197 3.3.3.1 Quasi-Two-Dimensional Boiling System ...............................................................197 3.3.3.2 Nucleate Boiling Curve and CHF in Quasi-Two-Dimensional Space ......................198 3.3.3.3 Bubble Structures ..............................................................................................199 Boiling. DOI: http://dx.doi.org/10.1016/B978-0-08-101010-5.00003-8 Copyright © 2017 Elsevier Ltd. All rights reserved.

145

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3.3.4 Observation of Liquid
Solid Contact Situations During Cooling by Liquid Jet or Spraying ............................................................................................................ 203 3.3.4.1 Experimental Setup and Conditions.....................................................................203 3.3.4.2 Leidenfrost Temperature and Limit of Liquid Superheat of the Test Liquid ............204 3.3.4.3 Liquid
Solid Contact Situations While Liquid Spray Cooling .................................204 3.3.4.4 Liquid
Solid Contact Situations with Liquid Jet Impingement ..............................206 3.3.5 Conclusion............................................................................................................. 210 3.4 Critical Heat Flux Enhancement in Saturated Pool Boiling............................................................. 212 3.4.1 Introduction ........................................................................................................... 212 3.4.2 Fundamental Effects of HPP on the CHF Enhancement ............................................. 214 3.4.2.1 Effect of Micropores and Vapor Escape Channels on the CHF..............................214 3.4.2.2 Effects of the Heights in HPPs δh on the CHF......................................................215 3.4.2.3 The CHF Model Based on Capillary Limit ............................................................217 3.4.2.4 Optimization in Geometry of HPP........................................................................218 3.4.2.5 Effect of Heater Size on the CHF Enhancement...................................................219 3.4.3 Further CHF Enhancement Techniques by HPP ......................................................... 220 3.4.3.1 Two-Layer Structured HPP..................................................................................220 3.4.3.2 Combination of HPP, Nanoparticle-Coated Surface, and Honeycomb Solid Structures (HSSs) in Pure Water.................................................................221 3.4.3.3 Combination of HPP and Nanofluid.....................................................................223 3.4.4 Conclusion............................................................................................................. 225 3.5 Dependence of Critical Heat Flux on Heater Size ......................................................................... 227 3.5.1 Introduction ........................................................................................................... 227 3.5.2 CHF on Wires and Cylinders .................................................................................... 229 3.5.2.1 Available CHF Data Correlations ..........................................................................229 3.5.2.2 Recent Experimental Study and Results ..............................................................231 3.5.2.3 Discussions and Remaining Problems.................................................................234 3.5.3 CHF on Plates ........................................................................................................ 236 3.5.3.1 CHF on a Plain Surface ......................................................................................236 3.5.3.2 CHF on Chips with Modified Surfaces .................................................................236 3.5.4 CHF Data Correlation on Heaters of Various Shapes and Configurations ....................... 238 3.5.5 Parameters and Factors Affecting CHF ..................................................................... 239 3.5.6 Summary and Concluding Remarks .......................................................................... 241 3.6 Stability of Transition Boiling...................................................................................................... 243 3.6.1 Introduction ........................................................................................................... 243 3.6.2 Attempt to Attain Steady Transition Boiling by Low-Resistance Heat Exchange ............ 243 3.6.2.1 Heating with Steam ............................................................................................243 3.6.2.2 Heating with Convective Cooling/Heating .............................................................246 3.6.2.3 Temperature Stabilization by Conduction to the Surroundings for a Small Surface .....246 3.6.3 Automatic Temperature Control................................................................................ 246 3.6.4 Temperature Uniformity Across the Surface .............................................................. 248 3.6.4.1 In the Case of Steady Boiling ..............................................................................248 3.6.4.2 In the Case of Transient Boiling...........................................................................251 3.6.5 Conclusion............................................................................................................. 251

CHF—TRANSITION BOILING

147

3.7 Derivations of Correlation and Liquid
Solid Contact Model of Transition Boiling Heat Transfer ...... 254 3.7.1 Introduction ........................................................................................................... 254 3.7.2 Experimental Apparatus and Procedure .................................................................... 255 3.7.2.1 Experimental Apparatus......................................................................................255 3.7.2.2 Experimental Procedure .....................................................................................256 3.7.2.3 Stable Conditions for Steady Transition Boiling.....................................................257 3.7.2.4 Experimental Uncertainty....................................................................................257 3.7.3 Experimental Results and Discussion ....................................................................... 258 3.7.3.1 Heat-Transfer Characteristics: Boiling Curve ........................................................258 3.7.3.2 Liquid
Solid Contact Fraction: Correlation ..........................................................259 3.7.3.3 Void Fraction Near Heating Surface ....................................................................260 3.7.4 Modeling and Discussion......................................................................................... 262 3.7.4.1 First Model.........................................................................................................262 3.7.4.2 Present Model ....................................................................................................263 3.7.4.3 Application to Rewetting .....................................................................................265 3.7.4.4 Application to Core Cooling .................................................................................266 3.7.5 Conclusion............................................................................................................. 268 3.8 Critical Heat Flux in Subcooled Flow Boiling................................................................................ 271 3.8.1 Introduction ........................................................................................................... 271 3.8.2 Criterion for the Judgement of Flow Pattern Development .......................................... 273 3.8.3 CHF Prediction for the Subcooled Flow Boiling of the Conventional Flow Pattern ......... 276 3.8.3.1 Introduction........................................................................................................276 3.8.3.2 Liu
Nariai Model ...............................................................................................280 3.8.3.3 Validation of the Proposed CHF Model ................................................................286 3.8.4 CHF Prediction for the Subcooled Flow Boiling of the Homogeneous-Nucleation-Governed Flow Pattern ...................................................... 288 3.8.4.1 CHF Triggering Mechanism and Prediction..........................................................288 3.8.4.2 Validation of the Proposed Model ........................................................................289 3.8.5 Conclusion............................................................................................................. 292 3.9 Convective Boiling Under Unstable Flow Conditions ..................................................................... 297 3.9.1 Introduction ........................................................................................................... 297 3.9.2 The Definition of Flow Instability ............................................................................. 298 3.9.3 The Historical Background ...................................................................................... 299 3.9.4 Simple Model—Quasi-Steady Assumption ................................................................ 301 3.9.5 Estimation by Lumped-Parameter Model—Dumping Effect of Two-Phase .................... 305 3.9.6 Dry-Out Under Natural Circulation Loop—Flow Oscillation Caused by the System ........................................................................................................ 308 3.9.7 More Detailed Discussion of Boiling Phenomena under Oscillatory Flow Conditions...................................................................................................... 311 3.9.8 Conclusion............................................................................................................. 313 3.10 Film Flow on a Wall and Critical Heat Flux .................................................................................. 316 3.10.1 Introduction ......................................................................................................... 316 3.10.2 Minimum Wetting Rate ......................................................................................... 317 3.10.2.1 Analytical Model of MWR............................................................................... 318

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CHAPTER 3 CHF—TRANSITION BOILING

3.10.2.2 Measurement of MWR, Contact Angle, and Wave Characteristics.................... 319 3.10.2.3 Results.......................................................................................................... 320 3.10.2.4 Effect of Waves on MWR ............................................................................... 326 3.10.3 CHF of Film Flow ................................................................................................. 328 3.10.4 CHF of Mini-Channel ............................................................................................ 333 3.10.5 Characteristics of Falling Film Flow........................................................................ 337 3.10.5.1 Wave Profile .................................................................................................. 338 3.10.5.2 Film Thickness .............................................................................................. 339 3.10.5.3 Wave Velocity ................................................................................................ 344 3.10.5.4 Wavelength ................................................................................................... 345 3.10.5.5 Development of Correlations of Wave Properties ............................................. 346 3.10.6 Conclusion........................................................................................................... 350 3.11 Boiling Transition and CHF for the Fuel Rod of a Light Water Reactor ............................................ 354 3.11.1 Introduction ......................................................................................................... 354 3.11.2 Prediction of the Heat-Removal Limit..................................................................... 354 3.11.2.1 Design-CHF Correlation for an LWR Fuel Assembly ........................................ 354 3.11.2.2 CHF Prediction Using a Film Dry-Out Model for a Vertical Tube ...................... 355 3.11.2.3 Analysis of Critical Power Prediction for BWR Fuel Assembly.......................... 359 3.11.2.4 Enhancement of Heat-Removal Limit ............................................................. 362 3.11.2.5 Post-BT Criteria ............................................................................................. 365 3.11.3 Conclusion........................................................................................................... 366

This chapter deals with topics on critical heat flux (CHF) point and transition boiling in aspects of heat-transfer mechanisms based on both model simulations and measurements of each authors’ research in recent decades. The first three sections report on heat-transfer modeling on CHF based on measurements and visualization results, i.e., macrolayer dry-out model (see Section 3.1), microlayer evaporation model (see Section 3.2), and contact-line-length density model (see Section 3.3). Section 3.4 demonstrates unique surface structures for enhancement of CHF. The following three sections cover other aspects of CHF and transition boiling mechanisms. Section 3.5 reports on unified explanations for heater size dependence of CHF. Section 3.6 shows the unique characteristics of transition boiling, i.e., negative differential resistance, and focuses on uniformity of surface temperature and heat flux during transition boiling. Section 3.7 discusses liquid
solid contact fraction in the transition boiling region and derives the correlation for the transition boiling curve. The last four sections deal with CHF in flow boiling conditions. Section 3.8 discusses CHF triggering mechanisms and prediction methods in subcooled flow boiling. Section 3.9 shows the influence of flow oscillation on convective boiling phenomena. Section 3.10 reports on the relation between the appearance of dry patches and CHF in forced flow boiling. The last section (see Section 3.11) focuses on boiling transition phenomena and CHF for boiling water reactor fuel assembly.

3.1.2 PREVIOUSLY PROPOSED CHF MECHANISMS FOR POOL BOILING

CRITICAL HEAT FLUX AND NEAR-WALL BOILING BEHAVIORS IN POOL BOILING

149

3.1 Hiroto Sakashita

Hokkaido University, Sapporo, Japan

3.1.1 INTRODUCTION In 1934, Nukiyama [1] published a paper entitled Maximum and Minimum Values of Heat Q Transmitted from Metal to Boiling Water Under Atmospheric Pressure—a milestone paper that was the first to show the existence of an upper limit of heat removal (critical heat flux, CHF) in boiling heat transfer. Following this pioneering research, numerous studies of CHF in pool boiling have been carried out, and a number of CHF models have been proposed. However, the mechanism of CHF has not been fully elucidated. This section reviews the research conducted by the group of the present author on CHF in (1) subcooled boiling on upward surfaces, (2) saturated boiling on inclined surfaces, (3) saturated boiling of binary aqueous mixtures, and (4) saturated boiling of nanofluids. These four kinds of boiling conditions have the common characteristic that it is possible to change the CHF in a controlled manner. This common characteristic makes it possible to hypothesize that if it is possible to identify a CHF model that consistently predicts the CHF behaviors in these four different boiling conditions, a mechanism developed from that model is a likely candidate to be close to the actual CHF mechanism. The following sections present experimental results of liquid
vapor behaviors close to heating surfaces measured with fine conductance probes. Based on these results, a possible mechanism of the CHF and the reasons why the CHF changes in the above four boiling conditions are examined.

3.1.2 PREVIOUSLY PROPOSED CHF MECHANISMS FOR POOL BOILING Zuber [2] postulated that vapor escapes from a heating surface as large vapor jets and proposed a hydrodynamic instability model in which the Helmholtz instability at the interface between the vapor jets and the surrounding liquid causes the CHF. Katto and Yokoya [3] proposed a different idea, where the CHF occurs when a liquid layer (a so-called macrolayer) which has formed beneath a large vapor mass dries out immediately before the departure of the vapor mass. This idea was further developed and formulated by Haramura and Katto [4], and has been termed the “macrolayer

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dry-out model.” Unal et al. [5] focused on the phenomena occurring on the heating surface and proposed a model in which the CHF is reached when a dry area on a heating surface reaches a temperature at which the liquid can no longer maintain contact. Theofanous et al. [6] proposed a similar model where irreversible temperature excursions of dry-spots beneath the primary bubble base become the CHF trigger. Howard and Mudawar [7] carried out experiments to observe boiling behaviors on vertical and inclined surfaces and proposed the following CHF model: at high heat fluxes near the CHF, the heating surface is covered with a wave-shaped vapor layer and wetted only by the wave troughs (termed the “wetting fronts”), which repeatedly sweep across the surface and remove heat from the heating surface. The CHF is triggered by the separation of the most upstream wetting front from the heating surface. Kandlikar [8] proposed a model incorporating the effect of the contact angle on the CHF, by considering the lateral forces acting on a bubble attached to a heating surface. When the force arising from changes in the momentum due to evaporation at the bubble interface exceeds the forces working to maintain the bubble in place, due to gravity and surface tension, then the bubble base (the dry area) spreads along the heating surface, leading to the CHF. The above models are based on different CHF mechanisms, but all involve the common assumption that there is a trigger causing the CHF. This would suggest that there will be some noticeable change, noticeable as a difference in the state of the liquid
vapor behaviors close to the heating surface before and after the CHF. There are also models that consider the boiling behavior to shift smoothly from nucleate boiling and pass through the CHF to transition boiling, and here the CHF is obtained as the maximum heat flux point along the continuous boiling curve. In these models, the CHF is determined from a competition between the heat-transfer enhancement with increasing wall superheat and a deterioration in the heat transfer by the expansion of the dry areas on the heating surface. Based on these models, there would be no distinct change in the apparent boiling behaviors before and after the CHF, differing from the models that propose the existence of a trigger for the occurrence of the CHF. Models categorized into this type are the stationary vapor stem model proposed by Dhir and Liaw [9], the triple contact line density model by Nishio et al. [10], the microlayer model by Zhao et al. [11], and the dry-spot model by Ha and Ma [12].

3.1.3 CHF IN SUBCOOLED POOL BOILING ON UPWARD SURFACES [13,14] 3.1.3.1 CHARACTERISTICS OF CHF IN SUBCOOLED POOL BOILING It has been widely accepted that with increases in subcooling the CHF for subcooled boiling markedly increases to values greatly above the CHF in saturated boiling. Fig. 3.1.1 shows the variation in CHF with subcooling measured on horizontal upward-facing copper surfaces (diameters 10 mm or smaller) in water boiling [13,15
17]; here the CHF increases linearly with increases in the subcooling. Fig. 3.1.2 shows the appearances of vapor bubbles in boiling on 8-mm-diameter surfaces near the CHF for saturated boiling (Fig. 3.1.2A) and subcooled boiling of 40 K subcooling (Fig. 3.1.2B). The appearances of the bubbles are little different, other than that the vapor mass in the subcooled boiling is slightly smaller. (In both the saturated and subcooled boiling in

3.1.3 CHF IN SUBCOOLED POOL BOILING ON UPWARD SURFACES

151

CHF (MW/m2)

6 Ono (d=8 mm) [13] Inada (d=10 mm) [15] Yokoya (d=10 mm) [16] Li (d=10 mm) [17]

4

2 Upward disk

0

(d: diameter of heating surface) 0

10

20 30 Subcooling (K)

40

50

FIGURE 3.1.1 Variation in CHF with subcooling (upward-facing surfaces) [14].

FIGURE 3.1.2 Appearances of bubbles at boiling in (A) saturated (ƒTsub 5 0K, q 5 1.5 MW/m2) and (B) subcooled (ƒTsub 5 40K, q 5 5 MW/m2) boiling near CHF [18].

Fig. 3.1.2A and B, the heating surface is completely covered with the vapor masses, which form and detach periodically, with a period of 25
40 ms.). Despite the similarities in the boiling appearances in saturated and subcooled boiling, the CHF at the 40 K subcooling is more than twice that of the CHF in the saturated boiling, as suggested by Fig. 3.1.1. It may therefore be expected that the causes of the increase in CHF with the increases in subcooling could be related to the liquid
vapor structure beneath the vapor masses. To establish more details of the CHF mechanism in saturated and subcooled boiling, the author and coworkers carried out experiments to measure the liquid
vapor behaviors near the heating surface using conductance probes, as will be further detailed in the following.

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CHAPTER 3 CHF—TRANSITION BOILING

FIGURE 3.1.3 Experimental apparatus and setup for measuring liquid
vapor behaviors [13].

3.1.3.2 EXPERIMENTAL APPARATUS FOR MEASURING LIQUID
VAPOR BEHAVIORS Fig. 3.1.3 shows the experimental apparatus. The experiments were conducted using water at atmospheric pressure over a range of subcooling from 0 to 40 K. The top surface of a conical copper block served as the heating surface making it possible to realize a heat flux up to 10 MW/m2. The diameter of the heating surface is 8 mm and a vapor mass covers the whole of the area of the heating surface at high heat fluxes near the CHF at the 40 K subcooling. A conductance probe method was adopted for the measurements of the liquid
vapor behaviors close to the heating surface. The tip of the conductance probe was thinned to less than 5 μm by electro-polishing, and the conductance probe was connected to a three-dimensional (3D) moving stage with a positioning accuracy of 0.5 μm in the perpendicular and 10 μm in the horizontal directions (the moving probe in the following, the A-probe in Fig. 3.1.3). A further probe was used to selectively measure the behaviors of vapor masses (the fixed probe in the following, the B-probe in Fig. 3.1.3). The fixed probe was placed near the center of the heating surface and 4 mm over the surface. During the measurements, potassium chloride was added to the water to increase the electro-conductivity, and an AC voltage of 24 kHz was applied between the conductance probe and the heating surface.

3.1.3.3 THE LIQUID
VAPOR STRUCTURE BENEATH VAPOR MASSES Fig. 3.1.4 shows the moving probe signals measured at different heights over the heating surface. In each graph, the top signals are the raw probe signals and the bottom signals are the respective digitized signals, where a high voltage of the raw signal shows that the tip of the probe is in contact with vapor and a low voltage that it is in contact with the liquid. The continuous wide vapor signals observed far from the heating surface (h ^ 0.241 mm) correspond to the vapor mass signals. Closer to the heating surface, the vapor mass signals display discontinuities (h 5 0.141 mm). When

3.1.3 CHF IN SUBCOOLED POOL BOILING ON UPWARD SURFACES

153

FIGURE 3.1.4 Probe signals recorded at different heights (h) over the heating surface [18].

approaching the surface further, the wide pulses disappear and the signals appear as an aggregation of narrow pulses (h 5 0.051 mm, 0.031 mm). Finally, close to the heating surface, high-voltage signals have disappeared and there are only the fine low-voltage signals, indicating that there is only liquid at this height (h 5 0.011 mm). Fig. 3.1.5 shows the vertical distributions of time-averaged void fractions calculated by averaging the moving probe signals. The void fraction distributions are similar for all subcooling conditions: it has a value around unity far from the surface and decreases to zero as it approaches the heating surface. Here, it must be borne in mind that the heat fluxes for the 20 K and 30 K subcooling shown in Fig. 3.1.5 exceed the CHF for saturated boiling (qCHF 5 2.09 MW/m2). The results in Figs. 3.1.4 and 3.1.5 suggest that the heating surface is always covered with liquid and that there is a liquid-rich zone between the vapor masses and the heating surface, where liquid or vapor dominates in turn. This liquid-rich zone between the vapor masses and a heating

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CHAPTER 3 CHF—TRANSITION BOILING

1

ΔT sub= 0K 2 q=1.41MW/m

Void fraction

0.8

ΔT sub=10K 2 q=1.43MW/m ΔT sub=20K 2 q=2.51MW/m ΔT sub=30K 2 q=2.77MW/m

0.6 0.4 0.2 0 0.001

0.01

0.1

1

Distance from heating surface (mm) FIGURE 3.1.5 Vertical distributions of time-averaged void fractions [13].

Macrolayer thickness (μm)

500

ΔT sub 0K 20 K 30 K 40 K

100 50 Eq. (3.1.1) Eq. (3.1.3)

10

Eq. (3.1.2) 5

1

2

3

4

5

2

Heat flux (MW/m ) FIGURE 3.1.6 Thickness of macrolayer formed under vapor masses in saturated and subcooled boiling [18].

surface corresponds to the so-called “macrolayer,” and here the term macrolayer will be used for this in the following. Fig. 3.1.6 shows the macrolayer thicknesses for the saturated and subcooled boiling conditions. The macrolayer thickness was determined from the position where the vapor mass signals disappear, and is based on the assumption that the region from the heating surface to the height below which the oscillation of the interface at the bottom of the vapor mass does not reach corresponds to the macrolayer. Further details of the method to determine the macrolayer thickness are represented in Ref. [13]. As suggested by the probe signals at h 5 0.141 mm or 0.101 mm in Fig. 3.1.4, the bottom of the vapor mass oscillates violently, and the macrolayer thickness also fluctuates with time. In Fig. 3.1.6, the symbols represent the thickness of the macrolayer with the highest formation

3.1.3 CHF IN SUBCOOLED POOL BOILING ON UPWARD SURFACES

155

frequency and the ends of the vertical bars at each symbol indicate the minimum and maximum values of the fluctuating macrolayer thickness. The lowest heat flux in all of the subcooled conditions, except for the saturated condition, is the heat flux at which a large vapor mass covering the whole area of the heating surface starts to form—the lowest heat flux of the vapor mass region. (At heat fluxes lower than this lowest heat flux, therefore, no macrolayer is formed on the heating surface.) Fig. 3.1.6 also shows the macrolayer thicknesses calculated with the empirical correlation proposed by Bhat et al. [19] for water at atmospheric pressure, with the semi-theoretical correlation by Haramura and Katto [4], and with the modified Haramura and Katto correlation by Rajvanshi et al. [20]. These correlations are given as (a) Bhat et al. [19]: δ 5 1:585 3 105 q21:527 :

(3.1.1)

(b) Haramura and Katto [4]:     22 σ ρv 0:4 ρ q 11 v : ρv ρl ρv Hfg ρl

(3.1.2)

    22 σ ρv 0:4 ρ q 11 v ; ρv ρl ρv Hfg ρl

(3.1.3)

δ 5 0:00535

(c) Rajvanshi et al. [20]: δ 5 0:0107

where δ is the macrolayer thickness, and the units of δ and q in Eq. (3.1.1) are m and W/m2, respectively. The macrolayer thicknesses for saturated boiling lie relatively close to the values of the empirical and the semi-theoretical correlations. However, the macrolayer thicknesses for subcooled boiling show different tendencies at different subcooling conditions, and the macrolayer formed near the lowest heat fluxes of the vapor mass region (this heat flux is far higher than the CHF of saturated boiling) is considerably thicker than would be expected by an extrapolation of the macrolayer thickness for saturated boiling to higher heat flux regions.

3.1.3.4 BEHAVIOR OF SURFACE DRY-OUT 3.1.3.4.1 The detection of surface dry-out by conductance probe The previous section (see Section 3.1.3.3) showed that the heating surface is covered by liquid even at very high heat fluxes in subcooled boiling, above the CHF of saturated boiling. This section shows measured results of the dry-out behavior of the heating surface at heat fluxes close to the CHF. The measurements were made by utilizing the features of the conductance probe used in the present experiments, as will be detailed next. Fig. 3.1.7 shows the measured output voltage from the moving probe (A-probe in Fig. 3.1.3) when the probe was pushed down from the atmosphere above the water layer and into the water (or pulled up from the water into the atmosphere) when the water and the heating surface were not heated and the water layer covering the heating surface was several millimeters thick. The 0-mm distance corresponds to a location where the tip of the probe touches the water surface. Here, at the water surface, the voltage falls instantaneously to about half the maximum voltage when the probe tip-water contact is established, after this it decreases further as the probe tip penetrates deeper

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CHAPTER 3 CHF—TRANSITION BOILING

FIGURE 3.1.7 Conductance probe signals recorded in and above water [18].

below the surface of the water, and reaches an almost constant low value when the probe tip is below a depth of around 0.4 mm. This result is made possible due to the high sensitivity of the conductance probe tip, and the probe outputs the intermediate value between high and low voltages (about 55% of the maximum voltage in Fig. 3.1.7) just when the probe tip comes in contact with the liquid. Fig. 3.1.8 shows the probe signals obtained at a high heat flux (81% of the CHF; Fig. 3.1.8A) and near the CHF (97% of the CHF; Fig. 3.1.8B) at 20 K subcooling. In the figures, the top signals are obtained with the moving probe fixed a few μm above the heating surface, and the bottom signals are from the fixed probe, representing the behavior of the vapor masses. In Fig. 3.1.8A, the signals from the moving probe near the heating surface record low voltages, indicating the existence of a liquid layer beneath the vapor masses. In Fig. 3.1.8B very close to the CHF, the signals from the moving probe reach higher voltages in the latter half of the vapor mass hovering periods. Fig. 3.1.9 represents Fig. 3.1.8B signals of the moving and fixed probes during one hovering cycle of a vapor mass. The moving probe signals can be divided into three regions (A, B, and C) according to the magnitude of the output voltage. From the correspondence with the static characteristics in Fig. 3.1.7, it may be assumed that region A (low-voltage signal region) corresponds to a situation where the whole of the probe is covered with liquid, region B (intermediate-voltage signal region) is where the tip of the probe is in contact with liquid and the remaining part of the probe is covered with vapor, and region C (high-voltage signal region) is where all of the probe is enclosed in vapor. With the experimental results that the signals accompanying region C appear only near the CHF, it may be suggested that the signals of Fig. 3.1.9 present evidence of the occurrence of surface dry-out at the probe location. It is, therefore, considered that the duration of region A indicates a period during which the formation of the large vapor mass is progressing, the duration

3.1.3 CHF IN SUBCOOLED POOL BOILING ON UPWARD SURFACES

157

Voltage (V)

(A) ΔT sub=20 K, q=2.55 MW/m2, h=1 μm 5 0 5 0 –5

Voltage (V)

0 0.1 (B) ΔT sub=20 K, q=3.05 MW/m2, h =5 μm

0.2

Dryout

5 0 5 0

–5

0

0.1

0.2

Time (s) (Upper signal: moving probe. Lower signal: fixed probe.)

FIGURE 3.1.8 Probe signals recorded near heating surface in nucleate boiling region and near CHF [14].

B

C

Voltage

A

Dry-out period Vapor mass hovering period 0.09

0.1

0.11

0.12

0.13

Time (s)

FIGURE 3.1.9 Regions of probe signals recorded under surface dry-out conditions [14].

of region B indicates the lifetime of the macrolayer under the large vapor mass, and the duration of region C indicates a period of surface dry-out. From these results, it is suggested that at high heat fluxes near the CHF the temporal variation of wet and dry states of the heating surface occurs not randomly or in an irregular manner but in the following sequential process: with the detachment of a vapor mass, there is inflow of bulk liquid, followed by the formation of a vapor mass and a macrolayer beneath the vapor mass, leading to surface dry-out by consumption of the macrolayer.

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CHAPTER 3 CHF—TRANSITION BOILING

3.1.3.4.2 The 2D behaviors of surface dry-out Figs. 3.1.8 and 3.1.9 show results of the dry-out behaviors at one position at the center of the heating surface. To examine the 2D dry-out behaviors across the heating surface, measurements were conducted at 121 grid points arranged at 0.1-mm intervals in a 1 mm 3 1 mm region at the center of the heating surface. The probe traversed the area horizontally at a height of 3
5 μm from the heating surface and the fractions of dry-out time to the measurement time (termed “dry-out void fraction”) were obtained at the 121 measuring points. Fig. 3.1.10 shows the 2D distributions of the dry-out void fractions obtained at two different heat fluxes near the CHF for 20 K subcooling (brighter color shows higher dry-out void fractions). In Fig. 3.1.10A with the heat flux q 5 2.97 MW/m2 (94% of the CHF) at which the dry-out begins to appear, here the dry-out is limited to some areas and the dry-out void fractions are small with values of less than 1.5%. In Fig. 3.1.10B where the heat flux is slightly higher at q 5 3.01 MW/m2 (95% of the CHF), the dryout areas enlarge greatly and the dry-out void fractions also increase to a maximum of about 21%.

3.1.3.5 THE MECHANISM OF CHF AND THE CAUSE OF THE INCREASE IN CHF IN SUBCOOLED BOILING The results of the foregoing sections may be summarized as: (1) the occurrence of dry-out commences as the heat flux approaches the CHF, (2) the dry-out occurs in the latter half of the vapor mass hovering period, (3) the dry-out area expands rapidly over the heating surface with slight increases in the heat flux. These findings strongly suggest that the dry-out of the macrolayer formed on the heating surface is the trigger of the CHF. 10

10

9

9

8

8

7

7 6

6 1 mm

5

5

4

4

3

3

2

2

1

1

0

0

1

2

3

4

5

6

7

8

0

9 1.5

(A) 2.97 MW/m2 (ΔTsub=20 K)

10

0

0

1

2

3

4

5

6

7

8

0

9 21

(B) 3.01

MW/m2

(ΔTsub=20 K)

FIGURE 3.1.10 2D map of dry-out void fractions (brighter color shows higher dry-out void fractions) [14].

10

3.1.3 CHF IN SUBCOOLED POOL BOILING ON UPWARD SURFACES

159

To verify and elucidate details of this deduced trigger mechanism, the transient behaviors of liquid/vapor signals close to the heating surface from the nucleate boiling region through the CHF to the transition boiling region were measured under transient heating modes, realized by stepwise increases in the heat input to the copper block initially kept at steady-state conditions at high heat fluxes in nucleate boiling. Fig. 3.1.11 shows the signals of the moving probe positioned 10 μm above the heating surface together with the changes in the surface superheat. Fig. 3.1.11 shows the behaviors of the surface superheat and the probe signals from 40 to 80 s after the start of measurements. There is a sudden increase in the surface superheat at 73 s, showing the occurrence of the CHF. At this time, the probe signals change suddenly from the fine irregular signals corresponding to the primary bubbles to signals showing surface dry-out. As above, all the experimental results discussed in Section 3.1.3 strongly support the following CHF mechanism: a macrolayer formed on the surface is consumed during vapor mass hovering and, as a consequence, the dry area expands rapidly across the heating surface, leading to CHF. Among the various models described in Section 3.1.2, this CHF mechanism is in good agreement with that assumed by the macrolayer dry-out model. Therefore, at least for the CHF in saturated and subcooled pool boiling of water on a copper heating surface with large heat capacity, the macrolayer dry-out model proposed by Katto and coworkers [3,4] would appear to be the most appropriate model of CHF, and the causes of the CHF increase with increasing subcooling are likely to be that a thick macrolayer is able to form in subcooled boiling as shown in Fig. 3.1.6, and further that the lowest heat flux of the vapor mass region shifts towards the higher heat flux. The reason why a thicker macrolayer is formed in subcooled boiling may be qualitatively explained as follows: as the vapor masses are formed by the coalescence of smaller bubbles (primary bubbles or coalesced bubbles formed by coalescence of the primary bubbles) generated on the heating surface immediately after the departure of the preceding vapor mass, it may be postulated that the macrolayer thickness is closely related to the behavior of the bubbles forming the vapor masses. In subcooled boiling at the vapor mass region, the boiling behaviors near the heating surface are affected by the subcooling only during the period from the detachment of the preceding until the formation of the succeeding vapor mass. The bubbles generated during this period grow and coalesce to form larger vapor masses affected by the subcooling, with the effect being stronger

FIGURE 3.1.11 Appearance of probe signals before and after CHF [14].

160

CHAPTER 3 CHF—TRANSITION BOILING

when the bulk liquid subcooling is stronger. When bubbles grow in a subcooled environment, the growth rate of the bubbles slows down due to condensation effects, and the slower growth rate reduces reaction forces acting on the bubbles. The reduction in the reaction forces results in bubbles that are closer to spherical, and this may explain the thicker macrolayer.

3.1.4 CHF IN SATURATED BOILING ON INCLINED SURFACES [21] A large number of studies have been conducted to examine the effect of the surface orientation on the CHF, and have reported that the CHF decreases drastically as the orientation changes from vertical to downward-pointing horizontal. Fig. 3.1.12 shows an experimental apparatus developed to investigate the mechanism of CHF in boiling on inclined surfaces. The boiling vessel is made of transparent polycarbonate, 160 mm3 140 mm3 400 mm high. The rectangular heating surface was placed at a side wall, and a conductance probe is inserted via the opposite wall. The upper surface of the copper block, 4 mm wide and 48 mm long, served as the heating surface, and the conductance probe was located at 38 mm from the lower edge of the copper block, along the vertical axis of the heating surface. The boiling vessel is placed on a rotating metal frame (not shown in Fig. 3.1.12), and the orientation of the heating surface can be changed from θ 5 90˚ (vertical) to θ 5 170˚ (almost horizontal downward facing) by inclining the boiling vessel. Fig. 3.1.13 shows the changes in the CHF versus the angle of inclination, the CHF decreases with increased angle of inclination, as has been reported in other studies. Fig. 3.1.14 shows the distributions of the time-averaged void fractions normal to the heating surface for four different angles of inclination at q 5 0.69 MW/m2 (“h” of the horizontal axis is the distance from the heating surface to the tip of the probe). Similar to the results for the upward-facing surface in Fig. 3.1.5,

FIGURE 3.1.12 Experimental arrangement for saturated boiling on vertical and inclined surfaces [21].

3.1.4 CHF IN SATURATED BOILING ON INCLINED SURFACES

161

2.5

CHF (MW/m2)

Measured data 2 1.5 1 0.5 80

Predicted values with Haramura Eq. (3.1.2) with Rajvanshi Eq. (3.1.3) 100 120 140 160 Angle of inclination (degrees)

180

FIGURE 3.1.13 Changes in CHF with angle of inclination, experimental and calculated values [18].

100

Void fraction (%)

q =0.69 MW/m2 80 60

θ=90º θ=130º θ=150º θ=170º

40 20 0 0.001

0.01

0.1

1

10

h (mm) FIGURE 3.1.14 Void fraction distributions on inclined surfaces [21].

the void fraction decreases to zero near the heating surface, indicating the existence of the continuous liquid layer (macrolayer) beneath the vapor masses moving upward along the heating surface. The measured results of the macrolayer thickness are shown in Fig. 3.1.15. Fig. 3.1.15 shows the macrolayer thicknesses versus the angle of inclination under constant heat flux conditions. Fig. 3.1.15 also shows the calculated results with the correlations by Bhat et al. (see Eq. 3.1.1), Haramura and Katto (see Eq. 3.1.2), and Rajvanshi et al. (see Eq. 3.1.3). These correlations do not include the gravitational acceleration, g, and hence predict constant macrolayer thicknesses independent of the angle of inclination. As shown in Fig. 3.1.15, the present results of the macrolayer thicknesses obtained at the constant heat fluxes are almost completely independent of the angle of inclination, indicating that the formation process of the macrolayer is little affected by the magnitude of the gravitational acceleration. This suggests that the change in the CHF with the angle of inclination in Fig. 3.1.13 is not caused by changes in the macrolayer thickness.

CHAPTER 3 CHF—TRANSITION BOILING

Macrolayer thickness (μm)

162

500 Rajvanshi, Eq.(3.1.3) 100 50

Bhat, Eq. (3.1.1) Haramura, Eq. (3.1.2) Measured data (q=0.76 – 0.82 MW/m2)

10 80

100 120 140 160 Angle of inclination (degrees)

180

FIGURE 3.1.15 Liquid layer thicknesses vs angle of inclination of heating surface [18].

One difference between the inclined and upward horizontal surfaces is that for the inclined surface the period during which the heating surface is covered by the vapor masses varies greatly with the angle of inclination. As the angle of inclination becomes larger, huge vapor masses with lengths almost equal to the heater length are formed and move upward along the heating surface. Fig. 3.1.16 shows the spectrums of the contact times of the probe-tip with the vapor (termed the pulse width, see top figure of Fig. 3.1.16). In Fig. 3.1.16, the horizontal axis expresses the pulse width, and the vertical axis shows the number of pulses at each pulse width (the total pulse number obtained in one run was 4096 or 8192). The heat flux conditions were similar (q 5 0.54
0.58 MW/m2), and the probe locations were h 5 1
2.6 mm away from the heating surface, inside the vapor masses. The peak in each spectrum (the region indicated by a horizontal arrow) corresponds to the vapor mass signals. For example, at θ 5 144 , the contact time of the probe tip with the vapor mass (period of passage of a vapor mass) distributes from about 15 to 55 ms and the most frequently appearing passage period is around 30 ms. The pulse width spectrum shifts toward the wider pulse width side with increasing angle of inclination, showing that the heating surface at larger angles of inclination is covered with vapor masses in contact with the probe tip for longer times. As described above, the liquid
vapor structures near the heating surfaces for the inclined surfaces are similar to those for the upward-facing surfaces. This suggests that the CHF of the inclined surfaces is triggered by the consumption of the macroleyer, like with the CHF for the upward-facing surface. When the CHF is triggered by the dry-out of the macrolayer during the period of the vapor mass passage, the CHF is approximately expressed with the following energy balance relation. qCHF  τ 5 ρl Hfg δ;

(3.1.4)

where qCHF is the critical heat flux, δ is the maximum (or initial) macrolayer thickness (thickness of macrolayer formed beneath the forefront of a vapor mass moving along the heating surface), τ is the length of the period of the passage of the vapor masses. As shown in Fig. 3.1.15, the macrolayer thicknesses distribute over a range of thicknesses, but the existing correlations appear to approximately predict the average values of the present macrolayer thicknesses. Here, Eq. (3.1.2) by Haramura and Katto and Eq. (3.1.3) by Rajvanshi et al. are used for the macrolayer thickness, δ, and the values of the most frequently appearing vapor masses (the peak values of the pulse width

3.1.5 CHF IN SATURATED BOILING OF BINARY AQUEOUS SOLUTIONS

163

digitized probe signal pulse width

q = 0.54–0.58 MW/m2

h=1–2 mm

150 θ =90º

100 50 0 0 150

40

80

120 θ =130º

100

Data number (–)

50 0 0 150

40

80

120 θ=144º

100 50 0 0 150

40

80

120 θ =156º

100 50 150

0

40

80

120 θ =170º

100 50 0

0

40 80 Pulse width (ms)

120

FIGURE 3.1.16 Pulse width spectrums for different inclinations of heating surfaces [18].

spectrums) are used as the duration of vapor mass passage, τ. The CHF estimated using these macrolayer thicknesses and vapor mass passage periods with Eq. (3.1.4) are plotted in Fig. 3.1.13 (the symbols are the predicted values and the solid and broken lines are interpolations through the discrete predicted values), showing qualitative agreement with the measured CHF. Overall, it may be concluded that the macrolayer dry-out model is a physically appropriate model of the CHF for inclined surfaces, and that the decrease in the CHF with the increasing angle of inclination is primarily caused by a lengthening in the duration of passage of the vapor masses moving along the heating surface.

3.1.5 CHF IN SATURATED BOILING OF BINARY AQUEOUS SOLUTIONS [22] It has been established that the CHF in pool boiling of water is often increased when small amounts of alcohols or ketones are added to the water. Several mechanisms causing the increases in the

164

CHAPTER 3 CHF—TRANSITION BOILING

CHF of such binary mixtures have been proposed, however, no generally agreed mechanism for the CHF enhancement has been established. To examine this phenomenon experimentally, the author and coworkers [22] have investigated the CHF for 2-propanol/water mixtures during pool boiling on an upward-facing heating surface under atmospheric pressure. The experimental apparatus is outlined in Fig. 3.1.17. The upper end of a copper rod, 12 mm in diameter, served as the heating surface, and the conductance probe was placed above the heating surface to measure liquid
vapor behaviors close to the heating surface. Fig. 3.1.18 shows photos of the appearance of boiling water and a 3.0-mol% 2-propanol/water mixture at high heat fluxes. At low heat fluxes (the isolated bubble region), the departure diameter of the bubbles becomes remarkably smaller by addition of 2-propanol. At high heat fluxes, large vapor masses covering the heating surface completely are formed with both water and the 2-propanol/ water mixture, as suggested in Fig. 3.1.18. Fig. 3.1.19 shows the CHF measured with varying concentrations of 2-propanol. The data scatter somewhat, but the CHF is the most enhanced, about 1.7-times compared to the CHF of water, at around 3.0
4.7 mol% of 2-propanol. The situation with the CHF considerably enhanced despite the similarities in the apparent boiling appearances is similar to that of subcooled boiling, discussed in Section 3.1.3.1 (Fig. 3.1.2). Fig. 3.1.20 shows the vertical distributions of time-averaged void fractions for water and 2-propanol/water mixture (3.0 mol%). For both the water and 2-propanol mixture, the void fraction decreases close to the heating surface where it reaches zero, suggesting the existence of a macrolayer on the heating surface. However, there are considerable differences in the void fraction profiles of the water and the 2-propanol/water mixture, despite the measurements taking place at similar heat fluxes (1.25 MW/m2 for water and 1.23 MW/

FIGURE 3.1.17 Experimental apparatus for boiling measurements in 2-propanol
water mixtures [23].

3.1.5 CHF IN SATURATED BOILING OF BINARY AQUEOUS SOLUTIONS

165

FIGURE 3.1.18 Photos of boiling behaviors for (A) water (q 5 1.3 MW/m2) and the (B) 2-propanol/water mixture (3.0 mol%) (q 5 1.7 MW/m2) at high heat fluxes [18].

3 CHF/CHF (water)=1.69

CHF/CHF (water)=1.72

CHF (MW/m2)

2.5

2

1.5 CHF (water) 1

0

Measured CHF

2 4 6 Concentration of 2-propanol (mol%)

8

FIGURE 3.1.19 Changes in CHF with the concentration of 2-propanol [18].

m2 for the 2-propanol mixture). The void fraction with the 2-propanol/water mixture begins to decrease further from the heating surface than water in the h , 1 mm region. Fig. 3.1.21 shows the thickness of the macrolayer formed beneath large vapor masses; the concentration of 2-propanol in Fig. 3.1.21 is 3.0 mol%. The data for water lie close to the results predicted with the previous correlations; however, the data for the 2-propanol/water mixture show a considerably thicker macrolayer than the data for water, as could be expected from the vertical profiles of the void fractions (Fig. 3.1.20). As the heat flux increases to approach the CHF of the mixture, the macrolayer rapidly thins and approaches the extrapolated values of the water data. Fig. 3.1.22 shows the macrolayer thicknesses measured by varying the concentration of 2-propanol under similar heat flux (1.58
1.64 MW/m2) conditions. The macrolayer thickness increases with

166

CHAPTER 3 CHF—TRANSITION BOILING

100 q=1.2–1.25 MW/m2 Void fraction (%)

80

2-propanol (3.0 mol%) Water

60 40 20 0 0.001

0.01

0.1 Height (mm)

1

10

FIGURE 3.1.20 Vertical distributions of void fractions for water and the 2-propanol/water mixture (3.0 mol%) [18].

Macrolayer thickness (μm)

5000 1000

100

10

(Water) Eq. (3.1.1) Eq. (3.1.2) Eq. (3.1.3)

1 0.7 0.8 0.9 1

Present data Water 2-propanol aq.(3.0 mol%) 2

3

Heat flux (MW/m2)

FIGURE 3.1.21 Macrolayer thickness for water and the 2-propanol/water mixture (3.0 mol%) [18].

increasing concentrations of 2-propanol, reaches a maximum at around 3.0
4.3 mol%, then tends to decrease with further increases in the 2-propanol concentration. It is worthy of note that this tendency is similar to the dependence of the CHF on the concentration of 2-propnaol shown in Fig. 3.1.19. The results shown above suggest that the characteristics of the CHF for 2-propanol
water mixtures can be explained based on the changes in the macrolayer thicknesses, and that the macrolayer dry-out model may be considered a physically appropriate model for the CHF of water/2-propanol mixtures. However, the reasons why a thicker macrolayer is formed with 2-propanol/water mixtures remain unclear. Further study will be necessary to elucidate this.

3.1.6 CHF IN BOILING OF WATER ON A HEATING SURFACE

167

Macrolayer thickness (μm)

5000 1000

100

(Water, q =1.6 MW/m2) Eq. (3.1.1) q=1.58–1.64 MW/m2 Eq. (3.1.2) Eq. (3.1.3)

10

1 0

1 2 3 4 5 6 Concentration of 2-propanol (mol%)

7

FIGURE 3.1.22 Changes in macrolayer thickness versus concentration of 2-propanol [18].

3.1.6 CHF IN BOILING OF WATER ON A HEATING SURFACE COATED WITH NANOPARTICLES [23] Nanofluids are suspensions of nanoparticles dispersed in a base-liquid. In 2003, You et al. [24] carried out experiments with pool boiling on an upward-facing surface with Al2O3-water nanofluid at 0.02 MPa and found that the CHF of the nanofluid was twice that of the CHF of pure water. Since then, other research has measured the CHF in nanofluid boiling using various kinds of nanoparticles (CuO, TiO2, SiO2, ZnO, and diamond nanopowder), and reported that the CHF is markedly enhanced compared with the CHF of water, similar to the results by You et al. It has been established that nanoparticles are deposited on heating surfaces during boiling of nanofluids and that the wettability of the surfaces with nanoparticles deposited is significantly improved (the static contact angle decreases significantly). Some of these reports have assumed that the CHF enhancement is caused by improvements in the wettability due to the nanoparticle deposition, but the actual mechanism has not been fully elucidated. To investigate the mechanism of CHF enhancement with nanofluids, the author has been carrying out experiments with pool boiling of water on an upward-facing surface coated with nanoparticles. This section presents the results obtained up to the present. The experimental apparatus used in this study is that shown in Fig. 3.1.17, the same as in the experiments with boiling of 2-propanol
water mixtures. The experiments used TiO2 nanoparticles with an average size of 25 nm. The TiO2-coated surface was prepared by nucleate boiling of TiO2
water nanofluid (the concentration of TiO2 0.011 wt%) for several minutes at a heat flux of 1 MW/m2. Fig. 3.1.23A and B shows the appearance of the TiO2-coated heating surface. In Fig. 3.1.23A, showing the whole surface (the 12-mm-diameter heating surface encircled with a broken line), some areas near the periphery of the heating surface remain uncoated, but the central part of the surface appears to be coated uniformly. Fig. 3.1.23B is an enlargement of a 1-mm square area from the central part of the surface, showing that a uniform coated layer is covering the

168

CHAPTER 3 CHF—TRANSITION BOILING

FIGURE 3.1.23 Images of a TiO2-coated surface [23]. (A) Whole surface (the circle shows the 12-mm-diameter heating surface). (B) Enlargement of the area of the central part of the heating surface.

FIGURE 3.1.24 Static contact angles, β, for a water droplet on (A) an uncoated surface (β 5 75 ) and (B) a TiO2-coated surface (β 5 5 ) [23].

surface. The thickness of the TiO2-coated layer was estimated to be thinner than 1 μm. Measurements of the liquid
vapor behaviors with the conductance probe were carried out at the center of the heating surface, and Fig. 3.1.24 shows water droplets (3 μL) placed on the uncoated surface (Fig. 3.1.24A) and on the TiO2-coated surface (Fig. 3.1.24B). As in previous studies, the 75 static contact angle β of the uncoated surface is much smaller, 5 , with the TiO2-coated surface, indicating an improvement in wettability due to the deposition of the TiO2 nanoparticles. Fig. 3.1.25 shows the boiling curves measured with the uncoated and the TiO2-coated surfaces. The CHF of the water boiling on the TiO2-coated surface was enhanced 1.8 times compared with that of the uncoated surface. Fig. 3.1.26 shows the vertical distributions of the time-averaged void fractions for the uncoated surface and the TiO2-coated surface measured at the center of the heating surface. There are no marked differences between the void fraction profiles of the uncoated and the coated surfaces, the void fraction increases when approaching the heating surface, reaches a maximum, and then decreases steeply. Further, the void fractions reach zero or a constant value very close to zero near the surface, indicating that there is a macrolayer between the heating surface and

3.1.6 CHF IN BOILING OF WATER ON A HEATING SURFACE

169

5 Uncoated surface (CHF=1.31 MW/m2) TiO2 coated surface (CHF=2.40 MW/m2)

q (MW/m2)

1 0.5

0.1 0.05

1

5

10

50

100

Δ Tsat (K)

FIGURE 3.1.25 Boiling curves for uncoated and TiO2-coated surfaces. 100

Void fraction (%)

Uncoated surface 80

q=1.22 MW/m2

60

TiO 2 coated surface q =2.0 MW/m2

40 20 0 0.001

0.01

0.1 Height (mm)

1

10

FIGURE 3.1.26 Void fraction distributions for uncoated and TiO2-coated surfaces.

the vapor mass. The heat flux in Fig. 3.1.26 for the coated surface (2.0 MW/m2) is much higher than the CHF of the uncoated surface (1.3 MW/m2). Even at this high heat flux, the void fraction is zero close to the heating surface, showing that the macrolayer does not dry out but remains on the TiO2-coated surface at the departure of vapor masses. Fig. 3.1.27 shows the macrolayer thicknesses for the uncoated and TiO2-coated surfaces. The data for the uncoated surface lie between the predicted results with Eq. (3.1.2) by Haramura and Katto and Eqs (3.1.1) and (3.1.3) by Bhat et al. or Rajvanshi et al. However, the data for the TiO2-coated surface show thicker layers than the data for the uncoated surface as well as that the macrolayer is thicker than the extrapolations of the various correlations to higher heat flux regions.

170

CHAPTER 3 CHF—TRANSITION BOILING

Macrolayer thickness (μm)

500

100 50

10 5

uncoated TiO2 coated Eq. (3.1.1) CHF (uncoated) Eq. (3.1.2) CHF (TiO2 coated) Eq. (3.1.3)

1 0.7 0.8 0.9 1

2

3

Heat flux (MW/m2)

FIGURE 3.1.27 Macrolayer thicknesses for the uncoated and TiO2-coated surfaces [23].

100 TiO2 coated surface

q (MW/m2)

60 heat flux [MW/m2]

40

void fraction (h=15 μm, 0.5s ave.)

1.5

20

Void fraction (%)

80 2

0 1 0

20

40

60 Time (s)

80

100

120

FIGURE 3.1.28 Changes in heat fluxes and void fractions at h 5 15 μm before and after the CHF with the TiO2-coated surface [23].

The results shown in Figs. 3.1.26 and 3.1.27 suggest the possibility that the thicker macrolayer is responsible for the enhancement of the CHF of the TiO2-coated surface, if the CHF is triggered by dry-out of the macrolayer as assumed by the macrolayer dry-out model. Therefore, the trigger mechanism of the CHF for the TiO2-coated surface was examined using the method detailed in Section 3.1.3.5, where the changes in the void fraction close to the heating surface before and after CHF were measured under transient heating. Fig. 3.1.28 shows the void fractions obtained by averaging the probe signals for every 0.5-s period together with the corresponding surface heat fluxes for the TiO2-coated surface, with the probe placed 15 μm over the heating surface. The heat flux starts to fluctuate from 80 s after the measurements were commenced, then decreases sharply at 100 s, showing that the CHF has been

NOMENCLATURE

171

reached. The void fraction averaged for every 0.5 s remains at small values close to zero until 80 s (the heat fluxes in this period are far higher than the CHF of the uncoated surface.), then the void fractions show large fluctuations, and abruptly rise at almost the same time as the occurrence of CHF at around 100 s. From this result, it may be concluded that the TiO2-coated surface is covered with a macrolayer before the CHF even at the far higher heat flux than that of the CHF for the uncoated surface, and that the dry-out of this macrolayer triggers the occurrence of the CHF. Therefore, the trigger mechanism of the CHF appears to be very similar to that with the macrolayer dry-out model and the cause of the CHF enhancement for the TiO2-coated surface can most likely be ascribed to the thick macrolayer as also suggested in Fig. 3.1.27. The reasons why the thicker macrolayer is formed on the TiO2-coated surface have not been satisfactorily explained, but Wang and Dhir [25] and Imai et al. [26] have reported that improvements in surface wettability can significantly reduce nucleation site density. The author here has not measured the nucleation site density, but it may be considered that there is a possibility that the nucleation site density is lowered by the TiO2 coating of the surface due to the improved wettability. As mentioned in Section 3.1.3.5, the vapor masses are formed by the coalescence of smaller bubbles (primary bubbles or coalesced bubbles formed by coalescence of the primary bubbles). It may therefore be hypothesized that the macrolayer thickness is closely related to the size of the bubbles at coalescence. Here, a reduction in the nucleation site density results in an increase in the size of the bubbles at coalescence, and hence could result in a thickening of the macrolayer. The improvement in surface wettability may, therefore, be one of the factors in the formation of the thicker macrolayer.

3.1.7 CONCLUSION This section reviews research conducted by the author’s group on pool boiling CHF for (1) subcooled boiling on upward surfaces, (2) saturated boiling on inclined surfaces, (3) saturated boiling of 2-propanol/water mixtures, and (4) saturated boiling on upward-facing surfaces coated with nanoparticles. The characteristics of the CHF in these four boiling conditions are satisfactorily explained when it is assumed that the CHF is triggered by the dry-out of the macrolayer formed beneath large vapor masses, and up to the present there is no experimental evidence contrary to suggesting this as the trigger mechanism. Therefore, certainly for pool boiling on surfaces with large heat capacities at pressures around atmospheric pressure, it may be concluded that among the various CHF models, the macrolayer dry-out model offers the better explanation of the actual CHF mechanism.

NOMENCLATURE h Hfg q qCHF β

distance from the heating surface to the tip of the probe latent heat of vaporization heat flux critical heat flux static contact angle

172

ΔTsub σ ρl ρv τ θ

CHAPTER 3 CHF—TRANSITION BOILING

subcooling surface tension density of liquid density of vapor length of the period of the passage of the vapor masses angle of inclination of the heating surface measured from the upward position

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311. [13] A. Ono, H. Sakashita, Liquid
vapor structure near heating surface at high heat flux in subcooled pool boiling, Int. J. Heat Mass Transfer 50 (2007) 3481
3489. [14] A. Ono, H. Sakashita, Measurement of surface dryout near heating surface at high heat flux in subcooled pool boiling, Int. J. Heat Mass Transfer 52 (2009) 814
821. [15] S. Inada, Y. Miyasaka, R. Izumi, M. Kobayashi, Studies on boiling curves in subcooled pool boiling (4th, heat transfer mechanism in transition boiling region), Trans. JSME 47 (423) (1981) 2199
2208. [16] S. Yokoya, M. Watanabe, M. Shoji, Critical heat flux in high subcooled pool boiling, in: Proceedings of 37th National Heat Transfer Symposium of Japan, 2000, pp. 65
66. [17] J. Li, S. Yokoya, M. Watanabe, H. Yoshii, M. Shoji, Study of critical heat flux in subcooled pool boiling, in: Proceedings of 36th National Heat Transfer Symposium of Japan, 1999 pp. 391
392. [18] H. Sakashita, Critical heat flux mechanism in pool boiling, J. Heat Transfer Soc. Jpn. 49 (209) (2010) 53
62. [19] A.M. Bhat, J.S. Saini, R. Prakash, Role of macrolayer evaporation in pool boiling at high heat flux, Int. J. Heat Mass Transfer 11 (1986) 1953
1961.

3.2.1 INTRODUCTION

173

[20] A.M. Rajvanshi, J.S. Saini, P. Prakash, Investigation of macrolayer thickness in nucleate pool boiling, Int. J. Heat Mass Transfer 35 (1992) 343
350. [21] H. Sakashita, A. Ono, J. Nyui, Critical heat flux and near-wall boiling behaviors in saturated and subcooled pool boiling on vertical and inclined surfaces, J. Nucl. Sci. Technol. 46-11 (2009) 1038
1048. [22] H. Sakashita, A. Ono, Y. Nakabayashi, Measurements of critical heat flux and liquid
vapor structure near heating surface in pool boiling of 2-propanol/water mixtures, Int. J. Heat Mass Transfer 53 (2010) 1554
1562. [23] H. Sakashita, CHF and near-wall boiling behaviors in pool boiling of water on a heating surface coated with nanoparticles, Int. J. Heat Mass Transfer 55 (2012) 7313
7320. [24] S.M. You, J.H. Kim, K.H. Kim, Effect of nanoparticles on critical heat flux of water in pool boiling heat transfer, Appl. Phys. Lett. 83 (16) (2003) 3374
3376. [25] C.H. Wang, V.K. Dhir, Effect of surface wettability on active nucleation site density during pool boiling of water on a vertical surface, J. Heat Transfer 115 (1993) 659
669. [26] Y. Imai, K. Okamoto, H. Madarame, T. Takamasa, Reduction of active nucleation site density under gamma ray irradiation, Thermal Sci. Eng. 13 (5) (2005) 17
23.

MICROLAYER MODELING FOR CRITICAL HEAT FLUX IN SATURATED POOL BOILING

3.2 Takaharu Tsuruta

Kyushu Institute of Technology, Kitakyushu, Japan

3.2.1 INTRODUCTION The heat-transfer mechanism of the critical heat flux (CHF) is very important, not only for the practical use of boiling in a thermal energy system, but also from an academic viewpoint. Even for a fundamental situation, such as saturated pool boiling on a smooth surface, a significantly large number of investigations have been conducted in the past several decades, including comprehensive reviews presented by Katto [1] and Lienhard [2]. Recently, many studies on CHF, including nanoparticle, nanoscale structured surface, and microchannel, have been carried out; research under the conditions of flow boiling or high-pressure systems has also been conducted. In this chapter, however, we focus on the theoretical study of CHF in saturated pool boiling. The main theoretical models of CHF are divided into three categories by considering where the key phenomenon occurs: the far-field model, the near-field model, and the on-surface model.

174

CHAPTER 3 CHF—TRANSITION BOILING

The far-field model is also termed the “hydrodynamic instability model” and was first presented in the foundational work by Zuber [3] for predicting the CHF over horizontal surfaces in saturated pool boiling. It was further developed to evaluate the CHF for pool boiling on wires, ribbons, etc., by Lienhard and Dhir [4]. This model has been used extensively because its final correlation takes the same form as the semi-empirical model by Kutateladze [5]. The hydrodynamic instabilities usually refer to two types: the Taylor instability along the boiling surfaces, and the Kelvin
Helmholtz instability along the vapor escape path. A Taylor instability is very likely to occur once the vapor width is larger than the instability wavelength, so as to play a dominant role in the width of departure vapor mushrooms. However, for many boiling surfaces, even for enhanced heat-transfer surfaces such as some porous surfaces, on which the CHF can be up to almost twice that seen in normal pool boiling, the hydrodynamic instability model can give a unique value of CHF. This implies that some other mechanisms are at work on the CHF, at least for normal pool boiling. The near-surface model is also termed the “macrolayer dry-out model” and was developed by Haramura and Katto [6] based on a series of experimental observations, including Gaertner’s [7]. This model postulates that a liquid sublayer (macrolayer) that is formed on the heater surface with an initial thickness is evaporated away during the hovering period of the overlying vapor mass, when the CHF appears. The macrolayer dry-out model is based on the condition of the dryout of the macrolayer without liquid resupply, due to hydrodynamic instability throughout the period of the vapor mushroom. Ono and Sakashita [8,9] measured the dynamic structure of the macrolayer at high heat flux in subcooled boiling and suggested that the macrolayer dry-out model is an appropriate model for the CHF in subcooled boiling. As the hydrodynamic triggering mechanism in the macrolayer, Mudawar et al. [10] presented a lift-off model of the wetting front due to the high vapor momentum flux corresponding to the vapor-stem model in Haramura and Katto [6]. They suggest that when the vapor momentum flux is sufficient to lift the liquid macrolayer from the heating surface, a transition from nucleate to film boiling occurs. This lift-off model was developed based on vertical surfaces, and Guan et al. [11] modified it for pool boiling on horizontal surfaces. The third model is the on-surface model. The present “microlayer model” is included in this category. Ideas have been proposed to explain the complex phenomena of the CHF in both of the above models, which disregard the detailed processes of heat and mass transfer on the boiling surfaces, so that the fluid and solid contact structures were greatly simplified and assumed to be time-independent. Nelson and his coworkers [12] performed a study based on the macrolayer dry-out model, in which the dominant heat transfer is attributed to the evaporation at the liquid
vapor
solid contact point (the so-called ‘triple point’). Other studies have been performed by Dhir and Liaw [13,14], in which the heat flux was related to the void fraction. By employing the value of the experimentally observed void fraction, the nucleate boiling (in the high heat flux region) and transition boiling heat fluxes, including the maximum and minimum heat fluxes, are predicted from the model. Furthermore, Lay and Dhir [15] proposed a vapor stem model and performed a dynamic analysis of it, from which a stable vapor stem is possible. These models have shown that only the evaporation of the so-called microlayer (which is much thinner than the macrolayer) can contribute the high heat flux in fully developed nucleate boiling. These two kinds of models seem to be successful at predicting the CHF in a variety of

3.2.2 MICROLAYER MODEL

175

situations; however, some questions about both of the models have been raised [16]. Theofanous et al. [17] observed the boiling surface directly, and they indicated that the hot spots formed within the bubble bases were identified as dry spots, which serve as precursors to burnout at high heat fluxes. They also indicated that the wetted area exists as a network of continuous wriggling canals of liquid near the CHF [18]. Similar wetted patterns were observed in the pool boiling of R113 on a horizontal surface by Nishio et al. [19], who pointed out the different boiling structures from the physical image given by the macrolayer model of the CHF. They observed that the macrolayers never dry completely, either at the CHF point or at the transition boiling. By considering these situations, they focused on the liquid
vapor
solid contact lines and found that the dependence of the length density of contact line upon the surface superheat is very similar to the boiling curve. Nishio and Tanaka [20] confirmed the idea that the boiling curve is a continuous curve in the fully developed region, which includes the CHF; namely, there is no triggering at the CHF point. They also insisted that the contact line length density represents an important index of boiling heat transfer. The findings by Nishio’s research group are very important, but the concept of contact line has a disadvantage in the explanation of heat transfer, i.e., because the heat-transfer area is necessary to estimate the heat transfer rate in every situation. The heat-transfer characteristics near the triple point should be expressed in the modeling for the CHF. This is the microlayer model presented by Zhao et al. [21], which is shown in this chapter.

3.2.2 MICROLAYER MODEL FOR FULLY DEVELOPED NUCLEATE BOILING AND CHF 3.2.2.1 BASIC IDEAS OF THE MICROLAYER It has been clarified that only the evaporation of the microlayer can contribute the high heat flux at CHF, i.e., the microlayer is important for exploring the mechanism of the detailed evaporation process. The typical studies on the thin liquid layer were performed by Cooper and Lloyd [22] and Cooper et al. [23], such as a microlayer is the same as the bottom area of the bubbles on the wall. A typical bubble grows hemispherically, forming a microlayer on the surface. Cooper and Lloyd [22] measured the surface temperature with thin-film thermocouples and indicated an initial sharp drop in temperature as the microlayer evaporated, followed by a recovery in temperature after the formation of a dry spot, then a small drop in temperature and subsequent recovery as the liquid re-wetted the surface during bubble departure. Conversely, Kim [24] insisted in his review paper that the heat transfer through the microlayer and at the three-phase contact line do not contribute more than about 25% of the overall heat transfer. Recently, Yabuki and Nakabeppu [25] measured the surface temperature transient for a single bubble with a microelectromechanical system (MEMS) sensor. They obtained precise local temperatures and wall heat-transfer rates, by which they concluded that the microlayer evaporation plays a central role in the wall heat transfer. To grow a single bubble, they suggest that microlayer evaporation contributes about 50% of the required heat, while the remaining heat can be supplied from the superheated liquid around the bubble. A similar contribution from the microlayer

176

CHAPTER 3 CHF—TRANSITION BOILING

FIGURE 3.2.1 Dynamic formation processes of micro- and macrolayers due to the growth of an individual bubble.

evaporation was also reported by Utaka et al. [26] from measurements of microlayer thickness by the laser extinction method. As shown in Fig. 3.2.1, the growth of individual bubbles can be divided into two periods, i.e., the initial growth period and the final growth period. During the initial growth period, the bubble grows in a semi-spherical shape with a microlayer formed beneath it. The shape of the bubble changes from semi-spherical to a spherical segment geometry because of the evaporation of the microlayer. In the final growth period, a liquid layer thicker than the microlayer is formed under the bubble and among the adjacent individual bubbles. This layer is termed the macrolayer in this model. The formation mechanism of the microlayer has been studied both theoretically and experimentally, and its thickness can be expressed by the following equation [22,23]: pffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffi δ0mi 5 0:8 ν l t 5 cαUt

0 # t # tg

(3.2.1)

where c 5 0.64Pr. Here the effect of surface tension can be neglected because the duration of initial growth is usually very short. For fully developed nucleate boiling under a high heat flux condition, Zhao et al. [21] considered the situation in which individual bubbles under the coalescence bubble (or vapor mushroom) are generated and depart from the heated surface periodically, as shown in Fig. 3.2.2. Experimental observations in water boiling on a horizontal Pt-wire within a narrow space [27] clearly indicate that the individual boiling bubbles are formed and depart periodically from the boiling surfaces into the upper coalescence bubbles. The vapor stems and the dry-out of the macrolayer have not been observed near the CHF. The measured dynamic distribution of the liquid layer near the wall, including results in the report by Hohl et al. [28], supports the periodical existence of the individual bubbles instead of the stationary vapor stems.

3.2.2.2 DESCRIPTION OF HEAT TRANSFER IN FULLY DEVELOPED NUCLEATE BOILING Fig. 3.2.3 shows a physical model for explaining the configuration of individual bubbles, the vapor mushroom, and the micro-/macrolayers in the microlayer model [21]. Two situations are depicted, depending on the departing mechanism of the individual bubbles. For fluids with a large value of

3.2.2 MICROLAYER MODEL

177

FIGURE 3.2.2 Modeling of individual bubbles under vapor mushroom for high heat flux nucleate boiling and experimental snapshot observed by Zhao et al. [27].

klρlcpl such as water, the growth rate is fast, and the interface between the individual bubbles and the vapor mushroom can easily be broken down. As a result, the coalescence occurs in the normal direction, as shown in Fig. 3.2.2A. For small-klρlcpl fluids like fluorocarbons, the growth rate is slow, and the coalescences occur among the individual bubbles on the surface, as observed by Nishio et al. [19]. The distance between centers for the individual bubbles is assumed to be 2d in case (a) and Dd in case (b). In both cases, the micro- and macrolayers exist on the heated surface under the individual bubbles, and the macrolayer never dries out, because of a continuous liquid resupply. The heat-transfer surface can be divided into three regions: the dry-out area, the microlayer area, and the macrolayer area. Evaporation occurs mainly in the microlayer area formed underneath the primary bubble, whereas evaporation of the liquid macrolayer is small and can be neglected. The areas of the three parts change dynamically with time. The dry-out region, with a zero initial area, develops because of the evaporation of the liquid microlayer during the period of the individual bubble. As a result, the microlayer area decreases with time. Here, it is supposed that no liquid is resupplied into the tremendously thin microlayer, because of the very small interfacial curvature. After individual bubbles depart from the boiling surface, the old microlayer area is replaced by fresh liquid from the macrolayer. It is assumed that the surface temperature is uniform throughout the boiling surface, it maintains a constant value during the period of vapor mushroom, and the waiting time of nucleation is negligible. Then, the local surface flux can be given as follows: 8 0; > > > > dδ k ΔT > > < 2ρl hfg mi 5 l sat ; dt δmi qðr; tÞ 5 > > > kl ΔTsat > > pffiffiffiffiffiffiffi ; > : πat

d r # rðtÞ ; d rðtÞ , r # d=2;

(3.2.2)

d=2 , r

d where r(t) is the radius of the dry-out area and δmi is the thickness of the microlayer. The heat flux in the dry-out area is small enough to be neglected. In contrast, the heat flux by the microlayer

178

CHAPTER 3 CHF—TRANSITION BOILING

FIGURE 3.2.3 Physical model of droplets arrangement for fully developed nucleation boiling.

evaporation is very large, because of its small thickness. By increasing the superheat ΔTsat, the evaporation rate increases and causes faster development of the dry-out, which has two opposite contributions to the average heat flux. The heat flux in the macrolayer area (d/2 , r) can be evaluated by the periodically transient heat conduction in a semi-infinite liquid layer. Here, we neglect the effect of macrolayer evaporation occurring at the liquid
vapor interface for the case in which the superheat boundary layer grows into the macrolayer. The effect was included, however, in Zhao et al. [21]. The mean wall heat flux over the heat-transfer area Ad can be derived by considering Eq. (3.2.2): qw 5

ð ð

ð ð 1 1 τd 1 τD kl ΔTs pffiffiffiffiffiffiffi dA dt qðr; tÞdA dt 1 Ad τ d 0 Ab τ D 0 Ad 2Ab πat

(3.2.3)

where τ d is the departure period of the individual bubble. The second term on the right-hand side represents transient heat conduction initiation due to the departure of the vapor mushroom. Its cycle

3.2.2 MICROLAYER MODEL

179

is expressed by τ D, and we can use Hanamura
Katto’s model [6]. At the CHF point on the boiling curve, the mean wall heat flux should have a maximum value: @qw =@ΔTsat 5 0

as

CHF ΔTsat 5 ΔTsat

(3.2.4)

3.2.2.3 MICROLAYER THICKNESS AND DRY-OUT RADIUS BENEATH AN INDIVIDUAL BUBBLE As stated in Section 3.2.1, the growth of the individual bubble is characterized by two different mechanisms. In the initial growing stage, the effect of heat transfer is dominant, while the kinetic effect plays an important role in the final growing stage. The total period τ d of the bubble growth should be divided into two stages: the initial growth stage for 0 # t # tg , and the final growth stage for tg # t # τ d . During the initial growth stage, the semi-spherical bubbles grow from active nuclei. The growth equation of an individual bubble can be derived from the heat balance between the latent heat of microlayer evaporation and the conduction heat through the microlayer. That is,   ðr d 2 3 ΔTsat πr ρv hfg 5 kl 2πr dr; dt 3 δmi 0

0 # t # tg

(3.2.5)

By utilizing Cooper’s equation (see Eq. 3.2.1) for the initial thickness of the microlayer, the bubble radius is obtained as r5

2kl ΔTsat 1=2 pffiffiffiffiffiffi t ρv hfg cα

(3.2.6)

At the end of the initial growth of the individual bubble, i.e., at t 5 tg, the bubble diameter d will be d5

4kl ΔTsat 1=2 pffiffiffiffiffiffi t ρv hfg cα g

(3.2.7)

From Eq. (3.2.6), we can obtain the time tg at which the front edge of the semi-spherical bubble reaches the radial position r, where the bubble radius is the same as the coordinate position, i.e., tg 5

pffiffiffiffiffiffi

2 cαρv hfg r ; r # d=2 2kl ΔTsat

(3.2.8)

Therefore, the initial thickness of the microlayer at any position rðr # d=2Þ can be given as δ0mi 5

pffiffiffiffiffiffiffiffiffiffiffi cαρv hfg r cαUtg 5 2kl ΔTsat

(3.2.9)

The heat conducted from the heating surface through the microlayer causes the consumption of the microlayer due to evaporation: 2ρl hfg

dδmi kl ΔTsat 5 dt δmi

(3.2.10)

180

CHAPTER 3 CHF—TRANSITION BOILING

Hence, the thickness of the microlayer can be derived with the initial condition Eq. (3.2.9) as δmi 5

" #1=2 3 cαρv hfg r 8cpl kl2 ΔTsat ðt2tg Þ U 12 2kl ΔTs c2 αh3fg ρ2v r 2

(3.2.11)

Therefore, the radius of the dry-out area (δmi 5 0) will be obtained as follows: "

d rðtÞ

#1=2 3 8cpl kl2 ΔTsat ðt2tg Þ 5 c2 αh3fg ρ2v

(3.2.12)

Eqs. (3.2.2) and (3.2.11) into Eq. (3.2.3) and neglecting the higher-order terms of 2  d Substituting rðtÞ =d2 , the mean wall heat flux can be derived as qw 5

" #   2 8cpl k2 ΔT 3 τ d 2kl2 dΔTsat πd 2 2kl ΔTsat 1 2 2 l 3 2sat 2 1 1 2 pffiffiffiffiffiffiffiffiffiffiffiffi πατ D cαρv hfg Ad 4Ad c αhfg ρv d

(3.2.13)

The CHF can thus be calculated, if the diameter d (or Dd) and the departure periods τ d and τ D are known.

3.2.2.4 BUBBLE DYNAMICS DURING THE FINAL GROWTH PERIOD The departure period of the individual bubble depends on the bubble dynamics and growth rate. The forces acting on the bubbles are illustrated in Fig. 3.2.4. The equation of motion is given as follows, by considering the forces due to inertia, buoyancy, and surface tension:

d ds ðξρl 1 ρv ÞV 5 ðρl 2 ρv ÞVg 1 f ðσÞ; t . tg dt dt

(3.2.14)

where V is the volume of the bubble and s is the vertical distance between the mass center of the bubble and the wall. The inertia term includes the effect of liquid accompanying the moving bubble using the volumetric ratio ξ. For the case of non-absorption by the vapor mushroom, the value of 11/16 is used as ξ [6]. For water, the bubbles are absorbed into the vapor mushroom, then a half value, 11/32, is used in the model. The surface tension force is written as

FIGURE 3.2.4 Forces acting on departing bubble: (A) isolated bubble; (B) bubble coalescing into vapor mushroom.

3.2.3 RESULTS AND DISCUSSION

( f ðσÞ 5

d 22π rðtÞ σ sin θ; nonabsorption d σ sin θÞ; absorption πσðd 2 2rðtÞ

181

(3.2.15)

For the case in which the individual bubble is merged into the vapor mushroom, the surface tension at the interface between them promotes the bubble departure from the heated surface. The volume of bubble V is obtained by the following equation: V5

1 πd 2 πd 3 1 12 4

ðt  tg

 qev dt ρv hfg

(3.2.16)

In addition, the initial height of the center of mass of a semi-spherical bubble s is given by s5

3kl ΔTsat 1=2 pffiffiffiffiffiffi t ; 4ρv hfg cα

t # tg

(3.2.17)

From these equations, the relationships between the departure times of each individual bubble (t 5 τ d) can be obtained.

3.2.3 RESULTS AND DISCUSSION For the case of water, the mean wall heat flux of Eq. (3.2.13) results in the following form: " #  3 2 8cpl kl2 ΔTsat τd πkl2 ΔTsat π  2kl ΔTsat 12 2 3 2 2 1 12 qw 5 pffiffiffiffiffiffiffiffiffiffiffiffi 16 πατ D 2cαρv hfg d c αhfg ρv d

(3.2.18)

The critical heat flux qCHF is obtained by following the differential procedure shown in Eq. (3.2.4). The calculated qCHF is plotted as a function of d in Fig. 3.2.5, for a contact angle θ 5 22 , which is expressed by a regression as qCHF 5 4:5 3 104 d20:44

(3.2.19)

The size d is the only unknown physical factor in the present model. Essentially, it depends on the nucleation site density N on the surface, but characterizes the fundamental heat-transfer model in Fig. 3.2.3. That is, the relation d 5 1=ð2N 1=2 Þ was assumed in the model. Concerning the relationship between the density of active sites N and the heat flux q, Gaertner and Westwater [29] presented the experimental result as q 5 117 N 2=3

Therefore, based on the assumption of d 5 1=ð2N be given as

1=2

(3.2.20)

Þ, the diameter of an individual bubble can

d 5 17:8 q20:75

(3.2.21)

By utilizing both Eqs (3.2.19) and (3.2.21), the following results can be obtained for the CHF point for water under atmospheric pressure: d 5 0:45 mm;

ΔTsat  20:9 K;

qCHF 5 1:33 3 106 W=m2

182

CHAPTER 3 CHF—TRANSITION BOILING

Heat flux q, W/m2

Calculation Eq.(3.2.19) Ref. [29] Present CHF

106

Critical heat flux Kutateladze [5] Gaertner -Westwater [29]

0.0001

0.001

Diameter of individual bubble d, m FIGURE 3.2.5 Relation between heat flux and individual bubble size for water based on the present model.

As shown in Fig. 3.2.5, the present result of qCHF agrees well with the CHF data reported by Kutateladze [5] and Gaertner and Westwater [29]. The calculated boiling curve of water is drawn in Fig. 3.2.6 for the fully developed nucleate boiling region. It is seen that there is good agreement between the microlayer model and the experimental data reported in the literature. The calculated mean dry-out area fraction at the CHF was predicted to be about 16.5%, which was very close to the result obtained by Shoji [30] for water. Since the area ratio of the microlayer to the heat-transfer surface is estimated as ðπd2 =4Þ=ð2dÞ2 5 π=16 5 0:196, most of the microlayer is dried out at the CHF condition. The departure periods of individual bubbles are plotted in Fig. 3.2.7. It is not a monotonic function of the wall superheat ΔTsat, but a peak value exists near the CHF. The bubble departure periods and the fluctuation periods of the local wall temperature are of the same order as the values measured by experiments [31,32]. Additionally, the detected dynamic signals of the liquid
vapor fluctuations near the boiling surface seen by Hohl et al. [28] can be explained by the present results. Thus, it seems that the proposed microlayer model successfully predicts the heat transfer in fully developed nucleate boiling regions including the CHF, although the effect of the coalescences among the individual bubbles is disregarded in the present microlayer model. For actual pool boiling, such coalescences should occur in some concentrated areas of the active sites. Furthermore, with the proposed microlayer model, the departure periods of the individual bubbles significantly affect the CHF, which increases with decreasing departure period. It is possible to develop the present model to predict the heat flux in subcooled boiling if the bubble collapse due to the condensation is considered [33,34]. For possible practical engineering applications, this model indicates that the CHF will be augmented if the departure of the individual bubbles is promoted, as in the situation of microbubble emission boiling.

3.2.3 RESULTS AND DISCUSSION

183

Present model

Heat flux q, W/m2

106

Typical experimental data

Gaertner –Westwater [29]

105 1

10

100

Wall superheat ΔT sat, K

FIGURE 3.2.6 Comparison of boiling curves of water.

3 Saturated water

Bubble cycle τd, ms

2.5 2 1.5 1 0.5 0

0

5

10 15 20 Wall superheat ΔTs, K

25

30

FIGURE 3.2.7 Theoretical estimation of individual bubble cycle τ d as a function of wall superheat ΔTsat for water. (A) Initial growing stage, (B) final growing stage.

184

CHAPTER 3 CHF—TRANSITION BOILING

3.2.4 CONCLUSION The microlayer model developed by Zhao et al. [21] is shown to theoretically discuss the mechanism of heat transfer in fully developed nucleate boiling regions, including the CHF. The model considered a dynamic structure of vapor
liquid
solid contacts and pointed out that the boiling heat transfer is primarily attributed to the evaporation of the microlayer that is formed during the initial growth period of individual bubbles. By considering the bubble dynamics, the microlayer thickness, the dryout area, and the wall heat flux, are formulated as functions of superheat, and a continuous boiling curve is predicted. The initial thickness of the microlayer becomes thinner with increasing wall superheat, and both the evaporation and the partial dry-out speed of the microlayer increase. As a result, the time-averaged heat flux during the departure period of individual bubbles has a maximum point on the plane of q vs ΔTsat. This maximum heat flux for nucleate boiling is the CHF.

NOMENCLATURE Ab Ad cp Dd Dt d g hfg kl N q qc qev R r rc rd s t tg T ΔTsat V v1 td

microlayer area (5 π(d/2)2), m2 the largest cross-sectional area of individual bubble, m2 specific heat of liquid, J/(kg K) departure diameter of individual bubble, m instantaneous diameter of individual bubble, m diameter of individual bubble at the end of initial growth, m gravitational constant, m2/s latent heat of evaporation, J/kg thermal conductivity, W/(m K) number of active sites in unit area, 1/m2 wall heat flux, W/m2 transient heat conduction in the liquid macrolayer, W/m2 evaporation heat flux on microlayer, W/m2 radius of individual bubble, m coordination, m position at which the superheat boundary layer reaches the liquid
vapor interface, m radius of dry-out area, m normal distance of center of gravity of individual bubble above heated surface, m time, s period of initial growth, s temperature, K wall superheat, K volume of bubble, m3 volumetric growth rate of bubble, m3/s departure time period, s

GREEK SYMBOLS α θ

thermal diffusivity of liquid, m2/s contact angle, degrees

REFERENCES

δ δ0 λC λD ρ σ ξ

185

thickness, m initial thickness, m Taylor instability wavelength, m most dangerous Taylor instability wavelength, m density, kg/m3 surface tension, N/m volumetric ratio of accompanying liquid to the moving bubble

SUBSCRIPTS d D g l ma mi v

individual bubble vapor mushroom initial growth liquid macrolayer microlayer vapor

REFERENCES [1] Y. Katto, Critical heat flux, Int. J. Multiphase Flow 20 (Suppl) (1994) 53
90. [2] J.H. Lienhard, Snares of pool boiling research: putting our history to use, in: Proc. 10th Int. Heat Transfer Conf., Brighton, UK, vol. 1, 1994, pp. 333
348. [3] N. Zuber, On the stability of boiling heat transfer, Trans. ASME J. Heat Transfer 80 (3) (1958) 711
720. [4] J.H. Lienhard, V.K. Dhir, Hydrodynamic prediction of peak pool-boiling heat fluxes from finite bodies, Trans. ASME J. Heat Transfer 95 (1973) 152
158. [5] S.S. Kutateladze, A hydromechanical heat transfer crisis model in a boiling liquid with free convection, Zh. Tekhc. Fiz. ð:T/Þ 20 (11) (1950) 1389
1392. [6] Y. Haramura, Y. Katto, A new hydrodynamic model of critical heat flux, applicable widely to both pool and forced convection boiling on submerged bodies in saturated liquids, Int. J. Heat Mass Transfer 26 (1983) 389
399. [7] R.F. Gaertner, Photographic study of nucleate pool boiling on a horizontal surface, Trans. ASME J. Heat Transfer 87 (1965) 17
29. [8] A. Ono, H. Sakashita, Liquid
vapor structure near heating surface at high heat flux in subcooled pool boiling, Int. J. Heat Mass Transfer 50 (17) (2007) 3481
3489. [9] A. Ono, H. Sakashita, Measurement of surface dryout near heating surface at high heat fluxes in subcooled pool boiling, Int. J. Heat Mass Transfer 52 (3) (2009) 814
821. [10] I. Mudawar, A.H. Howard, C.O. Gersey, An analytical model for near-saturated pool boiling critical heat flux on vertical surface, Int. J. Heat Mass Transfer 40 (10) (1997) 2327
2339. [11] C.K. Guan, J.F. Klausner, R. Mei, A new mechanistic model for pool boiling CHF on horizontal surfaces, Int. J. Heat Mass Transfer 54 (2011) 3960
3969. [12] K.O. Pasamehmetoglu, P.R. Chappidi, C. Unal, R.A. Nelson, Saturated pool nucleate boiling mechanisms at high heat fluxes, Int. J. Heat Mass Transfer 36 (1993) 3859
3868. [13] S.P. Liaw, V.K. Dhir, Void fraction measurements during saturated pool boiling of water on partially wetted vertical surfaces, Trans. ASME J. Heat Transfer 111 (1989) 731
738. [14] V.K. Dhir, S.P. Liaw, Framework for a unified model for nucleate and transition pool boiling, Trans. ASME J. Heat Transfer 111 (1989) 739
746.

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[15] J.H. Lay, V.K. Dhir, Shape of a vapor stem during nucleate boiling of saturated liquids, Trans. ASME J. Heat Transfer 117 (1995) 394
401. [16] P. Sadasivan, C. Unal, R. Nelson, Perspective: issues in CHF modeling—the need for new experiments, Trans. ASME J. Heat Transfer 117 (1995) 558
567. [17] T.G. Theofanous, J.P. Tu, T.N. Dinh, The boiling crisis phenomenon, Part I: nucleation and nucleate boiling heat transfer, Exp. Thermal Fluid Sci. 26 (2002) 775
792. [18] T.G. Theofanous, T.N. Dinh, J.P. Tu, A.T. Dinh, The boiling crisis phenomenon, Part II: dryout dynamics and burnout, Exp. Thermal Fluid Sci. 26 (2002) 793
810. [19] S. Nishio, T. Gotoh, N. Nagai, Observation of boiling structure in high heat-flux boiling, Int. J. Heat Mass Transfer 41 (1998) 3191
3201. [20] S. Nishio, H. Tanaka, Visualization of boiling structure in high heat-flux pool-boiling, Int. J. Heat Mass Transfer 47 (2004) 4559
4568. [21] Y.H. Zhao, T. Masuoka, T. Tsuruta, Unified theoretical prediction of fully developed nucleate boiling and critical heat flux based on a dynamic microlayer model, Int. J. Heat Mass Transfer 45 (2002) 3189
3197. [22] M.G. Cooper, A.J.P. Lloyd, The microlayer in nucleate pool boiling, Int. J. Heat Mass Transfer 12 (1969) 895
913. [23] M.G. Cooper, A.M. Judd, R.A. Pike, Shape and departure of single bubbles growing at a wall, in: Proc. 6th Int. Heat Transfer Conf., vol. 1, 1978, pp. 115
120. [24] J. Kim, Review of nucleate pool boiling bubble heat transfer mechanisms, Int. J. Heat Mass Transfer 35 (2009) 1067
1076. [25] T. Yabuki, O. Nakabeppu, Heat transfer mechanisms in isolated bubble of water observed with MEMS sensor, Int. J. Heat Mass Transfer 76 (2014) 286
297. [26] Y. Utaka, Y. Kashiwabara, M. Ozaki, Z. Chen, Heat transfer characteristics based on microlayer structure in nucleate pool boiling for water and ethanol, Int. J. Heat Mass Transfer 68 (2014) 479
488. [27] Y.H. Zhao, T. Masuoka, T. Tsuruta, Boiling bubble behavior and heat transfer characteristic on a horizontal Pt-wire within a narrow space, in: Proc. Heat Transfer Seminar of JSME in Okinawa, Japan, 1994, pp. 238
241. This is a part of Dr. Eng. Thesis, Kyushu Institute of Technology, 1999; Y.H. Zhao, Study on the mechanism of boiling heat transfer—Micro/macro-layer model. [28] R. Hohl, H. Auracher, J. Blum, W. Marquardt, Identification of liquid
vapor fluctuations between nucleate and film boiling in natural convection, 1997, p. II-5. [29] R.F. Gaertner, J.W. Westwater, Population of active sites in nucleate heat transfer, Chem. Eng. Symp. Ser. 56 (1960) 39. [30] M. Shoji, in: V.K. Dhir, A.E. Bergles (Eds.), Pool and External Flow Boiling, ASME, New York, 1992, p. 237. [31] Y. Haramura, Heat fluctuation while transition and film boiling, in: Proc. 31th National Heat Transfer Symposium of Japan, 1994, pp. 418
420 (in Japanese). [32] M. Shoji, S. Yokoya, H. Kuroki, in: Proc. 26th National Heat Transfer Symposium of Japan, 3, 1989, pp. 418
420 (in Japanese). [33] Y. Zhao, T. Tsuruta, Prediction of bubble behavior in subcooled pool boiling based on microlayer model, JSME Int. J. B 45-2 (2002) 346
354. [34] Y. Zhao, T. Tsuruta, T. Masuoka, Critical heat flux prediction of subcooled pool boiling based on the microlayer model, JSME Int. J. B 45-3 (2002) 712
718.

3.3.1 INTRODUCTION

HEAT-TRANSFER MODELING BASED ON VISUAL OBSERVATION OF LIQUID
SOLID CONTACT SITUATIONS AND CONTACT LINE LENGTH

187

3.3 Niro Nagai

University of Fukui, Fukui, Japan

3.3.1 INTRODUCTION The boiling phenomenon is important as an elementary process in energy equipment that utilize vapor such as power plants, and also in the cooling control systems utilizing high heat-transfer rates of boiling, such as cooling of steel plates and electronic chips. While these applications have promoted understanding of the heat transfer and structural aspects of the boiling phenomenon, the recent advent of microsystems such as bubble-jet printers and micro-actuators requires a better understanding of the boiling phenomenon from a structural viewpoint in particular. In general, the structure formation in the phase change of the liquid phase can be regarded as the result of the following series elementary processes: formation of supersaturated liquid phase, nucleation or activation of pre-existing nuclei, growth of new phase, and then formation of interface morphology. For example, Asai [1] has presented a boiling model for bubble-jet printers in which a smooth interface coalescent bubble grows as the result of the series of extremely superheated liquid phase, the spontaneous bubble nucleation, and the simultaneous growth of primary bubbles. As for the steady-state nucleate boiling at high heat fluxes, Gaertner [2] reported the following time-averaged structure based on still photographs and high-speed motion pictures of boiling. The first layer is the liquid layer including numerous columnar stems of vapor attached to the boiling surface. This layer has been called the “macrolayer.” The second layer includes large mushroom bubbles formed by coalescence of the vapor stems. Gigantic vapor slugs exist in the third layer and they result from coalescence of the mushroom bubbles rising up from the second layer. In this subchapter, this model is referred to as the “three-layered boiling-structure model.” The three-layered model is very important because it has provided the typical image of high heat-flux boiling including transition boiling. For example, based on this model, Haramura and Katto [3] proposed the “macrolayer dry-out model” and also Dhir and Liaw [4] proposed the “unified model” for the critical heat flux (CHF) in natural convection boiling. The existence of a liquid film under the mushroom bubble was observed certainly by Katto and Yokoya [5]. In their experiment, the behavior of the liquid film under a mushroom bubble was observed by setting an

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optical equipment very close to the surface and they reported that CHF in natural convection boiling is closely related to the dry-out of the liquid film (macrolayer) and the periodic departure of mushroom bubbles. However, the most important problem in the three-layered model is the structure of the first layer. The CHF models mentioned above assume stationary vapor stems of small diameters attached to the boiling surface, but this situation is very different from the results of observations reported by Nagai and Nishio [6] and Oka et al. [7]. A new attempt should thus be made to observe the boiling structures on/near the surface such as liquid
solid contact patterns and bubble structures. One of the difficulties in the observation of the real boiling structures is that the threedimensional (3D) and dynamic motion of bubbles obstructs our view of the real boiling structure on/near the boiling surface. In our study, thus, the following attempts were made to observe directly the boiling structures. One is an attempt to observe directly the dynamic behavior of liquid
solid contact from below the boiling surface using a horizontal plate of single crystal sapphire as the boiling surface. The other is an attempt to observe the sectional views of the bubble structures using a quasi-2D boiling system. The physical image of the boiling structures obtained in these attempts is much different from the three-layered model.

3.3.2 OBSERVATION OF LIQUID
SOLID CONTACT PATTERN AND CONCEPT OF CONTACT-LINE-LENGTH DENSITY 3.3.2.1 TOTAL REFLECTION TECHNIQUE Fig. 3.3.1 illustrates a schematic diagram of the experimental apparatus to observe directly the dynamic behavior of liquid
solid contact in natural-convection boiling. A Xenon light beam is introduced to a transparent boiling surface from below the surface through a silicone oil bath. The transparent boiling surface should be made of a highly conductive material because the thermal conductivity of the surface material has strong effects on the boiling curve (e.g., Nishio [8]). In this experiment, a plate of single crystal sapphire was selected as the boiling surface because its thermal conductivity is almost the same as stainless steel. When the incidence angle of the light beam is set adequately, total reflection occurs at the surface if the surface is dry and it does not occur if the surface is wetted by the liquid. So, clear pictures of the dynamic behavior of liquid
solid contact can be obtained by recording them using a high-speed video system [9]. The test liquid was R-113 at atmospheric pressure. The temperature of the liquid was maintained at the saturation temperature by an electric heater. The boiling surface was heated by supplying a DC electric current to an electro-conductive transparent thin film coated on the backside of the sapphire plate. In the nucleate and film boiling regions, the temperature of the silicone oil bath was controlled equal to that of the thin film to reduce heat loss from the film. For these regions, the observation was conducted under steady-state conditions by increasing or decreasing the DC current step by step. The surface temperature was measured with thermocouples attached to the surface and also with the electric resistance of the thin film. The heat flux was given by Joule heating of the thin film. As for the transition boiling region, the observation was conducted during the transition periods from nucleate to film boiling or from film to nucleate boiling. In this case, the

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SOLID CONTACT PATTERN

189

FIGURE 3.3.1 A schematic diagram of experimental apparatus to observe dynamic behavior of liquid
solid contact.

boiling curve was calculated using an inverse heat-conduction technique based on the surface temperature histories.

3.3.2.2 LIQUID
SOLID CONTACT PATTERNS Fig. 3.3.2 shows a typical set of pictures of liquid
solid contact patterns from the non-boiling to film boiling regions recorded by the high-speed video system. The white areas in each picture correspond to dry areas and the black areas to wetted areas. Using such video pictures and an image-processing technique, the distribution of the diameter of dry areas and the fraction of liquid
solid contact were calculated. The results were plotted in Figs. 3.3.3 and 3.3.4. The abscissa of Fig. 3.3.3 is the equivalent diameter, D, which is the diameter of the circle of the same area as the respective dry areas. Dividing the equivalent diameter to classes of ΔD 5 0.1 mm, the number of dry areas in each diameter class, nD, was counted during 400 ms for a surface area of 7.6 mm 3 7.6 mm. This number nD is the ordinate in Fig. 3.3.3. The fraction of liquid
solid contact averaged for 400 ms, Γw, was plotted to the normalized surface superheat ΔTws/ΔTCHF in Fig. 3.3.4 together with other data [10
14]. Fig. 3.3.2A corresponds to the non-boiling region because any dry area can not be observed. Fig. 3.3.2B shows the situation at a surface superheat just above the incipience of nucleate boiling,

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FIGURE 3.3.2 Dependence of liquid
solid contact pattern on surface temperature.

3.3.2 OBSERVATION OF LIQUID
SOLID CONTACT PATTERN

FIGURE 3.3.3 Distribution of dry-area size.

FIGURE 3.3.4 Experimental data of fraction of liquid
solid contact.

191

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and a few round dry areas appear which can be regarded as the bases of isolated bubbles. In this sub-chapter, the dry areas of such a round shape are referred to as the “primary dry areas.” In Fig. 3.3.2C and D, dry areas remain almost round but the number of dry areas increases with the increase in ΔTws. As shown in Fig. 3.3.2, the distribution of dry-area size is different from that of droplet size in dropwise condensation which has a fractal structure [15]. For example, at ΔTws 5 38 and 44 K corresponding to Fig. 3.3.2C and D, nD is almost independent of D for about D , 0.9 mm and it decreases rapidly for D . 0.9 mm. In the case of Fig. 3.3.2D corresponding to high heat-flux nucleate boiling, we can also observe some dry areas of which the shape becomes not round but slightly distorted due to coalescence of neighboring primary dry areas. The dry areas of such distorted shapes are referred to as the “secondary dry areas.” It is considered that dry areas in the constant nD region in Fig. 3.3.3 correspond to the primary dry areas and those in the rapidly decreasing nD region to the secondary dry areas. In Fig 3.3.2B
D, the wetted area is a continuous plane. The liquid
solid contact of this pattern is referred to as the “liquid
solid contact of the continuous plane pattern.” As shown in Fig. 3.3.4, the present data of the fraction of liquid
solid contact is smaller than 1 even at high-heat-flux nucleate boiling corresponding to ΔTws/ΔTCHF 5 0.94 (ΔTws 5 44 K). Fig. 3.3.2E shows the situation at the CHF point. As shown in Fig. 3.3.3, compared with the case at ΔTws 5 44 K, the constant nD region is shifted to smaller diameters and the numbers, nD, in a large-diameter region are increased. As a result, the fraction of liquid
solid contact is decreased below 60%. In this situation, dry areas become closely packed and the wetted area exists only as a network of wriggling continuous canals of liquid. In this sub-chapter, this situation of contact is referred to as the “liquid
solid contact of the network pattern.” The liquid
solid contact of the network pattern was observed also by Oka et al. [7], but it is much different from the three-layered boiling-structure model in which isolated vapor stems of small diameters are attached to the boiling surface. The result noted above indicates that the primary and secondary dry areas contribute to a decrease in the fraction of liquid
solid contact. In the case of Fig. 3.3.2F corresponding to high heat-flux transition boiling, there are extremely distorted and large dry areas which seem to result from coalescence of neighboring secondary dry areas. In this sob-chapter, such dry areas are referred to as the ‘tertiary dry areas’. In the tertiary dry areas, we can also find wetted areas which are isolated from the liquid network and include the primary or secondary dry areas. In this situation, as a result, dry areas are divided into the outer dry areas such as the tertiary dry areas and the inner dry areas located in the wetted area isolated from the liquid network. In Fig. 3.3.2G
I, the outer dry area comes to occupy the main portion of the boiling surface and the wetted areas exist only as isolated areas. In this sub-chapter, this situation is referred to as the “liquid
solid contact of the isolated pattern.” Fig. 3.3.2J shows the situation of film boiling at a low heat flux and any wetted area can not be observed.

3.3.2.3 CONTACT-LINE-LENGTH DENSITY As mentioned already, the fraction of liquid
solid contact is decreased not only by the tertiary or outer dry areas but also by the primary and secondary dry areas. Conversely, following the literature (e.g., Carey [16], and Dhir and Liaw [4]), very intensive evaporation occurs near the contact line. In addition, Graham and Hendricks [17] reported analytical results that the microlayer

3.3.2 OBSERVATION OF LIQUID
SOLID CONTACT PATTERN

193

evaporation contributes largely to the heat flux in high heat-flux nucleate boiling. So, to take account of the contribution of the three types of dry areas to boiling heat transfer, we should focus on the evaporation near the contact line surrounding each dry area. Then, to do this, we define the contact-line-length density, Φ, as the total length of contact lines existing on unit area of the boiling surface. The contact-line-length density is a concept different from the fraction of liquid
solid contact. As an example, we consider the following two cases with a same fraction of liquid
solid contact; the one is the case that there is only one large dry area, and the other is the case that there are many tiny dry spots. Comparing these two cases, the contact-line-length density in the former case is much smaller than that in the latter case. Fig. 3.3.5 shows experimental data of the fluctuation of the instantaneous contact-line-length density, Φ[t], calculated from the video pictures using the image-processing technique. Here, it should be noted that, as shown in Fig. 3.3.5, the instantaneous contact-line-length density shows dynamic behavior because an individual dry area grows and shrinks and it also migrates on the boiling surface. The contact-line-length density based on unit area of 1 m 3 1 m is as high as the order of magnitude of kilometers at ΔTws 5 47 K corresponding to the CHF point. The timeaveraged value of the contact-line-length density normalized by its maximum value, Φ/Φmax, is plotted in Fig. 3.3.6 together with the normalized boiling curve measured in this experiment, q/qCHF. As seen from the figure, the dependence of Φ/Φmax on the surface superheat is very similar to that of the normalized boiling curve. This result indicates that the contact-line-length density must be one of the very important quantities representing the boiling structures and also it is a more direct measure compared with the fraction of liquid
solid contact. The reason why contact-line-length density has a peak value as shown in Fig. 3.3.6 can be explained as follows. The primary dry areas as seen in Fig. 3.3.2B
D successively experience the process of generation, growth, shrinkage, and disappearance. So, the primary dry areas have peak

FIGURE 3.3.5 Fluctuation of contact-line-length density.

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FIGURE 3.3.6 Normalized contact-line-length density and boiling curve.

FIGURE 3.3.7 Maximum diameter of primary dry area.

values in their time variation. The measured maximum values of primary dry areas, Dp,max, are plotted against surface superheat in Fig. 3.3.7. The maximum value of primary dry areas gradually increases as surface superheat increases. Also, the nucleation site density rapidly increases as surface superheat increases. Therefore, contact-line-length density increases as surface superheat increases while the coalescence of dry areas rarely occur. Conversely, the increase in nucleation

3.3.2 OBSERVATION OF LIQUID
SOLID CONTACT PATTERN

195

site density and Dp,max induce the dense packing of dry areas, resulting in formation of secondary or tertiary dry areas. These secondary or tertiary dry areas decrease the number density of dry areas of smaller diameter, and at the same time increase the number density of dry areas of larger diameter, as shown in Fig. 3.3.3. Consequently, contact-line-length density decreases after it reaches the maximum value as surface superheat increases. Next, to examine the relation of the value of the contact-line-length density to the boiling curve, we tried to predict the boiling curve using the experimental data of the contact-line-length density. Following Dhir and Liaw [4], the heat-transfer rate per unit contact line length, QL,90 (W/m), can be calculated by the following equation if the contact angle is assumed as θ 5 90 (see Fig. 3.3.8). QL;90 5 2CΔTws

N X sin 2λn bð1 2 exp½ 2λn hÞ

ð2λn b 1 sin 2λn bÞλn sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi M C 5 αρv hlv 2 2πR0 Tsat 3

(3.3.1)

n51

FIGURE 3.3.8 Boiling-structure model by Dhir and Liaw [4].

(3.3.2)

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CHAPTER 3 CHF—TRANSITION BOILING

Cb k sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 1 pffiffiffiffiffiffi 2 Dm b5 2 ND λn b tan λn b 5

(3.3.3) (3.3.4)

Here, α is the evaporation coefficient, ρv is the density of vapor, hlv is the latent heat of vaporization, M is the molecular weight, R0 is the universal gas constant, Tsat is the saturation temperature, k is the thermal conductivity of liquid, ND is the number density of dry areas, and Dm is the averaged equivalent diameter of the dry areas. The values of ND and Dm can be calculated from the data shown in Fig. 3.3.3. Coupling the above equations with the experimental data of Φ, the heat flux at evaporating contact lines, qcl[ΔTws], can be calculated by the following simple equation: qcl ½ΔTws  5 F½θQL;90 ½ΔTws Φ½ΔTws 

(3.3.5)

In this equation, F[θ] is a function representing the effect of the contact angle on evaporation near the contact line. In this sub-chapter, this function is estimated from the graphical result presented by Dhir and Liaw [4]. Based on our preliminary calculations changing h 5 1
10 mm, it was concluded that qcl[ΔTws] does not depend strongly on the value of h. Thus, the boiling curves calculated from Eq. (3.5.5) for h 5 1 mm and θ 5 10 , 30 and 90 are shown in Fig. 3.3.9 together with the boiling curves measured in this experiment. As shown in this figure, the boiling curve calculated for θ 5 30 is similar to the experimental result. It is considered that this value is reasonable for the combination of R-113 and sapphire. Summarizing the results mentioned above, it can be concluded that the contact-line-length density is one of the very important quantities directly representing the boiling structures.

FIGURE 3.3.9 Comparison between predicted and measured boiling curves.

3.3.3 OBSERVATION OF CROSS-SECTIONAL STRUCTURE OF BOILING

197

3.3.3 OBSERVATION OF CROSS-SECTIONAL STRUCTURE OF BOILING As mentioned in the previous section, the liquid network coexisting with the closely packed dry areas was observed at heat fluxes near CHF and this situation is very different from the threelayered boiling-structure model. In this section, a quasi-2D boiling system is proposed to observe the sectional views of the boiling structures and some experimental results are summarized.

3.3.3.1 QUASI-TWO-DIMENSIONAL BOILING SYSTEM A schematic diagram of the experimental apparatus used in this experiment is shown in Fig. 3.3.10A. The test liquid was ethanol at atmospheric pressure and it was stored in a glass vessel of 110 mm width, 25 mm depth, and 80 mm height. The test liquid was held at the saturation temperature by an electric heater which was set alongside the test section. A schematic diagram of the boiling surface is shown in Fig. 3.3.10B. The boiling surface was an epoxy resin plate with a copper film of 30 μm thickness on one side. The thickness of the epoxy resin plate was 1.6 mm. The length of the test section of the copper film was 40 mm which was larger than the most dangerous wavelength of Rayleigh
Taylor instability for ethanol (17 mm). As shown in Fig. 3.3.10B, the boiling surface was sandwiched by two vertical glass plates to realize a quasi-2D boiling space. The width of the boiling surface or the gap between the vertical glass plates was much smaller than the most dangerous wavelength (W 5 0.5, 1.0, and 2.0 mm). The height of the glass plates was changed from H 5 0 to 15 mm. Boiling of the test liquid was activated by flowing a DC current in the copper film. A block of epoxy resin of 9 mm thickness was attached to the backside of the boiling surface to reduce heat

FIGURE 3.3.10 Schematic diagram of experimental apparatus to observe bubble structures in quasi-2D space.

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loss through the epoxy resin plate. To calculate the temperature of the copper film from its electric resistance, the DC current flowing in the film and the voltage between the voltage taps shown in Fig. 3.3.10B were measured. The measurement was repeated by increasing the electric current step by step, and it was continued until burnout of the copper film occurred. The calibration of the electric resistance to temperature was conducted for each boiling surface. The surface of the copper film was polished with #3000 emery papers to make the experimental condition uniform. The boiling structures between the glass plates were observed through the glass plate using the high-speed video system (500 and 1000 frames/s).

3.3.3.2 NUCLEATE BOILING CURVE AND CHF IN QUASI-TWO-DIMENSIONAL SPACE Fig. 3.3.11 shows experimental data of the nucleate boiling curve together with that predicted from the correlation of Nishikawa and Fujita [18] and the value of CHF predicted from the theoretical model by Zuber et al. [19]. As seen from the figure, no remarkable effect of W on the nucleate boiling curve is found. In Fig. 3.3.12, the experimental data of CHF normalized by the Zuber equation, qCHF/qCHF,Z, are plotted to the surface width normalized by the Laplace length, W/λcp. In the figure, experimental data for H 5 0 mm reported by Shoji and Kuroki [14] are also plotted. It is found from the figure that, in the case of H 5 0 mm, the normalized CHF starts to increase if the normalized width is decreased below about 2. It is found further that the normalized CHF is about unity regardless of the width if H is larger than 2 mm. Summarizing the results mentioned above, boiling heat transfer in the quasi-2D space used in this experiment is not much different from that in usual 3D spaces.

FIGURE 3.3.11 Nucleate boiling curves in quasi-2D space (H 5 2 mm).

3.3.3 OBSERVATION OF CROSS-SECTIONAL STRUCTURE OF BOILING

199

FIGURE 3.3.12 Critical heat flux in quasi-2D space.

3.3.3.3 BUBBLE STRUCTURES Fig. 3.3.13 shows typical video pictures obtained in this observation at three heat-flux levels for W 5 0.5 mm and H 5 2 mm. The left-side pictures at each heat-flux level are two successive closeup pictures taken at 1000 frames/s. The right-side picture is a distant-view picture taken at 500 frames/s to give a whole image of nucleate boiling. In the case of Fig. 3.3.13A at q 5 0.15qCHF, bubbles are isolated with each other as shown in the right-side picture, but, as shown in the left-side picture, the bubble departure is suppressed due to the vertical coalescence of a departure bubble with a small bubble growing beneath the departure bubble. The left-side pictures of Fig. 3.3.13B at q 5 0.3qCHF indicates the initiation of the lateral coalescence of neighboring primary bubbles. As a result, as shown in the right-side picture, bubbles of large vapor mass are produced. In the case of Fig. 3.3.13C at q 5 0.92qCHF, bubbles of very large mass, which can be referred to as the “filmwise bubbles,” are formed. The left-side pictures in Fig. 3.3.13C show the structure under the filmwise bubble. It is clearly seen that a liquid film does exist between the surface and the filmwise bubble and also vigorous bubble generation does occur in the liquid film. The boiling structure at this heat flux level is more clearly shown in Figs. 3.3.14 and 3.3.15. This result gives an image of the boiling structure different from the three-layered model, but it is similar to the results obtained by Galloway and Mudawar [20] for forced convection boiling in a narrow channel. In this sub-chapter, following their paper, the liquid film including bubble generation is referred to as the “liquid subfilm.” It is considered that the physical situation named as the liquid
solid contact of the network pattern results from the formation of the liquid subfilm. The microlayer under the primary bubbles

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FIGURE 3.3.13 Dependence of bubble structure on heat flux (W 5 0.5 mm, H 5 2 mm).

growing in the liquid subfilm seems to easily dry-out because such bubbles grow like vapor domes and they would not easily depart from the surface. In this situation, wetted areas exist only between such bubbles like domes and then a network like canals is formed. In the existing CHF models (e.g., Haramura and Katto [3]), the lateral pitch of departure of coalescent bubbles has been assumed equal to the most dangerous wavelength of Rayleigh
Taylor instability. Based on the physical image given by the three-layered model, however, there is no physical process producing such an instability at the interface of the mushroom bubbles. As shown in the right-side picture in Fig. 3.3.13C, the upper surface of the filmwise bubble was wavy and the bubble departure occurred at the convex part of the wave. Fig. 3.3.16 shows the experimental data of the lateral pitch of the bubbles departing from the filmwise bubble. The experimental data are located near the most dangerous wavelength, λ2,d. These results indicate that bubble departure from the filmwise bubbles is controlled by the Rayleigh
Taylor instability at the upper interface of the filmwise bubbles.

3.3.3 OBSERVATION OF CROSS-SECTIONAL STRUCTURE OF BOILING

201

FIGURE 3.3.14 Dynamic behavior of filmwise bubble (W 5 0.5 mm, H 5 2 mm, q 5 0.92qCHF).

FIGURE 3.3.15 Close-up picture of liquid film under filmwise bubble (W 5 0.5 mm, H 5 2 mm, q 5 0.92qCHF).

In the CHF model proposed by Haramura and Katto [3] based on the three-layered boilingstructure model, macrolayer thickness is one of the most important quantities which determine the critical heat flux. So, the liquid subfilm thickness under coalescent bubbles are discussed here. Fig. 3.3.17 shows the liquid subfilm thickness under coalescent bubbles measured from magnified video pictures. The data shown by open symbols are the thickness of subfilm liquid layer, δl,min, and the data shown by solid symbols are the liquid subfilm thickness including the averaged height

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FIGURE 3.3.16 Pitch of departure bubbles.

FIGURE 3.3.17 Liquid subfilm thickness under coalescent bubbles.

of vapor domes, δl,max. In Fig. 3.3.17, the experimental results on macrolayer thickness by Rajvanshi et al. [21] and the calculation results of macrolayer thickness in Haramura and Katto model are also plotted. The results of δl,max show almost the same tendency with the results on macrolayer thickness. Conversely, δl,min are much smaller than the results on macrolayer thickness.

3.3.4 OBSERVATION OF LIQUID
SOLID CONTACT SITUATIONS

203

3.3.4 OBSERVATION OF LIQUID
SOLID CONTACT SITUATIONS DURING COOLING BY LIQUID JET OR SPRAYING 3.3.4.1 EXPERIMENTAL SETUP AND CONDITIONS The experimental apparatus is schematically shown in Fig. 3.3.18. The test liquid was HFE-7100, whose boiling point is approximately 60 C. The solid surface was made of single-crystal sapphire, 50 3 50 3 5 t mm, which has relatively high thermal conductivity k 5 42 W/(m  K). The sapphire plate was put on a silicone oil bath, the temperature of which was controlled by cartridge heater up to 300 C. Both surface temperatures of the sapphire plate were measured by K-type thermocouples attached to it. The temperature of test liquid, TL, was changed to room temperature (23
28 C), 38 C, and 50 C, by controlling heat input to the heater in the test liquid tank. The test liquid was pumped to the nozzle set just above the sapphire plate, through the controlling valve, flow meter, and pressure sensor. The visual images of liquid
solid contact situations were obtained from below the surface through silicone oil by total reflection method as denoted before and recorded by high-speed video camera at 1000 frames/s and 1/10,000 shutter constant. Where the surface is dry, incident light from below the surface is totally reflected on the surface and the area looks light in the camera. Conversely, where the surface is wet, the incident light is not totally reflected and the area looks dark. Boiling situations were also recorded by handy camera, about 60 frames/s from above the sapphire plate. For the liquid spray experiment, two types of nozzles were used. The first one was a full _ was 350 mL/min (liquid volume flow density corn nozzle, for which liquid volume flow rate, V,

FIGURE 3.3.18 Visualization experiment setup for liquid spraying and jet impingement.

204

CHAPTER 3 CHF—TRANSITION BOILING

3.86 L/(m2･s)). The other was a narrow-angle nozzle, for which V_ was 920 mL/min (liquid volume flow density 184 L/(m2･s)). For the liquid jet impingement experiment, the nozzle was changed to a laminar nozzle. The velocity of the liquid jet, VL, was changed to 1.26, 1.70, and 2.94 m/s, which corresponded to the liquid jet diameters 2.9, 2.5, and 1.9 mm, respectively, where liquid volume flow rate was constant.

3.3.4.2 LEIDENFROST TEMPERATURE AND LIMIT OF LIQUID SUPERHEAT OF THE TEST LIQUID Preliminary experiments on measuring evaporation curves of a single liquid droplet on the sapphire plate showed that Leindenfrost temperature of HFE-7100 of TL 5 28 C was about TLeid 5 125 C. According to the correlation by Lienhard and Karimi [22] on limit temperature of liquid superheat, i.e., the temperature when the spontaneous nucleation becomes dominant, limit of liquid superheat of HFE-7100 was about Ttls 5 154 C. These two temperatures, Leidenfrost temperature, TLeid, and limit of liquid superheat, Ttls, are important index for considering liquid
solid contact on a superheated surface.

3.3.4.3 LIQUID
SOLID CONTACT SITUATIONS WHILE LIQUID SPRAY COOLING Fig. 3.3.19 shows visual images of liquid
solid contact situations just after the sapphire plate was cooled by liquid spraying under the following conditions: liquid temperature, TL, was room temperature and the nozzle was full corn jet type. The upper images were taken from above the surface by handy camera, while the lower images were taken from below the surface by high-speed camera. The initial surface temperature, Twi, for Fig. 3.3.19A was 100 C, and Twi 5 180 C for Fig. 3.3.19B. As shown in Fig. 3.3.19A of Twi 5 100 C, the surface was almost wetted from the beginning with many tiny dry spots included, which corresponds to typical nucleate boiling. Conversely, as shown in Fig. 3.3.19B of Twi 5 180 C, the surface was totally dry with no wetted area, which corresponds to typical film boiling. The liquid
solid contact situations shown in Fig. 3.3.19 are not our major concerns because the surface was always wetted or dry.

FIGURE 3.3.19 Snapshots of visual images of liquid
solid contact situations just after the liquid spraying started.

3.3.4 OBSERVATION OF LIQUID
SOLID CONTACT SITUATIONS

205

Fig. 3.3.20 shows sequential visual images of liquid
solid contact situations while the sapphire plate was cooled by liquid spraying under the following conditions: initial surface temperature Twi 5 140 C, liquid temperature, TL, was room temperature, and the nozzle was full corn jet type. The left-side images were taken from below the surface, while the right-side images were taken from above the surface. As shown in Fig. 3.3.20, initially the surface was totally dry. However, after a “certain time” had passed, a localized liquid
solid contact appeared and gradually expanded. The localized liquid
solid contact area consisted of many tiny wetted and dry spots, then in this sub-chapter, this localized liquid
solid contact area is referred to as “liquid
solid contact group.” The initial surface temperature of Fig. 3.3.20 was Twi 5 140 C, and local surface temperature must be gradually decreased due to liquid spray cooling, not measured in this experiment. Therefore, the situations shown in Fig. 3.3.20 correspond to stages from film boiling, through MHF point, to transition boiling region. Thus, during liquid spraying, it was successfully visualized how and when the localized liquid
solid contact initiated and expanded on superheated surface. Based on visual images like Fig. 3.3.20, the time history of the “liquid
solid contact group” was examined using an image-processing technique. The outer diameter of the liquid
solid contact group, L, was evaluated by image processing and plotted versus liquid spraying time in Fig. 3.3.21. In the case of Twi 5 140 C and TL 5 23 C, shown by the black circle symbol in Fig. 3.3.21, just after liquid spraying started (t 5 0), the diameter of the liquid
solid contact group, L, was zero.

FIGURE 3.3.20 Sequential snapshots of visual images of liquid
solid contact situations while liquid spraying for Twi 5 140 C (film to transition boiling).

206

CHAPTER 3 CHF—TRANSITION BOILING

FIGURE 3.3.21 Time history of diameter of liquid
solid contact group at V_ 5 350 mL/min (effect of liquid temperature and initial surface temperature).

However, after 2 s had passed (t 5 2 s), a liquid
solid contact group appeared on the surface and its diameter gradually increased to L 5 30 mm after t 5 4.2 s. From Fig. 3.3.21, the following were deduced. (1) When liquid temperature, TL, was constant, the appearance of liquid
solid contact group delayed as the initial surface temperature, Twi, increased. (2) When Twi was constant, the appearance of liquid
solid contact group delayed as the liquid temperature, TL, increased. (3) In the case of Twi 5 120 C, an increasing rate of L (mm/s) was relatively high compared to that for other initial surface temperatures. These results (1
3) imply that localized liquid
solid contact initiates when the surface temperature is about 120 C, which is very close to Leidenfrost temperature TLeid 5 125 C. With regards to the effect of liquid volume flow density, not shown in figures, comparing experimental results between by narrow-angle nozzle and by full corn nozzle, higher liquid flow density caused earlier appearance of liquid
solid contact group. When initial surface temperature, Twi, was 170 C, there were not any liquid
solid contact groups found at full corn nozzle (liquid volume flow density 3.86 L/(m2･s)) during visualized time of about 4.5 s. However, at narrow-angle nozzle (liquid volume flow density 184 L/(m2･s)), after about 0.2 s, a liquid
solid contact group appeared when Twi 5 170 C.

3.3.4.4 LIQUID
SOLID CONTACT SITUATIONS WITH LIQUID JET IMPINGEMENT Fig. 3.3.22 shows liquid
solid contact situations with liquid jet impingement at the initial surface temperature Twi 5 140 C, liquid jet velocity VL 5 1.26 m/s and liquid temperature TL 5 40 C. Time

3.3.4 OBSERVATION OF LIQUID
SOLID CONTACT SITUATIONS

207

FIGURE 3.3.22 Sequential snapshots of visual images of liquid
solid contact situations with liquid jet impingement for Twi 5 140 C (film to transition boiling).

t means elapsed time after the liquid jet impinged on the surface. Photos of bottom view, righthand side at each time, were taken by the total reflection method as mentioned previously. The same as with situations of liquid spraying, after a “certain time” had passed after the liquid jet impinged on the surface, small circular-shaped liquid
solid contact initiated just beneath the nozzle (between t 5 500 ms and 1000 ms in the case of Fig. 3.3.22) and the size of localized liquid
solid contact expanded after that. Hereafter, we will refer to the circular-shaped liquid
solid contact as “liquid
solid contact group,” as with liquid spraying, and the time when the liquid
solid contact was first observed as “incident time of the liquid
solid contact group.” When the initial surface temperature Twi was much higher than 140 C, a liquid
solid contact group was not observed during recording the duration of the high-speed video camera, 4.5 s. Conversely, when initial surface temperature Twi was sufficiently lower than 140 C, a liquid
solid contact group was observed from t 5 0 s, with whole surface wet conditions. Fig. 3.3.23 denotes time history of liquid
solid contact group diameter when the initial surface temperature was changed as Twi 5 130
160 C with the same liquid jet velocity as in Fig. 3.3.23. For comparison, the data for spray cooling as explained in the former section are also plotted. It is clearly shown in the figure that the incident time of the liquid
solid contact group becomes later and the expanding speed of the liquid
solid contact group becomes slower as the initial surface temperature becomes higher. Comparing the liquid jet diameter of 2.9 mm with the liquid
solid contact group diameter, the liquid
solid contact group rapidly expanded until its diameter reached around two-times that of the liquid jet diameter, and expanded gradually after that. Fig. 3.3.23 also shows the difference between liquid spraying and liquid jet impingement tested in these experiments. When the initial surface temperature Twi 5 140 C, the incident time for liquid jet

208

CHAPTER 3 CHF—TRANSITION BOILING

FIGURE 3.3.23 Time history of liquid
solid contact group diameter with liquid jet impingement and liquid spraying.

FIGURE 3.3.24 Incident time of liquid
solid contact group (Twi).

impingement was about 0.5 s, while the incident time for liquid spraying was about 3.2 s. This difference was mainly caused by a difference in local liquid volume flow rate density; liquid volume flow rate density of a liquid jet is much higher than that of liquid spraying at the center part of the surface. The incident time of the liquid
solid contact group is assumed to be the time when the local surface temperature decreased to a “certain” value. The authors tried to estimate the “certain” surface

3.3.4 OBSERVATION OF LIQUID
SOLID CONTACT SITUATIONS

209

FIGURE 3.3.25 Incident time of liquid
solid contact group (TL).

FIGURE 3.3.26 Incident time of liquid
solid contact group (VL).

temperature at the incident time of the liquid
solid contact group based on the initial surface temperature Twi and film boiling heat transfer of liquid jet impingement. Unfortunately, the film boiling heattransfer coefficient of HFE-7100 is not clear; thus the incident time of the liquid
solid contact group is qualitatively discussed here. In Figs. 3.3.24
3.3.26, the incident time of the liquid
solid contact group is plotted versus three parameters: initial surface temperature Twi, liquid temperature TL, and liquid jet velocity VL. From these figures, incident time becomes earlier at lower liquid temperature and larger

210

CHAPTER 3 CHF—TRANSITION BOILING

liquid jet velocity. And the most influential parameter on the incident time is initial surface temperature. In addition, considering the solid
liquid interface temperature by transient heat conduction problem of two semi-infinite bodies, the surface temperature at the incident time of the liquid
solid contact group is considered to be significantly lower than the limit of liquid superheat Ttls 5 154 C.

3.3.5 CONCLUSION The observation in this work revealed the following boiling structures in high heat-flux boiling. The liquid network coexisting with closely packed dry-areas corresponds to the liquid
solid contact structure, and the sectional structure is composed of the filmwise bubbles and the liquid subfilm with bubble formation. Based on these results, the contact-line-length density was proposed as a measure of the contribution of liquid
solid contact to high heat-flux boiling heat transfer. As for liquid
solid contact situations during cooling by liquid jet or spraying, the obtained results were summarized as follows. (1) Initial surface temperature Twi, liquid velocity or flow rate density, and liquid temperature TL affect the liquid
solid contact situations considerably. (2) As the TL and Twi increase, the elapsed time when the liquid
solid contact initiated after the liquid jet or spray firstly impacted on the surface is delayed. (3) The situations when and how the liquid
solid contact area initiates and expands on the surface are different between liquid jet and spraying.

NOMENCLATURE b C D Dm Dp,max h hlv H k M nD ND q qcl qCHF qCHF,Z QL,90 R0 t Tsat Tw W

half value of the averaged distance between the centers of dry areas heat-transfer coefficient of vaporization equivalent diameter of dry areas averaged equivalent diameter of dry areas maximum value of equivalent diameter of a primary dry area height of liquid
vapor interface latent heat of vaporization height of the glass plates thermal conductivity of liquid molecular weight the number of dry areas in each diameter class number density of dry areas heat flux heat flux at evaporating contact lines critical heat flux critical heat flux value estimated by Zuber equation heat-transfer rate per unit contact line length universal gas constant time saturation temperature temperature of boiling surface width of the boiling surface

REFERENCES

211

GREEK SYMBOLS α δ l,max δ l,mix ΔTCHF ΔTws Φ Φmax Γw λcp λn θ ρv

evaporation coefficient liquid subfilm thickness under coalescent bubbles including the averaged height of vapor domes liquid subfilm thickness under coalescent bubbles surface superheat at CHF point surface superheat contact-line-length density measured maximum value of contact-line-length density time- and space-averaged fraction of liquid
solid contact laplace length answers of Eq. (3.5.3) contact angle density of vapor

REFERENCES [1] A. Asai, Application of the nucleation theory to the design of bubble jet printers, Jpn. J. Appl. Phys. 28 (1989) 909
915. [2] R.F. Gaertner, Photographic study of nucleate pool boiling on a horizontal surface, Trans. ASME J. Heat Transfer 87 (1965) 17
29. [3] Y. Haramura, Y. Katto, A new hydrodynamic model of critical heat flux, applicable widely to both pool and forced convection boiling on submerged bodies in saturated liquids, Int. J. Heat Mass Transfer 26 (1983) 389
399. [4] V.K. Dhir, P. Liaw, Framework for a unified model for nucleate and transition pool boiling, Trans. ASME J. Heat Transfer 111 (1989) 739
746. [5] Y. Katto, S. Yokoya, Principal mechanism of boiling crisis in pool boiling, Int. J. Heat Mass Transfer 11 (1968) 993
1002. [6] N. Nagai, S. Nishio, A method for measuring the fundamental quantities on liquid
solid contact in pool boiling using an image processing technique, Flow Visual. Image Process. Multiphase Syst., FEDV.209, ASME, 1995, pp. 73
79. [7] T. Oka, Y. Abe, Y.H. Mori, A. Nagashima, Pool boiling of n-pentane, CFC-113, and water under reduced gravity: parabolic flight experiments with a transparent heater, Trans. ASME J. Heat Transfer 117 (1995) 406
417. [8] S. Nishio, Cooldown of insulated metal plates, in: Proceedings of 1983 ASME/JSME Thermal Engineering Joint Conference, vol. 1, Hawaii, 1983, pp. 103
109. [9] N. Nagai, S. Nishio, Leidenfrost temperature on an extremely smooth surface, Exp. Thermal Fluid Sci. 12 (1996) 373
379. [10] H.S. Ragheb, S.C. Cheng, Surface wetted area during transition boiling in forced convective flow, Trans. ASME J. Heat Transfer 101 (1979) 381
383. [11] L.Y.W. Lee, J.C. Chen, R.A. Nelson, Liquid
solid contact measurements using a surface thermocouple temperature probe in atmospheric pool boiling water, Int. J. Heat Mass Transfer 28 (1985) 1415
1423. [12] D.S. Dhuga, R.H.S. Winterton, Measurement of surface contact in transition boiling, Int. J. Heat Mass Transfer 28 (1985) 1869
1880. [13] S. Neti, T. Butrie, J.C. Chen, Fiber-optic liquid contact measurements in pool boiling, Rev. Sci. Instrum. 57 (1986) 3043
3047.

212

CHAPTER 3 CHF—TRANSITION BOILING

[14] M. Shoji, H. Kuroki, Non-linear aspects of high heat flux nucleate boiling heat transfer-formulation & results, Proc. 1994 IMECE, HTD-V.298, ASME, 1994, pp. 91
114. [15] I. Tanasawa, Advances in condensation heat transfer, Adv. Heat Transfer, 21, Academic Press, Orlando, 1991, pp. 55
139. [16] P. Van Carey, Liquid
Vapor Phase-Change Phenomena, Hemisphere, New York, 1992, Chapters 2 and 7. [17] R.W. Graham, R.C. Hendricks, Assessment of convection, conduction, and evaporation in nucleate boiling, NASA Technical Note (1967) 1
42, TN D-3943. [18] K. Nishikawa, Y. Fujita, Nucleate boiling heat transfer and its augmentation, Adv. Heat Transfer, 20, Academic Press, Orlando, 1990, pp. 1
82. [19] N. Zuber, M. Tribus, J.W. Westwater, The hydrodynamic crisis of pool boiling of saturated and subcooled liquids, Int. Dev. Heat Transfer (1963) 230
235, ASME, New York. [20] J.E. Galloway, I. Mudawar, CHF mechanism in flow boiling from a short heated wall—I. Examination of near-wall conditions with the aid of photomicrography and high-speed video imaging, Int. J. Heat Mass Transfer 30 (1993) 2511
2526. [21] A.K. Rajvanshi, J.S. Saini, R. Prakash, Investigation of macrolayer thickness in nucleate pool boiling at high heat flux, Int. J. Heat Mass Transfer 35 (1992) 343
350. [22] J.H. Lienhard, A. Karimi, Homogeneous nucleation and the spinodal line, Trans. ASME J. Heat Transfer C 103 (1981) 61
64.

3.4

CRITICAL HEAT FLUX ENHANCEMENT IN SATURATED POOL BOILING

Shoji Mori Yokohama National University, Yokohama, Japan

3.4.1 INTRODUCTION Pool boiling has been used for cooling in numerous thermal energy dissipation systems, such as high-power electronics, heat exchangers, and nuclear reactors. The advantage of pool boiling is that a high heat flux can be removed passively while maintaining a low superheat, as compared with natural/forced convection without phase change. However, the heat removal capacity is limited by the upper limit of cooling, i.e., the critical heat flux (CHF), where the heat-transfer coefficient decreases dramatically because the boiling regime is changed from nucleate boiling to film boiling. Therefore, the CHF enhancement is of great interest to engineers and researchers.

3.4.1 INTRODUCTION

213

Gambill and Lienhard [1] showed the theoretical upper limit of cooling for evaporation, neglecting condensation on the liquid
vapor interface. The theoretical maximum heat flux is given by qvmax 5 ρv hfg

rffiffiffiffiffiffiffiffiffiffi RTsat 2πM

(3.4.1)

where ρv, hfg, R, Tsat, and M are the density of the vapor, the latent heat of evaporation, the universal gas constant, the saturation temperature, and the molecular mass, respectively. Using Eq. (3.4.1), the theoretical maximum heat flux for water is 223.2 MW/m2 and that for FC-72 is 46.7 MW/m2 under atmospheric pressure conditions. In general, the achievable CHF for a plain surface without using external power is smaller than the theoretical upper limit for evaporation by one or two orders of magnitude, which indicates that CHF enhancement may be possible. Except for pool boiling, there are several interesting approaches to extremely high heat flux removal in passive thermal devices for electronic cooling. For the vapor chamber of a high-power electronic device, Semenic et al. [2] applied a bi-porous wick consisting of clusters of fine powder to dissipate approximately 10 MW/m2 (heat source area: diameter 6.4 mm, water, P 5 6.77 kPa, qCHF,max 5 9.9 MW/m2, ΔTSAT,CHF 5 147 K). Hashimoto et al. [3] removed approximately 8.5 MW/m2 using CNT-coated copper particles (heat source area: 5 mm 3 5 mm, water, qmax 5 8.5 MW/m2, ΔTSAT 5 75 K). Weibel et al. [4] proposed a vapor chamber using CNT-coated patterned sintered power, which can dissipate 5 MW/m2 or more (heat source area: 5 mm 3 5 mm, water, P 5 0.1 MPa, qCHF,max 5 5.6 MW/m2, ΔTSAT,CHF 5 134 K). These values are higher than achievable CHF enhancement in a saturated pool boiling of water. In these studies, water was selected as the test fluid because water has a high surface tension and a large latent heat of vaporization. The reason for the much higher heat flux removal, as compared with the saturated pool boiling CHF for the plain surface (approximately 1 MW/m2) [5], is that these vapor chambers eliminate the effect of large bubbles formed on the heated surface near CHF conditions in pool boiling. However, the heat-removal performance using these techniques in a vapor chamber depends significantly on the characteristic length of the heated surface because liquid is pumped toward the center of the heated surface by capillary suction [6]. Accordingly, there is an advantage to pool boiling in not only removing high heat flux, but also being applicable to large heated surfaces. One of the applications for cooling of a large heated surface is in-vessel retention (IVR) of corium debris in severe accidents at nuclear power plants [7]. Approaches for increasing the IVR capability must be simple and installable at low cost. In general, the CHF decreases as the heater size increases as stated above [8]. Arik and Bar-Cohen [8] proposed CHF correlation considering the effect of heater size using the dimensionless heater size, L0 : L L0 5 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi σ=gðρl 2 ρv Þ

(3.4.2)

where L is the characteristic heater length. Based on the obtained results, the heat-transfer area can be regarded as infinite when L0 exceeds approximately 20. Various surface modifications of the heated surface, for example, by porous coating due to welding, sintering, or brazing of particles, electrolytic deposition, flame spraying, bonding of

214

CHAPTER 3 CHF—TRANSITION BOILING

FIGURE 3.4.1 Dimensions of the honeycomb porous plate.

particles by plating, galvanizing, plasma spraying of a polymer, or metallic coating of a foam substrate, deposition of nanofluid, and a honeycomb porous plate, have been proven to effectively enhance the heat-transfer coefficient and the CHF in saturated pool boiling [9
18]. Based on the review of CHF enhancement by surface modification in saturated pool boiling [9
18], CHF is enhanced generally by (1) porous coatings (uniform or modulated) and (2) structures of various sizes fabricated/installed on the heated surface. In general, CHF enhancement in saturated pool boiling is a result of the effects of extended surface area, nucleation site density, wettability, capillary wicking, and wavelength decrease based on the modified Zuber hydrodynamic stability model [19]. The exact contribution of each effect has not yet been clarified. A number of combined techniques for CHF enhancement have been proposed. In particular, Mori and Okuyama [20] proposed a novel CHF enhancement technique using a honeycomb-structured ceramic porous plate (see Fig. 3.4.1), which is commercially available as a filter for purifying exhaust gases from combustion engines, for CHF enhancement. This honeycomb porous plate (HPP) has considerably smaller micropores of the order of 0.1 μm, as compared with those for sintered metal powders, and is simply attached to the test surface without any treatment, such as spraying or sintering. So far the saturated pool boiling CHF (heated surface diameter: 30 mm) is enhanced significantly up to 3.2 MW/m2 at maximum [21]. To the best of the author’s knowledge, the highest value of CHF (3.2 MW/m2) was obtained for a large heated surface having a diameter of 30 mm.

3.4.2 FUNDAMENTAL EFFECTS OF HPP ON THE CHF ENHANCEMENT 3.4.2.1 EFFECT OF MICROPORES AND VAPOR ESCAPE CHANNELS ON THE CHF [20] Fig. 3.4.2 shows the boiling curves for different structures of porous plates, i.e., an HPP, a honeycomb solid plate without micropores, which was fabricated by impregnating an HPP with adhesive, and a solid porous plate without vapor escape channels, having a height of 5.0 mm. Experiments using a honeycomb solid plate without micropores and a solid porous plate without vapor escape

3.4.2 FUNDAMENTAL EFFECTS OF HPP ON THE CHF ENHANCEMENT

q (MW/m2)

3

Water P = 0.1 MPa Δ TSUB = 0 K δ h = 5.0 mm

2

215

Honeycomb porous plate Plain surface Honeycomb solid plate Solid porous plate

1.40 MW/m

2

1.01 MW/m 2 0.88 MW/m 2

1

0.36 MW/m

0

0

10

20

Δ Tsat (K)

2

30

FIGURE 3.4.2 Boiling curves for different structures of porous plates.

channels was carried out in order to clarify the effect of a capillary suction and the effect of vapor channels to avoid an excessive pressure increase in the porous structure on the CHF, respectively. The arrows indicated in Fig. 3.4.2 correspond to the CHF condition. As clearly seen from Fig. 3.4.2, the CHF for HPP is 1.4 MW/m2, which is approximately 1.6 times and 4 times that of the honeycomb solid plate (0.88 MW/m2) and the solid porous plate (0.36 MW/m2), respectively. These results signify that micropores provide strong capillary suction and vapor escape channels are necessary to improve the CHF. That is, the CHF enhancement is attributed to the automatic liquid supply due to capillary action and the reduction of the liquid
vapor counterflow resistance adjacent to the heated surface due to the separation of the liquid and vapor flow by the honeycomb structure.

3.4.2.2 EFFECTS OF THE HEIGHTS IN HPPS δ H ON THE CHF [20] The saturated boiling curves of the HPPs at different heights and that of a plain surface are compared in Fig. 3.4.3. As shown clearly in the figure, the CHF is increased dramatically with the decrease in heights of the HPPs. In particular, a HPP for a height of 1.2 mm can remove a heat flux of 2.5 MW/ m2, which is approximately 2.5-times that of a plain surface (1.0 MW/m2). The difference in the values of heat-transfer coefficients between different heights (δh 5 1.2 mm, 5.0 mm, and 10.0 mm) of HPPs are not obvious, although they are significantly large compared with that of a plain surface. Fig. 3.4.4 shows the relationship between the CHF and heights of HPPs. The solid line and the dash-dotted line in this figure indicate the viscous-drag limit predicted by Eq. (3.4.8) and the hydrodynamic limit calculated by the model proposed by Liter and Kaviany [19], respectively. Eq. (3.4.8) will be derived in the following section. Comparison of these results will be discussed later. As can be seen in this figure, the CHF increases with the decrease in the height of the HPPs. The three possible CHF enhancement mechanisms for the use of porous media have been considered. The first is the capillary suction effect, the second is an extended surface area effect, and the third is the effect of a decrease in the flow-critical length scale, or the distance between vapor columns, which is regulated by the modulation in a porous layer, corresponding to Rayleigh
Tayer wavelength in Zuber’s hydrodynamic model, as suggested by Liter and Kaviany [19].

216

CHAPTER 3 CHF—TRANSITION BOILING

Water P = 0.1 MPa Δ TSUB = 0 K

2

q (MW/m )

3

2.51 MW/m

2

δ h = 1.2 mm δ h = 5.0 mm δ h = 10.0 mm

2

Plain surface

1.40 MW/m

2

1.04 MW/m 2

1

0

1.01 MW/m

0

10

20

2

30

Δ Tsat (K)

FIGURE 3.4.3 Boiling curves for honeycomb porous plates of different heights.

qCHF (MW/m2)

δh

5 4 Experimental values Viscous-Drag limit by Eq. (3.4.8) Hydrodynamic limit (Liter and Kaviany,2001)

3 2 1 0

0

2

4

6

8

10

δh (mm) FIGURE 3.4.4 Relationship between qCHF and height ofthe honeycomb porous plate.

As shown in Fig. 3.4.4, the CHF increases significantly as the height of the HPP decreases, which indicates the decrease in the extended surface area. Moreover, considering the low thermal conductivity in the HPPs and the thermal contact resistance between an HPP and a heated surface, the CHF enhancement mechanism in the present phenomena is not related to the extended surface area effect. The hydrodynamic liquid choking limit for the case less than the HPPs height δh of approximately 1.2 mm is smaller than the calculated value by the present model as shown in Fig. 3.4.4. However, the hydrodynamic limit also may be unrelated to the mechanism in the CHF presented herein even in the case of an HPP height δh of 1.2 mm. As a result, the CHF may be governed by the capillary suction effect. Therefore, it is assumed that the CHF occurs within the porous layer when the viscous drag surpasses the available capillary pumping. In order to clarify the CHF mechanism, a simplified 1-dimensional (1D) model, which is similar to the capillary limit model for a conventional heat pipe, applied to the phenomenon, and the calculated results are compared with the observed results.

3.4.2 FUNDAMENTAL EFFECTS OF HPP ON THE CHF ENHANCEMENT

217

3.4.2.3 THE CHF MODEL BASED ON CAPILLARY LIMIT [20] Fig. 3.4.5 shows a schematic diagram of the steam and water flows in an HPP. As shown in the figure, liquid is transported toward the heated surface within the porous medium by capillary force, and vapor generated in close vicinity to the heated surface escapes upward through the vapor channels. It is assumed that dry-out inside the porous material in close to the heated surface does not occur, that is, the inside of the porous material is completely filled with water in order to simplify the model. The CHF is considered to be achieved under conditions such that the maximum capillary pressure Δpc;max is equal to the sum of the pressure losses along the vapor
liquid path in the following: Δpc;max 5 Δpl 1 Δpv 1 Δpa

(3.4.3)

where Δpl and Δpv are the frictional pressure drops caused by the liquid flow in the porous medium and the vapor flow through the channels, respectively, and Δpa is the accelerational pressure drop caused by phase change from liquid to vapor. The maximum capillary pressure Δpc;max can be calculated by Δpc;max 5

2σ reff

(3.4.4)

where reff is the effective pore radius and σ is the surface tension. The pressure drop Δpl using Darcy’s law is expressed as Δpl 5

μl Qmax δh KAW ρl hfg

(3.4.5)

where μl is the viscosity of the liquid, Qmax is the maximum heat-transfer rate, δh is the height of the HPPs, K is the permeability, ρl is the density of a liquid, Aw is the contacted area of the HPP with the heated surface, and hfg is the latent heat of vaporization.

FIGURE 3.4.5 Schematic diagram of steam and water flows in a honeycomb porous plate.

218

CHAPTER 3 CHF—TRANSITION BOILING

The vapor pressure drop Δpv in a laminar incompressible flow (Reynolds number of vapor flow in present work is less than approximately 850) is given by Δpv 5

32μv δh Qmax ρv ndv 4 hfg

(3.4.6)

where μv is the viscosity of the vapor and n is the number of vapor escape channels on the heated surface. The accelerational pressure drop can be obtained as Δpa 5

 2 ρv Qmax 2 ðρv ndv2 Þhfg

(3.4.7)

The following CHF is obtained by substituting Eqs (3.4.4) to (3.4.7) into Eq. (3.4.3) and using the heated surface area A (approximately 7.07 cm2), as follows: 2B 1 Qmax 5 qCHF 5 A

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi B2 1 4Cð2σ=reff Þ μl δ h 32μv δh 1 ; ; B5 KAW ρl hfg 2AC ρv ndv 4 hfg

0 12 ρv @ 1 A C5 2 ðρv ndv2 Þhfg

(3.4.8)

where the permeability K and the effective pore radius reff were determined by experimental measurements (K 5 2:4 3 10214 m2 , reff 5 1.6 μm). As shown in Fig. 3.4.4, both the measured values and the values calculated by Eq. (3.4.8) increase as the height of the HPP decreases. Moreover, considering that the values of the observed CHF are explained roughly by the 1D model, which means that the 2D effect is not significant on the CHF, the cooling technology using HPPs presented herein may apply to large heated surface area cooling with high heat flux in saturated pool boiling.

3.4.2.4 OPTIMIZATION IN GEOMETRY OF HPP The CHF performance using HPPs depends on the pore radius reff, the permeability K, the height of the porous media δh, the vapor escape channel width dv, and the wall thickness δs of the porous medium between vapor escape channels. These parameters must be optimized in order to achieve the maximum CHF. In particular, the effect of the vapor escape channel width dv on the CHF is examined in the following three cases, i.e., (a) Δpc;max 5 Δpl 1 Δpv 1 Δpa , (b) Δpc;max 5 Δpl 1 Δpv , and (c) Δpc;max 5 Δpl . Fig. 3.4.6 shows the CHF values calculated as a function of the vapor channel width dv, for the HPPs height δh of 1.2 and 5.0 mm in the above cases (a)
(c), together with the measured results. The wall thickness δS between the neighboring vapor channels was fixed to 0.4 mm, which is equal to that of the tested plates. The predicted CHF in the above three cases ((a)
(c)) are almost the same for the case of more than the channel width dV of 0.3 mm, it is obvious that the CHFs for the region is dominated by the frictional pressure loss Δpl of liquid flow inside the porous medium. Moreover, considering that the difference of the value between cases (a) and (b) is small, accelational pressure loss does not dramatically influence the CHF. The CHF increases significantly with the decrease in the width of the vapor channel at larger widths (dv . 0.16 mm)and decreases markedly at smaller widths (dv , 0.16 mm). The increase in the CHF with the reduction of the channel width at

3.4.2 FUNDAMENTAL EFFECTS OF HPP ON THE CHF ENHANCEMENT

2

qCHF (MW/m )

10

(a) Δ Pc,max= Δ Pl+ Δ Pv+ Δ Pa (b) Δ Pc,max= Δ Pl+ Δ Pv (c) Δ Pc,max= Δ Pl

8 6

219

δ h = 1.2 mm

dv δ h = 5.0 mm

4

0.4 mm 2 0 0.01

0.05 0.1 0.5 dv (mm)

1

FIGURE 3.4.6 qCHF as a function of dv.

large widths is due to the increase in the contact area of the porous plate with the heat-transfer surface area. The increase in the contact area reduces the mass flux and pressure drop of the liquid flow in the porous wall, resulting in the higher allowable evaporation rate over the entire heattransfer surface. Whereas, smaller channel widths (dv , 0.16 mm) cause a significant increase in the pressure drop for the vapor flow in the escape channel, which results in a smaller CHF. Because of the difference in the limiting mechanisms, the calculated CHF shows the maximum values, which are approximately 8.0 MW/m2 and 2.0 MW/m2 at the channel width dv of approximately 0.16 mm for the plate thicknesses δh of 1.2 and 5.0 mm, respectively. The calculated results suggest that the optimum width for maximizing the CHF would be much smaller than that of the tested plates. The relationship between the CHF and the specification of the HPP was generalized [20]. Moreover, the effect of the channel width on the saturated pool boiling CHF of water has been investigated experimentally [22]. The vapor escape channel width was varied in the range of 1.4
7.9 mm, which was smaller than the Taylor instability wavelength for saturated water (approximately 15.6 mm). As a result, the primary mechanisms for CHF enhancement using a HPP are due to liquid supply to the heated surface caused by not only capillary suction but also the inflow of liquid through the vapor escape channels from the top surface due to gravity. The ratio of the contributions of the various mechanisms of CHF enhancement depends on the cell width.

3.4.2.5 EFFECT OF HEATER SIZE ON THE CHF ENHANCEMENT Several studies have examined the effect of heater size on the CHF [23]. In general, the CHF increases as the heater size decreases. The heat-transfer area can be regarded as infinite when L0 exceeds approximately 20. Fig. 3.4.7 indicates the effect of heater size on the CHF as a result of surface modification [24]. As shown in this figure, the increase in L0 from 4 to 12 diminishes the CHF enhancement of the nanoparticle-deposited surface (NDS). Conversely, the best-performing

220

CHAPTER 3 CHF—TRANSITION BOILING

q"CHF /q"Zuber (–)

3

2

1

0

0

10

20 L' (–)

30

40

Plain surface, Mori et al. (2015) Honeycomb porous plate installed on a nano-particle deposited surface, Mori et al. (2015) Nano-particle deposited surface, Kwark et al. (2010) Nanoparticle deposited surface, Mori et al. (2015) Si Nano-wire array, Lu et al. (2011)

FIGURE 3.4.7 Relationship between the CHF and the size of heated surfaces with various surface modifications.

surface modification for CHF enhancement was confirmed to be an HPP installed on an NDS [24]. Under the best-performing surface modifications, the CHF for L0 5 4.1, 12.2, and 20.4 (10-mm-, 30-mm-, and 50-mm-diameter surfaces, respectively) was enhanced up to 2.9-, 2.0-, and 1.9 times (3.1, 2.3, and 2.2 MW/m2, respectively) compared with Zuber’s CHF prediction. Therefore, high heat flux removal for a large heated surface can be achieved by installation of an HPP on the deposited nanoparticles [24].

3.4.3 FURTHER CHF ENHANCEMENT TECHNIQUES BY HPP 3.4.3.1 TWO-LAYER STRUCTURED HPP According to a previous study we conducted [20], the second and third terms on the right-hand side of Eq. (3.4.3) are negligible when the size in the vapor escape channels is of millimeter order, and the equation to predict the CHF can be simplified as qCHF 5

2σKρl hfg Aw Qmax 5 Δpl 5 A reff μl δh A

(3.4.9)

According to Eq. (3.4.9), the CHF is moved toward the infinite value at height δh of zero. However, the pool boiling CHF should be the same with that of plain surface (1.0 MW/m2) when the height δh of HPP is approaching to zero. This contradiction is caused by the fact that the capillary limit model does not consider the unsteady nature of the pool boiling near the CHF condition,

3.4.3 FURTHER CHF ENHANCEMENT TECHNIQUES BY HPP

221

as pointed out by Haramura and Katto [25]. Therefore, this signifies that there is an optimum height of HPP for CHF enhancement in a pool boiling. Accordingly, in order to prevent the inside of the HPP from drying out during the bubble hovering period on the plate, Mori et al. [26] pointed out that HPPs for CHF enhancement in saturated pool boiling must be constructed by the superposition of two kinds of porous materials (see Fig. 3.4.8), and each of the HPPs must fulfill two conditions. First, a HPP simply attached to a heated surface should have very fine pores to supply water to the heated surface due to strong capillary action, and the plate thickness should be as thin as possible to decrease the frictional pressure drop caused by internal water flow. Second, the other HPP, stacked on top of the thin HPP, needs to be structured to hold a sufficient amount of water in order to prevent the inside of the HPP from drying out during the bubble hovering period on the HPP.

3.4.3.2 COMBINATION OF HPP, NANOPARTICLE-COATED SURFACE, AND HONEYCOMB SOLID STRUCTURES (HSSs) IN PURE WATER [27] The experiments have been performed to clarify the effect of heated surface modification by NDS, honeycomb solid plate, and HPP attachment (see Fig. 3.4.9), on CHF enhancement as shown in Table 3.4.1. Fig. 3.4.10 illustrates the results of CHF values obtained from a pool boiling experiment with different heated-surface conditions. As can be seen in the figure, CHF is enhanced for all surface modifications in comparison with a plain surface (0.95 MW/m2). It was found that the combination of three elements (NDS 1 HPP 1 HSS) show a higher CHF than that obtained with other surface modifications. In conclusion, the following mechanisms are important for the CHF enhancement in a saturated pool boing. Namely, CHF is enhanced by (1) good wettability of the heated surface contributed to by nanoparticle-deposition, (2) automatic liquid supply by capillary action, and (3) selection of the cell size (vapor escape channel size) taking hydrodynamic theory into consideration.

FIGURE 3.4.8 Schematic drawing of two-layer structured honeycomb porous plate.

222

CHAPTER 3 CHF—TRANSITION BOILING

FIGURE 3.4.9 Schematic drawing of (A) HPP, (B) honeycomb solid structure, (C) nanoparticle deposition in surface modification.

Table 3.4.1 Experimental Matrices and Their Abbreviations Abbreviations

Surface Modification Details

PS NDS HSS HPP NDS 1 HSS NDS 1 HPP HPP 1 HSS NDS 1 HPP 1 HSS

Plain surface Nanoparticle-deposited surface Honeycomb solid structure attachment Honeycomb porous plate attachment Honeycomb solid structure attachment on nanoparticle-coated surface Honeycomb porous plate attachment on nanoparticle-coated surface Honeycomb solid structure attachment on honeycomb porous plate Honeycomb solid structure and honeycomb porous plate attachment on nanoparticle-coated surface

qCHF (MW/m2)

2

P = 0.1 MPa, heated surface diameter: 30mm, distilled water

1.87

*2.47 1.98 2.06 1.64

1.32 1.51

1 0.95

0

PS

NDS

NDS+HPP

–1

HSS HPP+HSS

HPP

Heated surface conditions

FIGURE 3.4.10 CHF values with different heated surface modification.

NDS+HSS

NDS+HPP+HSS

3.4.3 FURTHER CHF ENHANCEMENT TECHNIQUES BY HPP

223

3.4.3.3 COMBINATION OF HPP AND NANOFLUID [21]

Temperature in TC1 (°C)

Temperature in TC1 (°C)

For CHF enhancement in a real IVR application, CHF performance must be considered for conditions such as an HPP in water with fine particles, rather than pure water, because the HPP may become clogged with particles, resulting in the reduction of CHF. Accordingly, durability tests have been performed for the case of a HPP using nanofluid. Fig. 3.4.11 shows the time changes of temperature in TC1 which was installed 10.0 mm below the boiling surface resulting from the addition of nanofluid to pure water in the presence of an attached HPP. The experiment was conducted as follows. First, 900 mL of distilled water was boiled in the presence of an attached HPP. After a steady state was achieved, 100 mL of condensed nanofluid at room temperature was added to boiling pure water so that the final concentration was 0.001 vol.% or 0.1 vol.%. Heat flux was set to approximately 1.8 MW/m2, which was less than the CHF for the case of an attached HPP in pure water. Interestingly, CHF did not occur under either experimental condition for more than 2 h. The wall temperature increased suddenly just after the addition of nanofluid because the nanoparticles were deposited on the heated surface. The thickness of nanoparticle deposition related to thermal resistance depends on the nanofluid concentration, which is why the temperature increment in thicker nanofluid (0.1 vol.%) is higher than that in thinner nanofluid (0.001 vol.%). The temperature in TC1 then saturates at approximately 100 min in both cases. The amounts of nanoparticles deposited on and detached from the heated surface are considered to be approximately the same. Subsequently, CHF experiments were performed because no burnout is observed under these conditions. Fig. 3.4.12 shows the relationship between the CHF and concentration of nanofluid. As shown in this figure, for the case of a nanofluid only, the CHF increases up to 1.7 MW/m2 (pure water: 1.0 MW/m2), and the CHF is not affected by the nanofluid concentration. Conversely, the CHF is increased up to more than 2 MW/m2 by attaching an HPP to the heated surface in pure water as reported in a previous study [20]. The CHF with an HPP increases as the nanofluid concentration increases, and, surprisingly, the CHF reaches approximately 3.2 MW/m2 at maximum for 0.1 vol.% nanofluid. The CHF was increased significantly, by approximately three-times that for the case of pure water on a plain surface.

(A) Honeycomb porous plate with nanofluid (TiO2, 0.001 vol.%)

180

q =1.8 MW/m 2, P = 0.1 MPa 170

160 0

50

100 t (min)

150

180

170

(B) Honeycomb porous plate with nanofluid (TiO2, 0.1 vol.%)

160

q =1.8 MW/m , P = 0.1 MPa

2

0

50

100

t (min)

FIGURE 3.4.11 Time variation of TC1 just after the addition of nanofluid to pure water (final nanofluid concentration: (A) 0.001 vol.%, (B) 0.1 vol.%.

150

224

CHAPTER 3 CHF—TRANSITION BOILING

4

Honeycomb porous plate Plain surface

q (MW/m2)

3

2

1

0

0

0.1 0.001 Volume concentration (%)

FIGURE 3.4.12 Schematic drawing of two-layer structured honeycomb porous plate.

FIGURE 3.4.13 SEM images of the bottom surface of a honeycomb porous plate (A) before the boiling experiment and (B) after the boiling experiment (nanofluid: 0.1 vol.%).

Detailed SEM observations were carried out in order to clarify the behavior at the clearance between the HPP and the heated surface. Fig. 3.4.13 shows SEM images below the surface of the HPP attached to the heated surface (a) before and (b) after the CHF experiments for 0.1 vol.% nanofluid. As shown in the figures, nanoparticles were deposited beneath the HPP after the experiment. Moreover, microchannels of several tens of micrometer in width were formed just below the HPP. Microchannels formed near the heated surface may decrease the flow resistance for escaping vapor in the porous layer due to nanoparticle deposition, resulting in increased CHF enhancement.

NOMENCLATURE

225

Based on the above discussion, the CHF enhancement mechanism resulting from the combination of an HPP and a nanofluid is considered as follows. A nanoparticle deposition layer is formed on the heated surface. The surface wettability and capillary wicking performance are improved due to the NDS. Therefore, dry-out is retarded due to nanoparticle deposition once a liquid is supplied by gravity to the heated surface through vapor escape channels from the top surface, in addition to this effect, liquid is supplied to the heated surface due to capillary action by the HPP, as shown in previous studies [20,24], resulting in significant CHF enhancement. As a result of the attachment of an HPP to a heated surface in a nanofluid, CHF enhancement in saturated pool boiling occurs due to the effects of wettability, capillary wicking, the inflow of liquid through vapor escape channels, and vapor escaping macro- and microchannels. The exact contribution of each effect has not yet been clarified.

3.4.4 CONCLUSION CHF enhancement in saturated pool boiling is a result of the effects of extended surface area, nucleation site density, wettability, capillary wicking, and change of hydrodynamic wavelength. The exact contribution of each effect has not yet been clarified. A number of combined techniques for CHF enhancement have been proposed. In this section, CHF enhancement technique using HPP in saturated pool boiling was introduced. A honeycomb-structured porous plate is commercially available as a filter for purifying exhaust gases from combustion engines, and this method can be applicable to high heat flux removal (up to approximately 3.2 MW/m2 combining the HPP and nanofluid) for large heated surfaces. Moreover, several further CHF enhancement techniques by HPP were shown in this section.

NOMENCLATURE Aw dV hfg K L L0 M P R reff q qCHF Tsat Δpa Δpc;max Δpl Δpv ΔTSAT

contacted area of the HPP with the heated surface vapor channel width latent heat of evaporation permeability characteristic heater length dimensionless heater size molecular mass pressure universal gas constant effective pore radius heat flux critical heat flux the saturation temperature accelerational pressure drop caused by phase change from liquid to vapor maximum capillary pressure frictional pressure drops caused by the liquid flow in the porous medium frictional pressure drops caused by the vapor flow through the channels superheat

226

CHAPTER 3 CHF—TRANSITION BOILING

σ μl δh ρl ρv CHF HPP NDS HSS PS

surface tension viscosity of the liquid height of HPP density of a liquid density of the vapor critical heat flux honeycomb porous plate nanoparticle deposited surface honeycomb solid structure attachment plain surface

REFERENCES [1] W. Gambill, J. Lienhard, An upper bound for the critical boiling heat flux, J. Heat Transfer 111 (3) (1989) 815
818. [2] T. Semenic, I. Catton, Experimental study of biporous wicks for high heat flux applications, Int. J. Heat Mass Transfer 52 (21
22) (2009) 5113
5121. [3] M. Hashimoto, H. Kasai, K. Usami, H. Ryoson, K. Yazawa, J.A. Weibel, et al., Nano-structured twophase heat spreader for cooling ultra-high heat flux sources, in: the 14th International Heat Transfer Conference, Washington, DC, 2010. [4] J. Weibel, S. Kim, T.S. Fisher, S.V. Garimella, Carbon nanotube coatings for enhanced capillary-fed boiling from porous microstructures, Nanoscale Microscale Thermophys. Eng. 16 (1) (2012) 1
17. [5] N. Zuber, Hydrodynamic aspects of boiling heat transfer AECU-4439, Physics and Mathematics, US Atomic Energy Commission, 1959. [6] T. Semenic, High Heat Flux Removal Using Biporous Heat Pipe Evaporators, University of California, Los Angeles, 2007. [7] J.L. Rempe, K.Y. Suh, F.B. Cheung, S.B. Kim, In-vessel retention of molten corium: lessons learned and outstanding issues, Nucl. Technol. 161 (2007) 210
267. [8] M. Arik, A. Bar-Cohen, Effusivity-based correlation of surface property effects in pool boiling CHF of dielectric liquids, Int. J. Heat Mass Transfer 46 (20) (2003) 3755
3764. [9] H.S. Ahn, M.H. Kim, A review on critical heat flux enhancement with nanofluids and surface modification, J. Heat Transfer 134 (2) (2012) 024001. [10] J.N. Chung, T. Chen, S.C. Maroo, A review of recent progress on nano/micro scale nucleate boiling fundamentals, Front. Heat Mass Transfer 2 (2) (2011) 1
19. [11] R. Kamatchi, S. Venkatachalapathy, Parametric study of pool boiling heat transfer with nanofluids for the enhancement of critical heat flux: a review, Int. J. Thermal Sci. 87 (2015) 228
240. [12] H. Kim, Enhancement of critical heat flux in nucleate boiling of nanofluids: a state-of-art review, Nanoscale Res. Lett. 6 (1) (2011) 415. [13] Y.W. Lu, S.G. Kandlikar, Nanoscale surface modification techniques for pool boiling enhancement: a critical review and future directions, Heat Transfer Eng. 32 (10) (2011) 827
842. [14] S.M.S. Murshed, C.A. Nieto de Castro, M.J.V. Lourenc¸o, M.L.M. Lopes, F.J.V. Santos, A review of boiling and convective heat transfer with nanofluids, Renew. Sustain. Energy Rev. 15 (5) (2011) 2342
2354. [15] C.M. Patil, S.G. Kandlikar, Review of the manufacturing techniques for porous surfaces used in enhanced pool boiling, Heat Transfer Eng. 35 (10) (2014) 887
902. [16] X.-Q. Wang, A.S. Mujumdar, Heat transfer characteristics of nanofluids: a review, Int. J. Thermal Sci. 46 (1) (2007) 1
19. [17] R.L. Webb, The evolution of enhanced surface geometries for nucleate boiling, Heat Transfer Eng. 2 (3
4) (2007) 46
69. [18] J.M. Wu, J. Zhao, A review of nanofluid heat transfer and critical heat flux enhancement—Research gap to engineering application, Progr. Nucl. Energy 66 (2013) 13
24.

3.5.1 INTRODUCTION

227

[19] S.G. Liter, M. Kaviany, Pool-boiling CHF enhancement by modulated porous-layer coating: theory and experiment, Int. J. Heat Mass Transfer 44 (22) (2001) 4287
4311. [20] S. Mori, K. Okuyama, Enhancement of the critical heat flux in saturated pool boiling using honeycomb porous media, Int. J. Multiphase Flow 35 (10) (2009) 946
951. [21] S. Mori, S. Mt Aznam, R. Yanagisawa, K. Okuyama, CHF enhancement by honeycomb porous plate in saturated pool boiling of nanofluid, J. Nucl. Sci. Technol. (2015) 1
8. [22] S. Mori, L. Shen, K. Okuyama, Effect of cell size of a honeycomb porous plate attached to a heated surface on CHF in saturated pool boiling, the 14th International Heat Transfer Conference, ASME, Washington, DC, 2010. [23] S.M. Kwark, M. Amaya, R. Kumar, G. Moreno, S.M. You, Effects of pressure, orientation, and heater size on pool boiling of water with nanocoated heaters, Int. J. Heat Mass Transfer 53 (23
24) (2010) 5199
5208. [24] S. Mori, S. Mt Aznam, K. Okuyama, Enhancement of the critical heat flux in saturated pool boiling of water by nanoparticle-coating and a honeycomb porous plate, Int. J. Heat Mass Transfer 80 (2015) 1
6. [25] Y. Haramura, Y. Katto, A new hydrodynamic model of critical heat flux, applicable widely to both pool and forced convection boiling on submerged bodies in saturated liquids, Int. J. Heat Mass Transfer 26 (3) (1983) 389
399. [26] S. Mori, N. Maruoka, K. Okuyama, CHF enhancement of pool boiling using a honeycomb porous plate with two-layer structure, in: 9th Minsk International Seminar “Heat Pipes, Heat Pumps, Refrigerators, Power Sources”, Minsk, Belarus, 2015. [27] S.M. Aznam, S. Mori, K. Okuyama, The effect of nanoparticle deposited surface, a honeycomb solid structure and a honeycomb porous plate on the critical heat flux in a saturated pool boiling, in: The Ninth Korea-Japan Symposium on Nuclear Thermal Hydraulics and Safety, Buyeo, Korea, 2014.

DEPENDENCE OF CRITICAL HEAT FLUX ON HEATER SIZE

3.5 Masahiro Shoji University of Tokyo, Tokyo, Japan

3.5.1 INTRODUCTION Heat transfer of nucleate boiling locally fluctuates on a heated surface. It is also not uniform in time. So the heat flux usually used is the value averaged both in time and space. Most of the

228

CHAPTER 3 CHF—TRANSITION BOILING

boiling performance and knowledge has been obtained by the experiments or analysis of steady state or quasi-steady state. Even for such cases, the averaging is required at least for the space. Namely, the average heat flux is evaluated by q5

1 A

ð qðsÞds

(3.5.1)

A

where “A” represents the integration area taken on a heated surface. For the average to have stochastically meaningful results, “A” must be sufficiently large and there is a minimum size, i.e., Amin. Amin may be large at low heat flux nucleate boiling since nucleation sites are apart. In contrast, at high heat fluxes including critical heat flux (CHF), Amin would be relatively small since the bubbles or vapor masses generate densely, neighboring each other closely. If the heater size is equivalent to or less than this Amin, the influence of the heater size on boiling heat flux becomes significant. This is the ‘heater size effect’ of boiling heat transfer. The nucleate boiling is the efficient heat-transfer mode of boiling, and the upper limit of it is CHF. CHF is important for the engineering applications because it relates to the safety problem of thermal damage of the heater. So much attention has been paid to the CHF in the past boiling researches and much knowledge has been accumulated. The size effect of CHF has historically been correlated in the form of q 

qCHF qCHF 5 5 fnðL0 Þ qInfinite flat plate qZuber

where π qZuber 5 ρV hfg 24

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4 ðρL 2 ρV Þgσ ; ρV 2

(3.5.2)

L L0  pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi σ=ðρL 2 ρV Þg

The formula (3.5.2) was firstly introduced to correlate CHF data on cylinders by Bobrovich et al. [1] and Lienhard and Watanabe [2] independently, and has been successfully used until today. CHF is affected by many parameters except heater size. The parameters include: system pressure, gravity, liquid properties, and liquid subcooling, heater material, gas or oil contaminations in liquid, heater surface properties such as roughness and wettability due to oxidization and fouling, etc. Among them, the effects of system pressure, gravity and liquid properties may be considered as being included in the correlation (see Eq. 3.5.2). Actually, in the correlation (see Eq. 3.5.2), the effects of system pressure may be evaluated via ρv ðρL Þ, the effects of gravity via g, and liquid properties via ρL ; ρv ; hfg , and σ. It is noted here that the effects of heater material and the surface properties are not directly included in the correlation (see Eq. 3.5.2). In particular, the surface properties of the heater are nuisance factors that are difficult to deal with. Boiling research has actively been performed over the past 80 years, and numerous papers dealing with the CHF have been published. Most of the researches at an early stage until 1980 concern boiling on wires or cylinders. The experimental system employing a wire as a heater is the simplest system and it is easy to perform the experiment in a laboratory since the required power is small, and it is easy to observe the phenomena and to address the fundamental issues of boiling and heat transfer. Under these situations, the main focus of this sub-chapter will be on the CHF of pool saturated boiling on a wire or a cylinder. As the researches of CHF on plates and other shapes and configurations are limited, only a brief survey will be given in the later sections.

3.5.2 CHF ON WIRES AND CYLINDERS

229

In this sub-chapter, the term “wire” represents the cylindrical heater of small diameter and “cylinder” the cylindrical heater of relatively large diameter.

3.5.2 CHF ON WIRES AND CYLINDERS 3.5.2.1 AVAILABLE CHF DATA CORRELATIONS Boiling has been studied actively in the past relating to the applications to nuclear, chemical, electronic, and other industries. Many of the researches concern the boiling on a wire or a cylinder, and numerous CHF data have been accumulated and published in the literatures. The correlation of CHF data was reported by Kutateladze et al. [3], Sun and Lienhard [4], Bakhru and Lienhard [5], Park and Bergles [6], Di Marco and Grassi [7] and Sasaki et al. [8]. In the correlations, data of CHF from many sources for various liquids, various gravities and various pressures are correlated in the form of Eq. (3.5.2) as q 

qCHF qCHF p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 5 f ðR0 Þ 5 4 qZuber ðπ=24ÞρV hfg ððρL 2 ρV ÞgσÞ=ρV 2

where

rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi σ R0  d=2 ðρL 2 ρV Þg

All of the correlations are summarized in Fig. 3.5.1 in which only the data range (upper and lower envelopes of the plotted data) is shown for simplicity. The detailed information about the data and the data range in each correlation are summarized in Table 3.5.1. The correlation of later years essentially involves the data in the former correlations. It is especially mentioned here that Hong BakhruDi-Marco-Grassi Lienhard 2.0

Park-Bergles Park-Bergles

qCHF’

Kutateladze

1.0 Sun-Lienhard Park-Bergles Sasaki-Shoji Mohan-Ro 0.0

0.01

Sun-Lienhard 0.1

1.0 R’

FIGURE 3.5.1 Correlations of CHF data on wires and cylinders.

10

230

CHAPTER 3 CHF—TRANSITION BOILING

Table 3.5.1 Data Range and Include Data in the Correlations for the CHF on Wires and Cylinders Researchers

Data Range 0

Kutateladze et al. [3]

0.003 , R , 8

Sun-Lienhard [4]

0.15 , R0 , 10, RN 5 3.47

Bakhru-Lienhard [5]

0.015 , R , 0.08

Park and Bergles [6]

0.003 , R0 , 12

DiMarco-Grassi [7]

004 , R0 , 0.5 0.006 , R0 , 0.045

Sasaki et al. [8] Shoji et al. [9]

0.01 , R0 , 0.35 0.015 , R0 , 0.4

Data Details Seven liquids (water, methanol, buthanol, propanol, ethanol, benzene carbon-tetrachloride) Nine liquids (water, acetone, methanol, ethanol, benzene, isopropanol, carbontetrachloride, nitrogen, oxygen) for 0.0123 , p , 0.0216 and g/ge , 1. Their own data: 4-inch-long Nichrome wire from 0.005 to 0.080 inch diameter (0.4 , R0 , 11.5), including four liquids (acetone, methanol, benzene, isopropanol) for centrifugal force elevated gravity, 1 , g/ge , 67.1 Data of Sun
Lienhard, Siegel
Howell, Kutateladze. Their own data for Pt wire: 0.0076 , R0 , 0.0806 (1 mm diameter). Five liquids (acetone, benzene, methanol, isopropanol, water) for g , ge 2377 data for 0.003 , R0 , 12, 47 data sources. Their own data: 10 liquids: acetone, benzene, isopropanol, methanol, water, ethanol, N2, O2, R-113, R-11 20 sources, over 150 data, three correlations of Sun
Lienhard, Hong, Muhan
Rao Four sources of Elkasabgi
Lienhard, three correlations of Sun
Lienhard, and Hong, Muhan
Rao for two liquids of FC-72, R-113, and for 0.76 , p , 1.1 and 0.02ge , g , 1ge. Their own .70 data for platinum wire, gravity and pressure varied, slightly subcooled condition Data of seven investigators, mainly Japanese researchers Their own .1000 data for four liquids of water, ethanol, isopropanol, and butanol, and for four heater materials of platinum, stainless-steel, nichrome and kantal for a pressure range of 0.1
1.0 Mpa

Sasaki et al. mainly correlated the data of Japanese researchers including Nukiyama [10], the pioneer in the research of boiling. The equations to estimate CHF are given by Sun and Lienhard [4], Mohan Ro and Andrew [11], Park and Bergles [6], and Hong [12]. They are shown by the lines in Fig. 3.5.1, and the equations are summarized in Table 3.5.2. Most of them except the one by Sun and Lienhard are the empirical equations derived as the curve to best fit the data. As shown in Fig. 3.5.1, CHF data scatter is wide. However, except for the data of Di Marco and Andrew under microgravity, the CHF data show a similar trend in variation to that shown in Fig. 3.5.2 which was first pointed out by Di Marco and Grassi [7]. Some of the data of Di Marco and Andrew under microgravity were obtained under slightly subcooled conditions so that the CHF takes relatively higher values. The variation trend in Fig. 3.5.2 has the shape of an inverted capital ‘N,’ and it is possible to classify it into four regimes. Namely, with increasing wire diameter, in regime I of very small wires, CHF decreases; in regime II of small wires, CHF turns to increase;

3.5.2 CHF ON WIRES AND CYLINDERS

231

Table 3.5.2 Correlated Equations for the CHF on Wires and Cylinders

pffiffiffiffiffiffiffiffiffiffipffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qCHF 5 0:131 ρv hfg 4 σgðρl 2 ρv Þ pffiffiffiffiffi q 5 0:893 1 2:27expð23:44 R0 Þ for 0:15 , R0   22:2 23=4 q 5 1:60 for 0:02 , R0 , 0:15 R0 11 R02

Zuber [15] Sun-Lienhard [4] Mohan Rao and Andrews [11]

q 5 1:235 2 0:687X 2 0:590X 2 1 0:987X 3 1 0:673X 4 2 0:296X 5 2 0:330X 6 2 0:090X 7 2 0:008X 8 X 5 log R0 pffiffiffiffiffi q 5 6:79 1 9:01expð22:56 R0 Þ for 0:15 , R0 , 3:5

Park and Bergles [6] Hong et al. [12] q 5

qCHF qCHF;Zuber

5

K 0:131

qCHF where K 5 Kutateladze number 5 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4 ρv hfg

σgðρl 2 ρv Þ

qCHF/qZuber

Data scatter: large

Trend is not clear

Infinite surface

I II

III R’1

IV

R’2

(R’3) ln R’

FIGURE 3.5.2 Variation trend of CHF dependence on heater size.

in regime III, CHF turns around to decrease and tends gradually to the value of Zuber [15] for the infinite surface (regime IV). The values of R0 at the boundary of the regimes are summarized by Di Marco and Grassi [7] as shown in the upper table of Table 3.5.3. If we estimate those values from the correlations in Fig. 3.5.1, they take the values as given in the lower table of Table 3.5.3. It is mentioned here that the probable value of R0 1 is around 0.02, R0 2 around 0.2 and R0 3 around 3
4. The actual wire diameters corresponding to those values are approximately 0.1, 1.0, and 15 mm in water, respectively. In organic liquids, they become smaller as the capillary length is smaller.

3.5.2.2 RECENT EXPERIMENTAL STUDY AND RESULTS The variation in Fig. 3.5.2 is acceptable but yet the data is widely scattered, especially in regimes I and II, and so the definite variation trend is not clear enough. To confirm and to find the definite variation trend in the small wire regimes of I and II, Shoji and his coworkers [14] have recently performed systematic experiments by changing parameters in wide ranges. They employed four

232

CHAPTER 3 CHF—TRANSITION BOILING

Table 3.5.3 The Values of R0 at the Boundary of the Regimes Researcher 

Mohan Rao and Andrews [11] Lienhard & Dhir [13] Kutateladze et al.† [3] Sun and Lienhard† [4] Park-Bergles [6]† DiMarco-Grassi [7]† Sasaki et al.† [8] 

R2

R3

0.02 0.03 0.023 (0.02) 0.04 0.02 0.03

0.5 0.12 0.25 0.15 0.20 0.15
0.20 0.10

From DiMarco-Grassi; †from data correlations.

Water Ethanol Butanol IsoPropanol

Sun-Lienhard

qCHF / qZuber

2

BahkuLienhard Hong

MohanRao

Water : Pt : SUS : Ni-Cr

SasakiShoji 1

Sun-Lienhard Over 900 data

Kutateladze 0 0.01

Over 1000 Water data 0.1

1

0.1 MPa 0.5 Mpa 1.0 MPa 10

R’

FIGURE 3.5.3 Data correlation of all CHF data over 1000 effects of surface finish.

kinds of test heater materials (platinum, stainless-steel, nichrome, and tungsten), four test liquids (water, methanol, ethanol, and butanol), and have accumulated CHF data by changing wire diameter from 0.05 to 2.0 mm under various system pressures from 0.05 to 1.0 MPa and for various liquid subcoolings from 0 K to 50 K. Over 1000 CHF data have been accumulated in the experiments and they are plotted in Fig. 3.5.3. Although the bubbling features and aspects of boiling are different depending on the parameter employed, CHF data are rather well correlated in the relationship

3.5.2 CHF ON WIRES AND CYLINDERS

233

of the form of Eq. (3.5.2). It is noted that the effects of heater material are not included in the Eq. (3.5.2) so that the results of Fig. 3.5.3 indicate that its effect on CHF is not significant. As seen in Fig. 3.5.3, data scatter in very wide. To find the reason for the scatter, Shoji et al. conducted another test by paying attention to the nuisance variables that are presumed to affect CHF. Namely, using a platinum
water boiling system, they repeated the tests under the same experimental conditions to investigate the influence of cleanliness of test liquid, freshness of test heater, heater surface roughness, and heater annealing. As a result, they found that only the effect of surface roughness control is significant and polishing the surface to have uniform roughness decreases the data scatter. It should be pointed out here that the value of CHF is different depending on the roughness level and generally takes a lower value on the surface having uniform roughness. It is also mentioned that the band of data scatter differs depending on the size of the heater and the data fluctuation is small on very small wires whereas the fluctuation is large on relatively large-diameter wires. The data carefully obtained by paying attention to surface treatment are correlated in Fig. 3.5.4. From the results, Shoji et al. concluded that the curious dependence of CHF on wire size comes from the possible existence of two different CHF mechanisms, i.e., the one on small wires and the other on relatively large cylinders. Also they presumed that the CHF dependence on wire size in q vs R0 may be classified into three regions, i.e., the two regions corresponding to the two CHF mechanisms and the transition region between the two. In the transition region, the two mechanisms coexist in a random manner on the heater so that the value of CHF is likely to scatter over a wide range. In the region of large cylinders in Fig. 3.5.4, the so-called hydrodynamic CHF mechanism (models of Zuber, Kutateladze, and Haramura and Katto) holds and governs CHF. In contrast, in the region of small wires, another type of mechanism would determine the critical condition but the mechanism has not been made clear and remains unknown.

Present data ShojiSasaki

2

qCHF / qZuber

BakhruLienhard

Pt wire no-polish polish SUS pipe polish Sun-Lienhard Over 900 data

1

IV

III

Estimated model Shoji et al. over 1000 data II (I)

Small.d.. Transition 0 0.01

Large d.

0.1

1 R’

FIGURE 3.5.4 Correlation of CHF data: the final results.

10

234

CHAPTER 3 CHF—TRANSITION BOILING

Fig. 3.5.5 shows the photographs of boiling for different wire diameters in the case of the platinum-wire
water system. When the wire diameter is small, only isolated bubbles appear, and when the wire becomes large, say d . 0.40 mm (R0 . 0.08), the coalescence vapor bubbles cover the wire as in the case of a large flat surface. In case of a small wire, nucleate boiling occurs only in the narrow region of boiling curve close to the critical point. At the critical point, independent of wire diameter, the transition from nucleate to film boiling takes place in most cases, but in some cases the wire burns out.

3.5.2.3 DISCUSSIONS AND REMAINING PROBLEMS As for the CHF on a very small wire, Bakhru and Lienhard [5] already pointed out the following features. Namely, when nucleation occurs on a wire, the bubbles grow and spread horizontally until the wire is partially blanketed with a vapor patch. The blanketed portions of the wire are fully covered with vapor and there is no liquid-to-heater contact. The vapor patches flicker on and off from place to place. As the heat flux increases, the patches spread steadily until the wire is totally blanketed, then transition to film boiling takes place. Generally, the regimes of nucleate boiling and transition boiling are absent, and in place, three modes of heat removal (natural convection, a mixed natural convection and film boiling, and pure film boiling) are identified. Even if the regimes of nucleate and transition boiling exist, boiling aspects and mechanisms may be quite different in character where the force of gravity is over-balanced by the capillary force. The transition from nucleate to film boiling takes place but the boiling curve becomes continuous and the maximum

FIGURE 3.5.5 Variation of boiling aspects with wire diameter in platinum wire
water system.

3.5.2 CHF ON WIRES AND CYLINDERS

235

and the minimum heat fluxes vanish. The transition is clear in water but in organic liquids, it is not so clear. The critical condition takes place at a single bubble site on a wire. Namely, the hydrodynamic CHF theories such as those of Zuber [15], Sun and Lienhard [4], and Haramura and Katto [16] break down and another type of mechanism governs the critical condition. So the values of CHF in this region hitherto reported may be either the heat flux at the inception of film boiling, or the heat flux when the heater temperature begins to increase, or the heat flux when the heater first glow red. These boiling features were observed and confirmed also by Shoji et al. [14] and give valuable information as to when we consider the unknown mechanism of CHF and formulate its model. The dimensionless radius employed in the CHF data correlation may be considered as the ratio of heater wire radius against vapor bubble size. Actually, according to Friz [17], Cole and Rohsenow [18], and Katto and Yokoya [19], the departure size of an isolated bubble as well as a vapor mass (a coalescence bubble) is a function of capillary length. The dimensionless radius of the departing bubble Dd, is given as R0d 5

Dd 5 0:01045φ 2lcr

(3.5.3)

by Friz where Dd is the departure diameter of an isolated bubble, lcr is the capillary length and φ is the contact angle (degrees). It is given by Cole and Rohsenow as R0d 5

Dd ρ cPL Tsat 5 7:5 3 1025 Ja1:25 for water; and Ja 5 l : Jacob number 2lcr ρv hfg

(3.5.4)

where ρL , ρv , cpL , hfg , and Tsat are the density of liquid, density of vapor, specific heat of liquid, latent heat of vaporization and saturation temperature of liquid, respectively. If we assume here φ 5 60280 for saturated water on a heated surface (such as a copper), Eqs (3.5.3) and (3.5.4) yield R0d 5 0:63 2 0:84 and R0d 5 0:484;

respectively. These values are for a flat surface, and if we consider the equivalent radius of the wire in which the periphery is equal to the departure bubble size, the respective dimensionless radius Re ð 5 R0d =πÞ becomes R0e 5 0:20 2 0:27ðFrizÞ and R0e 5 0:154 ðCole and RohsenowÞ:

In the CHF data correlation of Fig. 3.5.4, these wire radii coincide rather well with the size where CHF mechanisms change from the one to the other. As for the departure diameter of a vapor mass, Katto and Yokoya [19] give the following expression: R0d

 

Dd 2 11 ρL 11 5 5 0:0385Ar 16 ρv 2lcr

(3.5.5)

where Ar represents the area ratio of the heated surface covered by a macrolayer at the base of a vapor mass. As is usual, Ar takes the value of 0.2
0.3, the dimensionless departure size of a vapor mass and its corresponding equivalent wire radius becomes R0d 5 1:6923:85 and R0e 5 0:5421:23, respectively. This equivalent radius coincides rather well with the value where CHF on a cylinder is close to the CHF on an infinite flat surface. By employing the departure bubble radius in place of capillary length, it may be possible to correlate CHF of subcooled pool boiling in the same form as the case of saturated pool boiling.

236

CHAPTER 3 CHF—TRANSITION BOILING

Gogonin-Kutateladze

Dimensionless CHF, qCHF /qZuber

2.0

Insulated backside Insulated backside: Ethanol Lienhard-Dhir

1.0

Gogonin-Kutateladze Insulated upper side 0 0.01

0.1

1.0

10

100

200

Dimensionless heater length, L’

FIGURE 3.5.6 CHF data correlations on flat plain plates.

3.5.3 CHF ON PLATES 3.5.3.1 CHF ON A PLAIN SURFACE The research on the size effect of CHF on a plate is rather limited. The exceptional studies of Lienhard and Dhir [13] and Gogonin and Kutateladze [20] are shown in Fig. 3.5.6. The detailed information of the data are summarized in Table 3.5.4. Data of Lienhard and Dhir includes the data of four sources, and the data of Gogonin and Kutateladze are for two liquids of ethanol and helium. Among the data of Gogonin and Kutateladze, in Fig. 3.5.6, the open symbols represent the data on upward-facing surfaces and the closed symbols on downward-facing surfaces. As is clear in the figure, CHF decreases monotonously with increasing size on an upward-facing surface and becomes almost constant in the region of L0 being larger than 2 or 3. In contrast, on a downward-facing surface, CHF monotonously decreases even when L0 becomes large. Thus, the CHF value changes depending on the surface orientation. Even if the size of the heater is identical, CHF on a plate differs depending also on the other situations and configurations of the shape of the surface (circle, square, or ribbon), side surface conditions, whether the side surface is insulated or not, and the supporting systems of the heated portion. These effects, however, have not yet been fully made clear.

3.5.3.2 CHF ON CHIPS WITH MODIFIED SURFACES Recently electronic devices loaded with highly integrated chips have been developed, and the cooling techniques for the chips with high power density have attracted attention and active research

3.5.3 CHF ON PLATES

237

Table 3.5.4 Data Information of the Correlations of CHF on Plain Plates Researchers

Data Range

Data

0

Lienhard-Dhir [13]

22 , L , 157

Gogonin-Kutateladze [20]

0.025 , L0 , 85

Four sources including Five liquids of acetone, n-pentane, carbontetrachloride, water, ethanol. Their own data: eight liquids of water, methanol, ethanol, isopropanol, aceton, benzene, n-pentane, carbon-tetrachloride) for 4 , g/ge , 17 Two liquids of ethanol and helium for p 5 0.1
5.2 Mpa, heater, thickness 0.5 mm, 150 mm long, width of 5
50 mm, insulated top side (downward facing), insulated bottom side (upward facing)

3.0

Dimensionless CHF, qCHF /qZuber

Mori et al. honeycomb porous

Mori et al. honeycomb porous on nanoparticle deposited

Kwark et al. 2.0

Rainey et al. nanoparticle deposited

Mori et al. plain 1.0

Data range of Gogonin-Kutateladze and Lienhard-Dhir Saylor et al. Rainey et al. plain FC-72 plain Correlation of Bar-Cohen-McNeil

Park-Bergles vertical chips 0 0.01

0.1

1.0

10

100

200

Dimensionless heater length, L’ FIGURE 3.5.7 CHF data correlations on chips.

into boiling has been made. In the research, the influence of size of the chip to the heat transfer was studied. CHF data of the representative researches of Park and Bergles [21] for plain chips, of Rayney and You [22], Saylor et al. [23], Kwark et al. [24], and Mori et al. [25] for chips with various modified surfaces, are plotted in Fig. 3.5.7 in comparison with Fig. 3.5.6. Here the modified surfaces include the surface of porous, honeycomb, and micropower deposited, and their

238

CHAPTER 3 CHF—TRANSITION BOILING

Table 3.5.5 Data Information of the Correlations of CHF on Chips Researchers Saylor et al. [23] Rainey and You [22] Kwark et al. [24] Mori et al. [25]

Bar
Cohen
McNeil [26] Park
Bergles [21]

Heater Surface Plain Microporous Nanoparticle deposited Nanoparticle deposited, honeycomb porous Honeyecomb porous on a nanoparticle deposited Correlation Vertical square chips one side insulated

Data Range 0

6 , L , 27 15 , L0 , 70 S 5 1.0 cm2, 4.0 cm2, 25 cm2 7 , L0 , 20 10 , L0 , 50 D 5 10 mm, 30 mm, 50 mm Infinite for L0 . 23 4 , H0 , 80  0:14 q 5 qCHF =qZuber 5 0:86 11 H152 03:29

Liquid FC-72 FC-72 Water Water

R113

combinations. The detailed information of the data and the test conditions are summarized in Table 3.5.5. In Fig. 3.5.7 and Table 3.5.5, the correlated equation of Bar-Cohen and McNail [26] derived to correlate the data of Saylor and You are included. As is clear from Fig. 3.5.7, the CHF variation trend with heater size in the case of plain chips is similar to the plain plates. The decreasing rate with the size in a small size region, however, seems to be sharper and the transition point from which CHF becomes constant is larger, about 10-times than that of a plain plate. Generally, the CHF on modified surfaces is highly enhanced especially in small chips, and it may be said that modification of the surface is a useful technique for the efficient cooling of high-density electronic chips.

3.5.4 CHF DATA CORRELATION ON HEATERS OF VARIOUS SHAPES AND CONFIGURATIONS CHF relates closely to the vapor removal patterns. Actually, Zuber’s CHF model [15] closely relate to the Taylor as well as the Helmholtz instability, both of which would be affected by the vapor removal pattern. In the CHF model of Haramura and Katto [16], CHF is governed by the macrolayer consumption which depends on the thickness of the macrolayer as well as the departure period of vapor mass, both of which are affected by the vapor removal pattern. Lienhard and Dhir [13] summarized the vapor removal patterns on various heater shapes and configurations, as shown in Fig. 3.5.8. In the case of flat surfaces, even if the size is the same, CHF takes different values depending on the shape (circular, square, or ribbon), the heater configuration (horizontal, vertical, or inclined), the heater supporting system (whether or not the insulating portion is attached to the periphery of the heater), and other affecting factors. In particular, on a vertical surface or a slender ribbon, CHF depends strongly on whether the side surface is insulated or not (one side is insulated or both sides are insulated). Actually, on a vertical plate, Park and Bergles [21] pointed out that CHF dependence on the width and the height are different. Lienhard and Dhir [13] presented the correlations for various shapes of heaters and configurations as shown in Fig. 3.5.9 and in Table 3.5.6.

3.5.5 PARAMETERS AND FACTORS AFFECTING CHF

239

FIGURE 3.5.8 Vapor removal patterns on various configuration heaters summarized by Lienhard and Dhir.

3.5.5 PARAMETERS AND FACTORS AFFECTING CHF In this sub-chapter, CHF on a wire or a cylinder set horizontally in a saturated liquid pool is discussed. In the CHF on a vertical wire, the length of the heater affects CHF relating to the shape of the vapor film periodically formed in columns along the heater. In the case of a flat surface, as was shown by Rainey and You [22], the inclination of the heated surface causes the reduction of CHF values. Thus the orientation of the heater must be considered when we discuss the heater size effects.

240

CHAPTER 3 CHF—TRANSITION BOILING

FIGURE 3.5.9 Correlations for various heater shapes and configurations, correlated by Lienhard and Dhir.

Table 3.5.6 Correlations Equations Derived by Lienhard and Dhir for Various Heater Shapes and Configurations Geometry Sphere Cylinder Plate Ribbon (vertical, two sides insulated) Ribbon (vertical, one side insulated)

Small Size pffiffiffiffiffi qCHF =qZuber 5 1:734= R0 pffiffiffiffiffi qCHF =qZuber 5 0:94= 4 R0 For long slender heaters pffiffiffiffiffi qCHF =qZuber 5 0:94= 4 P0 pffiffiffiffiffi qCHF =qZuber 5 0:18= 4 H 0 pffiffiffiffiffi qCHF =qZuber 5 1:4= 4 H 0

Large Size qCHF =qZuber 5 0:84 qCHF =qZuber 5 0:904 For large heaters qCHF =qZuber 5 0:90 For infinite heaters qCHF =qZuber 5 1:14 qCHF =qZuber 5 0:90 qCHF =qZuber 5 0:90

P, length of perimeter of cross section of long slender heater; H, vertical dimension of horizonatal ribbon.

As was indicated by Liaw and Dhir [27], heater surface wettability to the liquid (usually represented by the contact angle) has a strong influence on CHF. It is known that increasing the contact angle decreases the value of CHF. Thus the heater surface properties except the wettability including roughness, oxidation, and fouling must be considered when we discuss CHF. Depending on the liquid subcooling, CHF is different: it is well known that CHF increases with the increase in liquid subcooling. Unfortunately, however, the heater size effects of subcooled CHF

REFERENCES

241

have not been systematically investigated until now. The only exception to this statement may be the study and the discussion of Elkassabgi and Lienhard [28] for CHF on a wire in pool subcooled boiling, but no correlation was given. Considering that subcooled boiling is important for engineering applications, this remains an important problem to be solved in future.

3.5.6 SUMMARY AND CONCLUDING REMARKS 1. The size dependence of saturated pool boiling CHF on a wire or a cylinder is well correlated in the form of dimensionless CHF as a function of dimensionless radius. The variation with size shows a curious nature. CHF takes nearly a constant value at small diameters and with the increase in diameter, CHF starts to increases but turns to decrease at a certain diameter, and then gradually tends to the value for the infinite plate. The variation seems to be classified into three regions, i.e,. the one for small wires, the other for relatively large cylinders, and the region between the two. These regions would be caused by the possible existence of two different mechanisms of CHF. On the cylinders, the so-called hydrodynamic mechanism governs CHF but on small wires, while another mechanism, which is quite different from the hydrodynamic mechanism, determines the CHF. The latter mechanism has not yet been made clear and remains unknown. 2. Although the CHF on an upward-facing flat surface is correlated well in the same form between dimensionless CHF and dimensionless size, CHF data for small sizes are very limited. The data accumulation as well as a more detailed correlation of CHF on plates is required by considering the shape, orientation, configuration, heater supporting systems, and other affecting factors. 3. The CHF of subcooled boiling is important from the point of view of engineering applications. However, even in the simple mode of pool boiling, no correlation has been reported until today.

REFERENCES [1] G.I. Bobrovich, et al., Influence of size of heater surface on the peak pool boiling heat flux, J. Appl. Mech. And Tech., Phys. 4 (1964) 137
138. [2] J.H. Lienhard, K. Watanabe, On correlating the peak and minimum boiling heat fluxes with pressure and heater configuration, J. Heat Transfer 88 (1966) 94
100. [3] S.S. Kutateladze, et al., Influence of heater size on the peak heat flux in saturated liquids, Inz. Phyz. Zh 12 (1967) 569
575. [4] K.H. Sun, J.H. Lienhard, The peak pool boiling heat flux on horizontal cylinders, Int. J. Heat Mass Transfer 13 (1970) 1425
1439. [5] N. Bakhru, J.H. Lienhard, Boiling from small cylinders, Int. J. Heat Mass Transfer 15 (1972) 2011
2025. [6] K.A. Park, A.E. Bergles, Energy R.&D., Korean Institute of Energy and Resources, 9-4, 1986, p.16. See the article of “Elements of boiling heat transfer,” Boiling Heat Transfer, R.T. Lahey (Ed.), Elsevier Science Publishers, 1992, p. 414.

242

CHAPTER 3 CHF—TRANSITION BOILING

[7] P. Di Marco, W. Grassi, About the scaling of critical heat flux with gravity acceleration in pool boiling, in: 17th UIT National Heat Transfer Conference, Ferrara, June, 1999. [8] K. Sasaki et al., Critical heat flux on a fine heated wire in pool subcooled nucleate boiling, in: 43rd Japan National Heat Transfer Symposium, Nagoya, J233, 2006, pp. 567
568 (in Japanese). [9] M. Shoji et al., Critical heat flux on a horizontal wire, in: 50th Japan Heat Transfer Symposium, Sendai, E112, 2013, pp. 100
101 (in Japanese). [10] S. Nukiyama, The maximum and minimum values of the heat Q transmitted from metal to boiling water under atmospheric pressure, Trans. JSME 37 (206) (1934) 367
374. [11] P.K. Mohan Rao, D.G. Andrews, Effect of heater diameter on critical heat flux from horizontal cylinders in pool boiling, Can. J. Chem. Eng. 54 (1976) 403
412. [12] Y.S. Hong, et al., Critical heat flux mechanisms on small cylinders, Transport Phenomena in Heat Transfer Engineering, Begell House, New York, 1993, pp. 411
416. [13] J.H. Lienhard, V.K. Dhir, Hydrodynamic prediction of peak pool boiling heat fluxes from finite bodies, J. Heat Transfer 97 (1973) 152
158. [14] M. Shoji et al., 43rd Nagoya, 2006. J233, pp. 567
568; 44th Nagasaki, 2007, A240, pp. 335
336, and A241, pp. 337
338; 45th Tsukuba, 2008, D224, pp. 543
544, and D234, pp. 553
554; 46th Kyoto, 2009, B133, pp. 21
22, and B134, pp. 23
24; 47th Sapporo, 2010, G224, pp. 439
440; 48th Okayama, C221, pp. 335
336, 2011 (all in Japanese). [15] N. Zuber, Hydrodynamic aspects boiling heat transfer, AEC Report, AECU-4439, 1959. [16] Y. Haramura, Y. Katto, New hydrodynamic model of critical heat flux applicable widely to both pool and forced convection boiling on submerged bodies in saturated liquids, Int. J. Heat Mass Transfer 26 (1983) 379
399. [17] W. Friz, Maximum volume of vapor bubbles, Phys. Zeitschr. 36 (1935) 379
384. [18] R. Cole, W.M. Rohsenow, Correlations of bubble departure diameter for boiling of saturated liquids, Chem. Eng. Prog. Symp. Ser. 65
92 (1969) 211
213. [19] Y. Katto, S. Yokoya, Behavior of a vapor mass in nucleate and transition pool boiling, Heat Transfer Jpn. Res. 5-2 (1976) 45
65. [20] I.I. Gogonin, S.S. Kutateladze, Critical heat flux as a function of heater size for a liquid boiling in a large enclosure, J. Eng. Phys. 33 (1977) 1286
1289. Original: Trans. Inzhenerno-Fizicheskii Zhurnal, 33-5, 1977, 802
896. [21] K.A. Park, A.E. Bergles, Effects of size of simulated microelectronic chips on boiling and critical heat flux, J. Heat Transfer 110 (1988) 728
734. [22] K.A. Rainey, S.M. You, Effects of heater size and orientation on pool boiling heat transfer from microporous coated surfaces, Int. J. Heat Mass Transfer 44 (2001) 2589
2599. [23] J.R. Saylor et al., The effect of a dimensionless length scale on the critical heat flux in saturated pool boiling, ASME HTD-108, 1989, pp. 71
80. [24] S.M. Kwark, et al., Effects of pressure, orientation, and heater size on pool boiling of water with nanocoated heaters, Int. J. Heat Mass Transfer 53 (23
24) (2010) 5199
5208. [25] S. Mori, et al., Enhancement of the critical heat flux in saturated pool boiling of water by nanoparticlecoating and a honeycomb porous plate, Int. J. Heat Mass Transfer 80 (2015) 1
6. [26] A. Bar-Cohen, A. McNeil, Parametric effects of pool boiling critical heat flux in dielectric liquids, ASME Pool and External Flow Boiling, 1992, pp. 171
175. [27] S.P. Liaw, V.K. Dhir, Effect of surface wettability on transition boiling heat transfer from a vertical surface, in: Proc. 8-IHTC, vol. 4, 1988, pp. 2031
2038. [28] Y. Elkassabgi, J.H. Lienhard, Influences of subcooling on burnout of horizontal cylindrical heaters, J. Heat Transfer 110 (1988) 479
486. [29] S.S. Kutateladze, Heat transfer in condensation and boiling, USAEC Report, AECU-3370, 1952.

3.6.2 ATTEMPT TO ATTAIN STEADY TRANSITION BOILING

243

3.6

STABILITY OF TRANSITION BOILING

Yoshihiko Haramura Kanagawa University, Yokohama, Japan

3.6.1 INTRODUCTION Transition boiling is unstable if constant heat flux is applied to the heating surface as in electric heating. Since heat flux in the transition boiling region decreases with increasing wall temperature, occasional rise of wall temperature results in short heat removal, then makes the temperature higher. To maintain transition boiling in a steady manner, heat input must be controlled to overcome this unstable nature. There are three types of ways to keep wall temperature constant. The first is heating with condensing steam, as conducted by Berenson [1]. The second is electric heating accompanied by convective cooling, as conducted by Hotta and Issiki [2]. The last is automatic heat input control, as conducted by Peterson and Zaalouk [3], and Sakurai and Shiotsu [4] for platinum wire in the old days, and by Blum et al. [5] rather recently for a circular surface of a block. In the analyses shown below, the boiling curve is approximated linearly as qw 5 ΓðT 2 TN Þ; ðΓ , 0Þ

(3.6.1)

This condition is described with the inclined line in the upper figure of Fig. 3.6.1. The steady temperature distribution in the heater block is also shown in the bottom-right figure.

3.6.2 ATTEMPT TO ATTAIN STEADY TRANSITION BOILING BY LOW-RESISTANCE HEAT EXCHANGE 3.6.2.1 HEATING WITH STEAM The heat-transfer coefficient of condensing heat transfer is so large that the heat input to the wall decreases rapidly when the wall temperature rises. We can compensate therefore for a decrease in heat removal when wall temperature rises. Haramura [6], however, pointed out the importance of keeping steam temperature constant. The unstable heat-transfer characteristics in transition boiling may cause instability of steam temperature in a closed steam supply system. He postulated that the

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CHAPTER 3 CHF—TRANSITION BOILING

qw

Γ

z

Tw

Tw

z =H (boiling surface)

z =0 (heat input surface)

T∞

z

r

qw λ

T

FIGURE 3.6.1 Assumed boiling curve and steady tempearture profile.

FIGURE 3.6.2 Heat flow in a steam heating system [6].

boiling test system consists of a heater block and steam supplying vessel with water cooling (convective heat exchange) as shown in Fig. 3.6.2. Heat flows are written as Q1 5 Aw ΓðTw 2 TN Þ;

(3.6.2)

Q2 5 Aw K w ðTs 2 Tw Þ;

(3.6.3)

3.6.2 ATTEMPT TO ATTAIN STEADY TRANSITION BOILING

245

and Q3 5 AC K C ðTS 2 TC Þ;

(3.6.4)

where Aw is the area of the boiling surface and it is assumed to be the same as the condensing surface, AC is the surface area of the cooling coil, Kw and Kc are the overall heat-transfer coefficients from steam to the boiling surface and steam to cooling water. The condition to keep steady state is that net heat flow from any control volume increases when its temperature increases. It is written as Eq. (3.6.5) for the heated block and as Eq. (3.6.6) for steam. dQ1 dQ2 2 . 0: dTw dTw

(3.6.5)

dQ2 dQ3 dQ4 1 2 .0 dTs dTs dTs

(3.6.6)

Q4 is heat flow from the heater and is usually constant. In Eq. (3.6.6) derivative respect to Ts should not be performed as Tw is constant, but assuming that Tw varies as heat flow, as Q2 5 A K0 ðTs 2 TN Þ;

(3.6.7)

1 1 1 5 1 ; K0 Kw Γ

(3.6.8)

where

which is derived from Eqs (3.6.2) and (3.6.3) setting Q1 5 Q2 and eliminating Tw. K0 in Eq. (3.6.8) is negative when Eq. (3.6.9) is satisfied and Γ , 0. When Q4 is assumed constant (without automatic control of steam temperature), the conditions in Eqs (3.6.5) and (3.6.6) with Eq. (3.6.8) are written as Kw . ð2ΓÞ

and Ac Kc . Að2K0 Þ

or

  1 1 1 , 2 Ac Kc Að2ΓÞ AKw

(3.6.9)

(3.6.10)

Equation (3.6.10) shows the necessity of convective cooling from the steam-supplying vessel. It sometimes becomes necessary to cool with rather hot water to make AcKc large keeping the total cooling rate Q3 low. This convective cooling may be replaced by the relief of steam to the outside to make the steam pressure constant. It is also very important to make Kw large to eliminate instability. Since it is determined by the sum of heat resistances of condensation and heat conduction through the heater block, it is necessary to make them both as small as possible. In a steam heating system, temperature uniformity across the surface discussed in Section 3.6.4 will be attained independent of the surface size when the heater temperature is kept constant. Haramura [6] built an apparatus with a cooling coil and then measured the boiling curve for R-113 at atmospheric pressure. To reduce the heat resistance on the condensing surface, rotating wiper driven by steam jet was equipped. Using about 50 C cooling water and additional automatic control of steam temperature, he attained steady transition boiling up to about 20 kW/(m2 K) negative gradient.

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CHAPTER 3 CHF—TRANSITION BOILING

3.6.2.2 HEATING WITH CONVECTIVE COOLING/HEATING Hotta and Isshiki [2] attained steady transition boiling by electric heating with air cooling. The block diagram of their temperature control system is the same as that for steam heating except that heat flow Q4 in Fig. 3.6.2 is added directly to the heater block. Since Q4 is assumed constant and does not appear in the stability analysis of the heating system, the location of heat addition does not affect the stability. Further, the block diagram of the temperature control system is the same independent of whether convective heat transfer is used to cool or heat. To keep steady state, it is necessary to make the heat conductance to the cooling system large to overcome the negative resistance due to the transition boiling nature. However, heat resistance between the cooler wall and the boiling surface is also important because it may spoil the stability. Both Eqs (3.6.9) and (3.6.10) must be satisfied to establish steady transition boiling even in this system.

3.6.2.3 TEMPERATURE STABILIZATION BY CONDUCTION TO THE SURROUNDINGS FOR A SMALL SURFACE When a boiling surface is small, transition boiling characteristics, i.e., negative slope of boiling curve, are sometimes measured. It is considered that heat leakage to the surroundings stabilizes the instability. When the wall temperature rises in the transition boiling region, boiling heat flow decreases but heat conduction to the surroundings via a supporting or sealing element increases. Using the notations above, this situation corresponds to the case where Kw approaches infinity, Ac Kc is the conductance between the boiling surface and the surroundings, and Tc is the bulk temperature of the surroundings. In this case, the stability criterion is written as Ac Kc $ Aw ð2ΓÞ:

(3.6.11)

Ac Kc is not so large, but this condition can be satisfied to some negative slope
Γ when Aw is very small. It should be noted that Eq. (3.6.11) is valid when the surface temperature is uniform, and the precise condition should be derived by solving the heat conduction in the heater block and the surrounding elements.

3.6.3 AUTOMATIC TEMPERATURE CONTROL Automatic control is the best way to control heater temperature. Blum et al. [5] presented the stable criteria in PI (proportion and integral) control when sensor temperature just below the surface is fed back. The heater block has a stepwise change in cross-sectional area along the heat flow as shown in Fig. 3.6.3 [5]. The total height of the heater block is H, and the height of the wider portion is HS. The radii of the wider portion and the boiling surface are r1 and r2, respectively. They applied Laplace transform to one-dimensional unsteady heat conduction equation @T λ @2 T 5 @t ρcp @z2

(3.6.12)

3.6.3 AUTOMATIC TEMPERATURE CONTROL

247

FIGURE 3.6.3 Heater block of Blum et al. [5].

in a heater block with boundary conditions @T 5 q0 at heat input surface ðz 5 0Þ; @z

(3.6.13)

@T 5 ΓðT 2 TN Þ at boiling surface ðz 5 HÞ @z

(3.6.14)

2λ 2λ

and the continuation conditions of heat flow and temperature at the connecting plane, and derived the transfer function GIM(s) from heat input to the temperature of a sensor located at zM from the heat input surface as  

 1 r1 2 Γ sinh γðH 2 zM Þ cosh γðH 2 zM Þ 1 λγ r2 λγ ( GIM ðsÞ 5  2 )

 (3.6.15) Γ r1 Γ sinh γHS coshγðH 2 HS Þ 1 cosh γH 2 1 2 sinh γðH 2 HS Þ sinh γH 1 r2 λγ λγ

where γ 5 ðρcp s=λÞ1=2 . Their control system is a simple feedback loop shown in Fig. 3.6.4 and the transfer function of the controller is expressed as   1 1 GC ðsÞ 5 Kc 1 1 ; τ I s ð11τ 1 sÞ2

(3.6.16)

where τ 1 is the time lag of the circuit and it is assumed that the feedback system contains two time-lag elements. The stable condition is that all of the solutions of equation 1 1 GIM ðsÞGC ðsÞ 5 0

have negative-real values, i.e., the real part of each solution must be less than zero.

(3.6.17)

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CHAPTER 3 CHF—TRANSITION BOILING

Temperature

Heat flux Heater block

Power supply

Controller

FIGURE 3.6.4 Feedback system to control heater block temperature.

FIGURE 3.6.5 Stability limit. Theoretical and experimental limits are plotted. (τ I 5 6 s, τ 1 5 0.3 s. K1 is identical to Γ.) [5].

One of their results on stability criteria is shown in Fig. 3.6.5. There are lower and upper limits of gain to keep steady transition boiling. There is also a stable limit gradient (Γ  235 kW/m2) of the boiling curve at which no stable gain exists any more for a given dimension and material of the heater block. Blum et al. [7] showed the effect of τ I and τ 1 for a simple columnar block. Marquart and Auracher [8] dealt with a thick tube, where boiling occurred in a tube and the outer surface is heated. In this study, a cylindrical coordinate was used.

3.6.4 TEMPERATURE UNIFORMITY ACROSS THE SURFACE 3.6.4.1 IN THE CASE OF STEADY BOILING Even in the case where steady transition boiling is maintained with automatic temperature control, only the uniform mode is usually stabilized. So other modes may be remain unstable. Haramura [9] made clear the stability criteria for a heater block of a circular column. When the z-axis defined as

3.6.4 TEMPERATURE UNIFORMITY ACROSS THE SURFACE

249

the boiling surface is at z 5 H and heat input surface is at z 5 0, the temperature response is expressed with the sum of the products of radial (indicated with integer j), circumferential (indicated with integer s) and axial (indicated with l, zero or positive real numbers) modes as

 X qw ðH 2 zÞ qw Tðr; φ; z; tÞ 5 TN 1 As;j;l Js ðksj rÞeisφ coshfðyl 1 iml Þzgeðβ sjl 1iωsjl Þt 1 1 Γ λ s;j;l

(3.6.18)

where qw is heat flux at a neutral point and expressed by Eq. (3.6.1), λ the thermal conductivity of the heater block, As,j,l the amplitude of mode s, j and l. Js ðr1 Þ is s’th order Bessel function that is finite at r1 5 0. ksj are solutions of J 0s ðksj R0 Þ 5 0 ðadiabatic at r 5 R0 ; the outer surfaceÞ:

(3.6.19)

  Γ  ðγ 1im ÞH  e l l 1 e2ðγl 1iml ÞH 5 0 ðγ l 1 iml Þ eðγl 1iml ÞH 2 e2ðγl 1iml ÞH 1 λ

(3.6.20)

γ l and ml satisfy from the boundary condition on the boiling surface. The diverging rate β sjl and the vibration frequency ωsjl of each mode is determined by β sjl 1 iωsjl 5

o λ n ðγ l 1iml Þ2 2 ksj2 : ρcp

(3.6.21)

If at least one mode is unstable (β sjl . 0), temperature distribution diverges from that of the steady state. It is assumed that the uniform mode in circumferential (s 5 0) and radial (j 5 0) directions is assumed to be stabilized by the temperature control. Then other modes are considered here. Since ml acts to weaken the instability, it is enough to consider only the lowest mode (let l 5 0) among axial modes that satisfies γ 0 H tanhðγ 0 HÞ 5 2ΓH=λ

m0 5 0

and

(3.6.20a)

from Eq. (3.6.20). In this case, the real part of Eq. (3.6.21) becomes β sj0 5

o λ n 2 γ 0 2 ksj2 ρcp

(3.6.21a)

and the condition to keep uniform is written as γ 0 # ksj

(3.6.22)

with Eq. (3.6.20a). ksj’s for low-order modes are summarized in Table 3.6.1. The most unstable mode other than the uniform is that for s 5 1 and j 5 1. The wave number of which k11 is Table 3.6.1 Wave Numbers ksj s

0

1

2

3

4

5

j

0

1

1

2

1

2

1

1

1

ksj R0

0.0

3.832

1.841

5.331

3.054

6.706

4.201

5.318

6.416

All other ksj R0 are greater than 7.

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CHAPTER 3 CHF—TRANSITION BOILING

1.841/R0. It is concluded that the condition to keep uniform temperature distribution across the surface is γ 0 R0 # 1:841:

(3.6.23)

γ 0 H tanhðγ 0 HÞ 5 2ΓH=λ

(3.6.20a)

and This condition is shown in Fig. 3.6.6. Block temperature will be uniform when the parameters are in the region below the curve. The maximum
Γ for a given thickness is proportional to R022 for a sufficiently thin block and proportional to R0
1 for a sufficiently thick block. There is a maximum radius 1.841λ/(
Γ) for the uniformity corresponding to a given negative slope, if the control is performed with a single control circuit. If temperatures at multiple locations are controlled individually, some other lower modes can be stabilized. In that case the wave number of the most dangerous mode should be taken from Table 3.6.1 to determine the stability limit. For a rectangular surface, the uniform condition is written as γL # π

(3.6.24)

γH tanhðγHÞ 5 2ΓH=λ;

(3.6.20a)

and where L is the length of the longer side of the rectangle. Here, the mode along the shorter side is put uniform and the half wavelength of the mode along the longer side is put the length of the side. For small surfaces, the adiabatic condition on the periphery is not met due to heat conduction to the surrounding material. This suppresses the instability then a steady and uniform situation may be attained beyond the theoretical limit.

–Γ R 0 / λ

–Γ0 Uniform β