A new interpretation of the characteristic area and frequency appearing in the wall nucleation source from the point of view of the stochastic nature of this phenomenon is presented in this paper. This analysis shows important drawbacks in the standard interpretation of these terms, such as a strong bias in the characteristic area and high sensitivity to experimental conditions for the frequency. Finally, methods to improve the measurement of the corresponding mean values as well as estimators for their uncertainties based on the definition of a generalized probability density function (PDF) are provided.
Issue Section:
Evaporation, Boiling, and Condensation
References
1.
Collier
, J. G.
, and Thome
, J. R.
, 1994
, Convective Boiling and Condensation
, 3rd ed., Oxford University Press
, Oxford, UK
.2.
Ishii
, M.
, and Hibiki
, T.
, 2010
, Thermo-Fluid Dynamics of Two-Phase Flow
, 2nd ed., Springer
, New York
.10.1007/978-1-4419-7985-83.
Behar
, O.
, Khellaf
, A.
, and Mohammedi
, K.
, 2013
, “A Review of Studies on Central Receiver Solar Thermal Power Plants
,” Renewable Sustainable Energy Rev.
, 23
, pp. 12
–39
.10.1016/j.rser.2013.02.0174.
Ishii
, M.
, and Mishima
, K.
, 1984
, “Two-Fluid Model and Hydrodynamic Constitutive Relations
,” Nucl. Eng. Des.
, 82
(2–3
), pp. 107
–126
.10.1016/0029-5493(84)90207-35.
Kocamustafaogullari
, G.
, and Ishii
, M.
, 1995
, “Foundation of the Interfacial Area Transport Equation and Its Closure Relations
,” Int. J. Heat Mass Transfer
, 38
(3
), pp. 481
–493
.10.1016/0017-9310(94)00183-V6.
Ishii
, M.
, and Kim
, S.
, 2004
, “Development of One-Group and Two-Group Interfacial Area Transport Equation
,” Nucl. Eng. Des.
, 146
(3
), pp. 257
–273
.7.
Hibiki
, T.
, and Ishii
, M.
, 2003
, “Active Nucleation Site Density in Boiling Systems
,” Int. J. Heat Mass Transfer
, 46
(14
), pp. 2587
–2601
.10.1016/S0017-9310(03)00031-08.
Klausner
, J. F.
, Mei
, R.
, Bernhard
, D. M.
, and Zeng
, L. Z.
, 1993
, “Vapor Bubble Departure in Forced-Convection Boiling
,” Int. J. Heat Mass Transfer
, 36
(3
), pp. 651
–662
.10.1016/0017-9310(93)80041-R9.
Situ
, R.
, Mi
, Y.
, Ishii
, M.
, and Mori
, M.
, 2004
, “Photographic Study of Bubble Behaviors in Forced Convection Subcooled Boiling
,” Int. J. Heat Mass Transfer
, 47
(17–18
), pp. 3659
–3667
.10.1016/j.ijheatmasstransfer.2004.04.00510.
Brooks
, C. S.
, Ozar
, B.
, Hibiki
, T.
, and Ishii
, M.
, 2013
, “Interfacial Area Transport of Subcooled Boiling Flow in a Vertical Annulus
,” Nucl. Eng. Des.
, 268
, pp. 152
–163
.10.1016/j.nucengdes.2013.04.04111.
Situ
, R.
, Ishii
, M.
, Hibiki
, T.
, Tu
, J. Y.
, Yeoh
, G. H.
, and Mori
, M.
, 2008
, “Bubble Departure Frequency in Forced Convective Subcooled Boiling Flow
,” Int. J. Heat Mass Transfer
, 51
(25–26
), pp. 6268
–6282
.10.1016/j.ijheatmasstransfer.2008.04.02812.
Koumoutsos
, N.
, Moissis
, R.
, and Spyridonos
, A.
, 1968
, “A Study of Bubble Departure in Forced-Convection Boiling
,” ASME J. Heat Transfer
, 90
(2
), pp. 223
–229
.10.1115/1.359748313.
Abdelmessih
, A.
, Hooper
, F. C.
, and Nangia
, S.
, 1972
, “Flow Effects on Bubble Growth and Collapse in Surface Boiling
,” Int. J. Heat Mass Transfer
, 15
(1
), pp. 115
–124
.10.1016/0017-9310(72)90170-614.
Akiyama
, M.
, and Tachibana
, F.
, 1974
, “Motion of Vapor Bubbles in Subcooled Heated Channel
,” Bull. JSME
, 17
(104
), pp. 241
–247
.10.1299/jsme1958.17.24115.
Unal
, H. C.
, 1976
, “Maximum Bubble Diameter, Maximum Bubble Growth Time and Bubble Growth Rate During Subcooled Nucleate Flow Boiling of Water Up to 17.7 MN/m2
,” Int. J. Heat Mass Transfer
, 19
(6
), pp. 643
–649
.10.1016/0017-9310(76)90047-816.
Klausner
, J. F.
, Mei
, R.
, Bernhard
, D. M.
, and Zeng
, L. Z.
, 1993
, “Vapor Bubble Departure in Forced-Convection Boiling
,” Int. J. Heat Mass Transfer
, 36
(3
), pp. 651
–662
.10.1016/0017-9310(93)80041-R17.
Klausner
, J. F.
, Mei
, R.
, and Zeng
, L. Z.
, 1997
, “Predicting Stochastic Features of Vapor Bubble Detachment in Flow Boiling
,” Int. J. Heat Mass Transfer
, 40
(15
), pp. 3547
–3552
.10.1016/S0017-9310(97)00012-418.
Kenning
, D. B. R.
, 1991
, “Wall Temperature Patterns in Nucleate Boiling
,” Int. J. Heat Mass Transfer
, 35
(1
), pp. 73
–86
.10.1016/0017-9310(92)90009-H19.
Kenning
, D. B. R.
, and Yan
, Y. Y.
, 1996
, “Pool Boiling Heat Transfer on a Thin Plate: Features Revealed by Liquid Crystal Thermography
,” Int. J. Heat Mass Transfer
, 39
(15
), pp. 3117
–3137
.10.1016/0017-9310(96)00006-320.
Pasamehmetoglu
, K. O.
, and Nelson
, R. A.
, 1991
, “Cavity-Tocavity Interaction in Nucleate Boiling: The Effect of Heat Conduction Within the Heater
,” AIChE Symp. Ser.
, 87
(28
), pp. 342
–351
.21.
Maity
, S.
, 2000
, “Effect of Velocity and Gravity on Bubble Dynamics
,” Ph.D. thesis, Mechanical Engineering, University of California, Los Angeles, CA.22.
Basu
, N.
, Warrier
, G. R.
, and Dhir
, V. K.
, 2005
, “Wall Heat Flux Partitioning During Subcooled Flow Boiling: Part II—Model Validation
,” ASME J. Heat Transfer
, 127
(2
), pp. 141
–148
.10.1115/1.184278523.
Basu
, N.
, 2003
, “Modeling and Experiments for Wall Heat Flux Partitioning During Subcooled Flow Boiling of Water at Low Pressures
,” Ph.D. thesis, Mechanical Engineering, University of California, Los Angeles, CA.24.
Situ
, R.
, Ishii
, M.
, Hibiki
, T.
, Tu
, J. Y.
, Yeoh
, G. H.
, and Mori
, M.
, 2008
, “Bubble Departure Frequency in Forced Convective Subcooled Boiling Flow
,” Int. J. Heat Mass Transfer
, 51
(25–26
), pp. 6268
–6282
.10.1016/j.ijheatmasstransfer.2008.04.02825.
Murshed
, S. M. S.
, Vereen
, K.
, Strayer
, D.
, and Kumar
, R.
, 2010
, “An Experimental Investigation of Bubble Nucleation of a Refrigerant in Pressurized Boiling Flows
,” Energy
, 35
(12
), pp. 5143
–5150
.10.1016/j.energy.2010.07.05226.
Chen
, D.
, Pan
, L.
, Yuan
, D.
, Zhang
, H.
, Xu
, J.
, and Huang
, Y.
, 2011
, “The Nature of Bubble Growth Under Different System Pressures in a Narrow Channel
,” Nucl. Eng. Des.
, 241
(3
), pp. 785
–791
.10.1016/j.nucengdes.2010.12.01327.
Euh
, D.
, Ozar
, B.
, Hibiki
, T.
, Ishii
, M.
, and Song
, C.-H.
, 2010
, “Characteristics of Bubble Departure Frequency in a Low-Pressure Subcooled Boiling Flow
,” J. Nucl. Sci. Technol.
, 47
(7
), pp. 608
–617
.10.1080/18811248.2010.972095828.
Harada
, T.
, Nagakura
, H.
, and Okawa
, T.
, 2010
,”Dependence of Bubble Behavior in Subcooled Boiling on Surface Wettability
,” Nucl. Eng. Des.
, 240
(12
), pp. 3949
–3955
.10.1016/j.nucengdes.2010.03.01629.
Brooks
, C. S.
, Silin
, N.
, Hibiki
, T.
, and Ishii
, M.
, 2013
, “Experimental Investigation of Bubble Departure Diameter and Bubble Departure Frequency in Subcooled Flow Boiling in a Vertical Annulus
,” ASME
Paper No. HT2013-17308.10.1115/HT2013-1730830.
Okawa
, T.
, Kubota
, H.
, and Ishida
, T.
, 2007
, “Simultaneous Measurement of Void Fraction and Fundamental Bubble Parameters in Subcooled Flow Boiling
,” Nucl. Eng. Des.
, 237
(10
), pp. 1016
–1024
.10.1016/j.nucengdes.2006.12.01031.
Cho
, Y.-J.
, Yum
, S.-B.
, Lee
, J.-J.
, and Park
, G.-C.
, 2011
, “Development of Bubble Departure and Lift-Off Diameter Models in Low Heat Flux and Low Flow Velocity Conditions
,” Int. J. Heat Mass Transfer
, 54
(15–16
), pp. 3234
–3244
.10.1016/j.ijheatmasstransfer.2011.04.00732.
Kenney
, J. F.
, and Keeping
, E. S.
, 1951
, Mathematics of Statistics
, Part 2, 2nd ed., Van Nostrand, Princeton
, NJ
.33.
Young
, H. D.
, 1962
, Statistical Treatment of Experimental Data
, McGraw-Hill
, New York
.34.
Scholz
, F. W.
, and Stephens
, M. A.
, 1987
, “K-Sample Anderson-Darling Tests
,” J. Am. Stat. Assoc.
, 82
(399
), pp. 918
–924
.10.2307/2288805Copyright © 2015 by ASME
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