Research Papers: Evaporation, Boiling, and Condensation

A Unified Three-Dimensional Numerical Model for Boiling Curve in a Temperature Controlled Mode1

[+] Author and Article Information
Deepak Garg

Department of Mechanical
and Aerospace Engineering,
University of California,
Los Angeles 420 Westwood Plaza,
Los Angeles, CA 90095
e-mail: deepakgarg@ucla.edu

V. K. Dhir

Department of Mechanical
and Aerospace Engineering,
University of California,
Los Angeles 420 Westwood Plaza,
Los Angeles, CA 90095
e-mail: vdhir@seas.ucla.edu

2Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received September 15, 2017; final manuscript received September 17, 2018; published online November 21, 2018. Assoc. Editor: Debjyoti Banerjee.

J. Heat Transfer 141(1), 011504 (Nov 21, 2018) (13 pages) Paper No: HT-17-1542; doi: 10.1115/1.4041798 History: Received September 15, 2017; Revised September 17, 2018

In the present study, level set method is used to simulate the entire boiling curve in a temperature-controlled mode spanning all the three regimes viz., nucleate, transition, and film boiling with a unified numerical model supplemented with correlations specifying nucleation site density and waiting time between successive nucleations. In order to improve the performance of the code, parallel computing has also been implemented. Vapor evolution process along with temporal- and spatial-averaged wall heat flux and wall void fraction are computed for a uniform wall superheat case. Wall void fraction is found to increase with increase in wall superheat nonlinearly as different regimes of boiling were traversed. Energy partitioning from wall into liquid, interface, and microlayer has also been examined where it is found that as the wall void fraction increases, the percent energy going into liquid decreases while the microlayer contribution peaks around critical heat flux (CHF). Numerical simulations are carried out in 3D with water as test liquid and contact angle of 38 deg.

Copyright © 2019 by ASME
Your Session has timed out. Please sign back in to continue.


Nukiyama, S. , 1934, “ The Maximum and Minimum Values of the Heat Transmitted From Metal to Boiling Water Under Atmospheric Pressure,” J. Jpn. Soc. Mech. Eng., 37(206), pp. 367–374. http://www.htsj.or.jp/wp/media/IJHMT1984-3.pdf
Pioro, I. L. , Rohsenow, W. , and Doerffer, S. S. , 2004, “ Nucleate Pool-Boiling Heat Transfer—Part I: Review of Parametric Effects of Boiling Surface,” Int. J. Heat Mass Transfer, 47(23), pp. 5033–5044. [CrossRef]
Dhir, V. K. , 1998, “ Boiling Heat Transfer,” Annu. Rev. Fluid Mech., 30(1), pp. 365–401. [CrossRef]
Dhir, V. K. , 1991, “ Nucleate and Transition Boiling Heat Transfer Under Pool and External Flow Conditions,” Int. J. Heat Fluid Flow, 12(4), pp. 290–314. [CrossRef]
Chekanov, V. V. , 1977, “ Interaction of Centers in Nucleate Boiling,” Teplofiz. Vys. Temp., 15(1), pp. 121–128. http://adsabs.harvard.edu/abs/1977HTemS..15..101C
Basu, N. , Warrier, G. R. , and Dhir, V. K. , 2002, “ Onset of Nucleate Boiling and Active Nucleation Site Density During Subcooled Flow Boiling,” ASME J. Heat Transfer, 124(4), pp. 717–728. [CrossRef]
Dhir, V. K. , and Liaw, S. P. , 1989, “ Framework for a Unified Model for Nucleate and Transition Pool Boiling,” ASME J. Heat Transfer, 111(3), pp. 739–745. [CrossRef]
Liaw, S. P. , and Dhir, V. K. , 1989, “ Void Fraction Measurements During Saturated Pool Boiling of Water on Partially Wetted Vertical Surfaces,” ASME J. Heat Transfer, 111(3), pp. 731–738. [CrossRef]
He, Y. , Shoji, M. , and Maruyama, S. , 2001, “ Numerical Study of High Heat Flux Pool Boiling Heat Transfer,” Int. J. Heat Mass Transfer, 44(12), pp. 2357–2373. [CrossRef]
Luttich, T. , Marquardt, W. , Buchholz, M. , and Auracher, H. , 2004, “ Towards a Unifying Heat Transfer Correlation Along the Entire Boiling Curve,” Int. J. Therm. Sci., 43(12), pp. 1125–1139. [CrossRef]
Son, G. , and Dhir, V. K. , 2008, “ Numerical Simulation of Nucleate Boiling on a Horizontal Surface at High Heat Fluxes,” Int. J Heat Mass Transfer, 51(9–10), pp. 2566–2582. [CrossRef]
Yu, B. , and Cheng, P. , 2002, “ A Fractal Model for Nucleate Pool Boiling Heat Transfer,” J. Heat Transfer, 124(6), pp. 1117–1124. [CrossRef]
Yazdani, M. , Radcliff, T. , Soteriou, M. , and Alahyari, A. A. , 2016, “ A High Fidelity Approach Towards Simulation of Pool Boiling,” Phys. Fluids, 28(1), p. 012111. [CrossRef]
Zhang, L. , Li, Z. , Li, K. , Li, H. , and Zhao, J. , 2015, “ Influence of Heater Thermal Capacity on Bubble Capacity in Nucleate Pool Boiling,” Appl. Therm. Eng., 88, pp. 118–126. [CrossRef]
Son, G. , Dhir, V. K. , and Ramanujapu, N. , 1999, “ Dynamics and Heat Transfer Associated With a Single Bubble During Nucleate Boiling on a Horizontal Surface,” ASME J. Heat Transfer, 121(3), pp. 623–631. [CrossRef]
Lay, J. H. , and Dhir, V. K. , 1995, “ Shape of a Vapor Stem During Nucleate Boiling of Saturated Liquids,” ASME J. Heat Transfer, 117(2), pp. 394–401. [CrossRef]
Sussman, M. , Smereka, P. , and Osher, S. J. , 1994, “ A Level Set Approach for Computing Solutions to Incompressible Two-Phase Flow,” J. Comput. Phys., 114(1), pp. 146–159. [CrossRef]
Brackbill, J. U. , Kothe, D. B. , and Zemach, C. , 1992, “ A Continuum Method for Modeling Surface Tension,” J. Comp. Phys., 100(2), pp. 335–354. [CrossRef]
Gibou, F. , Chen, L. , Nguyen, D. , and Banerjee, S. , 2006, “ A Level Set Based Sharp Interface Method for the Multiphase Incompressible Navier Stokes Equations With Phase Change,” J. Comput. Phys., 222(2), pp. 536–555. [CrossRef]
Croce, R. , Gribel, M. , and Schweitzer, M. A. , 2004, “ A Parallel Level-Set Approach for Two Phase Flow Problems With Surface Tension in Three Space Dimensions,” Preprint 157, Sonderforschungsbereich 611. https://ins.uni-bonn.de/media/public/publication-media/lsm.pdf
Mukherjee, A. , and Dhir, V. K. , 2004, “ Study of Lateral Merger of Vapor Bubbles During Nucleate Pool Boiling,” ASME J. Heat Transfer, 126(6), pp. 1023–1039. [CrossRef]
Collange, S. , Defour, D. , Graillat, S. , and Iakymchuk, R. , 2015, “ Numerical Reproducibility for the Parallel Reduction on Multi- and Many-Core Architectures,” Parallel Computing, 49, pp. 83–97.
Jézéquel, F. , and Chesneaux, J. M. , 2008, “ CADNA: A Library for Estimating round-Off Error Propagation,” Comput. Phys. Commun., 178(12), pp. 933–955. [CrossRef]
Kocamustafafaogullari, G. , and Ishill, M. , 1983, “ Interfacial Area and Nucleation Site Density in Boiling System,” Int. J. Heat Mass Transfer, 26(9), pp. 1377–1387. [CrossRef]
Dusan , 1979, “ On the Spreading of Liquids on Solid Surface: Static and Dynamic Contact Lines,” Annu. Rev. Fluid Mech., 11, pp. 371–400. [CrossRef]
Hsu, Y.-Y. , and Graham, R. W. , 1986, “ Transport Processes in Boiling and Two Phase Systems,” American Nuclear Society, Lagrange Park, IL, pp. 15–18.
Cornwell, K. , and Brown, R. D. , 1978, “ Boiling Surface Topography,” Sixth International Heat Transfer Conference, Vol. 1, Toronto, ON, pp. 157–161.
Gaertner, R. F. , 1963, “ Distribution of Active Sites in the Nucleate Boiling of Liquids,” Chem. Eng. Prog. Symp., 59(41), pp. 52–61. https://ci.nii.ac.jp/naid/10018605594/#cit
Sultan, M. , and Judd, R. L. , 1978, “ Spatial Distribution of Active Sites and Bubble Flux Density,” ASME J. Heat Transfer, 100(1), pp. 56–62. [CrossRef]
Shoji, M. , 2004, “ Study of Boiling Chaos: A Review,” Int. J. Heat Mass Transfer, 47(6–7), pp. 1105–1128. [CrossRef]
Stephan, K. , and Abdelsalam, M. , 1980, “ Heat Transfer Correlations for Natural Convection Boiling,” Int. J. Heat Mass Transfer, 23(1), pp. 73–87. [CrossRef]
Rohsenow, W. M. , 1951, “ A Method of Correlating Heat Transfer Data for Surface Boiling of Liquids,” Trans. ASME, 84, pp. 969–976. http://hdl.handle.net/1721.1/61431
Maracy, M. , and Winterton, R. H. S. , 1988, “ Hysteresis and Contact Angle Effects in Transition Pool Boiling of Water,” Int. J. Heat Mass Transfer, 31(7), pp. 1443–1449. [CrossRef]
Chu, H. , and Yu, B. , 2009, “ A New Comprehensive Model for Nucleate Pool Boiling Heat Transfer of Pure Liquid at Low to High Heat Fluxes Including CHF,” Int. J. Heat Mass Transfer, 52(19–20), pp. 4203–4210. [CrossRef]
Lienhard, J. H. , and Dhir, V. K. , 1973, “ Extended Hydrodynamic Theory of the Peak and Minimum Pool Boiling Heat Fluxes,” NASA Report No. CR-2270. https://ntrs.nasa.gov/search.jsp?R=19730019076
Zuber, N. , 1959, “ Hydrodynamic Aspects of Boiling Heat Transfer,” Ph.D. thesis, University of California, Los Angeles, CA. https://www.osti.gov/servlets/purl/4175511
Auracher, H. , and Marquardt, W. , 2004, “ Heat Transfer Characteristics and Mechanisms along the Entire Boiling Curves Under Steady-State and Transient Conditions,” Int. J. Heat Fluid Flow, 25(2), pp. 223–242. [CrossRef]
Witte, L. C. , and Lienhard, I. H. , 1982, “ On the Existence of Two ‘Transition’ Boiling Curves,” Int. J. Heat Mass Transfer, 25(6), pp. 771–779. [CrossRef]
Bjonard, T. A. , and Griffith, P. , 1977, “ PWR Blowdown Heat Transfer, Thermal and Hydraulic Aspects of Nuclear Reactor Safety,” Thermal and Hydraulic Aspects of Nuclear Reactor Safety, Vol. 1, O. C. Jones, Jr. and S. G. Bankoff, eds., ASME, New York, pp. 17–41.
Liaw, S. P. , and Dhir, V. K. , 1986, “ Effect of Surface Wettability on Transition Boiling Heat Transfer From a Vertical Surface,” Eighth International Heat Transfer Conference, San Francisco, CA, pp. 2031–2036.
Berenson, P. J. , 1962, “ Experiments on Pool-Boiling Heat Transfer,” Int. J. Heat Mass Transfer, 5(10), pp. 985–999. [CrossRef]
Lee, L. Y. W. , and Chen, J. C. , 1985, “ Liquid Solid Contact Measurements Using a Surface Thermocouple Temperature Probe in Atmospheric Pool Boiling Water,” Int. J. Heat Mass Transfer, 28(8), pp. 1415–1423. [CrossRef]
Ragheb, H. S. , and Cheng, S. C. , 1979, “ Surface Wetted Area During Transition Boiling in Forced Convective Flow,” ASME J. Heat Transfer, 101(2), pp. 381–383. [CrossRef]
Tong, L. S. , and Young, J. D. , 1974, “ Phenomenological Transition and Film Boiling Heat Transfer Correlation,” Heat Transfer, 4, pp. 120–124. https://inis.iaea.org/search/search.aspx?orig_q=RN:7220488
Buchholz, M. , Auracher, H. , Luttich, T. , and Marquardt, W. , 2006, “ A Study of Local Heat Transfer Mechanisms Along the Entire Boiling Curve by Means of Microsensors,” Int. J. Therm. Sci., 45(3), pp. 269–283. [CrossRef]
Berenson, P. J. , 1961, “ Film Boiling Heat Transfer From a Horizontal Surface,” ASME J. Heat Transfer, 83(3), pp. 351–356. [CrossRef]
Son, G. , and Dhir, V. K. , 1997, “ Numerical Simulation of Saturated Film Boiling on a Horizontal Surface,” ASME J. Heat Transfer, 119(3), pp. 525–533. [CrossRef]
Garg, D. , 2017, “ A Unified Numerical Model for Pool Boiling Curve With Parallel Computing,” Ph.D. thesis, University of California, Los Angeles, CA. https://escholarship.org/uc/item/5q61h0pq
Dhir, V. K. , 2006, “ Mechanistic Prediction of Nucleate Boiling Heat Transfer—Achievable or a Hopeless Task,” ASME J. Heat Transfer, 128(1), pp. 1–12. [CrossRef]
Stephan, K. , Fuchs, T. , Wagner, E. , and Schweizer, N. , 2009, “ Transient Local Heat Fluxes During the Entire Vapor Bubble Lifetime,” ECI International Conference on Boiling Heat Transfer, Florianopolis, Brazil, May 3–7.


Grahic Jump Location
Fig. 1

Numerical model showing micro region and macro region [15]

Grahic Jump Location
Fig. 14

Simulated boiling curve and wall void fraction in a temperature controlled mode

Grahic Jump Location
Fig. 13

Film boiling heat flux

Grahic Jump Location
Fig. 12

Bubble evolution at film boiling (Z = 3.49 mm, ΔT = 130 °C): (a) (time = 186 ms), (b) (time = 217 ms), (c) (time = 235 ms), and (d) (time = 240 ms)

Grahic Jump Location
Fig. 11

Bubble evolution at transition boiling (Z = 3.49 mm, ΔT = 40 °C): (a) (time = 0.00 ms), (b) (time = 6 ms), (c) (time = 16 ms), and (d) (time = 41 ms)

Grahic Jump Location
Fig. 10

F-factor for transition boiling regime

Grahic Jump Location
Fig. 9

Normalized transition boiling curve

Grahic Jump Location
Fig. 8

Computed CHF value in comparison to data reported in the literature

Grahic Jump Location
Fig. 7

Nucleate boiling regime

Grahic Jump Location
Fig. 6

Wall heat flux and wall void fraction variation (ΔT = 15 °C)

Grahic Jump Location
Fig. 5

Bubble evolution at CHF (Z = 3.49 mm, ΔT = 27 °C): (a) (time = 1.47 ms), (b) (time = 4.00 ms), (c) (time = 4.94 ms), and (d) (time = 6.12 ms)

Grahic Jump Location
Fig. 4

Bubble evolution at nucleate boiling (Z = 3.49 mm, ΔT = 15 °C): (a) (time = 0.0 ms), (b) (time = 13.0 ms), (c) (time = 22.3 ms), and (d) (time =30.2 ms)

Grahic Jump Location
Fig. 3

Validation of bubble diameter and Nu (ΔT = 10 °C, ϕ = 54 deg)

Grahic Jump Location
Fig. 2

Validation of three bubble merger (ΔT = 10 °C, ϕ = 54 deg, Mukherjee and Dhir [21])

Grahic Jump Location
Fig. 15

Wall heat flux partitioning

Grahic Jump Location
Fig. 16

Comparison of nucleate boiling curve for different grid density



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In