Abstract

Nucleate boiling has significant applications in earth gravity (in industrial cooling applications) and microgravity conditions (in space exploration, specifically in making space applications more compact). However, the effect of gravity on the growth rate and bubble size is not yet well understood. We perform numerical simulations of nucleate boiling using an adaptive moment-of-fluid (MoF) method for a single vapor bubble (water or Perfluoro-n-hexane) in saturated liquid for different gravity levels. Results concerning the growth rate of the bubble, specifically the departure diameter and departure time, have been provided. The MoF method has been first validated by comparing results with a theoretical solution of vapor bubble growth in superheated liquid without any heat-transfer from the wall. Next, bubble growth rate, bubble shape, and heat transfer results under earth gravity, reduced gravity, and microgravity conditions are reported, and they are in good agreement with experiments. Finally, a new method is proposed for estimating the bubble diameter at different gravity levels. This method is based on an analysis of empirical data at different gravity values and using power-series curve fitting to obtain a generalized bubble growth curve irrespective of the gravity value. This method is shown to provide a good estimate of the bubble diameter for a specific gravity value and time.

References

1.
Siegel
,
R.
, and
Usiskin
,
C.
,
1959
, “
A Photographic Study of Boiling in the Absence of Gravity
,”
ASME J. Heat Transfer-Trans. ASME
,
81
(
3
), pp.
230
236
.10.1115/1.4008192
2.
Siegel
,
R.
, and
Keshock
,
E. G.
,
1964
, “
Effects of Reduced Gravity on Nucleate Boiling Bubble Dynamics in Saturated Water
,”
AIChE J.
,
10
(
4
), pp.
509
517
.10.1002/aic.690100419
3.
Qiu
,
D. M.
,
Dhir
,
V. K.
,
Chao
,
D.
,
Hasan
,
M. M.
,
Neumann
,
E.
,
Yee
,
G.
, and
Birchenough
,
A.
,
2002
, “
Single-Bubble Dynamics During Pool Boiling Under Low Gravity Conditions
,”
J. Thermophys. Heat Transfer
,
16
(
3
), pp.
336
345
.10.2514/2.6710
4.
Lee
,
H. S.
,
Merte
,
H.
, and
Chiaramonte
,
F.
,
1997
, “
Pool Boiling Curve in Microgravity
,”
J. Thermophys. Heat Transfer
,
11
(
2
), pp.
216
222
.10.2514/2.6225
5.
Kannengieser
,
O.
,
Colin
,
C.
, and
Bergez
,
W.
,
2010
, “
Pool Boiling With Non-Condensable Gas in Microgravity: Results of a Sounding Rocket Experiment
,”
Microgravity Sci. Technol.
,
22
(
3
), pp.
447
454
.10.1007/s12217-010-9211-z
6.
Raj
,
R.
,
Kim
,
J.
, and
McQuillen
,
J.
,
2012
, “
Pool Boiling Heat Transfer on the International Space Station: Experimental Results and Model Verification
,”
ASME J. Heat Transfer-Trans. ASME
,
134
(
10
), p.
101504
.10.1115/1.4006846
7.
Warrier
,
G. R.
,
Dhir
,
V. K.
, and
Chao
,
D. F.
,
2015
, “
Nucleate Pool Boiling Experiment (NPBX) in Microgravity: International Space Station
,”
Int. J. Heat Mass Transfer
,
83
, pp.
781
798
.10.1016/j.ijheatmasstransfer.2014.12.054
8.
Merte
,
H.
, Jr.
,
1994
, “
Pool and Flow Boiling in Variable and Microgravity
,” NASA Conference Publication, pp.
265
265
.
9.
Merte
,
H.
,
Lee
,
H.
, and
Keller
,
R.
,
1995
, “
Report on Pool Boiling Experiment Flow on STS-47, STS-57, STS-60
,” Technical Report. No. UM-MEAM-95-01.
10.
Merte
,
H.
,
Lee
,
H. S.
, and
Keller
,
R. B.
,
1998
,
Dryout and Rewetting in the Pool Boiling Experiment Flown on STS-72 (PBE-II B) and STS-77 (PBE-II A).
National Aeronautics and Space Administration, Lewis Research Center
, Hanover, MD.
11.
Usiskin
,
C. M.
, and
Siegel
,
R.
,
1961
, “
An Experimental Study of Boiling in Reduced and Zero Gravity Fields
,”
ASME J. Heat Transfer-Trans. ASME
,
83
(
3
), pp.
243
251
.10.1115/1.3682248
12.
Straub
,
J.
,
Zell
,
M.
, and
Vogel
,
B.
,
1990
, “
Pool Boiling in a Reduced Gravity Field
,”
Proceedings of the Ninth International Heat Transfer Conference
, Jerusalem, Israel, Aug. 19–24, pp.
91
112
.
13.
Zhao
,
J.-F.
,
Li
,
J.
,
Yan
,
N.
, and
Wang
,
S.-F.
,
2009
, “
Bubble Behavior and Heat Transfer in Quasi-Steady Pool Boiling in Microgravity
,”
Microgravity Sci. Technol.
,
21
(
S1
), pp.
175
183
.10.1007/s12217-009-9151-7
14.
Lee
,
R. C.
, and
Nydahl
,
J. E.
,
1989
, “
Numerical Calculation of Bubble Growth in Nucleate Boiling From Inception Through Departure
,”
ASME J. Heat Transfer-Trans. ASME
,
111
(
2
), pp.
474
479
.10.1115/1.3250701
15.
Mei
,
R.
,
Chen
,
W.
, and
Klausner
,
J. F.
,
1995
, “
Vapor Bubble Growth in Heterogeneous Boiling—II. Growth Rate and Thermal Fields
,”
Int. J. Heat Mass Transfer
,
38
(
5
), pp.
921
934
.10.1016/0017-9310(94)00196-3
16.
Welch
,
S. W.
,
1995
, “
Local Simulation of Two-Phase Flows Including Interface Tracking With Mass Transfer
,”
J Comput. Phys.
,
121
(
1
), pp.
142
154
.10.1006/jcph.1995.1185
17.
Kunkelmann
,
C.
, and
Stephan
,
P.
,
2009
, “
CFD Simulation of Boiling Flows Using the Volume-of-Fluid Method Within OpenFOAM
,”
Numer. Heat Transfer Part A: Appl.
,
56
(
8
), pp.
631
646
.10.1080/10407780903423908
18.
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-Trans. ASME
,
121
(
3
), pp.
623
631
.10.1115/1.2826025
19.
Abarajith
,
H. S.
, and
Dhir
,
V. K.
,
2002
, “
A Numerical Study of the Effect of Contact Angle on the Dynamics of a Single Bubble During Pool Boiling
,” The Office of Scientific and Technical Information (
OSTI
) of the Department of Energy, Technical Report, pp.
467
475
.https://www.osti.gov/biblio/404769
20.
Abarajith
,
H.
,
Dhir
,
V.
,
Warrier
,
G.
, and
Son
,
G.
,
2004
, “
Numerical Simulation and Experimental Validation of the Dynamics of Multiple Bubble Merger During Pool Boiling Under Microgravity Conditions
,”
Ann. N. Y. Acad. Sci.
,
1027
(
1
), pp.
235
258
.10.1196/annals.1324.020
21.
Tanguy
,
S.
,
Sagan
,
M.
,
Lalanne
,
B.
,
Couderc
,
F.
, and
Colin
,
C.
,
2014
, “
Benchmarks and Numerical Methods for the Simulation of Boiling Flows
,”
J Comput. Phys.
,
264
, pp.
1
22
.10.1016/j.jcp.2014.01.014
22.
Shin
,
S.-W.
,
Abdel-Khalik
,
S. I.
, and
Jurić
,
D.
,
2005
, “Direct Three-Dimensional Numerical Simulation of Nucleate Boiling Using the Level Contour Reconstruction Method”.
23.
Wu
,
J.
, and
Dhir
,
V. K.
,
2011
, “
Numerical Simulation of Dynamics and Heat Transfer Associated With a Single Bubble in Subcooled Boiling and in the Presence of Noncondensables
,”
ASME J. Heat Transfer-Trans. ASME
,
133
(
4
), p. 041502.10.1115/1.4000979
24.
Juric
,
D.
, and
Tryggvason
,
G.
,
1998
, “
Computations of Boiling Flows
,”
Int. J. Multiphase Flow
,
24
(
3
), pp.
387
410
.10.1016/S0301-9322(97)00050-5
25.
Sato
,
Y.
, and
Ničeno
,
B.
,
2013
, “
A Sharp-Interface Phase Change Model for a Mass-Conservative Interface Tracking Method
,”
J. Comput. Phys.
,
249
, pp.
127
161
.10.1016/j.jcp.2013.04.035
26.
Gibou
,
F.
,
Chen
,
L.
,
Nguyen
,
D.
, and
Banerjee
,
S.
,
2007
, “
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
.10.1016/j.jcp.2006.07.035
27.
Kwatra
,
N.
,
Su
,
J.
,
Grétarsson
,
J. T.
, and
Fedkiw
,
R.
,
2009
, “
A Method for Avoiding the Acoustic Time Step Restriction in Compressible Flow
,”
J. Comput. Phys.
,
228
(
11
), pp.
4146
4161
.10.1016/j.jcp.2009.02.027
28.
Sussman
,
M.
,
Almgren
,
A. S.
,
Bell
,
J. B.
,
Colella
,
P.
,
Howell
,
L. H.
, and
Welcome
,
M. L.
,
1999
, “
An Adaptive Level Set Approach for Incompressible Two-Phase Flows
,”
J. Comput. Phys.
,
148
(
1
), pp.
81
124
.10.1006/jcph.1998.6106
29.
Jemison
,
M.
,
Sussman
,
M.
, and
Arienti
,
M.
,
2014
, “
Compressible, Multiphase Semi-Implicit Method With Moment of Fluid Interface Representation
,”
J. Comput. Phys.
,
279
, pp.
182
217
.10.1016/j.jcp.2014.09.005
30.
Li
,
G.
,
Lian
,
Y.
, and
Sussman
,
M.
,
2013
, “
Simulations of Gas-Liquid Two-Phase Jet Flows Using the Moment of Fluid Method
,” Fluids Engineering Division Summer Meeting, Vol. 55560.
31.
Jemison
,
M.
,
Loch
,
E.
,
Sussman
,
M.
,
Shashkov
,
M. J.
,
Arienti
,
M.
,
Ohta
,
M.
, and
Wang
,
Y.
,
2013
, “
A Coupled Level Set-Moment of Fluid Method for Incompressible Two-Phase Flows
,”
J. Sci. Comput.
,
54
(
2–3
), pp.
454
491
.10.1007/s10915-012-9614-7
32.
Dyadechko
,
V.
, and
Shashkov
,
M.
,
2005
, “
Moment-of-Fluid Interface Reconstruction
,”.
33.
Arienti
,
M.
, and
Sussman
,
M.
,
2014
, “
An Embedded Level Set Method for Sharp-Interface Multiphase Simulations of Diesel Injectors
,”
Int. J. Multiphase Flow
,
59
, pp.
1
14
.10.1016/j.ijmultiphaseflow.2013.10.005
34.
Lian
,
Yongsheng
,
2014
, “
Numerical Simulation of Supercooled Large Droplets Using the Moment of Fluid Method
,” 52nd Aerospace Sciences Meeting,
p. 0740
.
35.
Lian
,
Y.
,
Guo
,
Y.
,
Work
,
A.
, and
Sussman
,
M.
,
2014
, “
Multiphase Flow Simulation Using Moment of Fluid Method
,”
8th International Conference on Computational Fluid Dynamics
, Chengdu, Sichuan, China, Oct. 10.
36.
Weymouth
,
G.
, and
Yue
,
D. K.-P.
,
2010
, “
Conservative Volume-of-Fluid Method for Free-Surface Simulations on Cartesian-Grids
,”
J. Comput. Phys.
,
229
(
8
), pp.
2853
2865
.10.1016/j.jcp.2009.12.018
37.
Scriven
,
L.
,
1959
, “
On the Dynamics of Phase Growth
,”
Chem. Eng. Sci.
,
10
(
1–2
), pp.
1
13
.10.1016/0009-2509(59)80019-1
38.
Urbano
,
A.
,
Tanguy
,
S.
,
Huber
,
G.
, and
Colin
,
C.
,
2018
, “
Direct Numerical Simulation of Nucleate Boiling in Micro-Layer Regime
,”
Int. J. Heat Mass Transfer
,
123
, pp.
1128
1137
.10.1016/j.ijheatmasstransfer.2018.02.104
39.
Guion
,
A.
,
Afkhami
,
S.
,
Zaleski
,
S.
, and
Buongiorno
,
J.
,
2018
, “
Simulations of Microlayer Formation in Nucleate Boiling
,”
Int. J. Heat Mass Transfer
,
127
, pp.
1271
1284
.10.1016/j.ijheatmasstransfer.2018.06.041
40.
Tryggvason
,
G.
, and
Lu
,
J.
,
2015
, “
Direct Numerical Simulations of Flows With Phase Change
,”
Proc. IUTAM
,
15
, pp.
2
13
.10.1016/j.piutam.2015.04.002
41.
Dhir
,
V. K.
,
2001
, “
Numerical Simulations of Pool-Boiling Heat Transfer
,”
AIChE J.
,
47
(
4
), pp.
813
834
.10.1002/aic.690470407
42.
Ajaev
,
V. S.
,
Gambaryan-Roisman
,
T.
, and
Stephan
,
P.
,
2010
, “
Static and Dynamic Contact Angles of Evaporating Liquids on Heated Surfaces
,”
J. Colloid Interface Sci.
,
342
(
2
), pp.
550
558
.10.1016/j.jcis.2009.10.040
43.
Mukherjee
,
A.
, and
Kandlikar
,
S. G.
,
2007
, “
Numerical Study of Single Bubbles With Dynamic Contact Angle During Nucleate Pool Boiling
,”
Int. J. Heat Mass Transfer
,
50
(
1–2
), pp.
127
138
.10.1016/j.ijheatmasstransfer.2006.06.037
44.
Jo
,
H.
,
Kim
,
S.
,
Kim
,
H.
,
Kim
,
J.
, and
Kim
,
M. H.
,
2012
, “
Nucleate Boiling Performance on Nano/Microstructures With Different Wetting Surfaces
,”
Nanoscale Res. Lett.
,
7
(
1
), pp.
1
9
.https://doi.org/10.1186/1556-276X-7-242
45.
Jiang
,
T.-S.
,
Soo-Gun
,
O.
, and
Slattery
,
J. C.
,
1979
, “
Correlation for Dynamic Contact Angle
,”
J. Colloid Interface Sci.
,
69
(
1
), pp.
74
77
.10.1016/0021-9797(79)90081-X
46.
Kistler
,
S. F.
,
1993
, “
Hydrodynamics of Wetting
,”
Wettability
, Vol. 6, pp.
311
430
.
47.
Ikalo
,
Tropea
,
C.
, and
Gani
,
E.
,
2005
, “
Dynamic Wetting Angle of a Spreading Droplet
,”
Exp. Therm. Fluid Sci.
,
29
(
7
), pp.
795
8020
.
48.
Dhir
,
V. K.
,
Warrier
,
G. R.
,
Aktinol
,
E.
,
Chao
,
D.
,
Eggers
,
J.
,
Sheredy
,
W.
, and
Booth
,
W.
,
2012
, “
Nucleate Pool Boiling Experiments (NPBX) on the International Space Station
,”
Microgravity Sci. Technol.
,
24
(
5
), pp.
307
325
.10.1007/s12217-012-9315-8
You do not currently have access to this content.