Abstract

The process involving heat and mass transfer during filmwise condensation (FWC) in the presence of noncondensable gases (NCG) has great significance in a large variety of engineering applications. Traditionally, the condensation heat transfer is expressed in the literature as a function of the degree of subcooling—reckoned as the difference between the ambient dry bulb temperature and the condenser wall temperature. However, in the presence of NCG, there exists a finite gradient of vapor mass fraction near the condenser plate, which directly influences the vapor mass flux to the condenser surface, thus limiting the condensation rate. The effects of both these influencing thermodynamic parameters, i.e., the degree of subcooling and the difference of humidity ratio (between the freestream environment and on the condenser plate), have been characterized in this work both experimentally and through a mechanistic model. The vapor mass flux during condensation on a subcooled vertical superhydrophilic surface under free convection regime is experimentally measured in a controlled environment (temperature and humidity) chamber. The mechanistic model, based on the similarity of energy and species transports, is formulated for the thermogravitational boundary layer over the condenser plate and tuned against the experimental results. Further, the model is used to obtain comprehensive data of the condensate mass flux and condensation heat transfer coefficient (CHTC) as functions of the salient thermal operating conditions over a wide parametric range. Results indicate that humidity ratio difference has a more pronounced influence on the condensation mass transfer rather than the degree of subcooling. Regime maps of condensate flux and CHTC show how these can be explicitly identified in terms of the degree of subcooling and humidity ratio difference, regardless of the prevailing thermal and humidity conditions at the freestream and the condenser plate. The mechanistic model thus lends to the development of empirical correlations of condensate mass flux and CHTC as explicit functions of these two parameters for easy use in practical FWC configurations.

References

1.
Lee
,
Y.-G.
,
Jang
,
Y.-J.
, and
Choi
,
D.-J.
,
2017
, “
An Experimental Study of Air–Steam Condensation on the Exterior Surface of a Vertical Tube Under Natural Convection Conditions
,”
Int. J. Heat Mass Transfer
,
104
, pp.
1034
1047
.10.1016/j.ijheatmasstransfer.2016.09.016
2.
Beér
,
J. M.
,
2007
, “
High Efficiency Electric Power Generation: The Environmental Role
,”
Prog. Energy Combust. Sci.
,
33
(
2
), pp.
107
134
.10.1016/j.pecs.2006.08.002
3.
Zhang
,
F. Y.
,
Yang
,
X. G.
, and
Wang
,
C. Y.
,
2006
, “
Liquid Water Removal From a Polymer Electrolyte Fuel Cell
,”
J. Electrochem. Soc.
,
153
(
2
), pp.
A225
A232
.10.1149/1.2138675
4.
Miljkovic
,
N.
, and
Wang
,
E. V.
,
2013
, “
Condensation Heat Transfer on Superhydrophobic Surfaces
,”
MRS Bull.
,
38
(
5
), pp.
397
406
.10.1557/mrs.2013.103
5.
Enright
,
R.
,
Miljkovic
,
N.
,
Alvarado
,
J. L.
,
Kim
,
K.
, and
Rose
,
J. W.
,
2014
, “
Dropwise Condensation on Micro-and Nanostructured Surfaces
,”
Nanoscale Microscale Thermophys. Eng
,,
18
(
3
), pp.
223
250
.10.1080/15567265.2013.862889
6.
Chang
,
H. C.
,
Rajagopal
,
M. C.
,
Hoque
,
M. J.
,
Oh
,
J.
,
Li
,
L.
,
Li
,
J.
,
Zhao
,
H.
,
Kuntumalla
,
G.
,
Sundar
,
S.
,
Meng
,
Y.
,
Shao
,
C.
,
Ferreira
,
P. M.
,
Salapaka
,
S. M.
,
Sinha
,
S.
, and
Miljkovic
,
N.
,
2020
, “
Composite Structured Surfaces for Durable Dropwise Condensation
,”
Int. J. Heat Mass Transfer
,
156
, p.
119890
.10.1016/j.ijheatmasstransfer.2020.119890
7.
Cha
,
H.
,
Vahabi
,
H.
,
Wu
,
A.
,
Chavan
,
S.
,
Kim
,
M.-K.
,
Sett
,
S.
,
Bosch
,
S. A.
,
Wang
,
W.
,
Kota
,
A. K.
, and
Miljkovic
,
N.
,
2020
, “
Dropwise Condensation on Solid Hydrophilic Surfaces
,”
Sci. Adv.
,
6
(
2
), p.
eaax0746
.10.1126/sciadv.aax0746
8.
Carey
,
V. P.
,
2020
,
Liquid-Vapor Phase-Change Phenomena: An Introduction to the Thermophysics of Vaporization and Condensation Processes in Heat Transfer Equipment
, 3rd ed.,
CRC Press
,
Boca Raton, FL
.
9.
Bum-Jin
,
C.
,
Sin
,
K.
,
Chan
,
K. M.
, and
Ahmadinejad
,
M.
,
2004
, “
Experimental Comparison of Film-Wise and Drop-Wise Condensations of Steam on Vertical Flat Plates With the Presence of Air
,”
Int. Commun. Heat Mass Transfer
,
31
(
8
), pp.
1067
1074
.10.1016/j.icheatmasstransfer.2004.08.004
10.
Oh
,
S.
, and
Revankar
,
S. T.
,
2006
, “
Experimental and Theoretical Investigation of Film Condensation With Noncondensable Gas
,”
Int. J. Heat Mass Transfer
,
49
(
15–16
), pp.
2523
2534
.10.1016/j.ijheatmasstransfer.2006.01.021
11.
Colburn
,
A. P.
, and
Hougen
,
O. A.
,
1930
, “
Studies in Heat Transmission II—Dehumidification
,”
Ind. Eng. Chem. Res.
,
22
(
5
), pp.
525
534
.10.1021/ie50245a028
12.
Huang
,
J.
,
Zhang
,
J.
, and
Wang
,
L.
,
2015
, “
Review of Vapor Condensation Heat and Mass Transfer in the Presence of Non-Condensable Gas
,”
Appl. Therm. Eng.
,
89
, pp.
469
484
.10.1016/j.applthermaleng.2015.06.040
13.
Colburn
,
A. P.
, and
Hougen
,
O. A.
,
1934
, “
Design of Cooler Condensers for Mixtures of Vapors With Noncondensing Gases
,”
Ind. Eng. Chem. Res.
,
26
(
11
), pp.
1178
1182
.10.1021/ie50299a011
14.
Sparrow
,
E. M.
,
Minkowycz
,
W. J.
, and
Saddy
,
M.
,
1967
, “
Forced Convection Condensation in the Presence of Noncondensables and Interfacial Resistance
,”
Int. J. Heat Mass Transfer
,
10
(
12
), pp.
1829
1845
.10.1016/0017-9310(67)90053-1
15.
Zhang
,
C.
,
Cheng
,
P.
, and
Minkowycz
,
W. J.
,
2017
, “
Lattice Boltzmann Simulation of Forced Condensation Flow on a Horizontal Cold Surface in the Presence of a Non-Condensable Gas
,”
Int. J. Heat Mass Transfer
,
115
, pp.
500
512
.10.1016/j.ijheatmasstransfer.2017.08.005
16.
de la Rosa
,
J. C.
,
Escrivá
,
A.
,
Herranz
,
L. E.
,
Cicero
,
T.
, and
Muñoz-Cobo
,
J. L.
,
2009
, “
Review on Condensation on the Containment Structures
,”
Prog. Nucl. Energy
,
51
(
1
), pp.
32
66
.10.1016/j.pnucene.2008.01.003
17.
Corradini
,
M. L.
,
1984
, “
Turbulent Condensation on a Cold Wall in the Presence of a Noncondensable Gas
,”
Nucl. Technol.
,
64
(
2
), pp.
186
195
.10.13182/NT84-A33341
18.
Alshehri
,
A.
,
Andalib
,
S.
, and
Kavehpour
,
H. P.
,
2020
, “
Numerical Modeling of Vapor Condensation Over a Wide Range of Non-Condensable Gas Concentrations
,”
Int. J. Heat Mass Transfer
,
151
, p.
119405
.10.1016/j.ijheatmasstransfer.2020.119405
19.
Al-Diwany
,
H. K.
, and
Rose
,
J. W.
,
1973
, “
Free Convection Film Condensation of Steam in the Presence of Non-Condensing Gases
,”
Int. J. Heat Mass Transfer
,
16
(
7
), pp.
1359
1369
.10.1016/0017-9310(73)90144-0
20.
Lee
,
K. Y.
, and
Kim
,
M. H.
,
2008
, “
Experimental and Empirical Study of Steam Condensation Heat Transfer With a Noncondensable Gas in a Small-Diameter Vertical Tube
,”
Nucl. Eng. Des.
,
238
(
1
), pp.
207
216
.10.1016/j.nucengdes.2007.07.001
21.
Su
,
J.
,
Sun
,
Z.
,
Fan
,
G.
, and
Ding
,
M.
,
2013
, “
Experimental Study of the Effect of Non-Condensable Gases on Steam Condensation Over a Vertical Tube External Surface
,”
Nucl. Eng. Des.
,
262
, pp.
201
208
.10.1016/j.nucengdes.2013.05.002
22.
Bae
,
B. U.
,
Kim
,
S.
,
Park
,
Y. S.
, and
Kang
,
K. H.
,
2020
, “
Experimental Investigation on Condensation Heat Transfer for Bundle Tube Heat Exchanger of the PCCS (Passive Containment Cooling System)
,”
Ann. Nucl. Energy
,
139
, p.
107285
.10.1016/j.anucene.2019.107285
23.
Punetha
,
M.
, and
Khandekar
,
S.
,
2017
, “
A CFD Based Modelling Approach for Predicting Steam Condensation in the Presence of Non-Condensable Gases
,”
Nucl. Eng. Des.
,
324
, pp.
280
296
.10.1016/j.nucengdes.2017.09.007
24.
Ganguli
,
A.
,
Patel
,
A. G.
,
Maheshwari
,
N. K.
, and
Pandit
,
A. B.
,
2008
, “
Theoretical Modeling of Condensation of Steam Outside Different Vertical Geometries (Tube, Flat Plates) in the Presence of Noncondensable Gases Like Air and Helium
,”
Nucl. Eng. Des.
,
238
(
9
), pp.
2328
2340
.10.1016/j.nucengdes.2008.02.016
25.
Zhang
,
W.
,
Wang
,
S.
, and
Lianbo
,
M.
,
2021
, “
Analytical Modeling for Vapor Condensation in the Presence of Noncondensable Gas and Experimental Validation
,”
ASME J. Heat Transfer
,
143
(
1
), p.
011601
.10.1115/1.4048251
26.
Akaki
,
H.
,
Kataoka
,
Y.
, and
Murase
,
M.
,
1995
, “
Measurement of Condensation Heat Transfer Coefficient Inside a Vertical Tube in the Presence of Noncondensable Gas
,”
J. Nucl. Sci. Technol.
,
32
(
6
), pp.
517
526
.10.1080/18811248.1995.9731739
27.
Dharma Rao
,
V.
,
Murali Krishna
,
V.
,
Sharma
,
K. V.
, and
Sarma
,
P. K.
,
2007
, “
A Theoretical Study on Convective Condensation of Water Vapor From Humid Air in Turbulent Flow in a Vertical Duct
,”
ASME J. Heat Transfer
,
129
(
12
), pp.
1627
1637
.10.1115/1.2767678
28.
Denny
,
V. E.
,
Mills
,
A. F.
, and
Jusionis
,
V. J.
,
1971
, “
Laminar Film Condensation From a Steam-Air Mixture Undergoing Forced Flow Down a Vertical Surface
,”
ASME J. Heat Transfer
,
93
(
3
), pp.
297
304
.10.1115/1.3449814
29.
Wu
,
X. M.
,
Li
,
T.
,
Li
,
Q.
, and
Chu
,
F.
,
2017
, “
Approximate Equations for Film Condensation in the Presence of Non-Condensable Gases
,”
Int. Commun. Heat Mass Trans.
,
85
, pp.
124
130
.10.1016/j.icheatmasstransfer.2017.05.007
30.
Gupta
,
R.
,
Das
,
C.
,
Datta
,
A.
, and
Ganguly
,
R.
,
2019
, “
Background Oriented Schlieren (BOS) Imaging of Condensation From Humid Air on Wettability-Engineered Surfaces
,”
Exp. Therm. Fluid Sci.
,
109
, p.
109859
.10.1016/j.expthermflusci.2019.109859
31.
Siddique
,
M.
,
Golay
,
M. W.
, and
Kazimi
,
M. S.
,
1993
, “
Local Heat Transfer Coefficients for Forced-Convection Condensation of Steam in a Vertical Tube in the Presence of a Noncondensable Gas
,”
Nucl. Technol
,.,
102
(
3
), pp.
386
402
.10.13182/NT93-A17037
32.
Oh
,
S.
, and
Revankar
,
S. T.
,
2005
, “
Effect of Noncondensable Gas in a Vertical Tube Condenser
,”
Nucl. Eng. Des.
,
235
(
16
), pp.
1699
1712
.10.1016/j.nucengdes.2005.01.010
33.
Lee
,
K. W.
,
No
,
H. C.
,
Chu
,
I. C.
,
Moon
,
Y. M.
, and
Chun
,
M. H.
,
2006
, “
Local Heat Transfer During Reflux Condensation Mode in a U-Tube With and Without Noncondensable Gases
,”
Int. J. Heat Mass Transfer
,
49
(
11–12
), pp.
1813
1819
.10.1016/j.ijheatmasstransfer.2005.11.011
34.
Liu
,
T. J.
,
2001
, “
Reflux Condensation Behavior in a U-Tube Steam Generator With or Without Noncondensables
,”
Nucl. Eng. Des.
,
204
(
1–3
), pp.
221
232
.10.1016/S0029-5493(00)00313-7
35.
Li
,
H.
, and
Peng
,
W.
,
2014
, “
A Study on Gas–Liquid Film Thicknesses and Heat Transfer Characteristics of Vapor–Gas Condensation Outside a Horizontal Tube
,”
ASME J. Heat Transfer
,
136
(
2
), p.
021501
.10.1115/1.4025501
36.
Memory
,
S. B.
, and
Rose
,
J. W.
,
1995
, “
Forced Convection Film Condensation on a Horizontal Tube—Influence of Vapor Boundary-Layer Separation
,”
ASME J. Heat Transfer
,
117
(
2
), pp.
529
533
.10.1115/1.2822559
37.
Michael
,
A. G.
,
Rose
,
J. W.
, and
Daniels
,
L. C.
,
1989
, “
Forced Convection Condensation on a Horizontal Tube—Experiments With Vertical Downflow of Steam
,”
ASME J. Heat Transfer
,
111
(
3
), pp.
792
797
.10.1115/1.3250753
38.
Bhanawat
,
A.
,
Yadav
,
M. K.
,
Punetha
,
M.
,
Khandekar
,
S.
, and
Sharma
,
P. K.
,
2020
, “
Effect of Surface Inclination on Filmwise Condensation Heat Transfer During Flow of Steam–Air Mixtures
,”
J. Therm. Sci. Eng. Appl.
,
12
(
4
), pp.
41028
41040
.10.1115/1.4046867
39.
Kang
,
H. C.
, and
Kim
,
M. H.
,
1994
, “
Effect of Non-Condensable Gas and Wavy Interface on the Condensation Heat Transfer in a Nearly Horizontal Plate
,”
Nucl. Eng. Des.
,
149
(
1–3
), pp.
313
321
.10.1016/0029-5493(94)90297-6
40.
Bhanawat
,
A.
,
Yadav
,
M. K.
,
Punetha
,
M.
, and
Khandekar
,
S.
,
2019
, “
Effect of Surface Inclination on Film Condensation Heat Transfer in the Presence of Air
,”
Proc. Int. Conf. Nucl. Eng. (ICONE), Jpn. Soc. Mech. Eng.
,
27
, p.
2133
.10.1299/jsmeicone.2019.27.2133
41.
Mahapatra
,
P. S.
,
Ghosh
,
A.
,
Ganguly
,
R.
, and
Megaridis
,
C. M.
,
2016
, “
Key Design and Operating Parameters for Enhancing Dropwise Condensation Through Wettability Patterning
,”
Int. J. Heat Mass Transfer
,
92
, pp.
877
883
.10.1016/j.ijheatmasstransfer.2015.08.106
42.
Gupta
,
R.
,
Das
,
C.
,
Roy
,
A.
,
Ganguly
,
R.
, and
Datta
,
A.
,
2018
, “
Arduino Based Temperature and Humidity Control for Condensation on Wettability Engineered Surfaces
,” Emerging Trends in Electronic Devices and Computational Techniques (
EDCT
), IEEE, GNIT, Kolkata, India, Mar. 8–9, pp.
1
6
.10.1109/EDCT.2018.8405062
43.
Rausch
,
M. H.
,
Fröba
,
A. P.
, and
Leipertz
,
A.
,
2008
, “
Dropwise Condensation Heat Transfer on Ion Implanted Aluminum Surfaces
,”
Int. J. Heat Mass Transfer
,
51
(
5–6
), pp.
1061
1070
.10.1016/j.ijheatmasstransfer.2006.05.047
44.
Rausch
,
M. H.
,
Leipertz
,
A.
, and
Fröba
,
A. P.
,
2010
, “
Dropwise Condensation of Steam on Ion Implanted Titanium Surfaces
,”
Int. J. Heat Mass Transfer
,
53
(
1–3
), pp.
423
430
.10.1016/j.ijheatmasstransfer.2009.09.014
45.
Incropera
,
F. P.
,
Lavine
,
A. S.
,
Bergman
,
T. L.
, and
DeWitt
,
D. P.
,
2007
,
Fundamentals of Heat and Mass Transfer
, 6th ed.,
Wiley
,
Hoboken, NJ
.
46.
Lawrence
,
M. G.
,
2005
, “
The Relationship Between Relative Humidity and the Dewpoint Temperature in Moist Air: A Simple Conversion and Applications
,”
Bull. Am. Meteorol. Soc.
,
86
(
2
), pp.
225
234
.10.1175/BAMS-86-2-225
47.
Lin
,
H. T.
, and
Wu
,
C. M.
,
1995
, “
Combined Heat and Mass Transfer by Laminar Natural Convection From a Vertical Plate
,”
Heat Mass Transfer
,
30
(
6
), pp.
369
376
.10.1007/BF01647440
48.
Goff
,
J. A.
,
1957
, “
Saturation Pressure of Water on the New Kelvin Temperature Scale
,”
Trans. Am. Soc. Heat. Ventil. Eng.
, 63, pp.
347
354
.
49.
Faghri
,
A.
, and
Zhang
,
Y.
,
2006
,
Transport Phenomena in Multiphase Systems
, 1st ed.,
Academic Press
,
Burlington, MA
.
50.
Hammoudi
,
D.
,
Benabdesselam
,
A.
,
Azzi
,
A.
, and
Kassim
,
M. A.
,
2018
, “
Numerical Modeling of Steam Condensation in Vertical Channel in Presence of Noncondensable Gas
,”
Int. J. Therm. Sci.
,
126
, pp.
263
271
.10.1016/j.ijthermalsci.2017.12.032
51.
Tagami
,
T.
,
1966
,
Interim Report on Safety Assessments and Facilities
,
Japanese Atomic Energy Research Agency
, Ibaraki, Japan.
52.
Uchida
,
H.
,
Oyama
,
A.
, and
Togo
,
Y.
,
1965
, “
Evaluation of Post-Incident Cooling Systems of Light Water Power Reactors
,”
Proc. Int. Conf. Peaceful Uses At. Energy
,
13
, pp.
93
102
.https://www.osti.gov/biblio/4023463-evaluation-post-incident-cooling-systems-light-water-power-reactors
53.
Kataoka
,
Y.
,
Fukui
,
T.
,
Hatamiya
,
S.
,
Nakao
,
T.
,
Naitoh
,
M.
, and
Sumida
,
I.
,
1992
, “
Experiments on Convection Heat Transfer Along a Vertical Flat Between Pools With Different Temperatures
,”
Nucl. Technol.
,
99
(
3
), pp.
386
396
.10.13182/NT92-A34722
54.
Dehbi
,
A.
,
2015
, “
A Generalized Correlation for Steam Condensation Rates in the Presence of Air Under Turbulent Free Convection
,”
Int. J. Heat Mass Transfer
,
86
, pp.
1
15
.10.1016/j.ijheatmasstransfer.2015.02.034
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