The dropwise condensation heat transfer
characteristics of CNT/OTS layered surface associated with non-condensable gas effect
Taeseok Kim
Advisor professor: Sung Joong Kim
Advanced Thermal-Hydraulics Engineering for Nuclear Application lab.
Department of Nuclear Engineering at Hanyang University
2020. 12. 16 ~ 18
Introduction
Dropwise condensation
Dropwise Filmwise
Large thermal resistance
Easy to contact Steam on surface
Droplet sweeping and re-nucleation Hard to contact
Steam on surface
Introduction
Dropwise condensation (Constriction resistance)
3
• Constriction resistance is caused by the bending of the heat flux lines in substrate
• It causes non-uniform heat flux and surface temperature on dropwise condensation
B. B. MIKIC, “On mechanism of dropwise condensation,” International Journal of Heat and Mass Transfer 12 10, 1311 (1969);
https://doi.org/10.1016/0017-9310(69)90174-4.
Time
Heat flux line
Temperature fluctuation Droplet distribution
Introduction
Dropwise condensation (Constriction resistance)
4
• High thermal conductive material can reduce the constriction resistance
• The substrate material is often limited by its mechanical strength and integrity
• Changing the substrate material is impractical in many industrial applications
High thermal conductivity of surface
High heat transfer coefficient High thermal conductive material coatings
Can reduce the constriction resistance
without substrate change
Introduction
Surface modification technique
5
Substrate
Vacuum
Source (Target)
Coating
• Surface modification can change the surface material without altering substrate
• CVD and PVD are well known surface modification techniques
• However, it needs high temperature or vacuum condition
• It is difficult to apply the commercial heat transfer tubes such as heat exchanger
PVD CVD
Introduction
The objective of this study
• Useful surface modification technique(Layer-by-layer) was selected.
• High thermal conductive material(Multi-walled carbon nanotube) was deposited
• Condensation heat transfer experiment was conducted on modified surface
High thermal conductive coatings
Condensation heat transfer experiment
Surface modification
LbL assembled MWCNT coating
7
PEI
waterCNT
water10 min
SS316LRinsing 10 min Rinsing
Substrate
(+) Polyethyleneimine(PEI) (-) Multi-walled CNT(MWCNT)
10 bi-layer
2 bi-layer LbL-assembled PEI/MWCNT
One bi-layer Tensile strength ↑
Thermal conductivity ↑
Easy to deposit Capable on complicated
or large area
MWCNT
Layer-by-Layer(LbL)
Surface modification
LbL assembled MWCNT coating
Coating material CNT
Bi-layer 10
Pore size ~ 64 nm
Thickness ~ 760 nm (ref) Contact angle ~ 20
oPore size distribution
Contact angle SEM image
~ 20 o
Surface modification
Hydrophobic coating
9
Octadecyltrichlorosilane(OTS)
Methyl group (Hydrophobic)
Head group (Silane)
~ 2 h dipping Annealing
Chemical adsorption
Substrate
Van der Waals force
Columnar structure OTS
Covalent bonding
Si
Cross linking
Si Si
Si
OTS
solution
Surface modification
Surface preparation
(b)
Bare CNT CNT+HPo
• Three surface were prepared for the condensation heat transfer experiment
• The substrate was selected to commercial stainless-steel (Bare)
• LbL-assembled MWCNT surface(CNT) cannot promote the dropwise condensation
• Hydrophobic coatings on the CNT surface was deposited (CNT+HPo)
CA ~ 85
oCA ~ 20
oCA ~ 105
oMethod
Experimental set up (Test Loop)
11
Air injection line
Coolant line Steam line
Test section
Method
Experimental set up (Test section)
Steam flow area 0.02 m
2Test specimen Length
1.18 m
Test specimen diameter
19.05 mm
Steam pressure 1 bar
Steam mass flux 0.1 kg/m
2s ( ~ 0.16 m/s) Coolant mass flux 1600 kg/m
2s
( ~ 1.6 m/s)
1.18m
Result
Condensation heat transfer coefficient
13
CNT+HPo
Bare
CNT
Result
Droplet morphology
14
CNT+HPo
Bare Sliding
Flooding
Miljkovic et al. (2013)
Result
Droplet morphology (Regime map)
15
Cassie state
Wenzel state
• Droplet morphology regime map was developed by Enright et al.
• CNT+HPo surface was in Wenzel state region, and it caused flooding condensation
R. ENRIGHT et al., “Condensation on Superhydrophobic Surfaces: The Role of Local Energy Barriers and Structure Length Scale,” Lang muir 28 40, 14424 (2012); https://doi.org/10.1021/la302599n.
Enright et al. (2012)
Result
Droplet morphology (Condensation heat transfer)
16
• Flooding has no enhancement of condensation heat transfer than the sliding Wen et al. (2018) Miljkovic et al. (2013)
HTC enhancement of CNT+HPo
was not caused by nanostructure
Result
Effect of the constriction resistance
17
• The CNT layers of the CNT+HPo surface can reduce the constriction resistance
• Constriction resistance was inserted to the condensation HTC model
B. B. MIKIC, “On mechanism of dropwise condensation,” International Journal of Heat and Mass Transfer 12 10, 1311 (1969); https://
doi.org/10.1016/0017-9310(69)90174-4.
𝑅 𝑐𝑠 ≈ 𝛽 2 1 − 𝛽 2
𝜓 4𝑘 𝑠 𝑟 𝑅 = 𝑅 𝑙𝑣 + 𝑅 𝑑𝑟𝑜𝑝 + 𝑅 𝑐𝑜𝑎𝑡 + 𝑅 𝑙𝑠 + 𝑅 𝑐𝑠
(previous)
Coating effect (present)
𝑅𝑐𝑠of CNT+HPo
𝑅𝑐𝑠of Bare
Thermal resistance of the single droplet
Result
Effect of the constriction resistance
18
• The present model (with constriction) is in line with the experimental result
Result
Effect of the non-condensable gas
19
• The condensation HTC of each surface decreased as air mass fraction increased
A. DEHBI, “A generalized correlation for steam condensation rates in the presence of air under turbulent free convection,” Internation al Journal of Heat and Mass Transfer 86, 1, Elsevier Ltd (2015); https://doi.org/10.1016/j.ijheatmasstransfer.2015.02.034.
Bare CNT+HPo CNT
Result
Effect of the non-condensable gas
20
• Dropwise condensation HTC was similar with the filmwise as air fraction increased
W
air~ 3% W
air~ 6%
W
air~ 9% W
air~ 15%
Conclusion
21
Effect of CNT layers on the dropwise condensation
LbL assembled CNT coatings
Reduce the constriction resistance
Condensation HTC enhancement
Acknowledgement
This work was supported by the National Research Foundation of Korea
(NRF) funded by the Ministry of Science & ICT (MSIT, Korea) grant numbers
[NRF-2016R1A5A101391921]
Thank you
for your
attention
Appendix
Data reduction (LMTD method)
𝑈 = 𝑄
𝐴 𝑠𝑢𝑟𝑓𝑎𝑐𝑒 ∆𝑇 𝐿𝑀𝑇𝐷
𝑄 = ሶ 𝑚𝐶
𝑝𝑇
𝑜𝑢𝑡− 𝑇
𝑖𝑛∆𝑇
𝐿𝑀𝑇𝐷= 𝑇
𝑜𝑢𝑡− 𝑇
𝑖𝑛𝑙𝑛 𝑇
𝑠𝑡𝑒𝑎𝑚− 𝑇
𝑖𝑛𝑇
𝑠𝑡𝑒𝑎𝑚− 𝑇
𝑜𝑢𝑡𝑁𝑢 = 0.023𝑅𝑒 0.8 𝑃𝑟 0.4
ℎ = 1
1
𝑈 − 𝑑 𝑜 𝑑 𝑖
1
ℎ 𝑐𝑜𝑛𝑣 − 𝑑 𝑜
𝑘 𝑙𝑛 𝑑 𝑜 𝑑 𝑖 𝑅 𝑐𝑜𝑛𝑑 = 𝑙𝑛 𝑟 2 Τ 𝑟 1
2𝜋𝑘𝐿
𝑇 𝑠𝑢𝑏 = 𝑄
T
u
b
e
w
a
l
l
Appendix
25
Dropwise condensation HTC model
∆𝑇 = ∆𝑇 𝑐𝑢𝑟𝑣 + ∆𝑇 𝑙𝑣 + ∆𝑇 𝑑𝑟𝑜𝑝 + ∆𝑇 𝑙𝑠 + ∆𝑇 𝑐𝑜𝑎𝑡 + 𝑞 𝑑 × 𝑅 𝑐𝑠
∆𝑇 𝑐𝑢𝑟𝑣 = 2𝑇 𝑠𝑎𝑡 𝜎 ℎ 𝑓𝑔 𝜌 𝑙 𝑟
∆𝑇 𝑙𝑣 = 𝑞 𝑑
2𝜋𝑟 2 1 − cos 𝜃 ℎ 𝑙𝑣
∆𝑇 𝑑𝑟𝑜𝑝 = 𝜃𝑞 𝑑 4𝜋𝑟𝑘 𝑙 sin 𝜃
∆𝑇 𝑙𝑠 = 𝑞 𝑑
𝜋𝑟 2 sin 2 𝜃 ℎ 𝑙𝑠
∆𝑇 𝑐𝑜𝑎𝑡 = 𝛿𝑞 𝑑
𝜋𝑟 2 sin 2 𝜃 𝑘 𝑐𝑜𝑎𝑡
∴ 𝑞 𝑑 =
∆𝑇 − 2𝑇 𝑠𝑎𝑡 𝜎 ℎ 𝑓𝑔 𝜌 𝑙 𝑟 𝛿
𝑘 𝑐𝑜𝑎𝑡 sin 2 𝜃 + 𝑟𝜃
4𝑘 𝑙 sin 𝜃 + 1
2ℎ 𝑙𝑣 (1 − cos 𝜃) + 1 ℎ 𝑙𝑠 sin 2 𝜃
D. NIU et al., “Dropwise condensation heat transfer model considering the liquid-solid interfacial thermal resistance,” International Journal of Heat a nd Mass Transfer 112, 333 (2017); https://doi.org/10.1016/j.ijheatmasstransfer.2017.04.061.
Appendix
26
𝐴 1 = ∆𝑇 2ℎ 𝑓𝑔 𝜌 𝑙
𝐴 2 = 𝜋𝑟(1 − cos 𝜃)(𝑅 𝑑𝑟𝑜𝑝 + 𝑅 𝑐𝑠 )
𝐴 3 = 𝜋𝑟 2 (1 − cos 𝜃)(𝑅 𝑣𝑙 + 𝑅 𝑙𝑠 + 𝑅 𝑐𝑜𝑎𝑡 )
𝐵 1 = 𝐴 2 𝜏𝐴 1
𝑟 𝑒 2 − 𝑟 2
2 + 𝑟 𝑚𝑖𝑛 𝑟 𝑒 − 𝑟 − 𝑟 𝑚𝑖𝑛 2 ln 𝑟 − 𝑟 𝑚𝑖𝑛 𝑟 𝑒 − 𝑟 𝑚𝑖𝑛 𝐵 2 = 𝐴 3
𝜏𝐴 1 𝑟 𝑒 − 𝑟 − 𝑟 𝑚𝑖𝑛 ln 𝑟 − 𝑟 𝑚𝑖𝑛 𝑟 𝑒 − 𝑟 𝑚𝑖𝑛 𝜏 = 3𝑟 𝑒 2 𝐴 2 𝑟 𝑒 + 𝐴 3 2
𝐴 1 (11𝐴 2 𝑟 2 − 14𝐴 2 𝑟 𝑒 𝑟 𝑚𝑖𝑛 + 8𝐴 3 𝑟 𝑒 − 11𝐴 3 𝑟 𝑚𝑖𝑛 )
𝑛 𝑟 = 1
3𝜋𝑟 𝑒 3 𝑟 𝑚𝑎𝑥
𝑟 𝑒 𝑟 𝑚𝑎𝑥
− 2
3 𝑟(𝑟 𝑒 − 𝑟 𝑚𝑖𝑛 ) 𝑟 − 𝑟 𝑚𝑖𝑛
𝐴 2 𝑟 + 𝐴 3
𝐴 2 𝑟 𝑒 + 𝐴 3 exp(𝐵 1 + 𝐵 2 )
Dropwise condensation HTC model
𝑅 𝑐𝑠 ≈ 𝛽 2 1 − 𝛽 2
𝜓 4𝑘 𝑠 𝑟
𝛽 = 𝑟 2 𝑏 2 𝜓 = 32
3𝜋 2 1 − 𝑟 𝑏
1.5
Appendix
27
𝑁 𝑟 = 1
3𝜋𝑟 2 𝑟 𝑚𝑎𝑥
𝑟 𝑟 𝑚𝑎𝑥
− 2 3
𝑞 𝑑𝑟𝑜𝑝 ′′ = (න
𝑟
𝑚𝑖𝑛𝑟
𝑒𝑞 𝑑𝑟𝑜𝑝 𝑟 𝑛 𝑟 𝑑𝑟 + න
𝑟
𝑒𝑟
𝑚𝑎𝑥𝑞 𝑑𝑟𝑜𝑝 𝑟 𝑁 𝑟 𝑑𝑟) 𝑟 𝑚𝑎𝑥 = 6 cos 𝜃 𝑟 − cos 𝜃 𝑎 sin 𝜃
𝜋(2 − 3 cos 𝜃 + cos 3 𝜃) 𝜎 𝑙𝑣 𝜌 𝑙 𝑔
0.5
Dropwise condensation HTC model
𝑟 𝑒 = 4𝑁 𝑠 −1/2 𝑁 𝑠 = 0.037
𝑟 𝑚𝑖𝑛 2
S. KIM and K. J. KIM, “Dropwise Condensation Modeling Suitable for Superhydrophobic Surfaces,” Journal of Heat Transfer 133 8, 081502 (2011); htt ps://doi.org/10.1115/1.4003742.
Appendix
28
Dropwise condensation HTC model
∆𝑔 = ℎ 𝑓𝑔 𝑇 𝑙 − 𝑇 𝑠𝑎𝑡
𝑇 𝑠𝑎𝑡 + 𝜈 𝑙 𝑝 𝑙 − 𝑝 𝑠𝑎𝑡 𝑇 𝑠𝑎𝑡
∴ ∆Ψ = 𝜌 𝑙 𝜋𝑟 3 sin 3 𝜃 න
0 𝜃
ℎ 𝑓𝑔 𝑇 𝑠𝑎𝑡
1 − cos 𝜙 2 sin 4 𝜙 ×
−∆𝑇 𝑠𝑢𝑏 + 𝑞 𝑑𝑟𝑜𝑝 𝑟 𝛿
𝜋𝑟 2 sin 2 𝜃 𝑘 𝑐𝑜𝑎𝑡 + 𝑞 𝑑𝑟𝑜𝑝 (𝑟)𝜙
4𝜋𝑟 sin 𝜃 𝑘 𝑙 + 𝑞 𝑑𝑟𝑜𝑝 𝑟
𝜋𝑟 2 sin 2 𝜃 ℎ 𝑙𝑠 𝑑𝜙 +𝜎 𝑙𝑣 2 − 3 cos 𝜃 + cos 3 𝜃 𝜋𝑟 2
𝝏∆𝜳 ቤ
𝝏𝒓 𝒓=𝒓
𝒎𝒊𝒏= 𝟎
∆Ψ 𝑟 = න[∆𝑔 + 𝑝 𝑠𝑎𝑡 𝑇 𝑠𝑎𝑡 − 𝑝 𝑙 𝑣 𝑙 𝑑𝑚 𝑙 + 𝜎 𝑙𝑣 𝐴 𝑙𝑣 + 𝜎 𝑠𝑙 𝐴 𝑠𝑙 − 𝜎 𝑠𝑣 𝐴 𝑠𝑣
𝑑𝑣 = 𝐴 𝑠 𝑑 ҧ 𝜀 = 𝜋𝑟 3 sin 3 𝜃 1 − cos 𝜙 2
sin 4 𝜙 𝑑𝜙
Appendix
29
Dropwise condensation HTC model
𝐴 𝑑 = න
𝑟
𝑚𝑖𝑛𝑟
𝑒𝜋𝑟 2 sin 2 𝜃 𝑛 𝑟 𝑑𝑟 + න
𝑟
𝑒𝑟
𝑚𝑎𝑥𝜋𝑟 2 sin 2 𝜃 𝑁 𝑟 𝑑𝑟 𝐴 𝑁𝑢 = ℎ 𝐹 𝑙
𝑘 𝑣 = 0.664𝑅𝑒 1/2 𝑃𝑟 1/3 𝑅𝑒 < 5 × 10 5 𝑁𝑢 = 0.037𝑅𝑒 0.8 − 871 𝑃𝑟 1/3 , 𝑅𝑒 > 5 × 10 5
𝑞 𝑐𝑣 ′′ = 𝐴 𝑠𝑜 + 𝐴 𝑙𝑣 ℎ 𝐹 ∆𝑇/𝐴 𝑞 𝑐𝑣 ′′
𝐴 𝑠𝑜 = 𝐴 − 𝐴 𝑑 𝐴 𝑙𝑣 = න
𝑟
𝑚𝑖𝑛𝑟
𝑒2𝜋𝑟 2 (1 − cos 𝜃)𝑛 𝑟 𝑑𝑟 + න
𝑟
𝑒𝑟
𝑚𝑎𝑥2𝜋𝑟 2 (1 − cos 𝜃)𝑁 𝑟 𝑑𝑟 A 𝐴 𝑠𝑜
𝐴 𝑙𝑣
∴ 𝑞 ′′ = 𝑞 𝑐𝑣 ′′ + 𝑞 𝑑𝑟𝑜𝑝 ′′
𝐴 𝑑
J. WANG et al., “Improved modeling of heat transfer in dropwise condensation,” International Journal of Heat and Mass Transfer 155, Elsevier Ltd (2 020); https://doi.org/10.1016/j.ijheatmasstransfer.2020.119719.