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Experimental and theoretical study of frost melting water retention on fin surfaces with different surface characteristics
Accepted Manuscript Experimental and theoretical study of frost melting water retention on fin surfaces with different surface characteristics Caihua Liang, Feng Wang, Yan Lü, Mingtao Yang, Xiaosong Zhang PII: DOI: Reference:
S0894-1777(15)00291-5 http://dx.doi.org/10.1016/j.expthermflusci.2015.10.015 ETF 8605
To appear in:
Experimental Thermal and Fluid Science
Received Date: Revised Date: Accepted Date:
5 November 2014 9 October 2015 14 October 2015
Please cite this article as: C. Liang, F. Wang, Y. Lü, M. Yang, X. Zhang, Experimental and theoretical study of frost melting water retention on fin surfaces with different surface characteristics, Experimental Thermal and Fluid Science (2015), doi: http://dx.doi.org/10.1016/j.expthermflusci.2015.10.015
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Experimental and theoretical study of frost melting water retention on fin surfaces with different surface characteristics
Caihua Liang a,*, Feng Wang a, Yan Lü a,b, Mingtao Yang a, Xiaosong Zhang a
a
School of Energy and Environment, Southeast University, 2 SiPaiLou Road, Nanjing 210096, P R China b
Jiangsu Huasheng Architecture Design Co., Ltd, Xuzhou 221006, P R China
* Corresponding author. Tel.: +86 25 83792692. E-mail addresses: [email protected] (C. H. Liang)
ABSTRACT There is some frost melting water retention on the surface of fin-tube heat exchanger during defrosting process. It takes much time and energy to evaporate the retained water. In this paper, the effect of fin surface characteristic on frost melting water retention is investigated experimentally. Visualization experiment shows that fin surface characteristic has a significant influence on water retention. The retained water forms a thin water film on the hydrophilic fin, while only a few small spherical droplets stay on the superhydrophobic fin. The retained water mass of the superhydrophobic fin decreases by 79.82%, 75.82% and 66.15% compared with that of the hydrophilic, bare and hydrophobic fins, respectively. The frosting time over 30 min has a subtle effect on retained water mass of the hydrophobic and superhydrophobic fins. A mathematical model, which considers the surface contact angle and contact angle hysteresis, is further developed to predict the maximum retained droplet radius and retained water mass. The model is verified to be accurate when the contact angle lied in the range of 110°-150°. Keywords: fin surface; frost melting water retention; contact angle; contact angle hysteresis; mathematical model
1. Introduction With the development of surface treatment technology in recent years, various surface-treated materials have been widely applied to various domains, such as anti-frosting for fin surfaces in air source heat pumps. It is 1
well-known that the phenomenon of frost formation on fin surfaces of the outdoor heat exchanger is unavoidable when an air source heat pump is used for heating in winter. Frost layer adversely affects the performance of the heating unit due to the increase of the heat transfer resistance and air pressure drop, and even result in the mechanical failure of the heating unit [1,2]. Therefore, the effective anti-frosting method is significant to improve the heating efficiency of air source heat pump. There have been some researches on the effect of surface characteristic on droplet condensation and frost growth. Dietz et al. [3] investigated the droplet departure frequency with the help of environmental scanning electron microscopy and its implications to enhancing the rate of dropwise condensation on superhydrophobic surfaces. Rykaczewski [4] and Enright et al. [5] carried out experiments to study the droplet condensation mechanisms on superhydrophobic surfaces. Enright et al. [5] also elucidated how local energy barriers were essential to understand non-equilibrium condensed droplet morphologies and how the wetting states were affected by the nucleation density of the droplets. Huang et al. [6] experimentally investigated the effect of contact angle on water droplet freezing and the experimental results showed that the contact angle has a strong influence on water droplet freezing time. Okoroafor and Newborough [7] tested the restrained frost ability of a hydrophilic surface in over two hours and the results indicated that the reduction in the frost growth rate and frost thickness lied in the range of 10%–30%. Wang et al. [8] prepared a hydrophobic surface whose contact angle was 147° and the frost on the surface was delayed for 60 minutes compared with that of a neat surface. Liu et al. [9] and Cai et al. [10] studied and compared the growth characteristics of the frost layer on different surfaces, such as the frost thickness, frost mass and frost morphology. There have been a few researches on the effect of surface characteristic on defrosting process. Kim et al. [11] investigated the characteristics of frosting and defrosting on a fin according to its surface contact angle and results showed that the effect of surface treatment on defrosting time was insignificant. Jhee et al. [12] reported the effects of the surface characteristics on frosting/defrosting behavior in a fin-tube heat exchanger and revealed that the amount of retained water on the surface-treated heat exchangers was smaller than that of the bare heat exchanger. Rahman et al. [13-15] studied the drainage of frost melting water from a number of microgrooved brass surfaces in multiple frost/defrost/refrost cycles, and their experiments showed that microgrooved surfaces drained up to 70% more condensate than the flat baseline did. There is some water retention on fin surfaces after frost melting because of the adhesive force. It takes much more time and energy to evaporate the retained water compared with those of frost melting. If the retained water is not evaporated completely, it will freeze again and form a dense frost layer in the next frost period. In a word, the retained water has an adverse influence on both 2
frosting and defrosting processes. Therefore, an in-depth understanding of frost melting water retention on fin surfaces is significant to reduce the retained water and improve the defrosting efficiency. In this paper, a series of fin samples with different surface characteristics were prepared and the effect of surface characteristic on frost melting water retention was investigated experimentally. A mathematical model, which considered the surface characteristics including the contact angle and contact angle hysteresis, was further developed to predict the maximum retained droplet radius and retained water mass.
2. Experiments 2.1. Experimental platform and procedure Fig. 1 is the schematic diagram of the experimental platform [16]. A cold platform was used to implement the frosting process and defrosting process of the fin. The semiconductor thermoelectric refrigeration was applied for the cold platform. The surface temperature of the cold platform was regulated from -20 to 150 °C by using a temperature controller. The cold platform was placed vertically in the experiment and the fin was fixed on it. An image acquisition system, which includes a CCD video camera, an asana microscope and image acquisition cards, was used to observe and record the behaviors of the frost melting water retention. The side and front photographs of the water retention were recorded by the CCD video camera and asana microscope, respectively, and then were transmitted to a computer. In the experiment, four types of fins with different surface characteristics were prepared, and the contact angle θ and contact angle hysteresis △θ were measured, as shown in Fig. 2. The measurement of the contact angle was performed using OCA 15 Pro apparatus by the pendant drop method, and the volume of the water droplet was 4μL. The measurement of the contact angle hysteresis was performed by the tilting plate method. A water droplet with volume of 10μL was dropped on the sample platform of the OCA 15 Pro apparatus, and then the sample platform was continuous tilted. When the water droplet just rolled, the tilt angle of the sample platform was the contact angel hysteresis. The hydrophilic and bare fins were directly obtained from fin-tube heat exchangers of air source heat pumps. The hydrophobic and superhydrophobic fins were prepared by using the sodium hydroxide solution etching method. The size of the fins is 4 cm × 4 cm. Before the experiment, the fin was fixed on the platform vertically. The surface temperature of the cold platform was set to -10 °C for frosting. After frosting, the platform temperature was raised to 50 °C (at a temperature rise rate of 8 °C/s) for defrosting. When there was no melting water flowing from the fin surface, the retained water mass was measured. The experimental conditions were the air temperature of 4.5 °C and air relative humidity of 65%. 3
2.2. Parameters measurement The most important parameters were the retained droplet radius r and retained water mass m. The retained droplet radius was measured by a comparative method. In Fig. 3(a), the length of each grid in the scale plate is 0.1 mm. The photographs of the droplets were compared with the scale plate under the same magnification. As shown in Fig. 3(b), the measured value dc was calculated through the number of the grids occupied by the droplet, and the r was calculated according to the relationship between r and dc. An electronic balance, with accuracy of 0.001 g and measuring range of 0–220 g, was used to weight the retained water. After frost melting, a piece of absorbent paper, which attracts water very well, was used to absorbed the retained water quickly and thoroughly, and then the retained water was weighed together with the absorbent paper. In order to verify the accuracy of the measurement process of retained water mass, an independent experiment was carried out. Firstly, the mass of a fin was weighted by the electronic balance and some water was dropped on the fin surface. Then the fin with the water on its surface was weighted together. The difference value between the two weighted values was the actual water mass on the fin surface. Next, a piece of the absorbent paper was used to absorbed the retained water quickly and thoroughly and then the retained water was weighed together with the absorbent paper. Compared the value measured by the method above with the actual retained water mass, the measuring error is shown in Fig. 4. The measuring error was less than 3% in 7 times repeated testing. Therefore, the measured method of retained water mass was verified to be accuracy.
3. Experimental results Fig. 5 shows the distribution of retained water on four types of fin surfaces after frosting for 60 min. The retained water spreads on the hydrophilic surface and looks like a thin water film. The retained water droplets gather into irregular shapes because of the effect of the surface tension, which are irregular in arrangement and density on the bare surface. Most of the frost melting water drains from the hydrophobic surface. The shape of the retained droplets is spherical and the distribution is sparse. The surface wettability has a significant effect on the shapes of the retained droplets on these fin surfaces. It is well-known that the contact angle θ is the measurement of the surface wettability. The bigger the contact angle is, the better the surface wettability is. Thus, the hydrophilic fin shows the best surface wettability among the four types of fins, which leads to a water film forms on its surface. Besides the shapes of the retained droplets, the sizes of them are observed to be different. The sizes of the retained droplets on the hydrophobic surface are smaller than those on the hydrophilic surface. It may be caused by the adhesive force which is produced on the fin surfaces. The adhesive force is against the gravity to keep the frost melt water retention on fin surfaces. The adhesive force of the hydrophobic surface 4
is smaller than that of the hydrophilic surface, so the retained droplet will depart from the hydrophobic surface if the size is too big. For the superhydrophobic surface, the frost layer rolls up from the edge of it at the beginning of the defrosting process, and directly departs from the surface, as shown in Fig. 6. Therefore, the superhydrophobic surface looks dry and only a few tiny droplets stay on it. The frost layer at the bottom of the fin surface melts firstly because of the rise of the surface temperature. The molten water is hard to stay on the vertical surface because of the strong hydrophobicity of the superhydrophobic fin. However, the frost layer above the molten water behaves like a hydrophilic medium. The molten water is absorbed by the hydrophilic frost layer and departs from the surface with the frost layer. Fig. 7 shows the retained water mass on four types of fin surfaces. The retained water mass is 0.109, 0.091, 0.065 and 0.022 g, respectively, which decreases with the increase in the contact angle and decrease of the contact angle hysteresis. The retained water mass on the superhydrophobic fin decreases by 79.82%, 75.82% and 66.15% compared with that on the hydrophilic, bare and hydrophobic fins, respectively. The decrease in the retained water mass can reduce the energy consumption for water evaporation. The results suggest that the superhydrophobic fin can restrain the frost melting water retention and then improve the defrosting efficiency. In order to study the effect of frosting time on retained water mass of different fins with different surface characteristics, the frosting time was set to 30, 60 and 90 min, respectively. The retained water mass on four types of fin surfaces under different frosting time is shown in Fig. 8. The changing trends of the fins show obvious differences. The frosting time has a great effect on the retained water mass of the hydrophilic and bare fins, which can be seen from the almost straight curves. However, the frosting time has a diminutive effect on the retained water mass of the hydrophobic fin. The largest fluctuation of the retained water mass in three tests is less than 5%. The retained water mass of the superhydrophobic fin is relatively stable, which is hardly affected by the frosting time. The frost melting water tends to depart from the vertical fin surface after frost melting under the effect of the gravity, while the surface produces adhesive force against the gravity. In other word, the phenomenon of the frost melting water retention is caused by the adhesive force. So it is easy to achieve a balance between the adhesive force and the retained water mass. When the frosting time increases, the frost mass increases, and the frost melting water increases in turn. If the adhesive force and the retained water mass reaches a balance, the surface is unable to provide more adhesive force to retain the added frost melting water. As a rsult, the added frost melting water will depart from the vertical surface and the retained water mass will remain the same. In this case, the surface can be seen as a saturated surface for frost melting water retention. This point can be verified by 5
the invariable retained water mass on hydrophobic and superhydrophobic surfaces (as shown in Fig. 7). As the adhesion of the hydrophobic and superhydrophobic surfaces is small, it is easy to reach saturation for frost melting water retention. Therefore, the retained water mass has nothing to do with the initial frosting condition when it is saturated.
4. Mathematical model 4.1. Description of model When a droplet is on an vertical fin surface, the contact angle (receding contact angle θr) that the liquid-solid interface instead of the gas-solid interface and the contact angle (advancing contact angle θa) that the gas-solid interface instead of the liquid-solid interface are different. This phenomenon is called the contact angle hysteresis, as shown in Fig. 9. The contact angle hysteresis △θ is the difference value between the receding contact angle θr and advancing contact angle θr. The adhesive force Fc is expressed as [17]
Fc r sin (sin r sin a )(
1 1 )
(1)
The retained droplet is approximately considered to be spherical crown, as shown in Fig. 9. Thus, the volume V and gravity Fg of the retained droplet are
V
Fg
2 3cos cos3 3
2 3cos cos3 3
r3
(2)
r3 g
(3)
The maximum retained droplet radius Rmax is calculated based on the force balance between the adhesive force and gravity 1
rmax
1 1 2 3 sin (sin r sin a )( ) g 2 3cos cos3
(4)
The experiment results in Fig. 8 show that the frosting time over 30 min has a subtle effect on retained water mass of the hydrophobic and superhydrophobic fins. From the analysis above we have known that the retention ability of the frost melting water on the surface is easy to reach saturation point because of the adhesive force. Similarly, the condensate droplets retention is also caused by the adhesive force. The small droplet can stay on the cold surface, but it will shed when it grows bigger and bigger. When the condensation develops into a balance stage, the growth of the droplets is equal to the shedding of the droplets. In consequence, the mass of the 6
condensate droplets is invariable. So the physical processes of the frost melting water retention and droplet condensation retention have something in common because of the effect of the surface adhesion. Thus, the mass of the condensate droplets is considered to be equal to the retained water mass when the process is saturated. So the retained water mass can be predicted with the aid of the calculation of the condensate droplets mass although the droplet distribution density may exist some difference. N(r) and n(r) refer to the distribution density of large condensate droplets and small droplets, respectively. They predict the distribution of droplets on the fin surface well. The references [18-20] give the details of N(r) and n(r). The mass of large condensate droplets is
mN
r
rmax
m r N r dr
e
rmax
r
N r
2 3 cos cos 3
πr dr 3
(5)
3
e
The mass of small condensate droplets is
mn
r
re
m r n r dr
min
r
re
n r
2 3 cos cos
min
3
πr dr 3
(6)
3
Therefore, the total mass m is
m mN
mn
5.2. Model Verification A series of fin samples with different surface characteristics were prepared to verify to the accuracy of the model. Fig. 10. shows the contact angle and contact angle hysteresis of the fins for model verification. Fig. 11. is the comparison of maximum retained droplet radius between experimental and calculated values. When the contact angle lies in the range of 110-150°, the relative error is less than 15%, which shows good accuracy for predicting the maximum retained droplet radius. However, when the contact angle is 98°, the relative error is more than 20%, which shows poor accuracy. Because the retained droplet is considered to be spherical crown in the model. It is different from the irregular retained droplets on surface with contact angle of 98°. The comparison of retained water mass between experimental and calculated values is shown in Fig. 12. When the contact angle is in the range of 110–150°, the model is accurate with a relative error less than 11%. However, the accuracy of the model was poor for bare and superhydrophobic surfaces. In the model, the retained droplet was considered to be spherical crown. However, the shape of the retained droplet was irregular on the bare surface (as shown in Fig.5). While on the superhydrophobic surface, the frost layer was directly released 7
(7)
from the surface at the beginning of the defrosting process. Unlike the defrosting process of the hydrophobic surface, the frost layer did not experience a melting process, which led to few droplets retained on the superhydrophobic surface. As a result, the model does not function well on the bare and superhydrophobic surfaces. The model may be improved in the future via amending the shape of the retained droplet on the bare surface and assessing the retained water mass that being adsorbed by the released frost layer on the superhydrophobic surface. 5.3. Numerical results Fig. 13 shows the effects of surface characteristics on maximum retained droplet radius. The maximum retained droplet radius decreases with the increase in contact angles. When the contact angle hysteresis is 5°, the maximum droplet radius decreases from 0.48 to 0.15 mm quickly as the contact angle increases from 110 to 160°. The greater contact angle hysteresis causes the maximum retained droplet radius to decrease faster; this can be seen clearly from the slope of the curve. Another significant finding is that the maximum droplet radius increases with the increase in the contact angles hysteresis. When the contact angle is 120°, the maximum droplet radius increases from 0.19 to 0.59 mm as the contact angle hysteresis increases from 1 to 10°. The effects of surface characteristics on retained water mass are shown in Fig. 14. The retained water mass is based on per square meter of the fin surface. The retained water mass decreases with the increase in the contact angle. When the contact angle hysteresis is 5°, the retained water mass decreases from 35.96 to 19.01 g with the contact angle increased from 110 to 160°. The greater contact angle hysteresis causes the values to decrease faster. Another finding is that the retained water mass increases with the contact angle hysteresis increasing.
5. Conclusions A frosting/defrosting experimental system was constructed to study the effects of surface characteristics of fins on frost melt water retention. Meanwhile, a mathematical model, which considered the effects of surface characteristics including the contact angle and contact angle hysteresis, was developed for predicting the maximum retained droplet radius and retained water mass. The effects of surface characteristics on frost melt water retention were observed to be significant. The retained water formed a thin water film on the hydrophilic fin while only a few small spherical droplets stayed on the super hydrophobic fin. The retained water mass of the superhydrophobic fin decreased by 79.82% compared with that of the hydrophilic fin. In addition, the frosting time over 30 min was found to have no effect on the retained water mass of the hydrophobic and superhydrophobic fins. The model was verified to be accurate 8
when the contact angle lied in the range of 110°-150°. However, the accuracy of the model was poor for bare and superhydrophobic surfaces. Thus, the model needs to be improved in the future.
Acknowledgements This work is supported by the National Natural Science Foundations of China (51106023), the 12th Five Year Science and Technology Support Key Project of China (2011BAJ03B10) and the Scientific Research Foundation of Graduate School of Southeast University (YBJJ1506).
References [1] Lee H, Shin J, Ha S, et al. Frost formation on a plate with different surface hydrophilicity[J]. International Journal of Heat and Mass Transfer, 2004, 47(22): 4881-4893. [2] Hakkaki-Fard A, Aidoun Z, Ouzzane M. Applying refrigerant mixtures with thermal glide in cold climate air-source heat pumps[J]. Applied Thermal Engineering, 2014, 62(2): 714-722. [3] Dietz C, Rykaczewski K, Fedorov A G, et al. Visualization of droplet departure on a superhydrophobic surface and implications to heat transfer enhancement during dropwise condensation[J]. Applied Physics Letters, 2010, 97(3): 033104. [4] Rykaczewski K. Microdroplet growth mechanism during water condensation on superhydrophobic surfaces[J]. Langmuir, 2012, 28(20): 7720-7729. [5] Enright R, Miljkovic N, Al-Obeidi A, et al. Condensation on superhydrophobic surfaces: The role of local energy barriers and structure length scale[J]. Langmuir, 2012, 28(40): 14424-14432. [6] Huang L, Liu Z, Liu Y, et al. Effect of contact angle on water droplet freezing process on a cold flat surface[J]. Experimental Thermal and Fluid Science, 2012, 40: 74-80. [7] Okoroafor E U, Newborough M. Minimising frost growth on cold surfaces exposed to humid air by means of crosslinked hydrophilic polymeric coatings[J]. Applied Thermal Engineering, 2000, 20(8): 737-758. [8] Wang Z J, Kwon D J, DeVries K L, et al. Frost formation and anti-icing performance of a hydrophobic coating on aluminum[J]. Experimental Thermal and Fluid Science, 2015, 60: 132-137. [9] Liu Z, Zhang X, Wang H, et al. Influences of surface hydrophilicity on frost formation on a vertical cold plate under natural convection conditions[J]. Experimental Thermal and Fluid Science, 2007, 31(7): 789-794.
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[10] Cai L, Wang R, Hou P, et al. Study on restraining frost growth at initial stage by hydrophobic coating and hygroscopic coating[J]. Energy and Buildings, 2011, 43(5): 1159-1163. [11] Kim K, Lee K S. Frosting and defrosting characteristics of a fin according to surface contact angle[J]. International Journal of Heat and Mass Transfer, 2011, 54(13): 2758-2764. [12] Jhee S, Lee K S, Kim W S. Effect of surface treatments on the frosting/defrosting behavior of a fin-tube heat exchanger[J]. International Journal of Refrigeration, 2002, 25(8): 1047-1053. [13] Rahman M A, Jacobi A M. Drainage of frost melt water from vertical brass surfaces with parallel microgrooves[J]. International Journal of Heat and Mass Transfer, 2012, 55(5): 1596-1605. [14] Rahman M A, Jacobi A M. Condensation, Frost Formation, and Frost Melt-Water Retention Characteristics on Microgrooved Brass Surfaces Under Natural Convection[J]. Heat Transfer Engineering, 2013, 34(14): 1147-1155. [15] Rahman M A, Jacobi A M. Study of frost properties and frost melt water drainage on microgrooved brass surfaces in multiple frost/defrost/refrost cycles[J]. Applied Thermal Engineering, 2014, 64(1): 453-461. [16] Liang C, Wang F, Lü Y, et al. Experimental study of the effects of fin surface characteristics on defrosting behavior[J]. Applied Thermal Engineering, 2015, 75: 86-92. [17] Min J C, Peng X F, Wang X D. Departure diameter of a drop on a vertical plate[J]. Journal of Basic Science and Engineering, 2002, 10(1): 57-62. (in Chinese) [18] Kim S, Kim K J. Dropwise condensation modeling suitable for superhydrophobic surfaces[J]. Journal of Heat Transfer, 2011, 133(8): 081502. [19] Abu-Orabi M. Modeling of heat transfer in dropwise condensation[J]. International journal of heat and mass transfer, 1998, 41(1): 81-87. [20] Vemuri S, Kim K J. An experimental and theoretical study on the concept of dropwise condensation[J]. International Journal of Heat and Mass Transfer, 2006, 49(3): 649-657.
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Nomenclature Fc
adhesive force (N)
r
radius of retained droplet (mm)
θ
contact angle (°)
θr
receding contact angle (°)
θa
advancing contact angle (°)
V
volume of retained droplet (m3)
Fg
gravity of retained droplet (N)
Ns
nucleation site density (1/cm2)
m
retained water mass (kg)
Greek symbols σ
surface tension (N/m)
ρ
density of retained droplet (kg/m3)
11
Figure Captions: Fig. 1. Schematic diagram of experimental platform. Fig. 2. Contact angle and contact angle hysteresis of prepared fins. Fig. 3. Measuring principle of retained droplet radius r. Fig. 4. Measuring error of retained water mass. Fig. 5. Distribution of retained water on four types of fin surfaces (frosting for 60 min). Fig. 6. Frost layer departure from surface of superhydrophobic fin. Fig. 7. Retained water mass on four types of fin surfaces. Fig. 8. Effect of frosting time on retained water mass on four types of fin surfaces. Fig. 9. Force analysis of retained droplet on fin surface. Fig. 10. Contact angle and contact angle hysteresis of prepared fins for model verification. Fig. 11. Comparison of maximum retained droplet radius between experimental and calculated values. Fig. 12. Comparison of retained water mass between experimental and calculated values. Fig. 13. Effect of surface characteristics on maximum retained droplet radius. Fig. 14. Effects of surface characteristics on retained water mass.
12
CCD camera (side)
Temperature controller
Cold platform
Fin
Computer
Microscope (front)
Cooling water bath
Fig. 1. Schematic diagram of experimental platform.
(a)
(b)
(c)
(d)
Fig. 2. Contact angle and contact angle hysteresis of prepared fins. (a) Hydrophilic fin: θ=15°, △θ=140°; (b) Bare fin: θ=98°, △θ=36°; (c) Hydrophobic fin: θ=137°, △θ=19°; (d) Superhydrophobic fin: θ=160°, △θ=5°.
13
(a)
(b)
Fig. 3. Measuring principle of retained droplet radius r. (a) Scale plate with grids and photograph of frost melt water retention; (b) The relationship between r and measured value dc.
5 4 3
Error / %
2 1 0 -1 -2 -3 -4 1
2
3
4
5
6
Experiment times Fig. 4. Measuring error of retained water mass.
14
7
Hydrophilic fin
Bare fin
Hydrophobic fin
Superhydrophobic fin
Fig. 5. Distribution of retained water on four types of fin surfaces (frosting for 60 min).
0.2 cm Fig. 6. Frost layer departure from surface of superhydrophobic fin.
15
0.12
Retained water mass / g
0.109 0.10
0.091
0.08 0.064 0.06 0.04 0.022 0.02 0.00 Hydrophilic
Bare
Hydrophobic Superhydrophobic
Fig. 7. Retained water mass on four types of fin surfaces.
0.16
Retained water mass / g
0.14 0.12
Hydrophilic Bare Hydrophobic Superhydrophobic
0.10 0.08 0.06 0.04 0.02 0.00 30
60
90
Frosting time / min Fig. 8. Effect of frosting time on retained water mass on four types of fin surfaces.
16
Fig. 9. Force analysis of retained droplet on fin surface.
Contact angle hysteresis / o
40 35 30 25 20 15 10 5 0 90
100
110
120
130
140
Contact angle /
150
160
170
o
Fig. 10. Contact angle and contact angle hysteresis of prepared fins for model verification.
17
1.8
Maximum radius / mm
1.6
Experimental values Calculated values
1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 90
100
110
120
130
140
Contact angle /
150
160
170
o
Fig. 11. Comparison of maximum retained droplet radius between experimental and calculated values.
0.14
Retained water mass / g
0.12 0.10 0.08 0.06 0.04 0.02 0.00 90
100
110
120
130
140
Contact angle /
150
160
170
o
Fig. 12. Comparison of retained water mass between experimental and calculated values.
18
Maximum radius / mm
1.0
0.8
0.6
0.4
0.2
0.0 100
110
120
130
140
Contact angle /
150
160
o
Fig. 13. Effects of surface characteristics on maximum retained droplet radius.
Fig. 14. Effects of surface characteristics on retained water mass.
19
Highlights The effects of fin surface characteristics on frost melt water retention were studied. The effect of frosting time on retained water mass was investigated. A mathematical model was developed for predicting the maximum retained droplet radius and retained water mass. The model was verify to be accurate when the contact angle lied in the range of 110°-150°.
20
S0894-1777(15)00291-5 http://dx.doi.org/10.1016/j.expthermflusci.2015.10.015 ETF 8605
To appear in:
Experimental Thermal and Fluid Science
Received Date: Revised Date: Accepted Date:
5 November 2014 9 October 2015 14 October 2015
Please cite this article as: C. Liang, F. Wang, Y. Lü, M. Yang, X. Zhang, Experimental and theoretical study of frost melting water retention on fin surfaces with different surface characteristics, Experimental Thermal and Fluid Science (2015), doi: http://dx.doi.org/10.1016/j.expthermflusci.2015.10.015
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Experimental and theoretical study of frost melting water retention on fin surfaces with different surface characteristics
Caihua Liang a,*, Feng Wang a, Yan Lü a,b, Mingtao Yang a, Xiaosong Zhang a
a
School of Energy and Environment, Southeast University, 2 SiPaiLou Road, Nanjing 210096, P R China b
Jiangsu Huasheng Architecture Design Co., Ltd, Xuzhou 221006, P R China
* Corresponding author. Tel.: +86 25 83792692. E-mail addresses: [email protected] (C. H. Liang)
ABSTRACT There is some frost melting water retention on the surface of fin-tube heat exchanger during defrosting process. It takes much time and energy to evaporate the retained water. In this paper, the effect of fin surface characteristic on frost melting water retention is investigated experimentally. Visualization experiment shows that fin surface characteristic has a significant influence on water retention. The retained water forms a thin water film on the hydrophilic fin, while only a few small spherical droplets stay on the superhydrophobic fin. The retained water mass of the superhydrophobic fin decreases by 79.82%, 75.82% and 66.15% compared with that of the hydrophilic, bare and hydrophobic fins, respectively. The frosting time over 30 min has a subtle effect on retained water mass of the hydrophobic and superhydrophobic fins. A mathematical model, which considers the surface contact angle and contact angle hysteresis, is further developed to predict the maximum retained droplet radius and retained water mass. The model is verified to be accurate when the contact angle lied in the range of 110°-150°. Keywords: fin surface; frost melting water retention; contact angle; contact angle hysteresis; mathematical model
1. Introduction With the development of surface treatment technology in recent years, various surface-treated materials have been widely applied to various domains, such as anti-frosting for fin surfaces in air source heat pumps. It is 1
well-known that the phenomenon of frost formation on fin surfaces of the outdoor heat exchanger is unavoidable when an air source heat pump is used for heating in winter. Frost layer adversely affects the performance of the heating unit due to the increase of the heat transfer resistance and air pressure drop, and even result in the mechanical failure of the heating unit [1,2]. Therefore, the effective anti-frosting method is significant to improve the heating efficiency of air source heat pump. There have been some researches on the effect of surface characteristic on droplet condensation and frost growth. Dietz et al. [3] investigated the droplet departure frequency with the help of environmental scanning electron microscopy and its implications to enhancing the rate of dropwise condensation on superhydrophobic surfaces. Rykaczewski [4] and Enright et al. [5] carried out experiments to study the droplet condensation mechanisms on superhydrophobic surfaces. Enright et al. [5] also elucidated how local energy barriers were essential to understand non-equilibrium condensed droplet morphologies and how the wetting states were affected by the nucleation density of the droplets. Huang et al. [6] experimentally investigated the effect of contact angle on water droplet freezing and the experimental results showed that the contact angle has a strong influence on water droplet freezing time. Okoroafor and Newborough [7] tested the restrained frost ability of a hydrophilic surface in over two hours and the results indicated that the reduction in the frost growth rate and frost thickness lied in the range of 10%–30%. Wang et al. [8] prepared a hydrophobic surface whose contact angle was 147° and the frost on the surface was delayed for 60 minutes compared with that of a neat surface. Liu et al. [9] and Cai et al. [10] studied and compared the growth characteristics of the frost layer on different surfaces, such as the frost thickness, frost mass and frost morphology. There have been a few researches on the effect of surface characteristic on defrosting process. Kim et al. [11] investigated the characteristics of frosting and defrosting on a fin according to its surface contact angle and results showed that the effect of surface treatment on defrosting time was insignificant. Jhee et al. [12] reported the effects of the surface characteristics on frosting/defrosting behavior in a fin-tube heat exchanger and revealed that the amount of retained water on the surface-treated heat exchangers was smaller than that of the bare heat exchanger. Rahman et al. [13-15] studied the drainage of frost melting water from a number of microgrooved brass surfaces in multiple frost/defrost/refrost cycles, and their experiments showed that microgrooved surfaces drained up to 70% more condensate than the flat baseline did. There is some water retention on fin surfaces after frost melting because of the adhesive force. It takes much more time and energy to evaporate the retained water compared with those of frost melting. If the retained water is not evaporated completely, it will freeze again and form a dense frost layer in the next frost period. In a word, the retained water has an adverse influence on both 2
frosting and defrosting processes. Therefore, an in-depth understanding of frost melting water retention on fin surfaces is significant to reduce the retained water and improve the defrosting efficiency. In this paper, a series of fin samples with different surface characteristics were prepared and the effect of surface characteristic on frost melting water retention was investigated experimentally. A mathematical model, which considered the surface characteristics including the contact angle and contact angle hysteresis, was further developed to predict the maximum retained droplet radius and retained water mass.
2. Experiments 2.1. Experimental platform and procedure Fig. 1 is the schematic diagram of the experimental platform [16]. A cold platform was used to implement the frosting process and defrosting process of the fin. The semiconductor thermoelectric refrigeration was applied for the cold platform. The surface temperature of the cold platform was regulated from -20 to 150 °C by using a temperature controller. The cold platform was placed vertically in the experiment and the fin was fixed on it. An image acquisition system, which includes a CCD video camera, an asana microscope and image acquisition cards, was used to observe and record the behaviors of the frost melting water retention. The side and front photographs of the water retention were recorded by the CCD video camera and asana microscope, respectively, and then were transmitted to a computer. In the experiment, four types of fins with different surface characteristics were prepared, and the contact angle θ and contact angle hysteresis △θ were measured, as shown in Fig. 2. The measurement of the contact angle was performed using OCA 15 Pro apparatus by the pendant drop method, and the volume of the water droplet was 4μL. The measurement of the contact angle hysteresis was performed by the tilting plate method. A water droplet with volume of 10μL was dropped on the sample platform of the OCA 15 Pro apparatus, and then the sample platform was continuous tilted. When the water droplet just rolled, the tilt angle of the sample platform was the contact angel hysteresis. The hydrophilic and bare fins were directly obtained from fin-tube heat exchangers of air source heat pumps. The hydrophobic and superhydrophobic fins were prepared by using the sodium hydroxide solution etching method. The size of the fins is 4 cm × 4 cm. Before the experiment, the fin was fixed on the platform vertically. The surface temperature of the cold platform was set to -10 °C for frosting. After frosting, the platform temperature was raised to 50 °C (at a temperature rise rate of 8 °C/s) for defrosting. When there was no melting water flowing from the fin surface, the retained water mass was measured. The experimental conditions were the air temperature of 4.5 °C and air relative humidity of 65%. 3
2.2. Parameters measurement The most important parameters were the retained droplet radius r and retained water mass m. The retained droplet radius was measured by a comparative method. In Fig. 3(a), the length of each grid in the scale plate is 0.1 mm. The photographs of the droplets were compared with the scale plate under the same magnification. As shown in Fig. 3(b), the measured value dc was calculated through the number of the grids occupied by the droplet, and the r was calculated according to the relationship between r and dc. An electronic balance, with accuracy of 0.001 g and measuring range of 0–220 g, was used to weight the retained water. After frost melting, a piece of absorbent paper, which attracts water very well, was used to absorbed the retained water quickly and thoroughly, and then the retained water was weighed together with the absorbent paper. In order to verify the accuracy of the measurement process of retained water mass, an independent experiment was carried out. Firstly, the mass of a fin was weighted by the electronic balance and some water was dropped on the fin surface. Then the fin with the water on its surface was weighted together. The difference value between the two weighted values was the actual water mass on the fin surface. Next, a piece of the absorbent paper was used to absorbed the retained water quickly and thoroughly and then the retained water was weighed together with the absorbent paper. Compared the value measured by the method above with the actual retained water mass, the measuring error is shown in Fig. 4. The measuring error was less than 3% in 7 times repeated testing. Therefore, the measured method of retained water mass was verified to be accuracy.
3. Experimental results Fig. 5 shows the distribution of retained water on four types of fin surfaces after frosting for 60 min. The retained water spreads on the hydrophilic surface and looks like a thin water film. The retained water droplets gather into irregular shapes because of the effect of the surface tension, which are irregular in arrangement and density on the bare surface. Most of the frost melting water drains from the hydrophobic surface. The shape of the retained droplets is spherical and the distribution is sparse. The surface wettability has a significant effect on the shapes of the retained droplets on these fin surfaces. It is well-known that the contact angle θ is the measurement of the surface wettability. The bigger the contact angle is, the better the surface wettability is. Thus, the hydrophilic fin shows the best surface wettability among the four types of fins, which leads to a water film forms on its surface. Besides the shapes of the retained droplets, the sizes of them are observed to be different. The sizes of the retained droplets on the hydrophobic surface are smaller than those on the hydrophilic surface. It may be caused by the adhesive force which is produced on the fin surfaces. The adhesive force is against the gravity to keep the frost melt water retention on fin surfaces. The adhesive force of the hydrophobic surface 4
is smaller than that of the hydrophilic surface, so the retained droplet will depart from the hydrophobic surface if the size is too big. For the superhydrophobic surface, the frost layer rolls up from the edge of it at the beginning of the defrosting process, and directly departs from the surface, as shown in Fig. 6. Therefore, the superhydrophobic surface looks dry and only a few tiny droplets stay on it. The frost layer at the bottom of the fin surface melts firstly because of the rise of the surface temperature. The molten water is hard to stay on the vertical surface because of the strong hydrophobicity of the superhydrophobic fin. However, the frost layer above the molten water behaves like a hydrophilic medium. The molten water is absorbed by the hydrophilic frost layer and departs from the surface with the frost layer. Fig. 7 shows the retained water mass on four types of fin surfaces. The retained water mass is 0.109, 0.091, 0.065 and 0.022 g, respectively, which decreases with the increase in the contact angle and decrease of the contact angle hysteresis. The retained water mass on the superhydrophobic fin decreases by 79.82%, 75.82% and 66.15% compared with that on the hydrophilic, bare and hydrophobic fins, respectively. The decrease in the retained water mass can reduce the energy consumption for water evaporation. The results suggest that the superhydrophobic fin can restrain the frost melting water retention and then improve the defrosting efficiency. In order to study the effect of frosting time on retained water mass of different fins with different surface characteristics, the frosting time was set to 30, 60 and 90 min, respectively. The retained water mass on four types of fin surfaces under different frosting time is shown in Fig. 8. The changing trends of the fins show obvious differences. The frosting time has a great effect on the retained water mass of the hydrophilic and bare fins, which can be seen from the almost straight curves. However, the frosting time has a diminutive effect on the retained water mass of the hydrophobic fin. The largest fluctuation of the retained water mass in three tests is less than 5%. The retained water mass of the superhydrophobic fin is relatively stable, which is hardly affected by the frosting time. The frost melting water tends to depart from the vertical fin surface after frost melting under the effect of the gravity, while the surface produces adhesive force against the gravity. In other word, the phenomenon of the frost melting water retention is caused by the adhesive force. So it is easy to achieve a balance between the adhesive force and the retained water mass. When the frosting time increases, the frost mass increases, and the frost melting water increases in turn. If the adhesive force and the retained water mass reaches a balance, the surface is unable to provide more adhesive force to retain the added frost melting water. As a rsult, the added frost melting water will depart from the vertical surface and the retained water mass will remain the same. In this case, the surface can be seen as a saturated surface for frost melting water retention. This point can be verified by 5
the invariable retained water mass on hydrophobic and superhydrophobic surfaces (as shown in Fig. 7). As the adhesion of the hydrophobic and superhydrophobic surfaces is small, it is easy to reach saturation for frost melting water retention. Therefore, the retained water mass has nothing to do with the initial frosting condition when it is saturated.
4. Mathematical model 4.1. Description of model When a droplet is on an vertical fin surface, the contact angle (receding contact angle θr) that the liquid-solid interface instead of the gas-solid interface and the contact angle (advancing contact angle θa) that the gas-solid interface instead of the liquid-solid interface are different. This phenomenon is called the contact angle hysteresis, as shown in Fig. 9. The contact angle hysteresis △θ is the difference value between the receding contact angle θr and advancing contact angle θr. The adhesive force Fc is expressed as [17]
Fc r sin (sin r sin a )(
1 1 )
(1)
The retained droplet is approximately considered to be spherical crown, as shown in Fig. 9. Thus, the volume V and gravity Fg of the retained droplet are
V
Fg
2 3cos cos3 3
2 3cos cos3 3
r3
(2)
r3 g
(3)
The maximum retained droplet radius Rmax is calculated based on the force balance between the adhesive force and gravity 1
rmax
1 1 2 3 sin (sin r sin a )( ) g 2 3cos cos3
(4)
The experiment results in Fig. 8 show that the frosting time over 30 min has a subtle effect on retained water mass of the hydrophobic and superhydrophobic fins. From the analysis above we have known that the retention ability of the frost melting water on the surface is easy to reach saturation point because of the adhesive force. Similarly, the condensate droplets retention is also caused by the adhesive force. The small droplet can stay on the cold surface, but it will shed when it grows bigger and bigger. When the condensation develops into a balance stage, the growth of the droplets is equal to the shedding of the droplets. In consequence, the mass of the 6
condensate droplets is invariable. So the physical processes of the frost melting water retention and droplet condensation retention have something in common because of the effect of the surface adhesion. Thus, the mass of the condensate droplets is considered to be equal to the retained water mass when the process is saturated. So the retained water mass can be predicted with the aid of the calculation of the condensate droplets mass although the droplet distribution density may exist some difference. N(r) and n(r) refer to the distribution density of large condensate droplets and small droplets, respectively. They predict the distribution of droplets on the fin surface well. The references [18-20] give the details of N(r) and n(r). The mass of large condensate droplets is
mN
r
rmax
m r N r dr
e
rmax
r
N r
2 3 cos cos 3
πr dr 3
(5)
3
e
The mass of small condensate droplets is
mn
r
re
m r n r dr
min
r
re
n r
2 3 cos cos
min
3
πr dr 3
(6)
3
Therefore, the total mass m is
m mN
mn
5.2. Model Verification A series of fin samples with different surface characteristics were prepared to verify to the accuracy of the model. Fig. 10. shows the contact angle and contact angle hysteresis of the fins for model verification. Fig. 11. is the comparison of maximum retained droplet radius between experimental and calculated values. When the contact angle lies in the range of 110-150°, the relative error is less than 15%, which shows good accuracy for predicting the maximum retained droplet radius. However, when the contact angle is 98°, the relative error is more than 20%, which shows poor accuracy. Because the retained droplet is considered to be spherical crown in the model. It is different from the irregular retained droplets on surface with contact angle of 98°. The comparison of retained water mass between experimental and calculated values is shown in Fig. 12. When the contact angle is in the range of 110–150°, the model is accurate with a relative error less than 11%. However, the accuracy of the model was poor for bare and superhydrophobic surfaces. In the model, the retained droplet was considered to be spherical crown. However, the shape of the retained droplet was irregular on the bare surface (as shown in Fig.5). While on the superhydrophobic surface, the frost layer was directly released 7
(7)
from the surface at the beginning of the defrosting process. Unlike the defrosting process of the hydrophobic surface, the frost layer did not experience a melting process, which led to few droplets retained on the superhydrophobic surface. As a result, the model does not function well on the bare and superhydrophobic surfaces. The model may be improved in the future via amending the shape of the retained droplet on the bare surface and assessing the retained water mass that being adsorbed by the released frost layer on the superhydrophobic surface. 5.3. Numerical results Fig. 13 shows the effects of surface characteristics on maximum retained droplet radius. The maximum retained droplet radius decreases with the increase in contact angles. When the contact angle hysteresis is 5°, the maximum droplet radius decreases from 0.48 to 0.15 mm quickly as the contact angle increases from 110 to 160°. The greater contact angle hysteresis causes the maximum retained droplet radius to decrease faster; this can be seen clearly from the slope of the curve. Another significant finding is that the maximum droplet radius increases with the increase in the contact angles hysteresis. When the contact angle is 120°, the maximum droplet radius increases from 0.19 to 0.59 mm as the contact angle hysteresis increases from 1 to 10°. The effects of surface characteristics on retained water mass are shown in Fig. 14. The retained water mass is based on per square meter of the fin surface. The retained water mass decreases with the increase in the contact angle. When the contact angle hysteresis is 5°, the retained water mass decreases from 35.96 to 19.01 g with the contact angle increased from 110 to 160°. The greater contact angle hysteresis causes the values to decrease faster. Another finding is that the retained water mass increases with the contact angle hysteresis increasing.
5. Conclusions A frosting/defrosting experimental system was constructed to study the effects of surface characteristics of fins on frost melt water retention. Meanwhile, a mathematical model, which considered the effects of surface characteristics including the contact angle and contact angle hysteresis, was developed for predicting the maximum retained droplet radius and retained water mass. The effects of surface characteristics on frost melt water retention were observed to be significant. The retained water formed a thin water film on the hydrophilic fin while only a few small spherical droplets stayed on the super hydrophobic fin. The retained water mass of the superhydrophobic fin decreased by 79.82% compared with that of the hydrophilic fin. In addition, the frosting time over 30 min was found to have no effect on the retained water mass of the hydrophobic and superhydrophobic fins. The model was verified to be accurate 8
when the contact angle lied in the range of 110°-150°. However, the accuracy of the model was poor for bare and superhydrophobic surfaces. Thus, the model needs to be improved in the future.
Acknowledgements This work is supported by the National Natural Science Foundations of China (51106023), the 12th Five Year Science and Technology Support Key Project of China (2011BAJ03B10) and the Scientific Research Foundation of Graduate School of Southeast University (YBJJ1506).
References [1] Lee H, Shin J, Ha S, et al. Frost formation on a plate with different surface hydrophilicity[J]. International Journal of Heat and Mass Transfer, 2004, 47(22): 4881-4893. [2] Hakkaki-Fard A, Aidoun Z, Ouzzane M. Applying refrigerant mixtures with thermal glide in cold climate air-source heat pumps[J]. Applied Thermal Engineering, 2014, 62(2): 714-722. [3] Dietz C, Rykaczewski K, Fedorov A G, et al. Visualization of droplet departure on a superhydrophobic surface and implications to heat transfer enhancement during dropwise condensation[J]. Applied Physics Letters, 2010, 97(3): 033104. [4] Rykaczewski K. Microdroplet growth mechanism during water condensation on superhydrophobic surfaces[J]. Langmuir, 2012, 28(20): 7720-7729. [5] Enright R, Miljkovic N, Al-Obeidi A, et al. Condensation on superhydrophobic surfaces: The role of local energy barriers and structure length scale[J]. Langmuir, 2012, 28(40): 14424-14432. [6] Huang L, Liu Z, Liu Y, et al. Effect of contact angle on water droplet freezing process on a cold flat surface[J]. Experimental Thermal and Fluid Science, 2012, 40: 74-80. [7] Okoroafor E U, Newborough M. Minimising frost growth on cold surfaces exposed to humid air by means of crosslinked hydrophilic polymeric coatings[J]. Applied Thermal Engineering, 2000, 20(8): 737-758. [8] Wang Z J, Kwon D J, DeVries K L, et al. Frost formation and anti-icing performance of a hydrophobic coating on aluminum[J]. Experimental Thermal and Fluid Science, 2015, 60: 132-137. [9] Liu Z, Zhang X, Wang H, et al. Influences of surface hydrophilicity on frost formation on a vertical cold plate under natural convection conditions[J]. Experimental Thermal and Fluid Science, 2007, 31(7): 789-794.
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[10] Cai L, Wang R, Hou P, et al. Study on restraining frost growth at initial stage by hydrophobic coating and hygroscopic coating[J]. Energy and Buildings, 2011, 43(5): 1159-1163. [11] Kim K, Lee K S. Frosting and defrosting characteristics of a fin according to surface contact angle[J]. International Journal of Heat and Mass Transfer, 2011, 54(13): 2758-2764. [12] Jhee S, Lee K S, Kim W S. Effect of surface treatments on the frosting/defrosting behavior of a fin-tube heat exchanger[J]. International Journal of Refrigeration, 2002, 25(8): 1047-1053. [13] Rahman M A, Jacobi A M. Drainage of frost melt water from vertical brass surfaces with parallel microgrooves[J]. International Journal of Heat and Mass Transfer, 2012, 55(5): 1596-1605. [14] Rahman M A, Jacobi A M. Condensation, Frost Formation, and Frost Melt-Water Retention Characteristics on Microgrooved Brass Surfaces Under Natural Convection[J]. Heat Transfer Engineering, 2013, 34(14): 1147-1155. [15] Rahman M A, Jacobi A M. Study of frost properties and frost melt water drainage on microgrooved brass surfaces in multiple frost/defrost/refrost cycles[J]. Applied Thermal Engineering, 2014, 64(1): 453-461. [16] Liang C, Wang F, Lü Y, et al. Experimental study of the effects of fin surface characteristics on defrosting behavior[J]. Applied Thermal Engineering, 2015, 75: 86-92. [17] Min J C, Peng X F, Wang X D. Departure diameter of a drop on a vertical plate[J]. Journal of Basic Science and Engineering, 2002, 10(1): 57-62. (in Chinese) [18] Kim S, Kim K J. Dropwise condensation modeling suitable for superhydrophobic surfaces[J]. Journal of Heat Transfer, 2011, 133(8): 081502. [19] Abu-Orabi M. Modeling of heat transfer in dropwise condensation[J]. International journal of heat and mass transfer, 1998, 41(1): 81-87. [20] Vemuri S, Kim K J. An experimental and theoretical study on the concept of dropwise condensation[J]. International Journal of Heat and Mass Transfer, 2006, 49(3): 649-657.
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Nomenclature Fc
adhesive force (N)
r
radius of retained droplet (mm)
θ
contact angle (°)
θr
receding contact angle (°)
θa
advancing contact angle (°)
V
volume of retained droplet (m3)
Fg
gravity of retained droplet (N)
Ns
nucleation site density (1/cm2)
m
retained water mass (kg)
Greek symbols σ
surface tension (N/m)
ρ
density of retained droplet (kg/m3)
11
Figure Captions: Fig. 1. Schematic diagram of experimental platform. Fig. 2. Contact angle and contact angle hysteresis of prepared fins. Fig. 3. Measuring principle of retained droplet radius r. Fig. 4. Measuring error of retained water mass. Fig. 5. Distribution of retained water on four types of fin surfaces (frosting for 60 min). Fig. 6. Frost layer departure from surface of superhydrophobic fin. Fig. 7. Retained water mass on four types of fin surfaces. Fig. 8. Effect of frosting time on retained water mass on four types of fin surfaces. Fig. 9. Force analysis of retained droplet on fin surface. Fig. 10. Contact angle and contact angle hysteresis of prepared fins for model verification. Fig. 11. Comparison of maximum retained droplet radius between experimental and calculated values. Fig. 12. Comparison of retained water mass between experimental and calculated values. Fig. 13. Effect of surface characteristics on maximum retained droplet radius. Fig. 14. Effects of surface characteristics on retained water mass.
12
CCD camera (side)
Temperature controller
Cold platform
Fin
Computer
Microscope (front)
Cooling water bath
Fig. 1. Schematic diagram of experimental platform.
(a)
(b)
(c)
(d)
Fig. 2. Contact angle and contact angle hysteresis of prepared fins. (a) Hydrophilic fin: θ=15°, △θ=140°; (b) Bare fin: θ=98°, △θ=36°; (c) Hydrophobic fin: θ=137°, △θ=19°; (d) Superhydrophobic fin: θ=160°, △θ=5°.
13
(a)
(b)
Fig. 3. Measuring principle of retained droplet radius r. (a) Scale plate with grids and photograph of frost melt water retention; (b) The relationship between r and measured value dc.
5 4 3
Error / %
2 1 0 -1 -2 -3 -4 1
2
3
4
5
6
Experiment times Fig. 4. Measuring error of retained water mass.
14
7
Hydrophilic fin
Bare fin
Hydrophobic fin
Superhydrophobic fin
Fig. 5. Distribution of retained water on four types of fin surfaces (frosting for 60 min).
0.2 cm Fig. 6. Frost layer departure from surface of superhydrophobic fin.
15
0.12
Retained water mass / g
0.109 0.10
0.091
0.08 0.064 0.06 0.04 0.022 0.02 0.00 Hydrophilic
Bare
Hydrophobic Superhydrophobic
Fig. 7. Retained water mass on four types of fin surfaces.
0.16
Retained water mass / g
0.14 0.12
Hydrophilic Bare Hydrophobic Superhydrophobic
0.10 0.08 0.06 0.04 0.02 0.00 30
60
90
Frosting time / min Fig. 8. Effect of frosting time on retained water mass on four types of fin surfaces.
16
Fig. 9. Force analysis of retained droplet on fin surface.
Contact angle hysteresis / o
40 35 30 25 20 15 10 5 0 90
100
110
120
130
140
Contact angle /
150
160
170
o
Fig. 10. Contact angle and contact angle hysteresis of prepared fins for model verification.
17
1.8
Maximum radius / mm
1.6
Experimental values Calculated values
1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 90
100
110
120
130
140
Contact angle /
150
160
170
o
Fig. 11. Comparison of maximum retained droplet radius between experimental and calculated values.
0.14
Retained water mass / g
0.12 0.10 0.08 0.06 0.04 0.02 0.00 90
100
110
120
130
140
Contact angle /
150
160
170
o
Fig. 12. Comparison of retained water mass between experimental and calculated values.
18
Maximum radius / mm
1.0
0.8
0.6
0.4
0.2
0.0 100
110
120
130
140
Contact angle /
150
160
o
Fig. 13. Effects of surface characteristics on maximum retained droplet radius.
Fig. 14. Effects of surface characteristics on retained water mass.
19
Highlights The effects of fin surface characteristics on frost melt water retention were studied. The effect of frosting time on retained water mass was investigated. A mathematical model was developed for predicting the maximum retained droplet radius and retained water mass. The model was verify to be accurate when the contact angle lied in the range of 110°-150°.
20