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An experimental study of the effect of air quality on frosting on cold flat surface
International Communications in Heat and Mass Transfer 82 (2017) 139–144
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International Communications in Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ichmt
An experimental study of the effect of air quality on frosting on cold flat surface Jianying Gong a,⁎, Jinjuan Sun b, Guojun Li a a b
MOE Key Laboratory of Thermo-Fluid Science and Engineering, School of Energy and Power Engineering, Xi'an Jiaotong University, Xi'an 710049, China School of Mechatronic Engineering, Xi'an Technological University, Xi'an 710021, China
a r t i c l e Available online xxxx Keywords: Freezing of droplet Supercooling degree PM2.5 concentration Frost formation
i n f o
a b s t r a c t The effects of air quality in the freezing process of droplets and the frost crystal growth on cold flat plate are studied experimentally. It is found that the air quality has important influence in the frosting process. The supercooling degree and freezing time change with solution concentration on different solutes. When supercooled droplets are in the instability state, the composition and concentration of solution can affect the nucleation and heat transfer, and most of the solute can increase the degree of supercooling and accelerate the freezing process. Solutions with cation of strong electrolyte have higher supercooling degree because the weak cation will hydrolyze. The hydrated ion can accelerate the formation of ice crystal. In addition, the frosting process on cold flat plate under different fine particle (PM2.5) concentrations is also studied in form of frost height and mass variations. The result shows that the greater the PM2.5 concentration is, the thicker the frost layer is and the greater the amount of the frost crystal is. This is because suspended particles in the air that can act as nucleating substrate to promote heterogeneous nucleation and the frost crystals are more easily deposited. © 2017 Elsevier Ltd. All rights reserved.
1. Introduction Frost formation has important effects in many fields, such as refrigeration industry, air-conditioning, aviation, etc. The process of frost formation associated with transient heat and mass transfer is extremely complex, whatever frost forms only if the temperature of cold flat plate is less than zero degrees Celsius and the ambient dew point temperature. The presence of frost will deteriorate refrigeration capacity due to decreased heat transfer coefficient and increased pressure drop, and defrosting will lead to higher energy consumption and operation cost. It is therefore essential to investigate physical mechanism on the frost formation. Over the last several decades, research on frost formation has been studied both experimentally and theoretically. Frost growth was studied through experimental [1–3]. Hayashi et al. [4] photographed the whole process of frost formation, which was divided largely into three stages: crystal growth period, frost layer growth period and frost layer full growth period. As the inception of crystal growth period, the solidification of water droplet has an essential role in the whole process of frosting and attracted further attention in recent times. Wu et al. [5] investigated the freezing of supercooled condensate droplets in the frost formation, and the freezing onset time and diameter of condensate
⁎ Corresponding author. E-mail address: [email protected] (J. Gong).
http://dx.doi.org/10.1016/j.icheatmasstransfer.2017.02.013 0735-1933/© 2017 Elsevier Ltd. All rights reserved.
droplets were characterized. Tan et al. [6] studied the occurrence of supercooling of water correlated with the ability of the chilling medium to promptly nucleate ice. Bahadur et al. [7] developed a physical model to predict ice formation on cooled superhydrophobic plates resulting from the impact of supercooled water droplets, and this modeling approach analyzed the multiple phenomena influencing ice formation on superhydrophobic plates. The frost layer composed of a large number of frost crystals behaves as a porous medium into which diffusion of water vapor leads to an increase of both thickness and density [8]. The models through the correlations to conform the experimental data were established for predicting frost growth by Parish and Sepsy [9]. Yang et al. [10] attempted to develop a mathematical model that can predict the characteristics of the frost growth and the heat transfer under turbulent flow. Lee et al. [11,12] presented a different theoretical model by considering the frost layer as porous media. Sahin [13] found that frost density was not the sole parameter affecting effective frost thermal conductivity. The foregoing studies focused on the laws of frost layer height, frost density, frost surface temperature, and frost thermal conductivity influenced by some factors such as cold flat surfaces temperature, environmental air humidity, temperature and velocity, etc. In the refrigeration industry, air-conditioning, aviation, and other engineering fields, many suspended particles exist in the frosting environment and the frost formation process mostly happens in the atmospheric environment. The air is not pure, and is affected by the haze. The air quality will affect the frosting process, however very few studies have considered the influence of particles in the air.
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Nomenclature C d h m FRH T t u V
PM2.5 concentration (μg m−3) particle diameter (nm) frost height (mm) frost crystal mass (kg m−2) relative humidity temperature (°C) time (s or min) velocity of air (m/s) volume of water droplet (μl)
Greek symbols ΔT supercooling degree (°C) Subscripts and superscripts a air w cold flat plate f freezing
The purpose of this paper is to build an experimental system to study the effects of air quality on the characteristics of the freezing process of droplets and the frost crystal growth on cold flat plate. Section 2 describes an experimental system for frost formation. The variations of the supercooling degree and freezing time of variety solutions at different concentrations and the process of frost layer growth under different PM2.5 concentrations are obtained in Section 3, followed by a brief conclusion in Section 4. 2. Experimental method 2.1. Experimental setup An experimental system is set up to study the frost formation process on cold flat plate, which consists of a list of components as shown in Fig. 1.
An isolated organic glass tunnel is designed and built to avoid the interference of environment, which has two quartz glass viewing ports on both top and side of the tunnel to observe frost formation by the microscopic image system. The test section is made of red copper sized at 60 mm × 40 mm × 8 mm, which is cooled by the semiconductor chilling plate (C-1208). The circulated cooling water piped from the lowtemperature thermostat bath (DC-4015, ±0.1 °C) is used as the chiller for the hot side of the semiconductor chilling plate. The five T-type thermocouples (GBTS200, ±0.1 °C) are used to measure the cold plate temperature. Fig. 2 shows the exact locations of thermocouples inserted in the cold flat plate. All the thermocouples are located at the same level of 1 mm beneath the surface of copper plate. Relative mean deviations (RMD) are listed in Table 1, which indicates that relative mean deviations of the temperatures among these points are less than 1.0%. On the other hand, another T-type thermocouple is inserted into the droplet which can capture center temperature of droplet [14]. The enhancement of heat transfer by thermocouple will lead to the higher measured temperature of droplet than its actual value. To correct the measured temperature, we insert thermocouple into ice-water mixture in a refrigerator and the insertion depth is equal to that in droplet. It is found that the mean temperature measured by thermocouple is about 0.45 °C higher than ice-water (0 °C). Thus the present measured temperatures of droplet are corrected according the above error analysis. The accuracy of center temperature measurement is about ±0.1 °C. Contact digital temperature and humidity sensor (JWSH-5VBDD, ±0.5 °C & ±3% RH) is installed for monitoring and recording data on humid air condition. A data acquisition system (Agilent-34970A) is used to collect all data in present experimental system to facilitate the following research. The microscopic image system consists of stereomicroscope, camera and a luminescence house/annular illuminator unit. The stereomicroscope (SZX-ZB7, OLYMPUS) is used to observe the microcosmic frosting process, whose magnification is from 12 to 84. The CCD microscope camera (Moticam2506) can automatically capture momentary frosting phenomenon. The luminescence house/annular illuminator unit (MLC150C, MOTIC) can emit luminescence light without thermal radiation for observation. The frost height is directly measured by image analysis system when the experimental image has been collected. The freezing time is defined as the period from the moment when the cold surface temperature begins to decrease to the time when water droplets freezes
Fig. 1. Schematic illustration of experimental system.
J. Gong et al. / International Communications in Heat and Mass Transfer 82 (2017) 139–144
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In order to investigate the impact of air cleanliness on the frosting process, air quality detector (DC1700) is used to monitor and record PM2.5 concentration value. 3. Results and discussion 3.1. Solidification of solution droplet on a cold flat plate
totally [15]. The moment of the decrease of cold surface temperature can be recorded from the collected data. And the time of complete freezing of water droplets can be obtained through analyzing the captured images. In this way, the freezing time is measured.
2.2. Test details Fine particle (PM2.5) refers to a particle which has an aerodynamic equivalent diameter less than or equal 2.5 μm. PM2.5 has small particle size and large specific surface area which makes it suspended in the air for long time, and it is an important index of air quality. Research suggests that the proportion of fine particles in the air is rising [16]. The water soluble ion is an important chemical component of PM2.5, including sulfate, nitrate, chloride, ammonium, etc. [17–22]. Dust particle is one of the important types of atmospheric particles and the composition of dust particles silica has is more than 50% [23]. In summary, the particles in the air are mainly sulfate, nitrate, ammonium, chloride and silica, etc. The effects of solute variety and concentration on droplet freezing are studied. The double distilled water is used to eliminate the effects of nonvolatile electrolyte and colloid and some soluble gas in water (such as carbon dioxide and ammonia) as far as possible. Analytical reagents with a concentration of 99.5% are used in the experiments, and the solutions are prepared by gradient dilution method. The water droplet is distributed by a microliter syringe on the center of plate. The microliter syringe has a droplet size deviation of 0.01 μl. The solvents include NaCl, Na2SO4, NH4Cl, (NH4)2SO4 and SiO2, and the concentrations are 10−1, 10−2, 10−3, 10−4, 10− 5, 10− 6, 10− 7, 10− 8, 10− 9, 10− 10 and 10−11 mol l−1 respectively.
3.1.1. Freezing process of solution droplets Fig. 3 shows the comparisons of variation of supercooling degree of various solution droplets with pure water droplets at different concentrations values. As shown in Fig. 3, the supercooling degree is very low in the freezing process of pure water droplets. In Na2SO4, NaCl and (NH4)2SO4 solutions, the supercooling degrees of solution droplets are higher than that of pure water droplets and the solution droplets are more prone to freeze. It is also seen that the supercooling degrees are different for solution droplets at different concentrations. For example, in Na2SO4 solution, the supercooling degree increases with increasing concentration in the range of 10−11 to 10− 8 mol l− 1. And then the supercooling degree basically remains unchanged and keeps stable in the range of 10−8 to 10−5 mol l−1, which is about five degrees Celsius higher than that of pure water droplet. However, when the concentration in the range of 10−5 to 10−1 mol l−1, the supercooling degree subsequently falls with the concentration increasing. In NaCl and
-5
-10
T/ C
Fig. 2. Locations of thermocouples inserted in the cold flat plate.
The air quality is one of the influencing factors in the solidification process of droplets. Therefore, the purpose of this section is to experimentally study the effects of solute variety and concentration on the droplet freezing, and lay the foundation for further research on the frosting process. This section mainly focuses on the study of the droplet freezing characteristics for different solutions at different concentrations. Therefore the environment experimental conditions (air temperature, humidity and velocity), the set value of cold flat plate temperature and volume of droplet are kept constant. The temperature of air Ta = 17.0 °C, the relative humidity of air RH = 71.8%, and the velocity of air u = 0.171 m/s. The cold plate temperature Tw decreases from 0 °C to the set value −23.9 °C. The volume of droplet V = 15 μl. The cold plate cools as the semiconductor chilling plate temperature decreases, and the freezing temperature and time of droplets are collected and recorded in turn with a decrease in temperature. After finishing the experiment, the cold plate is heated to 0 °C by reverse voltage to melt the solid droplet. In the end, the cold plate is washed repeatedly in order to make next experiment.
-15 Table 1 Experimental data by five T-type thermocouples. Time (s)
Point 1 (°C)
Point 2 (°C)
Point 3 (°C)
Point 4 (°C)
Point 5 (°C)
RMD (%)
0.0 1.0 2.0 3.0 4.0
−14.955 −15.102 −15.225 −15.336 −15.406
−14.916 −15.036 −15.149 −15.250 −15.325
−15.083 −15.216 −15.334 −15.444 −15.522
−14.806 −14.915 −14.993 −15.115 −15.196
−14.698 −14.747 −14.861 −14.998 −15.145
0.750 0.918 0.981 0.904 0.774
NH4Cl
(NH4)2SO4
NaCl
Na2SO4
H2O -20 -12 10
-10
10
-8
10
10
-6
-4
10
concentration/mol·L
-1
-2
10
0
10
Fig. 3. Supercooling degree variations of various solution droplets at different concentrations.
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(NH4)2SO4 solutions, the supercooling degree shows a similar trend, however the influence becomes smaller than that in Na2SO4 solution. The effect of the NH4Cl solution is considering complex at different concentrations. In NH4Cl solution, the supercooling degree is slightly higher than that of pure water droplet in the low concentration of 10−11 mol l−1 and the solution plays a role in promoting the freezing process. When the concentration increases in the range of 10− 10 to 10−5 mol l−1, the promotion no longer works, even in the concentration of 10− 9 mol l− 1, the supercooling degree is lower than that of pure water droplet. Then the promotion of freezing comes back and the supercooling degree improves with the concentration increases from 10−6 to 10−3 mol l−1. Nevertheless, as the concentration in the range of 10−2 to 10−1 mol l−1, the supercooling degree is once again lower than that of pure water droplet and the solution plays a role in restraining the freezing process. Fig. 4 shows the comparisons of freezing time variations of various solution droplets with pure water droplets at different concentrations values. In Na2SO4 solution, the freezing time decreases with an increasing concentration in the range of 10−11 to 10−8 mol l−1. And then the freezing time basically remains stable in the range of 10− 8 to 10−5 mol l−1. Subsequently, the freezing time increases with the concentration increasing from 10−5 to 10−1 mol l−1. The changes of the freezing time in NaCl and (NH4)2SO4 solutions are similar to that in Na2SO4 solution. For NH4Cl solution, when the concentration is low in 10−11 mol l−1, the freezing time is slightly lower than that of pure water droplet and the solution plays a role in promoting the freezing process. However, the promotion no longer works as the concentration increasing from 10−10 to 10−5 mol l−1, even in the concentration of 10−9 mol l−1, the freezing time is higher than that of pure water droplet and the solution plays a role in restraining the freezing process. And then the promotion of freezing returns and the freezing time decreases with the concentration increases from 10−6 to 10−3 mol l−1. When the concentration is in the range of 10−2 to 10−1 mol l−1, the freezing time is once again higher than that of pure water droplet. From the foregoing comparisons in Figs. 3 and 4, for a given solution the variation of the freezing time shows a reverse trend to that of the supercooling degree. This means the supercooling degree directly affects the freezing time as one would expect. The effect of concentration on the supercooling degree and freezing time are different for different solutes. Because the composition and concentration of the unstable solution droplet can affect the nucleation and heat transfer. Based on the above analysis, it can be seen that the coupled effect of cation and anion strongly influences the freezing time and supercooling degree. In high concentration ranges, the supercooling degree difference among solutes is small. The difference of supercooling degree
among different solutes mainly occurs when the solute concentrate is smaller than 10−4 mol/l. For cations, it is shown that the solution containing Na+ with different anion (SO24 − and Cl−) has higher supercooling degree than that containing the NH+ 4 . At the same time, it can also be observed that the solution containing SO24 − has higher supercooling degree than that containing Cl−. Compared with NH+ 4 , Na+ is a stronger electrolyte. Therefore, it can be concluded that strong electrolyte of cation has higher supercooling degree. The reason is that the weak cation NH+ 4 hydrolyzes which may capture water molecules from unit cell of the ice and prevent the formation and growth of ice in the water existed as hydrated crystal. On the other hand, the SO2− 4 ion, which picks up water molecules by hydrogen bond, acts as the has role of unit cell of the ice crystal. As a result, the solution of SO2− 4 higher supercooling degree than those of Cl−. From Fig. 3, it can also be observed that the influence of anion on supercooling degree is stronger than that of cation. The above analysis is aimed at the lower concentrate solute which is smaller than 10−4 mol/l. When the solute concentration is larger, it can be found that the freezing time becomes shorter. The main reason is that the polarization effect becomes dominant which prevents the generation of hydrogen bond. Hydrogen bond is the basic bridge forming the ice crystal structure. Therefore, the freezing process is delayed when the solute concentration is larger.
3.1.2. Freezing process of droplets mixed SiO2 Fig. 5 shows the comparisons of supercooling degree variations of various droplets mixed SiO2 with pure water droplets at different concentrations values. The particle diameters are respectively 12 nm and 40 nm. As shown in Fig. 5, when the concentration increases from 10−11 to −7 10 mol l−1, the supercooling degree is constantly lowered as the SiO2 particle d = 12 nm, which is in an inverse relationship as the SiO2 particle d = 40 nm. All the solutions mixed SiO2 except the concentration of the particle d = 40 nm is 10−11 mol l−1 play a role in promoting freezing. The supercooling degree increases to a certain peak with the concentration of the solution mixed SiO2 particle d = 12 nm increasing to 10−6 mol l− 1. And then the supercooling degree starts to reduce to the minimum with the concentration increasing to 10−4 mol l−1. The supercooling degree decreases with the concentration of the solution mixed SiO2 particle d = 40 nm increasing from 10−7 to 10−4 mol L−1. When the concentration is in the range from 10−4 to 10− 1 mol l−1, the supercooling degree of both solutions mixed different sizes SiO2 increases continually. When the particle diameter d is 40 nm, the supercooling degree is in basic agreement on that of pure water droplets. When the particle diameter d is 12 nm, the supercooling degree is
-5
100 80
-10
tf/s
T/ C
60 40
-15 20 0 -12 10
NH4Cl
(NH4)2SO4
NaCl
Na2SO4
SiO2 40 nm H2O
H2O -10
10
-8
10
-6
10
-4
10
concentration/mol·L
-1
SiO2 12 nm
-2
10
0
10
Fig. 4. Freezing time variations of various solution droplets at different concentrations.
-20 -13 10
-11
10
-9
10
-7
10
-5
10
concentration/mol·L
-3
-1
10
-1
10
Fig. 5. Supercooling degree variations of droplets mixed SiO2 at different particle sizes.
J. Gong et al. / International Communications in Heat and Mass Transfer 82 (2017) 139–144
143
6
100
m / kg·m
-2
80
tf/s
60 40
5
4 SiO2 12 nm
20
SiO2 40 nm H2O
0 -13 10
-11
10
-9
-7
10
10
-5
10
concentration/mol·L
-3
-1
10
-1
10
3
0
100
200
C /µg·m
300
-3
Fig. 6. Freezing time variations of droplets mixed SiO2 at different particle sizes.
Fig. 8. Frost crystal mass variations at different PM2.5 concentration values.
obviously lower than that of the pure water droplets and the silica particle plays a role in inhibiting the freezing process. Fig. 6 shows the comparisons of freezing time variations of various droplets mixed SiO2 with pure water droplets at different concentrations values. From the Fig. 6, the freezing time of droplets mixed SiO2 particle d = 40 nm is shorter than that of pure water droplets in the range of 10−9 to 10−5 mol l−1 and 10−3 to 10−1 mol l−1. When the particle diameter d is 12 nm, the freezing time of droplets mixed SiO2 is obviously shorter than that of pure water droplets in the range of 10−11 to 10−5 mol l−1 and the silica particle plays a role in inhibiting the freezing process. In short, from Figs. 5 and 6, the solutions mixed SiO2 especially the concentration of the particle d = 12 nm in the range of 10− 11 to 10−9 mol l−1 and 10−6 to 10−5 mol l−1 play a role in promoting freezing. The freezing time of droplets mixed SiO2 particle d = 40 nm is shorter than that of pure water droplets in the range of 10−9 to 10−5 mol l−1 and 10−3 to 10−1 mol l−1.
u = 0.160 m/s, and the cold plate temperature Tw = − 16.5 °C. For the three cases studied, the PM2.5 concentration values are22 μg m−3, 143 μg m−3 and 257 μg m−3 respectively. Figs. 7 and 8 show the variation of frost heights and frost crystal mass with time at different PM2.5 concentration values. The greater the PM2.5 concentration value is, the faster the frost crystal growth rate is, the thicker the frost layer is, and the greater amount of the frost crystal is. In Fig. 7, the frost heights at PM2.5 concentration C = 143 μg m−3 and C = 257 μg m−3 are respectively 9.5% and 18.7% higher than that at PM2.5 concentration C = 22 μg m−3. In Fig. 8, the frost crystal mass increases with the PM2.5 concentration value increasing. This is because suspended particles in the air can act as nucleating substrate and the Gibbs free energy for heterogeneous nucleation is smaller than that for homogeneous nucleation. When the PM2.5 concentration value is larger, the frost crystal nucleation is promoted and the frost crystals are more easily deposited. 4. Conclusion
3.2. Experimental study on frosting at different PM2.5 concentration values on cold flat plate This research focuses on the effect of air quality on frost height and frost crystal mass in frosting process. The temperature of air Ta = 10.8 °C, the relative humidity of air RH = 41.2%, the velocity of air 3.0 2.5
C= -3
22 µg·m -3 143 µg·m -3 257 µg·m
h/mm
2.0 1.5 1.0 0.5 0.0
0
60
120
180
240
300
t/min Fig. 7. Frost height variations with time at different PM2.5 concentration values.
This paper has experimentally studied the effects of solute variety and concentration on droplet freezing and the process of frost layer growth under different PM2.5 concentrations. The results indicate that for a given solution the variation of the freezing time showed a trend opposite to that of the supercooling degree. The supercooling degree directly affects the freezing time. The supercooling degree and freezing time change with solution concentration on different solutes. The three solutions including Na2SO4 solution, NaCl solution and (NH4)2SO4 solution show good promoting effect in the freezing process. The effect of the NH4Cl solution is more complex at different concentrations. The solutions mixed SiO2 especially the concentration of the particle d = 12 nm in the range of 10− 11 to 10−9 mol l−1 and 10− 6 to 10−5 mol l−1 play a role in promoting freezing. When the solute concentrate is smaller than 10−4 mol/l, the solution of Na+ has higher supercooling degree than those of the NH+ 4 and the has higher supercooling degree than those of the Cl−. solution of SO2− 4 The formation process is disrupted by the hydrolyzation process generated by the weak cation. At the same time, the hydrated ion generated which acts as unit cell enhances the formation process of by the SO2− 4 ice crystal. The effect of anion on supercooling degree is much obvious than the cation. For high solute concentration range, the polarization effect becomes dominant which prevents the generation of hydrogen bond and the formation of ice crystal. In addition, the results indicate that the greater PM2.5 concentration is, the thicker of the frost layer is, and the greater amount of the frost
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crystal is, which is due to suspended particles in the air that can act as nucleating substrate and the Gibbs free energy for heterogeneous nucleation is smaller than that for homogeneous nucleation. The frost crystal nucleation is promoted and the frost crystals are more easily deposited when the greater of the PM2.5 concentration value is.
Acknowledgments The present paper is financially supported by the National Natural Science Foundation of China (No. 51106013, 50806059, 51109174), China Postdoctoral Science Foundation (No. 2012M511998). References [1] M. Kandula, Frost growth and densification in laminar flow over flat surfaces[J], Int. J. Heat Mass Transf. 54 (15–16) (2011) 3719–3731. [2] M. Kandula, Frost growth and densification on a flat surface in laminar flow with variable humidity[J], Int. Commun. Heat Mass 39 (8) (2012) 1030–1034. [3] K. Matsumoto, M. Honda, Y. Ito, et al., Study on measurement of frost dimensions/ distribution and frost crystals scraping force using scanning probe microscope (investigation on influence of humidity)[J], Int. J. Refrig. 38 (2014) 341–351. [4] Y. Hayashi, A. Aoki, S. Adachi, et al., Study of frost properties correlating with frost formation types[J], J. Heat Transf. 99 (1977) 239–245. [5] X. Wu, W. Dai, W. Xu, et al., Mesoscale investigation of frost formation on a cold surface[J], Exp. Thermal Fluid Sci. 31 (2007) 1043–1048. [6] K.C. Tan, W. Ho, J.I. Katz, et al., A study of the occurrence of supercooling of water[J], Am. J. Phys. 84 (4) (2016) 293–300. [7] V. Bahadur, L. Mishchenko, B. Hatton, et al., Predictive model for ice formation on superhydrophobic surfaces[J], Langmuir 27 (2011) 14143–14150. [8] C.J.L. Hermes, R.O.J.R. Picucco, B. Jr, et al., A study of frost growth and densification on flat surfaces[J], Exp. Thermal Fluid Sci. 33 (2) (2009) 371–379.
[9] H.C. Parish, C.F. Sepsy, A numerical analysis of frost formation under forced convection[J], ASHRAE Semiannual Meet. 2331 (1972) 236–251. [10] D.K. Yang, K.S. Lee, D.J. Cha, Frost formation on a cold surface under turbulent flow[J], Int. J. Refrig. 29 (2) (2006) 164–169. [11] K.S. Lee, W.S. Kim, T.H. Lee, A one-dimensional model for frost formation on a cold flat surface[J], Int. J. Heat Mass Transf. 40 (18) (1997) 4359–4365. [12] K.S. Lee, S. Jhee, D.K. Yang, Prediction of the frost formation on a cold flat surface[J], Int. J. Heat Mass Transf. 46 (20) (2003) 3789–3796. [13] A.Z. Sahin, Effective thermal conductivity of frost during the crystal growth period[J], J. Heat Mass Transf. 43 (4) (2000) 539–553. [14] J.P. Hindmarsh, A.B. Russell, X.D. Chen, Experimental and numerical analysis of the temperature transition of a suspended freezing water droplet[J], Int. J. Heat Mass Transf. 46 (2003) 1199–1213. [15] L.Y. Huang, A Study on the Effects of Cold Surface Characteristics on Frost Formation[D]Doctoral dissertation Beijing University of Technology, Beijing, 2011. [16] Z.P. Bai, B.Q. Wang, Pollution and Control of Particulates in the Air[M], Chemical Industry Press, Beijing, 2011. [17] S. Liu, M. Hu, S. Slanina, et al., Size distribution and source analysis of ionic compositions of aerosols in polluted periods at Xinken in Pearl River Delta (PRD) of China[J], Atmos. Environ. 42 (25) (2008) 6284–6295. [18] K. Acker, S. Mertes, D. Möller, et al., Case study of cloud physical and chemical processes in low clouds at Mt. Brocken[J], Atmos. Res. 64 (1) (2002) 41–51. [19] J.H. Seinfeld, S.N. Pandis, Atmospheric Chemistry and Physics: From Air Pollution to Climate Change[M], John Wiley & Sons, New York, 2012. [20] R.K. Pathak, W.S. Wu, T. Wang, Summertime PM 2.5 ionic species in four major cities of China: nitrate formation in an ammonia-deficient atmosphere[J], Atmos. Chem. Phys. 9 (5) (2009) 1711–1722. [21] T. Anttila, A. Kiendler-Scharr, R. Tillmann, et al., On the reactive uptake of gaseous compounds by organic-coated aqueous aerosols: theoretical analysis and application to the heterogeneous hydrolysis of N2O5[J], J. Phys. Chem. 110 (35) (2006) 10435–10443. [22] M. Hallquist, D.J. Stewart, S.K. Stephenson, et al., Hydrolysis of N2O5 on sub-micron sulfate aerosols[J], Phys. Chem. Chem. Phys. 5 (16) (2003) 3453–3463. [23] L. Wei, F. Qi, W. Tao, et al., Physicochemistry and mineralogy of storm dust and dust sediment in northern China[J], Adv. Atmos. Sci. 21 (5) (2004) 775–783.
Contents lists available at ScienceDirect
International Communications in Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ichmt
An experimental study of the effect of air quality on frosting on cold flat surface Jianying Gong a,⁎, Jinjuan Sun b, Guojun Li a a b
MOE Key Laboratory of Thermo-Fluid Science and Engineering, School of Energy and Power Engineering, Xi'an Jiaotong University, Xi'an 710049, China School of Mechatronic Engineering, Xi'an Technological University, Xi'an 710021, China
a r t i c l e Available online xxxx Keywords: Freezing of droplet Supercooling degree PM2.5 concentration Frost formation
i n f o
a b s t r a c t The effects of air quality in the freezing process of droplets and the frost crystal growth on cold flat plate are studied experimentally. It is found that the air quality has important influence in the frosting process. The supercooling degree and freezing time change with solution concentration on different solutes. When supercooled droplets are in the instability state, the composition and concentration of solution can affect the nucleation and heat transfer, and most of the solute can increase the degree of supercooling and accelerate the freezing process. Solutions with cation of strong electrolyte have higher supercooling degree because the weak cation will hydrolyze. The hydrated ion can accelerate the formation of ice crystal. In addition, the frosting process on cold flat plate under different fine particle (PM2.5) concentrations is also studied in form of frost height and mass variations. The result shows that the greater the PM2.5 concentration is, the thicker the frost layer is and the greater the amount of the frost crystal is. This is because suspended particles in the air that can act as nucleating substrate to promote heterogeneous nucleation and the frost crystals are more easily deposited. © 2017 Elsevier Ltd. All rights reserved.
1. Introduction Frost formation has important effects in many fields, such as refrigeration industry, air-conditioning, aviation, etc. The process of frost formation associated with transient heat and mass transfer is extremely complex, whatever frost forms only if the temperature of cold flat plate is less than zero degrees Celsius and the ambient dew point temperature. The presence of frost will deteriorate refrigeration capacity due to decreased heat transfer coefficient and increased pressure drop, and defrosting will lead to higher energy consumption and operation cost. It is therefore essential to investigate physical mechanism on the frost formation. Over the last several decades, research on frost formation has been studied both experimentally and theoretically. Frost growth was studied through experimental [1–3]. Hayashi et al. [4] photographed the whole process of frost formation, which was divided largely into three stages: crystal growth period, frost layer growth period and frost layer full growth period. As the inception of crystal growth period, the solidification of water droplet has an essential role in the whole process of frosting and attracted further attention in recent times. Wu et al. [5] investigated the freezing of supercooled condensate droplets in the frost formation, and the freezing onset time and diameter of condensate
⁎ Corresponding author. E-mail address: [email protected] (J. Gong).
http://dx.doi.org/10.1016/j.icheatmasstransfer.2017.02.013 0735-1933/© 2017 Elsevier Ltd. All rights reserved.
droplets were characterized. Tan et al. [6] studied the occurrence of supercooling of water correlated with the ability of the chilling medium to promptly nucleate ice. Bahadur et al. [7] developed a physical model to predict ice formation on cooled superhydrophobic plates resulting from the impact of supercooled water droplets, and this modeling approach analyzed the multiple phenomena influencing ice formation on superhydrophobic plates. The frost layer composed of a large number of frost crystals behaves as a porous medium into which diffusion of water vapor leads to an increase of both thickness and density [8]. The models through the correlations to conform the experimental data were established for predicting frost growth by Parish and Sepsy [9]. Yang et al. [10] attempted to develop a mathematical model that can predict the characteristics of the frost growth and the heat transfer under turbulent flow. Lee et al. [11,12] presented a different theoretical model by considering the frost layer as porous media. Sahin [13] found that frost density was not the sole parameter affecting effective frost thermal conductivity. The foregoing studies focused on the laws of frost layer height, frost density, frost surface temperature, and frost thermal conductivity influenced by some factors such as cold flat surfaces temperature, environmental air humidity, temperature and velocity, etc. In the refrigeration industry, air-conditioning, aviation, and other engineering fields, many suspended particles exist in the frosting environment and the frost formation process mostly happens in the atmospheric environment. The air is not pure, and is affected by the haze. The air quality will affect the frosting process, however very few studies have considered the influence of particles in the air.
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Nomenclature C d h m FRH T t u V
PM2.5 concentration (μg m−3) particle diameter (nm) frost height (mm) frost crystal mass (kg m−2) relative humidity temperature (°C) time (s or min) velocity of air (m/s) volume of water droplet (μl)
Greek symbols ΔT supercooling degree (°C) Subscripts and superscripts a air w cold flat plate f freezing
The purpose of this paper is to build an experimental system to study the effects of air quality on the characteristics of the freezing process of droplets and the frost crystal growth on cold flat plate. Section 2 describes an experimental system for frost formation. The variations of the supercooling degree and freezing time of variety solutions at different concentrations and the process of frost layer growth under different PM2.5 concentrations are obtained in Section 3, followed by a brief conclusion in Section 4. 2. Experimental method 2.1. Experimental setup An experimental system is set up to study the frost formation process on cold flat plate, which consists of a list of components as shown in Fig. 1.
An isolated organic glass tunnel is designed and built to avoid the interference of environment, which has two quartz glass viewing ports on both top and side of the tunnel to observe frost formation by the microscopic image system. The test section is made of red copper sized at 60 mm × 40 mm × 8 mm, which is cooled by the semiconductor chilling plate (C-1208). The circulated cooling water piped from the lowtemperature thermostat bath (DC-4015, ±0.1 °C) is used as the chiller for the hot side of the semiconductor chilling plate. The five T-type thermocouples (GBTS200, ±0.1 °C) are used to measure the cold plate temperature. Fig. 2 shows the exact locations of thermocouples inserted in the cold flat plate. All the thermocouples are located at the same level of 1 mm beneath the surface of copper plate. Relative mean deviations (RMD) are listed in Table 1, which indicates that relative mean deviations of the temperatures among these points are less than 1.0%. On the other hand, another T-type thermocouple is inserted into the droplet which can capture center temperature of droplet [14]. The enhancement of heat transfer by thermocouple will lead to the higher measured temperature of droplet than its actual value. To correct the measured temperature, we insert thermocouple into ice-water mixture in a refrigerator and the insertion depth is equal to that in droplet. It is found that the mean temperature measured by thermocouple is about 0.45 °C higher than ice-water (0 °C). Thus the present measured temperatures of droplet are corrected according the above error analysis. The accuracy of center temperature measurement is about ±0.1 °C. Contact digital temperature and humidity sensor (JWSH-5VBDD, ±0.5 °C & ±3% RH) is installed for monitoring and recording data on humid air condition. A data acquisition system (Agilent-34970A) is used to collect all data in present experimental system to facilitate the following research. The microscopic image system consists of stereomicroscope, camera and a luminescence house/annular illuminator unit. The stereomicroscope (SZX-ZB7, OLYMPUS) is used to observe the microcosmic frosting process, whose magnification is from 12 to 84. The CCD microscope camera (Moticam2506) can automatically capture momentary frosting phenomenon. The luminescence house/annular illuminator unit (MLC150C, MOTIC) can emit luminescence light without thermal radiation for observation. The frost height is directly measured by image analysis system when the experimental image has been collected. The freezing time is defined as the period from the moment when the cold surface temperature begins to decrease to the time when water droplets freezes
Fig. 1. Schematic illustration of experimental system.
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In order to investigate the impact of air cleanliness on the frosting process, air quality detector (DC1700) is used to monitor and record PM2.5 concentration value. 3. Results and discussion 3.1. Solidification of solution droplet on a cold flat plate
totally [15]. The moment of the decrease of cold surface temperature can be recorded from the collected data. And the time of complete freezing of water droplets can be obtained through analyzing the captured images. In this way, the freezing time is measured.
2.2. Test details Fine particle (PM2.5) refers to a particle which has an aerodynamic equivalent diameter less than or equal 2.5 μm. PM2.5 has small particle size and large specific surface area which makes it suspended in the air for long time, and it is an important index of air quality. Research suggests that the proportion of fine particles in the air is rising [16]. The water soluble ion is an important chemical component of PM2.5, including sulfate, nitrate, chloride, ammonium, etc. [17–22]. Dust particle is one of the important types of atmospheric particles and the composition of dust particles silica has is more than 50% [23]. In summary, the particles in the air are mainly sulfate, nitrate, ammonium, chloride and silica, etc. The effects of solute variety and concentration on droplet freezing are studied. The double distilled water is used to eliminate the effects of nonvolatile electrolyte and colloid and some soluble gas in water (such as carbon dioxide and ammonia) as far as possible. Analytical reagents with a concentration of 99.5% are used in the experiments, and the solutions are prepared by gradient dilution method. The water droplet is distributed by a microliter syringe on the center of plate. The microliter syringe has a droplet size deviation of 0.01 μl. The solvents include NaCl, Na2SO4, NH4Cl, (NH4)2SO4 and SiO2, and the concentrations are 10−1, 10−2, 10−3, 10−4, 10− 5, 10− 6, 10− 7, 10− 8, 10− 9, 10− 10 and 10−11 mol l−1 respectively.
3.1.1. Freezing process of solution droplets Fig. 3 shows the comparisons of variation of supercooling degree of various solution droplets with pure water droplets at different concentrations values. As shown in Fig. 3, the supercooling degree is very low in the freezing process of pure water droplets. In Na2SO4, NaCl and (NH4)2SO4 solutions, the supercooling degrees of solution droplets are higher than that of pure water droplets and the solution droplets are more prone to freeze. It is also seen that the supercooling degrees are different for solution droplets at different concentrations. For example, in Na2SO4 solution, the supercooling degree increases with increasing concentration in the range of 10−11 to 10− 8 mol l− 1. And then the supercooling degree basically remains unchanged and keeps stable in the range of 10−8 to 10−5 mol l−1, which is about five degrees Celsius higher than that of pure water droplet. However, when the concentration in the range of 10−5 to 10−1 mol l−1, the supercooling degree subsequently falls with the concentration increasing. In NaCl and
-5
-10
T/ C
Fig. 2. Locations of thermocouples inserted in the cold flat plate.
The air quality is one of the influencing factors in the solidification process of droplets. Therefore, the purpose of this section is to experimentally study the effects of solute variety and concentration on the droplet freezing, and lay the foundation for further research on the frosting process. This section mainly focuses on the study of the droplet freezing characteristics for different solutions at different concentrations. Therefore the environment experimental conditions (air temperature, humidity and velocity), the set value of cold flat plate temperature and volume of droplet are kept constant. The temperature of air Ta = 17.0 °C, the relative humidity of air RH = 71.8%, and the velocity of air u = 0.171 m/s. The cold plate temperature Tw decreases from 0 °C to the set value −23.9 °C. The volume of droplet V = 15 μl. The cold plate cools as the semiconductor chilling plate temperature decreases, and the freezing temperature and time of droplets are collected and recorded in turn with a decrease in temperature. After finishing the experiment, the cold plate is heated to 0 °C by reverse voltage to melt the solid droplet. In the end, the cold plate is washed repeatedly in order to make next experiment.
-15 Table 1 Experimental data by five T-type thermocouples. Time (s)
Point 1 (°C)
Point 2 (°C)
Point 3 (°C)
Point 4 (°C)
Point 5 (°C)
RMD (%)
0.0 1.0 2.0 3.0 4.0
−14.955 −15.102 −15.225 −15.336 −15.406
−14.916 −15.036 −15.149 −15.250 −15.325
−15.083 −15.216 −15.334 −15.444 −15.522
−14.806 −14.915 −14.993 −15.115 −15.196
−14.698 −14.747 −14.861 −14.998 −15.145
0.750 0.918 0.981 0.904 0.774
NH4Cl
(NH4)2SO4
NaCl
Na2SO4
H2O -20 -12 10
-10
10
-8
10
10
-6
-4
10
concentration/mol·L
-1
-2
10
0
10
Fig. 3. Supercooling degree variations of various solution droplets at different concentrations.
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(NH4)2SO4 solutions, the supercooling degree shows a similar trend, however the influence becomes smaller than that in Na2SO4 solution. The effect of the NH4Cl solution is considering complex at different concentrations. In NH4Cl solution, the supercooling degree is slightly higher than that of pure water droplet in the low concentration of 10−11 mol l−1 and the solution plays a role in promoting the freezing process. When the concentration increases in the range of 10− 10 to 10−5 mol l−1, the promotion no longer works, even in the concentration of 10− 9 mol l− 1, the supercooling degree is lower than that of pure water droplet. Then the promotion of freezing comes back and the supercooling degree improves with the concentration increases from 10−6 to 10−3 mol l−1. Nevertheless, as the concentration in the range of 10−2 to 10−1 mol l−1, the supercooling degree is once again lower than that of pure water droplet and the solution plays a role in restraining the freezing process. Fig. 4 shows the comparisons of freezing time variations of various solution droplets with pure water droplets at different concentrations values. In Na2SO4 solution, the freezing time decreases with an increasing concentration in the range of 10−11 to 10−8 mol l−1. And then the freezing time basically remains stable in the range of 10− 8 to 10−5 mol l−1. Subsequently, the freezing time increases with the concentration increasing from 10−5 to 10−1 mol l−1. The changes of the freezing time in NaCl and (NH4)2SO4 solutions are similar to that in Na2SO4 solution. For NH4Cl solution, when the concentration is low in 10−11 mol l−1, the freezing time is slightly lower than that of pure water droplet and the solution plays a role in promoting the freezing process. However, the promotion no longer works as the concentration increasing from 10−10 to 10−5 mol l−1, even in the concentration of 10−9 mol l−1, the freezing time is higher than that of pure water droplet and the solution plays a role in restraining the freezing process. And then the promotion of freezing returns and the freezing time decreases with the concentration increases from 10−6 to 10−3 mol l−1. When the concentration is in the range of 10−2 to 10−1 mol l−1, the freezing time is once again higher than that of pure water droplet. From the foregoing comparisons in Figs. 3 and 4, for a given solution the variation of the freezing time shows a reverse trend to that of the supercooling degree. This means the supercooling degree directly affects the freezing time as one would expect. The effect of concentration on the supercooling degree and freezing time are different for different solutes. Because the composition and concentration of the unstable solution droplet can affect the nucleation and heat transfer. Based on the above analysis, it can be seen that the coupled effect of cation and anion strongly influences the freezing time and supercooling degree. In high concentration ranges, the supercooling degree difference among solutes is small. The difference of supercooling degree
among different solutes mainly occurs when the solute concentrate is smaller than 10−4 mol/l. For cations, it is shown that the solution containing Na+ with different anion (SO24 − and Cl−) has higher supercooling degree than that containing the NH+ 4 . At the same time, it can also be observed that the solution containing SO24 − has higher supercooling degree than that containing Cl−. Compared with NH+ 4 , Na+ is a stronger electrolyte. Therefore, it can be concluded that strong electrolyte of cation has higher supercooling degree. The reason is that the weak cation NH+ 4 hydrolyzes which may capture water molecules from unit cell of the ice and prevent the formation and growth of ice in the water existed as hydrated crystal. On the other hand, the SO2− 4 ion, which picks up water molecules by hydrogen bond, acts as the has role of unit cell of the ice crystal. As a result, the solution of SO2− 4 higher supercooling degree than those of Cl−. From Fig. 3, it can also be observed that the influence of anion on supercooling degree is stronger than that of cation. The above analysis is aimed at the lower concentrate solute which is smaller than 10−4 mol/l. When the solute concentration is larger, it can be found that the freezing time becomes shorter. The main reason is that the polarization effect becomes dominant which prevents the generation of hydrogen bond. Hydrogen bond is the basic bridge forming the ice crystal structure. Therefore, the freezing process is delayed when the solute concentration is larger.
3.1.2. Freezing process of droplets mixed SiO2 Fig. 5 shows the comparisons of supercooling degree variations of various droplets mixed SiO2 with pure water droplets at different concentrations values. The particle diameters are respectively 12 nm and 40 nm. As shown in Fig. 5, when the concentration increases from 10−11 to −7 10 mol l−1, the supercooling degree is constantly lowered as the SiO2 particle d = 12 nm, which is in an inverse relationship as the SiO2 particle d = 40 nm. All the solutions mixed SiO2 except the concentration of the particle d = 40 nm is 10−11 mol l−1 play a role in promoting freezing. The supercooling degree increases to a certain peak with the concentration of the solution mixed SiO2 particle d = 12 nm increasing to 10−6 mol l− 1. And then the supercooling degree starts to reduce to the minimum with the concentration increasing to 10−4 mol l−1. The supercooling degree decreases with the concentration of the solution mixed SiO2 particle d = 40 nm increasing from 10−7 to 10−4 mol L−1. When the concentration is in the range from 10−4 to 10− 1 mol l−1, the supercooling degree of both solutions mixed different sizes SiO2 increases continually. When the particle diameter d is 40 nm, the supercooling degree is in basic agreement on that of pure water droplets. When the particle diameter d is 12 nm, the supercooling degree is
-5
100 80
-10
tf/s
T/ C
60 40
-15 20 0 -12 10
NH4Cl
(NH4)2SO4
NaCl
Na2SO4
SiO2 40 nm H2O
H2O -10
10
-8
10
-6
10
-4
10
concentration/mol·L
-1
SiO2 12 nm
-2
10
0
10
Fig. 4. Freezing time variations of various solution droplets at different concentrations.
-20 -13 10
-11
10
-9
10
-7
10
-5
10
concentration/mol·L
-3
-1
10
-1
10
Fig. 5. Supercooling degree variations of droplets mixed SiO2 at different particle sizes.
J. Gong et al. / International Communications in Heat and Mass Transfer 82 (2017) 139–144
143
6
100
m / kg·m
-2
80
tf/s
60 40
5
4 SiO2 12 nm
20
SiO2 40 nm H2O
0 -13 10
-11
10
-9
-7
10
10
-5
10
concentration/mol·L
-3
-1
10
-1
10
3
0
100
200
C /µg·m
300
-3
Fig. 6. Freezing time variations of droplets mixed SiO2 at different particle sizes.
Fig. 8. Frost crystal mass variations at different PM2.5 concentration values.
obviously lower than that of the pure water droplets and the silica particle plays a role in inhibiting the freezing process. Fig. 6 shows the comparisons of freezing time variations of various droplets mixed SiO2 with pure water droplets at different concentrations values. From the Fig. 6, the freezing time of droplets mixed SiO2 particle d = 40 nm is shorter than that of pure water droplets in the range of 10−9 to 10−5 mol l−1 and 10−3 to 10−1 mol l−1. When the particle diameter d is 12 nm, the freezing time of droplets mixed SiO2 is obviously shorter than that of pure water droplets in the range of 10−11 to 10−5 mol l−1 and the silica particle plays a role in inhibiting the freezing process. In short, from Figs. 5 and 6, the solutions mixed SiO2 especially the concentration of the particle d = 12 nm in the range of 10− 11 to 10−9 mol l−1 and 10−6 to 10−5 mol l−1 play a role in promoting freezing. The freezing time of droplets mixed SiO2 particle d = 40 nm is shorter than that of pure water droplets in the range of 10−9 to 10−5 mol l−1 and 10−3 to 10−1 mol l−1.
u = 0.160 m/s, and the cold plate temperature Tw = − 16.5 °C. For the three cases studied, the PM2.5 concentration values are22 μg m−3, 143 μg m−3 and 257 μg m−3 respectively. Figs. 7 and 8 show the variation of frost heights and frost crystal mass with time at different PM2.5 concentration values. The greater the PM2.5 concentration value is, the faster the frost crystal growth rate is, the thicker the frost layer is, and the greater amount of the frost crystal is. In Fig. 7, the frost heights at PM2.5 concentration C = 143 μg m−3 and C = 257 μg m−3 are respectively 9.5% and 18.7% higher than that at PM2.5 concentration C = 22 μg m−3. In Fig. 8, the frost crystal mass increases with the PM2.5 concentration value increasing. This is because suspended particles in the air can act as nucleating substrate and the Gibbs free energy for heterogeneous nucleation is smaller than that for homogeneous nucleation. When the PM2.5 concentration value is larger, the frost crystal nucleation is promoted and the frost crystals are more easily deposited. 4. Conclusion
3.2. Experimental study on frosting at different PM2.5 concentration values on cold flat plate This research focuses on the effect of air quality on frost height and frost crystal mass in frosting process. The temperature of air Ta = 10.8 °C, the relative humidity of air RH = 41.2%, the velocity of air 3.0 2.5
C= -3
22 µg·m -3 143 µg·m -3 257 µg·m
h/mm
2.0 1.5 1.0 0.5 0.0
0
60
120
180
240
300
t/min Fig. 7. Frost height variations with time at different PM2.5 concentration values.
This paper has experimentally studied the effects of solute variety and concentration on droplet freezing and the process of frost layer growth under different PM2.5 concentrations. The results indicate that for a given solution the variation of the freezing time showed a trend opposite to that of the supercooling degree. The supercooling degree directly affects the freezing time. The supercooling degree and freezing time change with solution concentration on different solutes. The three solutions including Na2SO4 solution, NaCl solution and (NH4)2SO4 solution show good promoting effect in the freezing process. The effect of the NH4Cl solution is more complex at different concentrations. The solutions mixed SiO2 especially the concentration of the particle d = 12 nm in the range of 10− 11 to 10−9 mol l−1 and 10− 6 to 10−5 mol l−1 play a role in promoting freezing. When the solute concentrate is smaller than 10−4 mol/l, the solution of Na+ has higher supercooling degree than those of the NH+ 4 and the has higher supercooling degree than those of the Cl−. solution of SO2− 4 The formation process is disrupted by the hydrolyzation process generated by the weak cation. At the same time, the hydrated ion generated which acts as unit cell enhances the formation process of by the SO2− 4 ice crystal. The effect of anion on supercooling degree is much obvious than the cation. For high solute concentration range, the polarization effect becomes dominant which prevents the generation of hydrogen bond and the formation of ice crystal. In addition, the results indicate that the greater PM2.5 concentration is, the thicker of the frost layer is, and the greater amount of the frost
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crystal is, which is due to suspended particles in the air that can act as nucleating substrate and the Gibbs free energy for heterogeneous nucleation is smaller than that for homogeneous nucleation. The frost crystal nucleation is promoted and the frost crystals are more easily deposited when the greater of the PM2.5 concentration value is.
Acknowledgments The present paper is financially supported by the National Natural Science Foundation of China (No. 51106013, 50806059, 51109174), China Postdoctoral Science Foundation (No. 2012M511998). References [1] M. Kandula, Frost growth and densification in laminar flow over flat surfaces[J], Int. J. Heat Mass Transf. 54 (15–16) (2011) 3719–3731. [2] M. Kandula, Frost growth and densification on a flat surface in laminar flow with variable humidity[J], Int. Commun. Heat Mass 39 (8) (2012) 1030–1034. [3] K. Matsumoto, M. Honda, Y. Ito, et al., Study on measurement of frost dimensions/ distribution and frost crystals scraping force using scanning probe microscope (investigation on influence of humidity)[J], Int. J. Refrig. 38 (2014) 341–351. [4] Y. Hayashi, A. Aoki, S. Adachi, et al., Study of frost properties correlating with frost formation types[J], J. Heat Transf. 99 (1977) 239–245. [5] X. Wu, W. Dai, W. Xu, et al., Mesoscale investigation of frost formation on a cold surface[J], Exp. Thermal Fluid Sci. 31 (2007) 1043–1048. [6] K.C. Tan, W. Ho, J.I. Katz, et al., A study of the occurrence of supercooling of water[J], Am. J. Phys. 84 (4) (2016) 293–300. [7] V. Bahadur, L. Mishchenko, B. Hatton, et al., Predictive model for ice formation on superhydrophobic surfaces[J], Langmuir 27 (2011) 14143–14150. [8] C.J.L. Hermes, R.O.J.R. Picucco, B. Jr, et al., A study of frost growth and densification on flat surfaces[J], Exp. Thermal Fluid Sci. 33 (2) (2009) 371–379.
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