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The behavior of frost layer growth under conditions favorable for desublimation
International Journal of Heat and Mass Transfer 120 (2018) 259–266
Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
The behavior of frost layer growth under conditions favorable for desublimation Jaehwan Lee, Kwan-Soo Lee ⇑ School of Mechanical Engineering, Hanyang University, 222 Wangsimni-ro, Seongdong-gu, Seoul 04763, Republic of Korea
a r t i c l e
i n f o
Article history: Received 29 September 2017 Received in revised form 7 December 2017 Accepted 8 December 2017
Keywords: Conditions favorable for desublimation Initial frost crystal morphology Frost layer growth behavior Frost thickness Frost density
a b s t r a c t The purpose of this study is to understand the behavior of frost layer growth under conditions favorable for desublimation. The frosting experiments were conducted on a horizontal cooling surface. Condensation did not occur at the initial stage of frosting, and feather-shaped frost crystals were formed on the cooling surface. These frost crystals grew one-dimensionally while maintaining their shapes. In addition, the effects of operating conditions (air temperature, air velocity, air absolute humidity, cooling surface temperature) on frost layer growth under the conditions favorable for desublimation were investigated. As the cooling surface temperature decreased, the increase in the amount of frost was insignificant. Additionally, an increase in air velocity increased the frost density but not the thickness of the frost layer. Ó 2017 Elsevier Ltd. All rights reserved.
1. Introduction Frosting processes generally begin when supercooled condensate water is generated on a cooling surface. After this condensed water is formed, it changes to a solid state, and frost columns and branches grow on the frozen water [1]. When frosting occurs by freezing after condensation, the frost formation processes are divided into periods of crystal growth, frost layer growth, and frost layer full growth [2,3]. However, when the cooling surface temperature is very low, desublimation can occur instead of freezing after condensation. According to Pablo [4], the minimum temperature to which water can be supercooled under atmospheric pressure is approximately 42 °C. Nath and Boreyko [5] found that desublimation can occur depending on the cooling surface temperature and contact angle. If desublimation occurs, the growth behavior and physical properties of the frost layer can be significantly different from those of a frost layer formed by freezing after condensation. Therefore, it is necessary to study the growth behavior and physical properties of the frost layer under conditions favorable for desublimation. A number of studies have been conducted to develop a fundamental understanding of frosting phenomena. Studies typically focus on frost layer growth behavior [6–8] and frost crystal morphologies [9–12]. Experimental correlations between the physical properties of the frost layer have also been proposed by various ⇑ Corresponding author. E-mail address: [email protected] (K.-S. Lee). https://doi.org/10.1016/j.ijheatmasstransfer.2017.12.039 0017-9310/Ó 2017 Elsevier Ltd. All rights reserved.
researchers [13–17]. However, these studies were conducted at cooling surface temperatures higher than 35 °C [6–17], and the cooling surface temperatures considered in each study are summarized in Table 1. Because frost formation occurs mainly in the form of freezing after condensation in such a cooling surface temperature range, it is difficult to understand the frosting phenomenon associated with desublimation from these research results. To fundamentally understand the frosting phenomenon caused by desublimation, various experimental studies at lower cooling surface temperatures are required. There are only a few studies on frosting at low cooling surface temperatures where desublimation can occur [18,19]. Biguria and Wenzel [18] conducted frosting experiments on a 96 °C to 29 °C horizontal plate under forced convection conditions, and they proposed a correlation between the thermal conductivity and density of the frost layer. Cremers and Mehra [19] conducted frosting experiments at 90 °C to 60 °C using vertical cylinders under natural convection, and they proposed a correlation of frost thickness and density. Both studies focused on the observation of the physical properties of the frost layer rather than a fundamental understanding of frosting phenomena. Moreover, there is a limitation in that those studies did not clarify the effects of the four main operating conditions (air temperature, air velocity, air absolute humidity, cooling surface temperature) on the growth of the frost layer. The purpose of this study is to fundamentally understand frosting behavior occurring under conditions favorable for desublimation. For this purpose, frosting experiments were conducted on a horizontal plate at a temperature lower than 30 °C. In particular,
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Nomenclature a A h hm L m N P T u V w D
actual area per one pixel (m2) frost layer frontal area (m2) heat transfer coefficient (W/m2°C) mass transfer coefficient (kg/m2 s) horizontal length of frost layer (m) mass (kg) number of pixels in edge of frost layer pressure (kPa) temperature (°C) velocity (m/s) volume of frost layer (m3) width of test surface (m) relative uncertainty
e q x
average thickness (m) measurement error density (kg/m3) absolute humidity (kg/kg)
Subscript a atm f s w
air atmospheric frost saturation test surface
d
Table 1 Cooling surface temperature in previous studies. Reference
Cooling surface temperature, °C
Cheng and Shiu [6] Kandula [7] Wu et al. [8] Lee et al. [9] Wu et al. [10] Da Silva et al. [11] Wu et al. [12] Ostin and Andersson [13] Yang and Lee [14] Kim et al. [15] Negrelli and Hermes [16] Kim et al. [17]
18 to 0 18 to 10 19 to 10 28.4 to 11.6 20 to 0 10 to 3 16 to 10 20 to 7 35 to 15 32 to 20 30 to 4 27 to 15
experiments were carried out with cooling surfaces at temperatures below 40 °C; only a few studies have addressed this temperature regime. The initial frost layer growth process was observed, and the effects of cooling surface temperature, air temperature, air velocity, and air absolute humidity on the physical properties of the frost layer were investigated. 2. Experiments 2.1. Experimental setup The experimental apparatus was constructed in the same manner as has been done in previous studies [1,15], and the test section was constructed as shown in Fig. 1. As shown in the figure, each side of the test surface was insulated. Fig. 2 presents the test surface. In this experiment, a bare surface (Aluminum 6061, 5 5 cm) with a contact angle of 75 ± 1° was used, and the surface temperature was measured by an inserted type-T thermocouple. Both the refrigeration cycle and the thermoelectric cooler were used at the same time to control the temperature of the test surface. In the experiment, the temperature of the test surface was maintained by controlling the output of the thermoelectric cooler. The inlet temperature of the refrigerant was 30 °C, and the rated output of the thermoelectric cooler was 24 V, 350 W. The average thickness of the frost layer was measured by image processing. High-resolution photographs were obtained with a Nikon D800E camera and an AF-S Micro Nikkor 60 mm f/2.8G ED lens. The actual area occupied by a pixel in photographs was very small, approximately 4 1010 m2. The frost layer frontal area was calculated using ImageJ software, based on the pixel information. A
Fig. 1. Schematic diagram of the test section.
digital balance with an accuracy of 0.0001 g was used to measure the mass of the frost layer. 2.2. Experimental method Experiments for measuring the average thickness df and the density qf of the frost layer were carried out by the following procedure. Step 1. Cover the insulation on the top of the test surface to prevent heat and mass transfer between humid air and the test surface. Step 2. After setting the operating conditions according to the experimental conditions, remove the insulation and start the frosting experiment. Step 3. When the desired experiment time is reached, take a photograph.
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261
Fig. 2. Schematic diagram of the test surface.
Step 4. Separate the test surface from the test section, and measure the mass of the test surface.
Ddf ¼
Experimental data were measured at 5, 10, 20, 30, 40, 50, and 60 min, and df and qf were calculated as follows.
df ¼
qf ¼
A L mf mf ¼ V Aw
ð1Þ
@ qf @A
Dqf ¼
¼
eA
2 1=2 ¼
df
ð2Þ
Here, A is the frontal area of the frost layer, L is the horizontal length of the frost layer, mf is the mass of the frost layer, V is the volume of the frost layer, and w is the width of the test surface. Fig. 3 shows the image processing procedure. Fig. 3(a) is a photograph of the front part of the frost layer. The frost layer frontal area (A), which excludes the area of the test surface, can be obtained as shown in Fig. 3(b). The average thickness of the frost layer (df) can be calculated by substituting A into (1). The mass of the frost layer (mf) was calculated by subtracting the weight of the pure test surface from the mass measured in Step 4. The frost layer density (qf) can be calculated by substituting mf and A into (2). The uncertainty of the frost thickness (Ddf) and the uncertainty of the frost density (Dqf) are calculated as follows:
@df @A
eA
2
þ
@ qf @mf
eA
ð3Þ
Ldf
emf
2 2
qf
2 2 1=2 m 1 A2 wf eA þ Aw emf
qf
ð4Þ
In this study, the measurement error (eA) of the frost layer frontal area was defined as the area of the pixels constituting the frost layer boundary. In other words, the area of the pixels surrounded by the red dotted line in Fig. 4 is the measurement error (eA) of the frost layer frontal area. This value is calculated as the product of the number of pixels occupying the boundary line of the frost layer (N) and the area of each pixel (a), as follows:
eA ¼ Na ¼ a1=2 ð2df þ LÞ
ð5Þ
Here, N is given by
N¼
2df þ L a1=2
ð6Þ
The uncertainties and the accuracies of the parameters in the experiment are summarized in Table 2.
(a) original image
(b) processed image Fig. 3. Illustration of the image processing.
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Fig. 4. Measurement error of frost layer frontal area.
Table 2 Uncertainties of parameters. Parameter
Accuracy (Measured)Uncertainty (Calculated)
Measured
Temperature Relative humidity Air flow rate Digital balance
±0.2 °C ±1.0% ±1.9% ±0.0001 g
Calculated
Frost thickness Frost density
±2.99% ±3.05%
Table 3 Experimental conditions. Experiment number
Tw, °C
Ta, °C
xa, kg/kg (RH, %)
ua, m/s
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
30 30 30 40 40 40 40 40 40 40 40 40 40 40 45 45 45 50 50 50
8 8 8 4 8 12 8 8 8 4 12 8 8 8 8 4 8 8 12 8
0.0033 0.0033 0.0046 0.0033 0.0033 0.0033 0.0020 0.0046 0.0033 0.0033 0.0033 0.0020 0.0046 0.0033 0.0033 0.0033 0.0046 0.0033 0.0033 0.0020
0.75 1.5 1.5 1.5 1.5 1.5 1.5 1.5 0.75 0.75 0.75 0.75 0.75 2.25 1.5 1.5 1.5 1.5 1.5 1.5
(50%) (50%) (70%) (66%) (50%) (38%) (30%) (70%) (50%) (66%) (38%) (30%) (70%) (50%) (50%) (66%) (70%) (50%) (38%) (30%)
(a) Exp #2
(b) Exp #5
The experimental conditions were set up to investigate how the four main operating conditions (air temperature Ta, air velocity ua, and air absolute humidity xa, cooling surface temperature Tw) affect the growth behavior of the frost layer. The experimental conditions are represented in Table 3. 3. Results and discussion 3.1. Frost layer growth behavior in the early stage of frosting Condensed water was not observed for all experimental conditions, and desublimation occurred. When frosting occurs via freezing after condensation, the density of the frost layer is generally in the range of 50–100 kg/m3 at the initial stage [20,21]. However, the density of the frost layer at 5 mins was very low (about 20–30 kg/ m3) for most experimental conditions, and it increased to about 50–100 kg/m3 at one hour. Therefore, when desublimation occurred, the frost layer density at the initial stage of frost formation was significantly lower than when freezing after condensation occurred.
(c) Exp #7 Fig. 5. Initial frost morphologies under various experimental conditions (at 1 min).
Wu et al. [10] studied the morphologies of initial frost crystals formed on the frozen condensate water at a cooling surface temperature of 20 °C to 0 °C, and they suggested a frost crystal morphology map based on cooling surface temperature and degree of supersaturation. Initial frost crystal morphologies appeared as
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(a) Initial frost crystal formation (at 1 min)
(b) Crystal growth (at 2 min)
263
feather-shaped frost crystals appeared. In this study, the initial frost crystal morphology appeared as feather shapes under all experimental conditions, as shown in Fig. 5. In particular, as shown in Fig. 5(c), feather-shaped frost crystals were observed even at conditions of low degree of supersaturation (Exp #7, cooling surface temperature 40 °C, degree of supersaturation 0.0019 kg/ kg). Thus, when desublimation occurred at a low cooling surface temperature, the morphologies of the initial frost crystal were feather-shaped rather than the needle and a column shaped even at low degrees of supersaturation. When the initial feather shaped frost crystals appeared, the growth process of frost crystals was observed as shown in Fig. 6. The frost crystals in the circle of the figure indicate an example of typical frost crystals during the growth process. Fig. 6(a) shows feather-shaped frost crystals formed on the cooling surface at the initial stage of frost formation. These frost crystals grow over time, as shown in Fig. 6(b). The frost crystals grow one-dimensionally while maintaining their shape. Only existing frost crystals grow, and no new frost crystals are formed. During growth, the spacing between the frost crystals does not decrease much; thus, the frost density does not increase. As shown, the frost crystals grow largely in the direction perpendicular to the surface in the process of crystal growth in the circle. Therefore, in this frost crystal growth process, most of the mass transfer increases the frost thickness and not the density. Fig. 6(c) represents the state in which the frost crystals have grown enough to start interacting with each other. In this process, the frost crystals are combined to form a frost layer surface, and the crystals interact and grow until the surface becomes flat. Once the frost crystals form the frost surface, some of the water vapor diffuses inside the frost layer. During this process, the porosity inside the frost layer decreases and the density of the frost layer increases.
(c) Crystal interactions (at 3 min) Fig. 6. Initial stages of frosting (Exp #5).
3.2. Effects of operating conditions on the behavior of frost layer growth _ per unit area is expressed in terms of The mass transfer rate (m) the mass transfer coefficient (hm), air absolute humidity (xa), saturation humidity (xw, s) at cooling surface temperature (Tw) as
_ ¼ hm ðxa xw;s Þ m
Fig. 7. Saturation of absolute humidity at 1 atm.
feather shapes or needle and pole shapes in the cooling surface temperature range of 20 °C to 15 °C. When the degree of supersaturation was low, needle and column shaped frost crystals appeared; when the degree of supersaturation degree was high,
ð7Þ
Here, xw,s is a function of cooling surface temperature (Tw), and hm is determined by the air velocity (ua). Therefore, the mass transfer rate is determined by the cooling surface temperature (Tw), air velocity (ua), and air absolute humidity (xa). Previous research results have showed that these three operating conditions have a major influence on the properties of the frost layer [20,22]. To investigate how these operating conditions affect the growth behavior of the frost layer under conditions favorable for desublimation, frost layer thickness and density were observed under various experimental conditions. According to previous studies conducted at a cooling surface temperature above 35 °C [14,23,24], the amount of frost (mf) increases with decreasing cooling surface temperature (Tw). This is because the degree of supersaturation (xa xw;s ) increases. This increased amount of frost (mf) contributes to the growth of the thickness (df) of the frost layer. Thus, the density (qf) of the frost layer decreases owing to the increased thickness. Similarly, under conditions favorable for desublimation, the thickness (df) of the frost layer increases and the density (qf) decreases when the cooling surface temperature (Tw) decreases. The degree of supersaturation (xa xw;s ) hardly increases even if the cooling surface temperature (Tw) decreases; thus, the increase in frost mass (mf) is insignificant.
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The saturated water vapor pressure Ps is related to the temperature of the humid air, as follows, based on the correlation given by Buck [25]:
Ps ¼ 0:61115exp
Ta Ta ðT a 6 0 CÞ 23:036 333:7 279:82 þ T a
ð8Þ Here, the saturation humidity according to the temperature of the humidifier under 1 atm is given by
xs ¼ 0:622
Ps Patm Ps
ð9Þ
Fig. 7 shows the saturation humidity as a function of temperature of humid air at 1 atm. As shown in the figure, the saturation humidity at 40 °C is close to zero (about 8 105 kg/kg), and the variation in saturation humidity is also very small. Therefore, under these conditions, even if the cooling surface temperature (Tw) decreases, the driving force for mass transfer hardly increases. The results of the experiments showed that the increase in frost mass was less than 3% when the cooling surface temperature decreased from 40 °C to 50 °C (Exp # 5 ? Exp # 18). Fig. 8 shows the change in frost thickness (df) with the change of the air velocity (ua). As shown, frost thickness (df) did not increase even though air velocity (ua) increased under various experimental
Fig. 8. Change in frost average thickness due to air velocity at various test conditions.
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Table 4 Effects of operating conditions on the frost properties under conditions favorable for desublimation. Parameters
Tw Ta ua
xa
Effect on mf
df
qf
– – " "
; ; – "
" " " "
": Increased when the parameter increased. ;: Decreased when the parameter increased.
Fig. 9. Frost density at various air velocities.
conditions. The observation that the increase in air velocity does not increase the thickness of the frost means that the air velocity has exceeded a certain critical velocity. Thus, the critical velocity for the frost thickness is very low under conditions favorable for _ as desublimation. This is expressed by the heat transfer rate (q) follows:
q_ ¼ hðT a T w Þ
ð10Þ
Here, h is the heat transfer coefficient, which is proportional to _ increases as the velocthe air velocity, so the heat transfer rate (q) ity increases. Ta – Tw is large under conditions favorable for desublimation because the cooling surface temperature (Tw) is low. _ increases greatly even if the Therefore, the heat transfer rate (q) air velocity increases only slightly. When heat transfer is promoted, the surface temperature of the frost layer increases [14,15,26], thus the thickness of the frost layer decreases and the density increases [23,27]. An increase in air velocity does not increase frost thickness even though mass transfer is promoted owing to the effect of the increase in frost surface temperature. As shown in Fig. 9, frost layer density (qf) increases with increasing air velocity (ua). This means that mass transfer is promoted owing to an increase in air velocity (ua), which contributes to the growth in frost density (qf). Fig. 10 shows the frost layer after 5 min at air velocities of 0.75 m/s (Exp #10) and 2.25 m/s (Exp #11). When the air velocity (ua) was low, voids between the frost crystals are large, resulting in a highly porous frost layer. In contrast, the porosity of the frost layer is low for high air velocities (ua). Therefore, when the air velocity (ua) increases under conditions favorable for desublimation, the frost thickness does not increase, but the frost density increases because the diffusion of the water vapor into the porous frost layer are promoted.
(a) ua = 0.75 m/s (Exp #9)
Air absolute humidity (xa) was the operating parameter that dominated the frost growth behavior. This result is the same as those obtained in previous studies where frosting occurred via freezing after condensation. Both frost thickness (df) and density (qf) increased significantly with increasing air absolute humidity (xa). An increase in driving force due to increased air absolute humidity (xa) contributed to increasing thickness (df) and density (qf) of the frost layer. Table 4 summarizes the effects of cooling surface temperature, air temperature, air velocity and air absolute humidity on the properties of the frost layer under conditions favorable for desublimation. The decrease in cooling surface temperature no longer increases the total amount of frost, and an increase in air velocity increased frost density, not frost thickness. 4. Conclusion The initial frosting stage was observed when desublimation occurred. Under all experimental conditions, feather-shaped initial frost crystals were formed directly on the test surface and these frost crystals grew while maintaining their feather-like shape. At this point, frost crystals that had already been formed grew onedimensionally, and no new frost crystals were created. In this process, the porosity of the frost layer hardly decreased, so the frost thickness grew but the density did not increase. Eventually, the frost crystals grew enough such that they interacted with each other and formed a frost surface. The effects of cooling surface temperature, air temperature, air velocity, and air absolute humidity on the frost layer properties were investigated for conditions favorable for desublimation. The effects of air temperature and air absolute humidity on the properties of the frost layer were similar to those observed in previous studies. However, the decrease in cooling surface temperature did not increase the amount of frost, and an increase in air velocity only increased frost density, not frost thickness. Acknowledgements This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korean Government (MSIT) (No. 2016R1A2B4012954).
(b) ua = 2.25 m/s (Exp #14)
Fig. 10. Frontal images of frost layers at 5 min.
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Conflict of interest We declare no conflict of interest in this paper. References [1] D. Kim, H. Kim, S.W. Kim, D.R. Kim, K.-S. Lee, Experimental investigation of frost retardation for superhydrophobic surface using a luminance meter, Int. J. Heat Mass Transfer 87 (2015) 491–496. [2] Y. Hayashi, A. Aoki, S. Adachi, K. Hori, Study of frost properties correlating with frost formation types, J. Heat Transfer 99 (1977) 239–245. [3] M.-H. Kim, H. Kim, K.-S. Lee, D.R. Kim, Frosting characteristics on hydrophobic and superhydrophobic surfaces: a review, Energy Convers. Manage. 138 (2017) 1–11. [4] G.D. Pablo, Supercooled and glassy water, J. Phys. Condens. Matter. 15 (2003) R1669. [5] S. Nath, J.B. Boreyko, On localized vapor pressure gradients governing condensation and frost phenomena, Langmuir 32 (2016) 8350–8365. [6] C.-H. Cheng, C.-C. Shiu, Frost formation and frost crystal growth on a cold plate in atmospheric air flow, Int. J. Heat Mass Transfer 45 (2002) 4289–4303. [7] M. Kandula, Frost growth and densification on a flat surface in laminar flow with variable humidity, J. Phys. Condens. Matter. 39 (2012) 1030–1034. [8] X. Wu, S. Hu, F. Chu, Experimental study of frost formation on cold surfaces with various fin layouts, Appl. Therm. Eng. 95 (2016) 95–105. [9] H. Lee, J. Shin, S. Ha, B. Choi, J. Lee, Frost formation on a plate with different surface hydrophilicity, Int. J. Heat Mass Transfer 47 (2004) 4881–4893. [10] X. Wu, W. Dai, W. Xu, L. Tang, Mesoscale investigation of frost formation on a cold surface, Exp. Therm. Fluid. Sci. 31 (2007) 1043–1048. [11] D.L. da Silva, C. Melo, C.J.L. Hermes, Effect of frost morphology on the thermalhydraulic performance of fan-supplied tube-fin evaporators, Appl. Therm. Eng. 111 (2017) 1060–1068. [12] X. Wu, F. Chu, Q. Ma, B. Zhu, Frost formation and frost meltwater drainage characteristics on aluminum surfaces with grooved structures, Appl. Therm. Eng. 118 (2017) 448–454.
[13] R. Östin, S. Andersson, Frost growth parameters in a forced air stream, Int. J. Heat Mass Transfer 34 (1991) 1009–1017. [14] D.-K. Yang, K.-S. Lee, Dimensionless correlations of frost properties on a cold plate, Int. J. Refrig. 27 (2004) 89–96. [15] J.-S. Kim, D.-K. Yang, K.-S. Lee, Dimensionless correlations of frost properties on a cold cylinder surface, Int. J. Heat Mass Transfer 51 (2008) 3946–3952. [16] S. Negrelli, C.J.L. Hermes, A semi-empirical correlation for the thermal conductivity of frost, Int. J. Refrig. 58 (2015) 243–252. [17] K. Kim, J.-S. Kim, K.-S. Lee, Characteristics of frost formation on twodimensional fins and its empirical correlations, Int. J. Heat Mass Transfer 53 (2010) 2670–2675. [18] G. Biguria, L.A. Wenzel, Measurement and correlation of water frost thermal conductivity and density, Indust. Eng. Chem. Fundament. 9 (1970) 129–138. [19] C.J. Cremers, V.K. Mehra, Frost formation on vertical cylinders in free convection, J. Heat Transfer 104 (1982) 3–7. [20] A. Léoni, M. Mondot, F. Durier, R. Revellin, P. Haberschill, State-of-the-art review of frost deposition on flat surfaces, Int. J. Refrig. 68 (2016) 198–217. [21] K.-S. Lee, S. Jhee, D.-K. Yang, Prediction of the frost formation on a cold flat surface, Int. J. Heat Mass Transfer 46 (2003) 3789–3796. [22] C.J.L. Hermes, R.O. Piucco, J.R. Barbosa, C. Melo, A study of frost growth and densification on flat surfaces, Exp. Therm. Fluid Sci. 33 (2009) 371–379. [23] A. Leoni, M. Mondot, F. Durier, R. Revellin, P. Haberschill, Frost formation and development on flat plate: experimental investigation and comparison to predictive methods, Exp. Therm. Fluid Sci. 88 (2017) 220–233. [24] M. Kandula, Frost growth and densification in laminar flow over flat surfaces, Int. J. Heat Mass Transfer 54 (2011) 3719–3731. [25] A.L. Buck, New equations for computing vapor pressure and enhancement factor, J. Appl. Meteorol. 20 (1981) 1527–1532. [26] K.-S. Lee, W.-S. Kim, T.-H. Lee, A one-dimensional model for frost formation on a cold flat surface, Int. J. Heat Mass Transfer 40 (1997) 4359–4365. [27] H.W. Schneider, Equation of the growth rate of frost forming on cooled surfaces, Int. J. Heat Mass Transfer 21 (1978) 1019–1024.
Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
The behavior of frost layer growth under conditions favorable for desublimation Jaehwan Lee, Kwan-Soo Lee ⇑ School of Mechanical Engineering, Hanyang University, 222 Wangsimni-ro, Seongdong-gu, Seoul 04763, Republic of Korea
a r t i c l e
i n f o
Article history: Received 29 September 2017 Received in revised form 7 December 2017 Accepted 8 December 2017
Keywords: Conditions favorable for desublimation Initial frost crystal morphology Frost layer growth behavior Frost thickness Frost density
a b s t r a c t The purpose of this study is to understand the behavior of frost layer growth under conditions favorable for desublimation. The frosting experiments were conducted on a horizontal cooling surface. Condensation did not occur at the initial stage of frosting, and feather-shaped frost crystals were formed on the cooling surface. These frost crystals grew one-dimensionally while maintaining their shapes. In addition, the effects of operating conditions (air temperature, air velocity, air absolute humidity, cooling surface temperature) on frost layer growth under the conditions favorable for desublimation were investigated. As the cooling surface temperature decreased, the increase in the amount of frost was insignificant. Additionally, an increase in air velocity increased the frost density but not the thickness of the frost layer. Ó 2017 Elsevier Ltd. All rights reserved.
1. Introduction Frosting processes generally begin when supercooled condensate water is generated on a cooling surface. After this condensed water is formed, it changes to a solid state, and frost columns and branches grow on the frozen water [1]. When frosting occurs by freezing after condensation, the frost formation processes are divided into periods of crystal growth, frost layer growth, and frost layer full growth [2,3]. However, when the cooling surface temperature is very low, desublimation can occur instead of freezing after condensation. According to Pablo [4], the minimum temperature to which water can be supercooled under atmospheric pressure is approximately 42 °C. Nath and Boreyko [5] found that desublimation can occur depending on the cooling surface temperature and contact angle. If desublimation occurs, the growth behavior and physical properties of the frost layer can be significantly different from those of a frost layer formed by freezing after condensation. Therefore, it is necessary to study the growth behavior and physical properties of the frost layer under conditions favorable for desublimation. A number of studies have been conducted to develop a fundamental understanding of frosting phenomena. Studies typically focus on frost layer growth behavior [6–8] and frost crystal morphologies [9–12]. Experimental correlations between the physical properties of the frost layer have also been proposed by various ⇑ Corresponding author. E-mail address: [email protected] (K.-S. Lee). https://doi.org/10.1016/j.ijheatmasstransfer.2017.12.039 0017-9310/Ó 2017 Elsevier Ltd. All rights reserved.
researchers [13–17]. However, these studies were conducted at cooling surface temperatures higher than 35 °C [6–17], and the cooling surface temperatures considered in each study are summarized in Table 1. Because frost formation occurs mainly in the form of freezing after condensation in such a cooling surface temperature range, it is difficult to understand the frosting phenomenon associated with desublimation from these research results. To fundamentally understand the frosting phenomenon caused by desublimation, various experimental studies at lower cooling surface temperatures are required. There are only a few studies on frosting at low cooling surface temperatures where desublimation can occur [18,19]. Biguria and Wenzel [18] conducted frosting experiments on a 96 °C to 29 °C horizontal plate under forced convection conditions, and they proposed a correlation between the thermal conductivity and density of the frost layer. Cremers and Mehra [19] conducted frosting experiments at 90 °C to 60 °C using vertical cylinders under natural convection, and they proposed a correlation of frost thickness and density. Both studies focused on the observation of the physical properties of the frost layer rather than a fundamental understanding of frosting phenomena. Moreover, there is a limitation in that those studies did not clarify the effects of the four main operating conditions (air temperature, air velocity, air absolute humidity, cooling surface temperature) on the growth of the frost layer. The purpose of this study is to fundamentally understand frosting behavior occurring under conditions favorable for desublimation. For this purpose, frosting experiments were conducted on a horizontal plate at a temperature lower than 30 °C. In particular,
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Nomenclature a A h hm L m N P T u V w D
actual area per one pixel (m2) frost layer frontal area (m2) heat transfer coefficient (W/m2°C) mass transfer coefficient (kg/m2 s) horizontal length of frost layer (m) mass (kg) number of pixels in edge of frost layer pressure (kPa) temperature (°C) velocity (m/s) volume of frost layer (m3) width of test surface (m) relative uncertainty
e q x
average thickness (m) measurement error density (kg/m3) absolute humidity (kg/kg)
Subscript a atm f s w
air atmospheric frost saturation test surface
d
Table 1 Cooling surface temperature in previous studies. Reference
Cooling surface temperature, °C
Cheng and Shiu [6] Kandula [7] Wu et al. [8] Lee et al. [9] Wu et al. [10] Da Silva et al. [11] Wu et al. [12] Ostin and Andersson [13] Yang and Lee [14] Kim et al. [15] Negrelli and Hermes [16] Kim et al. [17]
18 to 0 18 to 10 19 to 10 28.4 to 11.6 20 to 0 10 to 3 16 to 10 20 to 7 35 to 15 32 to 20 30 to 4 27 to 15
experiments were carried out with cooling surfaces at temperatures below 40 °C; only a few studies have addressed this temperature regime. The initial frost layer growth process was observed, and the effects of cooling surface temperature, air temperature, air velocity, and air absolute humidity on the physical properties of the frost layer were investigated. 2. Experiments 2.1. Experimental setup The experimental apparatus was constructed in the same manner as has been done in previous studies [1,15], and the test section was constructed as shown in Fig. 1. As shown in the figure, each side of the test surface was insulated. Fig. 2 presents the test surface. In this experiment, a bare surface (Aluminum 6061, 5 5 cm) with a contact angle of 75 ± 1° was used, and the surface temperature was measured by an inserted type-T thermocouple. Both the refrigeration cycle and the thermoelectric cooler were used at the same time to control the temperature of the test surface. In the experiment, the temperature of the test surface was maintained by controlling the output of the thermoelectric cooler. The inlet temperature of the refrigerant was 30 °C, and the rated output of the thermoelectric cooler was 24 V, 350 W. The average thickness of the frost layer was measured by image processing. High-resolution photographs were obtained with a Nikon D800E camera and an AF-S Micro Nikkor 60 mm f/2.8G ED lens. The actual area occupied by a pixel in photographs was very small, approximately 4 1010 m2. The frost layer frontal area was calculated using ImageJ software, based on the pixel information. A
Fig. 1. Schematic diagram of the test section.
digital balance with an accuracy of 0.0001 g was used to measure the mass of the frost layer. 2.2. Experimental method Experiments for measuring the average thickness df and the density qf of the frost layer were carried out by the following procedure. Step 1. Cover the insulation on the top of the test surface to prevent heat and mass transfer between humid air and the test surface. Step 2. After setting the operating conditions according to the experimental conditions, remove the insulation and start the frosting experiment. Step 3. When the desired experiment time is reached, take a photograph.
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Fig. 2. Schematic diagram of the test surface.
Step 4. Separate the test surface from the test section, and measure the mass of the test surface.
Ddf ¼
Experimental data were measured at 5, 10, 20, 30, 40, 50, and 60 min, and df and qf were calculated as follows.
df ¼
qf ¼
A L mf mf ¼ V Aw
ð1Þ
@ qf @A
Dqf ¼
¼
eA
2 1=2 ¼
df
ð2Þ
Here, A is the frontal area of the frost layer, L is the horizontal length of the frost layer, mf is the mass of the frost layer, V is the volume of the frost layer, and w is the width of the test surface. Fig. 3 shows the image processing procedure. Fig. 3(a) is a photograph of the front part of the frost layer. The frost layer frontal area (A), which excludes the area of the test surface, can be obtained as shown in Fig. 3(b). The average thickness of the frost layer (df) can be calculated by substituting A into (1). The mass of the frost layer (mf) was calculated by subtracting the weight of the pure test surface from the mass measured in Step 4. The frost layer density (qf) can be calculated by substituting mf and A into (2). The uncertainty of the frost thickness (Ddf) and the uncertainty of the frost density (Dqf) are calculated as follows:
@df @A
eA
2
þ
@ qf @mf
eA
ð3Þ
Ldf
emf
2 2
qf
2 2 1=2 m 1 A2 wf eA þ Aw emf
qf
ð4Þ
In this study, the measurement error (eA) of the frost layer frontal area was defined as the area of the pixels constituting the frost layer boundary. In other words, the area of the pixels surrounded by the red dotted line in Fig. 4 is the measurement error (eA) of the frost layer frontal area. This value is calculated as the product of the number of pixels occupying the boundary line of the frost layer (N) and the area of each pixel (a), as follows:
eA ¼ Na ¼ a1=2 ð2df þ LÞ
ð5Þ
Here, N is given by
N¼
2df þ L a1=2
ð6Þ
The uncertainties and the accuracies of the parameters in the experiment are summarized in Table 2.
(a) original image
(b) processed image Fig. 3. Illustration of the image processing.
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Fig. 4. Measurement error of frost layer frontal area.
Table 2 Uncertainties of parameters. Parameter
Accuracy (Measured)Uncertainty (Calculated)
Measured
Temperature Relative humidity Air flow rate Digital balance
±0.2 °C ±1.0% ±1.9% ±0.0001 g
Calculated
Frost thickness Frost density
±2.99% ±3.05%
Table 3 Experimental conditions. Experiment number
Tw, °C
Ta, °C
xa, kg/kg (RH, %)
ua, m/s
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
30 30 30 40 40 40 40 40 40 40 40 40 40 40 45 45 45 50 50 50
8 8 8 4 8 12 8 8 8 4 12 8 8 8 8 4 8 8 12 8
0.0033 0.0033 0.0046 0.0033 0.0033 0.0033 0.0020 0.0046 0.0033 0.0033 0.0033 0.0020 0.0046 0.0033 0.0033 0.0033 0.0046 0.0033 0.0033 0.0020
0.75 1.5 1.5 1.5 1.5 1.5 1.5 1.5 0.75 0.75 0.75 0.75 0.75 2.25 1.5 1.5 1.5 1.5 1.5 1.5
(50%) (50%) (70%) (66%) (50%) (38%) (30%) (70%) (50%) (66%) (38%) (30%) (70%) (50%) (50%) (66%) (70%) (50%) (38%) (30%)
(a) Exp #2
(b) Exp #5
The experimental conditions were set up to investigate how the four main operating conditions (air temperature Ta, air velocity ua, and air absolute humidity xa, cooling surface temperature Tw) affect the growth behavior of the frost layer. The experimental conditions are represented in Table 3. 3. Results and discussion 3.1. Frost layer growth behavior in the early stage of frosting Condensed water was not observed for all experimental conditions, and desublimation occurred. When frosting occurs via freezing after condensation, the density of the frost layer is generally in the range of 50–100 kg/m3 at the initial stage [20,21]. However, the density of the frost layer at 5 mins was very low (about 20–30 kg/ m3) for most experimental conditions, and it increased to about 50–100 kg/m3 at one hour. Therefore, when desublimation occurred, the frost layer density at the initial stage of frost formation was significantly lower than when freezing after condensation occurred.
(c) Exp #7 Fig. 5. Initial frost morphologies under various experimental conditions (at 1 min).
Wu et al. [10] studied the morphologies of initial frost crystals formed on the frozen condensate water at a cooling surface temperature of 20 °C to 0 °C, and they suggested a frost crystal morphology map based on cooling surface temperature and degree of supersaturation. Initial frost crystal morphologies appeared as
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(a) Initial frost crystal formation (at 1 min)
(b) Crystal growth (at 2 min)
263
feather-shaped frost crystals appeared. In this study, the initial frost crystal morphology appeared as feather shapes under all experimental conditions, as shown in Fig. 5. In particular, as shown in Fig. 5(c), feather-shaped frost crystals were observed even at conditions of low degree of supersaturation (Exp #7, cooling surface temperature 40 °C, degree of supersaturation 0.0019 kg/ kg). Thus, when desublimation occurred at a low cooling surface temperature, the morphologies of the initial frost crystal were feather-shaped rather than the needle and a column shaped even at low degrees of supersaturation. When the initial feather shaped frost crystals appeared, the growth process of frost crystals was observed as shown in Fig. 6. The frost crystals in the circle of the figure indicate an example of typical frost crystals during the growth process. Fig. 6(a) shows feather-shaped frost crystals formed on the cooling surface at the initial stage of frost formation. These frost crystals grow over time, as shown in Fig. 6(b). The frost crystals grow one-dimensionally while maintaining their shape. Only existing frost crystals grow, and no new frost crystals are formed. During growth, the spacing between the frost crystals does not decrease much; thus, the frost density does not increase. As shown, the frost crystals grow largely in the direction perpendicular to the surface in the process of crystal growth in the circle. Therefore, in this frost crystal growth process, most of the mass transfer increases the frost thickness and not the density. Fig. 6(c) represents the state in which the frost crystals have grown enough to start interacting with each other. In this process, the frost crystals are combined to form a frost layer surface, and the crystals interact and grow until the surface becomes flat. Once the frost crystals form the frost surface, some of the water vapor diffuses inside the frost layer. During this process, the porosity inside the frost layer decreases and the density of the frost layer increases.
(c) Crystal interactions (at 3 min) Fig. 6. Initial stages of frosting (Exp #5).
3.2. Effects of operating conditions on the behavior of frost layer growth _ per unit area is expressed in terms of The mass transfer rate (m) the mass transfer coefficient (hm), air absolute humidity (xa), saturation humidity (xw, s) at cooling surface temperature (Tw) as
_ ¼ hm ðxa xw;s Þ m
Fig. 7. Saturation of absolute humidity at 1 atm.
feather shapes or needle and pole shapes in the cooling surface temperature range of 20 °C to 15 °C. When the degree of supersaturation was low, needle and column shaped frost crystals appeared; when the degree of supersaturation degree was high,
ð7Þ
Here, xw,s is a function of cooling surface temperature (Tw), and hm is determined by the air velocity (ua). Therefore, the mass transfer rate is determined by the cooling surface temperature (Tw), air velocity (ua), and air absolute humidity (xa). Previous research results have showed that these three operating conditions have a major influence on the properties of the frost layer [20,22]. To investigate how these operating conditions affect the growth behavior of the frost layer under conditions favorable for desublimation, frost layer thickness and density were observed under various experimental conditions. According to previous studies conducted at a cooling surface temperature above 35 °C [14,23,24], the amount of frost (mf) increases with decreasing cooling surface temperature (Tw). This is because the degree of supersaturation (xa xw;s ) increases. This increased amount of frost (mf) contributes to the growth of the thickness (df) of the frost layer. Thus, the density (qf) of the frost layer decreases owing to the increased thickness. Similarly, under conditions favorable for desublimation, the thickness (df) of the frost layer increases and the density (qf) decreases when the cooling surface temperature (Tw) decreases. The degree of supersaturation (xa xw;s ) hardly increases even if the cooling surface temperature (Tw) decreases; thus, the increase in frost mass (mf) is insignificant.
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The saturated water vapor pressure Ps is related to the temperature of the humid air, as follows, based on the correlation given by Buck [25]:
Ps ¼ 0:61115exp
Ta Ta ðT a 6 0 CÞ 23:036 333:7 279:82 þ T a
ð8Þ Here, the saturation humidity according to the temperature of the humidifier under 1 atm is given by
xs ¼ 0:622
Ps Patm Ps
ð9Þ
Fig. 7 shows the saturation humidity as a function of temperature of humid air at 1 atm. As shown in the figure, the saturation humidity at 40 °C is close to zero (about 8 105 kg/kg), and the variation in saturation humidity is also very small. Therefore, under these conditions, even if the cooling surface temperature (Tw) decreases, the driving force for mass transfer hardly increases. The results of the experiments showed that the increase in frost mass was less than 3% when the cooling surface temperature decreased from 40 °C to 50 °C (Exp # 5 ? Exp # 18). Fig. 8 shows the change in frost thickness (df) with the change of the air velocity (ua). As shown, frost thickness (df) did not increase even though air velocity (ua) increased under various experimental
Fig. 8. Change in frost average thickness due to air velocity at various test conditions.
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Table 4 Effects of operating conditions on the frost properties under conditions favorable for desublimation. Parameters
Tw Ta ua
xa
Effect on mf
df
qf
– – " "
; ; – "
" " " "
": Increased when the parameter increased. ;: Decreased when the parameter increased.
Fig. 9. Frost density at various air velocities.
conditions. The observation that the increase in air velocity does not increase the thickness of the frost means that the air velocity has exceeded a certain critical velocity. Thus, the critical velocity for the frost thickness is very low under conditions favorable for _ as desublimation. This is expressed by the heat transfer rate (q) follows:
q_ ¼ hðT a T w Þ
ð10Þ
Here, h is the heat transfer coefficient, which is proportional to _ increases as the velocthe air velocity, so the heat transfer rate (q) ity increases. Ta – Tw is large under conditions favorable for desublimation because the cooling surface temperature (Tw) is low. _ increases greatly even if the Therefore, the heat transfer rate (q) air velocity increases only slightly. When heat transfer is promoted, the surface temperature of the frost layer increases [14,15,26], thus the thickness of the frost layer decreases and the density increases [23,27]. An increase in air velocity does not increase frost thickness even though mass transfer is promoted owing to the effect of the increase in frost surface temperature. As shown in Fig. 9, frost layer density (qf) increases with increasing air velocity (ua). This means that mass transfer is promoted owing to an increase in air velocity (ua), which contributes to the growth in frost density (qf). Fig. 10 shows the frost layer after 5 min at air velocities of 0.75 m/s (Exp #10) and 2.25 m/s (Exp #11). When the air velocity (ua) was low, voids between the frost crystals are large, resulting in a highly porous frost layer. In contrast, the porosity of the frost layer is low for high air velocities (ua). Therefore, when the air velocity (ua) increases under conditions favorable for desublimation, the frost thickness does not increase, but the frost density increases because the diffusion of the water vapor into the porous frost layer are promoted.
(a) ua = 0.75 m/s (Exp #9)
Air absolute humidity (xa) was the operating parameter that dominated the frost growth behavior. This result is the same as those obtained in previous studies where frosting occurred via freezing after condensation. Both frost thickness (df) and density (qf) increased significantly with increasing air absolute humidity (xa). An increase in driving force due to increased air absolute humidity (xa) contributed to increasing thickness (df) and density (qf) of the frost layer. Table 4 summarizes the effects of cooling surface temperature, air temperature, air velocity and air absolute humidity on the properties of the frost layer under conditions favorable for desublimation. The decrease in cooling surface temperature no longer increases the total amount of frost, and an increase in air velocity increased frost density, not frost thickness. 4. Conclusion The initial frosting stage was observed when desublimation occurred. Under all experimental conditions, feather-shaped initial frost crystals were formed directly on the test surface and these frost crystals grew while maintaining their feather-like shape. At this point, frost crystals that had already been formed grew onedimensionally, and no new frost crystals were created. In this process, the porosity of the frost layer hardly decreased, so the frost thickness grew but the density did not increase. Eventually, the frost crystals grew enough such that they interacted with each other and formed a frost surface. The effects of cooling surface temperature, air temperature, air velocity, and air absolute humidity on the frost layer properties were investigated for conditions favorable for desublimation. The effects of air temperature and air absolute humidity on the properties of the frost layer were similar to those observed in previous studies. However, the decrease in cooling surface temperature did not increase the amount of frost, and an increase in air velocity only increased frost density, not frost thickness. Acknowledgements This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korean Government (MSIT) (No. 2016R1A2B4012954).
(b) ua = 2.25 m/s (Exp #14)
Fig. 10. Frontal images of frost layers at 5 min.
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