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Mesoscale investigation of frost formation on a cold surface
Experimental Thermal and Fluid Science 31 (2007) 1043–1048 www.elsevier.com/locate/etfs
Mesoscale investigation of frost formation on a cold surface Xiaomin Wu a
a,*
, Wantian Dai a, Wangfa Xu b, Liming Tang
c
Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Thermal Engineering, Tsinghua University, Beijing 100084, PR China b Department of Mechanical Engineering, Tongji University, Shanghai 200092, PR China c Department of Chemical Engineering, Tsinghua University, Beijing 100084, PR China Received 1 September 2005; received in revised form 20 July 2006; accepted 2 November 2006
Abstract Frost formation on a horizontal flat copper surface was experimentally investigated using microscopic observations. The experiments were carried out on 20 to 0 °C copper surfaces with 22 °C air and 15–85% relative humidities. The experiments showed that the frost formation on a cold surface generally begins with the formation and growth of condensate droplets, freezing of the super-cooled condensate droplets, formation and growth of initial frost crystals on the frozen droplets, growth of frost crystals accompanied by the collapse of some of the crystals, and finally frost layer growth. The freezing onset time and diameter of the super-cooled condensate droplets were characterized. The initial frost crystals can be classified into four groups according to their appearance and shape, with the variations of the frost crystal shape as a function of the cold surface temperature and air humidity. Ó 2006 Elsevier Inc. All rights reserved. Keywords: Frost formation; Super-cooled droplets; Frost crystals; Freezing onset time; Frost crystal shape
1. Introduction When humid air comes in contact with a cold surface whose temperature is below both the dew point of the air and the freezing point of water, frost may form on the surface. The occurrence of frosting is undesirable for most industrial applications such as air conditioners and refrigerators. A frost layer formed on an evaporator not only increases the air side thermal resistance, but also reduces the airflow area, both of which reduce the evaporator performance. Besides, frost on aircraft wings may cause serious safety problems. Therefore frosting has attracted increasing attention in recent years. Although many studies have been done on frost formation, most have focused only on a fully-grown frost layer. The thickness growth rate, density, and thermal conductivity of the fully-grown frost layer [1], as well as the influence of frost on evaporators with different type geometries [2,3] *
Corresponding author. Tel./fax: +86 10 62770558. E-mail address: [email protected] (X.M. Wu).
0894-1777/$ - see front matter Ó 2006 Elsevier Inc. All rights reserved. doi:10.1016/j.expthermflusci.2006.11.002
have been extensively studied. Several models have also been proposed to clarify the effects of environmental parameters and to predict the frost layer growth rate [4,5]. However, few studies have been done to investigate the frosting phenomena in the early stage of frost formation. Hayashi et al. [6] photographically investigated the process of frost formation on stainless steel surfaces and subdivided the process into three periods: crystal growth, frost layer growth, and frost layer fully growth. Cheng et al. [7] studied frost formation and frost crystal growth on a cold plate and found that the frost layer structure was like a forest with variant kinds of growing trees. Recently Na and Webb [8] presented a theoretical analysis of the nucleation process for frost formation on a cold surface and pointed out that the air at the cold surface should be supersaturated for frost nucleation to occur. They [9] further proposed a supersaturation model to predict the frost growth rate. Although the frosting phenomena have been studied extensively, information on the fundamental features of frost formation in the early stages is still limited. The present research seeks to provide such information.
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X.M. Wu et al. / Experimental Thermal and Fluid Science 31 (2007) 1043–1048
Nomenclature Ai N Ts RH
Surface area occupied by the freezing droplets in the observation field, m2 Total number of particles in the field of observation Surface temperature (°C) Air relative humidity (%)
Greek symbols Freezing onset time (s) sf / Freezing droplet diameter (m) DC Vapor concentration difference between the ambient air and the copper surface (g/kg)
Our previous studies showed that frost formation on a cold surface is not a simple process of direct conversion from vapor to frost, the incipient frost development is generally characterized by the formation of super-cooled water droplets on the cold surfaces. The frost formation processes on a hydrophobic surface were also found to differ from those on a bare copper surface and a hydrophilic surface [10,11]. The present study seeks to clarify the fundamental nature of frost formation at its initial stage including the freezing onset time and diameter of the super-cooled condensate droplets, as well as the shapes of the initial frost crystals. 2. Experiments 2.1. Experimental apparatus and procedure Fig. 1 schematically illustrates the experimental apparatus used in this research, which consists mainly of a test section, a data acquisition system, and a microscopic image acquisition system. The details of the test section are shown in Fig. 2. A thermoelectric cooler was used to provide a cooling source for the frosting surface. The thermoelectric cooler is a small heat pump, which operates on direct current and may be used for cooling or heating by reversing the current flow direction [12]. The cold side of the thermoelectric cooler was horizontally attached by thermal grease to a 1 mm thick by 50 mm square copper test plate. The hot side of the thermoelectric cooler was mounted with thermal grease on a heat sink. A plexiglas duct allowed cooling water to flow through the heat sink for heat removal from the hot side of the thermoelectric cooler. The surface temperature of the copper plate was measured using three 0.1 mm T-type thermocouples buried in
Fig. 1. Schematic diagram of the experimental apparatus.
Fig. 2. Test section details. (a) Layout of test plate. (b) Thermocouple locations.
grooves on the backside of the plate, as shown in Fig. 2. Because the copper plate had a very high thermal conductivity, the average thermocouple reading was used as the test surface temperature (Ts). The accuracy of the thermocouples was ±0.1 °C. The surface temperature of the copper plate could be adjusted by changing the input voltage of the semiconductor thermoelectric cooler and the water flow rate. The ambient air temperature (Tair) and relative humidity (RH) were measured using a temperature and humidity sensor (Model M23D4HT-3, ROTRNIC) installed above the test surface. The sensor accuracy was ±1.5% of full range for the relative humidity and ±0.3 °C for temperature. The thermocouples used in the experiment were all precisely calibrated before tests. All of the temperature and humidity measurements were recorded at time intervals of 2.5 s by a data acquisition system (Model 34970 A, Agilent) connected to a computer. The processes of frost formation on the surface were observed and recorded using a microscopic image acquisition system connected to the computer. The microscopic image system consisted of a zoom stereo microscope (Model SZ1145TR, OLYMPUS), a CCD camera (Model WAT-505EX, Watec), a image processor (Model Metor-II/Multi-Channel, Matrox), and a self-programmed program GRAB to
X.M. Wu et al. / Experimental Thermal and Fluid Science 31 (2007) 1043–1048
take the picture. The images were recorded every 2.5 s at magnifications up to 480 times. Tests were performed for copper surface temperatures between 20 °C and 0 °C. At the beginning of each test, the surface was at the cooling water temperature, then the thermoelectric cooler was turned on and the surface temperature was reduced to the desired temperature in a minute. The ambient air temperature was about 22 °C and the relative humidity was varied from 15% to 85%. 2.2. Test surface The static contact angles of the droplets on the surface were measured by the sessile drop method using a goniometer (Model JC2000C1, POWEREACH). The measured contact angle for the copper surface was 84°. Before each test, the surface was cleaned by acetone and then dried with cotton. 3. Results and discussion 3.1. Mesoscale frost formation processes The mesoscale frost formation processes on the cold copper surface for different test conditions were observed using the microscope. Although the frost formation mechanism is quite complicated, the observations showed that for the test conditions the frost formation on a cold surface generally began with the formation and growth of water droplets, then freezing of the super-cooled condensate droplets, then formation of initial frost crystals on the frozen droplets, then growth of frost crystals accompanied by falling down of some of the crystals, then formation and growth of the frost layer and finally aging of the frost layer. Fig. 3 demonstrates a typical frost formation process for a final copper temperature of 12 °C with 22 °C and 50% relative humidity air. The vapor in the moist air began to condense onto the copper plate when the plate surface temperature dropped below the dew point of the moist air. The resulting small condensate droplets (Fig. 3b) grow through direct condensation of vapor onto the droplets and coalescence with adjacent droplets (Fig. 3c and d). The condensate droplets remained liquid even when the copper surface dropped below 0 °C, with this super-cooled state continuing for a period of time before the freezing began. The super-cooled condensate droplets froze and became ice beads (Fig. 3e and f) once the water embryos in the droplets overcame the Gibbs energy barrier [13,14]. The vapor in the moist air then de-sublimated (vapor-to-ice transformation) onto the surfaces of the ice beads to form frost crystals (Fig. 3g). The frost crystals initially grew in one direction (Fig. 3g and h), but later in three dimensions (Fig. 3i and j). The frost crystals then began to grow across each other to form a frost layer consisting of ice beads, frost crystals and moist air on the cold copper surface (Fig. 3k). The frost layer became thicker and denser as it grew (Fig. 3l).
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During the frosting formation process, some of the crystals fell down, which makes the structure and growth of the frost layer even more complex, but none of the existing frosting models account for these facts. Thus further studies are needed to create a more practical and accurate frost formation model. 3.2. Freezing onset time and diameter The onset time of freezing can be judged from changes in the appearance of the condensate droplets. The condensate droplets were fully transparent before freezing (Fig. 3c and d) but turned whitish after freezing (Fig. 3e and f). The copper surface temperature corresponding to Fig. 3d was about 12 °C, so the condensate droplets in Fig. 3d were super-cooled. For convenience of explanation, sf is used to express the freezing onset time with the average diameter of the freezing droplets at sf as vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u N uX / ¼ 2t Ai =ðpN Þ ð1Þ i¼1
where Ai is the surface area occupied by the ith freezing droplet, N is the total number of droplets in the field of observation. Fig. 4 shows the variation of the freezing onset time (sf) with copper surface temperature (Ts) and relative humidity (RH). The freezing onset time decreases, as the surface temperature decreases and as the relative humidity increases, but the influence of surface temperature and relative humidity on the freezing onset time decreases as the surface temperature decreases. Fig. 5 shows the variation of the average freezing droplet diameter (/) with copper surface temperature and relative humidity. The freezing droplet diameter (/) decreases as the surface temperature decreases, and as the relative humidity decreases. 3.3. Initial frost crystal shapes The microscope observations showed that the initial frost crystals formed on the ice beads can be classified into four groups as irregular crystals, flake crystals, needle and pole crystals, and feather crystals, as shown in Fig. 6. The irregular crystals (Fig. 6a) have no clear regular shape with the frost crystals combining with tiny ice particles sprinkled not only on the top of the ice bead but also on the sides. Compared with the irregular crystals, the flake crystals (Fig. 6b) have a more regular shape with the copper surface temperature corresponding to the flake crystals being somewhat lower than that for the irregular crystals. Also the flake crystals do not have any of the tiny ice particles that were seen on the irregular crystals. The needle crystals are shown in Fig. 6c with the pole crystals in Fig. 6d. The formation conditions for these two types of crystals are very similar. They often appear at the same time, with more pole crystals tending to appear at lower copper surface
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Fig. 3. Top view of the frost formation process on the surface for Ts = 12 °C, RH = 50% and Tair = 22 °C.
temperatures. Unlike the irregular and flake crystals, the needle and pole crystals appear only on top of the ice bead. The feather crystals shown in Fig. 6e and f form at higher relative humidies and show more complex branching characteristics.
Fig. 7 illustrates the dependence of the frost crystal shape on Ts and DC, where the DC expresses the vapor concentration difference between the bulk air and the air at the copper surface. The vapor concentration at the copper surface was assumed to be the saturation vapor concentration
X.M. Wu et al. / Experimental Thermal and Fluid Science 31 (2007) 1043–1048
1600 RH=35% RH=50% RH=85%
Tf /s
1200 800 400 0 -6
-8
-10
-12
-14
-16
-18
TS / ºC Fig. 4. Variation of the freezing onset time with copper surface temperature and relative humidity.
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corresponding to the copper surface temperature. In crystallography, the frost crystal shape is generally considered to be mainly affected by the temperature of the substrate on which the frost forms and the vapor supersaturation degree at the substrate surface. For the present tests, the ice bead surface was the substrate for the initial frost formation. However, since the ice bead surface temperature was hard to measure, the ice bead surface temperature was assumed to be close to the copper surface temperature. Then, the vapor concentration difference between the ambient air and the copper surface is equal to the vapor super-saturation degree. The numbers I, II, III, IV and V in Fig. 7 identify the regions of super-cooled condensate drops, irregular crystals, flake crystals, needle and pole crystals, and feather crystals. The figure shows that the cold surface temperature is the primary factor affecting the frost
500 12 RH=85% RH=50% RH=35%
9
300
ΔC / g /kg
φ /μm
400
200
6
3
100 0 -4
0
-8
-12
-16
-20
TS / ºC Fig. 5. Variation of the freezing droplet diameter with copper surface temperature and relative humidity.
0
-5
-10
-15
-20
Ts / °C Fig. 7. Dependence of initial frost crystal shape on surface temperature and humidity I: super-cooled water droplets, II: irregular crystals, III: flake crystals, IV: needle and pole crystals, V: feather crystals.
Fig. 6. Four typical shapes of initial frost crystals (a) irregular crystals (b) flake crystals (c, d) needle and pole crystals (e, f) feather crystal.
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crystal shape, while the relative humidity has a minor effect on the frost crystal shape. 4. Conclusions Mesoscale frost formation processes on a cold copper surface were observed for different surface temperatures and relative humidities using a microscope. Following are the conclusions drawn from this research: 1. The super-cooled condensate droplets freeze earlier at lower surface temperatures and higher relative humidities, with the freezing droplets being smaller at lower surface temperatures and lower relative humidities. 2. The frost formation on a cold surface is generally characterized by the initial formation and growth of condensate droplets followed by freezing of the super-cooled droplets, formation and growth of initial frost crystals on the frozen droplets, growth of frost crystals accompanied by falling down of some of the crystals, and finally frost layer growth. 3. The initial frost crystals can be classified into four groups as irregular crystals, flake crystals, needle and pole crystals, and feather crystals. 4. The surface temperature is the primary factor affecting the frost crystal shape, with the relative humidity having less effect on the frost crystal shape. Acknowledgement This work was financially supported by the National Natural Science Foundation of China (No. 50476011), which is gratefully acknowledged.
References [1] A. Luer, H. Beer, Frost deposition in a parallel plate channel under laminar flow conditions, International Journal of Thermal Science 39 (2000) 85–95. [2] S.N. Kondepudi, D.L. O’Neal, The effects of different fin configuration on the performance of finned-tube heat exchanger under frosting conditions, in: ASHRAE Transactions, 96 (1990) part. 2, no. SL-90-1-1. [3] S.N. Kondepudi, D.L. O’Neal, Frosting performance of tube fin heat exchanger with wavy and corrugated fins, Journal of Experimental Thermal and Fluid Science 4 (1991) 613–618. [4] K.A.R. Ismail, C.S. Salinas, Modeling of frost formation over parallel cold plates, International Journal of Refrigeration 22 (1999) 425–441. [5] K.-S. Lee, S. Jhee, D.-K. Yang, Prediction of the frost formation on a cold surface, International Journal of Heat and Mass Transfer 46 (2003) 3789–3796. [6] Y. Hayashi, A. Aoki, S. Adachi, K. Hori, Study of frost properties correlating with frost formation types, Journal of Heat Transfer 99 (1977) 239–245. [7] C.H. Cheng, C.C. Shiu, Frost formation and frost crystal growth on a cold plate in atmospheric air flow, International Journal of Heat and Mass Transfer 45 (2002) 4289–4303. [8] B. Na, R.L. Webb, A fundamental understanding of factors affecting frost nucleation, International Journal of Heat and Mass Transfer 46 (2003) 3797–3808. [9] B. Na, R.L. Webb, New model for frost growth rate, International Journal of Heat and Mass Transfer 47 (2004) 925–936. [10] X.M. Wu, R.L. Webb, Investigation of the possibility of frost release from a cold surface, Experimental Thermal and Fluid Science 24 (2001) 151–156. [11] X.M. Wu, X.F. Shan, W.C. Wang, L.M. Tang, Meso-scale visual observation of frost formation on cold surfaces, Journal of Tsinghua University (Science and Technology) 43 (10) (2003) 1437–1440. [12] D.M. Rowe, CRC Handbook of Thermoelectrics, CRC Press, New York, USA, 1995. [13] X.M. Wu, W.C. Wang, Theoretical analysis of initial behavior of frost formed on a cold surface, Journal of Engineering Thermophysics 24 (2) (2003) 286–288. [14] X.M. Wu, W.T. Dai, X.F. Shan, W.C. Wang, Meso-scale visual observations and analyses of frost formation on cold surfaces in the early stage, Proceedings of 13th International Heat Transfer Conference, no. MHP-30, August 13–18, 2006, Sydney, Australia.
Mesoscale investigation of frost formation on a cold surface Xiaomin Wu a
a,*
, Wantian Dai a, Wangfa Xu b, Liming Tang
c
Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Thermal Engineering, Tsinghua University, Beijing 100084, PR China b Department of Mechanical Engineering, Tongji University, Shanghai 200092, PR China c Department of Chemical Engineering, Tsinghua University, Beijing 100084, PR China Received 1 September 2005; received in revised form 20 July 2006; accepted 2 November 2006
Abstract Frost formation on a horizontal flat copper surface was experimentally investigated using microscopic observations. The experiments were carried out on 20 to 0 °C copper surfaces with 22 °C air and 15–85% relative humidities. The experiments showed that the frost formation on a cold surface generally begins with the formation and growth of condensate droplets, freezing of the super-cooled condensate droplets, formation and growth of initial frost crystals on the frozen droplets, growth of frost crystals accompanied by the collapse of some of the crystals, and finally frost layer growth. The freezing onset time and diameter of the super-cooled condensate droplets were characterized. The initial frost crystals can be classified into four groups according to their appearance and shape, with the variations of the frost crystal shape as a function of the cold surface temperature and air humidity. Ó 2006 Elsevier Inc. All rights reserved. Keywords: Frost formation; Super-cooled droplets; Frost crystals; Freezing onset time; Frost crystal shape
1. Introduction When humid air comes in contact with a cold surface whose temperature is below both the dew point of the air and the freezing point of water, frost may form on the surface. The occurrence of frosting is undesirable for most industrial applications such as air conditioners and refrigerators. A frost layer formed on an evaporator not only increases the air side thermal resistance, but also reduces the airflow area, both of which reduce the evaporator performance. Besides, frost on aircraft wings may cause serious safety problems. Therefore frosting has attracted increasing attention in recent years. Although many studies have been done on frost formation, most have focused only on a fully-grown frost layer. The thickness growth rate, density, and thermal conductivity of the fully-grown frost layer [1], as well as the influence of frost on evaporators with different type geometries [2,3] *
Corresponding author. Tel./fax: +86 10 62770558. E-mail address: [email protected] (X.M. Wu).
0894-1777/$ - see front matter Ó 2006 Elsevier Inc. All rights reserved. doi:10.1016/j.expthermflusci.2006.11.002
have been extensively studied. Several models have also been proposed to clarify the effects of environmental parameters and to predict the frost layer growth rate [4,5]. However, few studies have been done to investigate the frosting phenomena in the early stage of frost formation. Hayashi et al. [6] photographically investigated the process of frost formation on stainless steel surfaces and subdivided the process into three periods: crystal growth, frost layer growth, and frost layer fully growth. Cheng et al. [7] studied frost formation and frost crystal growth on a cold plate and found that the frost layer structure was like a forest with variant kinds of growing trees. Recently Na and Webb [8] presented a theoretical analysis of the nucleation process for frost formation on a cold surface and pointed out that the air at the cold surface should be supersaturated for frost nucleation to occur. They [9] further proposed a supersaturation model to predict the frost growth rate. Although the frosting phenomena have been studied extensively, information on the fundamental features of frost formation in the early stages is still limited. The present research seeks to provide such information.
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X.M. Wu et al. / Experimental Thermal and Fluid Science 31 (2007) 1043–1048
Nomenclature Ai N Ts RH
Surface area occupied by the freezing droplets in the observation field, m2 Total number of particles in the field of observation Surface temperature (°C) Air relative humidity (%)
Greek symbols Freezing onset time (s) sf / Freezing droplet diameter (m) DC Vapor concentration difference between the ambient air and the copper surface (g/kg)
Our previous studies showed that frost formation on a cold surface is not a simple process of direct conversion from vapor to frost, the incipient frost development is generally characterized by the formation of super-cooled water droplets on the cold surfaces. The frost formation processes on a hydrophobic surface were also found to differ from those on a bare copper surface and a hydrophilic surface [10,11]. The present study seeks to clarify the fundamental nature of frost formation at its initial stage including the freezing onset time and diameter of the super-cooled condensate droplets, as well as the shapes of the initial frost crystals. 2. Experiments 2.1. Experimental apparatus and procedure Fig. 1 schematically illustrates the experimental apparatus used in this research, which consists mainly of a test section, a data acquisition system, and a microscopic image acquisition system. The details of the test section are shown in Fig. 2. A thermoelectric cooler was used to provide a cooling source for the frosting surface. The thermoelectric cooler is a small heat pump, which operates on direct current and may be used for cooling or heating by reversing the current flow direction [12]. The cold side of the thermoelectric cooler was horizontally attached by thermal grease to a 1 mm thick by 50 mm square copper test plate. The hot side of the thermoelectric cooler was mounted with thermal grease on a heat sink. A plexiglas duct allowed cooling water to flow through the heat sink for heat removal from the hot side of the thermoelectric cooler. The surface temperature of the copper plate was measured using three 0.1 mm T-type thermocouples buried in
Fig. 1. Schematic diagram of the experimental apparatus.
Fig. 2. Test section details. (a) Layout of test plate. (b) Thermocouple locations.
grooves on the backside of the plate, as shown in Fig. 2. Because the copper plate had a very high thermal conductivity, the average thermocouple reading was used as the test surface temperature (Ts). The accuracy of the thermocouples was ±0.1 °C. The surface temperature of the copper plate could be adjusted by changing the input voltage of the semiconductor thermoelectric cooler and the water flow rate. The ambient air temperature (Tair) and relative humidity (RH) were measured using a temperature and humidity sensor (Model M23D4HT-3, ROTRNIC) installed above the test surface. The sensor accuracy was ±1.5% of full range for the relative humidity and ±0.3 °C for temperature. The thermocouples used in the experiment were all precisely calibrated before tests. All of the temperature and humidity measurements were recorded at time intervals of 2.5 s by a data acquisition system (Model 34970 A, Agilent) connected to a computer. The processes of frost formation on the surface were observed and recorded using a microscopic image acquisition system connected to the computer. The microscopic image system consisted of a zoom stereo microscope (Model SZ1145TR, OLYMPUS), a CCD camera (Model WAT-505EX, Watec), a image processor (Model Metor-II/Multi-Channel, Matrox), and a self-programmed program GRAB to
X.M. Wu et al. / Experimental Thermal and Fluid Science 31 (2007) 1043–1048
take the picture. The images were recorded every 2.5 s at magnifications up to 480 times. Tests were performed for copper surface temperatures between 20 °C and 0 °C. At the beginning of each test, the surface was at the cooling water temperature, then the thermoelectric cooler was turned on and the surface temperature was reduced to the desired temperature in a minute. The ambient air temperature was about 22 °C and the relative humidity was varied from 15% to 85%. 2.2. Test surface The static contact angles of the droplets on the surface were measured by the sessile drop method using a goniometer (Model JC2000C1, POWEREACH). The measured contact angle for the copper surface was 84°. Before each test, the surface was cleaned by acetone and then dried with cotton. 3. Results and discussion 3.1. Mesoscale frost formation processes The mesoscale frost formation processes on the cold copper surface for different test conditions were observed using the microscope. Although the frost formation mechanism is quite complicated, the observations showed that for the test conditions the frost formation on a cold surface generally began with the formation and growth of water droplets, then freezing of the super-cooled condensate droplets, then formation of initial frost crystals on the frozen droplets, then growth of frost crystals accompanied by falling down of some of the crystals, then formation and growth of the frost layer and finally aging of the frost layer. Fig. 3 demonstrates a typical frost formation process for a final copper temperature of 12 °C with 22 °C and 50% relative humidity air. The vapor in the moist air began to condense onto the copper plate when the plate surface temperature dropped below the dew point of the moist air. The resulting small condensate droplets (Fig. 3b) grow through direct condensation of vapor onto the droplets and coalescence with adjacent droplets (Fig. 3c and d). The condensate droplets remained liquid even when the copper surface dropped below 0 °C, with this super-cooled state continuing for a period of time before the freezing began. The super-cooled condensate droplets froze and became ice beads (Fig. 3e and f) once the water embryos in the droplets overcame the Gibbs energy barrier [13,14]. The vapor in the moist air then de-sublimated (vapor-to-ice transformation) onto the surfaces of the ice beads to form frost crystals (Fig. 3g). The frost crystals initially grew in one direction (Fig. 3g and h), but later in three dimensions (Fig. 3i and j). The frost crystals then began to grow across each other to form a frost layer consisting of ice beads, frost crystals and moist air on the cold copper surface (Fig. 3k). The frost layer became thicker and denser as it grew (Fig. 3l).
1045
During the frosting formation process, some of the crystals fell down, which makes the structure and growth of the frost layer even more complex, but none of the existing frosting models account for these facts. Thus further studies are needed to create a more practical and accurate frost formation model. 3.2. Freezing onset time and diameter The onset time of freezing can be judged from changes in the appearance of the condensate droplets. The condensate droplets were fully transparent before freezing (Fig. 3c and d) but turned whitish after freezing (Fig. 3e and f). The copper surface temperature corresponding to Fig. 3d was about 12 °C, so the condensate droplets in Fig. 3d were super-cooled. For convenience of explanation, sf is used to express the freezing onset time with the average diameter of the freezing droplets at sf as vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u N uX / ¼ 2t Ai =ðpN Þ ð1Þ i¼1
where Ai is the surface area occupied by the ith freezing droplet, N is the total number of droplets in the field of observation. Fig. 4 shows the variation of the freezing onset time (sf) with copper surface temperature (Ts) and relative humidity (RH). The freezing onset time decreases, as the surface temperature decreases and as the relative humidity increases, but the influence of surface temperature and relative humidity on the freezing onset time decreases as the surface temperature decreases. Fig. 5 shows the variation of the average freezing droplet diameter (/) with copper surface temperature and relative humidity. The freezing droplet diameter (/) decreases as the surface temperature decreases, and as the relative humidity decreases. 3.3. Initial frost crystal shapes The microscope observations showed that the initial frost crystals formed on the ice beads can be classified into four groups as irregular crystals, flake crystals, needle and pole crystals, and feather crystals, as shown in Fig. 6. The irregular crystals (Fig. 6a) have no clear regular shape with the frost crystals combining with tiny ice particles sprinkled not only on the top of the ice bead but also on the sides. Compared with the irregular crystals, the flake crystals (Fig. 6b) have a more regular shape with the copper surface temperature corresponding to the flake crystals being somewhat lower than that for the irregular crystals. Also the flake crystals do not have any of the tiny ice particles that were seen on the irregular crystals. The needle crystals are shown in Fig. 6c with the pole crystals in Fig. 6d. The formation conditions for these two types of crystals are very similar. They often appear at the same time, with more pole crystals tending to appear at lower copper surface
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X.M. Wu et al. / Experimental Thermal and Fluid Science 31 (2007) 1043–1048
Fig. 3. Top view of the frost formation process on the surface for Ts = 12 °C, RH = 50% and Tair = 22 °C.
temperatures. Unlike the irregular and flake crystals, the needle and pole crystals appear only on top of the ice bead. The feather crystals shown in Fig. 6e and f form at higher relative humidies and show more complex branching characteristics.
Fig. 7 illustrates the dependence of the frost crystal shape on Ts and DC, where the DC expresses the vapor concentration difference between the bulk air and the air at the copper surface. The vapor concentration at the copper surface was assumed to be the saturation vapor concentration
X.M. Wu et al. / Experimental Thermal and Fluid Science 31 (2007) 1043–1048
1600 RH=35% RH=50% RH=85%
Tf /s
1200 800 400 0 -6
-8
-10
-12
-14
-16
-18
TS / ºC Fig. 4. Variation of the freezing onset time with copper surface temperature and relative humidity.
1047
corresponding to the copper surface temperature. In crystallography, the frost crystal shape is generally considered to be mainly affected by the temperature of the substrate on which the frost forms and the vapor supersaturation degree at the substrate surface. For the present tests, the ice bead surface was the substrate for the initial frost formation. However, since the ice bead surface temperature was hard to measure, the ice bead surface temperature was assumed to be close to the copper surface temperature. Then, the vapor concentration difference between the ambient air and the copper surface is equal to the vapor super-saturation degree. The numbers I, II, III, IV and V in Fig. 7 identify the regions of super-cooled condensate drops, irregular crystals, flake crystals, needle and pole crystals, and feather crystals. The figure shows that the cold surface temperature is the primary factor affecting the frost
500 12 RH=85% RH=50% RH=35%
9
300
ΔC / g /kg
φ /μm
400
200
6
3
100 0 -4
0
-8
-12
-16
-20
TS / ºC Fig. 5. Variation of the freezing droplet diameter with copper surface temperature and relative humidity.
0
-5
-10
-15
-20
Ts / °C Fig. 7. Dependence of initial frost crystal shape on surface temperature and humidity I: super-cooled water droplets, II: irregular crystals, III: flake crystals, IV: needle and pole crystals, V: feather crystals.
Fig. 6. Four typical shapes of initial frost crystals (a) irregular crystals (b) flake crystals (c, d) needle and pole crystals (e, f) feather crystal.
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X.M. Wu et al. / Experimental Thermal and Fluid Science 31 (2007) 1043–1048
crystal shape, while the relative humidity has a minor effect on the frost crystal shape. 4. Conclusions Mesoscale frost formation processes on a cold copper surface were observed for different surface temperatures and relative humidities using a microscope. Following are the conclusions drawn from this research: 1. The super-cooled condensate droplets freeze earlier at lower surface temperatures and higher relative humidities, with the freezing droplets being smaller at lower surface temperatures and lower relative humidities. 2. The frost formation on a cold surface is generally characterized by the initial formation and growth of condensate droplets followed by freezing of the super-cooled droplets, formation and growth of initial frost crystals on the frozen droplets, growth of frost crystals accompanied by falling down of some of the crystals, and finally frost layer growth. 3. The initial frost crystals can be classified into four groups as irregular crystals, flake crystals, needle and pole crystals, and feather crystals. 4. The surface temperature is the primary factor affecting the frost crystal shape, with the relative humidity having less effect on the frost crystal shape. Acknowledgement This work was financially supported by the National Natural Science Foundation of China (No. 50476011), which is gratefully acknowledged.
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