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An experimental study of frost formation on a horizontal cylinder under cross flow
International Journal of Refrigeration 24 (2001) 468±474
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An experimental study of frost formation on a horizontal cylinder under cross ¯ow Y.B. Lee a, S.T. Ro b,* a Institute of Advanced Machinery and Design, Seoul National University, Seoul 151-742, South Korea School of Mechanical and Aerospace Engineering, Seoul National University, Seoul 151-742, South Korea
b
Received 14 March 2000; received in revised form 11 August 2000; accepted 11 August 2000
Abstract Frost layers formed on the front and rear surfaces of a horizontal cylinder during cross ¯ow are found to be thicker than those at the top and bottom surfaces where the ¯ow separation is nearly initiated. This observation was obtained in an experimental study carried out to examine frost formation on a horizontal cylinder given a cross ¯ow condition. The thickness of the frost layer and the temperature distribution in the cylinder were measured for various experimental conditions. The local heat ¯ux around the cylinder and the eective thermal conductivity of the frost layer were likewise evaluated, while thickness and surface temperature of the frost layer around the cylinder were measured periodically. These measurements were obtained by varying the Reynolds number, temperature, and humidity. The dew point temperature of the inlet air, however, was kept below the freezing point throughout the experiment. Results also reveal that inlet air velocity, temperature, and humidity aect thickness and thermal conductivity of the frost layer. # 2001 Elsevier Science Ltd and IIR. All rights reserved. Keywords: Tube; Temperature; Humid air; Frost; Forced convection; Heat transfer; Test; Measurement
Etude expeÂrimentale sur le formation de givre sur un cylindre horizontal dans des conditions de convection forceÂe ReÂsume Les couches de givre qui se forment sur les surfaces devant et aÁ l'arrieÁre d'un cylindre horizontal sont plus eÂpaisses que celles qui se forment sur les surfaces supeÂrieures et infeÂrieures ou la seÂparation des ¯ux deÂbute. On a observe ce pheÂnomeÁne lors d'une eÂtude expeÂrimentale eectueÂe a®n d'eÂtudier la formation de givre sur un cylindre horizontal dans des conditions de convection forceÂe. L'eÂpaisseur de la couche de givre et la distribution de la tempeÂrature dans le cylindre ont eÂte mesureÂes sous diverses conditions expeÂrimentales. Le ¯ux thermique local autour du cylindre et la conductibilite thermique de la couche de givre ont eÂte eÂgalement eÂvalueÂs, alors que l'eÂpaisseur et la tempeÂrature super®cielle de la couche de givre autour du cylindre ont eÂte mesureÂes aÁ intervalles. Les auteurs ont obtenus ces mesures en variant le nombre de Reynolds, la tempeÂrature et l'humiditeÂ. On a maintenu la tempeÂrature du point de roseÂe de l'air aÁ l'entreÂe en dessous du point de congeÂlation pendant toute la dureÂe de l'expeÂrience. Les reÂsultats obtenus montrent que la vitesse de l'air aÁ l'entreÂe, la tempeÂrature et l'humidite in¯uencent l'eÂpaisseur et la conductivite thermique de la couche de givre. # 2001 Elsevier Science Ltd and IIR. All rights reserved. Mots cleÂs : tube ; tempeÂrature ; air humide ; givre ; convection forceÂe ; transfert de chaleur ; essai ; mesure
* Corresponding author: Tel.: +82-2-880-7111; fax +82-2-883-0179. E-mail address: [email protected] (S.T. Ro). 0140-7007/01/$20.00 # 2001 Elsevier Science Ltd and IIR. All rights reserved. PII: S0140-7007(00)00073-6
Y.B. Lee, S.T. Ro / International Journal of Refrigeration 24 (2001) 468±474
Nomenclature k l q0 R Re T w
thermal conductivity (W/mK) length (mm) heat ¯ux (W/m) thermal resistance (mK/W) Reynolds number temperature ( C) humidity ratio (g/KgDA)
Subscripts a air f frost s cylinder
1. Introduction Frost begins to form when humid air comes into contact with a cold surface that is kept below freezing temperature. This process aects the heat transfer rate particularly in air-conditioners, refrigerators, and heat pumps. The frost layer initially acts as a ®n and enhances the heat transfer rate, but after a while, the frost layer thickens and its structure changes, and consequently acts as an insulating layer and reduces the area of air ¯ow. Accordingly, defrosting should follow, and eective defrosting is possible only when both analytic tools and comprehensive experimental data on frost formation are available. It remains dicult, however, to analyze the frost formation process because it is a composite unsteady heat and mass transfer problem. This is aggravated by the variation in the roughness of the frost surface in relation to time, a function that causes turbulence in the boundary layer. A melting and refreezing cycle (known as the melt-back phenomenon) occurs when the air-frost surface temperature reaches the freezing point. This cycle changes the structure of the frost layer, increases the density and enhances thermal conductivity of the frost. These eects are more likely to happen in high-humidity and/or high-temperature environments than in low-humidity and/or low-temperature conditions [1]. A number of researches on frost formation have been carried out. Lee et al. [2] presented computational and experimental results of frost formation on a cold ¯at plate, while forced convection to a ¯at plate was studied by Yonko and Sepsy [3], Brian et al. [4], Yamagawa et al. [5], and Tokura et al. [6]. The properties of frost formed on parallel plates were published by O'Neal and Tree [7], LuÈer and Beer [8], and Han and Ro [9], while Aoki et al. [10] investigated frost on a vertical cylinder. Though many papers have been published, there are few experimental studies that deal with cylindrical geometry.
469
In this study, experiments are carried out using low humidity air conditions, which indicate that the dew point temperature of the free stream air is below the freezing point of water. When air temperature is 10 C in winter, relative humidity very often has the value of 30 50%, whose dew point is below freezing point. 2. Experiment 2.1. Experimental apparatus Fig. 1 illustrates the experimental apparatus used in this research. It consists of a cylindrical test section and an air circulation loop with an air-controlling chamber, ¯ow laminators, a square duct, a fan, a return duct and an ori®ce. The ori®ce located in the return duct measured the ¯ow rates, while the temperature and humidity of the incoming free stream air are controlled in the air controlling chamber, which is composed of a heater, a refrigerator and humidi®er. The cylindrical test section is placed in a 160 210 mm square duct. The test cylinder made of stainless steel 304 with outer and inner diameter of 70.0 and 17.0 mm, respectively, as shown in Fig. 2, is cooled using a 50/50 ethylene-glycol/water solution. Coolant temperature is lowered to about 30 C to obtain the cylinder surface temperature of 17 C. A stainless steel pipe is inserted in the cylinder, then coolant ¯ows into the test section through the pipe and ¯ows out through the annular space, reversing its direction. This con®guration of coolant ¯ow reduces a longitudinal temperature gradient. Small holes of 0.9 mm in diameter were drilled at four circumferential positions of 0, 90, 180 and 270 , with radial positions at 9, 21.75 and 34.5 mm to measure the temperature distribution in the cylinder. Three locations in the longitudinal direction were chosen to result in a total of 36 thermocouples to measure the temperature distribution in the hollow cylinder.
Fig. 1. A schematic diagram of the experimental apparatus. Fig. 1. ScheÂma de l'appareil expeÂrimental.
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The uncertainties for air temperature and absolute humidity are found to be 0.2 C and 1.09210 4 kgw/ kga, respectively. The uncertainty on the frost thickness is 0.02 mm. The uncertainty relating to eective thermal conductivity is 9.0%. 2.2. Measurements of frost surface temperature Thermocouples are used to measure frost surface temperature by direct contact or extrapolation of the temperature distribution in the frost layer [3,11]. Infrared thermometers can also be adopted as a non-contact tool for measurement [9,13]. For this experiment, a thermocouple (type T) was attached to a micrometer and was tipped parallel to the freezing surface, as shown in Fig. 3(a). This method enables us to measure the surface temperature and the thickness of the frost layer simultaneously, reducing the disturbance of air ¯ow. The possibility of the frost surface melting due to conduction is also reduced considerably compared to a perpendicular, direct-contact measurement. Four identical measuring sets were provided to measure the temperature of the frost surface and the thickness of the layer. As shown in Fig. 3(b), four circumferential positions were selected: front, top, rear and bottom.
longitudinal temperature gradient is ignored and the measured data at the center of three longitudinal locations are used. The circumferential dierences are minor: less than 0.5 C with an average dierence of 0.3 C at the top and bottom, and less than 0.2 C with an average dierence of 0.1 C at the rear. Based on the well-known conduction equation [12], the radial heat ¯ux is given by the following equation 2ks Ts;in Ts;out q0t 1 ln rs;out =rs;in
3. Reduction of experimental data 3.1. Heat ¯ux The cylinder is used as a heat ¯ux meter. Heat ¯ux can be calculated from the radial temperature distribution given a known thermal conductivity of the cylinder. The cylinder is made of stainless steel 304 and its thermal conductivity (ks) is known to be 14.0 W/mK [14,15]. The temperature gradient of the longitudinal direction is small enough to be ignored. The maximum temperature dierence in the longitudinal direction is less than 0.5 C with an average dierence of 0.1 C. Therefore, the
Fig. 2. A schematic diagram of the test section. Fig. 2. ScheÂma de la section eÂtudieÂe.
Fig. 3. A schematic diagram of measuring frost surface temperature and frost layer thickness. Fig. 3. ScheÂma du dispositif permettant de mesurer la tempeÂrature du givre super®ciel et l'eÂpaisseur du givre.
Y.B. Lee, S.T. Ro / International Journal of Refrigeration 24 (2001) 468±474
where ks stands for thermal conductivity of the cylinder, r is radius, Ts,in and Ts,out represent cylinder temperatures at the inner and outer sides, respectively. Three points were chosen to measure temperature as a function of radius: two at the almost inner and outer surfaces of the cylinder and one at the middle. The analytically obtained temperatures at the middle point are compared to verify Eq. (1). The dierence between the two temperatures does not exceed 0.2 C, the average being 0.1 C. 3.2. Heat transfer within the frost layer A simple equation may be used to describe heat conduction within a frost layer. If we assume that the properties of the frost layer are uniform at a certain instance, eective thermal conductivity of the frost layer can be calculated from the heat ¯ux measured, the overall temperature dierence across the frost layer, and the thickness. 2kf Tf;b Tf;sur 0 qt 2 ln lf rs;out =rs;out In Eq. (2), kf stands for eective thermal conductivity of the frost layer, lf is layer thickness, and Tf,b and Tf,sur represent the temperature of the frost layer at the base and surface, respectively. The temperature at the base is assumed to be the same as the temperature at the cylinder surface. From Eqs. (1) and (2), the eective thermal conductivity of the layer can be evaluated, and the eective thermal resistance of the layer can be expressed as follows: ks Ts;in Ts;out ln lf rs;out =rs;out kf 3 Tf;b Tf;sur ln rs;out =rs;in Rf
ln rs;out lf =rs;out 2kf
471
number based on the outer diameter of the cylinder. The frost layer increases in thickness with respect to time in all positions, this increase diers among positions. Frost layers formed on the front and rear positions are thicker than those on the top and bottom. This can be attributed as follows. At =0 , there is a stagnation point that causes the formation of thicker frost layer. At = 180 , vortices in the wake region increase the mixing eect and diusion, thereby enlarging heat and mass transfer [10]. Fig. 5 illustrates the change in eective thermal conductivity of the frost layer. Three hours after frost formation started, the value of eective thermal conductivity is still less than 10% of that of ice: about 2 W/mK. It can be presumed from this ®nding that the structure of the frost layer is still porous. With the growth of the frost layer, the density of the frost layer is enlarged and consequently eective thermal conductivity of the frost layer increases. However, the growth of the whole thickness of the frost layer, that acts as an insulating layer, produces eective thermal Table 1 Experimental conditions Tableau 1 Conditions expeÂrimentales Parameter
Range
Time (min) Air humidity ratio (g/kgDA) Air temperature ( C) Reynolds number
0±180 2.50±3.54 9.6±20.3 10 430±18 200
4
4. Results and discussions Data obtained from the experiments are presented as a function of time for given sets of experimental conditions with the following variables: temperature, humidity and air ¯ow rate. The outer surface temperature of the cylinder is maintained at 17 C, through a modulation of the coolant temperature. Table 1 summarizes the experimental conditions. Variations of the frost layer thickness with respect to time are plotted in Fig. 4. In the ®gure, the legend denotes each circumferential position (front =0 , top =90 , rear =180 , and bottom =270 ). Tair is the free stream air temperature, w humidity ratio of free stream air, and Red Reynolds
Fig. 4. Frost thickness as a function of time (Tair=9.9 C, Red=10 480, w=3.17 g/kgDA). Fig. 4. Epaisseur du givre en fonction de la dureÂe Tair=9,9 C, Red=10 480, w=3,17 g/kgDA).
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resistance of the frost layer to become larger. The variation in eective thermal resistance is shown in Fig. 6. The eect of humidity ratio on the growth of the frost layer can be seen in Fig. 7. It has been acknowledged that a higher humidity ratio in the free stream causes a
Fig. 5. Eective thermal conductivity of the frost layer as a function of the frost layer thickness (Tair=9.9 C, Red=10 480, w=3.17 g/kgDA). Fig. 5. Conductibilite thermique de la couche de givre en fonction de son eÂpaisseur (Tair=9,9 C, Red=10 480, w=3,17 g/kgDA).
Fig. 6. Eective thermal resistance of the frost layer as a function of the frost layer thickness (Tair=9.9 C, Red=10 480, w=3.17 g/kgDA). Fig. 6. ReÂsistance thermique de la couche de givre en fonction de son eÂpaisseur (Tair=9,9 C, Red=10 480, w=3,17 g/kgDA).
greater driving potential of mass transfer between free stream and frost surfaces, and the frost layer becomes thicker [2]. The present experiment con®rms it, as shown in the ®gure. The eect of inlet air temperature on frost layer thickness is given in Fig. 8. Even though air temperature eect is minor to air humidity eect, there is some tendency in air temperature eect. It is found that given higher inlet air temperature, a thicker frost layer is formed. According to Ref. [11], which dealt with the conditions of a high humidity ratio, a higher inlet air temperature raises the air-frost interface temperature and causes the air humidity ratio in the vicinity of the frost surface to increase, due to slight sublimation from the frost surface to the vicinity of frost surface. It lessens the concentration driving force, that is, the dierence between the humidity ratio of the air in the free stream and that of the air±frost interface. This reduces frost deposition rate and consequently the frost layer thickness [11]. Melting process with increasing air temperature was raised for another cause [7]. On the other hand, there is a research ®nding [16] that supports the present experimental results. The research contains a computational analysis for the eect of inlet air temperature given a low humidity ratio. They claimed that if there is no melting±refreezing cycle occurring near the frost surface that is adjacent to the air stream, the frost growth is primarily dominated by sublimation±ablimation processes that are in¯uenced by the heat transfer from the air stream and through the frost layer. It was
Fig. 7. Frost layer thickness as a function of time (case 1: Tair=9.2 C, Red=18 200, w=2.50 g/kgDA; case 2: Tair=9.6 C, Red=18 140, w=3.54 g/kgDA). Fig. 7. Epaisseur de la couche de givre en fonction de la dureÂe (cas 1 : Tair=9,2 C, Red=18 200, w=2,50 g/kgDA ; cas 2 : Tair=9,6 C, Red=18 140, w=3,54 g/kgDA).
Y.B. Lee, S.T. Ro / International Journal of Refrigeration 24 (2001) 468±474
473
Fig. 8. Frost layer thickness as a function of time (case 1: Tair=9.9 C, Red=10 480, w=3.17 g/kgDA; case 2: Tair=16.5 C, Red=10 430, w=3.31 g/kgDA; case 3: Tair=20.3 C, Red=10 430, w=3.00 g/kgDA). Fig. 8. Epaisseur de la couche de givre en fonction de la dureÂe (cas 1 : Tair=9,9 C, Red=10 480, w=3,17 g/kgDA ; cas 2 : Tair=16,55 C, Red=10 430, w=3,31 g/kgDA ; cas 3 : Tair=20,3 C, Red=10 430, w=3,00 g/kgDA).
concluded that a higher inlet air temperature generates a thicker frost layer [16]. Results of previous studies and those obtained from this study demonstrate the eects of air temperature, and these can be summarized as follows. There is many factors aecting the frost growth: transfer coecients, driving potentials in the heat and mass transfer, and melting on the frost surface. These factors are complexly coupled with each other. In the case of higher humidity, water particles are absorbed into the inner side of frost layer and prefer to contribute to density growth than to thickness growth; moreover, local melting at the frost surface is more likely to occur. In the case of this study, the value of frost surface temperature is below 0 C during the 3 h run and consequently there is no reason for reducing of frost layer thickness by melting-refreezing cycle. If the dew point is lower than the freezing temperature, sublimation is a dominant process; see Fig. 9(a) and (b). In the frost formation process, a concentration-driving force causes the mass transfer of vapor molecules from the air-to-frost layer. The deposition of vapor near the cooling plate induces a concentration dierence, which is a vapor partial pressure discrepancy at the vicinity of the surface and in the free stream air. It is supposed that the concentration gradient becomes steeper as the dierence in temperature
Fig. 9. Water vapor changing processes in dierent cases. Fig. 9. Processus de transformation de vapeur d'eau pour les dieÂrents cas.
between the frost surface and the free stream air becomes larger. As a result, the concentration-driving force is enlarged and the growth rate of the frost layer becomes even higher. Even though air temperature aects the thickness of frost layer, it should be kept in mind that air temperature eect is secondary factor in comparison with air humidity eect. 5. Conclusions Frost formation on a horizontal cylinder under cross ¯ow is examined experimentally and the eect of free stream air temperature and humidity ratio on thickness, eective thermal conductivity and eective thermal resistance of the frost layer is presented. Contrary to previous studies that mainly presented experimental and computational results for high humidity ratio, this research carried out experiments for low humidity conditions. Low humidity indicates that dew points of the free stream air are kept below freezing point. In all cases, the values of frost layer thickness at the front and rear sides of the cylinder are greater than those at the top and bottom sides. As the humidity ratio of free stream rises,
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a thicker frost layer is formed. As for the eect of air temperature, the present results suggest that a higher air temperature causes a thicker frost layer to be formed, and this is interpreted as a unique characteristic of the frost formation process occurring at low air humidity conditions. Further observation including measurements of the frost layer density may support the validity of this conclusion. Acknowledgements This research was supported in part by a grant from the BK-21 Program for Mechanical and Aerospace Engineering Research at Seoul National University. References [1] Padki MM, Sherif SA, Nelson RM. A simple method for modeling the frost formation phenomenon in dierent geometries. ASHRAE Transactions 1989;95(2):1127±37. [2] Lee KS, Kim WS, Lee TH. A one-dimensional model for frost formation on a cold ¯at surface. International Journal of Heat and Mass Transfer 1997;40(18):4359±65. [3] Yonko JD, Sepsy CF. An investigation of the thermal conductivity of frost while forming on a ¯at horizontal plate. ASHRAE Transactions 1967;73(1):1.1±11. [4] Brian PLT, Reid RC, Brazinsky I. Cryogenic frost properties. Cryogenic Technology 1969;5:205±12. [5] Yamakawa N, Takahkshi N, Ohtani S. Forced convection heat and mass transfer under frost conditions. Heat Transfer Japanese Research 1972;1:1±10.
[6] Tokura I, Saito H, Kishinami K. Study on properties and growth rate of frost layers on cold surfaces. Journal of Heat Transfer 1983;105:895±901. [7] O'Neal DL, Tree DR. Measurement of frost growth and density in a parallel plate geometry. ASHRAE Transactions 1984;90:278±90. [8] A. LuÈer and H. Beer, Frost formation on cooled parallel plates in laminar forced convection, In: Proceeding of 11th IHTC, Vol. 7, 1998. p. 157±62. [9] Han HD, Ro ST. The characteristics of frost growth on parallel plates, In: Advances in cold-region thermal engineering and sciences, Part I, 1999. p. 55±64. [10] Aoki H, Yamakawa N, Ohtani S. Forced convection heat transfer around a vertical cylinder under frosting conditions. Heat Transfer-Japanese Research 1981;1:53±63. [11] Sherif SA, Raju SP, Padki MM, Chan AB. A semiempirical transient method for modelling frost formation on a ¯at plate. Rev Int Froid 1993;16(5):321±9. [12] Hayashi Y, Aoki A, Adachi S, Hori K. Study of frost properties correlating with frost formation types. Journal of Heat Transfer 1977;99:239±45. [13] Tokura I, Saito H, Kishinami K. Prediction of growth rate and density of frost layers under forced convection. Warme und StouÈbertragung 1988;22:285±90. [14] Incropera, F. P. & Witt, D. P. Fundamentals of heat and mass transfer. 3rd ed., 1990. [15] Hong K, Weckman DC, Strong AB. The in¯uence of thermo¯uids phenomena in gas tungsten arc welds in high and low thermal conductivity metals. Canadian Metallugical Quarterly 1998;37(3±4):293±303. [16] Tao Y-X, Mao Y, Besant RW. Frost growth characteristics on heat exchanger surfaces. HTD-vol. 286. Fundamentals of phase changes: sublimation and solidi®cation. ASME, 1994. pp 29±38.
www.elsevier.com/locate/ijrefrig
An experimental study of frost formation on a horizontal cylinder under cross ¯ow Y.B. Lee a, S.T. Ro b,* a Institute of Advanced Machinery and Design, Seoul National University, Seoul 151-742, South Korea School of Mechanical and Aerospace Engineering, Seoul National University, Seoul 151-742, South Korea
b
Received 14 March 2000; received in revised form 11 August 2000; accepted 11 August 2000
Abstract Frost layers formed on the front and rear surfaces of a horizontal cylinder during cross ¯ow are found to be thicker than those at the top and bottom surfaces where the ¯ow separation is nearly initiated. This observation was obtained in an experimental study carried out to examine frost formation on a horizontal cylinder given a cross ¯ow condition. The thickness of the frost layer and the temperature distribution in the cylinder were measured for various experimental conditions. The local heat ¯ux around the cylinder and the eective thermal conductivity of the frost layer were likewise evaluated, while thickness and surface temperature of the frost layer around the cylinder were measured periodically. These measurements were obtained by varying the Reynolds number, temperature, and humidity. The dew point temperature of the inlet air, however, was kept below the freezing point throughout the experiment. Results also reveal that inlet air velocity, temperature, and humidity aect thickness and thermal conductivity of the frost layer. # 2001 Elsevier Science Ltd and IIR. All rights reserved. Keywords: Tube; Temperature; Humid air; Frost; Forced convection; Heat transfer; Test; Measurement
Etude expeÂrimentale sur le formation de givre sur un cylindre horizontal dans des conditions de convection forceÂe ReÂsume Les couches de givre qui se forment sur les surfaces devant et aÁ l'arrieÁre d'un cylindre horizontal sont plus eÂpaisses que celles qui se forment sur les surfaces supeÂrieures et infeÂrieures ou la seÂparation des ¯ux deÂbute. On a observe ce pheÂnomeÁne lors d'une eÂtude expeÂrimentale eectueÂe a®n d'eÂtudier la formation de givre sur un cylindre horizontal dans des conditions de convection forceÂe. L'eÂpaisseur de la couche de givre et la distribution de la tempeÂrature dans le cylindre ont eÂte mesureÂes sous diverses conditions expeÂrimentales. Le ¯ux thermique local autour du cylindre et la conductibilite thermique de la couche de givre ont eÂte eÂgalement eÂvalueÂs, alors que l'eÂpaisseur et la tempeÂrature super®cielle de la couche de givre autour du cylindre ont eÂte mesureÂes aÁ intervalles. Les auteurs ont obtenus ces mesures en variant le nombre de Reynolds, la tempeÂrature et l'humiditeÂ. On a maintenu la tempeÂrature du point de roseÂe de l'air aÁ l'entreÂe en dessous du point de congeÂlation pendant toute la dureÂe de l'expeÂrience. Les reÂsultats obtenus montrent que la vitesse de l'air aÁ l'entreÂe, la tempeÂrature et l'humidite in¯uencent l'eÂpaisseur et la conductivite thermique de la couche de givre. # 2001 Elsevier Science Ltd and IIR. All rights reserved. Mots cleÂs : tube ; tempeÂrature ; air humide ; givre ; convection forceÂe ; transfert de chaleur ; essai ; mesure
* Corresponding author: Tel.: +82-2-880-7111; fax +82-2-883-0179. E-mail address: [email protected] (S.T. Ro). 0140-7007/01/$20.00 # 2001 Elsevier Science Ltd and IIR. All rights reserved. PII: S0140-7007(00)00073-6
Y.B. Lee, S.T. Ro / International Journal of Refrigeration 24 (2001) 468±474
Nomenclature k l q0 R Re T w
thermal conductivity (W/mK) length (mm) heat ¯ux (W/m) thermal resistance (mK/W) Reynolds number temperature ( C) humidity ratio (g/KgDA)
Subscripts a air f frost s cylinder
1. Introduction Frost begins to form when humid air comes into contact with a cold surface that is kept below freezing temperature. This process aects the heat transfer rate particularly in air-conditioners, refrigerators, and heat pumps. The frost layer initially acts as a ®n and enhances the heat transfer rate, but after a while, the frost layer thickens and its structure changes, and consequently acts as an insulating layer and reduces the area of air ¯ow. Accordingly, defrosting should follow, and eective defrosting is possible only when both analytic tools and comprehensive experimental data on frost formation are available. It remains dicult, however, to analyze the frost formation process because it is a composite unsteady heat and mass transfer problem. This is aggravated by the variation in the roughness of the frost surface in relation to time, a function that causes turbulence in the boundary layer. A melting and refreezing cycle (known as the melt-back phenomenon) occurs when the air-frost surface temperature reaches the freezing point. This cycle changes the structure of the frost layer, increases the density and enhances thermal conductivity of the frost. These eects are more likely to happen in high-humidity and/or high-temperature environments than in low-humidity and/or low-temperature conditions [1]. A number of researches on frost formation have been carried out. Lee et al. [2] presented computational and experimental results of frost formation on a cold ¯at plate, while forced convection to a ¯at plate was studied by Yonko and Sepsy [3], Brian et al. [4], Yamagawa et al. [5], and Tokura et al. [6]. The properties of frost formed on parallel plates were published by O'Neal and Tree [7], LuÈer and Beer [8], and Han and Ro [9], while Aoki et al. [10] investigated frost on a vertical cylinder. Though many papers have been published, there are few experimental studies that deal with cylindrical geometry.
469
In this study, experiments are carried out using low humidity air conditions, which indicate that the dew point temperature of the free stream air is below the freezing point of water. When air temperature is 10 C in winter, relative humidity very often has the value of 30 50%, whose dew point is below freezing point. 2. Experiment 2.1. Experimental apparatus Fig. 1 illustrates the experimental apparatus used in this research. It consists of a cylindrical test section and an air circulation loop with an air-controlling chamber, ¯ow laminators, a square duct, a fan, a return duct and an ori®ce. The ori®ce located in the return duct measured the ¯ow rates, while the temperature and humidity of the incoming free stream air are controlled in the air controlling chamber, which is composed of a heater, a refrigerator and humidi®er. The cylindrical test section is placed in a 160 210 mm square duct. The test cylinder made of stainless steel 304 with outer and inner diameter of 70.0 and 17.0 mm, respectively, as shown in Fig. 2, is cooled using a 50/50 ethylene-glycol/water solution. Coolant temperature is lowered to about 30 C to obtain the cylinder surface temperature of 17 C. A stainless steel pipe is inserted in the cylinder, then coolant ¯ows into the test section through the pipe and ¯ows out through the annular space, reversing its direction. This con®guration of coolant ¯ow reduces a longitudinal temperature gradient. Small holes of 0.9 mm in diameter were drilled at four circumferential positions of 0, 90, 180 and 270 , with radial positions at 9, 21.75 and 34.5 mm to measure the temperature distribution in the cylinder. Three locations in the longitudinal direction were chosen to result in a total of 36 thermocouples to measure the temperature distribution in the hollow cylinder.
Fig. 1. A schematic diagram of the experimental apparatus. Fig. 1. ScheÂma de l'appareil expeÂrimental.
470
Y.B. Lee, S.T. Ro / International Journal of Refrigeration 24 (2001) 468±474
The uncertainties for air temperature and absolute humidity are found to be 0.2 C and 1.09210 4 kgw/ kga, respectively. The uncertainty on the frost thickness is 0.02 mm. The uncertainty relating to eective thermal conductivity is 9.0%. 2.2. Measurements of frost surface temperature Thermocouples are used to measure frost surface temperature by direct contact or extrapolation of the temperature distribution in the frost layer [3,11]. Infrared thermometers can also be adopted as a non-contact tool for measurement [9,13]. For this experiment, a thermocouple (type T) was attached to a micrometer and was tipped parallel to the freezing surface, as shown in Fig. 3(a). This method enables us to measure the surface temperature and the thickness of the frost layer simultaneously, reducing the disturbance of air ¯ow. The possibility of the frost surface melting due to conduction is also reduced considerably compared to a perpendicular, direct-contact measurement. Four identical measuring sets were provided to measure the temperature of the frost surface and the thickness of the layer. As shown in Fig. 3(b), four circumferential positions were selected: front, top, rear and bottom.
longitudinal temperature gradient is ignored and the measured data at the center of three longitudinal locations are used. The circumferential dierences are minor: less than 0.5 C with an average dierence of 0.3 C at the top and bottom, and less than 0.2 C with an average dierence of 0.1 C at the rear. Based on the well-known conduction equation [12], the radial heat ¯ux is given by the following equation 2ks Ts;in Ts;out q0t 1 ln rs;out =rs;in
3. Reduction of experimental data 3.1. Heat ¯ux The cylinder is used as a heat ¯ux meter. Heat ¯ux can be calculated from the radial temperature distribution given a known thermal conductivity of the cylinder. The cylinder is made of stainless steel 304 and its thermal conductivity (ks) is known to be 14.0 W/mK [14,15]. The temperature gradient of the longitudinal direction is small enough to be ignored. The maximum temperature dierence in the longitudinal direction is less than 0.5 C with an average dierence of 0.1 C. Therefore, the
Fig. 2. A schematic diagram of the test section. Fig. 2. ScheÂma de la section eÂtudieÂe.
Fig. 3. A schematic diagram of measuring frost surface temperature and frost layer thickness. Fig. 3. ScheÂma du dispositif permettant de mesurer la tempeÂrature du givre super®ciel et l'eÂpaisseur du givre.
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where ks stands for thermal conductivity of the cylinder, r is radius, Ts,in and Ts,out represent cylinder temperatures at the inner and outer sides, respectively. Three points were chosen to measure temperature as a function of radius: two at the almost inner and outer surfaces of the cylinder and one at the middle. The analytically obtained temperatures at the middle point are compared to verify Eq. (1). The dierence between the two temperatures does not exceed 0.2 C, the average being 0.1 C. 3.2. Heat transfer within the frost layer A simple equation may be used to describe heat conduction within a frost layer. If we assume that the properties of the frost layer are uniform at a certain instance, eective thermal conductivity of the frost layer can be calculated from the heat ¯ux measured, the overall temperature dierence across the frost layer, and the thickness. 2kf Tf;b Tf;sur 0 qt 2 ln lf rs;out =rs;out In Eq. (2), kf stands for eective thermal conductivity of the frost layer, lf is layer thickness, and Tf,b and Tf,sur represent the temperature of the frost layer at the base and surface, respectively. The temperature at the base is assumed to be the same as the temperature at the cylinder surface. From Eqs. (1) and (2), the eective thermal conductivity of the layer can be evaluated, and the eective thermal resistance of the layer can be expressed as follows: ks Ts;in Ts;out ln lf rs;out =rs;out kf 3 Tf;b Tf;sur ln rs;out =rs;in Rf
ln rs;out lf =rs;out 2kf
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number based on the outer diameter of the cylinder. The frost layer increases in thickness with respect to time in all positions, this increase diers among positions. Frost layers formed on the front and rear positions are thicker than those on the top and bottom. This can be attributed as follows. At =0 , there is a stagnation point that causes the formation of thicker frost layer. At = 180 , vortices in the wake region increase the mixing eect and diusion, thereby enlarging heat and mass transfer [10]. Fig. 5 illustrates the change in eective thermal conductivity of the frost layer. Three hours after frost formation started, the value of eective thermal conductivity is still less than 10% of that of ice: about 2 W/mK. It can be presumed from this ®nding that the structure of the frost layer is still porous. With the growth of the frost layer, the density of the frost layer is enlarged and consequently eective thermal conductivity of the frost layer increases. However, the growth of the whole thickness of the frost layer, that acts as an insulating layer, produces eective thermal Table 1 Experimental conditions Tableau 1 Conditions expeÂrimentales Parameter
Range
Time (min) Air humidity ratio (g/kgDA) Air temperature ( C) Reynolds number
0±180 2.50±3.54 9.6±20.3 10 430±18 200
4
4. Results and discussions Data obtained from the experiments are presented as a function of time for given sets of experimental conditions with the following variables: temperature, humidity and air ¯ow rate. The outer surface temperature of the cylinder is maintained at 17 C, through a modulation of the coolant temperature. Table 1 summarizes the experimental conditions. Variations of the frost layer thickness with respect to time are plotted in Fig. 4. In the ®gure, the legend denotes each circumferential position (front =0 , top =90 , rear =180 , and bottom =270 ). Tair is the free stream air temperature, w humidity ratio of free stream air, and Red Reynolds
Fig. 4. Frost thickness as a function of time (Tair=9.9 C, Red=10 480, w=3.17 g/kgDA). Fig. 4. Epaisseur du givre en fonction de la dureÂe Tair=9,9 C, Red=10 480, w=3,17 g/kgDA).
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resistance of the frost layer to become larger. The variation in eective thermal resistance is shown in Fig. 6. The eect of humidity ratio on the growth of the frost layer can be seen in Fig. 7. It has been acknowledged that a higher humidity ratio in the free stream causes a
Fig. 5. Eective thermal conductivity of the frost layer as a function of the frost layer thickness (Tair=9.9 C, Red=10 480, w=3.17 g/kgDA). Fig. 5. Conductibilite thermique de la couche de givre en fonction de son eÂpaisseur (Tair=9,9 C, Red=10 480, w=3,17 g/kgDA).
Fig. 6. Eective thermal resistance of the frost layer as a function of the frost layer thickness (Tair=9.9 C, Red=10 480, w=3.17 g/kgDA). Fig. 6. ReÂsistance thermique de la couche de givre en fonction de son eÂpaisseur (Tair=9,9 C, Red=10 480, w=3,17 g/kgDA).
greater driving potential of mass transfer between free stream and frost surfaces, and the frost layer becomes thicker [2]. The present experiment con®rms it, as shown in the ®gure. The eect of inlet air temperature on frost layer thickness is given in Fig. 8. Even though air temperature eect is minor to air humidity eect, there is some tendency in air temperature eect. It is found that given higher inlet air temperature, a thicker frost layer is formed. According to Ref. [11], which dealt with the conditions of a high humidity ratio, a higher inlet air temperature raises the air-frost interface temperature and causes the air humidity ratio in the vicinity of the frost surface to increase, due to slight sublimation from the frost surface to the vicinity of frost surface. It lessens the concentration driving force, that is, the dierence between the humidity ratio of the air in the free stream and that of the air±frost interface. This reduces frost deposition rate and consequently the frost layer thickness [11]. Melting process with increasing air temperature was raised for another cause [7]. On the other hand, there is a research ®nding [16] that supports the present experimental results. The research contains a computational analysis for the eect of inlet air temperature given a low humidity ratio. They claimed that if there is no melting±refreezing cycle occurring near the frost surface that is adjacent to the air stream, the frost growth is primarily dominated by sublimation±ablimation processes that are in¯uenced by the heat transfer from the air stream and through the frost layer. It was
Fig. 7. Frost layer thickness as a function of time (case 1: Tair=9.2 C, Red=18 200, w=2.50 g/kgDA; case 2: Tair=9.6 C, Red=18 140, w=3.54 g/kgDA). Fig. 7. Epaisseur de la couche de givre en fonction de la dureÂe (cas 1 : Tair=9,2 C, Red=18 200, w=2,50 g/kgDA ; cas 2 : Tair=9,6 C, Red=18 140, w=3,54 g/kgDA).
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Fig. 8. Frost layer thickness as a function of time (case 1: Tair=9.9 C, Red=10 480, w=3.17 g/kgDA; case 2: Tair=16.5 C, Red=10 430, w=3.31 g/kgDA; case 3: Tair=20.3 C, Red=10 430, w=3.00 g/kgDA). Fig. 8. Epaisseur de la couche de givre en fonction de la dureÂe (cas 1 : Tair=9,9 C, Red=10 480, w=3,17 g/kgDA ; cas 2 : Tair=16,55 C, Red=10 430, w=3,31 g/kgDA ; cas 3 : Tair=20,3 C, Red=10 430, w=3,00 g/kgDA).
concluded that a higher inlet air temperature generates a thicker frost layer [16]. Results of previous studies and those obtained from this study demonstrate the eects of air temperature, and these can be summarized as follows. There is many factors aecting the frost growth: transfer coecients, driving potentials in the heat and mass transfer, and melting on the frost surface. These factors are complexly coupled with each other. In the case of higher humidity, water particles are absorbed into the inner side of frost layer and prefer to contribute to density growth than to thickness growth; moreover, local melting at the frost surface is more likely to occur. In the case of this study, the value of frost surface temperature is below 0 C during the 3 h run and consequently there is no reason for reducing of frost layer thickness by melting-refreezing cycle. If the dew point is lower than the freezing temperature, sublimation is a dominant process; see Fig. 9(a) and (b). In the frost formation process, a concentration-driving force causes the mass transfer of vapor molecules from the air-to-frost layer. The deposition of vapor near the cooling plate induces a concentration dierence, which is a vapor partial pressure discrepancy at the vicinity of the surface and in the free stream air. It is supposed that the concentration gradient becomes steeper as the dierence in temperature
Fig. 9. Water vapor changing processes in dierent cases. Fig. 9. Processus de transformation de vapeur d'eau pour les dieÂrents cas.
between the frost surface and the free stream air becomes larger. As a result, the concentration-driving force is enlarged and the growth rate of the frost layer becomes even higher. Even though air temperature aects the thickness of frost layer, it should be kept in mind that air temperature eect is secondary factor in comparison with air humidity eect. 5. Conclusions Frost formation on a horizontal cylinder under cross ¯ow is examined experimentally and the eect of free stream air temperature and humidity ratio on thickness, eective thermal conductivity and eective thermal resistance of the frost layer is presented. Contrary to previous studies that mainly presented experimental and computational results for high humidity ratio, this research carried out experiments for low humidity conditions. Low humidity indicates that dew points of the free stream air are kept below freezing point. In all cases, the values of frost layer thickness at the front and rear sides of the cylinder are greater than those at the top and bottom sides. As the humidity ratio of free stream rises,
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a thicker frost layer is formed. As for the eect of air temperature, the present results suggest that a higher air temperature causes a thicker frost layer to be formed, and this is interpreted as a unique characteristic of the frost formation process occurring at low air humidity conditions. Further observation including measurements of the frost layer density may support the validity of this conclusion. Acknowledgements This research was supported in part by a grant from the BK-21 Program for Mechanical and Aerospace Engineering Research at Seoul National University. References [1] Padki MM, Sherif SA, Nelson RM. A simple method for modeling the frost formation phenomenon in dierent geometries. ASHRAE Transactions 1989;95(2):1127±37. [2] Lee KS, Kim WS, Lee TH. A one-dimensional model for frost formation on a cold ¯at surface. International Journal of Heat and Mass Transfer 1997;40(18):4359±65. [3] Yonko JD, Sepsy CF. An investigation of the thermal conductivity of frost while forming on a ¯at horizontal plate. ASHRAE Transactions 1967;73(1):1.1±11. [4] Brian PLT, Reid RC, Brazinsky I. Cryogenic frost properties. Cryogenic Technology 1969;5:205±12. [5] Yamakawa N, Takahkshi N, Ohtani S. Forced convection heat and mass transfer under frost conditions. Heat Transfer Japanese Research 1972;1:1±10.
[6] Tokura I, Saito H, Kishinami K. Study on properties and growth rate of frost layers on cold surfaces. Journal of Heat Transfer 1983;105:895±901. [7] O'Neal DL, Tree DR. Measurement of frost growth and density in a parallel plate geometry. ASHRAE Transactions 1984;90:278±90. [8] A. LuÈer and H. Beer, Frost formation on cooled parallel plates in laminar forced convection, In: Proceeding of 11th IHTC, Vol. 7, 1998. p. 157±62. [9] Han HD, Ro ST. The characteristics of frost growth on parallel plates, In: Advances in cold-region thermal engineering and sciences, Part I, 1999. p. 55±64. [10] Aoki H, Yamakawa N, Ohtani S. Forced convection heat transfer around a vertical cylinder under frosting conditions. Heat Transfer-Japanese Research 1981;1:53±63. [11] Sherif SA, Raju SP, Padki MM, Chan AB. A semiempirical transient method for modelling frost formation on a ¯at plate. Rev Int Froid 1993;16(5):321±9. [12] Hayashi Y, Aoki A, Adachi S, Hori K. Study of frost properties correlating with frost formation types. Journal of Heat Transfer 1977;99:239±45. [13] Tokura I, Saito H, Kishinami K. Prediction of growth rate and density of frost layers under forced convection. Warme und StouÈbertragung 1988;22:285±90. [14] Incropera, F. P. & Witt, D. P. Fundamentals of heat and mass transfer. 3rd ed., 1990. [15] Hong K, Weckman DC, Strong AB. The in¯uence of thermo¯uids phenomena in gas tungsten arc welds in high and low thermal conductivity metals. Canadian Metallugical Quarterly 1998;37(3±4):293±303. [16] Tao Y-X, Mao Y, Besant RW. Frost growth characteristics on heat exchanger surfaces. HTD-vol. 286. Fundamentals of phase changes: sublimation and solidi®cation. ASME, 1994. pp 29±38.