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Heat transfer coefficient of a snow bag
International Journal of Refrigeration 25 (2002) 1043–1046 www.elsevier.com/locate/ijrefrig
Heat transfer coefficient of a snow bag W.R. da Veigaa, J.P. Meyerb,* a
Department of Mechanical Engineering, Rand Afrikaans University, PO Box 524, Auckland Park, Johannesburg 2006, South Africa b Department of Mechanical and Aeronautical Engineering, University of Pretoria, Pretoria 0002, South Africa Received 18 September 2001; received in revised form 13 May 2002; accepted 15 May 2002
Abstract In snow shooting, pressurised liquid carbon dioxide is injected via a lance into a permeable snow bag mounted near the ceiling of an insulated transport container. The decrease in pressure causes the liquid carbon dioxide to convert to ‘‘snow’’ and vapour inside the snow bag. The snow bag acts as a phase separator, allowing the sublimated snow to keep the preserving temperature inside a container. In this paper the heat transfer coefficient of such a snow bag was determined experimentally. The average heat transfer coefficient was found to be 3.80 Wm2 K1. # 2002 Elsevier Science Ltd and IIR. All rights reserved. Keywords: Carbon dioxide; Dry ice; Manufacturing; Storage; Heat transfer; Coefficient; Application; Container
Coefficient de transfert de chaleur d’un « sac de neige » carbonique Mots cle´s : Dioxyde de carbone ; Neige ; Fabrication ; Reservoir ; Coefficient ; De transfert de chaleur ; Application ; Conteneur
1. Introduction Refrigerated transport equipment, can be broadly classified by the type of refrigeration system used. These types are ventilation, product subcooling, water ice, dry ice (carbon dioxide), liquid nitrogen or liquid carbon dioxide spray, eutectic plates for holdover, mechanical refrigeration and snow shooting. All these types of refrigeration systems are discussed in detail in the ASHRAE [1] handbook. Snow shooting should not be confused with liquid carbon dioxide spray. It is a new technology on which no literature has been published as far as could be determined. It has been recently patented in South Africa [2]. After loading the cargo into the insulated
* Corresponding author. Tel.: +27-12-420-3104; fax: +2712-362-5087. E-mail address: [email protected] (J.P. Meyer).
body the doors are closed and pressurised liquid carbon dioxide (R-744), at a pressure of 2 MPa (gauge) and a temperature of 17 C, is injected via a ‘‘snow’’ lance into a permeable snow bag mounted near the ceiling of an insulated container. The decrease in pressure causes the liquid carbon dioxide to convert to ‘‘snow’’ and vapour inside the snow bag. At an atmospheric pressure of 101.325 kPa 1 kg of liquid carbon dioxide expands to form 0.54 kg of gas at a temperature of approximately 78.5 C as well as 0.46 kg of solid snow, also at a temperature of 78.5 C. The snow bag is designed so that only the snow particles are retained, thus allowing the cold vapour to escape and pre-cool the container walls and product. The permeable snow bag acts as a phase separator, separating the carbon dioxide snow from the gas. The snow in the snow bag sublimes to cold carbon dioxide gas and then flows down the cargo keeping it cold. The snow is not in direct contact with the product or the container walls; therefore this method can be used
0140-7007/02/$20.00 # 2002 Elsevier Science Ltd and IIR. All rights reserved. PII: S0140-7007(02)00027-0
1044
W.R. da Veiga, J.P. Meyer / International Journal of Refrigeration 25 (2002) 1043–1046
Nomenclature A area (m2) h average heat transfer coefficient (Wm2 K1) enthalpy (J kg1) m mass (kg) Q heat transfer rate (W) T temperature ( C) t time in which temperature changes (s) U overall heat transfer coefficient (Wm2 K1) w width of the snow bag (m) z average height of the snow in the snow bag (m)
Subscripts a ambient outside container c container (inside) g saturated vapour i saturated solid o outside walls of container s snow
for most chilled as well as frozen products. Semi-compaction of the solid carbon dioxide snow phase occurs during charging, which reduces the sublimation rate of the snow, resulting in a more controlled release of the refrigeration capacity. Presently the size of the snow bag and the length of filling for a particular journey are determined through practical experience with similarly insulated and sized vehicles and not from fundamental heat transfer calculations. It is therefore the purpose of this paper to determine the heat transfer coefficient of a snow bag. This could be used in future to predict the amount of snow and/or size of the snow bag for a given size of body and heat load.
2. Experimental set-up A snow bag was installed in a thermal insulated container used for refrigerated transport of dairy products. The container was 6045 mm in length and had a width and height of 2430 mm. The wall thickness of the container was 140 mm at the top, bottom, back and front with the sides 130 mm thick. The insulation material used was polyurethane. The snow bag construction had a length of 3980 mm, width of 480 mm and a height of 150 mm and was manufactured from shade netting. The snow will therefore stay in the bag while the gas is released to the inside
of the container. The experiments were conducted at an ambient pressure of approximately 84 kPa, for which CO2 has a solid temperature of 80.8 C. A cross-section of the snow bag is shown in Fig. 1. A thermocouple was placed in the centre of the container and six other thermocouples were placed on the inner face of each of the container walls. Another six thermocouples were placed on the outer face of each of the container walls to determine the average temperature on the inside and outside of the container. The thermocouples were K-type thermocouples calibrated to an inaccuracy of 0.5 C. For heating the inside of the container six 1 kW electric heating elements were placed at even intervals inside the container. Four fans were placed inside the container to circulate the air to ensure a uniform temperature inside the container. The fans were placed to create a rotation of airflow over the electric heating elements in the container. In order to measure the heat load inserted into the container via the heating elements a kw-h meter was connected to the power supply line of the heating elements. The kilowatt-hour meter had an inaccuracy of 2%. The snow bag construction was suspended from the roof of the container with two s-type load cells to measure the weight of the snow inside the snow bag. The load cells were calibrated to within 0.03% inaccuracy. Three wooden depth gauges with polystyrene bases were positioned through the roof of the container to measure the average heights of the snow in the snow bag at different positions during the experiment without opening the doors of the container.
3. Data reduction and discussion of results 3.1. Overall heat transfer coefficient of container The overall heat transfer coefficient of the container walls was determined experimentally. The inside of the container was heated with the electric heating elements, until a steady state temperature difference of approximately 50 C between ambient conditions and the container inside was reached as shown in Fig. 2. The tests were conducted early in the morning to ensure a low ambient temperature.
Fig. 1. Cross-section of the snow bag.
W.R. da Veiga, J.P. Meyer / International Journal of Refrigeration 25 (2002) 1043–1046
The high temperature difference was used to ensure a more accurate overall heat transfer coefficient. The kw-h meter connected to the power supply measured the transmitted heat load represented by the electric heating elements. As soon as the required temperature difference was reached the fans were switched off and the temperatures were taken. The overall heat transfer coefficient based on the outside area (Ao) of the container was determined as 0.64 Wm2 K1. By determining the maximum possible error due to inaccuracy of the kw-h meter and the K-type thermocouples the inaccuracy of the overall heat transfer coefficient of the insulated container was determined to be a maximum of 4%. 3.2. Heat transfer coefficient of the snow bag The heat transfer from the snow with temperature Ts to the ambient temperature in the container (Tc) is Qs ¼ hs As ðTc Ts Þ
ð1Þ
The snow temperature was verified with measurements to be the same as the theoretical predicted value (80.8 C), at a height of 1935 m above sea level, where the measurements were conducted. Therefore the heat transfer coefficient of the snow can be determined from
1045
Eq. (1) by determining the heat transfer Qs from the determined overall heat transfer coefficient.
hs ¼
Uo Ao ðTa Tc Þ As ðTc TÞs
ð2Þ
For the measurement of the heat transfer coefficient after the snow bag was filled, the fans were not used since the circulation of the carbon dioxide inside the container had a significant effect on the heat transfer coefficient of the snow. The outer surface area of the snow was calculated without entering the container. This was done by measuring the height of the snow as the average of the three depth gauges. It was found that the upper surface of the snow bag was reasonably flat as the snow level moves down during sublimation. Therefore, as the snow sublimates it moves to the sides of the snow bag and it is only the height that decreases. To ensure that an accurate energy balance was obtained over the control volume the mass of snow sublimating per time period was measured with the load cells. By using the difference in enthalpy as 571 kJ kg1 [3], Eq. (3) could be used to calculate the heat absorbed by the snow sublimation.
Fig. 2. Average inner and ambient temperature versus time with four elements and fans switched off after 2 h.
Fig. 4. Total mass and average height of the snow in the snow bag.
Fig. 3. Average inner and ambient temperatures after snow shooting.
Fig. 5. Experimental heat transfer coefficient (hs) of the snow bag.
1046
Qs ¼ ms hg hi =t
W.R. da Veiga, J.P. Meyer / International Journal of Refrigeration 25 (2002) 1043–1046
ð3Þ
This absorbed heat should be the same as the heat transfer in Eq. (1) to ensure an energy balance. The differences were less than 10%. The measured results are shown in Figs. 3 and 4. In Fig. 3 the average temperature of the carbon dioxide gas in the container and the ambient temperature outside the container are given. Although there is a drop in temperature over the first 1.5 h, the temperature inside the container stayed fairly constant for a period of approximately 16 h from 7 to 23 h, even though the ambient temperature decreased from 29 to 14 C, during the same period. After 23 h there was a steep increase in the container temperature as the heat transfer through the container walls was too large in comparison to the heat that can be absorbed by the snow bag. In Fig. 4 the total mass of the snow in the snow bag and the height of the snow are given. Both decrease approximately linearly as function of time over the first 15 h after which it levels off (gradient decreases) as the snow finishes. After 25 h the height of the snow is zero but the mass is not. Through observation it was found that this is because of ice that forms on the snow bag from the moisture in the air inside the snow bag. The experimental predicted heat transfer coefficient is shown in Fig. 5. The heat transfer coefficient varies between a maximum of 5.15 Wm2 K1 and a minimum
of 2.73 Wm2 K1 (while there is snow). There is also an almost linear decrease in the measured heat transfer coefficient. The average heat transfer coefficient is 3.80 Wm2 K1. It was also observed that a layer of ice forms on the snow bag from the moist air. This creates an insulation layer that prevents the snow from sublimating at a higher rate. This is probably the reason that the heat transfer coefficient decreased.
4. Conclusions Experimental work has been done to determine the heat transfer coefficient of snow in a snow bag. The heat transfer coefficient varies between the maximum of 5.15 Wm2 K1 and a minimum of 2.73 Wm2 K1. The average heat transfer coefficient is 3.80 Wm2 K1.
References [1] ASHRAE, Handbook fundamentals. Atlanta (GA, USA): American Society of Heating, Refrigerants and Air-conditioning Engineers, Inc.; 1994. [2] Patent number 91/5027 held by African Oxygen Limited, South Africa, 1991. [3] CGA. Carbon dioxide. 4th ed. USA: Compressed Gas Association, Inc.; 1984. p. 7.
Heat transfer coefficient of a snow bag W.R. da Veigaa, J.P. Meyerb,* a
Department of Mechanical Engineering, Rand Afrikaans University, PO Box 524, Auckland Park, Johannesburg 2006, South Africa b Department of Mechanical and Aeronautical Engineering, University of Pretoria, Pretoria 0002, South Africa Received 18 September 2001; received in revised form 13 May 2002; accepted 15 May 2002
Abstract In snow shooting, pressurised liquid carbon dioxide is injected via a lance into a permeable snow bag mounted near the ceiling of an insulated transport container. The decrease in pressure causes the liquid carbon dioxide to convert to ‘‘snow’’ and vapour inside the snow bag. The snow bag acts as a phase separator, allowing the sublimated snow to keep the preserving temperature inside a container. In this paper the heat transfer coefficient of such a snow bag was determined experimentally. The average heat transfer coefficient was found to be 3.80 Wm2 K1. # 2002 Elsevier Science Ltd and IIR. All rights reserved. Keywords: Carbon dioxide; Dry ice; Manufacturing; Storage; Heat transfer; Coefficient; Application; Container
Coefficient de transfert de chaleur d’un « sac de neige » carbonique Mots cle´s : Dioxyde de carbone ; Neige ; Fabrication ; Reservoir ; Coefficient ; De transfert de chaleur ; Application ; Conteneur
1. Introduction Refrigerated transport equipment, can be broadly classified by the type of refrigeration system used. These types are ventilation, product subcooling, water ice, dry ice (carbon dioxide), liquid nitrogen or liquid carbon dioxide spray, eutectic plates for holdover, mechanical refrigeration and snow shooting. All these types of refrigeration systems are discussed in detail in the ASHRAE [1] handbook. Snow shooting should not be confused with liquid carbon dioxide spray. It is a new technology on which no literature has been published as far as could be determined. It has been recently patented in South Africa [2]. After loading the cargo into the insulated
* Corresponding author. Tel.: +27-12-420-3104; fax: +2712-362-5087. E-mail address: [email protected] (J.P. Meyer).
body the doors are closed and pressurised liquid carbon dioxide (R-744), at a pressure of 2 MPa (gauge) and a temperature of 17 C, is injected via a ‘‘snow’’ lance into a permeable snow bag mounted near the ceiling of an insulated container. The decrease in pressure causes the liquid carbon dioxide to convert to ‘‘snow’’ and vapour inside the snow bag. At an atmospheric pressure of 101.325 kPa 1 kg of liquid carbon dioxide expands to form 0.54 kg of gas at a temperature of approximately 78.5 C as well as 0.46 kg of solid snow, also at a temperature of 78.5 C. The snow bag is designed so that only the snow particles are retained, thus allowing the cold vapour to escape and pre-cool the container walls and product. The permeable snow bag acts as a phase separator, separating the carbon dioxide snow from the gas. The snow in the snow bag sublimes to cold carbon dioxide gas and then flows down the cargo keeping it cold. The snow is not in direct contact with the product or the container walls; therefore this method can be used
0140-7007/02/$20.00 # 2002 Elsevier Science Ltd and IIR. All rights reserved. PII: S0140-7007(02)00027-0
1044
W.R. da Veiga, J.P. Meyer / International Journal of Refrigeration 25 (2002) 1043–1046
Nomenclature A area (m2) h average heat transfer coefficient (Wm2 K1) enthalpy (J kg1) m mass (kg) Q heat transfer rate (W) T temperature ( C) t time in which temperature changes (s) U overall heat transfer coefficient (Wm2 K1) w width of the snow bag (m) z average height of the snow in the snow bag (m)
Subscripts a ambient outside container c container (inside) g saturated vapour i saturated solid o outside walls of container s snow
for most chilled as well as frozen products. Semi-compaction of the solid carbon dioxide snow phase occurs during charging, which reduces the sublimation rate of the snow, resulting in a more controlled release of the refrigeration capacity. Presently the size of the snow bag and the length of filling for a particular journey are determined through practical experience with similarly insulated and sized vehicles and not from fundamental heat transfer calculations. It is therefore the purpose of this paper to determine the heat transfer coefficient of a snow bag. This could be used in future to predict the amount of snow and/or size of the snow bag for a given size of body and heat load.
2. Experimental set-up A snow bag was installed in a thermal insulated container used for refrigerated transport of dairy products. The container was 6045 mm in length and had a width and height of 2430 mm. The wall thickness of the container was 140 mm at the top, bottom, back and front with the sides 130 mm thick. The insulation material used was polyurethane. The snow bag construction had a length of 3980 mm, width of 480 mm and a height of 150 mm and was manufactured from shade netting. The snow will therefore stay in the bag while the gas is released to the inside
of the container. The experiments were conducted at an ambient pressure of approximately 84 kPa, for which CO2 has a solid temperature of 80.8 C. A cross-section of the snow bag is shown in Fig. 1. A thermocouple was placed in the centre of the container and six other thermocouples were placed on the inner face of each of the container walls. Another six thermocouples were placed on the outer face of each of the container walls to determine the average temperature on the inside and outside of the container. The thermocouples were K-type thermocouples calibrated to an inaccuracy of 0.5 C. For heating the inside of the container six 1 kW electric heating elements were placed at even intervals inside the container. Four fans were placed inside the container to circulate the air to ensure a uniform temperature inside the container. The fans were placed to create a rotation of airflow over the electric heating elements in the container. In order to measure the heat load inserted into the container via the heating elements a kw-h meter was connected to the power supply line of the heating elements. The kilowatt-hour meter had an inaccuracy of 2%. The snow bag construction was suspended from the roof of the container with two s-type load cells to measure the weight of the snow inside the snow bag. The load cells were calibrated to within 0.03% inaccuracy. Three wooden depth gauges with polystyrene bases were positioned through the roof of the container to measure the average heights of the snow in the snow bag at different positions during the experiment without opening the doors of the container.
3. Data reduction and discussion of results 3.1. Overall heat transfer coefficient of container The overall heat transfer coefficient of the container walls was determined experimentally. The inside of the container was heated with the electric heating elements, until a steady state temperature difference of approximately 50 C between ambient conditions and the container inside was reached as shown in Fig. 2. The tests were conducted early in the morning to ensure a low ambient temperature.
Fig. 1. Cross-section of the snow bag.
W.R. da Veiga, J.P. Meyer / International Journal of Refrigeration 25 (2002) 1043–1046
The high temperature difference was used to ensure a more accurate overall heat transfer coefficient. The kw-h meter connected to the power supply measured the transmitted heat load represented by the electric heating elements. As soon as the required temperature difference was reached the fans were switched off and the temperatures were taken. The overall heat transfer coefficient based on the outside area (Ao) of the container was determined as 0.64 Wm2 K1. By determining the maximum possible error due to inaccuracy of the kw-h meter and the K-type thermocouples the inaccuracy of the overall heat transfer coefficient of the insulated container was determined to be a maximum of 4%. 3.2. Heat transfer coefficient of the snow bag The heat transfer from the snow with temperature Ts to the ambient temperature in the container (Tc) is Qs ¼ hs As ðTc Ts Þ
ð1Þ
The snow temperature was verified with measurements to be the same as the theoretical predicted value (80.8 C), at a height of 1935 m above sea level, where the measurements were conducted. Therefore the heat transfer coefficient of the snow can be determined from
1045
Eq. (1) by determining the heat transfer Qs from the determined overall heat transfer coefficient.
hs ¼
Uo Ao ðTa Tc Þ As ðTc TÞs
ð2Þ
For the measurement of the heat transfer coefficient after the snow bag was filled, the fans were not used since the circulation of the carbon dioxide inside the container had a significant effect on the heat transfer coefficient of the snow. The outer surface area of the snow was calculated without entering the container. This was done by measuring the height of the snow as the average of the three depth gauges. It was found that the upper surface of the snow bag was reasonably flat as the snow level moves down during sublimation. Therefore, as the snow sublimates it moves to the sides of the snow bag and it is only the height that decreases. To ensure that an accurate energy balance was obtained over the control volume the mass of snow sublimating per time period was measured with the load cells. By using the difference in enthalpy as 571 kJ kg1 [3], Eq. (3) could be used to calculate the heat absorbed by the snow sublimation.
Fig. 2. Average inner and ambient temperature versus time with four elements and fans switched off after 2 h.
Fig. 4. Total mass and average height of the snow in the snow bag.
Fig. 3. Average inner and ambient temperatures after snow shooting.
Fig. 5. Experimental heat transfer coefficient (hs) of the snow bag.
1046
Qs ¼ ms hg hi =t
W.R. da Veiga, J.P. Meyer / International Journal of Refrigeration 25 (2002) 1043–1046
ð3Þ
This absorbed heat should be the same as the heat transfer in Eq. (1) to ensure an energy balance. The differences were less than 10%. The measured results are shown in Figs. 3 and 4. In Fig. 3 the average temperature of the carbon dioxide gas in the container and the ambient temperature outside the container are given. Although there is a drop in temperature over the first 1.5 h, the temperature inside the container stayed fairly constant for a period of approximately 16 h from 7 to 23 h, even though the ambient temperature decreased from 29 to 14 C, during the same period. After 23 h there was a steep increase in the container temperature as the heat transfer through the container walls was too large in comparison to the heat that can be absorbed by the snow bag. In Fig. 4 the total mass of the snow in the snow bag and the height of the snow are given. Both decrease approximately linearly as function of time over the first 15 h after which it levels off (gradient decreases) as the snow finishes. After 25 h the height of the snow is zero but the mass is not. Through observation it was found that this is because of ice that forms on the snow bag from the moisture in the air inside the snow bag. The experimental predicted heat transfer coefficient is shown in Fig. 5. The heat transfer coefficient varies between a maximum of 5.15 Wm2 K1 and a minimum
of 2.73 Wm2 K1 (while there is snow). There is also an almost linear decrease in the measured heat transfer coefficient. The average heat transfer coefficient is 3.80 Wm2 K1. It was also observed that a layer of ice forms on the snow bag from the moist air. This creates an insulation layer that prevents the snow from sublimating at a higher rate. This is probably the reason that the heat transfer coefficient decreased.
4. Conclusions Experimental work has been done to determine the heat transfer coefficient of snow in a snow bag. The heat transfer coefficient varies between the maximum of 5.15 Wm2 K1 and a minimum of 2.73 Wm2 K1. The average heat transfer coefficient is 3.80 Wm2 K1.
References [1] ASHRAE, Handbook fundamentals. Atlanta (GA, USA): American Society of Heating, Refrigerants and Air-conditioning Engineers, Inc.; 1994. [2] Patent number 91/5027 held by African Oxygen Limited, South Africa, 1991. [3] CGA. Carbon dioxide. 4th ed. USA: Compressed Gas Association, Inc.; 1984. p. 7.