Heat and Mass Transfer in M a king Artificial Snow Jamin Chen' and Victor Kevorkian' Ingersoll Rand Research, Inc., Princeton, N . J . 08540 Artificial snow is used increasingly at ski resorts to ensure good skiing conditions. It is made by spraying mixtures of water and compressed air into the freezing atmosphere.
This paper describes analytical and experimental work which was carried out in heat and mass transfer to study the thermodynamics and mechanism of making artificial snow. In addition, the performance of different types of snow nozzles were studied under freezing conditions. The heat of fusion must be rejected to the cold ambient air. Water droplets must be seeded to initiate the freezing process and avoid supercooling which would otherwise occur. Although various seeding materials may be used-e.g., kaolinite-compressed air i s the most convenient. It not only supplies seeds upon expansion, but also serves to atomize the water and promote heat transfer with the cold ambient air.
O r d i n a r i l y , to cover a bare ski slope, 10 to 15 commercial snow guns (nozzles in which water and air are combined, usually a t 100 psig) are used, each operating a t about 10 gallons of water per minute (Moxey, 1967; Pierce, 1954). They operate for 10 hours during the night when the temperature drops below 32'F. Since the heat of fusion of water is 143 Btu per pound, about 12,000 Btu per minute must be removed to freeze the water sprayed by each gun. The gun also handles about 100 standard cubic feet per minute of air (8 pounds per minute). The air reaches the gun presumably at 32OF and 100 psig, and expands to sonic velocity at the nozzle throat. The air temperature a t the throat therefore is -50OF. Assume further t h a t all of the expanded air will be heated from -50" to 3 2 ° F by the water in the immediate vicinity outside of the gun. The maximum amount of heat t h a t could be absorbed by the expanded air is therefore 164 Btu per minute, which is only 1 . 4 5 of the amount to be removed. Therefore, the role of compressed air in the snow gun is not to absorb the heat of fusion directly, b u t to promote heat transfer from the water droplets to the cold ambient air. I t does this by causing turbulence and by producing water droplets of desirable diameter. A detailed discussion of the latter has already been presented (Chen and Kevorkian, 1968). I n addition, compressed air supplies ice seeds upon expansion which initiate the freezing process. A substantial amount of air is needed to freeze 10 gallons of water per minute. If the air is bone-dry, the minimum amount required varies from 13,000 scfm a t 8OF to 33,000 scfm at 30°F. Nevertheless, such large quantities of air may be supplied by winds of even moderate velocity (1 to 10 feet per second). Heat and Mass Transfer
During the snow-making process, heat transfer occurs by two different mechanisms: Convective heat transfer and evaporation of water. Radiative heat transfer under these conditions is insignificant. I
Present address, The Lummus Co., Bloomfield, S . J. 07003
' T o whom correspondence should be addressed.
Heat- and mass-transfer correlations have the following forms (Treybal, 1955):
h = ( h , / d ) [2.0 + P ~ ( ( N RNp; ~
')"'"I
(1)
and
h, = ( D / d ) [2.0 +
Ns~'~)"~''] (2)
where the heat transfer rate due to convection is q = h1T and the heat transfer rate due to mass transfer is qm = h,H+H. Comparison of these two modes of heat transfer may be made, assuming a water droplet size of 600 microns falling a t its terminal velocity. 8.3 feet per second (Perry, 1950), through still air. Although 9. depends on the humidity as well as the temperature of the ambient air, the comparison shows t h a t a t ambient air temperatures above 20' F , qnz predominates. while q< becomes increasingly important as the ambient air temperature decreases below 20" F. Size of Water Droplets
Equations 1 and 2 indicate that a smaller droplet diameter yields larger heat and mass transfer coefficients and larger area per unit mass. However. there is a lower limit for the droplet diameter; the residence time of a water droplet of given diameter is dependent on the wind velocity. Thus, the droplet diameter has to be small enough to result in a sufficiently long residence time in the air and a sufficiently high heat transfer rate t o complete the freezing process. However, in addition, it has t o be large enough so that water droplets will not be carried far away by the wind to cause difficulty in depositing artificial snow on the desired area. A water droplet of 100-micron diameter has a terminal velocity of about 1 foot per second (Perry, 195O)-le., it can be carried away by a wind having a vertical velocity component greater than this. On the other hand, a 700micron droplet has a terminal velocity of about 10 feet per second. From this consideration, the optimum droplet size is closer to 700 microns than to 100 microns. As mentioned above, the entire process of snow formation has to be completed within the residence time of the water droplet in the atmosphere. Residence times Ind. Eng. Chem. Process Des. Develop., Vol. 10, No. 1, 1971
75
were calculated for water droplets of various sizes ejected with various initial vertical velocity components from 3 feet above the ground (about that for a snow gun) into still air. When the vertical velocity component is greater than 20 feet per second (which is generally true for the way snow guns are operated), the residence times will be a t least 20 seconds. T h e optimum size of a water droplet for snow-making is accordingly determined by the rate of heat transfer. which must be sufficient to freeze the droplet in less than 20 seconds. The time required to freeze droplets of different diameters was calculated as a function of relative velocity between the water droplets and the atmosphere for typical snow-making conditions. These calculations indicated that droplets ranging in diameter from 200 to 700 microns will freeze in less than 15 seconds. The most desirable droplet size is therefore in the range of 200 t o 700 microns. Seeding
Even with the above requirements satisfied by water droplet size, spray trajectory, and wind velocity, snow may still not be made successfully. This is because water droplets of small sizes may supercool. LVhen a water droplet supercools, its temperature drops below 3 2 O F before solidification takes place; thus, the vapor pressure lowers. and the overall heat transfer rate decreases. A supercooled droplet may only partially freeze before it falls to the ground. I t s supercooled water is then frozen by conductive heat transfer with the cold ground, forming sheets of ice instead of "snow." One method for avoiding the undesirable supercooling of water droplets is seeding. Various seeding techniques are possible-use of solid particles. sonic vibration, etc. In the solid seeding of water droplets, many materials are available-e.g., silver iodide, whose threshold temperature (the highest temperature a t which solidification may occur) is 2S°F, cupric sulfide (21°F). and kaolinite (14'F) (Mason. 1963). If tiny ice crystals are used for seeding, the threshold temperature may be as high as 32°F. for both the seed and the droplet are of the same material. The production of tiny ice crystals for seeding purposes can be achieved by expanding compressed moist air t o the spontaneous nucleation temperature, which is -40" F for a 1-micron water droplet (Mason, 1963). T o seed effectively with ice crystals, the water has to be supercooled a t the point of seeding. If the water is above its freezing point. the seeds which come into contact with the warm water droplets will be melted and destroyed. I f air seeding is introduced into a water jet a t a point very near t o the water nozzle, or if the seed-laden air comes out from the same nozzle with the water, the water has t o be cooled very rapidly t o supercooled conditions. This requires a low water supply temperature and rapid heat transfer immediately outside the nozzle. In summary, the following requirements have to be satisfied for successful artificial snow-making: iVater must break up into droplets of proper size (200 t o 700 microns). Water droplets must be seeded. When seeding with ice crystals, the water droplets have to be supercooled before they are seeded. The trajectory of water droplets has to provide a 76
Ind. Eng. Chern. Process Des. Develop., Vol. 10, No. 1, 1971
sufficient residence time with the ambient air t o transfer the heat of fusion by both heat and mass transfer. Experimental
Three types of nozzles were used for the experimental studies carried out in the field under freezing conditions. External-mixing concentric convergent nozzles. Studies were made with air supplied t o the inner nozzle and water to the outer nozzle, and vice versa. Internal-mixing convergent nozzle. The air and water were premixed and then ejected from a single convergent nozzle. External-mixing cross-fZou nozzle. Water was ejected from a central nozzle while air streams intersected it from two nozzles on either side a t an angle of about 45". The experiments had a twofold objective. First, the criteria hypothesized above for successful snow-making were examined. Second. the performance of each nozzle type was studied under various atmospheric conditions and water and air pressures and rates. Seeding. Two series of experiments were made t o determine if seeding is essential. Conditions for the first series were: Ambient air temperature, 24°F: ambient air humidity, approximately SO'?; water temperature, 50' F: water supply pressure: 100 and 400 psig; water rate. 9 gallons per minute; and water nozzles, circular and annular. Compressed air was not used. The water droplets produced were about 200 microns. The trajectories of these water droplets were over 100 feet; therefore, they had ample opportunity to freeze. However, they reached the ground as water. and froze there to produce sheets of ice. T o ensure that the water supply was not too warm, it was mixed with snow in a tank to cool it to about 33°F before it was pumped. However, snow failed to form. A small expanded air stream was then directed against the water jet as it emerged from the nozzle. The air line had a small fitting on it which acted as a crude converging nozzle. As soon as this air stream was directed against the water stream, snow was produced. There was a possibility that this air stream promoted snow formation by improving the circulation of ambient air through the water spray. The fitting was accordingly removed from the air line and the experiment repeated. Under these conditions, snow was not produced. The second series was conducted under the following conditions: Ambient air temperature, 10" F ; ambient air humidity. 6 0 7 : water temperature, 40" F; water supply pressure, 425 psig; water rate, 10 gallons per minute: and water nozzle, annular. Compressed air was not used. Snow was not made. However, when either kaolinite powder or cupric sulfide powder was sprinkled into the water jet about 3 feet from the nozzle, snow was formed. These experiments clearly showed that. although the ambient air was cold enough and the water droplet size was proper, snow could not be made unless the water droplets were seeded. The solid seeding tests indicated t h a t water droplets produced with a pressure of 425 psig were suitable for snow-making without further breakup. I t also showed t h a t the trajectory of a 425 psig water jet was sufficient for removing the heat of fusion. When the two series are compared, it is seen that the function of air in the first series was t o seed the water droplets. The failure of air seeding caused by the removal
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Figure 1. Snow-making performance of internal-mixing convergent nozzle of the orifice-like fitting on the air line suggested the following air seeding mechanism: With a small fitting in the air line, the air would be subjected to a sudden expansion a t the orifice. Such an expansion would be isentropic and the air, after expansion. would be very cold. If the air supply temperature was 44'F or below, its temperature after expansion would be not higher than -40" F. the spontaneous nucleation temperature for 1-micron water droplets (Mason, 1963). Thus. the moisture content of the expanded air would be frozen into tiny ice particles, which, in turn, would seed the mass of water droplets. Air Humidity. A test was made at midday under the following conditions: Ambient air temperature, 31" F: water supply temperature. 50' F; water supply pressure, 425 psig: air supply pressure, 100 psig; water rate. 10 gallons per minute: air rate, 61 scfm; and, nozzle, externalmixing concentric. The sun was out. and there was a gusty wind. Snow was made. Although no measurement of air humidity was made. it was believed to be very low. Thus, with a fairly dry atmosphere and high wind velocity. it was possible to make snow in rather warm weather. Wind Velocity. An experiment was carried out a t about midnight with the following conditions: Ambient air temperature. 16"F: water supply temperature, SOOF; water supply pressure, 425 psig; air supply pressure. 100 psig; water rate. 10 gallons per minute; air rate. 100 scfm: and nozzle. external-mixing concentric. Snow was not made. There was no wind. The water droplets fell to the ground almost vertically. Also, soon after the water was turned on, the temperature of the ambient air surrounding the water spray increased to 32' F. At the same time. the water droplets were cooled from 50; to 32" F. This experiment showed that without the help of moving cold air, the sensible heat of water would heat the still ambient air to the freezing point, halting heat transfer before the solidification of water could be completed. Supercooling. As mentioned above under Seeding, droplets should be supercooled before they are seeded. Otherwise. the seeds will be destroyed. To check this point, an experiment was made with warm water under the following conditions: Ambient air temperature. 21" F; water supply temperature. 50' F: water
supply pressure, 425 psig; air supply pressure. 100 psig; water rate. 7.2 gallons per minute; air rate, 71 scfm: and nozzle, external-mixing concentric. Snow was not made. However, after the water supply temperature was lowered to 35"F, snow was made under the same conditions. These results were ascribed to supercooling. When the water supply temperature was 50" F, water droplets probably had not reached a subfreezing temperature when they intermixed with ice seeds from the air jet. Consequently, the seeds were destroyed, and the water droplets did not freeze. However. when the water supply temperature was lowered sufficiently, water droplets probably were subcooled when they contacted ice seeds. The seeds were not melted, and freezing of water droplets was initiated. Performance of Snow Guns
Internal-Mixing Convergent Nozzle. This type of snow gun is the most popular at ski resorts. I t s characteristics were examined under a variety of operating and atmospheric conditions. Results are shown in Figure 1 with the air-water ratio as a parameter. The air and water pressures are supply pressures, before the streams are mixed in the gun. Hence, the air-water ratio is varied by altering the supply pressure of either stream. Operators make artificial snow with this gun by beginning with a relatively low air-water ratio and low supply pressures to first deposit a layer of wet snow to serve as a good base. The ratio is then increased until the top layer is powder-like, or dry. This technique may be followed by reference to Figure 1. Dry snow can be made by operating at an air pressure above 70 psig and a water pressure above 50 psig. If the initial settings are such that the air supply pressure is less than 40 psig and the air-water ratio 3 scfm per gallon per minute, no snow will form. While maintaining this ratio and increasing the supply pressures. very wet, wet, and then dry snow can be made. Snow quality improves with these conditions because the water droplets become smaller, affording better opportunity to freeze completely. The expanding air not only seeds the droplets, but also serves to atomize the water. Hence, a t a given water supply pressure (and. therefore, rate), there is a practical upper limit to the air supply pressure. As the air supply pressure is increased a t a fixed water pressure--l e . . as the air-water ratio is increased-the snow quality. of course, improves. However, the droplets become so small that they are easily blown away by the wind and are not deposited on the ski slope. If the air-water ratio is decreased a t a fixed air supply pressure. snow quality will improve slightly as the water pressure is increased, owing to smaller droplets. However, the improvement is not as dramatic as when air pressure is increased because the latter has a much stronger influence on droplet size. There is a lower limit of air pressure below which snow will not be made, irrespective of the air-water ratio. After atomizing the water stream, the air must still be able to expand to a very low temperature where its water content will spontaneously freeze to form seeds. External-Mixing Concentric Nozzles. Studies were made under freezing conditions with the air supplied to the inner nozzle and water to the outer, and vice versa. Mixing Ind. Eng. Chem. Process Des. Develop., Vol. 10, No. 1, 1971
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AIR TEMPERATURE 9’-30’ F AIR PRESSURE 20-100 P S I G
100 200 300 400 WATER PRESSURE P S I G
0
500
Figure 2. Snow-making performance of external-mixing concentric nozzles
external-mixing concentric one. T h a t is, a t these pressure levels, the droplets were of proper size (200 t o 400 microns) for snow-making and the air stream merely provided the seeds. Under these conditions, dry snow was produced a t air-water ratios below 3 scfm per gallon per minute. However, a t pressures below 300 psig, unlike the external-mixing concentric nozzle, dry snow could still be made, providing the air-water ratio was sufficiently high. Undoubtedly, under these conditions the expanding air also acted to reduce the size of the water droplets. A series of tests was made a t an air-water ratio of 2.5 scfm per gallon per minute. Starting a t a water supply pressure of 300 psig, the water pressure (and, therefore. its rate) was increased while maintaining the same airwater ratio. This showed t h a t very high snow-making rates can be attained from one nozzle if the proper airwater ratio is maintained. Snow was made a t the rate of 40 gallons per minute. The test series terminated a t this point because the capacity of the air compressor was reached. The maximum rate a t which snow may be, made when operating in this fashion is determined by the ability of the ambient air to absorb the heat of fusion. This nozzle arrangement is perhaps the most preferable of the three studied. I t has a wider range of operability than the external-mixing concentric nozzle. Since the flow rates of water and air may be varied independently, control of this nozzle is considerably simpler than the internalmixing one. In the latter nozzle, it is somewhat difficult to balance the air and water flows a t the desired values. Nomenclature
H
a n 2
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Figure 3. Snow-making performance of external-mixing crossflow nozzles
of the two streams occurred in the open atmosphere. Since no significant difference was found between the two types of operation. the results were combined (Figure 2). Results were somewhat erratic, presumably because external mixing of concentric streams may not be reproducible because of factors such as changing wind direction. I n an unpublished study. Chen and Kevorkian (1963) found that a circular orifice nozzle operating under a water supply pressure of 350 psig produces droplets of about 300 microns. Figure 2 shows t h a t dry snow can be made a t water pressures above 300 psig and a t airwater ratios above 2 scfm per gallon per minute. The snow quality deteriorates a t lower pressures because the resulting droplets become too large. These results, therefore, also indicate that the expanding air stream was ineffective in breaking up the water stream, and served only to seed the droplets. External-Mixing Cross-Flow Nozzles. Results of these tests made under freezing conditions are shown in Figure 3. I t is seen t h a t a t water supply pressures above 300 psig, this type of snow nozzle behaved similarly to the 78
Ind. Eng. Chem. Process Des. Develop., Vol. 10, No. 1, 1971
= heat transfer coefficient B t u / (hr) (ft’) (” F) k , = thermal conductivity of air, B t u / (hr)(ft’) (O F / f t ) d = water droplet diameter, ft NRe = Reynolds number Np, = Prandtl number k , = mass transfer coefficient, f t / h r D = diffusivity of water vapor in air, ft2/hr Nsc = Schmidt number 9. = convective heat transfer rate, Btui (hr) (ft’) IT = temperature difference between water droplet and air, O F q. = heat transfer rate due to mass transfer, B t u / (hr) (ft’) Hi = heat of vaporization of water, Btuilb AH = difference between saturation vapor pressure of water a t the droplet temperature and humidity of the air, lb/ft3 Literature Cited
Chen, J., Kevorkian, V., Ind. Eng. Chem. Process Des. Develop., 7, 586-90 (1968). Chen, J., Kevorkian, V., unpublished data, 1963. Mason, B. J., “Ice. The Art and Science of Growing Crystals,” J. J. Gilman, Ed., pp 124-125, Wiley, Xew York, 1963. Moxey, R. L., Compress, A i r , 72 (6), 4-7 (1967). Perry, J. H., Ed., “Chemical Engineers’ Handbook,” 3rd ed., p 1021, McGraw-Hill, New York, N. Y., 1950. Pierce, W. M., Jr., U.S. Patent 2,676,471 (April 27, 1954). Treybal, R. E., “Mass-Transfer Operations,” pp 54-55, McGraw-Hill, New York, Y . Y., 1955.
RECEIVEDfor review February 11, 1970 ACCEPTED August 18, 1970
