1、NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS TECHNICAL NOTE 3143 Washington Mach 1954 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-TECH LIBRARY KAFB, NM If lllll lill Ill I !Ill1 111 !I IIII NATIONAL ADVISClRY COW- FCW AERONAUTICS TECHNICAL NOTE 31
2、43 WERIMENTAL DETEfKEWTIm OF TBERMAL CONDUCTNITY (SF Lm-DENSITY ICE BY willma D. Coles SUMMARY The thermal conductivity of law-density ice has been coquted from data obtained in an experimental investigation of the heat transfer and mass transfer by srhlimation for an iced surface on a flat plate in
3、 a high-velocity tangential air stream. The results are compared with data from several sources on the thermal conductivity of packed snow and solid glaze ice. The results show good agreement with the equations for the thermal conductivity of packed snow as a function of snow density. The agreement
4、of the curves for packed snow near the solid ice regime with the values of thermal conductivity of ice indicates that the curves are applicable over the entire ice-density range. Removal of ice formations Which accrete on aircraft surfaces from the Fmpingement and freezing of cloud droplets has been
5、 the sject of a considerable amount of research in recent years. The accumulation of ice on aircraft surfaces occurs over a range of air teqperatures from 32O F to as low as -40 F (ref. 1). The ice formations may be nearly clear glaze ice with little porosity, such as those formed at air tem- peratu
6、res near the freezing point, or they may be of the very porous type characterized by frost or ice formed at low teqeratures. Some factors which affect the nature of the ice formations are the speed of the aircraft and the cloud droplet size and droplet size distribution. Very few data me available o
7、n the physical properties of ice formations having a density other than that of clear, solid ice. Since much of the de-icing of aircraft is currently accomplished by the application of . heat to the surface to be de-iced, knuwledge of the thermal conductivity of ice is of importance in determining t
8、he heat lost through the ice. * A similar problem is encountered in the determination of heat-transfer Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-rates for frosted refrigeration equipment surfaces. A study of the mass transfer by s6bllmstion and
9、 the heat transfer for an iced surf ace in a high-velocity air stream (ref. 2) required the determination of ice den- sity, ice surface temperature, and rate of heat flow through the ice. From these data, the thermal conductivity of low-density ice has been determined for several values of ice densi
10、ty. The results obtained are.presented herein and are conibined wfth information from several sources to make possible a more complete evaluation of the thermal conductivity of ice over the entire range of ice density. The in- vestigation was conducted in a 3.84- by 10-inch tunnel. at the NACA Lewis
11、 laboratory. METBOD, APPARATUS, m PROCEDURE The thermal conductivity of a sribstance is usually determined by means of standard laboratory procedures and equipment. Few such deter- .- minations have been made for law-density ice, however; and since the investigation reported in reference 2 supplied
12、all the data necessary for the determination of thermal conductivity, the computations were made and are presented herein. The ice formations to be studied were formd on a section of the upper surface of a f lat-plate model which was mounted in the test sec- tion of the 3.84- by 10-inch tunnel. The
13、ice which formed on the sur- face was then maintained at constant thickness (no net transfer of mass by sublimation or condensation) while the heat-f low rate and the tem- perature were measured. The condition of constant ice thickness was necessary for two reasons : (1) The stream-side surf ace tem
14、perature could be readily obtained only for the condition for which the surface temperature was equal to the temperature of saturation of the air stream, and (2) the thermal conductivity must be determined for steady-state conditions for a constant ice thickness. The flat -plate model (sham in fig.
15、1) was 18 inches long, 0.75 inch thick, and 3.84 inches wide and was made of wood to minimize heat conduction through the model. One section of the upper surface of the model consisted of .a 3.84- by 5.75-inch copper plate 1/16 inch thick 7 set flush in the surface and located vith its leading edge
16、% inches from the leading edge of the model. The copper plate was the upper sur- face of a multipass copper box through which cold alcohol could be pumped. Five thermocouples were located in the surface of the cop-per -! plate spaced at linch intervals along the center line. The thermo- 8 couple lea
17、ds passed though tubes in the alcohol chamber, and the thermocouple junctions were made flush with the outer plate surface. The taes were soldered to the copper plate and to the bottom of the Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-copper box
18、. Additional thermocouples were located in the tunnel plenum chamber to measure the total temperature of the air stream and in the alcohol inlet and outlet lines to the copper box. A schematic diagram of the alcohol and thermocouple system is inclllaed in figure 1. A supply of refrigerated air, init
19、ially at approximately -20 F and with a specific humidity of approximately 5.00 pounds of water per pound of dry air, was ccpditioned to provide the desired temperatures and humidities at the tunnel test section. The humidity of the air stream was controlled by means of steam injected at a point suf
20、ficiently far upstream to insure thorough mlxing at the test section. The mass-transfer investigation reported in reference 2 placed cer- tain restrictions on the method of forming the ice which were best met by causing the water vapor in the humidity-controlled air stream to con- dense directly to
21、the solid state on the surface of the cold capper plate. The plate was cooled to a teqerature below that of the frost point of the air stream by the flow of cold alcohol throw the capper box. The alcohol was cooled in an alcohol - dry ice bath heat exchanger. The resultant ice formation thus took th
22、e form of a dense frost-like formation as shown in figure 2. Ice formations were deposited on the refrigerated surface of the cop-per plate at nemly constant values of 5000 feet pressure altitude and 45O F total tewerature of the air stream for Mach nwibers of 0.4, 0.6, and 0.8. The thickness of the
23、 ice forma- tion, which is dependent upon the humidity, velocity, and static pres- sure of the air stream, was controlled through regulation of the steam supply used for humidification of the air stream. The ice was allowed to form until a thickness of approximately 0.20 centheter had been ob- taine
24、d. Measurements of the ice thickness while the tunnel was in oper- ation were made through a windaw in the tunnel wall by the use of a short-focal-length telescope mounted on a vernier carriage. The tele- scope was focused on the pointer (fig. 2) which was directly above the center line of the coppe
25、r plate. The depth of focus of the telescope was. less than 3/4 inch; therefore, with the pointer in focus the ice surface viewed was within the range of approximately f5/8 inch from the center line. The mean height of the ice surface was used in order to account for roughness projections and depres
26、sions. To obtain measurements of ice density, a 2- by 4-inch sheet of brass 0.002 inch thick was wetted on one side and frozen to the copper plate. Ice was then formed by condensation on the thin brass sheet for each Mach nmiber condition. The ice thickness was measured with the telescope, and then
27、the brass sheet and the ice were 13fted fromthe cold plate and removed from the tunnel to determine the ice weight and the average ice density. The density of the ice was assumed to be uni- form throughout its thickness and at all points on the surface. Provided by IHSNot for ResaleNo reproduction o
28、r networking permitted without license from IHS-,-,-The heat-transfer rate through the ice could not be measured directly from the heat gained by the alcohol in flowing through the copper box, as there was some contribution to the total heat gained by the alcohol from conduction through the wood mod
29、el. The total heat transferred to the alcohol was determined from measurements of the al- cohol flow rate, alcohol inlet temperature,.and change in temperature between inlet and outlet to the capper box. The Dewar flasks and stirrer shown in figure 1 ensured uniform temperawe of the alcohol across t
30、he tubing cross section at the points of temperature measurement. The al- cohol flow rate was measured immediately following the temperature measurements by diverting the flow and obtaining volume measurements over a 45-second time interval. Values of the specsic gravity of the alcohol at the temper
31、atures used were determined experimentally, and values of the specific heat of the alcohol for the temperature and water content conditions existing during the investigation were obtained from reference 3. It was necessary to determine the heat gained by conduction through the model, which must be s
32、dtracted from the total heat gained by the alcohol to determine the heat flow through the ice. For this purpose an insulating material (cork bomd) of known thermal conductivity was cemented to the surface of the copper plate. The total heat gained by the alcohol with the cork in place is the sum of
33、the conduction heat - flow through the model and through the cork. For a good insulating material such as cork, the surface temperature on the stream side is approximately equal to the adiabatic wall temperature; thus the heat transfer through the cork can be calculated from the adiabatic wall tem-
34、perature, the measured plate surface temperature beneath the cork, and the conductivity of cork board (ref. 4 and the manufacturers data). The use of the adiabatic wall temperature (computed frm measurements of the total temperature and the total and static pressure) for the sur- face temperature of
35、 the cork during heat transfer through the cork re- sults in an error of approximately 5 percent of the heat flow through the cork. However, because the heat conducted thrdugh the cork is a relatively small proportion of the total hgat gained by conduction, the resulting error in the determimtion of
36、 the heat conducted through the wood model is approximately 1 percent. Values of the heat gained by conduction were determined for the various Mach ders, pressure alti- tudes, and alcohol bulk temperatures. A conduction correction factor for the heat gained through the model was aetermined which is
37、a function of Reynolds nuuiber, as the heat conducted through the wood was first transferred to the wood by convection from- the air stream. By use of the conduction correction factor, values of the heat gained by conduc- tion through the wood were obtained and were stibtracted from the total heat g
38、ain measured with ice on the surface to determine the rate of heat transfer through the ice. Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-In order that the heat transfer to the alcohol should not include any heat required for the transfer of mass
39、either to or from the ice sur- face, the humidity of the ah stream was adjusted mtil the ice remained at constant thickness. With constant ice thickness there is no net mass transfer; that is, sdlimation of the ice and condensation of the vapor from the air on the ice surface occur at the sme rate.
40、Under these conditions, the surface temperature of the ice is the temperature of saturation of the air stream (fro determination of the ice thickness was estimated to be within *2 percent of the average ice thick- ness over the entire plate. The measurements of the average ice surface temperature (f
41、rost-point temperature-) were estimated to be in error by less than it appears prob- able that the use of the van Dusen curve my result in values of thermal conductivity which are too law for ice at very 1m temperatures. CONCLUDING REMAFKS Values of the thermal conductivity of low-density ice formed
42、 by a condensation process on a cold surface have been determined. The data show good agreement with the equations of van men and Devswr for the thermal conductivity of packed snow as a function of the snow density. Lewis Flight Propulsion Laboratory National Advisory Committee for Aeronautics Cleve
43、land, Ohio, January 15, 1954 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-8 NACA TN 3143 REFERENCES 1. Lewis, William, and Bergrun, Norman R. : A Probability Analysis of the Meteorological Factors Conducive to Aircra2-t Icing in the United States.
44、 NACA TN 2738, 1952. 2. Coles, Willard D., and Ruggeri, Robert S.: Experimental hvestiga- tion of Sublimation of Ice at Subsonic and Supersonic Speeds and its Relation to Beat Transfer. NACA TN 3104, 1954. 3. Anon.: International Critical Tablee. Vol. V. McGraw-HI11 Book Co., Inc., 1929, pp. ll4-116
45、, 216-217. - 4. Anon.: International Critical Tables. Vol. 11. McGraw-Hill Book Co., Inc., 1927, pp. 315-316. 5. Walker, William H., Lewis, Warren K., McAdams, William H., and Gilliland, Edwin R.: Principles of Chemical mineering. Third ed., McGraw-Hill Book Co., Inc., 1937, pp. 695-696. 6. Dorsey,
46、N. Eknest: Properties of Ordinmy Water-S&stance. Reinhold Pub. Corp. (ew ork), 1940, pp. 481-484. 7. Devaux, J.: Radiothermic Economy of Fields of Snow and Glaciers. Sci. Abs., ser. A, vol. 36, 1933, pp. 980-981. (bs. from Ann. d. Phys., Bd. 20, July-Aug. 1933, pp. 5-67.,. Provided by IHSNot for Res
47、aleNo reproduction or networking permitted without license from IHS-,-,-Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-Figure 2. - Ice formstion deposited on flat-plate model by condensation of water vapor from air stream. Provided by IHSNot for Res
48、aleNo reproduction or networking permitted without license from IHS-,-,-.40 .45 .50 -55 .60 .65 .70 .75 .80 .85 Mach number Figure 3. - Density of ice formed by condensation from air stream as a function of Mach number. Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-s3 i5 P Density of ice or snow, g/cu cm W I- Figure 4. - Thermal conductivity of ice and packed snow as function of density. bF. W oiid / / , / / I I I / ,/ Dusen - Devaux (packed snow) 2 4 20 - d 4 -. I I Temperature, Oc 1-90 74 Eil 4- /- - 7 0 , .1 .2 .3 .4 .5 .6 .7 .8
