T h e interaction of solvent with drying agent may also play a part in the drying process, but no measurements of this factor have been made. This study of the drying rates of organic solvents with various drying agents has enabled the design of industrial drying rquipment to be carried out with greater precision than heretofore. Both the operation of existing drying units and their service life before regeneration are now more closely controlled. Acknowledgment
We express our thanks to W. Cooper and G. Vaughan for their interest in this work, and to the Dunlop Rubber Co., Ltd., for permission to publish this paper.
literature Cited
(1) Bevington, J. C., Eaves, D. E., Makromol. Chem. 36, 145 (1960). (2) Black, C., Joris, G. G., Taylor, H. S., J . Chem. Phys. 16, 537 (1 948). (3) British Ceca Co., Ltd., technical information. (4) Carter, J . W., Institute of Fuel, Reprint 8, (January 1951). (5) Davis, D. S., Chern. Process Ens. 39, 99 (1958). (6) Derr, R. B., Willmore, C. B., Ind. Eng. Chem. 31, 866 (1939). (7) International Critical Tables, Vol. 111, p. 386, McGraw-Hill, New York, 1933. (8) Miller, A. W., Roberts, C. W., Ind. Chem. 34, 141 (1958). (9) Wymore, C. E., IND.ENG.CHEM.,PROD.RES.DEVELOP. 1, 173 ( 196 2 ) . RECEIVED for review October 3, 1963 ACCEPTEDFebruary 20, 1964 Division of Petroleum Chemistry, 145th Meeting, ACS, New York, N. Y . , September 1963.
VAPOR CONDENSATION ON A HORIZONTAL TUBE USING TEFLON T O PROMOTE DROPWISE CONDENSATION C R E I G H T O N A . DEPEW A N D
R O N A L D L . REISBIG’
Unioerstty of Washington, Seattle, W a s h .
Quantitative measurements of condensing steam were made, using a 0.00025-inch thick film of polytetrafluoroethylene (Teflon) to promote dropwise condensation. The condensing surface was a horizontal l / Z inch O.D. aluminum tube. Both dropwise and filmwise modes of condensation were studied using steam. For each mode, steam-side film coefficients were determined as a function of the temperature drop between the saturated vapor and the outer surface of the condenser tube. Results show conclusively that coating surfaces with Teflon provides a practical scheme for promoting dropwise condensation. Thin Teflon coatings adhered well to stainless steel and copper, as well as aluminum. The heat transfer results were in good agreement with existing theory and with data from other studies.
can condense on a surface in either of two ways: filmwise,)’ wherein the condensate forms a continuous liquid film on the surface; and “dropwise,” wherein the condensate forms discrete droplets. Both mechanisms produce surface heat transfer coefficients that are large when compared with coefficients produced by’ ordinary convective processes, but dropwise condensation normally produces heat fluxes that are an order of magnitude larger than those associated with filmwise condensation. Previous methods used to promote dropwise condensation involved using chemical additives in the vapor or oily materials applied directly to the condensing surface. Examples of such additives are stearic ;and oleic acid, mercaptans, waxes, and oils. The common failing of all these techniques is that replenishment is required-i.e., the effectiveness of the promoter diminishes with time. Baer and McKelvey ( 7 ) have demonstrated the deterioration of a silicone grease surface in 4 hours of testing and compared their results with a Teflon surface which was unchanged in 7 hours of operation with condensing steam. Another disadvantage is that these promoters are not usable on all base materials. O n the other hand, Teflon is a long-lived coating which forms a strong mechanical bond with all .naterials commonly used in con-
A
VAPOR “
’ Present
Mich.
address, Michigan State University, East Lansing;
denser tubing. This scheme for promoting dropwise condensation was introduced by Topper and Baer (78) in 1955 and was subsequently used by Baer and McKelvey ( 7 ) in 1958. The research reported in this paper demonstrated the effectiveness of Teflon as a promoter of dropwise condensation, in addition to presenting fundamental heat transfer results for both modes of condensation. Filmwise condensation has been studied extensively by many researchers ( 4 , 6 , 7, 74,76, 79, ZO), and experimental results have shown good agreement with theoretical relations developed by Nusselt (72) in 1916. Peck and Reddie ( 7 3 ) extended Nusselt’s analysis to include the effects of inertia forces. The inclusion of these forces results in a dimensionless parameter, X p / k ( T a u- T,), which is applied as a correction to the film coefficient derived by Nusselt. O n the basis of this derived parameter and approximately 200 measurements by 19 different authors, Peck and Reddie proposed the following equation :
The first systematic study of dropwise condensation was made by Schmidt, Schurig, and Sellschopp ( 7 5 ) in 1930. Drew, Nagle, and Smith ( 3 ) conducted basic studies in 1935 to determine the conditions that favor dropwise condensation. VOL. 3
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OCTOBER 1964
365
t VENT -100
PSlG STEAM
STEAM COLLECTION
COOLING WATER METER
Figure 1.
Diagram of condensation apparatus
Fatica and Katz ( 4 )improved the existing theory by proposing a model that allows for conduction across the droplet and the growth of the droplet to a critical size. Their analysis results in a n equation involving a n experimentally determined constant, which accounts for track width, drop growth rate, and maximum drop size. T h e condensation heat transfer coefficient is presented in terms of the over-all heat transfer coefficient. This is a major drawback. Other factors such as the fraction of surface covered by droplets, advancing and receding contact angle, and surface tension between liquid and vapor must be determined experimentally for a given system. I n 1952 Sugawara and Michiyoski ( 7 7 ) extended Fatica’s analysis to include the sweeping cycle as well as the adhering period. Although the individual theories differ considerably from one another, they all assume that the condensate is deposited primarily at the edge of the droplet. High speed, magnified motion pictures taken for this study, as well as films taken by Welch (20, 27), tended to validate this hypothesis. Another important advance in the theory was made by Kelvin (2),who proved that for drops smaller than 1 micron the vapor pressure is substantially higher than for a plain liquid surface. This fact accounts for the rapid growth of microscopic drops and gives credence to Euken’s theory (5) that the drops are nucleated rather than formed by an unstable condensate film. A recent investigation by Welch (20) has contributed significantly to the knowledge of the mechanism of dropwise condensation. A major portion of Welch’s work consisted of making high speed motion pictures of condensing steam vapor through a microscope. Welch’s experimental results have been successfully analyzed by McCormick and Baer (70) with a new theory \vhich assumes that heat is transferred by conduction through microdrops which grow from randomly distributed nucleation sites. Further verification of the theory and the influence of surface roughness appears in subsequent work by McCormick and Baer ( 7 7 ) . 366
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PROCESS DESIGN A N D DEVELOPMENT
Apparatus
T h e test apparatus is shown schematically in Figure 1. T h e heat transfer surface in this apparatus consisted of a single horizontal 0.500-inch O.D., 0.020-inch-wall seamless 6 0 6 1 - 0 aluminum tube. Both bare and Teflon-coated tubes were used as described below. Cooling water was forced through the 42.6-inch-long test section at a controlled rate as measured by a calibrated rotameter. Calibrated copperconstantan thermocouples \vere used to measure bulk water temperatures a t the inlet and outlet. T h e cooling water temperature was controlled by the rate a t which cold tap water was admitted to the surge tank. T h e entire steam chamber was constructed of 3-inch borosilicate glass tee sections, providing excellent visibility of the heat transfer surface. Untreated, saturated plant steam at a pressure of 1-inch H g gage was admitted at two locations through moisture separators. Steam chamber pressure was measured with a mercury manometer; steam and condensate temperatures (ahvays identical) were measured with calibrated copper-constantan thermocouples. The steam chamber was vented to the atmosphere continuously to remove noncondensable gases; ho\vever, steam velocity within the chamber was minimal. T h e entire tube surface was continually observed during a test run to assure that the proper condensation mechanism was being maintained. T h e condensed steam was collected in a trough in which it flowed by gravity into a 500-ml. buret. T h e condensate rate was thus obtained by measuring the time required to fill the buret. T h e bare aluminum tube used for the filmwise condensation tests \vas initially polished with No. 1 emery paper, washed with soap and water, and rinsed with bvater daily. For the dropwise condensation tests, a tube was coated with polytetrafluoroethylene (Teflon). Other than an initial washing with soap and water, the Teflon-coated condenser tube received n o further treatment before being placed in the test chamber. The Promoter
Teflon is chemically inert a n d is not wetted by most solvents. It was found (74) that Teflon is not wetted by fluids which have surface tensions greater than 18 dynes per cm. and that the wettability of a fluorinated bulk polymer is a
t
RANGE OF SCATTER FOR ALL DATA
PRESENTED IN REF. 13
la
05
c
I
0
10
Figyre 2.
A
0
-e-.
20
Filmwise condensation of steam Results of single investigators ( 1 3 )
direct function of the amount of fluorine in the compound. Thus, fluorocarbons r a n be used to promote dropwise condensation with almost any known fluid. Teflon coatings produced by spraying with a Teflon emulsion and curing a t 700" F. were very tough and adhered well to copper and stainless steel; however, the strongest bond was formed with aluminum. This can be explained by the fact that aluminum oxide is porous and adheres well to the parent metal. When Teflon is melted on this slightly oxidized aluminum surface, it tends to fill these tiny pores, forming a very strong mechanical bond. The Teflon film was 0.0005 inch thickjust after the condenser tubes were coated. This thickness was reduced to 0.00025 inch by buffing the film with a high speed cloth wheel. This technique produced a very smooth finish on the film surface as well as demonstrating its durability. Topper and Baer (78) report durable Teflon films as thin as 0.0001 inch. Since Teflon has a low thermal conductivity, the promoter film should be as thin as possible The production of very thin Teflon films or methods of improving their thermal conductivity should be the object of future research. T h e thickness and thermal conductivity of the ultimate Teflon coating are two important parameters in the determination of the dropwise heat transfer 'coefficient. A value of thermal conductivity of 0.14 B.t.u./hr. sq. ft. OF./inch has been reported (8). The method of preparing the original film and the subsequent buffing probably had an effect on the thermal Conductivity. The actual value is unknown, and the above reported value was used in all calculations. T h e coated tube was selected from a batch of six tubes for its uniformity. Two hundred systematic measurements of the outside diameter of the uncoated tube were made with a micrometer. After coating and buffing, the same 200 locations were measured. T h e deviation in film thickness was no more than =t0.00005 inch.
of testing yielded data for dropwise condensation on a Tefloncoated tube. T h e system was designed to yield values of heat flux as a function of mean cooling water temperature and cooling water velocity. A heat balance was made on all runs to compare the cooling water measurements with the condensate measurements. In all cases the heat transfer rates agreed to within 15%, with a n average difference of 5%. With the aid of Wilson's graphical technique ( g ) , it was possible to obtain steam-side film coefficients as a function of the temperature difference between the saturated vapor and the tube surface: The intercept of a plot of l/Uo us. 1 / P S is the value of the combined steam and tube wall resistance. In the case of the coated tube, the intercept also includes the resistance of the Teflon coating. As previously noted, the steam state was held constant for all tests. Consequently, each curve was established for a different, but constant, value of (T,, - Tu): T h e scatter in the data represents an average deviation in the raw data-heat flux u s . water velocity of +2%, with a maximum deviation of 5.9%. I t is concluded that the range of water velocities (0.5 to 15 feet per second) is adequate to determine the intercept with sufficient accuracy for the purpose of this work. A separate curve is required for each resulting value of h when Wilson's graphical technique is used. If the condensing film coefficient is constant, the method is exact; however, h is a function of ( T , , - T s ) ,which in turn depends on the heat flux. T h e accuracy of the method, then, depends on the variation of heat flux, and more accurate results should be produced when the water velocity is large and the water-side resistance is comparable in size to the other resistances. This condition was fulfilled in the current experiments, and it is believed that the method yields more accurate results than can be obtained with an estimated value of the water-side coefficient.
Heat Transfer Measurements
The experiments were carried out in two phases studied over the same range of variables. During the first phase, tests were made for filmwiije condensation. The information obtained from these tests was compared with the existing theory and with the dropwise condensation data. T h e second phase
Filmwise Results
Filmwise condensation heat transfer mined from these data over a (Tsn 61.4' F. These results are presented 2 and 3. Figure 2 shows that these VOL. 3
NO. 4
coefficients were deter;
T,) range from 6.6' to graphically in Figures film coefficients are as
OCTOBER 1 9 6 4
367
PO,
*+A A A
A
.
11%,1 e
e
* A
4
m
b x
L
I2 ,
3
Figure 3. tion
4
1 6 7 8 9 1 0TS"
- Ts
eo
30
405060
801
Comparison of dropwise and filmwise condensaI
A 0 W
Results from (20) Dropwise results Filmwise results
Figure 4. studies
much as 25y0 lower than the Nusselt theory w h m AT is large and 10% lower for the smallest AT. However, they are well within the data envelope used by Peck and Reddie to develop their equation. Only the results for condensing steam from Peck and Reddie ( 7 3 ) are shown in Figure 2, while 186 points for condensing organic vapors have been omitted for clarity. T h e data used to develop Figure 2 were a t the most about 40Y0 lower than the Nusselt equation for small values of and [2~1;1] A!J
about 40% higher for large values.
0
2
0
3
3
4
0
5
0
6
0
Tsv - TS Comparison of dropwise results with other
41
In
general. the d a t a for horizontal tubes d o not agree as well with Nusselt's theory as d a t a obtained from vertical plates. T h e heat transfer coefficient for horizontal tubes is a strong function of tube diameter. This fact partially accounts for the d a t a envelope shown in Figure 2. The d a t a obtained in this study are almost parallel to the Peck and Reddie curve but are about 2070 lower. T h e results of this investigation are correlated well by the following equation, which is similar to Peck and Reddie's expression : 0
Dropwise Results
Dropwise condensation film coefficients were determined over a ( T s 0- T,) range from 4.8' to 46.5' F. These results are shown graphically in Figure 3, which shows that the d a t a obtained in this study are in good agreement with an extensive array of d a t a by Welch (20). The dropwise and filmwise curves converge as ( T , , - T,) gets large. This is caused by the rapid formation of drops which tend to blanket the condenser surface with liquid a t high heat fluxes. Figure 4 compares the data from this study with d a t a by Westwater (27), Shea (76), and Fatica ( 4 ) . The d a t a by Shea are somewhat higher, which can be explained by the fact that the steam vapor velocity was 25 feet per second across the condenser surface. Welch, Shea, and Fatica obtained their data from flat vertical condenser surfaces ranging in height from 3 inches to 2 feet. The fact that these d a t a are in good agreement with the data taken in this study for a '/*-inch O.D. horizontal tube is most interesting. O n e might conclude that 368
l&EC
PROCESS DESIGN A N D DEVELOPMENT
Figure 5. ance A.
E. C.
l
I
1
I
0
o
m
3
3
I 4
o
I 5
0
I 6
0
TSv-Tw Comparison of condenser tube perform-
Estimated performance for dropwise condensation on Teflon film 0.00005 inch thick Dropwise condensation on the Teflon film 0.00025 inch thick Filmwise condensation on b a r e tube
dropwise condensation is not significantly influenced by condenser surface geometry. Figure 4 shows that the results of these tests are in excellent agreement with the equation proposed by Fatica and Katz. Figure 5 is a comparison of the over-all thermal performance betbveen a Teflon-coated tube and a bare condenser tube. T h e Teflon-coated tube performs 507, better than the bare tube when ( T , , - T,) is small; ho\vever. for larger values of (T,? - T,), the improvement is only about 307,. The Teflon film was 0.00025 inch thick and provided 12.5 times as much thermal resistance as the 0.020-inch-thick aluminum
wall of the condenser tube and about three times more than the condensing film itself. This shows that the thickness of the Teflon film should be reduced to improve the over-all performance of the Teflon-coated condenser tube. These films can be made to l , ’ 5 as thick as the one used in this program; however, the production of such a thin film is most difficult. T h e estimated performance of a n aluminum tube with a Teflon coating 0.00005 inch thick is also shown in Figure 5. Comparison of the top and bottom curves shows that heat fluxes 1007‘ greater than with uncoated tubes can be obtained with Teflon-coated tubes. Conclusions
Filmwise steam condensation heat transfer in horizontal condenser tubes can be adequately predicted by Peck and Reddie’s (73) equation. Dropwise steam condensation heat transfer can be adequately predicted by Fatica and Katz’s (4) equation, although practical difficulties in its use are involved. Teflon is a. good promoter for dropwise condensation, and it can offer heat transfer rates increased u p to 1 0 0 ~ o when the film is made 0.00005 inch thick. Nomenclature h = heat transfer coefficient, B.t.u./hr. sq. ft. F. h x u = filmwise condensation heat transfer coefficient pre-
dicted from Nusselt’s theory, B.t.u./hr. sq. ft.
k
T,
= thermal conductivity, B.t.u./hr. ft. = temperature of condensing surface,
’F.
F. ’ F.
T,, = saturated vapor temperature, ’ F. Go = over-all heat transfer coefficient, B.t.u./hr. sq. ft. O F: V = average cooling water velocity, ft./sec. X 1.1
= =
Literature Cited (1) Baer, E., McKelvey, J. M., Delaware Science Symposium,
,4CS, University of Delaware, Newark, Del., February 1958. (2) Davies, J. T., Rideal, E. K., “Interfacial Phenomena,” p. 7, Academic Press, New York, 1961. (3) Drew, T . B., Nagle, W. M., Smith, W. G., Trans. A m . Znst. Chem. Engrs. 31, 605 (1935). (4) Fatica, N., Katz, D. L., Chem. Eng. Progr. 45, 66’. (1949). (5) Groher, H., Erk, S., Grigull, J., “Fundamentals of Heat Transfer,” p. 353, McGraw-Hill, New York, 1961. (6) Hampson, H., Engineering 172, 221 (1951). (7) Hampson, H., “International Developments in Heat Transfer, Part 11,’‘p. 310, Am. SOC.Mech. Engrs., New York, 1961. (8) Hodgman, C. D., ed., “Handbook of Chemistry and Physics,” 36th ed., Chemical Rubber Publishing Co., Cleveland, Ohio, 1954. (9) McAdams, W. H., “Heat Transmission,” 3rd ed., p. 345, McGraw-Hill, New York, 1960. (10) McCormick, J. L., Baer, E., J . Colloid Sci. 18, 208 (1963). (11) McCormick, J. L., Baer, E., 8th Midwestern Mechanics Conference, Case Institute of Technology, Cleveland, Ohio, April 1963. (12) Nusselt, W., 2. Ver. Deut. Ingr. 60, 541 (1916). (13) Peck, R. E., Reddie, W. A , , Ind. Eng. Chem. 43, 2926 (1951). (14) Pierce, 0. R., Intern. Sci. Technol. No. 11, 31 (1962). (15) Schmidt, E., Schurig, W., Sellschopp, W., Tech. Mech. u . Thermodynam. 1, 53 (1930). (16) Shea, F. L., Krause, N. W., Trans. A m . Znst. Chem. Engrs. 36, 463 (1940). (17) Sugawara, S., Michiyoski, N., Proc. 2nd Japan. Natl. Congr. Appl. Mech., Part 111, p. 289, 1952. (18) Topper, L., Baer, E. J., J . ColloidSci. IO, 225 (1955). (19) Watson, R. G., Brunt, J. J., Birt, D. C., “International Developments in Heat Transfer, Part 11,” Am. SOC. Mech. Engrs., p. 296, 1961. (20) Welch, J. F., Ph.D. dissertation, University of Illinois, Urbana, Ill., 1960. (21) Westwater, J. W., Welch, J. F., “International Developments in Heat Transfer, Part 11,” p. 302, Am. SOC.Mech. Engrs., 1961.
heat of vaporization, B.t.u./lb. viscosity, lb./ft. sec.
RECEIVED for review September 23, 1963 ACCEPTED December 10, 1963
ANALOG COMPUTER METHOD FOR DESIGNING A COOLER-CONDENSER WITH FOG FORMATION D.
R. COUGHANOWR AND E. 0. STENSHOLT,
School of Chemical Engineering, Purdue University, Lafayette, Ind. An analog computer method is given for designing a cooler-condenser for the separation of a condensable vapor from an inert gas accompanied b y fog formation. The design equations which describe the process are applied to an example (air-benzene) in which fog i s likely to form. The unique feature is the method b y which the heat balance is modified when fog is present and the computer implementation which decides when the heat balance should b e modified. A comparator monitors the difference between the gas temperature and the saturation temperature. Whenever the two temperatures become equal, a relay operated by the comparator changes the circuit to modify the heat balance. HE basic design equations for the condensation of mixed Tvapors were presented by Colburn and Drew (2). Colburn and Hougen (4)developed design equations for removal of condensable from an inert gas. O’Brien and Franks ( 6 ) have recently discussed the design of a cooler-condenser by means of a n analog computer for the H20-CO2 system. They mention that fog may be formed, but d o not solve this case; however, they refer to the work of Schuler and Abell ( 8 ) ,who account 1 Present Sorway.
address,
Institut
for Kjemiteknikk,
Trondheim,
for the formation of fog in a n experimental study of the condensation of Tic14 from N2. T h e purpose of the present work is to show what modifications are needed in the usual design equations to account for fog formation, a n d how the equations can be solved by analog computation. Design Equations
T h e following design equations are developed for a doublepipe condenser in which the gas flows through the center tube and cooling water flows cocurrently to the gas outside the tube. VOL. 3
NO. 4
OCTOBER 1964
369
