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Dropwise condensation of steam at atmospheric and above atmospheric pressures
Chemical Engineering
Science, 1967, Vol. 22, pp. 1305-1314. Pergamon Press Ltd., oxford.
Printed in Great Britain.
Dropwise condensation of steam at atmospheric and above atmospheric pressures J. T. O’BARA~, E. S. KILLIAN: and L. H. S. ROBLEE, JR Department
of Chemical Engineering, University of Massachusetts,
Amherst, Massachusetts
(Received 22 August 1966; accepted 7 March 1967) Abstrad-The results of the initial phases of a study concerned with the mechanism of the dropwise condensation of steam are presented. In the first phase of this work, equivalent heat transfer coetl% cients at atmospheric pressure for the dropwise condensation of steam on a vertical surface were determined experimentally. The coefficients ranged from 1140 to 37,000 B.t.u./hr-ft*-“F for heat fluxes of 29,900 up to 167,000 B.t.u./hr-ft* with surface temperature differences varying from 45 to 2”F, respectively. Vapor velocities varied from 1.75 to 752 ft/sec with the flow directed down the vertical condensing surface. Observations indicated that the vapor velocity across the condensing surface has a significant effect on the equivalent transfer corfficient with the coefficient exhibiting a maximum with increasing vapor velocity. It is believed that this maximum reflects the transition between dropwise and mixed condensation resulting from the greater vapor-liquid interfacial shear stress developed at the higher vapor velocities. Visual observations of the condensation phenomenon were also made at pressures ranging from atmospheric to 200 psig. These observations showed that, as the pressure increases, a transition from dropwise tomixedcondensationoccursbetween 25 to 50 psig. This transition is posited to be associated with the decreased surface tension of the condensed phase at the higher saturation temperatures. A theoretical analysis is presented which is consistent with the experimental observations.
RECENT technological advances, e.g. space power systems and sea water desalination, have brought about a renewed interest in the phenomenon of dropwise condensation. In these cases, as contrasted with more conventional systems, the resistance to heat transfer provided by the condensing steam is a significant part of the total resistance so that an increase in the steam-side coefficient can have a measurable influence on the overall performance of the system.
In addition to the heat flux, several variables such as vapor velocity, condensing surface characteristics, promoter and inert gas concentration affect dropwise condensation. Unfortunately, in most investigations, the influence of one or more of these variables has not been adequately accounted for with the result that there are little reproducible data available. Also, relatively few studies have been made concerning the mechanism of the process.
Various theories on the mechanism of dropwise condensation have been proposed. EMMONS [l] proposed a mechanism that assumes a bare area exists on the condensing surface between droplets. Vapor molecules impinging on this area rebound at the temperature of the surface and consequently, as they are at a lower temperature than the saturated vapor above the area, form a subcooled vapor layer over the condenser surface between the droplets. When this vapor layer comes in contact with the surface of a drop, the layer rapidly condenses and produces a local reduction in pressure which gives rise to eddy currents between the drops. Emmons theorised that these currents cause the higher heat transfer coefficients. A different theory has been proposed by JAKOB [2]. In this theory, the cooling surface is assumed to be covered by a very thin layer of water which continually and quickly grows in thickness until it fractures to form droplets. As the droplets coalesce and roll off the surface, a portion of dry surface is exposed and almost instantaneously covered by condensation of fresh
t Esso Research and Engineering Company, Florham Park, New Jersey. 2 American Cyanamid Company, Wayne, New Jersey.
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J. T. O’BARA,E. S. KILLIANand L. H. S. ROBLJX,JR steam such that the process can repeat itself. Jakob theorised that the high heat transfer coefficient was caused by the direct contact of the dry surface and the steam streaming to it. Jakob’s theory obtains support from an investigation by WELCHand WESTWATER [3,4]. This study involved photographing the phenomenon at speeds ranging from 250 to 3000 frames per second and magnifications of about 1 to 11 x on the negative. These pictures indicate that the drops visible to the eye grow mainly by numerous coalescenses which, upon forming, result in the vibration of the new drop that sweeps up the liquid film nearby. Apparently, condensation takes place preferentially on the swept regions and only slightly on the drops. The film which then forms on the swept regions builds up to a critical thickness--estimated at about 05 /l-before fracturing to form new drops. The creation of an essentially “bare” surface between drops provides the explanation of the high heat transfer coefficients obtained in the dropwise condensation process. In contrast with Westwater’s film fracture theory, UMUR and GRIFFITH [5] conclude from a recent investigation on dropwise condensation that a film no greater than a monolayer thick can exist in the area between drops. This finding is based on both theoretical considerations from a thermodynamic point-of-view and on an optical study. The optical study involved determining film thickness by noting the change in the elliptic&y of plane polarised light when reflected from the metallic condensing surface. These investigators also proposed a model for drop growth at atmospheric and at lower pressures which is consistent with experimentally observed values which have shown that growth rate is a function of vapor pressure. In addition to the experimental studies to elucidate the mechanism, a few theoretical approaches have been attempted. In 1949 FATICAand KATZ [6] and later, in 1956, SUGWARAand MICHIY~KI [7] developed quantitative expressions to predict dropwise heat transfer coefficients. The derived expressions are based on a number of assumptions and in both cases it is assumed that drop size distribution and percentage of area covered by condensate is uniform. While it is difficult to assess the importance of these assumptions, the principal
shortcoming of the final expressions lie in the fact that the dropwise transfer coefficient is expressed in terms of the overall heat transfer coefficient. Thus, while advances have been made, the mechanism of dropwise condensation is far from being clearly understood. There are a number of approaches to this complex problem. One involves extending Jakob’s theory to saturation pressures above atmospheric. At higher temperatures and pressures. the surface tension of the water condensate-vapor interface decreases appreciably. Also it is known that the number of condensate nuclei formed at a given temperature follows a Boltzmann law in which the condensate surface tension (surface free energy) appears in the exponential term. The functional dependence is such that a decrease in surface tension decreases the exponential term. Thus, at higher temperatures and pressures a decrease in surface tension results in an exponential decrease in the number of nucleation sites available for condensation so that less drops form on the surface. In addition, the decreased surface tension of the liquid-vapor interface would also cause the equilibrium interfacial force to be directed more parallel to the condensing surface. Consequently, the drops would tend to flatten out so that at some sufficiently high temperature and pressure the phenomenon of dropwise condensation could be maintained no longer and mixed, followed by filmwise, condensation would ensue. The ultimate goal of the present study is to test this theory both through heat transfer measurements and through the use of highspeed motion picture photography. This paper is a report of two phases of this study. One involved obtaining reproducible data and determining the effect of vapor velocity at atmospheric pressure on heat transfer coefficients for dropwise condensation, while the second dealt with preliminary observations of the condensation phenomenon at pressures up to 200 psig. THEORETICAL CONSIDERATIONS It is often observed experimentally that a liquid in contact with a solid surface will not wet the surface but exist as a drop with a definite angle of contact between the liquid and solid phases. This
1306
Dropwise condensation of steam at atmospheric and above atmospheric pressures
is depicted in Fig. 1. For this system, the change in surface free energy, AP, resulting from a small
Conditions prevailing at equilibrium for a saturated vapor, a liquid and a solid surface can be obtained from a consideration of the rate of condensation on a unit area of surface developed from the kinetic theory as (7)
p
and the evaporation rate from the surface which follows a Boltzmann law
1
1 %L SV FIG. 1. Surface tensions acting on a drop.
N- = B&exp(
change in the area of the drop, AA, is
AFS=AA(YSL-Y,,o)+AAy,,ocos(O-At?)
(I)
At equilibrium lim (AF”/AAj = 0 AA-0
so
(2)
- WsLo/RT,)
(8)
Equilibrium requires that the temperature of the system be uniform and that the two rates expressed in Eqs. (7) and (8) be equal at the liquid-vapor interface and at the solid surface. Consequently, recognisingf, is unity, a relation giving the fraction of the solid surface covered with absorbed molecules, fsLo, is obtained
that Eq. (1) becomes
YLyocos~=YsyO-YSL
(3)
The work of adhesion, WsLo, can be expressed in terms of the respective surface tensions as WW = Ysvo+ YLVO -
YSL
(4)
And similarly, the work of cohesion, WCis W,=&LP
(5)
Combining Eqs. (3), (4) and (5) an expression giving the ratio of the work of adhesion to the work of cohesion is obtained w,,,/ w, = +( 1 + cos e)
(6)
Equation (6) shows that for dropwise condensation (a nonspreading liquid) wherein 8, the contact angle, is greater than zero, the ratio of W,,,/ WCis less than unity so that the work of cohesion within the liquid is greater than the work of adhesion between the liquid and the solid.
For dropwise condensation, WsLo/WC, is less than unity and under these conditions, the ratio of the condensation coefficients aSLo/@,is also less than unity because the liquid-vapor force field is stronger than that of the solid surface [5]. The work of cohesion, WC, is roughly equal to the latent heat of vaporisation. Thus, as the saturation pressure in a particular system is increased, WC decreases. Unfortunately there is relatively little information on WsLo, the work of adhesion between available
solid and liquid surfaces. However, data indicates that the change in W,,
with temperature or pressure is negligible compared with the changes in WC. Consequently, as saturation pressures increase the ratio W,,,/ WC increases and tends toward unity. Thus, for this situation a consideration of Eqs. (6) and (9) shows that a greater fraction of the surface should be covered with liquid and that the drops should tend to spread out. Therefore, it would be anticipated, depending upon the solid surfaces involved, that at some sufficiently high saturation pressure dropwise condensation no longer could be maintained.
1307
J. T.
O’BARA, E. S. KILLUN and L. H. S. ROBLEE, JR
The effect of pressure and temperature on drop growth is also significant. In the case of net condensation, involving nonequilibrium conditions, an expression [S] for the net condensation per unit interfacial area, N, is given as
I I
OUTLET C:OOLING WA1 TER THERMOIPLES>
Since the saturation pressure increases faster than the saturation temperature, Eq. (10) indicates that as the saturation pressure is increased the net rate of condensation increases. Thus, in dropwise condensation one would expect to see drops growing more rapidly as saturation pressures are increased in addition to observing that the drops cover a larger fraction of the surface and tend to flatten out. Up to this point only forces involving surface tensions have been considered. Usually, for condensation in a confined space the condensate which forms enters as vapor. Depending upon the particular geometry of the system the vapor velocity may be quite high and exert a considerable shear stress at the liquid-vapor interface and thereby influence the heat transfer tYrn coefficient. That this is the case for film condensation has been amply demonstrated [9], For dropwise condensation it would be expected that as the shear stress, or alternatively the vapor velocity, increased from essentially zero values, the effect would be to increase the equivalent heat transfer coefficient, h,, in much the same way as it does for film condensation. However, at sufficiently high velocities, it would be expected that the shear stress would be great enough to disrupt drop formation leading first to mixed and finally film condensation with lower transfer coefficients as compared with those of dropwise condensation. EXPERIMENTAL APPARATUSANDPROCEDURE The arrangement of the experimental apparatus is shown in Fig. 2. Gas-free saturated steam produced from distilled water was generated in the boiler and supplied to the condensing chamber through lagged piping. Preliminary studies with an iron boiler showed that boiler contamination
COOLING
CHAMBER
CONDENSING
CHAMBER
Iz!E~N~ Jb””
I WA1 ‘ER
THERMO-
1 COUPLE
I
WATER FROM LABORATORY LINE
FIG. 2. Experimental arrangement.
interfered with the maintenance of dropwise condensation. Consequently, in these studies all internal surfaces including piping were constructed of stainless steel. Cupric oleate was used as a promoter in all runs and was added to the boiler water to give a concentration of about 72 ppm. Condensate from the test chamber was returned to the boiler while uncondensed steam was condensed in the auxiliary condenser and then returned to the boiler. The condensing chamber was formed by bolting together two stainless steel plates and a copper plate. All the plates were 6 in. dia. (see Fig. 3). The front steel plate was fitted with a centrally located window through which condensation could be observed. The window was made of electrically conducting glass which when heated eliminated fogging. A centrally located tapered hole was cut from the 1 in. thick condensing chamber plate which was held between the front steel plate and the copper plate. The assembly was vertically oriented. The tapered hole on the viewing port side was 23 in. dia. and on the condensing side, i.e. the side against the copper plate, it was 2 in. dia. The surface of this tapered hole formed the radial wall of the condensing chamber. Thus, the shape of the condensing chamber was the frustum
1308
Dropwisecondensationof steam at atmosphericand above atmosphericpressures of a right cone. Steam inlet and outlet, each & in. i.d., were located at the top and bottom of the The condensing chamber plate, respectively. entire assembly was bolted together and to a 2 in. i.d. cooling chamber secured to the backside of the copper plate. Water, circulating through this chamber, absorbed the heat of condensation flowing through the copper plate from the condensing surface. The water entered the cooling chamber along the central axis and impinged on the copper surface which was parallel with and of the same area as the condensing surface. The water left the chamber through two outlets, one at the top and one at the bottom. The piping was arranged to insure that the chamber was always completely filled with water.
couples were wired in parallel. Also, at the cross section nearest the condensing surface, two thermocouples were placed in holes drilled radially at angles of 45” and 225” measured clockwise from the top thermocouple. One of these couples measured the temperature at the plate axis and the other at a point one inch out from the axis. Prior to fitting in the copper plate each thermocouple was passed through a short length of copper tube, the junction fused to the end of the tube and the tube then turned down to 0*0930 in. o.d. to provide a press fit in the drilled holes. Based on the thermocouple readings, the temperature gradient in the copper plate was calculated and from this the thermal flux through the system. Also, by extrapolation of these temperatures, the effective condensing and cooling surface temperatures were determined. These ELECTRICALLY CONDENSING values along with the steam temperature as trv:NAoii SURFACE measured by a thermocouple in the steam vapor STEAM INLET \ / space and thermocouples in the cooling chamber COOLING WATER determined the AT’s at each end of the copper \ OUTLET plate, The equivalent heat transfer coefficient, h,, on the condensing side was evaluated using AT, and the flux through the system. The vapor velocity was determined by an energy balance around the boiler, transfer lines and condensing chambers. Heat flux determined by this balance and a balance on the cooling chamber was in reasonable agreement with that calculated from conduction measurements in the copper plate. As described previously, thermocouples were placed at various radial depths in the copper plate at the cross section nearest the condensing surface. Temperatures indicated by these thermocouples during runs established that there was essentially no radial temperature difference in the center portion of the plate and hence, little radial heat transfer. Because of this and because alI of the FIO. 3. Half section of condensing chamber. thermocouple leads were brought out of the plate radially, the temperature measurements in the The copper plate, e in. thick, was provided plate are believed to be quite accurate. The absence with a total of 14 thermocouples made from No. 24 of any appreciable radial gradient implies that gauge copper-constantan wire. At each of three heat flow through the plate should be axial and cross sections, four thermocouples spaced 90” thus, linear. Experimentally, a slight departure apart were placed in holes drilled radially to within from linearity was observed which was the result one-half in. of the center of the plate. To obtain of the nonuniform temperature distribution over an average reading at a cross section, the thermothe condensing surface. This slight variation was
I
/
1309
J. T.
O’BARA. E. S. KILLIAN and
caused by the steam entering at the top of the plate at a somewhat higher temperature than that leaving at the bottom of the plate. In the initial phases of this investigation data were obtained with a test cell essentially the same as that described above with the exception of the dimensions of the copper plate. In these earlier studies [lo], a copper slug 14 in. dia. and 14 in. long was used. While in this case the entire face was used for condensation so that the area available for condensation was the same in either cell, the diameter-length ratio was much less than that of the large disc. Consequently, radial heat transfer was important. While this problem was solved by adequately insulating the slug, the experience with this assembly prompted the design of the second. It is important to note, however, that identical results, within the limits of experimental error, were obtained with both setups and thus, provide oonsiderable assurance that the results reported are accurate. Prior to a set of runs the condensing surface was polished by hand with jeweler’s rouge until it appeared that all copper oxide had been removed. After polishing, the surface was rinsed first with acetone and then several times with distilled water until a continuous film of water adhered to it. In a typical run the cooling water was set at a desired rate and the Variac controlling the input to the boiler adjusted. After temperatures stabilised, the inert gases in the system were removed using a water aspirator connected to the open end of the auxiliary condenser. Throughout the investigation the inert gas concentration was checked using a Classen-type apparatus proposed by FURMANand HAMPSON[Ill. These measurements showed the noncondensible concentration to always be less than O-0036 wt. “lo. Following aspiration, the cooling water flow rate to the auxiliary condenser was adjusted such that condensation could always be observed in the condenser. This assured that there was no backflow of air into the system. After equilibrium had been attained, temperature readings were made throughout the system. These measurements and flow rates provided data for calculating the thermal flux and the equivalent heat transfer film coefficient. Additional runs were
L.
H. S. ROBLEE, JR
made by setting up new flow rates aud energy inputs.
RENJLTAND Heat transferjIm
DISCUSSION
coeficients-atmospheric
pressure
(i) Experimental results. Experimental results are presented in Figs. 4 through 8. The individual points on the graphs are averages of several runs. While Figs. 4 and 5 could be combined into one, two graphs have been used for greater clarity. Heat fluxes ranged from 167,000 down to 29,900 B.t.u./hr-ft2 for AT, ranging from 2 to 44*7”F. The equivalent film coefficients ranged from 1140 to 37,200 B.t.u./hr-ft2-“F and vapor velocities from l-75 to 7.52 ft/sec. Because of condensation, the vapor velocity varies continuously over the condensing surface from a maximum value at the steam inlet to a minimum at the outlet. Consequently, there is an arbitrariness associated with the definition of the vapor velocity. In this investigation the vapor velocity reported is the arithmetic mean of the inlet and outlet values calculated from energy balances. The crosssectional area used in determining these velocities was the same for both inlet and outlet and was taken as the area perpendicular to the condensing surface through which the steam passed just before contacting the condensing surface. Detailed experimental results can be obtained from [lo] and [12].
1310
VAPOR VELOCITY. v 1.75
FTlSEC
b 2.42 0 314 0 402
0 0
5
IO
IS
20
ATa,
lF
25
30
35
40
45
Fro. 4. Variation of steam-sideheat transfer coefficientswith AT. for dropwise condensation.
Dropwise condensation of steam at armospneric and above atmospheric pressures
at the low velocity of 1.75 ft/sec. This effect is clearly shown in Fig. 6 where, with AT, as a parameter, the film coefficient is plotted against vapor velocity. The figure, obtained from Figs. 3 and 4, shows that for each AT, there is a maximum vapor velocity at which dropwise condensation exists and that this maximum increases slightly as AT, decreases. For the AT, of this investigation, the maximum vapor velocity obtainable in dropwise condensation lies in the range from 5 to about 6.5 ftlsec.
35 VAPOR VELOCITY,
FTISEC
25
40
I&. 30 : “k
25
i
20
3 2
I5
n 0
IO
=
5 0 0
5
IO
I5 AT,.
20
30
35
45
lF
FIG. 5. Variation of steam-side heat transfer coefficient with AT, for dropwise condensation.
35 ‘-
(ii) Error analysis. The most probable error associated with the effective heat transfer coefficient was determined by a propagation of error analysis. In this analysis the estimated average error in temperature measurements was taken as +O*YF. The thermal conductivity of copper was assumed constant at 218 B.t.u./hr-ft2 (“F/ft) and the error in thermocouple position was considered zero. An analysis of a typical run for an h, of 1470 B.t.u./hr-ft2-“F, a AT, of 29.22”F and a heat flux of 43,000 B.t.u./hr-ft2 showed that at the 99.7 per cent confidence level the most probable error in h, was less than or equal to 14.1 per cent. The analysis further revealed that the probable error is most strongly influenced by AT,, becoming quite small for high values but large for low values even when thermocouple temperatures are known as accurately as within 0.5 per cent. (iii) Discussion. Figures 4 and 5 show that the equivalent filmcoefficient, h,, plotted on theordinate, has its maximum value at low AT, and decreases to an essentially constant value (depending on vapor velocity) above a AT, of about 35°F. These figures show the pronounced effect vapor velocity has on h,. For example, at a AT, of 9°F h, is about 4800 B.t.u./hr-ft2-“F at a vapor velocity of 1.75 ft/sec. At this AT,, the coefficient steadily increases by approximately three and one-half times to 16,800 B.t.u./hr-ft2-“F as the vapor velocity increases to 5.54 ft/sec. Interestingly, as the vapor velocity is further increased an abrupt drop in h, is observed. In fact, at a velocity of 7.25 ft/sec the coefficient is essentially the same as
0
I
2 VAPOR
FIG.
3 VELOCITY,
4
5
6
7
S
FTlSEC
6. Influence of vapor velocity of steam-side heat transfercoefficients.
The reason a maximum vapor velocity exists in dropwise condensation appears to be an effect of the shear stress between vapor and drops. As the vapor velocity increases, the shear stress also increases and tends to disrupt the drops, inducing coalescence and, hence, the formation of a liquid film. The shift in the maximum value is explained by the fact that at low AT, drops are relatively small and drop growth rate is low so that more shear stress is necessary to bring about this transition. In contrast, at higher AT, the drops are larger and growth rate higher so that less shear stress, i.e. lower vapor velocity, is required to produce the same effect. In Figs. 7 and 8, the results of this work are compared with those of FATEA and KATZ [a], and WELCH [4]. Although the results of Fatica and Katz are for steam condensing on nickel, chromium, as well as on copper, using stearlc and oleic acid as promoters, there was very good agreement between their work and the present study.
1311
J. T. O’BARA, E. S. KILLIAN and L. H. S. ROBLEE,JR
Their vapor velocity, while not stated, was assumed negligible. In Fig. 8, this work is compared with Westwater’s. In order to make a valid comparison, the vapor velocities should be roughly the same. The apparent discrepancy here in comparing results at a vapor velocity of 2.42 and 10.2 ft/sec lies in the definition of vapor velocity, specifically the areas on which the velocity calculations are based. As mentioned previously, the area used to determine vapor velocities in this work was taken as the area perpendicular to the condensing surface through which the steam passed prior to contacting the condensing surface. Because of the geometry of the condensing chamber this area is about four times that of the steam inlet (or outlet) area. Thus, if vapor velocities in the present work were based simply on inlet and outlet steam line cross sections, as were Westwater’s, a velocity of 2.42 ft/sec would correspond to a velocity of
35 .IL
JO--
NL
25--
‘s ,E
15
0
IO
i
5
VAPOR VELOCITY, v 1.75
FA,ICA AND KATZ
:‘_i_: 0 0
5
IO
15
20
25
30
35
FTISEC
!
!
40
45
ATS , *F
Fro. 7. Comparison of experimental results with those of Fatica and Katz.
35 u :
30
Nk
21
.$
20
VAPOR VELOCITY, FT/SEC A 2.42 (THIS WORK) 0 10.2 (WESTWATER)
2 2
15
>_
10
‘Y
s 0 0
5
D
I5
20
25
30
35
40
45
approximately 10 ft/sec. With this in mind, the agreement between the two studies is very close over a broad range of AT, and only departs significantly at low values of AT,, a range in which, in this type of study, experimental error is large.
High pressure study-visual observations
(i) Experimental results. In addition to determining heat transfer coefficients at atmospheric pressure, preliminary studies were made which involve visual observations of the dropwise condensation phenomenon at high pressure. The experimental procedure at high pressure was essentially that at atmospheric pressure with the exception that the glass auxiliary condenser was replaced by a closed metal condenser. Also, the system was purged of noncondensable gases by directly venting steam to the atmosphere. The observations which follow were made under continuous operation as the steam pressure was increased from 0 to 200 psig. 25 psig Steam Pressure (267”F)t The conditions were much the same as at atmospheric pressure. The drops looked essentially the same, but they appeared to reside longer on the surface. 50 psig Steam Pressure (301°F) A noticeable change occurred by the time this pressure was reached. Drops cycled very slowly and changed from the rain drop shape at atmospheric pressure to a more flat and almost circular shape. They seemed to merge much more slowly and grow quite large before merging took place.
75 psig Steam Pressure (320°F) There was not much change from the conditions at 50 psig pressure. The surface appeared to be covered with a layer of condensate and drops seemed to adhere to this layer rather than the metal surface.
ATs,*F
FIO. 8. Comparison of experimental those of Westwater.
results with
t The values in parenthesis are the saturation tures corresponding to the pressures cited.
1312
tempera-
Dropwise condensation
of steam at atmospheric
100 psig Steam Pressure (338°F) No large change was observed. However, drop density seemed smaller and individual drops appeared to be larger than those at lower pressures. 125 psig Steam Pressure (353°F) The surface appeared the same as it did at 100 psig. 150 psig Steam Pressure (367°F) At this pressure it was difficult to define the beginning and end of a drop. All drops appeared very flat on the surface.
and above atmospheric
vapor velocity is increased from relatively low values, the transfer coefficient increases significantly. Above a certain critical velocity, however, the coefficient rapidly decreases. Visual observations of the condensation phenomenon at pressures above atmospheric indicate that in the pressure range between 25 and 50 psig the phenomenon undergoes a transition from dropwise to mixed followed by filmwise condensation. Acknowledgment-The authors gratefully acknowledge the fmancial support of this investigation by the Office of Naval Research Contract Nonr #3357 (02).
175 psig Steam Pressure (377°F) The condensation appeared to be more filmwise than dropwise.
NOTATION %
fc
200 psig Steam Pressure (388°F) Filmwise condensation appeared to be the predominant mode of condensation. (ii) Discussion. Although these studies are only preliminary, they reveal that dropwise condensation is affected by pressure and that a transition from dropwise to mixed condensation appears to occur at pressures in the neighborhood of 50 psig. While it could be argued that the transition reflects a chemical change in the promoter at the higher temperatures, this does not appear to be the case as no hysteretic effects were observed as the pressures were varied up or down. Based on the evidence available it is believed that the transition observed is a consequence of the decreased surface tension of the condensate at the higher pressures and saturation temperatures. Thus, as the cohesive forces are reduced the forces of adhesion become relatively more important. This, along with the greater rate of condensation and actual pressure on the drops at higher pressures, promotes the formation of filmwise as contrasted with dropwise condensation.
pressures
fSLO
area increment change in surface free energy fraction of a liquid surface covered with condensate fraction of a surface covered with absorbed molecules gravitational constant equivalent heat transfer coefficient on the steam condensing surface net condensation rate per unit area condensation rate per unit area evaporation rate per unit area equilibrium pressure corresponding to temperature of liquid-vapor interface vapor pressure universal gas constant temperature surface temperature vapor temperature difference between steam temperature and condensing surface temperature work of cohesion work of adhesion condensation coefficient-fraction of molecules striking a surface that condense fraction of molecules striking a liquid surface that condense fraction of molecules striking a solid surface that condense proportionality constant surface tension of liquid in equilibrium with its vapor interfacial tension between a solid and a liquid surface tension of solid-gas interface in equilibrium with saturated vapor contact angle of a drop
h”. NN
N+_ pi
PO
R T T, Tv AT,
WC WSLO o!
EC asL B YLVO
CONCLUSIONS
YSL
The experimental findings indicate that vapor velocity has an important effect on the equivalent heat transfer coefficient for condensing steam. As 1313
YSVO 0
J. T. O’BARA, E. S.
ILLIAN
and L. H. S. ROBLEE,JR
REFERJ~NCES
[l] EMMONSH., The mechanism of drop condensation. Trans. Am. Inst. Chem. Engrs 1939 35 109-125. Mech. Engng 1936 58 729-739. [2] JAKOBM., Heat transfer in evaporation and condensation-II. [3] WELCH J. F. and WESTWATERJ. W., Microscopic study of dropwise condensation. Proceedings of the International Heat Transfer Conference 1961 11 302-309. [4] WELCHJ. F., Ph.D. Thesis, University of Illinois 1960. [5] UMUR A. and GRIFFITHP., Mechanism of dropwise condensation. J. Heat Transfer 1965 87 Series C No. 2 275-282. Chem. Engng Prog. 1949 45 661-674. [a FATICAN. and KATZ D. L., Dropwise condensation. [I SUGWARA S. and MICHNOSKII., Dropwise condensation. Memoris of Faculty of Engineering, Kyoto University 1956 18 No. 2 84-111. [8] SILVERR. S. and SIMPSONH. C., The condensation of superheated steam. Proceedings of a Conference held at the National Engineering Laboratory, Glasgow, pp. 39-69, 1961. [9] ROHSENOWW. M. and CHIO H. Y., Heat, Mass and Momentum Transfer, Prentice-Hall 1963. [lo] Q’BARA J., M.Sc. Thesis, University of Massachusetts 1964. [ll] FIJRMANT. and HAMPSONH., Experimental investigation into the effect of cross flow with condensation of steam and steam-gas mixtures on a vertical tube. Proc. Inst. Mech. Engrs 1959 173 147-169. [12] KILLIANE. S., M.Sc. Thesis, University of Massachusetts 1966.
R&n&-Les resultats des phases initiales dune etude concernant le mecanisme de la condensation de la vapeur goutte a goutte sont present& dans la premiere partie de cette etude. Les coefficients equivalents du transfert de la chaleur a la pression atmospherique, pour la condensation de la vapeur goutte a goutte sur une surface verticale, ont &C determines de facon experimentale. I_es coefficients varient respectivement de 1.140 a 37.200 B.t.u./heure pied car& “F. Les velocites de la vapeur varient de 1,75 a 7,52 pied/set., le courant &ant dirige vers le bas de la surface verticale de condensation. Les observations indiquent que la v&cite de la vapeur a travers la surface de condensation a un effet significatif sur le coefficient de transfert equivalent, le coefficient montrant un maximum pour une v&cite croissante de la vapeur. On pense que ce maximum reflete la transition entre la condensation goutte 51goutte et mixte, resultant de la plus grande tension du dechirement exe& a l’interface vapeur[ liquide qui se developpe pour des valeurs plus Blevees de la v&cite de la vapeur. Des observations visuelles du phenomene de condensation ont aussi ette faites 51des pressions s’&chelonnant de la pression atmospherique a 200 Ib/pouce*. Ces observations ont montre que, comme la pression augmente, il se produit une transition de la condensation goutte a goutte la condensation mixte pour des pressions entre 25 et 50 lb/pouce*. Cette transition est enonc& comme &ant associee il la tension d&roissante a la surface de la phase conden& B des temperatures de saturation plus &levees. Une analyse thbrique est presented qui est en accord avec les observations exp&imentales.
Zusannnenfassnng-Die in den Anfangsstadien einer Untersuchung des Mechanismus der tropfenweisen Kondensation von Dampf erzielten Resultate werden im ersten Teil dieses Referats behandelt. Gleichwertige Wtimeiibertragungs-Koeflizienten bei atmosphkischem Druck werden experimentell durch die tropfenweise Kondensation von Dampf auf einer senkrechten FlaChe bestimmt. Die Koeffizienten variierten zwischen 1.140 und 37.200 B.t.u./hr Fuss* “F. Die Dampfgeschwindigkeiten variierten zwischen 1,75 und 7,52 Fuss/set, wobei die Stromung an der senkrechten Kondensationsfliiche entlang abw%rts gerichtet war. Die Beobachtungen deuten darauf hin, dass die Dampfgeschwindigkeit entlang der Kondensationsfltihe eine bedeutende Wirkung auf den iiquivalenten Ubertragungs-Koeffizienten austibt, wobei der Koethzient bei zunehmender Dampfgeschwindigkeit einen maximalen Wert erreicht. Man glaubt, dass dieser maximale Wert den Ubergang zwischen der tropfenweisen und der gemischten Kondensation widerspiegelt, bedingt durch die griissere Querspannung an der GrenzflLhe zwischen Dampf und Fltlssigkeit, wie sie bei hiiheren Dampfgeschwindigkeiten entwickelt wird. Visuelle Beobachtungen der Kondensationserscheinung wurden such bei Drticken vom atmospharischem Druck bis zu 200 lb/Zoll* lfberdruck durchgefiihrt. Diese Beobachtungen erweisen, dass mit zunehmenden Druck ein Ubergang von tropfenweiser zu gemischter Kondensation zwischen 25 und 50 lb/Zoll* Uberdruck eintritt. Es wird angenommen, dass dieser Ubergang mit der abnehmenden ObertXchenspannung der kondensierten Phase bei hiiherer Stittigungstemperatur im Zusammenhang steht. Es wird eine theoretische Analyse geboten, die den Versuchsergebnissen gerecht wird.
1314
Science, 1967, Vol. 22, pp. 1305-1314. Pergamon Press Ltd., oxford.
Printed in Great Britain.
Dropwise condensation of steam at atmospheric and above atmospheric pressures J. T. O’BARA~, E. S. KILLIAN: and L. H. S. ROBLEE, JR Department
of Chemical Engineering, University of Massachusetts,
Amherst, Massachusetts
(Received 22 August 1966; accepted 7 March 1967) Abstrad-The results of the initial phases of a study concerned with the mechanism of the dropwise condensation of steam are presented. In the first phase of this work, equivalent heat transfer coetl% cients at atmospheric pressure for the dropwise condensation of steam on a vertical surface were determined experimentally. The coefficients ranged from 1140 to 37,000 B.t.u./hr-ft*-“F for heat fluxes of 29,900 up to 167,000 B.t.u./hr-ft* with surface temperature differences varying from 45 to 2”F, respectively. Vapor velocities varied from 1.75 to 752 ft/sec with the flow directed down the vertical condensing surface. Observations indicated that the vapor velocity across the condensing surface has a significant effect on the equivalent transfer corfficient with the coefficient exhibiting a maximum with increasing vapor velocity. It is believed that this maximum reflects the transition between dropwise and mixed condensation resulting from the greater vapor-liquid interfacial shear stress developed at the higher vapor velocities. Visual observations of the condensation phenomenon were also made at pressures ranging from atmospheric to 200 psig. These observations showed that, as the pressure increases, a transition from dropwise tomixedcondensationoccursbetween 25 to 50 psig. This transition is posited to be associated with the decreased surface tension of the condensed phase at the higher saturation temperatures. A theoretical analysis is presented which is consistent with the experimental observations.
RECENT technological advances, e.g. space power systems and sea water desalination, have brought about a renewed interest in the phenomenon of dropwise condensation. In these cases, as contrasted with more conventional systems, the resistance to heat transfer provided by the condensing steam is a significant part of the total resistance so that an increase in the steam-side coefficient can have a measurable influence on the overall performance of the system.
In addition to the heat flux, several variables such as vapor velocity, condensing surface characteristics, promoter and inert gas concentration affect dropwise condensation. Unfortunately, in most investigations, the influence of one or more of these variables has not been adequately accounted for with the result that there are little reproducible data available. Also, relatively few studies have been made concerning the mechanism of the process.
Various theories on the mechanism of dropwise condensation have been proposed. EMMONS [l] proposed a mechanism that assumes a bare area exists on the condensing surface between droplets. Vapor molecules impinging on this area rebound at the temperature of the surface and consequently, as they are at a lower temperature than the saturated vapor above the area, form a subcooled vapor layer over the condenser surface between the droplets. When this vapor layer comes in contact with the surface of a drop, the layer rapidly condenses and produces a local reduction in pressure which gives rise to eddy currents between the drops. Emmons theorised that these currents cause the higher heat transfer coefficients. A different theory has been proposed by JAKOB [2]. In this theory, the cooling surface is assumed to be covered by a very thin layer of water which continually and quickly grows in thickness until it fractures to form droplets. As the droplets coalesce and roll off the surface, a portion of dry surface is exposed and almost instantaneously covered by condensation of fresh
t Esso Research and Engineering Company, Florham Park, New Jersey. 2 American Cyanamid Company, Wayne, New Jersey.
1305
J. T. O’BARA,E. S. KILLIANand L. H. S. ROBLJX,JR steam such that the process can repeat itself. Jakob theorised that the high heat transfer coefficient was caused by the direct contact of the dry surface and the steam streaming to it. Jakob’s theory obtains support from an investigation by WELCHand WESTWATER [3,4]. This study involved photographing the phenomenon at speeds ranging from 250 to 3000 frames per second and magnifications of about 1 to 11 x on the negative. These pictures indicate that the drops visible to the eye grow mainly by numerous coalescenses which, upon forming, result in the vibration of the new drop that sweeps up the liquid film nearby. Apparently, condensation takes place preferentially on the swept regions and only slightly on the drops. The film which then forms on the swept regions builds up to a critical thickness--estimated at about 05 /l-before fracturing to form new drops. The creation of an essentially “bare” surface between drops provides the explanation of the high heat transfer coefficients obtained in the dropwise condensation process. In contrast with Westwater’s film fracture theory, UMUR and GRIFFITH [5] conclude from a recent investigation on dropwise condensation that a film no greater than a monolayer thick can exist in the area between drops. This finding is based on both theoretical considerations from a thermodynamic point-of-view and on an optical study. The optical study involved determining film thickness by noting the change in the elliptic&y of plane polarised light when reflected from the metallic condensing surface. These investigators also proposed a model for drop growth at atmospheric and at lower pressures which is consistent with experimentally observed values which have shown that growth rate is a function of vapor pressure. In addition to the experimental studies to elucidate the mechanism, a few theoretical approaches have been attempted. In 1949 FATICAand KATZ [6] and later, in 1956, SUGWARAand MICHIY~KI [7] developed quantitative expressions to predict dropwise heat transfer coefficients. The derived expressions are based on a number of assumptions and in both cases it is assumed that drop size distribution and percentage of area covered by condensate is uniform. While it is difficult to assess the importance of these assumptions, the principal
shortcoming of the final expressions lie in the fact that the dropwise transfer coefficient is expressed in terms of the overall heat transfer coefficient. Thus, while advances have been made, the mechanism of dropwise condensation is far from being clearly understood. There are a number of approaches to this complex problem. One involves extending Jakob’s theory to saturation pressures above atmospheric. At higher temperatures and pressures. the surface tension of the water condensate-vapor interface decreases appreciably. Also it is known that the number of condensate nuclei formed at a given temperature follows a Boltzmann law in which the condensate surface tension (surface free energy) appears in the exponential term. The functional dependence is such that a decrease in surface tension decreases the exponential term. Thus, at higher temperatures and pressures a decrease in surface tension results in an exponential decrease in the number of nucleation sites available for condensation so that less drops form on the surface. In addition, the decreased surface tension of the liquid-vapor interface would also cause the equilibrium interfacial force to be directed more parallel to the condensing surface. Consequently, the drops would tend to flatten out so that at some sufficiently high temperature and pressure the phenomenon of dropwise condensation could be maintained no longer and mixed, followed by filmwise, condensation would ensue. The ultimate goal of the present study is to test this theory both through heat transfer measurements and through the use of highspeed motion picture photography. This paper is a report of two phases of this study. One involved obtaining reproducible data and determining the effect of vapor velocity at atmospheric pressure on heat transfer coefficients for dropwise condensation, while the second dealt with preliminary observations of the condensation phenomenon at pressures up to 200 psig. THEORETICAL CONSIDERATIONS It is often observed experimentally that a liquid in contact with a solid surface will not wet the surface but exist as a drop with a definite angle of contact between the liquid and solid phases. This
1306
Dropwise condensation of steam at atmospheric and above atmospheric pressures
is depicted in Fig. 1. For this system, the change in surface free energy, AP, resulting from a small
Conditions prevailing at equilibrium for a saturated vapor, a liquid and a solid surface can be obtained from a consideration of the rate of condensation on a unit area of surface developed from the kinetic theory as (7)
p
and the evaporation rate from the surface which follows a Boltzmann law
1
1 %L SV FIG. 1. Surface tensions acting on a drop.
N- = B&exp(
change in the area of the drop, AA, is
AFS=AA(YSL-Y,,o)+AAy,,ocos(O-At?)
(I)
At equilibrium lim (AF”/AAj = 0 AA-0
so
(2)
- WsLo/RT,)
(8)
Equilibrium requires that the temperature of the system be uniform and that the two rates expressed in Eqs. (7) and (8) be equal at the liquid-vapor interface and at the solid surface. Consequently, recognisingf, is unity, a relation giving the fraction of the solid surface covered with absorbed molecules, fsLo, is obtained
that Eq. (1) becomes
YLyocos~=YsyO-YSL
(3)
The work of adhesion, WsLo, can be expressed in terms of the respective surface tensions as WW = Ysvo+ YLVO -
YSL
(4)
And similarly, the work of cohesion, WCis W,=&LP
(5)
Combining Eqs. (3), (4) and (5) an expression giving the ratio of the work of adhesion to the work of cohesion is obtained w,,,/ w, = +( 1 + cos e)
(6)
Equation (6) shows that for dropwise condensation (a nonspreading liquid) wherein 8, the contact angle, is greater than zero, the ratio of W,,,/ WCis less than unity so that the work of cohesion within the liquid is greater than the work of adhesion between the liquid and the solid.
For dropwise condensation, WsLo/WC, is less than unity and under these conditions, the ratio of the condensation coefficients aSLo/@,is also less than unity because the liquid-vapor force field is stronger than that of the solid surface [5]. The work of cohesion, WC, is roughly equal to the latent heat of vaporisation. Thus, as the saturation pressure in a particular system is increased, WC decreases. Unfortunately there is relatively little information on WsLo, the work of adhesion between available
solid and liquid surfaces. However, data indicates that the change in W,,
with temperature or pressure is negligible compared with the changes in WC. Consequently, as saturation pressures increase the ratio W,,,/ WC increases and tends toward unity. Thus, for this situation a consideration of Eqs. (6) and (9) shows that a greater fraction of the surface should be covered with liquid and that the drops should tend to spread out. Therefore, it would be anticipated, depending upon the solid surfaces involved, that at some sufficiently high saturation pressure dropwise condensation no longer could be maintained.
1307
J. T.
O’BARA, E. S. KILLUN and L. H. S. ROBLEE, JR
The effect of pressure and temperature on drop growth is also significant. In the case of net condensation, involving nonequilibrium conditions, an expression [S] for the net condensation per unit interfacial area, N, is given as
I I
OUTLET C:OOLING WA1 TER THERMOIPLES>
Since the saturation pressure increases faster than the saturation temperature, Eq. (10) indicates that as the saturation pressure is increased the net rate of condensation increases. Thus, in dropwise condensation one would expect to see drops growing more rapidly as saturation pressures are increased in addition to observing that the drops cover a larger fraction of the surface and tend to flatten out. Up to this point only forces involving surface tensions have been considered. Usually, for condensation in a confined space the condensate which forms enters as vapor. Depending upon the particular geometry of the system the vapor velocity may be quite high and exert a considerable shear stress at the liquid-vapor interface and thereby influence the heat transfer tYrn coefficient. That this is the case for film condensation has been amply demonstrated [9], For dropwise condensation it would be expected that as the shear stress, or alternatively the vapor velocity, increased from essentially zero values, the effect would be to increase the equivalent heat transfer coefficient, h,, in much the same way as it does for film condensation. However, at sufficiently high velocities, it would be expected that the shear stress would be great enough to disrupt drop formation leading first to mixed and finally film condensation with lower transfer coefficients as compared with those of dropwise condensation. EXPERIMENTAL APPARATUSANDPROCEDURE The arrangement of the experimental apparatus is shown in Fig. 2. Gas-free saturated steam produced from distilled water was generated in the boiler and supplied to the condensing chamber through lagged piping. Preliminary studies with an iron boiler showed that boiler contamination
COOLING
CHAMBER
CONDENSING
CHAMBER
Iz!E~N~ Jb””
I WA1 ‘ER
THERMO-
1 COUPLE
I
WATER FROM LABORATORY LINE
FIG. 2. Experimental arrangement.
interfered with the maintenance of dropwise condensation. Consequently, in these studies all internal surfaces including piping were constructed of stainless steel. Cupric oleate was used as a promoter in all runs and was added to the boiler water to give a concentration of about 72 ppm. Condensate from the test chamber was returned to the boiler while uncondensed steam was condensed in the auxiliary condenser and then returned to the boiler. The condensing chamber was formed by bolting together two stainless steel plates and a copper plate. All the plates were 6 in. dia. (see Fig. 3). The front steel plate was fitted with a centrally located window through which condensation could be observed. The window was made of electrically conducting glass which when heated eliminated fogging. A centrally located tapered hole was cut from the 1 in. thick condensing chamber plate which was held between the front steel plate and the copper plate. The assembly was vertically oriented. The tapered hole on the viewing port side was 23 in. dia. and on the condensing side, i.e. the side against the copper plate, it was 2 in. dia. The surface of this tapered hole formed the radial wall of the condensing chamber. Thus, the shape of the condensing chamber was the frustum
1308
Dropwisecondensationof steam at atmosphericand above atmosphericpressures of a right cone. Steam inlet and outlet, each & in. i.d., were located at the top and bottom of the The condensing chamber plate, respectively. entire assembly was bolted together and to a 2 in. i.d. cooling chamber secured to the backside of the copper plate. Water, circulating through this chamber, absorbed the heat of condensation flowing through the copper plate from the condensing surface. The water entered the cooling chamber along the central axis and impinged on the copper surface which was parallel with and of the same area as the condensing surface. The water left the chamber through two outlets, one at the top and one at the bottom. The piping was arranged to insure that the chamber was always completely filled with water.
couples were wired in parallel. Also, at the cross section nearest the condensing surface, two thermocouples were placed in holes drilled radially at angles of 45” and 225” measured clockwise from the top thermocouple. One of these couples measured the temperature at the plate axis and the other at a point one inch out from the axis. Prior to fitting in the copper plate each thermocouple was passed through a short length of copper tube, the junction fused to the end of the tube and the tube then turned down to 0*0930 in. o.d. to provide a press fit in the drilled holes. Based on the thermocouple readings, the temperature gradient in the copper plate was calculated and from this the thermal flux through the system. Also, by extrapolation of these temperatures, the effective condensing and cooling surface temperatures were determined. These ELECTRICALLY CONDENSING values along with the steam temperature as trv:NAoii SURFACE measured by a thermocouple in the steam vapor STEAM INLET \ / space and thermocouples in the cooling chamber COOLING WATER determined the AT’s at each end of the copper \ OUTLET plate, The equivalent heat transfer coefficient, h,, on the condensing side was evaluated using AT, and the flux through the system. The vapor velocity was determined by an energy balance around the boiler, transfer lines and condensing chambers. Heat flux determined by this balance and a balance on the cooling chamber was in reasonable agreement with that calculated from conduction measurements in the copper plate. As described previously, thermocouples were placed at various radial depths in the copper plate at the cross section nearest the condensing surface. Temperatures indicated by these thermocouples during runs established that there was essentially no radial temperature difference in the center portion of the plate and hence, little radial heat transfer. Because of this and because alI of the FIO. 3. Half section of condensing chamber. thermocouple leads were brought out of the plate radially, the temperature measurements in the The copper plate, e in. thick, was provided plate are believed to be quite accurate. The absence with a total of 14 thermocouples made from No. 24 of any appreciable radial gradient implies that gauge copper-constantan wire. At each of three heat flow through the plate should be axial and cross sections, four thermocouples spaced 90” thus, linear. Experimentally, a slight departure apart were placed in holes drilled radially to within from linearity was observed which was the result one-half in. of the center of the plate. To obtain of the nonuniform temperature distribution over an average reading at a cross section, the thermothe condensing surface. This slight variation was
I
/
1309
J. T.
O’BARA. E. S. KILLIAN and
caused by the steam entering at the top of the plate at a somewhat higher temperature than that leaving at the bottom of the plate. In the initial phases of this investigation data were obtained with a test cell essentially the same as that described above with the exception of the dimensions of the copper plate. In these earlier studies [lo], a copper slug 14 in. dia. and 14 in. long was used. While in this case the entire face was used for condensation so that the area available for condensation was the same in either cell, the diameter-length ratio was much less than that of the large disc. Consequently, radial heat transfer was important. While this problem was solved by adequately insulating the slug, the experience with this assembly prompted the design of the second. It is important to note, however, that identical results, within the limits of experimental error, were obtained with both setups and thus, provide oonsiderable assurance that the results reported are accurate. Prior to a set of runs the condensing surface was polished by hand with jeweler’s rouge until it appeared that all copper oxide had been removed. After polishing, the surface was rinsed first with acetone and then several times with distilled water until a continuous film of water adhered to it. In a typical run the cooling water was set at a desired rate and the Variac controlling the input to the boiler adjusted. After temperatures stabilised, the inert gases in the system were removed using a water aspirator connected to the open end of the auxiliary condenser. Throughout the investigation the inert gas concentration was checked using a Classen-type apparatus proposed by FURMANand HAMPSON[Ill. These measurements showed the noncondensible concentration to always be less than O-0036 wt. “lo. Following aspiration, the cooling water flow rate to the auxiliary condenser was adjusted such that condensation could always be observed in the condenser. This assured that there was no backflow of air into the system. After equilibrium had been attained, temperature readings were made throughout the system. These measurements and flow rates provided data for calculating the thermal flux and the equivalent heat transfer film coefficient. Additional runs were
L.
H. S. ROBLEE, JR
made by setting up new flow rates aud energy inputs.
RENJLTAND Heat transferjIm
DISCUSSION
coeficients-atmospheric
pressure
(i) Experimental results. Experimental results are presented in Figs. 4 through 8. The individual points on the graphs are averages of several runs. While Figs. 4 and 5 could be combined into one, two graphs have been used for greater clarity. Heat fluxes ranged from 167,000 down to 29,900 B.t.u./hr-ft2 for AT, ranging from 2 to 44*7”F. The equivalent film coefficients ranged from 1140 to 37,200 B.t.u./hr-ft2-“F and vapor velocities from l-75 to 7.52 ft/sec. Because of condensation, the vapor velocity varies continuously over the condensing surface from a maximum value at the steam inlet to a minimum at the outlet. Consequently, there is an arbitrariness associated with the definition of the vapor velocity. In this investigation the vapor velocity reported is the arithmetic mean of the inlet and outlet values calculated from energy balances. The crosssectional area used in determining these velocities was the same for both inlet and outlet and was taken as the area perpendicular to the condensing surface through which the steam passed just before contacting the condensing surface. Detailed experimental results can be obtained from [lo] and [12].
1310
VAPOR VELOCITY. v 1.75
FTlSEC
b 2.42 0 314 0 402
0 0
5
IO
IS
20
ATa,
lF
25
30
35
40
45
Fro. 4. Variation of steam-sideheat transfer coefficientswith AT. for dropwise condensation.
Dropwise condensation of steam at armospneric and above atmospheric pressures
at the low velocity of 1.75 ft/sec. This effect is clearly shown in Fig. 6 where, with AT, as a parameter, the film coefficient is plotted against vapor velocity. The figure, obtained from Figs. 3 and 4, shows that for each AT, there is a maximum vapor velocity at which dropwise condensation exists and that this maximum increases slightly as AT, decreases. For the AT, of this investigation, the maximum vapor velocity obtainable in dropwise condensation lies in the range from 5 to about 6.5 ftlsec.
35 VAPOR VELOCITY,
FTISEC
25
40
I&. 30 : “k
25
i
20
3 2
I5
n 0
IO
=
5 0 0
5
IO
I5 AT,.
20
30
35
45
lF
FIG. 5. Variation of steam-side heat transfer coefficient with AT, for dropwise condensation.
35 ‘-
(ii) Error analysis. The most probable error associated with the effective heat transfer coefficient was determined by a propagation of error analysis. In this analysis the estimated average error in temperature measurements was taken as +O*YF. The thermal conductivity of copper was assumed constant at 218 B.t.u./hr-ft2 (“F/ft) and the error in thermocouple position was considered zero. An analysis of a typical run for an h, of 1470 B.t.u./hr-ft2-“F, a AT, of 29.22”F and a heat flux of 43,000 B.t.u./hr-ft2 showed that at the 99.7 per cent confidence level the most probable error in h, was less than or equal to 14.1 per cent. The analysis further revealed that the probable error is most strongly influenced by AT,, becoming quite small for high values but large for low values even when thermocouple temperatures are known as accurately as within 0.5 per cent. (iii) Discussion. Figures 4 and 5 show that the equivalent filmcoefficient, h,, plotted on theordinate, has its maximum value at low AT, and decreases to an essentially constant value (depending on vapor velocity) above a AT, of about 35°F. These figures show the pronounced effect vapor velocity has on h,. For example, at a AT, of 9°F h, is about 4800 B.t.u./hr-ft2-“F at a vapor velocity of 1.75 ft/sec. At this AT,, the coefficient steadily increases by approximately three and one-half times to 16,800 B.t.u./hr-ft2-“F as the vapor velocity increases to 5.54 ft/sec. Interestingly, as the vapor velocity is further increased an abrupt drop in h, is observed. In fact, at a velocity of 7.25 ft/sec the coefficient is essentially the same as
0
I
2 VAPOR
FIG.
3 VELOCITY,
4
5
6
7
S
FTlSEC
6. Influence of vapor velocity of steam-side heat transfercoefficients.
The reason a maximum vapor velocity exists in dropwise condensation appears to be an effect of the shear stress between vapor and drops. As the vapor velocity increases, the shear stress also increases and tends to disrupt the drops, inducing coalescence and, hence, the formation of a liquid film. The shift in the maximum value is explained by the fact that at low AT, drops are relatively small and drop growth rate is low so that more shear stress is necessary to bring about this transition. In contrast, at higher AT, the drops are larger and growth rate higher so that less shear stress, i.e. lower vapor velocity, is required to produce the same effect. In Figs. 7 and 8, the results of this work are compared with those of FATEA and KATZ [a], and WELCH [4]. Although the results of Fatica and Katz are for steam condensing on nickel, chromium, as well as on copper, using stearlc and oleic acid as promoters, there was very good agreement between their work and the present study.
1311
J. T. O’BARA, E. S. KILLIAN and L. H. S. ROBLEE,JR
Their vapor velocity, while not stated, was assumed negligible. In Fig. 8, this work is compared with Westwater’s. In order to make a valid comparison, the vapor velocities should be roughly the same. The apparent discrepancy here in comparing results at a vapor velocity of 2.42 and 10.2 ft/sec lies in the definition of vapor velocity, specifically the areas on which the velocity calculations are based. As mentioned previously, the area used to determine vapor velocities in this work was taken as the area perpendicular to the condensing surface through which the steam passed prior to contacting the condensing surface. Because of the geometry of the condensing chamber this area is about four times that of the steam inlet (or outlet) area. Thus, if vapor velocities in the present work were based simply on inlet and outlet steam line cross sections, as were Westwater’s, a velocity of 2.42 ft/sec would correspond to a velocity of
35 .IL
JO--
NL
25--
‘s ,E
15
0
IO
i
5
VAPOR VELOCITY, v 1.75
FA,ICA AND KATZ
:‘_i_: 0 0
5
IO
15
20
25
30
35
FTISEC
!
!
40
45
ATS , *F
Fro. 7. Comparison of experimental results with those of Fatica and Katz.
35 u :
30
Nk
21
.$
20
VAPOR VELOCITY, FT/SEC A 2.42 (THIS WORK) 0 10.2 (WESTWATER)
2 2
15
>_
10
‘Y
s 0 0
5
D
I5
20
25
30
35
40
45
approximately 10 ft/sec. With this in mind, the agreement between the two studies is very close over a broad range of AT, and only departs significantly at low values of AT,, a range in which, in this type of study, experimental error is large.
High pressure study-visual observations
(i) Experimental results. In addition to determining heat transfer coefficients at atmospheric pressure, preliminary studies were made which involve visual observations of the dropwise condensation phenomenon at high pressure. The experimental procedure at high pressure was essentially that at atmospheric pressure with the exception that the glass auxiliary condenser was replaced by a closed metal condenser. Also, the system was purged of noncondensable gases by directly venting steam to the atmosphere. The observations which follow were made under continuous operation as the steam pressure was increased from 0 to 200 psig. 25 psig Steam Pressure (267”F)t The conditions were much the same as at atmospheric pressure. The drops looked essentially the same, but they appeared to reside longer on the surface. 50 psig Steam Pressure (301°F) A noticeable change occurred by the time this pressure was reached. Drops cycled very slowly and changed from the rain drop shape at atmospheric pressure to a more flat and almost circular shape. They seemed to merge much more slowly and grow quite large before merging took place.
75 psig Steam Pressure (320°F) There was not much change from the conditions at 50 psig pressure. The surface appeared to be covered with a layer of condensate and drops seemed to adhere to this layer rather than the metal surface.
ATs,*F
FIO. 8. Comparison of experimental those of Westwater.
results with
t The values in parenthesis are the saturation tures corresponding to the pressures cited.
1312
tempera-
Dropwise condensation
of steam at atmospheric
100 psig Steam Pressure (338°F) No large change was observed. However, drop density seemed smaller and individual drops appeared to be larger than those at lower pressures. 125 psig Steam Pressure (353°F) The surface appeared the same as it did at 100 psig. 150 psig Steam Pressure (367°F) At this pressure it was difficult to define the beginning and end of a drop. All drops appeared very flat on the surface.
and above atmospheric
vapor velocity is increased from relatively low values, the transfer coefficient increases significantly. Above a certain critical velocity, however, the coefficient rapidly decreases. Visual observations of the condensation phenomenon at pressures above atmospheric indicate that in the pressure range between 25 and 50 psig the phenomenon undergoes a transition from dropwise to mixed followed by filmwise condensation. Acknowledgment-The authors gratefully acknowledge the fmancial support of this investigation by the Office of Naval Research Contract Nonr #3357 (02).
175 psig Steam Pressure (377°F) The condensation appeared to be more filmwise than dropwise.
NOTATION %
fc
200 psig Steam Pressure (388°F) Filmwise condensation appeared to be the predominant mode of condensation. (ii) Discussion. Although these studies are only preliminary, they reveal that dropwise condensation is affected by pressure and that a transition from dropwise to mixed condensation appears to occur at pressures in the neighborhood of 50 psig. While it could be argued that the transition reflects a chemical change in the promoter at the higher temperatures, this does not appear to be the case as no hysteretic effects were observed as the pressures were varied up or down. Based on the evidence available it is believed that the transition observed is a consequence of the decreased surface tension of the condensate at the higher pressures and saturation temperatures. Thus, as the cohesive forces are reduced the forces of adhesion become relatively more important. This, along with the greater rate of condensation and actual pressure on the drops at higher pressures, promotes the formation of filmwise as contrasted with dropwise condensation.
pressures
fSLO
area increment change in surface free energy fraction of a liquid surface covered with condensate fraction of a surface covered with absorbed molecules gravitational constant equivalent heat transfer coefficient on the steam condensing surface net condensation rate per unit area condensation rate per unit area evaporation rate per unit area equilibrium pressure corresponding to temperature of liquid-vapor interface vapor pressure universal gas constant temperature surface temperature vapor temperature difference between steam temperature and condensing surface temperature work of cohesion work of adhesion condensation coefficient-fraction of molecules striking a surface that condense fraction of molecules striking a liquid surface that condense fraction of molecules striking a solid surface that condense proportionality constant surface tension of liquid in equilibrium with its vapor interfacial tension between a solid and a liquid surface tension of solid-gas interface in equilibrium with saturated vapor contact angle of a drop
h”. NN
N+_ pi
PO
R T T, Tv AT,
WC WSLO o!
EC asL B YLVO
CONCLUSIONS
YSL
The experimental findings indicate that vapor velocity has an important effect on the equivalent heat transfer coefficient for condensing steam. As 1313
YSVO 0
J. T. O’BARA, E. S.
ILLIAN
and L. H. S. ROBLEE,JR
REFERJ~NCES
[l] EMMONSH., The mechanism of drop condensation. Trans. Am. Inst. Chem. Engrs 1939 35 109-125. Mech. Engng 1936 58 729-739. [2] JAKOBM., Heat transfer in evaporation and condensation-II. [3] WELCH J. F. and WESTWATERJ. W., Microscopic study of dropwise condensation. Proceedings of the International Heat Transfer Conference 1961 11 302-309. [4] WELCHJ. F., Ph.D. Thesis, University of Illinois 1960. [5] UMUR A. and GRIFFITHP., Mechanism of dropwise condensation. J. Heat Transfer 1965 87 Series C No. 2 275-282. Chem. Engng Prog. 1949 45 661-674. [a FATICAN. and KATZ D. L., Dropwise condensation. [I SUGWARA S. and MICHNOSKII., Dropwise condensation. Memoris of Faculty of Engineering, Kyoto University 1956 18 No. 2 84-111. [8] SILVERR. S. and SIMPSONH. C., The condensation of superheated steam. Proceedings of a Conference held at the National Engineering Laboratory, Glasgow, pp. 39-69, 1961. [9] ROHSENOWW. M. and CHIO H. Y., Heat, Mass and Momentum Transfer, Prentice-Hall 1963. [lo] Q’BARA J., M.Sc. Thesis, University of Massachusetts 1964. [ll] FIJRMANT. and HAMPSONH., Experimental investigation into the effect of cross flow with condensation of steam and steam-gas mixtures on a vertical tube. Proc. Inst. Mech. Engrs 1959 173 147-169. [12] KILLIANE. S., M.Sc. Thesis, University of Massachusetts 1966.
R&n&-Les resultats des phases initiales dune etude concernant le mecanisme de la condensation de la vapeur goutte a goutte sont present& dans la premiere partie de cette etude. Les coefficients equivalents du transfert de la chaleur a la pression atmospherique, pour la condensation de la vapeur goutte a goutte sur une surface verticale, ont &C determines de facon experimentale. I_es coefficients varient respectivement de 1.140 a 37.200 B.t.u./heure pied car& “F. Les velocites de la vapeur varient de 1,75 a 7,52 pied/set., le courant &ant dirige vers le bas de la surface verticale de condensation. Les observations indiquent que la v&cite de la vapeur a travers la surface de condensation a un effet significatif sur le coefficient de transfert equivalent, le coefficient montrant un maximum pour une v&cite croissante de la vapeur. On pense que ce maximum reflete la transition entre la condensation goutte 51goutte et mixte, resultant de la plus grande tension du dechirement exe& a l’interface vapeur[ liquide qui se developpe pour des valeurs plus Blevees de la v&cite de la vapeur. Des observations visuelles du phenomene de condensation ont aussi ette faites 51des pressions s’&chelonnant de la pression atmospherique a 200 Ib/pouce*. Ces observations ont montre que, comme la pression augmente, il se produit une transition de la condensation goutte a goutte la condensation mixte pour des pressions entre 25 et 50 lb/pouce*. Cette transition est enonc& comme &ant associee il la tension d&roissante a la surface de la phase conden& B des temperatures de saturation plus &levees. Une analyse thbrique est presented qui est en accord avec les observations exp&imentales.
Zusannnenfassnng-Die in den Anfangsstadien einer Untersuchung des Mechanismus der tropfenweisen Kondensation von Dampf erzielten Resultate werden im ersten Teil dieses Referats behandelt. Gleichwertige Wtimeiibertragungs-Koeflizienten bei atmosphkischem Druck werden experimentell durch die tropfenweise Kondensation von Dampf auf einer senkrechten FlaChe bestimmt. Die Koeffizienten variierten zwischen 1.140 und 37.200 B.t.u./hr Fuss* “F. Die Dampfgeschwindigkeiten variierten zwischen 1,75 und 7,52 Fuss/set, wobei die Stromung an der senkrechten Kondensationsfliiche entlang abw%rts gerichtet war. Die Beobachtungen deuten darauf hin, dass die Dampfgeschwindigkeit entlang der Kondensationsfltihe eine bedeutende Wirkung auf den iiquivalenten Ubertragungs-Koeffizienten austibt, wobei der Koethzient bei zunehmender Dampfgeschwindigkeit einen maximalen Wert erreicht. Man glaubt, dass dieser maximale Wert den Ubergang zwischen der tropfenweisen und der gemischten Kondensation widerspiegelt, bedingt durch die griissere Querspannung an der GrenzflLhe zwischen Dampf und Fltlssigkeit, wie sie bei hiiheren Dampfgeschwindigkeiten entwickelt wird. Visuelle Beobachtungen der Kondensationserscheinung wurden such bei Drticken vom atmospharischem Druck bis zu 200 lb/Zoll* lfberdruck durchgefiihrt. Diese Beobachtungen erweisen, dass mit zunehmenden Druck ein Ubergang von tropfenweiser zu gemischter Kondensation zwischen 25 und 50 lb/Zoll* Uberdruck eintritt. Es wird angenommen, dass dieser Ubergang mit der abnehmenden ObertXchenspannung der kondensierten Phase bei hiiherer Stittigungstemperatur im Zusammenhang steht. Es wird eine theoretische Analyse geboten, die den Versuchsergebnissen gerecht wird.
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