to calculate the performances of basins operating under the following ranges of conditions: pd = 312 lb./cu. ft. pL = 62.4 lb./cu. ft. g = 0.04 lb./ft. min. (water temp. = 72’ F.)
Q 100
500 1000
L 33 67 100
W
D
10 15 20
5.0 7.5 10.0
The data were smoothed by plotting S.I. us. Q/W’L at constant values of L and D,then tabulated as S.I. us. Q / W D a t constant values of QIPVL. The latter values are plotted in Figure 4. The curves of Figure 4 clearly define points of opti-
mum performance and should be useful for preliminary design purposes as well as for estimating the effects of allowing a basin to accumulate deposited solids. Similar sets of curves can, of course, be constructed for other ranges of basin dimensions, flow rates, solids density, and water temperature. Literature Cited (1) Bramer, H. C., Hoak, R. D., IND. ENG. CHElrl., PROCESS DESEXDEVELOP. 1, 185 (1962). ( 2 ) Hughmark, G. .4., Znd. Eng. Chem. 53, 389 (1961).
RECEIVED for review January 9, 1963 ACCEPTED May 31, 1963 Contribution from the Water Resources Research Project, sustained at Mellon Institute since 1938 by the American Iron and Steel Institute.
CONDENSING HEAT TRANSFER IN STEAM-AIR MIXTURES IN TURBULENT FLOW PAUL B. STEWART, JAMES L. CLAYTON,’ B E N I G N 0 LOYA,Z AND STANLEY E. H U R D Department of Mechanical Engineering and Sea Water Conversion Laboratory, C’nzverstty of California, Berkeley 4,Calif.
Graphical correlations and empirical equations show the effects of mixture composition over the complete range, of gas phase turbulence, and of liquid layer thickness on the over-all heat transfer coefficient. The latter two variables are correlated in terms of Reynolds numbers. The condensing surface used was a vertical tube with gas flow vertically down.
at present sufficiently high, are the major factor militating against the more widespread demineralization of saline waters than is currently practiced. Current research and development work in this field are directed, in the final analysis, to this fundamental goal of cost reduction. Among the approaches envisioned are the synthesis of a process not now in use and the improvement of existing methods. In this latter category much attention is being focused on the reduction of both energy costs and capital costs. The utilization of the so-called “free” energy, such as solar energy, and existing bodies of saline water at a higher temperature than some available sink has been under investigation a t the University of California for more than a decade now. This latter possibility, the reduced pressure flashing of a vapor produced from warm saline water and its subsequent condensation to demineralized water led to the work reported here. Deaeration of the feed stream would certainly reduce the temperature potential available for the process. On the other hand, failure to deaerate would increase the cost of the condenser and its associated gas pumping equipment. Originally it was planned to limit the work to the experimental study of the effect of inert (noncondensable ) gas concentration on the surface heat transfer coefficient. Subsequently two other factors, the free stream gas-phase Reynolds number and the liquid or condensate-phase Reynolds number, OSTS,
Present address, Space Technology Laboratory, Pasadena, Calif. Present address, Lockheed Missiles and Space Co., Palo Alto, Calif. 2
48
I&EC P R O C E S S DESIGN A N D DEVELOPMENT
appeared to be of sufficient importance to warrant extending the investigation to include these variables. Prior Work
The prior work reported upon in the technical literature on the general subject of the condensing heat transfer surface coefficient is voluminous. As with most phenomena involving fluid mechanics, it is not only convenient but almost necessary to consider separately the cases of the gas phase in laminar and in turbulent floiv. Only the latter of these, turbulent flow, and that further restricted to forced convection, is discussed here. To subdivide the field still further, the nature of the gas phase prior to the condensation process, whether a one-component vapor, a one-component vapor plus a noncondensable component, or a multicomponent system. seems logical. Multicomponent systems are also excluded from consideration here. The one paper in the field of condensing heat transfer cited by practically all writers on the subject since its publication is that by Nusselt (27) in 1916. Kusselt considered the simplest possible case analytically-that of a pure vapor condensing filmwise on a vertical isothermal surface, the condensate layer being in laminar flow so that all heat must be transported through it by pure conduction, and that gravity forces are the only body forces acting on the condensate layer. The Nusselt equation, as reported by Kreith (78),is
Even though the rather severe restrictions made in setting u p Nusselt’s model for the subsequent mathematical analysis
S T E A M MAIN
I
WATER MAlh
IESENC ~HERMOCOPLE
t"
@ @ @
'a
&$$ ?
x
0 0
XI
HAVOYETES
SATE?
YETE"
DRESSUSE Gii'FlCE S T E A M SEPARATCR S T E A M .ET STEAM
@ @
M
VAL~E P?ESSU*E RESULAT \ G
I
W
)
1
E.ESTCi
TRAF
C30LINS
VALiE
WATER
5
STEAM
A
AIR
C
CON3ENSATE
h'
C N R - S T E A M MlXT!JRE
3-
might seem, a t least at first glance, to limit its utility, such has not been the case. All of the restrictions tend to make surface coefficients computed by this equation conservative. McAdams (79) suggests a simple rule-of-thumb based on experimental work:
1.2 hxu =
h
oLriii
Figure 2.
Test condenser
(2)
Subsequent investigators (7-6, 70, 77, 73-15, 77, 22, 23, 25-27), whether using the analytical or the experimental approach to the condensation of pure vapors, have concerned themselves with factors excluded in the Nusselt derivation. These include initial superheat in the vapor, condensing surfaces other than vertical flat plates, the orientation of condensing surface and gas- or vapor-phase flow, turbulence in the gas phase, turbulence in the condensed liquid phase, condensation rate, and physical property (Prandtl number) variation. Results are usually expressed in terms or dimensionless groups as graphs or empirical equations. The introduction of a second and noncondensable component into the vapor phase adds another resistance to the several already in series in the over-all heat transfer process. This resistance, unlike the others, is a mass transport phenomenon (at least in part) and therefore subject to a concentration potential rather than a temperature difference. A41thoughfragmentary earlier work exists on this subject ( 2 4 , it was clearly recognized and treated at some length by Colburn and Hougen (8)Y). They not only correlated extensive experimental work in terms of heat and mass transfer coefficients, but developed a method for condenser design calculation. Subsequent work in this area (2, 12, 20, 22, 28, 30) has extended the Colburn and Hougen treatmenr to other geometries and other Prandtl and Schmidt numbers, expanded the Reynolds number range, and suggested modifications to their computation method. Equipment
.4flow diagram of the experimental equipment is given in Figure 1 and a cross-section drawing of the test condenser is shown in Figure 2.
The test condenser was fabricated from standard weight brass pipe and plate with all joints being brazed. Crosshatched components, for either aerodynamic streamlining or thermal insulation, were of phenolic plastic. The entering gas-vapor mixture flowed vertically downward and parallel to the condensing surface. The outside surface of the shell was covered with insulation. Temperatures were measured by calibrated thermocouples, copper-constantan or ironconstantan. Sampling ports were located as shown. Essential dimensional constants of the system are : Length of test condenser, L , 2.14 feet Outside diameter of test condenser, d, 1.90 inches Surface area of test condenser, A , 1.065 sq. feet Cross-sectional flow area of annulus, 0.1195 sq. foot Steam was supplied from campus steam mains, and throttled down to the system pressure from the 100-p.s.i.g. supply. Auxiliaries in the steam supply system included a condensate separator, pressure-regulating valve to ensure essentially constant downstream (throttled) pressure, a n orifice flowmeter, and a small desuperheating heat exchanger. Air was supplied from one of two alternate sources. For mixtures of 60 volume % or more steam the air was drawn in from the room by a steam jet ejector. The air was metered by a n ASME standard orifice in a surge drum prior to entering the ejector and its flow was regulated by a valve. For mixtures containing 507, or more air, the air was supplied by the building compressed air system, the ejector being used as the steam-air mixer, and the air flow measured by a standard calibrated orifice meter. Condensate and cooling water flow rates were determined by weighing the amount collected in a timed interval. Steam not condensed in the test condenser was condensed in aftercondensers, and the sum of all condensate rates from all condensers was taken as the steam rate, since the final aftercondenser was vented to the atmosphere, which made it easy to check whether complete condensation was being achieved. Draft gages, manometers, thermocouple switch gear, and similar equipment shown in Figure 1 completed the assembly. VOL. 3
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1964
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50
I & E C PROCESS D E S I G N AND DEVELOPMENT
Experimental Procedure
The experimental procedure requires but little comment. Two hours or more were usually required to bring the assembly into steady-state operation, verified by checking the constancy of the experimental variables such as flow rates, pressures, and temperatures. The data for each experimental point are the average of those taken on three consecutive 20-minute “runs.” Concentration data were obtained in one of two ways, or sometimes both: air rate from the calibrated orifice meter, and steam rate by weighed condensate; or (particularly in the low steam concentration range) by aspirating out ahead of the test condenser a steam-air sample and pulling it through a n absorption tube to remove water and a wet-test meter i o measure the air. The water in the sample was determined by weighing the absorption tube before and after. Results and Discussion
Effect of Vapor Phase Concentration. The early data taken were in the high steam concentration range, and show a somewhat greater scatter than those taken later. Among
04
Equation 1 \vas used to determine a mean coefficient, and the ratio of I;/h?;, \vas calculated to serve as a means of relating the effect of a n inert gas on the transfer of energy. The ratio is tabulated in Tables I and I1 and shown in graphical form in Figure 3. The adverse effect of air upon the transfer of energy is brought out by comparing the ratio for pure steam (1.3) to that for a mixture containing 6.4% steam by \veight (0.0088). An empirical equation which correlates the data is :
P
1
u
- = 1.12 e I l , 0 5 3 6 ( 1 0 0 - - T )
‘“r
C6
,
0
- T h i s Work
u = 26.5@ . 0 3 4 8
. hleisenburg
‘0
OoLY
Weight
20 percent
35
en.n332 Y
(5)
where Y is per cent of steam by volume. The correlation equation for the data of this work only is:
- . Harnpson
Figure 4. work
where Y is the per cent by volume of steam in the mixture. This relationship is valid for the range of 10 to 99% steam by volume and correlates the low steam concentration range data with a n aveiage deviation of less than 4,575 and a maximum deviation of 12.3%. The data in the high steam concentration range are more divergent. as noted earlier. having a n average deviation of 12.4% and a maximum deviation of 45.6%. The differing procedures for measuring A T account for a t least part of this scatter, since an error of 0.1” F. in each reading for a temperature difference of 4” F. would introduce a relative error of 5% in the heat rate. The data of Colburn, Meisenberg. Robinson, and Vishneoskii (7. 8, 20. 2d, 29) and of this investigation were correlated as shown in Figures 4 and 5. The greater coefficients obtained by Colburn and Hougen (Figure 5) can be accounted for by the higher velocities of floiv used in their investigations. The correlation equation for all the data is:
u = 28.5
c4-
(4)
hNu
Figure 3. Effect of noncondensable on mean heat transfer coefficient
1
the significant differences in the earlier and later data. those in the higher and lower steam concentration ranges. are smaller variations in gas-phase Reynolds number and in the heat flux which is nearly proportional to the cooling water flow rate in the later work. Also, the cooling water temperature measuring system was changed to a differential thermocouple for the later work from the individual thermocouples used earlier to increase the accuracy in temperature difference data. Even though the calculation of a total transport coefficient for a combined mass and heat transfer process as if it were a heat transport process only does not correspond to the physical picture in the case of condensation in the presence of noncondensables. this technique has several features to recommend it : It is simple, and it permits a ready and direct evaluation of the resistance offered bv the inert. Accordinglv. the results are expressed in this manner. The temperature rise and flov rate of the cooling !rater were used in the determination of the heat flux. The driving force for the energv transferred \vas taken as the average temperature difference between the main stream and test surface.
40
Nan - C o n d e n m b l e
Comparison with previous
P
(6)
where, again, Y is per cent steam by volume. These two equations are considered to be in excellent agreement. Effect of Flow Variables. As noted earlier, comparison of this work with that of Colburn and Hougen (7, 8 ) led to the suspicion that the gas-phase Reynolds number was a n important variable. Fortunately, this had been held essentially constant in this work on the effect of gas-phase concentration. VOL. 3
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51
c
Y
52
l&EC PROCESS DESIGN A N D DEVELOPMENT
c
0
L o w Range
0
-
D
- Votta and Waikei
--
High Range Robinson
D - Colburn
0 -
- hougen
Meisenburg
'0 20
40 60 S t e o m by V o l u m e , Y
Peweni
Figure 5.
\
80
IO0
Correlation of previous work
,
Overoll H e a t Transfer C o e f f i c i e n t ( 8 5 % Steam by v o l u m e )
-.. \
Nusselt Equation
6oi,
l 80 oo1
L
400
' 4 0
'
A
-
D
n
-5500'
/lllllllllll'tlll 70 I00
130
160
190
R e s ( C o n d e n s o t e Film R e y n o l d s N u m b e r )
Figure 6.
looc[
A third series of experiments was then carried out in which the concentration of the entering gas phase was held essentially constant. The results of these experiments were calculated to 857, steam concentration, using Equation 5. The usual correction was small. Thus, the significant variables were reduced to two : the entering gas-phase Reynolds number, and the condensate film Reynolds number. In the first of these the length dimension is the difference between the outside and inside diameters of the annulus, and in the second it is the thickness of the condensate layer evaluated a t the bottom of the test section. Figures 6 and 7 show these results with the over-all heat transfer coefficient from bulk gas phase to tube wall plotted against the condensate film (6) Reynolds number and the free stream (D)Reynolds number, respectively. Experimental points are shown on Figure 6. Figure 7 is a cross plot of Figure 6 using the values from the curves drawn thereon. The original data and calculations summaries are given in Table 111. Although a n excellent qualitative picture of the events taking place during the condensation of a vapor from a vapor-noncondensable mixture has been available for over 30 years now, since the work of Colburn and Hougen, attempts to interpret these phenomena quantitatively in terms of boundary layer, heat transfer, and mass transfer theory have met with but little success. Votta and Walker (30) attempted to eliminate one of the difficulties-the existence of the two transport potentials, temperature and concentration differences-by the use of an available energy function. The major barrier to a rational approach, setting u p differential equations and integrating between limits, is the lack of knowledge of the intermediate limits. The only locations where existing instrumentation permits the measurement of temperature and composition without seriously disturbing the system, if at all possible, are in the bulk of the gas phase and a t the metal wall. At and near the liquid-gas interface in both phases conditions are unknown, as is also the variation with location. Consequently a n empirical approach must be used in treating data such as those of this investigation. As with any empirical correlation it is desirable not only to have consistent new data, but also new information that does not disagree with that previously available which has achieved acceptance. Therefore certain data from the literature, in addition to those from this investigation, are plotted on Figures 6 and 7 . In Figure 6 the Susselt equation is plotted as slightly modified by Kirkbride (76) after further adjustment on the basis of this work to take into account the presence of the noncondensable gas. Essentially all of the experimental points fall below this dashed curve, again shoiving its utility as a limiting case. Jakob's ( 7 5 ) equation for the condensation of pure steam on a vertical tu be is :
Over-all heat transfer coefficient
Ovewll Heal Transfer Coefftclenl
Re, = 170
h,[B.t.u./hr.-sq. ft.-" F.] = 0.205 (3400
-
where V , is the vapor velocity in meters per second and L the length of the tube in meters. For comparison purposes this equation was converted to a function of free stream Reynolds number and corrected to 85 volume % steam, becoming: h,[B.t.u./hr.-sq. 0 " 2000
"
4000
'
" " ' 6000 8000
(Re)D
Figure 7.
'
' ~ ' 10000 12000
14000
16000
i E n t e r i n q Free S t r e o m R e y n o l d s N u m b a r )
Over-all heat transfer coefficient
ft.-' F.] = 0.152 (3400
-
0.060 Reo) (8)
For free stream Reynolds numbers above 9000, Jakob's data correlate closely lvith those of this investigation for a condensate film Reynolds number of about 110. Although no conVOL. 3
NO. 1
JANUARY
1964
53
densate film Reynolds number information was reported by Jakob in this instance, his relation for mean heat transfer coefficient tends to minimize the effect of free stream Reynolds number and is consistent with this investigation, considering a film Reynolds number of 110 as a median for this range of data. A relation reported by Hebbard (74), while condensing pure steam on vertical tubes, is also recorded on Figure 4. The relation h,,,[B.t.u./hr.-sq. ft.-O F.] = 38.2 (Ren) 0.238
(9)
was obtained from a set of curves he presented, using the one corresponding to a liquid boiling point of 100’ C. This relation also has been converted to consider 85 volume % steam in the mixture. KO condensate film Reynolds number information was presented in conjunction with Hebbard’s data, so only a qualitative comparison is possible. He obtained over-all heat transfer coefficients about 50% lower than those reported in this investigation for a film Reynolds number of 50; however, Hebbard’s relation demonstrates the same weak dependence on free stream Reynolds number, producing a line almost parallel with that of Jakob in the range of data reported. Several points obtained from the data of Votta and Walker (30) were also plotted on Figure 7. In all cases here the condensate Reynolds number was very low, about 5 ; this indicates that they had a very thin condensate film, leaving most of the resistance to heat transfer in the air film. These data were corrected for air percentage but may not be sufficiently accurate, since large corrections were necessary (some of the points correspond to only 17% steam by volume). An attempt was made to correlate these points with a dashed line on Figure 4. This line demonstrates a larger dependence on free stream Reynolds number than the other relations considered; this would be expected, since the air film was the controlling factor. Some of the scatter of the data points in Figure 6 is possibly due to the change in the free stream Reynolds number because of steam condensation as the fluid flowed through the annulus. Many of the points farthest from the correlation curves were for runs where upward of 30% of the entering steam was condensed instead of the usual 10 tc 15%. Nomenclature
A = area, sq. ft. CW = cooling water C = concentration, yo by vol. or wt. d = diameter of tube, ft. D = effective diameter of annulus, it. g = gravitational constant, 32.2 ft./sec.2 h = average surface heat transfer coefficient, B.t.u./hr.sq. ft.-’ F. k = thermal conductivity, B.t.u./hr.-sq. ft.-’ F./ft. L = length, ft. P = pressure, atm. or inches H g R e = Reynolds number, dimensionless T , t = temperature, ’ F. U = over-all heat transfer coefficient, B.t.u./hr.-sq. ft.-’ F. V = velocity, ft./sec. w = weight rate of flow, lb./hr. x = concentration, wt. % of air Y = concentration, vol. of steam r = weight rate of flow of condensate per unit breadth, Ib./hr.-ft. 6 = thickness of condensate layer, ft.
54
l & E C PROCESS D E S I G N A N D D E V E L O P M E N T
A
X
= a difference = latent heat of condensation (vaporization), B.t.u./lb.
1.1 p
= viscosity, lb./ft.-sec. or lb./ft.-hr. = density, lb./cu. ft.
SUBSCRIPTS C.W. = cooling water D = in Ren is Reynolds number based on vapor phase velocity, and annulus diameter = DVp/p, a t inlet conditions m = average (mean) Nu = Nusselt (refers to Equation 1) sat = saturation 4x7, 6 = in Re8 is condensate film Reynolds number = __ evaluated at liquid outlet
P
literature Cited (1) Badger, W.L.. Monrad, C. C., Diamond, H. I+‘., Ind. Eng. (1) Chem. 22, 700 (1930). (2) Baker, E. M., Kazmark, E. IV., Stroebe, E. IV., Trans. A m . Znst. Chem. Engrs. 35, 127 (1939). (3) Bromlev. L. A.. Ind. Ene. Chem. 44. 2966-9 (1952). (4) Carpenter, F. ’S., Colbyurn, A. P., “Proce‘edings of General Discussion of Heat Transfer,” Inst. Mech. Engrs. and Am. SOC.
Mech. Engrs., pp. 20-26, 1951. (5) Chari, K., J . Sci.Znd. Res. (India) 10A, 1047-51 (1938). (6) Chu, J. C., Flitcraft, R. K., Holeman, M. R., Ind. Eng. Chem. 41, 1789-94 (1949). (7) Colburn. A. P., Trans. Inst. Chem. Engrs. (London) 30, 187-93 (1933-34). (8) Colburn, A. P., Hougen, 0. A , , Ind. Eng. Chem. 26, 1178 (1934). (9) Colburn, A. P., Hougen, 0. A,, “Studies in Heat Transmission,” Bull. Univ. Wisconsin Expt. Sta., No. 70 (1930). (10) Fritz, W.,Z. Ver. Deut. Zng., Bcih. Verfahrenstechnik 1937, 127-32. (11) Grigull, U., Forsch. Gehiete Ingenieurw. 13, No 2, 49-57 (1942). (12) Hampson, H., “Proceedings of General Discussion on Heat Transfer,” Inst. Mech. Engrs. and Am. SOC.Mech. Engrs., New York. 1951. (13) Hassan, K., Jakob, M., Trans. Am. Soc. Mech. Engrs. 80, 887-94 (1958). (14) Hebbard, G. M., Badger, W. L., Trans. Am. Znst. Chem. Engrs. 30, 194 (1933). (15) Jakob, M.: Mech. Eng. 58, 729 (1936). 16) Kirkbride, C. G., Ind. Eng. Chem. 26, 425 (1934). 17) Kirschbaum, E., iVetjen, A. K., Chem. Zng. Tech. 23, 361-7 (1951). (18‘) Krkith, Frank, “Principles of Heat Transfer,” pp. 424-6, International Textbook Co., Scranton, Pa.. 1958. (19) McAdams, iV. H., “Heat Transmission,” 3rd ed., p. 335, McGraw-Hill, New York, 1954. (20) Meisenburp. S. J.. Trans. A m . Znst. Chem. Eners. 31.622 (1935). (21j Kusselt, W7,’Z. Vir. Deut. Zng. 60, 541 (1916j. (22) Othmer, D. F., Znd. Eng. Chem. 21, 576 (1949). (23) Quigg, H. T., Zhid., 30, 1047-51 (1938). (24) Robinson. C. S.. J . Ind. Ene. Chem. 12. 644 (1920). i25/ Rohsenow. W.. Trans. A-m. Soc. .kfech. E n u s : 78, 1645-8 ‘ (1957). (26) Rohsenow, LV., Webber, J. H., Ling, A . T.: Ibid., 78, 1637-43 I
,
11957).
(2?i~Seban,R. A , , Ihzd., 76, 299-303 (1954). (28) Smith, J., Znd. Eng. Chem. 34, 1248-52 (1942). (29) Vishneoskii, K. P., T r . Kutbyshev. Ind. Znst. 4, 161-7 (1953). (30) Votta, F., W’alker. C. A,, A.Z.Ch.E. J . 4, 413 (1958). RECEIVED for review February 25, 1963 ACCEPTED August 5, 1963 Division of \Vater and \Vaste Chemistry, 144th Meeting, ACS, Los Angeles, Calif.. April 1963. Funds for the support of this work are furnished by the State of California, and allocated by the Water Resources Center of the university. Donald R. Burnett, as part of an M.S. in mechanical engineering project, designed the equipment used, and aided in its installation and calibration.
