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Nomenclature Cp
D
= specific heat at constant pressure
= diameter,ft.
t. u./ (hr.)(sq. ft.) (: F.) thermal conductivity, B. t. u./(hr.)(sq. ft.)(’ F./ft.) length of tube, ft. heat transferred Der unit time, B. t. u. specific gravity average li uid temperaturoe, F. vapor heal temperature, F. liquid film temperature difference, F. over-all temperature difference = t, - tu specific volume, cu. ft./lb. weight of feed, lb./hr. surface tension, dynes/cm. viscosity, lb./(ft.)(hr.)
hL
= boiling liquid film heat transfer coefficient, B.
k
= = =
L a
3
=
= t, = A ~ L= AT0 = v = = w u = p = t~
O
Literature Cited Baker, Kazmark, and Btroebe, IND. ENa:CFxzhf., 31, 214 (1939). (IA) Boarts, Badger, and Meisenburg, Trans. Am. Inst. Chem. Engrs., 33, 363 (1937). (2) Brooks and Badger, Ibid., 33, 392 (1937). (3) Cleve, Milt. u . Forschungsarb., 322, 1 (1929). (1)
VOL. 31, NO. 2
(4) Cryder and Finalborgo, Trans. Am. Inat. Chem Engrs., 33, 346 (1937). ENG.CHEM.,24,1382 (1932). (5) Cryder and Gilliland, IND. (6) Drew and Mueller, Trans. Am. Inst. Chem. Engrs., 33, 449 (1937). (7) Fritz, Physik. Z.,36, 379 (1936). (8) Fritz and Ende, Ibid., 37,391 (1936). (9) Hebbard and Badger, IND. ENQ.CHEM.,26, 420 (1934). (IO) Hebbard and Badger, Ibid., Anal Ed., 5, 359 (1933). (11) Jakob, Mech. Eng., 58, 643 (1936). (12) Jakob, Z. Ver. deut. Ing., 76, 1161 (1932). (13) Jakob and Fritz, Forsch. Bebiete. Ingenieurw., 2, 435 (1931). (14) Jakob and Linke, Ibid., 4, 75 (1933). (15) Jakob and Linke, Phyaik. Z., 36, 267 (1935). (16) King, Refrig. Eng., 25, 83 (1933). (17) Kirkbride, Trans. Am. Inst. Chem. Engrs., 30, 170 (1933). (18) Kirschbaum, Kranz, and Starok, Forsch. Gebiete. Ingenieurw., B6, Forscltungsheft 375, 1 (1935). (19) Linden and Montillon, Trans. Am. Inst. Chem. Engrs., 24, 120 (1930). (20) Logan, Fragen, and Badger, IND.ENG.CHXIX., 26, 1044 (1934). (21) Mueller, A. C., personal communication. (22) Stewart and Hechler, Refrig. Eng., 31, 107 (1936). RECFJVBDNovember 3,1938. Presented before the meeting of the Amerioan Institute of Chemical Engineers, Philadelphia, Penna., November 9 to 11, 1938. Submitted by G.W. Stroebe in partial fulfillment of the requirementi for the Ph.D. degree, University of Miohigan.
Liquid Velocity and Coefficients of Heat Transfer in a Natural-Circulation Evaporator
T
I
ALAN S. FOUST AND EDWIN IM.BAKER, University of Michigan, WALTER L. BADGER, Dow Chemical Company, Ann Arbor, Mich.
HIS investigation was undertaken in an attempt to help bridge the gap between the science of heat transfer and the art of evaporation. The basket-type evaporator, which was studied in this research, has been in use for many years, and is typical of those developed in advance of a full understanding of the fundamental principles of heat transfer. Design of evaporators of this class has been based largely on experience and rule of thumb ( I ) ; without these, the design of such an evaporator presents a well nigh impossible problem. It was the purpose of this investigation to study the influence of boiling point, temperature drop, and liquor level on the behavior of a basket-type evaporator of semicommercial size as the first step of an attempt to relate rate of circulation of the liquor and coefficient of heat transfer to the fundamental variables involved. The difficulty of measuring the rate of liquid circulation under normal operating conditions has prevented the securing of accurate data on this vital and somewhat neglected variable. Those factors which appeared most important were: (a) the temperature drop under which the evaporator is operating; (6) the boiling point of the liquid (which, in turn, introduces as dependent variables viscosity, vapor density, and liquid density); (c) viscosity of the liquid; ( d ) density of liquid; (e) “liquor” &vel; (f) ratio of tube length to diameter; and (8) latent heat of evaporation. This investigation has also tentatively indicated the importance of the width of the annulus of the evaporator.
The effects of boiling point, temperature drop, and liquor level on the rate of circulation and on the coefficient of heat transfer when evaporating distilled water have been investigated in this research. Equations have been developed which relate these quantities, either directly or through fundamental variables which are dependent on them.
Historical Background Webre and Robinson (18) presented a theoretical analysis of the rate of liquid circulation in evaporators based on the velocity of vapor leaving the tubes. His analysis balanced the head available in the annulus by virtue of the circulating liquid agbinst the velocity head imparted to the ascending stream, and by a comparison of the weights of the two columns he arrived at the velocity of liquid entering the tube. This analysis necessarily neglected the slip between liquid and vapor in the ascending stream in the evaporator tube. Without knowledge of the temperature a t the top of the tube, there was no basis for calculating the amount of vapor present in the stream leaving the tube and the amount formed by flashing afterward. This method was also limited in its applicability in that it did not investigate the behavior when operating with liquor levels above the top tube sheet. Linden and Montillon ( l a ) presented an accurate study of circulation in an inclined-tube evaporator with one 4-fOOt tube. Their study covered a rather narrow range of temperatures and liquor level conditions. Circulation was measured
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INDUSTRIAL AND ENGINEERING CHEMISTRY
Experimental data are presented on liquid velocity and coefficients of heat transfer in a basket-type evaporator of semicommercial size when evaporating water. The results are submitted in the form of equations which relate each of these quantities with three important operating variables investigated, either directly or through fundamental variables dependent on them. Both coefficients and rate of circulation increase with increasing temperature drop and higher boiling point. Coefficients increase with lowered liquor level, over the range investigated; liquid velocity reaches a maximum when the liquor level is somewhat above the top tube sheet, and decreases at a fairly regular rate as the liquor level is either increased or decreased. Temperature measurements of the stream in the tubes indicate that boiling takes place in a smaller portion of the tube than had been realized. Liquid temperatures throughout the tube are found to approach vapor temperatures much more closely than had been previously thought to be the case.
by the elongation of a fine phosphor bronze wire coil spring supporting a circular disk of wire gauze in the vertical return pipe of their evaporator. This device had been calibrated by suspending it in a water stream of known velocity and measuring the elongation of the spring. Their results led them to an expression of the boiling film coefficient in terms of liquid circulation and Prandtl number of the liquid as follows:
In this equation all factors are represented by conventional symbols except the velocity, V,, which is taken as a logarithmic mean of steam and liquid rates. This equation is undoubtedly accurate for an evaporator of the type they studied, but its direct transposition to the common basket-type evaporator is questionable. Kirschbaum’s study (11) of the long-tube type of evaporator included measurement of the amount of liquor circulating by virtue of natural convection. From his measurements on a tube 16 feet long, there seems little justification for predicting the rate of circulation in a basket-type evaporator with conventional short tubes. His study does give information on the effect of the ratio of tube length to diameter, which has not been investigated in this research. His measurements of the rate of circulation were by means of an orifice in the return lime, with consequent impediment in flow more serious than that introduced by the gauze disk of Linden and Montillon. Cleve (4)is one of many investigators of the rate of circulation in boilers operating a t pressures above atmospheric. The importance of circulation as a controlling factor in the
207
performance of water tube boilers for raising steam has long been recognized by the mechanical engineering profession and has been the subject of much study. Cleve’s work, along with that of most investigators who have attacked this phase of boiler design and performance, was concerned primarily with cases of heavier loading of the heating surface than is customary in evaporator practice. His results were reported only qualitatively and extended well into the range where rate of circulation decreased as a result of increased friction of the greatly expanded stream. Under such conditions heat transfer coefficients decreased, probably on account of blanketing of the heating surface by vapor under the influence of a high temperature drop. These two effects are recognized and have been found in other conditions of heating, but no case has been found where this falling off of circulation or coefficient is reported for apparatus similar t o the basket-type evaporator. This statement, of course, does not include the generally recognized effect of very low liquor level on operation of natural-circulation evaporators. Cleve’s measurements of rate of circulation in large experimental apparatus were made by means of a Venturi tube; in several smaller apparatus, weirs were used.
Apparatus The evaporator studied in this investigation was a 30-inch diameter, semicommercial Swenson basket-type evaporator (Figure 1). Connections to the vapor space and stuffing boxes for connections to the steam basket were carried in a reinforcing pad cast on one side of each section of the body. In the bottom section were two stuffing boxes, one for removal of drips from the steam basket, and one for a manometer connection for measurin the ressure in the basket. Feed and wash lines were connectei to t t e middle section. Vapor space pressure was measured by a manometer connected t o the top section. The steam inlet was carried through a stuffing box in the top section. The vapor outlet was a complicated cross fitting through which also passed an auxiliary steam line. (This connection was arranged to permit use of the evaporator as the second effect of a double-effect evaporator and was not used in this investigation.) Manifold connections permitted the use of either 40 or 125 pounds per square inch of steam, with coarse and fine adjustment of each. Liquor level was indicated by a gage glass on the evaporator body. The cone bottom of the evaporator carried a propeller-type agitator which was left in place but not used during this work. The basket was cylindrical, 25 inches 0. d. and 48 inches high, supported in the bottom section of the evaporator by four angleiron brackets at its bottom. The steam inlet was a standard 6inch pipe in the center of the top tube sheet. Drips were removed through a 2-inch outlet on the side 1 inch above the bottom tube sheet. The pressure manometer connection was a 0.5-inch pipe, 2 feet above the bottom tube sheet. There were thirt one 10gage carbon steel tubes, 2.5 inches 0. d. Twelve of t l i m were spaced on a l4inch circle and nineteen on a 20-inch circle. The coefficients of heat transfer were calculated on the basis of the total “effective” area of 102 square feet. The construction of the basket obviously gave a stagnant layer of condensed steam in the bottom of the basket, approximately 1 inch deep, and the area of the tubes, bottom tube sheet, and basket wall so blanketed was not included in the effective area. Measurement of the stream temperature along the center of one tube while operating was accomplished by means of a travelin thermocouple of the type developed by Boarts, Badger, an6 Meisenberg (3). The couple was copper-constantan, No. 28 B & S gage, enameled and silk-covered wire, and was sealed into a protecting tube of soft drawn brass, 0.086 inch 0. d. and 0.050 inch i. d. The couple projected 0.5 inch from the end of the tube, and was sealed in place with litharge and glycerol cement drawn into the tube by vacuum. The assembly was centered in the tube by Chrome1 wire fins and could be moved through the length of the tube by means of a closed-circmt pull wire. The pull wire carried indicators showing the position of the couple. A sketch of the assembly is shown in Figure 2. The cold junction was maintained at 32” F., and the electromotive force was measured by means of a Leeds & Northrup type K2 potentiometer. It was possible to duplicate readings to about 0.10’ F., which was felt to be the limit of accuracy of the apparatus. The couple was calibrated “in place” against saturated steam in the vapor space; the divergence between the temperature corresponding t o the pressure (13) and that corre-
208
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A
q-
SKETCH OF APPARATUS FIGURE1. GENERAL
c o w ne sse D
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INDUSTRIAL AND ENGINEERING CHEMISTRY
sponding to the electromotive force ( 7 ) was applied to the thermocouple reading as a correction. The pressure in the vapor space was maintained automatically by means of an electric breaker circuit. A contact in the atmospheric leg of the vapor space manometer was set at such position that when the pressure in the evaporator decreased below the desired value, a relay circuit was opened. This in turn opened a solenoid-operated valve which admitted air t o the vapor head, raising the pressure to the desired point; at that time the relay circuit was closed and the admission of air stopped. Steam pressure and liquor level were manually controlled by the operator. Steam condensate and overhead drips were collected in calibrated cylindrical tanks (D,C , G, and F of FiFure l), equipped wTith gage glasses, which permitted the level t o be read, and therefrom, the weight of condensate collected over any given interval to be calculated. Pressures were indicated by manometers of special construction, generally used in this laboratory. They are made of 5-mm. glass tubing clamped into end blocks by rubber stoppers compressed by a follower strip of steel. The end blocks of 1 X 1 X 4 inch steel are drilled for appropriate connections to traps at the top and drain valves at the bottom. The whole assembly, together with a brass scale one meter long, is bolted to a rugged wooden back. In all measurements mercury was used under air saturated with water vapor at the pressure of operation. Such a manometer (inverted) was also used on the Pitot tube; thus each glass tube became a gage glass under a loop of vapor, since the usual bottom block was connected to the vapor space of the evaporator. A Pitot tube was used to measure the flow of liquid because it introduced less hindrance to flow than any other usable device. It was constructed of brass tubing (No. 12 Birmingham wire gage with No. 26 gage wall). It was necessary that the leads be brought out of the evaporator below the liquid level in order to avoid vaporization in the tubes. This would result since the pressure in the tubes would be less than in the vapor space, owing to the negative head of water in that part of the tube above liquid level. The impact jet of the Pitot tube was bent into a loop one inch above the end; the suction jet was straight, and the ends of both were tapered for streamlining. They were held in proper relation to one another by being silver-soldered to a nickel plate 0.5 inch long, 0.15 inch wide, and 0.03 inch thick. The center line distance between the jets was therefore maintained at 0.25 inch. The whole assembly was supported in an evaporator tube 3 inches from the bottom, by loops of No. 16 Chrome1 wire silversoldered to the to of the Pitot tube. These loops were of such size that they wo& s ring against the inside tube wall and hold it parallel to the line of iow, in which position it was placed (Figure 3) *
The velocity head in the tube was indicated by two gage glasges, each connected between one jet of the Pitot tube and the vapor space of the evaporator. The level in each varied with the level in the evaporator, but the fairly steady difference between the two gave a satisfactory measure of the velocity of liquid circulation. The Pitot tube was calibrated under conditions as nearly identical with operating conditions as it was possible to attain outside the evaDorator. The calibration amaratus consisted of a length of 2.5-iGch pipe connected by a flaige t o a 6-inch pipe. The Pitot tube was inserted 3 inches from the end of the smaller pipe, and water was pumped through the assembly. The 2.5-inch pipe was chosen since it had nearly the same diameter as the evaporator tubes. By calibrating over the velocity range indicated by a preliminary trial in the evaporator, the effect of stream contraction could be eliminated. The 6-inch pipe was chosen to give the same reduction in area as would obtain when the Pitot tube was installed in the basket. A logarithmic plot of the indicated head us. the linear velocity of the water pumped was a straight line, of which the slope was 0.5 (Figure 4).
Operating Procedure Measurements for one condition were made over a 20minute interval, and the averages were taken for the readings during that period-ten readings on each manometer, five on each thermometer, and four or more on the traveling thermocouple for the liquor temperature at each position in the tube. These measurements were taken after sufficient time was allowed for the evaporator to reach stable conditions. The last measurement t o respond to any change in operating conditions was the temperature of the overhead drips; after this temperature had remained constant for 5 minutes with operating variables constant, it was assumed that steady
209
operation had been attained. At the start and end of the run the drip tanks were gaged, and on alternate minutes through the operation period manometers were read on the vapor space, steam space, and Pitot tube. Temperatures were recorded for the feed, steam drips, and overhead drips every 4 minutes, since these were substantially constant. Also, the variation of the liquor level from the predetermined value was observed and recorded throughout the run. These readings allowed the calculation of coefficients and rate of circulation for known conditions of temperature drop, boiling point, and liquor level. The temperature of the liquid was measured at 6-inch intervals along the center line of the tube as rapidly as it was possible to balance the potentiometer. The thermocouple was in direct contact with the liquid, and there was no observable lag in reading. Thia gave accurately the temperature of the liquid and hence a true temperature drop measurement, in addition to the usual apparent temperature drop calculated on the basis of vapor head pressure. Measurements were made with vapor head temperatures of 140°, 155', 170", 185', and 205' F. with liquor levels from 12 inches below the top tube sheet to 20 inches above, over the range of temperature drops practically operable for the unit (15" to 45" F.),ordinarily a t 10" F. intervals. At the start of the investigation there were 110 guides to the changes in the rate of circulation under the effect of changes in liquor level, except the variation of the coefficient reported by Badger and Shepard (2) and the theoretical analysis by Webre and Robinson (18). Operating levels were arbitrarily chosen at 4-inch intervals from the top tube sheet, and measurements were made a t these liquor levels in the early part of the experimental work. Measurements made at three boiling points indicated that the decrease in circulation was quite regular as the liquor level was lowered, but that the change was rapid for levels just above the top tube sheet. When this was discovered, the choice of levels for measurement was altered to give a greater concentration of work in the region of maximum circulation. During later measurements, data were taken a t 6-inch intervals below the tube sheet and at 3-inch intervals above. The limits of liquor level studied include the conditions of operation for most commercial evaporators. There is theoretical interest but little practical value in extending the range of conditions studied downward through the generally recognized peak in coefficients which occurs at a liquor level about one-third of the height of the tubes, since operation with such a level is complicated by severe salting or scaling of the tubes with the solid contained in the liquor. Measurements of circulation were subject to three difficulties. For satisfactory operation it was found necessary to use the Pitot legs full of water, and since the tube was of rather small diameter the response of the manometer to the small heads available resulted in some lag in the reading. At first, considerable difficulty was experienced in eliminating all air pockets from the leads, but a technique was later developed for purging these pockets by means of the liquid in the evaporator which contained no dissolved gases. As a consequence, it is felt that the danger of air pockets in the leads was negligible on the runs which were accepted. Results of these runs and calculations leading to the correlation are shown in Table 1.1 Despite frequent cleanouts, some difficulty was encountered from the accumulation of a small amount of iron oxide in the condensate water used for the experiments. Occasionally a small particle of rust would block the Pitot tube. When the flow of water into or out of the Pitot tube was impeded, the manometer responded more slowly to changes in 1 Only selected rune are reported here. The complete table of data will be given in the February 25, 1939, issue of the Trans. A n . Insc.
Cham. Engre.
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VOL. 31, NO.2
SILVER-SOLDERED
..
s g9
BRASS TUBE
16 CHROMPL WIRE
ILVER-SOLDERED ITHARGE 8 GLYCERINE T.C. JUNCTION PULLING BRIDLE
16 CHROMEL WIRE
B
FIGURE2. TRAVELING THERMOCOUPLE
velocity, and erroneous readings resulted. These factors led to the discrediting of certain runs which were obviously in error. Some of the runs which appeared acceptable were vitiated by an inherent tendency of the evaporator t o surge and boil unsteadily a t particular operating conditions. This was especially noticeable in runs boiling a t 170" F. with the liquor level a t the top tube sheet and a t 205" F. with the liquor level 6 inches above the top tube sheet. The coefficients so measured checked in trend the coefficients reported by Badger and Shepard (2) and by various other investigations of similar evaporators. That is, coefficients increased with increasing boiling point, with increasing temperature drop, and with decreasing liquor level. The rates of circulation followed the coefficients in that they increased with boiling point and with tempersture drop. With varying liquor levels, circulation was found to reach a maximum when the liquor was slightly above the top tube sheet and decreased a t an approximately uniform rate as the liquor level was changed from this point in either direction. Results from these measurements of rate of circulation were inspected for consistency by plotting liquid velocity against temperature drop for lines of constant liquor level and constant boiling point. One such typical plot is shown in Figure 5 . Discrepancies from
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INDUSTRIAL AND ENGINEERING CHEMISTRY
MANOMETER READING
- MM
211
plus the hydrostatic head of the fluid above the liquor for most conditions of evaporation, it was concluded that most of the heat transfer was to nonboihg liquid. For this reason it was desirable to arrive a t an equation expressing the effect of changes in Prandtl number, which would parallel the Dittus and Boelter equation.2 Investigation of the relation of liquid velocity to coefficient by plotting these two against one another for conditions of constant boiling point and constant liquor level indicated that the coefficient was proportional t o t h e l i q u i d velocity raised to the 0.35 power as expressed by the equation:
OF WATER
FIGURE 4. CALIBRATION OF PITOT TUBE
U , = ~ 0 . 3 6 4 (boiling point and liquor level) (3)
FIGURE 3. PITOT TUBE
In order, then, to arrive a t a relation connecting the coefficient with the P r a n d t l number raised to the 0.4 power, it was necessary that the liquid velocity be proportional to the Prandtl number raised to the 1.15power.
smooth curves were rather small, b u t some were found which led t o a repetition of measAtd-'F. urements a t certain FIGURE 5 . VARIATION OF LIQUIDVELOCITY WITH TEMPERATURE DROP o p e r a t i n g conditions. Cross Dlots (Figure 6) of rate of circulation against liquor level for lines of constant temperature drop and constant boiling point indicated that there was reasonable consistency among the results of the various measurements.
Correlation of Data
It was a t first hoped to arrive a t a dimensionless equation expressing the results of this study, but the investigation of only three independent variables hardly seemed to justify this in view of the complexity of the problem. From the beginning of the study, it was obvious that temperature drop was a major factor in circulation. The influence of this variable was studied by logarithmic plots of Reynolds number us. temperature drop for lines of constant liquid level and constant boiling point. A typical plot is shown in Figure 7. For all conditions studied, the average slope of these plots, all of which were straight lines, was 0.8. The slope increased slightly for higher liquor levels; the extreme slopes for all conditions studied were 0.5 and 1.1. The data were thus expressed by the equation:
0-12
-8
-4
0
LIQUOR L E V E L
).4
- INCHES FROM
i.8
+I2
+I6
KO
TOP TUBE SHEET
FIGURE 6. VARIATION OF LIQUIDVELOCITY WITH LIQUOR LEVEL 45 40
35
30
Re =
Ato0.8 q4
(boiling point and liquor level)
(2)
A consideration of this function, 4, in terms of fundamental variables involved by changes in temperature, indicated that circulation was dependent on both specific volumes of the liquid and the vapor and on Prandtl number for the fluid being boiled. Since it had been observed that the temperature of the liquid in the greater part of the tube was below the boiling point a t a pressure equal to the sum of vapor bead pressure 8 Undergraduate research on coefficients to sugar solutions in the same evaporator indicates t h a t this may not be a justifiable assumption, but that the exponent of the Prandtl number may be a s low as -0.85. The amount and accuracy of this work do not appear t o justify the use of t h a t exponent instead of 0.4; the correlation given by the use of such a negative power is not as satisfartory as the one offered. 4
25
3 a 20
/
0 V
I167 1417
BOILING POINT- 170'5 11
4
s
e
7 8 9 1 0 REYNOLDS NUMBER x IO-'
I5
FIGURE 7. VARIATIOY OF REYNOLDS NUMBERWITH
TEMPERATURE DROP
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VOL. 31, NO. 2
of being dimensionless. The data so plotted are shown in Figure 9. The empirical equation representing these data takes the form:
A plot of
against the expansion volume of the water a t various boiling points (that is, the difference in specific volumes of steam and water) A xId3(AVC) yielded almost Atc- Pr"l s t r a i g h t lines of FIGVRE 8, VARIATION OF CIRCoLATIoN slope - 1.1, This FUNCTION WITH BOILING POINT plot is shown i n F i g u r e 8, using average values only. This indicated that a t constant liquor level the value
was constant. The slight variation of these plots from a straight line indicated omission of some other factor which should be taken into account. This factor may be the thermal coefficient of expansion of the liquid, but the introduction of the Grashof group did not g h e a correlation. The importance of surface tension and interfacial tension has been recognized (&,IO,16), but there is no agreement as to the exact relation. Attempts to measure the effect of surface tension in the basket-type evaporator by evaporating "Duponol" solution were unsuccessful because of severe foaming. Interpretation of the effect of liquor level is complicated by a lack of understanding of the factors entering into the friction of unregulated turbulence which occurs in operations a t high liquor levels. It was thought possible to represent the effect of liquor level on rate of circulation over the range investigated by a simple empirical formula since a plot of these data took the form of a parabolic curve. Submergence ratio-i. e., the ratio of the total height of the liquid above the bottom tube sheet divided by the length of the tube-was substituted for the simple linear measurement of the depth of liquor from any convenient basis point, since this seems to be a more nearly fundamental quantity and has the further advantage
ReVjg'.'
At,0.8 p~1.16=
a
+ b R, + c
(4)
~~2
where a, b, and c are constants to be evaluated. Substitution of numerical values in this equation yields:
g,,,,6
bt,o.s Rev
1.1
= 1.597 (2.204 Ra-R,'
- 1.006) lo6
The function as determined indicated that the maximum circulation occurs with the liquor level a distance above the top tube sheet approximately equal to the width of the annulus of this evaporator. This leads to the presumption that a sounder equation would result if, rather than a submergence ratio referred to tube length, the basis were taken as the tube length plus that height of liquid which would give smooth weir flow just filling the annulus. This factor remains to be investigated by the use of baskets of different sizes, or by the insertion of cylinders t o reduce the width of the annulus. Since for design purposes it is desirable to be able to predict a coefficient for known boiling point, temperature drop, and liquor level conditions, a function relating these appears desirable. Plots of over-all coefficient against temperature drop indicated that the coefficient was proportional to Plotting the value
against specific volume for constant liquor level gives lines with a slope of -0.37 (Figure 10). The arbitrary choice of the exponent for the Prandtl number was on the basis of temperature measurements which indicated that most of the heat was transferred to nonboiling liquid. In order to parallel the Dittus and Boelter equation the same exponent (0.4) was selected for the Prandtl number. The variation of coefficients with liquor level was studied by plotting this function against submergence ratio as shown in Figure 11. The empirical equation for this correlation is
400
40 0
350
350
300
300
250
250
200
I50
150
100
IO0
50 0.7
50
0.8
0.9
I .o
1.2
1.1
R,- SUBMERGENCE
1.3
RATIO
FIGURE 9. VARIATION OF CIRCULATION FUNCTION WITH SUBMERGENCE RATIO
IA
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INDUSTRIAL AND ENGINEERING CHEMISTRY
Application of this equation to a design demands a knowledge of actual liquid temperature. Investigation of the data has revealed no quantitative expression for the difference between the vapor temperature and the average liquid temperature. Qualitatively this difference appears to average about 1O F. for operation with the liquor level near the tube sheet. If this correction is subtracted from the apparent temperature drop, the error introduced by using this result as the corrected temperature drop becomes very small, since it enters the expression to the power 0.22.
Discussion of Results The explanation of the unexpected difference in behavior of circulation and coefficient as the liquor level is lowered probably lies in the increasing fraction of the stream evaporated a t lower levels of operation. An interpretation of this effect would require a knowledge of the viscosity of a water-steam mixture in an unknown state of subdivision, and of varying proportions up the tube. We have chose ver the I
I
I
I
I
I
I
1
%,cu.FT./LB.
FIGURE 10.
VARI.4TION OF COEFFICIENT FUXCTION WITH
BOILING POINT
entire length of the tube the Reynolds number for water instead of attempting to arrive a t a true average value. The error thus introduced appears defensible] since most of the tube is filled with nonboiling liquid, and the fraction evaporated is small. The range of this fraction evaporated is 0.001 to 0.0025, and much of this evaporation occurs after the liquid has left the tube. The expressions derived for rate of circulation and for coefEcient of heat transfer imply that both of these d u e s increase with heavier loading of the evaporator. Many investigators report decreasing coefficients with extremely heavy loading and attribute the decrease to blanketing action of vapor formed on the heating surface and to decreased circulation as a result of friction from the largely expanded stream. These reports were based in most cases on apparatus which was small or which did not allow free circulation of the boiling stream parallel to the heating surface. No such phenomenon has been observed in vertical-tube evaporators, in which the circulation, parallel to the tube axis, prevents the formation of a blanketing film of vapor a t temperature drops in practical use. The correlation on the basis of temperature drop and physical properties of the liquid being evaporated is considered t o be of greater utility to the designer than a relation between coefficient and circulation, such as was offered by Linden and Montillon. Their investigation, however, was on the much more sound basis of film measurements and is consequently better suited to fundamental analysis. I n contrast with the work of Linden and Montillon, this research was made with an evaporator whose size and operating conditions approached commercial practice. The desira-
213
bility of measuring film coefficients in the evaporator was and is recognized. Comparison of the measured over-all coefficients with expected steam film coefficients indicates that the resistance of the liquid film controls heat transfer. On this basis it was decided to forego the measurement of film coefficients, since a calandria permitting their measurement was not available. The construction of such a basket was considered too elaborate a program without more knowledge of the importance of certain variables and more certainty of the feasibility of the whole program. When a theoretical evaluation of the “drag forces” of bubbles rising in a liquid is made and confirmed, it will undoubtedly include other density relations for the fluid and its vapor instead of the simple difference in specific volumes. When made, this modification will represent a refinement of the present prediction. The difference in specific volumes is important in determining bubble size, as well as the available head for causing circulation, and hence is cohsidered to be the most important single property for correlation a t this stage of the investigation. That portion of the driving force of circulation originating in the difference in density between the fluid in the annulus and in the tube can be approximated, but an accurate evaluation of the drag force of rising bubbles has not been made. Fritz (8) developed an expression for the maximum aize of bubbles in terms of fairly readily available data. High-speed photography has reached such a point of developmert that it is possible to study accurately the shape assumed by rising bubbles. Application of these techniques should make possible the computation of the lifting force by the methods of hydrodynamics (6). The solution will not be straightforward but will involve a trial-and-error solution. Even so, it should be more satisfactory than the application of any available air-lift formula. The action probably parallels airlift action, but computations (14,17) now used on lifts involve exponential functions of submergence, and it should be borne in mind that the boiling length of the tube is far from constant.
0.75
0.8
0.9
I 1.1 1.2 SUBMERGENCE RAT1 0
1.3
1.4
5
FIGURE11. VARIATION OF COEFFICIENT FUNCTION WITH SUBMERGENCE RATIO
The existence of turbulence effects in the bottom of the evaporator must be recognized. There is no measure of the energy dissipated by the conflicting horizontal flow of liquid over the top of the basket and upward flow of liquid out of the tubes. The observation that maximum circulation was attained with the liquor level a distance above the top of the calandria approximately equal to the width of the annulus indicates that the weir action of the edge of the basket may exercise an important influence on the turbulent flow across the tube ends. The unproved hypothesis is advanced that the maximum velocity occurs a t such apparent liquor level as will result in smooth weir action, witli the liquid flowing off of the calandria and just filling the annulus.
INDUSTRIAL AND ENGINEERING CHEMISTRY
214
The use of an empirical parabolic function in terms of basic quantities such as this research has developed, appears to be a satisfactory method of expressing the effects of changes in submergence ratio on the rate of circulation and the coefficient of heat transfer.
Nomenclature a, b, c = = C, = D = h
constants specific heat of liquid (9) inside diameter of tube, ft. film cpefficient of heat transfer, B. t. u./(hr.)(sq. ft.) IQn\
1.J
= thermal conductivity (16)
k R,
submergence ratio apparent over-all temperature d$p, O F. true over-all temperature drop, F. ap arent over-all coefficient of heat transfer, €3. t. u./ phr.) (sq. ft.) ( O F.) = true over-all coefficient of heat transfer, B. t. u./(hr.) (sq. ft.) ( O F . ) = liquid velocity, ft./seq. = difference in specific volumes of steam and water, cu. ft./lb. = mean velocity = volumetric coefficient of expansion 1/ F. =’a general function = viscosity of water, lb./(ft.)(h.) (9) = density of water, lb./cu. ft. (13) = Prandtl No. = C,p/k in consistent units = Reynolds No. = D u p / ~in consistent units = = = =
Ata At0
U.
UC
P
Pr Re
Literature Cited (1) Badger, W. L., “Heat Transfer and Evaporation,” New York, Chemioal Catalog Co., 1926.
VOL. 31, NO. 2
(2) Badger, W. L., and Shepard, P. W., C h m . C Met. Eng., 23,237, 281,390 (1920). (3) Boarts, R. M.,Badger, W. L., and Meisenbefg, S. J., Trans. Am. Inst. C h m . Ew.,33,363 (1937). (4) Cleve, Mitt. u. Forsch&gsarb., 322, 1 (1929). (5) Cryder, D.S., and Gilliland, E. R., IND. ENQ.CHBM.,24, 1382 (1932). (6) Dodge, R. A., and Thompson, M. J., “Fluid Mechanica,” New York, McGraw-Hill Book Co., 1937. (7) Foote, P. D.,Fairchild, C. O., and Harrison, T. R., U. S. Bur. Standards, Tech. Paper 170 (1921). Physik. Z., 36, 379 (1936). (8) Frite, W., (9) International Critical Tables, New York, McGraw-Hill Book co., 1929. (10) Jakob, M.,Mech. Eng., 58, 643 (1936). (11) Kirschbaum, Krans, and Starck, Forsch. Gebiete Ingenieurw., B6, Forschungsheft 375, 1 (1935). (12) Linden, C. M., and Montillon, G. H., Trans. Am. Inst. Chem. Engrs., 24, 120 (1930). (13) Peabody, “Steam and Entropy Tables,” (in Hodgman and Lange’s Handbook of Chemistry and Physics, 18th ed., Chemical Rubber Pub. Co., Cleveland, 1934). (14) Perry, J. H.,Chemical Engineers Handbook, New York, McGraw-Bill Book Co.. 1934. (15) Schmidt, E., and Sellschopp, W., Forsch. Gebiete Ingenieurw., 3,277 (1932). (16) Stroebe, G. W.,Baker, E. M., and Badger, W. L., IND.ENQ. CHEM.,31, 200 (1939). (17) Ward, C. N., and Kesaler, L. H., Univ. Wis., Bull. 9,No. 4 (1924). (18) Webre, A. L.,and Robinson, C. S., “Evaporation,” New York, Chemical Catalog Go., 1926. RECEJVED November 3,1938. Presented before the meeting of the American Institute of Chemioal Engineers, Philadelphia, Pa., November 9 to 11, 1938. Submitted by A. 8. Foust in partial fulfillment of the requirements for the Ph.D. degree, Univeraity of Miahigan.
Steam-Film Heat Transfer Coefficients for Vertical Tubes E. M. BAKER, E. W. KAZMARK,lAND G. W. STROEBEl University of Michigan, Ann Arbor, Mich.
T
HE application of heat transmission from condensing
steam to vertical tubes is found primarily in the various forms of vertical tube evaporators, although condensers are occasionally built to operate in this manner. The data available on heat transfer through condensed steam films outside vertical tubes are rather limited. This is possibly due to the fact that interest has centered on the heat transfer through the films on the inside of such tubes, which have usually offered greater resistance than the steam films, as shown by the generally lower liquid film coefficients. However, with the development of the forced-circulation and the long-tube vertical evaporators, the liquid-ftlm coefficients have been increased until they are of the same general magnitude as the steam-film coefficients, and the latter have acquired increasing importance. I n the accompanying paper by Stroebe, Baker, and Badger (Y), dealing with boiling-liquid-& coefficients in a long-tube vertical evaporator, the liquid-film coefficients were consistently 50 to 100 1 Preaent
address, 804 Hudson Avenue, Rochester, N. Y. Present address, Standard Oil Company of California, Riohmond, Cahf.
per cent greater than the steam-iilm coefficients. In such a case the latter coefficients are controlling, and it is important that the designer have some knowledge of the behavior of steam-film coefficients for such tubes. There is little agreement among the available data on heat transfer coefficients for steam condensing on vertical tubes, and there have been few attempts to find a correlation between various sets of data. Most of the correlations have been based on the theoretical equations developed by Nusselt, though few have agreed with these equations; the majority of the data has given coefficients somewhat higher than predicted by the Nusselt relation. Hebbard and Badger (4) obtained some consistent results using steam outside a 12-foot long, 1-inch 0.d., vertical tube. Their results checked the Nusselt equation, if a constant factor of 1.2513 was applied. However, as pointed out in a discussion of this paper by McCormick (6),other data, using different types of apparatus, have been correlated satisfactorily with the Nusselt equation by applying factors different from that used by Hebbard and Badger. Apparently
