INDUSTRIAL AND ENGINEERING CHEMISTRY
1044
ACKNOWLEDGMENT The author wishes to acknowledge the assistance of H. H. Thompson and L. V. Sorg, who aided in the gathering of data herewith presented. Thanks are also due Mr. Sorg for the drawings.
LITERATURE CITED (1) Am. SOC. Testing Materials, Proceedings, 32, 407 (19.32) (2) Gray, T . T . , U. S. Patents 1.340,889 (1920); 1,759,812, 1,759,813,
Vol. 26, No. 10
1,759,814 (1930); 1,853,671 (1932) ; 1,908,599 (1933); Mandelbaum, M . R., paper presented before World Petroleum Congress, July, 1933; Cooke, M. B., and Hayford, A. W., Refiner & Natural Gasoline M f r . , 13, 83 (March, 1934). (3) Rogers, Bussies, and Ward, IND.ENQ.CHEM.,25, 397 (1933). (4) Sorg, L. V., paper presented before Division of Petroleum Chemistry a t Twelfth Midwest Regional Meeting of Am. Chem. SOC., Kansas City, Mo., May 3 t o 5, 1934. RECEIVEDMay 25, 1934. Presented before the Division of Petroleum Chemistry at the Twelfth Midwest Regional Meeting of the American Chemical Society, Kansas City, Mo., May 3 to 5 . 1934.
Liquid Film Heat-Transfer Coefficients in a Vertical-Tube Forced-Circulation Evaporator L. A. LOGAN,'N. FRAGEN, AND W. L. BIDGER,University of Michigan, Ann Arbor, Mich. Film heat-transfer coeficients f o r liquids in forced convection through 8-foot, 0.75-inch i. d., vertical copper tubes hare been measured directly in a semi-commercial evaporator and correlated within *10 per cent by means of the following dimensionless equation:
hD/k
=
properties of the liquid, and an equation for liquid film coefficients based on the physical properties has been found to have wide application. Consequently this investigation was conducted for the purpose of obtaining a correlation of the liquid film coefficients in evaporators by means of an equation involving the physical properties of the liquid being evaporated.
0.0205 (Dup/p)O (C,u/k)O
This equation applies with the aboiie accuracy between the following limits: Reynolds' number, 7500 to 250,000; Prandtl's number, 2 to 50; liquor inlet velocity, 7 to 17 feet per second: riscosity, 1 to 20 pound-7 per hour per foot.
T
HE available data on heat transfer through liquid
films deal almost entirely with nonboiling liquids. Some information may be found in the literature concerning liquid film coefficients for boiling liquids. The latest contributions in this field were made in 1931 by Jacob and Fritz (5) and in 1932 by Cryder and Gilliland ( 3 ) . Linden and hlontillon ( 7 ) also measured the individual film coefficients in an inclined-tube natural-circulation evaporator. Both of these investigations showed that with natural circulation the values of the liquid film coefficients increase with increases in temperature drop. There is also considerable information available on over-all coefficients in evaporators. Badger and Shepard (1) and Linden and Montillon (7') found that over-all coefficients increased with increased boiling temperatures. Claassen ( 2 ) and Kerr (6) studied the effect of the concentration of boiling sugar solutions on the over-all coefficients and found that an increase in the percentage solids caused a decrease in the coefficient. It is probable that the changes in over-all coefficients with changes in boiling point and concentration are due mostly to the effect of these variables on the liquid film coefficient. The earlier investigations of heat-transfer coefficients in evaporators expressed the changes in the coefficient in terms of the previously mentioned variables-namely, temperature drop, boiling point, and concentration. Expressions involving these variables limit the application of the results obtained to the particular liquid being evaporated. A change in the variables causes a change in the physical 1 Present address, Union Carblde and Carbon Research Laboratories, Inc , Long Island City, New York.
TO STORACE
FIGURE 1. E V A P O ~ A AND T O RFLOWSHEET 110-gallon feed tank with heating cojl 2. Belt-driven centrifugal feed pump 3. Kinney positive pressure circulatinn DumD 4. Main bo& of evaporator 5. Surface condenser 6. Jet condenser 7. Wet vacuum pump 8. Upper section of heating element 9. Lower section of heating element 10. Asbestos insulation 1.
11.
12. 13. 14. 15.
16.
A.
B. C.
Twelve capper tubes 8 feet long. eleven tubes '(8 inch 0.d.,'16 B.W. G . (Birmingham wire gage) wall: one tube 1 incho. d . , 11 B. W. G. wall, Steelshell around upper casting Steam baffle Sampling tube Steam drip tanks Overhead drip tanka Vacuum manometer with arrangementa for automatic oontrol Pressure drop manometer Steam pressure manometer
October, 1934
1045
INDUSTRIAL AND ENGINEERING CHEMISTRY
The physical properties that are considered t o affect the film heat-transfer coefficient most a r e the viscosity, thermal conductivity, specific heat, and density of the liquid. I n order to obtain a wide range of values of those physical constants, sucrose solutions were used at rarious concentrations and t e m p e r a t u r e s . The physical constants were determined from known relationships with the concentration and temperature of the solution.
I
EXPERIMEKTAL PROCEDURE The experimentd unit used was a Swenson semi-commercial forced-circulation e v a p o r a t o r with a heating surface of 18.4 square feet. Figure 1 is a diagram of the evaporator and the flow sheet used for these experiments. Since the upper section of the heating element is surrounded by the boiling liquid, it had to be insulated to prevent the flow of heat through the walls of the casting t o the liquid. This was accomplished by building a shell of sheet steel around the heating element and filling the space between the shell and the casting with several layers of asbestos paper. The flox sheet is self-explana-
FIGURE 2 . DIMENSIONLESS
PLOT OF
RUNS
each run. These samples were cooled and the percentage sugar determined by means of a Brix hydrometer.
tnrv. I _ _
'fhe tube wall thermocouples were installed by the method The tube wall temperatures and liquid temperatures were developed recently by Hebbard and Badger (4). This installa- plotted against distance from the bottom of the tube ( r' I' gure tion gave consistent and accurate results. Single couples were also placed in the suction line to the pump, in the steam line on 5), and the area between the curves was determined by the low-pressure side of the control valve, and in the liquor just graphical integration. This area, divided by the tube length, below the lower tube sheet. A means was devised for measuring gave the true average drop in liquor film temperature. the temperature of the liquid in the tubes a t intervals from the bottom of the tubes to the top. This consisted of a thermoCORRELATION OF DATA couple mounted in the end of a aO-foot, 0.25-inch 0 . d. nickel tube which could be moved up or down inside one of the 0.75-inch The data were correlated by the following equation which tubes in the evaporator. The readings of all thermocouples has been derived by means of dimensional analysis, and is were made with a Leeds & Northrup type K potentiometer. It was found while making preliminary test runs that, owing to usually known as the Dittus and Boelter equation (8): radiation losses and moisture in the steam from the low-pressure hD/k = T (Dup/p)"' ( C p / k ) " mains, consistent heat balances were not obtained. To decrease the radiation losses, the portion of the steam chest exposed to the The dimensionless groups were first calculated for each run air was lamed with a laver of magnesia. and the steam was taken from the KGh-pressure line a t 1255ounds per square inch. It was and plotted as in Figure- 2. This plot gave three separate then found that the steam entering the heating element was always bands for the three series of runs at different concentrations of superheated. The degree of superheat was measured by means of The approxinlate 'lope Of each Of these bands is Oa8* a thermocouale in the steam line. All subseauent heat balances "gar. checked n,ithin 10 Assuming that the exper cent. p o n e n t of Reynolds' In the experimental criterion (Dup/,u) was procedure, the principal 0.8, t h e d a t a w e r e variables and the ranges plotted as in Figure 3. covered were: concenThis drew all the points tration of sugar in solution, 20 to 65 per cent; into one band which apparent boiling point of h a d ' a n approximate the solution, 160"to 210" F.; ve1ocit)y of liquid slope of 0.4. entering the tubes, 7 to Assuming t h a t the 17 feet per second; and exponent of Prandtl's apparent over-all temcriterion ( C p / k ) was perature drop, 5" to 42" 0.4, it was then necesF. The system of changing these variables was sary to recheck the exsuch that sets of experi0 p o n e n t of Reynolds' ments could be found in number. T h i s was which any three Of the FIGURE 3. DIMENSIONLESS PLOT O F R U N S WITH REYNOLDS-CRITERIONdone by means of Figvariables were constant, EXPONENT OF 0.8 ivhile the fourth covered ure 4. It was found the entire range. that the best slope for The experimental runs were all made in pairs. The normal this band was still 0.8. The values of the exponents are now length of a single run was 15 minutes. The steam drips were and 72 = 0.4* The Of were read at the beginning, at the end of the first run, and at the end of fixed at the second run. The second run in each case was merely a con- lated for each run, and the average of these values was found tinuation of the first but was calculated separately. The POt o be 0.0205. The final equation is: tentiometer readings taken during each run were for the liquor inlet, liquor outlet, steam, tube couples, and nine positions of the h D / k = 0.0205 ( D ~ p / g ) "(Cplk)'.' ~ (1) traveling liquor couple. It was found possible to read each of these two or three times during each double run. Distilled water Of the 400 runs which were completed, 271 were CaIculated. was introduced as feed a t a rate equal to the rate of evaporation. Of these 271 runs, 201 Rere correlated by the above equation Thus by maintaining the constant liquor level, the concentration t'o within * 10 per cent and 117 t o lVithin* per cent. of sugar in solut,ion was kept fairly constant during the run. Mcddams (8) recommends the following equation as the Samples of the solution were taken at the beginning and the end of
1046
INDUSTRIAL AND ENGINEERING CHEMISTR Y
Vol. 26, No. 10
degree of accuracy the rate of heat transfer to the supposed boiling section. The reason for this was that the length of the nonboiling section is about seven times that of the boili n g s e c t i o n , and thus the calculations involved the subtraction of two large quantities w h i c h w e r e n e a r l y equal. However, the liquid film coefficients calculated by the equation resulting from this investigation (Equation l ) are so little different from those obtained for nonboiling liquids under the same conditions (Equation 2) that any such effects in the boiling section are of little importance. The correlation resulting in Equation 1 was not based on theoretical considerations but is merely an empirical means of best representing the experimental results of this investigation. Since Equation 1 is almost entirely empirical, it can be applied only to 8-foot tubes of 0.75 inch inside diameter. A l i m i t a t i o n exists in the application of Equation 1 in the calculation of liquid film heat-transfer coefficients in forced-circulation e v a p o r a t o r s . The equation is based on a mean drop in liquid film temperature determined by measuring the change in liquor temperature as i t passes through the tube. Only the apparent temperature drop based on the FIGURE4. PLOTFOR CHECKING REYNOLDS-CRITERION EXPONEXT temperature of the liquid in equilibrium with best general correlation for the heating of nonboiling liquids vapor at the pressure existing in the vapor space of the evaporator can be readily obtained or estimated. Table I shows in turbulent flow in horizontal pipes: both the apparent temperature drop and the actual mean hD/k = 0.0225 (Dup/p)O.* ( C ~ l k ) ' . ~ (2)
The coefficients calculated by means of this equation are slightly higher than those represented by Equation 1. It might seem, therefore, that the insulating effect of the vapors in contact with the tube wall in the boiling section tends to lower the coefficients. It is also logical to assume that the boiling at the top of the tube might i n c r e a s e the velocity and agitation of the liquid to such an extent that the coefficients in this section would be increased. Figure 5 shows that the liquor temperature curves, in every case, flatten out or reach a maximum at about a foot from the top of the tubes. This might indicate that boiling commences a t this point. The vaporization of part of the liquid at this point would r e s u l t in the sudden withdrawal of heat as latent heat of vaporization. Part of this heat would be removed from the remaining liquid with a resulting lowering of the liquid temperature. This might even result in r e m o v i n g heat from the tube wall at a greater rate than the rate of absorption of heat by the wall from the steam. This would cause a lowering of the wall temperature in this section of the tube. Some of the tube temperature curves also flatten out a t the top of the tube. I n this investigation it was found impossible to approximate with any
VELOCITY
IS
7 FEET PER
SECOND
VELOCITY
IS 10 FEET PER SECOND
234
224
230
220
220
210
I
I
I
LiauoR I
TUBE
TUBE
I
!
I
I
1 LOO
190
190
180
160
a
150
0
4 DISTAHCE ABOVE
THE BOTTOM
OF
THE
TUBES
N
FEET
FIGURE 5. TEMPERATURE DISTRIBUTION CURVES The apparent,over-all A T for these runs is 20' F. The legend for the concentration of solutions (in per cent sugar) is as follows: 0 = 18-20 48-50 A 00-06
-
IN D USTR I A L A N D EN G IN EE R I N G CH E M I ST R Y
October, 1934
temperature drop. No obvious relation seems to exist. The correlation of the liquid film heat-transfer coefficients calcu-
LIQUIDFILMTEMP Apparent True F. ' F. 24.4 18.7 16.4 21.9 20.6 16.7 18.6 15.1
OVER-ALL TEMP. -4pparent True F. F. 42.1 36.4 42.1 36.6 42.2 38.3 42.3 38.8
AP140 AP240 AP340 AP440
lated on the basis of the apparent temperature drop will be the subject of a later paper. .kCBNOWLEDGMENT
OF APPARENT AKD TRUE TABLE I. COMPARISON TEMPERATURE DROPS
RUN No.
1047
BP140 BP240 BP340 BP440
42.2 42.3 42.3 42.3
34.6 35.2 36.1 36.9
30.7 28.9 25.2 23.4
23.1 21.8 19.0 18.0
CP140 CP240 CP340
42.6 42.6 42.5
32.4 32.3 31.2
36.0 33.4 31.8
25.8 23.1 20.5
4L140 AL240 .4L340 -4L442
42.2 42.6 42.0 42.0
36.1 37.5 37.5 38.0
30.4 22.8 18.8 18.2
24.3 17.7 14.3 14.2
BL140 BL240 BL340
41.5 42.0 41.9
34.7 35.4 39.1
31.6
29.0 23.7
24.8 22.4 20.9
BL160 BL260
60.4 62.6
53.1 53.6
45.0 42.7
37.7 33.3
CL144 CL542 CL642
43.1 43.2 43.2
33.1 32.5 32.1
36.7 34.7 33.1
26.7 24.0 22.0
Appreciation is expressed to W. R. Kleckner and E. D. Allen for their assistance in obtaining the experimental data. Especial acknowledgment is also made to the National Research Council for a Grant-in-Aid that greatly expedited this work. LITER.4TURE CITED (1) Badger and Shepard. Trans. A m . Inst. Chem. Enyi's., 16, 159 (1928). (2) Claassen, Mitt.Forschungsarb., 7, 75 (1902). (3) Cryder and Gilliland, IND.ENG.CHEM.,24, 1382 (1932). (4) Hebbard and Badger, Ibid., Anal. E d . , 5 , 359 (1933). ( 5 ) Jacob and Fritz, Forsch. Gebiete Ingenieurw., 2, 434 (1931). (6) K e r r , E. W., Trans. A m . SOC.Mech. Engrs., 35,731 (1913). (7) Linden and Montillon, Trans. Am. Inst. Chem. Engrs., 24, 120 (1930). (8) McAdams, " H e a t Transmission," p. 169, McGraw-Hill Book Co., New York, 1933. RECEIVED July 26, 1934. Presented before the Division of Industrial and Engineering Chemistry a t the 88th Meeting of the American Chemical Society, Cleveland, Ohio, September 10 to 14, 1934. This article is part of the dissertation submitted by L. A. Logan in partial fulfilment of the requirements for the degree of doctor of science in the University of Michigan.
White Lead Effect of Chemical Structure on Physical Properties A. W. ,~NDERSOR;,Anaconda Zinc Oxide Department, International Lead Refining Company, East Chicago, Ind.
W
HITE lea,d is a basic carbonate of lead in which are
found two components: lead carbonate is considered crystalline, while lead hydroxide is considered amorphous. There are some differences of opinion as to the reaction involved in the formation of basic carbonates of lead. According to Liebig (5) it proceeds as follows:
+
+
Pb ~ C H ~ C O O H - + P ~ ( C H I C O O ) ~ Hz 2Pb(CHaC00)2 ~H~O+P~(CH~COO)~.P~I(OH)~ 2CH8COOH 3Pb(CH3COO)a.Pb(OH)2 4C02+2[2PbC03,Pb(OH)c] GCH&OOH
+
+
+
FIGURE 1
+
COhSTITUTION4L
DI4GR411
It is not definitely known what the actual constitutional formula is. However, according to Heaton ( 3 ) it is probable that a definite chemical compound is not formed but rather a mixture of complex basic carbonates which come to equilibrium a t the approximate ratio of 2PbCOJ Pb(0H)n. To correspond exactly to this formula the pigment s h o d d show the folloning percentage composition, Ha0
PbO
2.32 86.32
Pb
cot
80.14 11.35
corresponding to a component equivalent (given by Lambert, 4) of PbCOi Pb(0H)n
68.9 31.1
Theoretically the above formula is correct, and, as Thorpe
(7) found, the best samples show a ratio of components of two molecules of lead carbonate to one molecule of lead hydroxide. But the basic-carbonate white leads as used in the paint trade in many cases deviate from the above theoretical 'structure. Pigments having a lead carbonate content as low as 60 per cent and as high as 80 per cent have been encountered. Beyond these limits the valuable properties of the pigment may be lost. According to A. S. T. M. specifications the maximum lead carbonate content should be 75 per cent and the minimum 65 (1). The paint manufacturer, however, is interested in basiccarbonate white lead from the standpoint of its physical prope r t i e s , s u c h as oil a b s o r p t i o n , tinting s t r e n g t h , opacity, etc., rather than the c h e m i c a l structure. Severtheless, i t has been found that the physical p r o p e r t i es of w h i t e l e a d a r e FIGURE 2. SIZE-FREQUENCY CURVES affected by the chemical structure. The degree and direction of this change in physical properties will follow the varying ratio of lead carbonate to lead hydroxide. It may be that the older processes of manufacture limited the chemical structure
