I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
September 1949
(57) Siefert, Mills, Summerfield, Am. J . Phys., 15,255 (1947). (58) Silver, Phil. Mag., 7, 23,633 (1937). (59) Smith, Chem. Revs., 21,389 (1937). (60) Stipe, L'Aerotechnique, 7,191,141 (1938). (61) Tanford, J. Chern. Phys., 15,433 (1947). (62) Tanford and Pease, Ibid., p. 431. (63) Taylor and Maccoll, "Aerodynamic Theory," Division H., Vol. 111, edited by W. F. Durand, reprinted ed., Calif. Inst. of Technol., 1943. (64) Topler, Ann. Physik., 9, 502 (1880). (65) Townend, Chem. Revs., 21, 259 (1937). (66) Turner and Lord, Natl. Advisory Comm. Aeronaut., Tech. Mem., 1086 (1946). (67) Von Elbe and Mentser, J . Chem. Phys., 13,89 (1945).
1945
(68) Wang, J . Applied Mechanics, 13,A-85 (1946). (69) Wattendorf, Calif. Inst. Technol., Guggenheim Aeronautical Laboratory, Publication 45. (70) Way, "Open Duct Jet Propulsion," Westinghouse Research Report, SM-101 (July 1941). (71) Way, "Preliminary Experimental Study of Open Duct Propulsion Models." Ibid.. SR-114 (January 1942).
RECEIVED December 13, 1948. Presented before the Division of Gas a n d Fuel Chemistry a t the 112th Meeting of the AMERICAN CHEMICAL SOCIETY, New York, N. Y. This work was carried out for t h e Bureau of Ordnance. u. S. Navy, Contract NOrd 9756, as part of Project Bumblebee.
Heat Transfer at High Rates to Water with Surface Boiling W. H. McADAMS, W. E. KENNEL1, C. S. MINDEN2, RUDOLF CARL3, P. M. PICORNELL4, AND J. E. DEW5 Massachusetts Institute of Technology, Cambridge, Mass.
The main object of this research was to study heat transfer a t high density of heat flux from an electrically heated surface to water flowing i n annuli. I t was desired to determine the quantitative relations between density of heat flux, temperature difference, pressure, degree of subcooling, and water velocity. Degassed distilled water flowed upward through a vertical glass tube, containing a centrally located heater having an outside diameter of 0.25 inch.
T
HIS topic is of interest because of the very high densities of heat flux required i n regeneratively-cooled rockets and in other applications requiring unusually high rates of heat transfer per unit area, such as liquid-cooled aircraft engines, cyclotron targets, and apparatus for the continuous casting of steel. SURVEY OF LITERATURE
HEATTRANSFER WITHOUT CHANGE IN PHASE.For turbulent flow inside tubes or in annuli, the following equations are most widely used: Dittus and Boelter (8) for heating liquids: = 0.0265
, k
(",")"'" (y)"'"
Colburn ( d ) , for heating or cooling in tubes:
Sieder and Tate (go), for heating or cooling in tubes: (3)
Carpenter, Colburn, Schoenburn, and Wurster in an annulus:
(a), for heating (4)
Usually this equation is written as
_____ 1 9 8
4
6
Present Present Present Present Present
address, Standard Oil Company of Indiana, Whiting, Ind. address, Stanolind Oil & Gas Company, Tulsa, Okla. address, 1503 Stratford Rd., Lawrence, Kans. address, 309 Ayala Bldg., Juan Luna, Manila, P. I. address, 509 S. Locust A m . , Okmulgee. Okla.
For annuli, the equivalent diameter is taken as four times the hydraulic radius, based on total wetted perimeter. At the moderate values of At ordinarily used with heat transfer t o water, all these equations predict nearly the same values of the heat transfer coefficient. I n 1944, Hayes and Bartol ( 1 0 )employed densities of heat flux as high as 2,000,000 B.t.u. per hour per square foot and found that Equation 2 correlated their data. SURFACE BOILING.Surface or local boiling (9,1.d,16)is a form of nucleate boiling which occurs when a liquid a t a temperature below saturation is brought into contact with a metal surface hot enough to cause boiling at the surface of the heater. The vapor bubbles condense in the cold liquid and no net generation of vapor is realized with degassed liquid. Mosciki and Broder (17)were probably the first investigators to study local boiling. They used an electrically heated vertical platinum wire submerged in water at atmospheric pressure. The water temperature was varied from 68" to 212 O F. and the critical wire temperature (266' F.) a t the peak density of heat flux was essentially independent of the temperature of the water (15). With subcooled water a t 68' F. the estimated peak density of heat flux was 1,200,000 B.t.u. per hour per square foot, which was approximately seven times t h a t with water a t the boiling point. The same general effect of subcooling was noted by Nukiyama ( 1 8 ) who immersed a n electrically heated horizontal platinum wire in water a t 1 atmosphere. I n the preheating section of an experimental horizontal-tube evaporator heated externally by dropwise condensation of steam, Woods (23) found that the local over-all coefficients of heat transfer were four times those predicted for nonboiling conditions. This was explained as possibly being due t o local boiling a t the surface of the tube with subsequent condensation of the vapor in the cold liquid. Tibbetts and Cohen (22) connected a high amperage direct current generator t o a German silver tube (0.08 inch inside diameter) and passed t a p water through a t a velocity of 53.5 feet
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
1946
Figure 1.
Photograph of Test Section
per second. They attained a peak density of heat flux of 4,700,000 B.t.u. per hour per square foot before the tube melted. Taylor ($2) used an electrically heated stainless steel tube, 4.75 inches long with an inside diameter of 0.305 inch, with tap water entering at a velocity of 37 feet per second. Audible noise occurred a t a flux density of 2,000,000 and burnout occurred at 3,400,000 B.t.u. per hour per square foot. Colburn, Srhoenborn, and Sutton ( 5 ) obtained data for local boiling of tap water flowing upward a t velocities from 0.3 to 6 feet per second through an annulus having a central heated tube 1.66 inches in outside diameter and an unheated outer jacket 2.00 inches inside diameter. The heat transfer coefficients for local boiling were higher than predicted for nonboiling conditions and the increase was more pronounced with low velocity and high temperature difference. The highest flux density obtained was 69,000 B.t.u. per hour per square foot. Colburn and Gutton (6) obtained similar results nhen using methanol in the same apparatus. APPARATUS
Water was pumped through the calibratcd orifices, the prcheater, t,he test section, and the cooler and returned to the pump. The pressure in the flow circuit was maintained by boiling the water in the pressurizing t,ank a t constant, temperature, by means of a n immersion heater controlled by a thermoregulator. A pipe from the bottom of the pressurizing tank transmit,ted t'he hydraulic pressure to the flow circuit which wvas filled with liquid. The tank also served as a reservoir since it supplied any water lost by leakage from the flow system. A steam heated tank was mounted above the apparatus so that distilled matJer could be degassed by boiling before introduction into the syst,em. To prevent corrosion the flow circuit was constructed of stainless steel, and the inside of the pump was lined with enamel. TESTSECTION. As shown in Figures 1 and 2, t'he test section was a vertical annulus through which the water flowed upwards. The outer wall of the annulus was formed by heavy Pyrex tubing, 18 inches long, which was held at each end by packing glands in the large brass endpieces. The glass jackets had inside diameters
Vol. 41, No. 9
of 0.77, 0.73, and 0.43 inch. The brass endpieces permitted the entrance and exit of water from the test section and provided mountings for the insulated electrical leads. The electrical mounting in the lower brass head was provided with a flexible joint which allowed for thermal expansion of the heating unit. The heating element was centrally located mithin the outer glass tube and was supported by mountings in the endpieces. This element consisted of a Type 304 stainless steel tube, silver s o l d e i d a t its lower end to a solid copper rod and a t its upper end to a hollow capper tube. All the heating elements and copper leads 11ere 0.25 inch in diameter. M o s t of the heating elements were 3.75 inches long, had nominal wall thicknesses of 0.012 inch, and were m0untc.d to provide a 10-inch length of unheated annulus upstream of the heater. A few of the heating elements were 11.5 inches long and had nominal wall thicknesses of 0 035 inch; these were mounted to provide a 3-inch length of unheated annulus upstream of the heater. ELECTRICAL C o m o m m s . Power for the heating elements was supplied by a direct current generator rated at 15 volts and 1000 amperes. The generator had 36 commutator sections and was driven at approximately 1150 r.p.m. by an alternating current motor. The generator and exciter were equipped with rheostats which provided smooth control of the output from practically no load t o full power. Calibrated iron-constantan thermocouples were inserted through the hollow copper lead into the heating elements t o measure the temperature of the inside wall. Three or four thermocouples were equally spaced inside the 3.75-inch heating element. The 11.5-inch heater had five thermocouples spaced at 2inch intervals, starting 2 inches from the upstream (lower) end. Iron-constantan thermocouples were inserted in wells in the water stream also to measure the temperature of the water entering and leaving the test section. Prior to mounting a heating element in the test section, its length, diameter, and wall thickness were accurately measured. I n some cases (2, 16) the heating elements were calibrated to determine what fraction of the total power input to the test section was dissipated in the stainless steel. I n other cases ( 7 ) the resistance of the stainless steel portion of the heating element was measured for use in calculating the density of heat flux.
L NUT
HEAT/NG ELEMENT
COPPER
DROP TAP IS NOT SHOWN (2)ALL #ATEff/ALS ARE BRASS UNL OTHER W/SE INDICA TED PACKING N u r
L U
I
I, ,i,
INDUSTRIAL AND ENGINEERING CHEMISTRY
September 1949 I
, , ,
I
I
I , , ,
I I
TYPICAL CURVE FOR LOCAL BOILING
,
I
I
1 / I l l I I I I L
EFFECT OF V€'T'YM
-
100
I
I
I
I
I I I I
SUBCOOLING
EGASSfO DISTILLED WATER
RUN SCP. 4 F X PCR SECOND 60 P S t A , SO O F . SUECOOLED JACUET DIAMETER- 0.77 tNC.4
10
1947
60
A t ,'%
IO
io0 A t , OF
Figure 3
Figure 4 PROCEDURE
b
F
Distilled water was degassed by boiling in the degassing tank, prior to introduction into the flow circuit. The system was then flushed and filled with the degassed water. For further degassing, the water was circulated by means of the pump and boiled by means of the preheater. To remove any air which might have been trapped in the system, steam was vented a t the highest points in the cooler. The water in the pressurizing tank was boiled and some steam was vented in order to degas the water. This procedure ( 2 ) was sufficient to reduce the concentration of the dissolved air t o approximately 0.3 ml. of air per liter of water. By prolonging the degassing technique ( 7 ) , the concentration of dissolved gases could be reduced to not more than 0.06 ml. of air per liter. Samples of the water, degassed in this manner, were analyzed for dissolved oxygen by the Winkler technique. The vclocity, pressure, and water temperature were held constant while data were taken at several settings of power to the test section. The temperatures of the inside wall of the heating element and those of the inlet and outlet water were recorded. The density of heat flux from the heating element to the water was calculated from P R . For the 3.75-inch heating element, the temperature t, of the inside wall of the heating element was taken as the temperature of the central thermocouple, or as the average of the two middle thermocouples. The temperature, to, of the outside wall was determined by deducting the calculated temperature drop through the wall:
average of the temperatures of the water entering and leaving the test section. The temperature driving force, or At, was the difference between the outside wall temperature and the bulk temperature of the water. For the 1l.ri-inch heating elements the procedure was essentially the same except that outside wall temperatures of the heater, bulk water temperatuies, and values of At were determinod for the five positions a t which thermocouples were located inside the heating element. RESULTS
All the data obtained in over sixty runs ( 2 , 7 , 1 6 ) are given in tabular form in (11). Owing t o the use of stainless steel piping throughout the circuit and to the use of an enamel lining in the pump, the surface of the heater remained bright and clean throughout the runs. For conditions involving reasonably large rise in temperature of the water, heat balances closed to within a few per cent, based on total power input. Typical data are presented in the following illustrations t o show the effect of the several variables on the rate of heat transfer with and without local boiling. The runs are designated by 3 letter suffix as indicated. suffix M CP 1)
(5) or, more conveniently by
Equation 5 was derived by assuming uniform generation of electric heat, constant thermal conductivity, and constant electrical resistivity; Equation 5a follows on expansion of the logarithmic term. The bulk temperature of the water was taken as the arithmetic
BO
Inmstigator Minden Carl and Picornell Dew Special run t o determine peak density of heat flux
In all of the runs, except 14M and 15M, the water was degassed by boiling and stripping prior to use. Figure 3 defines the various regions of heat transfcr. The data are plotted on logarithmic paper with density of heat flux as abscissa. I n the range A B , the heat transfer followed thc usual laws for forced convection without surface boiling. This particular run was mnde with 50" of subcooling, which ineans that the average bulk temperature of the water was 50" F . below the saturation temperature. At a At of 50" F. the heater was
INDUSTRIAL AND ENGINEERING CHEMISTRY
1948
Vol. 41, No. 9
T
K
4 W
Q.
9
HEATING ELEMENT.
0 25 X 3 75 /NCH
io5
IO
100
600
At,OF: Figure 6
At,Y
Figure 5
t-l
A : NO SURFACE BO/IlNG
q / A = 32 000 8 7 U / CiiR)(SQ, f T.)
I-/
therefore at the snturntioii temperature, and a t \Talues of At greater than 50 O F., local boiling was tlieoreticnllg possible. Local boiling occurred in the region BC, point R representing the start of local boiling and point C representing the biiriiout of the heating element as it became blanketed with vapor. For purposes of estimation or design, only a srna.11 error is made if t,he
noriboiling and local boiling regions of the curve are considered to be straight lines, the intersection of which establishes the transition point, ( q / A ) a and ( At)rr. EFFECT OF VELOCITY. Figure 4 shows the effect of velocity a t 60 pounds per square inch absolute by comparing curves for water velocities of 1, 4, and 12 feet. per second, for several degrees of
September 1949
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INDUSTRIAL AND ENGINEERING CHEMISTRY
1949
subcooling. For the range in which local boiling did not occur, the data agree well with those predicted by conventional equations. Owing to superheating a t the surface of the heater, the curves of q / A against At do not inflect upwards until At is considerably i n excess of the degree of subcooling. For a given degree of subcooling, the curves for surface boiling merge into a common line. Figure 4 also shows EFFECT OF SUBCOOLING. the effect of varying the degree of subcooling. Runs were made a t average water temperatures of 20°, 50", loo", and 150" F. below saturation. I n t h e nonboiling range, the curves are displaced somewhat from each other, as expected because of variation in physical properties with temperature. I n the region of vigorous local boiling, the several curves are A B C displaced from each other horizontally by values q / A =480,000 q / A = 730,000 q / A = 1,090,000 A t = 91.3 A t = 97.4 A t = 104.8 of At corresponding closely to the differences in subcooling. EFFECT OF PRESSURE.Determination of the effect of total pressure over the range from 30 to 90 pounds per square inch absolute, a t a constant degree of subcooling, required extremely careful experimentation since the magnitude of the observed effect was slight. While varying the pressure, it was necessary to hold other variables, including the concentration of dissolved gas, a t substantially constant values, since a small shift in any of these more important variables could have readily masked the minor effect of pressure. Typical data are given in Figure 5. I n the range of surface boiling a t low density of heat flux, increase in pressure resulted in a small decrease in At for a given q j A . A similar effect of pressure was found in runs at higher velocities and with increased degrees of subcooling. At high densities of heat flux near the burnout point, pressure appeared D E F to have even less effect. q / A = 295,000 q / A = 510,000 q/A 830,000 A t = 83.6 A t = 89.7 A t = 96.7 MAXIMUM DENSITYOF HEAT FLUX. The Figure 9. Degassed Distilled Water at 50' C. and 30 Lb./Sq. In. Abs. peak density of heat flux was determined by increasing the power in a series of steps until the Flowing upward (top)at 12 feet per second and (bottom) at 4 feet per eecond. heater burned out. Table I summarizes the dahs on peak flux, which increased with increase in hydraulic diameter of 0.17 inch. Figure 6 shows the effect of both water velocity and degree of subcooling, and was insensitive subcooling. The trends are similar t o those for the larger anto pressure. nulus. Figure 7 shows wall temperatures and water temperatures at TABLE I. MAXIMUM DENSITIES OF HEATFLUX 2-inch intervals along a centrally located heater 11.5 inches in (Heater length, 3.75 inches; heater diameter, 0.25 inch; jacket diameter, length and 0.25 inch in diameter, in a n annulus having an equiv0.77 inch) alent hydraulic diameter of 0.52 inch. The water velocity was Pressure (q/A)ma=g 1 foot Per second, Pressure v a s 90 pounds per square inch abVelocity, Lb./Sq. 1;. tsat - t , B.t.u./(Hr.) Temperature Run No. Ft./Sec. Abs. F. (sq. *t.) Rise Ratioa solute. and subcooling was 50' F. At low densitv of heat flux 17CP BO-3 1 60 20 494,000 0.416 in the nonboiling region (Figure 7.4) the water temperature rose 0.217 1 60 651,000 50 l6CP: BO-2 only slightly, whereas the heater temperature rose more steeply, 0.140 1 60 854,000 15CP BO-1 100 4 60 1,030,000 0.086 5CP. BO-5 50 indicating a decrease in the heat transfer coefficient with increase 1,050,000 0.091 21CP 4 90 50 19CP,BO-4 12 60 1,170,000 0.082 20 in heated length. A t densities of heat flux in the range of surface 0,039 12 60 1,390,000 BO6 50 12 BO 100 2,010,000 0.027 boiling (Figure 7H),the heater temperature remained constant 9CP 12 30 1,850,000 24M 100 0.026 although the wa tev temperature rose 30' F. I€based on the total (q/A)max =- (tz - t 1 ) m a Defined as At, there would be an increase in the apparent coefficient of heat (w)( c ) ( t s s t - tl)/TDIL tsat - ti * transfer. The controlling potential for surface boiling is evidently the wall temperature less the saturation temperature. This potential, I, bat, is called Atmat,and is independent of the EFFECTO F DIMENSIONS OF ANNULUS. The results reported above were obtained with upward flow of watcv ill annuli having bulk temperature of the water. EFFECT OF Dissoi~v~m GASES. I n a few runs air was used in equivalent hydraulic diameters of 0.48 or 0.52 inch. Several runs were made with a smaller annulus having a n equivalent place of steam t o pressurize the water in the reservoir. Figure 8
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It
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1950
INDUSTRIAL A N D E N G I N E E R I N G CHE'MISTRY
Vol. 41, No. 9
indicates that substantially correct values of the thermal conductivity of the wall were employed. SUKIIACE RoII,iXG. Typical runs at several velocities and degrees of subcooling were &own in Figure 4, in n-hich the density of heat flux was p1ol)ted against the total At from thc henlcr to the subcooled water. This rnet,hod of plottirig shows thal, if the total At is adopted as IE prinie variable, the degree of subcooling and water velocity must enter the correlation in a complex way. Local boiling is a two-step process, involving generat,ion of vapor bubbles on the surface of the heater follomd by condensation in subcooled liquid. Tharefore the first step should be controlled by the potential At,,, =
tw.11
- L,
(7)
As shown in Figure 11, the flux denaity with surface boiling was a function of Atant: (p/A) = C'Atanr3.8G
shows a comparison between runs pressurized with air and steam. Although the curves coincide in the noriboiling mnge and also at high densities of heat flux, there is a considerable region in which the air-pressurized water gave higher density of heat flux for a given At than the degassed water. The magnitude of this effect was considerably less a t lower pressures. I n all airpressurized runs, bubbles started to form at lower values of At than in the degassed runs. PHorrocnAplric RESULTS. Figures 9A-9F are high speed Edgerton photographs showing sur6 face boiling on a stainless steel heater of 0.25 inch diameter. Water a t 30 pounds per square inch absolute, subcooled 50" F., mas flowing upward 4 at velocities of 12 and 4 feet per second. Comparisons between pictures A and E, and pictures A and If' show that there was less vapor presI h ent, for a given density of heat flux, at the k 2 0 higher water velocity.
2 7
DISCUSSION OF RESULTS
KONROII ITG Co~rwrross. All runs in which the temperature of the outer surface of the heater was b d w that of saturation were conipared with the equation
P
5
2
IO6
h Q $
8 6
? h
52
4
ti which was recommended by Biedcr and Tnte ( g o ) for turbulent flow of liquids in pipcs, with C of 0.027. CtLrpcAnter, Coiburri, Schoenburn, and Wurster (3)correlated d a t a for water flo\ving in an annulus, with C trf 0.023. The present results are correlated with C of 0.026 ns shown in Figure 10. All phyi.icu1 Ijroperties were evaluated at the avei'agc bulk temperature of the stream except p v , w h i ~ l iwas evaluated a t the surface temperaturr of the heater. At high densities of tieat flux, the temperature drop through the wall of the heater was a n important correction. As two wall thicknesses were employed, the good correlation of Figure 10
L . ?
$
5Q
8
6
4
(8)
and was independent of water velocity (1 to 36 feet per second), degree of subcooling (20' to 150 F.), pressure (30 to 90 pounds per square inch absolute), and equivalent diameter (0.17 to 0.48 inch). Evidently t,he boundnry lnyer on the surface of the heater is controlled by generation and condensation of vapor and is not affected by turbulence caused by the velocity of the flowing subcooled water. The value of C' decreased from 0.190 t o 0.074 as the concentration of dissolved gas decreased from 0.30 to 0.06 ml. of air a t standard conditions per liter of water.
HEATER
.' 0 25
/NCH 0.D X 3 75 /NCH€S LONG PRESSURE 30-90 P S / A SUBCOI)L/NG :P O - /50 OF
INDUSTRIAL AND ENGINEERING CHEMISTRY
September 1949
The slope of the curves for surface boiling of subcooled flowing water are almost identical with those obtained by Addoms (1) for boiling on a horizontal. platinum wire submerged in a saturated pool of water under conditions of natural circulation. TRANSITION TO SURFACX BOILINQ. The previous sections have presented equations for correlating data in the nonboiling and surface boiling regions, Equations 6 and 8. I n Figure 3 the transition point, was defined as the intersection of the two straight lines. Surface boiling begins at a "transition" At a t which the density of heat flux for nonboiling conditions: q/Ar = LI
hnb
(9)
Attr
is equal t o that for surface boiling: =
(q/-4)tr
C' At?::
(10)
tr
giving the transition rule:
This equation is slightly conservative because in the transition range the data lie a little above the transition point assumed in deriving the equation. The wall temperature f ,t r , at which the transition occurs is found by use of Equation 11, noting that AtsBt.tl =
t w tr
Att, = L,tr
= ( t ~t r,
-tsat)
- tea.* -t (tmt
(12a) Pb)
- t)
WC)
MAXIMUM DENSITY OF HEATFLUX. The peak density of heat flux in the range of surface boiling was determined by the point a t which the heater became insulated with a film of vapor and burned out. Values of the maximum density of heat flux were determined in several runs a t 60 pounds per square inch absolute BS shown in Figure 4. The condensing step is the bottleneck a t the burnout point, as is shown by the fact that burnout always occurred without warming the stream of subcooled water to the saturation temperature.
*
1951
The peak density of heat flux would probably be decreased by decreasing the clearltnce between the heater and the outer wall or by passing water through a heated tube. With surface boiling of gassed water, peak flux a t burnout may decrease with increase in heated length. Sufficient data on peak density of heat flux are not available to warrant a dimensionless correlstion. The water must have adequate heat absorbing capacity t o condense the vapor, which would introduce the dimensionless group c(t..t
- t)/X
(13)
where is the latent heat of condensation. The turbulence of the stream of water, in which the vapor condenses, introduces the Reynolds number, D,G/@. The peak flux could appear in one of several dimensionless moduli. On plotting peak flux for a given velocity against subcooling, extrapolation to zero subcooling gives an estimate of the peak flux with mturated liquid:
The peak density in excess of this value is plotted in Figure 12 as ordinate against the product ( t , t)Vsecl '%asabscissa, giving:
-
The maximum flux density was not a function of pressure, since points a t 30 and 90 pounds per square inch absolute were well correlated with the data a t 60 pounds per square inch absolute in Figure 12. The diameter of the annulus was not varied in the experiments on peak density of heat flux, hence the correlation applies only t o the 0.25-inch heater in the 0.77-inch glass tube. DIMENSIONSOF ANNULUS. For jacket diameters of 0.42 and 0.73 inch, Figure 11 showed that flux density depended only on Atsat in the region of surface boiling. I n the range of surface boiling, the temperature of the heater was uniform along the length of the heater, as shown in Figure 7. With high water velocity in the small annulus and with strong surface boiling, the drop in pressure lowered the saturation temperature and increased At.,t by as much as 20" F. VISUAL OBSERVATIONS. The high speed Edgerton photographs reproduced in Figure 9 showed that an increase in the water velocity decreased the number and size of the surface bubbles for a given density of heat flux. Visual observation of high speed motion pictures (7) showed that an increase in the degree of subcooling had a similar effect. At a water temperature of 150" F. below saturation, a water velocity of 4 feet per second, and a pressure of 30 pounds per square inch absolute, the high speed motion pictures revealed cyclical formution and condensation of the vapor bubbles on the surface of the heater. Thus, a t one instant numerous bubbles were seen on the heater, and 0.007 second later no bubbles were visible. The formation and collapse of the bubbles were repeated a t regular intervals, which were apparently not in phase with fluctuations in alternating or direct current power. RESULTSWITH GASSEDWATER. In the foregoing sections, the data for degassed distilled water have been discussed. I n Figure 8 i t was shown that the presence of dissolved gas increased the density of heat flux for a given At in the transition region. The presence of dissolved gases also made a distinct difference in the visual appearance of the surface boiling. The stream of water was cloudy, and many small gas bubbles were carried out in the water leaving the test section.
1952
INDUSTRIAL AND ENGINEERING CHEMISTRY
The runs reported in Figure 8 were made at a pressure of 90 pounds per square inch absolute and a temperature of 270" F. which is 50 O below the saturation temperature of 320' F. Coniputation shows t h a t the water could dissolve approximately 36 ml. of air per liter of water. I n the air-pressurized run (15M) reported in Figure 8, analysis of the water showed 69 ml. per liter. (This value is based on analysis for dissolved oxygen and the assumption that the ratio of dissolved nitrogen to dissolved oxygen is the same as that in water saturated with air. Solubilities are reported at standard conditions, 32" F. and 1 atmosphere.) Consequently, the water entering the test section was either supersaturated or contained gas bubbles. Computation shows t h a t gas theoretically could start t o be evolved a t 149" F. Actually the first vapor was observed when the wall temperature reached 288 O F., and the transition to surface boiling occurred a t a wall temperature of 302' F. Recent F o r k at high density of heat flux with gassed water has been reported by Hnowles ( I d ) and by Kreith and Summerfield ( l a ) . Knowles employed downflow of t a p water in a n annulus containing a centrally-located stainless steel tube heated by alternating current. Knowles obtained surface boiling as shown by increase in the heat transfer coefficient t o over four times the value predicted for nonboiling conditions. The highest density of heat flux was 2,300,000 B.t.u./(hr.)(sq. ft.). Knowles experienced considerable difficulty with deposition of scale on the heating element, which may account for the erratic results. Kreith and Summerfield employed distilled water flowing through a stainless steel tube which was heated by alternating current. This arrangement gave 100% active surface, as compared with the lower fraction of active suiface in the work which involved annuli with the central tube serving as the only heat source. The distilled water was probably in equilibrium with the atmosphere since no attempts at degassing were made. Both horizontal and vertical test sections n-ere employed. Under nonboiling conditions the data were closelv correlated by Equations 2 and 3. Excellent heat balances were obtained. The results for the vertical tube were plotted as density of heat flux against Atsat, with curves for the several pressures (16 t o 202 pounds per square inch absolute). The highest density of heat flux was 1,450,000 B.t.u./(hr.)(sq. ft.). Each curve showed a gradual transition from the nonboiling region to the surface boiling region. The degree of subcooling was not maintained constant, and the shift of the curves was attributed to the effect of total pressure, instead of t o the effect of subcooling on the start of local boiling as shown in the present investigation (Equation 11). Burnout data were reported only for one run. CONCLUSIONS
NOKBOILING CONDITIONS.Under nonboiling conditions both degassed and gassed distilled water gave results correlated by Equation 6 for turbulent flow in tubes or annuli. The best value of C was 0.026, and the maximum deviation of the data was 2070, Figure 10. SURFACEBOILINGOF DEGASSED DISTILLED WATER. Surface boiling of degassed water is a two-step process involving nucleate boiling at the heated surface and condensation of the vapor in the subcooletl liquid, Figure 9. At a given flux density, pressure, and temperature, an increase in velocity from 4 to 12 feet per second substantially decreased the volume of v:tpor on 01 near the surface of the hesitel, Figure 9. At a Rater temperature of 150' F. below saturation, a pressure of 30 pounds pel square inch absolute, and a velocitv of 4 feet per second, a high speed motion picture revealed c \ clical formation and complete condensation of vapor bubblcls o t 1 the suriace of the hcatei at I egular intervals. Densitirs of herit flux were correlated by a ciiiglc w r v e when plotted ag:iinbt the surface boiling potential, a(,,,= t, - fsat, and were indeperident of water velocity, pressu~c.degree of sub-
Vol. 41, No. 9
cooling, and dimensions of the annuli, Figure 11. Total At did not correlate the results, Figure 4. These results were correlated by the equation. q / A = C' At,,t3.86
for velocities ranging from 1 t o 36 feet per second, subcooling from 20" to 150" F., pressure from 30 to 90 pounds per squarr inch absolute, and equivalent diameter from 0.17 t o 0.52 inch The value of C' ranged from 0.190 to 0.074, depending on the, extent of degassing. At moderate density of heat flux, vapor formation occurred nt active nuclei on the heater. Bt a given moderate density of heat flux, increase in pressure from 30 to 90 pounds per square inch absolute caused a decrease in At less than 10" F. Below a flux density of 250,000 B.t.u. per hour per square foot, presence of dissolved air reduced the At required for a given flux density, Figure 8. PEAKDENSITY OF HEATFLUX. Visual observation of a high speed motion picture showed that burnout was caused by formntion of a blanket of vapor on the heater. T h e peak density of heat flux varied with the water velocity and the degree of subcooling. Peak densities a t 30 t o 90 pounds per square inch absolute were correlated by Equation 15. T h e peak densities of heat flux w r e three t o twelve times those for nonboiling conditions. TRANSITION TO SURFACE BOILING. When the surface temperature of the heater slightly exceeded the saturation temperature of the degassed water, surface boiling was theoretically possible. Owing t o the effect of superheating, the temperature of the heater was considerably greater than the saturation temperature before the transition to surface boiling actually occurred. T h e wall temperature a t the transition point is given by Equation 11. ACKNOWLEDGMENT
It is desired t o acknowledge the cooperation of W. H. Redlein and P;.R. Wilcox who participated in the design and construction of the apparatus. Thanks are due J. N. Addoms for assistance in preparation of this paper and to H. R.Carter for preparation of drawings. NOMENCLATURE
area of heat transfer surface, square feet, equals
TDIL
dimensionless constant in Sieder-Tate type of equation, recommended value of C is 0.026 dimensional constant in equation for surface boiling q / A = C'(Atsa~)3.86 specific heat of fluid, B.t.u./(lb.) (' F.) diameter, feet equivalent diameter, equal to four times the hydraulic radius based on total perimeter, feet; D, equals DZ - Dl inside (outside) diameter of annular passage, feet electromotive force, volts mass velocit of fluid through annulus, lb./(lir.) (sq. f t . ) ; w / S = 4 w / r ( D n 2- D l z ) heat transfer coefficient based on total At from heated wall to subcooled water, hnb = q / A ( t , t ) , B.t.u./(hr.) (sq. ft.) ( " F.) current, amperes conversion factor, 3.41 B.t.u./(hr.) (watt) thermal conductivity of fluid, B.t.u./(hr.) (ft.) ( O F . ) k a t film temperature, ti = (L t ) / 2 thermal conductivity of wall of hollow cylindrical heater, B.t.u./(hr.) (sq. ft.) ( " I{'./ft.) heatcd length, feet l i e ~ i r ~ ~ n ~ f einr rtest e d length L, B.t.u./hr.; p =
(f=
+
A1 "LL
density of heat flux, B.t.u./(hr.) (sq. ft.); q / A = K l 2 Li / T D1L pcalc dcnsitg of heat flux, B.t.u./(hr.) (sq. ft.) q / A a t transition point defined in Pigurd 3
INDUSTRIAL AND ENGINEERING CHEMISTRY
September 1949
= electrical resistance, ohms = radius of hollow heater; re for inside,
BIBLIOGRAPHY
ro for outside,
feet
= cross section for fluid flow, sq. ft.; S = rr(D22 = =
= = = =
*
W
=
XU
=
Y
=
At
-
Di2)/4 average temperature of bulk stream of water, O F., tl at inlet; t z at oytlet; t = ( t ~ t 2)/ 2 film temperature, F. (tw t)/2 saturation temterature of gas-free water from steam tables, F. temperature of outer wall of heater, ’F. value of tw at transition from nonboiling conditions t o surface boiling conditions, as defined by Figure 3 average velocity of bulk stream of water, ft./sec.; Vaeo= w/(3600)(PL)8, neglecting any bubbles water rate through test section, lb./hr. thickness of wall of hollow cylindrical heater, feet; xW = (Do - D i ) / 2 product of dimensionless ratios in correlation for nonboiling conditions:
+ +
= total t e m p e r a t y e difference, heated wall to subcooled liquid, F.; 1, - t =
temperature excess of heated wall over water, tw
-
O
F.;
t,at
surboiling conditions, as defined by Figure 3,
= At,., a t transition from nonboiling conditions to
cf:e
1953
F.; & t , t r t w t r - teat total temperature diherence at transitio: from nonboiling conditions to surface boiling, F. = drop in tempera:ure through wall of hollow cylindrical heater, F.; At, = tt - to, see Equation 5 = dimensionless constant, 3.1416 = latent heat of vaporization, B.t.u./lb. = viscosity of fluid, lb./(hr.) (ft.) = viscosity at tw = density of liquid, lb./cubic foot Dimensionless moduli Prandtl number, a t average bulk stream temperature Prandtl number at tf Reynolds number based on average bulk stream temperature and equivalent diameter, D, same as above but based on t j Nusselt number based on k a t t and De same as above but based on kr =
Addoms, J. N., Mass. Inst. Technol., Sc.D. thesis Chem. Eng. (1948).
Carl, R., and Picornell, P., Zbid., S. M. thesis Chem. Eng. (1948). Carpenter, F. G., Colburn, A. P., Schoenborn, E . M., and Wurster,A., Trans. Am. Inst. Chem. Engrs., 42, 165-87 (1947). Colburn, A. P., Ibid., 29, 174-210 (1933). Colburn, A. P., and Schoenborn, E. M., and Sutton, C. S., Natl. Advisory Comm. Aeronaut., Rept. UD-NI (March 1945) ; T N 1498, (March 1948). Colburn, A. P., and Sutton, C. S., Ibid., UD-N2 (February 1948) ; TN 1498, (March 1948). Dew, J. E., Mass. Inst. Teohnol., S. M. thesis Chem. Eng. (1948).
Dittus, F. W., and Boelter, L. M. K., Univ. CaZif. Pubs. Eng., 2 , 443 (1930).
Drew, T. B., and Mueller, A. C., Trans. Am. I n s t . Chem. Engrs., 33, 449-71 (1937).
Hayes, V. R., and Bartol, J. A., Mass. Inst. Technol., S.M. thesis in Naval Construction and Engineering (1944). Kennel, W. E., Ibid., DSc. thesis Chem. Eng., pp. 228-340 (October 1948). Knowles, J. W., Can. J.Research, 26, 268-70 (1948). Kreith, F., and Summerfield, M., Calif. Inst. Technol., Progress Rept. 4-68, JPL (April 1948); ASME Paper No. 48-A-38. McAdams, W. H., “Heat Transmission,” 2nd ed., Chap. IX, New York, McGraw-Hill Book Co., 1942. McAdams, W. H., Purdue Univ. Eng. Bull., Research Ser. 104, 32, 1-56 (March 1948). Minden, C. S., personal communication (1948). Mosciki, I., and Broder, J., Rocznicki Chem., 6 , 3 2 1 - 5 4 (1926). Nukiyama, S., J . SOC.Mech. Engrs. ( J a p a n ) , 37, 367-74; 553-4 (1934).
Redlien, W. H., and Wilcox, W. R., Mass. Inst. Technol., S.M. thesis Chem. Eng. (1947). Sieder, E. N., and Tate, G. E., IND. ENG.CHEM.,26, 1429-36 (1936).
Taylor, J., personal communication t o W. H. McAdams (1943). Tibbetts, E. G., and Cohen, J. B., informal report to A. R. Kaufmann, Mass. Inst. Technol. Woods, W. K., Mass. Inst. Technol., Sc.D. thesis Chem. Eng. (1940); McAdams, W. H., Woods W. K., and Bryan, R. L., Trans. Am, SOC. X e c h . Engrs., 63, 545-52 (1941).
RECEIVED January 31, 1949. Presented before the Meeting of the Division of Industrial and Engineering Chemistry, North Jersey Section, AMERICAN CHEMICAL SOCIETY,Newark, N. J., January 17, 1949.
A New Distillation Packing Rf. R. CANNON The Pennsylvania State College, State College, Pa.
z
new highly efficient distillation packing is made from protruded metal. Test data are given on two sizes of the packing i n 2 and 4 inch diameter columns. Because of the nature of the surface, the packing is readily wetted, requires no preflood, and attains equilibrium quickly. Consequently, considerable time is saved i n getting started. Since i t is made from flat metal, a relatively inexpensive starting material, i t i s less expensive than paclsings made from wire gauze or fine wire. I t is installed by simply pouring through a funnel.
\ I
HE new distillation packing described here consists of small units made from thin metal which has 1024 holes per square inch and is shaped into half cylinders with corners or edges bent inward to prevent nesting of one piece within another. Figure 1 illustrates the appearance of an individual piece. The holes are not clean cut but a protrusion or burr extends from one side. This surface has the unique property of being automatically wetted by liquid hydrocarbons. For example, if a strip of this
metal is partially submerged in a beaker of liquid hydrocarbon the liquid will crawl quickly up the surface of the metal. If the metal is touched with a blotter about 0.5 inch above the liquid level in the beaker, one can see absorption occur. The holes in the packing are not sealed by the liquid but both sides are wet. TEST EQUIPMENT AND PROCEDURE CoLirMNS. The test columns were made of 2- and 4-inch inside diameter Pyrex pipe with packed sections of 8.5 and 9.5 feet, respectively. Each column was offset from the still so t h a t all of the reflux from the column passed through a calibrated tube in which reflux rate could be measured accurately by closing the valve in this line and noting the rate of filling of the tube with the aid of a stop watch. The 2-inch diameter column was surrounded by a glass jacket which carried a resistance wire for heating. This jacket in turn was surrounded by a larger glass jacket t o reduce heat flow t o the room. Thermometers in the air space between the column and the heating jacket provided a means of determining the correct
