I
R.
F. KNOTT,' R. N. ANDERSON, ANDREAS ACRIVOS, and E. E. PETERSEN
Department of Chemical Engineering, University of California, Berkeley, Calif.
An Experimental Study of Heat Transfer to Nitrogen-Oil Mixtures These results are of interest to the design engineer confronted with the problem of predicting heat transfer coefficients to two-phase mixtures
ALTHOUGH two-phase gas-liquid flow processes are commonly used, no suitable correlations are known for predicting pressure drops and heat transfer coefficients in gas-liquid flow systems. Several types of flow patterns can occur, depending on relative amounts of each phase present and orientation of flow apparatus. Some investigators (3, 9) have chosen a homogeneous flow model where fluid properties such as density and viscosity are based upon relative amounts of each phase present. However, under most conditions the twophase mixture is nonhomogeneous, and weighted mixture properties cannot be used in conventional single-phase-flow heat transfer and pressure drop relationships. Furthermore, large deviations from single-phase behavior have been reported for the addition of small weight fractions of the gas phase ( 7 , 77). Several empirical relationships (2, 75) are available for correlating twophase gas-liquid pressure drop by heterogeneous models using parameters associated with pure gas and pure liquid properties. A typical example is the Martinelli method (75) in which experimental data on two-phase gas-liquid pressure drop are correlated to =t3oyO in terms of single-phase pressure drops and a flow parameter. Heat transfer investigations have generally lagged behind those of pressure drop in this field because of the more complicated analysis necessary. Early
Present address, Shell Development Co., Emeryville, Calif.
studies (3, 22) concerned the two-phase single-component problem in which vaporization is important, and several studies in this field have been undertaken recently ( 4 ) . Investigations of two-phase, two-component, gas-liquid systems have not been as widespread. However, Johnson (70, 77), Abou-Sabe (7), King (73), Fried (6, 7), Vershoor and Stemerding (ZO), and Novosad (77) have obtained a considerable amount of data from which qualitative conclusions can be drawn. The heterogeneous approach has been followed by Johnson and his group in their studies of horizontal flow systems. Abou-Sabe (7, 72) assumed that the two-phase heat transfer coefficient could be predicted from an expression of the form h T P = h L Z L -b h,Z, (1) where ZL and 2, are functions varying between the limits of zero and 1 depending upon the relative amounts of each phase present and hL and h, are the singlephase heat transfer coefficients for the liquid and gas, respectively, calculated as if each phase were flowing alone in the tube. A development closely paralleling that of the Martinelli pressure drop equations was used by Abou-Sabe in analysis of his air-water data. The function ZL depended upon the liquid volume fraction, the ratio APL/AP, = X z , and the singlephase gas Reynolds number while 2, appeared to be negligible even when the gas volume fraction approached 90%. King (73) and Fried (6, 7) investigated the dependence of the ratio hTP/hL = fiz
upon other system parameters, APTp/ AP, = $2 and X 2 . Through use of the heat transfer-pressure drop analogy Fried was able to correlate the air-water data of King and Abou-Sabe as well as his own within &30% by plotting $z us.
d2.
Johnson ( 7 7) has more recently confirmed the relationship between $2 and q 9 by correlating his experimental data on a mineral oil-air system within &20%. However, poor agreement between observed values of d' and those predicted by the Martinelli equation was noted a t high air rates. In general, introduction of the gas phase produced more marked increases in two-phase pressure drops and heat transfer coefficients than were evident in the airwater case, and therefore the plot of $* us. 42 for oil-air was found to lie above that for water-air. Verschoor and Stemerding's investigation (20) on a vertical air-water system is important as an additional source of data and for the qualitative observations involved. A gradual increase in twophase heat transfer coefficient over that obtainable in a single-phase flow was noted as the flow pattern progressed through the bubble region. The transition from bubble to slug flow at an airwater volumetric ratio of 2 was marked by an increase in slope for #*, with a maximum value observed a t a volumetric air-water ratio of 200-the transition point between slug and annular flow. As might be expected for a given volumetric air-water ratio, the value of fiz increased with increasing water rates. VOL. 51, NO. 1 1
NOVEMBER 1959
1369
was thermally and electrically insulated from the upper and lower calming sections by Bakelite disks in the mounting flanges. Losses by heat conduction along the copper bus bars could not be prevented so they were calculated from temperature gradient measurements. By suitable allowances for the above losses, heat transferred to the oil was accurately determined. Temperatures were measured at six points along the length of the tube by No. 22 copper-constantan thermocouples soft-soldered directly to the tube wall. Calculations showed a maximum temperature drop of less than 0.5" F. across the tube wall thickness, so peening the thermocouples into the tube wall was unnecessary. T h e lower calming section assembly consisted of a 2-foot length of stainless steel tube (similar to that used in the test section) concentrically jacketed by a steel pipe, ll/*-inch inside diameter, both of which were soldered to the bottom of the lower valve body. The fluid mixture entered the calming section assembly at a point just below the valve body, flowed down the annulus, made a 180' turn (where a thermocouple measured its temperature) and then passed up the inner tube into the heat exchanger. T h e upper calming section was similar in detail to the lower except that the orientation of the assembly and the fluid path through it were reversed. In addition the annulus was packed with steel shot. A thermocouple measured mixed mean fluid temperature at the base of the annulus. Nitrogen gas flowed from a high pressure nitrogen cylinder, through a regulator, a small flowmeter, and a tapered needle valve into the Venturi mixer. It was injected into the oil stream through four '/Sz-inch holes spaced at 90' intervals around the periphery of the Venturi throat. T h e pressure in the Venturi was held around 200 p.s.i. so that a good portion of the gas dissolved in the oil. T h e homogeneous mixture was made downstream of the Venturi where a right-
LOWER CALMING SECTION
C Y L I N ~ E RG E A R
PUMP
Test section and upper and lower calming sections were constructed of stainless steel
(1,17,20)
across the tube length. Varying amounts of heat could be generated within the tube wall by adjusting the voltage drop across the tube. Previous investigators in this field have used double pipe heat exchangers with either steam or cooling water as the shell side fluid.
( I , 19,20)
An Electrically Heated Test Section Has Several Advantages (12)
Previous Investigations Established Several Important Facts Close relationship of heat transfer to pressure drop in twophase flow Marked deviation of two-phase flow from single-phase liquid flow behavior with addition of significant amounts of gas phase Importance of flow pattern in any general correlation for two-phase heat transfer coefficient Greater sensitivity of two-phase heat transfer coefficient to parameters characterizing liquid phase Importance of gas hold-up and relative gas and liquid velocities
(I,6-7, 11-13)
( f , 6, 17)
(17)
In this study, the rate of heat transfer to two-phase mixtures of a viscous oil and nitrogen was measured. From the results it has been tentatively concluded that liquid-gas heat transfer coefficient in the bubble flow region is greater than the single-phase value a t the same liquid rate because the over-all mean velocity is increased by adding the gas phase (74). However, the disagreement between various investigators at V J V , > 1 suggests that more work is necessary to evaluate the different studies.
Energy input to the heat exchanger can be measured exactly in electrical quantities. Constant heat flux per unit length produces a linear average fluid temperature rise. A single film heat transfer coefficient is measured, rather than an over-all coefficient, which contains the contributions of two film coefficients and the effect of tube wall conductivity. Heat losses from the test section were minimized in several ways. T h e test section was insulated along its entire length by a thick layer of Fiberglas matting to reduce heat losses by radiation and natural convection. I t
I -
OIL
RUNS
I
W LL
3
+
Experimental
a LT
W
The vertical heat exchanger was a 5foot length of Type 304 stainless steel tube having a 0.028-inch wall thickness and an inside diameter of 0.506 inch. I t was connected at each end to an a.c. power supply rated at 10 volts and 230 amperes. T h e high specific resistance for stainless steel and the small tube wall thickness combined to produce a resistance of approximately 0.05 ohm
1 370
Figure 1 . Typical wall temperature profiles
INDUSTRIAL AND ENGINEERING CHEMISTRY
a
z W
I-
20
1 _I
4 A 60
D I S T A N C E FROM TEST SECTION ENTRANCE- inches
H E A T TRANSFER COEFFICIENTS leveled out at the end because of changes in the local heat transfer coefficient (Figure 1). Therefore a logarithrnic mean temperature difference was unsatisfactory, and an integrated incan temperature difference defined as
was used as the mean driving poteni.ia1 in the calculation of over-all heat transfer coefficient. Satisfactory agreement between the single-phase oil experiments and the Sieder and Tate equation is shown in Figure 2. Ninety-three nitrogen-oil runs were made over a range of Rei, from 6.7 to 162 and ReG from 126 to 3920. These data are shown in Figure 3 where h T P / ' h L is plotted cs. V B / V L ,where hTP and h L are the heat transfer coefficients calmlated from the two-phase experiments based upon the integrated mean temperature difference and the equation of Sieder and Tate, respectively, and V, and TIL are the volumetric feed rates of gas at mean exchanger pressure and oil (into the exchanger test section), respectively. Under the conditions of these experiments there is very little, if any, increase in the heat transfer coefficient
Figure 2. Single-phase oil data agreed well with results calculated from Sieder and Tate equation
anele needle valve adjusted to produce a pressure drop of over 100 p.s.i. created intense turbulence and caused the reappearance of some of the dissolved gas in the form of small bubbles. Visual observations of the mixtures were possible through Lucite viewing sections at either end of the test section. The oil used in these experiments was a commercially available, paraffin base petroleum oil having the following guaranteed specifications:
API gravity at 6Oo/6O0 F. Pour point, F. Viscosity, S.S.U. at 210' F.
ever, heat was transferred by a constant flux process in the equipment used in these experiments. While this resulted in a linear rise in average fluid temperature, it also produced a wall temperature profile that rose quite sharply in the first third of the heat exchanger and then
2 6 . 5 (min.) 10 (max.) 70-75
Information on the variation of specific gravity, thermal conductivity, and specific heat of the oil with temperature was provided by the manufacturer. The viscosity-temperature relationship was determined experimentally. The temperature variation ( O F.) of these properties is, respectively: S = 0.890[1
C, =
1
-t'S
(0.388
- 0.0004(t - 6 0 ) ]
+ 0.00045t) B.t.u.,'lb. ' F.
0.813 k = -- [ l - 0.0003(t - 3 2 ) ]
B.t.u./(hr. sq. ft.) ( " F./in.) Results and Discussion Twenty-nine single-phase oil runs were made to establish operating procedures and calibrate the equipment. T h e j factors calculated from these runs were compared with those calculated by the equation of Sieder and Tate (78). Strictly speaking, this equation applies only when the wall temperature of the heat exchanger is held constant How-
t ' 01 01
I
I 4
6
8
1
1
I,
I
!
!
'
I
l~
2
2 %/VL
Figure 3.
Two-phase heat transfer coefficients as a function of V,/VL
The disagreement among investigators points up the need for further evaluation of work in this field
VOL. 51, NO. 11
NOVEMBER 1959
1371
for injection of nitrogen at values of VQ/VLless than 0.2 As the quantity of nitrogen is increased, the heat transfer coefficient ratio increases to about 2 at V Q / V L= 10. The results of other workers have been included in Figure 3. Fried ( 6 ) , using an air-water system, reported results similar to those obtained in this work. T h e data of Vershoor and Stemerding (20) for air-water and of Johnson ( 7 7 ) for air-oil are much higher than those of Fried and the present investigators. Because of the wide variation in the results reported by different investigators it is worth while to focus attention on single phase heat transfer theory and its applicability to two-phase heat transfer. It is generally known that the main resistance to the transfer of heat to liquids (excluding, of course, liquid metals) is confined to a region in the vicinity of the heat transfer surface, and any mechanical agitation or decrease in the thickness of this region should result in an increase in the rate of heat transfer to the liquid. Accordingly, it is profitable to consider what effects the addition of a dispersed gas phase might have on this boundary layer region. At low gas volume fraction, the gas phase forms discrete bubbles which do not coalesce and results in a flow pattern known as bubble flow region in the literature. I n bubble flow there should be very little agitation in the boundary layer region due to the presence of the gas bubbles. I n fact, there is evidence indicating that particles in a laminar velocity field tend to move to a point of minimum gradient (76, 79). The authors are, therefore, led to the tentative conclusion that in the bubble flow region, the addition of the gas phase effectively increases the mean velocity of the fluid through the exchanger and correspondingly increases the heat transfer coefficient. T o a first approximation, then, hTp can be estimated by the equation of Sieder and Tate:
in the region near the heat transfer surface under the conditions of their experiments. However, for this to be true, the mixing action must be violent indeed, because the increase in the heat transfer coefficient which Gose, Petersen, and Acrivos ( 8 ) obtained when nitrogen was injected through the boundary layer into a water stream was less than the values reported by Vershoor and Stemerding at comparable Reynolds numbers. Injection of nitrogen through the boundary layer into an oil similar to that used by Johnson produced a value of h T p / h L of about 2 for equal volumes of each phase. It is difficult to visualize conditions under which more violent disturbance of the boundary layer can be effected than by gas injection through the boundary layer. Even pulsating two-phase flow seems like an unlikely explanation for these high values inasmuch as West and Taylor (27) found that the heat transfer coefficient to a pulsing single phase fluid (water) was increased to a maximum of twice its steady flow value at pulsation ratios of about 1.4. Undoubtedly, the key to understanding two-phase heat transfer lies in the quantitative characterization of twophase flow patterns.
Nomenclature = specific heat, B.t.u./(lb.)(" F.) = tube diameter. ft. = single-phase gas heat transfer
coefficient, B.t.u./(hr.)(sq. ft.) (" F.) = single-phase heat transfer coefficient, B.t.u./(hr.) (sq. ft.) (" F.) = two-phase heat transfer coefficient, B.t.u./(hr.) (sq. ft.) (" F.) - ( ~C) (G~ ) 2 ' 3 ( , > , ' * 4 , diI~
I
mensionless = thermal conductivity, B.t.u./
(hr.) (sq. ft.) (" F./ft.) = length of heated section, ft. = Nusselt number, dimensionless = single-phase liquid pressure
drop, p.s.i./ft. 1.86
(T
z> (--)"'"
X Pr X D
113
p
= single-phase gas pressure drop, p .s .i./ft = two-phase pressure drop, p s i . /
.
(3)
where V T p is the mean velocity based upon the total volume of fluid (gas and liquid) flowing, and where all of 'the thermal properties are those of the liquid phase. From Equation 3 it follows that:
ft .
= Prandtl number, = = =
=
(4) =
Equation 4 predicts the approximate trends of the results of Fried and the present investigators, although this equation predicts values of hTP/hL slightly higher than the experimental results. T h e results of Johnson and Vershoor and Stemerding indicate that the iniected phase is causing a mixing action
1 372
INDUSTRIAL AND ENGINEERING CHEMISTRY
=
=
= = =
dimensionless Reynolds number, dimensionless specific gravity, dimensionless tube wall temperature, O F. bulk fluid temperature rise through exchanger, F. inlet bulk fluid temperature, " F. outlet bulk fluid temperature, " F. gas flow rate, cu. ft./hr. a t 70" F., 1 atm. liquid flow rate, cu. ft./hr. a t 60" F. a n exponent or distance, ft. APL/AP,
Z,,
ZL =
8
=
/1
=
/1w
=
YL
=
e2
=
empirically determined parameter for the gas and liquid phases, respectively integrated mean temperature difference, " F. oil viscosity a t the mean bulk fluid temperature, O F. oil viscosity a t the mean wall temperature, O F. kinematic viscosity, sq. ft./hr. APTp/APL
= hT,/hL
Acknowledgment This work was supported in part by grants from the National Science Foundation and from the Petroleum Research Fund administered by the American Chemical Society.
literature Cited (1) Abou-Sabe, A. H., Ph.D. University of California, 1951.
thesis,
(2) Chenoweth, J. W., Martin, M. W., Petrol. Rejner 34, 155 (October 1955). (3) Dittus, F. W., Hildebrand, A., Trans. ' Am. Soc.'Mech. Engrs. 64, 185 (f'942). (4) Drew, T. B., Hoopes, J. W., Advances in Chemical Engineering," Vol. 1, pp. 2-73. Academic Press. New York. 1956. ( 5 ) I&., pp. 79-150. ' (6) Fried, L., Chem. Eng. Progr. Symp. Ser. 50,47-51 (1954). (7) Fried, L., M.S. thesis, University of California, 1953. (8) Gose, E. E., Petersen, E. E., Acrivos, A., J . Appl. Phys. 28, 1509 (1957). ( 9 ) Isbin, H. S.: others, "Two-Phase Pressure Drops," U. S. Atomic Energy Comm. AECU-2994 (1 954). (10) Johnson, H. A , , University of California, private communication, 1955. (11) Johnson, H. A , , Trans. Am. Soc. Mech. Engrs. 77, 1257 (1955). (12) Johnson, H. A , , Abou-Sabe, .4.H., Ibld., 74, 977 (1952). (13) King, C. D. G . , M.S. thesis, University of California, 1952. (14) Knott, R. F., Anderson, R. N., Acrivos, A , , Petersen, E. E., American Documentation Institute No. 6041, 1959. (15) Lockhart, R. W., Martinelli, R. C . , Chem. Eng. Progr. 45, 39 (1949). (16) Maude, A. D., Whitmore, R. L., Brtt. J . Appl. Phys. 7 , 98 (1956). (17) Novosad, Z., Collect. Czechoslov. Chem. Communs. 20, No. 2, 477 (1955). (18) Sieder, E. N., Tate, G. E., IND. ENG.CHEM.28, 1429 (1936). (19) Starkey, T. V., Brzt. J . Appl. Phys. 7 , 52 (1956). (20) Vershoor, H., Stemerding, S., Inst. Mech Engrs. Gen. Discussion on Heat Transfer. London,. England, September 1951, Sect. 2> p. 57. (21) West, F. B., Taylor, A. T., Chem. Eng. Progr. 48, 39 (1952). (22) Woods, W. K., McAdams, W. H., Trans. Am. Sod. Mech. Engrs. 64, 193 (1942). RECEIVED for review September 2, 1958 ACCEPTED July 13, 1959 Material supplementary to this article has been deposited as Document No. 6041 with the AD1 Auxiliary Publications Project, Photoduplication Service, Library of Congress, Washington 25, D. C. A copy may be secured by citing the document number and by remitting $1.25 for photoprints or $1.25 for 35-mm. microfilm. Advance payment is required. Make checks or money orders payable to Chief, Photoduplication Service, Library of Congress.
