I
JOHN L. LOCKARD and JAMES H. WEBER
I
Department of Chemical Engineering, University of Nebraska, Lincoln 8, Neb.
I
pined ubes..
.
in Cross-Flow Exchangers
Friction factors and heat transfer coefficients can be predicted from relationships based on experimental results
IN
A PREVIOUS study Hobson and Weber (,i)obtained performance data on concentric pipe heat exchangers in which the inner elements were spined tubes. In the study three different types of spined surfaces were used in a total of eight double pipe exchangers. Heat and momentum transfer data were obtained and the performance characteristics of these exchangers were compared with those of exchangers in which either a smooth pipe or another type of extended surface equipment was used as the inner element. These comparisons were made in the original study (5)and in a subsequent one ( 6 ) . The results of these studies show that the use of spined tubes in concentric pipe exchangers is, in general, not to be recommended because of the excessive pressure drop of the annular fluid. The loss of pressure and, in turn, increased fluid pumping costs would tend to outweigh any advantages which may be obtained from the better heat transfer characteristics. As a further test of spined tubes in heat exchangers, a study was undertaken to determine the heat and momentum transfer characteristics of this type of extended surface, when it is used in a
cross-flow exchanger. I n undertaking a study of this type it is necessary to limit the number of variables to be investigated. First, the spined tubes were arranged on centers of equilateral triangles. A “staggered” arrangement tends to give substantially higher heat transfer coefficients than does a n “in-line” arrangement (74). The choice of equilateral triangles was arbitrary but this arrangement has been used previously by many investigators. Second, the tubes were placed in five rows. I n the first, third, and fifth rows there were three tubes per row, while in the second and fourth rows, two tubes per row. I n order to keep a constant cross section normal to the direction of air flow, two baffles were , placed in each of the second and fourth rows. This helped to prevent the air from by-passing the heating surfaces in these rows. The number of rows was set at five, partially for practical reasons and partially because previous investigations showed that results obtained under these circumstances were representative. T h e greater the number of rows of tubes used in the tube bank, the greater the pressure drop. Because pressure drop of the fluid flowing across the tube bank
probably would be the most important drawback to the practical use of spined tubes, the reason for not using a large number of rows of tubes is apparent. Further, a number of studies (73-76) reviewed by McAdams (72) show that the mean values of the heat transfer coefficient for banks five rows deep were over 90% of the mean values for banks 10 rows deep. These results, of course, were obtained on equipment using banks of plain tubes, but it would appear that the percentage would be even higher for spined tubes, because the spines would increase the degree of turbulence in the fluid, Jameson ( 8 ) investigated the use of finned tubes in banks and found that the number of rows had only a slight effect on the heat transfer coefficient. Katz and others ( 9 ) made an extensive study of the use of extended surface heat transfer equipment in cross-flow exchangers and concluded that the value of the heat transfer coefficient was not affected by varying the number of rows of tubes in the exchanger. Further, they concluded that if the blower was located upstream, as was the case in the present investigation, there was little increase in heat transfer from the first to the second, or later rows. In a recent investigation Lapin and Schurig ( 7 7 ) obtained performance data on cross-flow exchangers in which finned tubes were used. These authors found that a t the higher Reynolds numbers (10,000 to 15,000) the heat transfer VOL. 52, NO. 1 1
NOVEMBER 1960
925
coefficient was independent of the number of rows if that number exceeded four. Because of the resulrs previously found, the compilation presented by McAdams (12): and the nature of the spined tubes, the conclusion was reached that performance data obtained on a cross-flow exchanger in which there \cere five rows of spined tubes would be suitable for design purposes. Fluid velocity and, in turn, Reynolds number is an important parameter in an investigation of this type. In this Tvork, the range of Reynolds numbers covered was 8.50 to 22,000, Experimental Equipment and Technique
The heat exchanger section with 3/8-inch spined tubes
112' SPINED TUBE
200
AND (13)
100
-. +
TUBE
.Y
0
0
P u w
50
m
z 3
+--I w
ul v)
z 3 20
800 1,000
3,000
5,000
10,000
30,000
D,Q,,,/y+
REYNOLDS N U M B E R
Figure 1. Cross-flow exchangers using spined tubes and smooth tubes give similar relationships for Nusselt vs. Reynolds numbers
In this study the same types of spined tubes were employed as in the previous study (5). Illustrations of the spined surfaces were included in the original work; consequently, they will be omitted. The three heat exchangers were of conventional design. The tubes were placed in a rectangular duct construcied of asbestos board and were in a vertical position. The heating medium, steam, was supplied to the tubes, individually, from a header. The steam condensate passed through a trap and was then cooled, collected, and weighed. T h e header, lead lines, and the exchanger were insulated with glass wool. From a series of blank runs, the heat loss from the equipment was determined to be 1100 l3.t.u. per hour. A blower was used to force air through the tube bank. The air rate was controlled by adjusting the size of air inlet to the blower. The air rate was measured by a Pitot tube used in a conjunction with a draft gase. l h e Pitot tube was located 6 feet below the exchanger in a 6-inch circular duct. At the lower rates a rotameter was occasionally employed. To ensure a uniform air velocity across the duct, a fine screen was fitted in the duct between the blower discharge and the heating section in such a manner as to give the desired condition. All temperatures were measured by copper constantan thermocouples used
Dimensions o f Cross-Flow Exchangers
0
o
0
0
\
@ @
THERMOCOUPLE
1
, PITOT TUBE
CONDENSATE
PRESSURE TAP
GRID OF 17 THERMOCOUPLES
\
A blower was located upstream of heating section and screen was used to obtain uniform air velocity across the duct
A typical exchanger.
926
INDUSTRIAL AND ENGINEERING CHEMISTRY
Nominal Tube Size, Inch -~
Item D o , ft. XT XL
114
Minimum free 0.1510 area," sq. ft. 5 Rows of tubes Tubes, total No. 13 Height of tubes, 0.462 ft. 0.0225 Baffle size, ft. a
Bared on D o .
1/2
3/8
0.0450 0.0563 2.86 3.42 2.46 2.97
0.0700 2.39 2.06
0.1510 0.1510
5 13 0.482 0.0281
5 13 0.502 0.0350
S P I N E D TUBES in conjunction with a Leeds & Northrup semiprecision potentiometer. The temperatures are accurate to zkO.5' F. Air temperatures were measured upstream of the heating section by a single thermocouple and immediately downstream, by 17 thermocouples located on a grid. Further downstream, approximately 6 feet and in a 6-inch circular duct, another thermocouple was located. The air temperature obtained at this point provided a check on the exit air temperature. Of course, a heat loss in the section of the equipment from the tube bank to the thermocouple had to be estimated to do this. The pressure differentials across the heating section were measured. Small differentials were read on a draft gage, and large ones, on a water filled U-tube manometer. The former gage could be read to k0.002 inch of water and the latter, to 1 0 . 0 2 inch. The experimental procedure was conventional. The runs were '/* to 2 hours in duration and prior to taking any data of record, the equipment was operated at the prescribed test conditions for 30 minutes. This period of time allowed conditions to stabilize. A series of runs in which the air input varied from 30 to 600 cubic feet per minute, measured at delivered conditions, was made on each of the three exchangers. Heat balances were made by determining the heat given up by the steam, by weighing the condensate, and equating this to the sum of heat absorbed by the air plus the heat lost from the exchanger. A run was not considered valid unless the heat balance checked within 1 5 % . For the experiments taken as a whole, percentage differences in the heat balances were random in nature. Treatment of Experimental Data
Heat transfer coefficients for the spined surfaces were calculated from the relationships q = UoAoAtm (1) = + xA,, + .1_A4 (2) U, h,, k Am h, Ai
a w
-
COLEURN (2)
-f
KAYS,LONDON,AND LO1 (IO)
U
3/8" SPINED TUBE
u)
K 4
vertical surface. The resistance offered by the condensate film was approximately. 10% .~ of the total resistance the Pipe and the resistance offered wall was approximately Hence, these values- could be' considerably in error and not affect materially the value of h, as determined by Equations 1 and
-
L.
A number of studies have been undertaken to determine the heat transfer coefficient in cross-flow exchangers. The early data were correlated by Colburn (2) who developed the equation
I n Equation 3 the subscript f,indicating the property or group of properties, is to be evaluated a t the film temperature. T h e relationship
was used to evaluate the film temperature.
1 1
Heat transfer rates, q, were obtained directly from the experimental results and the log mean temperature differences were calculated in the usual manner. The area of heat transfer was taken as the total outside area, primary and secondary of the tube. I n doing so, the assumption is made that the fin efficiency is 100%. This assumption is justified on the basis of the low air film coefficient and the high thermal conductivity of the copper spines. The condensate film coefficient, h,, was calculated from the Nusselt equation for filmwise condensation on a
0.006
118" SPINE0 TUBE
Grimison ( 3 ) used the same basic relationship as Equation 3. He presented a number of different intercept and slope values (for log-log plots of h,D,/k, US.
. Sx) for a variety I
Pf
I n Equation 3, Do is the nominal outside diameter of the tube, while G,,, is the maximum mass velocity. ,,G , would occur where the cross section for flow is a minimum. T h e experimental results of this investigation were correlated by a relationship of the form of Equation 3. I n Figure 1, the results are compared with smoothed data of Huge (7) and Pierson ( 7 3 ) . Figure 2 shows the correlation of the j , factor, defined by Colburn, as a function of DoGmax/pLf.For comparison a plot of Colburn's original relationship for plain tubes is included as well as a relationship given by Kays, London, and Loi (70). I n certain cases, as far as the magnitude of heat transfer coefficient at a given mass rate is concerned, the use of
0
0.6.
-
r
of situations.
/
0.5.
I / 2 " SPINED TUBE
P 0
5 0.3-+
"
"
I& r
z -0 0.2-
t
+
1/4"
SMOOTH TUBES
- X T = 2 43
GRIMISON ( 3 , 4 )
0.1 , 800 1000
I 3,000 REYNOLDS
5,000
I0,000
NUMBER
0, GmaX/p t
30,000
Figure 3. As expected, friction factors obtained on exchangers using spined tubes are higher than those obtained on smooth tube exchangers VOL. 52, NO. 11
NOVEMBER 1960
927
spined tubes in tube banks is to be preferred over the use of plain tubes. Experimental data on the momentum transfer characteristics were also obtained. From the experimental data, a modified friction factor (Figure 3) could be calculated from the expression presented by Chilton and Genereaux (7): (PI - P,) = 4f'NG2,,,/2pg,
(5)
The relationship of Chilton and Genereaux was developed to apply to banks of plain tubes. For comparison, modified friction factors obtained from the relationship presented by Grimison (3, 4) J' = ( 0 . 2 3
J-
were calculated and included on Figure 3. For calculation purposes XT was assigned a value of 2.43. This is approximately the valde of XT for the I, &-inchspined tubz exchanger. There was no necessity to calculate modified friction factcrs for other plain tube exchangers because X,, over the range of values involved, is not a critical factor. Values of the modified friction factor for the spined tube exchangers are from two to four times as great as the factors
for plain tube exchansers (Figure 3). This means, according to Equation 5, that the pressure drop under a specific set of conditions for the plain tube exchangers would be from one half to one quarter the magnitude of those obtained in this work. This is a significant difference and would mean that pumping costs for the type of exchanger used in this work would be considerably higher than those incurred for a similar type plain tube exchanger. The heat and momentum transfer characteristics were then combined in a power performance factor, B.t.u./hr.O F.-h.p., and this plotted us. the Reynolds number, Figure 4. 'The heat transfer data for the plain tubes presented in this plot are results obtained by Kays, London, and Loi (10). O n the basis of the power performance factors alone the performances of spined tube cross-floiv exchangers compare unfavorably with those of cross-flow exchangers using plain tubes. However, there are other factors, such as pressure drop, length, and size which may otherwise have a bearing on the choice between using spined or plain tubes in heat transfer systems. Nomenclature
A D
= area, sq. ft. = diameter, ft.
I00
inside diameter of base tube, I't. outside diameter of base tube, ft. diameter ofspines, ft. Ib./hr.-sq. ft. number of roxvs of tubes P = Dressure. lb./sa. ft. II = over-all heat transfer coefficient, B.t.u. {'hr. -ft .Z-O F . X , = longitudinal pitch ratio; 1ong.itudinal tube spacing divided by the outside tube diameter based on dimensions for pipe corresponding to nominal sizes X T = transverse pitch ratio; transverse spacing divided by the outside tube diameter based on dimensions for pipe corresponding to nominal sizes = heat capacity, B.t.u./lb.-o F. = friction factor,, dimensionless gc = gravitational constant, 32.134 lb.-ft.,'(lb.) sec.2 h = individual heat transfer coefficient, B.t.u.,/hr.-ft.z-oF. j, = heat transfer factor, dimensionless k = thermal conductivity, B.t.u./'hr.k2-" F./ft. = rate of heat transfer, B.t.u./'hr. q t = temperature, F. Atm = log mean temperature driving force for heat transfer, O F. x = wall thickness, ft. p = density, Ib./cu. ft. = viscosity, 1b.jft.-hr. Subscripts ( = Elin z = inside m = mean max = maximum value o = outside s = surrace
D, DO D, G
= = = = -I' =
j'
Literature Cited 50 30
10
(1) Chilton, T. H., Genereaux, R. P., T r a n s . A m . Znst. Chem. Engrs. 29, 161 (1933). (2) Colburn, A . P.: Z6id..p. 174. (3) Grimison. E. D., Ibid.,59, 583 (1937). (4) Z6id.,60, 381 (1938). (5) Hobson, M., Weber, J . H., IND.ENG. CHEM.46, 2290 (1954). 16) Hobson. M.. Weber. J. H..' PetTd. ReJiner 3 6 , No. '5. 2 3 9 (1957). (7) Huge. E. C.. T r a n s . Am. SOC.M c c h . Enqrs. 59, 573 11917). (8) J-ameson. ;. L., T r a n s . A m . Soc. M e c h . Engrs. 6 7 , 633 (1945). (9) Katz, D. L.. Young. E. H., Williams, R. B., Balekjian, G., Williamson. R . P., Project 1592, Engr. Res. Inst.. Cniv. of Michigan, 1959. (10) Kays, \V. M., London. X . L.. Loi, R. I
