u
f~
Elk
= collision diameter, Angstroms = collision integral which depends on parameter = ratio of energy to molecular gas constant, O K .
SUBSCRIPTS f o s
w
= = = =
pertains pertains pertains pertains
to to to to
exit conditions conditions in plasma core mean conditions a t s wall conditions
SUPERSCRIPTS m, n, r, t = constant exponents literature Cited (1) Bird, R. B., Hirsclifelder, J. O., Curtiss, C. F., Heat Transfer Division, ASME, Nov. 29-Dec. 4, 1953>New York. (2) Cann, G., private communication to W. von Jaskowsky.
(3) Freeman, M. P., Skrivan, J. F., A.I.Ch.E. J . 8, No. 4, 450-54 (1962). (4) Freeman, M. P., Skrivan, J. F., Hydrocarbon Process. Petrol. Refiner 41,No. 8 , 124-8 (1962). (5) Glasstone, S., “Thermodynamics for Chemists,” p. 53, Van Nostrand, New York, 1954. (6) Martinek, F., “Thermodynamic and Transport Properties of Gases, Liquids, and Solids,” p. 151, McGraw-Hill, New York, 1959. (7) Penner, S.S., “Chemical Reactions in Flow Systems,” Agardograph 7, Butterworths Scientific Publications, London, 1955. (8) Sanger-Bredt, I., Natl. Advisory Comm. Aeronaut., NASA Tech. Transl. F1 (1959). (9) Scala, S. M., Baulknight, C. W., A R S J . 29, 39-45 (1959). (10) Jliethern, R. J., Brodkey, R. S., A.I.Ch.E. J . 9, No. 1, 49-54 (1963). RECEIVED for review June 3, 1964 ACCEPTEDMarch 31, 1965
CONVECTIVE HEAT TRANSFER IN FLOW NORMAL T O BANKS OF TUBES A. A. A U S T I N , ’ R. B. B E C K M A N N , l R . R . ROTHFUS, AND R. I. KERMODE
Carnegie Institute of Technology, Pittsburgh, Pa. Heat transfer coefficients for individual tubes were determined in two cross-flow exchangers of 1 0-row depth having staggered and in-line tube arrangements on a pitch of 1.25 diameters. The transfer medium was pressurized water flowing a t Reynolds numbers from 10,000 to 180,000. Pressure drops across the staggered lcrttice were also measured, The jet of entering water was allowed to strike the tube bundle so that the effect of dissipation could b e studied. The heat transfer coefficient was found to b e strongly dependent on ithe transverse and longitudinal position of the tube in the first few rows. Deeper in the bank, the iet was lless a factor and the coefficients were more uniform from tube to tube. Their functional dependence on the Reynolds number was observed to change sharply a t a Reynolds number of about 80,000, apparently because of turbulence in the boundary layer. N STUDYISG
heat transfer in fluids flowing normal to banks of
I tubes, it has been usual to use air as the transfer medium
under uniform wind-tunnel conditions. Two notable examples are the investigations of Huge (8) and Pierson (77), whose extensive data \\ere correlated by Grimison (7). I n all, 22 staggered and 16 in-line tube arrangements, 10 rows deep, were studied by these investigators over the Reynolds number range from 2000 t o 40.1300. T h e correlation is summarized by McAdams (70). On the other hand, liquid floiv has not received much attention, although t\vo investigators have made especially significant contributions to irhe literature on the subject. Bergelin and associates (7-4) studied a number of tube banks, using a light spindle oil as the heat transfer medium, and reached a n upper Reynolds number of about 10,000. Dwyer and associates ( 6 ) studied heat transfer in water flowing a t Reynolds numbers up to 1,200,000 across a staggered arrangement of tubes. The present investigation of liquid flow was undertaken for two principal purposes: to extend the range of data to a higher Reynolds number, but with a lower pitch-to-diameter ratio 1 Present address, Esso Research and Engineering Co., Linden, N. J. 2 Present address, Department of Chemical Engineering, University of Maryland, College Park, Md.
than the 1.58 value used by Dwyer and his coworkers, in order to determine the effect of pitch on certain phenomena reported by these authors; and to investigate the manner in which the heat transfer coefficients for individual tubes in the bundle might be influenced by the impingement of a strong jet of entering liquid on the first row. The presence of such a n unrestricted jet is apt to be encountered in industrial exchanges handling liquids a t optimum velocities in the connecting lines. In dealing with flow normal to banks of tubes, it has been customary to define a Reynolds number based on the outside diameter of the tube, Do,and on the mass velocity, G,,, through the minimum area available for flow. For nonisothermal cases, the viscosity has been evaluated a t the “film” temperature in the usual way, yielding the Reynolds number in the form (DoGmax/gj). In the manner of Colburn ( 5 ) , the Nusselt number, h,D,/kj, and the Prandtl number, (C,g/k) have been related to the Reynolds number through equations of the form
The heat transfer coefficient in this case is averaged over the entire bank of tubes and is based on the rate of total heat transfer, the total outside area of the tubes, and the mean temperaVOL. 4
NO. 4
OCTOBER 1 9 6 5
379
ture difference between the surface of the tubes and the bulk of the flowing fluid. On the basis of early data, Colburn recommended that B be taken as 0.33 and n as 0.6 for gases flowing normal to deep banks of staggered tubes a t Reynolds numbers between 2000 and 32,000. For the corresponding case of flow through inline arrangements, B was to be taken as 0.26. O n the other hand, Grimison's correlations of data on air flow later showed both B and n to be functions of longitudinal pitch, transverse pitch, and arrangement of tubes. For the particular case of staggered tubes on equilateral centers, the Nusselt numbers a t a pitch-diameter ratio of 1.25 were found to be somewhat higher than those a t ratios of 1.50 or more. For square in-line arrangements, however, the Nusselt numbers were not significantly affected by the ratio. The exponent n was slightly greater for the in-line arrangements than for the staggered ones, but the Nusselt numbers were about the same in the upper range of Reynolds numbers studied. Bergelin and associates studied heat transfer in a light oil flowing normal to triangular, square-staggered, and square inline tube arrangements having pitch-diameter ratios of 1.50 and 1.25 with 3/8-inch and 3/4-inch tubes a t Reynolds numbers from 10 to 10,000. When data were presented as graphs of j factor against Reynolds number, the lines defining the various tube bundles tended toward coincidence a t Reynolds numbers above 6000. Dwyer and associates dealt with the flow of water a t about 360' F. and a t Reynolds numbers between 30,000 and 1,200,000 normal to an equilateral staggered lattice of tubes. The tubes had a n outside diameter of 0.81 inch and a pitch-diameter ratio of 1.58. The bank was 10 tubes wide and 20 tubes deep. Data were obtained on individual tubes and, since the Prandtl number was essentially copstant, the results were presented as graphs of the average coefficient for the tube under consideration against the Reynolds number. U p to a Reynolds number of 80,000 the tubes well within the bank exhibited coefficients in agreement with Colburn's form of Equation 1. At 80,000, however, an abrupt break occurred on the logarithmic graph and a t higher Reynolds numbers exponent n was about 0.8 instead of 0.6. It was found that the tubes situated adjacent to the wall of the duct had average heat transfer coefficients about 15% higher than those of the tubes within the bank. The duct leading to the exchanger was roughly the same size as the exchanger itself, being a 13-inch i.d. pipe with no screens or straightening vanes ahead of the first row of tubes. The front row coefficients increased as the Reynolds number was raised to the 0.65 power over the whole range of flow rates and were about 30% lower than those within the bank at a Reynolds number of 100,000. The tubes in the third row had the same coefficients as those farther back in the bank, so the entrance effect did not persist beyond the point which might be expected. The data of Dwyer and associates were taken on individual tubes and the coefficients are therefore not the same as the average ones for which Equation 1 was initially written. Agreement with Colburn's form of the equation implies that the behavior of the tubes well within a sufficiently deep bank largely fixed the transfer characteristics of the bundle as a whole. On the other hand, the influence of entrance effects on the coefficients of individual tubes in the first two or three rows is felt appreciably in the average coefficient over a bank as much as six or seven rows deep, as shown by Kays and Lo (9). Experimental Equipment
T h e circulating system was a hydraulic loop carrying pressurized, deionized water a t temperatures u p to 300' F. Flow 380
l&EC PROCESS D E S I G N AND D E V E L O P M E N T
SUPPLY
Figure 1.
TANK'
Flow sheet of experimental apparatus
w12"-.i,
KNIFE EDGE-
.
075" HOLES 0911"CENTERS
I 2 3 4 5 6 7 8 910 R O W NUMBER
Figure 2. Tube sheet layout for staggered bank showing method of specifying tube position
COMPENSATION HEATER
/
/TEFLON
SLEEVE
THERMOCOUPLE
I t
\ALUMINUM
FOIL LAYER
Figure 3. Heated tube with thermocouple installation
through a 4-inch steel line equipped with appropriate meters, heat exchangers, and accessories was maintained by two 500gallon-per-minute purnps capable of producing heads u p to 175 p.s.i.g. and arranged for series, parallel, or separate operation. The test fluid was steam condensate intermittently recirculated through beds of deoxygenating resin and anionand cation-exchange resins. The experimental heat exchanger !vas installed in a 2I/2-inch bypass line in the main loop. T h e rate of water flow in the test section was controlled by means of a n air-operated valve and measured by means of a standard orifice meter. IVater temperatures within the exchanger and in the hydraulic loop \cere measured by means of thermocouples. The flow scheme is shown in Figure 1. The experimental exchanger consisted of a rectangular shell through xvhich the water flowed in the horizontal direction perpendicular to a bank of vertical tubes 12 tubes wide and 10 ro\\.s deep in the direci:ion of flow. The shell, which !vas constructed of lll'e-inch mild steel plate, had a 12- X 12-inch internal cross section and a total length of 63 inches. T h e transition from the standard 2I,'2-inch supply pipe to the crosssectional area of the tube bank Ivas made through a smooth expansion section of 'i'l-inch steel plate, 24 inches long, placed inside the shell. Pressure taps were installed 27 and 55 inches from the inlet end of the shell for the purpose of measuring pressure drop across the tube bundle and the \rater temperature was measured a t the latter point by means of a thermocouple probe. The tubes had an outside diameter of 0.75 inch and \rere arranged on 0.94-inch centers, yielding a pitch-diameter ratio of 1.25. T ~ v oarrangements were studied, a staggered equilateral lattice and ,a square in-line lattice. The tubes \rere held in place by tube sheets xvhich lay flush against the top and bottom of the shell \vith their leading edges beveled to a 7' knife. The layout of a tube sheet and the method of numbering tubes and ro\vs are illustrated in Figure 2. Most of the members of each bundle xvere dummy steel tubes 12 inches long Ivhich terminated at the interior of the shell. The bundle was held rigidly in plaize by six longer tubes \vhich penetrated the shell in any one o f the odd-numbered roivs and in tube positions 1, 3> 5, 8: lO> and 12. These tubes passed through the ~ i - a lof l the shell 41 inches doivnstream from the inlet end and \vere sealed by header plates and O-rings so they could be removed. Thus the bundle could be moved backlvard or forlvard and the tubes could be rearranged so a heated tube might replace one of the long dummies a t any one of a number of positions \vithin the bank. T h e heated tube \vas of copper, 25 inches long, Lvith an outside diameter of 0.75 inch over the central 10 inches and of ll,'lR inch out to the ends. Teflon sleeves: 1 # 1 3 ! inch thick and 4l,'! inches long. adjoined the 10-inch section and insulated each end of the tube from the shell and seal. Heating coils \\.rapped around the m d s of the tube compensated for any heat loss to the surroundings. The main heater ivas a 220volt a.c.. 1250-1vatt cartridge unit 10 inches long lvhich \vas Ivrapped closely \\-ith aluminum foil and installed centrally within the tube. The heater \vas connected to a L-ariac and a single-phase source, and an ammeter and voltmeter \rere used to determine the poxver input. Surface thermoc installed 90' apart on the periphery of the tube 4> 10 inches from one end of the 10-inch heated section. The last was used in compensating for heat losses: the first three in obtaining data. The tube \vas allvays aligned ivith the flow in such a \vay that surface temperatures ivere obtained at the front and rear stagnation points and a t one point midxvay betiveen them. T h e thermocouple installation is illustrated in Figure 3. Experimental Procedure
After the tube bundle had been installed with the live tube in the desired position: the water ivas raised to approximately the operating temperature by circulation through a heater in the main loop and air was bled from the system. Before each run, the surface thermocouples \rere checked against the bulk temperature of the \rater and poiver was supplied to the live tube only after null points had been determined. .4s the poirer to thc main heater \vas iincreased to nearly the maximum value of 1230 ivatts, it \\-as necessary to supply 10 to 15 \vatts to the compensating heaters a t the ends of the live tube in order to keep the surface temperatures uniform over the heated length.
Since the total heat loss was only about 2% of the input, compensation based on one thermocouple was judged to be satisfactory. The single live tube added only a small amount of heat to the rapidly circulating vater. In spite of the large capacity of the system, however. the water temperature increased very gradually, mainly because of the action of the pumps. Since the change over any one run was negligible, no attempt \%as made to hold the temperature constant over a series of experiments or other\+ise to eliminate the influence of fluid properties. The data l+ere therefore treated in the manner of Colburn. using a "film" temperature equal to the arithmetic mean of the surface and bulk fluid temperatures and a constant exponent on the Prandtl number. Thus the relationship of concern ivas of the form
for a given tube position and geometry. Since the local heat flux a t a given point on the periphery of the tube was not measured, coefficient \+-asdefined through the equation q = KA(t,3
- t),
\\.here q is the rate of total heat transfer across the outside surface area: A ? of the heated section of the live tube. The quantity (t.3 - t ) m is the mean temperature difference bet1veen the surface of the tube and the bulk of the fluid obtained by applying Simpson's rule to the differences measured at the points 90' apart over the periphery. I n no case did the extremes of these differ by more than a quarter of the average temperature difference; so this means of integration yielded satisfactory results. Tubes in the vicinity of the shell \vere rotated so measurements of the surface temperature could not be made on both sides of the stagnation point, since symmetry could not be assumed in such cases. Several sets of runs were made ivith first one and then another thermocouple facing upstream. No effect of position could be noted. Thus there appeared to be no significant axial variation of ivall temperature over the central portion of the heated tube. Heating runs \\-ere made with the live tube at various positions in both the staggered and in-line bundles. The bulk temperature of the Ivater ranged from 230' to 310' F. and the Reynolds numbers from 10.000 to 190,000. Pressure drops across the staggered array Tvere measured in a separate series of runs. Experimental Results
The method of specifying the position of a particular tube in the bank can be understood by referring to the numbers of tubes and roi\s sho\\n in Figure 2. The row number is given the prefix R and the tube number in that row the prefix T. Thus, for example. the tube specified as R3T10 is in the third ron from the upstream side of the bank and is the tenth tube from the reference end of that row. The T 5 tubes are therefore in a file close to the center of the bank and the T12 tubes are in the file adjacent to one of the walls. Some of the data for the fifth file of the staggered arrangement and also for one tube of the in-line bank are shonn in Figures 4 and 5 to illustrate typical experimental solutions of Equation 2. The points on the logarithmic coordinates can be represented satisfactorily by t\\ o straight-line segments. Therefore, over limited ranges of Reynolds numbers. Equation 2 can be evaluated in the simple form =
VOL. 4
K(Re,)m
NO. 4
OCTOBER 1 9 6 5
(3) 381
iT IC
Figure
tI ),O0 0
4. Heat transfer data for fifth file of first row A 0
Staggered In-line
NRI
Figure 5. Heat transfer data for ile of third, seventh, and ninth rows of staggered arrangement D Tube R3T5 A Tube R9T5
V 382
l & E C PROCESS D E S I G N A N D DEVELOPMENT
Tube R7T5
Constants K and m are seen to depend on the position of the tube Lvithin the bank a s well as on the Reynolds number range under investigation. 'Table I summarizes the values of the constants obtained from the experimental data a t various positions in the staggered bank and for the in-line lattice. In general, the constants indicate similar behavior in the tivo types of lattices. In the in-line case, holvever, the tubes near the \Val1 of the exchanger exhibit a different dependence on Reynolds number in the 50:OOO to 70>000range. This is very evident in the data for tube R9T12 Ivhich are shown in Figure 6. The two straightline segments do not intersect as in the case of the staggered lattice and there is a clistinct displacement along the Reynolds number scale in the area of the transition. The behavior of the \Val1 tubes in the staggered array is shown in Figure 7 by Lvay of comparison. \\'hen the constants from Table I are inserted in Equation 3, the numerical results presented in Table I1 are obtained. As expected, the influence of the entering jet on the heat transfer coefficients is most apparent in the data for the centrally situated tubes in the first few ro\vs a t high Reynolds numbers. In the low Reynolds number range the transverse pattern is very uniform, even in the upstream part of the lattice. As the Reynolds number is increased, the jet causes a progressive increase in the cocffic.ients of the T5 file relative to the other files in the first fexv rc)\vs. At the same time, the coefficients of the T12 (Xvall) file in these rows are relatively decreased to some extent. Even at the highest Reynolds numbers investigated here, however, the jet is largely dissipated over the first half dozen roIvs and the coefficients in the rest of the lattice are almost independent of the rank or file of the tube. Once the jet is dissipated, the coefficients for the tubes in the doxvnstream parts of both the staggered and in-line lattices attain about the same values a t a given Reynolds number. Both the longitudinal and transverse effects of the jet: ho\\ever, are someivhat more strongly manifested in the in-line lattice where the tubes do nc't have as good an opportunity to block the flow. The pressure measiurements were made in the staggered lattice under the influence of the jet and \vith the Lvater a t a variety of temperatures. The effect of fluid properties on the pressure drop was assumed to follo\v the Jakob equation
Table 1.
Effects of Tube Position and Reynolds Number on Constants of Equation 3
K
Tube AYo.
RlT5 R3T5 R5T5 R7T5 R9T5 RlTlO
R3T10 R7T10 RlT12 R3T12 R7T12
STAGGERED TUBES 0.28 0.6 0.0044 1. 0 0.31 0.6 0.013 0.9 0.32 0.6 lOl000- 40;OOO 40.000-110.000 0,038 0.8 0.33 0.6 10.000- 80,000 0.034 0.8 80,000-190,000 0.33 0.6 10,000- 80,000 80,000-150,000 0.034 0.8 0.11 0.7 10 000-1 50,000 0.32 0.6 10.000- 70.000 0.011 0.9 70:000-180;000 0.31 0.6 10.000- 80,000 80,000-180,000 0,032 0.8 0.11 0.7 10,000-150,000 0.34 0.6 10,000-150,000 0.11 0.7 10,000-200,000 ~
IN-LINE TUBES 0.28 0.6 1. o 0,0044 R3T5 0.13 0.7 0.044 0.8 0.10 R6T5 0.7 R9T5 0.32 0.6 0.32 0.8 R3T10 0.12 0.7 ~ 6 ~ 1 0 0.28 0.6 0.033 0.8 0.10 0.7 R9T10 0.033 0.8 R3T12 0 016 0 9 0 026 0 8 R6T12 0 11 0.7 0,032 0.8 R9T12 0.14 0.7 0.11 0.7
R1T5
Table 11.
Re1.8:
Re = 5 x 104
=
R1T5
R3T12 R5Tj R7T5 R.7T10 R7T12 R9T5
70 69 70 78 80 85 80 83 78 70 83
R1T5 R3T5 R3T10 R3T12 R6T5 R6T10 R6T12 R9T5 R9T10 R9T12
70 82 76 64 63 70 69 80 63 88
RlTlO
RlT12 R3T5 R~TIO
(5)
The measured pressure drop was much less than that due to friction alone since the jet expanded Xvithin the lattice, but the details of the expansion were not investigated. To estimate the pressure drop in the absence of any jet: the entire expansion \vas assumed to take place jvithin the bank in the manner of a simple expansion with uniform velocities a t every transverse plane. The pressure gain obtained from the momentum balance over the simple expansion from the inlet pipe to the empty shell was added to the measured pressure drop in each
~
iVu , P r j -1)
Re
104
Ap (inches of water a.t 70' F.) = 7.6 X
10:OOO- 33:OOO 33,000-120,000 10,000- 36:000 36.000-120.000 10 000-1 30 I000 10,000- 88:000 88,000-130,000 10,000-130,000 10,000- 45,000 45,000-120,000 10 000.- 50,000 70,000-180,000 10,000- 40,000 70.000-1 20,000 10,000- 40,000 70.000-150.000 10.000- 40.000 70~000-150,000
Values of (NujPrj-'I3) Obtained from Equation 3 with Constants from Table I
Tube
where x i is the ratio of' transverse pitch to tube diameter and ;V is the number of ro\vs of tubes in the bundle. IYith this as a basis, the measured pressure drops \vere adjusted to a common \vater temperature of 300' F. Since the pressure measurements were made in a separate series of runs, no heating was done with the live tube and the film temperature \vas therefore the same as the bulk temperature of the water. The measured pressure drops corrected to 300' F. could be correlated by the equation
Reynolds ~VO. Range
m
3
Re
=
105
STAGGERED TUBES 220 440 210 350 220 350 220 420 210 350 220 340 220 380 220 340 200 320 220 350 220 340 IN-LINETUBES 220 250 230 220 200 190 220 210 200 240
VOL. 4
NO. 4
440 440 380 260 320 330 320 320 330 350
Re = 1.5 X 105
660 460 460 590 500 440 530 470 460 460 470
660 610 500 360 420 460 450
450 460 460
OCTOBER 1 9 6 5
383
instance. T h e results are shown in Figure 8 and can be represented by the equation
Ap (inches of water a t 70’ F.)
= 4.84
X 10-9
(6)
Discussion of Results
As in the case of Dwyer’s work, it is estimated that the heat transfer coefficients presented here are accurate within 15% and the water flo\v rates uithin 5%. T h e heat transfer coefficients for tubes R5T5, R7T5, R7T5, and R7T10 in the staggered lattice are within 10% of those found by Divyer
in the main part of his tube bank. This indicates that the tubes situated in the part of the bank unaffected by the iet or I+alls have essentially the same coefficients in a n equilateral lattice with a pitch ratio of 1.25 as in one \\ith a ratio of 1.58. Tubes R 7 T j . R7T5, and R7T10 in the staggered lattice exhibit the same abrupt change of exponent m at the same Reynolds number of 80.000 as do Dwyer’s tubes. I t appears, therefore, that the break point is not appreciably influenced by the pitch ratio, provided the tube under consideration is situated in the central part of the lattice and sufficiently far downstream from the leading row. O n the other hand, the CO-
1,000
x -1
z;loo 52 z v
1,000 Figure 6.
384
10,000
NR,
100,000
Heat transfer data for tube R9T12 of in-line lattice showing transitional behavior
I & E C PROCESS D E S I G N A N D D E V E L O P M E N T
efficients for the R l T 5 , R3T5, and R5T5 tubes in the staggered lattice exhibit break points a t Reynolds numbers between 33,000 and 40,000. Although it could not be determined precisely, there appears to be a n upward progression in the Reynolds number of the break with increased depth of penetration into the lattice. The break point is almost surely associated with turbulence iin the boundary layers on the individual tubes. TVith the Reynolds number defined on the basis of a n over-all flow rate, the variation in break point is to be expected. I n cases where the first row is exposed to an essentially uniform velocity of approach with no entering jet present, investi-
Table 111. Average \/slues of ( N u ~ P r j - ' / ~over ) Tube Banks of Various Depths in Presence of Entering Jet of Type Investigated Aierage (-VujPrf-l 3, f a r Bank AVO. of ~ . _ _ R o r ~ sin Re = Re = Re = Re = Bad 704 5 x IO' 706 7.5 X 105 SjTAGGERED
7
70 73 75 75 76 76 76
1
70
21 5
72
220
73 72 71 70
230 220 215 21 5
1
2 3 4 5 6
215 220 220 215 215 215 215
LATTICE 390 390 390 380 370 370
540 540 530 530 520 510
360
51 0
IN-LISELATTICE
2 3 4
5 6
390 390 380 380 370
540 540 530 510 500
36 0
49n
gators have consistently found that the coefficients for the first row in both staggered and in-line lattices are 30 to 40% lower than those for, say, the tenth row. I n the present \vork, the front roiv tubes, R l T l O and R l T 1 2 , of the staggered lattice lay outside the direct circle of the impinging jet. The scale of the turbulence confronting them, hoivever, was in all probability smaller than it \vould have been had the scale been fixed by the empty shell alone. In this respect it came closer to resembling the turbulence within the lattice. The front row tubes in the present experiments exhibited coefficients ivhich were only a little loiver than those farther back in the lattice a t low Reynolds numbers and about equal to them a t higher Reynolds numbers. There \vas no break point evident ivithin the investigated range and exponent m remained constant a t 0.7. The variation \vith Reynolds number was therefore the same as observed by Drvyer, but the coefficients in the present case \vere uniformly greater than his a t a given Reynolds number value, almost certainly because of the nature of the initial flow. TVhen the present results are extrapolated to much higher Reynolds numbers than those investigated. the front row COefficients become markedly loiver than those in the main bank because their rate of change with Reynolds number is smaller. Again, this is qualitatively the same behavior as observed by Dyer. Snyder (72) observed that in staggered? isosceles lattices a t Reynolds numbers from 8000 to 2 j ; O O O the coefficients increase steeply from the first to third rows! drop somewhat in the fourth and fifth ro\vs? and then rise again to a constant value for the sixth and folloiving roJvs. LVhen the numbers in Table I1 are plotted against longitudinal position in the lattice (not done here because the intermingling lines make for a tonfusing presentation), the coefficients can best be interpolated if a dip is assumed to occur after the third roiv. It appears, however, that the eventual rise to a constant downstream value happens more slo~vlyfor the tubes near the ivall than for those near the center of the bank. The dip is more pronounced and the recovery in general is more delayed in the in-line lattice xvhere the jet persists longer than in the staggered lattice. It thus appears that the robbing of the xvall tubes by the jet is a factor in the transverse profiles even lvell back in the bank and that in this respect the influence of the jet penetrates the lattice appreciably deeper than might be concluded from study of the centrally situated files alone. The peculiar transitional behavior of some of the in-line tubes. as illustrated in Figure 6 >has not been explained on the basis of the present data. The hydraulic conditions a t tubes near the rvall must be complicated by asymmetry and reflection of the ivakes from the flat surface. The in-line lattice has the end tubes in every row equally close to the lvall) Lvhile the staggered lattice has only the tubes a t the ends of alternate ro\vs equally close. I t is not surprising, therefore, that the transitional characteristics in the tivo geometries should be different. The difference seems to be largely a jvall phenomenon, since the central tubes sho\v about the same transitional behavior in the t\\-okinds of lattices. The pressure drop due to friction, sho\\-n in Figure 8 and Equation 6: is about 227, loiver than predicted by Equation 4. The latter is based on the data of Pierson for the flou. of air normal to staggered tubes at Reynolds numbers from 200 to 40,000. DIt-yer and his colvorkers found that their data for a staggered lattice ivith 1.58 pitch-diameter ratio fitted the extrapolation of the Jakob equation up to a Reynolds number of 106. O n the other hand, Huge measured pressure drops across staggered banks ivith a 1.25 pitch ratio and obtained results 20 to 257, lower than those of Pierson. I t appears in the VOL. A
NO.
4 OCTOBER 1 9 6 5
385
Figure
9.
Average Nusselt numbers for staggered and in-line banks 10 rows deep
present case, therefore, that the treatment of the jet as an ordinary expansion is adequate for practical purposes even though the model is oversimplified. The results thus obtained are within the spread of previous data and very close to Huge’s observations a t the same ratio of pitch to tube diameter. To complete the picture, the data of Table I1 Ivere smoothed transversely and longitudinally through the lattices and the averages for banks of various depths were calculated (Table 111). The influence of the jet is clearly significant in banks less than six or seven ro\vs deep. Even a t a Reynolds number as low as 10,000 the average coefficients do not increase markedly with depth in the usual way. O n the other hand, the average coefficient for a staggered lattice 10 rows deep obeys the Colburn equation up to the transitional point and is in agreement xvith Dwyer’s mainbank data a t still higher Reynolds numbers. This re:ult, sho\vn in Figure 9, indicates that the effect of the jet has been overcome. Grimison’s correlation for a 10-row staggered bank lies about 10% above the Colburn line a t a pitch-diameter ratio of 1.25, although the lines are close together for ratio of 1.5. The difference is unresolved, since the results of the present Ivork indicate no significant change in going from Dwyer’s ratio of 1.58 to the present ratio of 1.25. Figure 9 sholvs that there is little difference between a staggered lattice of 10 rows and an in-line one, on the average. The coefficients for the in-line lattice are about 3% lower than those for the staggered bank. This is almost exactly the percentage difference observed by Grimison at the same pitch-diameter ratio and is much less than the 217, difference originally suggested by Colburn. At Reynolds numbers below 2000, however, Bergelin and his coworkers (7-4) have found that the coefficients for an in-line bank are much lower than those for the corresponding staggered lattice. Therefore, the present results can be extrapolated downward through only a very limited range of the Reynolds number scale.
SUBSCRIPTS f = film temperature b = bulk temperature m = mean value
Acknowledgment
literature Cited
One of the authors (A.A.A.) received educational fellowships from the Dow Chemical Co., E. I. du Pont de Nemours 8r Co.,
(1) Bergelin, 0. P., Brown, G. A., Colburn, A. P., Trans. Am. SOC. Mech. Engrs. 73, 841 (1951).
386
I&EC PROCESS DESIGN A N D DEVELOPMENT
and the Allied Chemical Corp. The two large pumps in the main loop were obtained through a grant from the Esso Education Foundation. Nomenclature
A
= outer tube-wall area through which heat is transferred,
B
= constant? dimensionless
C,
=
constant-pressure heat capacity of fluid, B.t.u./(lb.)
Do
=
gc
=
G,,,
=
outer diameter of tube, ft. conversion factor = 32.2 (lb. mass)(ft.)/(lb. force) (sq. sec.) mass velocity of fluid through minimum cross-sectional area available for flow, lb./(hr,) (sq. ft.) heat transfer coefficient for one tube, defined by Equation 3: B.t.u./(hr.) (s4. ft.)(OF.) average heat transfer coefficient for entire bank of tubes: B.t.u./(hr.) (sq. ft.) (OF.) thermal conductivity of fluid, B.t.u./(hr.) (ft.) (OF.) constant, dimensionless constant: dimensionless constant: dimensionless number of ro\vs oftubes in bank, dimensionless Nusselt number, hD,/k, or h,D,/k, dimensionless pressure drop across bank, lb. force/:q. inch Prandtl number, C,p/k. dimensionless total rate of heat transfer across area A? R.t.u./hr. Reynolds number, Do GmaX/p,dimensionless bulk average of fluid, OF. temperature of outer tube-\vall surface, O F . ratio of transverse pitch to tube diameter, dimensionless viscosity of fluid, lb. mass/(hr.)(ft.) density of fluid, lb. mass/cu. ft. function, dimensionless
sq. ft.
(OF.)
=
h,
=
k K m n
= = = =
Pr
= = = =
q
=
Nu
Ap Re t t, xt p
p
9
= =
= = = = =
(2) Bergelin, 0. P., Brown, G. A., Doberstein, S. C., Ibid.,74, 953
(1952). (3) Bergelin, 0. P., Brown, G. A., Hull, H. L., Sullivan, F. IV.,
(10) McAdams, \V. H., “Heat Transmission,” 3rd ed., p. 273, McGraw-Hill, New York, 1954. (11) Pierson, 0. L., Trans. Am. Soc. Mech. Engrs. 59, 563 (1937).
zbid., 72, 881 (1950). (4) Berg-elin, 0. P., DaLis, E. S., Hull, H. L., Ibid., 81, ser. C, 369 (1959j. (5) Colburn, A. P., Trans. Am. Znst. Chem. Engrs. 29, 174 (1933). ,(6) Dwyer, 0. E., Sheehan, T. V., IVeisman, J., Horn, F. L., Znd. E q . Chem. 48, 1836 (1956). (7) Grimison, E. D., Trans. Am. Soc. Mech. Engrs. 59,583 (1937). (8) Huge, E. C., Zbid.,5!), 573 (1937). (9) K ; I ~ . s\V, , M., Lo: K . K., Department of Mechanical Engineering. St i*iford Univeraity, Calif., Tech. Rept. 15, NR-035-104 (-4ug. 13, 1952).
ACCEPTED June 14, 1965 Based on material submitred in partial fulfillment of the requirements for the degree of doctor of philosophy at the Carnegie Institute of Technology. Original data contained in thesis “Forced Convection in Banks of Tubes” by A. A. Austin, Department of Chemical Engineering, 1959, available on interlibrary loan from the Hunt Library, Carnegie Institute of Technology. Project sponsored by the U. S. Atomic Energy Commission.
(12) Snyder, N. IV., “Heat Transfer Symposium,” Am. Inst. Chem. Engrs. Syrnp. Ser. 1 6 (December 1951). RECEIVED for review November 9, 1964
FUSED-SALT FLUORIDE-VOLATI LlTY PROCESS FOR RECOVERING URANIUM FROM SPENT ALUMINUM-BASED FUEL ELEMENTS M . R . B E N N E T T , G. I . C A T H E R S , R. P. M I L F O R D , W . W . P I T T , JR., AND J. W . U L L M A N N Oak Ridge ATational Laboratory, O a k Ridge, Tenn.
A molten-salt fluoride-volatility process for dissolving aluminum-based nuclear reactor fuel elements and recovering the uranium as u F 6 has been demonstrated at laboratory and engineering scales. Aluminumuranium is dirsolved in KF-ZrFd-AIF3 at 575” C. by reaction with HF, and the uranium is then converted to volatile UFe with fluorine. Further purification steps are identical to those used in the Zr-U alloy process. Corrosion has, been studied; pilot plant tests with irradiated fuel are under way.
fluoride-volatility process has been developed to recover the uranium from spent nuclear reactor fuels that consist of a n alloy of aluminum and highly enriched uranium clad in alumi.num. T h e process has been tested a t laboratory and engineering scales (semiworks). A pilot plant study began in July 1964. This paper describes only the laboratory and engineering-scale studies. T h e \vork is part of an AEC-sponsored program to develop fluoride-volatility methods as alternatives to aqueous methods for processing various spent reactor fuels. Analogous studies using fluidizedbed methods (70, 79) and the Nitrofluor process (20) have been conducted a t Argonne and Brookhaven Sational Laboratories. Although an aqueous process for aluminum-based fuels ( 9 ) is in use, a commercial fuel-processing plant using the fluoridevolatility method will need a method for aluminum-based fuels, since a major part of the highly enriched reactor fuel load is aluminum-based. Development of this process for AI-U alloy fuels is a continuation of a program a t Oak Ridge National Laboratory in Lvhich fluoride-vo1atilii.y methods have been applied to the processing of molten salt (2) and Zr-U alloy (4,5) fuels. I n both processes, conversion of the uranium to volatile U F 6 with fluorine in a mixture of molten fluorides is the key step. Molten-salt fuels are fluorinated directly; Zr-U alloy fuels are first dissolved in a fluoride melt by reaction with H F . T h e UFB is separated from the volatile fluorides of contaminating elements with beds of NaF and MgF2. Details of the UFO
A
MOLTES-SALT
purification steps in the A1-U alloy fuel process are identical with those reported elsewhere for the Zr-U alloy process ( 3 ) . Advantages of Process
Like its counterpart for Zr-U alloys, the process for AI-U alloy fuels appears particularly attractive from the standpoint of directly yielding its highly radioactive waste as a low volume of solids. T h e process has minimal problems of nuclear safety. From the standpoint of chemical safety, the reactions are easily controlled; no reservoirs of liquid oxidants are present; and the process operates a t practically atmospheric pressure. By analogy to the Zr-U alloy process, the degree of decontamination of the uranium from fission products should be exceptionally high, and uranium losses have been shown to be low. Points of Concern. As in most fuel-recovery processes, corrosion of process equipment must be considered. By normal standards, corrosion in molten-salt fluoride-volatility processes is high. However, our data indicate that corrosion rates in the dissolution, or hydrofluorination, step are similar for the zirconium and aluminum processes. Unfortunately, one recent study indicates that corrosion during the fluorination step may be worse. T h e proximity of the temperature of the melt during the dissolution step to that of the melting point of the A1-U alloy has been of concern, but laboratory tests and calculations indicate that the accidental melting of a fuel element during fullscale operation should not lead to any serious consequences. VOL. 4
NO. 4
OCTOBER 1 9 6 5
387
