Cooling of Gases through Packed Tubes MAX LEVA, MURRAY WEINTRAUB, MILTON GRUMMER, AND E. L. CLARK Central Experiment Station,
U. S . Bureau
of Mines, Pittsburgh, Pa.
The coefficient h of the first equation was differentir with respect to D, a t Dt and G = constant, and a m mum heat transfer coefficient was predicted for a -ti DP - = 0.153. This was verified experimentally.
H e a t transfer coefficients were determined for the flow of heat from hot air and carbon dioxide to cooling water. Tests were made with a 2-inch and a S/d-inch standard packed pipe. The packing material was of low thermal conductivity, spherical, and smooth. The ratio of particle to tube diameter varied from about 0.08 to 0.27. The gas flow range was characterized by the modified Reynolds number interval 250-3000. Two dimensionally homogeneous equations were proposed correlating film coefficient h w i t h the physical properties of the system. Thus:
Dt
second equation is not quite so precise as the first fc but for most engineering work it is accurate enough, on account of its greater simplicity should be prefe to Equation 1. Both equations state that h is pro tional to
($).
This was proved by determining
transfer coefficients for carbon dioxide. The value of group is 229’0 smaller for carbon dioxide than for air. check between the air data and carbon dioxide data excellent. The possible inclusion of the Prandtl nul is discussed as well as the application of the equatioi tube sizes larger than 2 inches.
and, by an approximation of Equation 1,
E
ARLIER work (1) in this field revealed t h a t heat transfer
ture. The air outlet of the small tube was open, and then two copper-advance thermocouples which, for all the experir were approximately l / 4 inch below the adjustable screen a inch apart from each other. The temperature gradieni served were negligible in all cases. The water jacket me2 36 inches on the large and 14 inches on the small tube.
coefficients of gases passing through packed tubes could be correlated by the equation:
The validity of this expression for a wide range of gas. heating operations was stressed a t that time. There was, however, no experimental evidence to show whether this equation could also be used to estimate heat transfer coefficients for gas cooling operations. A few orienting experiments with a 2-inch tube were sufficient t o indicate t h a t the above equation did not apply t o cooling operations. The experimental findings were about 15y0 higher than the calculated values. It appeared, therefore, that typical data were required if a correlation was to be achieved which would permit the prediction of gas cooling coefficients.
f
valve I
,
va
\0
Thermometer Thermocouple
UNIT AND OPERATION
Figure 1 shows essential details of the experimental equipment. Two tubes served as test units. Measured quantities of air could be admitted to either the 2-inch or a/*-inch tube. By proper manipulation of valves 1 and 2, the temperature of t h e air arriving a t the tubes.could be controlled satisfactorily. To induce good mixing and thereby avoid temperature grtdients, the air entered the tubes sidewise through tees. At this point the inlet air temperature was measured by mercury thermometers. The air left the large tube through a reducer and throttle valve. Horizontal temperature explorations revealed t h a t this device was well suited for equalizing the air tempera-
\Thennometar Blower
Water inlet
Figure 1. Unit for Determination of Cooling Coeffi
747
INDUSTRIAL AND ENGINEERING CHEMISTRY
748 TABLE I.
5;; -. _.
ZU
COLLECTED WITH
DATA
G
Re
ti
575
498 426 349 328 268 215 160
327.5 330,b 324 324 5 337.0 330.3 331
tz
tw
%INCH
TUBE
At
Q
78.6 77.5 74.0 73.0 65.9 61.6 33.4
2370 2058 1648 1557 1348
h
hDt k
D p = 0.169 1n.b 41.6 35.6 29.2 27.4 22.4 17.95 13.40
1-a b
8 7 ,5 86.5 86.0 85 83 82 80.5
Dp 2-a b c d e f g
39.2 30.1 25.6 21.5 18.18 15.01 11.37
1681 1291 1098 905 765 632 479
478 367 312 258 218 180 137
324 337 337 338 335.5 327.5 333
3-a b
51.4 44.5 37.0 29.06 25.8.5 20.9 17.28
2205 1910 1588 1248 1110 896 740
841 730 606 476 420 339 280
331.5 331.5 338.5 336.5 326 329 328.5
48.5 43.1 40.0 34.9 29.8
2078 1840 1720 1498 1277
780 695 643 561 480
335 339.5 330.5 337 329.5
57.7 49.8 42.4 30.2 30.2 25.4 19.61
2480 2140 1819 1295 1295 1090 841
1583 1367 1161 827 827 697 537
325.5 335.5 336 333.5 330 331 333.5
1690 1556 1465 1230 912 1551 1386 1260
382 397.5 397.5 398.5 398.5 394 361 366.5 363.5
2230 2080 1745 1360 985 852 691 561
1430 1330 1120 870 631 546 443 360
329 337 333.5 334 330.5 321 5 328.5 335
3158 2836 2432 2105 1767 1470 1215 1063 923 785 654 543
265.5 2384 2045 1770 1485 1284 1020 895 776 660 550 457
331.5 336 335 325 325 339 329.5 330 324.5 325 329 335
2690 2450 1982 1561 1287 1055 857 679 513
2258 2058 1663 1312 1086 886 720 570 430
323.5 333.5 336 337,5 332,5 331.5 330 330 328
75.5 75.5 76 76 77.5 77.5
77
795
20.2 18.0 15.0 14.3 13.7 11.5 8.90
192 170 142 135 130 109 84.0
71.9 71.9 70.0 69.1 65.8 62.8 60.8
2210 1802 1535 1300 1091 874 679
20.6 16.7 14.8 12.6 11.0 9.0 7.50
195 158 140 119 104 85 71
84.8 82.9 81.8 75.4 72.0 70 4 67.7
2978 2590 2223 1684 1493 1230 1019
24.0 21.0 18.3 15.0 14.0 11.7 10.0
227 199 173 142 133 111 95
87.8 87.4 83.5 82 1 76.9
2830 2468 2310 2076 1735
21.6 19.0 18.6 17.1 15.2
205 180 176 162 144
80.3 79.8 78.9 73.9 71.4 70.5 66.7
3240 2932 2510 1786 1768 1497 1174
27.6 25.0 21.5 16.1 16.7 14.1 11.9
262 238 204 153 159 134 113
105 105 103 104 100.3 88 93.5 93.2 93.0
4358 4294 4045 3392 2530 1832 3724 3400 3070
28.3 27.2 27.0 22.0 17.0 14.0 27.2 25.0 22.5
271 260 258 210 162 134 2 52 231 208
81
72.5 64.3 64 62.2 60
2980 2790 2400 1880 1360 1140 950 795
25.0 22.5 21.4 17.5 14.1 11.9 10.0 8.50
237 213 203 166 134 113
97.6 93.2 88.1 83.3 78.9 78.2 73.0 70.8 68.5 66.0 64.0 63.6
4180 3850 3116 2765 2342 2085 1668 1470 1250 1061 911 779
29.8 28.3 24.0 22.5 20.0 18.0 15.2 14.0 11.7 10.7 9.50 8.00
280 a67 226 212 188 170 143 132 110 101 90 75
30.0 28.5 23.5 18.3 17.2 14.6 12.5 10.2 7.70
285 271 223 174 164 139 119 97 73
1057
= 0.169 I n .
86.0 84.5 84.0 83.0 82.5 82.0 81.0
77.0 77.0
77.0 76.5
77.0 77.0
77.0
D p = 0.228 In.
c
d e f g
87
86 85 82 81.5 80.5 79.5
72.5 72.5 73 73 73 73 73
D p = 0.228 In. 4-a b c d
e
89 88 87 86 84
73 73 73 73.5 73.5
a
D p = 0.388 In. 5-a b c d e f g
88.5 87 86.5 84 83 82.5 81
75.5 75.5
75.5 75 75 75 75
D p = 0.388 In.
e f
i?
i
63.3 58.4 54.9 46.1 34.2 24.6 57.1 51.0 46.3
657
71.5
io
71 71.5 71.5 71 71.5 70.5 69.5
D p = 0.388 I n . 7-a b c d e f
51.7 48.1 40.4 31.4 22.8 19.8 16.0 13.0
Dp 8-2
b
: e
f
85 83.5 82 81
78
77.5
77
76.5
72.5 73 72.5 73 73 72 72.5 73
84 76
95 80
= 0.5075 I n .
92
00 .~
88 86.5 84.5 82 80.5 79.5 78 ’ 78 77 76
70 71 72 72 72.5 72 72 72 72 72 72 72.5
D p = 0 . SO75 In. 9-a b
ki
62.7 57.1 46.2 36.4 30.0 24.6 19.98 15.83 11.96
a Runs
75 7.5
82 81 80 79 79
74.5 74.5 85 75 75 75 75
79.8 80.2 80.1 74.1 69.5 66.7 63.6 60.4
60.0
1 to 7, inelwive, were made with glass beads of diameters as indicated: runs 8 and
9 were made with porcelain balls. b Packing height in all cases was 36 inches; air was used f o r eYery run.
Vol. 40, No. 4
the pipes were assembled, they were cleaned of all dirt, but the surfaces were not etched or polished. The circulation rate of the cooling water was kept at. t,he fairly high ve1ocit.y of 3 feet per second through the large, and 9 feet per second t,hrough the small annulus. -4s ,the temperature rise of the water a t these rates was negligible, it was sufficient to record only the inlet, water temperat,ure. For each of the various paclrings investigated, the following readings were made: air rate through tube; inlet and exit air temperatures; and wat,er temperature. On the basis of the inside packed-hibe diameter, the height, of the pacliing in the tube, and the assumpt,ion that a logarithmic temperat,ure difference prevailed betn-cen air and water, heat-transfer coefficients were calculated. All physical properties of the fluids were evaluated at, the average bulk temperatures. PACKISGMATERIALS.Low thermal conductivity [
