Gas-Liquid Contacting by Mixers A. e. q d f 3.c.
M d , E*td #. A. RudhhW
UNIVERSITY OF VIRGINIA, CHARLOTTESVILLE, VA.
7 Results are presented on the dispersion of air in water by means of a disperser-type mixer. The amount of air held u p o r retained in bubble form in a cylindrical tank Filled w i t h water has been measured end i s considered t o b e useful in estimating the ability of mixers to disperse gases in liquids. A term called "contact time" has been Calculated and i s related to p o w e r input and air velocity for one ratio of tank to impeller diameter. The data are taken from experiments in small vessels, 1 foot in diameter, to large tanks, 8 feet in diameter. The tanks were baffled, and the disperser was rotated on a vertical shaft on the tank axis. Liquid quantities ranged from 5 to 2250 gallons. A i r flows ranged from 1 foot per minute superficial
velocity to 5 feet per minute, Power was measured over a range of 0.01 to 6.5 horsepower. O v e r this w i d e range of conditions a general relation holds:
G
1. For the container: size and shape, depth of liquid, baffles (number, position, size). 2,. For the agitator, any one design: positipn of axis (vertical, horlzontal, angular, centered, etc.), position of impeller (depth of immersion, relation t o gas inlet), size (diameter, blade width and angle), speed, and power. 3. For the gas: position of distributor, rate of flow, temperature and pressure, bubble size, 4. For the liquid: batch or continuous flow (rate of flow), temperature, density, viscosity, and other physical properties.
ASES and liquids are normally contacted in towers where
they flow past each other by gravity and often through a tortuous path. When agitation Of liquid is desired, it is sometimes advantageous to effect the gas-liquid contact in a vessel equipped for mechanical agitation. Many forms of agitators can be used for such an operation, but one of the most promising types is the disperser (Figure 1) recently developed by the Mixing Equipment Company. Preliminary labomtory tests indicated that this disperser has operating advantages over other types of impellers; accordingly, it was selected as the basis of a study of the interrelation of numerous physical factors encountered in the contacting of gas and liquid by a n agitator. Further, the data reported here deal Only with the contacting of air (saturated) and water; continuing experiments with various watecsolutions confirm the generalizations presented, although actual relations differ in magnitude. Many physivariables aff e e t t h e performanee of an agitator in gasliquid contacting. The more important ones are:
h/f = e
= c(hp.)"/VF
The data also cover several positions of impeller w i t h regard to liquid depth. The data are useful in predicting gas dispersion as a function of the p o w e r input, and relations are given showing h o w to handle larger o r smaller volumes of gas i n order to achieve equal, lesser, o r greater contact time. Data dre included to show the effect of air flow on the p o w e r consumed at given impeller speeds.
A number of these variables are interrelated but they can be one at a time to isolate their effects. The following were kept constant throughout all the work: The tank cyfinflabbottomed, and equipped with vertical baffles. The axis of rotation of the impeller was vertical and centered on the axis of the tank. Gas inlet was a single opening immediately below the center of the impeller. A disperser (Figure 1) was used for all runs. Air pressure was approximately atmospheric (sufficiently greater to produce the required flow). Temperature of air and water were each within a few degrees of room temperature, varying between 70" and 80" F. All operations were batchwise for the liquid. Most of the runs were made in a glass walled tank, 12.5 i.d.; others were made in a metal tank, 8 feet i.d. and 8 feet deep. With the small tank the liquid depth was 9.75 to 13 inches (5 to 7 gallons). Two, three, or four baffles were used, full depth, equidistant, and touching tank side; the baffle dimensions were
ROTAMETER
4 Figure 1. Diagram of Disperser (Dimensions in Inches)
Figure
517
2.
Flow Sheet for
DRAIN
Gas Holdup Determinations
818
INDUSTRIAL AND ENGINEERING CHEMISTRY
Figure 3.
Diagram of Level Taking Device
B X ‘/le inch. The disperser (Figure 1) wa5 one third the tank diameter, used either a t one half or, preferably, two thirds the liquid depth; its speed was 410 to 854 r.p.m. The air inlet had a single opening directly below the center of the disperser. The superhial air flow was approximately 1 t o 5 feet per minute a t operating (liquid) temperature and at pressure equivalent to disperser depth. With the large tank the liquid depth was 61/, feet (2250 galPons). Three or four baffles, 2 X 8 inches, were used full depth equidistant, and touching the tank side. The disperser (similar to Figure 1 with ten blades 20 inches in diameter) was one fifth the tank diameter, used at one half or, preferably, two thirds the liquid depth, with a speed of 85 to 300 r.p.m. The air inlet had a single opening directly below the center of the disperser. The superficial air flow was 1 to 3 feet per minute. The principal variables studied were speed of impeller, air flow, depth of liquid and impeller, and number of baffles. Power input was measured and was the result of the impeller size and speed and the air flow. Thus, no attempt was made t o hold power constant during the runs, but instead power measurements were considered as resultant from and dependent upon the other variables. I n addition to the variables controlled or measured, another factor, holdup, was evaluated. It seems apparent that the amount of gas actually retained in intimate contact with the liquid in the form of bubbles at a n y one time is an important consideration in gas-liquid contacting. Furthermore, if the amount of gas retention is known, it is possible to determine a n average time of contact between gas and liquid for any given rate of gas flow. This latter can be called “contact time”. The actual retention or holdup of gas in liquid can be obtained by a n accurate measurement of the volume of liquid in the tank before and during aeration. The difference between the two volumes represents volume of air entrained or held up, and can be represented either as a percentage of the original or final mixture volume, or as the average increase in height of the liquid (Figure 5 ) . Holdup varied between 2 and 10% of original liquid depth. Average contact time between gas and liquid can be found by dividing the holdup by the air flow. As used in the correlations which follow, the vertical holdup divided by the superficial air velocity, in feet per second, is called “contact time”. The volume of gas in the holdup is ealculated a t a pressure equal t o one half liquid depth. APPARATUS
A flow sheet for the test system (Figure 2) shows the use of a glass-sided tank and is similar in all respects to the larger system
Vol. 36, No. 6
where the 8-foot-diameter tank was used. Compressed air was fed to appropriate reducing control valves. For small tank runs a rotameter measured the air flow; for large-scale runs in the 8foot tank, a calibrated orifice meter was used. The metered air was passed through a short packed tower for humidification or was by-passed if desired. After this operation the air passed to a separator where air temperature was measured. A manometer gave the pressure of the air before it entered the mixing tank. A tube was led into the tank beside one of the baffles, extended t o the bottom, and then turned u p a t the center of the tank, opening immediately below the stirrer shaft. Section A , Figure 2, shows the air inlet tube in relation t o the stirrer shaft. It was found to be most important to have uniform distribution of air. This was accomplished by drilling the end of the shaft along its axis and then drilling four holes equally spaced to permit gas to bubble out around the shaft just below the disperser. This method resulted in uniform surface contours throughout the runs, showing that the gas was fed uniformly to all parts of the underside of the disperser. The surface contour and level of the liquid was obtained in all runs by means of a so-called level taker, shown in cross section in Figure 3. It consists of two concentric copper tubes, ‘/a and l/4 inch in diameter, with a number of nonconcentric holes drilled in the upper portion of the tubes. This unit served as a device for obtaining a calm and average level surface for the small area of the surface at which it was placed. The small inner tube was led downward a considerable distance, turned up, and brought out of the tank, The level taker was clamped in such a fashion as to be easily moved to different points across any radius of the tank, The tubing was led to either a sensitive liquid-differential manometer or, more often, t o a small hook gage. Accurate readings of the level in the tank at any desired point were possible with this setup. The disperser was ER placed at the end of a half-inch shaft supported on bearings above the tank. IMPELLER A spring dynamometer was attached to the end of this shaft and made the c o u p ling between the stirrer shaft and the drive shaft. T h e ELD spring dynamometer arrangement is shown in more detail in Figure 4. A stroboscope was placed in position t o flash upon the calibrated disk Figure 4. Spring Dynamometer and pointer of the dvnamometer. The relative position of the pointer attached to the impeller shaft and the calibrated disk attached t o the drive shaft could be noted easily by the arresting action of the stroboscope, and thus the torque between the two shafts could be observed. The spring dynamometer was calibrated repeatedly and after each set of runs was checked at two points in its calibration. The dynamometer was run in air before and after each set of runs to account for the power required by the bearings. During most of the runs the helical spring of the dynamometer was one which had a maximum torque of 10 inch-pounds for two complete revolutions. Horsepowers up to 0.10 were measured satisfactorily with this dynamometer. The drive shaft had a step-cone pulley
June, 1944
519 Table 1.
Data on 4-Inch Six-Blade Disperser in Water
%$,:7t
Impeller Power Air Power Function, Speed Input, Flow, Hold- Depth HP. No. R2.M’. HP. Ft./Sec. UP, Ft. Sec./Fi. (Cu.Ft.) (Ft./Sea.) 13-In. Water Depth, Impeller 43/8 In. above Bottom, 4 Baffles 1915.0 488 0.0331 0 0 1915.1 575 0.0258 0.0238 0.0443 1165 1 if3 1915.2 582 0.0248 0.0300 0.0488 1 43 0.895 1915.3 605 0.0224 0.0425 0.0580 1.19 0.571 1915.4 614 0.0198 0.0544 0.0677 1.08 0.394 1915.5 626 0.0179 0.0665 0.0744 0.97 0.290 1915.6 630 0.0165 0.0822 0.0788 0.83 0.218 1917.0 645 0.0750 0 0 1917.1 720 0.0554 0.0238 0.0676 2:46 2:520 1917.2 724 0.0520 0.0300 0.0744 2.14 1.878 1917.3 747 0.0480 0.0425 0.0835 1.68 1.223 1917.4 763 0.0435 0.0544 0.0951 1.49 0.866 1917.5 777 0.0397 0.0665 0.1044 1.32 0.647 1917.6 792 0.0343 0,0822 0.1180 1.19 0.452 13 In. Water, Impeller 6l/2 In. from Bottom, 3 Baffles 1336.1 605 0.0278 0.0300 0.0437 1.30 i 1.005 1336.2 605 0.0192 0.0544 0.0531 0.86 0.382 1336.3 605 0.0165 0.0822 0.0589 0.63 0.218 1345.08 562 0.0457 0 0 1345.1A 702 0.0456 0.0300 0.0610 1 :?7 11647 1345.2A 778 0.0444 0.0544 0.0750 1.19 0.885 1345.3A 850 0.0822 0.0980 1.01 0.0398 n 0.524 1345.OB 0.0146 ” 380 0 1345.1B 534 0.0159 0.0300 0.0350 1 :05 0 15?4 1345.2B 578 0.0151 0.0544 0.0500 0.81 0.301 1345.3B 611 0.0150 0.0822 0.0550 0.59 0.197 n 1346.0 393 0.0160 0 1346.1 508 0.0163 0.01’37 6.0259 i:is 0:866 1346.2 522 0.0163 0.0238 0.0330 1.25 0.742 1346.3 530 0.0161 0.0281 0.0357 1.14 0.620 1346.4 533 0.0158 0.0300 0.0370 1.10 0.571 1346.5 0.0159 0.0367 0.0420 1.01 554 0.469 1346.6 562 0.0157 0.0425 0.0462 ’ 0.97 0.401 1346.7 573 0.0155 0.0482 0.0492 0.349 0.90 581 1346.8 0.0152 0.0544 0.0531 0.86 0.304 1346.9 589 0.0149 0.0603 0.0570 0.83 0.268 1346.10 603 0.0147 O.OG65 0.0597 0.239 0.79 1346.11 0.0146 0.0735 0.0625 0.74 617 0.216 1346.12 622 0.0142 0.0822 0.0632 0.187 0.67 1349.0 575 0.0485 0 0 1349.1 681 0.0476 0.0197 0.0470 2:io 2:iiio 1349.2 692 0.0468 0.0238 0,0520 1.92 2.125 1349.3 0,0455 0.0281 0.0560 697 1.75 1.755 1349.4 703 0.0452 0.0300 0.0600 1.75 1.630 1349.5 735 0.0462 0.0367 0.0660 1.365 1.57 1349.6 746 0.0442 0.0125 0.0700 1.43 1.128 1349.7 758 0,0434 0.0482 0.0740 1.32 0.975 1349.8 780 0,0435 0.0544 0.0790 1.25 0.866 1349.9 796 0.0438 0.0603 0.0820 1.17 .O.787 1349.10 808 0.0417 0.0665 0.0860 1.10 0.679 1349.11 828 0.0412 0.0735 0.0900 1.04 0.606 1349.12 854 0.0403 0.0822 0.0950 0.99 0.530 1353.0 465 0.0270 0 0 1353.1 585 0.0272 0.0197 0.0468 2:ii 1:i94 1353.2 595 0,0272 0.0238 0.0502 1.86 1.240 1353.3 603 0.0270 0.0281 0.0533 1.041 1.67 1353.4 611 0,0264 0.03no 0.0562 0.853 1.64 1353.5 638 0.0265 0.0367 0.0613 1.46 0.782 1353.6 647 0,0286 0.0425 U ,0642 1.32 0.652 1353.7 657 0.0255 0.0482 0.0675 0.573 1.21 1353.8 672 0,0256 , 0.0544 0.071’3 1.13 0.510 1353.9 685 0.0249 0.0603 0.0745 1.07 0.448 1353.10 701 0.0242 0.0665 0.0781 0.394 1.01 1353.11 717 0.0230 0.0735 0.0813 0.339 0.94 1353.12 743 0.0232 0 .OS22 0.0851 0.89 0.306
Run
:
93/4 In. Water, Impeller 31/4 In. from Bottom, 4 Baffles 1808.0 0.0203 0 0 1808.1 0.0160 0.0238 0.0321 1:io 0:6?4 1808.2 0.0146 0.0300 0.0354 1.39 0.706 1808.3 0.0137 0.0425 0.0429 1.18 0 467 1808.4 0.0125 0.0544 0.0452 0.97 0.334 1808.5 0.0121 0.0665 0.0430 0.76 0.264 1808.6 0.0115 0.0822 0.0420 0.60 0.203 1809.0 500 0.0368 0 0 1809.1 581 0.0281 0.0238 0.0394 1:94 1 :?io 1809.2 596 0.0263 0.0300 0.0437 1.71 1.270 1809.3 617 0,0230 0.0425 0.0528 1.43 0.785 1809.4 629 0.0212 0.0544 0.0620 130 0.566 1809.5 641 0.0187 0.0665 0.0656 1.13 0.407 1809.6 650 0.0175 0.0822 0.0685 0.94 0.309 * . 1813.0 450 0.0282 0 0 1813.1 553 0.0228 ’ 0.0238 0.0368 1:83 1:iis 1813.2 568 0.0214 0.0300 0.0420 1.64 1.032 1813.3 587 0.0195 0.0425 0.0470 1.28 0.665 1813.4 604 0.0187 0.0544 0.0497 1.05 0.499 1813.5 618 0.0175 0.0665 0.0564 0.98 0.382 1813.6 626 0.0166 0.0822 0,0634 0.88 0.293 1842.0 370 0.0161 0 0 1842.1 429 0 0103 0 0238 0 0184 0:b 0:iis 1842.2 431 0 0096 0 0300 0 0248 0.99 * 0.464 1842.3 434 0 0089 0 0425 0 0297 0.83 0.303 1842.4 435 0 0090 0 0544 0 0347 0.76 0.240 1842.6 437 0 0086 0 0665 0.0347 0.61 0.187 3842.6 438 0 0083 0 0822 0 0352 0.51 0.146 I
Run
NO.
Impeller Speed, R.P.M.
Power In ut,
Air Flow I&. Ft./Seb.
Contact ~ i Power ~ Function, ~ / Hold- Depth HP. UP, Ft. Sec./Ft: (C.uFt.) (Ft./Sec.) . . .
1853.0 1853.1 1853.2 1853.3 1853.4 1853.5 1853.6 1854.0 1854.1 1854.2 1854.3 1854.4 1854.5 1854.6
93/4 In. Water, Impeller 31/4 In. from Bottom, 3 Bataes 500 0.0319 0 0 591 0.0248 0.0238 0.0306 1:53 i:Sio 610 0.0242 0,0300 0.0360 1.41 1.170 631 0.0217 0.0425 0.0482 1.31 0.740 649 0.0195 0.0544 0.0580 1.23 0.519 660 0.0176 0.0665 0.0640 1.09 0.384 669 0.0161 0.0822 0.0647 0.90 0.284 600 0.0565 0 0 680 0.0427 0.0238 0.0384 1:89 2:600 692 0.0405 0.0300 0.0377 1.48 1.958 711 0.0379 0.0425 0.0428 1.18 1.294 729 0.0332 0.0544 0.0510 1.09 0 885 0.0278 0.0665 0.0691 1.18 0.606 750 708 0.0254 0.0822 0.0795 1.09 0.448
1814 0 1814.1 1814 2 1814.3 1814 4 1814.5 1814.6 1815.0 1815.1 1815.2 1815.3 1815.4 1815.5 1815 6 1833.0 1833.1 1833.2 1833.3 1833.4 1833.5 1833.6 1836.0 1836.1 1836.2 1836.3 1836.4 1836.5 1836.6 1843.0 1843.1 1843.2 1843.3 1843.4 1843.5 1843.6
Sa/, In. Water, Impeller 47,’s In. from Bottom, 3 Baffles 404 0.0190 0 0 504 0 0160 0.0238 0.0178 0’90 0 : 975 508 0.0149 0.0300 0.0222 0.89 0.720 521 0 0143 0.0425 0.0314 0.88 0.487 539 0.0130 0.0544 0.0386 0.83 0.346 544 0 0121 0.0665 0.0392 0.69 0.264 543 0.0120 0.0822 0.0278 0.40 0.212 500 0.0340 0 0 601 0.0284 0.0238 0.0246 1:23 1:+30 606 0.0270 0.0300 0.0322 1.27 1.305 625 0.0248 0.0425 0.0369 1.02 0.845 644 0.0232 0.0544 0.0432 0.92 0.619 663 0.0210 0.0665 0.0575 0.99 0.458 674 0.0198 0.0822 0.0613 0.86 0.350 605 0.0556 0 0 680 0.0422 0.0238 0.0348 1:i3 2 1575 691 0.0400 0 0300 0.0439 1.70 1.935 710 0.0356 0.0425 0.0503 1.37 1.215 725 0.0332 0.0544 0.0572 1.21 0.885 740 0.0293 0.0665 0.0641 1.11 0.638 761 0.0269 0.0822 0.0685 0.94 0.474 490 0.0322 0 0 585 0.0247 0.0238 0.0304 1:62 1 505 598 0.0238 0.0300 0.0365 1.44 1.150 620 0.0226 0.0425 0.0422 1.16 0.772 636 0.0208 0.0544 0.0490 1.04 0.555 647 6.0185 0.0665 0.0550 0.96 0.403 657 0.0175 0.0822 0.0550 0.77 0.309 370 0.0152 0 0 423 0.0102 0.0238 0.0120 0:62 0:110 427 0.0099 0.0300 0.0169 0.67 0.478 433 0.0093 0.0425 0.0222 0.62 0.316 435 0.0090 0 0544 0.0229 0.50 0.239 437 0.0086 0.0665 0.0239 0.187 0.43 441 0.0079 0.0822 0.0246 0.36 0.140
:
and was connected to another stepcone pulley attached to a variable-speed l/r-hp. motor. The dynamometer used in the 8-foot-diameter tank was differential in design, and was described on page 500 and previously by Riegell. With this dynamometer, power inputs were measured from 2 hp. to 6.25 hp. PROCEDURE
Each run was made on a given batch of liquid a constant rate of air flow and a constant speed of agitation. Liquid level W M measured before, during, and after the run. During the run the liquid level was obtained across one or more radii of the surfabe in order t o plot a profile of the surface from which the holdup wad calculated. The tank was filled with water t o the desired level, the impeller was put a t the proper position on the shaft and in the tank, and the level taker was placed 1inch from the side of the tank midway between two bafftes. The connecting tubing between level taker and gage was flushed t o remove all bubbles from this part of the system. After steady conditions were reached, the water level in the tank and the gage were determined. It is believed that the accuracy of the hook gage was approximately 0.005 inch. The agitator was then started and the speed adjusted to the desired amount. A reading was made on the dynamometer for the purpose of recording horsepower under load without air flow. Air was then turned on until a desired air flow was obtained. Readings were again taken on the dynamometer and on the hook gage. The speed was kept constant (the stroboscope was used to measure speed as well as t o “stop” the dynamometer). The level taker was then moved t o five or more equidistant positions across the 1 Riegel, E. R., “Chemical Machinery”. New York, Reinhold Pub. Gorp., 1944.
.
Vol. 36, No. 6
INDUSTRIAL AND ENGINEERING CHEMKSTRY
820
FTI 400 7
a006
aoos
a004 a003 0.002
QIQOI
0.000
1
Figure 6 Variation of Horsepower with Air Flow for Disperser Contacting Air and Water
TO
BorroN Figure
5.
Sectional Plot of Tank Illustrating Holdup
Dotted vertioal lines are travene points.
by the free cross-sectional area Of the tank. I n general i t is believed that so-called floodine of the disperser occurs at high superficial air velocities, where the power absorbed by the impeller is approximately 25% 01. less of the amount i t would absorb if running under air-free conditions. Even for a superficial air velocity of 0.02 foot per sccond, the power consumption of the disperser is only 55% of that if no air were present. At superficial air velocities of 0.07 to 0.08 foot per second and a disperser speed of 550 r.p.m., the disperser behaves as though air flooding were occuring, and large bubbles begin to make their appearance. At lower superficial air velocities practically no large bubble5 appear. It was found posaiblc to correlate the data in terms ot holdup and contact timr by the folloning general equation:
H = t o t a l holdup In feeti nor$-hatched area i s holdup.
Y
radius of the tank. This was done by swinging the instrument in an arc approximately on a radius and equidistant between two baffles. Levels at the different positions were recorded, care being taken to eliminate all air bubbles from any interconnecting tubing and to account for liquid transfer to the gage. Humping immediately before and aft,er each baffle was neglected. It a a i felt that the hump on the leading side of the baffle was compcnsated for by the depression on the following side. Furthermore, the effect was small compared to the total area of the surface of the liquid. For each impeller speed used, six different air velocities were studied. Temperature, pressure, and flow mcasurernents were recorded; and when a complete traverse had been made, the tank was drained and the impeller run at, thc same speed in air. The same procedure was folloved in run 8-foot-diameter tank, although fewer numbei RESULTS
Data for the experimental runs are given in Table I. Figure 5 is an illustration of the increase in water depth due to holdup of air during agitation. It shows actual conditions during one of the rum and likewise illustrates the average holdup as derived from the actual contour measurements. The actual level measurements were recorded and plotted so as to give a surface contour. The surface of the liquid was divided into equal area annuli, care being taken to compute these equal areas so as to account for the area occupied by the shaft, the baffles, the inlet air tube, and thc lever-taker tube. The center points of these equal areas were dekrmined and from the smooth curve plots of the contour, values mere read for each of the center points considered. By adding the center point readings found in this way and dividing by the number of center points, an integrated average height of liquid was obtained. This increase in average height above the quietliquid air-free height is called "holdup". This method is believed to be accurate, and a number of experiments were performed with and without baffles and without air flow where a known quantity of liquid was present. Surface contours determined by the level t.aker were then used to compute total volume of liquid in the container. It was found possible t o check thcse volumes within 0. I %. There is a considerable decrease in the power absorbed by an impeller held a t constant speed, as gas is fed to it. This is shox-n graphically for the disperser in Table I1 and Figure 6. The air flow is used in the form of superficial air velocity-Le., cubic feet of air flowing per second at, the expcrimontxl condit,ions divided
where H h
=
F
=
6
=
=
hp. =
V
y
c, n
= = =
total holdup, f t . holdup per ft. depth of liquid = H/y air velocity (superficial), ft./sec. av. contact time per ft. of liquid depth horsepower volume of air-free water, cu. ft. av. liquid depth, ft. constants
Data from Table I are plotted in Figure 7'. Equation I applied as evidenced by the straight lines. The slope of the lines is constant in all four cases, giving the value of 0.47 for n of Equation I .
Table Run So.
14 15 16 17 18 19
11.
Data on 20-Inch Ten-Blade Disperser in Water
e,S,",,"Ft
Power Function, HP. Depth Ft. Seo./Fd. (Cu. Ft.)(Ft./Sec.) Ft,./dc. Hp. R.P.M. 6'/r Ft.Water. ImDeller 2 F t . from Bottom, 4 Baffles 0,402 0.298 0.945 220 0.23Y 0.181 0.588 180 0.148 0.126 0.410 150 0.404 0.232 0.930 200 0.248 0.159 0.650 164 1 ,030 0.089 0.770 188 0 300 0.089 0.770 140 6l/f F t . Water, Impeller 3 Ft, from Bottom, 3 Baffles 0.830 0.400 0.272 6.25 0.0497 225 0.216 0.450 0.140 3.30 0.0487 180 1.010 0.513 0.255 6.23 0.0367 216 0.232 0 . 1 1 0 0 . 4 4 0 0,03R9 165 2.83 0.816 0.940 0.132 5.61 0.0219 102 0,470 0 307 0.0220 0.065 140 2.12
Impeller Speed,
Power Input,
Air Flow
Holdup,
521
June, 1944
The constant c differs for each set of conditions of liquid depth, impeller immersion, and number of baffles. Figure 8 is a composite of the graphs of Figure 7 with the experimental points omitted, and allows for easier direct comparison of the variables mentioned. Four baffles gave only slightly higher curves than three baffles, with all other conditions constant. Three baffles gave appreciably higher values than two b d e s . Line 1-1 (Figure 8) represents the optimum conditions, corresponding to initial depth of liquid equal to tank diameter, and with the disperser two thirds immersed. Compared with line 2-2, it is seen that less contact time results per unit of power when the impeller immersion 0.I 0.2 0.3 0.9 a5 0.6 a8 I 2 9 4 is reduced t o one half liquid depth. This is directly indicated by the value of c (Equation 1) which is 1.65 for line 1-1 and 1.43 for line 2-2. Lines 3-3and 4-4 show the same effect of impeller immersion with lower liquid levels. Visual observations showed that immersion of more than two thirds gave no improvement in holdup or contact time. The effect of liquid depth is seen from Unes 1-1 and 3-3,and lines 2-2 0.I 0.2 0.8 04 QS a6 au I 2 3 4 and 4-4. For the same impeller immersion, the greater depth gives increased holdup and contact time. These curves represent data over a wide range of air velocities and impeller speeds (horsepower input) and a considerable range in tank size. Data from the large-diameter tank fit well with the data from the small tank, and it appears possible to apply this correlation to tanks of any intermediate size, provided, however, that the same ratio of tank diameter to 0.1 0.2 0.9 0.4 0.506 a9 I P 3 4 impeller diameter is followed. This form of correlation is useful, not only UORSEPO WE& F U N C T / O N in that the power required to obtain a definite contact time can be oalcuFigure 7. Data Points and Curve for Air-Water Contacting, Giving the Equation lated, but also becaus the relation of h / F = c (hp./VF)o.47 power requirements to various sized equipment can be estimated. The correlation makes use of contact time per foot of depth of liquid. The total contact time depends not only on the contact time per foot of depth, but also on the actual size of the tank. 3 For example, if data are obtained from an experimental model in a given absorption, it is possible to determine the horsepower necessary and the contact time that will result for a larger
e
~p ,,
+ Figure 8.
Cuive No. 1-1 2-2 3-3
1-4
Curves for Air-Water Contacting, Giving Equation h / F = c (hp./VF)'.'' Depth Immersion No, of Baffles c Value 4 1.66 3 1.43 4 and 8 1.63 % diam. 3 1.26 % diam %
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INDUSTRIAL AND E N G I N E E R I N G C H E M I S T R Y
522
Vol. 36, No. 6
Figure 9 shows the relation between an increase in gas flow and its effect upon holdup and contact time. For the greater gas flows, holdup increases considerably but contact time decreaseb. For example, with a 50% increase in gas flow, the holdup is increased 25% but the contact time is decreased by 17% CONCLUSIONS
-
0
/O
20
90
40
% INCREU8K
60 IN
60
5RJ
70
80
90
100
FLOW
Figure 9. Effect of Increased Gas Flow on Total Contact Time and H o l d u p (Horsepower Input Constant)
piece of equipment. If it is desired to hold the power input per cubic foot of liquid constant, but to double the size of an existing operation, calculation shows that the tank-diameter will increase 26%, liquid depth 26%, and superficial air velocity 26%. If, then, the total horsepower is doubled, along with the gas flow and liquid voIume, the total contact time (from the use of Equation 1 and Figure 7A) will be increased hy 12%. Other similar relations can be derived froin this general expression.
It is believed that the generalized Equation 1 is useful i n evaluating the interrelation between important factors i n gitpliquid contact. The eqiiat,ion x a s derived from data over a wide range of air flosvs and power inputs and for a wide range in tank size. The concept of holdup or retention and contact time are useful tools, and seem to be related not only to air-water coiltacting but also to actual gas absorption. Other experiments now underway (not reported here) indicate a considerable difference in the holdup for solutions other than pure water. The data can he handled in the same way as indicated here. and will later. be extended to take into account changes in viscosity 8 8 n7cll a? ot,her solution properties. ACKNOWLEDGMENl
The authors wish to express their thanks to Mixing Equipment Company, Inc., for cooperation in this work; and also to E. E. Foerster, H. W. Tucker, L. Pancoast, and other students, who helped develop equipment and techniques which made this wnrk possible
HEAT TRANSFER in the VOTATOR.
04. q. 64dm
THE GIRDLER CORPORATION, LOUISVILLE, KY
7 Over-ail coefficients of 500 to 1150 B.t.u./(hour) (square foot) (" F.) are easily obtainable on water-to-water heat interchange using the Votator. H i g h agitation combined with scraping of the heat transfer wall produces thin films and high turbulence. The resul't is high rates of heat transfer even though the linear velocity through the Votator is less than 0.1 foot per second. This internal design leads to small size equipment which, in turn, allows high jacket velocities w i t h low pressure drops. The Dittus-Boelter equation is used to calculate film coeFficients on the jacket side where the flow i s helical. The coefficients thus obtained check the experimental results within 10%. Film coefficients on the Votator side are found to increase less rapidly above a blade peripheral velocity of 1 3 feet per second for waterlike materials in the particular Votator design used.
HE Votator has been used extensively for proce5sing margarine, shortening, and lard, because crystallization, plastization, emulsification, and heat transfer may be brought about simultaneously. Its main accomplishment is processing, so that little stress has been put on the high heat transfer efficiency of the Votator. This paper deals with a water-to-water heat interchanp test in which blade velocity, jacket-water velocity, and throuphput rates were studied in relation t o the over-all and film heat transfer coefficients. A laboratory Votator, 3 inches in diameter and equipped with a 2.25-inch diameter shaft and two stainless steel blades, was designed for use with both water and ammonia. For water n sleeve insert cuts the height of the annular space to l/( inch, and a baffle seal a t one end prevents by-passing the water flow through the ammonia section. Copper tubing ('/(-inch diametc7r) inside
T
the & w e tornis a hc.lic.al w i t w path around the nickel Votatoc tube. This method is apparently satisfactory since the heat balance-i.e., the quantity of heat flowing as measured from the jacket and Votator sides- rhecked to less than 2% for most ea The assembly of this unit i i shown in Figure 1. The method consisted in pumping hot water (175" F.) a t about 560 pounds per hour through the Votator and cooling it with a countercurrent flow of cold water (60' F.) on the jacket. Speeds of the mutator (a shaft with blades) were 300,400, 500, 700, 1000, and 1900 r.p.m. Jacket-water velocities of 4.7, 5.1, 6.5, 7.5, 9.3, 12.9, 18.1, and 25.9 feet per second were tried. These corresponded to pressure drops through the jacket of 0.5, 1, 2, 3, 5, 10, 20, and 40 pounds per square inch. I n two cases, 1900 and 400 r.p.ni., the throughput rate was changed from 560 to 340 and 1800 pounds per hour, respectively. I n all cases calibrated thermometers (0.2' F. subdivisions) were used, and the water rates were determined with a stop watch and scale tank. Thirt\ pounds of votated water and 86 pounds of jacket water w r v weighed. Check readings were made t o ensure that the equipment had come to equilibrium. The mutator speed was 1v+ rtccurate since the speed indicator could not be reliably read bettcar than * 10 r.p.m. Three points should be coneiclered for accurate analysis of t h t data-errors due t o ( a ) movement in stagnant layer of water outd e the sleeve insert, (6) any flow by-passing from one helical turn to the next, and ( c ) cxpansion and contraction losses at entrance and exit of jacket. This work neglects these errors since they are small and are apparently within the a c ( w a r v of th(b data-namely, 2%.
