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 xas 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 to 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 ac(warv of th(b data-namely, 2%.
523
June, 1944 HEAT BALANCE
The quantity of heat flowing per hour was determined by multiplying the average specific heat by the weight rate of water flow and the temperature change of the water. This change in heat content of water flowing through the Votator and jacket were separately calculated; values checked in most cases to less than 2%. The correction for average specific heat was found unnecessary with the present accuracy. Table I summarizes the data. Figure 2, constructed from the data of Table I, shows how the quantity of heat flowing, Q, varied with changes in mutator speed for several jacket-water (jw)velocities. It illustrates that the amount of heat flowing through the 0.7 square foot of cooling surface reached as high as 52,000 B.t.u. per hour, with 37,000 B.t.u. as about the average flow. Increased mutator speed increased the heat flow considerably, but the increase at the higher mutator speeds was much smaller, as shown by the following data taken at a jacket-water velocity of 9.3 feet per second ( AP = 5 pounds per square inch, 2900 pounds per hour) :
WATER JACKET
PRODUCT INLET
BAFFLED FOR WATER
OUTLET
Figure 1. Longitudinal and Cross-Sectional View of Ammonia-Jacketed Laboratory Votator Baffled for Water
I n going from 300 to 500 r.p.m., 2050 B.t.u. per hour more could be removed; in going from 700 to 1000 r.p.m., the increase was less than half as much. 1000 B.t.u. Der hour. Obviously 'there should b e a'selection of the highest mutator speed which is consistent with power load, tube, Table I. Data for Water-to-Water Heat Translei blade, and bearing wear. Temperature, F. Black dots in Figure 2 indicate Rate, Lb./Hr. Heat, B.T.U./Hr. Vot. the few cases where the heat balance Jacket soln. Jaoket Vot. Vot. AP, did not check closely. For this U out out in LMTD soln. Jacket soln. Jacket Jacket reason the values obtained from the 300 Revolutions per Minute votated water side were used where 67.2 113.1 700* 62.8 76.31 584.4 8158 37,410' 35:850 40 the data were more reliable, since 69.0 116.1 665' 62.8 584.3 20 77.94 5612 36,300' 34,750 71.5 119.2 626 10 34,690 62.8 79.21 581.7 3993 34740 low rates and large temperature 74.0 122.7 581* 5 62.8 80.55 32,320 577.1 2890 32:750* 76.3 63.0 80.62 124.8 562 30,420 582.5 2292 31,720 3 differences existed. By this pro515 1 80.9 128.7 64.7 80.25 28,620 581.4 1602 29,240 cedure the curves became consistent 400 Revolutions per Minute with one another throughout all this 71.9 148.9 62.7 96.41' 1790 5649 64,420 20 788 61,900 work. Other points on the graph 111.4 69.6 20 736 02.8 37,990 74.35 673.1 5594 38,580 1 81.9 126.0 556 63.0 78.92 581.5 30,500 1617 30,910 * are an average of the data obtained from the jacket and Votator 500 Revolutions per Minute sides. 103.1 68.8 63.8 67.83 555.3 8042 40,640 40,160 40 861 63.8 69.44 70.5 38,280 20 106.2 559.3 5721 39 320 798 The bottom curve a t a jacket 72.8 36,490 110.0 63.8 71.09 553.3 10 737 4060 36:690 water velocity of 5 feet per second 114.2 63.8 73.06 75.6 682 555.3 2192 34,990 a4no 5 77.4 116.4 64.0 73.66 552.3 2457 33.650 32,870 3 645 is smooth, but all other curves show 79.9 119.2 64.0 74.22 555.3 32,360 62 1 2039 32,170 2 82.2 121.9 590 1 64.2 75.01 30,750 659.3 1712 31,200 a sharp break at 500 r.p.m. Also, the greatest increase in heat transfer 700 Revolutions per Minute for jacket-water velocities, 9 feet 68.1 100.6 63.0 67.83 44,630* 8096 41,240 40 70.1 62.8 68.82 103.4 41,880 5780 42,070 20 per second and above, occurred in 72.5 62.8 69.92 106.9 4080 39,320 39,450 10 805 112.2 76.0 62.8 72.93 2874 37,870 5 going from 600 to 700 r.p.m.; a t 5 37,760 741 78.3 63.0 73.21 114.8 35,420 2315 35,350 691 3 feet per second the sharpest increase 83.0 120.2 63.1 74.58 1624 32,250 32,520 1 620 84.6 63.3 74.37 121.6 1465 31,140 31,230 '/* 583 occurred a t 300 to 500 r.p.m. The facts are explained later where i t 1000 Revolutions per Minute is more clearly shown that full tur70.5 102.1 02.5 68.54 593.7 5646 44,410 45,110 20 933 73.0 62.5 70.03 105.6 42,400 565.3 4044 41,670 858 10 bulence apparently does not occur 109.8 76.0 62.6 71.41 39,710 563.6 2968 38,840 6 786 113.6 78.6 62.6 72.74 569.4 2329 36,970 37,200 3 728 until a jacket-water velocity of 7.5 84.1 119.7 1 62.7 74.15 666.3 1569 33,330 33,500 643 feet per second is obtained.
Mutator Speed, R.P.M 300 500
B.T.U. Removed per Hour 32,750 34,800
Mutator Speed, R.P.M. 700 1000
B.T.U. Removed per Hour 37,800 38.800
O
Vot.
a?!".
in
179.3 178.8 179.2
179.4 178.0 176.8 179.0 178.2 178.4 177.8 179.6 179.4 178.8 178.6 178.6 178.3 177.5 176.5 170.0 170.5 171.8 175.0
3
63.7 65.6 69.1 61.1 63.1 60.1 70.0
90.5 93.3 100.0 75.7 79.4 85.0 91.0
56.8 56.6 56.7 56.8 56.8 56.9 57.2
1900 Revolutions per Minute 66.08 61,640 67.43 48,050 70.54 43 020 51.38 31'400* 54.40 30:640* 58.66 30 560* 62.80 30:050*
51,620 48 090 49:890 32,650 34 080 33'670 32:860
40 20 10 40 20 10 5
Ill6 1018 890 872* 806* 746* 684*
* Over-all coeffioient U based on heat removed from votated water. All other coefficients calculated from average heat balance.
.
INDUSTRIAL AND ENGINEERING CHEMISTRY
524
Yol. 36, No. 6
OVER-ALL COEFFICIENTS
The over-all coefficients were calculated from the average quantity of heat flowing, (3, by the following equation:
Q
Figure 2.
Table Jacket Pressure Drop Lb./Sq. Id. 40 20 10 5
3
2 1 0'. 5
.
II. Inlet and Outlet Jacket-Water Averages -Av.
300
r.p.m.
65.0 65.9 67.2 68.4 69.7 72:O
..
Jacket-Water Temp., 500 700 r.p.m. r.p.m. 65.6 66.5 67.7 69.4 70.7 ?3:1
74.0
F.-----. 1000
r.p.m. &:5
67.8 69.3 70.6 73:4
Ovar-all Av. Jacket Temp.,' F. 65.6 66.6 67.8 69.2
70.4 71.8 72.8 74.0
(1)
The amount of heat being transferred per hour, Q,is proportional to the cooling surface area, A,, and the driving force, L M T D . Cooling area A, was 0.7 square foot of scraped surface for our unit. This figure was based on the assumption that the flanged heads of the jacket (Figure 1) were only half effective for cooling and that the cooling space occupied by the helical baffle was negligible. Certainly the cooling area will not be appreciably larger than this, and if the baffle does effectively occupy space, the calculated over-all coefficient, U,is on the conservative side. The over-all Coefficients were calculated on the basis of effective scraped surface. EFFECT OF MUTATOR SPEED. The effect of mutator speed in the range 300-1900 r.p.m. on over-all coefficient U is shown in Figure 3. In contrast to the heat quantity curves (Figure 2), these curves are smooth and do not show the pronounced break a t 500 r.p.m. Here, as previously discussed, the points a t 1900 r.p.m. are extrapolated values. The largest U obtained was about 1140 B.t.u./(hour)(square foot)( F.), and the average was close to 800. The most rapid change in U occurred a t the lower speeds The increase in U slowed down after 600 r.p.m. It would obviously be poor efficiency to operate below 600 r.p.m. for thin liquids, and as discussed in the section on Heat Balance, it is advisable to use the highest mutator speed consistent with wear and power. The peripheral speed a t 600 r.p.m. was 7.8 feet per second. As a result of the high over-all coefficient U obtained by scraping, the size of equipment is small, and high jacket-water velocities and film coefficients can be obtained with small pressure drops.
Effect of Blade Speed on Heat Transfer for Several Jacket Conditions
The data a t 1900 r.p.m. do not fall on the 26, 18, and 13 foot per second linei. The correct velocities for these are 24, 17, and 11.6 feet per second; consequently, extrapolated values are included in Figure 2 to make the picture complete. To simplify calculations on the jacket side, an over-all average was made of the average jacket temperatures obtained at various pressure drops. The inlet and outlet jacket-water temperatures were averaged for each Votator condition. Since these averages were quite close for different conditions on the Votator side, they were again averaged (Table 11) in order to calculate the physical properties of the jacket water as given in Table 111. A plot of variation in transfer of heat with changes injw velocities for the several mutator speeds showed that, up to 9 feet per second, the heat transfer increased linearly with increased velocity; above this value the increase tapered off. At a mutator speed of 700 r.p.m., 3700 more l3.t.u. per hour were transferred in going from a jw velocity of 5 to 8 feet per second; in going from 20 to 23 feet per second, the increase was only 2100 l3.t.u. per hour. Even the latter amount is considerable, so it is advisable to use the highest jw velocity possible and economical with the water pressure available. Table I11 indicates that a t 300-1000 r.p.m. a velocity of 25 feet per second required 8000 pounds of water flow per hour and a pressure drop of 40 pounds per square inch. Unless the water is to be used later at low pressure for further processing, these conditions are impractical without a booster pump. Values above 9 feet per second should be used in all possible installations since the amount of transferred heat increases a t its maximum rata up to this point.
= UA, L M T D
Figure 3. Effect of Blade Speed on Over-all Coefflciant of Heat Transfer 6or Several Jacket Conditions
June, 1944
525
-
Pressure drop Ib./sq. ’in. 40 20
10 5 3 2 1
‘/2
Av.
tyy.,
Table
-
111. Jacket Average Data
(Annular space 1.395 X 10-8 sq. ft., equivslent diameter D I 0.0324 ft.) 300-1000 R.P.M.. 1900 G Density, Viscosity, Vat. Pressure lb./sd. ft./ lb./ ceptiV soh. drop sec. ou. ft. poises ft./dec. Re lb./hr. Ib./ss. ’in. 1612 25.88 40 680 1128 20 18.10 804.3 12.91 10 581.6 9.33 467.3 40 7.51 340 405.9 6.52 20 316.8 5.09 10 291.7 5 4.69
Av. rate, lb./hr.
65.6 66.6 67.8 69.2 70.4 71.8 72.8 74.0
R.P.M. Av.
tyy., 60.25 61.1 62.9 59 60 62.9 63.6
__
7
Av.
V, ,i?ji% ft./sec. 7485 5347
3627 7596 5413 3662 2540
23.9 17.08 11.6 24.25 17.0 11.75 8.i a
film, (2) metal, and (3)jacket-water film. The heat equation is then
Q Q Q Figure
4.
Effect
of Changes in Rate and Temperature of Votated Water on O v e r - a I I Coefficient
340 IB.PER W R , APPROX.
I
I
I
I
I
- lmv) h , A e ( t m v - 1rnJ = h j A c ( t m j - ti) = hoAc(tu
(2A)
E
(2B)
Proportionality constants he, h,, and 4 apply to Votator water, metal, and jacket-water film, respectively; t,,, t,,, ti, and tmi apply to temperature of votated water, metal surface on VoCator side, jacket-water, and metal surface on jacket side, respectively. The area stays constant. This is an arbitrary assumption because U is based on the Votator side; this means only that the h values, even though applying to different films, are based on the area of the inside scraped surface. To convert to the outside area-e.g., Q = hfoAo(tm5 t,) = h,
