INDUSTRIAL AND ENGINEERING CHEMISTRY
1082
Vol. 40, No. 6
L I T E R A T U R E CITED teniperaturr difFer~11t~~ in F. lx~twt~cn [~SI)(~I,~II~~.II~~~! cylinder wall and air 11) C'liilton, T. 11.. and ( ' ( J I ~ U ~ I A. I , P., ISU.KXG. CHEM..26. (1931). 'L = velocity of main air stream, it. per ser. ( 2 ) C'lapp, J. T.. PIi.1). the&, G I i i v . of Illiriois. 1932. = distance from grid t o some point donnstreani, f t . z (31 Drvdeii. 11. L.. Ibid.. 31. 41ti (1939). xu = distance b c t w e n hot, wire and thermocouple, it. Z = turbulence level, c h a = measured angle of turbulence (to = angle due t o hest transfer by conduction NT = corrected angle of turbulencr 6 = film thickness p = viscosity, Ib. per f t . see. p = density of air, Ib. per cu. ft. b, J I , /3 = constants LYs,, = S u s w l t group h,d %j
~t
=
= Hi~ynoldsnumber
Ilk:
ulted in Irhat i, norniall>- thought i i f as c r o ~ s flon on the heating pipes. APPARATUS
E'igu1.c 1 is R diagrammatic view ~f the i iiiportant c~lt~me~rlts and ai~i~aiigenicnt for t t i i q ~ v o r l ; .
tlic,ii,
The iron tank \vas c\.lindricaI, tiat-t)ottonicd, 4 f w t in diamc'ter, and 5 fcet high. Tlic turbines n.cre mounted 011 a shaft iron1 a dynamoinc~tcrand thc, axis n-as located o n thc vertiral ccntc~i, line of ihc t a n k . Thrl hc~iitirig pipe hafflcs ~ r c ~ t ~ emade : of galvatiizctl iron pipe,, 1-iiich standard iron pipe qizt'. Four pip(>.qn-IW ronnected togrLthcr with standard (,I1 and tcc: fittings to l0rni a h:iffli* and :ii.i,ang(d . per minute n-aq supplied t o earh bank. I n a similar Ilisrd H u t~ t V a t_ r r Coil Turbine, abovr Kater . _ _ manner cold water at 53.4"F Ruu Diain., Bottoili, Jprwi. T ~ I I I ~ , . , .\ i:* ' I ' ~ n 1 1 ~ . 'renip. Flos, n-as fed t o each of the two No. Incheq Inches R.P.11. F. X 1 0 ~ ir:. O F. < ] ' i t , F. l h , / m h . "? he,:, i h e s ~ cooling banks at a tota 27 .i 250 16 24 ti6 i 139.0 972 13 103.3 2.64 124.2 rate of 124 pound? per 14 16 66.7 103.8 2 ,6tj 142.3 29.3 232 28 1 2 6 .2 972 minute, split so that half 16 16 16 66.7 102.8 2.61 139.6 12 3 , 3 229 711 28.5 LO" (5 16 12 148.9 :i(i, 1 236 883 3.81 130.4 15 100 of the flow went t o e a r t 16 16 ~8 h 1.36 ti 121.1 29.6 262 988 20 100 3.80 bank. Actually, only t h t 22 16 24 100 56.1 3 . ti4 141.2 122.; 265 1060 34.9 2 3,; total hot and total cold water 147.9 16 12 66 i 95.0 129.8 37 3 229 640 24 2 . u !92,8 134.6 883 25 16 32 66.7 118.1 32,5 239 flows were measured. Tfit. 13i.i 34 ;, "6 39a 16 20 66.7 91.0 "30 117.2 983 flow through each individuab bank was regulated by valve>, so t'hat identical exit wat,er temperatures were obtained ((11tmiic-li heating baIlli, alii! itleutical exit water temperatures for pipes in series. Each bank of pipes was placed so t h a t it extended 11 inches toward the center of the tank, with a 1-inch cleitrance the cooling banks. Measurements preliminary t o the main run& indicated that for equal temperature drop in either the heating betTT-een the tank wall and the heat'ing pipe nearest it. The $pace between pipes was approximately 1.5 inches. Tees were or cooling banks, the floiv of water through the banks was equal. provided for thermocouple measurements of temperature at the For the illustrat'ive run, steady temperature of 93.1 F. for the points marked t in each bank. For all the runs reported a liquid mixing water was obtained and with all other temperatures condept,h of 4 feet was used, and the area of heating surface exposed st,ant i t was used as a base for calculat,ions. This temperat,urc to the mixing liquid for each bank of pipes was 5.22 square feet. was measured by means of a thermometer inserted in the tank TWOdifferent sizes of flat-blade turbines of standard design. through the upper surface of liquid. One position was chosen such as shown in Figure 2, were used. One was 12 inches in difor temperature measurement of the mixed water; its location ir ameter and had four flat blades, the other Fas 16 inches in dianishown in Figure 1. I n a number of runs temperatures were eter with six flat, blades. The dynanioniet.er was of a differential taken a t different points through the surface of the water and type similar t o one described rleeir-here ( 1 ) . it x a s found t h a t uniform temperature was present over rimsidcrable areas between sets of baffles. Turbine Position
~
@
,
O P E R A T I O N OF E Q U I P M E N T
H E A T TRANSFER C O E F F I C I E N T S
Figure 3 is a flag sheet showing the apparatus with auuliary equipment and actual operating conditions for one of the runs Hot water, used as the heating medium, was made by direct injection of steam into the circulating hot water system. It n-as circulated by a rotary pump bypassed for temperature and flow control to the hot water reservoir. The hot water was sent to two of the pipe baffles, located opposite each othei. Cold water from a n overhead t a n k supplied by city water waa sent t o the other two sets of baffles. The supply of water in both case? n a> put into the pipe closest to the center of the tank and taken out from the pipe next to the tank wall. The water in the mixing tank was thus heated by hot water in two opposite sets of heating pipes and cooled by the cold water in the other two banks of pipea Bv this arrangement i t was possible to reach steady conditions of heat transfer, and temperatures and flows were recorded i n order t o calculate coefficients only when steady conditionq prpvailed.
r,
Over-all heat transfer coefficients, n-ere determined oil r,hr hasis of the hot water flow and its temperature difference. This quantity of heat per hour was divided hy the area of both heating banks a.nd log mean At ( A t n ' , resulting in the coefficient U . The A f n b was calculated by taking the logarithmic mean between temperature differences entering and leaving, the entering temperature difference being the differerm between entering hot water and mixed water; and the leaving temperature difference beiiig the differencebetween exit hot water and the mixed water. Heat balances (from data in Table 11) are considered satisfactory. Seveial runs Jvere made t.o determint heat loss from t,he equipment through the walls and free surface of liquid, by using the heating banks only. The heat loss througb the equipment is in the order of 5 to 105%of the total heat supply No nieasurements were made of pipe wall temperatures; herlce no direct data are available for the temperature difference tet.n-een pipe wall and mixed water. Therefore, only over-al: remperature differences are takt:ri into account. The mixed For example, for the run shown in the flag &et with the t u bine rotating at 55 r.p.m. hot water at 135.2' F. was sent t o the liquid flow pattern \?as such that there was definite cross f l o ~ around the hcatinr tubes as v,-ell as both unxvard and do\~nn-ardf l o along ~ the tubes. Thus, in ad, were some areat dit,ion to sonie cross f l o ~ there along the tubes where countercurrent flon e x i s t d . 1200 and others n-here cocurrent flow took place. 131;I100 cause the flow inside the tubes of a baffle b a l k 3tarted from the top, and passed downnarc hhmt 1000 ihrough the first tube, u p through the seconci (1on.nin thc third, and u p in the fourth, it is c l t w 900 that flows m r e reversed in consecutive tubes whert ~ doR-nnard, an^ the mixed FTater f l is ~essentially B.T.U. ~ h e r cnould exist cocurrent and countercurrenl (H R) (saFT.)(P. ) flow ior successive heat tubes in any one bank. In addition, there would be some cross flow at the 600 same time. The Afm defined above was assunied 500 to be applicable t o such cross and mixed flow. 0.5 1.0 I .5 2.0 2.5 3.0 3.5 .iccordinrlv. - - the film coefficient for heat transfer on the outqide of the heating pipes (here desigIMPELLER POSITION (FT.) ABOVE TANK BOTTOM nated as \$as calculated from the over-all Figure 4. Effect of Impeller Position on Film Coefficient of H e a t coefficient, taking into account the resistance oi Transfer the pipe rlall and the coefficient of heat transfer for Liquid depth 4 feet. Sixteen-inch 6-flat-blade t u r b i n e ivatcr flonirig ill thr vtlitical heating pipes. Thiz I
,
I'
INDUSTRIAL AND ENGINEERING CHEMISTRY
lune 1948
1085
1500 I500
1000
hheot
8oo
600 B.T.U. (HRXSQ.FTX-F)
600
4 00
B.T.U. (HR](SO.FT.)('E)
3 00
400
/
300
i'
I ~
200
~1
2
ix 105
4
3
5
6XId
200
1x18
2
3
4
5X05
N,,
=
Figure 6. Relation between F i l m Coefficient of H e a t Transfer and Reynolds N u m b e r
Figure 5. Relation between F i l m Coefficient of H e a t Transfer and Reynolds N u m b e r
Four-flat-blade turbine and t a n k diameter-turbine diameter ratio of 4
Six-flat-blade turbine and t a n k diameter-turbine diameter ratio of 3
l a t r v r coefficient was coiiiputecl tJS the classical S u s e l t method: 'iquid properties evaluated at aw!apP liquid temperature. The simplified relation, IO00
i ~ l ~ r *C r eis the over-all coefficient aiid R is the resistance due to * h i : water film inside the tube plus the resistance of the iron wall all based on outside pipe area was used to compute h. Clean ralvanized iron pipe was used to construct the heating pipes and -7,is asjunied that the pipes remained clean throughout the n-ork. Ttiis assumption is substantiated hy the fact that t,he data lvere Iciwmulated over sc ral moiiths, and the latest, runs made gave data that correlated ne11 n i t h earl>-runs. Sodium dichromate was used in the recirculated hot x a t e r stream to inhibit wrrorion. Visual inspection nf the pipe s h o m d no dirt, ac,wmulation on the pipe walls.
h 600
8 ,
*. 400 300
200
L
I x 100
I
1 2
I 3
I 4
1 5
1 6
1 I J 7 8 9 lXIOB
RESULTS
tem for heat transfer Oiie uf the variables involved in :his $rid mixing is t,he position of the turbine above the bottom of the :ank. Inasmuch as flon. from turbine type agitators travels t u 'he walls of the vessel and then divides into upward and d o m Tard flom Then baffles are present, the position of the impeller :an be made to produce various ratios of flovi in the tank above and belon- the turbine. To determine whether position Ivould Xffect. the heat transfer coefficient, several series of runs xere niade lyirh the 16-inch turbine at varxing speeds and a t approsimatel? constant Atrn. These are summarized in Table I and Figure 4, Film coefficients are plotted in Figure 4 against the iosition of the impeller above the hottom of t,he tank. The quid dept,h in all cast's xas 4 feet su t h a t the 2-foot position was at t,he mid-point of the TT-ater and approximately the half-height position of the heating tubes. There is an appreciable effect oi impeller position on the coefficient and from these data i t is evident t h a t the highest coefficients are ,rbtained when this radial flow turbine operat,es a t approximately one-half liquid depth. The coefficient,s drop as the turbine is raised above the mid-point. .It these high positions there was considerable srrirl and a large :-ortex was formed. Ordinarily, t,urbine impellers of this type are operated approsilllately one impeller diameter above the loottom of the tank and the iiiipeller~themselves are approximatply one-third tank diameter.
Figure 7.
Comparison of H e a t Transfer Coefficients for B o t h Heating and Cooling
By visual observation of the surface conditions and flon- pattern of the liquid, i t appeared that for positions up to the mid-point of t,he tank, good mixing conditions existed. If solids are t o be suspended x i t h this type of turbine and heating baffles, the mid-point position of the impeller might not be sufficient for adequate suspension and i t might be necesssry t o lower the impeller to t,he one-third point or even lower, and it would be expected that the heat transfer coefficient would decrease as indicated in Figure 4. The remainder of the data taken were all for t,he impeller position a t one-half immersion. Figure 4 also s h o w directly the effect. of increased speed (and consequently the effect of increased pon-er) on the over-all coefficient. It is clear that increased rotational speeds of the turbine increase the heat transfer coefficients. More data on this effect are evident from the general correlations shown in Figures 5 , 6 , and 7 . Table I1 is a summary of the data for the 16-inch-diameter &blade and the 12-inch-diameter 4-bla,de turbines. Heat transfer data in mixing as in other operations can be correlated
1086
INDUSTRIAL AND ENGINEERING CHEMISTRY
null
rurbinr Diarn..
SO.
in clip^
30 36 31
1(i 1I; 16 1 fi
4i 38 1'i 28
I'oncr. H.P. 0 024 0.173 0 , 088 0 . 0,59
I li I fi
1'(7 33 22 Hi 44 4:1 :i 4 :i:i
82 42 4 .?I 31,
U.OY8
I li I li 1li
0 023 0 031 0,1,5.5 0 0 4 ~
1f i
0.310
10
I (i
0.173 0.293
Iii
0.100
I li
0 028
16 It i
0.014 0,086 0.013 0 3i0 0 . I02 0 039 0.120 0.3i0 0.1P.i 0 275
I6 I ti I ii
:;3 6
Ili 16 lli 1 li If i
;I2
58 I4
1, 12 15 I'
0 390 (1 3 3 3 0.018 0 .08(1 I1 390 0 043 U 13.5
I5 12 I2
0.063 0.540 I) ilil
I2 I2 I2
,?!I
64 61 ti8
68 li0
84 69 71
!I0 i 94 2 90.3 !i7 4 9.5 3 !*0 4
I2!J 0 1.36 ii 11'l , :i 138 (1 138
1.30
,
93 I
1:3n 2 I gij :3
4
140.0 141.2 144.0 144 3
!I2 i !ii
Yci I 4 7 1;
96.5 tl6.n 98 2 97.9 98.6 100 0 100.4 !)!I !I 101.0 101 s 102.0 101 . 0 100.4 100 0 u9.u 93 ii 113. 2 9 1 ,j
Y3.2
%j.8 94. 93.0 UI
Vol. 40, No. 6
,x
144.2 144 0 143.G 148 9
147.1 I T,P , 0
Lil 0 153.1 1.54.8 155.8 154 2
133 8
1.50 X 148..i
142 6 147 0
144 8 14ti ,> 148.3 147.2 147.4 I47 :i
by means of dimensionless groups such ah the 1~c~yiiiild.i iiuinhi,i,
(3,.4). The Iteyriolds number for mixing is
IP.\'p
.
proportioriat t o the fluid displaceinenl (ut, this turbinr, when i t LE placcti mid-ivay in the depth of the liquitl. Figure ti sliows data for a 12-inch, I-blade turbine iri a ~ - ~ ' ( J I > I diameter lank (7' 'I1 = 4. In ihis case the slope of the lint, j b 0.70. The difference in slope b t ~ t w t ~this n arrangement arid tlic 16-inch iiiipeller is no doubt tiuc to t h c faint that the two arc not, dimrn~ionallyequalill : this 16-inch turbine cont hladcs whcre thc 12-inch turbine had four tiladrs, and tlic ratill of tank diameter to t,urbine diamcter was 3 for thc 16-inch turtiiiit, arid 4 for the 12-inch turhinr,. 111 this configuration of irn-
Valucii of C for both heating and cooling pipes aye tlcsipiatcti Corresponding values of the film coefficieiit and 17coa~. urside of the pipes are tabulated in the last t w v col Somi; values of hroolare higher than for h h P a r hut the a values of hi,,.,t are a little higher than for h,, > I . Figure 5 shows a correlation of the data for the 16-inrh, tiblade turbine in a 4-foot diameter tank ( T / D = 3), operating at various speeds in water at different temperatures. Thc V R I U I ~ S pcller, tank, and tubes, the film coefficients are proportioiial r ( 1 of li are for the film coefficient on the heating surfacr. T h i ~ the 0.70 power of specd and likcwiw t o the 0.70 pon-cr of t h t . Reynolds number range is that ordinarily existing i Huitl tlisplacc~ment(81. operations involving water and other liquids of IonFigure 7 bho\v,? the corrc
