of the Divisiott of
Frankl Regenerator Packings Heat Transfer and Pressure Drop Characteristics GUNNAR L U N D A N D B A R N E T T YALE UNIVERSITY.
F. D O D G E
NEW HAVEN, C O N N .
O v e r - a l l heat transfer coefficients and f r i c t i o n factors were determined f o r a i r flowing t h r o u g h F r a n k l regenera t o r packings a t pressure a n d temperature conditions in t h e range encountered in a i r separation plants. T h e effects of variables such as reversal t i m e , i n l e t temperature, i n l e t humidity, flow rate, packing geometry, a n d r a t i o of l e n g t h t o diameter, o n t h e heat transfer coeffi-
c i e n t were studied a n d a n equation is developed w h i c h correlates t h e experimental results well. Comparison is made w i t h d a t a previously published a n d t h e a p p l i c a b i l i t y of t h e correlated results t o t h e design of large scale regenerators is discussed. T h e effects of i m p o r t a n t operating variables o n regenerator design are shown b y examples in w h i c h correlated results of t h i s investigation are applied.
T
investigation \vas utidr l i e ~ iu i i ( I i 3 t . ~,i~titrac*t \ v i t h thtx Office of Scientific Research ai Drve~lopnicnt. F h l y r c d t s of the experimental studica have h s e n reporttd by 1)odge arid Bliss (2, 3, 4,5'1. The heat trariafi~t,,pi~'ss"ureitrojl, imtl purification perl'orm:~nce of a variclty of Fi~iinltl pavkingi \VCTC> $tudicd ant1 onipiriwl correlations of t h c s c ~ ~ p t ~ t ~ i m r~c~ruli c ~ n t as l\ v ( ~ t ~~Iitaincd. ~c~
HE developnic.nt of large scalca ail, sc*paration p1:trits in Germany dui,ing the middle 1920's gavt. rise to a nretl for heat exchangers of high capacit,y and high t.firiency for the transfer of heat from the inconling process air t o t,hc effluent gases-i.e., nitrogen and osygcn. Coiirrntional rtwperativt. heat. exchangers for this scirvice n-ere extrenwl!~ largr tiwausc, of the small pressure' loss allo\v:ihle. This and thr resulting high cost of f a h i r a t ion lit1 to tievcJlopment s in the uso of rcgcnrr:itivc~type
CONSTRUCTION
p~'occsraii~1)y Iii('ans of the regenerator rather than h>- c.licniica1 means, as had been the general practiw u p t o that timcx. Despite the widespread use of Frankl packinga i i i IO\\. tc.nipi'i'aturc heat eschange, particularly in Germany, thcrtl h a w h t ~ n published very fen- heat transfer data that can he used in the design of such regenerat,ors. This lack war cxmphasizrd at t h e outset of World Il-ar 11, when some thought !vas given t o t h e use of regenerative hrat exchangers Frank1 pacliiilga i n portable oxygen plants for military It was to provide sonie data for use in the design of these regenvrators that this
OF F R ~ N K LPACKINGS
E'riirikl n:genc'rator parliirip~;ti'i% I i i a t i ~f~r ( ~ n nic,t:rllic* i i,il)hoiis ha\-ing roirugations running ac'i'oss 1111, rihhoti at itti :ingle 0'X5 with the. r i h h n idye,. TWJsilc.!i 1,ihlioIis arc. placwl Aatn-iw one against thr n t h t ~ rwith ~ t hi, cx)rrugaticliis of 0 1 at~ right ~ ang1i.s t o the coinigntion:: of t h o c ~ t h c ~xt ~n t. i t!ic,n t l i c two are wound spirally t o torin a disk OF tltt' 1 1 c ~ i i . r dtliaiiic~tt~r anti of R height q u a l to the. i~itibtrn width (Fipurc I I. Tlicw pacliiiigs are iilaccd on(' upon the other iiisitlc, the, ri~gt~nc~i~ator shell as show1 iri Figure 2. Sonicst imcis a s p a i ~ ~isr ustd I)et,\vcac>n t h e elcnii'nts and i n ot Iivr cahw t h c h packiiigs at'(' placed c l r i s c ~ l yone upon anot1it.r. For regenc.ratoi'.: 01' I:trgi, size it has sonictinic~s tiwn ne ry to (':tulli tlic s p a e ~tit~twec~ri the packing disks and the regt>noi'atorshell in ordtxr to jiwvi'nt by-passing of gas around t h e packing. Iron, coppcr, ani1 aluniinurn have been used as materials of twristructiori lor tlic packing clenients and some variations in geometry have h e n t i , i c d -4argely variations in the dimerisionb C I thc ~ corrugations and the width of t,he ribbon.
1019
1020
INDUSTRIAL AND ENGINEERING CHEMISTRY
ameter and from 12 to 15 feet high. I n addition to their heat transfer function, the regenerators serve to remove carbon dioxide and water from the process air, eliminating the need for preliminary purification. The impurities present in the air from the compressor are precipitated out as the air is cooled in the regenerator and then during the next phase of the cycle are evaporated into the returning product stream.
v
SPACLR
ASSEMBLED CLEMENT
Figure 1.
Frankl Regenerator Packing
USE I N AIR SEPARATION PLANTS '
Vol. 40, No, 6
T o indicate more clearly how Frankl regenerators are operated theif use in a typical low pressure air separation plant is described briefly. Figure 3 is a diagram of a Linde-Frank1 plant, FThich shows the position of the regenerative heat eschangers with respect t,o the other equipment. Two sets of regenerators will be noted: one is for heat interchange between process air and nitrogen product and the ot,her is for heat int,erchange betlyeen process air and osygen product.
T o avoid the accumulation of impurities in t,he regenerator, the deposit laid down during the high pressure phase of a cycle must be completely evaporated during the lo^ prcssurc~ phase of the cycle. This requiies a careful control of t,he temperature differences in the regcnerat'or; at the cold end the temperature differences must, be small. Because of their high heat transfer capacity per unit volume, low pressure drop, purification acFigure2. Regenerator Packed tion, andease of fabriw i t h Frankl Elements cation, regenerators cont.aining Frankl paclcings have been used extensively in low pressure air separation plants such as the one described. During the last two decades over seventy plants of this type have been erected in Germany.
b
Adirfrom the low pressure turbocompressor, a t a pressure of approximately 100 pounds per square inch absolute, alternately passes down through each regenerator in a set and in transit is cooled to a temperature close to its dew point. Leaving the regenerat,ors, the air passes to the bottom of the high pressure section of the fractionating tower, where it is separated into oxygen and nitrogen product. The osygen product, withdraivn from the bottom of the low pressure section of the tower, returns through an oxygen regenerator and leaves tjhe system a t essentially atmospheric conditions. The overhead from the fractionating tower is the nitrogen product which, after exchanging some heat with FRACTIONAT1NG the liquid nitrogen feed from the high pressure SET- . tion, passes through a nitrogen regenerator and out of the system. The two rt.gr:rierators in a set are periodically switched, so that heat stored in one by the incoming air during oiie phascb of the reversal cycle is traiisferred to the outgoing nitrogeii or osypc~n during the succeeding phase of the cycle. Iic~vc~rsal times of from 2 to 5 minutes are ordinarily used. Very high heat transfer eficiencies have been reported for the Frankl I't~&yn(mtors~std in plants {jf this type: a AMMONIA COOLER TURBO-EXPANDER warm end approach of less HIGH PRESSURE t h a n 2 " F . is not uncommon. COWPRESSOR The regenerators are ordinarily about 3 f'rc~r in diFigure 3. Regenerators in a Linde-Frank1 Air Separation Plant
a
June 1948
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
J021
tained at' about I10 pounds per square inch absolute and the expander discharge ranged from 6 to 12 pounds. The expanded air returned through the other regenerator in the slstem, taking up heat from the packing as it passed through and eventually leaving the system a t essentially atmospheric conditions. P The t n o regenerators were switched periodically, so that they R ere alternately cooled and heated by the outgoing and incoming gas, respectively. This reversal of the regenerators was accomplished by a four-way plug valve a t the warm end and a chech valve assembly a t REGENERATORS the cold end which responded automatically to the warm end change. The s a r m end plug valve mas activated by an air cilinder that was controlled by a standard timing device. By means of the timer, the reversal time could be varied from 0.75 to 6 minutes. Because of the verv 105% temperatures existing within the unit, all the cold parts mere carefully insulated by placing them i n large metal containers which were aftciwards packed with insulation. Pressure and temperature points vere located a t positions of interest throughout the apparatus; calibrated Bourdon pressure gages were used for the measurement of pressure Figure 4. Apparatus for Testing Regenerator Packings and calibrated copper-constantan thermocouples with bare junctions were used for the measurement of temperatures. For APPARATUS solid surface temperatures, the thermocouples were soldered to the surface and for gas temperatures the thermocouples n ere placed In the course of thls Investigation five different regenerator in a restricted line nhere high velocities existed. On the regenerators themselves, gas temperatures were measured at each packings were tested and for each a different eyperlmental asend and on some test setups solid temperatures were measured used, The basic form of each assembly was the sembly along the radius and the length of the packed bed. same, however. The basic components of each test unit are shown in the generalized flow sheet of Figure 4. The Frank1 packings tested in the above apparatus and their assemblage in the testunits are described in Table I. The intake of the air compressor was provided with a caustic The equivalent diameters and free cross-sectional areas of the scrubbing tower for removing carbo],. dioxide from the process air packings were calculated on the assumption that the basic flow when desired. The discharge from the compressor passed to a receiver and then through two filters to removeentrained water and oil. From the filters, the air passed through Table I. Construction Data for Regenerator Setups a pressure regulat'or t'o a satuRegenerator Setup A B C D E-1 E-2 E-3 ration system consisting of a water pump, which injected Packing material Steel Steel Aluminum Aluminum Copper Copper Copper Diameter of element, in. 6.78 6.75 2.875 6.738 4.33 4.33 4.33 water directly into the air Widthof c o r r u p a t e d r i b h o n , i n . 0.875 0.875 0.844 0.845 0.969 0.969 0.969 line, a gas-fired heater, and a 73.56 Total length of corrugated rib104.4 11.42 30.43 30.43 30.43 61.82 knockout drum. This perbon per element, ft. Angle of crimp, 45 45 45 45 45 45 45 mitted saturation of the air Crimp pitch along edge, in. 0.1780 0.0891 0.1780 0.1778 0.1343 0 1343 0.1343 ivith water a t the temperaOrthogonal crimp pitch, in. 0.1259 0.0630 0.1257 0,1259 0,0951 0,0951 0.0951 ture and pressure at rq-hich it Over-all height of corrugations 0.0383 0.0281 0.0463 0,0470 0,0436 0.0436 0.0436 Ribbon thickness (av. measured 0.011 0.011 0.013 0.013 0.014 0.014 0.014 was t o enter the regenerators. value), in. The air from the saturator Over-all height minus thickness, 0.0296 0 0296 0.0296 0 0273 0.0111 0.0333 0,034 system passed down through in. Weight per packing element. lb. 2.747 3 82 1,710 1 710 1.710 0.2029 0.9058 one regenerator and in transit h-0, of elements per regenerator 58 58 244 60 118 95 72 was cooled down to a temperature of about -250" F. Total packing >!-eight, Ib. per 160 202 162.5 123.5 49 3 54.9 226 regenerator I t then proceeded to a n exSone S o n e Sone Wire triangle '/winch thick None Ppzcers pansion engine which proCopper Copper Copper Copper Copper Copper Material of shell Copper vided the refrigeration necesInside diameter of shell, in. 4.334 4.334 4.334 2 995 6.81 6.81 6.81 0.083 0.083 0 083 Thickness of shell, in. 0.095 0.095 0.065 0.095 sary for the low temperature 8.46 6.44 Length of regenerator shell, it. 4 50 4.50 4.50 20.29 10.50 operation of the regenerators. 4 29 Actual packed height, ft. 10.0 8.03 6.11 19.96 Following the expander there Effective packed height, ft. 4:23 4123 Q.53 7.67 5.81 4.22 17.18 Equivalent diameter, ft. 0,00412 0 , 0 0 2 4 6 0.00409 0.00409 0.00409 0.00481 0.00488 was a knockout drum for the Free cross-sectional a r e a per 0.0832 0,0532 0.0532 0.1191 0.1059 0 0225 0.1238 removal of any solids that element, sq. i t . 700 505 427 454 691 1030 Area per regenerator, sq. ft. 605 might have precipitated out 716 716 716 Area per unit volume of pack- 650 5 35 980 580 during the expansion. The ing, sq. ft./cu. it. pressure in the system on the 207 207 207 214.5 64 52.5 Apparent density of packing, 1 5 0 . 3 lh./cu. f t . high pressure side of the expander was usually main~~
.
'
1022.
Vol. 40, No. 6
INDUSTRIAL AND ENGINEERING CHEMISTRY Symbols Used in Table 11.
I-'
prtwure of liigli pi.essure air entering regenerator, pounds per square inch absolute r l I = integral average temp;rature of high pre-suri~ air entering regeric,rator, F. I = integral averagt' tcniprrature of high prcssurc~ air leaving regt:iiorator, F. 11' = pressure chop t hrough regenerator during high prc'ssure phase of cyclr, inches of water for setups .\, €3, and D : inches of nirrcury for setups C, E-1, E;-2, and E-3 Y',) = saturation tt,mpc'raturis of rntering high pressure a i r , =
, I
F. AH = enthalpy changc of high pressurr air i r i passing through regencrator, B.t.u. per hour L' = flow rate of high pi .urt' air, pounds per hour
I"
of entering Ion- pressure air, pounds prr square inch absolutt. 7'; = tcmprrature of entering loiv pressure air, ' F. 7'; = ttmperaturci of exit low pressure' air, F. AP' = pressure drop through rcgcnr~ator for lo\\. iirc's-iire phase of cyclr: saint' unitr as for AP AH' = rnthalpy change i F' = How rate of lo\\- p (2., = htxat leak per reg(' A(,( = m r m riid teniprir Ati = cold end temperature differeiicr, F. A / , n = log mean temperaturc diffrwrirc~,' F. I . = ovc.r-all heat transfer c.ocifficiriit based on siirlwi, Nroa of both rcgenerators in a wt ltt-',,. = avvragr Ittyioltls iiuniber for t h r tivo pha regenerator cycle (bawd on eqnivaltnt tiiw free cross-stmion area) I-cle,denoting upisrat irig ~~quilii)i~ium. 1,:x:wt :maIytic.:d aulut i o t i * for tlic, regc'nerator probleni Iiavc~ bacxn tlvrived only for c mat(' an actual condition. The siniplificatioris umptiotis a s t o the h a p e or nature of the
INDUSTRIAL AND ENGINEERING CHEMISTRY
June 1948
Table I I . .\-I
10!4 i4
.1-2 lo!(. i 7 3 .I
2 .>
-204 3 0 ti 73 I 14.093 196 17.3 -243.8 70.1 5.8 15.447 196
-232.7 2 4 74.3 15,537 lY6 17.4 -268 67.1 4.8 16.419 196 431 7.4 35.3 17.Y 0 645 203 210 0.244 180 0 158 0.709 3,49
670 c) . 0 3Y.3 16.7 0.640 199 204 0.280 180 0.156 0.712 3.44
.1-2 108 4 74.7 -230 2 1 il i4 7 1G.348 20s 18.0 -2G9.7 66.8 4 ;i 17,492
lo8
,>,2
7 9
39.3 19.6 0.623 217 223 0.210 800
0 279 0 320 4.60
S u m m a r y of Experimental and Calculated Results
.1-4
.i-5
108 8 76 0 -192 5 2 8 76.0 14,007 203 li.4 -23Y . 8
'2 1 3
.0
14..518 184 256 3 3 4i.3 17.2 0 600 194 190 0 302 180 0.1.50 0 722 3.19
.i-6
1 0 2 .(i 106.2 102.4 129.1 -189.8 -203.5 1.7 2 6 102.4 129 1 13.452 17,159 liil 178 17.1 li.5 -233.0 -241.4 97.1 120.7 3.1 6.0 13,276 18,174 lis 171 - 88 ,508 5.3 8.4 37 , ? I 43.2 18.1 19 6 0.6.7 0.643 171 178 17: 174 0,333 0.296 180 90 0 077 0.149 0.725 0 851 2.92 3 41
B-2 B-3 R-4 B-5 B-6 111 .5 100.8 113 3 113.3 i9 9 69.1 tl.5 68 9 72.8 10.7 -187.4 -209.6 -210.2 -187.8 -220.2 4 0 4.4 4.3 72 8 66 1 70.0 71.5 '68.9 16.679 14,33!l 19.540 13,724 13.130 208 202 272 2'26 208 20 2 20.6 25.7 20.0 20.8 18.4 - 249 . .i - 2 4 0 . ; - 2 2 7 3 - 2.54 , 0 -220.4 -241.3 6.j 2 62 4 61 8 63 6.5.8 58.9 15 6 13.2 15.0 12.3 13,242 17,RO.j 15,203 11.939 id.iO9 1.5.634 272 208 226 i21 208 202 739 1232 585 463 ,>, .I 333 .5 7 10 0 7 4 7.6 7.3 7.0 30 j 33.8 1 1 .i 39.0 39.9 30.7 17 .i I9 5 19.2 19 2 16 1 19.8 0.402 0 427 0 Pi9 0 3ifi n 364 0.608 13SI 140 I38 107 140 187 14X 143 161 142 190 110 0 362 .. 0.474 0,353 0.3!lO 180 90 180 180 90 180 0 052 0.090 0 120 0.069 0 184 0,088 n 659 0.828 0 775 0 867 0.831 0.899 1 61 2.12 2 82 1 8!1 1 29 1 99
B-1 113.8 69 8 -200.0 2.6 6Y 8 10,789 137
,
c-I Y8 0
63.0 -231.1 1.2 60 7.269 97.2 26.3 -249.0 53.2 6.3 8.3911 lL.0 065 9 8 17 9 13.4 0 64.i 680 737 0 201 180 0 140 0.74 14 98 P 1)'
Tb AH
F
r' *
l',' T?'
1PJ
.lH' 1J I.
11
,
11,
iL,,
r.
Re,av.
Re'
i
*
(1 -
01>
c-4 99.8 115.0 -202.6 2.0 115.0 9.639 109.4
4 5
98.0 107.4 -225 2 1 3 107.4 8.508 94 0 23.9 -240.3 92.8 6 0
6.868 93.0 470 8.2 10.8
107 0 480 14 6 15.1
0.I 60 5.928 78.8 23.5 -245 5 52.8
9 6
0 .i 3 3 ,559 611 0.186 180 0 116 0.78 16.22
C-17 YS..i 99.8 100 7 1 14 , ,-, ll0.Y 114.0 -239.8 - 2 3 6 i -23" 1 43 1 .68 1.3i 110 9 114 ,5 114.0 10,933 11.107 11,331 113 8 117 0 114 2 25 2 ".a 24.5 - 2 5 3 . 4 -249.7 - 2 3 4 . 4 103.4 87.0 Yi.O 8 4 9.3 9 0 12.20% 12.143 11 837 130 0 130 0 129 433 363 605 17.0 23 9 11.1 1 7 , .i 1 4 . 6 16.7 16 R 14.1 18 8 n. 765 0.90: 0 6i T68 id0 770 822 80.5 830 0.181 0.183 0.185 180 180 180 O.li4 0.171 0.171 0.682 0 687 0.68i 19.28 22.7 17 2
"
7': 7'1
c-3
(2-2 98 9 61.0 -234.2
0,468
14
0 665 618 668 O.li3 180 0.139 0 742 15.42 C-18 100.7 116.0 -223.8 2 2 116.0 12,191 129.3 25.7 -248 2 91 3 10.8 12,131 131 0 - 30 24 3 24.4 24 5 0 54.7 ' 802 828 0.216 180 0.174 0 674 13.9
1023
23.7 -234 6
89.1 6.8 9.959 113.0 160 25.9 32.0 28 , 0 375 Bi5 705 0.187 I80 0.150 0 723 8 93 C-1Y 100.8 113 4 -242 3 1 8'' 113 4 11.837 121 2,3., -2.53 2 104 8 10.4 12.877 i3;! n 520 8 6 10 9 9 8 1 39 794 845 0 194
,o
-_ I d
0.076 0 853 28.0
c-5 98 Y 6.3.4 -233;, 0 1.5 65 4 8,.535 111 0 26.4 -248.9 .I8 3 8 3 9,715 127 0 ,590 7.1 13 9 10 1 0 2x4:
,
i i
832 0 194 120 0.10; I1 747 21 3
C-0
.1-7 105.3 134.3 -209.1 1.9 134.3 18,400 182 17.2 -251.5 120.1 4.4 19,383 182 492 14 2 42.4 25.8 0 53 17; 181 0.233 180 0 1.58
-1-8 106.2 130.5 -212.4 1.3 130.5 18,345 184 17.4 -255 1 109.1
0 708
0 343 3.09
2.86
B-7 99.9 72.2 -183.9 4.3 72.2 13,842 211 20.7 -227.7 63.9 14.9 13,467 2111 813 8 3 43.8 21.4 0.333 142 143 0 348 300 0 128 n 760 1.68
r-i
98 (I '39 9 110 4 (1.3 -219 I - 2 3 2 . 8 1 .i 1 73 110 4 71.5 9,108 8.730 114.1 96. t 23 S 21.7 -239.0 -242 6 67.7 96.8 7.3 8.3 $4,830 Y ,928 110 0 128.0 350 410 13.6 3.8 19 9 9 8 16 6 6.3 0 613 1 66.J 774 632 684 825 0.202 0.181 120 180 0 1.56 0.111 0 806 0.712 35 4 14 86
5.7 18,932 184 304 21.4 42.7 30.8 0.438 180 186 0.306 300 n.263
8-8 113 3
72.3
-207 8 3.8
A-10
.i-!3
111 .i 133 4 -231 1 1 , .i li33.4 2Y,23!l 2 7 .'i 20 I -268.!i 116.0 10 1 3.l 12,213 29.83!1 273 12 .i 3111 300 17.4 11 3 36.3 37.8 21 6 26.1 0.815 0.397 270 118 120 277 0 385 0.284 180 I80 0.109 0,241 0 794 0-375 1 (42 3.44
B-'I 113 3 12Y 6 -1Y0 4
B-10 113.3
1:34 8
- 189.8
18 .5 0.61 173 177 0 2Y4 180 0 l:1G 0, 74.1 3 I :3
13-11 113 ;3 132 2 -186.2
H-12 11:3 14 13.3 , 1
- lf8.1
.,
4 ,f j i 10 4.4 4.6 134 8 132.2 133.4 72.3 129.6 18,062 17,537 18,643 18.136 14.449 195 I !+4 204 203 190 20, 20.2 21.3 20.4 20.7 -227 8 -230.9 -232 ? - 2 1 9 , 4 -249.5 117.2 111 ..> 119.3 119 8 63.9 18 I 15.9 15.6 13 8 16 9 18,1321 19,303 15,890 18.?~06 19,540 lY0 190 203 195 194 243 485 449 62 1 721 !4 1 17.6 14.1 9 8 8 4 51.3 41.1 37.4 41 i 47., 20 6 28.0 28.8 '0 8 27.8 0 334 0,324 0.310 0 353 0.426 121 123 124 124 140 125 123 128 143 123 0.417 0.387 0 463 0 353 0.450 180 300 90 180 300 0 031 0,062 0,036 0.078 0 107 0.8 i ( l 0 !13!l 0.880 0.929 0 798 1 46 1 2 i 1 70 1.86 1 38
x
c'-8 Y!4 9
64.9 -234.Y 1.6 64 9 9,008 117.4 24.9 -249 J
.is, 7
7.9 9.868 130 0 430 9.2 14.6 11.7 0.883 804 853 0.163 120 0.111 0 806 18.92
c-9 9Y $1 60 9 -249 1 1 4 60 9 9,488 120 0 24 3 - 2.59 , 3 33 1
7 0 10,198 132.0 35.5
7.8
10 2
9 0
1 20.5
833 880
0 146 90 0 086 0.835 24 8
C-10 '38 0 119 3 -240.2 1.6 112 3 11,751 121 0 25.2 -251 6 9s 6 8 8 12 , j 31 134.0 390 13.7 11.4 12.5 1.07 791 842 0 167 90 0 090 0 828
22 2
C-21 C,'-22 C-23 C-24 C-25 100.8 100 3 100.8 99 8 99 8 110 .? 121.3 I23 9 122 2 110.2 -218 6 -21,; 0 - 2 1 4 . 9 - 2 4 2 8 -2.51 .i -227,' 2 3' 132 2.3 2 . 1.7 1 28 1 8 122 2 I 16 .-I I 2 3 ii 110 2 121.3 107.8 12,101 12,O"i 12.240 12.342 11.993 11.414 122 3 119 7 12 3 . .i 12.5 0 I29 2 127 1 "4 6 2,j 7 25.7 26 2 24 !I 25.4 - 2 5 2 , .i -244 8 -244 ,5 - 2 4 6 1 -2.3 2 -263.4 97.3 4.5 , 3 92 i 103 4 109 1 100.2 10 2 9 ,3 10 .3 10 1 10 2 8.R 12,732 12,781 12.055 12.140_ 12.823 12,274 I :Xl .5 133 0 133.0 128 0 128 , 133 0 224 290 20.5 430 340 20 li.9 10.5 23.8 14.8 22 0 14.Y 23 3 11,9 26.2 2 9 , .i 31 2 10 4 20 A 21 3 26 4 1 0 ,.i "4 2 13 4 0 i2.i I) ,749 0 On3 1.243 1 02.5 0 ILjO 770 802 788 8 1:3 783 7i8 796 810 80.5 830 839 866 0 192 0 . 1 ~ 4 0 217 0 212 0 144 0.111 2i0 270 860 in , .> 180 0 li7 0 272 0 363 0,075 0 . CI76 0 268 0 536 0 ,5317 0 40G 0.856 0 833 0 677 22 2 20 6 21 0 21 0 24 9 13.9 (Continued ,n next p a g e ) ('-2fl ion 8 10i 8
,A- 12
h-11
A - L:i
.A- I 4
93.3 129.p - 181. i 1.3 129 d 1 1,673 12.5 16.5 -218.0 118.G
('-11 Y8.0
117.2 - 2 2 3 . $1 2.2
117.2 11,980 12.5 not great enough to be detected in the correlation of the r r d t . of this inveqtigation. bscuniple 3. I n Example 2, assume that the inlet air enters saturated mith nater a t 130" F. and compare the regenerator de-ign n i t h that for the caw nhere the air enters dry a t 130" F. The added heat load due to water must be calculated. The vapor pressure of a a t r r at 130" F. is 2.221 pounds per q u a r e inch absolute (14).
moles of water rno1e.q of air piuncis of \rater -~ pound.: of air
2.221 = = ~-
,).0227
100-2.22
=
0.0227
x
Inlet Teinp..
'
1.'.
0 100
130 130
(I
IC,,
2980 4180
1 10,350 14,480
L>irig saturatrd air, thc volunii, of regcBncrator is ahout 4O'C grtiatclr thari IV I). EE'FE(.T OF TEIIPER.ITT-RF: I)I rcgc'nerator required for a givcn si~r~victt by the \\arm cncl teniperaturc ap~)i~oac*!! IT hich i,q rpecifird.
Exnniple 4. A4ssume a warm r i ~ t l Example 1, using a 3-niinutrb I! nerator design with that for a 3 Solving hy the procetlure previou>ly (l~~scribeci. Ivt? obtain:
5110 137.50
20:x 3990
I t i- apparcnt that as the re1 11 time increases the required rcyq'nerator size increases rapidly. For t,his particular case a 30' C increase in w i g h t , of packing is required when the reversal tinit, i* iricwaued from 3 to 5 minutes. B. EFFECTO F ISLETTEMPERATERE. It would be expected that as the inlet temperature of the high pressure air is increased holding a ci)iistant cold end temperat,ure level, the result,ing inmeasp in heat load will require a larger regenerator for a given n-arm end trmperature approach. This is illustrated by the iollon-ing example:
Inlrr Tam!,.,
cl = 43Nl iu4.3 14; = 497,000 13.t.u. per hour. Calculating rhe rt~gt~rii*ix~or G i 7 t . :+,. t v ~ t o wgivrli thr following results:
18 - = 0.0141 20
Fur till: clost~r tcniperat urc' a p l ~uacati, i appr,oxim:btcly 4091, difference apmore pavl;iiig is required. .Is thP tri~iperat~ure proacZhe3 zero, the rr,quired regeneration size will increase rapidly. E. EFFECT O F ALLOWABLE PRE. R E DROP. As the allowable pressure drop for a regenerator design is increased the diameter n-ill become smaller, the length will tiecome larger, and the total packing requirement. will tend T O diminish. Example 5. Assume, in Exampic 1. thar the allon.able pressure drop is 3.0 pounds per square inch and compare the regenerator design x i t h that for the case where the allowable pressure drop is 2.0 pounds per square inch. Cse a 3-minute reversal cycle. The design calculations led to the following comparison: Allowable A p
L
D
JP
WJ
A
2.0 3.0
6.8 7.42
1.53 1.42
2.07 1.96
2630 2420
9110 8400
Using the higher pressure drop. a11 8 5 reduction in packing volume r e d t s . FLOW.As the total air capacity of a F. EFFECTOF TOTAL regenei ator is increased for a specified heat transfer efficiency, the required diameter of the regenerator increases and because of the change in L I D ratio, the heat transfer coefficient is improved and the height becomes less.
Ezanip(e 6. For the conditions of Lxample 1, compare regenerator designs for air flows of 1000 and 2000 standard cubic feet per minut? using a %minute reverqal time. Calculations of the regenerator sizes for these two different flows gave the following result.: Total Flow, Standard Cu. Ft. 31in.
L
u
Ap
W'J
1000
6.8 5.8
1.53 2.08
2.07 2.01
2630 4115
moo
A
9,110 14,240
.llthongh the flow rate is double, the volume of packing required i i only about 60% greater. G. EFFECTOF P.4cerrY.c L ~ T E R I A LFrank1 . packirigs may be made of a variety of different metals and the question arises as t,o how the choice of metal will affect the design of a regenerator. The folloiv-ing ?sample illustrates the effect of packing material on de$igii:
Example 7 . I n Example 1, use packing elements made of aluminum instead of copper and compare results. The packing dimension5 are to be the same and a 3-minute reversal time will be used. Carrying out, the design calculations for aluminum which has markedly different properties than copper, !\-e obtain: Packinp 3Iaterial Copper Ali~minam
L
D
AP
WI
1
6.8 8.58
1.53 1.64
2 07
2630 1141
9,110 13,000
LU2
IND U S T R IAL. A N D EN G INEERIN G CHEM1STRY
1032
Using aluminum instead of copper, t,he required packing weight is reduced by 5 5 7 , but t,he packing volume and area increase by 40%. H. EFFECT OF P-4CKISG GEOMETRY. The geometry of the packing used will influence the regenerator design.
Ezaniple 8. For the conditions of Esaniple 1, design a regenerator using copper packings having the saiiie basic geometry as the iron packing of esperimental setup B and compare tyith the design of Example 1. The comparison in results for the two geometries is as follows: Packing Geometry
d e , Foot
L
D
Ap
US
-4
Volu111r Cu. F t .
E-1
0.00409 0.00246
6.8 5.80
1.53 1.99
2.07 1.99
2630 4420
9,110 17,GOO
12.5 18.1
B
The more finely crimped packing gives a regenerator that is: considerably larger in volume and heavier in weight, because of the low Reynolds number required and the resulting lorn heat transfer coefficient. OF FLOW RATIO. If the quantit,y of returning air I. EFFECT is less than that of the incoming air, the cold end teiiiperature difference will De greater for a given warin end difference, and because of the larger temperature driving force the required regenerator will be smaller in size than for the case where thp Bows are equal. Ezample 9. Assume in Example 1 that the return air is 95CG of the incoming air, and compare the regenerator design \vith that, for equal flows using a 3-minute reversal time. The following tabu1ation:'compares t'he t,wo regenerator designs: Flow Ratio
L
D
1 .o 0.95
6.8 4.7
1.53 1.39
AP 2.07 1. s i
a'* 2630 1480
A 9110 5110
As t'he ratio of returning to incoming air is reduced, the regenerator required for a specified warm end temperature difference becomes smaller. SUMMARY
The heat transfer performance of a number of Frank1 regener-
ator packings was studied and an equation based upon the analogy to a recuperative type of heat exchanger was used to cor-
Vol. 40, No. 6
relate the experimental r e d t s . This equation, of the form G = B(Re)=(l - Qp,'Wsr,&)m, correlated the data for each packing tested, fairlj- m l l . By int,roduction of the ratio ( L I D ) into the equation a single function was derived which corrc:lat,ed the results for all the packings tested. This function was detcrmined t,o be:
C = 0.00123(Re)'
(1
-
&)*
(3*
Friction factors w r e correlated with Reynolds nuniher arid the effects of various operating variables on regenerator design were discuswd. LITERATURE CITED
(1) hckerman, G., Z. angew!. Math. N e c h . , 11, 192 (1931). ( 2 ) Bliss, Harding, Office of Publication Board, PB 9387 (1943).
(3) Bliss, Harding, and Dodge, B. F., I b i d . , PB 9390 (1943). (4) I b i d . , PB 8606 (19453. (5) Dodge, B. F., Ibid., PB 8318 (1912). (6) FrBnkl, Mathias, U. S. Patent 1,890,646 (Dec. 13, 1932). (7) I b i d . , 1,910,299 (Aug. 14, 1934). (8) Glaser, H., Z . V e r . deut. Ing., Beiheft Folge, 1938, No. 4, 112. (9) I b i d . , 53, 925 (1939). (10) Hausen, H., 2. angew. Math. Mech., 9, 173 (1929). (11) Ibid., 11, 105 (1931). (12) Hausen, H., 2. tech. ;Ifech. Thermodynamik,1, 219 (1930). (13) Hausen, H., Z . Ver. deut. Ing.,Verfahrenstechnik, 1937, 62. (14) Keenan, J. H., and Keyes, F. G., "Thermodynamic Properties of Steam,'' New York, John Wiley 8: Sons. 1936. (15) Lobo, W.E., Office of Publication Board, PB 8900 (1945). (16) Lobo, TV. E., and Skaperdas, G. T., Chem. Eng. Progress, 1, N o . 2; Trans. Am. Inst. Chem. Engrs., 43, 69 (1947). (11) Lowan, A. TY., Phil. Mag., 17,914 (1934). (18) Schack, A, "Industrial Heat Transfer," tr. by Goldschmidt and Partridge, New York, John TTiley & Sons, 1933. (19) Schmeidler, W., Z. angew. Math. Mech., 8, 385 (1928). (20) Trumpler, P. R., Trans. Am. SOC.Jfech. Engrs., 6 8 , 487 (1946). RECEIVED J a n u a r y 22, 1948. Based on a dissertation presented by G. Lund t o t h e faculty of t h e School of Engineering, Yale University, in partial fulfillm e n t of t h e requirements for the degree of doctor of engineering. Experimental work on which dissertation was based was performed a t Yale under Contract O E M s r 355 with t h e Office of Scientific Research a n d Development. B a r n e t t F. Dodge was t h e official investigator for t h e S,D,R.C. under thie contract,.
Design of TemDerature-Measuring Elements v
H
M A R I O T.ClCHELLl MELLON INSTITUTE, P I T T S B U R G H . PA.
M e t h o d s are presented for determining t h e length of temperature-measuring elements t h a t m u s t extend i n t o a gaseous atmosphere t o reduce t h e error of reading due t o conduction of heat along t h e u n i t t o less t h a n a certain value. T h e solution of t h i s problem and a n u m b e r of sample calculations are given for most standard types of thermometer and thermocouple installations.
T
HE accurate nieasurement of the teiiipei ature of gaqi ouk systenis is frequently the aiin of research norhtxis and process engineeis. I n steady-state systems, beveral factors prevent a temperature-measuring element from attaining the same temperature as the gas surrounding it-naniclv, ielativelj poor heat transfer betncen the gas and the element: radiation between the element and surfaces having a different tenipeiature from the gas being measured; and conduction of heat along the element bet-wecn its point of attachment and its point oi nirasuiement. In most case* it is difficult to determine accurately the correc-
tion that must, be added to, or subtracted from, the measured temperature t o yield the true gas temperature. This results partly from the fact that the heat, transfer properties of a system are generally not knorvn t o a high degree of accuracy, and partly from the fact t,hat when second order effects are included, such as variations in the heat transfer coefficient with position along the element, the equation obtained for a differential length of element becomes esceedingly complex. Complications such as these make solution of the exact, problem very difficult, but t,hey do not rule out the solution of the following important problems: K h a t is the masinium value of the error in reading of a particular temperature-measuring element? Conversely, hoiv long a temperature-measuring unit is needed to control the error i n reading due to conduction along the unit to less than a certain preassigned value'? These problems are more readily solved because t,hey allow the use of safe or conservative approsiinatioiis wherever uncertain values or effects which cause excessive complication occur. ThiP paper develops and presents the procedure for making
