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Juice Heating
29. Juice Heating We have seen that in the course of the clarification process it is necessary to heat the juice at least once. Even when using defecators, it would be very expensive, from the point of view of steam consumption, to carry out all the heating in the defecators, which use direct steam. A preliminary heating is carried out, by means of exhaust steam or bled vapour, to bring the juice to a temperature of about 90°C (195°F). Stop valve Air cock
Ammoniacal vapours Juice inlet and outlet
Steam entry
Condensate outlet
Drain valves
Fig. 200. Juice heater (Fives-Lille).
29
CALCULATIONS FOR HEATERS
313
In any case, therefore, it is necessary to have a heat exchanger to heat the juice by exhaust steam or bled vapour; these are the juice heaters. The juice heater (Fig. 200) consists of an assembly of tubes: the juice circulates through the tubes, and the vapour outside them. Suitable headers force the juice to pass a certain number of times from bottom to top and from top to bottom of the heater by restricting the juice each time to a few of the tubes. Specific heat of sugar solutions
The specific heat c of sucrose solutions is given, to a close approximation, by the equation: c = 1 — 0.006£
(255)
B = brix of the solution. This formula may be applied without serious error to juices, syrups and molasses of different purities. It follows that a typical mixed or defecated juice, of 16° or 17° brix, will have a specific heat of approximately 0.9. Using this value for juice will never involve a serious error. For greater precision, when the brix differs appreciably from the mean, it will be preferable to use the value given by eqn. (255), which moreover is simple and readily calculated. According to the most recent determinations (Gucker and Ayres, I.S.J., (1941) p. 154), more accurate values would be obtained by replacing the coefficient 0.006 by 0.0056 in eqn. (255). Loss of h e a t
According as the lagging of the heater is more or less effective (and, for batteries of heaters, the lagging of the piping connecting the heater to the following one), the loss of heat, which determines the efficiency of the heat exchange operation, will range from about 4 to 8%, averaging 5% for a heater suitably lagged and covered with wooden battens. Calculations f o r h e a t e r s
Calculations for heaters are complicated by the fact that, while one of the fluids, the vapour, is at constant temperature, the other, i.e., the juice, is at a varying temperature in its passage from entry to exit. This introduces an integral which is expressed by a logarithm. This renders the calculation somewhat lengthy, but any precise calculation would not be possible otherwise. It will be seen, moreover, in the following example, that the resulting complication is indeed minimised: there is not even need for a table of logarithms; a simple slide rule will furnish results sufficiently precise for practical requirements. The whole calculation for heaters is contained in the 3 equations following: (a) Quantity of heat transmitted: _kS
M = pc{T —to)(l—e
p*)
(256)
(b) Temperature obtained: kS
(c) Heating surface:
t= T—(T—to)e~pc
(257)
5 = - ^ l n J ^ L k T—t
(258)
314
JUICE HEATING
29
M = quantity of heat transferred to the juice, in B.Th.U. S = heating surface of the heater, in sq.ft. p — weight of juice to be heated, in lb./h c = specific heat of the juice (approx. 0.9) T = temperature of the heating vapour, in °F. to = initial temperature of the cold juice, in °F t — final temperature of the hot juice, in °F k = coefficient of heat transfer, in B.Th.U./sq.ft./h/°F. (Recalling that the expression: y = e~x reduces to: — x=\ny=
23 logy
(259)
Hence: _*s kS log e vc = -0.4343—
(260)
and that, when a logarithm has a negative value, we must write for example: log x = —0.372 = Γ.628) Value of k. All authors are in agreement in indicating the marked influence exerted on the heat transfer coefficient k by the velocity V of the juice circulation in the tubes; but opinions differ concerning the law expressing the relationship of these two quantities. Hausbrand (p. 331) gave: 3
k = 103 ]/ V + 0.023
(261)
k = heat transfer coefficient of the heater, in B.Th.U./sq.ft./h/°F V = velocity of juice in the tubes, in ft./sec. However, his work was done on clean tubes. An expression previously used in Australia was (I.S.J., (1936) p. 438): k = 100 ]/v Speyerer (Perk, 9th Congr. LS.S.C.T.) gives for V = 1 m/sec (3.28 ft./sec): fc= 45 + 0.41 (T— 32) The present author has suggested (La Sucrerie de Cannes, French edn.): k = 0.3(Γ— 32)
J/KTÖ."13
(262)
T = temperature of the vapour used for heating, in °F. However, these formulae have the disadvantage of taking into account only the effect of heat transfer from tube (or scale) to juice in which the juice velocity is important. It is desirable to take into account equally the resistance offered to heat transfer: (a) from vapour to metal, (b) across the tube, (c) from tube to scale, (d) across the scale, which should introduce an additive term and not a multiplying factor in the total resistance. Crawford and Shann (9th Congr. LS.S.C.T.) have thus obtained an expression in the form: Τ=0·°°2
+
-256Τ^
(263)
29
CALCULATIONS FOR HEATERS
315
This expression, obtained over weeks of about 140 hours, but on tubes which had been thoroughly cleaned, gives values too high for ordinary practice, and takes no account of the influence of the heating steam. Accepting its logical form, and adjusting it to suit industrial operating conditions, we shall write: Π k
I
T—12 I 22
a9+
(264>
—I
k = heat transfer coefficient for the heater, in B.Th.U./sq.ft./h/°F T = temperature of the heating steam, in °F V = velocity of the juice in the tubes, in ft./sec. The index 0.8 is actually a necessary refinement for a scientific or precise determination, but it introduces a superfluous complication for normal industrial calculations. The first term of the denominator (0.9) corresponds to the resistance to heat transfer due to factors (a) to (c) discussed above. It obviously varies, during the week and during the season, depending on the severity of scale formation; and the value indicated by the formula is a mean operating figure. The second term corresponds to the resistance to heat transfer from tube (or scale) to juice, which is the only one in which the juice velocity intervenes. An indication of the variability of the term 0.9 will be given by the following small table, quoted by Perk (9th Congr. LS.S.C.T.) and originating from an investigation carried out in Java in 1940 on the value of the overall coefficient k, for the various vertical heaters of 9 factories: Value ofk
fkcallm2lhl°C) Heaters Heaters Heaters Heaters Heaters
using exhaust steam using vapour from 1st effect using vapour from 2nd effect using vapour from 3rd effect using vapour from last effect
225-1,127 212-1,080 201- 630 129- 612 276- 517
On account of the variability of the coefficient k, it is advisable to determine it for the existing heaters of the factory, to deduce from it the value of the term independent of V in the deno minator (close to 0.9 above) and, from the various values found, to apply eqn. (264) using the value which appears most probable for the case under consideration. Velocity of circulation. The velocity of circulation of juice in the tubes plays an important part in the efficacy of a heater. It is for this reason that heaters are divided into compartments by baffle plates. For effective use of this equipment, it is advisable that the juice velocity should not fall below 3 ft./sec. In fact, not only would the heat transfer coefficient be lower on Monday morning, but the heater would foul more rapidly, and the temperature of the hot juice would fall all the more rapidly during the week. On the other hand, at high velocities, the passage of the juice through the heater causes a very marked pressure drop, which rapidly becomes prohibitive. For this reason, a velocity of 6.5 ft./sec, already high, is seldom exceeded, and the best velocities to be aimed at, from the economic viewpoint, are between 5 and 6 ft./sec.
316
29
JUICE HEATING
Pressure drop
According to the Darcy formula, the pressure drop for water flowing in a pipe of diameter D has a value of: J=U—
V2
(265)
j = pressure drop expressed as hydraulic gradient (dimensionless) b = coefficient varying slightly with D V = velocity of flow, in ft./sec D = diameter of pipe, in ft. Using the following approximations: (1) replacing b by its approximate value for tube diameters of the order of 1 \ in., say: 0.00015, (2) neglecting the viscosity of juice relative to water, and assuming the same value as for water, (3) assuming the loss of head due to the 180° change of direction undergone at each pass, as equivalent to a length of tube of 3.3 ft., we may write: J = 0.0006 - ^ - (3.3C + L)
(266)
J = total loss of head for a heater, in ft. head of water V = velocity of juice in the heater, in ft./sec D = diameter of the tubes, in ft. C = number of passes in the heater L = total length of juice path, in ft. = Cl I = length of each tube, in ft. When the tubes are encrusted with scale, the value found should be increased by 10-20%, according to the deposit. Eqn. (266) may also be written: J = 0.0006 -1— C(i -f 3.3)
(267)
Temperature margin
Practical application of juice heater calculations shows that, if excessive values of heating surface are to be avoided, it is desirable to arrange for a certain margin between the temperature T of the heating vapour and the temperature t required for the heated juice leaving the heater. With the object of economy, one should strive to limit the temperature t required, in such a way as to maintain the margins of temperature given in Table 51. TABLE 51 MARGIN OF TEMPERATURE TO BE ALLOWED IN JUICE HEATERS
Heating medium Exhaust steam Vapour from 1st vessel Vapour from other vessels
Temperature margin T — t,°F 11-14 18-22 27-36
29
DESIGN OF A BATTERY OF HEATERS
317
Otherwise, the excessive heating surface which will be necessary to obtain a hotter juice would be out of proportion to the gain in temperature so obtained. Juice heating is generally done in stages, at least in the main battery of heaters, by taking vapours from the various vessels of the multiple effects in turn, and finishing with exhaust steam; thus a battery will be obtained having a reasonable number of heaters of optimal heating surface. Design of a battery of heaters
Data. Suppose: Crushing rate of the factory 49 t.c.h. Weight of mixed juice produced 100% on cane Density of mixed juice 65.5 lb./eft. Temperature of cold juice 86°F Back-pressure 7 p.s.i. Quadruple effect, 4 equal vessels each 3,875 sq.ft. We shall also assume that this quadruple effect operates under the following scale of pres sures : Temp. T Latent heat r (°F) (B.Th.U.jlb.) Steam to 1st effect Vapour from 1st effect Vapour from 2nd effect Vapour from 3rd effect Vapour from 4th effect
232 216 196 178 140
957 968 980 991 1,014
and that the evaporation capacity of each effect is according to the following scale (cf. p. 424): H.S. Evap. rate Evap. capacity (sq.ft.) (lb.lsq.ft.jh) (lb./h) 1st effect 2nd effect 3rd effect 4th effect
3,875 3,875 3,875 3,875
7.4 6.1 4.9 4.1
28,675 23,640 19,000 15,900
Choice of heating stages. We shall strive to utilise to the best advantage the possibilities of each vessel by bleeding from each the quantity of vapour which it can supply above that necessary for the following vessel. However, we shall not make use of the excess of the 3rd effect over the 4th, which is not worth the trouble. We shall suppose then that the last 2 vessels each furnish 15,900 lb./h (actually, they can in these conditions give slightly more). Heater No. 1. The surplus of the 2nd effect is therefore: 23,640 — 15,900 = 7,740 lb./h Using this in a heater receiving the cold juice, we may heat this juice to a temperature /, such that: 49 x 2,240 x 0.9(ii — 86) 7,740 = 980 x 0.95
318
JUICE HEATING
29
whence: h = 159°F or say 158°F. Heater No. 2. In its turn, the 1st effect has a surplus of 28,675 — 23,640 = 5,035 lb./h and could thus heat the juice leaving No. 1 heater to a temperature t% such that: 49 x 2,240 x 0.9(/2— 158) 968 x 0.95
~
whence:
U = 205°F.
We shall stop at 194°F to maintain an economic margin (T = 216°F) and avoid a heater which would be unnecessarily expensive. Heater No. 3. It remains then to raise the juice from 194°F to 217° or 221°F by means of exhaust steam. Calculation of heating surfaces. We shall select from Table 52, (p. 324) a series of heaters of 880 mm diameter, with 16 passes each of 13 tubes of 31 x 34 mm. The volume of juice to be heated is: 49 x 2,240 Λ „ r * —£— = 1,676 cu.ft.
Λ
Q=
65.5
As these heaters give (see table) an output of 35,2001/h for a velocity of 1 m/sec or 379 cu.ft./h for a velocity of 1 ft./sec, the velocity of circulation for an output of 1,676 cu.ft. (47,600 1) of juice will be: 1,676 379
4.42 ft./sec
This is a rather low velocity, but acceptable; we shall therefore retain the series of heaters chosen. Heater No. L The heat transfer coefficient of the 1st heater will be: ki =
196 °· 9
32 — = 117 B.Th.U./sq.ft./h/°F + 74.42 77
and its heating surface:
or:
pc , T— to 49 x 2,240 x 0.9 , 196 — 86 Si = -T— In — = — In 117 196 — 158 98,784 110 Si = - ^ y - x 2.3 log — = 900 sq.ft.
We shall use 2 heaters of 500 sq.ft. (45 m2) each. Heater No. 2. In the same way we have: A:2 =
216
~ ~ ^ = 132 B.Th.U./sq.ft./h/°F
°·9+Ϊ42
29
DEFINITION OF HEATING SURFACE
319
And: 62 =
4 9 x 2 , 2 4 0 x 0 . 9 , 216—158 In 132 216—194
or: 98,784 52=
X2
58 31
g
n32- - ° 22=725SC1-ft· We shall use the heater (from table) of 750 sq.ft. (70 m2). Heater No. 3. In the same way: ks =
232
32 — = 143 B.Th.U./sq.ft./h/°F 0.9+ — ^ 4.42
And: 3
49 x 2,240 x 0.9 143
Π
232—194 232 — 219
or: 98,784 38 Λ = - y ^ - x 2.3 log — = 740 sq.ft. We shall again use the 750 sq.ft. (70 m2) heater. Comments. 1. Since heater No. 1 has been calculated, as a first approximation, according to the maximum possibilities of the 2nd vessel, it will be advisable to see that it is not allowed to rise above 160°F, otherwise there will be danger of depriving the 3rd effect of some of the vapour which it needs. In the same way, No. 2 heater should theoretically not exceed 205°F. 2. In such batteries of heaters, it is necessary always to plan the connections allowing No. 1 heater to be connected to the 1st effect, and No. 2 to exhaust steam, in order to be able to cope with unfavourable conditions which may be encountered; scale, low back pressure, etc., without risk of allowing the juice temperature to fall below 216°F, which would be detrimental to the subsidation. 3. A temperature of 221°F should not be exceeded; Webre (T.S.J., (April 1951) p. 25) considers that, the higher the temperature reached, the greater is the risk that waxes, which are molten at such temperatures, will emulsify when subject to the ebullition taking place in the flash tank preceding the clarifier. They then become very difficult to separate. 4. It is equally advisable to provide a spare heater, using exhaust steam, so as to be able to clean, at leisure, the units which need cleaning, without interfering with the operation of the factory. Definition of heating surface The heating surface of a juice heater refers to the inside area of the tubes. This convention is not universal, but it is general in France, and it is logical, since it is the coefficient of transfer from tube to juice that is the limiting factor; transmission from vapour to outer surface of the tube is much more rapid. It is therefore the area of the boundary between tube and juice
320
JUICE HEATING
29
which determines the capacity of the heater, and it is certainly that surface which is the best measure of capacity. The area of tube plate between the tubes is neglected. However, certain manufacturers, who neglect this, take it into account in some measure by calculating the area from the overall length of the tubes, between outer faces of the tube-plates. This is the system adopted in par ticular by French manufacturers. English manufacturers calculate the heating surface from the outside of the tubes (Perk, 9th Congr. I.S.S.C.T.). Total heating surface required
What is the total heating surface required in an ordinary cane sugar factory, using defecation or sulphitation? Noel Deerr (p. 273) specifies 45 sq.ft./t.c.h., Tromp (p. 360) 35-45 sq.ft./t.c.h. In South Africa (I.S.J., (1933) p. 243) installations vary from 24 to 100 sq.ft./t.c.h., 45 being considered a standard figure. In Cuba (F.A.S., (April 1940) p. 30) 32 sq.ft./t.c.h. is recommended for a juice velocity of 6 ft./sec. In Porto-Rico, the mean for all factories for the 1948 campaign (T.S.J., (1950) p. 53) gave 36 sq.ft., the extreme figures being 22 and 56 sq.ft./t.c.h. If heating is to be done in stages, with vapour bleeding from at least 2 effects, it is necessary to reckon on: 44-55 sq.ft./t.c.h. for the main battery: 11-16 sq.ft./t.c.h. more, in the case of fractional liming and double heating: or, 16-22 sq.ft./t.c.h. for secondary juice, in the case of compound clarification. Addition of a heater-condenser would increase these figures appreciably. Construction of heaters
The cylindrical shell containing the tube-plates is extended at each end beyond the tube-plate, the extended portion being divided into compartments by baffles. Except for the first compartment, by which the juice enters, and the last, or outlet, both of which are located in the top upper recess for vertical heaters, each compartment provides for 2 passes: upward and downward. If there are 10 tubes per pass, for example, there will be 20 tubes for each compartment, 10 for upward and 10 for downward flow. We give (Fig. 201) a view from above of the top compartment and of the bottom cover, showing the mode of circulation. The shell is generally of mild steel plate. The extension and the cover are most often of cast iron, but are much stronger if made of cast steel. The doors also should be of steel, if they are to withstand the pressures produced by the pressure drops corresponding to high velocities in long batteries of heaters. The tube-plates should preferably be of the same metal as the tubes, in order to avoid electrolytic effects. The tubes are sometimes in semi-stainless steel, more often in steel or brass. The brass most often encountered, and the most suitable, corresponds to the composition: 70% copper, 29% zinc, 1% tin. The commonest dimensions for brass (with Continental manufacturers) are 30 x 33, 31 X 34, 31.5 x 35 or 32 x 35 mm. It would be desirable for manufacturers to
29
CONSTRUCTION OF HEATERS
321
adopt standard diameters for heaters identical with those which they provide for the tubes of the multiple effects. When the heater is fed with cold juice, large temperature differences between tubes and shell are produced, causing bending and distortion of the tubes. Sometimes the manufacturer supplies curved tubes, to minimise the effects of expansion. When these tubes are cleaned by hand scraper, unfortunately, they wear more along one side. On account of these expansion effects, a tube length greater than 13-15 feet is avoided. Each heater should be provided with thermometers, easily read, giving temperatures of juice entering and leaving. Section at top (view f r o m above)
Θ φ
Tubes in which the juice rises Tubes in which the juice descends Section at bottom (view f r o m above)
Fig. 201. Juice heater. Juice circulation.
Horizontal and vertical heaters. The British practice is to build heaters with the axis horizontal while the French use vertical types. The latter arrangement generally allows the heaters to be accommodated more easily. Incondensable gases. Heaters using exhaust steam are generally provided with a simple incondensable gas pipe discharging to atmosphere, and it is sufficient to leave this just "cracked" open. Heaters working on bled vapour on the other hand demand a generously designed incon densable gas pipe. The withdrawal should be made with a drop of one stage of pressure when
322
JUICE HEATING
29
the heater is close to the evaporator (the incondensables from a heater using 1st effect vapour should be taken to the top of the 2nd effect), but of 2 stages if the heater is at a distance 1st to 3rd effect). The incondensables should be withdrawn from the top as well as from the bottom of the shell. The withdrawal pipe serving the bottom of the heater should terminate 4 inches from the bottom, in order to avoid picking up condensate. The incondensable gas pipe should have a cross-section of at least 1 sq.in. per 700 sq.ft. of heating surface. Condensates. Condensate outlets from the heater should be sufficient to ensure that the velocity of flow of the water does not exceed 3 ft./sec. Vapour pipes. The steam and vapour pipes should be so designed that the velocity of the vapour does not exceed 100 ft./sec. They are generally calculated for a velocity of 70-80 ft./sec. The vapour entry should be placed about one quarter of the length down from the top of the heater (in the case of a vertical heater). This arrangement avoids excessive vibrations and breakages of tubes, and facilitates escape of condensate along the tubes (Perk, 9th Congr. LS.S.C.T.y Pressure test. Heaters are tested, according to the intended vapour pressure: Vapour side: at 20 or 40 p.s.i. Juice side: at 70 p.s.i. It will be advisable to insist on this test as a minimum for the juice side, to avoid possible failure of the bottom or top of the first heater of the battery under the pressure due to the accumulated head losses, when the velocity of circulation of the juice reaches high values. Pressures on bottom doors
The pressure on the lower doors and bottom portions of the heaters is calculated as follows: we take the delivery head of juice from the heater outlet to the final juice discharge level; we add the height of juice in the heater, the loss of head in the heaters following it; and it is assumed that the pressure due to the loss of head in the heater under consideration is equal to half the total loss of head for that heater. Generally the difference in density between juice and water is neglected, and the height of juice above the bottom is taken as equal to the height of the tubes. Example. To calculate the pressure acting on the bottom of the first heater (obviously the heaviest loaded) of a battery of 3 heaters of 16 passes each of 13 tubes of 31 mm (1.22 in.) inside diameter, heating 2,472 cu.ft./h of juice. Height of juice discharge above the outlet of the heaters: h = 6.5 ft. Length of tubes of each heater: / = 12 ft. 2 in. Solution. Cross-section of juice passage in the heaters: s
n x 1 222 = I x -: 'ΤΤΓ = 0.1055 sq.ft. 3
4 x 144
29
323
HEATER-CONDENSER
Juice flow: 2,472 Q = ^ΓΤ^Γ = °· 68 66 cu.ft./sec ; 3,600 Velocity of juice in the heaters: ¥,
0.6866
r c
.
Loss of head in each heater (eqn. 267): 6.52 0.0006 x —— x 16(12.17 x 3.30) = 64 ft. Pressure acting on the bottom of the first heater: Loss of head in the delivery pipe (estimated) 3 ft. Height of delivery above the heaters 6 ft. Height of juice in the heater 12 ft. Loss of head in the last 2 heaters: 64 x 2 128 ft. Mean loss of head in the 1st heater: 64/2 32 ft. 181 ft. If it were desired to calculate the delivery pressure at the pump pumping the juice through the heaters, we should have: Loss of head in the delivery pipe (pump to heaters 4- heaters to final discharge) 5 Discharge head from pump to heaters 15 Height of delivery from heaters to final level 6 Loss of head in the 3 heaters: 64 x 3 192
ft. ft. ft. ft.
218 ft. It will be seen that high velocities of circulation lead to high pressures for the tube sizes normally employed by French manufacturers. The heaters and their pumps should be designed accordingly. Heater-condenser
It will be seen in Chapter 31 (see p. 413) that the further advanced the vessel from which the vapour bleeding is done, the greater is the steam economy. If it is the vapour from the last effect that is utilised, economy will be complete, since this vapour would otherwise go to the condenser and be lost. Further, by utilising this vapour, the load on the condenser is reduced by reducing the weight of vapour to be condensed. Hence a heater is sometimes interposed, called a heater-condenser, in the vapour pipe between the last effect and the condenser. This heater can work only on cold juice, since the temperature of the hot juice which it can deliver is limited by that of the vapour, that is, by the vapour temperature corresponding to the vacuum in the condenser (50-60°C or 120-140°F). It is difficult, in these conditions, to maintain an economic margin of temperature, between vapour and hot juice, and this leads to large heating surfaces, and hence to an expensive unit. It will be necessary to balance its cost against the small gain in heat units to be expected from it. Similarly, the extra length
324
29
JUICE HEATING
of juice piping required, sometimes rather long and complicated, must be taken into account. The heater-condenser is calculated as for an ordinary heater. When one is installed, it amounts in itself to about 33 sq.ft./t.c.h. Series of heater sizes
In order to give an idea of the heaters offered by the manufacturers, from which heaters to be ordered must be chosen, we give in Table 52 one of the 2 series constructed by Fives. This firm actually offers 2 series: the "old" and the "new". The new series consists of heaters with brass tubes of 31 x 34 mm (1.22 x 1.34 in.). The length of tubes indicated in the table is taken between exterior surfaces of the plates (for the length of replacement tubes, add 5 mm). The heating surface indicated corresponds to the interior surface of the tubes calculated on a length equal to the distance between exterior faces of the tube plates. TABLE 52 FIVES HEATERS. NEW SERIES
640
725
790
880
960
1050
25.2
28.5
31.1
34.6
37.8
41.3
Number of passes
16
16
16
16
12
12
Tubes per pass
6
8
10
13
19
26
Total no. of tubes
96
128
160
208
228
312
0.0486
0.0649
0.0812
0.1054
0.1542
0.2110
175
223
292
379
555
760
63.0 78.7 94.5 110.2 126.0 141.9
— —
— — — —
— — — — — —
— — — — — — — — —
Diameter
in inches
Area of passage (sq.ft.) Juice flow (cu.ft./h) at V = 1 ft./sec Length of tubes (in inches) for H.S. of: m2
15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 ^5 J00 110 120 130
sq.ft.
161 215 269 323 377 431 484 538 592 646 700 753 807 861 915 969
1023 1076 1184 1292 1399
63.0 84.1 105.1 122.2
— — — — — — — — — — — — — —
— — — — — — — — — — —
75.6 88.4 101.0 113.6 126.2 138.8 150.6
— — — — — — — —
77.6 87.2 97.0 106.7 116.6 126.2 135.8 145.7
— — — — —
88.8 97.8 106.7 115.6 124.6 133.5 142.3 151.2 160.0 169.1 178.0
90.6 99.6 103.6 112.6 116.6 122.6 129.3 142.3 155.3 168.3
Ammoniacal vapours Juice inlet and outlet
Steam entry
Condensate outlet
Drain valves
Fig. 200. Juice heater (Fives-Lille).
29
CALCULATIONS FOR HEATERS
313
In any case, therefore, it is necessary to have a heat exchanger to heat the juice by exhaust steam or bled vapour; these are the juice heaters. The juice heater (Fig. 200) consists of an assembly of tubes: the juice circulates through the tubes, and the vapour outside them. Suitable headers force the juice to pass a certain number of times from bottom to top and from top to bottom of the heater by restricting the juice each time to a few of the tubes. Specific heat of sugar solutions
The specific heat c of sucrose solutions is given, to a close approximation, by the equation: c = 1 — 0.006£
(255)
B = brix of the solution. This formula may be applied without serious error to juices, syrups and molasses of different purities. It follows that a typical mixed or defecated juice, of 16° or 17° brix, will have a specific heat of approximately 0.9. Using this value for juice will never involve a serious error. For greater precision, when the brix differs appreciably from the mean, it will be preferable to use the value given by eqn. (255), which moreover is simple and readily calculated. According to the most recent determinations (Gucker and Ayres, I.S.J., (1941) p. 154), more accurate values would be obtained by replacing the coefficient 0.006 by 0.0056 in eqn. (255). Loss of h e a t
According as the lagging of the heater is more or less effective (and, for batteries of heaters, the lagging of the piping connecting the heater to the following one), the loss of heat, which determines the efficiency of the heat exchange operation, will range from about 4 to 8%, averaging 5% for a heater suitably lagged and covered with wooden battens. Calculations f o r h e a t e r s
Calculations for heaters are complicated by the fact that, while one of the fluids, the vapour, is at constant temperature, the other, i.e., the juice, is at a varying temperature in its passage from entry to exit. This introduces an integral which is expressed by a logarithm. This renders the calculation somewhat lengthy, but any precise calculation would not be possible otherwise. It will be seen, moreover, in the following example, that the resulting complication is indeed minimised: there is not even need for a table of logarithms; a simple slide rule will furnish results sufficiently precise for practical requirements. The whole calculation for heaters is contained in the 3 equations following: (a) Quantity of heat transmitted: _kS
M = pc{T —to)(l—e
p*)
(256)
(b) Temperature obtained: kS
(c) Heating surface:
t= T—(T—to)e~pc
(257)
5 = - ^ l n J ^ L k T—t
(258)
314
JUICE HEATING
29
M = quantity of heat transferred to the juice, in B.Th.U. S = heating surface of the heater, in sq.ft. p — weight of juice to be heated, in lb./h c = specific heat of the juice (approx. 0.9) T = temperature of the heating vapour, in °F. to = initial temperature of the cold juice, in °F t — final temperature of the hot juice, in °F k = coefficient of heat transfer, in B.Th.U./sq.ft./h/°F. (Recalling that the expression: y = e~x reduces to: — x=\ny=
23 logy
(259)
Hence: _*s kS log e vc = -0.4343—
(260)
and that, when a logarithm has a negative value, we must write for example: log x = —0.372 = Γ.628) Value of k. All authors are in agreement in indicating the marked influence exerted on the heat transfer coefficient k by the velocity V of the juice circulation in the tubes; but opinions differ concerning the law expressing the relationship of these two quantities. Hausbrand (p. 331) gave: 3
k = 103 ]/ V + 0.023
(261)
k = heat transfer coefficient of the heater, in B.Th.U./sq.ft./h/°F V = velocity of juice in the tubes, in ft./sec. However, his work was done on clean tubes. An expression previously used in Australia was (I.S.J., (1936) p. 438): k = 100 ]/v Speyerer (Perk, 9th Congr. LS.S.C.T.) gives for V = 1 m/sec (3.28 ft./sec): fc= 45 + 0.41 (T— 32) The present author has suggested (La Sucrerie de Cannes, French edn.): k = 0.3(Γ— 32)
J/KTÖ."13
(262)
T = temperature of the vapour used for heating, in °F. However, these formulae have the disadvantage of taking into account only the effect of heat transfer from tube (or scale) to juice in which the juice velocity is important. It is desirable to take into account equally the resistance offered to heat transfer: (a) from vapour to metal, (b) across the tube, (c) from tube to scale, (d) across the scale, which should introduce an additive term and not a multiplying factor in the total resistance. Crawford and Shann (9th Congr. LS.S.C.T.) have thus obtained an expression in the form: Τ=0·°°2
+
-256Τ^
(263)
29
CALCULATIONS FOR HEATERS
315
This expression, obtained over weeks of about 140 hours, but on tubes which had been thoroughly cleaned, gives values too high for ordinary practice, and takes no account of the influence of the heating steam. Accepting its logical form, and adjusting it to suit industrial operating conditions, we shall write: Π k
I
T—12 I 22
a9+
(264>
—I
k = heat transfer coefficient for the heater, in B.Th.U./sq.ft./h/°F T = temperature of the heating steam, in °F V = velocity of the juice in the tubes, in ft./sec. The index 0.8 is actually a necessary refinement for a scientific or precise determination, but it introduces a superfluous complication for normal industrial calculations. The first term of the denominator (0.9) corresponds to the resistance to heat transfer due to factors (a) to (c) discussed above. It obviously varies, during the week and during the season, depending on the severity of scale formation; and the value indicated by the formula is a mean operating figure. The second term corresponds to the resistance to heat transfer from tube (or scale) to juice, which is the only one in which the juice velocity intervenes. An indication of the variability of the term 0.9 will be given by the following small table, quoted by Perk (9th Congr. LS.S.C.T.) and originating from an investigation carried out in Java in 1940 on the value of the overall coefficient k, for the various vertical heaters of 9 factories: Value ofk
fkcallm2lhl°C) Heaters Heaters Heaters Heaters Heaters
using exhaust steam using vapour from 1st effect using vapour from 2nd effect using vapour from 3rd effect using vapour from last effect
225-1,127 212-1,080 201- 630 129- 612 276- 517
On account of the variability of the coefficient k, it is advisable to determine it for the existing heaters of the factory, to deduce from it the value of the term independent of V in the deno minator (close to 0.9 above) and, from the various values found, to apply eqn. (264) using the value which appears most probable for the case under consideration. Velocity of circulation. The velocity of circulation of juice in the tubes plays an important part in the efficacy of a heater. It is for this reason that heaters are divided into compartments by baffle plates. For effective use of this equipment, it is advisable that the juice velocity should not fall below 3 ft./sec. In fact, not only would the heat transfer coefficient be lower on Monday morning, but the heater would foul more rapidly, and the temperature of the hot juice would fall all the more rapidly during the week. On the other hand, at high velocities, the passage of the juice through the heater causes a very marked pressure drop, which rapidly becomes prohibitive. For this reason, a velocity of 6.5 ft./sec, already high, is seldom exceeded, and the best velocities to be aimed at, from the economic viewpoint, are between 5 and 6 ft./sec.
316
29
JUICE HEATING
Pressure drop
According to the Darcy formula, the pressure drop for water flowing in a pipe of diameter D has a value of: J=U—
V2
(265)
j = pressure drop expressed as hydraulic gradient (dimensionless) b = coefficient varying slightly with D V = velocity of flow, in ft./sec D = diameter of pipe, in ft. Using the following approximations: (1) replacing b by its approximate value for tube diameters of the order of 1 \ in., say: 0.00015, (2) neglecting the viscosity of juice relative to water, and assuming the same value as for water, (3) assuming the loss of head due to the 180° change of direction undergone at each pass, as equivalent to a length of tube of 3.3 ft., we may write: J = 0.0006 - ^ - (3.3C + L)
(266)
J = total loss of head for a heater, in ft. head of water V = velocity of juice in the heater, in ft./sec D = diameter of the tubes, in ft. C = number of passes in the heater L = total length of juice path, in ft. = Cl I = length of each tube, in ft. When the tubes are encrusted with scale, the value found should be increased by 10-20%, according to the deposit. Eqn. (266) may also be written: J = 0.0006 -1— C(i -f 3.3)
(267)
Temperature margin
Practical application of juice heater calculations shows that, if excessive values of heating surface are to be avoided, it is desirable to arrange for a certain margin between the temperature T of the heating vapour and the temperature t required for the heated juice leaving the heater. With the object of economy, one should strive to limit the temperature t required, in such a way as to maintain the margins of temperature given in Table 51. TABLE 51 MARGIN OF TEMPERATURE TO BE ALLOWED IN JUICE HEATERS
Heating medium Exhaust steam Vapour from 1st vessel Vapour from other vessels
Temperature margin T — t,°F 11-14 18-22 27-36
29
DESIGN OF A BATTERY OF HEATERS
317
Otherwise, the excessive heating surface which will be necessary to obtain a hotter juice would be out of proportion to the gain in temperature so obtained. Juice heating is generally done in stages, at least in the main battery of heaters, by taking vapours from the various vessels of the multiple effects in turn, and finishing with exhaust steam; thus a battery will be obtained having a reasonable number of heaters of optimal heating surface. Design of a battery of heaters
Data. Suppose: Crushing rate of the factory 49 t.c.h. Weight of mixed juice produced 100% on cane Density of mixed juice 65.5 lb./eft. Temperature of cold juice 86°F Back-pressure 7 p.s.i. Quadruple effect, 4 equal vessels each 3,875 sq.ft. We shall also assume that this quadruple effect operates under the following scale of pres sures : Temp. T Latent heat r (°F) (B.Th.U.jlb.) Steam to 1st effect Vapour from 1st effect Vapour from 2nd effect Vapour from 3rd effect Vapour from 4th effect
232 216 196 178 140
957 968 980 991 1,014
and that the evaporation capacity of each effect is according to the following scale (cf. p. 424): H.S. Evap. rate Evap. capacity (sq.ft.) (lb.lsq.ft.jh) (lb./h) 1st effect 2nd effect 3rd effect 4th effect
3,875 3,875 3,875 3,875
7.4 6.1 4.9 4.1
28,675 23,640 19,000 15,900
Choice of heating stages. We shall strive to utilise to the best advantage the possibilities of each vessel by bleeding from each the quantity of vapour which it can supply above that necessary for the following vessel. However, we shall not make use of the excess of the 3rd effect over the 4th, which is not worth the trouble. We shall suppose then that the last 2 vessels each furnish 15,900 lb./h (actually, they can in these conditions give slightly more). Heater No. 1. The surplus of the 2nd effect is therefore: 23,640 — 15,900 = 7,740 lb./h Using this in a heater receiving the cold juice, we may heat this juice to a temperature /, such that: 49 x 2,240 x 0.9(ii — 86) 7,740 = 980 x 0.95
318
JUICE HEATING
29
whence: h = 159°F or say 158°F. Heater No. 2. In its turn, the 1st effect has a surplus of 28,675 — 23,640 = 5,035 lb./h and could thus heat the juice leaving No. 1 heater to a temperature t% such that: 49 x 2,240 x 0.9(/2— 158) 968 x 0.95
~
whence:
U = 205°F.
We shall stop at 194°F to maintain an economic margin (T = 216°F) and avoid a heater which would be unnecessarily expensive. Heater No. 3. It remains then to raise the juice from 194°F to 217° or 221°F by means of exhaust steam. Calculation of heating surfaces. We shall select from Table 52, (p. 324) a series of heaters of 880 mm diameter, with 16 passes each of 13 tubes of 31 x 34 mm. The volume of juice to be heated is: 49 x 2,240 Λ „ r * —£— = 1,676 cu.ft.
Λ
Q=
65.5
As these heaters give (see table) an output of 35,2001/h for a velocity of 1 m/sec or 379 cu.ft./h for a velocity of 1 ft./sec, the velocity of circulation for an output of 1,676 cu.ft. (47,600 1) of juice will be: 1,676 379
4.42 ft./sec
This is a rather low velocity, but acceptable; we shall therefore retain the series of heaters chosen. Heater No. L The heat transfer coefficient of the 1st heater will be: ki =
196 °· 9
32 — = 117 B.Th.U./sq.ft./h/°F + 74.42 77
and its heating surface:
or:
pc , T— to 49 x 2,240 x 0.9 , 196 — 86 Si = -T— In — = — In 117 196 — 158 98,784 110 Si = - ^ y - x 2.3 log — = 900 sq.ft.
We shall use 2 heaters of 500 sq.ft. (45 m2) each. Heater No. 2. In the same way we have: A:2 =
216
~ ~ ^ = 132 B.Th.U./sq.ft./h/°F
°·9+Ϊ42
29
DEFINITION OF HEATING SURFACE
319
And: 62 =
4 9 x 2 , 2 4 0 x 0 . 9 , 216—158 In 132 216—194
or: 98,784 52=
X2
58 31
g
n32- - ° 22=725SC1-ft· We shall use the heater (from table) of 750 sq.ft. (70 m2). Heater No. 3. In the same way: ks =
232
32 — = 143 B.Th.U./sq.ft./h/°F 0.9+ — ^ 4.42
And: 3
49 x 2,240 x 0.9 143
Π
232—194 232 — 219
or: 98,784 38 Λ = - y ^ - x 2.3 log — = 740 sq.ft. We shall again use the 750 sq.ft. (70 m2) heater. Comments. 1. Since heater No. 1 has been calculated, as a first approximation, according to the maximum possibilities of the 2nd vessel, it will be advisable to see that it is not allowed to rise above 160°F, otherwise there will be danger of depriving the 3rd effect of some of the vapour which it needs. In the same way, No. 2 heater should theoretically not exceed 205°F. 2. In such batteries of heaters, it is necessary always to plan the connections allowing No. 1 heater to be connected to the 1st effect, and No. 2 to exhaust steam, in order to be able to cope with unfavourable conditions which may be encountered; scale, low back pressure, etc., without risk of allowing the juice temperature to fall below 216°F, which would be detrimental to the subsidation. 3. A temperature of 221°F should not be exceeded; Webre (T.S.J., (April 1951) p. 25) considers that, the higher the temperature reached, the greater is the risk that waxes, which are molten at such temperatures, will emulsify when subject to the ebullition taking place in the flash tank preceding the clarifier. They then become very difficult to separate. 4. It is equally advisable to provide a spare heater, using exhaust steam, so as to be able to clean, at leisure, the units which need cleaning, without interfering with the operation of the factory. Definition of heating surface The heating surface of a juice heater refers to the inside area of the tubes. This convention is not universal, but it is general in France, and it is logical, since it is the coefficient of transfer from tube to juice that is the limiting factor; transmission from vapour to outer surface of the tube is much more rapid. It is therefore the area of the boundary between tube and juice
320
JUICE HEATING
29
which determines the capacity of the heater, and it is certainly that surface which is the best measure of capacity. The area of tube plate between the tubes is neglected. However, certain manufacturers, who neglect this, take it into account in some measure by calculating the area from the overall length of the tubes, between outer faces of the tube-plates. This is the system adopted in par ticular by French manufacturers. English manufacturers calculate the heating surface from the outside of the tubes (Perk, 9th Congr. I.S.S.C.T.). Total heating surface required
What is the total heating surface required in an ordinary cane sugar factory, using defecation or sulphitation? Noel Deerr (p. 273) specifies 45 sq.ft./t.c.h., Tromp (p. 360) 35-45 sq.ft./t.c.h. In South Africa (I.S.J., (1933) p. 243) installations vary from 24 to 100 sq.ft./t.c.h., 45 being considered a standard figure. In Cuba (F.A.S., (April 1940) p. 30) 32 sq.ft./t.c.h. is recommended for a juice velocity of 6 ft./sec. In Porto-Rico, the mean for all factories for the 1948 campaign (T.S.J., (1950) p. 53) gave 36 sq.ft., the extreme figures being 22 and 56 sq.ft./t.c.h. If heating is to be done in stages, with vapour bleeding from at least 2 effects, it is necessary to reckon on: 44-55 sq.ft./t.c.h. for the main battery: 11-16 sq.ft./t.c.h. more, in the case of fractional liming and double heating: or, 16-22 sq.ft./t.c.h. for secondary juice, in the case of compound clarification. Addition of a heater-condenser would increase these figures appreciably. Construction of heaters
The cylindrical shell containing the tube-plates is extended at each end beyond the tube-plate, the extended portion being divided into compartments by baffles. Except for the first compartment, by which the juice enters, and the last, or outlet, both of which are located in the top upper recess for vertical heaters, each compartment provides for 2 passes: upward and downward. If there are 10 tubes per pass, for example, there will be 20 tubes for each compartment, 10 for upward and 10 for downward flow. We give (Fig. 201) a view from above of the top compartment and of the bottom cover, showing the mode of circulation. The shell is generally of mild steel plate. The extension and the cover are most often of cast iron, but are much stronger if made of cast steel. The doors also should be of steel, if they are to withstand the pressures produced by the pressure drops corresponding to high velocities in long batteries of heaters. The tube-plates should preferably be of the same metal as the tubes, in order to avoid electrolytic effects. The tubes are sometimes in semi-stainless steel, more often in steel or brass. The brass most often encountered, and the most suitable, corresponds to the composition: 70% copper, 29% zinc, 1% tin. The commonest dimensions for brass (with Continental manufacturers) are 30 x 33, 31 X 34, 31.5 x 35 or 32 x 35 mm. It would be desirable for manufacturers to
29
CONSTRUCTION OF HEATERS
321
adopt standard diameters for heaters identical with those which they provide for the tubes of the multiple effects. When the heater is fed with cold juice, large temperature differences between tubes and shell are produced, causing bending and distortion of the tubes. Sometimes the manufacturer supplies curved tubes, to minimise the effects of expansion. When these tubes are cleaned by hand scraper, unfortunately, they wear more along one side. On account of these expansion effects, a tube length greater than 13-15 feet is avoided. Each heater should be provided with thermometers, easily read, giving temperatures of juice entering and leaving. Section at top (view f r o m above)
Θ φ
Tubes in which the juice rises Tubes in which the juice descends Section at bottom (view f r o m above)
Fig. 201. Juice heater. Juice circulation.
Horizontal and vertical heaters. The British practice is to build heaters with the axis horizontal while the French use vertical types. The latter arrangement generally allows the heaters to be accommodated more easily. Incondensable gases. Heaters using exhaust steam are generally provided with a simple incondensable gas pipe discharging to atmosphere, and it is sufficient to leave this just "cracked" open. Heaters working on bled vapour on the other hand demand a generously designed incon densable gas pipe. The withdrawal should be made with a drop of one stage of pressure when
322
JUICE HEATING
29
the heater is close to the evaporator (the incondensables from a heater using 1st effect vapour should be taken to the top of the 2nd effect), but of 2 stages if the heater is at a distance 1st to 3rd effect). The incondensables should be withdrawn from the top as well as from the bottom of the shell. The withdrawal pipe serving the bottom of the heater should terminate 4 inches from the bottom, in order to avoid picking up condensate. The incondensable gas pipe should have a cross-section of at least 1 sq.in. per 700 sq.ft. of heating surface. Condensates. Condensate outlets from the heater should be sufficient to ensure that the velocity of flow of the water does not exceed 3 ft./sec. Vapour pipes. The steam and vapour pipes should be so designed that the velocity of the vapour does not exceed 100 ft./sec. They are generally calculated for a velocity of 70-80 ft./sec. The vapour entry should be placed about one quarter of the length down from the top of the heater (in the case of a vertical heater). This arrangement avoids excessive vibrations and breakages of tubes, and facilitates escape of condensate along the tubes (Perk, 9th Congr. LS.S.C.T.y Pressure test. Heaters are tested, according to the intended vapour pressure: Vapour side: at 20 or 40 p.s.i. Juice side: at 70 p.s.i. It will be advisable to insist on this test as a minimum for the juice side, to avoid possible failure of the bottom or top of the first heater of the battery under the pressure due to the accumulated head losses, when the velocity of circulation of the juice reaches high values. Pressures on bottom doors
The pressure on the lower doors and bottom portions of the heaters is calculated as follows: we take the delivery head of juice from the heater outlet to the final juice discharge level; we add the height of juice in the heater, the loss of head in the heaters following it; and it is assumed that the pressure due to the loss of head in the heater under consideration is equal to half the total loss of head for that heater. Generally the difference in density between juice and water is neglected, and the height of juice above the bottom is taken as equal to the height of the tubes. Example. To calculate the pressure acting on the bottom of the first heater (obviously the heaviest loaded) of a battery of 3 heaters of 16 passes each of 13 tubes of 31 mm (1.22 in.) inside diameter, heating 2,472 cu.ft./h of juice. Height of juice discharge above the outlet of the heaters: h = 6.5 ft. Length of tubes of each heater: / = 12 ft. 2 in. Solution. Cross-section of juice passage in the heaters: s
n x 1 222 = I x -: 'ΤΤΓ = 0.1055 sq.ft. 3
4 x 144
29
323
HEATER-CONDENSER
Juice flow: 2,472 Q = ^ΓΤ^Γ = °· 68 66 cu.ft./sec ; 3,600 Velocity of juice in the heaters: ¥,
0.6866
r c
.
Loss of head in each heater (eqn. 267): 6.52 0.0006 x —— x 16(12.17 x 3.30) = 64 ft. Pressure acting on the bottom of the first heater: Loss of head in the delivery pipe (estimated) 3 ft. Height of delivery above the heaters 6 ft. Height of juice in the heater 12 ft. Loss of head in the last 2 heaters: 64 x 2 128 ft. Mean loss of head in the 1st heater: 64/2 32 ft. 181 ft. If it were desired to calculate the delivery pressure at the pump pumping the juice through the heaters, we should have: Loss of head in the delivery pipe (pump to heaters 4- heaters to final discharge) 5 Discharge head from pump to heaters 15 Height of delivery from heaters to final level 6 Loss of head in the 3 heaters: 64 x 3 192
ft. ft. ft. ft.
218 ft. It will be seen that high velocities of circulation lead to high pressures for the tube sizes normally employed by French manufacturers. The heaters and their pumps should be designed accordingly. Heater-condenser
It will be seen in Chapter 31 (see p. 413) that the further advanced the vessel from which the vapour bleeding is done, the greater is the steam economy. If it is the vapour from the last effect that is utilised, economy will be complete, since this vapour would otherwise go to the condenser and be lost. Further, by utilising this vapour, the load on the condenser is reduced by reducing the weight of vapour to be condensed. Hence a heater is sometimes interposed, called a heater-condenser, in the vapour pipe between the last effect and the condenser. This heater can work only on cold juice, since the temperature of the hot juice which it can deliver is limited by that of the vapour, that is, by the vapour temperature corresponding to the vacuum in the condenser (50-60°C or 120-140°F). It is difficult, in these conditions, to maintain an economic margin of temperature, between vapour and hot juice, and this leads to large heating surfaces, and hence to an expensive unit. It will be necessary to balance its cost against the small gain in heat units to be expected from it. Similarly, the extra length
324
29
JUICE HEATING
of juice piping required, sometimes rather long and complicated, must be taken into account. The heater-condenser is calculated as for an ordinary heater. When one is installed, it amounts in itself to about 33 sq.ft./t.c.h. Series of heater sizes
In order to give an idea of the heaters offered by the manufacturers, from which heaters to be ordered must be chosen, we give in Table 52 one of the 2 series constructed by Fives. This firm actually offers 2 series: the "old" and the "new". The new series consists of heaters with brass tubes of 31 x 34 mm (1.22 x 1.34 in.). The length of tubes indicated in the table is taken between exterior surfaces of the plates (for the length of replacement tubes, add 5 mm). The heating surface indicated corresponds to the interior surface of the tubes calculated on a length equal to the distance between exterior faces of the tube plates. TABLE 52 FIVES HEATERS. NEW SERIES
640
725
790
880
960
1050
25.2
28.5
31.1
34.6
37.8
41.3
Number of passes
16
16
16
16
12
12
Tubes per pass
6
8
10
13
19
26
Total no. of tubes
96
128
160
208
228
312
0.0486
0.0649
0.0812
0.1054
0.1542
0.2110
175
223
292
379
555
760
63.0 78.7 94.5 110.2 126.0 141.9
— —
— — — —
— — — — — —
— — — — — — — — —
Diameter
in inches
Area of passage (sq.ft.) Juice flow (cu.ft./h) at V = 1 ft./sec Length of tubes (in inches) for H.S. of: m2
15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 ^5 J00 110 120 130
sq.ft.
161 215 269 323 377 431 484 538 592 646 700 753 807 861 915 969
1023 1076 1184 1292 1399
63.0 84.1 105.1 122.2
— — — — — — — — — — — — — —
— — — — — — — — — — —
75.6 88.4 101.0 113.6 126.2 138.8 150.6
— — — — — — — —
77.6 87.2 97.0 106.7 116.6 126.2 135.8 145.7
— — — — —
88.8 97.8 106.7 115.6 124.6 133.5 142.3 151.2 160.0 169.1 178.0
90.6 99.6 103.6 112.6 116.6 122.6 129.3 142.3 155.3 168.3