The CRC Handbook of Mechanical Engineering. Chapter 4. Heat and Mass Transfer (776127), страница 43
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The first step is to calculate or estimate LMTDcountercurrent from Equation (4.5.89)and then estimate F as follows:1. If the two streams are in countercurrent flow, F = 1.2. If the two streams are in a combination of countercurrent and cocurrent flows (i.e., multiple tubepasses) and the outlet temperatures of the two streams are equal, F = 0.8.3. If the exchanger has multiple passes and Th,o > Tc,o, then 0.8 < F < 1.0, with the actual valuedepending upon the temperature ranges of the two streams and (Th,o – Tc,o). It is usually sufficientlyaccurate to take F = 0.9 in this case, but a more accurate value can be obtained from the earlierhalf of this section by Shah.4. Design of a multiple tube pass exchanger with Th,o < Tc,o (i.e., a temperature cross) leads to F <0.8, which is inefficient, of uncertain inaccuracy, and perhaps even thermodynamically impossible.The problem can be handled with multiple shells in series.
Consult Shah’s discussion.5. Then, MTD = F(LMTD)countercurrent, (Equation 4.5.91).Estimation of Uo. The best way to estimate Uo is to use Equation (4.5.94), together with values of ho,hi, Rf,o, and Rf,i, chosen from Table 4.5.10. This table includes ranges of values that are typical of thefluids and services indicated assuming normally allowable pressure drops, exchanger construction, andfouling. However, care should be taken in selecting values to consider possible unusual conditions, e.g.,especially high or low velocities (implying correspondingly high or low allowable pressure drops), andespecially fouling.
In selecting values from the table, the user should carefully read the footnotes foreach entry.Calculation of Ao. The total outside tube heat transfer area required in the heat exchanger is now foundfrom Equation (4.5.88).Estimation of Exchanger Dimensions. Figure 4.5.20 shows the relationship among Ao, effective tubelength L, and inside shell diameter for a fully tubed, fixed tubesheet heat exchanger with one tube-sidepass, with 3/4 in. (19.05 mm) plain tubes on a 15/16 in. (23.8 mm) pitch equilateral triangular tube layout.These curves are constructed using tube count tables (e.g., Saunders, 1988). The dashed lines marked3:1, 6:1, 8:1, 10:1, and 15:1 indicate ratios of tube length to shell inside diameter for guidance inselection. Exchangers of less than 3:1 ratio are expensive because of the large-diameter shell andtubesheet, with more holes to be drilled and tubes rolled and/or welded, and shell-side flow distributionis likely to be poor and lead to excessive fouling.
Exchangers greater than 15:1 ratio are probably beyondthe point of saving money by reducing shell diameter and number of tubes and may require excessiveclear way for pulling the bundle; the bundles may be springy and difficult to handle during maintenance.Most heat exchangers fall into the 6:1 to 10:1 range.Figure 4.5.20 is a very specific case which is used as a reference. In order to extend its usefulness toother tube diameters, layouts, bundle constructions, etc., Equation (4.5.97) is used:Ao¢ = Ao F1 F2 F3(4.5.97)where Ao¢ is the value to be used with Figure 4.5.20, Ao is the required area calculated from Equation(4.5.88), andF1 is the correction factor for the tube layout. F1 = 1.00 for 3/4 in.
(19.05 mm) outside diameter tubeson a 15/16 in. (23.8 mm) triangular pitch. Values of F1 for other tube diameters and pitches aregiven in Table 4.5.11.F2 is the correction factor for the number of tube-side passes. F2 = 1.00 for one tube-side pass, andTable 4.5.12 gives values of F2 for more passes.© 1999 by CRC Press LLC4-178Section 4FIGURE 4.5.20 Heat transfer area as a function of shell inside diameter and effective tube length for 19.05 mm(3/4 in.) tubes on a 23.8 mm (15/16 in.) equilateral triangular tube layout, fixed tubesheet, one tube-side pass, fullytubed shell. (From Schlünder, E.
U., Ed. Heat Exchanger Design Handbook, Begell House, New York, 1983. Withpermission.)F3 is the correction factor for shell construction/tube bundle configuration. F3 = 1.00 for fixed tubesheet,fully tubed shells, and Table 4.5.13 gives values of F3 for the standard TEMA types.Once a value of Ao¢ has been calculated from Equation (4.5.97), enter the ordinate of Figure 4.5.20 atthat value and move horizontally, picking off the combinations of shell inside diameter and tube lengththat meet that requirement.
The final choice can then be made from among those possibilities.Example of the Approximate Design MethodProblem Statement. Estimate the dimensions of a shell-and-tube heat exchanger to cool 100,000 lbm/hr(12.6 kg/sec) of liquid toluene from 250 to 110°F (121.1 to 43.3°C) using cooling tower water availableat 80°F (26.7°C). Use split-ring floating head construction (TEMA S) with 3/4 in. (19.05 mm) outsidediameter ´ 14 BWG (0.083 in. = 2.11 mm wall) low-carbon steel tubes on 15/16 in. (23.8 mm) equilateraltriangular pitch. This construction implies one shell-side pass and an even number of tube-side passes— assume two for the present.
Choose cooling water exit temperature of 100°F (37.8°C). Specific heatof toluene is 0.52 Btu/lbm°F (2177 J/kgK) and viscosity at 180°F (82.2°C) is 0.82 lb/m/ft hr (0.34 ´ 10–3Nsec/m2 or 0.34 cP).© 1999 by CRC Press LLC4-179Heat and Mass TransferTABLE 4.5.11 Values of F1 for Various Tube Diameters and Layouts(Heat transfer area / cross - sectional area of unit cell)ReferenceNew CaseThis table may also be used for low-finned tubing in the following way.
The value estimated forho from Table 4.5.10 should be multiplied by the fin efficiency (usually between 0.75 and 1 fora good application; 0.85 is a good estimate) and used in Equation 4.5.92 with A* = Ao, the totaloutside heat transfer area including fins. Then this value of Ao is divided by the ratio of thefinned tube heat transfer area to the plain tube area (per unit length).
The result of this calculationis used as Ao in Equation 4.5.96 to find Ao¢ to enter Figure 4.5.20.Source: Schlünder, E.U., Ed., Heat Exchanger Design Handbook, Begell House, New York,1983. With permission.F1 =(Heat transfer area / cross - sectional area of unit cell)TABLE 4.5.12 Values of F2 for Various Numbers of Tube Side PassesaF2 Number of Tube-Side PassesInside Shell Diameter, in. (mm)2468Up to 12 (305)131/4 to 171/4 (337 to 438)191/4 to 231/4 (489 to 591)25 to 33 (635 to 838)35 to 45 (889 to 1143)48 to 60 (1219 to 1524)Above 60 (above 1524)1.201.061.041.031.021.021.011.401.181.141.121.081.051.031.801.251.191.161.121.081.04—1.501.351.201.161.121.06aSince U-tube bundles must always have at least two passes, use of this table isessential for U-tube bundle estimation.
Most floating head bundles also requirean even number of passes.Source: Schlünder, E.U., Ed., Heat Exchanger Design Handbook, Begell House, NewYork, 1985. With permission.Solution.qT = (100, 000 lb m hr ) (0.52 Btu lb m °F) (250 - 110) °F= 7.28 ´ 10 6 Btu hr = 2.14 ´ 10 6 W© 1999 by CRC Press LLC4-180Section 4TABLE 4.5.13 F3 for Various Tube Bundle ConstructionsF3 Inside Shell Diameter, in. (mm)Type of TubeBundle ConstructionUp to 12(305)13–22(330–559)23–36(584–914)37–48(940–1219)Above 48(1219)Split backing ring (TEMA S)Outside packed floating heat (TEMA P)U-Tube* (TEMA U)Pull-through floating head (TEMA T)1.301.301.12—1.151.151.081.401.091.091.031.251.061.061.011.181.041.041.011.15aSince U-tube bundles must always have at least two tube-side passes, it is essential to use Table 4.5.12 alsofor this configuration.Source: Schlünder, E.U., Ed., Heat Exchanger Design Handbook, Begell House, New York, 1983.
Withpermission.LMTD countercurrent =(250 - 100) - (110 - 80)ln250 - 100110 - 80= 74.6°F = 41.4°CSince there are at least two tube-side passes, flow is not countercurrent, and Th > Tc , estimate F » 0.9.ooTherefore, MTD = 0.9 (74.6°F) = 67.1°F = 37.3°C.Estimation of Uo. Light organic liquid cooled by liquid water. (Note that 1 Btu/hr ft2 °F = 5.678W/m2K).Water (in tubes) hiToluene (in shell) hoTube-side fouling R f1000 Btu/hr ft2 °F300 Btu/hr ft2 °F0.001 hr ft2 °F/Btu5700 W/m2K1700 W/m2K1.8 ´ 10–4 m2K/WiShell-side fouling R f0.0005 hr ft2 °F/Btu8.8 ´ 10–5 m2K/WoTube wall resistance (for estimation purposes, this term can be approximated by xw/kw,where xw is the wall thickness):xw0.083 in.hr ft 2 °Fm2K== 2.7 ´ 10 -4= 4.6 ´ 10 -5BtuWkw (12 in. ft ) (26 Btu hr ft °F)Then,Uo =10.001(0.750)0.7501++ 2.7 ´ 10 -4 + 0.0005 +1000(0.584)0.584300= 150 Btu hr ft °F = 848 W m 2 KAo =7.28 ´ 10 6 Btu hr= 723 ft 2 = 67.7 m 2150 Btu hr ft 2 °F (67.1°F )()Correct for changes in construction features (preliminary examination of Figure 4.5.20 indicates shellinside diameter will be in the range of 500 mm, or 20 in.):F1: F1 = 1.00 since the same tube size and layout is used;F2: F2 = 1.04, assuming two passes;F3: F3 = 1.15, TEMA S construction;© 1999 by CRC Press LLC4-181Heat and Mass TransferAo¢= (723 ft2) (1.00)(1.04)(1.15) = 865 ft2 = 81 m2.From Figure 4.5.20, entering at Ao¢ , pick off the following combinations of shell inside diameter andtube length:Shell Inside Diameterin.2725231/4211/4191/4171/4mm686635591540489438Effective Tube Lengthft6.67.59.210.813.116.7m2.02.32.83.34.05.1L/Ds2.93.64.76.18.211.6Any of these combinations would supply the desired area; the 211/4 in.
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