BOOKCOMP, Inc. — John Wiley & Sons / Page 1389 / 2nd Proofs / Heat Transfer Handbook / Bejan COLUMNS AND OTHER CONTACTORS 1389 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [1389], (31) Lines: 947 to 965 ——— 0.0pt PgVar ——— Normal Page PgEnds: T E X [1389], (31) important in vaporizing systems, where the droplets can grow in size quite substan- tially throughout the column. Generally, heat transfer per unit of droplet surface area decreases as the droplet grows. Another positive factor is that the wake behind the droplet can be stripped away at each tray. The net result of both of these aspects is that the heat transfer can be increased substantially compared to a corresponding spray column. 19.4.3 Packed Columns Another approach to improving on spray column performance is to use packed-bed arrangements. In this configuration, the main contacting zone (as shown in the spray column diagram) would be filled with objects of potentially any shape. Both packed beds and baffled towers can be contrasted to spray columns in several ways. Certainly, the cost is higher than the latter for either of these options. The spray column can yield higher performance than that for columns with internals [see, e.g., the report by Kunesh (1993)]. However, there are situations when backmixing can seriously degrade performance of spray columns. Also, if a vapor is introduced into a thick layer of liquid such as might be the case for a spray column, a significant pressure drop through the liquid might be encountered. This would increase the power required for moving the vapor. In both of these cases, packed columns or other devices with internals might offer beneficial performance improvements. Usually, packings are used when a liquid is in contact with a gas or vapor. It is desired to have as much liquid surface in contact with the vapor or gas as possible. As the liquid flows over the packings, essentially wetting the latter, the area in contact between the two fluids is related to the area of the packing. Packings can also be used in liquid–liquid systems to assist in removing the wake from the dispersed liquid and increasing the heat transfer. Although a simple configuration can be imagined where packed spheres are used, in fact, this is not a normally favored approach because of trade-offs between cost and performance. Instead, more complicated shapes such as structured packings are used. Some examples of these are shown in Fig. 19.11. Objects like those have a very high surface-area-to-volume ratio. These products can achieve ratios up to about 1000 m 2 /m 3 . In contrast, this ratio might be a couple of orders of magnitude smaller for spheres. Another factor of concern is the pressure drop for any flows through the bed. Generally, this is related to the solid volume fraction of packing. For solid spheres this is on the order of 40 to 50%, but for some modern packing shapes, this fraction might be less than a few percent. This is accomplished with a low total weight in modern packings, simplifying the design and construction of the column. Another appealing factor about some modern packing materials is that they fill the bed quite uniformly without special attention being required to remove large void spaces. The latter can affect bed performance negatively. Packings of these types can be made of one of a variety of materials, depending on the application requirements. Plastic can be used for low-cost applications where the working temperatures are not too high. On the other hand, metals or ceramics can be used for higher-temperature applications. BOOKCOMP, Inc. — John Wiley & Sons / Page 1390 / 2nd Proofs / Heat Transfer Handbook / Bejan 1390 DIRECT CONTACT HEAT TRANSFER 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [1390], (32) Lines: 965 to 968 ——— 0.097pt PgVar ——— Normal Page * PgEnds: Eject [1390], (32) Figure 19.11 Types of bed packings:(above) Jaeger Tripaks (in North America) or Hacketten (in Europe) (printed with permission of Jaeger Products, Inc.); (below) Cascade MiniRings (printed with permission from Century Plastics, Inc. and Jaeger Products, Inc., the exclusive licensee for the product in North America). Heat transfer data in theliterature for systems with packings are limited. Part ofthis paucity of data is due to the fact that there are so many forms and sizes of packings. When this is coupled with the range of heat transfer stream compositions, the range of possibilities is virtually unlimited. Despite this, some data are given in the literature. Thomas et al. (1979) reported a study of condensation of R-113 on water using ceramic spheres or Berl saddles. They also considered Cheng’s (1963) results for Aroclor–steam in a bed of Raschig rings and the methylene chloride–water data of Harriott and Weigandt (1964). A relationship that provides a reasonable fit for all these data is as follows: BOOKCOMP, Inc. — John Wiley & Sons / Page 1391 / 2nd Proofs / Heat Transfer Handbook / Bejan COLUMNS AND OTHER CONTACTORS 1391 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [1391], (33) Lines: 968 to 1052 ——— 6.89127pt PgVar ——— Normal Page PgEnds: T E X [1391], (33) St ≡ U V ˙m V C P,V a(a w /a t ) = 0.4Ja ·C −0.21 H −0.67 (19.65) where Ja ≡ h fg C P,V (T s − T a ) C ≡ ˙m L C P,L ˙m V C P,V and H represents the packing height Z ratioed to the characteristic packing diameter. A factor is included to account for the packing wetted area and the total packing area. Others have focused on the details of particular bed configurations and the heat transfer that results. For example, Fair and his co-workers were quite active in this area. Results for a variety of packings, including Raschig rings, Intalox saddles, Pall rings, and HyPak rings, were reported for an air–water or oil system (Huang and Fair, 1989; Fair, 1990). Key aspects of these data are presented in Table 19.3. All are for some combination of liquid and gas. The correlation equations are of the form U v = c 1 G c 2 G G c 3 L (19.66) In some cases the data are presented for the volumetric heat transfer coefficient on either the gas or liquid side separately. These data were reported as being for h G a or h L a and are so denoted in the table, but all are correlated with the same form as shown above. When the component values are given, the overall value can be found from the following equation U V = 1 (1/h G a) + (1/h L a) (19.67) TABLE 19.3 Summary of Heat Transfer Correlations Appearing in the Literature System Coefficient Packing a c 1 c 2 c 3 Air/oil U V RR-1 1.15 0.54 0.067 U V RR-0.5 0.0032 1.57 0.14 U V RR-1 0.083 0.94 0.25 Air/water h G a RR 0.0201 0.7 0.7 h G a RR-1, RR-1.5 0.117 1.0 0.2 h L a RR-1, RR-1.5 8.0 0.0 0.80 h G a RR-1 1.78e 0.0023Tf 0.7 0.07 h L a RR-1 0.82 0.7 0.5 U V PR-2 0.0279 0.57 0.806 Source: Adapted from data presented by Huang and Fair (1989). a RR-0.5, RR-1, and RR-1.5 denote Raschig rings of 0.5-, 1.0-, 1.5-in. size, while PR-2 denotes Pall rings of 2.0-in. size. BOOKCOMP, Inc. — John Wiley & Sons / Page 1392 / 2nd Proofs / Heat Transfer Handbook / Bejan 1392 DIRECT CONTACT HEAT TRANSFER 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [1392], (34) Lines: 1052 to 1062 ——— 0.28006pt PgVar ——— Normal Page PgEnds: T E X [1392], (34) TABLE 19.4 Heat Transfer Correlation Constants for Air–Water Packed-Bed Systems Size Packing (cm) Coefficient c 1 c 2 c 3 Raschig rings 2.5 h L a 26,680 0.51 0.63 h G a 6,947 1.10 0.02 3.8 h L a 46,060 0.48 0.75 h G a 6,130 1.45 0.16 Intalox saddles 2.5 h L a 36,900 0.20 0.84 h G a 7,228 1.01 0.25 3.8 h L a 42,570 0.20 0.69 h G a 6,174 1.38 0.10 Pall rings 2.5 h L a 33,460 0.45 0.87 h G a 5,065 1.12 0.33 3.8 h L a 32,910 0.31 0.80 h G a 5,310 1.28 0.26 HyPak rings 3.0 h L a 43,670 0.15 0.76 h G a 8,150 0.99 0.18 Source: Adapted from data presented by Huang and Fair (1989). The results shown in Table 19.3 were determined using columns ranging from 0.1016 to 0.76 m in diameter. It is interesting to note the wide variation in the results for these types of systems, even for the same-size columns. Huang and Fair (1989) also reported some heat transfer measurements of their own on air–water systems. For these studies they used a variety of packing materials. Work was performed in a square column, modified to eliminate corner effects. The net cross-sectional area of the column was 0.079 m 2 . A summary of these experiments is shown in Table 19.4. Again it is assumed that a form like eq. (19.66) represents the performance. There is interest in the operation of packed-bed condensers when noncondensables are present, as noncondensables are frequently found in these types of systems. One such reported study uses water to condense steam in a steam–carbon dioxide mixture (Bontozolou and Karabelas, 1995). It was found that the region along the column where the bulk of the condensation takes place can be controlled by a suitable choice of the steam–water ratio. The amount of CO 2 dissolution in the water was found to be unexpectedly high and a strong function of liquid temperature. 19.5 CONCLUDING COMMENTS It is hoped that the information included in this chapter will help engineers become more familiar with the various options available through the use of direct contact heat transfer. The methods of analysis outlined here, and the correlations included, BOOKCOMP, Inc. — John Wiley & Sons / Page 1393 / 2nd Proofs / Heat Transfer Handbook / Bejan NOMENCLATURE 1393 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [1393], (35) Lines: 1062 to 1127 ——— -0.69815pt PgVar ——— Normal Page PgEnds: T E X [1393], (35) should facilitate this. Although designs can be performed for many types of systems with the computer approach outlined, still missing from this field is something akin to the effectiveness–NTU approach to closed exchangers. Hopefully, designers will recognize the significant performance improvements possible for many applications with the use of direct contact processes. NOMENCLATURE Roman Letter Symbols a area of bubbles/droplets per unit volume of column, m −1 A flow area, m 2 B combination of variables defined below eq. (19.25) Bi Biot number, dimensionless c 1 ,c 2 , constants, dimensionless C ratio of mass-flow-rate specific heat products, dimensionless C D drag coefficient on a single droplet, dimensionless C P specific heat at constant pressure, kJ/kg · K d droplet diameter, m D column diameter or impeller diameter, m f friction factor of the nozzle, dimensionless Fo Fourier number, dimensionless Fr Froude number, dimensionless g acceleration of gravity, 9.8 m/s 2 G mass flow flux, kg/m 2 · s h heat transfer coefficient, W/m 2 · K ¯ h average heat transfer coefficient, W/m 2 · K h enthalpy, kJ/kg h fg latent heat of vaporization, kJ/kg H ratio: packing height to packing diameter, dimensionless Ja Jakob number, dimensionless k thermal conductivity, W/m · K K factor used in eq. (19.5), dimensionless LMTD log mean temperature difference, K m mass, kg empirical exponent, dimensionless ˙m mass flow rate, kg/s M molecular weight, dimensionless n empirical exponent, dimensionless N number of bubble trains in a column, dimensionless ˆ N mass transfer rate, kg/s NTU number of transfer units, dimensionless P pressure, kPa Pr Prandtl number, dimensionless Q heat transfer, W BOOKCOMP, Inc. — John Wiley & Sons / Page 1394 / 2nd Proofs / Heat Transfer Handbook / Bejan 1394 DIRECT CONTACT HEAT TRANSFER 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [1394], (36) Lines: 1127 to 1154 ——— -1.32632pt PgVar ——— Long Page PgEnds: T E X [1394], (36) r radius of sphere, m R droplet radius, dimensionless volumetric flow ratio, dispersed to continuous, dimensionless R m mass flow ratio, dispersed to continuous, dimensionless R average dimension radius, [≡ (R 2 0 + R 2 )/2R 0 R], dimensionless Ra Rayleigh number, dimensionless Re Reynolds number, dimensionless St Stanton number, dimensionless Ste Stefan number, dimensionless T temperature, K quantity defined below eq. (19.22), dimensionless U overall heat transfer coefficient, W/m 2 · K U V volumetric heat transfer coefficient, W/m 3 · K[= Ua for a direct contact device] v velocity, m/s 2 V volume, m 3 V volume of influence of a single column of bubbles, m 3 ˙ V volumetric flow rate, m 3 /s ˜ V denotes superficial or slip velocity, m 3 /s We Weber number in a bubble column, σ/ρ ˜ V 2 D We im Weber number in an agitation system, [= σ/ρN 2 D 2 im ], dimensionless X jet length or travel distance, m z local height, m (ft) Z total height of column or active zone, m Greek Letter Symbols a thermal diffusivity, m 2 /s β term defined in eqs. (19.22 and 19.31) vapor half opening angle, deg coefficient of thermal expansion, dimensionless γ function defined in eq. (19.38), dimensionless δ film thickness, m ζ exponent defined below eq. (19.47), dimensionless η fraction of heat transfer from dispersed to continuous phase, dimensionless λ eigenvalue, m −1 µ dynamic viscosity, N/m · s ν kinematic viscosity, m 2 /s ρ density, kg/m 3 σ surface tension, N/m φ local holdup (fraction of volume occupied by droplets), dimensionless ¯ φ averaged holdup over whole column, dimensionless BOOKCOMP, Inc. — John Wiley & Sons / Page 1395 / 2nd Proofs / Heat Transfer Handbook / Bejan REFERENCES 1395 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [1395], (37) Lines: 1154 to 1203 ——— 3.1951pt PgVar ——— Long Page PgEnds: T E X [1395], (37) χ function defined under eq. (19.2), dimensionless ψ function defined below eq. (19.25), dimensionless Subscripts a onset of agglomeration a w air c continuous condensate column column d dispersed droplet e external value f flooding value fg heat of vaporization g, G gas or vapor i considered element of a series or internal value im impeller jet jet L liquid max maximum value nozzle nozzle rough rough nozzle surface value S thermal sink slip slip component of velocity smooth smooth nozzle surface value T height of single tray zone or total or terminal V volume vapor w wall interface water 0 initial value 1, 2 ends of heat exchanger constant indices ∞ ambient condition REFERENCES Ahmad, G. R., and Yovanovich, M. M. (1994). Approximate Analytical Solution of Forced Convection Heat Transfer from Isothermal Spheres for All Prandtl Numbers, J. Heat Trans- fer, 116, 838–843. ASHRAE (2000). Cooling Towers, in ASHRAE Systems and Equipment Handbook, ASHRAE, Atlanta, GA, 36.1–36.19. Ay, H., Johnson, R., and Yang, W J. (1994). 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BOOKCOMP, Inc. — John Wiley & Sons / Page 1396 / 2nd Proofs / Heat Transfer Handbook. (1991). Direct-Contact Heat Transfer for Air Bubbling through Water, J. Heat Transfer, 113, 71–74. BOOKCOMP, Inc. — John Wiley & Sons / Page 1397 / 2nd Proofs / Heat Transfer Handbook / Bejan REFERENCES 1397 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [1397],. Cloud Heat Exchanger: Air and Particle Flow and Heat Transfer, Heat Recov. Syst., 1(2), 133–138. Sagoo, M. S. (1982). The Falling Cloud Heat Exchanger Commercial Pilot Plant Operation, Heat Recov.