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
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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 increasedsubstantially comparedto 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) wouldbe filledwith objects of potentially any shape Both packed beds andbaffledtowers can be contrastedto spray columns in several ways Certainly, the cost is higher than the latter for either of these options The spray column can yieldhigher 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 liquidsuch 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, packedcolumns or other devices with internals might offer beneficial performance improvements
Usually, packings are usedwhen a liquidis in contact with a gas or vapor It is desiredto have as much liquidsurface in contact with the vapor or gas as possible
As the liquidflows 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–liquidsystems to assist in removing the wake from the dispersedliquidand increasing the heat transfer
Although a simple configuration can be imaginedwhere packedspheres are used,
in fact, this is not a normally favoredapproach because of trade-offs between cost andperformance Instead, more complicatedshapes such as structuredpackings 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
m2/m3 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 relatedto the solidvolume fraction of packing For solidspheres 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 accomplishedwith 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 requiredto remove large voidspaces The latter can affect bedperformance negatively
Packings of these types can be made of one of a variety of materials, depending
on the application requirements Plastic can be usedfor low-cost applications where the working temperatures are not too high On the other hand, metals or ceramics can
be usedfor higher-temperature applications
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Figure 19.11 Types of bedpackings: (above) Jaeger Tripaks (in North America) or Hacketten (in Europe) (printed with permission of Jaeger Products, Inc.); (below) Cascade MiniRings (printedwith permission from Century Plastics, Inc andJaeger Products, Inc., the exclusive licensee for the product in North America)
Heat transfer data in the literature for systems with packings are limited Part of this paucity of data is due to the fact that there are so many forms and sizes of packings
When this is coupledwith 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 bedof Raschig rings andthe methylene chloride–water data of Harriott and Weigandt (1964) A relationship that provides a reasonable fit for all these data is as follows:
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˙mV C P,V a(a w /a t ) = 0.4Ja · C −0.21 H −0.67 (19.65)
where
C P,V (T s − Ta )
C ≡ ˙m ˙m L C P,L
V C P,V
andH represents the packing height Z ratioedto the characteristic packing diameter.
A factor is includedto account for the packing wettedarea andthe total packing area
Others have focusedon the details of particular bedconfigurations andthe heat transfer that results For example, Fair andhis co-workers were quite active in this area Results for a variety of packings, including Raschig rings, Intalox saddles, Pall rings, andHyPak rings, were reportedfor an air–water or oil system (Huang andFair, 1989; Fair, 1990) Key aspects of these data are presented in Table 19.3 All are for some combination of liquidandgas The correlation equations are of the form
U v = c1G c2
G G c3
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 forh G a
orh L a andare so denotedin the table, but all are correlatedwith the same form as
shown above When the component values are given, the overall value can be found from the following equation
(1/h G a) + (1/h L a) (19.67)
TABLE 19.3 Summary of Heat Transfer Correlations Appearing in the Literature
Source: Adaptedfrom data presentedby Huang andFair (1989).
aRR-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.
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TABLE 19.4 Heat Transfer Correlation Constants for Air–Water Packed-Bed Systems
Size
Source: Adaptedfrom data presentedby Huang andFair (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 andFair (1989) also reportedsome heat transfer measurements of their own on air–water systems For these studies they used a variety of packing materials
Work was performedin a square column, modifiedto eliminate corner effects The net cross-sectional area of the column was 0.079 m2 A summary of these experiments is shown in Table 19.4 Again it is assumedthat 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 andKarabelas, 1995) It was foundthat 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 CO2 dissolution in the water was found to
be unexpectedly high anda strong function of liquidtemperature
19.5 CONCLUDING COMMENTS
It is hopedthat the information includedin 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,
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shouldfacilitate this Although designs can be performedfor many types of systems with the computer approach outlined, still missing from this field is something akin
to the effectiveness–NTU approach to closedexchangers 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
B combination of variables defined below eq (19.25)
c1, c2, 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 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/s2
h heat transfer coefficient, W/m2· K
¯h average heat transfer coefficient, W/m2· K
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 usedin eq (19.5), dimensionless LMTD log mean temperature difference, K
empirical exponent, dimensionless
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
Pr Prandtl number, dimensionless
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R droplet radius, dimensionless
volumetric flow ratio, dispersed to continuous, dimensionless
R m mass flow ratio, dispersed to continuous, dimensionless
R average dimension radius, [≡ (R2
0+ R2)/2R0R],
dimensionless
Ra Rayleigh number, dimensionless
Re Reynolds number, dimensionless
St Stanton number, dimensionless Ste Stefan number, dimensionless
quantity defined below eq (19.22), dimensionless
U overall heat transfer coefficient, W/m2· K
U V volumetric heat transfer coefficient, W/m3· K [= Ua for a
direct contact device]
V volume of influence of a single column of bubbles, m3
˙V volumetric flow rate, m3/s
˜V denotes superficial or slip velocity, m3/s
We Weber number in a bubble column,σ/ρ ˜V2D
Weim Weber number in an agitation system, [= σ/ρN2D2
im],
dimensionless
X jet length or travel distance, m
Z total height of column or active zone, m
Greek Letter Symbols
a thermal diffusivity, m2/s
β term definedin eqs (19.22 and19.31)
vapor half opening angle, deg coefficient of thermal expansion, dimensionless
γ function defined in eq (19.38), dimensionless
ζ exponent defined below eq (19.47), dimensionless
η fraction of heat transfer from dispersed to continuous phase,
dimensionless
µ dynamic viscosity, N/m· s
ν kinematic viscosity, m2/s
φ local holdup (fraction of volume occupied by droplets),
dimensionless
¯φ averaged holdup over whole column, dimensionless
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χ function defined under eq (19.2), dimensionless
ψ function defined below eq (19.25), dimensionless
Subscripts
condensate
droplet
i considered element of a series or internal value
rough rough nozzle surface value
slip slip component of velocity smooth smooth nozzle surface value
T height of single tray zone or total or terminal
vapor
interface water
1, 2 ends of heat exchanger
constant indices
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