Heat Transfer Handbook part 137 pps

BOEHM University of Nevada–Las Vegas Las Vegas, Nevada 19.1 Introduction 19.2 Sensible heat exchange 19.2.1 General comments 19.2.2 External convection to spheres 19.2.3 Heat transfer in

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CHAPTER 19

Direct Contact Heat Transfer

ROBERT F BOEHM

University of Nevada–Las Vegas Las Vegas, Nevada

19.1 Introduction 19.2 Sensible heat exchange 19.2.1 General comments 19.2.2 External convection to spheres 19.2.3 Heat transfer inside spheres 19.3 Evaporation andcondensation 19.3.1 General considerations 19.3.2 Condensation of a vapor on or in a liquid Film condenser

Condensation on liquid droplets Condensation on liquid jets Condensation in a liquid 19.3.3 Evaporation of a liquidby a surrounding vapor, gas or liquid Droplet evaporation in a vapor or gas

Droplet evaporation in a liquid 19.4 Columns andother contactors

19.4.1 Spray columns Global treatments Differential treatment Melting andsolidification applications 19.4.2 Baffledcolumns

19.4.3 Packedcolumns 19.5 Concluding comments Nomenclature

References

19.1 INTRODUCTION

Direct contact heat transfer can occur whenever two substances at different

temper-atures touch each other physically The implication is that there is not an interven-ing wall between the two substances Heat transfer where there is a surface between

the two streams is sometimes called indirect, or the heat transfer device is one of

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the closed types The physical interaction of the two streams can accomplish heat

transfer very efficiently Without an intervening wall, the energy transport between the two streams can take place across small thermal resistances In addition, the fact that a wall is not present can allow a mass transfer process to take place In some cases, this is a desirable phenomenon (open cooling towers), but in other cases it may not be

Costs are often more favorable for direct contact heat transfer devices than for their closedcounterparts The thermal resistances present in closedheat exchangers result

in less heat transfer than might be accomplishedin direct contact, andthis often trans-lates to lower operating costs for the latter In addition, the equipment to accomplish the direct contact processes is generally less expensive than the counterpart closed heat exchangers Both aspects can result in considerable life-cycle cost savings for the direct contact approach over that of the closed type of heat exchanger

Some potential limitations are inherent in direct contact processes There is a requirement that the two streams be at the same pressure Although this requirement does not often cause significant problems, it could be very important Also, as noted above, the mass transfer possibility in direct contact may not be desirable

Direct contact heat transfer is a fieldwith a wide range of potential applications

The actual situation is that with some notable exceptions, such as open feedwater heaters andwet cooling towers, few of these applications have been usedto any great extent Reasons for this are numerous, but one of the main reasons is that engineers are not as knowledgeable as they might be about the design of these types of systems

This chapter is an attempt to expose some of these possibilities so that the design of more efficient industrial processes might result

To present a description of direct contact processes within the limited space of this chapter, some restriction in scope is necessary Because the direct contact of any number of generic streams is possible (andmost have in fact been proposed

to transfer heat), only some of the more important applications will be notedhere

Solid–solid transfer processes are not covered, nor are high-temperature situations included where radiative heat transfer is important Open cooling towers are not discussed here to any great extent, even though they are the single most widely-appliedtype of direct contact heat exchangers Although some information related

to cooling towers is provided in the Section 19.4, this will by no means cover a very significant fraction of the total literature on the subject The previous work on cooling towers is voluminous andtends to use quite specializeddesign approaches Interested readers can findcurrent overviews by ASHRAE (2000) andMills (1999) An earlier review of the literature on the numerical modeling developed to predict cooling tower performance was given by Johnson et al (1987)

The literature contains reports of studies of interaction between different sub-stances as well as the same subsub-stances For example, a great deal of interest has been directed to the use of water in phase-change situations, particularly the condensation

of steam on liquid water On the other hand, interest has also been directed to the use

of fluids of different types For example, a great deal of literature on heat transfer in immiscible liquids was cited years ago by Sideman (1966), and many studies on this topic have appearedsince then

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Generally, the prediction of mass transfer has been given more attention over the years than has the fieldof direct contact heat transfer Because of mass transfer and heat transfer analogies, some information from the mass transfer literature can be used in direct contact heat transfer design This analog is exposed minimally here, however Emphasis here is on surveying predictions and applications, the main thrusts

of benefit to designers

19.2 SENSIBLE HEAT EXCHANGE 19.2.1 General Comments

Heat transfer from a continuous fluidto droplets or bubbles of another fluidis a com-plicatedsituation involving not only the typical convection-relatedvariables (e.g., geometry, velocity, andthermophysical properties) but also the proximity of the ob-jects to one another where more than one is present The latter characteristic can be

handled in an overall way through the definition of the void fraction or holdup, the

latter denoted here by the symbolφ Either of these relates to the volumetric ratio of

the amount of the dispersed phase (droplet or bubble) to the total volume Holdup has

a profoundeffect on direct contact heat transfer, as notedseveral times in this chapter

Another aspect that influences the heat transfer to droplets or bubbles is the shape

of these objects It has been well documented that droplets and bubbles can experience

a wide variety of shapes, depending on the object size and the flow situation (Grace, 1983) Despite this, much work has been done on a variety of systems assuming that the droplet is spherically-shaped A great deal of the early work was reviewed by Sideman (1966)

19.2.2 External Convection to Spheres

Convection to spheres has been the focus of many studies Some benchmark work

on this was that of Vliet andLeppert (1961) for a single sphere in forcedconvection with water The examination of their data for convection from water to solid spheres,

as well as existing data from others, led them to propose the following correlation:

hd

k =

1.2 + 0.53Re0.54

Pr0.3

µ

c

µw

0.25

(19.1)

which is statedto holdfor 1< Re < 300,000 and2 < Pr < 380.

More recently, AhmadandYovanovich (1994) have revisitedthis problem They recommendthe following correlation for swarms of spherical andrigiddroplets for situations when the holdup is less than 5%:

hd

k = 2 +

0.775Pr1/3[Re/(2χ + 1)]1/2

1+ [1/(2χ + 1)3Pr]1/6 (19.2) whereχ = 1.0/Re1/4forχ < 1 and χ = 1.0 for χ > 1.

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For holdups greater than 5%, the problem becomes much more complicated Here interactions with the other droplets in the swarm change the continuous fluid flow pattern over each individual droplet Wilson and Jacobs (1993) used a numerical approach to show that the heat transfer on individual particles in this more populous situation is given by the following:

hd

k = [1 − 0.186(φ − 0.42)]

0.877Re1/2+ 0.152Re2/3

Pr1/3 (19.3)

In this correlation, the velocity usedin the Reynolds number is the superficial value

19.2.3 Heat Transfer inside Spheres

Interior to droplets andbubbles, the heat transfer is affectedby the amount of circula-tion andwhether or not impurities are present Although the latter is more generally viewedas a problem of correctly identifying the appropriate properties to use, the former can be very difficult to predict If there is no circulation at all, a conduction solution will apply For a spherically shapedbubble or droplet without circulation, the solution to the transient conduction problem using a convective boundary condi-tion to a constant environmental temperature (this may not always be an appropriate assumption) gives the following:

T − T∞

T o − T∞ = 2

∞



n=1

sinλn R − λ n R cos λ n R

λn R − sin λ n R cos λ n R

sinλn r

λn r exp

−λ2

n R2· Fo (19.4) Here theλnare the infinite number of roots to the transcendental equation:

λn R cos λ n R = (1 − Bi) sin λ n R

For the other extreme, which finds a great deal of internal circulation within the droplet, Sideman (1966) recommends the following correlation after examining the results that were known at the time of his review:

hd

andwhere

K ≡ 1 − 2.9 + 4.35(µ d /µ c )

1+
ρdµd /ρ cµc1/2Re

−1/2

This equation holds for Re· Pr  1

Intermediate between the conduction limit and the well-mixed limit is an area in-vestigatednumerically andexperimentally by Hutchins andMarschall (1989) They found that natural convection is a major mode of transfer in addition to conduction

The internal heat transfer coefficient was seen to decrease with time until a “nearly

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constant” value was reached, and this value was set by natural convection as repre-sentedby

¯h d d

k d = 0.806(Ra)0.2321 = 0.806



gβd3(T W − T0)

να

0.2321

(19.6)

A problem that involves primarily sensible heat exchange, but where some evapo-ration also plays a part, is the bubbling of air into a stagnant column of water Ghazi (1991) reported such a study The results were given in a different form from some other relations presentedhere Data correlatedwith the following relationship:

UL

kair

L is the depth of the water pool, and the overall heat transfer coefficient U was

determined from the equation

UA = ˙mairC p,air (Tair,out− Tair,in)

withA as a reference area, taken as that for the orifice in this correlation.

19.3 EVAPORATION AND CONDENSATION 19.3.1 General Considerations

Lock (1994) has summarized the various modes in which condensation and evapora-tion can take place in simple direct contact systems These include the evaporaevapora-tion–

condensation interactions with droplets and jets in the presence of an incondensable gas Consider a representation of the regimes shown in Fig 19.1 In this figure the italic notations relate to the state of the vapor, with four regions defined by the in-tersection of the interface isobar andthe interface isotherm The nonshadedareas, hot evaporation on the upper right andcoldcondensation on the lower left, are the normally anticipatedregions where those phenomena occur Above the isothermT I

the region of vapor heat gain is demarcated from the region of vapor heat loss

In the hot evaporation region, the vapor–gas mixture is at a higher temperature than the liquid This superheated mixture drives the process by the transfer of heat to the cooler liquid Below the isotherm, but still on the same side of the isobar, the process can take place only if the liquidis superheatedandthus furnishes the heat necessary for the evaporation process Cool evaporation is limitedby the liquidsuperheat, as wouldbe representedby the liquidJakob number

Condensation processes take place in the region shown to the left of the interface isobar in Fig 19.1 These are normally considered to occur when the vapor is cooler than the liquid, andthis region is denotedas coldcondensation (lower left)

Clearly, the liquidsource or sink available for evaporation or condensation is limitedin real situations Hence the finite heat capacity of the liquidis a critical

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T

T l

Saturation curve

Condensation isobar

Warm condensation Cold

condensation

Interface isobar

Hot evaporation

Cool evaporation

Evaporation isobar Saturation

curve

s

Entropy

Figure 19.1 Four regimes of a vapor–gas mixture (Adapted from Lock, 1994.)

element in the determination of the amount of heat and mass transfer that can occur

For the cool evaporation andwarm condensation regions, this can be assessedby examining the Jakob number for the liquid By examining a simple energy balance, it can be shown that the mass of vapor that can be added to or removed from the liquid

by a change of phase is given by

m v ≤ m L JaL

where JaL = C P,L |T I − T0|/h fgandJaV = C P,V |T∞− T I |/h fgrepresent, respec-tively, the liquidandvapor Jakob numbers The Jakob number plays an important descriptive role in virtually all direct contact processes that involve a change of phase

For direct contact situations where cool evaporation or warm condensation occurs, the interface temperature is very close to the saturation temperature This results in a vapor Jakob number that is quite small In this case the equation shown above for the amount of mass of vapor formedor removedreduces to the following

Often in these situations, the liquidJakob number is very small, andvery large amounts of liquidwill be requiredto condense or evaporate small amounts of vapor

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A practical issue that can arise is the presence of a noncondensable gas, often air,

in a condensing or evaporating system In evaporating systems, small amounts of a component of this type do not cause much effect, and the phase-change processes are relatively unimpeded In condensing systems, the situation is quite different

Here the phase-change process can be grossly hindered Thus it is very important

in condensing systems to know the extent of the presence of noncondensables and account for them appropriately

19.3.2 Condensation of a Vapor on or in a Liquid

Condensation of a vapor on or in a liquid, whether or not that liquid is the same substance as the vapor, is commonly encounteredin engineering systems Direct contact processes differ from their indirect counterparts in many respects already noted In indirect transfer, the extent of the process is limited by the area of the surface andthe heat transfer rate possible through the surface In direct contact processes, the situation is limitedby the interplay between the latent heat of condensation andthe amount of sensible heat the liquidcan absorb The amount of the liquidusedfor condensing purposes and its subcooling determines the extent of condensation that can be accomplished

The presence of noncondensables during the condensation process affects perfor-mance in negative ways Details of the many studies of this will not, in general, be summarizedhere because of the effects of the multitude of variables that influence individual situations Condensation of a vapor that contains noncondensable elements

on a surface finds that a noncondensable layer builds up near the surface This causes both a heat transfer and a mass transfer resistance that impedes the basic condensa-tion process In many respects this is similar to what is foundin surface condensers when noncondensable gases are present In vapor droplet direct contact condensation

in a liquid, this same phenomenon is present at the inner interface of the bubble

Additionally, though, the presence of noncondensables results in a decreased vapor pressure inside the bubble compared to that of a pure substance in the same situation

This then lowers the condensation temperature, decreasing the driving potential for heat transfer

Many studies of direct contact condensation are reported in the literature An extensive review of this literature was given by Sideman and Moalem-Maron (1982)

primarily for visualization purposes This is the direct contact film condenser shown

in Fig 19.2 In this situation, a bulk vapor is condensed on another liquid, the latter serving as the sink Patternedafter the model usedfor Nusselt’s solution for laminar film condensation, and described in most elementary heat transfer texts, the concepts form a basis for other systems that follow below

Consider the heat transfer processes that occur in the direct contact film condenser

The pure saturatedvapor condenses on the liquidof the same substance Heat then flows by conduction through the condensed liquid to the sink liquid Since it is assumedhere that there is no other place for the heat to be absorbedultimately than

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Figure 19.2 Some details of a direct-contact film condenser where a vapor condenses on the liquid

the sink liquid, the heat capacity of that liquid is the determining factor for the duty possible from devices of this type

The heat transfer processes that must be analyzedfor this type of system are the diffusion phenomena through the two liquidfilms For short times, the sink liquidis consideredas being semi-infinite at the interface between it andthe condensedliquid

drop-lets Here spheres of the cooler sink fluidare sprayedat a velocityv into the saturated

vapor of the fluidof interest Due to heat exchange between the warmer vapor and cooler sink fluid, the vapor condenses and builds up a film on the droplets This process then slows with time because the fluid film that builds up on the droplet causes increasing thermal resistance to heat flow (although this effect can often be neglectedin analyses because the film thickness is small) Also, the temperature of the sink fluid increases, causing a diminishing temperature driving force, a true limit

to the process Consider the situation when the equality sign holds in eq (19.10) For

a film thickness ofδ, this equation can be written as

4π

d

2

2

δ · ρc= 4π

3

d

2

3

yielding

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δ = d

6

ρS

Generally, the densities of the two liquids are of the same order of magnitude If the Jakob number of the sink is very much less than unity, the condensate thicknessδ

will be small relative to the sink droplet diameter In this situation, the heat transfer across the condensedfilm can be assumedto be by conduction

Heat transfer in the droplet can also be assumed to be by conduction The govern-ing descriptive equation for temperature is then one-dimensional conduction in spher-ical coordinates With this model, the heat transfer into the composite film/droplet is given by (Lock, 1994)

¯h x x

k S =

2

π1/2



vX

αS

1/2

(19.13)

whereX is defined here as the droplet travel distance in the vapor: X ≡ vt These

results holdfor the times andsituations when the film thickness is small The term in

parentheses is sometimes calledthe travel P´eclet number.

viewpoint than the situation of condensation on droplets, condensation on jets yields

to direct analysis Again assume that the thermal transport in the jet is due primarily

to heat conduction and neglect the thermal resistance of the condensate film As is often the case, the Jakob number in the vapor is assumedto be small An alternative phrasing of this assumption is that the vapor superheat is assumednot to be large For this situation, the average heat transfer is given as (Lock, 1994)

¯h S djet

k S = 2

π1/2



v0d2 jet

αS X

1/2

(19.14)

The combination of variables in the parentheses is the Graetz number, basedon the assumedconstant diameter of the jet, andv0is the jet velocity

Several researchers have reported experimental studies, including Celata et al

(1989) An empirical relationship that does not require all of the idealizations inherent

in the equations given above was publishedby Kim andMills (1989):

hdjet

k = 3.2

v

0djet

ν

0.8 α

0.3f

rough

fsmooth

0.18ρν2

σdjet

0.19d

jet

L

0.57

(19.15)

Here the symbolf denotes the friction factor of the nozzle and σ represents the

surface tension

Condensation in a Liquid

Single-Bubble Studies The condensation of a single bubble in a liquid of the same component or a liquidof a different component has been of great interest to researchers over the years Included have been studies of a stationary bubble in a

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liquid of the same or a different liquid, as well as a moving bubble in the same or a different liquid A primary motivation for this has been to develop an understanding that might be applicable to more realistic systems that consist of many bubbles When

fluids of different types are involved (called three-phase exchanges because the liquid

andvapor of the condensing component as well as the liquidof the sink are present), the number of variables that influence performance goes up significantly over that for two-phase-exchange systems As shown in a review of this work by Sideman and Moalem-Maron (1982), most studies tendto focus on the time requiredto condense the bubble in a given situation Hence the bubble radius variation with time is an oft-citedresult

Some measuredresults for the condensation heat transfer coefficient were given recently by Terasaka et al (1999) They also comparedthe measurements to some theoretical predictions andfoundthe results to compare quite well In the experiments reported, they condensed single bubbles of hexane and, separately, vinyl acetate in water The experimental results fit the following equations For hexane,

h d = 7√.89 × 104

while for vinyl acetate, the following was found:

h d = 8√.77 × 104

These relationships can be comparedto the theoretical result:

h d = h fg

M W

2ρV

In this result,M W denotes the molecular weight of water

Bubble Trains A train of single bubbles is a more-complicatedidealization of more realistic systems consisting of swarms of condensing bubbles In this model, some degree of interaction of individual bubbles, including the effects of local heating of the bulk liquid, can be analyzed Another important aspect that can be examined

in the train studies is the effect on rise velocity of preceding bubbles This has a significant impact on the liquidheight necessary to accomplish a desiredamount of condensation

The transport properties of fluids involved in the condensing systems have a pro-foundimpact on the magnitude of the heat transfer coefficients This is like the sit-uation in surface condensers In direct contact, the properties of the fluid where the condensation is taking place add an additional effect An example quoted in Side-man andMoalem-Maron (1982) serves to illustrate this effect The relative ratios

of heat transfer coefficients for pentane condensing in pentane to those for pentane condensing in water to those for a water–water system are 1 : 1.5 : 3.9 The superior heat transfer performance of water over organic fluids can be seen in these ratios

of heat transfer coefficients for pentane condensing in pentane to those for pentane condensing in water to those for a water–water system are : 1.5 : 3.9 The superior heat transfer performance... properties of fluids involved in the condensing systems have a pro-foundimpact on the magnitude of the heat transfer coefficients This is like the sit-uation in surface condensers In direct contact, the... In this model, some degree of interaction of individual bubbles, including the effects of local heating of the bulk liquid, can be analyzed Another important aspect that can be examined

in