FILM AND DROPWISE CONDENSATION

OF STEAM-AIR MIXTURES

FILM AND DROPWISE CONDENSATION

OF STEAM-AIR MIXTURES

By

Emile Nenni ger, Jr.

A Thesis submitted to the Fa.culty of Graduate Studies and Research at

MCGill University, in partial tulfilment of the requirements for the Degree of

Master of Engineering

MCGill University August 1951

ACKNOWIEOOEMENT

The author wishes to express his gratitude

to Dr. J.B. Phillips, Chairman of the Department

of Chemical Engineering, for his assistance and

advice during this investigation.

The writer also vishes to acknowledge the

National Research Council for their financial

assistance in the form of a Bursary and a Summer

Supplement.

INDE X

SUMMARY 1

INTRODUCTION 2

HISTORICAL REVIEW 3

THEORETICAL DISCUSSION 11

( 1) Fundamentals of He at Transfer 11

( 2) The Nus sel t Equation 12

(3) Presence of a Non-Condensing Gas 13

(4) Three-Variable Concept adapted for this Thesis 14

(5) Theory of' DropWise Condensation 16

(a) Simple Bxplanation of High He at Trans:f'er Coeffiéients 16

(b) Kinetic Theory of' Condensation 17

( c ) SUrface Tension and the Spreading Coefficient 22

( d) Promoter Action 23

DESCRIPI'ION OF EXPERIMENTAL APP.ARATUS 26

Vapor Flow Apparatus 26

Cooling Water Apparatus 27

The Condenser 28

EXPERIMENTAL PROCEDURE 32

Maintenance of Film-Type Condensation 32

Maintenance of Dropwise Condensation 32

Experimental Rune and Tabulation of Data 33

RESULTS

Explanation and Presentation of Data

Development of the Empirical Equation

36

36

48

DISCUSSION OF EXPERIMENTAL RESULTS

OVerall Comparison of Dropwise and Film-Type Condensation 51

Effect of Air Velocity on 'h' 52

Stability of Dropwise Condensation 52

Effect of Air Velocity on 'hse' 53

The Empirical Equation 53

Sources of Experimental Error 54

( 1) Thermocouple Errors 54

(2) Radiation losses 55

(3) Fogging in the Condenser 55

( 4) Sc ale Formation 56

LIST OF SYMBOLS 57

REFERENCES 59

APP.ENDIX 62

1-

SUMMARY

This thesis presents a comparison of the steam-side heat-transfer

coefficients of condensing steam-air mixtures during film-type and

dropwise condensations. Condensation took place on the outside of a

vertical five-foot length of li--inch extra-heavy copper pipe. Dropwise

condensation was produced by the application of a film of octyl

mercaptan to the copper surface.

Dropwise condensation gave higher heat-transfer coefficients from

zero to twenty nol percent air. Further increase in the concentration

of air resulted in identical coefficients for the two modes of

condensation.

An empirical equation was developed to predict the steam-side heat­

transfer coefficients during film-type condensation in the range of ten

to twenty-five mol percent air in the inlet steam.

2-

INTRODUŒ'ION

Although the condensation of steam was the first system to be

studied in the field of condensing vapors, there is still a great deal

that is unknown about the mechanism of this process.

The presence of air in steam has long been known to inhibi t the

condensation process. In many industries it is impossible to prevent

the accumulation of air in the steam. This creatly lowers its value,

and in sorne cases the steam is simply vented to the atmosphere after

serving its original purpose.

With certain types of surface active agents, the condensing surface

may be altered to produce dropwise condensation of the steam instead of

the usual film-type condensation. With pure steam it has been shown

that heat transfer coefficients on the steam side can be increased from

five- to ten-fold by using a dropwise promoter.

The idea was conceived that perhaps dropvise condensation would

provide an answer to the problem of steam with air present. In this

thesis an attempt was made to study the steam-side coefficients of steam

and air mixtures during both dropwise and film-type condensations.

3-

HISTORICAL REVIEW

The high coefficient of heat transfer was one ot the first

properties to be noted in the condensation of steam. Reynolds (35)

believed it to be infinite tor pure steam, but with the development

ot better techniques this proved to be wrong.

Great advances were made in the study of the condensation of

steam, in both theory and actual experimental knowledge, during the

period from 1890 to 1930. With the sudden growth of the petroleum

and the chemical industries, during and atter the First World War,

the field ot study broadened immensely to include not only the

condensation of steam, but also organic vapors, mixed vapors, and

mixtures of vapors and inert gases.

Joule (19) in 1860 was probably one of the first scientiste to

record an investigation on the subject. He built a condenser, similar

to the types which are found in almost all chemical laboratories today,

consisting of two concentric cylinders. Cooling water was circulated

in the annulus while steam entered the inside tube. The condensate

was collected and measured in a reservoir, In order to increase the

turbulence and bence the a.mount of he at transferred, Joule introduced

a spiral wire in the annular space and tound that the rate of beat flow

was increased several times. A similar attempt on the ste am side had

little effect, shoW'ing that the water-side resistance to beat transfer

was the greater. Joule also tried using air as a cooling medium and

found that the resistance of the air film was large compared to the steam.

4-

Joule concluded, "The resistance to conduction is attributed

a.liOOst entirely to the film of water in iDDilediate contact wi th the

inside and outside surfaces of the tube, and is little influenced by

the kind of metal of which the tube is composed, or by its thickness

in the limite of ordinary tubes, or even by the state of its surface

as to greasiness or oxidation11•

This is an important conclusion for it shows that Joule understood

that the resistance to the flow of beat was mainly in the films of

material on both sides of the wall through which the heat was flowing.

Although he was mistaken about the effects of grease or oxide films

on the surface, it is true that often the resistance of the tube wall

to the conduction of heat is negligible compared with that of the fluid

film on either side.

In 1873, Osborne Reynolds (35) presented a paper to the Royal

Society of London, in which he described the research of Pasely, a

student at Owens College, on the condensation of mixtures of air and

steam. The apparatus used was quite simple, consisting of a condensing

surface in the f'orm of' a 1U1 tube exposed to an atmosphere of steam

and air inside a flask. The rate of' heat transf'er was measured merely

by counting the drops of condensate falling from the tube in a unit of

time. It was found that the rate of condensation dropped about 7(J{o in

the range of 0 to l~ air. Reynolds attributed this decrease to the

presence of a stagnant layer of air in immediate contact with the

condensate film, opposing the flow of steam.

5-

Reynolds stated, "--- in fact, there is no limit at which pure

ste am will condense but the power of the surface to carry off he at 11•

Kelvin (22) in 1889 agreed with Joule in that there is also a

resistance to the flow of he at on the condensing steam side. However,

he realized that it is almost impossible to determine the thickness of

the film of condensate since in most fluid-to-solid beat transfer,

convection as well as conduction is involved. Kelvin suggested the

use of the term "he at transfer coefficient" for this case, and d.efined

the coefficient as the quanti ty of beat flowing through unit surface in

unit tilœ per unit temperature difference. This term bas been universally

adopted.

Callendar and Nicolson ( 4) in 1897 described experimente they had

performed at MCGill University on the condensation of steam vith the id.ea

of examining previous concepts (probably Reynolds statement about the

infinite rate of pure steam condensation). They condensed steam on the

inside of a thick cylinder, which bad mercury therJOOmeters inserted at

various distances from the condensing surface; in this way they hoped to

be able to estima te the wall temperature. Discrepancies were noted in

the temperature readings, hovever, which vere thought to be caused by

the uneven flow of he at around the thermometer wells. They concluded that

"if the rate of condensation vere infinite it should have been possible

to obtain a rate of condensation many times greater than the limit deduced

from the cylinder-condensation experimenta above mentioned 11• Renee the

rate of condensation vas found to depend mainly on the temperature

6-

difference between the saturated ste am and the surface on which i t

was condensing.

In 1915, Wilson { 44) published a paper dealing wi th a method of

obtaining steam film coefficients in cases where the wall temperature

was unk:nown. It bad long been known that the water-film coefficient

was an exponential function of i ts veloci ty. He assumed that the

resistance on the vapor aide and the resistance of the wall were

independent of the water velocity. Binee the total resistance is equal

to the sum of the se three, he was able to deduce the resistance of the

vapor film by Plotting the sum of the resistances against the water

velocity expressed in its exponential form. The intercept representa

the value of the vapor resistance plus the wall resistance. The wall

r~sistance can easily be. calculated and bence the vapor film resistance

determined. This method in a sligbtly modified form is used today in

industrial work to determine condensing-vapor-film coefficients {20).

Since the resistance varies inversely as the conductance, this method

of cal.cu1ation is subject to large errors when the stea.m-side coefficient

is large compared with the water-side coefficient.

In 1916 Nusselt (31) presented a mathematical paper deal.ing with the

condensation of vapors. This paper is probably the IOOst important of

all that have been presented on this subject, for his equations are still

used today as a basie for the calculation of condensing-film coefficients.

Almost every paper dealing with the condensation of vapors uses one of

the Nusselt equations as a starting point, and describes deviations

7-

~rom it. Although the equations involve several assumptions, some

o~ which are known to be unwarranted, their simplicity maltes them

o~ great practical value. Monrad. and Bad.ger (28) give a good summa.ry

o~ the derivation of the Nusselt equation ~or vertical tubes.

The effect of air in ste am vas studied by Orrok ( 32) who ~ound that

the overall coef~icient o~ steam-to-water varied as the square o~ the

volume percentage of steam. Kerr (23), in a paper deecribing the use o~

multiple-effect evaporators for the sugar industry, found the beat

transfer coefficient to be a function of the fourth power of the volume

percentage of steam in the mixture. However, in a wri tten discussion

(33), Orrock points out that this is one of the _most complicated problems

in the beat-transmission field. The resulte for various tests up to this

point had shown a great deal of scattering which made the correlation o~

data di~ficult.

The effect of air in steam has also been discussed by Hoeffner (16)

and Josse (18) but with no quantitative relations. In 1920 Robinson (37)

described a method of obtaining an empirical equation relating the heat

tranefer coefficient with the percent air present, using the data provided

by Kerr ( 23). B .F .Dodge ( 10) developed equations to enable approxima te

calculations to be made when non-condensables are present in vapors.

He describes systems containing several vapor components which obey

Raoult' s law.

In 1929, D.F. othmer (34) inveetigated the film-type condensation

of ste am containing 0 to 6. 59;, air by volume, on a horizontal tube.

8-

He stated that the decrease in the coefficient of heat transfer,

due to very small amounts of air present, indicates that the air must

be localized around the tube.

Colburn and Hougen (7) in 1930 gave resulta obtained in a vertical

tubular condenser using air-stea.m mixtures. It was found that the

date varied over each section of the tube, and they tried to give a set

of resulte for each foot of length. In 1934 they (8) developed a trial-

and -error method of designing tubular condensera for mixtures of vapors

and non-condensing gases. The sensible beat loss plus the latent beat

loss due to diffusion througb the condensate film, is equated to the

he at transferred through the condensa te, tube wall, and the cooling water

film. This requires a knowledge of the temperature of the interface

between the condensate and the vapor, and the corre sponding vapor

pressure of the condensate. Smith (41) in 1942, pointed out that this

procedure had neglected the he at los ses of the condensate. If the

latent heat of the vapor is high, as in the case of steam, the error

woul.d be sma.ll, but f'or some organic va pors the error could amount to

Chilton and Colburn ( 6) showed a method of estimating mass transfer

' coefficients for design calculations based on Reynolds analogy between

beat transfer and fluid friction (36).

The effect of the length of the vertical condensing tube is

discussed by Baker, Kazmark and Stroebe (2), (3), {43). They found

that the vapor-side beat transfer coefficient varies inversely as the

square root of the length. The error is about t 2~.

9-

McCormick (26) in 1933, while discussing the work of Hebbard and

Bad.ger ( 15) and other workers, came to the conclusion that i t is

impossible to correlate the resulte by applying factors to the Nusselt

equation. Possibly some of the d:tscrepancies he noted were due to the

presence of dropwise condensatiDD.

A method of determining the surface temperature of the condensate

has long been sought by workers in this field. Kirkbride (24) tried

measuring the thickness with a micrometer screw, but was not very

successful because of the ripples in the film. A photographie method,

based on the gradient of optical density in gases due to the temperature

gradient, is described by s. Ruppricht (38).

The marked differences between the beat transfer coefficients of

dropwise and film-type condensation were first brought to light by Schmidt,

Schurig and Sellschopp (39) in 1930. They condensed steam on a round

copper plate 5.28 inches in diameter. When the surface became slightly

oily due to contamination of the steam, the mode of condensation changed

to dropwise and the beat transfer coefficient increased from roughly

1000 to 80oo B.t.u./(hr.)(sq.ft.)(°F.}.

Spoelstra ( 42) was attracted to this field of study by the curious

heat transfer phenomenon found when testing fouled tubes in Javanese

sugar mills. In a great many cases it was found that when the badly­

fouled tubes were cleaœd, the heat transf'er became less efficient. In

his research Spoelstra f'ound that the scale on the tubes contained enough

oil to promote dropwise condensation, and the overall heat transfer

increased in spite of the added resistance in the scale.

10-

In 1933, Nagle end Drew ( 29) f'ound. that wi th ordinSJ:"Y' copper

surfaces there is a tendency f'or steam to condense in a dropwise :manner

af'ter long periode of' operation. This again was probably caused by the

presence of' oil in the steam. Af'ter more caref'ul experimentation (30)

(11), the ef'f'ect of' surf'ace-acti ve agents on the condensing surf' ace vas

def'initely established.

Steam-side coefficients renging from 6800 to 16,400 were reported

in experimente done on a vertical copper tube by Fi tzpatrick, Baum and

Mc Adams ( 13) in 1938. Benzyl mercaptan vas used as a promoter and i t

caused a substantial increase in the steam-side coefficient f'or both

Admiralty metal and copper tubes.

The ef'f'ect of' vapor velocity was described by Shea and Krase (40) in

1940. They f'ound that as the vapor velocity increased, the coefficient

increased slowly to a maximum and then decreased quite rapidly. No

f'urther work bas been done on this phase of' dropwise condensation.

Much light was thrown on the mechanism of' pr~ter action by

Emmons (12). He applied molecul.ar layera to surfaces in def'inite known

thicknesses and then studied their eff'ect on the steam side coefficients.

He f'ound that the promoters generally :form in a monomolecular layer

af'ter a short period o:f operation.

11-

THEORETICAL DISCUSSION

( 1) Fundamental.s of Heat Trans fer.

Heat may flow by three distinct mechanisms:

Conduction: The transfer of heat with no appreciable displacement

of the particles of the conducting medium.

Convection: The transfer of beat in a fluid due to maas-motion

of the fluid.

Radiation: The trans fer of beat by electromagnetic wave motion from

one body to another.

The transfer of heat by conduction may be expressed as

where

dq = -kd.A dt ds

(1)

dq "' instantaneous rate of heat trans:fer, B.t. u. per hr. dA= differentia! area, in sq.ft. through which the beat

is flowing - dt

dx = temperature gradient at rigbt angles to the flow of he at, ( °F. per foot )

k .. Specifie thermal cotxluctivity of the substance.

When heat transfer takes place between a solid and a fluid the

mechanism becomes somewhat complicated, for both conduction and convection

are usually involved, and sometimes, radiation. To overcome this

difficulty the :following equation is used:

where dq = hdA (t - t 8 ) (2)

h = beat transfer coefficient througb the fluid film on the surface of the solid

t = bulk temperature of the fluid t 8 = surface temperature of the solid.

12-

(2) The Nusselt Equation.

Nusselt (31) derived theoretical equations in order to be able

to predict the beat transfer coefficients for pure condensing vapors.

His equation for the condensation of vapors on vertical surfaces is

h"' ~~~'3)~1.410f; Y' (3)

The derivation of this equation depends on seven sim:plifying

assumptions:

(1) The film of condensate is so thin that the temperature gradient

through it may be considered as being linear

( 2) All the he at is carried to the œtal surf' ace by pure conduction

in a direction perpendicular to the surface

(3) The physical properties of' the condenaate are talœn at the mean

film temperature.

( 4) The surface is considered as being smooth and clean

(5) The film always moves in viscous motion

( 6) The curvature of the film may be neglected

( 7) The temperature of' the sol id surface is constant.

Most of' these assumptions are quite valid. Probably the greatest

error is in the assumption that the film always f'lovs in viscous motion.

In almost all condensera there is an appreciable vapor velocity past the

condensing surface, causing ripples and small local disturbances in the film,

vhich tend to increase the rate of beat transfer.

13-

(3) Presence of a Non-condensable Gas.

The presence of a non-condensable gas in the vapor greatly

complicates the theoretical approach to this problem. The vapor can

no longer be considered as haVing a constant temperature, for as it

passes through the condenser its temperature will decrease vith the

removal of the condensable portion. As the condensable flows toward

the cool surface, the non-condensables are drawn along Vith it, tending

to form an inert layer on the surface. This layer acta as an added

resistance, for the condensable vapors must diffuse through it before

they reach the condensing surface.

No satisfactory theoretical equation bas yet been derived which

will predict the beat transfer coefficient for this case. In 1935,

Meisenburg, Boarts and Badger (27) presented one of the best papers on

the film type condensation of steam vith air present. They expressed

their experimental resulte in the form of the Nusselt equation vith

extra factors to take care of the effect of air in concentrations from

0 to 4 percent by weight. The ir equation is

h = 1t [k'!p2:J À J ~ (...L \0·11 s s l L p L\ t] Ç ) (4)

Tr5 is a factor which depends on the amount of air present in the

steam. Since the amount of non-condensables vas small it vas not found

necessary to include the mass-veloci ty effect of the non-condensable

gas.

14-

(4) Three-Variable Concept adapted for this Thesis.

As the amount of air present in the condensing steam increases,

the effect of its mass-velocity becomes an important factor. In the

work done for this thesis in the range of 7 to 25 mol percent air, the

mass-veloci ty proved to be an important variable and could not be

neglected. Also, the variation of vapor temperature was appreciable,

eliminating the possibility of expressing the resulte in the form of a

modified Nusselt equation.

It was d.ecided that perhaps the simplest approach would be the

best, and an attempt was made to find a three-variable correlation from

the experimental data. The most fundamental. variables pertaining to

design conditions were chosen. They are:

( 1) a = mol percent air present in the ente ring ste am

(2) G :::: maas velocity of the air through the condenser

(3) h :o the vapor-side heat transfer coefficient.

It was found that

h = F(a,G) al.eo

where x is a constant and

K = F(a)

the re fore

h = Gx F(a)

(5)

(6)

{7)

(8)

The resulta for film-type condensation of steam-air mixtures

conformed fairly well with an equation of type (8).

15-

VAPOR

'---- PlPE WALL

CONOE.NS~\E __ _/

Fig.l- Hypothetical View of Condensate on Pipe Wall.

16-

(5} Theory of Dropwise Condensation.

(a) Simple Explanation of High Heat-Tranefer Coefficients.

For a long time the early papers dealing with dropwise condensation

vere unable to give a clear reason why the beat transfer coefficient should

increaae so definitely when this phenomenon occurred. In 1924 Ginabat

( 14} gave a simple explanation as summarized by Nagle and Drew ( 29) in

1933.

It ~ be assumed that the condensate covers the cooling surface in

the manner shown in Fig.l and that there are two adjacent surfaces of equal

area A covered by condensate of average thicknesses 'a' and 'b'. Let ~

and cq, be the heat transferred through areas •a• and 'b' respectively.

The total beat transferred through areas a and b will be

+ KAA.t b

=KA At [ ~+ ~]

For an illustration let a+ b -: 6

If the condensation is film type a= b and

Qa,+~ = KAàt [ ~+ ~]

:0.67 KAÂt

However if the relative thicknesses are such that a::. 1 and b = 5 then

Qa,+ cq, = KAA t [ î + ~] ~ 1.2 KAAt

The at!J:)unt of heat transferred through the seme area and seme amount

of condensa te is almost twice as much in the second case.

17-

In d.ropwise condensation, the nature of the condensa te layer

between the drops is still an enigma. It is the belief of sone workers

( 12), and of the author of this the sis, that the surface is actually

dry between the droplets. A film of supersaturated vapor is thlrught

to exist in place of the film of condensate. However, whether the film

between the drops is actually vapor or liquid, the equivalent thiclme ss

woul.d only be a minute fraction of the drop-thickness, and this would

cause a great increase in the rate of heat transfer as shown above.

The foregoing illustration also indicates the significance of

ripples in the condensate layer during the more normal film-type

condensation.

{b) Kinetic Theory of Condensation.

The mechanism of dropwise condensation has been definitely shown to

depend on the nature of the molecules of the vapor, condensate and

condensing surface. Emm.ons (12), in 1939, presented a paper dealing with

the published etudies of the behavior of molecules at surfaces. The

kinetic molecular theory may be applied to dropwise condensation as

follows:

The rate of arri val of molecules at a condensing surface may be

expressed as

U= p 1

( e.n \<.bT~) ï. gm. per sq.èm.sec. (9)

The rate of evaporation of molecules from a surface is

gm. per sq.cm.sec. {10)

18-

M:>lecules at the condensing surface Will accumulate at the rate

U - V 6

• If a layer of condensa te builds up on the surface, the rate

of evaporation will change, for it depends on the nature and temperatures

of the surface, while the rate of arrival of vapor ~lecules will be

constant for it is independent of the surface condition.

The rate of evaporation from the condensate surface may now be

expressed as

gm.per sq.cm.sec. (11)

If the condensate layer is assumed to be monomolecula.r, the wall

temperature T8 may be assumed to be the sa:me as the vapor-liquid surfaces

temperature of the condensate, Ti.

According to Emmons ( 12} the beat of evaporation in this case Will

vary With the affinity that the vapor molecules have for each other and

that of the vapor melecules for the surface. If the surface has a

greater affinity for the vapor molecules than they have for each other, À$

will be greater than À.t and from equations (10, 11) V 8

will be less than

vi.

Since the rate of evaporation from the bare surface is lesa than

that of the liquid-vapor interface, any ba.re spot~ on the surface will

eventually be covered vith a film of condensate, and film-type condensation

will ensue. The film will build up in thickness until an equilibrium is

established between the rate of heat transfer through it and the effect

of gravity in removing the film. The Nusselt equation, which bas been

universally accepted for the prediction of beat transfer coefficients for

film type condensation of pure vapors, is based on a consideration of this

equilibrium.

19-

In dropwise condensation the surface is believed to have lesa

atfini ty for the vapor molecules than they have for each other. In this

case Ài will be grea ter than "-• and consequently v 8 will be grea ter than

vi. Since the rate of evaporation in this case is greater from the bare

surface than from the condensate surface, there will be a tendenoy for

the oondensing surface to remain dry. Because of the stress put on the

system due to the temperature gradients, condensation naturally will

take place on the surface.

Since it is impossible to have the surface perfectly uniform, the

nuclei for the drops probably form on the most advantageous parts of the

surface where perhaps there are weaknesses in the layer of the dropwise

promoter. It has been shown quite conclusively by Emmons (12) that the

layer of promoter on a condensing surface will exist as a monom.olecular

film atter a few hours of operation regardless of the number of molecular

layera that may have existed originally. This layer will undoubtedly

contain the irregularities necessary to act as nuclei for the droplets.

During the experimental work for this thesis, it was oberved that

at the start of an experimental dropwise run, the surface immediately

became covered with a silvery layer of countless minute water droplets

whioh tended to coalesce as they grew. Finally, when they reached a

aize of roughly an eighth of an inch in diameter, the drops would run down

the surface gathering any ether droplets in their path, and sweep the

surface clean for the process to commence again.

20-

H Emmons ( 12} postulated tha.t a layer of supersaturated vapor

would be present between the drops of condensate on the pipe wall.

In the experimental work done for this thesis, the present author

found that the temperature of any point on the surface of the pipe was

a.l.lra.ys below tha.t of the adjacent vapor; therefore, it may be assumed

that the surface between the drops is below the saturation temperature

of the vapor. Thus, a temperature gradient must exist between the bulk

of the saturated vapor and the surface, and this in turn must exist in

a layer of supersaturated vapor, or in ave~ thin film of liquid or both.

After watching this phenomenon for many hours in the laboratory, the

author of this thesis believes that the surface between the drops is

dry, and. covered by a film of supersaturated vapor.

It is suggested that this blanket of supersaturated vapor over the

dry surface between the drops terminates at the edges of the drops them­

selves, thus exposing a highly unstable vapor to a very attractive

condensing surface. Local drops in pressure might occur as the vapor

condenses rapidly. The se drops in pressure would cause a great deal of

turbulence on the surface in general. This theory was borne out by

experimental observations.

21-

LlQU\0 GAS

50l\D

Fig.2 - Interracial Tensions Among Solid Liquid and Gas.

22-

(c) SUrface Tension and the Spreading Coefficient.

The attraction of the va.rious phases for each other and the

tendency for a liquid to form in drops rather than in a film on a

surface can be expressed in terms of the spreading coefficient which

involves surface tension effects.

The spreading coefficient Z is defined by N.K.Adam (1) as

Z = '( sg - '( lg - G 81 dynes/cm. (12)

(Figure 2)

If Q is made equal to zero, it is possible to get a physical picture

of the meaning of Z. The solid-gas interfacial tension is opposed to

the sum of the liquid-gas and the solid-liquid interfacial tensions, and

clea.rly if Z is zero or positive, the liquid will spread out in a film

over the surface. Therefore, the condition necessary for dropwise

condensation is thet Z will be negative.

If Z ie negative the liquid will withdraw from the surface until an

equilibrium is established according to the equation

osg = o1g cos et ~81 (13)

Substituting this in equation {12)

Z • D1g (cos 6 - 1) (14)

This provides a simple way of determining the value of Z from liquid

surface tension and contact-angle measurements.

The viscosity, however, of the condensate also plays an important

part, for if it is high the drops will merge slowly with each other and

the 'hold up' on the condensing surface will be large. An experiment is

described ( 12) where aniline was condensed on a copper surface promoted

with heptyl mercaptan. The value of Z was negative, but the drops were

23-

so sluggish that the surface vas soon entirely covered by a film of

drops that bad coalesced.

(d.) Promoter Action.

Most vapors when condensing on a clean metallic surface will wet

the surface. A notable exception to this rule is the condensation of

steam on chromium (29). It has been found, however, that these

surfaces may be treated with compounds which will promote dropwise

condensation. The greatest success so fa.r bas been obtained with copper

surfaces exposed to steam.

In order to al ter the surface propertie s so that the spreading

coefficient will be negative, it is necessa.ry to use a substance which

will have a high attraction for the metal surface to prevent it from

washing off. At the sam.e time it must exhibit a 'repellent • action for

the condensa te. It has been shown that the promoter will exist in a

monomolecula.r layer ( 12); therefore 1 the molecules of the promoter must

possess the se properties. This is the reason why the mercaptans a.re so

successful on copper. The active end o:f the molecule containing the

sulfur will adhere to the surface very tenaciously, while the other end,

being a hydrocarbon, repels the steam condensate.

The dropwise condensation of any vapor aay be obtained on any

surface if the following prol_)8rties can be found in the promoter (12):

( 1} One part of the promoter molecule must have a very weak.

affinity for the vapor molecule

( 2) Another part of the promoter molecule must have a great

affinity for the cooling surface

24-

(3) These two parts of the molecule should exist in an arrangement

such tha.t in a. monomolecular layer the molecules will be able to orientate

themselves in such manner as to have one active and one inactive surface.

A table of promoters and their relative effectiveness on various

surfaces is given by Drew, Nagle & Smith ( l\).

25-

Fig. 3 - Photograph of the Condensing-Vapor Apparatus.

26-

DESCRIPriON OF EXPERIMEN!'AL APPARATUS

The apparatus used in this investigation was almost the same as

that used by G.E. Charles (5) in 1950 for the atudy of dehumidification.

It consisted essentially of a vertical tubular condenser designed for

the flow of vapor down the out si de, and water up the inside of a copper

pipe. A schematic flow-sheet is shown in Fig. 4.

Vapor Flow Apparatus.

Air, from the University compressed-air system, passed through a

standard instrument disk-type fil ter, before being throttled through a

globe valve into the apparatus. The flow of air was metered by a aharp­

edged orifice (diam.O. 500 inch) eut from a 1/16-inch aluminum sheet. The

orifice was calibrated by placing it in series with a standard orifice.

steem, from the University mains, was throttled through another

globe valve, and entered the system after the air orifice. The mixture

of steem and air passed tbrough a small saturation condenser, followed

by a separation chamber, to the top of the experimental condenser.

Carefully standardized thermometers graduated in tenths of a degree,

Centigrade, and manometers for measuring the atatic pressure of the vapor,

were located at the condenser inlet and outlet. The excess va:pors from

the conde11ser outlet were vented to the atmosphere, while the condensa te

was collected in tared bucket s and weighed.

WATER OUT - 1 -'

'-..,J

AIR .~~~~

0

0

t ......._,

SA:TUR.Ait011 1

CONDENSER 1 1

1

1

COOLlNG 1 W ~TER --tJ1o 1

T

.. E )\CESS VAPOR

M MA.NOMETER 0 OR\F\CE T THERMONIE.TE R

T

T

...... _

T

M

. M

5TEAM

T

~1

1

~

27-

WATER lN

CONSTANT f HEAD TANK -----

EXPER\MENTAL CONDENSER

[ CONOENSAïE .....-•----, B ALÂ NC E

,;._.,....

.,.

Fig.4 - Schematic View of Condensing Vapor Apparatus.

28-

The Cooling Water Apparat us.

It is essential in experimenta ot this type to keep the rate ot

flow of cooling water constant. Kemmett (21 ), while working at M::Gill

University on a horizontal condenser, attributed a good part ot his

experimental error to variations in the rate of flow of cooling water.

Consequently, a constant-head tank was designed and built to deliver

up to a maximum of four gallons of water a minute to the condenser at

constant rates ot flow. The possibility of using an electrically-driven

centritugal pump connected to a reservoir was also investigated, but

variations in the power lines rendered this method useless.

The water floved from the constant-head tank through a controlling

globe valve to the condenser. Mercury thermometers measured the

temperature of the water at the inlet and outlet ot the condenser.

Thermocouples vere tried, but unsatistactory resulta were obtained,

pro}»ably due to conduction of beat along the copper tubing in which

they vere inserted. The water was metered be tore going to the drain,

by an orifice which had been calibrated in place.

The Condenser.

Condensation took place on the outside of a vertical (1*'-inch

extra-heavy-copper) pipe over five feet of its length. The pipe was

jacketed by a pyrex tube (4-inches I.D. ), wbich was insula.ted except

tor a narrow observation elit down one aide. The vapor temperature

was determined by tive thermocouples located at one-foot intervals in

the vapor space, starting at six incbes from the top and ending at six

inches from the bottom. Pipe wall temperatures vere measured by nine

constantan-copper thermocouples placed at six-inch intervals on alternate

aides of the tube.

A- À

29-

f.X T2A. HE.A.VV coPPtR. PIPE

----- Wllt.E. c~&LE.

JUNCTIOtot

WIRE.. C~f,LE.

MIL.LED Glt.OOVE

JUNCiiON.

--SOLDE~

bR.ASS FoU ..

~~ IWSUL.~TE.O

CONS T~li T~H WIR.t

E.N LA~GE.D VIF.W OF VER-TICAL ûROOVE.

Foll.

Fig.5 - Installation of the Thermocouples in the Pipe Walls.

30-

Considerable time vas spent in the installation of the couples

in the pipe wall. A similar tube (5 ) had previously been built

according to vbat vas presumed the beat method found described in the

literature. In spite of the care and hard work involved, the tube had

four faulty couples out of nine. Another survey of the literature on

this subject was made, and after much experimentation on copper tubing,

it vas decided to use the folloving technique:

Two longitudinal grooves (1/10-inch deep, 1/16-inch vide) vere

milled on opposite aides of the tube. Horizontal slots (lt inches long,

1/16-inch vide) vere eut in the outside surface of the tube vi th a saw,

and were branched at right angles to the main grooves at the location of

the thermocouples, as shawn in F1g.5. Only constantan vires (#30 A.V.G.

double fibreglass insulation) were placed in the grooves, because the

pipe served as a common junction and lead for the copper side of the

thermocouples. When the vires for one side had all been eut to the

proper length, they were wrapped together vith a strip of brass foil

(0.001-inch thick, 3/16-inch wide) in a he1ical f'ashion. The wires at

the Junctions projected tangentia11y f'rom the helix and were soldered in

the horizontal slots to gi ve a reading of the surface temperature of

the pipe about one and one-half inches away from the longitudinal groove.

The bund.led vires were pressed to the bottom of the groove; the tube vas

heated vith an mey-acetylene torch, and the groove vas filled vith a low­

melting-solder. When this had been done on bath sides, the tube was

carefully polished vith steel vool. Each couple vas tested and all were

found to be operating properly.

31-

The advantages of this method are:

( 1) The use of' the copper pipe as part of each thermocouple

insures good thermal contact with the surface.

(2) There is only one lead in the pipe wall for each couple

( 3) The brass foil wrapping prevents damage to the fi ber glass

insulation on the wires when the solder is applied

(4) The brass helix gives the cable good physical contact with

the bot tom of the groove and prevents 1 t from f'loating to the surface

when the molten solder is applied.

32-

EXPERIMENTAL PROCEDURE

Maintenance of Film-type Condensation.

Small amounts of im:purities in the condensing vapor will some­

times cause dropwise condensation to take place on portions of the

condensing surface. The compressed air vras found to have soœ oil

mist in it vrhich made it impossible to maintain complete film-type

condensation for any length of time. Much better resulta vrere

obtained after placing a good filter in the air line.

Before the experimental runs vrere started, the condenser vras

dismantled to clean the pipe surface. The pipe vras first vrashed w1 th

very dilute nitric acid to remove the scale, and then vrashed several

times vith the household detergent 'Surf'. The surface was tested by

placing drops of water on the pipe and noting vrhether they spread

immediately into a thin film. The condenser vras then re-assembled,

and the film-type experimental rune were made. From time to time the

condenser vras cleaned by injecting small amounts of the powdered

detergent into the vapor line, and flushing the suds out with wet

ste am.

Maintenance of Dropwise Condensation.

Octyl mercaptan was used on the surface as a promoter of dropwise

condensation. Preliminary experimenta showed that the injection of a

mere cubic centimeter of this mercaptan into the vapor stream caused

the surface (2.17 sq.ft.) to change over completely from film-type to

dropwise condensation. In order to parallel the procedure used for

33-

film-type condensation, the condenser was dismantled once more and

the tube washed and polished vith a cotton cloth containing a few

cubic centimeters of the mercaptan. The condenser was then re­

assembled and the dropwise runs were made. Al though i t was probably

unnecessary, another cubic centimeter of octyl œrcaptan was

injected into the vapor stream atter about twenty hours of operation.

Experimental Runa and Tabulation of Data,

Eighty half' -hour runa were made, but occasionally accidents

occurred, and some of these rune had to be discarded.

Before each run, the barometric pressure was determined, the

water rate was set, and the saturation temperature of the vapor inlet

was adjusted to give the desired steam-air composition. When the system

had reached a steady state, the run was started, and the following data

were recorded every ten minutes:

(1) Air rate

(2) Static pressure at the vapor inlet

( 3) static pressure at the vapor outlet

( 4) OUt let vapor temperature

( 5 ) Cooling water temperature bef' ore the condenser

( 6) Cooling water temperature atter the condenser

(7) Vapor temperatures given by the five thermocouples in the

condenser

( 8) Pipe wall temperatures gi ven by the nine thermocouples in the

pipe wall

( 9) Condensate temperature

( 10) OUtside surface temperature of the insulation on the condenser.

34-

In addition, the condensate was weighed at the conclusion of

each run.

La..l 0 ...::(;

~

" t--;;z: w \J

\Il a...J ...... Dl.

" ....... 0

...... al :::2 t--ce ~ ....... 0-::ii ....... t-

loo

~0

8o

1o

Go

5

4o

0

TOP

35-

L .... V4POit TEMPE~ATUR.E

PIPE WALL TEMPERA TU ~f.

R.UN N°. S'l

4

LENGiH OF CONDENSING SU~fACE.

IN FE ET

Fig.6 - Temperature Profiles in Condenser during a Typical Run.

& bOTTOM

1

36-

RESULTS

Explanation and Presentation of Data.

A few remarks should be made at this point to clarify the

resulta as expressed in Tables I, II, and Figures 7, 8, 9, 10 and

11.

a ; the mol tfo air in the inlet steam, calculated for

each run from accurate temperature and pressure

measurements of the saturated mixture. During the

runs, the"camposition of the inlet vapor varied

slightly from the desired value. It wa.s necessary,

therefore, to average the inlet compositions for each

group of runa. The avera.ged values are shown in

Figures 7 and 8.

G = the mass velocity of the air in pounds per hour per

square foot of a.nnular space in the condenser.

h ::: the ateam-side beat transfer coefficient, calculated

for each run by means of the equation:

where

qw-:::. beat absorbed by the cooling wa.ter (B.T.U./hr.)

A ::: a.rea of condensing slirface (sq.ft.)

Average temperature difference between the va.por and the pipe wall, obta.ined by graphical integration of the temper­ature profiles which were plotted for each run (Fig.6) (OF).

37-

he = The steam-side heat transfer coefficient for film-type

condensation calculated by the empirical equation developed

in this thesis:

he= 5600 G.33 a-1.44

hse ::: the sensible beat transfer coefficient calculated from the

equation:

where

hse = MC (t1 - "t2) A (tg - tw) ave.

M = air rate lb./hr.

C ::: specifie beat of air-steam mixture at average vapor temperature (B.T.U./{°F.)(lb.air)

t 1 :;; inlet vapor temperature °F.

t2 = outlet vapor temperature ~.

The curves shown in Figures 9, 10 and 11 represent values obtained

from the parallel lines in Figures 7 and 8. The resulte of the pure

steam runs and the runs in which mixed film-type and dropwise condensation

occurred are not included in Tables I and II. f.bre complete tables of

the experimental data and the calculated values are given in the appendix.

38-

TABLE I FILM-TYPE CONDENSATION

Run No. a G h he h - (a.ctual) ( emperieal) (sensR1e)

lb. Air/ B.T.U./ bt>1 ~ Air In ~hr. ){,sg..ft.) ~hr.!{sg..tt.!~°F)

20 9.22 13.1 439 554 1.33

21 9.19 17.3 515 539 1.93

22 9.62 11.5 495 482 1.29

23 9.52 15.9 587 543 1.91

24 12.6 8.3 290 293 0.91

25 12.5 12.0 345 336 1.16

26 12.8 16.8 389 364 1.46

27 13.5 21.5 426 360 1.73

28 14.65 12.0 258 266 1.07

29 15.2 17.0 309 284 1.33

30 15.5 18.8 327 287 1.54

31 15.6 25.4 392 311 1.93

32 19.0 15.0 199 199 1.15

33 19.2 20.5 251 215 1.41

34 19.5 24.2 273 223 1.73

35 19.8 28.8 303 231 2.00

36 22.5 12.9 129 147 1.07

37 22.7 18.9 182 165 1.38

38 22.9 26.6 223 183 1.81

39 23.1 31.8 255 190 2.08

40 25.1 12.6 112 124 1.11

39-

TABLE I FILM-TYPE CONDENSATION ( Continued)

Run No. a G h he hse - (actual) ( emperical) (sensible)

lb.Air/ B.T.U./ Mol! Air In (hr. )(sg.ft.) (hr.)~s~.ft.)~°F~

41 25.2 19.0 149 141 1.45

42 25.3 24.0 179 154 1.66

43 25.6 33.9 215 168 2.07

44 27.7 16.4 112 118 1.30

45 27.7 19.9 128 123 1.40

46 27.8 22.6 149 131 1.50

47 28.0 32.3 185 145 1.95

48 30.4 15.2 99.5 100 1.19

49 30.5 17.3 112 lo4 1.29

50 30.6 24.2 143 116 1.55

51 30.7 31.8 169 129 1.97

40-

TABLE II DROPWISE CONDENSATION

Run No. a G h hfe (actÜal) (sens ble)

B. T.U./ Mol 1o Air In 1b.AirL{hr.){sg.ft.) (hr.){sg.tt.~{°F.)

54 4.11 4.6 1095 1.42

55 4.o8 4.6 1020 1.41

56 5-33 6.9 1245 2.19

57 6.44 3.5 620 0.70

58 7.00 6.9 706 1.36

59 10.1 8.1 444 1.03

60 10.6 10.4 452 1.50

61 10.95 15.8 638 2.23

62 7.24 10.4 878 2.34

63 14.5 8.1 256 0.95

64 14.7 13.8 390 1.87

65 15.2 20.8 405 2.18

66 18.0 13.3 162 0.99

67 18.15 16.4 218 1.42

68 18.6 23.7 367 2.20

69 17.2 9.2 188 0.97

70 20.1 9.8 128 0.97

71 20.1 9.2 145 0.92

72 20.1 14.4 193 1.33

73 20.2 19.6 248 1.42

41-

TABLE II DROPWISE CONDENSATION (Continued)

Run No. a G h h - (actual) ( sensi:gÏe)

Mol% Air In lb.Air/(hr.)(sq.ft.) B.T.U./

(hr.)(sq.ft.)(°F.)

74 22.8 12.5 141 1.14

75 23.0 16.4 180 1.28

76 23.1 22.2 213 1.52

77 25.5 12.0 111 1.06

78 25.7 17.3 145 1.36

79 25.9 30.0 201 2.07

1000----------------------------------------------------------------------~

-~ "" w 3 lOO

w 0 ~ 150 • ~ w t-<1') 10

~

5

b.

9·S CIJo ~\~ o

~~0 ~

\0 15 G - A \R \1 EL OC.\ 'T't'

0

zo ts lb.fChr.) (s,. ft.)

Fig.7 - Relation between Gand h obtained in Film-Type Condensation.

•

30 35

+:"' 1\) 1

-a..:

1400

l'lOO

~·000-10 -tt 9oo ~800 .: 100

é '='­? ..-:: c:o

t-z 400 w -0 -..... J.a,. 300 laJ 0 \,)

w ~ lOO ' ~ .c( w ~

~,d'Jo------

----b~ 1::1.----

"!-

... ~ /

~·

• ~~> 1-

'7

b~ ~fl'l ~· .,.. -,o

~ t!l·o ~•/ • ~ . 1"1· / ~ t.S·

/

~ 0.

.t'. lOC ,.,... <il

5 •o tS to 25 30 G AIR \IE.LOC.\\'( lb.j(hr.)t~.ft.)

Fig.8 - Relation between G and h at various Inlet Compositions for Dropwise Condensation.

~ w 1

-u.. ~lOOO ~ *C300

'" ~ :) 800 t-=. Ul

t­%

100

LtJ 600 -() -t soo uJ 0 V .(OO

"' 0 - 300 'f ~ 4 f&o 111 :;;

lOO

.J:

5

b

"'" \ " .

~~~=~o16.4J~Â .

10

MOL

~. n~~~~!-J . . .o .~. ~ .. ---------==-~~~~~ ·--------·-·- . ""'"•- -·-

IS t.O

Ofo A.\ R \ N \ N LE.\

tS

ST~ÂN\

30

'·

35

Fig.9 - Effect of Inlet Steam Composition on Heat Transfer Coefficient in Film-Type Condensation.

+:-­+:--1

7000

6

5000

4000

30GO

tooo

lOO }-% 600 ..... -~ soo ...... w.. ~ 400' u

0:: LaJ 3oo ..... (f)

z < ~ 2

~ ..... :t

100·~--~--~--~--~--~--~--~--~--~--~--~--~--~ 0 2. 4- E> 8 \0 \'l, \4. \E:. \ ~ 20 -e~ ?4 ,,

MOL or. AH\ \N \ NlE "T S 'TE~N\

1700

1500

1460

1300

ltOO

t-700 % Ul o U)O -... ... wSOO 0 0

w400 a .,.,

J 300 ~ 4. ~too .,

lOO .t:

46-

OROPWlSE CONO~t\S~T\ON

l=lLNI-lYPE C Ot\OEN5~T\ON

0 ~----=---------------------------------------~~--~ s 10 15 to -z.s MOl O'fo A.\R lN ENTER\NG ~\EA.M

Fi~.ll - Comparison of Steam-side Coe~~icients ip Dropwise & Film-Type

47-

·66 = O.t06 G~

r·o.___:;.... ______ ~-----~~--~--~~"" IO tS 2.0 30 40 50

G AIR VE\.OC.\T'f \b. /[hr. ){s'\. ft.)

Fig.l2 - Relation between Sensible Beat Transfer Coefficient and Mass Velocity of Air in Film-Type Condensation between 12.5 and 30 Mol i air.

48-

Development of the Eœpirical Equation.

The equation for film-type condensation of steam with air present

was developed by a method shown by Davis (9).

The following is an outline of the standard method of obtaining

a three-variable correlation:

(1) One variable is held constant while the relation between

the other two is found. This is repeated for as many

values of the first variable as possible

( 2) The constants of the two-variable equations obtained in

( 1) are plotted against the :tiret variable, and the

relation between each one of them and the first variable

is found

(3) The relation between the first variable and the constants

are combined w1 th the equations found in ( 1) and the final

equation is obtained.

The method was applied to the resulta for film-type condensation

in the :tollowing way:

(1) The inlet composition 'a' was held constant while a

relation between Gand h was found as shown in Fig.7.

The best relation seemed to be

h = KGX

where x is a constant which is independent of 'a' (Table III).

a

9-5

12.8

15.3

TABLE III

x

.30

.29

.31

\ ê

2.3

2.2 ! f .

Z.l

2.0

1.9

~ L8

§

\.0

; .

\.\

LOG a

\.2

49-

LOG K=- -1. 4.4LOG9-+l147 .. ~ -~ -:;;;:r.4;:a=---t

K= 5600a.

\.3 l.4-

Fig.l3 - Correlation between K and a for Film-Type Condensation.

50-

TABLE III (Cont'd)

a x

19.4 .36

22.8 .36

25.3 .34

27.8 .35

30.5 .36

Average x ::. 0.33

(2) A relation between K and 'a' was found (Table IV).

a

9.5

12.8

15.3

19.4

22.8

25.3

TABIB IV

Log a

0.978

1.107

1.185

1.288

1.358

1.4o8

Example for G =15

r.os K = r.os h - .33 r.os a

2.342

2.192

2.o62

1.912

1.792

1.707

A plot of log •a• against log K gave the relation shown in Fig.l3.

log K = -1.44 log (a)+ 3. 747 or

K = 5600 a-1.44 (7)

( 3) Equation 7 was combined wi th equation 8 to obtain the final

results:

h ::: 56oo a-1.44a.33 (8}

This equation may be applied to film-type condensation over the range:

G = 10 to 25 lbs. Air/(hr. )(sq.ft.)

a =- 10 to 25 mol ~ Air.

51-

DISCUSSION OF EXPERIMENTAL RESULTS

Overall Comparison of Dropwise and Film-type Condensation.

A number of runs with pure steam were made before the experimenta

with steam-air mixtures were tried. The resulte are shown in the

appendix. It was found that the vapor velocity of the pure steam had

an appreciable effect on the steam-side heat transfer coefficient in

the case of film-type condensation, but the effect was almost negligible

with dropwise condensation. Although no quantitative measurements of

the pure-steam velocities were made, the resulte seem to support the

present author' s theory that significant turbulence is caused on the

surface by the erratic mechanism of dropwise condensation, as mentioned

in the theoretical discussion. When air was present, the vapor velocity

exhibited an effect similar to that of film-type condensation, as shown

in Figures 7 and 8. This was probably caused by the presence of a fairly

high concentration of air close to the condensing surface, which would

hinder the rapid condensation of the supersaturated vapor. As the air

concentration in steam increases, its condensation temperature decreases;

therefore, i t is possible that the air, which is drawn toward the surface

with the steam, would attain a sufficient concentration to prevent

supersaturation between the drops.

As the concentration of air in the entering steam was increased,

the steam-side coefficient for dropwise condensation approacbed that of

film-type condensation. When the inlet concentration of the air was

52-

about 2CJI,, the two coefficients became identical as shown in Fig.ll.

Several graphe were drawn similar to Fig.ll for the different mass­

velocities used in the experimental work, and the same trend was

noted.

Thus, probably the most important conclusion to be drawn in this

thesis is tha.t dropwise condensation of steam-air mixtures is desirable

up to about 20 mol percent air. At higher concentrations, dropwise

condensation does not beem to give a higher beat transfer coefficient.

Effect of Air Velooity on 'h'.

The effect of 'G' on 'h' is shown in Fig.7 for film-type condensation

and Fig.8 for dropwise condensation. It was found that on a log-log plot

the resulte could be expressed as a series of parallel lines. The average

slope for the film-type lines was 0.33 while that of the dropwise lines

was 0.34. This indicates tha.t the mass-velocity effect, when air is

present, is almost identical for the two modes of condensation.

Stability of Dropwise Condensation.

Jakob and Hawkins (17) stated that dropwise condensation is unstable,

and is unsuited for pra.ctical design work until this difficulty of

instability can be overcome.

The resulta in this thesis show good uniformity in the dropwise

condensation experimente. Immediately after the surface bad been coated

with the mercaptan, the coefficients vere somewhat erratic, but after a

few hours of operation it was always possible to get reproducible resulta.

53-

Perhaps octyl mercaptan f'orms a more stable :film on the surface than

the lower mercaptans of' the paraff'in series which are sometimes used.

At one point, during the runs, a cubic centimeter of the

mercaptan was injected into the vapor stream, and erra.tic resulta

were obtained for a. :f'ew runs immediately f'olloWing this treatment,

as shown by the 18.~ line in Fig.8. The subsequent resulta were in

accordance With the general trend.

The eff'ect of' the Air Mass-Velocity on the Sensible-Hea.t Transfer

Coe:f':f'icient.

When the calcula.ted values :for the sensible-heat transf'er

coefficient were plotted on a log-log diagram (Fig.l2), it wa.s :f'ound

that a correlation could be obtai~n for the film-type data between 12.5

and 30 mol percent air. The resulta for less than 12.5 percent air showed

no such trends; the data for dropwise condensation disclosed a Wide

scattering on the various plots constructed, and made impossible any

correlation.

The Empirical Eguation.

The empirical equation was developed to attempt to show the general

trend in film-type condensation with air present. Table I illustrates

how the values :from the empirical equation compare wi th the experimental

resulta. The coefficients calculated from the equàtion are usually on

the low side, - the sa:f'e side for design purposes. If this equation

should be used for design, it must be kept in mind that it applies only

54-

over the range stated in the derivation, and perhaps only to the type

of condenser used in the experimental work. Further investigation is

needed in this field if a more general relation is desired.

An attempt was made to derive another equation to predict the

steam-side coefficients of condensing steam during dropwise condensation.

No simple correlation was found and it was decided that the resulte

could best be expressed in graphical form as show in Figures 8, 10 and

11.

Sources of Experimental Error.

( 1) Thermocouple Errors.

Ju, F1itcraft and Ho1eman (20) c1aim that it is impossible to get

accurate pipe-wall temperature readings with inserted thermocouples,

because of the disturbance caused to the flow of heat and the fluid

condensa te on the surface. In the ir paper on film coefficients of

condensing organic vapors they used a modified form of the Wilson Plot

(mentioned in the Historical Survey) to obtain their resulta. The

a.ccuracy of' this method is somewhat questionable (25).

It is the opinion of the present investigator that the best

procedure is still the installation of thermocouples in the pipe-wall.

They can be located with the minimum amount of disturbance of the

condensing surface, and, if necessary, the pipe can be electroplated to

gi ve i t a uniform surface.

•· <

55-

During the experimental work for this the sis, repeated

calibrations of' the pipe-wall thermocouples showed no appreciable

variations. In each run the maximum variation of any pipe-wall

temperature reading f'rom its average was about one degree Centigrade.

Usually the variations were much lesa than this.

(2) Radiation Lasses.

The outside temperature of the insulation on the condenser was

observed for each run and the radiation losses were calculated. On

the average, the beat lost by radiation and convection amounted to

about f'i ve percent of the he at g1 ven up by the vapor. This loss did

not appear in the calculation of the heat-transfer coefficients,

because all the beat trans:ferred through the condensate film was

measured by an increase in the beat-content of the cooling-water.

Fogging in the Condenser.

The presence of fog in the condenser considerably complicates the

overall picture. In normal condensation, the vapor does not condense

until it reaches the eondensate on the eooling surface. This means

that all the latent beat is liberated on the eondensing surface and

only sensible heat is transferred through the gas film covering the

surface. When a mist or fog appears in the condenser, some of the

latent beat as well as the sensible beat is transferred through the

gas film, and the mechanism of the process is changed. In some of the

runa a tendency towards fog formation was evident when the air

concentration approached thirty percent.

56-

Scale Formation.

The resulta shown in this thesis pertain onl.y to the condensing

film on the outside of the tube, and are, therefore, independent of

any ecale which may have formed on the inside of the tube. During the

film-type runs, the condensing surface was kept clean by washing 1 t

occasionally wi th the detergent 'Surf' • During the dropwise runs, the

surface was not cleaned for fear of disturbing the promoter layer. No

visible changes in the surface were. noted while the dropwise runs were

being made.

A

a

c

c

e

G

g

K

k

p

Ts,Tw

u

v

z

57-

LIST OF SYMBOLS

Area of heat-transfer surface, square feet.

Mol percent air in entrance steam.

Weight percent air in entrance steam.

Specifie heat of steam-air mixture B.T.U./(°F.){lb.Air).

Base of Napierian or natural logari tbms.

Mass-velocity of the air in the condenser lb./{hr.)(sq.foot annular space).

Acceleration due to gravity, 4.17 x 108 ft./(hr.){hr.).

Mean coefficient of heat transfer, from vapor to pipe wall B.T.U./(hr.)(sq.ft.){°F.)

Mean coefficient of sensible heat transfer from vapor to pipe wall. B.T.U./(hr.}(sq.ft.)(~.}

Constant used in the derivation of the empirical equation.

Specifie thermal conductivity B.T.U./(hr.)(sq.f't.)(°F. per foot)

The Bol tzman gas constant.

Air velocity lb./hr.

Pressure of the vapor in consistent unite.

Temperature of the vapor 0 c. or °F.

Temperature of the vapor-liquid interface 0 c. or ~.

Temperature of the surface or pipe wall.

Rate of condensation by Kinetic Theory, gm. per sq.cm. sec.

Rate of evaporation by Kinetic Theory, gm. per sq.cm. sec.

Spreading coefficient, dynes/cm.

At

58-

Interracial tension, dynes/cm.

3.1414

Constant-depending on amount of air present.

Mass rate of flow of condensate from lowest point on the condensing surface, divided by the breadth, lb./(hr.)(ft.)

Temperature difference, degrees Fahrenheit - for condensing vaporà 1\t is tg - ty.

Heat of evaporation or latent heat of condensation.

Absolute viscosity of condensate film,lb./(hr.)(ft.).

59-

REFERENCES

1. Adam N.K. Phys. and Chem. of Surfaces, Clarendon Press (1930)

2. Baker E.M., E.W .Kazmark & G.W. Stroebe, Trans.Am. Inst.Chem. Engrs. 35, 127 {1939)

3. Baker E.M., E.W.Kazmark & G.W.Stroebe, Ind.Eng.Chem.31, 214-8 {1939)

4. Calendar H.L. & J.T. Nicol.son, Engineering 64, 481. (1897)

5. Charles G.E. Heat and Maas Transfer in Debumidification, M.Eng. Tbesis McG111 - 1951.

6. Cbilton T.H. and A.P. Co1burn, Ind. Eng.Cbem. 26 1183-7 (1934)

7. Colburn A. P. and O.A. Hougen, Studies in Heat Transmission, Bulletin of the University of Wisconsin #70 (1930)

8. Co1burn A. P. and O.A. Hougen, Ind.Eng.Chem., 26, ll78 (1934)

9. Davis D.s. Empirical Equations and Nomography, McGraw-Hill, (1943)

10. Dodge B.F. Ind.Eng.Chem., 14, lo62, (1922)

11. Drew T.B., W.M.Nagle, and W.Q.Smith, Trans.Am.Inst.Cbem.Engrs. 31 605 (1935)

12. Emm.ons H. Trans.Am.Inst.Cbem.Engrs., 35, 109 (1939)

13. Fitzpatrick J.P., S. Ba.um, a:nd W.H. McAd.ams, Trans.Am. Inst.Cbem. Engrs. 35, 97, (1939)

14. Gina.bat, Warme 47, 573, 588 (1924)

15. Hebbard G.M. & W.L. Badger Trane.Am.Inst.Cbem.Engrs. 30 194 (1933)

16. Hoeffner - Z. Ver. Deut. Ing. 63 629, 650 ( 1919)

17. Jacob M. and Hawkins G.A. Elements of Heat Transfer and Insu1ation -John Wi;Ley and Sons - New York ( 1942)

18. Josse Z. Ver.Deut.Ind. ll 322 (1909)

19. Joule Trans.Royal Society 151, 133 {London 1896)

60-

20. Ju Chin Chu, R.K.Flitcraft and M.R.Holeman, Ind.Eng.Chem. 41, 1789 (1949)

21. Kennett F.W. The Determination of Film Coefficients for Condensing Vapors. M.Eng.Thesis MCGill - (1948)

22. Kelvin Phil.Mag. .2_, 24 {London 1889)

23. Kerr E.W. Trans.Am.Soc.Mech.Engrs. 38, 67 (1916)

24. Kirkbride C.G. Trans.Am.Inst.Chem.Engrs. 30, 179 {1933)

25. McMams W.H. Heat Transmission, 275 McGraw-Hill (1942)

26. MCCormick H. Trans.Am.Inst.Chem.Engrs. 30, 215 (1933)

27. Meisenburg S.J., R.M. Boarts and W.L. Badger, Trans.Am.Inst. Chem.Engrs. _ll; 622 {1935)

28. Monrad c.e. and w.L. Badger, Ind.Eng.Chem. 27, 1103 (1930)

29. Nag1e W.M. and Drew T.B. Trans.Am.Inst.Chem.Engrs. 30, 217 (1933)

30. Nagle W.M., G.S. Baya Jr., L.M.Blenderma.n, and T.B.Drew, Trans. Am.Inst.Chem.Engrs. 31, 593 (1935}

31. Nusselt z. Ver.Deut.Ing. 60, 541 (1916)

32. Orrok G.A. Trans.Am..Soc.Mech.Engrs. 34, 713 (1912)

33. Orrok G.A. Trans.Am.Soc.Mech.Engrs. 38, 67 (1916}

34. othmer D.F., Ind.Ens.Chem. 2J., 576 (J.929)

35. Reynolds 0. , Proc. Royal Society (London 1873) Vol. 21 p. 275

36. Reynolds o., Scientific Papers of Osborne Reynolds Vol. II Cambridge, London ( 1901)

37. Robinson c.s., Ind.Eng. Chem. 12, 644, 1920

38. Rupricht S. Refrig. Eng. 26, 19 {1933}

39. Schmidt E., W.Schurig, and W.Sellschopp, Tech. Mech.Thermodynam., .!_, 53 {1930)

61-

40. Shea. F.L., a.nd. N.W. Kra.se, Tra.ns.Am.Inst.Chem.Engrs. 36, 463 (194o)

41. Smith J.C., Ind.Eng.Chem. 34, 1248, (1942)

42.

43.

Spoe1stra H.J. Arch.Suikerind in Nedev-Indes, Part III No.23 905 (1931)

Stroebe G.W., E.M.Bak.er, a.nd. W.L.Ba.dger Ind.Eng.Chem. 31, 200 (1939) --

44. Wilson E.E. Tra.ns.Am.Soc .Mech.Engrs. 37, 47, (1915)

62-

APPENDIX

~_!. Q!&9.lJl!A!IQ.N'_Ql.11.:0lQ!J..~ C011]:.;;::.'F;;:::.;IC=-=I=ENT:.:::.S

b. T ° F. Vater Rate tw1-t w2 B.T.U.s per OF

Ryn N:o. 1b/hr~ ~~ hour __ to water h Remarks

1 33.7 1524 46.1 70,.300 961 Film-type

2 32.4 1524 46.1 70,.300 1000 a a

3 28.8 1524 58 • .3 ss,soo 952 tf • 5 3.3.6 1524 52.2 79,600 1090 n n

7 30.2 1248 57.6 71,900 1098 tt n

8 23.4 1248 65.1+ 81,500 1605 u n

52 5.94 1524 60.8 92,700 7190 Dropwise Law Velocity

53 6.55 1524 61.4 9.3,500 6580 Dropwise High Velocity

TABLE VI

Vap.tem.p.in Vap.tem.p.out ~ Te>r pipe wall G Air B.T,U.s/hr. h Rux.!_ No, °C _ mol ~ Air in °C to va_ppr _ 1b/(h~..{§_q_._ft.) to_ ~t.~:r. __ B. ~_T,[d!_h_rllig_,J:tillo.El

9

ll

12

1.3

14

15

16

20

2],

22

23

98.8 5.56 94.0 46.2 7.93..;. 79,500

98.7 6.57 96.7 38.2 ll.4 )f; 86,.300

98.7 5.37 96.2 40.7 10.8 "" 59,400

98.4 5-47 96.0 36.7 9.1+5 * 56,000

98.7 4.94 96.8 .35.4 10.4 ~ 51,100

98.7 5.94 97 • .3 34.6 9.22 '* 53,500

97.6 7.87 83.6 64.4 7.5 ~ 54,700

97.3 9.22 9.3.6 46.1 1,3.1 39,500

97.2 9.79 93.8 41.8 17.3 4.3,900

97 • .3 9.62 9.3.S 42.8 ll.5 46,700

97.4 9.52 94.6 40.5 15.9 46,100

Mixed dropwise and film-type condensation took place in Runa 10, 17, lB, 19.

1r G calcula.ted from vapor pressure measurements - not reliable.

795

945

716

635

642

f::FJ6

729

283

4.39

515

495

TABLE __ VI (Continued)

Vap.tem.p.in Vap.temp.out AT~ pipe wall G Air B.T.U.s/hr. h RunNo. °C mol% Air_in °C to vaBor ·1b/(hr) ( sg .f't.) to water

24 96.1 12.6 S7.6 W.7 8.,3 .38,100 290

25 96.2 12.5 91 • .3 56.0 12.0 41,800 345

26 96.2 12.8 92.0 50.7 16.S 42,800 389

Z7 96.1 13.5 92 •. 4. 49 • .3 21.5 45,600 426

28 95.2 14.65 87.4 62.,3 12.0 .34,800 258

29 95.1 15.2 89.6 56.3 17.0 37,800 309

30 95.1 15.5 89.5 54.2 l.S.S 38,400 3Z7

31 95.2 15.6 91 • .3 48.0 25.4 40,800 392

32 94.1 19.0 85.4 6S.8 15.0 29,700 199

3.3 94.1 19.2 88.7 (:J).6 20.5 33,000 251

34 94.1 19.5 88.5 57.0 24.2 3.3,700 Z73

35 94.1 19.8 89.2 53.3 28.8 35,100 303

36 93.1 22.5 78.3 83.5 12.9 23,400 129

37 93.1 22.7 83.8 71.8 18.9 28,300 182

38 93.1 22.9 86.4 61.9 26.6 29,900 223

TABLE VI (Continued)

Vap.temp.in Vap.tem.p.out àT <? pipe wall G Air B.T.U .. s/hr. h Ryn_NQ,• °C mol 2! .Air in oc to WJ.P.Q.r 1b/(hr}(sg.f~;"•l to water B.T.U./(hr)(sg.ft.H";F1

39 93.1 23.1 87.1 59.6 31.8 33,000 255

JJJ 92.0 25.1 73.3 85.0 12.6 20,600 112

41 92.0 25.2 79.6 76.5 19.0 24,700 149

42 92.0 25.3 83.0 70.7 24.8 27,400 179

43 92.0 25.6 84.8 66.2 33.9 30,800 215

JJ. 91.0 27.7 74.9 81.7 16.4 19,750 112

45 91.0 27.7 78.0 80.1 19.9 22,200 128

46 91.0 27.S 80.5 74.4 22.6 24,100 149

47 91.0 28.0 82.6 70.2 32.3 28,100 185

48 89.9 30.4 72.0 83.9 15.2 18,100 99.5

49 89.9 30.5 74.2 81.5 17.3 19,750 112

50 89.9 30.6 78.9 74.2 24.2 23,000 143

51 89.9 30.7 80.7 68.1 31.8 25,000 169

TABLE_ .ii! STEAM-SIDE (h)' s FOR DRDPWISE C,ONDENSATI,ON 0}!' STE.AM, AIR MIX:l'URES

Vap.temp.in Vap.temp.out 6T OF pipe wall Run No. °C mol % Air in °C :!i.9 vruw::

B.T.U.sjhr. h to water B.T.U./(hr)(sg.ft.)(Of)

54 99 • .3 4.11 c:n.l 2.3.4 4.6 55,600 1095

55 99.1 4.08 96.:3 24.1 4.6 5:3,200 1020

5.6 99.1 5-.33 c:n.o 20.7 6.9 55,900 1245

57 98.:3 6.44 94.3 32.9 3.5 44,200 620

58 98.2 7.00 94.7 .31.0 6.9 47,500 706

59 c:n.2 10.1 91.8 40.2 8.1 :38,400 444

60 97.1 10.6 92.4 .39.2 10.4 :38,400 452

61 97.2 10.95 94.0 .31.5 15.8 4.3,600 638

62 98.:3 7.24 95.4 25.4 10.4 48,400 878

6.3 96.1 1.4.5 87 • .3 56.9 8.1 31,600 256

64 96.1 1.4.7 90.0 40.5 13.8 :34,:300 390

65 96.1 15.2 91.6 4:3.0 20.8 :37,800 405

66 94.6 18.0 85.8 77.:3 13.:3 27,100 162

~-VII (Continued)

Vap.tem.p.in Run Jf.o_~ - --~C_

Vap. temp.•:mt mo_],_.%_ Ai:r_ in_ °C

~ T OF pipe wall G Air B.T.U.s/hr. h to_ .!liJ?..Or~ lbLÛl_rlli~f_t_.j_ ___io __ wat_E;l_:r.__ B. 'J,'_.JI..} l_h_rllsq. rt. )~

67 94.6 18.15 'i!r/.6 52.2 16.4 24,700 218

68 94.6 18.6 89.6 42.7 23.7 34,000 367

69 94.6 17.2 83.5 61.7 9.2 25,200 188

70 93.6 20.1 80.4 68.0 9.S 18,900 128

71 93.6 20.1 79.9 68.8 9.2 21,600 :145

72 93.6 20.1 84.1 59.6 14-4 25,000 193

73 93.6 20.2 88.0 53.5 19.6 28,800 248

74 92.6 22.8 79.8 67.3 12.5 20,600 1..4J.

75 92.6 23.0 83.0 60.5 16.1+ 23,600 180

76 92.6 23.1 85.4 57.1 22.2 26,400 213

77 91.6 25.5 76.0 74.1 12.0 17,800 111

78 91.6 25.7 81.0 65.3 17.3 20,600 145

79 91.6 25.9 84.2 57.8 30.0 25,200 201

TABLE VIII

CALCULATION OF SENSIBLE HEAT TRANSFER COEFFICIENTS h8e

FOR FILM-TYPE CONDENSATION

M - Air Rate tl - t2 Tave save MS(t1-t2)

lbs./br. Vapor 0 c 0 hse:

A(ts-tw>ave Run No. Vapor C Humid Heat

20 11.4 3.7 95.2 1.75 1.33

21 15.0 3.4 95.5 1.90 1.93

22 10.0 3.5 95.5 1.90 1.29

23 13.8 2.8 96.0 2.10 1.91

24 7.2 8.5 91.9 1.08 0.91

25 11.4 4.9 93.8 1.40 1.16

26 14.6 4.2 94.1 1.45 1.46

27 18.6 3.7 94.3 1.50 1. 73

28 10.4 7.8 91.1 0.99 1.07

29 14.7 5.5 92.4 1.11 1.33

30 16.3 5.6 92.3 1.10 1.54

31 22. 3.9 93.3 1.30 1.93

32 13 8.7 89.4 0.85 1.15

33 17.8 5.4 91.7 1.07 1.41

34 21 5.6 91.3 1.01 1.73

35 25 4.9 91.1 1.055 2.00

TABLE VIII (Continued)

CALCULATION OF SENSIBLE BEAT TRANSFER COEFFICIENTS h8e

FOR FILM-TYPE CONDENSATION

M - Air Rate tl - t2 Tave Save MS(t1-t2)

lbs./hr. Vapor °C Vapor 0 c hse=

A(tg-tw)ave Run No. Humid Heat

36 11.2 14.8 85.7 0.65 1.07

37 16.4 9-3 88.5 0.785 1.38

38 23 6.7 89.8 0.875 1.81

39 27.6 6.0 90.1 0.90 2.08

40 10.9 18.7 82.7 0.555 l.ll

41 16.5 12.4 85.8 0.655 1.45

42 21.5 9.0 87.5 0.730 1.66

43 29.4 7.2 88.4 o. 78o 2.07

44 14.2 16.1 83.0 0.560 1.30

45 17.2 13.0 84.5 0.605 1.40

46 19.6 10.5 85.8 .655 1.50

47 28.0 8.4 86.8 .698 1.95

48 13.2 17.9 81.0 .510 1.19

49 15.0 15.7 82.0 .535 1.29

50 21.0 11.0 84.4 .600 1.55

"51 27.6 9.2 85.3 .635 1.97

TABU: IX

CALCULATION OF SENSIBlE HEAT TRANSFER COEFFICIENTS b8e

FOR DROPWISE CONDENSATION

M - Air Rate tl - t2 Tave 6ave MS(t1-t2)

Vapor 0 c Vapor °C hsea

Run No. 1b./br. Humid Heat A(tg-twJave

54 4.0 2.2 98.2 4.55 1.42

55 4.0 2.8 97.7 3.65 1.41

56 6.0 2.1 98.1 4.35 2.19

57 3.0 4.0 96.3 2.30 0.70

58 6.0 3.5 96.5 2.42 1.36

59 7.0 5.4 93.5 1.32 1.03

60 9.0 4.7 94.8 1.68 1.50

61 13.7 3.2 95.6 1.93 2.33

62 9.0 2.9 96.9 2.75 2.34

63 7.0 8.8 91.7 l.o6 0.95

64 12.0 6.1 93.1 1.25 1.87

65 18.0 4.5 93.9 1.40 2.18

66 11.5 8.8 90.2 0.91 0.99

TABLE IX (Continued)

CALCULATION OF SENSIBLE BEAT TRANSFER COEFFICIENTS h8e

FOR DROPWISE CONDENSATION

M- Air Rate tl - t2 Tave save MS(t1-t2)

lb./hr. 0 Vapor °C hse=

A(tg-tw>ave Run No. Vapor C Humid Beat

67 14.2 7.0 90.1 0.90 1.42

68 20.5 5.0 92.1 1.10 2.20

69 8.0 11.1 89.0 0.816 0.97

70 8.5 13.2 87.0 0.707 0.97

71 8.0 13.7 86.7 0.693 0.92

72 12.5 9.5 88.8 0.805 1.33

73 17.0 5.6 90.8 0.96o 1.42

74 10.8 12.8 86.2 0.670 1.14

75 14.2 9.0 87.5 0.730 1.28

76 19.2 7.2 88.0 0.755 1.52

77 10.4 15.6 83.8 0.585 l.o6

78 15.0 10.6 86.3 0.675 1.36

79 26.0 7.4 87.9 0.750 2.07