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 selt 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
36
RESULTS
Explanation and Presentation of Data
36
Development of the Empirical Equation
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.
was collected and measured in a reservoir,
The condensate
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 oxidation
11
•
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
and air inside a flask.
1
U1 tube exposed to an atmosphere of steam
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 "heat transfer coefficient" for this case, and d.efined
the coefficient as the quantity 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;
be able to estimate the wall temperature.
in this way they hoped to
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 velocity.
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.
r~sistance
determined.
The wall
can easily be. calculated and bence the vapor film resistance
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.
o~
the derivation of the Nusselt equation
Monrad. and Bad.ger (28) give a good summa.ry
~or
vertical tubes.
The effect of air in ste am vas studied by Orrok ( 32) who
the overall
coef~icient o~
volume percentage of steam.
steam-to-water varied as the square
~ound
o~
that
the
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
data
o~
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 approximate
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 condensate, 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 vapors 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.
presence of' oil in the steam.
This again was probably caused by the
Af'ter more caref'ul experimentation (30)
(11), the ef'f'ect of' surf'ace-active 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 Fitzpatrick, 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'
Emmons (12).
pr~ter
action by
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:
The transfer of heat with no appreciable displacement
Conduction:
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
dq
=
(1)
-kd.A dt
ds
where
dq "' instantaneous rate of heat trans:fer,
dA= differentia! area, in sq.ft. through
is flowing
- dt
dx = temperature gradient at rigbt angles
he at, ( °F. per foot )
k .. Specifie thermal cotxluctivity of the
B.t. u. per hr.
which the beat
to the flow of
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 )
h
= beat
(2)
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
( 7)
The
may
be neglected
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~
s
s l L p L\t]
Tr5
steam.
(...LÇ \0·11
)
(4)
is a factor which depends on the amount of air present in the
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-velocity 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.
= mol
They are:
( 1)
a
(2)
G : : maas velocity of the air through the condenser
(3)
h
:o
percent air present in the ente ring ste am
the vapor-side heat transfer coefficient.
It was found that
h
al.eo
=
F(a,G)
(5)
(6)
where x is a constant and
K
= F(a)
{7)
= Gx
(8)
the re fore
h
F(a)
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'.
and
cq,
Let
~
be the heat transferred through areas •a• and 'b' respectively.
The total beat transferred through areas a and b will be
KAA.t
+
=KA At
[
b
~+ ~]
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
~
1.2
[ î + ~]
KAAt
The at!J:)unt of heat transferred through the seme area and seme amount
of condensate is almost twice as much in the second case.
17-
In d.ropwise condensation, the nature of the condensate 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
Emm.ons (12), in 1939, presented a paper dealing with
condensing surface.
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 condensate 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) V8 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 greater than "-• and consequently v 8 will be greater 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 themselves, 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.
experimental observations.
This theory was borne out by
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 -
G81
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
= o1 g 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 alter 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 condensate.
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.
successful on copper.
This is the reason why the mercaptans a.re so
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 condensate
was collected in tared bucket s and weighed.
27-
T
--
WATER
WATER OUT
1
lN
0
'
CONSTANT
HEAD TANK
'-..,J
T
.
AIR
0
SA:TUR.Ait011
-----
~1
M
......._,t
.~~~~
,;._.,....
1
.,.
CONDENSER 1
1
COOLlNG
W
~TER --tJ1o
f
EXPER\MENTAL
CONDENSER
1
1
1
1
T
......
5TEAM
_
T
..
E )\CESS VAPOR
M
0
T
Fig.4 -
MA.NOMETER
OR\F\CE
1
M
~
[ CONOENSAïE
.....-•----, B ALÂ NC E
T
THERMONIE.TE R
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.
29-
f.X T2A. HE.A.VV coPPtR. PIPE
- - - - - Wllt.E.
c~&LE.
MIL.LED Glt.OOVE
JUNCiiON.
--SOLDE~
bR.ASS FoU..
~~
IWSUL.~TE.O
CONS T~li T~H
WIR.t
JUNCTIOtot
A-
E.N LA~GE.D VIF.W
OF VER-TICAL ûROOVE.
À
Foll.
WIRE..
Fig.5 -
C~f,LE.
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 lowmelting-solder.
When this had been done on bath sides, the tube was
carefully polished vith steel vool.
found to be operating properly.
Each couple vas tested and all were
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 fiberglass
insulation on the wires when the solder is applied
(4)
The brass helix gives the cable good physical contact with
the bottom of the groove and prevents 1t 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 sometimes 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.
Although 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.
35-
L ..
loo
1
V4POit TEMPE~ATUR.E
La..l
0
...::(;
~0
~
"
t-
-;;z:
w
\J
\Il
a...J
......
Dl.
PIPE WALL
8o
TEMPERATU ~f.
1o
"
.......
0
Go
......
al
:::2
t-
-ce
~
.......
5
0-
::ii
.......
t-
R.UN N°. S'l
4o
4
0
TOP
bOTTOM
LENGiH OF
CONDENSING
SU~fACE.
IN FE ET
Fig.6 -
&
Temperature Profiles in Condenser during a Typical Run.
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:
hse
= MC
(t1 - "t2)
A (tg - tw) ave.
where
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
Run
No.
bt>1
FILM-TYPE
CONDENSATION
-a
G
~
Air In
lb.
~hr.
h
he
h
(a.ctual) (emperieal) (sensR1e)
Air/
B.T.U./
~hr.!{sg..tt.!~°F)
){,sg..ft.)
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
Run No.
FILM-TYPE
-a
Mol! Air In
CONDENSATION
G
( Continued)
h
(actual)
he
( emperical)
hse
(sensible)
B.T.U./
lb.Air/
(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
a
Run No.
CONDENSATION
G
h
(actÜal)
(senshfeble)
B. T.U./
Mol 1o Air In
(hr.){sg.tt.~{°F.)
1b.AirL{hr.){sg.ft.)
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
70
20.1
9.8
71
20.1
72
73
188
0.97
128
0.97
9.2
145
0.92
20.1
14.4
193
1.33
20.2
19.6
248
1.42
41-
TABLE II
Run No.
DROPWISE
-a
CONDENSATION
(Continued)
G
h
h
(actual)
( sensi:gÏe)
B.T.U./
(hr.)(sq.ft.)(°F.)
Mol% Air In
lb.Air/(hr.)(sq.ft.)
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----------------------------------------------------------------------~
0
9·S CIJo
~\~ o
•
-
b.
~
3"" lOO
w
w
0
~ 150
•
~
w
t-
<1')
~~0
10
~
~
5
\0
G Fig.7
-
A \R
15
\1 EL OC.\ 'T't'
+:"'
1\)
1
zo
ts
lb.fChr.) (s,. ft.)
Relation between Gand h obtained in Film-Type Condensation.
30
35
1400
-a..:
l'lOO
-tt
~·000-10
9oo
~800
1::1.----
~,d'Jo------
----b~
.: 100
é
'='?
..-::
c:o
t-
•
~~>
'7
z 400
--
w
0
.....
J.a,.
300
laJ
1-
b~
.,.. ~fl'l
-,o
~·
~ t!l·o
0
\,)
w
~ lOO
'
~
"!-
.c(
...~
w
~·
~
.t'.
/
lOC
,.,...
•o
5
G
Fig.8 -
AIR \IE.LOC.\\'(
~
0.
~•/ • ~ . 1"1·
/
~
t.S·
/
~
w
1
<il
tS
to
25
lb.j(hr.)t~.ft.)
Relation between G and h at various Inlet Compositions for Dropwise Condensation.
30
-
u..
~lOOO
~
*C300
'"
~
:) 800
t-=.
Ul
b
100
t-
%
-- 600
LtJ
()
tuJ
"
"'"
~~~=~o16.4J~Â
~. n~~~~!-J
soo
0
V .(OO
"'- 300
0
'f
~
4
111
.
\
'·
.
.~. ~ . ---------==-~~~~~
f&o
·--------·-·-
:;;
lOO
.J:
.
.
""'"•-
. .o
-·-
+:-+:-1
5
MOL
Fig.9 -
IS
10
Ofo
A.\ R
\N
t.O
\ N LE.\
tS
30
35
ST~ÂN\
Effect of Inlet Steam Composition on Heat Transfer Coefficient in Film-Type Condensation.
7000
6
5000
4000
30GO
tooo
}-
lOO
% 600
-
.....
~ soo
......
w..
~
u
400'
0::
LaJ 3oo
.....
(f)
z
<
~
2
~
:t
.....
100·~--~--~--~--~--~--~--~--~--~--~--~--~--~
,,
?4
-e~
20
\~
\E:.
\4.
\'l,
\0
8
E>
42.
0
MOL
or.
AH\
\N \ NlE "T
S 'TE~N\
46-
1700
1500
1460
1300
ltOO
OROPWlSE
t-700
CONO~t\S~T\ON
%
Ul
-....o..
U)O
wSOO
0
l=lLNI-lYPE
0
C Ot\OEN5~T\ON
w400
.,.,a
J
~
300
4.
~too
.,
.t:
lOO
0
~----=---------------------------------------~~--~
s
10
15
to
-z.s
MOl
Fi~.ll
-
O'fo A.\R lN ENTER\NG
Comparison of Steam-side
~\EA.M
Coe~~icients
ip Dropwise & Film-Type
47-
·66
= O.t06 G~
r·o.___:;....______~-----~~--~--~~""
IO
tS
G
AIR VE\.OC.\T'f
2.0
30
40
50
\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 w1th 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).
TABLE III
a
x
9-5
.30
12.8
.29
15.3
.31
49-
\
ê
2.3
2.2
;
.
LOG K=- -1. 4.4LOG9-+l147
!
f .
..
~ -~
-:;;;:r.4;:a=---t
K= 5600a.
Z.l
2.0
1.9
~
L8
§
\.0
\.\
\.2
\.3
l.4-
LOG a
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).
TABIB IV
Example for G =15
r.os
= r.os h
a
Log a
9.5
0.978
2.342
12.8
1.107
2.192
15.3
1.185
2.o62
19.4
1.288
1.912
22.8
1.358
1.792
25.3
1.4o8
1.707
K
- .33
r.os
a
A plot of log •a• against log K gave the relation shown in Fig.l3.
log K
or
K
( 3)
=
-1.44 log (a)+ 3. 747
= 5600
a-1.44
(7)
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
a =- 10 to 25
lbs. Air/(hr. )(sq.ft.)
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.
appendix.
The resulte are shown in the
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 massvelocities 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
and 30 mol percent air.
no such trends;
obtai~n
for the film-type data between 12.5
The resulta for less than 12.5 percent air showed
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
condensate 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 g1ven 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 1t
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.
57-
LIST OF SYMBOLS
A
Area of heat-transfer surface, square feet.
a
Mol percent air in entrance steam.
c
Weight percent air in entrance steam.
c
Specifie heat of steam-air mixture B.T.U./(°F.){lb.Air).
e
Base of Napierian or natural logari tbms.
G
Mass-velocity of the air in the condenser lb./{hr.)(sq.foot
annular space).
g
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.)(~.}
K
Constant used in the derivation of the empirical equation.
k
Specifie thermal conductivity B.T.U./(hr.)(sq.f't.)(°F. per foot)
The Boltzman gas constant.
Air velocity lb./hr.
p
Pressure of the vapor in consistent unite.
Temperature of the vapor 0 c. or °F.
Temperature of the vapor-liquid interface
0
c.
or ~.
Ts,Tw
Temperature of the surface or pipe wall.
u
Rate of condensation by Kinetic Theory, gm. per sq.cm. sec.
v
Rate of evaporation by Kinetic Theory, gm. per sq.cm. sec.
z
Spreading coefficient, dynes/cm.
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.)
At
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,
Engrs. 35, 127 {1939)
3.
Baker E.M., E.W.Kazmark & G.W.Stroebe,
{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,
10.
Dodge B.F.
Ind.Eng.Chem., 14,
11.
Drew T.B., W.M.Nagle, and W.Q.Smith,
Trans.Am.Inst.Cbem.Engrs. 31 605 (1935)
12.
Emm.ons H.
13.
Fitzpatrick J.P., S. Ba.um, a:nd W.H. McAd.ams,
Engrs. 35, 97, (1939)
14.
Gina.bat, Warme
15.
Hebbard G.M. & W.L. Badger Trane.Am.Inst.Cbem.Engrs. 30 194 (1933)
16.
Hoeffner - Z. Ver. Deut. Ing. 63
17.
Jacob M. and Hawkins G.A. Elements of Heat Transfer and Insu1ation John Wi;Ley and Sons - New York ( 1942)
18.
Josse Z.
19.
Joule
lo62,
Trans.Am.Inst.Cbem.Engrs.,
47,
573, 588
Ver.Deut.Ind.
ll
Trans.Am. Inst.Chem.
Ind.Eng.Chem.31,
214-8
(1943)
(1922)
35,
109
(1939)
Trans.Am. Inst.Cbem.
(1924)
629, 650
( 1919)
322 (1909)
Trans.Royal Society 151,
133
{London 1896)
60-
20.
Ju Chin Chu, R.K.Flitcraft and M.R.Holeman,
41, 1789
(1949)
21.
Kennett F.W. The Determination of Film Coefficients for
Condensing Vapors. M.Eng.Thesis MCGill - (1948)
22.
Kelvin Phil.Mag.
23.
Kerr E.W.
24.
Kirkbride C.G.
25.
McMams W.H.
Heat Transmission, 275 McGraw-Hill (1942)
26.
MCCormick H.
Trans.Am.Inst.Chem.Engrs. 30,
27.
Meisenburg S.J., R.M. Boarts and W.L. Badger,
Chem.Engrs. _ll; 622 {1935)
28.
Monrad
29.
Nag1e W.M. and Drew T.B.
30.
Nagle W.M., G.S. Baya Jr., L.M.Blenderma.n, and T.B.Drew,
Am.Inst.Chem.Engrs. 31, 593 (1935}
31.
Nusselt
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.
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
38.
Rupricht S.
39.
Schmidt E., W.Schurig, and W.Sellschopp, Tech. Mech.Thermodynam.,
.!_, 53 {1930)
.2_,
24
{London 1889)
Trans.Am.Soc.Mech.Engrs. 38,
c.e.
z.
Ind.Eng.Chem.
67
Trans.Am.Inst.Chem.Engrs.
(1916)
30,
215
and w.L. Badger, Ind.Eng.Chem. 27,
Ver.Deut.Ing.
c.s.,
{1933)
(1933)
Trans.Am.Inst.
1103
Trans.Am.Inst.Chem.Engrs.
60, 541
2J.,
Ind.Eng. Chem.
Refrig. Eng.
179
26,
19
30,
217 (1933)
Trans.
(1916)
576
12,
(1930)
(J.929)
644,
1920
{1933}
61-
40.
Shea. F.L., a.nd. N.W. Kra.se, Tra.ns.Am.Inst.Chem.Engrs.
41.
Smith J.C.,
42.
Spoe1stra H.J.
(1931)
43.
Stroebe G.W., E.M.Bak.er, a.nd. W.L.Ba.dger
(1939)
44.
Wilson E.E.
Ind.Eng.Chem.
34,
36,
463
(194o)
1248, (1942)
Arch.Suikerind in Nedev-Indes, Part III No.23 905
Tra.ns.Am.Soc .Mech.Engrs.
Ind.Eng.Chem.
37,
47,
(1915)
31,
--
200
62-
APPENDIX
Q!&9.lJl!A!IQ.N'_Ql.1 .:0lQ!J..~ C011]:.;;::.'F;;:::.;IC=-=I=ENT:.:::.S
1
~_!.
b. T
° F.
N:o.
Ryn
Vater Rate
tw1-t w2
OF
1b/hr~
~~
B.T.U.s per
hour__to water
h
Remarks
1
33.7
1524
46.1
70,.300
961
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
Film-type
TABLE VI
Rux.!_ No,
Vap.tem.p.in
°C _
mol
~
Air in
Vap.tem.p.out
°C
~
Te>r pipe wall
to va_ppr _
G Air
1b/(h~..{§_q_._ft.)
7.93..;.
9
98.8
5.56
94.0
46.2
ll
98.7
6.57
96.7
38.2
ll.4
12
98.7
5.37
96.2
1.3
98.4
5-47
14
98.7
15
B.T,U.s/hr.
h
to_ ~t.~:r. __ B. ~_T,[d!_h_rllig_,J:tillo.El
79,500
795
)f;
86,.300
945
40.7
10.8 ""
59,400
716
96.0
36.7
9.1+5
*
56,000
635
4.94
96.8
.35.4
~
51,100
642
98.7
5.94
97 •.3
34.6
9.22
'*
53,500
f::FJ6
16
97.6
7.87
83.6
64.4
7.5
~
54,700
729
20
97.3
9.22
9.3.6
46.1
1,3.1
39,500
283
2],
97.2
9.79
93.8
41.8
17.3
4.3,900
4.39
22
97 •.3
9.62
9.3.S
42.8
ll.5
46,700
515
23
97.4
9.52
94.6
40.5
15.9
46,100
495
Mixed
1r G
dropwise
and
film-type condensation took place in
10.4
Runa
10, 17, lB, 19.
calcula.ted from vapor pressure measurements - not reliable.
TABLE __VI (Continued)
RunNo.
Vap.tem.p.in
Vap.temp.out
°C
mol% Air_in
°C
AT~
pipe wall
to vaBor
G Air
·1b/(hr) (sg .f't.)
B.T.U.s/hr.
to water
h
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)
Ryn_NQ,•
Vap.temp.in
°C
mol
2!
.Air in
Vap.tem.p.out àT <? pipe wall
oc
to WJ.P.Q.r
G Air
B.T.U.. s/hr.
to water
1b/(hr}(sg.f~;"•l
h
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
mol % Air in
°C
B.T.U.sjhr.
h
to water B.T.U./(hr)(sg.ft.)(Of)
6T OF pipe wall
:!i.9 vruw::
Run No.
°C
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)
Run
Jf.o_~
Vap.tem.p.in
Vap. temp.•:mt
mo_],_.%_ Ai:r_ in_
°C
- --~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 h8 e
FOR FILM-TYPE CONDENSATION
M - Air Rate
Run No.
lbs./br.
tl - t2
Tave
Vapor 0 c
Vapor 0 C
Humid Heat
save
hse:
MS(t1-t2 )
A(ts-tw>ave
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 h 8 e
FOR FILM-TYPE CONDENSATION
M - Air Rate
Run No.
lbs./hr.
tl - t2
Vapor °C
Tave
Save
Vapor 0 c
Humid Heat
hse=
MS(t1-t2)
A(tg-tw)ave
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 b8 e
FOR DROPWISE CONDENSATION
M - Air Rate
Run No.
1b./br.
54
4.0
55
tl - t2
Vapor 0 c
Tave
6 ave
hsea
MS(t1-t2 )
Vapor °C
Humid Heat
2.2
98.2
4.55
1.42
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
A(tg-twJave
TABLE IX (Continued)
CALCULATION OF SENSIBLE BEAT TRANSFER COEFFICIENTS h8 e
FOR DROPWISE CONDENSATION
M- Air Rate
tl - t2
Vapor 0 C
Tave
save
hse=
MS(t1-t 2 )
Vapor °C
Humid Beat
7.0
90.1
0.90
1.42
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
Run No.
lb./hr.
67
14.2
68
A(tg-tw>ave