An experimental study was conducted on pool-boiling heat transfer from an electrically heated horizontal wire to saturated liquid nitrogen at atmospheric ...
Journal
of NUCLEAR SCIENCE and TECHNOLOGY, 18[7], pp. 501-513
Pool-Boiling
Heat
Transfer
(July 1981) .
in Liquid
501
Nitrogen*
Muneo KIDA, YoshihiroKIKUCHI:OsamuTAKAHASHI and
Department
Itaru
of Nuclear
MICHIYOSHI
Engineering,
Received
December
Kyoto University**
26,
1980
An experimental study was conducted on pool-boiling heat transfer from an electrically heated horizontal wire to saturated liquid nitrogen at atmospheric pressure. Experimental results of heat transfer characteristics in both nucleate- and film-boiling regimes, critical heat flux and minimum heat flux were analyzed and compared with various correlations. In addition, photography was used to obtain information concerning the vapor-bubble and vapor-film behaviors around the heating wire. These data of microcharacteristics were utilized for evaluating theoretical models of nucleate-boiling mechanism proposed by other investigators. Transient conduction to the relatively cold (saturated) liquid , which came into the space vacated by the departing bubble and contacted with the heating surface, was found to be important for high heat transfer rates associated with nucleate boiling. KEYWORDS: liquid boiling, bubble size, mum heat flux
nitrogen, heat transfer, pool boiling, nucleate boiling, film bubble frequency, nucleation sites, critical heat flux, mini-
I. In
recent
years
exceptionally for liquid
helium nitrogen,
needed
for
during
boiling,
at
for to
fundamental
room
cryogenic
cryogenic
is important
boiling
been
only
departing
bubbles
and
the
to
the
heat
examine
the liquid
obtained
on
heat
emphasis
on
the
formation
transfer
in nucleate
therefore, to
frequency
of
bubble
boiling,
the and
on
* Orally presented at 1980 Fall Meetings ** Yoshida , Sakyo-ku, Kyoto 606.
from
in
both
nucleation
vapor
in the
of At . Energy
25 -
of
are
paper
and
sites pattern
Soc.
of
Japan
for have
film
and
the
in film
(Sep.
studies
for
under-
with
boiling.
1980).
of
some
conducted
horizontal
frequency
heat size
deriving been
the
the
wire
experimental
boiling,
of
boiling
i.e.
important
the
between
Most
boiling,
heated
gives
are
espe-
Extensive
necessary
electrically
usually
transfer,
world(1).
are
by
which
difference
experiments
nucleate
flow
heat
boiling.
which
and
This
of
-
out
convection)
systems,
of
been
developed
by cryogens,
temperature gives
present an
pressure.
the
surfaces
macrocharacteristics
boiling
transfer
number
of
has
being
or forced
high-vacuum
large often
carried
the
temperature now
a knowledge
formation,
need,
low are
(pool
microcharacteristics
during
characteristics
in
the
on
heat
size,
been
investigate
this
cooling
extremely liquid
of
instance,
cooling
liquids
data
meet
of
pressures
limited
at atmospheric
transfer bubble
have,
To
pool-boiling nitrogen
the
a cryogenic
mechanism
formulations.
saturated
since
and
conducted
are
transfer
these
use
for
The
low
of
There
heat
magnets. very
experiments.
transfer.
standing
such
making
types
nucleonics
temperature
have
fields magnets,
Several
produce
storage
liquid
studies
technical
reactor.
proposed is used
and
cially
past
are
of
superconducting
fusion
In dealing
a solid
growth
Large
a Tokamak-type
liquid
of
the
rapid.
INTRODUCTION
to
results particular of
bubble
502
J. Nucl. Sci. Technol.,
II. Figure of
a
EXPERIMENTAL
1 shows
a schematic
double-walled
and
the
outer
gen,
from
walls
room
insulator outer
wall
for
in an
keep
and
the
inner
apparatus
diameter. wall,
A gap which
which
consisted
between
contained
the liquid
inner nitro-
Two
on
vapor-film
experimental
in inner
the
condition. the
side
records
of
behaviors
in
photographic
the
AND PROCEDURE
thermal
to
provided
of 90 mm
to isolate A
adiabatic were
of
evacuated
equipped
obtaining
vapor-bubble liquid
was
was
windows*
wall
diagram
chamber
temperature.
also
glass
glass
APPARATUS
nitrogen. The
heater
platinum diameters
of
connected
by
acrylic
an
izontally
to electrical
nitrogen.
direct
current
potential
the
two
was
placed surface
of
The
wire
heated
by
a shunt
power
a
measured
leads
60 mm
area
thus
wire
I was
apart, being
was
annealed
at approximately
of
1,000K and then cleaned chamber
liquid
nitrogen,
ually
heated
flux by
runs
was
control
heat
system,
in a film boiling
condition,
as shown
in Fig. 2.
film boil-
After
in, the
input power
further
increased
value.
Upon attaining
condition,
the
cooled down the
V and * For heat
heat
heat
wire
to zero flux.
the
the prescribed was,
transfer into
in turn, decreasing
through
The
resistance
leakage
was
up to a prescribed
by gradually
power
mum
apparatus
grad-
resulting
ing had set
Experimental
filled with
the wire power
1
the
with acetone.
was
up to the critical
the
of Fig.
set
the
means
(0.125 O).
to each
After
the 60 pD
in mm.
by
Prior wire
system. between
diameter
measured
hor-
specially
control
V was
D is the
resistor
was
from
transfer
current
supported
free
drop
mm2 where
leads
1.0 mm.
and
supplied
heat
Wire
to
the
electrical
effective
0.1
under
transistorized
The
smooth
length.
from
structure
liquid
a pure,
in
varied
150 mm
designed
was
60 mm
were
It was
The
element
wire
R(=V/I)
experiments liquid
a mini-
potential
drop of
, however, nitrogen.
Fig. another
2
Regimes
chamber
without
- 26 -
in boiling windows
heat was
transfer used
to minimize
Vol. 18, No. 7 (July 1981)
the
wire
were
503
measured
at the saturation
continuously
. During the runs, the liquid nitrogen corresponding to the atmospheric pressure .
temperature
was maintained
The power was readily calculated : W=VI. The mean temperature Tw of the wire obtained from the curve T(R)(2) , which was previously confirmed by measuring R at some different temperatures using a current of very low intensity . Because of the relatively was
high
thermal
conductivity
temperature 0.19 K and
gradient
lower
wire
than
and
the
in the cross the average
diameter
boiling diagram
of
the
was no appreciable temperature being
a condition
: heat
flux
of
2.4 x 105 Wm-2
AND DISCUSSIONS
Transfer
present
heat
flux
nucleate
and DTs
temperature
temperature
contains
wire , there surface
actual
on a log (q) i's. log (DTs)
wall
the saturation also
the
plotted
; q is the
excess
under
RESULTS Heat
3 shows
data
of the
of 0.5 mm.
Nucleate-boiling
Figure
diameter
; for instance,
temperature
III. 1.
small
section
other
the
Tw above
Ts.
The
figure
experimental
results
published to date(3)~(11). Complete agreement is lacking among the results since the nature of the surface has an important influence
on nucleate
other
things.
above-mentioned been and cause
the The
was
general solid
dicates
in
derived
organic
form,
after
data, would
of data. in the
figure
correlation(12)
for nucleate
and various by the
of taking
line drawn
Kutateladze's
variations
measurement
scatter
the
has yet
to this,
method
uncertainties
among
explains
successfully,
In addition
geometry,
process, which
effects
found.
in system
boiling
No theory,
boiling
liquids
in-
which of
water
and is represented
rearrangement,
Fig.
3
Nucleate-boiling
heat
transfer
( 1) where r
is the
the
surface
tion
due
are 2.
The
thermal
latent
conductivity, m
heat
subscripts l equation
the
of
vaporization,
and
v signify
represents
the
viscosity,
P the values
Cp the
pressure
pertaining
present
data
specific
and g
the
heat,
to liquid
and
well
although
fairly
a
acceleravapor, the
scattered. Critical 4
plots
scattered
the
Kutateladze's
Figure The
k the
hfg
to gravity.
respectively. data
density,
tension,
Heat
Flux
shows
reveal slightly.
the that This
effect the
of
CHF tendency
heater
diameter
increases
with
is
similar
liquid(13)~(15). - 27 -
D on increasing to
the
the
critical
heat
flux
(CHF) qmax-
diameter
although
the
data
experimental
results
of
ordinary
are
504
J. Nucl.
For
comparison,
tion(12)
is also
teladze
was
that
the
matter
indicated
in the
probably
critical
of
the
heat
flux
the
to
Kuta-
point
condition
From
final
figure.
equation
out was
stability
surface.
analysis,
correla-
first
hydrodynamic
horizontal
in the
Kutateladze's
Sci. Technol.,
on
a
a flat
the
dimensional
can
be
written
form
(2) where
B
is
Kutateladze between for
that
this
constant
0.19,
with
0.16 as average,
organics
0.16
of
CHF
boiling
Eq. ( 2 ).
theoretical
data
of
both
flat
on
cylinders
in
constant.
and
sets
horizontal
proportionality
found 0.13
several
and
a
(wires). The
line in the
varied
both plates
The
Effect
of heater
except
range
in Fig.
4 was
for D=0.1
of +-20%.
mm,
For
obtained agree
D-=0.1 mm,
fall below the line. This suggests a dependency of CHF on the heater Kutateladze et al.(16) found that Eq. ( 2 ) could be used to correlate data
for
and
horizontal
the
physical
cylinders
properties
heat
diameter flux
and
values,
scattering
4
on critical
solid line drawn
measured data
Fig.
water
if B could of the liquid.
vary
with
This
the
diameter
dependency
by
fairly
letting well
however,
diameter. pool-boiling by the
the
diameter
by
dimensionless
the
Laplace
diameter characteristic
of
the
heater,
length,
CHF
(or wire) relation
B=f (D*), where D*,
the
the plots
of the cylinder
is expressed
B=
with
(3) is
obtained
by
dividing
the
heater
or
(4) Figure
5 is a plot of Eq. ( 3 ) for the
present relations
experimental predicted
et a1.(16) also
Rao
indicated
results. CorKutateladze
by
& Andrews(17)
in this
teladze
et al. proposed
curve
for
14 sets
and 6 organics, over
wide
pressure, smooth
ranges
fitted
of water
were
lines drawn
Applying
in the figure
of the
Rao & Andrews
horizontal derived
and
kinds of surfaces. spread
a hydrodynamic
for
obtained
of diameter
represent the band these data. model
the best
and with different metallic heater
The broken
ity
Kuta-
of data
which
are
figure.
in
stabil-
Fig.
5
cylinders,
Generalized
plot
of dimensionless
the follow-
portionality - 28 -
of CHF heater
constant
B
data
showing
diameter
effect
D* on pro-
Vol. 18, No. 7 (July 1981)
ing
505
correlation
q max/qmaxF= 0.805/D*(D*2i+2)3/4, where
D*i is the
CHF
recommended
dimensionless
(5)
diameter
of vapor -liquid interface. rmax F is the well-known by Zuber(18) for infinite flat plates and is given by the following equa -
tion : (6)
which, except for the dashed line drawn in The proportional range of the present
coefficient , is identical to Eq. ( 2 ) derived by Kutateladze. A dot-andthe figure was obtained by letting D*i= D* in Eq . ( 5 ). constant B increases generally with increasing heater diameter in the heater diameter . Fairly good agreement is observed between the
present data and both correlations within the spread range of data. 3. Film-boiling Heat Transfer Film boiling as a cooling process has not had wide commercial applications because of the high surface temperatures. In cryogenic systems, however, a knowledge of film boiling is particularly important since the extremely large temperature difference between a equipment surface and a cryogenic liquid often causes film boiling during cooling down from the room temperature. Figure of
6 shows
film-boiling
heater
diameters.
excess
of the
saturation
the experimental
heat
transfer
The
wall
abscissa
the heat transfer As DTS
coefficient
increases,
In this
lower DTs
boiling
regimes
and the
various
is DTs,
the
above
the
temperature
temperature
results
for
ordinate
given
h first decreases region, exist
h,
by q/DTs. sharply.
nucleate-
and film-
simultaneously
along
the heating
wire, as clarified
later
by Photo.
1 (c).
boiling
more
dominant
Film
becomes
with increasing DTs, the
heat
transfer
higher DTs
region
is established
and extremely where
h increases
ing DTs.
For a given DTs,
solid
lines drawn
relations For
film is
boiling,
from
frictional
forces
arrived based
at on
increaswith and the the cor-
and Breen Fig.
respectively.
given,
radiation
are
by Bromley(19)
& Westwater(20), model
broken
in the figure
obtained
exists,
with
h decreases
The
the
film boiling boiling
slightly
diameter.
In
stable
and no nucleate
however, increasing
degrades
characteristics.
as
that the
the
molecular
on
compared vapor
heating the
following
with
is surface
vapor
film
equation
conduction
nucleate
generated
alone
at
through flowing
the on
representing : - —29—-
boiling, the
Film
By of
convective
a
transfer
well-known
interface
film.
outside the
boilingheat
a reasonably
liquid-vapor
vapor the
6
by
balancing horizontal heat
transfer
physical
conduction the
buoyant
tube,
and and
Bromley
coefficient
hc
506
J. Nucl. Sci. Technol.,
(7) where the
all
physical
properties
of
the
vapor
are
evaluated
at
the
average
temperature
of
film. Bromley
heat
also
suggested
an
expression
which
included
the
radiative
contribution
hr
to
transfer
h=hc+ 0.75 hr, for
hc>hr*.
He estimated
the
magnitude
of
hr
(8)
from
the
relation
(9) which
is the
equation
for net heat
In Eq. ( 9 ) e. is the Boltzmann
emissivity
transfer
by
of heating
radiation
surface, a
( 7 ) can be rearranged
where
into the dimensionless
parallel
of liquid
plates.
and k
Stefan-
the
subscript
the
diameter
for
isopropanol
Breen
D means
of
cylindrical
wires
(10)
NuD=hD/kv,
(11)
Ra*D=D3rv„(rl-rv)gCpv/(kvmv),
(12)
to
Freon-113,
large
tubes,
than
Rayleigh
numbers,
the
analyzed
and
rather
form
Nusselt
and
results
of
3)+0.4.
(13)
modified
Rayleigh
numbers
are
based
on
heater.
& Westwater
preferred
that
generalized
NuD=0.62(Ra*Dt')1/4,
t'=hfg/(CpvDT
fine
infinite
absorptivity
constant.
Equation
Here
between
the
the
the that
and diameter
were
concluded as
several
obtained
the
that
investigators,
on the
horizontal critical
characteristic
including cylinders
wavelength lc
length
in
the
their ranging
was Nusselt
own, from
sometimes
and
modified
where
(14)
They also found that, depending on the value of the dimensionless ratio lc/D, the boiling characteristics for a horizontal heater fell into three different regimes. However, they succeeded in correlating the data in all three by the equation Nulc=(0.59+0.069lc/D)(Ra*lct")1/4,
(15)
t"=[hfg /(CpvDTs)+0.34]2.
(16)
where
This
correlating
expression
All the measured and
agree
better
0.1 mm.
Similar
liquids.
For
* In total
the
tendency
present
heat
with
such
is obviously
values
cases
experiments
are higher
the
empirical
the
vapor
with
small
film thickness
radiative
contribution
transfer. -
form
of Eq. (10).
the calculated
correlation
was observed the
a modified than
30 -
of Breen diameter
results wires
is comparable was
of
Bromley's
& Westwater,
estimated
for water to the
equation
except and
wire
to be less
for
common
diameter
than
D=
20%
, as of the
Vol. 18, No. 7 (July 1981)
507
suggested by Bromley. The Bromley's model is not applicable for this physical situation. In the higher DTs region wave motion or turbulent flow is further observed, especially due to the intermittent release of bubbles from the vapor film, which is not considered in Bromley's model where the vapor-liquid interface is assumed to be completely smooth, i. e. no capillary nor standing waves existing. Figure 7 shows the generalized plots of film-boiling heat transfer data in the dimensionless form. The abscissa is lc/ D and the ordinate Nulc/(Ra*lct")1/4. The figure contains other experimental results(19)(20)(28)~(32)of water, organics and cryogenic liquids. The height of the bar indicated on the data does not mean the uncertainty range of the measured values, but the spread of each measurements.
Fig.
Correlations
7
predicted
Generalized
plot
of film-boiling
heat
by Bromley and Breen & Westwater
figure. In the region lc/D8, however,
transfer
are also indicated
in this
is observed between the experimental the measured values are higher than
the Bromley's prediction (broken line) and lower than the empirical correlation of Breen & Westwater (solid line). The plots diverge increasingly from the theoretical curves with increasing lc/D, i. e. with decreasing wire diameter. A dot-and-dashed line then gives a best fit for the data and is represented by the following equation : Nulc=(0.75+0.032lc/ 4. The minimum
Minimum transition heat
flux
Heat from
D)(Ra*lct")1-4.
(17)
Flux film boiling
q ruin (see Fig. 2).
to nucleate The
boiling
minimum -
31 -
occurs
heat
flux
at a heat
flux known
is normally
of
lesser
as the im-
508
J. Nucl.
portance
than
nucleate
boiling
lessens
the
need
to predict
loading
the
transition
Figure
on
In the
present
mum
heat
the
immediately
were
existing
The
minimum
on
increasing
large
the
data
at
the
transition
flux
correlations
and
of
this
&
Wong(21)
by
Berenson(22)
in
the
of
since
heat
many
the
transition
temperature
fluids , however, to nucleate
transition in
point
surface
transfer
and
one encounters boiling occurs
coefficient
applications
to then a at
during
the
.
mini-
moment partial
no
vapor
of heating
theoretical
Lienhard
data.
wire.
qmin decreases
In
the
design
flux
i.e.
diameter.
boiling
Technol.,
heater
from
boiling,
since changes
of
high
reduction In cryogenic
for
heat
the surface
heat
the
cylinders
the
flux
effect
taken
to nucleate
film
shown
the
with
system.
considered
minimum
before
boiling
the
The
experiments flux
in fluid a marked
heat
be
shows
on
flux
minimum
must
8
diameter
flat
heat
produces
temperatures.
boiling
film
critical
generally
thermal
operating
by
the
Sci.
with
figure
are
also
predicted
for
horizontal
for horizontal
plates. The
by the bules
film
boiling
steady at
formation
the
element.
to
the
and
release
Zuber(18)
Taylor
transition-
and
from
horizontal
a flat
following
is characterized
liquid-over-vapor
a heating apply
regime
over
was
first
the
instability
film-boiling
relation
of bub-
interface
heat
plate. for
theory
the
Fig.
to
8
Effect of heater diameter on minimum heat flux
transfer
Based
on
minimum
the
heat
analysis
flux
of
with
Zuber
film
boiling
, Berenson had determined the on a horizontal flat plate ,
(18) Accounting instability ing
for
of
the
correlation
the
effect
interface
of
for
surface
tension
a horizontal
in the
cylinder
traverse
, Lienhard
direction
upon
& Wong
the
Taylor
the
follow-
derived
:
(19) Although dominant
a partial at
theoretical 5.
curve
The
liquid
the
predicted
knowledge frequencies
mechanism
limited
film
in
boiling,
from
size
during of data
nitrogen
bubbles for
nucleate
growth
boiling. has
correlation
cryogenic
to examine
coexisting
measured
Lienhard
bubble
boiling,
is important
ordinary studied
liquids. the
of
of
rates,
For been
the
with
values & Wong
film
agree
boiling
well
with
, is the
.
Boiling
microcharacteristics and
boiling
experiments, the
of
of
i.e.
present
Microcharacteristics
departure
ture
qmin
liquids by
many
This
led
size
and
the
- 32 -
i. e. departure for
that
wet
the
heating
investigators(23). present
frequency
sizes
understanding
authors in saturated
of vapor
bubbles
the
transfer
heat
surface There
to carry pool
, the are
out boiling
depar-
, however, a study on .
,
Vol. 18, No. 7 (July 1981)
Photograph
509
1 (a) shows a typical
photograph of vapor bubble behavior on the heating wire (D=0.5 mm) during nucleate boiling. Small bubbles of 0.43 mm in average diameter stream forth from many nucleation sites on the wire. The number of nucleation sites is 9.55 x 105 m-2. The frequency of bubble formation is approximately 90 Hz which was determined from the photographic records taken by the high-speed camera. In film boiling, however, a film of vapor is always formed on the heating wire, as shown in Photo. 1 (b). Waves are observed along the top of the wire, and the crest-to-crest average distance for the waves on the top of the wire is 7.2 mm, a value close to the critical wavelength lc=6.6 mm. Larger bubbles of 3.6 mm in average diameter are released from the top of the wire. A decrease of heat flux produces a partial film boiling where film boiling and nucleate boiling exist simultaneously along the heating wire, as shown in Photo. 1 (c). From the above-mentioned observations, vapor bubbles or vapor films in liquid nitrogen are found to
Photo.
1
Bubble boiling
and film behavior in liquid nitrogen
during
behave quite similarly to those in noncryogens. Figure 9 shows the effect of changes in heat flux q on the number of nucleation sites per unit area of the heating surface n, the frequency of bubble formation f and the diameter of departing bubble d0 for the wire diameter of 0.5 and 1.0 mm. With the rise in heat flux the number of nucleation sites and the bubble diameter increase in the nucleateboiling regime, and film boiling produces much larger bubbles. In this figure are also shown the theoretical values of Fritz(24) and the empirical correlation of Verkin & Kirichenko(25) in nucleate boiling. Fritz considered a balance between buoyancy and surface tension forces to derive the expression
for departure
diameter (20)
where b
is the
conditions
appears
bubble to
contact be nearly
angle. constant
For at
most 45d. - 33 -
situations,
the
value
of b
under
dynamic
510
J. Nucl. Sci, Technol.,
Verkin & Kirichenko found that for 12 sets of data obtained on water, organics and 4 cryogenic liquids over the wide ranges of pressure and subcooling, both the diameter of departing bubbles and the frequency of bubble formation were correlated well with the reduced pressure P/ Pc, where Pc is the critical pressure. Applying their correlation to the present experimental condition (P/Pc = 3.0 x 10-2),d0=0.46 mm and f=100 Hz are obtained. It can be seen from the figure that the measured values of bubble diameter fall below the theoretical line derived from Fritz's equation, but agree fairly well with the correlation of Verkin & Kirichenko although the data are scattered. The microcharacteristics have often been used in deriving heat transfer correlations for saturated nucleate boiling*. Several correlations are based on one or more (simultaneous) contributions of the following mechanisms : (1)
Transient conduction to the relatively cold (saturated) liquid that comes into the space vacated by the departure of the bubble.
(2) Evaporation of a liquid microlayer the base of a growing bubble. (3)
Circulation of liquid in vicinity on vapor-liquid interface.
The
third
mechanism
was
Fig.
at
to cause
years, and on the analogy of heat transfer derived an equation of the following type
Effect
of heat
flux on number
bubble
the
high
due to thermocapillarity heat
transfer
in single-phase turbulent for nucleate pool-boiling
rates
effects for
Nub
liquid
Prandtl
is
the number
Rohsenow(26)
boiling
Nusselt
; A, m1 and
defined
a bubble
number, m2 are
Reb
the
boiling
Reynolds
number
and
Reynolds
number
by
the
* In the
present
was
evaluated
experiments
by liquid
the
(22) from
the
was -
maintained 34 -
heating
(23)
equation
nitrogen
the
relation
Nub=qd0/(DTski). flux
Prl
constants.
where Gb=(p/6)d30rvfn, the average mass velocity of vapor receding surface. He also defined the Nusselt number in Eq. (21) by the equation
heat
have
(21)
Reb=Gbd0/mt,
The
many
flow, investigators heat transfer
Nub=A(Reb)m1(Prl)m2, where
of
nucleation sites, frequency of bubble formation and bubble diameter in nucleate boiling
of a growing
thought
9
at saturation
temperature
.
Vol.
18, No. 7 (July
1981)
511
qnb=(p/6)hfg A different Their
nucleate-boiling
analysis
from
the
space
is based
heating
vacated
with
the
they
obtained
heating
on
surface by
the
heating
transfer
first
mechanism
is transient
departure
surface the
heat the
at
final
equation
correlation
the
bubble
After
the
the
to
the
of
the
and
(24)
was
that
conduction
of Tw
d30 rvfn
the
liquid
by Mikic
of
mode Ts
superheated
formulation
average
derived
significant
and
which layer
heat
.
transfer
comes
into
the
, and then contacts of related terms
integration
nucleate-boiling
& Rohsenow(27) of
heat
flux
over
the
,
whole
surface,
qnb=2(pkl rlCpl
f)1/2 d20nDTs.
(25)
Figure 10 shows a comparison of measured total heat flux q with nucleate-boiling heat flux qnb predicted by Eqs . (24) and (25). In the calculation of qnb,the measured values were applied to f, d0, n and DTs. line indicates a relation qne=q .
The solid
The measured values of q are much higher than the predicted values of qnb by Rohsenow's correlation, but agree well with the correlation of Mikic & Rohsenow. This means that the transient conduction to the relatively cold (saturated) liquid, which comes into the space vacated by the departure of the bubble, is dominant in the high heat transfer rates associated with nucleate boiling.
Fig.
10
Comparison of nucleate-boiling flux with total heat flux
heat
IV . CONCLUSIONS Saturated
pool-boiling
experiments
were
conducted
with an electrically
heated
wire in liquid nitrogen at atmospheric pressure. The wire diameter ranged 1.0 mm. In each run the heater power was gradually increased and decreased designed wire
power
were
control
measured
Comparison conclusions :
system.
during
Changes
boiling.
of the experimental
in the
Bubble results
potential
behaviors with
various
(1)
Nucleate-boiling heat Kutateladze's correlation,
(2)
The critical heat flux tends to be higher with ured values agree fairly well with the theoretical and
(3)
transfer characteristics although the data are
drop
and
the
were also recorded correlations
can be scattered.
increasing wire values predicted
from 0.1 to by a specially
resistance
of
the
on the photo-film.
yielded
represented
horizontal
the fairly
following well
by
diameter. The measby Kutateladze et al.
Rao & Andrews.
The diameter of departing bubble (0.3~0.9 mm) and the frequency tion (approximately 90 Hz) agree fairly well with the correlations chenko
for nucleate
to the cold
(saturated)
boiling. liquid
The
present
is much
more - 35 -
data
suggest
responsible
that
the
of bubble formaof Verkin & Kiritransient
conduction
for the high heat transfer
rates
512
J. Nucl. Sci. Technol.,
associated (4)
with
nucleate
boiling.
In film boiling the heat transfer coefficient decreases with increasing The measured values are higher than Bromley's correlation and agree the correlation of Breen & Westwater. servations that the turbulent wave the
(5)
heat flux measured
more
detailed
studies
are
knowledge
of
formation,
Transient
will
In order based
to on
the
the boiling
as cooling
boiling
required
about
microcharacteristics
such
This is suggested by the photographic obmotion of vapor film is caused along the top of
for film boiling decreases with values are in good agreement
predicted by Lienhard & Wong. The foregoing observations in liquid
bubble
diameter. well with
wire.
The minimum diameter. The
much
wire fairly
down
present
nucleate
rate occurs
in many
transient
steady-state
the bubble
in an
the
boiling
size
of
departing
and
the
number
Rapid
strength boiling
boiling
as
of
to those
analytically
film
accident
applications.
affect
need
of
are similar and
and
including
growth
significantly fill this
both
boiling,
also
nitrogen
experimentally
the increase of the wire with the theoretical values
of
well
as
temperature structures
experiments
in
cryogenic
in noncryogens, order
, of nucleation
change
some
the
the
especially
the
frequency sites .
of
normal
during
but
obtain
liquids,
bubbles
during
to
such
operations, transient
, which is important for are scheduled for coming
safety. years
,
experiments.
[NOMENCLATURE] A: B: Cp: D: Di: D* :
Proportionality constant in Eq. (21) Proportionality constant in Eq. ( 2 ) Specific heat Diameter of cylindrical heater Interfacial diameter of vapor film Dimensionless diameter of cylindrical heater, defined by Eq. ( 4 ) D*i : Same as D*, except that characteristic length is taken as Di d0 : Diameter of departing bubble f : Frequency of bubble formation g : Acceleration due to gravity h: Total heat transfer coefficient hc: Convective (based on molecular conduction) heat transfer coefficient hfg : Latent heat of vaporization hr : Radiation heat transfer coefficient I: Electric current flowing wire k: Thermal conductivity m 1, m2:Constant exponents in Eq. (21) n : Number of nucleation sites per unit area of heating surface Nub : Boiling Nusselt number, defined by Eq. (23) NuD: Nusselt number based on diameter of cylindrical heater, defined by Eq. (11) Nulc: Same as NuD, except that characteristic length is taken as lc P: Static pressure in liquid at boiling surface Pc: Critical pressure - 36 -
Pr: q: qmax.: axF : qmin,: qnb: R: Ra*D: Ra*lc: Reb: T: Ts: Tw.: Ts:
V: W: : : ' : ": : c:
Prandtl number (=Cpm/k) Total heat flux Critical heat flux Critical heat flux qm for horizontal flat plate, defined by Eq. ( 6 ) Minimum heat flux Nucleate-boiling heat flux Electric resistance of wire Modified Rayleigh number, defined by Eq. (12) Same as Ra*D, except that characteristic length is taken as lc Boiling Reynolds number, defined by Eq. (22) Temperature (K) Saturation temperature (K) Temperature of heating surface (K) Excess of temperature of heating D surface above saturation temperature (= Tw-Ts) Potential drop of wire Input power (= VI) a Thermal radiative absorptivity of liquid b Bubble contact angle Dimensionless heat t parameter , defined by Eq. (13) Dimensionless t heat parameter , defined by Eq. (16) k Stefan-Boltzmann constant, 5.669 x 10-6 Win-2 K-4 Critical wavelength,l defined by Eq. (14)
m
Vol. 18, No. 7 (July 1981)
513
: Viscosity r : 'Density s : Surface tension
(Subscripts) l : Liquid,
v:
Vapor
REFERENCES
(1) See, for instance, FROST, W. : "Heat Transfer at Low Temperatures" , (1975), Plenum Press, N ew York. (2) "Dennetsu Kogaku Shiryo", (3rd Ed.), (in Japanese), (1975), Japan Soc . Mech. Engrs., Tokyo. (3) LYON, D. N.: Int. J. Heat Mass Transfer, 7[10], 1097 (1964). (4) ROUBEAU, P. : Proc. 10th Int. Congress of Cryogen and Ref rigent, Copenhagen , 1959, Vol. 1, 49 (1960 ), Pergamon Press, Oxford. (5) COWLEY, C. W., et al.: Ind. Eng. Chem. Process Design Develop., 1[2], 81 (1962) . (6) FLYNN, T. M., et al.: "Advances in Cryogenic Engineering", Vol. 7, 539 (1962), Plenum Press , N ew York. (7) HASELDEN, G. G., PETERS, J. I. : Trans. Inst. Chem. Engrs., 27, 201 (1949). (8) WEIL, L., LACAZE, A.: Acad. Sci., Paris, 230[1], 186 (1950). (9) FRITZ, J. J., JOHNSON, H. L. : Rev. Sci. Instrum., 21[5], 416 (1950). (10) MERTE, H., CLARK, J. A. : Trans. ASME, J. Heat Transfer, Ser. C, 86, 351 (1964). (11) TAMAKI, E., WAKISAKA, N. : Liquid nitrogen boiling experiments, Preprint 7th Japan Nat . Heat Transfer Symp., (in Japanese), 73 (1970). (12) KUTATELADZE, S. S. : AEC-tr-3770, (1959). (13) SUN, K. H., LIENHARD, J. H. : Int. J. Heat Mass Transfer, 13, 1425 (1973). (14) BERNATH, L.: Chem. Eng. Progr. Symp. Ser., 56, 95 (1960). (15) IVEY, G. H., MORRIS, D. J. : Proc. 3rd Int. Heat Transfer Conf., Chicago, 1966, Vol. 3, 129 (1966). (16) KUTATELADZE, S. S., et al.: Teplofiz. Vys. Temp., 5, 841 (1967). (17) RAO, P. K. M., ANDREWS, D. G.: Proc. 6th Int. Heat Transfer Conf., Toronto, 1978, Vol. 1. 227 (1978). (18) ZUBER, N.: AECU-4439, (1959). (19) BROMLEY, L. A.: Chem. Eng. Progr., 46[5], 221 (1950). (20) BREEN, B. P., WESTWATER, J. W. : ibid., 56[7], 67 (1962). (21) LIENHARD, J. H., WONG, P. T. Y. : Trans. ASME, J. Heat Transfer, Ser. C, 88, 220 (1964). (22) BERENSON, P. J. : Transition-boiling heat transfer from a horizontal surface, Heat Transfer Lab. Tech. Rept. No. 17, (1960), M. I. T. (23) See, for instance, "Futto Netsudentatsu", (in Japanese), (1964), Japan Soc. Mech. Engrs., Tokyo. (24) FRITZ, W. : Phys. Z., 36[11], 379 (1935). (25) VERKIN, B. I., KIRICHENKO, Yu. A.: Proc. 7th Int. Cryogenic Eng. Conf., London, 1978, 505 (1978), IPC Sci. Technol. Press, Gildford. (26) ROHSENOW, W. M.: Trans. ASME, J. Heat Transfer, Ser. C, 74, 969 (1952). (27) MIKIC, B. B., ROHSENOW, W. M.: ibid., 91, 245 (1969). (28) INAI, N. : Film-boiling heat transfer in liquid helium, Preprint 14th Japan Nat, Heat Transfer Symp., (in Japanese), 133 (1977). (29) FREDERKING, T. H. K.: Amer. Inst. Chem. Engrs. J., 4, 403 (1959). (30) NUKIYAMA, S.: J. Japan Soc. Mech. Engrs., 37, 367 (1934). (31) MCADAMS, W. H., et al.: Chem. Eng. Progr., 44, 639 (1948). 32) BANCHERO, J. T., et al.: ibid., 51[17], 21 (1955). (
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