7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
The effect of system pressure on bubble growth in narrow channel
Deqi Chen, Liangming Pan* and Dewen Yuan
School of Power Engineering, Chongqing University, Chongqing 400044
Email: cneng @cqu.edu.cn
Keywords: bubble growth, system pressure, bubble sliding
Abstract
A visual research on bubble growth in vertical narrow channel with deionized water as working fluid at different system
pressures (110 bar) was carried out. It was found that the bubble size degreases obviously and the bubble growth is restrained
significantly with increasing system pressure. At lower system pressure (13 bar), the bubble grows at nucleation site and
begin to shrink due to condensation one it departs from the nucleation site. While at higher system pressure (610 bar), bubble
grows when it is sliding along the heating wall. It was also found that the power curve can predict nondimension bubble
growth at different system pressure. A theoretic analysis focusing on the effect of system pressure on bubble growth was also
presented in this paper; and it was found that the latent heat needed for a bubble with unit volume and the situation of heat
transfer happening on the heating wall will be different under different system pressure significantly, which results in distinct
difference in bubble growths at different system pressures.
Introduction
Bubble growth is one of the key issues included with the
study of nucleate boiling heat transfer. It is necessary to
study bubble growth in different working conditions
profoundly in order to understand the mechanism of
nucleate boiling heat transfer.
Many researchers have carried out experiments to
investigate bubble growth visually with high speed camera.
Thorncroft et al. (1998) visually investigated the vapor
bubble growth and departure in vertical upward flow and
downward flow in forced convection boiling with FC87 as
working fluid. The results showed that bubble growth rate
increased with Jacob number (increasing ATsat) under
otherwise identical conditions in upflow or downflow.
The authors also found that the vapor bubble growth could
be predicted by the power curve model, R=ktf, and in
which n ranged from 1/31/2.
Ma et al. (2001) conducted experiments in which a single
vapor bubble was nucleated and grew in a flow field of
FC72 on a flat surface in terrestrial gravity and
microgravity. And the single bubble generated on a thin
gold film semitransparent heater was investigated too. The
authors found that the dimensionless transient bubble
diameters (D/La) during growth are proportional to the
parameter of Re1/3t*1/3, where Re is the Reynolds number
and t is the dimensionless time.
Prodanovic et al. (2002) studied subcooled flow boiling of
water at pressures from 1.053 bar, bulk liquid velocity
ranged from 0.08 to 0.8 m/s, and subcooling at 1030 K.
Experiments were carried out on a vertical, annular test
section with inner heating surface and upward water flow
with highspeed camera capturing the bubble behavior from
inception to collapse. And the authors also found that the
bubble diameter decreases significantly with increasing
pressure.
Basu et al.(1993, 2005) measured the waiting time, growth
time, departure size and frequency in an upwardvertical
subcooled flow boiling facility using water as working
fluid. The authors found that the bubble waiting time was
correlated against wall superheat, while the bubble growth
time was correlated with bulk subcooling, bubble departure
diameter and superheated liquid layer. But it shall be noted
that the correlation was just proposed for limited test scope
and heated surface.
Siedel et al. (2008) carried out an experimental analysis of
bubble growth, departure and interactions during pool
boiling on artificial nucleation sites with 99% purity
npentane as the working fluid. Experiment had been
carried out under various wall superheat conditions which
were from 2.1 to 7.1 K. After the bubble volume has been
plotted as a function of time, they found that bubble growth
appears very reproducible, the volume at detachment being
independent of the wall superheat whereas the growth time
is dependent on the superheat.
Bubble growth rate and bubble size are affected by system
pressure significantly. Meanwhile, the vapour density
increases with system pressure. So with the same bubble
diameter, the one grows in higher system pressure will
need more heat transferred from heating wall. And due to
the effect of channel wall on bubble growing in narrow
channel when bubble reaches a certain size, bubble
behavior will differ with that in conventional channel.
While these characters still are not so clear. So the purpose
of present study is investigating the effect of system
pressure on bubble growth in vertical rectangular narrow
channel with 2 mm in gap. And the experiment has been
carried out in 1 to 10 bar system pressure with deionized
water as working fluid. High speed camera was adopted to
capture bubble behaviors on heating wall.
Nomenclature
D diameter (mm I m)
g gravitational constant (ms1)
G mass flux (kg/m2s)
hfg latent heat of evaporation
k coefficient in power law, R=kf
La Laplace number (mm)
n coefficient in power law, R=kf
P power (W)
p pressure (bar)
Qb latent heat needed for a bubble with unit
volume (kJ/m3)
q, heat flux (kW/m2)
R radius (mm m) ; resistance (mQ)
T temperature (C)
t time (ms I s)
V voltage (V); volume (mm3 m3)
Greek letters
P
Superscript
Superscript
*
density (kg/m3)
surface tension (N/m)
time factor (s)
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
The experimental loop system used in the current work is
showed in the schematic diagram Fig.1, deionized water
was selected as the working fluid and had been heated for
about 24 hours to eliminate the effects of noncondensing
gas. A pump was used realize forced convection in
experimental loop system.
An NV2118 Venturi flow meter was adopted to measure
the mass flux and it can be used in a wide range (351189
kg/h with p=917.68 kg/m3) with an accuracy of +0.5% of
the respective full scale.
And there are temperature and pressure measuring before
the Venturi flow meter by calibrated Ttype sheath
thermocouple with an accuracy of 0.5 C and a spring
manometer with an accuracy of 1%, respectively, so the
density of the water flowing through the Venturi flow meter
can be corrected and the exact mass flux through the loop
system can be obtained consequently.
1.2 Test section
heating side
oulet pressure
measruing hole
insulating part
gasket
substrate of heater stri
tempreture measuring
hole of heater
dimensionless
Subsripts
atmosphere
bubble
system
sealing part
electrod
inlet pressure
measruing hole
1 Experimental Facility
1.1 Test loop configuration
Valve 2 water
inlet
Preheater
Legend
Venture flow meter
Temperature measuring
SValve
P) Pressure measuring
Relief valve
Liquid level
Fig. 1 Schematic diagram of forced
convection loop for flow boiling
'

observation side
Slow direction
40
S" outlet
outlet mixing chamber
/ tempreture measuring
hole for fluid
heating strip
observing window
inlet
flow direction
 _inlet mixing chamber
narrow channel
Fig.2 Schematic diagram of visual test section
A rectangular narrow channel test section was fabricated
which consists of two thick stainless steel plate components,
as showing in Fig.2. The heating strip, with dimensions of
30 mm wide, 406 mm long and 2 mm thick, is made of
Cr20Ni80 material whose resistance is very stable with
varying temperature. For instance, if the temperature
coefficient of resistance of the heating strip is 1 at 200C
and then it is only 1.006 at 1000C, and 1.012 at 200 OC.
The resistance of the heating strip is 7.75 mQ at 250C
according to the 4wiresresistancemeasuring of Agilent
34970A. The gas of the narrow channel is 2 mm in present
work. The heating strip is powered by siliconcontrolled
D.C. power by the two electrodes on the left side of the test
section as showed in Fig.2.
1.3 Data acquisition
At present work, 1 mm sheath diameter Ttype
thermocouples (SICC) were adopted for temperature
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
measuring. All the Ttype thermocouples were calibrated by
a benchmark thermocouple to make sure all the Ttype
thermocouples are with an accuracy of 0.50C. As showed in
Fig.2, there are five temperature measuring holes for fluid
in observation side and other five for heating wall,
respectively. When measuring the fluid temperature, the
sensors of thermocouples were submerged in the fluid. For
the measuring of the heating wall temperature, the sensors
of thermocouples were attached to the heating strip. As
showed in Fig.2, the distance between two adjacent
thermocouples in both observation side and heating side of
the test section is 80 mm. The thermocouples measuring
heating wall temperature are at the center of a
corresponding observation windows, and the average of the
temperatures measured by the nearby two thermocouples
measuring fluid temperature is believed as the local fluid
temperature.
Regarding to the measuring of pressure in test section, the
pressure at the inlet was measured by a smallsmart
pressure transducer (Sicc, JXBY1700M) which can
translate the pressure signal to electric signal (D.C signal
range between 420 mA) by connecting the pressure sensor
to the inlet pressure measuring hole showed in Fig.2, with
accuracy of +0.25% of the full scale (10 bar).
As what is mentioned before, the resistance of heating strip
will change a little with the varying of temperature. After
correcting the temperature coefficient of resistance by the
instant measuring heating wall temperature, the exact
resistance R of the heating strip can be obtained. So the
power applied on the heating strip can be calculated by P =
V2/R if the voltage Vbetween the two electrodes are known.
In fact, during current study the instant voltage was
acquired by the Agilent 34970A Data Acquisition Unit.
To capture the fast boiling process, a high speed camera
(Redlake HG100K) was adopted in current study, and
10,000 fps (frame per second) capturing speed was adopted
in current study and the picture size is 256 pixelx 192 pixel.
When the system pressure is less than 10 bar, the area
captured by high speed camera is about 12.7 mmx9.5 mm
in the real dimensions, while it is about 4.7 mmx3.5 mm
when the system pressure is 10 bar. The 2nd window
(counted from the inlet of test section) was selected for
observation. MicroNikkon 60mm f/2.8D lens was
mounted on the high speed camera and the camera was
supposed to place in a position where the center line of the
lens was perpendicular to the heating surface in order to
reduce distortion because of refraction.
1.4 Working conditions
The working conditions carried out in present work is as
following,
System pressure: 110 bar
Mass flux: 86400 kg/(m2s)
Heat flux: 83.6188.6 kW/m2
Inlet temperature: 80154 C
2 Bubble growth in different system pressures
2.1 Bubble growth curves in different system
pressures
Fig.3 and Fig.4 are showing the typical bubble growing in
a p=l 3 bar, q84 5 kW/m2, G=399 6 kg/m2s, T108 8 OC, T=80 1 OC
b p=2 8 bar, q,85 1 kW/m2, G398 4kg/m2s, T,135 3 OC, T=110 2 OC
Fig.3 Classic bubble growths at lower system pressure
1 bar, 3 bar, 6 bar and 10 bar system pressures. As what we
can see from Fig.3 and Fig.4, the bubbles are growing at
the nucleation site when the system pressure is less than 6
bar, and the bubbles begin to shrink due to condensation
once they depart from nucleation site. While the bubbles
are sliding along heating wall when they are growing if the
system pressure is more than 6 bar. According to Fig.3 and
Fig.4, it is also very obvious that bubble size decreases
dramatically with increasing system pressure.
Fig. 5 is showing the bubble growth curve with different
system pressures, ranging from 110 bar; and for those
bubbles growing with about 1 or 3 bar system pressure,
bubbles are growing at the nucleation sites. With identical
other working conditions except system pressure which
varies from 1.2 bar to 2.9 bar (marked as "la" and "3a" in
Fig.5a, respectively), bubble size and bubble grow time
shrink significantly with system pressure, as what we can
see in Fig.5a; it is also shown that bubble growth rate (the
slop of curve) decreases with increasing system pressure in
Fig.5a. The maximum bubble radius reached in Run No. la
is 50% greater than that of Run No. 3a. Almost the same
phenomena is observed when system pressure raised from
6 bar to 10 bar as shown in Fig.5a; and the bubble radius of
Run. No.6b is about 60% greater than that of Run No.lOb.
What should be noted is that the bubble grows when it is
sliding along heating wall in Run No. 6b and 10b. When
comparing bubble growths in 1 bar, 6 bar and 10 bar
system pressure with other working conditions almost the
same, the effect of system pressure on bubble growth is
more obvious, as shown in Fig.5b. We can see that the
bubble radius at 1.5 ms of bubble growth time in Run No.
6c is about 80% less than that of Run No. Ic and 90% is
a p=6 Ibar, q58 2 kW/m2, G=76 6
kg/m2s, T 162 5 OC, T,=131 7 C
b p=9 9bar, q,84 3 kW/m2, G=99 9
kg/m2s, T,185 2 OC, TI=144 2 C
c p=10 2 bar, qa152 1 kW/m2, G=89 9 d p=9 6 bar, q148 5 kW/mz, G=203 4
kg/m2s, T 188 0C, T,=146 0C kg/m2s, T,186 30C, TI=147 4C
A : Sliding bubble growing
Fig. 4 bubble growth at higher pressure which sliding on
heating wall
09
o,
07 9la, p,= 2 bar, qw=1490kW/m, G=384 5 kg/m2s
06 R B3a, p,=2 9 bar, qw=149 4 kW/m2, G400 0 kg/m2s
mm 05 A6b, p,=6 5 bar, q,=84 1 kW/m2, G=86 7 kg/m2s
S4 xlOb, p,=9 9 bar, q,=84 3 kW/m2, G=99 8 kg/m2s
03
02 A A A 
01 wXXX  
0
0 2 4 6 8 10
t ms
1 
09
08
07
R 06
mm 05
04
Fig.5a
e 1c, p,=1 2 bar, q,=84 1 kW/m2, G=214 6 kg/m2S
B 6c, p=6 2 bar, q,=83 5 kW/m2, G228 6 kg/m2
A 10c, p,=9 9 bar, q=83 7kW/m2, G193 1 kg/m2s
(D
D
9
r
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
reached in Run No. 10c, which suggests that the effect of
system pressure on bubble growth is significant and this
effect decreases with increasing system pressure.
2.2 Nondimension bubble growth in different
system pressures
For simplification of data analyzing, bubble radius is
nondimensionalized by half Laplace number, La/2, as
following,
R* =R/(La/2) (1)
La = [c/1((p, P)g)11/2 (2)
Where R is bubble radius; c is surface tension force; pl
and pv is liquid density and vapor density, respectively.
And nondimension bubble growth time is defined by time
factor, J, as following,
t' =1/lxt (3)
4 La
S= p () 3 h, / q (4)
3 2
Where hfg is latent heat of working fluid; q, is heat flux.
According to Eq.(4), it is clear that 4 indicates the time
needed for vaporizing a liquid drop with radius of La/2
when heating power is equal to that of unit heating wall
with heat flux q,. It is obvious that 4 is dependent on liquid
properties and power of heating wall.
Nondimension bubble growth curves can be predicted
very well by power curve model, namely,
R* =kx t (5)
And all predicted and experimental results of
nondimension bubble growth curves are shown in Fig.6
from where we can see that the predicted nondimension
bubble growth curves agree well with the experimental
measured nondimension bubble growth curves; and the
error of most data is within 15% with specified values of
k and n for different Runs as shown in Fig.6.
3 Theoretical analysis about effect of system
pressure on bubble growth
1
09
08
07
R' 06
05
04
03
02
01
0
Run k n
Ola 0.224, 0.547
S ,. 3a 0.247, 0.447
A6b 0.110, 0.161
~ 0 lO0b 0.030, 0.226
S xlc 0.374, 0.386
x6c 0.094, 0.154
+ 10c 0.040, 0.276
 Predicted curves with R'=kxt
 & A  
00
X X o0
0 10 20 30 40 50 60
e~s a   
A
0 3 6 9 12 15
t ms
Fig.5b
Fig. 5 Bubble growths with different system
pressure
Fig.6 Bubble growths with different system
pressure
As mentioned before, bubble growth rate and bubble size
will decrease significantly with increasing system pressure.
According the nondimension bubble growths shown in
Fig.6, one also can see that the coefficient k of power
model (Eq.5) decreases with increasing system pressure;
when Run changes from Ic to 6c and 10c, k decreases by
75% and 89%, respectively. However, the coefficient n
shows uncertain trend with increasing system pressure.
According to the analysis of microlayer evaporation model
and relaxation model for bubble growth, coefficient k of
power model for predicting bubble growth will be affected
by heating conditions of heating wall (Sjoerd, et al, 1979)
significantly, such as heat flux, heating wall superheat, and
the coefficient k reflects bubble growth at a certain extend.
While it is more obvious that bubble growth is affected by
system pressure due to latent heat needed for a bubble with
unit volume, Qb, is affected by system pressure
significantly. When water is selected as working fluid,
water vapor density will increase with increasing system
pressure. In that case Qb of vapor bubble will increase with
system pressure dramatically although latent heat of water,
hfg, decreases with system pressure slightly too, as shown
in Fig.7.
Assuming that the latent heat needed for a bubble with unit
volume in 1 bar system pressure (po) is Qb(po), then one can
defined the latent heat factor, kQb at ps system pressure as,
k (ps)= Qb( ) / Q (o) (6)
kQb(Ps) indicates the latent heat needed for a bubble with
unit volume at system pressure ps based on that at
atmosphere pressure po. We also can see from Fig.7 that kQb
increases with system pressure significantly.
For a bubble growing system with heating wall surface A,
heat flux q,, and system pressure ps, let us assume that the
fraction of total power of heating wall for a certain bubble
growing is r7b(Ps). According to energy balance, the bubble
volume after tb bubble growth time can be written as,
S. A tb r, (ps)
k (ps) Qb (o)
In the same bubble growing system with the same q, and A,
and the same bubble growing time tb, the ratio of bubble
volume at ps system pressure to that at po (1 bar) system
pressure is as following,
k, ( Vbb Ps (8)
b (po) k~ (Ps) qb (Po)
If the heat transferring situation is exactly the same at
different system pressures, one can reach,
'b (P) = rb (P0) (9)
Upon Eq.(9), Eq.(8) can be written as,
k,,(ps)= Vb(ps)/Vb (p)=l /k (p) (10)
14000
12000
10000
8000
Qb
kJ/m 6000
4000
2000
Qb
kQb
0 1 2 3 4 5 6 7 8 9 10 11 12 13
p, bar
Fig. 7 Evaporation heat of bubble with unit volume
varying with system pressure
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
which means that bubble volume reached after a certain
bubble growing time varies inversely with latent heat
needed for a bubble with unit volume at system pressure ps.
However, according to experimental research as shown in
Fig.5b, with identical working conditions except system
pressure, at 1 ms bubble growth time the bubble radius is
0.89 mm, 0.16 mm and 0.08 mm at system pressure of 1
bar, 6 bar and 10 bar, respectively. In that cast, the
following results can be reached,
kv (6) = 0.0058 <<1/kQb (6) 0.2 (11)
kb (10) 0.00073 <
We can see that Eq.(ll) and Eq.(12) do not agree with
Eq.(10). So the assuming of Eq.(9) is impossible and the
following equation should be met in order to meet Eq(ll)
and Eq(12),
rb (Ps) b o) (13)
It suggests that the heat transferring situation is quite
different at different system pressures; and at higher system
pressure, the fraction of total power of heating wall for a
certain bubble growing is much lower. Because bubble
growth size decreases significantly with increasing system
pressure; and when the system pressure reaches a certain
value (6 bar as found according to current experimental
study), bubble grows when sliding along heating wall. All
this will lead to less contact surface between bubble base
and heating wall, and less bubble interface surface is
immerged in the thermal boundary layer, which will
diminish heat transferring from heating wall to the bubble
growing on heating wall. And this would be a good
explanation for the strong effect of system pressure on
bubble growth and why coefficient k decreases with
increasing system pressure.
4 Conclusions
According to current study on bubble growth in narrow
rectangular channel under different system pressures,
including experimental investigation and theoretical
analysis, there are a few conclusions obtained.
(1) According to experimental observation, it was
found that the bubble is growing at nucleation site at lower
system pressure (13 bar), while bubble is growing when
sliding along the heating wall under higher system pressure
(610 bar). Bubble size and growth rate diminish with
increasing system pressure.
(2) After nondimensionalizing bubble radius and
bubble growth time with half Laplace number, La/2, and
time factor, 4, respectively, power law can predict
nondimension bubble growth very well although the
system pressure ranges from 1 to 10 bar where different
bubble growing mode are included. And it was found that
the coefficient k of power model decreases with increasing
system pressure.
(3) Latent heat needed for a bubble with unit
volume, Qb, and latent heat factor, kQb, defined based on 1
bar system pressure increase significantly with increasing
system pressure, which will result in smaller bubble size
and lower bubble growth rate with coincident other
working conditions. And it was also found that the heat
transfer situation is quite different under different system
pressures, and the fraction of total power applied to the
heating wall for a certain bubble growing, 7b, is much less
at if the system pressure is higher.
Acknowledgements
The authors are grateful for the support of the National
Science Foundation of China (No.50406012) and the
support of the Researching Foundation of the Laboratory of
Bubble Physics and Nature Circulation of China at contract
of9140C7101020802.
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7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
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