Proceedings of ICMM2005
3rd International Conference on Microchannels and Minichannels
June 13-15, 2005, Toronto, Ontario, Canada
Paper No. ICMM2005-75110
AN EXPERIMENTAL INVESTIGATION INTO THE EFFECT OF SURFACTANTS ON AIR-WATER
TWO-PHASE FLOW IN MINICHANNELS
Nathan J. English
Rochester Institute of Technology
Satish G. Kandlikar
Rochester Institute of Technology
ABSTRACT
The complex interfacial phenomena involved in two-phase
gas-liquid flow have defied mathematical simplification and
modeling. However, the systems are used in heat exchangers,
condensers, chemical processing plants, nuclear reactor
systems, and fuel cells. The present work considers a 1 mm
square minichannel and adiabatic flows corresponding to
practical PEM fuel cell conditions. Pressure drop data is
collected over mass fluxes of 4.0 to 33.6 kg/m2s, which
correspond to superficial gas and liquid velocities of 3.19-10
m/s and 0.001-0.02 m/s respectively. The experiments are
repeated with water of reduced surface tension, caused by the
addition of surfactant, in order to quantify the surface tension
effects, as it is recognized that surface tension is an important
parameter for two-phase flow in minichannels. The accuracy
of various two-phase pressure drop models is evaluated. A new
model for laminar-laminar flow is developed.
NOMENCLATURE
Acs
a
b
Bo
C
Cs
C*
Ca
Cross-sectional area, m2
Channel width, m
Channel height, m
Bond number (non-dimensional), (ρ L − ρ G )gLc σ ,
note that Chen et al. (2002, 2001) use Lc = Dh/2,
whereas many authors use Lc = Dh.
Chisholm’s parameter (non-dimensional)
Surfactant concentration calculated on a % weight
basis (non-dimensional)
Modified Chisholm’s parameter (non-dimensional)
Capillary number (non-dimensional),
2
µG ρσ = We Re
Froude number (non-dimensional), G
Gravitational acceleration, m/s2
Mass flux, kg/m2s
j
L
Lc
Le
Superficial velocity, m/s, V& A cs
Length, m
Characteristic Length, m
Entrance length, m, Le ≅ 0.06 Re Dh
m&
N conf
Mass flow rate, kg/s
Confinement number (non-dimensional),
P
Pw
Re
(σ/g(ρL-ρG))0.5/Dh
Pressure, Pa
Wetted perimeter, m
Reynolds number (non-dimensional),
V&
Volumetric flow rate, m3/s
We
X
x
Weber number (non-dimensional), DhG ρσ
Lockhart-Martinelli Parameter (non-dimensional)
& G (m& G + m& L )
Mass quality (non-dimensional), m
GDh µ
2
Greek Symbols
D
Diameter, m
E, F, H Terms of the Friedel (1980) correlation
f
Friction factor (non-dimensional)
Fr
g
G
2
α
β
∆P
µ
Ω
ρ
σ
φ
Aspect ratio (non-dimensional), b/a assuming b < a
Void fraction (non-dimensional)
Change in pressure, Pa
Viscosity, kg/ms
Modification factor of Chen et al. (2002), (2001) (nondimensional)
Density, kg/m3
Surface tension, N/m
Two-phase friction factor (non-dimensional)
Subscripts
gDh ρ
2
G
Go
H
Calculated with the properties of the gas phase
Calculated as if the total mass flux has the fluid
properties of the gas phase
Homogenous
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Copyright © 2005 by ASME
h
L
Lo
T
Hydraulic
Calculated with the properties of the liquid phase
Calculated as if the total mass flux has the fluid
properties of the liquid phase
Two phase
INTRODUCTION
The behavior of single-phase internal flow is well
understood and predictable over a wide range of operating
conditions. Two-phase flows are also quite common, but are
not as well understood and involve significant error in
predictability. The fundamental physics has proved too
complicated to characterize by simplified mathematical models
of the governing equations. Likewise, the use of computers for
computational fluid dynamics (CFD) analysis has produced less
than satisfying results. Therefore, emphasis is placed on
experimentation derived from theoretical considerations.
The majority of the experimentation in two-phase flow
uses large diameter channels. It is recognized that as one
moves to flow in mini and microchannels the influence of
surface tension tends to increase, while that of gravity
decreases, which causes models intended for larger channels to
inaccurately predict the flow behavior. Such technologies as
compact heat exchangers, refrigeration systems, and micro-tube
condensers are progressing to smaller channels. Literature
specific to minichannels often focuses on flow regime analysis,
refrigerant flow, low mass quality flow, and relatively high
mass fluxes. Even for these, there is a dearth of quality data
published with enough information to be useable for
comparison and analysis. They are often based on limited
ranges of operating conditions and are not externally verified.
Furthermore, even though the effect of surface tension is
recognized it is not usually targeted in experimentation.
The present work focuses on an area with little
published literature, air-water adiabatic flow with low mass
fluxes (GT < 50 kg/m2s) and high mass quality (x > 0.1). For
industrial relevance, the flow conditions are chosen from works
done on proton exchange membrane (PEM) fuel cells. In a
PEM fuel cell, minichannels (typically rectangular, trapezoidal,
or semi-circular) are used as structural elements, as well as a
means of reactant fuel delivery. In the PEM fuel cell cathode,
water is produced along one wall of the channel and is pushed
by flowing air to create a two-phase flow. One would like to be
able to predict the channel pressure drop and flow conditions in
order to optimize the system and ensure adequate reactant
delivery. There is inherent heat transfer, mass transfer,
multiple materials, multiple channels and channel bends, but
the system will be simplified in order to focus on the two-phase
pressure drop and surface tension effects.
It should be noted that the term channel will be
considered equivalent to and substituted for words such as pipe
and tube. The channel classification developed by Kandlikar
and Grande (2002) is used and considers minichannels to be
within the range of 3 mm ≥ Dh > 200 µm. The channel used in
this investigation is nominally square and it is expected that the
flow behavior will be slightly different from most literature,
which often use non-square geometries (usually circular or high
aspect ratio rectangular).
OBJECTIVES
1. Collect two-phase pressure drop data under conditions
relevant to PEM fuel cells.
2. Use a surfactant to sequentially reduce the surface
tension and collect additional pressure drop data with
the new solutions.
3. Evaluate published models for adequate prediction of
the pressure drop and accurate representation of the
surface tension effects.
4. Make suggestions for improvement of the published
models.
OVERVIEW OF TWO-PHASE FLOW RESEARCH
Typical two-phase pressure drop models follow either of
two methods. The first correlates the two-phase pressure drop
to the single-phase pressure drops. This is accomplished by
either calculating the single-phase pressure drop as if one of the
phases is flowing alone in the channel at its mass flux (∆PL,
∆PG), or by using the total mass flux but using the fluid
properties of only one of the single phases (∆PLo, ∆PGo). The
second method collects non-dimensional numbers that involve
characteristic flow parameters and gives them correlated weight
in predicting the pressure drop. Using either method, a
researcher might refine the model by targeting a specific flow
regime.
Lockhart and Martinelli (1949) related the two-phase
pressure drop to the single-phase pressure drops with the
Lockhart-Martinelli Parameter, X:
X2 =
∆PL
∆PG
(1)
∆PT = φG2 ∆PG = φ L2 ∆PL
(2)
The equations were presented in conjunction with tables that
correlated the two-phase friction factors φG and φ L with X.
The equation used to calculate the single phase pressure drops
can be written as:
2 LµG
Dh2 ρ
4A
2ab
Dh = cs =
(a + b )
Pw
∆P = f Re
(3)
(4)
The friction factor defined by Kakac et al. (1987) is used to
calculate fRe as it applies to smooth rectangular channels under
laminar flow and is within 0.05% of the tabulated values:
1 − 1.3553α + 1.9467α 2 − 1.7012α 3 
 (5)
f Re = 24
4
5

 + 0.9564α − 0.2537α

The Lockhart and Martinelli tables are cumbersome to use
for engineering calculations, so Chisholm (1967) defined
approximate equations using the parameter C, which are
considered accurate for engineering predictions in large
diameter channels:
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Copyright © 2005 by ASME
C
1
+ 2
X X
2
φG = 1 + CX + X 2
φL2 = 1 +
(7)
Table 1: Values of Chisholm’s parameter C.
Laminar Liquid, Laminar Gas
Chisholm’s
Parameter C
5
Turbulent Liquid, Laminar Gas
10
Laminar Liquid, Turbulent Gas
12
Turbulent Liquid, Turbulent Gas
21*
µH =
xρ L + (1 − x )ρG
µ L µG
xµ L + (1 − x )µG
(8)
(9)
Beattie and Whalley (1982) modified the two-phase
homogenous viscosity to include consideration of the void
fraction:
ρL x
ρ L x + ρ G (1 − x )
µ H = µ L (1 − β )(1 + 2.5β ) + µ G β
β=
(10)
(11)
Friedel (1980) considered a wide body of experimental
data and developed a correlation weighted with the nondimensional Froude (16) and Weber (17) numbers (which
assume a homogenous two-phase density):
3.24 FH
FrT0.045WeT0.035
ρ f
2
E = (1 − x ) + x 2 L Go
ρ G f Lo
φ Lo2 = E +
F = x 0.78 (1 − x )
0.224
(12)
0.19
GT2 Dh
0.7
(15)
(16)
(17)
ρ Hσ
Other publications have attempted a similar method as
Friedel and used such non-dimensional groups as the
Confinement number (18) and Capillary number (19). The
Confinement number is a re-working of the Bond number Eq.
(27). It is important to note that the Weber, Confinement,
Capillary, and Bond (though not the Froude) numbers include
surface tension, and could prove useful in trying to quantify the
surface tension effects.


σ


g (ρ L − ρ G ) 

N conf =
Dh
We µG
Ca =
=
Re σρ
The homogenous flow model differs from the other models
in that it assumes the two-phase flow is a single-phase flow
having flow properties that are an average of the individual
phase properties. The total mass flux is used along with
averaging equations for density and viscosity:
ρ L ρG
 µG

 µL
WeT =
*Chisholm (1973)
ρH =
0.91
  µG 
 1 −

µ
L 
 
2
GT
FrT =
gDh ρ H2
(6)
The values of C appear in Table 1 and depend on whether the
single-phase flows are turbulent or laminar, as characterized by
the superficial Reynolds number. Hereafter, references to the
Lockhart-Martinelli model will assume the Chisholm
approximation.
Two-Phase Flow Characteristics
ρ 
H =  L 
 ρG 
0.5
(18)
(19)
It was recognized by the research of Chen et al. (2002),
Coleman and Garimella (1998), Fukano and Kariyasaki (1993),
Garimella (2004), and Triplett et al. (1999) that the surface
tension force becomes important for channels of hydraulic
diameter less than 10 mm (or rectangular channels with small
gap widths) and dominate below 5 mm. Often a bubble will not
rise solely from buoyancy below these dimensions. The
models developed for larger diameters give too much influence
to gravity and too little to surface tension and prove inaccurate
for minichannels.
However, little minichannel research
actually targets surface tension as an experimental parameter.
Weisman et al. (1979) investigated the effect of changing
liquid properties by independently altering the viscosity,
density and surface tension of water in an air-water system.
Unfortunately, the smallest diameter considered was 120 mm.
Therefore, they concluded that surface tension has little effect
on the pressure drop in two-phase flow.
Barajas and Panton (1993) considered the effect of
wettability by changing their channel material. They used
several partially wetting materials and one partially non-wetting
material. They found little difference among the partially
wetting materials, but a significant shift in flow regime
transitions for the partially non-wetting material.
Mishima and Hibiki (1996) modified the Chisholm
correlation to better match their data for minichannels:
C = 21(1 − e −333 D )
C = 21 1 − e −319 Dh
(13)
(
(14)
)
(20)
(21)
Equations (20) and (21) are for circular and non-circular
geometries respectively.
The equations create a direct
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Copyright © 2005 by ASME
dependence of the Chisholm parameter on channel size. For
channels of 0.01 m diameter or greater, the value approaches to
the turbulent-turbulent case given by Chisholm. The new
equations remove the dependence on superficial velocity, j, and
Reynolds number, as only the turbulent-turbulent value is used.
Figure 1 is a plot of the Mishima-Hibiki value for C as a
function of channel diameter in mm.
Mishima and Hibiki C Value
25
20
15
10
5
0
0
5
10
15
20
25
Hydraulic Diameter in mm
Fig. 1: Mishima and Hibiki modified value for C.
Rather than modify the Chisholm equation, Chen et al.
(2002), (2001) added a multiplication factor to the
Homogenous and Friedel correlations. Equation (22) is used
with Eq. (23) in the 2002 Homogenous modification and Eq.
(24) in the 2001 Homogenous modification. Equation (25) is
used with Eq. (26) for the 2001 Friedel modification. This
correction factor includes weighted non-dimensional groups
and gives recognition to the surface tension effects. Note that
they used Dh/2 for the Bond number characteristic length, but
many works use only Dh.
∆P = Ω∆PH
Ω=
(22)
−0.5
0.85 − 0.082 Bo
+
0.5
0.57 + 0.004 ReGo
+ 0.04 Fr −1
(
)
100 mm
Air Inlet
)
∆P = Ω∆PFriedel
 0.0333 Re 0Lo.45
for Bo < 2.5
 0.09
 Re G 1 + 0.4e − Bo
Ω=
We 0.2

for Bo ≥ 2.5
 (2.5 + 0.06 Bo )
(ρ − ρ G )g (Dh 2)2
Bo = L
σ
(
EXPERIMENTAL SETUP
Lexan is the selected test section material due to its
machineability and optical qualities. The channel is 321 mm
long and has two pressure taps that are centered 177.8 mm
apart. The first pressure tap is 110 mm downstream from the
entrance of the air and 100 mm from the entrance of the water.
Typical pressure tap lengths are between 200 – 300 mm in
published literature [Mishima and Hibiki 1996, Bao et al. 2000,
Zhao and Bi 2000, Barajas and Panton 1992, and Yang and
Shieh (2001)], however the present section is longer than Chen
et al. (2002) at 150 mm and Damianides (1987) at 60 mm.
These two works are very relevant to the present work, and the
length is close to the range found in the other works. Figure 2
is a cross-sectional view of the channel.
(23)
80We −1.6 + 1.76 Fr 0.068 + ln (ReGo ) − 3.34
1 + e(8.5 −1000 ρ A ρW )
1 + 0.2 − 0.9e − Bo
for Bo < 2.5
(24)
Ω=
0.2
Bo 0.3
− Bo
− 0 .9 e
for Bo ≥ 2.5
 1 + We e
(
In order to acceptably narrow the experimental focus and
provide industrial relevance, the flow conditions from PEM
fuel cells are considered. Trabold (2004) emphasized the need
for PEM fuel cell cathode flow to remain in the annular flow
regime, so that enough oxygen reaches the catalyst sites and to
avoid parallel flow mal-distribution problems. To achieve this,
he recommended maintaining a superficial air velocity of 5-6
m/s. The rate of water production is only dependant on the
chemical reactions, however the cells are not always operated
optimally and there is localized buildup in bends. Typically,
the mass quality is greater than 0.1 and often very close to one.
Wheeler et al. (2001) considered a slightly different
system than that described by Trabold. However, it was reemphasized that annular flow be maintained. A superficial air
velocity of 6 m/s was recommended as a minimum, though the
group investigated much larger velocities as well.
Ide and Fukano (2003) studied the flow of two-phase
air-water surfactant solutions and the surfactant’s impact on
flow patterns and pressure drop. They used a rectangular 1.0
mm x 10.0 mm channel and reduced the surface tension to
0.034 N/m. They found that the addition of surfactant caused
the pressure drop to increase for all the concentrations tested.
However, they also observed significant foaming of the fluid
caused by the surfactant addition. Therefore, the impact of the
surfactant on surface tension was not isolated from its impact
on the flow pattern and other fluid behavior.
)
(25)
(26)
(27)
177.8 mm
33.2 mm
Pressure Taps
Outlet
Water Inlet
Fig. 2: Geometry of the test section (not to scale).
The entrance and exit lengths are more of a concern
than the total channel length, as the flow pattern might be
developing or liquid might be held up at the exit. However,
due to the small dimensions and low flow rates there is a high
viscous damping that reduces the entrance length. Even for the
highest air flow rate tested, the single-phase entrance length
(Le) would be only 37.7 mm. Damianides found 100Dh to be
an acceptable entrance length for minichannels, independent of
the geometry of the entrance section, and indicates that even as
little as 20Dh may be acceptable. Therefore, there is 100Dh
distance for entrance effects and flow calming and a 33.2 mm
exit section. The last 2 mm of the channel bottom are removed
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Copyright © 2005 by ASME
and lead to an expanded chamber below the channel. From
there, the fluids drain from the test section and any liquid
buildup is in the chamber rather than the channel. The large
differential between the gas and liquid flow rates also reduces
the chance of buildup.
Two more pieces of lexan are sandwiched around the
center two and clamps compress the group. The edges of the
center pieces are machined to receive a strip of rubber that
compresses and prevents leakage. The pressure taps are 0.396
mm round holes that expand to fit aluminum tubing that
connects to opposing sides of a differential pressure transducer.
The reading from this transducer is the frictional pressure drop
along that section of channel, as the drops due to acceleration
and gravity are negligible.
Air is supplied by a pressurized tank and controlled by
a variable area flow meter. The inlet temperature and pressure
are recorded. Water is gravity fed and controlled by a precision
low flow variable area flow meter. All of the experiments use
distilled water that is degassed using the method of Kandlikar
et al. (2002).
At a low concentration, surfactants are capable of
reducing the surface tension of a liquid while negligibly
influencing other properties such as density and viscosity. Two
key drawbacks to their use are that they change the optical
qualities of the liquid and can cause it to foam. The first
influences photography of the flow, but should not influence
the experimental results. The second causes fluid behavior
uncharacteristic of water and is not acceptable. Upon the
recommendation of Shurell (2004), the surfactant TritonTM DF12 is used as it produces negligible foaming at room
temperature. It is capable of reducing the surface tension of
water to a static 0.034 N/m and dynamic 0.046 N/m at a
concentration of 0.1% by weight. Concentrations of 0.0208,
0.0369, 0.0719, and 0.1089% were used to achieve the static
surface tensions and three-phase contact angles listed in Table
2. Only the advancing contact angle is listed as the receding
contact angle proved so low as to be impossible to measure for
all cases (less than 5o). A Fischer “Surface Tensiomat” Model
21 is used for surface tension measurements with an accuracy
of 8%.
The standard deviation for the contact angle
measurement is 7o, so numerous measurements were taken to
reduce the uncertainty to ±0.5o.
Table 2: Measured values of surface tension and contact angle
for pure water and the surfactant solutions as designated by the
concentration, Cs, of TritonTM DF-12.
Measured Property
Water
0.0208
0.0369
0.0719
0.1089
Surface Tension (N/m)
0.073
0.048
0.0411
0.0354
0.0338
72
48
40
35
28
Advancing Contact
Angle (deg.)
Experimental Uncertainties
The channel dimensions are measured to be 1.124 mm
± 0.008 mm and 0.93 mm ± 0.02 mm for width and height
respectively, which result in a hydraulic diameter of 1.018 mm
and an aspect ratio of 0.827. There is a 5% uncertainty in the
fluid temperatures. The uncertainty in liquid flow rate varies
between 0.82-8.6%. The uncertainty in air flow rate varies
between 0.5-1.5%. The pressure drop length is measured to be
171.8 mm ± 0.6 mm. The error in pressure drop measurement
is less than 1.0% and if it is incorporated into the plots as error
bars on the data then the data points are larger than the error
bars themselves. The uncertainty in liquid flow rate impacts
the calculation of mass quality and so can be included as x-axis
error bars on the pressure drop data. The other uncertainties do
not impact the pressure drop reading, however they have a
significant effect on the calculation of the pressure drop
prediction models.
Therefore, the uncertainties can be
propagated through those models to find their minimum and
maximum predictions. Figure 9 is an example of applying the
uncertainties to the proposed model.
EXPERIMENTAL PROCEDURE
The test section is first cleaned with methanol and
distilled water to reduce contamination. Once fully assembled,
the air flow is regulated to the desired rate and the experiments
begun. The air flow rate and surfactant concentration are held
constant for each run, but are varied between runs. The
pressure drop is recorded for air flowing alone in the channel,
and then with successively greater water flow rates. The test
section is fully dried between runs, as any residual liquid leads
to a greater actual superficial liquid velocity than recorded.
Also, the liquid flow rate is increased slowly and given time to
reach equilibrium within the channel before taking each data
point, so as to avoid transient situations and to promote
comparability between runs. The pressure readings are time
averaged over a minute of recorded values, though the
fluctuations are typically slight.
To meet the recommendations of Trabold (2004) and
Wheeler et al. (2001), the air flow rate is set to target
superficial velocities of 4, 6, 8, and 10 m/s. Runs are
performed at these rates for pure water and for the surfactant
solution with the highest concentration. For the lower
concentration solutions, the runs are only performed with 6 and
10 m/s superficial air velocities targeted. The water flow rates
are selected to give an even distribution of data points for a plot
of pressure drop as a function of mass quality. They fall within
a mass quality range of 0.15 to 0.98, which covers the typical
operating range of PEM fuel cells. The range of room
temperature operating conditions can be seen in Table 3.
Table 3: Range of operating conditions encountered in
experimental data collection.
Mass Flux (kg/m2s)
Superficial Velocity (m/s)
Superficial Reynolds Number
Air
4.03-12.0
3.19-10.06
211-654
Water
0.49-21.6
0.0005-0.0217
0.56-24.6
RESULTS AND DISCUSSION
Single Phase Validation
In order to ensure that the test setup is performing
acceptably, single phase air data is collected over the relevant
range of air flow rates as seen in Fig. 3. The recorded pressure
drop is used to calculate the friction factor and is compared to
the theoretical prediction. There is an average 10.7% deviation
between the data and theoretical prediction, however the data
relies on measured values for the channel geometry, ambient
temperatures and fluid flow rates. If the measurement
uncertainty is included then there is good agreement between
the theoretical and experimental and the test setup is considered
5
Copyright © 2005 by ASME
to be operating acceptably. Any remaining disparity may be
attributed to slight imperfections in test section machining, and
minor fluctuations in channel size resulting from clamping the
fourth channel wall to the other three. In the following plots of
experimental two-phase data, the single phase data will be
included as the value at a mass quality of one.
also impacts whether that droplet spreads over the surface or
not. Also, it acts as a drag force between the gas and liquid.
The importance of the surface tension can be seen in the
pertinent non-dimensional numbers. The Froude Eq. (16),
Weber Eq. (17), Capillary Eq. (19) and Bond Eq. (27) numbers
are calculated over the range of experimental conditions
considered and are presented in Table 4.
0.10
Experimental
0.09
Table 4: Characteristic non-dimensional numbers calculated
over the experimental range for pure water and the surfactant
solutions with the lowest and highest concentrations of
TritonTM DF-12.
Theoretical
0.08
f
0.07
0.06
Cs
Fr
We
Ca
Bo
0.05
Pure Water
3206-9100
0.589-4.25
0.001-0.007
0.0353
0.04
0.0208
3235-9054
0.901-5.98
0.002-0.0092
0.0527
0.03
0.1089
3206-9055
1.252-8.60
0.003-0.013
0.0745
0.02
0.00
190
290
390
490
590
690
Reynolds Number
Fig. 3: Single phase air data taken over the experimental range
and compared to the theoretical values.
Flow Pattern Considerations
High speed video photography of the flow confirmed
that it is typically in the annular flow regime. However, a
stratified flow regime is occasionally observed in the corners of
the channel, though with no discernable pattern as to when it
occurs. For pure water, the stratified flow exhibits a discrete
three-phase contact line around dry wall patches. For the
surfactant solutions, there is no distinct three-phase contact line
and no clear incidence of stratified flow. No plug or slug flow
is observed under equilibrium conditions, however it is possible
to instigate them by quickly changing one or both of the flow
rates.
Almost all of the flow maps published under
conditions similar to those presently considered do not present
experimental data for such low liquid flow rates. The closest
are Damianides (1987) and Yang and Shieh (2001) which
predicted slug flow, though theirs were taken from circular
channels. Barajas and Panton (1993) and Coleman and
Garimella (1999) predicted a transition from slug to wavy flow
with increasing gas superficial velocity. Mishima and Hibiki
(1996) predicted a similar transition, but from churn to annular
flow. Bao et al. (1994) predicted stratified flow throughout.
Less related works such as Fukano and Kariyasaki (1993),
Wambsganss et al. (1992), Xu et al. (1999), Lowry and Kawaji
(1988), Wilmarth and Ishii (1994), Garimella (2004), and
Kawahara et al. (2002) predicted a variety of slug, churn, and
annular flow. However, many do not predict annular flow until
the superficial gas velocity is greater than 10 m/s.
Effect of Surfactant
There is a general agreement in the literature
pertaining to two-phase flow in minichannels that the surface
tension has an increasing effect on the flow behavior and
pressure drop as the channel diameter decreases. The surface
tension essentially acts as a resistance to the motion of a water
droplet as it is being blown along a solid surface, however it
The Froude number shows that the inertial forces
clearly dominate the gravitational effects. The Weber number
shows that for pure water at the lowest mass fluxes the surface
tension has more impact than the inertial forces, but for most of
the cases the inertial dominates the surface tension. The
Capillary number shows that in all cases the surface tension
force dominates that of viscosity. The Bond number shows that
the surface tension force dominates that of buoyancy, though
slightly less so in the surfactant solutions.
The Lockhart-Martinelli, Mishima-Hibiki, and
Homogenous flow models do not make any adjustments for
surface tension and predict the same pressure drop for the
surfactant solutions as for pure water, whereas all of the other
models make adjustment for it. However, over all of the cases
tested and even for the highest concentration of surfactant there
was little change in the data, as can be seen in Fig. 4. There is
less than a 5% deviation between the runs, which is within the
experimental uncertainty and slight variations in operating
conditions between runs.
More importantly, there is no
discernable progression to either a greater or lesser pressure
drops. Similar results were found for the case of a 10 m/s
superficial air velocity.
4.8
Pure Water
0.0208
4.6
Pressure Drop (kPa/m)
0.01
0.0369
4.4
0.0719
0.1089
4.2
4.0
3.8
3.6
3.4
3.2
3.0
0.25
0.35
0.45
0.55
0.65
0.75
0.85
0.95
Mass Quality x
Fig. 4: Comparison of pressure drops using surfactant
solutions as designated by concentration, Cs, Ga = 6.75 kg/m2s,
Ja = 5.66 m/s.
6
Copyright © 2005 by ASME
Accuracy of the Published Two-Phase Models
Figure 5 plots the relevant two-phase pressure drop
prediction models using pure water over the full range of mass
qualities. The particular sample case is at a nominal superficial
air velocity of 6 m/s. The other cases show similar trends,
though with higher and lower predictions, as the predicted
pressure drops increase with air flow rate. The models exhibit
similar behavior to each other and appear to predict similar
values, however for mass qualities of over 0.5 one can see that
there is as much as a 300% difference between the model’s
predictions. The present work focuses on this high quality
region, where the relationship between pressure drop and
quality is relatively linear.
As discussed in the experimental setup section, the
setup is designed to account for entrance, exit, or other effects
due to single phase hydrodynamic development. Therefore, the
experimental data is the frictional pressure drop alone. Figure 6
represents the actual data taken for the same case as for Fig. 5
and compares the closest predictions. The Friedel correlation is
not included in the plots as it over predicts the data very
significantly. Models by Chisholm (1973), Tran et al. (2000),
and Wambsganss et al. (1992) were also tested, but have not
been discussed as they were found very inaccurate. The simple
to calculate Beattie and Whalley (1982) model predicts the
pressure drop very accurately with a mean absolute deviation of
7.5-16% and also matches the curve of the data well. The Chen
et al. (2002) and the Chen et al. (2001) Friedel modification
were reasonably accurate, with mean absolute deviations of 1640% and 22-28% respectively. These values are averaged over
each run and the deviation may be higher at a given point.
Although the Chen models have low errors, Fig. 6 shows that
they do not match the curve of the data well. Furthermore, as
scaling modifications of other models, they are intrinsically
more complicated. Similar results are found under all of the
experimental conditions tested.
50
Lockhart-Martinelli
Pressure Drop (kPa/m)
45
Mishima-Hibiki
Homogenous Flow
40
Chen et al. 2002
35
Chen et al. 2001
Chen Modified Friedel
30
Single Phase Air
25
20
15
10
5
0
0
0.2
0.4
0.6
Mass Quality x
0.8
1
Fig. 5: Two-phase pressure drop predictions of relevant
models, Ga = 6.75 kg/m2s, Ja = 5.66 m/s.
12
Pressure Drop (kPa/m)
The addition of surfactant proved inadequate for
quantifying the effect of surface tension on pressure drop under
the present test conditions. It is possible that the surface
tension was not reduced enough for an observable change. It is
more likely that the impact of the inertial effects, as well as the
annular flow conditions do not lend themselves to the exposure
of surface tension effects. In laminar annular flow, there is less
of an interaction between the two phases than in bubble, plug,
or slug flow, and therefore less opportunity for surface tension
to exhibit itself. High speed photography does reveal that the
surfactant solutions are more wetting and spread around the
channel walls without the distinct three-phase interface where
the surface tension would exert itself most. The effects might
be more discernable at lower mass qualities or under turbulent
flow conditions. Certainly, the flow rates of the fluids appear
to contribute much more significantly to the pressure drop than
surface tension. It is possible that the particular surfactant
chosen was inappropriate, however a run with the surfactant
TritonTM EF-19 at a concentration of 0.0968% by weight was
performed and yielded similar results as those of Fig. 4. As
surfactant behavior is known to be temperature dependant, and
the ambient temperature is not precisely controllable, it is
possible that slight deviations in the temperature impacted the
results.
A reduction in the experimental uncertainties,
particularly those in the channel dimensions and the fluid flow
rates, would certainly help in discerning a change.
The results disagree with the findings of Ide and
Fukano (2003). However, the surfactant they used produced
noticeable foaming that increased with surfactant concentration.
No foaming is observed in the present work, which allows the
surfactant solution to act like pure water but with a reduced
surface tension. It is plausible that their foaming caused the
increase in pressure drop that they observed rather than the
change in surface tension. Certainly the foaming would work
against any drag reduction between the two fluids caused by
decreasing the surface tension.
Lockhart-Martinelli
Mishima-Hibiki
Homogenous Flow
Chen et al. 2002
Chen et al. 2001
Chen Modified Friedel
Beattie-Whalley
Experimental Data
10
8
6
4
2
0
0.25
0.35
0.45
0.55
0.65
0.75
Mass Quality x
0.85
0.95
Fig. 6: Experimental data plotted with the two-phase pressure
drop predictions of relevant models, Ga = 6.75 kg/m2s, Ja = 5.66
m/s.
New Model Development
The Mishima-Hibiki model modifies the LockhartMartinelli model for flow in minichannels under the turbulentturbulent flow condition. In Fig. 6 the model is being applied
outside of its intended range of operability. Indeed, it leads to a
C value of 5.74, very close to Lockhart-Martinelli value,
though actually higher when it needs to be lower for
minichannels. It is proposed that the following model is
applicable to laminar-laminar two-phase flow in minichannels
and the associated frictional pressure drop:
(
C = 5 1 − e −319 Dh
7
)
(26)
Copyright © 2005 by ASME
(
C = 5 1 − e −333 D
)
(27)
Likewise, it is theorized that Eq. (29) is applicable for
rectangular minichannels under any flow conditions, though no
experiments have been conducted in the laminar-turbulent and
turbulent-laminar ranges:
(
)
C* = C 1 − e −319 Dh
φG2 = 1 + C * X + X 2
(28)
∆PT = φG2 ∆PG
(30)
(29)
Figure 7 represents how well the proposed model matches the
data of Fig. 6.
10
Lockhart-Martinelli
Homogenous Flow
Beattie-Whalley
Friedel
Mishima-Hibki
Chen et al. 2002
Chen et al. 2001
Chen et al. Friedel
Proposed Model
10
58.6
55.9
8
60.3
29.8
7.46
16.00
9.83
1602
53.2
16.10
48.9
22.5
1944
72.2
39.7
61.0
27.6
1746
61.4
22.2
55.5
24.3
2.4
4.5
3.3
G = 6.75, J = 5.66
G = 11.33, J = 9.51
English-Kandlikar J = 5.66
English-Kandlikar J = 9.51
7
6
5
4
3
2
Homogenous Flow
1
0.15
Chen et al. 2002
8
Chen Modified Friedel
0.25
0.35
7
Experimental Data
English-Kandlikar
6
5
0.45
0.55
0.65
0.75
12
0.45
0.55
0.65
0.75
Mass Quality x
0.85
0.95
Fig. 7: Experimental data plotted with the proposed model, Ga
= 6.75 kg/m2s, Ja = 5.66 m/s.
The modification results in a 2.4-4.5% deviation when
averaged over the runs and with a greatest local deviation of
11%. That is a significant improvement over the other models
as can be seen in Table 5. Though it becomes slightly less
accurate as the water flow rate increases, the curve matches the
data more closely than any other model. The proposed model
works well over the range of gas and liquid flow rates that were
tested experimentally in the 1 mm square minichannel.
Figure 8 gives a comparison of the 4 data sets
collected for pure water as designated by mass flux and
superficial velocity. The new model predictions are also
plotted. As expected, the primary dependence is on the flow
rates of both fluids. The pressure drop clearly increases for
increasing gas and liquid flow rates, and follows a curve very
close to that produced with the model.
Pressure Drop (kPa/m)
0.35
0.95
Fig. 8: Comparison of the pure water data with the proposed
model and Beattie and Whalley’s predictions for different mass
fluxes, G = Ga, J = Ja.
4
3
0.85
Mass Quality x
Beattie-Whalley
2
0.25
43.5
19.7
G = 3.78, J = 3.19
G = 9.03, J = 7.58
English-Kandlikar J = 3.19
English-Kandlikar J = 7.58
9
Mishima-Hibiki
9
Pressure Drop (kPa/m)
Table 5: Absolute mean discrepancies of the two-phase
pressure drop models when averaged over the experimental
runs and with the best models highlighted.
Model
Lowest %
Highest % Average %
Pressure Drop (kPa/m)
It includes Chisholm’s value of C for laminar-laminar flow and
Mishima-Hibiki’s channel diameter adjustment. This causes
the value of C to go to the Chisholm’s value of C for channels
of hydraulic diameter greater than 0.01 m. No experiments
were performed with circular channels, but extension to circular
geometries seems reasonable:
Experimental Data
English-Kandlikar 2005
10
Minimum Prediction
Maximum Prediction
8
6
4
2
0
0.25
0.35
0.45
0.55
0.65
0.75
0.85
0.95
Mass Quality x
Fig. 9: Comparison of the experimental data with the proposed
model’s predictions and including experimental uncertainties,
Ga = 6.75 kg/m2s, Ja = 5.66 m/s.
Figure 9 shows that the experimental uncertainties do
not negatively impact the pressure drop prediction of the
proposed model. If a similar plot is generated for the BeattieWhalley Homogenous Flow model, one can see that the
uncertainty decreases the inaccuracy of the model, but not to
the point that it is as good as the proposed model. Likewise,
using the other models and including the uncertainty decreases
their inaccuracies, but not significantly enough to change the
findings of the previous section.
8
Copyright © 2005 by ASME
The experimental repeatability is tested by evaluating
the pressure drop under identical conditions on different days
and after disassembling the test setup. It is not possible to
duplicate the same mass quality between runs, however the
pressure drop values and overall trends match within 3.0%.
CONCLUSIONS
1. An experimental investigation into two-phase air-water
pressure drop was conducted for a 1 mm square
minichannel under conditions comparable to those found
in a PEM fuel cell: air mass fluxes of 4-12 kg/m2s, water
mass fluxes of 0.49-22 kg/m2s, mass qualities of 0.15 to
0.98.
2. The effect of the surface tension was studied by adding
the surfactant TritonTM DF-12 and reducing the surface
tension to 0.034 N/m. No quantifiable change in
pressure drop was observed using the surfactant
solutions. Primarily annular flow, but also some
stratified flow was observed with pure water. The
surfactant enhanced wetting in the channel and
consistently produced only annular flow which
prevented the exposure of the surface tension effects due
to the lack of a three-phase contact line region.
3. Of the existing two-phase pressure drop prediction
models, the Beattie and Whalley (1982) modification of
the Homogenous Flow model matches the experimental
data very well with an average mean deviation of 9.8%.
4. The Chen et al. (2002) correlation, the Chen et al. (2001)
modified Friedel correlation and the Homogenous Flow
model correlated the data with mean deviations of 22%,
24% and 30% respectively.
5. The Mishima and Hibiki (1996) model is extended to
laminar-laminar flow by replacing their constant, 21,
with the Chisholm value for laminar-laminar flow of 5.
The new model predicts the data with an average
deviation of 3.3% and is considered applicable to similar
low mass fluxes, high mass qualities and annular flow.
FUTURE WORK
It would be worthwhile to extend the investigation of
surface tension effects to a wider range of flow conditions,
mass qualities, and flow regimes. This could include work on
circular channels, as well as, rectangular. However, it is
recommended that precision made channels be used due to the
significant influence of channel diameter. Wettability effects
could also be studied independently by using different channel
materials. Study of how reduced tension liquids perform in
multiple channels and parallel flow or in channels with bends
would be beneficial to the field of fuel cell research. More
experimentation with other fluids is needed to fully understand
the influence of the various fluid properties. It is recommended
that the proposed model be tested in the laminar-turbulent and
turbulent-laminar flow conditions, and at different mass fluxes
and qualities.
ACKNOWLEDGMENTS
The work was performed in the Thermal Analysis and
MicroFluidics Laboratory of the Mechanical Engineering
Department of the Rochester Institute of Technology.
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