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An Experimental Investigation into the Effect of
Surfactants on Air-Water Two-Phase Flow in
Minichannels
a
a
Nathan J. English ; Satish G. Kandlikar
a
Mechanical Engineering Department, Thermal Analysis and Microfluidics
Laboratory, Rochester Institute of Technology. Rochester, New York. USA
To cite this Article: English, Nathan J. and Kandlikar, Satish G. , 'An Experimental
Investigation into the Effect of Surfactants on Air-Water Two-Phase Flow in
Minichannels', Heat Transfer Engineering, 27:4, 99 - 109
To link to this article: DOI: 10.1080/01457630500523980
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© Taylor and Francis 2007
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Heat Transfer Engineering, 27(4):99–109, 2006
C Taylor and Francis Group, LLC
Copyright ISSN: 0145-7632 print / 1521-0537 online
DOI: 10.1080/01457630500523980
An Experimental Investigation
into the Effect of Surfactants
on Air-Water Two-Phase
Flow in Minichannels
NATHAN J. ENGLISH and SATISH G. KANDLIKAR
Mechanical Engineering Department, Thermal Analysis and Microfluidics Laboratory, Rochester Institute of Technology,
Rochester, New York, USA
The complex interfacial phenomena involved in two-phase gas-liquid flow have defied mathematical simplification and
modeling. However, these 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 4.0–12.0 kg/m2 s for air and 0.5–21.6 kg/m2 s
for water, corresponding to superficial gas and liquid velocities of 3.19–10.06 m/s and 0.0005–0.022 m/s, respectively. The
experiments are repeated with water-surfactant mixtures of different concentrations 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, and a new model for laminar-laminar two-phase flow pressure drop
is developed.
INTRODUCTION
models intended for larger channels to inaccurately predict 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 cases, there
is a dearth of good quality data published with enough information to be useable for comparison and analysis. They are often
based on limited ranges of operating conditions. Furthermore,
even though the effect of surface tension is recognized, it has
not been studied extensively.
The present work focuses on an area with little published
literature, air-water adiabatic flow with low mass fluxes (G T <
50 kg/m2 s) 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 semicircular) 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
The behavior of single-phase internal flow is well understood
and predictable over a wide range of operating conditions. Twophase flows are also quite common but not as well understood
and involve significant error in predictability. The fundamental physics has proved too complicated to be characterized by
simplified mathematical models. Likewise, the use of computers
for computational fluid dynamics (CFD) analysis has produced
less than satisfying results. Therefore, emphasis is placed on
experimentation and model development based on 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, causing the
The work was performed in the Thermal Analysis and MicroFluidics Laboratory of the Mechanical Engineering Department of the Rochester Institute of
Technology.
Address correspondence to Dr. Satish G. Kandlikar, Mechanical Engineering
Department, Rochester Institute of Technology, Rochester, NY 14623. E-mail:
[email protected]
99
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100
N. J. ENGLISH AND S. G. KANDLIKAR
to optimize the system and ensure adequate reactant delivery.
There is inherent heat transfer, mass transfer, multiple materials,
and 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 [1] is used and considers minichannels to be within the
range of 3 mm ≥ D > 200 µm, with a modification that D represents the minimum channel dimension. The channel used in
this investigation is nominally square, and it is expected that the
flow behavior will be slightly different from most of the 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 pressure drop data with the different surfactant
concentrations.
3. Evaluate published models for 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 one 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 [2] related the two-phase pressure
drop to the single-phase pressure drops with the LockhartMartinelli parameter, X, where P = pressure, φ = two-phase
friction factor and subscripts, L = liquid, G = gas, and T =
two-phase:
X2 =
PT =
PL
PG
φ2G PG
=
φ2L PL
tion used to calculate the single phase pressure drops can be written as Eq. (3), where f = friction factor, Re = Reynolds number,
L = channel length, µ = dynamic viscosity, G = mass flux, Dh =
hydraulic diameter, ρ = density, Acs = cross-sectional area, a =
channel width, b = channel height, and Pw = wetted perimeter:
2LµG
Dh2 ρ
(3)
4Acs
2ab
=
Pw
(a + b)
(4)
P = f Re
Dh =
The friction factor defined by Kakac et al. [3] is used to calculate
f Re as it applies to smooth rectangular channels under laminar
flow and is within 0.05% of the tabulated values. It is only aspect
ratio-dependent (α = b/a), where α ≤ 1:
1 − 1.3553α + 1.9467α2 − 1.7012α3
f Re = 24
(5)
+0.9564α4 − 0.2537α5
The Lockhart and Martinelli tables for pressure drop calculations are cumbersome to use for engineering calculations, so
Chisholm [4] defined approximate equations using the parameter C, which are considered accurate for engineering predictions
in large diameter channels:
C
1
+ 2
X
X
(6)
φ2G = 1 + CX + X 2
(7)
φ2L = 1 +
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.)
The homogenous flow model differs from the other models
in that it assumes the two-phase flow as 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, where x = mass quality
(x = G G /(G G + G L )) and subscript H = homogenous:
ρH =
ρ L ρG
xρ L + (1 − x)ρG
(8)
µH =
µ L µG
xµ L + (1 − x)µG
(9)
Table 1 Values of Chisholm’s parameter C
(1)
Two-phase flow characteristics
Chisholm’s parameter C
(2)
Laminar liquid, laminar gas
Turbulent liquid, laminar gas
Laminar liquid, turbulent gas
Turbulent liquid, turbulent gas
5
10
12
21∗
The equations were presented in conjunction with tables that correlated the two-phase multipliers φG and φ L with X. The equaheat transfer engineering
∗ Chisholm
[31].
vol. 27 no. 4 2006
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N. J. ENGLISH AND S. G. KANDLIKAR
Beattie and Whalley [5] modified the two-phase homogenous
viscosity to include consideration of the void fraction, β:
ρL x
β=
(10)
ρ L x + ρG (1 − x)
µ H = µ L (1 − β)(1 + 2.5β) + µG β
(11)
Friedel [6] considered a wide body of experimental data
and developed a correlation weighted with the non-dimensional
Froude number, Fr, and Weber number, We (which assume a
homogenous two-phase density), and described through E, F,
and H in Eqs. (12–15), where g = gravitational acceleration,
σ = surface tension, and subscripts Lo, Go = calculated as if
the total mass flux has the properties of the liquid and gas phase,
respectively.
φ2Lo = E +
3.24FH
ρ f Go
E = (1 − x)2 + x 2 L
ρG f Lo
(13)
F = x 0.78 (1 − x)0.224
(14)
H =
ρL
ρG
0.91 µG
µL
0.19 µ
1− G
µL
0.7
(15)
Fr T =
G 2T
gDh ρ2H
(16)
WeT =
G 2T Dh
ρH σ
(17)
Other publications have attempted a similar method as Friedel
and used such non-dimensional groups as the Confinement number, Nconf , in Eq. (18) and the Capillary number, Ca, in Eq. (19).
The Confinement number is a re-working of the Bond number
in Eq. (27). It is important to note that the Weber, Confinement,
Capillary, and Bond numbers include surface tension, and could
prove useful in trying to quantify the surface tension effects.
σ 0.5
Nconf =
Ca =
Weisman et al. [12] 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 [13] 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 [14] modified the Chisholm correlation
to better match their data for minichannels where D = circular
channel diameter.
(12)
Fr0.045
We0.035
T
T
g(ρ L −ρG )
101
C = 21(1 − e−333D )
(20)
C = 21(1 − e−319Dh )
(21)
Equations (20) and (21) are for circular and non-circular geometries, respectively. The equations create a direct dependence of
the Chisholm parameter on channel size. For channels of a 0.01m
diameter or greater, the value approaches 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.
Rather than modifying the Chisholm equation, Chen et al.
[7, 15] added a multiplication factor, , to the homogenous and
Friedel correlations. Equation (22) is used with Eq. (23) in the
2002 homogenous modification [7] and Eq. (24) in the 2001
homogenous modification [15]. 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 Dh /2 is used for
the Bond number, Bo, characteristic length, but many works use
only Dh .
P = PH
(18)
Dh
We
µG
=
Re
σρ
(19)
It was recognized by the research of Chen et al. [7], Coleman
and Garimella [8], Fukano and Kariyasaki [9], Garimella [10],
and Triplett et al. [11] that the surface tension force becomes
important for channels of a hydraulic diameter less than 10 mm
(or rectangular channels with small gap widths) and dominate
below 5 mm. Often a gas 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.
heat transfer engineering
Figure 1 Values of C recommended by Mishima and Hibiki [14].
vol. 27 no. 4 2006
(22)
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102
=
N. J. ENGLISH AND S. G. KANDLIKAR
0.85 − 0.082Bo−0.5
−1
0.57 + 0.004Re0.5
Go + 0.04Fr
+
=
80We−1.6 + 1.76Fr0.068 + ln(ReGo ) − 3.34
1 + e(8.5−1000ρG /ρL )
(23)
1 + (0.2 − 0.9e−Bo )
0.3 1 + We0.2 /e Bo − 0.9e−Bo
(24)
for Bo < 2.5
for Bo ≥ 2.5
P = PFriedel




0.0333Re0.45
Lo
0.4e−Bo )
=
We


(2.5 + 0.06Bo)
Re0.09
G (1 +
0.2

Bo =
(ρ L − ρG )g(Dh /2)2
σ
Figure 2 Geometry of the test section (not to scale).
(25)
for Bo < 2.5
(26)
for Bo ≥ 2.5
(27)
In order to acceptably narrow the experimental focus and
provide industrial relevance, the flow conditions from PEM fuel
cells are considered. Trabold [16] 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 parallel flow
mal-distribution problems can be avoided. To achieve this, he
recommended maintaining a superficial air velocity of 5–6 m/s.
The rate of water production is only dependent 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. [17] considered a slightly different system than
that described by Trabold. However, it was re-emphasized 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 [18] 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 × 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 of 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.
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
heat transfer engineering
lengths are between 200–300 mm in published literature [13, 14,
19–21]; however, the present section is longer than Chen et al.
[7] at 150 mm and Damianides [22] 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.
The entrance and exit lengths are also of concern, 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 (L e ) would be only 37.7 mm. Damianides [22] 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 a 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 and lead to an expanded chamber below the channel.
From there, the fluids drain from the test section, and any liquid
buildup in the channel is avoided. The large differential between
the gas and liquid flow rates also reduces the chance of a liquid
buildup.
Two more pieces of lexan are sandwiched around the center, and two clamps are used to compress the assembly. 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 connecting opposing sides of a differential pressure transducer. The
reading from this transducer is the frictional pressure drop along
that section of the channel, as the pressure drops due to acceleration (adiabatic flow) and gravity (horizontal flow) are negligible.
Air is supplied by a pressurized tank and flow rate is measured
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. [23].
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 the photography
of the flow but should not influence the experimental results.
The second causes changes in the fluid behavior uncharacteristic of water and is not acceptable. Upon the recommendation
of Shurell [24], the surfactant TritonTM DF-12 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
vol. 27 no. 4 2006
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N. J. ENGLISH AND S. G. KANDLIKAR
103
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
Cs
Surface tension
(N/m)
Advancing contact
angle (deg.)
Water
0.073
72
0.021
0.048
48
0.037
0.0411
40
0.072
0.0354
35
0.109
0.0338
28
dynamic 0.046 N/m at a surfactant concentration of Cs = 0.1%
by weight. Concentrations of 0.021, 0.037, 0.072, and 0.109%
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 5◦ ). 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 7◦ , so numerous measurements
were taken to reduce the uncertainty to ±0.5◦ .
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 0.1◦ C uncertainty in
the fluid temperature measurement. The uncertainty in liquid
flow rate varies between 0.82–8.6%, and 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 thus can be included as x-axis error bars on the pressure drop data. The other
uncertainties do not impact the pressure drop measurements;
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 3 is an example of applying
the uncertainties to single phase data.
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 are
begun. The air flow rate and surfactant concentration are held
constant for each run but 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. Also, the liquid flow rate is increased
slowly and given time to reach equilibrium within the channel
heat transfer engineering
Figure 3 Single-phase air data taken over the experimental range and compared to the theoretical values.
before recording each data point so as to avoid transient situations and 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 [16] and Wheeler
et al. [17], 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.
RESULTS AND DISCUSSION
Single-Phase Validation
In order to validate the test setup, single phase air data are
collected over the relevant range of air flow rates, as seen in
Figure 3. The recorded pressure drop is used to calculate the
friction factor and is compared to the theoretical predictions.
There is an average 10.7% deviation between the data and theoretical predictions; however, the data rely on measured values
for the channel geometry, ambient temperatures, and fluid flow
Table 3 Range of operating conditions encountered in experimental data
collection
(kg/m2 s)
Mass flux
Superficial velocity (m/s)
Superficial Reynolds number
vol. 27 no. 4 2006
Air
Water
4.03–12.0
3.19–10.06
211–654
0.49–21.6
0.0005–0.0217
0.56–24.6
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104
N. J. ENGLISH AND S. G. KANDLIKAR
rates. If the measurement uncertainty is included, then there is
good agreement between the theoretical and experimental, and
the test setup is considered 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. 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.
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 or 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
[22] and Yang and Shieh [21], which predicted slug flow, but
their data were taken in circular channels. Barajas and Panton [13] and Coleman and Garimella [8] predicted a transition
from slug to wavy flow with increasing gas superficial velocity.
Mishima and Hibiki [14] predicted a similar transition, but from
churn to annular flow. Bao et al. [25] predicted stratified flow
throughout. Less related works such as Fukano and Kariyasaki
[9], Wambsganss et al. [26], Xu et al. [27], Lowry and Kawaji
[28], Wilmarth and Ishii [29], Garimella [10], and Kawahara
et al. [30] 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.
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
Cs
Fr
We
Ca
Bo
Pure water
0.0208
0.1089
3206–9100
3235–9054
3206–9055
0.589–4.25
0.901–5.98
1.252–8.60
0.001–0.007
0.002–0.0092
0.003–0.013
0.0353
0.0527
0.0745
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 inertia forces dominate the surface tension.
The Capillary number shows that in all cases, the surface tension force dominate over the viscous forces. 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 Figure 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 higher
or lower pressure drop. Similar results were found for the case
of a 10 m/s superficial air velocity.
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
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 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.
The Froude number shows that the inertial forces are significantly larger than the gravitational effects. The Weber number
heat transfer engineering
Figure 4 Comparison of pressure drops using surfactant solutions as designated by concentration, Cs , G a = 6.75 kg/m2 s, Ja = 5.66 m/s.
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N. J. ENGLISH AND S. G. KANDLIKAR
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 0.097% by weight was performed
and yielded similar results as those of Figure 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 [18].
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 that was caused by decreasing the surface
tension.
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
105
Figure 6 Experimental data plotted with the two-phase pressure drop predictions of relevant models, G a = 6.75 kg/m2 s, Ja = 5.66 m/s.
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 are the frictional pressure drop alone. Figure 6
represents the actual data taken for the same case as for Figure 5 and compares the closest predictions. The Friedel correlation is not included in the plots, as it overpredicts the data
very significantly. Models by Chisholm [31], Tran et al. [32]
and Wambsganss et al. [26] were also tested but not discussed,
as they were found very inaccurate. The Beattie and Whalley
[5] model is simple to calculate, 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. model [7] and
the Chen et al. [15] model with the Friedel modification were
reasonably accurate, with mean absolute deviations of 16–40%
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, Figure 6 shows that they do
not match 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.
New Model Development
Figure 5 Two-phase pressure drop predictions of relevant models, G a =
6.75 kg/m2 s, Ja = 5.66 m/s.
heat transfer engineering
The Mishima-Hibiki model modifies the Lockhart-Martinelli
model for flow in minichannels under the turbulent-turbulent
flow condition. In Figure 6 the model is being applied outside of its intended range of operability—indeed, it leads to
a C value of 5.74, which is very close to Lockhart-Martinelli
value but actually higher than what 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
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106
N. J. ENGLISH AND S. G. KANDLIKAR
Figure 7 Experimental data plotted with the proposed model, G a =
6.75 kg/m2 s, Ja = 5.66 m/s.
the associated frictional pressure drop:
C = 5(1 − e−319Dh )
(28)
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:
C = 5(1 − e−333D )
(29)
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, where: C ∗ = Chisholm’s modified for
flow in small channels. Figure 7 represents how well the proposed model matches the data of Figure 6.
C ∗ = C(1 − e−319Dh )
(30)
φ2G = 1 + C ∗ X + X 2
(31)
PT = φ2G PG
(32)
Figure 8 Comparison of the pure water data with the proposed model for
different mass fluxes, G = G a , J = Ja .
The modification results in a 2.4–4.5% deviation when averaged over the runs, 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 four 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 trend very close to that produced with the model.
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 Beattie-Whalley
Homogenous Flow model, one can see that the uncertainty
decreases the inaccuracy of the model, but not to the point that
Table 5 Absolute mean discrepancies of the two-phase pressure drop models
when averaged over the experimental runs. The best models are in bold
Model
Lowest %
Highest %
Average %
Lockhart-Martinelli
Homogenous flow
Beattie-Whalley
Friedel
Mishima-Hibki
Chen et al. [7]
Chen et al. [15]
Chen et al. Friedel
Proposed model
43.5
19.7
7.46
1602
53.2
16.10
48.9
22.5
2.4
58.6
55.9
16.00
1944
72.2
39.7
61.0
27.6
4.5
60.3
29.8
9.83
1746
61.4
22.2
55.5
24.3
3.3
heat transfer engineering
Figure 9 Comparison of the experimental data with the proposed model’s
predictions, including experimental uncertainties, G a = 6.75 kg/m2 s, Ja =
5.66 m/s.
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N. J. ENGLISH AND S. G. KANDLIKAR
107
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.
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 exactly
duplicate the same mass quality between runs; however, the
pressure drop values and overall trends match within 3.0%.
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.
CONCLUSIONS
cross-sectional area, m2
channel width, m
channel height, m
Bond number (non-dimensional), (ρ L − ρG ) gL2c /σ.
Note that Chen et al. [7, 21] use L c = Dh /2, whereas
many authors use L c = Dh .
C
Chisholm’s parameter (non-dimensional)
Cs
surfactant concentration calculated on a % weight
basis (non-dimensional)
C∗
Modified Chisholm’s parameter (non-dimensional)
Ca
capillary number (non-dimensional), µG/ρσ =
We/Re
D
diameter, m
E, F, H terms of the Friedel [6] correlation
f
friction factor (non-dimensional)
Fr
Froude number (non-dimensional), G 2 /gDh ρ2
g
gravitational acceleration, m/s2
G
mass flux, kg/m2 s
j
superficial velocity, m/s, V̇ /Acs
L
length, m
characteristic length, m
Lc
Le
entrance length, m, L e ∼
= 0.06ReDh
ṁ
mass flow rate, kg/s
Nconf
confinement number (non-dimensional), (σ/g(ρ L −
ρG ))0.5 /Dh
P
pressure, Pa
Pw
wetted perimeter, m
Re
Reynolds number (non-dimensional), GDh /µ
V̇
Volumetric flow rate, m3 /s
We
Weber number (non-dimensional), Dh G 2 /ρσ
X
Lockhart-Martinelli parameter (non-dimensional)
x
mass quality (non-dimensional), ṁ G /(ṁ G + ṁ L )
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/m2 s, water mass fluxes of
0.49–22 kg/m2 s, and mass qualities of 0.15–0.98.
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 were 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 [5] 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. [7] correlation, the Chen et al. [15] 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 [14] model is extended to laminarlaminar 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. It is recommended that the appropriate value of C for the laminar or turbulent cases be used
in extending the Mishima and Hibiki model to low flow rate
conditions.
NOMENCLATURE
Acs
a
b
Bo
Greek Symbols
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 ones. 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. A
heat transfer engineering
α
β
P
µ
ρ
σ
φ
aspect ratio (non-dimensional), b/a (≤1)
void fraction (non-dimensional)
change in pressure, Pa
viscosity, kg/ms
modification factor of Chen et al. [7, 21] (nondimensional)
density, kg/m3
surface tension, N/m
two-phase friction factor (non-dimensional)
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108
N. J. ENGLISH AND S. G. KANDLIKAR
Subscripts
G
Go
H
h
L
Lo
T
calculated with the properties of the gas phase
calculated as if the total mass flux has the fluid properties of the gas phase
homogenous
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
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Nathan English completed his Master of Science
program in mechanical engineering at RIT with a
concentration in thermo-fluids. This builds upon
the bachelor of science degree that he earned in
physics from Roberts Wesleyan College. In his
thesis, he investigated adiabatic two-phase pressure drop of air-water with and without surfactant
mixtures in minichannels. Currently he is a product engineer at the Ovonic Fuel Cell Company.
heat transfer engineering
109
Satish G. Kandlikar is the Gleason Professor of
mechanical engineering at RIT. He received his
Ph.D. degree from the Indian Institute of Technology in Bombay in 1975 and has been a faculty
member there before coming to RIT in 1980. His
current work focuses on the heat transfer and fluid
flow phenomena in microchannels and minichannels. He is involved in advanced single-phase and
two-phase heat exchangers incorporating smooth,
rough, and enhanced microchannels. He has been
published in over 130 journal and conference papers. He is a fellow member
of ASME and has been the organizer of the three international conferences on
microchannels and minichannels sponsored by ASME. He is a recipient of the
Eisenhart Outstanding Teaching award, IBM Faculty award, ASME Best Paper
Award at NHTC, and Journal of Heat Transfer Best Reviewer Award. He is the
founder of the ASME Heat Transfer chapter in Rochester and founder and first
Chairman of the E-cubed fair—a science and engineering fair for middle school
students in celebration of Engineers’ Week. He is the Heat and History Editor
for Heat Transfer Engineering journal and an associate editor for Journal of
Heat Transfer and Journal of Nanofluidics and Microfluidics.
vol. 27 no. 4 2006