1. Study of two-phase flow pressure drop characteristics
in Proton Exchange Membrane (PEM) fuel cell
flow channels of different geometries
Thesis Presentation
by
Ekramul Haque Ehite
04/04/2016
Advisor: Kazuya Tajiri, Ph.D.
Department of Mechanical Engineering-Engineering Mechanics
Michigan Technological University

2. Acknowledgement
2
 I deeply express my gratitude to Dr. Kazuya Tajiri for his
guidance, suggestions, and continuous support at every stage of
my research and graduate study.
 I cordially thank Dr. Amitabh Narain and Dr. Scott W. Wagner for
being in my thesis committee. Their valuable suggestions greatly
helped and guided me towards completion of this research.
 I am grateful to Udit Shrivastava, Ph.D., Jaime Patterson and
Paul Skuln for their assistance during the experimentation.
 I heartily thank the industry sponsors for providing the financial
support for my research and Master’s study.
 Special thanks to the members of Michigan Tech MUB Board,
Mind Trekkers, REAC and Quiz Bowl Club for their help.

3. Outline
3
 Introduction
 Significance of the research
 Research objectives
 Methodology
 Experimental design
 Test conditions
 Results
 Pressure drop vs air flow velocity
 Deviations from empirical model
 Water droplet velocity vs air flow velocity
 Summary and conclusions
 Future scope of work

4. Introduction
 Fuel cells
 Electrochemical energy conversion device
 chemical energy ⇒ electrical energy
 Continuous source of fuel (H2) and
Oxidizer (O2) required
 Site in the device for reaction ⇒ Electrolyte
 Proton Exchange Membrane (PEM) fuel cells
 Electrolyte: Polymer film
 Advantages
 Zero emission characteristics
 Low temp operation (50-100⁰ C)
 High operating efficiency
 Disadvantages
 Cost: Materials
 Fuel infrastructure
4
Schematic diagram of a PEM fuel cell,
http://physics.nist.gov/MajResFac/NIF/pemFuelCells

5. Flow channels in PEM fuel cell
5
Fuel Cell Assembly (Lee et al. 2009)
 Distribute fuel/oxidizer to
the catalyst layer
Flow channels
 Remove reaction product
from the catalyst layer
Parallel
Serpentine
Various flow channel
designs (Mench, 2008)

6. Water management in PEM fuel cell
 During electrochemical reaction, water is
produced in the channel
 Water production rate > water removal
rate ⇒ Water lens formation
 Channel flooding:
- Hinders supply of reactants
- lowers performance
 Hydration required for membrane
 Balanced water management is
necessary
6
Water generation in PEM fuel cell,
http://hycarus.eu/our-technologies

7. Two-phase flow in PEM fuel cell
 Liquid-water buildup in channel produces two-phase
flow, having different patterns
 Common flow patterns:
 corner flow (Low air and water production rate)
 annular film flow (Moderate air and water rate)
 slug flow (high air and water rate; dominant in PEM
fuel cell)
 Two-phase flow study in PEM fuel cells
 Direct method: neutron imaging, X-ray
microtomography
 Indirect method: measurement of parameters
produced due to water accumulation
7
Two-phase flow patterns in PEM fuel cell
(a) corner flow, (b) annular film flow,
(c) slug flow (Zhang et al., 2006)
Water droplets
Hydrophobic, rough
GDL surface
Hydrophilic, smooth
Walls
Gas Channel

8. Two-phase flow pressure drop in PEM fuel cell
 Indirect parameter: Two-phase flow pressure drop
 Plugging of the channel causes increase of pressure drop across channels
 Consequence:
 System requires stronger compressor
 Size ↑
 Cost ↑
 Overall efficiency ↓
 Each two-phase flow pattern has its particular pressure drop signature
 in-situ diagnostic tool for investigating water accumulation within the flow
channel
8

9. Two-phase flow pressure drop models
 The two-phase flow pressure drop is the sum of the frictional (ΔPTP,F),
gravitational (ΔPTP,G) and acceleration pressure drop (ΔPTP,A):
ΔPTP = ΔPTP,F + ΔPTP,G + ΔPTP,A
 In PEM fuel cell, only frictional pressure drop is important ⇒ ΔPTP = ΔPTP,F
9
Models for two-phase
flow pressure drop
estimation
Homogeneous
equilibrium model
Separated flow
model
(Treat two-phase flow
as pseudo-single phase
fluid)
(Multiply single phase
Pressure by two-phase
flow frictional multiplier,Φ 𝑓
2
)

10. Separated flow model
 Original equations developed by Lockhart-Martinelli (1949)
 Two-phase flow pressure drop,
𝑑𝑃
𝑑𝑧 𝑇𝑃
= Φ 𝑓
2 𝑑𝑃
𝑑𝑧 𝑓
 Two-phase frictional multiplier, Φ 𝑓
2
=
𝑑𝑃
𝑑𝑧 𝑇𝑃
𝑑𝑃
𝑑𝑧 𝑓
= 1 +
𝐶
𝑋
+
1
𝑋2
 Martinelli Parameter, 𝑋 =
𝑑𝑃
𝑑𝑧 𝑓
/
𝑑𝑃
𝑑𝑧 𝑔
1/2
10
∅ 𝑓
2
= two-phase frictional multiplier C = Chisholm parameter
𝑑𝑃
𝑑𝑧 𝑓
= Single phase pressure drop X = Martinelli parameter
Subscript TP = Two-phase
mixture
Subscript f = Liquid
Subscript g = Gas

11.  English and Kandlikar (2006)
11
𝐷ℎ = Channel hydraulic
diameter
D = Channel diameter
 C = 5 (1 − e−0.319𝐷ℎ) [For rectangular channel]
 C = 5 (1 − e−0.333𝐷
) [For circular channel]
 Chisholm Model (1967)
Depends on
Flow Regime
 Mishima and Hibiki (1996)
 C = 21 (1 − e−0.319𝐷ℎ) [For rectangular channel]
 C = 21 (1 − e−0.333𝐷
) [For circular channel]
Modified for
Channel size
Modified for
PEM fuel cell
channels
Chisholm parameter
Two-phase flow
characteristics
Chisholm’s
Parameter C
Laminar liquid-laminar gas 5
Turbulent liquid-laminar gas 10
Laminar liquid-turbulent gas 12
Turbulent liquid-turbulent gas 21
Range of Operation
Gas Water
Mass flux (kg/m2-s) 4.03-12.0 0.49-21.6
Superficial veloctity (m/s) 3.19-10.06 0.0005-0.0217
Superficial Reynolds No 211-654 0.56-24.6

12. Significance of the research
12
Unique characteristics of two-phase flow in
PEM fuel cell
 Liquid introduction through porous gas diffusion layer
(GDL)
 Distribution of two-phase flow along the channel
 Flow bounded by hydrophobic GDL at one wall, and
hydrophilic metal/graphite walls on the other walls
No reliable model
exists for a wide
range of operating
conditions
Hydrophobic GDL
Air
Water injection and distribution through porous GDL
Hydrophilic Wall
Experimental
data
Support
existing
models
Develop
more
accurate
and robust
models

13. Research objectives
Objective 1
13
Experimentally determine
Two-phase air-water flow
pressure drop along
minichannels
Rectangular
channel
Semi-circular
channel
Objective 2
Comparison of
experimental results with
theoretical results based
on existing most reliable
PEM fuel cell empirical
model

14. Methodology
Pressure drop
model selection
14
• Separated flow model (Lockhart and Martinell,
1949)
• Modified by English and Kandlikar (2006)
Flow channel
manufacturing
• Rectangular and semi-circular channels
• Machining the channels in brass plates
• 3d surface profiling
Pressure Drop
Experimentation
Comparison of
results
• Building experimental setup
 Test cell assembly
• Developing test conditions and protocols
• Calibration of equipment
 Pressure transducer, mass flow controllers
• Digital acquisition of data
• Conversion of digital reading to pressure drop
measurements
• Compare between experimental and
theoretical results
• Compare between rectangular and
semi-circular results

15. Flow channel manufacturing
15
Rectangular channel Semi-circular channel
• Machined in the machine shops of Michigan Technological University
• 3d surface profiling performed to find average surface profiles
h1
h2
v

16. Channel surface profiling
16
Rectangular channel Semi-circular channel
3.1
3.2
3.3
3.4
3.5
3.6
3.7
47 48 49 50 51
Verticallength(mm)
Horizontal length (mm)
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
48 48.5 49 49.5 50 50.5 51
Verticallength(mm)
Horizontal length (mm)
Rectangular channel Semi-circular channel
Parameter Dimension Parameter Dimension
Top width, h1 (mm) 1.009 ± 0.0202 Radius, R (mm) 0.485 ± 0.1759
Bottom width, h2 (mm) 0.738 ± 0.048 Depth, D (mm) 1.052 ± 0.0396
Depth, v (mm) 0.370 ± 0.2745
Roughness (mm) 0.032 ± 0.0627 Roughness (mm) 0.075 ± 0.1068
Cross-sectional area
(m2)
2.20×10-7 ± 1.16×10-7 Cross-sectional area
(m2)
3.70×10-7 ± 2.64×10-7
Hydraulic Diameter (m) 4.52×10-4 ± 3.42×10-4 Hydraulic Diameter (m) 5.74×10-4 ± 2.6×10-4

17. Experimental design - test cell
335mm
70mm 150mm
water injection
gas inlet water injection two-phase flow
outlet
single-phase
17
pressure drop
two-phase
pressure drop
Machined flow channel
Schematic Diagram of flow channel

18. Experimental design - test cell assembly
Bottom view
Side view
18
Water injection port
(Dia 1/16”)
Pressure ports
for transducer 1
Pressure ports
For transducer 2
Top view
Two-phase flow
OutletGas inlet
Channel plate

19. Experimental setup
• Conventional way of studying two-phase pressure drop
• Provide constant gas flow rate and constant liquid water flow rate, and
measure the two-phase pressure drop change with time
19Schematic Diagram of the experimental setup
Water
Porous
Carbon
Paper
Gas channel
Water
injection
port
Channel walls

20. Experimental setup
20
Syringe pump
Pressure transducer 1
Pressure transducer 2
Water injection
indicator
DAQ
Mass flow controller
PC
Test section

21. Test conditions: equations used
21
i = Current density (A/cm2)
A = Active electrode area (cm2)
F = charge carried on one
equivalent mole (C/eq)
SR= Stoichiometric Ratio
Molar flow rate of air, 𝑛 𝑎𝑖𝑟 =
𝑖𝐴
4𝐹
.
100
21
. 𝑆𝑅
Water generation rate, 𝑛 𝑤𝑎𝑡𝑒𝑟 =
𝑖𝐴
2𝐹
Required Oxygen Convert to air (Since,
air is 79% N2 and 21%
O2 on a mole basis)
=
Reactant feed
Reactant consumption

22. Test conditions summary
22
Parameter Range
Rectangular channel Semi-circular channel
Gas species Nitrogen (N2) Nitrogen (N2)
Mass quality 0.819, 0.850 0.819, 0.850
Stoichiometric ratio, SR 1.2, 1.5 1.2, 1.5
Current density (A/cm2) 0.2-4 0.2-4
Gas flow rate (sccm) 8.7-218 8.7-218
Water injection rate (ml/hr) 0.135-2.7 0.135-2.7
Gas Mass flux (kg/m2-s) 0.77-19.24 0.46-11.44
Water Mass flux (kg/m2-s) 0.17-3.39 0.10-2.02
Gas superficial velocity (m/s) 0.66-16.51 0.39-9.81
Water superficial velocity (m/s) 0.00017-0.0034 0.00010-0.002
Gas superficial Reynolds
number 18.56-464.95 14.03-351.63
Water superficial Reynolds
number 0.096-1.92 0.073-1.452

23. Test conditions: rectangular
23
Case Gas flow rate at
inlet
Water injection
Rate
Mass
quality, x
SR Condition equivalent to (20cm-
long) current density
(sccm) (mL/hr) (A/cm2)
1 8.7 0.135 0.819 1.2 0.2
2 17.4 0.27 0.819 1.2 0.4
3 26.1 0.405 0.819 1.2 0.6
4 34.8 0.54 0.819 1.2 0.8
5 43.5 0.675 0.819 1.2 1
6 52.2 0.81 0.819 1.2 1.2
7 60.9 0.945 0.819 1.2 1.4
8 69.6 1.08 0.819 1.2 1.6
9 78.3 1.215 0.819 1.2 1.8
10 87 1.35 0.819 1.2 2
11 104.4 1.62 0.819 1.2 2.4
12 121.8 1.89 0.819 1.2 2.8
13 139.2 2.16 0.819 1.2 3.2
14 156.6 2.43 0.819 1.2 3.6
15 174 2.7 0.819 1.2 4
16 10.9 0.135 0.850 1.5 0.2
17 21.8 0.27 0.850 1.5 0.4
18 32.7 0.405 0.850 1.5 0.6
19 43.6 0.54 0.850 1.5 0.8
20 54.5 0.675 0.850 1.5 1
21 65.4 0.81 0.850 1.5 1.2
22 76.3 0.945 0.850 1.5 1.4
23 87.2 1.08 0.850 1.5 1.6
24 98.1 1.215 0.850 1.5 1.8
25 109 1.35 0.850 1.5 2
26 130.8 1.62 0.850 1.5 2.4
27 152.6 1.89 0.850 1.5 2.8
28 174.4 2.16 0.850 1.5 3.2
29 196.2 2.43 0.850 1.5 3.6
30 218 2.7 0.850 1.5 4
Falls within
Kandlikar’s
Condition
range
Falls within
Kandlikar’s
Condition
range

24. Test conditions: semi-circular
24
Case Gas flow rate at
inlet
Water injection
Rate
Mass
quality, x
SR Condition equivalent to (20cm-
long) current density
(sccm) (mL/hr) (A/cm2)
1 8.7 0.135 0.819 1.2 0.2
2 17.4 0.27 0.819 1.2 0.4
3 26.1 0.405 0.819 1.2 0.6
4 34.8 0.54 0.819 1.2 0.8
5 43.5 0.675 0.819 1.2 1
6 52.2 0.81 0.819 1.2 1.2
7 60.9 0.945 0.819 1.2 1.4
8 69.6 1.08 0.819 1.2 1.6
9 78.3 1.215 0.819 1.2 1.8
10 87 1.35 0.819 1.2 2
11 104.4 1.62 0.819 1.2 2.4
12 121.8 1.89 0.819 1.2 2.8
13 139.2 2.16 0.819 1.2 3.2
14 156.6 2.43 0.819 1.2 3.6
15 174 2.7 0.819 1.2 4
16 10.9 0.135 0.850 1.5 0.2
17 21.8 0.27 0.850 1.5 0.4
18 32.7 0.405 0.850 1.5 0.6
19 43.6 0.54 0.850 1.5 0.8
20 54.5 0.675 0.850 1.5 1
21 65.4 0.81 0.850 1.5 1.2
22 76.3 0.945 0.850 1.5 1.4
23 87.2 1.08 0.850 1.5 1.6
24 98.1 1.215 0.850 1.5 1.8
25 109 1.35 0.850 1.5 2
26 130.8 1.62 0.850 1.5 2.4
27 152.6 1.89 0.850 1.5 2.8
28 174.4 2.16 0.850 1.5 3.2
29 196.2 2.43 0.850 1.5 3.6
30 218 2.7 0.850 1.5 4
Falls within
Kandlikar’s
Condition
range
Falls within
Kandlikar’s
Condition
range

25. Expected pressure drop characteristics
25
PressureDrop,∆P
Time, t
Single phase pressure drop (Transducer 1 Reading)
t = 0
Two-phase pressure drop (Transducer 2 Reading)
Water injection indicator pressure drop
(Transducer 3 Reading)
Segment where two-phase
pressure drop becomes steady

26. Pressuredrop vs air velocity - rectangular channel
26
Pressure Drop vs Air Velocity – Stoichiometric Ratio 1.2
• Theoretical pressure drop based on the separated flow model modified by Kandlikar et. al
Results
0.0E+00
5.0E+03
1.0E+04
1.5E+04
2.0E+04
2.5E+04
3.0E+04
3.5E+04
4.0E+04
4.5E+04
0 2 4 6 8 10 12 14
PressureDropperunitlength(Pa/m)
Air Velocity at the Inlet (m/s)
Theoretical single phase
Pressure per unit length
(Pa/m)
Experimental Single phase
pressure per unit length
(Pa/m)
Theoretical two phase
Pressure per unit length
(Pa/m)
Experimental two phase
pressure per unit length
(Pa/m)
* Cross-sectional
area, 2.20×10-7
m2
Re=
Reynolds No=225.33

27. Pressuredrop vs air velocity - rectangular channel
(Cont’d)
27
Pressure Drop vs Air Velocity - Stoichiometric Ratio 1.5
0.0E+00
1.0E+04
2.0E+04
3.0E+04
4.0E+04
5.0E+04
6.0E+04
0 2 4 6 8 10 12 14 16 18
PressureDropperunitlength(Pa/m)
Air Velocity at the Inlet (m/s)
Theoretical single
phase Pressure per
unit length (Pa/m)
Experimental single
phase pressure per
unit length (Pa/m)
Theoretical two
phase Pressure per
unit length (Pa/m)
Experimental two
phase pressure per
unit length (Pa/m)
Reynolds No=225.33

28. Pressuredrop vs air velocity - semi-circular channel
28
Pressure Drop vs Air Velocity - Stoichiometric Ratio 1.2
0.0E+00
5.0E+03
1.0E+04
1.5E+04
2.0E+04
2.5E+04
0 1 2 3 4 5 6 7 8 9
PressureDropperunitlength(Pa/m)
Air Velocity at the Inlet (m/s)
Theoretical single
phase Pressure per
unit length (Pa/m)
Experimental Single
phase pressure per
unit length (Pa/m)
Theoretical two
phase Pressure per
unit length (Pa/m)
Experimental two
phase pressure per
unit length (Pa/m)
* Cross-sectional
area, 3.70× 10-7
m2
Reynolds No=286.46

29. Pressuredrop vs air velocity - semi-circular channel
(Cont’d)
29
Pressure Drop vs Air Velocity - Stoichiometric Ratio 1.5
0.0E+00
5.0E+03
1.0E+04
1.5E+04
2.0E+04
2.5E+04
0 2 4 6 8 10 12
PressureDropperunitlength(Pa/m)
Air Velocity at the Inlet (m/s)
Theoretical single
phase Pressure per
unit length (Pa/m)
Experimental single
phase pressure per
unit length (Pa/m)
Theoretical two phase
Pressure per unit
length (Pa/m)
Experimental two
phase pressure per
unit length (Pa/m)
Reynolds No=286.46

30. Deviation from empirical model - Rectangular channel
30
Stoichiometric Ratio 1.2 Stoichiometric Ratio 1.5
0
20
40
60
80
100
120
0 2 4 6 8 10 12 14
Deviationfromempiricalmodel(%)
Air Velocity at the Inlet (m/s)
Single phase Two phase
0
5
10
15
20
25
30
35
40
0 5 10 15 20
Deviationfromempiricalmodel(%)
Air Velocity at the Inlet (m/s)
Single phase Two phase

31. Deviation from empirical model – semi-circular
channel
31
Stoichiometric Ratio 1.2 Stoichiometric Ratio 1.5
0
50
100
150
200
250
300
350
400
450
500
0 2 4 6 8 10
DeviationfromEmpiricalModel(%)
Air Velocity at the Inlet (m/s)
Single phase Two phase
0
50
100
150
200
250
300
350
400
0 2 4 6 8 10 12
DeviationfromEmpiricalModel(%)
Air Velocity at the Inlet (m/s)
Single phase Two phase

32. Pressuredrop comparison between channels
32
Stoichiometric Ratio 1.2
• Effect of Hydraulic Diameter: Semi-circular channel pressure drop<Rectangular channel pressure drop
0.0E+00
5.0E+03
1.0E+04
1.5E+04
2.0E+04
2.5E+04
3.0E+04
3.5E+04
4.0E+04
4.5E+04
0 2 4 6 8 10 12 14
Two-phaseflowpressuredrop(Pa/m)
Air velocity at inlet (m/s)
Rectangular Channel Semi-circular channel
0.0E+00
5.0E+03
1.0E+04
1.5E+04
2.0E+04
2.5E+04
3.0E+04
3.5E+04
4.0E+04
4.5E+04
0 2 4 6 8 10 12 14 16 18
Two-phaseflowpressuredrop(Pa/m)
Air velocity at inlet (m/s)
Rectangular Channel Semi-circular channel
Stoichiometric Ratio 1.5

33. Water droplet velocity comparison between channels
33
Stoichiometric Ratio 1.2
0.00E+00
2.00E-05
4.00E-05
6.00E-05
8.00E-05
1.00E-04
1.20E-04
1.40E-04
1.60E-04
1.80E-04
0 2 4 6 8 10 12 14
WaterDropletVelocity(m/s)
Air Velocity at the Inlet (m/s)
Rectangular Channel Semi-Circular Channel
0.00E+00
2.00E-05
4.00E-05
6.00E-05
8.00E-05
1.00E-04
1.20E-04
1.40E-04
1.60E-04
1.80E-04
2.00E-04
0 5 10 15 20
WaterDropletVelocity(m/s)
Air Velocity at the Inlet (m/s)
Rectangular Channel Semi-circular channel
• Droplet Velocity: Measured by finding the time between water emerging
into the channel and reaching the two-phase pressure drop zone
Stoichiometric Ratio 1.5

34. Summary and conclusion
34
 Experimental data supports the general trend of PEM fuel cell empirical
models
 Reasons behind deviation from empirical results
 Some test conditions of the experiment not within the range of
conditions for the empirical model
Parameters Gas Water
Mass flux
(kg/m2-s)
Rectangular Channel (Experimental) 0.77-19.24 0.17-3.39
Semi-circular Channel (Experimental) 0.46-11.44 0.10-2.02
English Kandlikar Model 4.03-12.0 0.49-21.6
Superficial velocity
(m/s)
Rectangular Channel (Experimental) 0.66-16.51 0.0001703-0.0034
Semi-circular Channel (Experimental) 0.39-9.81 0.000101-0.002
English Kandlikar Model 3.19-10.06 0.0005-0.0217
Superficial Reynolds
No
Rectangular Channel (Experimental) 18.56-464.95 0.096-1.92
Semi-circular Channel (Experimental) 14.03-351.63 0.073-1.452
English Kandlikar Model 211-654 0.56-24.6

35. Conclusion
35
 Reasons behind deviation from empirical results (Cont’d)
 Leakage losses
 Non-uniformity in channel dimensions
 Difference in surface characteristics between the GDL surface and
the channel walls

36. Future scope of work
36
 In-situ experiments with PEM fuel cells
 Use of other geometries (e.g. triangular, trapezoidal)
 Using micro-machining to obtain more accurate and uniform
channel dimensions
 Experimenting with two-phase flow of different mass qualities
 Determine the effect of GDL and wall surface properties (e.g.:
wettability) on two-phase flow pressure drop
 Development of a two-phase pressure drop model applicable over
wide range of operating conditions

37. Thank You!
Questions, Comments, &
Suggestions!

38. References
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[2] http://hycarus.eu/our-technologies, Retrieved March 19, 2016.
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[5] K. Mishima, T. Hibiki. Some characteristics of air-water two-phase flow in small diameter vertical
tubes. Int. J. Multiphas. Flow, 22:703-712, 1996.
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