DANSIS Møte, 26.Mars 2008
Application of Computational Fluid
Dynamics to Advance Fuel Cell
Technology
Torsten Berning
Assistant Professor
Institute of Energy Technology
Aalborg University
tbe@iet.aau.dk
1
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Overview
· Introduction to Fuel Cells
▫ Principle of operation
▫ Sample calculations for automotive applications
DANSIS Møte, 26.Mars 2008
▫ Current problems and challenges for
commercialization
· Introduction to Computational Fuel Cell
Dynamics
▫ Problem statements
▫ Literature overview
▫ Sample results
· Conclusions and Outlook
2
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DANSIS Møte, 26.Mars 2008
Introduction to fuel cells
3
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What are fuel cells?
· Fuel cells are:
▫ Electrochemical devices that continuously convert
the internal energy of gases directly into electricity,
e.g.:
DANSIS Møte, 26.Mars 2008
1
H 2 + O2 ⇒ H 2O (+ electricity + heat )
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▫ No energy storage devices (unlike batteries)
▫ “The opposite of electrolyzers”
▫ Heat is a (desired or not) waste product due to
inefficiencies
▫ Overall reaction is split up in half cell reactions that
occur at anode and cathode of fuel cell, e.g.:
Anode : H 2 ⇒ 2 H + + 2e −
4
1
Cathode : O2 + 2 H + + 2e − ⇒ H 2O
2
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Schematic and parts of a modern fuel cell
Bipolar plates BP (stainless steel)
▫
▫
▫
▫
provide convection path for gas and liquid phase
conduct electrons
non-permeate to gas phase
corrosion-free
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Porous diffusion media - GDM
(teflonated carbon fiber paper)
▫
▫
▫
provide diffusion path for gas phase
conduct electrons
transport liquid water
▫
assists in liquid water management
▫
▫
▫
▫
provide diffusion path for gas phase
conduct electrons
transport liquid water
conducts protons
▫
▫
▫
conducts protons
repels electrons
separates gas phases
e-
e-
H2/H2O
H2
Micro-porous layer – MPL
(carbon particles with Teflon)
H+
Catalyst layer – CL
Polymer electrolyte membrane – PEM
(polymer membrane with sulfuric or
phosphoric acid sites)
O2
Air/
H2O
Membrane-Electrode Assembly – MEA
5 ▫
combination of membrane and catalyst layers
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Air/
H2O
Example for stamped flow field plates
e.g. cathode
inlet port
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Active cell area
e.g. cathode
outlet ports
·
·
·
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Source:
www.techetch.com
Serpentine vs. straight flowfield vs. “interdigitated”
Anode/cathode land-channel width
Liquid water problem
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Sample calculation for automotive applications
Required stack volume
DANSIS Møte, 26.Mars 2008
·
·
·
Required power of a car is 90 kW
Maximum power density of a PEM
fuel cell is around 0.9 W/cm2
=> 100 000 cm2 total active area
Take a single cell active area to
be 15 cm × 25 cm = 375 cm2
=> need 267 cells in total
·
Source: [1]
How thick is one “unit cell”?
▫
Membrane:
25 μm
▫
Catalyst layers:
2 x 20 μm
▫
Diffusion layers:
2 x 230 μm
▫
Gas flow channels:
2 x 250 μm
▫
Bipolar plates:
2 x 250 μm
Ca. 1.5 mm in total
·
=>Total stack height is 40 cm (without stack manifold)
Assume an additional 125 cm2 area required in unit cell for
manifolding so that total single cell area is 500 cm2
·
Total volume is 20 000 cm3 = 20 l for stack alone
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[1]: R. O’Hayre et al.: Fuel Cell Fundamentals, Wiley, 2006
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display
Sample calculation for automotive applications
Current challenges: Pt cost
Platinum cost
▫
Current amount of Pt catalyst used: ≈ 0.4 mg/cm2
⇒ 40 g Pt per car
▫
Current cost of Pt: 2150 US$/(oz.tr.) (1 troy ounce = 31.1 g)
DANSIS Møte, 26.Mars 2008
⇒ more than 2500 US$ for (untreated) Pt per car!
⇒ Or, more general: ≈25 US$/kW for Pt catalyst material
(automotive cost target for fuel cell propulsion system: 50 $/kW)!
⇒ Still need to significantly reduce the required amount of Pt!
8
Source: www.rohstoffe-go.de
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Sample calculation for automotive applications
Current challenges: Pt cost
DANSIS Møte, 26.Mars 2008
Platinum cost
▫
1st optimization problem: more Pt per
cell increases cell performance (by
reducing “activation overpotential”)
and thus may help to reduce the total
number of cells required by increasing
power density
▫
2nd optimization problem: for catalyst,
surface area matters, i.e. Pt is
dispersed in nano-particles (2 - 3 nm
diameter) on carbon support (e.g. 20
% Pt on carbon).
Particle size increases with increased
wt%, hence increases activation
overpotential ( ), but catalyst layer
thickness decreases with increasing
wt% Pt, hence reduces the ohmic loss
due to protonic transport in CL (☺)
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Source: [2]
[2]Larminie & Dicks: Fuel cell systems explained, Wiley, 2003
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display
Sample calculation for automotive applications
Stack inlet velocity
·
·
·
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·
·
·
E.g. let the current load be at maximum of 1.5 A/cm2
Total stack current is 100 000 cm2 × 1.5 A/cm2 = 150 000 A
Need 150 000/4 × 96485 moles of O2 per second ≈ 0.4 mole/s O2,
at a stoichiometric flow of 2 we have 0.8 mole/s
Molar flow rate of dry air is 0.8 × (1/0.21) = 3.8 mole/s
=> Assume molar flow rate of humidified air to be 5.0 mole/s
Operate the cell at elevated pressure of P=1.5 bar and at a
temperature of 80 ºC = 353 K
Using ideal gas law the volumetric flow rate at the cathode side
is:
N& R T
PV& = N& RuT ⇒ V& =
u
P
5.0 mole s × 8.3143 Nm moleK × 353K
=
1.5 ×105 N m 2
3
m3
l
3 cm
= 98.8 × 10
≈ 100 × 10
= 100
s
s
s
−3
·
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Assuming a header area of 10 cm2 we have a velocity of 100 m/s
at the stack inlet (Re=250 000)!
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DANSIS Møte, 26.Mars 2008
FCs automotive applications
Current challenges: durability
▫
Required lifetime for a car: 5000 h
▫
Cells are stacked “in series”, i.e. the same current must flow (“is
drawn”) through every cell
▫
Current is still drawn in a cell when channels of a single cell are partially
blocked by liquid product water so that no fresh reactants can reach
catalyst
⇒ which reactions occur when no H2 is available?
⇒ “Carbon corrosion” at cathode, e.g. the protons and electrons required
for cathode half-cell reactions are provided by the neighboring region at
the cathode side by a reaction such as: C + 2H2O => CO2 + 4H+ + 4e- ,
also known as “carbon corrison”. Thus, carbon support for the Pt is
shrinking and the Pt particles form agglomerates & reduce surface area!
Source: Meyers, Darling, J. Electrochem. Soc., 153, 2006
Cathode CL
Membrane
Anode CL
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DANSIS Møte, 26.Mars 2008
Overview of automotive FCs
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·
Currently, most automotive manufacturers are putting
their main focus on low-temperature PEM Fuel Cells due
to the achievable high power density and cost targets
·
Catalyst cost are becoming a major concern with
respect to achieving a cost target of 50 US$/kW
·
Due to low operating temperature liquid water
management and its impact on durability is (still) one
of the main technological hurdles for commercialization
·
DOE has initiated several projects worth > 5 million
US$ to address liquid water management and modeling
in fuel cells
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DANSIS Møte, 26.Mars 2008
Introduction to
computational fuel cell dynamics
13
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Different Simulation Scales
1. Stack level
·
·
optimize reactant gas and coolant distribution from cell
to cell
optimize “header” geometry to minimize pressure drop
2. Single cell level
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·
gas and coolant flow-field design and optimization
regarding pressure drop, DM/BP contact area,
temperature distribution
3. Single channel level
·
·
provide fundamental understanding of reactant transport
through porous media and electrochemical reaction
provide fundamental understanding concerning the liquid
water transport through porous media and interaction of
liquid water with channel flow
4. “Microscopic Level” (non-CFD)
·
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phenomenological (1d) models to describe multi-phase
transport e.g. in electrolyte membrane and catalyst layer
depending on the micro-structure
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Water transport in fuel cells
▫
During FC operation there are two different sources of
liquid water
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1. Product water due to electrochemical reaction
▫
water is produced at the cathode but may diffuse back to anode
depending on local conditions
▫
whether product water is in liquid or gas phase depends on the local
conditions
2. Liquid water condensation due to reactant gas depletion
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▫
gases entering the cell are pre-humidified
▫
water vapor concentration along the channel and inside the porous media
increases due to reactant consumption
▫
when local relative humidity (RH) exceeds 100 % water will condense
▫
Water vapor leaves the cell via diffusion from the
catalyst region to the gas flow channels and convection
in the channels
▫
Liquid water has to leave the cell via capillary forces
inside the porous media and by “wicking” and convection
in the channels
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Liquid water transport through porous media
·
Capillary forces drive liquid water from regions of high
concentrations (“saturations”) to regions of low saturation
in a diffusion-like transport based on Darcy’s law
DANSIS Møte, 26.Mars 2008
⎛ kl ∂pcap ⎞
r
kl
kl
kl
kl
⎟⎟∇s
ul = − ∇pl = − ∇p g + ∇pcap = − ∇p g − ⎜⎜ −
μl
μl
μl
μl
⎝ μl ∂s ⎠
kl:
kdry:
relative permeability of liquid water, e.g. kl = s3 × kdry
dry permeability of porous medium
μl:
liquid water viscosity
capillary pressure pcap = pg - pl
“saturation”, i.e. porous volume fraction occupied by liquid phase
pcap:
s:
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Source: Nam & Kaviany, Int. J. Heat Mass Transfer., Vol. 46, Iss. 24, 2003
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display
Liquid water transport through porous media
·
·
Q.: how does the capillary pressure depend on the
1
saturation?
⎛ ε ⎞ 2
⎟ f (s )
A.: functional relationship pcap = σ cos φ ⎜
DANSIS Møte, 26.Mars 2008
σ:
φ:
ε:
f(s):
⎜k ⎟
⎝ dry ⎠
liquid/gas surface tension
contact angle: hydrophobic: φ > 90° (affected by aging)
dry porosity of diffusion media
functional relationship (“Leverett” function)
f (s ) = 1.417 × (1 − s ) − 2.12 × (1 − s ) + 1.263 × (1 − s )
2
3
Functional dependence f(s) [-]
0.6
0.5
0.4
0.3
0.2
0.1
0
0
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0.2
0.4
0.6
0.8
1
Saturation s [-]
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Modeling approaches
·
Two fundamentally different approaches :
1. Multiphase mixture model:
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▫
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CFD solver solves one set of conservation equations that includes both
phases (gas and liquid);
amount of liquid water in porous media determined in a post-iterative step;
Mathematically equivalent to two-fluid model with few exceptions, but
implementation is difficult
Frequently applied in Fluent, Star CD and CFD-ACE
2. Two-fluid model:
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▫
▫
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CFD solver solves two sets of conservation equations, one for each phase,
including exchange terms between the phases
Physically more complete than multiphase mixture model and straightforward to implement
Computationally expensive and requires full multi-phase solver (e.g. CFX-4)
Source: Luo, Ju and Wang, J. Electrochem. Soc., 154, 3, 2007
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DANSIS Møte, 26.Mars 2008
Sample results obtained with
two-fluid approach
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·
Left plot: predicted local amount of phase-change
inside the cathode side gas diffusion medium
·
Right plot: predicted liquid water saturation inside the
cathode side gas diffusion medium
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DANSIS Møte, 26.Mars 2008
Recent focus: boundary condition for the
liquid phase at channel/DM interface
·
Liquid phase description inside the porous media is (more
or less) understood, but what happens at the boundary
between channel and gas diffusion medium?
·
Current questions concerning water management include:
1. What is the correct boundary condition for the liquid water at
the channel interface?
2. How does the liquid water inside the channel affect the
channel flow, and what pressure drop is required to purge
the channels?
Source: Zhang, Yang and Wang, J. Electrochem. Soc., 153, 2, 2006
20
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Recent focus: boundary condition for the
liquid phase at channel/DM interface
Experiments are conducted to
understand droplet detachment
from diffusion medium
DANSIS Møte, 26.Mars 2008
·
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Source: Zhang, Yang and Wang, J. Electrochem. Soc., 153, 2, 2006
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display
Recent focus: boundary condition for the
liquid phase at channel/DM interface
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·
CFD modeling is required to understand droplet detachment
from diffusion medium
Source: Zhu, Sui and Djilali, J. Power Sources.,
172, 2007
Source: Kumbur, Sharp, Mench, J. Power Sources,
161, 2006
22
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Summary
DANSIS Møte, 26.Mars 2008
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·
·
CFD can be applied in all aspects of fuel cell operation
starting from “cold” flow and gas distribution in a stack
over simulating single cell behaviour down to providing
fundamental understanding with respect to liquid water
flow and its impact on the cell performance and aging
behavior
experimental efforts are required to verify CFD models
and provide functional relationships that describe multiphase behavior (e.g. capillary pressure vs. saturation)
Over the past years CFD has rapidly advanced in the
field of fuel cell design:
▫
▫
▫
▫
starting from 2D-single phase model (Gurau et al., 1998)
3D-single phase models (e.g. Shimpalee et al., 2000)
2D two-phase models (e.g. Chen et al., 2001)
3D, non-isothermal two-fluid model (e.g. Berning & Djilali,
2003)
▫ 3D, non-isothermal multi-phase mixture model with dryto-wet transition (Luo et al., 2007)
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