Modeling a Proton Exchange Membrane Fuel Cell Stack Cell by Cell: Illustration of a Mechanism for the Propagation of Degradations
Authors: Bahrami M. , Bligny R. , Dillet J. , Didierjean S. , Martin J. P. , Pierfederici S. , Maranzana G. 
Published: September 2021

This paper is devoted to the modeling of a PEMFC fuel cell stack. First, to justify the hypotheses, original experimental results are presented and show that the gas flow rates feeding a cell in its stack environment highly depend on the thermal management. Then, the generic model of a cell in its stack environment is presented. A two-phase flow model is implemented to calculate the gas flow rates as a function of the pressure drops and considering the amount of liquid water present in both compartments. In this way, the dispatching of the total active gases flow rate between the different cells can therefore be described. Finally, a stack of five cells is numerically assembled by describing the thermal coupling between the cells. Two application examples are conducted. A first one considers a cooling defect and a second one simulates the case where one cell is more degraded than the others. It is shown how these types of malfunction can cause a fuel starvation event. At the end, and for the first time as far as we know, a mechanism of propagation of degradations from cell to cell is proposed.

List of symbols

Symbol
Description
Unit
Symbol
Description
Unit

C

d
l

Double-layer capacity of the cell
F

R

m

Protonic resistance of the membrane and electrodes
Ω

C

v
a
p

water vapor concentration
mol m−3

R

t
h

Thermal resistance
K W−1

C

O

2

Oxygen Concentration
mol m−3

R

d
i
f
f

Mass transfer reisstance
s m−3

C

s
a
t

T

Concentration of the saturated vapor at T

mol m−3

S

w

Water saturation in the channels

C

p

Specific heat capacity of plate
J/K.kg

T

Temperature
K

D

v
a
p

⁎
,
G
D
L

Effective water vapor diffusion coefficient through the GDL
m2 s−1

U

Cell potential
V

D

m

H

2

O

Water diffusion coefficient in the membrane
m2 s−1

V

c
h

Volume of channels

m3

D

O

2

G
D
L

Effective oxygen diffusion coefficient through the GDL
m2 s−1

Greek Letters

e

G
D
L

Thickness of the GDL
m

α

o
x

Anodic charge transfer coefficient

E

0

Standard cell potential
V

α

r
e
d

Cathodic charge transfer coefficient

E
W

Equivalent weight of the membrane
kg mol−1

γ

Roughness factor of the electrode

F

Faraday constant
C mol−1

Δ
P

Pressure drop
Pa

I

Current intensity
A

ξ

Electro-osmosis coefficient

I

0

Exchange current density
A m−2

λ

Water content of the membrane

K

M
E
A

t
h

thermal capacity of the MEA
J K−1

λ

G
D
L

Effective thermal conductivity of GDL
W mK−1

K

p

t
h

thermal capacity of the anode/cathode plates
J K−1

ρ

Volumetric mass
kg m−3

L

Length of the active area
m

ϕ

Cathode electrode potential
V

L

v

Water latent heat
kJ mol−1

Upper & lower scripts

Δ

H

H

2

lower heating value of Hydrogen
kJ mol−1

in

Inlet

M

H

2

O

Molar mass of water
kg mol−1

out

Outlet

N

a
i
r

Dry air molar flow rate
mol s−1

c

Cathode

N

H

2

Dry hydrogen molar flow rate
mol s−1

a

Anode

N

v
a
p

Water vapor molar flow rate
mol s−1

ch

Channels

N

v
a
p

e
l
→
c
h

Water vapor flow rate from electrode to channels
mol s−1

el

Electrode

P

0

Atmospheric pressure
mol s−1

m

Membrane

P

a

Total pressure in the anode channels
Pa

cf

Cooling fluid

P

c

Total pressure in the cathode channels
Pa

n−1
Preceding electrode

R

Universal gas constant
J mol.K−1

n + 1
Following electrode

R

e

Electrical resistance of the cell
Ω