penga Ž, tolj i, barbir f, computational fluid dynamics study of pem fuel cell performance for...

ww.sciencedirect.com

i n t e r n a t i o n a l j o u r n a l o f h yd r o g e n e n e r g y x x x ( 2 0 1 6 ) 1e1 0

Available online at w

ScienceDirect

journal homepage: www.elsevier .com/locate/he

Computational fluid dynamics study of PEM fuelcell performance for isothermal and non-uniformtemperature boundary conditions

�Zeljko Penga, Ivan Tolj, Frano Barbir*

Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, University of Split, R Boskovica 32,

21000 Split, Croatia

a r t i c l e i n f o

Article history:

Received 19 April 2016

Received in revised form

11 July 2016

Accepted 12 July 2016

Available online xxx

Keywords:

Computational fluid dynamics

Segmented fuel cell

Non-uniform temperature field

Water transport

Thermal conductivity

* Corresponding author.E-mail address: [email protected] (F. Barbir

http://dx.doi.org/10.1016/j.ijhydene.2016.07.00360-3199/© 2016 Hydrogen Energy Publicati

Please cite this article in press as: Penga �Z, enon-uniform temperature boundary conj.ijhydene.2016.07.092

a b s t r a c t

Computational fluid dynamics (CFD) study of segmented proton exchange membrane fuel

cell (PEMFC) performance has been carried out, based on experimental setup and operating

parameters from previous studies. Two different temperature boundary conditions were

considered e isothermal and, a novel, non-uniform temperature profile calculated from

Mollier h-u chart. Implementation of non-uniform terminal temperature boundary con-

ditions resulted in close to 100% relative humidity along the cathode channel, resulting in

improvement of PEMFC performance without the need for external humidification. Model

polarization curve and relative humidity distribution along the cathode channel length are

in good agreement with experimental results. It was found that different current collector

materials, i.e., their thermal conductivity have major influence on temperature, thus on

relative humidity distributions along reactant gas channels. The membrane thickness af-

fects the net water transport across the membrane, thus also has influence on temperature

and relative humidity distribution along the reactant gas channels.

© 2016 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.

Introduction

Water and heat produced during an electrochemical reaction

inside a fuel cell can be used for internal humidification of

reactant gases, without the need for external humidifiers.

However, if non-humidified ambient air is introduced in an

isothermal fuel cell operating at 60 �C or higher, it would be

heated very quickly which would result in extremely low

relative humidity throughout the cathode channel, thus

causing drying of the polymer in the catalyst layer and the

membrane. This, in turn, would have adverse effects on fuel

cell performance and durability [1]. Tolj et al. [2] proposed and

).92ons LLC. Published by Els

t al., Computational fluidditions, International J

investigated a concept of an imposed variable temperature

profile along the cathode channel which resulted in 100%

relative humidity of reactant gas throughout the most of the

cathode channel without external humidification. Toyota also

relied on internal water and heat management to operate the

fuel cell stack in their Mirai vehicle without external humid-

ification [3].

High relative humidity along the cathode channel results

in higher protonic conductivity of the polymer membrane, as

demonstrated in studies by Zawodzinski et al. [4] and Hinatsu

et al. [5]. However, too much water inside the fuel cell may

result in flooding of the catalyst layer, the gas diffusion layer

and the channel. It would therefore be beneficial to keep

evier Ltd. All rights reserved.

dynamics study of PEM fuel cell performance for isothermal andournal of Hydrogen Energy (2016), http://dx.doi.org/10.1016/

mailto:[email protected]

www.sciencedirect.com/science/journal/03603199

www.elsevier.com/locate/he

http://dx.doi.org/10.1016/j.ijhydene.2016.07.092



i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n en e r g y x x x ( 2 0 1 6 ) 1e1 02

relative humidity around 100% inside the fuel cell. This is only

possible with adequate internal water and heat management.

Water management means balancing various water fluxes,

namely water generated in the electrochemical reaction on

the cathode side, electro-osmotic drag, i.e., water flux from the

anode to the cathode, and water diffusion through the mem-

brane as a result of water concentration and pressure

gradients.

Electro-osmotic drag is defined as a number of water

molecules NðH2OÞ dragged by a single hydrogen proton pass-

ing through the membrane. Water flux induced by electro-

osmotic drag is always from the anode to the cathode side of

themembrane. There have been numerous studies carried out

over the years to determine the correlation between electro-

osmotic drag coefficient and various operating parameters

for Nafionmembranes [6e16]. Experimental methods used for

electro-osmotic drag coefficient determination were concen-

tration cell [6e8], direct-methanol fuel cell analysis [10],

electrophoretic NMR techniques [11], and streaming poten-

tials [15].

However, results of parameter correlation from different

authors show high level of disagreement, although most of

them follow similar trends when dependency on different

operating conditions is considered. Model predictions from

various authors are considerably different in lowermembrane

water content (l) intervals. Almost every numerically imple-

mented model for determining electro-osmotic drag coeffi-

cient is dependent upon l, which is in defined as a function of

water activity, i.e. relative humidity. However, results from a

study by Jinnouchi et al. [17] showed that electro-osmotic drag

coefficient is not dependent on l, and that it increases only

slightly with increase in operating temperature. For this

reason, further investigation of electro-osmotic drag coeffi-

cient in an operating PEMFC is required.

Water flux resulting from a water concentration gradient

across the membrane is defined as diffusion if the flux direc-

tion is from the anode to the cathode side of the membrane,

and back-diffusion if the flux is in the opposite direction. In

most practical applications, during the flow of an electric

current, only back-diffusion is considered, because water

concentration on the cathode side of the membrane is always

higher. Large number of studies have been carried out in order

to determine diffusion coefficient by different groups of au-

thors [7,12,13,18e25]. Models of water diffusion through the

membrane also show significant disagreements between au-

thors using similar initial operating parameters.

Although most of measurement results show monotonic

dependency of water diffusion on l, some models predict a

relatively large spike in water diffusion for l intervals of 3e4,

which has not been physically explained so far. In work by

Olesen et al. [24] this phenomena was attributed to a purely

mathematical nature of derivation of fraction of natural log-

arithms of water activity versus natural logarithm of mem-

brane water content e because membrane water content

dependency on water activity was assumed to be a third de-

gree polynomial with origin in zero. This is not valid after

PEMFC break-in procedure, because the membrane will retain

a certain amount of water even if the reactants are completely

dry for some period of time. Experimental methods used

during the investigations were nuclear magnetic resonance

Please cite this article in press as: Penga �Z, et al., Computational fluidnon-uniform temperature boundary conditions, International Jj.ijhydene.2016.07.092

[14,18,19], transient sorption kinetics [20,21], steady-state

permeation [12,13,22,23], amongst others [26e29].

Almost every author referenced so far, when considering

membrane water content, has implemented empirical

expression for l derived by Zawodzinski et al. [4]. Zawod-

zinski et al. have carried out experiments at operating tem-

perature of 30 �C, which is unreasonably low when

considering common PEMFC operating temperatures (in

ranges of 60 �Ce80 �C). From this approach, one would sug-

gest that l would be the same for different temperatures

since it has temperature already incorporated in terms of

water vapor saturation pressure, which is used to calculate

water activity, i.e. relative humidity. However, in work of

Hinatsu et al. [5], l has been measured for an operating

temperature of 80 �C. The results of Hinatsu et al. [5] differ

significantly for higher intervals of water activity when

compared to results from Zawodzinski et al. [4], and subse-

quently requires further investigations.

Considering the above mentioned, changing temperature

on boundaries of a CFD model in order to achieve the desired

relative humidity profile along the reactant channels (result-

ing in higher PEMFC efficiency), has a high potential for error.

In order to determine the reliability of the implemented

models for water transport, in this work the CFD model is

validated with local and global operating parameters from

experiments of Tolj et al. [2].

The major outcome of this paper is outlining the fact that

temperature difference between reactant channels and cur-

rent collector terminals is significant, and that improper

definition of higher temperature boundary conditions during

the CFD analysis leads to under-prediction of the polarization

curve at higher current densities.

The common CFD modeling approach is defined by having

a uniform temperature field on anode and cathode terminals,

based on defining a single parameter of operating tempera-

ture. The temperature of an operating PEMFC is higher inside

the reactant channels e compared to the temperature along

terminals, and non-uniformly distributed due to heat release

induced by electrochemical reaction.

Although this is of minor importance for relatively low

current densities and fully humidified reactants, in cases

where higher current density is considered and where

partially humidified reactants are used, this must be consid-

ered. One way of minimizing this error would be to measure

the temperature along the anode and cathode terminals in

more physical points. This would result in a temperature

profile boundary condition and lead to a more realistic

boundary condition setup, as demonstrated in this work.

There are other methods of achieving self-humidification

of an operating cell [30e36], but they are based on devel-

oping new materials for the membrane, catalyst layers and

new types of porous layers, or the necessity for hydrogen

recirculation pump, which results in further increase in the

cost of the already costly membrane-electrode assembly or

the PEM fuel cell system. Thiswork is studying the economical

solution for self-humidification without the necessity for

developing new exotic materials or using additional system

components for achieving self-humidification. It is based on

establishing a temperature gradient along the cathode flow

field, which can be achieved by cooling channels configuration




i n t e r n a t i o n a l j o u r n a l o f h yd r o g e n e n e r g y x x x ( 2 0 1 6 ) 1e1 0 3

and coolant mass flow rate control which is a standard

component of PEM fuel cell stack systems.

Methodology

Experimental setup

In a previous study by Tolj et al. [2], measurements of polari-

zation curves and relative humidity profiles along the cathode

reactant channel were done using 5 single cell fuel cells

(segments) connected electrically in parallel, with counter-

flow setup. The results have been used to calibrate and vali-

date the developed CFD model.

Domains

Geometry for the CFD model has been developed from one

single cell used by Tolj et al. [2]. In order to implement

segmented temperature boundary condition, and represent

the experimental setup consisting of five segments, current

collector terminals from anode and cathode have been

divided into five equal parts (segments), Fig. 1.

Mesh

In order to enable study of different physical processes inside

PEMFC, a grid dependency study was carried out for various

mesh configurations by varyingmesh type and number of finite

volumes. Since geometry is simple, and has large difference in

scale size (edge length span from 10 mm e catalyst layer thick-

ness, to0.2meaxial lengthofPEMFC), itwasmostconvenient to

use a structured hexahedral mesh, i.e. Cartesian grid.

During the calculations, convergence monitors have been

defined to track the convergence history of average current

density on the cathode terminals, as well as the average

relative humidity on anode and cathode inlets and outlets. In

order to achieve a grid independent solution, the number of

mesh sub-divisions has been varied considerably. After

Fig. 1 e Numerical domains.


achieving a grid independent solution for an average current

density close to 500 mA cm�2, the relative humidity profile

along the cathode channel length has been compared to

experimental results with good agreement. Total number of

finite volumes was 1.547 million.

A comparison of mesh setup with the one used in work by

Arvay [37] showed a similar number of edge sub-divisions for

all domains besides the reactant channels. In this work, a

higher number of finite volumes in the channels have been

used to give a better representation of the relative humidity

profile along the cathode channel.

Governing equations and boundary conditions

Numerical calculations were carried out using ANSYS Fluent

16.2 PEM Fuel Cell Module. The operating parameters used in

the setup are shown in Table 1. The parameters used for the

model calibration were open-circuit voltage of 0.91 V, imple-

mented from the work of Tolj et al. [2], and the cathode

reference current density for the operating current density of

500 mA cm�2. The resulting value for cathode reference cur-

rent density used during the simulations was 0.0155 Am�2.

The remaining material parameters are kept on the default

values in PEM Fuel Cell Module, because the data was not

provided by the MEA manufacturer. Solution control and

recommended parameters are implemented from the manual

[38]. The novelty of this work is the implementation of

segmented temperature profiles which enables the study of

PEMFC operating parameters for different applied tempera-

ture profiles, i.e. temperature gradients.

The governing equations are based on mass, momentum,

energy and species conservations including appropriate source

terms described in the manual [38]. The type of analysis used

was steady-state and single-phase, including equations for

Joule heating, reaction heating, electrochemistry sources,

Butler-Volmer rate and membrane water transport. Water

transport equations consist of an equation for electro-osmotic

Table 1 e Operating parameters.

Parameter Values

Cathode stream abs. pressure 1.01325 bar

Anode stream abs. pressure 1.01325 bar

Cathode stream inlet temperature 30 �CAnode stream inlet temperature 25 �CFuel cell hardware temperature 60 �C or variable

Relative humidity of cathode stream inlet 75%

Relative humidity of anode stream inlet dry

Current density 500 mA=cm2

Stoichiometry, cathode 2.15

Stoichiometry, anode 1.2

Reactant straight channel length 200 mm

Channel width at anode and cathode 1 mm

Channel height at anode and cathode 1 mm

Membrane thickness (Nafion 212) 0.05 mm and 0.01 mm

Catalyst layer thickness 0.01 mm

Platinum loading 0.5 mg=cm2

Gas-diffusion layer thickness 0.38 mm

Effective area 2000 mm

Membrane dry density 2 g=cm3

Membrane molecular weight 1100 g=mol





drag coefficient by Springer et al. [26] and diffusion equations

by Motupally et al. [12] for different membrane water content

intervals. The membrane water content equation used in the

software was adopted from Zawodzinski et al. [4].

The governing equations of Fluent PEM fuel cell module

are based on energy, mass, momentum and species conser-

vation including appropriate sink and source terms [refer-

ence]. For steady-state simulations, time dependent

parameters are omitted from the equations. The resulting

equations are:

Continuity

V�rV!� ¼ Smass

Where Smass represents source term for continuity equation.

This term is only applicable for the triple-phase boundary

(catalyst) regions. Inside the gas channels, gas-diffusion

layers and the membrane, the source term Smass is set to

zero.

Momentum

1sð1� sÞV

�rV!

V!� ¼ �Vpþ 1

sð1� sÞV�mVV

!�þ rg þ Smom

Where Smom represents the source term for momentum

equation and applies only for the porous medium. For other

domains, Smom is set to zero.

Species

V�rV!Xi

� ¼ �VðrDiVXiÞ þ Si

where index i represents different speciese oxygen, hydrogen

and water vapor. Si represents the source and sink term for

the species inside the catalyst layers and accounts for the

reactant consumption in anode and cathode catalyst layers

and water generation inside the cathode catalyst layer. In

other domains, Si is set to zero.

Energy

V�rV!T� ¼ V

�keffVT

�þ ST

where ST represents the heat source term for the energy

equation. ST applies only for the cathode catalyst layer, for

other domains it is set to zero.

Water transport through the membrane

Electro-osmotic drag represents thewater flux from the anode

to the cathode side, and is defined by expression

nd ¼ 2:522

l

where nd represents electro-osmotic drag coefficient, and l

represents membrane water content, defined as

l ¼ 0:043þ 17:18a� 39:85a2 þ 36a3 ða<1Þ


l ¼ 14þ 1:4ða� 1Þ ða � 1ÞWhere a represents water activity, defined as

a ¼ pwv

psatþ 2s

Where pwv represents water vapor pressure, and psat repre-

sents water vapor saturation pressure. Since the model is

single phase, the Leverett function term 2s is set to zero.

Back-diffusion flux Jdiffw is defined as

Jdiffw ¼ � rm

MmMH2ODlVl

Where rm andMm represent density and the equivalent weight

of the dry membrane, respectively. The term Dl represents

membrane water diffusivity, defined as

Dl ¼ 3:1� 10�7l�e0:28l � 1

��e�

2346T

�ðl<3Þ

Dl ¼ 4:17e� 10�8l�1þ 161e�l

��e�

2346T

�ðl � 3Þ

Domain boundary conditions

The domain type for all domains is defined as fluid bodies,

except for current collectors which are defined as solid bodies.

In work of Tolj et al. [2] the current collector material was

stainless steel SS316L, therefore this material was selected in

this study as well.

It has been shown that the thermal conductivity of the

current collector material has a significant influence on rela-

tive humidity profile along the channel length. Thermal con-

ductivity affects the heat transfer rate between the reactant

channels which are at higher temperature, and the current

collector terminals, which are on lower temperature. Appli-

cation of current collector materials with low thermal con-

ductivity results in a higher temperature difference between

the channels and terminals. Reduction in heat transfer be-

tween the channels and terminals results in a temperature

gradient and reduced relative humidity profile along the entire

channel length. The temperature along the channel length

determines the water vapor saturation pressure, therefore it

has a direct influence on relative humidity distribution along

the channel, as well as PEMFC efficiency.

Inlet boundary conditions

The mass flow inlet boundary condition is defined for anode

and cathode inlets. The anode inlet hydrogen temperature

was set to 25 �C, with a relative humidity of 0%. Cathode inlet

air temperature was set to 30 �C, with a relative humidity of

75%. The anode mixture of gases consisted of hydrogen and

water vapor (while the mass fraction of water vapor was set

on zero on the anode inlet), the cathode mixture of gases

consisted of nitrogen, oxygen and water vapor.

Outlet boundary conditions

On the anode and cathode reactant channel outlets, the

pressure outlet boundary condition is applied with a zero




Fig. 2 e Effect of different thermal conductivity of current


gauge pressure and backflow total temperature set according

to the temperature field setup.

Wall boundary conditions

Non-slip boundary conditions were applied to the walls. The

temperature was fixed on segmented terminals of the anode

and cathode current collectors for isothermal and non-

uniform temperature field. The electric potential on the

anode terminals was set to zero. On the cathode terminals

different values of electric potential are defined in order to

extract the polarization curve. The remaining surfaces are

defined as walls by default.

collectors on relative humidity distribution along cathode

channel.
Results and discussions
Isothermal case experimental results for the polarization

curve and relative humidity profile along the cathode channel

are used for model calibration. The calibration consisted of

achieving grid independent solution and defining appropriate

material properties of current collectors.

In the work of Ozden et al. [39], the analysis was done for

similar isothermal setup, with difference from experimental

setup by Tolj et al. [2] by using aluminum as current collector.

In that work, the analysis was done for an electric potential of

0.548 V, resulting in a current density close to 500 mA cm�2.

The simulated operating point has shown good agreement

compared with experimental results of polarization curve

from Tolj et al. [2], while the difference in the relative hu-

midity profile along the cathode channel was notably

contrasted.

The first step during the calibration of the developedmodel

was to compare the operating point and the relative humidity

profile with the results reported in Ref. [39] when aluminum is

used as current collector. It was found that the results are in

good agreement.

Influence of thermal conductivity of current collectors onrelative humidity distribution along the reactant channels

After changing the current collector material properties to

represent stainless steel SS316L, the numerical simulation re-

sults showed even better agreement of relative humidity profile

along the cathode channel when compared with experimental

data fromTolj et al. [2]. It is found that the thermal conductivity

has significant influence on the relative humidity distribution.

Since the thermal conductivity of the current collectormaterial

used by Tolj et al. [2] was not measured experimentally, and

knowing that the thermal conductivity of SS316L ranges from

12 to 17Wm�1 K�1, the best agreement with experimental data

is achieved with a thermal conductivity of 13 Wm�1 K�1, as

shown in Fig. 2. The relative humidity shown in Fig. 2 repre-

sents the area-weighted average values for the cathode chan-

nel cross sections. The values of relative humidity from CFD

simulations are extracted for cross sections defined every 5% of

the channel length.

In order to explain this behavior, several things must be

considered. Aluminum has a higher thermal conductivity

compared to that of stainless steel (200 Wm�1 K�1 for


aluminum, vs. 12e17 Wm�1 K�1 for stainless steel). The rela-

tive humidity for fixed mass flow and pressure depends only

on temperature, since water vapor saturation pressure is only

a function of temperature [40]. For a fixed mass flow and

pressure, increasing the temperature along the reactant

channels results in a reduction of relative humidity profile

along the channel, and vice versa.

If the temperature is fixed on the terminals, it is clear that

higher temperature along the reactant channels must be pri-

marily caused by heat release during electrochemical reactions

inside the cathode catalyst layer. This leads to a conclusion that

in order to determine the relative humidity profile along the

channel length properly during CFD analysis, it is important to

apply realistic boundary conditions for temperature on the

anode and cathode terminals. In order to define realistic tem-

peratures on terminals, they would need to be measured

experimentally. Measuring the terminal temperature is espe-

cially important when current collector materials with low

thermal conductivity are used (e.g. stainless steel, graphite, ti-

tanium). In this work, it is shown that the temperature, for

isothermal boundary condition setup, is higher inside reactant

channels from 3 to 5 K when compared to the terminal tem-

perature for current density close to 500 mA cm�2. The tem-

perature difference between the two further increases with

increase in the operating current density.

Model validation

In order to determining the influence of different temperature

field configurations on PEMFC performance, two fixed temper-

ature fields on anode and cathode terminals are studied (anode

and cathode side have identical configuration). The first was

uniform temperature field, or the so-called isothermal, and the

other was non-uniform temperature field. To determine how

accurately does the model predicts PEMFC performance, the

simulation results were compared with the experimental ones.

The comparison of the results for the polarization curve and

relative humidity profile along the cathode channel length

shows good agreement with the simulation results.

Polarization curvesThe comparison of the simulated operating points with the

associated experimental polarization curves is done for two





different temperature fields. During the simulation setup,

potentiostatic boundary conditions were applied by defining

electric potential of 0 V on the anode and a fixed electric po-

tential for each calculation on the cathode terminals. In Fig. 3,

it can be seen that CFD prediction of polarization curve for

isothermal case for a 50 mmmembrane is very good. At higher

current densities it can be seen that CFD slightly under-

predicts current density when comparing to the experi-

mental results for both temperature fields.

The reason for this is that at higher current densities, more

heat is released during the electrochemical reaction inside the

cathodecatalyst layer.Thisresults inahigher temperaturealong

the reactant channels than that defined on the current collector

terminals. With an increase in temperature, for fixedmass flow

and ambient pressure, the relative humidity is decreased,

resulting indecreasing of themembranewater content (l). Since

the membrane protonic conductivity is proportional to l,

decrease in relative humidity results in a decrease of protonic

conductivity of themembrane, i.e. higher ohmic losses.

The temperature difference between the channels and

current collector terminals is more pronounced in non-

uniform temperature field case, where fixed temperature of

terminals is overall lower (35�Ce59 �C) when compared to

isothermal case. Heat release inside the cathode catalyst layer

in non-uniform temperature field case has a higher relative

influence on PEMFC performance drop at higher current

densities e resulting in increased heat release, since higher

temperature results in lower relative humidity of the reactant

gases. This can be accounted for by slightly lowering terminal

temperature on higher current densities to get desired tem-

perature profile along the channels.

Additionally, for non-uniform temperature field there is a

difference between the temperatures of the anode and cath-

ode reactants along the entire channel length. This is due to

much higher mass flow of air, compared to hydrogen, result-

ing in slower heating of the cathode air. The cathode air tends

to heat up slower than the anode hydrogen, therefore the

temperature along the anode channel is higher. Since heat is

released inside the cathode catalyst layer, it would be ex-

pected that the cathode channel has higher temperature, but

not in this case.

Relative humidity distributionThe relative humidity distribution along the reactant chan-

nels directly influences PEMFC performance. In the work of

Fig. 3 e Polarization curve comparison.


Tolj et al. [2], the relative humidity distribution and temper-

ature was measured at the inlet and outlet of cathode chan-

nels of each segment, making a total of six measurements

along the entire channel length. Measurements for anode side

of PEMFC were not performed.

In Fig. 4 it can be seen that the CFD results show good

agreement with experimental ones for the relative humidity

distribution along the cathode channel for a 50 mmmembrane.

In Fig. 5, the relative humidity distributions are shown for

non-uniform temperature field case. In order to get channels

temperature profiles close to the experimental ones presented

in Refs. [2], proper boundary conditions for the temperature

were applied. As a result, the CFD results of the relative hu-

midity in the cathode channel are in accordance with the

experimental data.

Temperature distribution along the reactant channelsIt is not clear what is the definition of the operating temper-

ature of PEMFC, especially if term isothermal setup is being

used. Most informative way to define PEMFC temperature

would be to define a temperature profile along the reactant

channels, however it is difficult to measure the temperature

along the reactant channels because the method is intrusive.

For this reason, some authors define the temperature of

the fuel cell as the averaged outlet temperature of coolant

fluid. This is justified if the coolant is characterized by a high

specific heat andmass flow rate, and its temperature gradient

over the entire flow field is relatively small. The coolant outlet

temperature approach is relatively simple and gives some

overall definition of PEMFC temperature. The problem with

coolant outlet temperature is that this temperature is close to

an averaged value between the channel and terminal tem-

perature, which is not very useful for CFD applications.

Measuring temperature on terminal boundaries would be

more effective for CFD application. It enables setting up

proper boundary condition values, however it is uncertain

what are the exact temperatures of reactant gases inside

channels. Since commonly used materials for current collec-

tors have low thermal conductivity, temperature along

channels is always higher than on the terminals.

In order to gain insight in prediction capabilities of CFD

model analysis, it would be most convenient to measure

temperature on the terminals, as well as relative humidity

Fig. 4 e Relative humidity distribution along anode and

cathode channel length, isothermal case for current

density of 550 mA cm¡2.





cathode channel length, non-uniform temperature field

case for current density of 550 mA cm¡2.


and temperature inside the reactant channels. This would

resolve large number of uncertainties regarding setup of

proper temperature boundary conditions and give a more

detailed insight in water transport through the membrane.

In this work, terms isothermal and non-uniform temper-

ature field are used to describe temperature boundary condi-

tions on anode and cathode segmented terminals, since

temperature field inside an operating fuel cell is certainly not

isothermal. During the CFD analysis, temperature was fixed

on anode and cathode terminals, and the rest of the temper-

ature field was calculated numerically.

In Fig. 6, it can be seen that for fixed terminal temperature

of 60 �C or 333 K on the anode and the cathode terminals for

the so-called isothermal setup, temperature along reactant

channels is overall higher than terminal temperature, except

in vicinity of the inlets.

This leads to difficulties during proper setup of CFD anal-

ysis which would represent realistic operating parameters of

PEMFC from which experimental data has been extracted.

During the CFD setup, terminal temperature or terminal heat

flux must be defined, which is unknown in this case because

temperature has only been measured along the cathode

channel length.

In Fig. 6, it can be seen that hydrogen temperature almost

instantly increases to approximately constant value along the

Fig. 6 e Temperature distribution along terminals and

reactant channels for current density of 550 mA cm¡2,

isothermal case.


entire channel, while temperature of air increases more

slowly, due to the fact that air mass flow is much higher (even

though hydrogen has a much higher specific heat).

Definition of terminal segment temperature during non-

uniform temperature field setup consisted of setting up

initial temperature field and gradually reducing temperature

on each segment to a certain extent and double-checking the

resulting temperature profile versus temperature profile

defined by Tolj et al. [2] along the cathode channel length. In

Fig. 7, it can be seen that terminal temperature profile is

overall lower by up to 5 K when compared to Tolj et al. [2]

segmented temperature profile (derived from Mollier h-u

chart).

From non-uniform temperature field CFD study, it can be

seen that there is an overall difference between temperatures

of anode and cathode reactant gases due to a large difference

in mass flow rates. Since air mass flow rate is much higher

than mass flow rate of hydrogen, temperature of air increases

slower than temperature of hydrogen along the entire channel

length, even though heat is released during electrochemical

reaction inside the cathode catalyst layer.

Temperature difference between anode and cathode

reactant gases, as well as terminals, leads to a conclusion that

in order to study water and heat transfer in detail, both anode

and cathode temperature and relative humidity must be

measured along the channel and on terminals as well.

It is clear that setting up non-uniform temperature profile

is challenging both numerically and experimentally. Practical

way of setting up non-uniform temperature profile on a single

cell, or a stack, would be by defining sufficiently lowmass flow

rate of the coolant fluid, which would enter the fuel cell at

certain temperature and gradually heat up during the passage

through the cell. In this way, it would be possible to impose

similar boundary conditions as the ones used in this work,

however, this approach is currently investigated for the next

work.

Investigation of a thinner membrane

In order to determine the influence of thinner membrane

(10 mm) on PEMFC performance, simulations are carried out

for identical operating conditions used in the 50 mm mem-

brane study. Fig. 8 shows that thinner membrane results in


reactant channels for 50mm membrane, non-uniform

temperature field case for current density of 550 mA cm¡2.




Fig. 8 e Polarization curve comparison for different

membranes.Fig. 10 e Temperature distribution along terminals and

reactant channels for current density of 550 mA cm¡2,

different membranes, isothermal case.


notably higher operating voltage for isothermal and non-

uniform temperature field setups, thereby improving overall

performance of the cell.

The performance gain is a result of lower ohmic resistance

of the thinner membrane, as well as better hydration of the

anode hydrogen due to increased back-diffusion.

In Fig. 9 it can be seen that relative humidity profile for the

thinner membrane along the reactant channel length is

notably different. Thinner membrane results in higher back-

diffusion, therefore the relative humidity profile along the

anode channel is higher. For the same operating conditions

and temperature profile on terminals used in the 50 mm

simulations, it would be expected to see a slight decrease of

relative humidity profile along the cathode channel. However,

relative humidity profile along the cathode channel is higher

for the thinner membrane for this particular isothermal case.

The reason for this can be seen in Fig. 10, which shows that

this is simply caused by lower temperature profile along the

channels for the thinner membrane case. Even though the

back-diffusion results in higherwater flux from the cathode to

the anode side, lower temperature profile results in overall

higher relative humidity profiles for both sides. For this reason

reduction in the actual water content on the cathode side can

not be seen from relative humidity profile shown in Fig. 9.

Lower temperature profile along the channels is a result of

higher operating voltage for the thinner membrane, i.e. lower

waste heat generation.


cathode channel length, isothermal temperature field case,

different membranes, for current density of 550 mA cm¡2.


The effect of back-diffusion on relative humidity profile is

more pronounced in non-uniform temperature field case.

Fig. 11 shows that relative humidity profile along the anode

channel is higher, and along the cathode channel is lower, as

expected to be. In order to establish close to 100% relative

humidity along the cathode channel, the temperature profile

on cathode terminals has to be slightly reduced.

Decrease in temperature profile along the cathode channel

results in increased relative humidity along the anode chan-

nels as well. Since relative humidity along the anode channel

was already 100% in regions close to the anode outlet, the

temperature profile along the anode terminals was slightly

reduced to keep the relative humidity profile along the anode

channel close to the initial one.

Temperature profiles for this setup are shown in Fig. 12. It

can be seen that difference between anode and cathode ter-

minal temperature is up to 15 K for this configuration, which is

impractical for stack applications. For this reason, tempera-

ture profile along the anode and cathode terminals was kept

the same during the simulations.

Practical solution for establishing a non-uniform temper-

ature profile with coolant can be done by introducing coolant

channels where the flow direction is co-flow with the cathode

reactant. Since the desired temperature profile is close to


cathode channel length, non-uniform temperature field

case, different membranes, for current density of

550 mA cm¡2.





reactant channels for 10 mm membrane, non-uniform

temperature field case for current density of 550 mA=cm2.


linear, it can be achieved with constant mass flow rate of the

coolant, where the slope of the temperature profile, i.e. tem-

perature gradient can be controlled by altering the mass flow

rate of the coolant. This approach could be used in stack

configurations as well, where different temperature profiles

can be established depending on operating conditions,

without the need for external humidification.

Conclusions

The CFD model shows good agreement with experimental

results fromTolj et al. [2] and outlines details which need to be

studied experimentally. The temperature distribution inside

an operating fuel cell is of critical importance when partially

humidified/dry reactants are considered, and needs to be

experimentally studied in more detail.

It is shown that the temperature inside an operating fuel

cell is highly non-uniform, and the temperature inside the

reactant channels is in overall higher than that of the current

collector terminals. In order to have a robust CFD model with

good prediction capacity for various operating parameters, the

temperature must be measured during experiments in more

points, and can not be simply defined as one operating

parameter. The temperature difference between the reactant

channels and terminals increases with the current density,

and CFD model must be calibrated to account for this tem-

perature difference at all times.

Non-uniform temperature field study has shown that there

is an additional difference between the temperature of re-

actants along the anode and cathode channels, due to signif-

icantly higher air mass flow of in the cathode channels. This

results in a lower temperature profile along the cathode

channel compared to that of the anode channel, even though

that heat is being generated inside the cathode catalyst layer.

This further complicates proper temperature field setup on

terminals, since experimental data for temperature was

available only along the cathode channel length.

It is demonstrated that the membrane thickness also in-

fluences the temperature inside reactant channels, dictating

the relative humidity distributions and the PEMFC efficiency.

Using thinner membrane is beneficial for fuel cell operation


without an external humidification, as it results in better hy-

dration of the anode side due to the increased back-diffusion

and lower temperature along the channels (lower ohmic los-

ses of the membrane).

Further studies will includemeasurement of water and tem-

peraturedistributionalongtheanodechannelusingasegmented

fuel cell. The experimental setup will also be used to verify the

results obtained numerically for a thinner (10 mm) membrane.

The performance at various current densities, including the

transients during the load changes, will also be studied.

Acknowledgments

The research leading to these results has received funding

from the Croatian Science Foundation project IP-11-2013-8700

“Water and Heat Management and Durability of PEM Fuel

Cells”. �Z. Penga also acknowledges support he has received

from EU FP7 Programme through Fuel Cells and Hydrogen

Joint Undertaking under grant agreement no 325275 (Project

SAPPHIRE).

Nomenclature

a water activity

CFD Computational fluid dynamics

Di gas diffusion coefficient

Dl membrane water diffusivity

g gravitational acceleration, ms�2

h enthalphy, J

Jdiffw back diffusion flux, kg m�3 s�1

keff thermal conductivity, Wm�1 K�1

Mm equivalent weight of the dry membrane, g mol�1

MH2O molar mass of water, g mol�1

nd electro-osmotic drag coefficient

p pressure, Nm�2

PEMFC proton exchange membrane fuel cell

psat water vapor saturation pressure, Nm�2

pwv partial pressure of water vapor, Nm�2

s liquid water saturation

Si source term for species, kg m�3s�1

Smass source term for continuity equation, kg m�3s�1

Smom source term for momentum equation, kg m�3s�1

ST source term for energy equation, kg m�3s�1

SS stainless steel

T temperature, K

V!

velocity vector

Xi species mass fraction

Greek symbols

l membrane water content

m dynamic viscosity, kg m�1s�1

r density, kg m�3

rm dry membrane density, kg m�3

u absolute humidity, kgH2Okg�1air





r e f e r e n c e s

[1] Yousfi-Steiner N, Mocoteguy Ph, Candusso D, Hissel D,Hernandez A, Aslaindes A. A review on PEM degradationassociated with water management: impacts, influentfactors and characterization. J Power Sources2008;183:260e74.

[2] Tolj I, Bezmalinovic D, Barbir F. Maintaining desired level ofrelative humidity throughout a fuel cell with spatiallyvariable heat removal rates. J Hydrogen Energy2011;36:13105e13.

[3] Konno N, Mizuno S, Nakaji H, Ishikawa Y. Development ofCompact and high-performance fuel cell stack. SAE Int. J AltPower 2015;4(1):123e9.

[4] Zawodzinski TA, Derouin C, Radzinski S, Sherman RJ,Smith VT, Springer TE, et al. Water uptake by and transportthrough Nafion 117 membranes. J Electrochem Soc1993;140:1041e7.

[5] Hinatsu JT, Mizuhata M, Takenaka H. Water uptake ofperfluorosulfonic acid membranes from liquid water andwater vapor. J Electrochem Soc 1994;141:1493e8.

[6] LaConti AB, Fragala AR, Boyack JR. Electrode materials andprocesses for energy conversion and storage. ElectrochemSoc Proc Ser Princet 1997;77(6):354.

[7] Zawodzinski TA, Springer TE, Davey J, Jestel R, Lopez C,Valerio J, et al. A comparative-study of water-uptake by andtransport through ionomeric fuel-cell membranes. JElectrochem Soc 1993;140(7):1981e5.

[8] Pivovar BS, Smyrl WH, Cussler EL. Nafion, Polystyrenesulfonic acid and polybenzimidazole as direct methanol fuelcell electrolytes. J Electrochem Soc 2005;152:A53e60.

[9] Xie G, Okada T. Water transport behavior in Nafion 117membranes. J Electrochem Soc 1995;142(9):3057e62.

[10] Ren X, Henderson W, Gottesfeld S. Electro-osmotic drag ofwater in ionomeric membranes. J Electrochem Soc1997;144:267e70.

[11] Ise M, Kreuer KD, Maier J. Aspects of the formation andmobility of protonic charge carriers and the stability ofperovskite-type oxides. Solid State Ionics1999;125(1):285e302.

[12] Motupally S, Becker AJ, Weidner JW. Diffusion of waterthrough Nafion 115 membranes. J Electrochem Soc2000;147:3171e7.

[13] Fuller TF, Newman J. Experimental determination of thetransport number of water in Nafion 117 membrane. JElectrochem Soc 1992;139:1332e7.

[14] Zawodzinski TA, Davey J, Valerio J, Gottesfeld S. The watercontent dependence of electro-osmotic drag in proton-conducting polymer electrolytes. Electrochim Acta1995;40(3):297e302.

[15] Weng D, Wainright JS, Landau U, Savinell RF. Electro-osmoticdrag coefficient of water and methanol in polymerelectrolytes at elevated temperatures. J Electrochem Soc1996;143(4):1260e3.

[16] Ye X, Wang CY. Measurement of water transport propertiesthrough membrane-electrode assemblies. J Electrochem Soc2007;154(7):B676e82.

[17] Jinnouchi R, Yamada H, Morimoto Y. Measurement ofelectro-osmotic drag coefficient of Nafion using aconcentration cell. 14th International Conference on theProperties of Steam in Kyoto 2004;32:403e406.

[18] Zelsmann HR, Pineri M, Thomas M, Escoubes M. Water self-diffusion coefficient determination in an ion exchangemembrane by optical measurement. J Appl Polym Sci1990;41(7e8):1673e84.

[19] Gong X, Bandis A, Tao A, Meresi G, Wang Y, Inglefield PT,et al. Self-diffusion of water, ethanol and decafluoropentane


in perfluorosulfonate ionomer by pulse field gradient NMR.Polymer 2001;42:6485e92.

[20] Morris DR, Sun XD. Water sorption and transport propertiesof Nafion 117. J Appl Polym Sci 1993;50:1445e52.

[21] Yeo SC, Eisenberg A. Physical properties and supermolecularstructure of perfluorinated ion-containing (Nafion) polymers.J Appl Polym Sci 1997;21(4):875e98.

[22] Rivin D, Kendrick CE, Gibson PW, Schneider NS. Solubilityand transport behavior of water and alcohols in Nafion.Polymer 2001;42(2):623e35.

[23] Ye X, LeVan MD. Water transport properties of Nafionmembranes. J Membr Sci 2003;221(1):163e73.

[24] Olesen AC, Berning T, Kaer SK. On the diffusion coefficient ofwater in polymer electrolyte membranes. ECS Trans2012;50(2):979e91.

[25] Husar A, Higier A, Liu H. In situ measurement of watertransfer due to different mechanisms in a proton exchangemembrane fuel cell. J Power Sources 2008;183(1):240e6.

[26] Springer TE, Zawodzinski TA, Gottesfeld S. Polymerelectrolyte fuel cell model. J Electrochem Soc1991;138(8):2334e41.

[27] Zhao Q, Majsztrik P, Benziger J. Diffusion and interfacialtransport of water in Nafion. J Phys Chem 2011;115:2717e27.

[28] Nguyen TV, White RE. A water and heat management modelfor proton-exchange-membrane fuel cells. J Electrochem Soc1993;140(8):2178e86.

[29] Vishnyakov A, Ravikovich PI, Neimark AV. Characterizationof micro-and mesoporosity in SBA-15 materials fromadsorption data by the NLDFT method. J Phys Chem2001;B105(29):6817e23.

[30] Breitwieser M, Moroni R, Schock J, Schulz M, Schilinger B,Pfeifer F, et al. Water management in novel direct membranedeposition fuel cells under low humidification. J HydrogenEnergy 2016;41:11412e7.

[31] Kim BJ, Kim MS. Studies on the cathode humidification byexhaust gas recirculation for PEM fuel cell. J Hydrogen Energy2012;37:4290e9.

[32] Su H, Xu L, Zhu H, Wu H, Wu Y, Yang L, et al. Self-humidification of a PEM fuel cell using a novel Pt/SiO2/Canode catalyst. J Hydrogen Energy 2010;35:7874e80.

[33] Staschewski D, Mao ZQ. Hydrogen-air PEMFC operation withextraordinarily low gas pressures and internalhumidification e concept and experimental prototype stack.J Hydrogen Energy 1999;24:543e8.

[34] Hou S, Liao S, Dang D, Zou H, Shu T, Du L. Self-humidifyingmembrane electrode assembly prepared by addingmicrocrystalline cellulose in anode catalyst layer as preservemoisture. J Hydrogen Energy 2014;39:12842e8.

[35] Lee SH, Choi SH, Gopalan SA, Lee KP, Gopalan AI. Preparationof new self-humidifying composite membrane byincorporating graphene and phosphotungstic acid intosulfonated poly(ether ether ketone) film. J Hydrogen Energy2014;39:17162e77.

[36] McKahn D. Influence of gas channel depth in self-humidifiedminiature PEM fuel cells with dead-ended anode. J HydrogenEnergy 2015;40:7168e81.

[37] Arvay A. Proton exchange membrane fuel cell modeling andsimulation using ANSYS Fluent. Arizona State University;2011 [Master Thesis].

[38] ANSYS Inc. ANSYS fluent 12.0 fuel cells module manual.ANSYS, Inc; 2009.

[39] Ozden E, Tolj I, Barbir F. Designing heat exchanger withspatially variable surface area for passive cooling of PEM fuelcell. Appl Therm Eng 2013;51(1e2):1339e44.

[40] Barbir F. PEM fuel cells, 2nd edition: theory and practice.Academic Press; 2012.


http://refhub.elsevier.com/S0360-3199(16)32079-1/sref1








































































































































































penga Ž, tolj i, barbir f, computational fluid dynamics study of pem fuel cell performance for...

Documents