Theoretical and experimental study of a 10 kilowatt …lib.tkk.fi/Dipl/2008/urn100393.pdfHELSINKI...

HELSINKI UNIVERSITY OF TECHNOLOGY

Faculty of Engineering and Architecture

Laboratory of Applied Thermodynamics

Jaana Viitakangas

Theoretical and experimental study of a 10 kilowatt

proton exchange membrane fuel cell’s thermal and mois-

ture system control

Master’s Thesis submitted in partial fulfillment of the requirements for the degree of Master of

Science in Technology.

Espoo, October 24, 2008

Supervisor: Prof. Markku Lampinen

Instructor: Jari Ihonen, Ph.D.(Tech.)

ii

HELSINKI UNIVERSITY ABSTRACT OF THE

OF TECHNOLOGY MASTER’S THESIS

Author: Jaana Viitakangas

Name of the thesis: Theoretical and experimental study of a 10 kilowatt proton exchange

membrane fuel cell’s thermal and moisture system control

Date: October 24, 2008 Number of pages: 67

Faculty: Faculty of Engineering and Architecture

Department: Department of Energy Technology

Professorship: Ene-39 Thermal Engineering

Supervisor: Prof. Markku Lampinen

Instructor: Jari Ihonen, Ph.D.(Tech.)

A fuel cell is an electrochemical device that converts fuel and oxidant into electricity. Fuel

cells are considered a promising future energy technology, due to their potential for efficient

and environmental energy production.

In this thesis a middle pressure, 10 kW scale electrical power proton exchange membrane

(PEM) fuel cell system has been studied, concentrating on air and moisture management. The

issue of whether a small pressurization could benefit the PEMFC system has been examined.

Since the examination is targeted to a real system that could be built of serial production com-

ponents, system component availability has also been mapped. It was notedthat there are no

commercial compressors for the PEMFC systems in this power range.

Pressurization is known to have many advantages over non pressurizedfuel cell systems,

namely pressurization makes the system smaller and lighter and therefore cheaper. Pressur-

ization also eases water management, since at higher pressures less wateris needed to reach

the same relative humidity levels. However, the high pressure systems are more complex and

costly to build because of required special equipment. In this work, middle pressure denotes

the pressures between atmospheric and 1.5 bar.

In this study net power gain was not achieved, mainly because of blowersin this range have

fairly low efficiencies and best efficiency area is typically narrow. The power density increases

by pressurization and this leads system size and cost reductions.

Keywords: PEMFC, air and water management, pressurization

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TEKNILLINEN KORKEAKOULU DIPLOMITYÖN TIIVISTELMÄ

Tekijä: Jaana Viitakangas

Työn nimi: 10 kilowatin polymeeripolttokennon lämpö- ja kosteudenhallintajärjestelmien

teoreettinen ja kokeellinen tutkimus

Päivämäärä: 24.10.2008 Sivuja: 67

Tiedekunta: Insinööritieteiden ja arkkitehtuurin tiedekunta

Laitos: Energiatekniikan laitos

Professuuri: Ene-39 Lämpötekniikka ja koneoppi

Työn valvoja: Prof. Markku Lampinen

Työn ohjaajat: Jari Ihonen, Ph.D.(Tech.)

Polttokenno on sähkökemiallinen laite, joka muuntaa polttoaineen ja hapen suoraan sähköksi.

Polttokennot ovat lupaava energiantuotantomuoto, sillä niillä on edellytykset tehokkaaseen ja

ympäristöystävälliseen energiantuotantoon.

Tässä diplomityössä on tutkittu sähköteholtaan 10 kW luokan keskipaine polymeeri elek-

trolyytti membraani polttokenno (PEMFC) järjestelmää. Työssä on keskitytty ilman- ja kosteu-

denhallintaan, tutkimalla voisiko pieni paineennosto hyödyttää PEM-polttokennojärjestelmiä.

Koska tarkastelussa on keskitetty rakennettavissa oleviin järjestelmiin, myös järjestelmäkom-

ponenttien saatavuutta on kartoitettu. Katsauksessa selvisi, ettei tämän kokoluokan PEM polt-

tokennoille ole kompressoreita markkinoilla.

Paineistuksen tiedetään tuovan useita etuja normaalissa ilmanpaineessa toimiviin PEM poltto-

kennoihin nähden. Keskipainejärjestelmästä tulee kevyempi, pienempi ja näin ollen halvempi.

Paineistus myös helpottaa kosteudenhallintaa. Korkeapainejärjestelmät ovatkuitenkin mon-

imutkaisempia ja vaadittavien erityiskomponenttien vuoksi kalliimpia rakentaa. Tässä työssä

keskipainejärjestelmällä viitataan paineisiin normaalin ilmakehän ja 1.5 bar välillä.

Tässä tutkimuksessa nettotehoja ei pienellä paineistamisella saavutettu, johtuen pääasiallis-

esti puhaltimen huonosta hyötysuhteesta sekä kapeasta parhaan hyötysuhteen alasta. Paineis-

taminen kuitenkin parantaa tehotiheyttä, joka tietyissä sovelluksissa voi olla hyötysuhdettakin

tärkeämpää.

Avainsanat: PEMFC, ilman- ja kosteudenhallinta, paineistus

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Acknowledgements

This Master’s thesis has been carried out in the Fuel cells and hydrogentechnology VTT Tech-

nical Research Center of Finland and is a part of the WorkingPEM project which is funded by

the Finnish Funding Agency for Technology and Innovation, Tekes.

I want to thank professor Markku Lampinen for supervising my Master’sthesis and Jari Ihonen

for guidance and sharing a great deal of fuel cell trivia.

I would also like to thank the whole staff of VTT Fuel cells and hydrogen technology as well

for introducing me into the world of fuel cells, as well as for the company forthe lunch and the

coffee breaks. I especially want to thank Timo Keränen who has patiently helped me out with

problems big and small. I also wish to thank the other Master’s thesis workers at VTT for “peer

support”. A special thanks goes to Marisol Herrera for proofreading.

My gratitude also goes to my parents who have always been there for me andhave let me find

my own paths.

Finally, I would like to thank Vipe, who’s overwhelming optimism has enlightened mylife.

Otaniemi, November 10, 2008

Jaana Viitakangas

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viii

Contents

Nomenclature xvi

List of Figures xviii

List of Tables xix

1 Introduction 1

1.1 Background of the project. . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 Problem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.3 Target and approach. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.4 Thesis outline. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2 Polymer electrolyte membrane fuel cell 5

2.1 What is PEM?. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.1.1 Structure and reactions. . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.1.2 Cell components. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.2 Thermodynamics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.2.1 Gibbs free energy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.2.2 Theoretical fuel cell potential. . . . . . . . . . . . . . . . . . . . . . 9

2.2.3 Nernst equation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.2.4 Theoretical fuel cell efficiency. . . . . . . . . . . . . . . . . . . . . . 11

2.3 Mass transfer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.4 Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

ix

2.4.1 Current density. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.4.2 Actual performance. . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.4.3 Actual cell voltage. . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.4.4 Actual fuel cell efficiency . . . . . . . . . . . . . . . . . . . . . . . . 17

2.5 Conservation laws for fuel cells. . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.5.1 Flux balance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.5.2 Energy balance for PEMFCs. . . . . . . . . . . . . . . . . . . . . . . 18

2.6 Water management. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.6.1 Humidification of air and hydrogen. . . . . . . . . . . . . . . . . . . 21

2.7 Degradation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3 PEM fuel cell systems 23

3.1 PEM fuel cell applications. . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.1.1 Fuel cell vehicles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.1.2 Heavy-duty vehicles and buses. . . . . . . . . . . . . . . . . . . . . . 25

3.2 The special needs of PEM systems. . . . . . . . . . . . . . . . . . . . . . . . 28

3.2.1 Water management. . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.2.2 Hydrogen storage. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.3 Challenges of PEM systems. . . . . . . . . . . . . . . . . . . . . . . . . . . 30

3.3.1 Hydrogen supply. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

3.3.2 Contamination. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

3.3.3 The demand and price of platinum. . . . . . . . . . . . . . . . . . . . 31

3.3.4 Other costs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

3.3.5 Incomplete society. . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

3.4 BoP - Balance of plant. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

3.4.1 Specific key components. . . . . . . . . . . . . . . . . . . . . . . . . 33

3.4.2 Other commercial components. . . . . . . . . . . . . . . . . . . . . . 34

3.4.3 Net system power and system efficiency. . . . . . . . . . . . . . . . . 35

3.5 System optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

x

3.5.1 Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3.5.2 Pressure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3.6 Air side fuel cell system modeling. . . . . . . . . . . . . . . . . . . . . . . . 37

3.6.1 PEMFC models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

3.6.2 Membrane humidifier models. . . . . . . . . . . . . . . . . . . . . . 38

4 Characterization 41

4.1 Testing of blowers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

4.1.1 Test system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

4.1.2 Ametek DC blower. . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

4.1.3 Ametek AC blower. . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

4.1.4 Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

4.1.5 Error factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

4.2 Stack characterization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

4.2.1 CEA/GENEPAC stack. . . . . . . . . . . . . . . . . . . . . . . . . . 45

4.2.2 3G stack . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

5 Air side calculations 51

5.1 The effect of temperature and pressure. . . . . . . . . . . . . . . . . . . . . . 52

5.1.1 The cost of pressurization. . . . . . . . . . . . . . . . . . . . . . . . 52

5.1.2 Cost of pressurization with a 3G stack. . . . . . . . . . . . . . . . . . 52

5.1.3 The effect of pressurization on water balance. . . . . . . . . . . . . . 53

5.2 Modeling with Matlab . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

5.2.1 Assumptions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

5.2.2 General discussion of the model. . . . . . . . . . . . . . . . . . . . . 59

6 Results 61

6.1 The effect of pressure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

6.1.1 Theoretical price. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

6.1.2 Efficiency. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

xi

6.2 Modeling results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

6.2.1 Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

7 Conclusions and Future Work 67

7.1 Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

7.2 Future work. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

A Matlab code 75

A.1 Main program. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

A.2 Sub programs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

B Stack energy balance 97

xii

Nomenclature

Roman symbols

a activity, Eq.2.24

A area (m2)

Cp heat capacity at constantp (JK−1)

Cp heat capacity at constantv (JK−1)

cp specific heat capacity at constantp (Jkg−1K−1)

cv specific heat capacity at constantv (Jkg−1K−1)

D diffusion coefficient (cm2s−1)

e charge of one electron = 1.602× 10−19 (moleculesmol−1)

E voltage (V )

F Faraday’s constant, Eq.2.19(Celectron−mol−1)

f fugasity

G Gibbs (free) energy (kJmol−1)

H enthalpy (J)

h specific enthalpy (Jkg−1)

I current (A)

i current density, Eq.2.32(Acm−2)

i0 exchange current density (Acm−2)

J flux (mols−1)

j flux per unit are (mols−1cm−2)

khyd hydraulic permeability coefficient, in Eq.2.65(?)

m mass (kg)

m mass flow (kgs−1)

M molecular weight (kg/mol)

n amount of substance (mol)

n molecular flow (mols−1)

xiii

NA Avogadro’s number, numbers of molecule per mole (moleculesmol−1)

P power (W )

p pressure (Pa, bar)

r area specific resistance (Ωcm−2)

R gas constant,R ≈ 8.314 Jmol−1K−1

RH relative humidity (%)

S entropy (JK−1)

s specific entropy (Jkg−1K−1)

T temperature (K)

U internal energy (J)

v specific volume, v = 1/ρ (m3/kg)

V voltage (V )

V volume (m3)

W work (Jmol−1)

x humidity (kgwater/kgair)

z number of electrons

Greek symbols

α charge transfer coefficient of reaction, in Eq.2.38

∆G reaction Gibbs energy (J/mol)

∆H reaction enthalpy (J/mol)

∆S reaction entropy (J/mol)

∆V voltage loss (V )

ǫ sensible, latent or enthalpy efficiency, Eq.3.15

η efficiency (%)

κ isentropic coefficient,κ =cpcV

λm membrane water content

µ chemical potential (J/mol2), Eq.2.16

ξ electroosmotic drag coefficient, in Eq.2.63

ρ density (kg/m3)

σm membrane conductivity

τ tortuosity, Eq.2.31

Φ porosity, Eq.2.30

φ relative humidity (%), Eq.2.68

xiv

Superscripts

at standard state,p = p0 = 1 bar

Subscripts

aux axillary system equipment

b bulk

comp air compressor

cons concentration

DC DC/DC or DC/AC power conversion

diff diffusion

FC fuel cell

gen generation

HHV higher heating value

i of species i

LHV lower heating value

ohm ohmic

PC power conversion and parasitic loss

sys system

xv

Abbreviations

AC Alternating current

ASR Area specific resistance

BoP Balance of plant

CGN compressed natural gas

DC Direct current

EMF Electromotive force

H2ICE Hydrogen powered internal combustion engine

HHV Higher heating value

ICE Internal combustion engine

LHV Lower heating value

lpm liter per minute

MEA Membrane electrode assembly

NREL The National Renewable Energy Laboratory

OCV Open circuit voltage

ORR Oxygen reduction reaction

PED Pressure equipment directive

PEM Polymer electrolyte membrane

PEMFC Polymer electrolyte membrane fuel cell

PTL Porous transport layer

rpm Rotations per minute

t oz Troy ounce (1 t oz∼= 0.0311 kg)

UPS Uninterruptible power supply

WRR Water recovery ratio

xvi

List of Figures

2.1 The basic principle of PEM fuel cell. Figure modified from [14]. . . . . . . . . 6

2.2 An example of a polarization curve.. . . . . . . . . . . . . . . . . . . . . . . 13

2.3 The energy balance of a PEMFC.. . . . . . . . . . . . . . . . . . . . . . . . . 18

3.1 Volumetric densities of hydrogen under various conditions [58, 35]. . . . . . . 29

3.2 The price development of platinum between 1992 and 2008 [5]. . . . . . . . . 32

4.1 Test system for Ametek two-phase blower.. . . . . . . . . . . . . . . . . . . . 42

4.2 Pressure losses in the test arrangement for blower testing.. . . . . . . . . . . . 43

4.3 The measured data points and characteristic curves of Ametek DC blower. . . . 44

4.4 The 3D efficiency plot of Ametek DC blower.. . . . . . . . . . . . . . . . . . 45

4.5 The measured data points and characteristic curves of Ametek AC blower. . . . 46



4.8 The manufacturers efficiencies of Ametek DC and AC blowers.. . . . . . . . . 48

5.1 The air side of the PEMFC system.. . . . . . . . . . . . . . . . . . . . . . . . 51

5.2 Net power per one cell.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

5.3 Change of voltage efficiency withp andT . . . . . . . . . . . . . . . . . . . . . 54

5.4 Influence of the operating pressure and relative humidity on the water content. . 54

5.5 Influence of the operating pressure on the water content.. . . . . . . . . . . . 55

5.6 General description of the model.. . . . . . . . . . . . . . . . . . . . . . . . . 56

6.1 The efficiencies (humidifier model FC 400-10).. . . . . . . . . . . . . . . . . 63

xvii

6.2 The powers.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

6.3 Efficiencies with OA 1050 compressor.. . . . . . . . . . . . . . . . . . . . . . 64

6.4 The calculated stack energy flows.. . . . . . . . . . . . . . . . . . . . . . . . 65

xviii

List of Tables

2.1 Lower and higher heating values of hydrogen and other fuels [31]. . . . . . . . 11

3.1 Major contaminants identified in the operation of PEM fuel cells [29]. . . . . . 31

4.1 The 3G cell voltages at 45C. . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

4.2 The 3G cell voltages with effect of temperature and pressure.. . . . . . . . . . 49

5.1 The 3G cell voltage efficiencies.. . . . . . . . . . . . . . . . . . . . . . . . . 53

5.2 The dimensions of the membrane tubes in Perma Pure humidifiers.. . . . . . . 58

6.1 The model coefficients.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

xix

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Chapter 1

Introduction

The era of abundant and cheap oil is coming to its end in the near future andseeking of alterna-

tives is gaining major attention. For certain applications, for example in transportation, energy

carriers will likely be required also in the future. Fuel cells could well be part of the solution.

At present, a majority of transport methods is fueled with raffinates of crude oil. Oil alterna-

tives have been investigated actively but no one candidate has emerged above the others. Fuel

cells continue to be far too expensive for cars and problems with production and storing of hy-

drogen remain for the most part unsolved. The question that might be raised then is whether

the fuel cells will ever really penetrate vehicle markets, or if a breakthrough will take place in

battery development and thus allowing vehicles with high-tech batteries to conquer the market.

At the same time a strong opinion also exist in favor of fuel cell vehicles. Unanimity only

exists in the context of the future of the conventional propulsion systems; oil will run out sooner

or later and therefore alternatives to internal combustion engines are needed. Another concern of

car manufacturers in the modern world is the actions they must take to mitigate climate change.

Mitigation of climate change obliges them to reduce CO2 emissions and the usage of fossil fuels.

Even though hydrogen is an abundant element present in a variety of chemical compounds,

on earth it is not present in a molecular form. Hydrogen is thus a fuel that must be produced

somehow. Hydrogen production with renewables is still too expensive andthe main means of

hydrogen production is by reforming fossil fuels. Naturally this does notreduce CO2 emissions.

The fuel cell is an electrochemical device that converts fuel and oxidant into electricity. Sim-

ilar to a combustion process, fuel cells convert chemical bonds into another form of energy. The

difference is that while combustion processes transform chemical energy into heat which can be

further converted into electricity in a power plant, the fuel cells convert chemical bond energy

directly into electrical energy. Therefore the fuel cell process is not restricted by Carnot effi-

ciency, and is potentially more efficient than the internal combustion engine. Fuel cell operation

is similar to that of a battery, with the difference that in a fuel cell system the reactants and

1

2 CHAPTER 1. INTRODUCTION

products are constantly supplied and removed.

Fuel cells are commonly classified by the type of electrolyte used in the cells; proton exchange

or polymer electrolyte membrane (PEMFC), alkaline (AFC), phosphoric acid(PAFC), molten

carbonate (MCFC) and solid oxide (SOFC). PEMFC seems to be the most attractive option for

mobile applications because of its low operating temperature, solid phase electrolyte and ability

to operate air with CO2.

1.1 Background of the project

This thesis was done for the Working PEM project which is part of the Tekes’ Fuel Cell Tech-

nology Program. In the Working PEM project, a 10 kW PEM fuel cell powerplant is developed

to be used in a working machine operating environment. For working machines, the price of the

propulsion system is not as critical as in passenger vehicles. Typically theweight and refueling

issues are also become more easier to handle.

The use of fuel cell propulsion systems would create many benefits in working machinery en-

vironments. Harbor vehicles would benefit from decreased emissions during vehicle usage, since

environmental considerations are receiving special attention in harborsand environmental poli-

cies are tightening emission limits. Naturally purity of air becomes an issue for vehicles operated

in indoor settings, such as in example in storehouses. In mining environments theconventional

propulsion system in heavy-duty vehicles set requirements for mechanical ventilation. If fuel

cell systems replaced the internal combustion engines, savings in the ventilation systems could

be achieved. The distribution of hydrogen in the harbors, mining area or warehouses would also

be simple enough to implement.

The main problems in implementing fuel cells in heavy-duty vehicles are operatinglife and

costs. Since fuel cell vehicles should be able to compete with existing options,they must have

roughly the same operating life as traditional machinery and the costs should not exceed mani-

fold. Somewhat higher costs for the propulsion system are tolerated sincethe secondary effects

can reduce costs in other parts of system. Clearly image issues in environmental matters have

attained importance especially within bigger companies and thereby could also be counted as

having a monetary value.

The competitor of a traditional propulsion system is expected to fit in roughly the same space

as in current vehicles. Hence the car industry would like to raise the operating temperature of

fuel cells to over 100C, optimally to 120C, in order to keep the size of a radiator reasonable.

Currently this would lead to catalyst and membrane problems. Better membrane materials have

made it possible to run a fuel cell at a temperature of about 90C. In the future, the fuel cell

vehicles will probably be operated with a moderate size fuel cell together witha heavier battery

in the system. Along with these hybrid vehicles perhaps temperatures of 90 - 95 C could be

1.2. PROBLEM 3

sufficient.

Thermal control has a direct effect on the operating life of a PEM fuel cell. Outside working

machines air temperatures may easily rise to 55C, which naturally leads to cooling system

problems for PEMFC since the operating temperature for current PEMFC isoften between 55

and 70C. This clearly implies that if PEM fuel cells will be chosen to replace their propulsion

systems, operating temperatures must be higher.

1.2 Problem

The industrial sector is demand for higher operating temperatures for PEMFCs lead to more

difficult water management issues. Elevating temperatures to about 90C raises the partial

pressure of steam and therefore lowers the partial pressure of oxygen in the same proportion.

In order for the fuel cell to receive the required amount of oxygen, asmall pressure increase is

required. However, higher temperatures generally lead to a higher cell potentials, even though

the theoretical voltages decrease. This is due to diminishing voltage losses when temperatures

rise.

However, in order to maintain the simplicity of the system, the pressurization should be con-

ducted so, that the pressure equipment directive, abbreviated PED, (97/23/EC) can be forgotten.

Pressure vessels designed for gas or liquid with a working pressure ofmore than 0.5 bar falls

within the scope of PED.

Therefore it is our intend to mainly keep the pressures under 0.5 bar, since the PED raises the

price of the system to such a degree that notably larger pressurizations would provide greater

benefits.

1.3 Target and approach

The target of this work is to study the effects of middle pressure for the PEMfuel cell sys-

tem, This work also aims to consider whether or not the proposed settings achieve gains when

compared with no pressurization systems.

It should be noted though that even PEMFC systems working at ambient air pressures need a

small pressurization to overcome the pressure losses of system components, pipes and connec-

tors. In the present work, the intention is to raise the pressure slightly overthis.

The approach is to study the optimal solutions for the air side of the fuel cell. The emphasis

in the study is primarily the optimization. Secondly, it is intented to characterize somereadily

existing and new components and use the experimental data achieved in the study. In those parts

where experimental data can not be obtained, equations from literature willbe used.

4 CHAPTER 1. INTRODUCTION

1.4 Thesis outline

This masters thesis concentrates on the control of air input (and moisture) ina middle pressure

PEMFC system. The middle pressure is considered to be the minimum pressure that the system

demands, to 0.5 bar overpressure, measured at the exit of the blower orcompressor.

First in Chapter2 the polymer electrolyte membrane fuel cell is introduced. Basic thermody-

namics, mass transfer and electro chemistry are introduced, and water management and degra-

dation issues shortly discussed. In Chapter3, PEMFC systems are more closely examined and

components, challenges and optimization of PEMFC system are described

In Chapter4 the results of blower and stack characterization are presented. The calculations

of the effect of temperature and pressure and the Matlab modeling are presented in Chapter5.

Finally in Chapter6 results are illustrated and in Chapter7 a summary of the conclusions and

future work is presented.

Chapter 2

Polymer electrolyte membrane fuel cell

2.1 What is PEM?

The PEM fuel cell is a low temperature fuel cell. It contains a polymer electrolyte membrane,

which must be humidified and therefore the operating temperature in the standard atmosphere

must be less than 100C. PEM operating temperature is usually from 60 to 80C. PEM cells

are very sensitive to impurities, such as CO, and therefore usually run onpure hydrogen.

PEMFCs are used in wide variety of applications and in many portable applications they are

a strong candidate for prime power for fuel cell vehicles, FCVs.

2.1.1 Structure and reactions

The reactions on the anode and cathode side are

H2 → 2H+ + 2e− (2.1)

1/2 02 + 2H+ + 2e− → H2O (2.2)

so the overall reaction is

H2 +1

202 → H2O. (2.3)

2.1.2 Cell components

The cell components are shown in Fig.2.1. The innermost part of the PEM fuel cell is the mem-

brane electrode assembly, MEA, which contains the membrane and the electrodes, commonly

manufactured directly onto the membrane surface. Between the bipolar platesand MEA is the

5

6 CHAPTER 2. POLYMER ELECTROLYTE MEMBRANE FUEL CELL

Figure 2.1: The basic principle of PEM fuel cell. Figure modified from [14].

gas diffusion layer, GDL. Because of the low voltage of one fuel cell, there are usually various

cells in series, forming a structure called a stack.

Membrane

Naturally high proton conductivity is the most important character of a membrane, but in order

to be functional, it also requires other qualities. The membrane must preventthe mixing of fuel

and reactant gases and it must be chemically and mechanically durable. When considering a real

commercial application, the low price of a membrane also has a great importance.

In PEMFCs the proton conductivity is strongly dependent on membrane structure and its wa-

ter content. PEM fuel cell membranes are commonly made of perfluorosulfonic acid (PFSA)

ionomer. Probably the best known membrane material is NafionTM , made by Dupont [14].

NafionTM has a Teflon-like PTFE backbone, where branches of vinyl ether chains leave, each

containing a sulphonic acid group, SO3H, in the end. Even though PTFE is highly hydrophobic,

this sulphonic acid group is highly hydrophilic and since the group is ionically bonded, it is ac-

tually an SO−3 ion with H+ ion. The weak binding between these ions enables the movement of

protons to the directions of proton gradient. Protons in a manner of speaking bounce from one

2.1. WHAT IS PEM? 7

sulphonic acid group to another, until they reach the cathode side surface of membrane and pop

out. This transport mechanism is called the Grotthus mechanism. In case thereis enough water

present to form free water which is not bound to vinyl ether chains, protons can also diffuse

within H3O+ ions through the membrane.

Electrodes

Electrodes are thin catalyst layers pressed between the membrane and the porous GDL. Together

with a membrane between them, they form the MEA. The electrochemical reactions in a fuel

cell take place in the electrodes. As the reactions in a low temperature and acidenvironment are

rather slow, the catalyst and extensive active surface are needed. The best known catalyst for

reduction reactions in PEMFC is platinum. Alternatives to the platinum catalyst are subject to

intensive research, since platinum prices have increased significantly inthe past decade. This

will be illustrated later, in Chapter3.3.3

Electrodes have a very porous structure. They are a mixture of an ionomer and catalyst on a

coal atoms. To be exact, the catalyst surface where the reactions occuris called the three phase

boundary. The name of the reaction surface comes from the fact that allthree species needed:

gases, electrons and protons are available only on that surface.

GDL

The gas diffusion layer, GDL, can be called by many names: gas diffusionbacking (GDB),

porous transport layer (PTL), porous backing layer (PBL). As the name used here, gas diffusion

layer, suggests, the GDL must be made of porous material so that the flow ofgases can easily

permeate it. The GDL does not directly participate in electrochemical reactions, but despite its

name, the GDL also has other tasks than only being a pathway for the reactants. It serves as a

current collector and therefore must be made of a material with good electrical conductivity. The

GDL also conducts the formed heat away and it functions as a mechanical support of MEA.

The GDL for PEMFCs are mostly carbon cloth or carbon paper. These are porous, conductive

and chemically enduring materials. The thickness of GDLs varies commonly between 0.017 to

0.04 cm, density from 0.21 to 0.73 g/cm3 and porosity between 70 % and 80 % [42].

Bipolar plates

Within PEMFCs, the flow channel plates are called bipolar plates if there are flow channels and

fuel cells on both sides of the plate. Bipolar plates can be manufactured of graphite, graphite-

polymer composites or metals. Graphites are light, chemically durable and easy tomachine.

But they are porous and therefore require an impregnant, and they arenot suitable for serial

production. Graphite-polymer composites are cheap but lack good conductivity. Metals, as


is well known, possess good conductivity, mechanical strength and gasimpermeability, but the

moisture conditions of PEM stacks make the environment corrosive and the coating again lowers

their conductivity.

Other

Other components in PEMFC are end plates, coolant channel plates and small assembly compo-

nents, such as bolts, seals and connectors.

2.2 Thermodynamics

2.2.1 Gibbs free energy

The Gibbs free energy is a thermodynamic potential measuring the available work from the

isothermal and isobar thermodynamic process

∆G = ∆H − T∆S, (2.4)

where∆H is the enthalpy change, or the heat, of a chemical reaction and the difference between

the enthalpy of formation of products and reactants, and∆S is the entropy difference between

the products and reactants.∆H also depicts the total thermal energy available and the term

T∆S likewise the unavailable energy arising from the entropy change.

The specific enthalpy and entropy at temperatureT and pressurep can be calculated from the

equations

hi(T, p) = hi +

∫ T

T0

cp(T, p0)dT −

∫ p

p0

[v(T, p)− T∂v

∂T(T, p))]dp (2.5)

si(T, p) = si +

∫ T

T0

cp(T, p0)

TdT −

∫ p

p0

∂v

∂T, (T1, p)dp. (2.6)

wherehi andsi are the specific enthalpy and entropy at the standard state,p0 = 1.0 bar, and

temperatureT0 = 298.15 K. We can also interprethi = ∆Hof (T0, p0), the enthalpy of formation

of compoundi at standard state and temperatureT0, andsi is the absolute entropy of compound

i. Absolute entropy at temperature 0 K is according to its definitionsi (T = 0K) = 0. The

specific enthalpy and specific entropy are related to enthalpy and entropy

H = hn (2.7)

S = sn. (2.8)

2.2. THERMODYNAMICS 9

wheren is molar amount of substance. In case the pressure is constant, Eq.2.5and2.6evidently

get a form

hi(T ) = hi +

∫ T

T0

cpdT (2.9)

si(T ) = si +

∫ T

T0

cpTdT. (2.10)

Also when a gas can be considered as an ideal gas, the Eq.2.9may be used, since the enthalpy

of an ideal gas is a function of temperature only,hidealgas(T, p) = h(T ). Since for ideal gas

v =RT

Mp, (2.11)

the entropy for ideal gas can be calculated from

si(T, p) = si +

∫ T

T0

cpTdT −

R

Mln

p

p0. (2.12)

As the heat capacity,cp, is a function of temperature, a tabular value must be used or it can be

calculated from polynomial function of temperature

cp = a+ bT + cT 2 + dT 3..., (2.13)

wherea, b, c andd are empirical constants also found in the tables. When considering water

and vapor in the tables and h,s-drawings, it is common to use a triple point (Tref = 273.16 K =

0.01C, pref = 0.006112 bar) as a reference state instead of standard state.

The Gibbs free energy for the chemical reaction is

∆G = Gproducts −Greactants, (2.14)

which for hydrogen oxidation reaction, Eq.2.3becomes

∆G = µH2O

− µH2

−

1

2µO2

(2.15)

whereµ is the chemical potential that is defined as

µi ≡G

ni. (2.16)

2.2.2 Theoretical fuel cell potential

The ideal fuel cell potential atp0, also called electromotive force, EMF, is the potential at zero

current (i.e. on open circuit). The maximum electrical work,Wel, that can be obtained from a

fuel cell with constant temperature and pressure, equals the Gibbs freeenergy

Wel = −∆G. (2.17)


If the cell is reversible and the potential equals the open circuit voltage, OCV, the maximum

achievable work is

W = zFE, (2.18)

wherez is the number of electrons,E is the ideal potential of the cell andF is the Faraday’s

constant, which is related to charge of an individual electron by

F = NAe ≈ 96584As/mol, (2.19)

whereNA is Avogadro’s number,NA ≈ 6.022× 1023 mol−1 ande charge of one electron =

1.602× 10−19. Thus the formulation for the ideal fuel cell potential becomes

E = −

∆G

zF. (2.20)

As Gibbs free energy is a function of temperature, raising the temperature decreases the term

−∆G. Therefore raising the temperature also lowers the theoretical fuel cell potentialE. At

the temperature of T = 25C, the theoretical fuel cell potential becomes

E =237340Jmol−1

2 ∗ 96485Asmol−1= 1.23V. (2.21)

2.2.3 Nernst equation

The ideal potentialE in the previous chapter was valid at standard state,po = 1 bar. Fuel cells

often operate at other pressures, and unless the effect of pressure was already counted in the

calculation of Gibbs energy, it can be taken into account with the calculation of potential with

the Nernst equation. The Nernst equation is

E = E +RT

zFln

faAf

bB

f cCf

dD

, (2.22)

wheref is fugacity. It is a function of pressuref(p) and is used in the case of real gases. When

considering ideal gases, activity can be used instead fugacity, and Eq.2.22can be written as

E = E +RT

zFln

aaAabB

acCadD

, (2.23)

where activity,a, is defined as

a =pip0

, (2.24)

wherepi is partial pressure of the gas andp0 standard pressure. When water is in liquid form,

aH2O = 1 and the Nernst equation for hydrogen oxidation reaction becomes

E = E +RT

2Fln

(

pH2

p0

pO2

p0

0.5)

. (2.25)

2.2. THERMODYNAMICS 11

It can be seen from Eq.2.23that the potentialE decreases when partial pressure of water vapor,

pH2O, increases as this lowers the partial pressure of the reactant gases,pH2andpO2

. In reality,

cell potential is essentially lower as calculated from the above equation. Thiswill be discussed

in section2.4.2.

2.2.4 Theoretical fuel cell efficiency

In generally any energy conversion device’s efficiency is defined asthe ratio between useful

energy output and energy input;

η =useful energy output

energy input. (2.26)

Assuming that all of the Gibbs free energy can be converted into electricalenergy, the efficiency

of a fuel cell is

ηteor =∆G

∆H. (2.27)

Both∆G and∆H are temperature dependent and the ideal efficiency decreases with the tem-

perature increaase.

There are two different heating values,∆H, used for fuels: the lower heating value, LHV, and

the higher heating value, HHV. The difference between these two heating values is the state in

which the water is assumed to be in Eq.2.27. With LHV water is assumed to be in vapor form,

whereas with HHV the water is considered to be in liquid form and the latent heat of vaporization

in the fuel and reaction products is recovered.

Selecting the LHV may be justified due to the possibility to compare directly a fuel cell with

internal combustion engines, but the use of HHV can also be rationalized. In a PEMFC the

product water comes out mostly in a liquid form and thereby the use of HHV could be preferable.

Despite the choice, in terms of the efficiencies, it is important to state clearly which heating value

has been used. In the Table2.1below, the heating values of hydrogen and a few other fuels are

listed.

Gaseous fuels Liquid fuels

Hydrogen Methane Gasoline Diesel Methanol Propane

kJ/g kJ/g kJ/g kJ/g kJ/g kJ/g

LHV 119.93 50.02 44.5 42.5 18.05 45.6

HHV 141.86 55.53 47.5 44.8 19.96 50.36

Table 2.1: Lower and higher heating values of hydrogen and other fuels[31].


2.3 Mass transfer

Fick’s law tells that the flux of a substance (mol/m2s) is proportional to concentration gradient.

Its one-dimensional form is

jA = −DAB∂cA∂z

, (2.28)

whereDAB is the diffusion coefficient between the components A and B,cA is a concentration

of component A andz is the diffusion distance. Fick’s diffusion in a porous material is

jA = −DABΦ

τ

∂cA∂z

, (2.29)

whereΦ is the porosity

Φ =V ∗

V= 1−

ρmeas

ρbulk, (2.30)

whereρmeas is the measured density of the porous material andρbulk is the density of the solid

material if porosity was pressed out, andτ is the tortuosity

τ =s

x, (2.31)

wheres is the real path length that particles move andx is the direct distance through the mate-

rial.

To be accurate, the Fick’s law is valid only for a two component diffusion and in multicom-

ponent cases other more complex formulae should be used.

2.4 Operation

2.4.1 Current density

The current densityi is commonly used in the fuel cell context instead of currentI, since it allows

the comparison between different surfaces per unit area basis. The current density (A/cm2) is

defined as

i =I

A, (2.32)

where A is the electrode active area.

Exchange current density

Exchange current,i0, density in electrochemical reactions is analogous to the rate constant in

chemical reactions, but unlike the rate constants, exchange current density is concentration de-

pendent. It is the rate at which oxidation and reduction reactions proceedat thermodynamical

2.4. OPERATION 13

equilibrium. At equilibrium the forward and reverse current densities mustbalance and therefore

the net current equals zero.

i0 = ARedexp

(

−

∆G0Red

RT

)

cA,ref = −AOxexp

(

−

∆G0Ox

RT

)

cB,ref , (2.33)

whereARed andAOx are the constants from Arrhenius equation for reduction and oxidation

reactions respectively.

2.4.2 Actual performance

As fuel cell power systems are highly interdisciplinary, there also exists a wide variety of names

standing for essentially the same matters. This is also the case for the voltage difference between

the theoretical potential of reversible cell and the actual polarization curve, seen in Fig.2.2.

Figure 2.2: An example of a polarization curve. The Roman numbers refer tothe losses defined

below.

From the thermodynamical point of view, voltage reduction is caused by irreversibilities. Elec-

trochemists call them overvoltage or overpotential, because it is a voltage superimposed over the

reversible (ideal) voltage. The disadvantage though is that the name implies that the voltage be-

comes higher, although in reality the overvoltage reduces the reversible voltage. Electrochemists


and others also call these losses a polarization.

Even thought it may seem too general, here we refer to the voltage reduction simply as voltage

losses that are caused by irreversibilities. The main losses are:

• Activation losses (I).These are caused by the slowness of the reactions taking place on the

catalyst surface. Slow reaction kinetics means high activation energy is required, and some

voltage difference from the equilibrium is needed to initiate electrochemical reactions.

Activation losses happens at both electrodes, but at the cathode side they are much greater,

due to the higher activation energy necessary for the oxygen reduction, and therefore due

to the slower reaction kinetics. The current potential equation to calculate activation losses

will be presented below. The Tafel equation is also commonly used. Using theTafel

equation below the activation losses can be computed. Activation losses canbe reduced

for example by raising the cell temperature, using a more efficient catalyst or increasing

the pressure.

• Ohmic losses (II).The resistance to the ion flow in the electrolyte and the electrical re-

sistance of the electrodes cause ohmic losses. Electrolyte and electrodes obey Ohm’s law

and the formulation for the calculation of ohmic losses is presented below.

• Mass transfer losses (III).Mass transfer losses, also known as concentration losses, follow

from difficulties in getting the reactants to the reaction sites. When a fuel cell isoperating,

the reactants on the reaction surface are constantly consumed, which in turn gives rise to

a concentration gradient, meaning that the partial pressure of the gas at the reaction site is

lower than partial pressure at bulk flow. Naturally a reduction in a gas pressure leads to a

reduction in voltage. In PEMFCs the removal of water can also cause mass transfer losses.

There is a difference in diffusivities of hydrogen and water, which may lead to a situation

where water vapor is not removed effectively enough and flooding occurs. Flooding in

turn deteriorates the mass transfer of oxygen.

• Internal currents and fuel crossover losses.If forming electrons cross the membrane in-

ternally, and not through the external circuit, they are called internal currents. Some fuel

may diffuse from the anode through the electrolyte to the cathode and reactdirectly with

the oxygen without producing any electricity. This waste fuel is known as fuel crossover.

This irreverssibility is least important in terms of energy loss. However in low-temperature

cells the voltage drop is significant. These losses may also be noted in an opencircuit volt-

age, unlike in the case of other losses mentioned above. With PEM fuel cells operating at

ambient air pressure, the voltage is usually at least 0.2 V less than the 1.23 V reversible

voltage [45].

2.4. OPERATION 15

Current potential equation

The relationship between current density, overpotential and concentration is also called the

Butler-Volmer equation;

i = i0

[

cAcA,ref

exp

(

−

αRdzFη

RT

)

−

cBcB,ref

exp

(

αOxzFη

RT

)]

(2.34)

whereαRd andαOx are experimental transfer coefficients for the reduction and oxidation reac-

tions respectively. Instead of transfer coefficient, symmetry factors are sometimes used. Sym-

metry factors may be used only for a single step reaction involving a single electron (z = 1). i0is exchange current density, the rate at which these reactions proceedat equilibrium.

The current potential equation is valid for both anode and cathode reactions. At the fuel cell

anode, where overpotential is low, a linear approximation can be calculatedwith the help of the

Taylor series:

ia = ia,0zFη

RT. (2.35)

In Eq.2.35the mass transfer is assumed to be fast and therefore it does not limit the operation.

For the cathode side, the Tafel equation is a suitable approximation.

The Tafel equation

On the cathode side it can be considered thatη « 0 and therefore the second term in Eq.2.34

approaches zero. If further mass transfer is not limiting the operation, a following form of current

potential equation is derived

ic = ic,0cA

cA,ref

exp

(

−

αzFη

RT

)

. (2.36)

This is called as the Tafel equation and it is commonly seen in the form

∆Vact = a+ b ln i, (2.37)

where the constantsa andb are defined as

a = −

RT

αzFln i0, (2.38)

b =RT

αzF. (2.39)

From Tafel plots, where overpotential is against thelog of current density or current density

log i against overpotential, the parameters a, b andi0 are easy to read: b being the slope of the

line, a the voltage wheni0 = 1 andi0 the current density when potential is 0 V.


Modified Ohm’s law

The Ohm’s law can be presented with the following equation

V = RI, (2.40)

whereR is the total resistance, and I the current through the cell. In order to make the for-

mulation consistent with the other voltage losses, commonly the Ohmic losses are presented as

∆Vohm = ir, (2.41)

wherer is called area specific resistance, ASR, (Ω/cm2), which is the total cell internal resis-

tance including ionic, electronic and contact resistance.

However, according to the Fuel Cell Handbook, it is important to verify thedefinition of

ASR when using literature data, since some researchers have defined ASR to include also the

activation and concentration polarization [42].

Concentration polarization

The concentration losses are determided by the equation

∆Vcons =RT

zFln

(

cscb

)

, (2.42)

wherecs is the concentration on the surface andcb is the bulk concentration. By using Fick’s

law, Eq.2.28and Faraday’s law, Eq.2.49, the Eq.2.42may also be written as

∆Vcons =RT

zFln

(

iLiL − i

)

, (2.43)

where currentiL is the limiting current density, which can be calculated from Eqs.2.28and2.49

by setting cs = 0:

iL =zFDcb

x(2.44)

However, it must be noted that these equations are not very accurate in describing the concen-

tration losses and some more accurate empirical equations have been developed. The first thing

one may notice, is the use of Fick’s law for the diffusion and its restrictions in describing only

one component diffusion.

Internal currents

When the fuel cell is at open circuit potential or when it operates at verylow current densities,

internal currents and crossover losses may have a substantial effecton cell potential.

2.5. CONSERVATION LAWS FOR FUEL CELLS 17

2.4.3 Actual cell voltage

Hence the actual cell voltage formula:

Vcell = E −∆Vact −∆Vohm −∆Vcons, (2.45)

whereE is the fuel cell open circuit voltage, Eq.2.23. All of the overpotentials had positive

values even in reality they describe the losses, hence the signs of deduction in the Eq.2.45.

Often an accurate approximation of the fuel cell polarization may be used, which assumes that

the anode losses are negligible [14]

Vcell = E −

RT

αFln

(

i

i0

)

−

RT

zFln

(

iLiL − i

)

− ir. (2.46)

More accurate but commonly semi-empirical formulae can be found in literature.

2.4.4 Actual fuel cell efficiency

The fuel cell efficiency is a product of theoretical efficiencyηteor, Eq.2.27, and a voltage effi-

ciencyηV

ηV =Ecell

E, (2.47)

whereEcell is the actual cell voltage andE the theoretical voltage, defined in Eq.2.20. The

voltage efficiency,ηV , takes into account the polarizations. Hence the formula of actual fuel cell,

ηfc, becomes

ηfc =Vcell

−∆H/zF. (2.48)

When hydrogen’s higher heating value, HHV, is used, the term−∆H/zF is the so called ther-

moneutral potential. At temperature T = 25C, the termoneutral potential has a value of 1.482 V.

In the chapter3.4.3the efficiency of the whole fuel cell system will be discussed.

2.5 Conservation laws for fuel cells

2.5.1 Flux balance

Using the Faraday’s law

I = zFJ, (2.49)

the flow rates of reactants (mol/s) as a function of current can be derived

n =I

zF, (2.50)


wherez is the number of electrons transferred per ion. Thereby

I

2F= nH2,need = nH2O,form = 2nO2,need, (2.51)

where nH2,need and nO2,need are the hydrogen and oxygen needed andnHO,form the water

formed, when a certain currentI is drawn from a fuel cell.

2.5.2 Energy balance for PEMFCs

The first law of thermodynamics states that the difference of the internal energy,U , of the system

is equal to the heat added to the system,Q, plus the work done for the systemW ;

∆U = U(B)− U(A) = Q(P ) +W (P ), (2.52)

where process P proceeds from the initial stateA to the final stateB. It should be remembered

that the signs are determined from the point of view of the particular system. Apositive sign

means that the heat is brought into the system and work done for the systemand a negative sign

means that the system produces heat and work is done by the system.

Figure 2.3: The energy balance of a PEMFC, with humid air but dry hydrogen.

The energy balance of a fuel cell is depicted in Fig.2.3. The energy balance indicates, that

the incoming energy equals the out coming energy. For a fuel cell at a stationary state, we may

formulate the energy balance as

[nH2hH2

+ nO2hO2

+ nN2hN2

+ nH2O,ghH2O,g]in =

[nO2hO2

nN2hN2

+ nH2O,ghH2O,g + nH2O,lhH2O,l]out +Φcool +Φloss + Pel, (2.53)

2.5. CONSERVATION LAWS FOR FUEL CELLS 19

where enthalpy,h, is used instead of specific internal energy,u.The enthalpy is defined as

h = u+ pv, (2.54)

wherepv is expansion work done by the system to the surroundings,p denoting pressure andv

specific volume. In Eq.2.53the kinetic and potential energies are negated.

Pel is the electrical work done by the stack

Pel = nUcellI, (2.55)

Φloss is the heat transferred via convection from the surface of the stack,

Φloss = αstackAstack,s (Tstack − T∞) , (2.56)

whereαstack is the heat transfer coefficient of the stack,Astack is the area of the surface of

the stack andTstack,s andT∞ are the temperatures of the stack surface and the environment,

respectively,andΦcool is the heat transferred by cooling fluid

Φcool = mcool∆hcool. (2.57)

The theoretical heat of fuel cell reactions may be calculated from

Φtheo = −nH2,need∆Hreac, (2.58)

and the latent heat of vaporization of waterΦlatent

Φlatent = nH2O,vap∆Hpc. (2.59)

The H2, need is the required hydrogen with currentI, ∆Hreac the reaction enthalpy of the

reaction2.3, ∆Hpc the heat of phase change andnH2O,vap the vaporized water, which is the

difference between the maximum amount of water vapor that air at that temperature can hold

and the water vapor in the incoming air,

nH2O,vap = nH2O,max,vap − ninH2O,g. (2.60)

It can be seen from the energy balance Eq.2.53above that theoretical heat of fuel cell reactions

may also be calculated as

Φtheo = Φcool +Φloss + Pel. (2.61)

Reactant and product flows are convenient to calculate with molar flow rates, since the Eq2.50

can be used to calculate them. However, in the case of the cooling circuit water in Eq.2.57, the

use of mass flow rate is more practical.


2.6 Water management

Water management is critical in PEMFC, since the membrane requires high watercontent in

order to maintain good proton conductivity. Low water content of the membrane reduces con-

ductivity, which in turn results increased ohmic losses and a drop in cell voltage. High humidifi-

cation may also be a problem if not properly managed. Excess water, particularly on the cathode,

can hinder reactant diffusion, causing increased mass transport losses. (mol s−1 cm−2)

jH2O,gen =i

2F, (2.62)

wherei is current density (A/cm2).

Water transport through the membrane has several mechanisms;

• Electro-osmotic drag. Water is been dragged from the anode to the cathode by protons

which are moving through the electrolyte. The water flux caused by electro-osmotic drag

is

jH2O,drag = ξ(λ)i

F, (2.63)

whereξ is electro-osmotic drag coefficient, meaning number of H2O molecules per pro-

ton. Electro-osmotic drag is a function of membrane hydration,λ, which is defined

as the number of H2O molecules per sulfonic acid groups present in the polymer,λ =

n(H2O)/n(SO3H).

• Back diffusion. A large concentration gradient across the membrane is formed due to

electrochemical water production and electro-osmotic drag and causes back diffusion from

cathode to anode. Obeying the Fick’s law, Eq.2.28, the rate of water diffusion is

jH2O,dif f = D(λ)∆c

∆z, (2.64)

whereD is the water diffusion coefficient in ionomer of water contentλ. To be accurate,

Fick’s first law is valid only in one component diffusion and does not take into account the

interactions between all of the species. If more accurate calculations in multicomponent

system are needed, the Maxwell-Stefan equation may be used.

• Hydraulic permeation. the pressure difference may cause the water to be pushed hydrauli-

cally from one side of the membrane to the other. The rate of hydraulic permeation is

jH2O,hyd = khyd(λ)∆p

∆z, (2.65)

where khyd is the hydraulic permeability coefficient of the membrane of water contentλ.

As can be seen from the mechanisms above, all formulae contain terms which are functions

of the water content of the membrane. Several empirical correlations havebeen developed to

calculate these coefficients but apparently none of them have attained general validity.

2.7. DEGRADATION 21

2.6.1 Humidification of air and hydrogen

As stated above, the performance of a PEMFC deteriorates notably if adequate water content is

not maintained in the membrane. Therefore both air and hydrogen must be humidified before

entering to the cell. On the other hand it must be assured that the overload offorming water does

not create flooding of the membrane and thereby deteriorate the mass transfer.

Air humidity is commonly expressed with two variables, the water contentx or the relative

humidityRH or φ. The humidity or the water contentx is defined as

x ≡

mh

mi, (2.66)

wheremh andmi are the mass of the water vapor and the mass of the air, respectively. In the

case of ideal gases, humidity can be expressed with partial pressures

x =Mh

Mi

phpi

, (2.67)

whereMh andMi are the molecular weights andph andpi the partial pressures of water vapor

and air, respectively. The relative humidity is the percentage proportion of water vapor compared

to the maximum amount of water vapor the air at certain temperature can carry

φ(T ) =ph

p′h (T ), (2.68)

whereph is the water vapor pressure andp′h (T ) the saturation vapor pressure at temperatureT .

2.7 Degradation

Degradation is one of the main problems for PEM fuel cell stacks, since it drastically reduces

the lifetime of a PEMFC. All components in PEMFCs suffer from degradation,but the most

deleterious degradation problems occur in the membrane and the catalyst layers.

Operational conditions are known to have an effect on a PEMFC’s durability. An improper

water balance, either too wet or too dry, has a long-term effect on cell degradation rates [43].

Low humidification results in reduced conductivity. Low water content may also accelerate the

physical degradation of a membrane and even result in membrane holes andreactant gas cross-

over [43].

Recently a comprehensive review of PEMFC degradation and durability has been written by

R.L. Borup et al. [18]. R.L. Borup et al. [19] have shown in their study, that both temperature

and relative humidity affect Pt particle growth, which leads to catalyst surface area loss. An

increase in operating temperature causes the rate of Pt particle size growthto increase more

rapidly. The lower the relative humidity, the less the platinum particles were observed to grow.

By lowering the relative humidity, carbon corrosion was also observed to increase.


Chapter 3

PEM fuel cell systems

3.1 PEM fuel cell applications

Fuel cells can be used in wide range of applications, since they can satisfythe electrical power

needs from a fraction of a watt to hundreds of kilowatts. A diverse variety of applications has

been under research and development. The most suitable PEMFC systems seem to be in portable,

special, and transportation applications.

In small portable applications, fuel cells may replace batteries. Demonstrations of many trans-

port applications have been already seen, from motorized bicycles to automobiles and heavy-

duty vehicles. Fuel cells are also ideal for distributed power generation,as in individual homes

and other buildings, and in applications situated in remote areas, such as UPSsystems in cellular

phone stations.

PEMFC systems have the potential to substitute for batteries and therefore to become the

power supplies for various portable equipment [34]. However, not all researchers share this

opinion. The main reasons are the challenge of a safe hydrogen supply and rapid development

of Li-based battery technology [59], as well as the generated waste heat. The crucial question

concerns the development of portable devices’ power consumption. Somepredict power con-

sumption to grow so fast that battery technology can not keep pace with it, while others predict

energy-saving equipment to rush into the market.

In stationary applications PEMFC systems have been developed for a stationary power gen-

erators [14], but other types of fuel cells are penetrating into markets in this range of nominal

power, commonly SOFC.

PEMFCs have been considered the most competitive option for transportation. The most

promising applications for PEMFCs are buses, recreation vehicles, and lightweight vehicles [59].

Vehicle developers have been interested in fuel cell powered alternatives since the 1990s when

environmental issues began to appear in the public debate and almost all majorcar manufacturers

23

24 CHAPTER 3. PEM FUEL CELL SYSTEMS

have demonstrated a prototype [14]. The seemingly zero emission propulsion system attracted

many, but there are still emissions formed during fuel production which mustbe considered.

Very recently Honda announced a mass production of FCVs. Honda began leasing its FCX

Clarity Fuel Cell Vehicle in California during the summer of 2008 and later this year in Japan

[3, 4]. Their aim is to lease about 200 FCVs within the next three years [3].

At the moment particular attention is directed to transit buses and other centrallyrefueled

vehicles, since infrastructure for the distribution of hydrogen could be built more easily than

for passenger vehicles. Furthermore, hydrogen tanks in the buses can be placed on the roof,

meaning that there are no strict space limits for hydrogen storage. Placing the hydrogen bottles

on the roof of the vehicle is also a safe option. The major advantage is that fuel cell buses

produce zero emissions during operation, which is important in densely populated cities.

For the heavy-duty vehicles such as mining and indoor vehicles, indoor airquality becomes

an important factor and switching to zero-emission vehicles would yield a positive side-effect:

savings in the ventilation system. Therefore the drive train equipment may cost slightly more.

On the other hand the yearly operating time of a working site vehicle may be far higher than for

passenger vehicles and this creates greater importance for refueling issues and requires longer

vehicle lifetime.

There are still many problems to overcome before the full commercialization of PEMFC

systems. This raises the possibility that PEMFCs may lose various application fields to other

types of fuel cell systems, such as molten carbonate fuel cells, solid oxidefuel cells, and direct

methanol fuel cell, and direct borohydride fuel cells as well as battery systems [59].

3.1.1 Fuel cell vehicles

The rapid development of Li-ion batteries is changing FCV design. Until now, all FCV demon-

strations have been made without hybridization but since heavy hybridization clearly enhance

fuel cell durability, it will feature in demonstrations in the near future.

The current status of FC technology shows its high potential, especially forpassenger cars [58,

38]. Nevertheless Demirdöven et al. [30] compared the energy efficiency of hybrid and FCVs

as well as conventional ICE vehicles in 2004. They concluded that priority should be placed

on hybrid vehicles, since analysis indicated that FCVs using hydrogen from fossil fuels offers

no significant energy efficiency over hybrid vehicles with ICE drive trains. Also Granovskii et

al. [38] showed in their analysis that hybrid and electric cars have advantages over conventional

ICE and FCVs.

Many researchers share the opinion that combustion engines will have a significant share of

passenger car propulsion systems in the near future [58, 30]. Full hybrids with potential plug-in

capabilities are seen as the next step of development and FCVs offering zero emissions could be

regarded as the final stage of development [58].

3.1. PEM FUEL CELL APPLICATIONS 25

A fuel cell propulsion system can be developed using only fuel cells without batteries, or with

batteries in a hybrid configuration, where the storage system has an important role. Hybridization

increase the working life of a stack, since it lowers the degradation that stems from voltage

cycling. Hybridization offers a number of other improvements for FCVs as well, such as stored

energy from regenerative braking and avoiding working regions of poor efficiency [16]. The

peak power declines and therefore the size of the stack and the FC systemdeclines. For long

PEMFC durability in a hybrid vehicle, an advanced energy management strategy is also needed

to split the power between the PEMFC and a battery [48].

As several alternative fuel pathways are being explored around the world, hydrogen fueled

transportation is emerging as one of the only technologies that can meet the demands for three

core concerns: lower greenhouse gas emissions, lower air pollutant emissions and independence

from imported crude oil [11].

3.1.2 Heavy-duty vehicles and buses

Since implementation of fuel cells in heavy duty vehicles is still rather rare, it is necessary to

survey fuel cell buses. Fuel cell buses belong to nearly the same power range as heavy-duty

vehicles and therefore experiences gained with fuel cell buses may give essential information.

Many fuel cell bus demonstrations have been mad; the largest and most successful FC bus

demonstrations being Clean Urban Transport for Europe, CUTE, and Sunline Transit Authority

in Palm Springs, California, where fuel cell buses have been operatingin regular service for

several years [14, 24]. The demonstration projects and FC buses will be discussed in greater

detail below.

The main obstacles for commercialization are fuel cell cost and durability; thelatter will be

mainly solved by hybridization. Cost is less predictable, but it is clear that economics of scale

will bring prices down. It seems that Li-ion batteries will penetrate into the market within next

few years and will be the main battery technology. The electrical plug-in vehicles and hybrids

will most likely also penetrate into the markets, but the time frame may be longer.

CUTE

In the EU fuel cell demonstration project, Clean Urban Transport for Europe (CUTE), 27 fuel

cell buses were operated in nine European cities; Amsterdam, Barcelona,Hamburg, London,

Luxembourg, Madrid, Porto, Stockholm and Stuttgart [8, 15]. The buses, were operated for 24

months in each of these cities until May 2006 when the project ended. Appropriate regional

hydrogen production and refueling infrastructures were also established but were not uniform

among the cities.

The buses were based on a conventional 12m Mercedes-Benz Citaro low-floor city bus by


DaimlerChrysler and the engine was designed around the Ballard Mk9 stack which uses gaseous

hydrogen, stored at 350 bar, as a fuel and atmospheric air as an oxidant [8]. The buses were

designed for a high reliability and durability, since one of the main goals of the project was to

show that buses running on fuel cells only were reliable enough to be used in normal operation.

Therefore there was no hybridization at all, which clearly affected the durability of the stacks.

The use of series-production components was maximized, even acknowledging that this may

have a negative impact on vehicles’ fuel economy.

The buses operated more than 62 000 hours, covered more than 850 000kilometers and carried

more than four million passengers. The results showed operating success: there were no major

breakdowns or problems and the buses were found to be reliable under European conditions, and

the result of a driver survey showed that most characteristics of the fuel cell buses were perceived

as the same or better than regular buses [8].

In the study of Saxe et al. [54] fuel cell system efficiencies were found to be high (36-41%),

but fuel consumption was higher for the fuel cell buses than for dieselbuses. Nevertheless the

authors of the Saxe study reminded that the CUTE buses were pre-commercial generation fuel

cell buses and calculated that a large fuel consumption reduction was possible; about 20% from

minimising the reliability measures, another 10% from lowering the weight by 2 tonnes and by

hybridisation of an additional 5-10% or more.

Simultaneously CUTE had a partner projects using the same Citaro FC buses: the Ecological

City Transport System (ECTOS) in Iceland, Sustainable Transport Energy for Perth (STEP) in

Australia and the hydrogen fuel cell bus project in Beijing, China, and thus another nine buses

were operating in Reykjavik, Perth and Beijing [8].

HyFLEET:CUTE

After the two-year period of CUTE, many of the FC buses have continued inthe HyFLEET:CUTE

program. In addition the hydrogen FC buses in nine cities, HyFLEET:CUTE includes operation

of 14 hydrogen powered internal combustion engine ,H2ICE, buses in Berlin [7].

SunLine Transit Agency in California

The National Renewable Energy Laboratory (NREL) reported evaluation results for one pro-

totype FC bus and one prototype H2ICE hybrid bus operating in Thousand Palms, California

[24, 23, 25, 26]. The 40-foot long FC bus was a Van Hool A330 transit bus chassis, redesigned

to integrate the fuel cell system. It used UTC Power’s PureMotionTM

120 Fuel Cell Power System

in a hybrid electric drive system designed by ISE. ZEBRAR© batteries (sodium/nickel chloride)

were used as an energy storage system. The fuel cell power system was a 120 kW PEM stack, op-

erating near ambient pressure and thereby without a compressor. The HHICE bus has essentially

3.1. PEM FUEL CELL APPLICATIONS 27

the same electric hybrid drive system from ISE Corp. as the fuel cell bus, but with ultracapac-

itors for energy storage and a Ford V10 Triton engine customized to operate on hydrogen fuel.

SunLines compressed natural gas (CNG) buses were used as a baseline.

By the release of the Third Evaluation Report [25], the entire evaluation period was 27 months,

from January 2006 through March 2008, for the FC bus and H2ICE bus, and 21 months, July

2006 through March 2008, for the CNG buses.

NREL found the energy efficiency (miles per gallon, diesel gallon equivalent) of the FC bus

to be 66% higher than that of the H2ICE bus. The FC bus efficicency was also 2.4 times higher

than their CNG bus fleet’s efficiency. However, the fuel economy of the fuel cell bus was found

to be 2.4 times higher than the CNG buses, and the fuel economy of the H2ICE bus 44% higher

than the CGN buses. The maintenance costs of the FC bus and the H2ICE bus were 47% higher

and 2 times higher respectively than the CNG bus ($0.30 per mile). Warranty costs were not

included. The economic merits of the FC bus and H2ICE bus were not especially beneficial

when compared with CGN bus; the bus purchase costs at SunLine were $3.1 million USD for

the FC bus, and $1-2 million USD for the H2ICE bus, while the conventional CNG bus price

was $375 000 USD.

NREL emphasized that the FC bus was at a test phase for the optimization of thesystem, and

not ready for the markets.

SunLine, FTA, UTC Power, and ISE Corp. have entered into a new agreement to operate a

new fuel cell power system for another two-year period [25]. The new power system is expected

to be much more durable than previous versions. This fuel cell power system was installed in

April 2008 and the bus has begun normal eight-hour service seven days per week.

Besides the SunLine Transit Agency in California, several other hydrogen fuel cell bus evalu-

ations are ongoing in the US. For more information about these projects, the reader is advised to

visit the NREL webpage [53].

NedStack city buses

At a Hannover fair ’Group Exhibit H2/FC 2008’, Dutch PEMFC manufacturer NedStack gave

a product data sheets of 18 meter long hybrid city buses and 26 meter long hybrid city buses

[10]. The 26 meter hybrid city bus has a rated net power of 160 kW, which is in the same size

class as working machines. On their webpage NedStack reports that they are currently seeking

partnerships with bus manufacturers [6].

Ballard HD6

Ballard has developed FC buses since 1992 and after successfully implementing Ballard Mk9for the 27 FC buses in the CUTE program, Ballard is already developing theirsixth generation


fuel cell module for the bus market [2]. The HD6 has a gross power of 75 kW or 150 kW and

a working life warranty of 12 000 hours or 5 years [1]. The fuel is gaseous hydrogen and the

working conditions are 63C, nominal hydrogen pressure 16 barg and air pressure 1.2 barg.

During the next Olympic Winter Games 2010 in Vancouver, Canada, Ballard will provide a 20

FC bus fleet [9]. The buses are intended to be showcased in the Resort Municipality of Whistler

during the 2010 Olympic and Paralympic Winter Games, and then be integrated intothe BC

Transit fleet [9].

3.2 The special needs of PEM systems

3.2.1 Water management

As discussed in Chapter2.6, water management is critical for polymer membrane operation.

Therefore water management is one of the main study subjects in relation to PEMFCs and

PEMFC systems.

In addition to the modeling and testing, one more method of water management is system

integration. The piping should be built as short as possible, which will alleviate water conden-

sation problems. In particular the pipes between the humidifier and the stack should be as short

as possible, one recommended option is to integrate the humidifier with the stack. However, this

internal humidification has been rather problematic to achieve.

3.2.2 Hydrogen storage

Hydrogen storage issues are a critical concern in FCVs. Fuel cell storage has a great influence

on vehicle cost. The key requirements for on-board hydrogen storagefor a vehicle are high

gravimetric and volume densities, fast kinetics, appropriate thermodynamics,long cycle life for

hydrogen charging and release, durability and tolerance of contaminants, as well as low system

costs, safety and minimal energy requirements and environmental impacts [32].

The volumetric densities of the four most common methods of hydrogen storageare depicted

in Fig. 3.1. The actual options outside the laboratory environment are compressed hydrogen and

liquid hydrogen. Metal hydrides may also be used, but their price and weight normally present

a hindrance. Chemical storage and carbon nanofibres are still in the study phase.

• Compressed hydrogen storage.Compressed hydrogen gas is stored in pressure vessels at

pressure of 35-70 MPa and at room temperature. Energy consumption for pressurization

is 15% for a 70-MPa pressure vessel and 12% for a 35-MPa vessel, based on the LHV of

hydrogen [58].

• Liquid storage.Liquid hydrogen is stored at temperatures of 20-30 K and pressure 0.5-1

3.2. THE SPECIAL NEEDS OF PEM SYSTEMS 29

Figure 3.1: Volumetric densities of hydrogen under various conditions [58, 35].

MPa. The boiling point of hydrogen isT = -252.9C (p = 1 atm). Liquefaction spends

30% of the chemical energy stored in hydrogen, based on LHV [58]. Evaporation losses

of hydrogen should be minimized.

• Metal hydrides.Metals can be combined with hydrogen to form metal hydrides according

to the equation:

(n/2)H2 +M MHn. (3.1)

Commonly the reaction of desorbting hydrogen requires heat to occur, meaning∆H > 0.

Hydrogen is absorbed if∆G of the reaction at chosen conditions is negative, and desorbted

if ∆G is positive. An important advantage of metal hydrides is their high volumetric

storage density, but the trade-off between weight/capacity and operatingconditions is quite

problematic [35].

• Chemical storage.Hydrogen can also be stored and released through chemical reactions.

Common reactions involve chemical hydrides and water or alcohols, which allare com-

mon liquids. Although liquid fuels have clear advantages, the disadvantage of chemical

storage is that the method is not reversible and during each refueling, byproducts must be

purged and new chemical hydrides and other reactants must be put into thevehicle. Cost,

life-cycle impacts and issues related to regeneration energy requirements are key technical

barriers currently under research [32].

• Carbon nanofibres.Certain nanostructures of carbon may achieve a large surface area and

therefore research has been done concerning absorption of hydrogen in these nanofibres.


There are three different types of nanostructure where hydrogen possibly could be stored:

sphere fullerenes, nanotubes and nanofibers.

Fullerenes are one of the carbon allotropes. They form only out of carbon atoms and

can be in the form of a hollow sphere, ellipsoid, tube, or plane. Both sphere fullerenes

and carbon nanotubes have an interesting ability to entrap atoms of other elements within

their molecular structure [33]. Hydrogen can be stored in nanotubes by chemisorption

or physisorption. Hydrogen can adsorb at the exterior of the tube wall by H-C bonds or

inside in a molecular form,H2. Nanotubes have shown good potential in hydrogen storage

systems, but prices are still too high [39].

Nanofibers are composed of graphite plates which are organized parallel, perpendicular

or at a certain angle (as ’fish bones’) in respect of the axis of the fiber.Nanofibers have

is a large surface area between the graphite plates where hydrogen canbe adsorbed. The

cyclic stability and other properties of the nanofibres are not well studied so that it is not

known whether or not this technology would be suitable for hydrogen storage [39].

3.3 Challenges of PEM systems

3.3.1 Hydrogen supply

For commercialization of PEMFC systems, the existence of a stable supply of high-purity hy-

drogen is essential. In Chapter3.2.2above, hydrogen storage methods were briefly introduced.

Besides hydrogen storage, steady and sustainable production and supply must also be solved

before a breakthrough can be achieved on the markets.

3.3.2 Contamination

Impurities in the fuel stream and pollutants in the air stream can contaminate the fuel cell in

many ways, causing performance degradation and even failures. Hydrogen impurities mainly

stem from the manufacturing process, while air impurities mainly result from vehicle exhaust

and industrial emissions. In Table3.1the majority of contaminants in the operation of fuel cells

are presented.

The contaminants in Table3.1 can harm fuel cell performance in different ways, which may

be categorized in three major types [29]:

• kinetic losses due to the poisoning of anode and cathode electrocatalysis,

• ohmic losses due to an increase in the resistance of cell components and

• mass transport losses due to changes in structure and hydrophobicity ofCLs, PEMs and

GDLs.

3.3. CHALLENGES OF PEM SYSTEMS 31

Impurity source Typical contaminant

Air N2, NOx, SOx, NH3, O3

Reformate hydrogen CO,CO2, H2S,NH3, CH4

Bipolar metal plates (end plates)Fe3+, Ni2+, Cu2+, Cr3+

Sealing gasket Si

Coolants, DI water Si,Al, S,K, Fe, Cu,Cl, V, Cr

Battlefield pollutants SO2, NO2, CO, propane, benzene

Compressors Oils

Table 3.1: Major contaminants identified in the operation of PEM fuel cells [29].

The primary contaminants are carbon monoxide- (CO) and sulfur- (S) containing species. CO

binds strongly to the platinum catalyst and blocks the active catalyst sites from hydrogen. Simi-

lar to CO adsorption, H2S and SO2 also strongly adsorb on the Pt catalyst. Even small amounts

of sulfur impurities on the cathode can cause a significant performance drop. As for other con-

taminants, ammonia causes membrane deterioration and alkali metals membrane deterioration

and also catalyst poisoning.

3.3.3 The demand and price of platinum

The catalyst is one of the two major high cost components in a PEMFC. Typicallythe catalyst

contains platinum 0.4 mg per cm2 of each electrode active area [14]. As the price of platinum has

been climbing in recent years, it has once again become an important factorin fuel cell prices.

The average monthly price of platinum was about 420 US$ per t oz April 1998 and 2000 US$

per t oz in April 2008, so that the platinum price has increased almost five-fold in the past 10

years [5]. During the past four months, the price of platinum has slightly decreased, as can be

seen from Fig.3.2. The troy ounce is a unit of weight traditionally used for precious metals, 1 t

oz equals to 0.0311 kg.

PEMFCs are considered to be the best option for the fuel cell automotive.To meet targets for

automotive commercialization, it is essential to reduce the Pt-loading from about 0.40 mg/cm2

to 0.10 mg/cm2 and thus raise the activity of Pt or Pt-alloy catalyst four-fold [36]. This should

be put into practice without any loss in a cell voltage and while maintaining maximum power

density and cell efficiency. In fuel cell vehicle applications the operational life is also important

factor where should be not compromised. It has been shown that the anode catalyst loading in a

state-of-the-art MEA operating on pure H2 may be reduced to 0.05 mg/cm2 without significant

voltage losses [37]. But because of the poor activity of Pt for the oxygen reduction reaction

(ORR), cathode loadings are more difficult to lower.


Figure 3.2: The price development of platinum between 1992 and 2008 [5].

Alternatively, an inexpensive base metal catalyst might come into question [37]. However,

catalysts made of carbon-supported Pt offer the highest ORR activity per unit mass and are

therefore likely to remain standard for platinum-based cathode materials [18].

3.3.4 Other costs

TIAX’s cost analysis of PEM fuel cell systems for transportation [20] determined the 80 kW

fuel cell system cost to consist 63% of a stack, 34% of BoP and 3% of assembly. The major

component of the stack cost was calculated to be the electrodes, accounting for 77% of the cost

of the stack. The catalyst containing platinum and the high price of platinum are naturally the

reason for the high costs of the electrodes.

Membrane is another costly part, but membrane manufacturers have estimatedthat for every

two orders of magnitude increase in manufacturing volume the price may be cutin half. The

third issue which clearly is cost related is the hydrogen storage.

3.3.5 Incomplete society

The end users will not accept hydrogen energy systems easily due to a lack of infrastructure

and uncertain safety regulations. The lack of infrastructure is a well-known ’chicken and egg’

3.4. BOP - BALANCE OF PLANT 33

problem which will require the intervention of political decision-makers. Thegeneral public

should be well informed about the current situation of the technology and it’spossibilities of

fuel cell technology, and that properly handled and managed hydrogen has no greater safety

risks than other transport fuels.

3.4 BoP - Balance of plant

The fuel cell BoP is commonly regarded to from four management systems: air supply, humidi-

fication, thermal management and fuel supply. In reality, however, they are not separate systems.

The air management system include air filtration and a blower or compressor.Water management

system takes care of the water balance in the stack with air and hydrogen humidifiers. The stack

cooling circuit is its thermal management system, including a pump and radiator. Fuel supply

system includes a pressure reducing valve and possibly a pump or ejectorfor recirculation.

3.4.1 Specific key components

The fuel cell specific components in the system are the compressor, air filter, pump or ejector

for hydrogen circulation and pressure reducer for hydrogen. These components play an impor-

tant role when building a fuel cell system, since their cost is commonly higher than the other

commercial components used.

Blower or compressor

There exists a wide variety of blowers and compressors on the market. Blowers and compressors

need not be fuel cell specific, as long as a few constraints are kept in mind. The blower must

be oil-free, as no contaminants should be allowed to enter a fuel cell. Diaphragm pumps may

not be the best choice for a fuel cell system, since uneven air flow may have a harmful effect

on fuel cell operating life. For industrial use, blowers and compressors are commonly designed

to operate near full power, which can be seen in the shape of the efficiency curve. The former

fuel cell systems without hybridization have been operated to a large degree at partial power.

Since heavy hybridization seems to be the future, choosing the blower or compressor becomes

easier since there will be only a few operating point defined in advance, and the system’s overall

efficiency will increase.

Blowers and compressors are manufactured by Ametek, Becker, ebm-papst and Iwaki, to

mention a few. Fuel cell-specific blower or compressor manufacturers are Opcon Autorotor,

Vairex and Scroll Giken.


Air humidifier

Small fuel cells operating at a maximum temperature of60C may be operated without addi-

tional humidifiers, but in larger ones this is rarely done due to durability and power density [45].

As maintaining the water balance is highly important in PEMFCs, the system is usually equipped

with a properly measured and reliable reactant humidifier, at least on the cathode side, to avoid

dehydration and flooding. The most commonly used humidifiers in PEMFC systems are nozzle

spray, gas bubbling, enthalpy wheel and membrane humidification. Enthalpywheel and mem-

brane humidifiers reuse a large amount of the heat and moisture carried bythe exhaust gas, and

thereby have proved to be a more viable technique for mobile applications [49]. The enthalpy

wheel requires a rotating hygroscopic core part driven by electric motor, whereas membrane

humidifiers do not need any moving parts. Therefore membrane type humidifiers are often pre-

ferred in vehicle applications [49]. The complexity and potential maintenance costs also make

enthalpy wheels less desirable to automakers [27]. The cathode side membrane humidifiers are

commonly tube and shell moisture exchangers, where water or moisture air flows in porous

tubes. The porous tubes, mostly made of NafionTM , allow only the the water molecules to pass

from the wet to the dry side. This transfer is driven by the water vapor partial pressure difference.

Membrane humidifier producers are e.g. Permapure, DPoint, Enerfuel and Freudenberg.

Air filter

When considering PEMFCs in vehicles, it must be noted that even though theusual air may be

clean enough, the local concentrations may easily climb above the limits e.g. whensurrounded

by other vehicles. As the airborne contaminants can quickly kill PEM cell , thesystem needs a

fuel cell specific air filter. At the moment, Freudenberg is the only PEMFC airfilter manufac-

turer.

3.4.2 Other commercial components

Aside from the above-mentioned components, a PEMFC system requires pumps and blowers

to circulate reactants and coolant water. Cooling circuits also require a radiator and possibly a

de-ionization filter to maintain clean cooling water. In case of pressurization,a compressor or

a compressor-expander will be used for air delivery. Sensors to monitor pressure, flow rate and

temperature are also needed to control the system.

3.4. BOP - BALANCE OF PLANT 35

3.4.3 Net system power and system efficiency

The efficiency of the fuel cell power system is, as in Eq.2.26, a ratio betweenPout andPin

ηsyst =Pout

Pin, (3.2)

where output electrical energyPout is

Pout = Pel − Paux, (3.3)

where the gross output power,Pel, was calculated in Eq.2.48 and the parasitic loads by all

auxiliary system equipment,Paux, is the sum of all parasitic loads, commonly

Paux = Pcomp + Ppump + Pfan + PDC , (3.4)

wherePcomp is the power of compressor or blower,Ppump power of hydrogen recirculation and

cooling circuit pumps,Pfan is power of cooling circuit fan, andPDC is the power lost in DC/DC

or DC/AC power conversion.Pin is the theoretical power of incoming fuel,

Pin = nH2,in∆HH2. (3.5)

So the system’s efficiency becomes

ηsyst = ηfcηIηaux =Ufc

−∆HH2/zF

IfczF nH2,in

Pel − Paux

UfcIfc, (3.6)

whereηfc is the fuel cell efficiency, Eq.2.48, ηaux product of efficiencies of the balance of plant

equipment andηI the current efficiency. The current efficiency is also called fuel efficiency,

since the highest current is drawn when 100% of fuel is used.

ηI =I

Itheor=

zF nH2,need

zF nH2,in=

1

λH2

, (3.7)

where theλH2is the stoichiometric ratio of hydrogen.

The efficiency of blower or compressor

The efficiency of a blower or compressor is commonly calculated as

ηblower =Pisent

Pshaft

, (3.8)

wherePshaft is the real measured shaft power andPisent is the isentropic power

Pisent = nRT0κ

κ− 1

[

(

p1p0

)κ−1

κ

− 1

]

, (3.9)


whereκ is an isentropic constant,κ =cpcV

. For air,κ = 1.4 at 20. Isentropic constant is a

function of temperature, but may be considered as a constant if temperature variations are not

large.

The shaft powerPshaft consists of the powersPactual, which is defined as the power required

for gas compression only, andPfriction, describing the friction losses, and may also be calculated

with mechanical efficiencyηmech

Pshaft = Pactual + Pfriction =Pactual

ηmech

. (3.10)

The power required for gas compression,Pactual, can be calculated from the energy balance

Pactual = ncp (T2 − T1) + Φ, (3.11)

whereΦ is the heat from the blower to the surroundings, commonly ignored in simple calcula-

tions. The electrical power drawn by the blower or compressor motor can be calculated from

Pel,blower =Pshaft

ηmotor=

Pisent

ηisentηmechηmotor. (3.12)

3.5 System optimization

In the present work, the air side of the PEMFC system is studied. In the following, the two main

parameters, temperature and pressure, are discussed.

3.5.1 Temperature

The increase in temperature lowers the EFM, Eq.2.20, since the so-called unavailable energy

termT∆S in Gibbs energy, Eq.2.4, grows with the temperature rise. It also causes a higher

Tafel slope,b, as seen from Eq.2.39and thereby a greater potential loss. Despite the losses, fuel

cell performance is in general increased by temperature rise. This is dueto the higher current

densities since mass transfer polarization and ohmic losses are reduced. Further, as is highly

appreciated in the fuel cell vehicles, the rejected heat has a higher quality.

3.5.2 Pressure

Fuel cell performance is improved when pressurized, but the cost of providing that pressure may

grow to that extent that the net gain becomes questionable. Fundamentally, pressurization is a

trade-off between improved performance (reduced cell area) and reduced piping insulation and

heat loss compared to increased parasitic load and capital cost [42]. The higher cell potential is

due to [14]:

3.6. AIR SIDE FUEL CELL SYSTEM MODELING 37

• The Nernst equation, Eq.2.23.

• An increase in exchange current density, Eq2.33, due to increased concentration of reac-

tant gases and thereby to accelerated kinetics.

Naturally large plants benefit most from pressurizing, while the costs in smallsystems easily

outweigh the benefits.

Pressurization also improves water management, since at higher pressures less water is needed

to reach the same relative humidity. This will be illustrated later in Chapter5.1.3.

3.6 Air side fuel cell system modeling

The air side of fuel cell systems has been intensely studied, mainly becausethe blower or com-

pressor is the largest single parasitic loss in the system and thus the importance of humidification

in PEMFCs.

B. Blunier and A. Miraoui [17] presented a simple mathematical model of a PEMFC system

including a PEMFC, compressor and humidifier. Their aim was to find the bestconditions on

the inlet air to maximize the net voltage. They concluded that operating with fully humidified

air at stack inlet is not a good for the operation at low mass rates, but is the best choice at high

flow rates. The optimum pressure was found to be less than 2.5 bar in all the cases.

3.6.1 PEMFC models

Currently a wide variety of PEMFC models exists. PEMFC models have been made for a steady

state [56, 12, 46] as well as for dynamic conditions for predicting transient responses [47, 50,

60, 22, 55]. There are models made for particular fuel cells where inputs values commonly are

feed gases, pressure and compositions, cell temperature and currentdensity [52, 51], and generic

models, where cell parameters such as active area and membrane thickness may also be included

[46].

While other models rely more on physical laws than other, the ohmic overvoltage, ∆Vohm,

is commonly somewhat empirically determined in all of the studies. Since the conductivity of

graphite is much greater than conductivity of membrane, usually the internal resistance is defined

as to equal to the membrane resistance.

In the beginning of the 1990s, T.E Springer [56] wrote a baseline model for the PEMFC. His

model was made for a PEMFC with a 117 NafionR© membrane. Later his empirical equations

for membrane conductivity,σm, and membrane water content,λm have been used by many

researchers in PEMFC models as well as models of membrane humidifiers.


3.6.2 Membrane humidifier models

As already introduced in Chapter3.4.1there are many types of humidifiers which can be used

in PEMFC systems. In this chapter we concentrate only on membrane humidifiers. Modeling of

membrane humidifiers has been done for two types which differ from each other according to the

geometry: to tube-and-shell humidifiers and plate-and-frame humidifiers. Commonly the heat

transfer in the membrane humidifier is modeled the same way as in the corresponding geometry

heat exchanger.

In general, the equations for determining the membrane diffusion coefficient are calculated

with the equations from T.E Springer [56]. The equations are empirical and derived for a single

type of PEMFC membrane, NafionTM117.

D. Chen and H. Peng have developed a thermodynamic model of a membrane humidifier

that captures the dynamic variables, and also a simple proportional controller to control the

humidifier operation [28]. The membrane humidifier is built from two plates with flow channels

having a square cross-section, clamped together with flows separating themembrane in between.

In the model, the humidifier consists of N humidifier units, which can be controlledindividually.

The model enabled both steady-state and dynamic analysis.

Later Chen et al. [27] validated basically the same model with a Perma Pure PH-60T-24SS

tube-and-shell type water-to-gas humidifier and obtained a new water transfer coefficient for the

Nafion membrane for dry air humidification with liquid water.

In the study of R. Huizing et al. [40] a design methodology for membrane-based plate-and-

frame fuel cell humidifiers was developed. The method is very simple and straightforward, using

the ratio,R, between the residence time of gas in the humidifier over the diffusion time of water

from the surface of the membrane into the channel as a design parameter. Atarget range forR

is identified to be between 2 and 4.

S.K. Park et al. [49] proposed a mathematical model for the tube-and-shell type gas-to-gas

humidifier using the principles of thermodynamics. Based on the results of the model they

concluded that the increased flow rate of the dry gas increased the heatand vapor mass transfer

rate. They also suggested that possibly the flow rate of the stack exhaustair can be used to

control the water balance at high currents by adding an extra valve to regulate the exhaust air.

P. Cave and W. Mérida [21] constructed a single channel Nafion membrane humidifier and

characterized it as single-phase vapor-to-vapor, counter flow operation. A method to quantify

heat loss to surroundings was developed, and the heat loss was foundto effect the overall perfor-

mance significantly. The moisture transfer was shown to be more influenced by the flow rate of

the dry side than of the wet side. They also observed that the trends of theeffect of the flow rates

on the humidifier performance will vary depending on the metric used to indicateperformance.

The different metrics will be introduced below.

3.6. AIR SIDE FUEL CELL SYSTEM MODELING 39

Performance metrics

Many metrics exist to measure a humidifier’s ability to transfer moisture. According to P. Cave

and W. Mérida [21] a comprehensive listing of the used metrics is introduced.

• The dew point approach temperature (DPAT).The difference in dew point between the

wet side inlet and dry side outlet.

• The total water transfer.The difference in the amount of water between the inlet and outlet

of either stream.

• The average water flux.The total water transfer normalized by total membrane area.

Jmem,H2O =mH2O,dry,out − mH2O,dry,in

A. (3.13)

• Water recovery ratio (WRR).The ratio of the total water transferred to the water available

in the wet stream.

WRR =mH2O,dry,out − mH2O,dry,in

mH2O,wet,in

. (3.14)

• The sensible, latent and enthalpy effectiveness (SE,LE and EE).The effectiveness factor

is defined as

ǫ =mair,dry,in (Xdry,out −Xdry,in)

mair,min (Xdry,out −Xdry,in), (3.15)

whereX is temperatureT (SE), humidity ratiox Eq. 2.66(LE) or enthalpyh (EE). The

LE is said to be best of these three in describing moisture-transfer effectiveness.


Chapter 4

Characterization

The aim was to achieve data of the main component of the air management system.The proper

compressor for a middle pressure 10 kW fuel cell system was not found, and two Ametek blowers

were characterized. In addition with compressor data, stack characterization data was needed.

The necessary stack data was run with VTT’s own 3G stack, but with restricted variable condi-

tions because of problems with the stack.

The suitable compressor should have been able to create 500 mbar over pressure with an air

flow up to 600 liter per minute (lpm). After browsing the options available on the market, the

selection of proper compressors was found to be very narrow. The best choice, the Vairex VV-

1020, was found to be too expensive for these purposes. Therefore performance data form a

compressor suitable for a middle pressure system was not obtained.

Opcon Autorotor OA1050 could have been considered for a larger PEMfuel cell system, as it

has a maximum air flow of 100 g/s, corresponding approximately 4720 standard lpm. Also the

technology of Scroll Giken looked promising, but the compressors are not in serial production

at the moment, so the price was not yet set.

4.1 Testing of blowers

Two Ametek blowers were chosen to be tested in a test bench. The objectivewas to obtain

their real characteristic curves on partial powers and learn the straightforward methodology to

calculate and represent the blower efficiencies on partial powers.

The aim was to measure characteristic curves with different constant speeds of revolution.

Since both of the blowers seem to have a peculiar inner control of speed of revolution, the

constant input voltage of speed of revolution ultimately did not provide a constant revolutions

per minute (rpm). However, the fluctuation is assumed to be very small, so with a constant

input voltage of rpm it is assumed to attain a constant rpm. Due to this inner control, it was not

41

42 CHAPTER 4. CHARACTERIZATION

possible to calculate the speeds of revolution with the data collected from the test arrangements.

4.1.1 Test system

The test system is depicted in Fig.4.1. Since the tests were conducted in the fuel cell test station,

the air filter was included in the test system. At each constant rpm, the pressure and flow were

varied by removing plugs from the splitter. Since this did not provide enoughdata points, SMC

fittings placed before the splitter were also removed one by one.

Figure 4.1: Test system for Ametek two-phase blower.

The test system created notable pressure losses, which then had to be eliminated from the

pressure data in order to obtain valid data. Because a proper size connector for pressure and

temperature sensors was lacking, the piping down from the blower had to bethrottled in to tubes

with a narrow diameter. The pressure loss of the air filter could be taken directly from the fit

based on measurements made earlier in the project. The flow meter’s pressure drop came from

the manufacturer’s data sheet. The pressure loss of the pipes and fittingsdownstream from the

blower was measured with an another test. The measured pressures werethen corrected with

total pressure loss correlation. The pressure losses are depicted in Fig. 4.2.

From Fig.4.2 we may see that flow in the air filter is laminar and thereby the pressure loss

growth with flow rate growth is tolerable, but the flow in the flow meter and piping isturbulent

and the pressure loss curve is proportional to the second power of flowrate and therefore the

losses grow notably with flow rate growth. We may conclude, that in the test systems described

above, even minor losses should be measured.

4.1.2 Ametek DC blower

The Ametek two-stage DC blower was tested. The measured data points and pressure-corrected

characteristic curves can be seen from Fig.4.3. The numbers in the legend are input voltage

values that adjust speed of rotation. The calculated efficiencies are depicted in the following

figure, Fig.4.4. The efficiencies are calculated by comparing the real power to isentropicpower.

Four Haze’s lead acid batteries were used as a blower power supply. The batteries were 12 V

each, connected two in series and these two two-packs were connected inparallel to obtain the

4.1. TESTING OF BLOWERS 43

0 100 200 300 400 500 600 7000

5

10

15

20

25

30

35

40

45Pressure losses in the test arrangement

Flow rate [lpm]

Pre

ssur

e lo

ss [m

bar]

Air filterFlow meterOutlet pipingTotal ∆p

Figure 4.2: Pressure losses in the test arrangement for blower testing.

required 24 V voltage. The real voltages were not measured during the tests and therefore the

real voltages of the stack of lead batteries were measured afterward with test loads.

4.1.3 Ametek AC blower

An Ametek AC blower was tested. In Fig.4.6the calculated efficiency of the Ametek AC blower

is shown at the tested range of data points, and in Fig4.7 the efficiencies are also depicted in

the 2D plot. The current and blower power measurements were carried out by using Fluke

measurement device.

4.1.4 Conclusions

The area of greatest efficiency is narrow, which should be noted whenchoosing a suitable blower

for a fuel cell system. The system’s characteristic curve should be at least roughly calculated

first, so that the blower may then be selected. The 3D efficiency plots can also be a good tool

when pressurization is achieved with a back pressure valve, and the operation point moves from

the system’s characteristic curve.

In both of the blower tests, the system’s pressure losses were so high thatwe were able to

measure only about one third of the characteristic curves. Therefore the area of maximum effi-

ciency was not reached and is not seen in the blower efficiency plots, Fig. 4.4 and Fig.4.6. In

Fig. 4.8, the efficiencies drawn according to the manufacturers maximum power characteristic

curve can be seen.

Another potential problem arises from the air temperature. The blower outlet temperatures in


0 50 100 150 200 250 300 350 400 450 5000

20

40

60

80

100

120

140

Flow rate [lpm]

Pre

ssur

e [m

bar]

Characteristic curves with pressure loss correction

2.533.544.555.566.5

Figure 4.3: The measured data points (asterisks) and pressure and voltage corrected character-

istic curves (solid lines) of Ametek DC blower. The black dashed line is the manufacturer’s

characteristic curve on maximum power and the legend numbers are input voltage values that

adjust speed of rotation.

the Ametek DC blower only rose up to less than 50C, but in the Ametek AC test we measured

temperatures around 95C. There were doubts that the high temperatures may have caused a

bending of the last characteristic curves with high speeds of revolution towards the lower rpm

curves.

4.1.5 Error factors

The zero level of the pressure sensor is moving as a function of temperature. Nonetheless, this

was not taken into account.

4.2. STACK CHARACTERIZATION 45

0100

200300

400500

0

50

100

1500

5

10

15

20

Flow rate [lpm]

Efficiency of Ametek 2−stage blower

Pressure [mbar]

η [%

]

Figure 4.4: The 3D efficiency plot of Ametek DC blower.

4.2 Stack characterization

4.2.1 CEA/GENEPAC stack

The stack is the core of the fuel cell system. In this case the system had to betaken into con-

sideration before the necessary information concerning the stack was obtained. This was due to

later stack delivery than expected in the beginning, as well as to problems withthe control code

of the test bench which was not working at the time. The data from the stack was not obtained

within the time limits of this work.

Originally this stack was assumed to be a good choice for a middle pressure system. However

the first test runs showed the pressure drop in the stack to be lower than expected, and therefore

perhaps it would be more suitable for a low pressure system.

4.2.2 3G stack

VTT’s own 3G stack was characterized in the Arbin test bench and the effects of pressurization

were studied. The stack consists of 5 cells, each having a reactive areaof 200 cm2. The stack


0 100 200 300 400 500 600 700 8000

50

100

150

200

250

300

350

400

450

Flow rate [lpm]

Pre

ssur

e [m

bar]

Characteristic curves with pressure loss correction

1.7522.252.52.7533.253.53.7544.254.54,7555.255.55.756Data sheet

Figure 4.5: The measured data points (asterisks) and pressure and voltage corrected character-

istic curves (solid lines) of Ametek AC blower. The black dashed line is the manufacturer’s

characteristic curve on maximum power and the legend numbers are input voltage values that

adjust speed of rotation.

had had some water management problems in the past, and even though some modifications to

the stack were done, it seemed that the problems were not totally overcome.

The purpose was to run three data sets. Each data set was run with four currents: 75 A,

100 A, 125 A and 150 A. All four currents were run with four differentcathode pressures:

ambient pressure, approximately 150 mbar, 300 mbar and 450 mbar over pressures. The anode

side pressure was kept constant at 1.2 bar. The measured cell voltages at 45C are presented

in Table 4.1. Table4.1 shows, that pressurization from the atmospheric pressure to 0.5 bar

overpressure raises the cell voltage at all measured currents by about 50 mV. It can be assumed,

that the voltage gain of the pressurization would be even higher if the stack was run with lower

air stoichiometry.

The three data sets were intended to be run with a different humidification conditions. How-

ever, the heating resistors were burned during the first test run, and this and a severe water


0200

400600

800

0100

200300

400

0

5

10

15

20

25

Flow rate [lpm]

Efficiency of Ametek AC blower

Pressure [mbar]

η [%

]


0 100 200 300 400 500 600 700 8000

50

100

150

200

250

300

350

400

450 Efficiency of Ametek AC blower

Flow rate [lpm]

Pre

ssur

e [m

bar]

5

10

15

20

25



0 500 1000 1500 20000

5

10

15

20

25

30

35Efficiency of Ametek DC blower

Flow rate [lpm]

η [%

]

0 500 1000 1500 2000 25000

5

10

15

20

25

30

35

40Efficiency of Ametek AC blower

Flow rate [lpm]

η [%

]

Figure 4.8: The efficiency fits for Ametek DC and AC blowers after the manufacturers maximum

power characteristic curve. Red dotted lines show the maximum flow rates reached in the tests

and manufacturers corresponding efficiencies.

I Pressurization

A 0 bar 0.1 bar 0.2 bar 0.3 bar 0.4 bar 0.5 bar

75 688.0 699.9 711.1 721.6 731.3 740.3

100 666.1 677.2 687.8 697.9 707.5 716.5

125 640.9 656.7 669.9 680.7 688.9 694.5

150 619.6 637.6 652.4 663.9 672.3 677.5

Table 4.1: The 3G cell voltages (mV) at 45C, with different currents and pressures.

management problem with the stack forced us to finish the test. Therefore theeffect of the hu-

midification has been estimated according to my thesis supervisor, J. Ihonen,and his studies [41];

the resistivity of the membrane was estimated to decrease 5 mΩcm2 per 10C. In Table4.2 the

cell voltages with increasing pressure and temperature are shown.

Because of the water management problems with the stack, we were obligated torun the stack

with an air stoichiometry of 5.22. However, the excess air could not cover the whole problem,

and after the incoming air heater broke down, we were not able to run the latter two data sets.

The cell average voltage is not an average voltage of all five cells, but of the three cells in

the middle, since the current collector material is not optimal and the higher currents in the

outermost cells also create a voltage loss.


Pressurization

Tdew point 0 bar 0.1 bar 0.2 bar 0.3 bar 0.4 bar 0.5 bar

42C 619.6 637.6 652.4 663.9 672.3 677.5

52C 623.3 641.3 656.1 667.7 676.1 681.2

62C 627.1 645.1 659.9 671.4 679.8 685.0

Table 4.2: The 3G cell voltages (mV) with increasing pressure and temperature, I = 150 A,

λair = 5.22. The voltages at 45C are real measured values and at 55C and 65C estimated

values according to [41].


Chapter 5

Air side calculations

A realistic air supply model is necessary for fuel cell system development.The main goal was

not to achieve an universally applicable model with accurate results, but rather to develop an

easy methodology that could be usable if the proper data was available.

The goal was to use experimental data as much as possible since a strongly theoretical models

of all the necessary components would have required resources that were not available. Therefore

the model presented and used here is a simple empirical model, and not a fundamental model

that would represent the physics of the processes involved.

At the end we were not able to obtain experimental data from those components that would

have been ideal for this study. Therefore the results should be taken asindicative results and the

goal for the work has been the methodology of developing easy tools whichcan be used when

building a middle pressure system. Devices considered in the air side of PEMFC system are

depicted in Fig.5.1.

Figure 5.1: The air side of the PEMFC system.

51

52 CHAPTER 5. AIR SIDE CALCULATIONS

5.1 The effect of temperature and pressure

5.1.1 The cost of pressurization

Pressurization increases the cell voltage but also the parasitic load of the blower. The net power

gain or loss can be simply calculated as

Pnet = Pel − Pel,blower. (5.1)

wherePel is electrical power, Eq.2.55, andPel,blower electrical power consumption of the

blower’s motor. The so called “energy payback” is the minimum power gain required from

the stack to overcome the excess power of the blower resulting from the pressurization

Ppayback = Pel,inc = ∆UI = Pblower,inc = ηel,blower∆Pisent. (5.2)

Using the equation above, it may be calculated how much the cell voltage shouldincrease in

order electrical power produced by the stack to overcome the extra power draw of the blower.

Or vice versa, if the cell voltage increase by the pressurization is known,how high the blower

efficiency should be in order to profit from the pressurization.

5.1.2 Cost of pressurization with a 3G stack

With a stack temperature of 45C and air stoichiometry,λair, of 5.22 it is presumable that no

power gain will be achieved with pressurization. In Fig.5.2 net power gain/loss per one cell is

presented withI = 150 A andλair of 5.22 and 2. In Table4.2 the cell voltages were presented,

from which the net power gain/loss was calculated as in Eq.5.1.

The voltage reduction caused by lowerλair is not taken into consideration, even though in

reality some Volts would apparently be lost, and for simplicity total blower efficiency is assumed

to be a constant 35%. The shape of the gain curve is greatly dependent on the efficiency plot

of a chosen blower/compressor. It may simply be noted, that with blowers thepeak gain will

probably be around 100 - 300 mbar gauge, since higher pressurizations will easily consume too

much power.

Increasing temperature should even increase net power gain, as we maysee from Table5.1,

where the voltage efficiencies, Eq.2.47, of the a 3G stack are calculated. The voltages of 3G

stack were presented in Table4.2. In Fig. 5.3 the voltage efficiency gains from Table5.1 are

illustrated in percentage units. Here we may see that in the measured 3G stack data set, the

pressurization from atmospheric pressure to 0.5 bar overpressure, the cell voltage efficiency has

increased by about 5%-units.

5.1. THE EFFECT OF TEMPERATURE AND PRESSURE 53

Pressurization

Tdew point 0 bar 0.1 bar 0.2 bar 0.3 bar 0.4 bar 0.5 bar

42C 51.7 53.2 54.5 55.4 56.1 56.6

52C 52.0 53.5 54.8 55.7 56.4 56.9

62C 52.3 53.8 55.1 56.0 56.7 57.2

Table 5.1: The 3G cell voltage efficiencies (%) with increasing pressure and temperature,

I = 150 A,λair = 5.22.

0 0.1 0.2 0.3 0.4 0.5−18

−16

−14

−12

−10

−8

−6

−4

−2

0

2

Pressurization [bar]

Net

pow

er [W

]

λair

=5.22

λair

=2

Figure 5.2: Net power per one cell, with a current of 150 A and air stoichiometry of 5.22. The

cell area is 200 cm2.

5.1.3 The effect of pressurization on water balance

Pressurization improves water management. From Fig.5.4we may see how much even a small

pressurization lowers the water content at 90C. The water content has been calculated with

Eqs.2.67and2.68. For example if relative humidity is chosen to be maintained at 100%, raising

the pressure by 300 mbar from ambient air pressure cuts the water content by half;

x =Mh

Mi·

RH ∗ p′h (T )

p−RH·′h (T )

x(p = 1bar) =18.016g/mol

28.856g/mol·

1 · 70170Pa

1 · 105Pa− 1 · 70170Pa∼= 1.47 kg water/kg dry air

x(p = 1.3bar) =18.016g/mol

28.856g/mol·

1 · 70170Pa

1.3 · 105Pa− 1 · 70170Pa∼= 0.73 kg water/kg dry air


0 0.1 0.2 0.3 0.4 0.50

1

2

3

4

5

6

Pressurization [bar]

[%]

42°C52°C62°C

Figure 5.3: Change of voltage efficiency by pressurization and dew point temperature rise in

percentage units [%].I = 150 A,λair = 5.22.

1 1.1 1.2 1.3 1.4 1.50

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

Operating pressure [bar]

Wat

er c

onte

nt [k

g w

ater

/ kg

dry

air]

Influence of the operating pressure and relative humidity on the water content, T = 90°C

60%70%80%90%100%

Figure 5.4: Influence of the operating pressure and relative humidity on the water content.

Fig. 5.5illustrates how drastically the water content increases by raising the temperature from

60C to 90C, and again how much it drops by slight pressurization of a few hundredmbars.

However, the temperature has an effect on other issues too. The contact angle of the water in the

GDL has been observed to be strongly dependent on temperature. This inturn will affect water

transfer through the porous GDL, and thereby affect the water balance.

5.2. MODELING WITH MATLAB 55

1

1.2

1.4

60

70

80

900

0.5

1

1.5

Operating pressure [bar]

Influence of the operating pressure on the water content, RH = 100%

Temperature [C]

Wat

er c

onte

nt [k

g w

ater

/ kg

dry

air]

0.2

0.4

0.6

0.8

1

1.2

1.4

Figure 5.5: Influence of the operating pressure on the water content.

5.2 Modeling with Matlab

The general description of the air side model is depicted in Fig.5.6.

First the parameters are set. The pressure vector,pyli, is the most important variable, but e.g.

the temperature of the stack,Tstack, air stoichiometry,λO2 and exchange current at operating

point iTP can also be adjusted. The pressure vectorpyli is the overpressure at the outlet of the

shell side of the humidifier. The user may input overpressures as high asdesires, but the program

automatically sets the maximum pressure to be 1.5 bar at the outlet of the blower, since it is not

wished to observe the pressures higher than this. The humidifier model mustalso be chosen

here.

In the initial calculations-section reactant flow rates are calculated, as wellas corresponding

pressure losses of the component.

The blower section iterates the electrical power consumed by the blower,Pblower, and the

efficiency of the blower,ηblower, according to the blower Eq.3.12. It also iterates the temperature

of the outcoming air,TTS,in using the Eqs.3.9 and 3.12 by assuming that efficiency,ηm =

ηmechηmotor, remains constant.

The fuel cell model is completely empirical, and the cell voltage,Ucell, is iterated from the

experimental stack data, Table4.1.

The humidifier section uses the approach temperature and approach dew point data to calculate

the air flow temperature to the stack,TTS,out and out of the stack,TSS,in as well as the approach

dew point temperature,Tapp,dp.


Figure 5.6: General description of the model.


The rest of the humidifier section makes first an assumption that the relative humidity of air

flow out of the stack,RHSS,in, is saturated. First the air flow dew point into the stack,TdpTS,out,

is calculated. After calculating the stack mass flow rates, the relative humidityRHSS,in can be

calculated and if the assumption of fully humidified air was not correct, a loop iterates new

values forTdpTS,out, RHSS,in and mass flows rates.

First in the energy balance section the electrical power,Pel, the heat needed for vaporization

of the forming water,Qform and latent heat of evaporating water,Qlatent, are calculated. Then

it is checked, if enough heat is formed for vaporization. However, newiteration of the calculated

variables was not created, since commonly heat of the reaction is more than enough.

The transferred heat,ΦTS , is calculated according to the energy balance and from there the

temperature of the fluid at the outlet of the shell side,TSS,out, is iterated. Also WRR, water

recovery ratio, is calculated from the water mass flows in the humidifier, Eq.3.14.

The heat energy flow from the stack,Φcool,con, and electrical power of the stack,Pel are

calculated at the section energy balance of the stack. Furthermore, the theoretical heat of the

reaction,Φtheo, and the latent heat of the evaporating water in the stack,Φlatent are calculated.

At the end the program calculates the efficienciesηtheo, ηV andηI according to Eqs.2.27,

2.47and3.7, and efficiency of the BoP,etaBoP , including here only the blower and finally the

efficiency of the system,ηsyst, Eq.3.6.

5.2.1 Assumptions

The ideal gas law has been applied to all gases. The ideal gas law is also applied to water steam

since PEMFCs operate at relatively low temperatures and pressures andany resulting error is

small.

Blower

Data obtained from blower characterizations were used.

The temperature in the blower outlet was measured during the blower tests, but considered

to be too inaccurate to use in this model. This inaccuracy stems from the fact that temperature

sensor had to be placed downstream from the blower and not immediately after the outlet because

of a lack of proper fitting for the sensors. Additionally when adjusting the back pressure by

taking off the plugs, it was not realized slowly enough so that the temperature of the metal fitting

and the sensor would have had time to steady themselves.

Therefore the temperature is calculated from the thermodynamical power ofthe blower by

iteration. Since only total efficiency can be calculated from the blower measurement data and

there is no available data for the motor only, a rough assumptions must be made.It is assumed the

efficiencyηm, which includes the motor efficiencyηmotor and the mechanical efficiencyηmech


to be constantηmech = 0.4 and only isentropic efficiency to alternate according the flow rate and

pressure.

It is understood that this is pessimistic value near blower operating point, butit may well be

close to real value at partial pressures.

Humidifier

The humidifier pressure drop has been calculated from manufacturer’sdata for humidifier model

FC200-780-10. The air flow in the membrane pipes is assumed to be laminar andhence the

pressure loss of membrane pipeploss to be directly proportional to the flow of airQ. This way

the equations for the pressure loss in a membrane pipe per meter of length (mbar/m) on the tube

side,ploss,TS , and shell side of the membrane,ploss,SS , receive a form

ploss,TS = 0.1052Q− 0.0032, (5.3)

ploss,SS = 0.0681Q− 0.0005. (5.4)

It should be noted though, that the dry air flow into the tube side of a humidifieris higher than

the oxygen depleted air flow into the shell side of the membrane.

The incoming air is assumed to be dry air. The heat exchange in the humidifier has been

calculated with counter current heat exchanger formulae, even thoughthe flows are not actu-

ally counter current. The heat exchange through the pipe’s membrane walls is assumed to be

conductive. In reality, the adsorption and desorption of water molecules inthe porous mem-

brane material binds and releases heat. Even so, the effect of sorptionand latent heats are not

considered in this study, or in the studies of many researchers [49, 27].

The water transfer performance of a Perma Pure humidifier is assumed to bethe same as in

the manufacturer’s data sheets. The approach dew point and the approach temperature data from

Perma Pure is used without any modifications. The humidifier models, that can be chosen in the

model, are FC 100-6, FC 200-7, FC 300-7, FC 300-10, and FC 400-10. The quantities of the

pipes,ntube, and pipe lengths,ltube, of these humidifiers are listed in Table5.2.

FC 100-6 FC 200-7 FC 300-7 FC 300-10 FC 400-10

ntube 80 780 1660 1660 2500

ltube [m] 0.1524 0.1778 0.1778 0.254 0.254

Table 5.2: The dimensions of the membrane tubes in Perma Pure humidifier models considered

in the model.


In addition it is assumed that the humid air from the stack is saturated and that thehumidifier

is perfectly insulated from the surroundings and no heat is transferredonly from the hot fluid to

the cold fluid.

Stack

The 3G stack data is used for polarization curves. It should be noted, that this data set was run

at a stack temperature of 45C, and therefore is not suitable to use with a model, where the stack

temperature is expected to be higher.

The pressure loss was estimated to be 100 mbar at flow rate of 300 lpm. The flow rate is

assumed to be laminar and therefore the pressure loss to be directly proportional to flow rate.

5.2.2 General discussion of the model

The allowed temperature range may become a problem, since in testing the AC Ametek blower

temperatures up to 95C were reached. The Perma Pure humidifiers data sheets allow operating

temperature ranges of 1 to 80 for FC 100 and FC 200 models, and 1 to 90 for FC 300 and

FC 400 models.


Chapter 6

Results

The methodology for simplified optimization of the air side of PEMFC system is described.

The lack of a suitable stack for characterization and testing was unfortunate. Since the behavior

and parameters of the stack remained unknown, it was difficult to select a suitable blower for

the system. The intention was to seek a proper new compressor or blower, purchase it and

characterize it, but at this power range the selection was noted to be very narrow. The most

promising air supply option was ultimately too expensive for this purpose, andit was obvious

that the Ametek blowers characterized within this work are not the most suitablefor the type of

system studied.

6.1 The effect of pressure

6.1.1 Theoretical price

The pressurization cost comes from the blower. Therefore the blower should be sized carefully

for the particular system to reach the optimum operating point.

There are two ways to adjust the blowers: by controlling the speed of revolution and throttling.

Controlling the speed of revolution is an optimal method, since if a blower is chosen so that the

operating point is at maximum efficiency, this adjustment maintains good efficiency. Nonethe-

less, controlling the speed of revolution adjusts only along the characteristiccurve of the system

and other pressure-flow rate ratios can not be achieved. With a fuel cell system, the flow rate

is commonly controlled directly by the current drawn from the fuel cell and the required sto-

ichiometry of air. Therefore after choosing a blower, only throttling can beused to adjust the

pressure. With a back pressure valve, the pressures higher than on the characteristic curve line

may be reached, but with the price of reduced blower efficiency.

61

62 CHAPTER 6. RESULTS

6.1.2 Efficiency

The overall efficiencies of blowers within the power range discussed are rather low. As we have

seen from Figs.4.4, 4.6and4.7, the efficiencies are quite poor and the power consumption rather

high.

6.2 Modeling results

The modeling results are run with a hypothetical stack having 70 cells and each cells area of

200 cm2. The temperature of the stack is 70C and the ambient temperature and pressure are

T0 = 25C andp0 = 1 bar. The coefficients are shown in Table6.1below.

Constants Set constants

TSPT 273.15 K Tstack 343.15 K

T0 298.15 K Acell 200 cm2

p0 1 bar ncell 70

κ 1.4 λO2 2

Mh 18.016·10−3 kg/mol λH2 1

Mi 28.965·10−3 kg/mol RHin,an 0 %

MO2 32.00·10−3 kg/mol RHTS,in 0 %

MN2 28.02·10−3 kg/mol pH2 1.2 bar

Table 6.1: The model coefficients.

As discussed above, the blower efficiencies are quite unsatisfactory atall conditions. A quick

comparison with efficiency data obtained from the Opcon Autorotor’s compressor OA 1050

demonstrates the efficiencies, if an OA 1050 compressor were used instead of a blower, Fig.6.3.

The efficiencies of the twin screw compressor are depend greatly on inner coating materials and

built-in pressures [13]. In the given data for the compressor below, the coating is Tufram and

built-in ratio 1.44 [13].

The OA 1050 compressor is clearly designed for a system significantly larger than the studied

system range here; the compressor has maximum flow rates high enough for example for a 75

kW Ballard HD6 fuel cell system. In any case, the comparison is made here,since the efficiency

curves of the OA 1050 have satisfying shapes. However, moving into the better efficiency range

would require higher flow rates. Additionally the price of this kind of a compressor is too high

compared to the systems in studied range, and therefore can not be considered in reality.

The stack energy flows of the test run presented in Fig.6.1 is presented in Appendix A. The

stack energy flows are illustrated as an example in Fig.6.4. The conditions in the Fig.6.4 are:

6.2. MODELING RESULTS 63

0 100 200 300 400 5000

10

20

30

40

50

η [%

]

Average pressurization of the stack [mbar]

i = 0.375 A/cm2

ηblower

ηfc

ηsyst

0 100 200 300 400 5000

10

20

30

40

50

η [%

]


i = 0.5 A/cm2

0 100 200 300 400 5000

10

20

30

40

50

η [%

]


i = 0.625 A/cm2

ηblower

ηfc

ηsyst

ηblower

ηfc

ηsyst

0 100 200 300 400 5000

10

20

30

40

50

η [%

]


i = 0.75 A/cm2

ηblower

ηfc

ηsyst

Figure 6.1: The efficiencies (humidifier model FC 400-10).

i = 0.75 A,Tstack = 70C, the humidifier model of 400.10, and pressurization of 200 mbar.

6.2.1 Conclusions

According to the modeling, a small pressurization does not raise the system efficiency. However,

the power density will be greater and thereby the system’s size and cost become smaller. Size of

the power supply is critical in some applications and the system cost reductionis essential in all

applications.

It may be noted though that running the model system with a current density of 0.75 A/cm2,

a pressurization of about 140 mbars does not decrease the system efficiency greatly. It can be


0 100 200 300 400 5000

1000

2000

3000

4000

5000

6000

7000

8000

P [W

]


i = 0.375 A/cm2

P

blower

Pfc

Psyst

0 100 200 300 400 5000

1000

2000

3000

4000

5000

6000

7000

8000

P [W

]


i = 0.75 A/cm2

Pblower

Pfc

Psyst

Figure 6.2: The powers.

0 100 200 300 400 5000

5

10

15

20

25

30

35

40

45

50

55

η [%

]


i = 0.75 A/cm2,

ηblower

ηfc

ηsyst

0 100 200 300 400 5000

1000

2000

3000

4000

5000

6000

7000

8000

P [W

]


i = 0.75 A/cm2

Pblower

Pfc

Psyst

Figure 6.3: Efficiencies with OA 1050 compressor.

concluded that if the model system had been ran with higher currents and air flows, a better

blower efficiencies would have been reached and possibly the system efficiency would have not

decreased at all by pressurization.

As the stack data utilized was very restricted, many important effects can notbe seen from the

results. The main deficiencies are the effects of the stack temperature,Tstack, air stoichiometry,

λair, and relative humidity of air in the stack,RH, on the efficiency of the cell voltage and thus

on the cell efficiency. At the moment only the effect of pressure on cell voltage is demonstrated.

6.2. MODELING RESULTS 65

Figure 6.4: The stack energy flows, withi = 0.75 A,Tstack = 70C, the humidifier model of

400.10, and pressurization of 200 mbar.


Chapter 7

Conclusions and Future Work

7.1 Conclusions

In this study, a simplified simulation method of air side of PEMFC system was described. The

main points that should be considered in constructing an air supply system for a PEMFC system

were also described.

The benefits of pressurization are greatly dependent of system’s size and the performance of

the chosen air delivery system. According to the results, it appears that even a small pressuriza-

tion may offer clear benefits in the operation of a fuel cell, but the additionalparasitic power of

the blower would be difficult to overcome. Within this size range, the blower easily consumes

a great deal of the electricity produced and increasing the pressure witha blower would appear

to be unfavorable deal. However, higher power density have certain benefits in some cases, and

therefore small pressurizations should not be totally rejected.

It should be noted however, that in the Matlab simulation the effect of the humidity and tem-

perature on cell voltage can not be seen because of restricted voltage data. In reality, both

humidity and temperature should have a notable effect on cell voltage.

7.2 Future work

In the present work, the cell voltage data measured has been remarkably retricted. Therefore it

would be very important to obtain data from different temperatures, different air stoichiometry

and different humidification levels, to be able to calculate these effects more accurately. Char-

acterization of a humidifier is also an important task to perform in order to obtainmore reliable

data on membrane humidifier efficiency.

67

68 CHAPTER 7. CONCLUSIONS AND FUTURE WORK

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Appendix A

Matlab code

A.1 Main program

% ------------ PROGRAM 1 ---------------

%---------------------------------------

% Laskee ilmapuolen hyötysuhteen paineen funktiona

%---------------------------------------

clear

R = 8.314; % [J/kgK]

F = 96485; % Faradayn vakio [C/mol]

T_STP = 273.15; % T at standard temperature & pressure [K]

T_0 = 298.15; %

p_0 = 1; % [bar]

k = 1.4; %

M_h = 18.016E-3; % [kg/mol]

M_i = 28.9635E-3; % [kg/mol]

M_O2 = 32E-3; % [kg/mol]

M_N2 = 28.02E-3; % [kg/mol]

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Asetetaan alkuarvot

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

T_stack = 70 + 273.15; % haluttu stackilämpötila [K]

A_cell = 200; % [cm2]

n_cell = 70; % kennojen lkm

lambda_O2 = 2; % ilmaylimäärä

X = 1; % muodostuvan veden osuus, mikä ulos katodilta

RH_TS_in = 0; % Ol. että sisään täysin kuivaa ilmaa

RH_SS_in = 100; % Alkuol. että stackin jälk. ilma kylläistä,

75

76 APPENDIX A. MATLAB CODE

% tarkistetaan myöhemmin

RH_out_cat = RH_SS_in;

lambda_H2 = 1; % vety-ylimäärä

RH_in_an = 0; % sisään menevän vedyn suht.kosteus

p_H2 = 1.2; % vedyn paine [bar]

i_tp = 0.75; % itseisvirrantiheys, joka toimintapisteessä

T_ymp = T_0; % ympäristön lämpötila [K]

p_ymp = p_0; % ympäristön ilmanpaine [bar]

p_yli = linspace(0,0.5,6); % Haluttu ylipaine kostuttimen jälkeen,

% eli ylim. paine systeemissä (vektori) [bar]

% HUOM! systeemin ylimääräinen paine! haluttu

% maksimi ei välttämättä sallittu maksimi (koska:

p_1_max = 0.5; % bar g !)

% Kostutin;

model = 400.10; % kostutinmalli, vaihtoehtoina Perma Puren FC sarjat:

% 100 200.7 300.7 300.10 400.7

if model == 100 % FC100-80-6

n_tube = 80;

l_tube = 6 * 0.0254;

elseif model == 200.7 % FC200-780-7

n_tube = 780;

l_tube = 7 * 0.0254;

elseif model == 300.7 % FC300-1660-7

n_tube = 1660;

l_tube = 7 * 0.0254;

elseif model == 300.10 % FC300-1660-10

n_tube = 1660;

l_tube = 10 * 0.0254;

elseif model == 400.10 % FC400-2500-10

n_tube = 2500;

l_tube = 10 * 0.0254;

end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Lähtölaskut

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Kennon vaatima ilmamäärä

I = i_tp * A_cell % yhden kennon virta

n_O2_need = n_cell * I / (4 * F) % tarvittu happimäärä [mol/s]

n_air_in = lambda_O2 * 100/21 * n_O2_need % ilmamäärä [mol/s]

m_i_in = n_air_in * M_i; % ilmamäärä [kg/s]

rho_ki = rho_dry_air(T_STP); % kuivan ilman tiheys [kg/m3]

Q_i_in = m_i_in/rho_ki * 60E3 % [slpm]

% Kennon vaatima vetymäärä

n_H2_need = 2 * n_O2_need; % [mol/s]

n_H2_in = lambda_H2 * n_H2_need; % [mol/s]

A.1. MAIN PROGRAM 77

% Ja polttokennoreaktioissa muodostuva vesi

n_H2O_form = n_H2_need; % [mol/s]

% Kostuttimen painehäviö tällä ilmavirralla (valmistajan datasta)

Q_i_in_pipe = Q_i_in/n_tube;

p_loss_TS = (0.1052 * Q_i_in_pipe - 0.0032) * l_tube * n_tube/1000; %[bar]

% Ilmavirtaus kuoripuolella pienempi, koska fc käyttää osa n hapesta

n_air_out = n_air_in - n_O2_need;

x_O2 = (lambda_O2 * n_O2_need - n_O2_need) / n_air_out;

M_i_out = x_O2 * M_O2 + (1-x_O2) * M_N2;

m_i_out = n_air_out * M_i_out;

Q_i_in_SS = m_i_out/rho_ki * 60E3;

Q_i_in_SS_pipe = Q_i_in_SS/n_tube;

p_loss_SS = (0.0681 * Q_i_in_SS_pipe - 0.0005) * l_tube * n_tube/1000; %[bar]

p_loss_hum = p_loss_TS + p_loss_SS %[bar]

% Stackin painehäviö tällä virtauksella, ol. virtaus lamin aarista

x_1 = 300; % [lpm]

y_1 = 0.1; % [bar]

Q_avg = (Q_i_in + Q_i_in_SS)/2;

p_loss_stack = y_1/x_1 * Q_avg; %[bar]

% Joten ilmapuolen kokonaispainehäviöt ovat (putkiston pa inehäviöitä ei

% huomioida)

p_loss_syst = p_loss_hum + p_loss_stack

% ja ylipaine vektori stackissa

if p_1_max < p_yli(end)

X_p = p_1_max; % X_p on suurin haluttu paine puhaltimen

else % ulostulossa

X_p = p_yli(end);

end

p_stack_ylip_avg = linspace((0.5 * p_loss_stack+p_loss_SS+p_yli(1)),...

(X_p-p_loss_TS-0.5 * p_loss_stack),length(p_yli))

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Puhallin

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% haluttu ylipaine puhaltimen ulostulossa, täytyy <=500 [m bar]

p_blower_ylip_mbar = (p_stack_ylip_avg + 0.5 * p_loss_stack + p_loss_TS) * 1000

% Jos käytetään Ametekin AC puhallindataa

load flowrate_AC.mat % sis. matriisit V , p ja P

x = V; % [lpm]


y = p; % [mbar gauge]

z = P; % [W]

% painekorjaus, y1 = painekorjausfunktio, y3 = korjatut pai nearvot

% matriisina

y1 = 5.6662E-5 * x.^2 + 0.0246 * x -0.3543;

y3 = y + y1;

% Hyötysuhde

p_Pa = 100 . * y3; % paine [Pa]

V_m3s = x ./ 60000; % tilavuusvirta [m3/s]

eta = p_Pa . * V_m3s ./ P . * 100; % hyötysuhde matriisi %

[XI,YI] = meshgrid(0:5:800, 0:5:450);

ZI = griddata(x,y,eta,XI,YI,’cubic’);

for i = 1:length(p_blower_ylip_mbar)

eta_blower(i) = interp2(XI,YI,ZI,Q_i_in,p_blower_ylip _mbar(i));

end

eta_blower

% Puhaltimen ottama teho

[XII,YII] = meshgrid(0:5:800, 0:5:450);

PI = griddata(x,y,z,XII,YII,’cubic’);

for j = 1:length(p_blower_ylip_mbar)

P_blower(j) = interp2(XII,YII,PI,Q_i_in,p_blower_ylip _mbar(j));

end

P_blower

% Lämpötila puhaltimen ulostulossa täytyy iteroida

% Ol. moottorin mek. hyötysuhteen ol. vakio: eta_blower_me ch = 0.4

eta_blower_mech = 0.4; %[0...1]

eta_blower_isent = eta_blower./100 ./ eta_blower_mech;

p_1 = p_blower_ylip_mbar/1000 + 1; % paine puhaltimen ulost ulossa[bar]

P_blower_isent = n_air_in * R * T_0 * (k/(k-1)) . * ...

((p_1./p_0).^((k-1)/k) - 1)

% Lasketaan ulostulolämpötila kaikille painevektorin mää rittämille

% puhaltimen ottotehoille.

for n = 1:length(P_blower_isent)

% iteroidaan T_TS_in

P_blower_thermo(1) = 0;

m = 1;

t(m) = T_ymp;

while P_blower_isent(n)/eta_blower_isent(n) - P_blower _thermo(end) > 0

if m > 1

t(m) = t(m-1)+0.1;

end


c_p_blower_avg(m) = (c_p_dry_air(T_ymp) * M_i + ...

c_p_dry_air(t(m)) * M_i) / 2;

P_blower_thermo(m) = n_air_in * c_p_blower_avg(m) * (t(m)-T_ymp);

m = m+1;

end

T_TS_in(n) = t(end);

if P_blower_isent(n) == 0

T_TS_in(n) = NaN

end

end

T_TS_in % Puhaltimen ulostulon lämpötilavektori[K]

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Kennon polarisaatiokäyrä

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Jännite-virta yhtälö;

V_p_45 =[688.0100 699.9217 711.1048 721.5592 731.2850 740 .2822;

666.1000 677.2104 687.8057 697.8858 707.4507 716.5005;

640.8600 656.6694 669.9396 680.6706 688.8624 694.5150;

619.5900 637.5861 652.3724 663.9489 672.3156 677.4725] * 1E-3; % [V]

% yhdelle kennolle

i_ = 0.375:0.125:0.750; % virrantiheys [A/cm2], vakio matr iisin riveillä

p_ = 0:0.1:0.5; % ylipaine [bar], vakio matriisin sarakkeil la

for l = 1:length(p_stack_ylip_avg)

U_cell(l) = interp2(p_,i_,V_p_45,p_stack_ylip_avg(l), i_tp);

end

U_cell

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Kostutin

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Q = Q_i_in;

% Approach temperature (sovitteet tehty valmistajan dataa n)

if model == 100

if Q > 0 && Q < 8

T_app = 0.075 * Q + 2.0833;

elseif Q >= 8 && Q <= 18

T_app = 0.2911 * Q + 0.325;

else

disp([’Flow rate out of the limits.’])

end

elseif model == 200.7

if Q > 0 && Q < 112


T_app = 0.0054 * Q + 2.0833;

elseif Q >= 112 && Q <= 280

T_app = 0.0208 * Q - 0.325;

else


end


if Q > 0 && Q < 240

T_app = 0.0025 * Q + 2.0833;

elseif Q >= 240 && Q <= 600

T_app = 0.0097 * Q - 0.325;

else


end


if Q > 0 && Q < 340

T_app = 0.0018 * Q + 2.0833;

elseif Q >= 340 && Q <= 850

T_app = 0.0068 * Q - 0.325;

else


end


if Q > 0 && Q < 500

T_app = 0.0012 * Q + 2.0833;

elseif Q >= 500 && Q <= 1250

T_app = 0.0047 * Q - 0.325;

else


end

else

disp([’Not known humidifier model.’])

end

T_TS_out = T_stack - T_app / 2; % T_stack_in

T_SS_in = T_TS_out + T_app; % T_stack_out

% Approach dew point; (sovitteet tehty valmistajan dataan)

if model == 100

if Q > 0 && Q < 8

T_app_dp = 0.2625 * Q + 2.7583;

elseif Q >= 8 && Q <= 18

T_app_dp = 0.6277 * Q - 0.0232;

else


end


if Q > 0 && Q < 112

T_app_dp = 0.0188 * Q + 2.7583;

elseif Q >= 112 && Q <= 280

T_app_dp = 0.0448 * Q - 0.0232;

else



end


if Q > 0 && Q < 240

T_app_dp = 0.0088 * Q + 2.7583;

elseif Q >= 240 && Q <= 600

T_app_dp = 0.0209 * Q - 0.0232;

else


end


if Q > 0 && Q < 340

T_app_dp = 0.0062 * Q + 2.7583;

elseif Q >= 340 && Q <= 850

T_app_dp = 0.0148 * Q - 0.0232;

else


end


if Q > 0 && Q < 500

T_app_dp = 0.0042 * Q + 2.7583;

elseif Q >= 500 && Q <= 1250

T_app_dp = 0.01 * Q - 0.0232;

else


end

else

disp([’Not known humidifier model.’])

end

disp(’T_app -- T_TS_out -- T_SS_in -- T_app_dp’);

disp([T_app T_TS_out T_SS_in T_app_dp]);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% LASKETAAN KAIKILLA HALUTUILLA PAINEILLA

for w = 1:length(p_yli)

T_dp_SS_in(w) = T_SS_in; % Ol. ensin että kaasu stackista ul os RH = 100 %

Tdp_TS_out(w) = T_dp_SS_in(w) - T_app_dp;

% RH_TS_out suhteellinen kosteus kostuttimen ulostulossa

RH_TS_out(w) = XSteam(’psat_T’,Tdp_TS_out(w)-273.15) / ...

XSteam(’psat_T’,T_TS_out-273.15) * 100 % [%]

%-------------------------------------------

% lämmönsiirto [kW], lasketaan keskimääräisistä arvoista , T_ka

% Olettaa, että putkipuolelta aina sisään kuivaa ilmaa

T_avg_TS(w) = (T_TS_in(w) + T_TS_out) / 2; % [K]

% kuivan ilman massavirta kostuttimeen sisään "tube side"

m_ki_TS = m_i_in; % [kg/s]

% Water vapor pressure p_v_TS_in

p_v_TS_in(w) = RH_TS_in/100 * XSteam(’psat_T’,(T_TS_in(w)-273.15)); % [bar]


% Water vapor pressure p_v_TS_out

p_v_TS_out(w) = RH_TS_out(w)/100 * XSteam(’psat_T’,(T_TS_out-273.15)); % [bar]

p_v_avg_TS(w) = (p_v_TS_in(w) + p_v_TS_out(w)) / 2; % [bar]

c_pm_TS(w) = spes_heat_capacity(T_avg_TS(w),p_v_avg_T S(w)); % [J/kgK]

p_stack_in(w) = p_1(w) - p_loss_TS; % paine stackiin sisaan ,(cat)[bar];

% Lasketaan massavirrat stackiin sisään ja ulos

stack_flows(w,:) = stack_flow2(T_TS_out,T_SS_in,lambd a_O2,i_tp,A_cell,...

n_cell,RH_TS_out(w),p_stack_in(w),p_loss_stack)

RH_stack_out(w) = stack_flows(w,7);

RH_SS_in(w) = RH_stack_out(w);

% Jos veikkaus RH_SS_in = 100 % meni pieleen, lasketaan uudel leen

if RH_stack_out(w) < 100

clear RH_stack_out_apu

clear stack_flows_apu

clear p_v_SS_in_apu

clear T_dp_SS_in_apu

clear Tdp_TS_out_apu

clear RH_TS_out_apu

RH_stack_out_apu(1) = RH_stack_out(w);

RH_stack_out_ed(1) = 1;

p_v_SS_in_apu(1) = 1;

stack_flows_apu(1,:) = stack_flows(w,:)

n = 1;

while RH_stack_out_apu(n)- RH_stack_out_ed(n) > 0.05

p_v_SS_in_apu(n) = (stack_flows_apu(n,4)/stack_flows_ apu(n,3) * ...

stack_flows_apu(n,6)/M_h * (p_yli(w)+p_0-p_loss_SS) * 1E5 / ...

(1 + stack_flows_apu(n,4)/stack_flows_apu(n,3) * ...

stack_flows_apu(n,6)/M_h)) / 1E5;

T_dp_SS_in_apu(n) = XSteam(’Tsat_p’,p_v_SS_in_apu(n)) +273.15; % [K]

Tdp_TS_out_apu(n) = T_dp_SS_in_apu(n) - T_app_dp;

RH_TS_out_apu(n) = XSteam(’psat_T’,Tdp_TS_out_apu(n)- 273.15) / ...

XSteam(’psat_T’,T_TS_out-273.15) * 100; % [%]

stack_flows_apu(n+1,:) = stack_flow2(T_TS_out,T_SS_in ,lambda_O2,i_tp,A_cell,...

n_cell,RH_TS_out_apu(n),p_stack_in(w),p_loss_stack) ;

RH_stack_out_ed(n+1) = stack_flows_apu(n+1,7);

n = n+1;


RH_stack_out_apu(n) = RH_stack_out_apu(n-1)-0.01;

end

RH_stack_out(w) = RH_stack_out_apu(end)


stack_flows(w,:) = stack_flows_apu(end,:)

p_v_SS_in(w) = p_v_SS_in_apu(end)

T_dp_SS_in(w) = T_dp_SS_in_apu(end)

Tdp_TS_out(w) = Tdp_TS_out_apu(end)

RH_stack_in(w) = RH_TS_out_apu(end)

RH_TS_out(w) = RH_stack_in(w);

else

p_v_SS_in(w) = XSteam(’psat_T’,(T_SS_in-273.15)); % [ba r]

end

n_H2O_vaporization(w) = (stack_flows(w,4)-stack_flows (w,2))/M_h

m_h_stack_in(w) = stack_flows(w,2);

m_h_TS_out(w) = m_h_stack_in(w);

m_h_stack_out(w) = stack_flows(w,4);

m_h_SS_in(w) = m_h_stack_out(w);

m_H2O_l_out(w) = stack_flows(w,5);

m_H2O_mahtuu(w) = stack_flows(w,4) - stack_flows(w,2);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Stacki (energiatase)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%-------------------------------------------------- -------------------

% Tarkistetaan muodostuuko tarpeeksi lämpöä höyrystämään kaikki vesi

% stackissa muodostuva lämpö, Q_form

% Reaktioentalpia lambda_H_reak lämpötilassa T_stack

h_mol_T_stack = h_mol_3(T_stack);

lambda_H_reak = h_mol_T_stack(4)-h_mol_T_stack(2)-...

0.5 * h_mol_T_stack(1); % HHV

Q_theo = - n_H2_need * lambda_H_reak;

P_el(w) = n_cell * U_cell(w) * i_tp * A_cell;

Q_form(w) = Q_theo - P_el(w)

% stakissa tarvittava latentti lämpö, Phi_latent

% Veden höyrystymislämpö lämpötilassa T_stack [J/mol]

Delta_H_vap = H_phase_change(T_stack) * M_h;

Q_latent(w) = n_H2O_vaporization(w) * Delta_H_vap

if Q_latent(w) > Q_form(w)

clear stack_flows_apu

clear Q_latent_apu


clear Q_form_apu

clear n_H2O_vaporization_apu

clear RH_in_apu

stack_flows_apu(1,:) = 0;

Q_latent_apu(1) = Q_latent;

clear n

n = 1;

RH_out_apu(n) = RH_stack_out(w) - 0.01;

while Q_latent_apu(end) - Q_form(w) > 0.1 % Convergence cri terion : 0.1

if n > 1

RH_out_apu(n) = RH_out_apu(n-1)-0.01;

end

p_h_apu_sat = XSteam(’psat_T’,T_SS_in-273.15)

p_h_apu = RH_out_apu(n)/100 * XSteam(’Tsat_p’,p_h_apu_sat)

T_dp_SS_in(w) = XSteam(’Tsat_p’,p_h_apu)

Tdp_TS_out(w) = T_dp_SS_in(w) - T_app_dp;

RH_in_apu(n) = XSteam(’psat_T’,Tdp_TS_out(w)-273.15) / ...

XSteam(’psat_T’,T_TS_out-273.15) * 100; % [%]

stack_flows_apu(n,:) = stack_flow2(T_TS_out,T_SS_in,l ambda_O2,i_tp,A_cell,...

n_cell,RH_in_apu(n),p_stack_in(w),p_loss_stack);

n_H2O_vaporization_apu(n) = (stack_flows_apu(n,4)-sta ck_flows_apu(n,2))/M_h

Q_latent_apu(w) = n_H2O_vaporization_apu(w) * Delta_H_vap;

n = n+1;

end

n_H2O_vaporization(w) = n_H2O_vaporization_apu(end)

RH_stack_out(w) = RH_apu(end)


Q_latent(w) = Q_latent_apu(end)

RH_stack_in(w) = RH_in_apu(end)

RH_TS_out(w) = RH_stack_in(w);

end

%-------------------------------------------

% Ja lämmönsiirto Phi_TS

p_v_TS_in(w) = RH_TS_in/100 * XSteam(’psat_T’,(T_TS_in(w)-273.15));

p_v_TS_out(w) = RH_TS_out(w)/100 * XSteam(’psat_T’,(T_TS_out-273.15));

p_v_avg_TS(w) = (p_v_TS_in(w) + p_v_TS_out(w)) / 2; % [bar]

T_avg_TS(w) = (T_TS_in(w) + T_TS_out) / 2;

c_pm_TS(w) = spes_heat_capacity(T_avg_TS(w),p_v_avg_T S(w));

m_avg_TS(w) = (m_h_stack_in(w) + m_h_stack_out(w))/2 + m_ ki_TS;

Phi_TS(w) = m_avg_TS(w) * c_pm_TS(w) * (T_TS_out - T_TS_in(w));

%-------------------------------------------


m_ki_SS = m_i_out;

% kostean ilmavirta sisään kostuttimeen

p_SS_in(w) = p_1(w) - p_loss_TS - p_loss_stack; % [bar]

m_SS_in(w) = m_h_stack_in(w);% kostean ilman massavirta [ kg/s]

%--------------------------------------------

% WRR, (Water Recovery ratio)

x_TS_in(w) = (M_h/M_i) * (p_v_TS_in(w) /(p_1(w) - p_v_TS_in(w)));

m_h_TS_in(w) = x_TS_in(w) * m_ki_TS;

WRR(w) = (m_h_TS_out(w) - m_h_TS_in(w))/m_h_SS_in(w) * 100; % [%]

%--------------------------------------------

% T_SS_out

% Water vapor pressure p_v_SS_out

p_TS_out(w) = p_1(w) - p_loss_TS;

x_TS_out(w) = (M_h/M_i) * (p_v_TS_out(w) /(p_TS_out(w) - p_v_TS_out(w)));

m_h_trans(w) = (x_TS_out(w) - x_TS_in(w)) * m_ki_TS; % vesi membraanin yli [kg/s]

m_h_SS_out(w) = m_h_SS_in(w) - m_h_trans(w);

x_SS_out(w) = m_h_SS_out(w)/m_ki_SS * M_i/M_h;

p_out(w) = p_yli(w) + p_ymp;

p_v_SS_out(w) = x_SS_out(w) / (1 + x_SS_out(w)) * p_out(w) ;

% ja keskimääräinen höyrynpaine SS

p_v_avg_SS(w) = (p_v_SS_in(w) + p_v_SS_out(w)) / 2;

% T_SS_out , lasketaan iteroimalla SS ulostulevan kaasun lä mpötila, ol. että

% lämmönsiirtoa ympäristön kanssa ei tapahdu

clear Phi_SS_apu

Phi_SS_apu(1) = 0;

clear t

n = 1;

t(n) = T_SS_in - 0.5;

while Phi_TS(w) - Phi_SS_apu(end) > 0.01 % Convergence crit erion : 0.01

if n > 1

t(n) = t(n-1)-0.01;

end

T_avg_SS(n) = (T_SS_in + t(n)) / 2;

c_pm_SS(n) = spes_heat_capacity(T_avg_SS(n),p_v_avg_S S(w)); % [J/kgK]

% Lämpötehojen laskemiseen on käytetty sisään menevää kaas uvirtaa m_SS_in

Phi_SS_apu(n) = m_ki_SS * c_pm_SS(n) * (T_SS_in - t(n));

n = n+1;

if t(end) < 274


disp(’Ulostulolämpötilan, T_SS_out, iterointi ei toimi’ )

T_SS_out = 0

break

end

end

Phi_SS(w) = Phi_SS_apu(end);

T_SS_out(w) = t(end);

end

T_stack_in = T_TS_out; % lämpötila stackiin sisään

T_stack_out = T_SS_in; % lämpötila stackista ulos

n_O2_in = 0.21 * n_air_in;

n_N2_in = 0.79 * n_air_in;

n_O2_out = n_air_in - n_O2_need;

h_mol_T_stack_in = h_mol_3(T_TS_out)

h_mol_T_stack = h_mol_3(T_stack)

h_H2_in = h_mol_T_stack(2);

h_O2_in = h_mol_T_stack_in(1);

h_N2_in = h_mol_T_stack_in(5);

h_H2O_g_in = h_mol_T_stack_in(3);

h_mol_T_stack_out = h_mol_3(T_SS_in)

h_O2_out = h_mol_T_stack_out(1);

h_N2_out = h_mol_T_stack_out(5);

h_H2O_g_out = h_mol_T_stack_out(3);

h_H2O_l_out = h_mol_T_stack_out(4)

H_H2_in = n_H2_in * h_H2_in

H_O2_in = n_O2_in * h_O2_in

H_N2_in = n_N2_in * h_N2_in

H_O2_out = n_O2_out * h_O2_out

H_N2_out = n_N2_in * h_N2_out

for w = 1:length(p_yli)

n_H2O_g_in(w) = m_h_TS_out(w) / M_h;

n_H2O_g_out(w) = m_h_SS_in(w) / M_h;

n_H2O_l_out(w) = m_H2O_l_out(w)/M_h;

H_H2O_l_out(w) = n_H2O_l_out(w) * h_H2O_l_out;

H_H2O_g_in(w) = n_H2O_g_in(w) * h_H2O_g_in;

H_H2O_g_out(w) = n_H2O_g_out(w) * h_H2O_g_out;

enthalpy_flow(w) = (H_O2_out + H_H2O_g_out(w) + H_H2O_l_o ut(w)) - ...

(H_H2_in + H_O2_in + H_N2_in + H_H2O_g_in(w));

Phi_cool_con(w) = -enthalpy_flow(w) - P_el(w);

end


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

disp(’Stacki taseista’);

disp(’m_h_TS_out -- m_h_SS_in -- m_H2O_l_out’);

disp([m_h_TS_out’ m_h_SS_in’ m_H2O_l_out’]);

disp(’m_H2O_l_out’);

disp(m_H2O_l_out);

disp(’P_el -- enthalpy_flow(out-in) -- Phi_cool_con’);

disp([P_el’ enthalpy_flow’ Phi_cool_con’]);

disp(’Q_theo’);

disp(Q_theo);

disp(’Q_latent’);

disp(Q_latent’);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Hyötysuhteiden laskenta

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%-------------------------------------------------- ---

% Stackin hyötysuhde, eta_fc (käyttäen alempaa lämpöarvoa , LHV)

%-------------------------------------------------- ---

load parametrit_thermo

G_reak_0_T = deltaG_0(T_stack)

% Teoreettinen hyötysuhde, eta_theo, lämpötilassa T_stac k

eta_theo = G_reak_0_T ./ lambda_H_reak

% Jännitehyötysuhde, eta_V, lämpötilassa T_stack

U_0_T = - G_reak_0_T ./ (2 * F);

eta_V = U_cell ./ U_0_T

% Virtahyötysuhde (= polttoainehyötysuhde)

eta_I = 1/lambda_H2;

% Polttokennon kokonaishyötysuhde, eta_fc

eta_fc = eta_theo . * eta_V . * eta_I

%-------------------------------------------------- -----

% Systeemin hyötysuhde

%-------------------------------------------------- -----

eta_BoP = (P_el - P_blower)./P_el

eta_syst = eta_fc . * eta_BoP

disp(’Kostuttimen arvoja:’);

disp(’T_TS_out[C]’);

disp([T_TS_out-273.15])


disp(’Tdp_TS_out[C] -- RH_TS_out’);

disp([[Tdp_TS_out-273.15]’ RH_TS_out’]);

disp(’WRR -- Phi_TS -- T_SS_out[C]’)

disp([WRR’ Phi_TS’ T_SS_out’-273.15]);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Piirretään kuvaajia

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%............esim. FIGURE 1..............

figure

%subplot(3,1,3)

subplot(2,2,1)

plot(p_stack_ylip_avg * 1000,eta_blower);grid on;hold on;

plot(p_stack_ylip_avg * 1000,eta_fc * 100,’r’);

plot(p_stack_ylip_avg * 1000,eta_syst * 100,’--m’,’LineWidth’,2)

set(gcf,’Color’,’w’)

axis([0 500 0 55])

ylabel(’\eta [%]’)

xlabel(’Average pressurization of the stack [mbar]’);

legend(’\eta_blower’,’\eta_fc’,’\eta_syst’)

title([’i = ’,num2str(i_tp),’ A/cm^2 , n\_cell = ’,num2str (n_cell),...

’ humidifier ’,num2str(model)]);

hold off;

A.2 Sub programs

c_p_dry_airThe fit for specific heat for dry air is from P.T. Tsilingiris [57].

function out = c_p_dry_air(T)

% Correlation for calculating the spesific heat of dry air in the temperature range

% -23 C <= t <= 777 C and at the total pressure of 1.013 bar.

% "Thermophysical and transport properties of humid air at t emperature range

%between 0 and 100 C"

% P.T. Tsilingiris

% INPUT

% T = temperature [K], can be vector

% OUTPUT

% c_pa = viscosity of vapor [J/kgK]

C0 = 0.103409E1;

C1 = -0.284887E-3;

A.2. SUB PROGRAMS 89

C2 = 0.7816818E-6;

C3 = -0.4970786E-9;

C4 = 0.1077024E-12;

c_pa_ = C0 + C1 * T + C2* T.^2 + C3 * T.^3 + C4 * T.^4; % [kJ/kgK]

c_pa = c_pa_ * 1E3; %[J/kgK]

out = c_pa;

c_p_vapor

The fit for specific heat for water vapor is from P.T. Tsilingiris [57].

function out = c_p_vapor(t)

% Correlation for calculating the viscocity of dry air in the temperature range

% 0 C <= t <= 120 C and at the total pressure of 1.013 bar.

% "Thermophysical and transport properties of humid air at t emperature range

%between 0 and 100 C"

% P.T. Tsilingiris

% INPUT

% t = temperature [C], can be vector

% OUTPUT

% c_pv = viscosity of vapor [J/kgK]

C0 = 1.86910989;

C1 = -2.578421578E-4;

C2 = 1.941058941E-5;

c_pv_ = C0 + C1 * t + C2 * t.^2; % [kJ/kgK]

c_pv = c_pv_ * 1E3; %[J/kgK]

out = c_pv;

deltaG_0

The parameters in the parametrit_thermo.mat file are Faraday constantF , gas constantR, ref-

erence temperatureTref , reference pressurepref , heat of formationmuod_entalpia, entropy of

formationmuod_entropia and coefficientsabcde. The coefficientsabcde are from M. Lampinen

[44].

function out = deltaG_0(T)


% Calculates the Gibbs free energy for hydrogen oxidation re action ar

% standard state and temperature T

% IN

% T temperature [K]

% OUT

% deltaG reaction Gibbs at p_0

for v = 1:length(T)

load parametrit_thermo

% Sensible entropy S for gases

for j = 1:5

% C = c_p / T

C = @(T)abcde(1,j) * T.^(-1)+abcde(2,j)+abcde(3,j) * T+abcde(4,j) * T.^2+...

abcde(5,j) * T.^3;

S(j) = quadgk(C,T_ref,T(v));

end

% Sensible entropy S for liquid water

muod_entropia(4) = 0;

% muod_entropia(i)+S(i), from JANAF tables

T_apu = [298.15 300:20:360 372.78];

S_apu = [69.950 70.416 75.279 79.847 84.164 86.808];

S(4) = interp1(T_apu,S_apu,T(v));

% Spesific entropy at reference pressure p_0 = 1 bar

for i = 1:5

s(i,:) = muod_entropia(i) + S(i);

end

s_0(v,:) = s;

h_0(v,:) = h_mol_3(T(v));

end

lambdaH_reak = h_0(:,4) - h_0(:,2) - 0.5 * h_0(:,1);

lambdaS_reak = s_0(:,4) - s_0(:,2) - 0.5 * s_0(:,1);

deltaG = lambdaH_reak - T’ . * lambdaS_reak;

out = deltaG


h_mol_3

The parameters in the parametrit_thermo.mat file are Faraday constantF , gas constantR, ref-

erence temperatureTref , reference pressurepref , heat of formationmuod_entalpia, entropy of

formationmuod_entropia and coefficientsabcde. The coefficientsabcde are from M. Lampinen [44].

function out = h_mol_3(T_in)

% Calculates enthalpies [O2 H2 H2O_g H2O_l N2] at temperatur e T_in

%INPUT

% T_in lämpötila (K) --- VAIN SKALAARI!

%

%OUTPUT

% out = h, molar spesific enthalpy (J/mol)

%

% O2 H2 H2O_g H2O_l N2

load parametrit_thermo.mat

T_C = T_in - 273.15;

% Sensible enthalpy H

for j = 1:5

c_p = @(T)abcde(1,j)+abcde(2,j) * T+abcde(3,j) * (T.^2)+abcde(4,j) * (T.^3)+...

abcde(5,j) * (T.^4); % [J/molK]

H(j) = quadgk(c_p,T_ref,T_in);

end

% Sensible enthalpy for water, from JANAF tables

T_apu = [298.15 300:20:360 372.78];

H_apu = [0 0.139 1.646 3.153 4.664 5.633] * 1000; %[J/mol]

H(4) = interp1(T_apu,H_apu,T_in);

for i = 1:5

h(i) = muod_entalpia(i) + H(i);

end

out = h;

H_phase_change

Fit is made for the values in the steam tables.


function out = H_phase_change(T)

% Latent heat of water at temperature T

% IN

% T = temperature [K]

% OUT

% H_phase_change [J/kg]

apu = [0 2501.4

5 2490.0

10 2478.7

15 2467.2

20 2455.4

25 2443.6

30 2431.6

35 2419.5

40 2407.2

45 2395.0

50 2382.9

55 2370.6

60 2358.3

65 2345.8

70 2333.4

75 2320.8

80 2308.2

85 2295.5

90 2282.8

95 2269.8

100 2256.8];

T_l = ones(size(apu));

T_l(:,1) = apu (:,1) + 273.15;

T_l(:,2) = apu (:,2) * 1E3;

R = polyfit(T_l(:,1),T_l(:,2),2);

H = R(1) * T^2 + R(2) * T + R(3);

out = H;

spes_heat_capacity

The fit for the specific heat capacity for moist air is from P.T. Tsilingiris [57].

function out = spes_heat_capacity(T,p_v)

% Calculates the spesific heat capacity of humid air (= mixtu re of dry air

% and vapor) at the total pressure of 1.013 bar.


%"Thermophysical and transport properties of humid air at t emperature range

% between 0 and 100 C"

% P.T. Tsilingiris

% INPUT

% T = Temperature [K]

% p_v = pressure of water vapor [bar]

%

% OUTPUT

% c_pm = spesific heat capacity of humid air [J / kgK]

M_a = 28.8558; % molecular mass of air [kg/kmol]

M_v = 18.016; % molecular mass of water [kg/kmol]

p_0 = 1.013E5; % total pressure [Pa]

T_C = T - 273.15; % temperature in degrees C

p_sv = XSteam(’psat_T’,T_C) * 1E5; % saturated vapor pressure [Pa]

% IDEAL GAS;

RH = p_v * 1E5 / p_sv; % [0...1]

x_v = RH * p_sv/p_0; % the molar fraction of water vapour

% for dry air, c_pa

c_pa = c_p_dry_air(T); % [J/kgK]

% for water vapor, c_pv

c_pv = c_p_vapor(T_C); % [J/kgK]

x_a = 1 - x_v;

M_m = M_a* x_a + M_v * x_v;

c_pm = c_pa * x_a * M_a/M_m + c_pv * x_v * M_v/M_m;

out = c_pm; % [J/kgK]

stack_flow2

function out = stack_flow2(T_in,T_out,lambda,i,A_cell, n,RH_in,p_in,p_loss)

% Calculates the mass flows in and out of the stack

% Parameters

% IN

% T_in = temp. of the gas in [K]

% T_out = temp. of the gas out (=T_SS_in) [K]

% lambda = stoichiometric coefficient of air

% i = current density [A/cm2]

% n = number of cells in stack


% A_cell = effective area of one cell [cm2]

% RH_in = relative humidity of incoming air [%]

% p_in = pressure at stack inlet [bar]

% p_loss = pressure loss of stack [bar]

%

%water vapor mass flow at stack inlet

% OUT = [m_i_in m_h_in m_i_out m_h_out m_H2O_l_out M_i_out R H_out]

% m_i_in = air mass flow at stack inlet [kg/s]

% m_h_in = water vapor mass flow at stack inlet [kg/s]

% m_i_out = oxygen depleted air mass flow at stack outlet [kg/ s]

% m_h_out = water vapor mass flow at stack outlet [kg/s]

% m_H2O_l_out = liquid water out of stack [kg/s]

% M_i_out = molar mass of outcoming oxygen depleted air [kg/m ol]

F = 96485; % Faradayn vakio [C/mol]

M_i = 28.8558E-3; % molecular mass of air [kg/mol]

M_h = 18.016E-3;% molecular mass of water [kg/mol]

M_O2 = 32E-3; % molecular mass of oxygen [kg/kmol]

M_N2 = 28.01E-3;% molecular mass of nitrogen [kg/kmol]

I = i * A_cell;

p_out = p_in - p_loss; % pressure at stack outlet

n_O2_need = n * I / (4 * F); % oxygen consumed at reactions [mol/s]

n_O2_in = lambda * n_O2_need;

n_air_in = 100/21 * n_O2_in;

% steam pressure [bar]:

p_h_in = RH_in/100 * XSteam(’psat_T’,(T_in-273.15));

x_in = (M_h/M_i) * p_h_in / (p_in - p_h_in); % humidity

m_i_in = n_air_in * M_i;

m_h_in = x_in * m_i_in;

n_air_out = n_air_in - n_O2_need;

x_O2 = (n_O2_in - n_O2_need) / n_air_out; % mole fraction of o xygen

% in outcoming oxygen depleted air

M_i_out = x_O2 * M_O2 + (1-x_O2) * M_N2;

m_i_out = n_air_out * M_i_out;

% Forming water

n_form_H2O = n * I / (2 * F);

m_form_H2O = n_form_H2O * M_h;

% The maximum water in the air at outlet

p_h_max = XSteam(’psat_T’,(T_out-273.15));

x_max_out = (M_h/M_i_out) * p_h_max / (p_out - p_h_max);

m_h_max = x_max_out * m_i_out;

m_mahtuu = m_h_max - m_h_in;

% The relative humidity at outlet


if m_mahtuu < 0

m_H2O_vaporization = 0;

m_h_out = m_h_max;

m_H2O_tiivistyy = - m_mahtuu;

RH_out = 100;

else

m_H2O_tiivistyy = 0;

if m_form_H2O >= m_mahtuu

m_H2O_vaporization = m_mahtuu;

m_h_out = m_h_in + m_H2O_vaporization;

RH_out = 100;

else

m_H2O_vaporization = m_muod_H2O;

m_h_out = m_h_in + m_H2O_vaporization;

p_h_out_Pa = (m_h_out/m_i_out) * (M_i_out/M_h) * p_out * 1E5 / ...

(1 + (m_h_out/m_i_out) * (M_i_out/M_h));

p_h_out = p_h_out_Pa / 1E5;

RH_out = p_h_out / XSteam(’psat_T’,T_out-273.15) * 100; %[%]

end

end

% Outcoming liquid water

m_H2O_l_out = m_form_H2O - m_H2O_vaporization + m_H2O_tii vistyy;

disp(’m_i_in -- m_h_in -- m_i_out -- m_h_out -- m_H2O_l_out -- M_i_out -- RH_out’);

out = [m_i_in m_h_in m_i_out m_h_out m_H2O_l_out M_i_out RH _out];

XSteam

XSteam is a function that calculates water and steam properties according toIAPWS IF-

97 standards. This freeware is coded by Magnus Holmgren and can be downloaded from

http://www.x-eng.com/.


Appendix B

Stack energy balance

Stack energy balance calculations are presented in the Table above. Conditions in the system are

as described in Chapter6.2and depicted in Fig.6.1.

97

98 APPENDIX B. STACK ENERGY BALANCE

i=0.375

∆p mbar 0 100 200 300 400 500

Qi,in(STP ) lpm 177.5

HH2,in J/s 35.39

HO2,in J/s 35.09

HN2,in J/s 130.7

HH2O,g,in J/s -11290 -10143 -9207 -8429 -7772 -7211

HO2,out J/sJ 18.47

HN2,out J/s 137.6

HH2O,g,out J/s -13538 -11978 -10740 -9734 -8901 -8199

HH2O,l,out J/s -5036 -5521 -5876 -6144 -6353 -6518

Pel W 3631 3685 3737 3785 3830 3872

enthalpy flow(out−in) W -7466 -7539 -7592 -7632 -7664 -7689

Φcool,con W 3835 3854 3856 3848 3834 3817

Φtheo W 7738

Φlatent W 394.0 321.7 268.9 228.9 197.9 173.3

i=0.5

∆p mbar 0 100 200 300 400 500


HH2,in J/s 47.19

HO2,in J/s 46.74

HN2,in J/s 174.2

HH2O,g,in J/s -14501 -13126 -11989 -11034 -10219 -9516

HO2,out J/s 24.65

HN2,out J/s 183.6

HH2O,g,out J/s -18067 -16075 -14478 -13170 -12079 -11155

HH2O,l,out J/s -6046 -6772 -7312 -7727 -8052 -8313

Pel W 4694 4758 4820 4879 4935 4989


Φcool,con W 5161 5205 5225 5228 5220 5206

Φtheo W 10317

Φlatent W 624.8 516.8 436.3 374.5 326.1 287.2

99

i=0.625

∆p mbar 0 100 200 300 400 500


HH2,in J/s 58.99

HO2,in J/s 58.38

HN2,in J/s 30.83

HH2O,g,in J/s -17475 -15933 -14640 -13542 -12597 -11775

HO2,out J/s 18.47

HN2,out J/s 229.6

HH2O,g,out J/s -22605 -20226 -18299 -16708 -15372 -14233

HH2O,l,out J/s -6767 -7751 -8496 -9076 -9536 -9909

Pel W 5677 5781 5871 5945 6005 6051


Φcool,con W 6523 6567 6589 6601 6610 6620

Φtheo W 12896

Φlatent W 898.7 752.2 641.2 554.9 486.4 430.9

i=0.75

∆p mbar 0 100 200 300 400 500


HH2,in J/s 70.79

HO2,in J/s 70.00

HN2,in J/s 260.8

HH2O,g,in J/s -20232 -18573 -17166 -15956 -14906 -13986

HO2,out J/s 37.03

HN2,out J/s 275.8

HH2O,g,out J/s -26704 -24029 -21840 -20017 -18475 -17154

HH2O,l,out J/s -7222 -8471 -9432 -10190 -10799 -11297

Pel W 6620 6750 6864 6955 7026 7079


Φcool,con W 7886 7943 7974 7996 8016 8037

Φtheo W 15475

Φlatent W 1212 1026 883.1 770.2 679.5 605.4

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