MODELING AND ANALYSIS OF PROTON EXCHANGE MEMBRANE FUEL CELL. A thesis presented to the Russ College of Engineering and Technology of Ohio University

Transcription

1 MODELING AND ANALYSIS OF PROTON EXCHANGE MEMBRANE FUEL CELL A thess presented to the Russ College of Engneerng and Technology of Oho Unversty In partal fulfllment of the requrements for the degree Master of Scence Harshl R. Parkh March 2004

2 Ths thess enttled MODELING AND ANALYSIS OF PROTON EXCHANGE MEMBRANE FUEL CELL BY HARSHIL R. PARIKH has been approved for the Department of Mechancal Engneerng and the Russ College of Engneerng and Technology by Bhavn Mehta Assocate Professor of Mechancal Engneerng R. Denns Irwn Dean Russ College of Engneerng and Technology

3 PARIKH, HARSHIL R. M.S. March Mechancal Engneerng MODELING AND ANALYSIS OF PHOTON EXCHANGE MEMBRANE FUEL CELL (pages 73) Drector of Thess: Bhavn Mehta Fuel cell technology s one of the emergng technologes for alternatve power supply. Dfferent types of fuel cells are avalable to serve n varous applcatons. Proton exchange membrane fuel cell (PEMFC), whch s the focus of ths work, s used wdely for portable applcatons. Present PEMFCs are expensve whch mpede ther commercalzaton. Better understandng of processes and the optmzaton of the fuel cell wll solve the problem. The focus of ths work s to numercally smulate the complex processes that take place wthn the fuel cell and to develop a typcal User Defned Functon (UDF). As mathematcal model of fuel cell s very complex, t s very dffcult to solve the problem analytcally. Numercal smulaton s the only economcal and fast method to understand the processes properly. The work also nvestgates the effects of change of parameters on the performance of the fuel cell. Approved: Bhavn Mehta Assocate Professor of Mechancal Engneerng

4 ACKNOWLEDGEMENTS I wsh to express my sncere grattude to Dr. Bhavn Mehta of Oho Unversty, my graduate faculty advsor, for hs support and encouragement durng the project. Workng wth hm on ths project was really good learnng experence. I would lke to thank Dr. Gerardne Botte of Oho Unversty for advsng me n ths project. Her techncal expertse and gudance made ths work possble. I would also lke to thank to the support group of FLUENT for answerng all my questons n clear and expedent manner.

5 5 TABLE OF CONTENTS ABSTRACT...3 ACKNOWLEDGEMENTS...4 TABLE OF CONTENTS...5 LIST OF FIGURES...7 CHAPTER 1: INTRODUCTION Overvew Hstory of Fuel Cells Types of Fuel Cells Dffcultes wth Commercalzaton of Fuel Cells Overvew of CFD Lterature Revew Scope and Outlne...22 CHAPTER 2: BASIC FLOW CONCEPTS The Contnuty Equaton The Momentum Equaton The Energy Equaton Conservaton of Chemcal Speces Modfed Equatons for The Porous Medum...27 CHAPTER 3: ELECTROCHEMICAL MODEL Transport Laws for Infntely Dlute Solutons Dervaton of Current Densty Voltage Equaton and Varous Losses n Fuel Cell...34 CHAPTER 4: DOMAIN DISCRITIZATION AND BOUNDARY CONDITIONS Computatonal Doman Boundary Condtons Contnuum Condtons Model Assumptons...47

6 6 CHAPTER 5: STUDY OF PROTON EXCHANGE MEMBRANE FUEL CELL Flow Feld Soluton Derved Quantty...59 CHAPTER 6: EFFECT OF CRITICAL PARAMETERS ON FUEL CELL PERFORMANCE Polarzaton Curve Power Densty Curve Effect of Porosty Effect of Cathode Pressure Effect of Number of Flow Channels...65 CHAPTER 7: CONCLUSIONS Conclusons Recommendaton and Future Work...68 REFERENCES...69 APPENDIX...72 A: Physcal Dmensons at the Base Condton...72 B: Operatonal Parameters at the Base Condton...72 C: Electrode Propertes at the Base Condton...72 D: Membrane Propertes at the Base Condton...73 E: Constants...73

7 7 LIST OF FIGURES: Fgure: 1.1 Grove s Fuel Cell...10 Fgure: 1.2 Schematc Representaton of PEMFC...12 Fgure: 1.3 The Multdscplnary Nature of CFD...19 Fgure: 3.1 Schematc Representaton of Electrcal Resstance of the Electrode...38 Fgure: 3.2 Schematc Representaton of the Flow Channel...38 Fgure: 4.1 Exploded Vew of PEMFC...40 Fgure: 4.2 Fully Meshed Flow Channel...42 Fgure: 4.3 Fully Meshed Electrode...42 Fgure: 4.4 Fully Meshed Catalyst Layer...43 Fgure: 4.5 Fully Meshed Membrane...43 Fgure: 4.6 Good and Bad Choces of Locaton of Outflow Boundary Condton...45 Fgure: 4.7 Boundary Condtons and Contnuum Condtons...47 Fgure: 5.1 Contours of Reynolds Number n the Cathode Flow Channel...50 Fgure: 5.2 Dstrbuton of Mass Fracton of Hydrogen n Anode Flow Channel...50 Fgure: 5.3 Dstrbuton of Mass Fracton of Hydrogen near the Entry of Anode...51 Fgure: 5.4 Dstrbuton of Mass Fracton of Hydrogen near the Ext of Anode...51 Fgure: 5.5 Dstrbuton of Mass Fracton of H + Ions n the Catalyst Layer...52 Fgure: 5.6 Magnfed Vew of Dstrbuton of Mass Fracton of H + Ions n the Anode Catalyst Layer...53 Fgure: 5.7 Dstrbuton of Mass Fracton of Hydrogen n Anode Catalyst Layer...53 Fgure: 5.8 Dstrbuton of Mass Fracton of H + Ions n the Membrane...54 Fgure: 5.9 Dstrbuton of Mass Fracton of Water n Cathode Catalyst Layer...55 Fgure: 5.10 Magnfed Vew of Dstrbuton of Mass Fracton of Water n the Cathode Catalyst Layer...55 Fgure: 5.11 Dstrbuton of Mass Fracton of Oxygen near the Entry of Cathode...56 Fgure: 5.12 Dstrbuton of Mass Fracton of Oxygen near the Ext of Cathode...56 Fgure: 5.13 Dstrbuton of Mass Fracton of Oxygen n Cathode Flow Channel...57 Fgure: 5.14 Dstrbuton of Mass Fracton of Water n Cathode Flow Channel...58

8 8 Fgure: 5.15 Contours of Concentraton of Oxygen n the Cathode...59 Fgure: 5.16 Contours of the Current Densty n A/m Fgure: 5.17 Contours of the Current Densty wth Magnfed Scale...60 Fgure: 6.1 Polarzaton Curve...61 Fgure: 6.2 Power Densty Curve...62 Fgure: 6.3 Effect of Porosty on Polarzaton Curve...63 Fgure: 6.4 Effect of Cathode Pressure on Polarzaton Curve...64 Fgure: 6.5 Effect of Number of Flow Channels on Polarzaton Curve...65

9 9 CHAPTER 1 INTRODUCTION 1.1 Overvew: Lmted resources of fossl fuels, ncreasng envronmental polluton, rsng costs of conventonal fuels, and lower effcency of converson of energy n exstng systems dctates the need of alternatve way of power generaton. Even though not mature fully, fuel cell s foreseen as a potental alternatve for power generaton. Fuel cells have to compete wth the other energy converson devces such as gas turbnes, gasolne engnes and batteres. A fuel cell s an electrochemcal devce whch converts chemcal energy of fuel and oxygen drectly nto electrcty. A fuel cell s a battery-lke devce but unlke a battery t provdes contnuous electrcty as long as fuel and oxygen are suppled. Ths technology s envronment frendly, requres low mantenance for the component and hgh theoretcal effcency due to drect converson of energy. For best performance hydrogen s used as fuel and oxygen as the oxdant. Due to dffcultes and rsk assocated wth the use of hydrogen drectly, other alternatves are used. Instead of drect hydrogen ol, methanol, natural gas etc. fuels are used wth the reformer whch can extract hydrogen from hydrocarbon fuels. Sometmes an onboard electrolyser s used to produce the pure hydrogen and oxygen from water usng electrolyss. The sngle cell produces the voltage of about 0.7V 0.8V whch s nsuffcent for any applcaton. Hgher voltages are obtaned by stackng of ndvdual fuel cells. Fuel cells are beng developed for a wde range of applcatons dependng on the sze and operatng temperature. Fuel cells are avalable for portable applcatons such n moble,

10 laptop; automoble applcaton and statonary applcatons lke resdental and power plant requrements Hstory of Fuel Cells: In 1800, Brtsh scentsts Wllam Ncholson and Anthony Carlsle descrbed the process of usng electrcty to decompose water nto hydrogen and oxygen. Wllam Robert Grove took the dea n reverse n He dscovered that by arrangng two platnum electrodes wth one end of each mmersed n a contaner of sulfurc acd and the other ends separately sealed n contaners of oxygen and hydrogen, constant current flows between electrodes. The sealed contaners held water as well as the gases, and he noted that the water level rose n both the tubes, as the current flowed. By combnng several sets of these electrodes n a seres crcut, he created Gas Battery the frst fuel cell. Grove s fuel cell s shown n the Fgure: 1.1. Fgure: 1.1 Grove s Fuel Cell In 1889, Ludwg Mond and Carl Langer used thn, perforated platnum electrodes.

11 11 Fredrch Wlhelm Ostwald descrbed fuel cell performance theoretcally. In 1893, he expermentally found the nterconnecton of fuel cell components. By relatng physcal propertes and chemcal reactons, he solved the puzzles of Grove s gas battery. Hs work became the base for later fuel cell researcher. In 1896, Wllam Jacques constructed a Carbon Battery n whch ar was njected nto an alkal electrolyte to react wth a carbon electrode. Eml Baur constructed wde rangng research nto dfferent types of fuel cells durng the frst half of the twenteth century. Francs Bacon began researchng an alkal electrolyte fuel cell n late 1930s and he bult a cell that used a nckel gauze electrode and operated under very hgh pressure. 1.3 Types of Fuel Cells: Varous types of fuel cells are avalable n the market for dfferent applcaton. Varous fuel cells are dfferentated by the electrolyte used n them. Even though other type of fuel cells are descrbed, ths work s only concentrated on the proton exchange membrane fuel cell. Proton Exchange Membrane Fuel Cell (PEMFC) PEMFC s also called the Polymer electrolyte membrane fuel cell as the electrolyte used s a sold organc polymer. The materal used conssts of a fluorocarbon polymer backbone, the same as Teflon. Solfonc acd groups are attached to t. The acd molecules are fxed to the polymer but the protons on the acd groups are free to mgrate through the membrane. The electrolyte s sandwched between two graphte papers wth the catalyst spread n the nterfaces. These two graphte papers are used as the anode and the cathode. Graphte papers, catalyst layers and the electrolyte together form the Membrane Electrode Assembly (MEA). On both the sdes of MEA, graphte plates wth grooves, whch form

12 the flow channels for hydrogen and oxygen, are attached. Fgure: 1.2 shows the typcal flow dagram of PEMFC. 12 Hydrogen passes through flow channels, dffuses through anode and reaches the catalyst layer. The catalyst splts hydrogen molecules nto hydrogen ons and electrons. Whle hydrogen ons mgrate from anode to cathode through electrolyte, electrons take the outer route. In the same way, oxygen flows through the oxygen flow channels, dffuses through the cathode and reaches the catalyst. Hydrogen ons from the electrolyte and electrons from outer crcuts combne at cathode sde and react wth oxygen molecules for form water and generate heat. Fgure: 1.2 Schematc Representaton of PEMFC Chemcal reactons on the anode and the cathode are shown below: Anode: 2H H e

13 13 Cathode: + 4 H + O + e H O + heat 2 2 Overall reacton: 2 H O H O + heat PEMFC operates at around 180 F whch s relatvely low. 50% of ts maxmum power s obtaned at room temperature. Due to a low operatng temperature, the start up tme s less, whch makes t sutable for automoble and other applcatons. PEMFC offers hghest power densty per unt area than any other type of fuel cell. As the sold electrolyte s used whch does not suffer loss, the lfe of PEMFC s not dependent on the electrolyte. As the sold membrane s used as electrolyte, sgnfcant pressure dfferental can be mantaned across the electrolyte to optmze the cell performance. Platnum, whch s used as a catalyst, s very senstve to CO posonng, so cheap technology s requred to clean the gases. Another barrer to commercalzaton s the hydrogen storage tank. As PEMFC uses hydrogen as a fuel t has to be stored as a compressed gas n a pressurzed tank whch s dangerous. As t offers low energy densty, t requres a large tank to use for a prolonged perod of tme wthout refll. Hgher densty fuel can be used onboard but t requres the reformer whch can produce pure hydrogen. Also, nfrastructure for hydrogen supply has to be developed. Current densty of 850 A/ft 2 s acheved at 0.7V/cell wth hydrogen and oxygen at 65 ps and over 500 A/ft 2 wth ar at same pressure. Phosphorc Acd Fuel Cell (PAFC) The Phosphorc Acd Fuel Cell s the most mature fuel cell technology. The PAFC was selected for substantal development a number of years ago because of the belef that,

14 among low temperature fuel cells, t was the only technology that showed relatve tolerance for reformed hydrocarbon fuels. 14 The PAFC uses lqud phosphorc acd, contaned n a Teflon bonded slcone carbde matrx, as the electrolyte. The porous matrx keeps the acd n place by capllary acton. Due to the loss of acd durng the operaton, addtonal phosphorc acd s requred after many hours of operaton. Porous carbon, coated wth platnum as a catalyst, s used as an electrode on anode and cathode sdes. The electrcal effcency of PAFC s about 40%. It has a power densty of 160 to 175 watts/ft 2 of actve cell area. The operatng temperature range s 300 to 400 F. PAFC s effcency s very hgh. Besdes that t can use mpure hydrogen as a fuel. Fuels wth CO concentraton of about 1.5% can be used n PAFC. It s not wdely used because of low current and power compared wth other fuel cells, ts large sze and heaver weght. At low temperature the byproduct water dssolves n the phosphorc acd and dlutes the phosphorc acd.. Dlute phosphorc acd has poor onc conductvty. Besdes ths problem, at lower temperatures carbon monoxde posonng of the platnum becomes severe. It can not be operated above 400 F because phosphorc acd begns to decompose at approxmately 410 F. Molten Carbonate Fuel Cell Molten carbonate fuel cell uses carbonate salt lke lthum, sodum or potassum carbonates as a electrolyte. Ths electrolyte s soaked n a matrx whch s sandwched between anode and cathode. At the anode, hydrogen reacts wth carbonate ons and produces carbon monoxde and electron. At the cathode, oxygen from ar and carbon doxde from fuel channel outlet react wth electrons and produce carbonate ons. Chemcal reactons at anode and cathode are as follows:

15 15 Anode reacton: 2 2H 2 + 2CO3 2H 2O + 2CO2 + 4e Cathode reacton: O 2 + CO2 + 4e 2 2 CO Overall reacton: 2 3 2H + CO 2 + O2 + 2CO2 2H 2O 2 2 Mature MCFC exhbts up to 60% effcency whch can be rased to 80-85% f waste heat s utlzed for cogeneraton. As salt carbonate requres a very hgh temperature to become onc conductve, the operatng temperature of the MCFC s about 1200 F. Hgh temperature offers many advantages ncludng hgh effcency. It s possble to extract hydrogen from many fuels at ths temperature, the fuel cell tself woks as an nternal reformer. Snce hgh temperature ncreases reacton rate, an nexpensve catalyst nstead of platnum can be used. Hgh temperature nduces thermal stresses n fuel cell components whch reduces the lfe of components and ncreases corroson. Sold Oxde Fuel Cell Sold Oxde Fuel Cell (SOFC) uses sold ceramc nstead of lqud as an electrolyte. The preferred ceramc materal s sold zrconum oxde and small amount of ytrra. Tubular desgn s wdely used n whch a tube s at the center, wrapped by cathode. Cathode s fully covered by sold electrolyte and anode. For a fuel cell stack multple cells are connected by a hgh temperature conductor. SOFC exhbts 60% effcency and can be rased to 85% wth cogeneraton. The operatng temperature of SOFCs s around 1800 F. At ths temperature sold electrolyte materal offers suffcent conductvty for negatve ons. A wde varety of fuels wth hgh percentages of sulfur can be used due to hgh temperature whch also offers nternal reformng. Unlke MCFC, at ths temperature carbon monoxde does not act as a poson and can be used drectly as a fuel. Start up tme s much hgher for SOFC due to the hgh

16 operatng temperature. The cell performance s very senstve to operatng temperature. Even smallest drop n the temperature results n sgnfcant drop n performance. 16 Alkalne Fuel Cell Alkalne Fuel Cell (AFC) was one of the frst fuel cell technology developed and t was the frst type wdely used n US space program. An aqueous soluton of alkalne potassum hydroxde, soaked n a matrx, was used as an electrolyte. As the onc conductvty of alkalne soluton s very hgh, OH - moves from cathode to anode through the electrolyte. These fuel cells can use comparatvely cheap metals as catalyst. As cathode reacton rate s very hgh for alkalne electrolyte, AFCs are consdered as hgh performance fuel cells. They are very effcent and exhbts effcency of 65-70% n space applcatons. The operatng temperature range of ths type of fuel cell s F. CO 2 s very posonous to AFC. It can not tolerate even a small percentage of CO 2. So AFCs requre extremely pure hydrogen and oxygen. The purfcaton technque s very expensve whch ncreases fuel cell cost. Drect Methanol Fuel Cell Drect Methanol Fuel Cell (DMFC) technology s relatvely new compared to other types of fuel cells. Lke PEMFC, t also uses polymer membrane as the electrolyte. Other types of fuel cells requre pure hydrogen as fuel or reformer to produce hydrogen from hydrocarbon fuels, but DMFC catalyst layer extracts hydrogen from methanol. So, drect methanol can be used as fuel. The operatng temperature range of DMFC s F. Effcency of DMFC s about 40%. At hgher temperatures hgher effcency can be obtaned. Snce methanol has hgher power densty than hydrogen, t solves the fuel tank problem. Even exstng nfrastructure can be used to supply methanol as t s a lqud lke gasolne. However, the major problem s unused fuel crossng from anode to cathode.

17 17 Regeneratve (Reversble) fuel cell Ths type of fuel cell was recently added to the fuel cell famly. In ths type of fuel cell water s splt nto hydrogen and oxygen by solar powered electrolyss process. Hydrogen and oxygen are fed to fuel cell. After the reacton water, heat and electrcty are generated. Generated water s agan suppled back to the solar electrolyser. Thus the power generaton process forms a closed loop. Ths technque s under development. 1.4 Dffcultes wth Commercalzaton of Fuel Cells: Even though the fuel cell s a polluton-free effcent devce and avalable n a wde varety for varous applcatons, t suffers some external and nternal obstacles n commercalzaton. Most of the fuel cells use hydrogen as a fuel. Gaseous hydrogen has low power densty whch requres a large storage tank. Lqud hydrogen reduces the storage tank sze but technology s very expensve to produce the lqud hydrogen. As hydrogen s explosve, ts storage s rsky. As fuel cell s the emergng technology, ts nfrastructure s not fully developed. Hydrogen dstrbuton systems are not developed fully as other fossl fuels. Cost of the fuel cell s another bg hurdle. As fuel cells use platnum, whch s very expensve, as a metal catalyst, cost ncreases whch results n hgher captal cost per klowatt. Water and thermal management and mass transport lmtatons are other mportant nternal ssues to deal wth for commercalzaton of fuel call as they affect prmarly the fuel cell performance. The membrane should be fully hydrated to mantan good conductvty. Water s generated due to chemcal reacton at cathode. Water s transported due to three dfferent phenomena; electro-osmotc drag, due to mgraton of proton through membrane from anode to cathode sde, back dffuson from cathode; and dffuson of water from fuel gas stream. Imbalance between water generaton and water

18 18 removal causes ether dehydraton of membrane or floodng of electrode. Both have adverse effect on the fuel cell performance. Dehydraton of membrane affects photonc conductvty of the membrane and over-floodng of electrode affects the mass transport of hydrogen or oxygen to the reacton ste. To mantan proper humdfcaton of membrane there must be balance between water generaton and water removal. Durng electrochemcal reactons at electrode lots of heat s released whch ncreases the operatng temperature of the fuel cell. Hgh temperature affects the hydraton of the membrane and also causes thermal stresses n the membrane. An effectve coolng system should be desgned to mantan the proper operatng temperature. To work on these dffcultes, a detaled understandng of fuel cell processes lke mass dffuson, speces transport, water and thermal dstrbuton, chemcal reacton etc. s requred. Due to the hghly reactve envronment of the fuel cell t s not possble to perform detaled n stu measurements durng the operaton. Ths type of nformaton s obtaned cost effectvely by modelng and smulaton of the processes. The branch dealng wth modelng and smulaton of flow s called Computatonal Flud Dynamcs (CFD). 1.5 Overvew of CFD: Computatonal Flud Dynamcs (CFD) s a part of computatonal mechancs that s a part of smulaton. Smulaton s used to forecast or reconstruct the behavor of product or physcal stuaton under assumed or measured boundary condtons. CFD allows studyng the flud flow, whch ncludes flud flow behavoral, heat and mass transfer, phase change, chemcal reacton, effect of mechancal movement. CFD s a very complcated feld whch s nter-related to many other dscplnes such as engneerng, physcs, mathematcs, computer scence, vsualzaton technques. Ths s depcted n the Fgure: 1.3.

19 19 Fgure: 1.3 The Multdscplnary Nature of CFD Followng are the reasons for the fast growng mportance of the CFD: Need to forecast performance of the product Expensve cost of experments Impossblty of some the experments Get detaled nsght of the process Avalablty of hgh speed and memory of the computer 1.6 Lterature Revew: Earler, Bernard and Verbrugge[1] and Sprnger et al.[2] developed one dmensonal, sothermal models of MEA. Rho et al.[3] studed the mass transport phenomena n PEM fuel cell usng dfferent mxtures of oxygen and nert gases. Cappadona et al.[4] studed the conductance of Nafon 117 membranes as a functon of temperature and the water content.

20 20 R.G. Reddy [5] worked on optmzaton of flow channel dmensons and shapes. Dmensons rangng from 0.5 to 4 mm for dfferent channel wdth, land wdth and channel depth were smulated and best combnaton for optmum performance was found. They also studed the effect of channel shape. They conclude that hemsphercal cross secton was more effectve compared to rectangular or trangular cross secton. R. G. Reddy [6] extended hs prevous work of a fuel cell model wth metal foam n flow feld of bpolar/ end plates nstead of conventonally used rectangular flow channels. In hs work, he proved that permeablty affects sgnfcantly the fuel cell performance. Research ndcated that decreasng permeablty of the flow feld results n better performance of the fuel cell. Due to the manufacturng lmtatons permeablty of the rectangular channel desgn can not be decreased below 10-8 m 2. But wth foam flow feld t s possble and performance of the fuel cell could be ncreased. E. Hontan o et al. [7] performed 3D numercal smulatons of the gas flow n the assembly of bpolar plates on fuel sde and anode. In hs study he made a comparson of groove plates wth parallel channels and porous materal. The new concept, equvalent permeablty has been defned. Equvalent permeablty means the permeablty of the porous medum whch causes the same pressure drop as groove plate. Bernng et al. [8] developed a non-sothermal, three-dmensonal computatonal model of PEM fuel cell. In the work, water management ssues along wth other ssues are dscussed. In the work, t has been proved that non-unform catalyst dstrbuton gves unform current densty that leads to optmum fuel cell performance. Ths model does not nclude the phase change phenomenon. M. Ells et al. [9] presented a mathematcal and computer model of a catalyst layer havng agglomerate structure. They conclude that vod fracton and characterstc agglomerate length of catalyst layer sgnfcantly affect the cell performance. In ther work they have used electron mcroscopy method to determne mportant physcal parameters such as vod fracton, agglomerate sze and catalyst layer thckness.

21 21 C. Wang et al. [10] presented sothermal, two-phase model for water management n fuel cell. They ntroduced threshold current densty to dstngush sngle phase and two-phase zones. If the fuel cell operates above threshold current densty, lqud water appears on cathode sde and two-phase zone forms. They conclude that n the two-phase zone of hydraulc structure water transportaton takes place manly due to capllary acton. Xanguo L et al. [11] proposed a one-dmensonal, non-sothermal PEMFC model. They have dscussed thermal response and water management problem wth fuel cell. They have also dscussed the temperature dstrbuton wthn the fuel cell. They conclude that water phase n the electrodes, sgnfcantly affects the temperature dstrbuton wthn the fuel cell. Xanguo L et al. [12] presented a mathematcal model, whch ncludes all the fundamental processes ncludng the effect of varable degree of water floodng n cathode catalyst layer. They observed that f cell pressure ncreases, water floodng n electrode ncreases sgnfcantly, whch lowers the performance of the cell. And the effect s more at low current densty. Hongton Lu et al. [13] performed a parametrc study of PEMFC performance usng experments and mathematcal model to fnd the effect of varaton of dfferent parameters on fuel cell performance. Ther results are mportant to valdate the future mathematcal or computer PEM fuel cell models X. L et al. [14] presented a smplfed mathematcal engneerng model of PEMFC to predct the performance more accurately. They fnd that f graphte s used as bpolar plates and electrodes, performance deterorates manly due to mass transport lmtaton. If conductng polymer s used nstead, performance mproves but suffers consderably at hgh current denstes due to ther reduced electrcal conductvty.

22 22 K.S. Chen et al. [15] presented a transent mult dmensonal computer model of PEMFC. They study the effect of hydrogen dluton when reformatted gas s fed at the anode nstead of pure hydrogen. They conclude that hydrogen dluton reduces the performance due to lmted transport of hydrogen to the reacton ste. Günther the [16] dscussed the problem n the optmzaton of the nterfaces n the fuel cell. He suggested that the nterfacal area of the three-phase boundary between gas, electrolyte and the electrode should be large and can be obtaned by the pore structure of the actve layer of the gas dffuson electrode. 1.7 Scope and Outlne: The purpose of ths work s to smulate the PEMFC and study the dstrbuton of the varous speces n the dfferent components of PEMFC. Ths work also deals wth the effects of varous parameters such as porosty, cathode pressure and number of tubes n flow channels, on fuel cell performance. Ths thess s dvded nto 7 chapters ncludng ths chapter. The Chapter 2 descrbes the fundamental concepts of flow and the modfed equatons used for the porous medum. Chapter 3 explans the concepts of electrochemcal systems. A mathematcal equaton s derved for current densty. The chapter also dscusses the varous losses n the fuel cell. Chapter 4 elucdates the scheme for doman dscretzaton, boundary condtons and contnuum condtons. Chapter 5 presents the results for dstrbuton of varous speces n dfferent components of the fuel cell.

23 Chapter 6 explans the effect of crtcal parameters such as porosty of the electrode, pressure on cathode sde and number of flow channels on fuel cell performance. 23 Chapter 7 summarzes the results and conclusons. The chapter also lsts the recommendatons for the future work.

24 24 CHAPTER 2 BASIC FLOW CONCEPTS The purpose of ths chapter s to hghlght the basc equatons and terms used by FLUENT to solve flow related problems. Detaled dscusson of all the topcs can be found n references [17] and [21]. The basc equatons are contnuty equaton or conservaton of mass, momentum equaton or conservaton of momentum and energy or conservaton of energy. The flow follows all these equatons. In addton to these equatons, equaton of conservaton of speces s also descrbed n terms of chemcal reacton. 2.1 The Contnuty Equaton: The contnuty equaton states that the mass s conserved for a closed system. The general contnuty accounts for conservaton of any quantty whch may be flowng n the system n terms of densty of the quantty at all the ponts and the rate of flow of the quantty from one pont to the another pont. Mathematcally t can be wrtten as, Dρ +. v = Dt ( ρ ) 0 where ρ s the densty and v s the velocty vector. s the dfferental operator defned n rectangular coordnates as, 2.1 = δ 2.2 x D where δ s the unt vector and x are the varables assocated wth three drectons. s Dt the total or substantal dervatve defned as,

25 D Dt where v s the th component of velocty vector v. 25 = + v 2.3 t x For ncompressble flud densty does not change wth pressure. A flud s usually consdered ncompressble. Although the gases are compressble for speeds < 100m/s, the fractonal change of absolute pressure n the flow s small. In ths type of case densty change n the flow s very small. So for ncompressble flud flow contnuty equaton reduces to, regardless of steady or unsteady flow. v = The Momentum Equaton: The prncple of conservaton of lnear momentum s derved from Newton s Second Law of moton. The prncple of conservaton of momentum states that tme rate of lnear change of lnear momentum of a gven set of partcles s equal to the vector sum of all the external forces actng on the partcles of the set provded Newton s Thrd Law of acton and reacton governs the nternal forces. Mathematcally ths can be wrtten as, Dv ρ = p + σ + ρf 2.4 Dt where σ s the Cauchy stress tensor and f s the body force vector. Ths equaton s also known as Naver Stroke equaton. The prncple of conservaton of angular momentum can be stated as the tme rate of change of the total moment of momentum of a gven set of partcles s equal to the vector sum of the moments of the external forces actng on the system. In the absence of dstrbuted couples, the prncple leads to the symmetry of the stress tensor,

26 26 σ = ( σ ) T where the superscrpt T denotes the transpose of the enclosed quantty. 2.3 The Energy Equaton: The energy equaton, whch s also a law of conservaton of energy, s based on the Frst Law of Thermodynamcs. Ths law states that the tme rate of change of the total energy s equal to the sum of rate of work done by appled forces and the change of heat content per unt tme. For ncompressble flud, the frst Law of Thermodynamcs can be expressed as, DT ρ C = q + Q + Φ 2.5 Dt where T denotes the temperature, q s the heat flux vector, Q s the nternal heat generaton, Φ s the vscous dsspaton functon and C s the specfc heat. Here specfc heat can be Cp at constant pressure process or C v at constant volume process. Other types of nternal heat generaton may arse from other physcal processes such as chemcal reacton or joule heatng. 2.4 Conservaton of Chemcal Speces: If m l denotes the mass fracton of a chemcal speces, the conservaton of m l s expressed as, ( ρ ml ) + ( vml + J l ) = R 2.6 l t

27 where the frst term s the rate of change of mass of chemcal speces per unt volume. The term ρ vml s the convecton flux of the speces, n other words the flux carred by the general flow feld ρ u. The term J l s dffuson flux caused by gradents of m l. The term on the rght hand sde R l s the rate of generaton of chemcal speces durng the chemcal reacton. Ths term can be postve or negatve dependng on the chemcal reacton. For nonreactng speces R l s zero Modfed Equatons for the Porous Medum: Modfed Momentum and Energy Equatons for Porous Medum: The prevously descred general governng equatons are defned for the flud medum.the porous medum s treated smlar to the flud medum. The porous medum offers flow resstance to the flud flowng through the medum. Whle modelng flow through porous medum, the followng lmtatons are encountered. Its very dffcult to model physcally presented volume blockage n the model. The effect of the porous medum on the turbulence feld s only approxmated. As one of the assumptons durng the study s that lamnar flow exsts throughout the flud flow regon, the second lmtaton s neglected. FLUENT overcomes the frst lmtaton by usng volumetrc flow rate based on superfcal velocty nsde the porous medum to satsfy the contnuty of velocty vector across the porous nterface. Ths s done by modfyng the momentum equaton and the energy equaton.

28 28 Momentum Equaton for Porous Medum: Porous medum s modeled by addng a source term to the governng dfferental equatons. The source term has two parts, vscous loss term and nertal loss term. The source term s gven by, µ 1 S = v + C2 ρ v v 2.7 α 2 where µ s the vscosty of the flud, α s the permeablty of the flud, C s the nertal resstance factor. 2 The source term can also be modeled by the power law of velocty magntude. ( C1 1) v S = C v where C and C 1 2 are user defned emprcal coeffcents. Darcy s Law n Porous Medum: If flow through the porous medum s lamnar then the pressure drop across the porous medum s proportonal to the velocty and the constant C can be assumed to be zero. So for porous medum Darcy s law reduces to, 2 where p p µ = v n α s the pressure loss across the porous medum, 2.9 n s the thckness of the porous medum.

29 29 Energy Equaton for Porous Medum: For porous medum, conducton term and transent term are added to the general energy equaton. The conducton term uses effectve conductvty of the sold regon and the transent term ncludes the thermal nerta of the sold regon. The energy equaton for the porous medum s gven by, t h ( E ( ) E ) v( E p) γρ + 1 γ ρ + ρ + = k T h J + τ v + S f f s s f f where E and E are the total flud and sold medum energy respectvely, γ s the f s eff f porosty of the porous medum, k eff s the effectve thermal conductvty of the medum, h τ s the shear stress and S f s the flud enthalpy source term. The effectve thermal conductvty of the medum k eff s calculated as the volume average of the flud conductvty and the sold conductvty. So the effectve thermal conductvty of the porous medum s gven by, k eff f ( γ ) k s = γk where γ s the porosty of the porous medum, k s the flud conductvty and k s the sold conductvty. f s

30 30 Chapter 3 Electrochemcal Model Movement of ons and electrons produces the current. The purpose of ths chapter s to dscuss varous electrochemcal equatons. A mathematcal equaton for current densty s derved for one dmensonal flow of ons. The equaton s vald for dlute solutons only. 3.1 Transport Laws for Infntely Dlute Solutons: Mass transfer n an electrolyte soluton depends on the movement of onc speces, materal balances, current flow, electroneutralty and flud mechancs. The flux densty of each dssolved speces s calculated as follows, N = z u Fc Φ D C c v where N s the flux densty of speces, z s the number of proton charges carred by ons, u s the moblty of the speces, F s the Faraday constant, c s the concentraton of speces, D s the dffuson co-effcent of speces, v s the bulk velocty of the flud, and Φ s the electrostatc potental, whose gradent, Φ, s the electrc feld. The frst term on the rght hand sde explans the speces transport due to mgraton. The second and the thrd terms descrbe the nonelectrolytc system. The second term refers to speces transport due to dffuson of speces. Speces dffuse from hgh concentraton regons to low concentraton regons. The last term descrbes speces transport due to convecton of the flud. Current due to moton of the charged partcles n the electrolyte soluton s expressed as follows,

31 31 where s the current densty. = F z N 3.2 Materal balance for the mnor component s expressed as follows, where c t c t = N + R s the accumulaton, N s the net nput and R s the producton per unt volume n homogeneous chemcal reactons. 3.3 For steady state process surface, R c t s zero. Because most of the reacton takes place on the s zero. So above equaton reduces to, N = 0 Electroneutralty s expressed as follows, zc = Ths type of electroneutralty s observed n a thn double charge layer near the electrode and other boundares. 3.2 Dervaton of Current Densty: c For steady state reacton, = 0 and as the reacton s takng place at the surface, t R = 0 So, Equaton 3.3 reduces to, n other words, N = 0

32 N x x N y + y N + z z 32 = 0 Consderng the flow of speces n one drecton, the gradent of flux n Y and Z drectons can be neglected. N x x dn = dx Flux densty of the dssolved speces n one dmenson s gven by, x = dφ dc N = zu Fc D + dx dx c v 3.6 Substtutng (3.6) n (3.5), d dx zu Fc dφ D dx dc dx + cv = 0 z u F d dx c dφ D dx d 2 2 dx c dc + v dx = 0 dc v dx = z u F d dx c dφ + D dx d 2 2 dx c Wrtng ths equaton for postve and negatve ons, dc v dx d = z u+ F c dx dφ dx + + D + d 2 2 dx c 3.7 dc v dx d = z u F c dx dφ dx + D d 2 2 dx c 3.8 Subtractng (3.8) from (3.7),

33 = dx c d D dx d c dx d F u z dx c d D dx d c dx d F u z φ φ Rearrangng the terms, ( ) ( ) = dx c d D D dx d c dx d F u z u z φ ( ) ( ) 2 2 dx c d u z u z F D D dx d c dx d = φ Integratng on both the sdes, ( ) ( ) dx dc u z u z F D D dx d c = φ So, ( ) ( ) dx dc u z u z F c D D dx d = φ 3.9 Substtutng (3.9) n (3.6), ( ) ( ) v c dx dc D dx dc u z u z D D u z N + = Accordng to the Nernst-Ensten equaton, RTu D =

34 34 where R s the unversal gas constant. So, Substtutng (8) nto (7), D u = 3.11 RT N z D ( D+ D ) ( z D z D ) dc dc D dx dx = c v Because current n an electrolyte soluton s due to the moton of the charged partcles, current densty s gven by, = F z N 3.12 Cell performance s always determned by the dependence of cell voltage on the cell current densty for varous operatng and desgned condtons. The plot of dependence of cell voltage on current densty of the cell s called Polarzaton Curve. 3.3 Voltage Equaton and Varous Losses n Fuel Cell: The cell voltage s determned by calculatng the reversble cell voltage E r and subtractng the losses. So cell voltage s gven by, E E r η act ηohmc, m ηohmc, e = 3.13 where E = cell voltage E r = reversble voltage

35 35 η act = loss, due to resstance to the electrochemcal reacton and to mass transfer lmtatons η ohmc,m = loss due to ohmc resstance n the membrane η ohmc,e = loss due to ohmc resstance n the electrode Reversble Voltage The reversble voltage s the maxmum voltage a cell can generate at thermodynamc equlbrum. It s calculated from a modfed form of the Nernst equaton. For standard values of change n Gbbs free energy G and change n entropy S, reversble voltage s gven by, E r = ( T ) T ln( ph ) + ln( p ) 2 O where T s the operatng temperature and p H 2 s the partal pressure of hydrogen and p O2 s the partal pressure of oxygen. Actvaton Potental Loss The actvaton potental loss s assocated wth electrochemcal reacton and mass transfer lmtaton to the reacton ste. Ths loss can be calculated usng the Butler-Volmer equaton as follows, α aη act F α cη act F = 0 exp exp 3.15 RT RT where s the current densty of the cell, 0 s the apparent current densty, α a s anodc transfer coeffcents, α c s the cathodc transfer coeffcents, η act s the actvaton

36 potental loss, F s the faraday s constant, R s the unversal gas constant, and T s the cell temperature. 36 The apparent current densty s the measure of the actvaton energy barrer requred for the electrochemcal reacton to take place. Membrane Loss The voltage loss n the membrane s due to resstance of membrane materal to the proton transfer. It s calculated from the one dmensonal expresson of Bernard and Verbrugge. F I + δ p E H η, = δ + ohmc m m 1 κ κµδ m µκ FK p K C where η ohmc, m s the voltage drop across the membrane, δ m s the membrane thckness, Iδ s the cell current densty, κ s the effectve conductvty of the membrane, K s the hydraulc permeablty of the membrane, K s the electrc permeablty of the 2 membrane, p s the pressure dfferental across the membrane, C s the concentraton of protons, and µ s the vscosty of the water. E H + p The effectve conductvty for the above equaton s gven by, where + D H 2 F C + D + H H κ = 3.17 RT s the protonc dffuson coeffcent n the membrane, R s the unversal gas constant.

37 37 Electrode Ohmc Loss The electrode acts as the passage for electrc current flow and supply reactant to the reactant stes. Loss assocated wth t s calculated accordng to Ohm s law. Electrcal resstance of the electrode s represented n electrcal crcut n Fgure: 3.1. From the Fgure: 3.1, electrons travel the average path length of ( w c + w s ) 4. So, usng Ohm s law the average resstance n the electrode per half flow channel s, ( w + w ) ρ eff c s R = δ L e where ρeff s the effectve resstvty of the electrode, δ e s the thckness of the electrode and L s the length of the electrode. Flow channel dmensons are shown n the Fgure: 3.2. Now f n g s the total number of flow channels on the plate, there wll be 2n g resstor n parallel. So equvalent resstance s gven by, R R ρeff e = = 2n 8n δ L + g g e ( wc ws ) 3.19 and the effectve resstvty for porous electrode s gven by, ρ eff ρ bulk = ( 1 φe ) 2 where ρ bulk s the bulk resstvty of the electrode materal and φ e s the vod fracton of the electrode.

38 38 Fgure: 3.1 Schematc Representaton of Electrcal Resstance of the Electrode [9] Fgure: 3.2 Schematc Representaton of the Flow Channel [9]

39 39 As both the electrodes are treated dentcal, ohmc lass for electrode s gven by, where I s the current densty. η R e I 3.21 ohmc, e = 2

40 40 CHAPTER 4 DOMAIN DISCRITIZATION AND BOUNDARY CONDITIONS The purpose of ths chapter s to explan the dscretsed the computatonal doman and the boundary condtons to solve the problem. A fuel cell conssts of flow channels for hydrogen and oxygen on ether sde of the membrane. Porous electrodes are next to flow channels on ether sde. A catalyst layer s sandwched between membrane and electrode. All the components are depcted n the Fgure: 4.1. Fgure: 4.1 Exploded Vew of PEMFC 4.1 Computatonal Doman: The whole computatonal doman s dvded nto flow channels, electrodes, catalyst layers and the membrane. All the components are meshed and assembled n two dfferent ways.

41 41 Method I In ths method only GAMBIT s used to mesh all the components. Each component s modeled n GAMBIT one by one and then they are moved so that they touch n logcal order. Now as two components have separate faces, when they are assembled the nterface wll have two faces. FLUENT requres one common face between adjonng components. Ths dffculty can be overcome by mergng two components, creatng a separate plane of requred sze and dvdng merged components usng that plane. Once all the components are assembled they are meshed usng structured mesh. Method II The second method s complcated but s more convenent. In ths method all the components are modeled n 3-D modelng software Pro-Engneer whch s relatvely easy. They are exported n IGES format and to GAMBIT separately. They are meshed separately usng structured mesh and then mesh fles are called n 2D or 3D Tmerge applcaton provded by FLUENT n logcal order to assemble the components. Ths assembled fle s agan read n GAMBIT to apply boundary condtons. Generated meshed fles are shown n Fgure: 4.2, Fgure: 4.3, Fgure: 4.4 and Fgure: 4.5. Due to very fne mesh, t s not vsble properly. So t s magnfed n the nset. 4.2 Boundary Condtons: The model s subjected to followng boundary condtons: Velocty Inlet Velocty nlet boundary condton s used to defne the flow velocty along wth other scalar propertes at nlet of the contnuum doman. Sometmes velocty boundary

42 42 Fgure: 4.2 Fully Meshed Flow Channel Fgure: 4.3 Full Meshed Electrode

43 43 Fgure: 4.4 Fully Meshed Catalyst Layer Fgure: 4.5 Fully Meshed Membrane

44 condton s used to defne the flow velocty at exst of contnuum doman. In ths case extremely care should be taken to satsfy the contnuty equaton n the doman. 44 Velocty nlet boundary condton s used to compute the mass flow nto the doman through nlet and to compute the fluxes of momentum, energy and speces through nlet Mass flow rate enterng the cell next to the nlet velocty boundary s calculated as follows, where m m = ρ v da 4.1 s the mass flow rate, ρ s the densty of the flud, whch can be constant or depends on temperature, pressure or speces mass fracton. Ths boundary condton s manly ntended for ncompressble fluds. Wth compressble flud sometmes t gves unrealstc results due to hghly non-unform stagnaton property dstrbuton. Outflow Outflow boundary condton s appled to the contnuum doman ext where pressure and velocty values are not known pror to the soluton whch s very common stuaton. Certan assumptons are made to solve the equatons wth ths boundary condton. Large peclet number, whch s the rato of strength of convecton and dffuson, s assumed near the boundary and flow exhbts one way behavor means downstream flow s not a nfluenced by upstream flow. The above two assumptons allow to extrapolate the pressure, velocty, and other quanttes from or wthn the doman. Flow should be fully developed to extrapolate the quanttes from or wthn the doman. Fully developed flow s defned as the flow n whch flow profles of velocty,

45 temperature etc. do not change n the flow drecton. Sometmes undeveloped flow gves unrealstc results or non-convergence of the soluton. 45 Fully developed flow s obtaned by proper selecton of locaton for outflow boundary condton as depcted n the fgure: 4.6. Wall Condton Wall boundary condton s used to bnd both flud and sold contnuum regons. No slp condton exsts at wall boundary condton. Slp condton s appled by specfyng shear at wall. For no slp boundary condton, shear stress at wall s predcted by the shear Fgure: 4.6 Good and Bad Choces of Locaton of Outflow Boundary Condton [18] stress n the regon near the wall. In lamnar flow shear stress depends on gradent of the velocty at the wall.

46 where v n 46 v τ w = µ 4.2 n s the normal velocty gradent and µ s the vscosty of the flud. For the nvscd flow, slp condton exst at the wall. They are consdered frctonless and there s no shear stress exerted on the adjacent flud. 4.3 Contnuum Condtons: There are manly two type of contnuum exsts, flud and sold. Group of cells through whch flud flows, s called flud zone. All the equatons are solved for ths contnuum. Wth ths defnton of flud contnuum, the porous contnuum s also consdered as a specal flud zone. Even though they are consdered as flud, they are treated dfferently. Dfferent sets of equatons are solved for the porous contnuum as descrbed n secton 2.5. On the other hand mpermeable contnuum through whch flow does not pass s called sold contnuum. Governng equatons are not solved for sold contnuum, only heat transfer equaton s solved. Flud contnuum can be treated as sold contnuum by specfyng zero convecton. Sold contnuum can be consdered as source of heat generaton. In ths problem flow channels are flud, catalyst layers are sold and electrodes and the membrane are porous contnuum. Fgure: 4.7 shows varous boundary condtons and contnuum condtons. Boundary condtons are ponted wth yellow lnes and contnuum condtons are ponted wth red lnes.

47 47 Fgure: 4.7 Boundary Condtons and Contnuum Condtons 4.4 Model Assumptons: 1. Steady state and statonary condtons exst n the sngle cell stack. 2. Effect of Gravty s neglected. 3. Heat conducton across the membrane s neglected. 4. Isothermal condtons exst n the cell doman. 5. Flow s assumed to be Lamnar and verfed durng post processng. 6. Flow through Membrane Electrode Assembly (MEA) s consdered one dmensonal 7. Permeablty of the porous materal s assumed to be sotropc.

48 48 8. Change of phase of the byproduct water s neglected. 9. Fuel gas and oxygen are assumed to be compressble deal gas. 10. Membrane s assumed to be fully humdfed. So electronc conductvty s assumed constant. 11. Membrane s assumed to be mpermeable for gas phase but permeable for lqud phase.

49 49 CHAPTER 5 STUDY OF PROTON EXCHANGE MEMBRANE FUEL CELL A Fuel cell s a complex electrochemcal devce n whch many processes such as mass dffuson, chemcal reacton, mass balance, flow through porous medum etc, take place. The fuel cell smulaton results are presented for detaled understandng of varous processes. In the present study the results are focused on dstrbuton of varous speces n the dfferent components of the fuel cell. As most of the other quanttes, such as molar concentraton of speces, current densty dstrbuton etc, have been affected drectly by mass fracton, mass fracton dstrbuton of varous speces are presented. 5.1 Flow Feld Soluton: One of the assumptons of lamnar flow wthn the flow doman s valdated by calculaton of Reynolds numbers n the flow doman. Fgure: 5.1 shows the contours of Reynolds number. As the Reynolds number s very low, the assumpton of lamnar flow s vald. The dstrbuton of mass fracton of hydrogen gas n the hydrogen flow channel s presented n the Fgure: 5.2. Ths fgure shows that the hghest mass fracton of hydrogen gas s at the nlet. As t flows through the hydrogen flow channel, more and more hydrogen s absorbed n the porous anode, whch reduces the mass fracton of the hydrogen n the hydrogen flow channel whle flowng towards the outlet. Fgure: 5.3 and Fgure: 5.4 show the dstrbuton of the hydrogen at the entry and ext of the porous anode. The mass fracton dstrbuton of hydrogen near the entry of the anode s dfferent than mass fracton dstrbuton near the ext, due to mass dffuson n the porous electrode.

50 50 Fgure: 5.1 Contours of Reynolds Number n the Cathode Flow Channel Fgure: 5.2 Dstrbuton of Mass Fracton of Hydrogen n Anode Flow Channel

51 51 Fgure: 5.3 Dstrbuton of Mass Fracton of Hydrogen near the Entry of Anode Fgure: 5.4 Dstrbuton of Mass Fracton of Hydrogen near the Ext of Anode

52 52 Fgure: 5.5 shows the dstrbuton of H + ons at the anode catalyst layer. Blue squares represent sold catalyst partcles. As the reacton n whch hydrogen s splt nto H + ons takes place at the anode catalyst layer, more H + ons are near the catalyst surface. Ths can be seen n the Fgure: 5.6, whch s the magnfcaton of Fgure: 5.5. Fgure 5.7: shows the hydrogen dstrbuton at the same cross secton. As all the hydrogen s splt nto H + ons, mass fracton of hydrogen s nearly zero at the anode catalyst layer. Fgure 5.8: shows the dstrbuton of H + ons n the membrane. Ths dstrbuton matches wth the dstrbuton n catalyst layer. Fgure: 5.5 Dstrbuton of Mass Fracton of H + Ions n the Catalyst Layer

53 53 Fgure 5.6: Magnfed Vew of Dstrbuton of Mass Fracton of H + Ions n the Anode Catalyst Layer Fgure 5.7: Dstrbuton of Mass Fracton of Hydrogen n Anode Catalyst Layer

54 54 Fgure 5.8: Dstrbuton of Mass Fracton of H + Ions n the Membrane H + ons from the anode and oxygen gas from the cathode combne at the cathode catalyst layer and produce water. Fgure: 5.9 shows the dstrbuton of mass fracton of water. A large mass fracton of water can be seen near the catalyst partcle n Fgure: Fgure: 5.11 and Fgure: 5.12 show the dstrbuton mass fracton of oxygen near entry the entry and ext of the cathode. By comparng the Fgure: 5.11 and Fgure: 5.12, the mass dffuson effect n the porous cathode can be verfed. Dstrbuton of mass fracton near the entry of the cathode s nearly same as that of the cathode flow channel dstrbuton.

55 55 Fgure 5.9: Dstrbuton of Mass Fracton of Water n Cathode Catalyst Layer Fgure 5.10: Magnfed Vew of Dstrbuton of Mass Fracton of Water n the Cathode Catalyst Layer

56 56 Fgure 5.11: Dstrbuton of Mass Fracton of Oxygen near the Entry of Cathode Fgure 5.12: Dstrbuton of Mass Fracton of Oxygen near the Ext of Cathode

57 57 Fgure 5.13: shows the dstrbuton of mass fracton of oxygen n the cathode flow channel. Mass fracton s at maxmum at the nlet. As flow proceeds towards the ext of the flow channel, oxygen s absorbed nto the porous cathode. Because of the absorpton, mass fracton of oxygen reduces. Here the reducton n mass fracton s less compared to the reducton n the hydrogen channel. The prmary reason for ths s the water content n the cathode due to chemcal reacton. The hgh water content obstructs the flow of oxygen whch reduces the oxygen absorpton n the cathode. Fgure 5.14: shows the dstrbuton of mass fracton of water n the cathode. As expected, there s a hgher water accumulaton of water movng towards ext of the flow channel. Fgure 5.13: Dstrbuton of Mass Fracton of Oxygen n Cathode Flow Channel

58 58 Fgure 5.14: Dstrbuton of Mass Fracton of Water n Cathode Flow Channel The concentraton of oxygen on the cathode sde s consdered as an mportant parameter for fuel cell performance. As stated earler n ths chapter, concentraton of the speces can be calculated usng mass fracton of the speces by the followng formula, M m 1 c = 5.1 V M w where c s the concentraton of the speces, M s the total mass of all the speces, m s the mass fracton of the speces, V s the volume of the cell and M w s the molecular weght of the speces. Fgure: 5.15 shows the concentraton contours of oxygen n the cathode. By comparng, Fgure: 5.12 and Fgure: 5.15, smlarty n dstrbuton can be found.

59 59 Fgure: 5.15 Contours of Concentraton of Oxygen n the Cathode 5.2 Derved Quantty: One of the mportant parameters n the smulaton and analyss s the current densty dstrbuton n the membrane, as t s the fnal output to measure fuel cell performance. User Defned Functon (UDF) s used to solve the electrochemcal equatons. Fgure: 5.16 shows the contours of current densty wth full range. As most of the porton of the membrane has hgher current densty, unform color can be seen. Varaton n the current densty dstrbuton can be seen by magnfyng the scale of Fgure: 5.16, n Fgure: The current densty s more on one sde of the membrane, due to hgher concentraton of H + ons. The current densty reduces whle movng towards the other end.

60 60 Fgure: 5.16 Contours of the Current Densty n A/m 2 Fgure: 5.17 Contours of the Current Densty wth Magnfed Scale