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Water Balance Considerations in Modeling of PEM Fuel Cell Systems


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WATER BALANCE CONSIDERATIONS IN MODELING OF PEM FUEL CELL SYSTEMS By ROHIT M. SHARMA A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2005

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Copyright 2005 by Rohit M. Sharma

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This document is dedicated to my parents who have supported me in all my endeavors

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ACKNOWLEDGMENTS First of all, I would like to thank Dr. William. E. Lear, the chairman of my graduate committee, for providing me with an opportunity to work under his guidance as a part of the fuel cell lab. Dr. Lear shared with me his extensive knowledge and always motivated me to perform better. I would also like to thank Dr. James Fletcher, the co-chair of my committee, for his efforts. It was fun working under his guidance as he shared a lot of his experiences. I would also like to acknowledge Dr. Herbert Ingley for being a part of my committee and for the time and support that he provided. In addition, I would like to thank the members of the fuel cell lab and my friends and colleagues for their support. Above all I would like to express my gratitude to my parents for their unwavering support and blessings. iv

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TABLE OF CONTENTS page ACKNOWLEDGMENTS .................................................................................................iv LIST OF TABLES ............................................................................................................vii LIST OF FIGURES .........................................................................................................viii NOMENCLATURE ..........................................................................................................xi ABSTRACT .....................................................................................................................xiv CHAPTER 1 INTRODUCTION........................................................................................................1 1.1 Fuel Cells Basics.....................................................................................................1 1.2 Type of Fuel Cells..................................................................................................3 1.2.1 Phosphoric Acid Fuel Cells (PAFC)............................................................4 1.2.2 Alkaline Fuel Cells (AFC)............................................................................4 1.2.3 Molten Carbonate Fuel Cells (MCFC).........................................................5 1.2.4 Solid Oxide Fuel Cells (SOFC)....................................................................5 1.2.5 Proton Exchange Membrane Fuel Cells (PEMFC)......................................6 1.3 Water Balance in PEM Fuel Cells..........................................................................8 1.4 General Arrangement of PEM Fuel Cell and Auxiliary Systems...........................9 2 LITERATURE REVIEW...........................................................................................13 2.1 Water Balance in PEM Fuel Cells........................................................................13 2.2 Configuration of Fuel Cell Stack and Its Auxiliaries...........................................16 2.3 Different Models to Predict Properties of Moist Air at Elevated Temperature and Pressure...........................................................................................................19 3 WATER BALANCE MODEL...................................................................................22 3.1 Expression for the Mass Flow Rate of Excess Water...........................................24 3.2 Procedure to Calculate excessM ..............................................................................28 3.3 Model Validation..................................................................................................33 4 RESULTS AND DISCUSSION.................................................................................36 v

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5 EFFECT OF CERTAIN NON-IDEAL COMPONENTS ON WATER BALANCE MODEL INPUTS.......................................................................................................49 5.1 Effect of a Non-Ideal Air Handling System on Model Inputs..............................49 5.1.1 Change in Pressure Ratio Developed by a Non-ideal Air Compressor and Its Effect on Water Balance......................................................................50 5.1.1.1 Performance characteristics of an Allied Signal compressor at part load conditions.................................................................................51 5.1.1.2 Relation for fraction of design current.............................................54 5.1.1.3 Variation of excessM with fraction of design current for part load operation of an Allied Signal compressor...............................................57 5.1.2 Change in Fraction of Excess Air due to Compressor Limitations............61 5.1.3 Change in Fraction of Excess Air due to Air Distribution Limitations......64 5.2 Effect of Non-Ideal Water Separator on Water-Balance Model Inputs...............67 5.2.1 Relation between liquidoutM and ...............................................................67 5.2.2 Design Case................................................................................................69 5.2.3 Variation of excessM for the Design Case.....................................................72 6 CONCLUSIONS........................................................................................................75 7 RECOMMENDATIONS............................................................................................77 LIST OF REFERENCES...................................................................................................78 BIOGRAPHICAL SKETCH.............................................................................................80 vi

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LIST OF TABLES Table page 3-1 Comparison of different values of at sea level.....................................................34 3-2 Comparison of different values of at 2250 meters................................................34 5-1 Values of different parameters at the 10 selected operating points of an Allied Signal compressor....................................................................................................54 vii

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LIST OF FIGURES Figure page 1-1 Cell voltage v/s current density for a general fuel cell. 3 ............................................3 1-2 General arrangement of PEM fuel cell and auxiliaries............................................10 2-1 General arrangement of fuel cell systems used by Haraldsson and Alvfors 7 in their analysis.............................................................................................................17 2-2 General arrangement of fuel cell systems used by Hussain et al. 14 in their analysis.....................................................................................................................18 3-1 Control volume defined for the general arrangement of PEM fuel cell and auxiliary systems......................................................................................................22 3-2 Different flow streams of water crossing the control volume boundary..................23 3-3 Comparison of model predictions with Hyland and Wexler data............................35 4-1 Excess water versus pressure ratio and fraction of excess air: sea level, very low depleted air temperature case...................................................................................43 4-2 Excess water versus pressure ratio and fraction of excess air: sea level, low depleted air temperature case...................................................................................44 4-3 Excess water versus pressure ratio and fraction of excess air: sea level, intermediate depleted air temperature case..............................................................44 4-4 Excess water versus pressure ratio and fraction of excess air: sea level, high depleted air temperature case...................................................................................45 4-5 Excess water versus pressure ratio and fraction of excess air: high altitude, very low depleted air temperature case............................................................................45 4-6 Excess water versus pressure ratio and fraction of excess air: high altitude, low depleted air temperature case...................................................................................46 4-7 Excess water versus pressure ratio and fraction of excess air: high altitude, intermediate depleted air temperature case..............................................................46 viii

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4-8 Excess water versus pressure ratio and fraction of excess air: high altitude, high depleted air temperature case...................................................................................47 4-9 Excess water versus pressure ratio and fraction of excess air: sea level, low depleted air temperature, humid ambient air case....................................................47 4-10 Excess water versus pressure ratio and fraction of excess air: sea level, low depleted air temperature, humid ambient air case....................................................48 4-11 Excess water versus pressure ratio for liquidoutM =0 and liquidoutM =0.1: sea level, high depleted air temperature...................................................................................48 5-1 Compressor map of an Allied Signal compressor....................................................52 5-2 Excess water versus fraction of design current and fraction of excess air: sea level, intermediate depleted air temperature, liquidoutM =0.......................................59 5-3 Excess water versus fraction of design current and fraction of excess air: sea level, high depleted air temperature, liquidoutM =0....................................................59 5-4 Excess water versus fraction of design current and fraction of excess air: high elevation, intermediate depleted air temperature, liquidoutM =0................................60 5-5 Excess water versus fraction of design current and fraction of excess air: high elevation, high depleted air temperature, liquidoutM =0.............................................60 5-6 Change in fraction of excess air due to compressor limitations for lower fractions of design current........................................................................................63 5-7 Excess water versus fraction of design current: compressor limitation: sea level, intermediate depleted air temperature, liquidoutM =0.................................................63 5-8 Change in fraction of excess air due to air distribution limitations for lower fractions of design current........................................................................................65 5-9 Excess water versus fraction of design current: air distribution limitation: sea level, intermediate depleted air temperature, liquidoutM =0.......................................66 5-10 Excess water versus fraction of design current: comparison of air distribution limitation versus compressor limitation: sea level, intermediate depleted air temperature, =0.........................................................................................66 liquidoutM 5-11 Mass flow rate of water entering and leaving the water separator and the control volume......................................................................................................................68 ix

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5-12 Variation of the excess water term with pressure ratio for liquidoutM =0 and the design case: high elevation, high depleted air temperature......................................74 5-13 Variation of the excess water term with pressure ratio for liquidoutM =0 and the design case: high elevation, low depleted air temperature.......................................74 x

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KEY TO SYMBOLS NOMENCLATURE m mass flow rate of water N molar flow rate y fraction of excess air M molecular weight M non-dimensional mass flow rate p pressure R gas constant T temperature a constant in Redlich-Kwong equation b constant in Redlich-Kwong equation g gibbs free energy f fugacity N rotational speed of a compressor F faradays constant number of cells in a fuel cell stack n number of electrons transferred in an electrochemical reaction I fuel cell stack current v velocity xi

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m mass flow rate of air V Volume A Area Greek relative humidity of ambient air specific volume efficiency of water separator ratio of inlet air temperature to reference temperature in a compressor ratio of inlet air pressure to reference pressure in a compressor 1 ratio of dimensional parameters of a compressor mole fraction density Subscripts H 2 O-in water that enters the control volume H 2 O-out water that leaves the control volume H 2 O-gen water generated inside the control volume H 2 O-excess excess water leaving the control volume mem water supplied back to the stack liquid-out liquid water leaving the control volume along with exit air design design point excess excess water leaving the control volume amb ambient r ratio xii

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t exit air properties 1 saturated exit air properties 2 modified saturated exit air properties real real gas properties liq liquid c critical correct corrected properties of gas a actual properties of gas humid properties of humidified air H 2 O -90% properties of vapor present in 90% humidified air dry dry conditions (relative humidity is zero) xiii

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Abstract of Thesis Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science WATER BALANCE CONSIDERATIONS IN MODELING OF PEM FUEL CELL SYSTEMS By Rohit M. Sharma August 2005 Chair: W. E. Lear Co-chair: J. Fletcher Major Department: Mechanical and Aerospace Engineering. In order for the potential of proton exchange membrane (PEM) fuel cells to be realized for automotive applications, several important system-level issues must be solved. One of the requirements placed on automobile engine operation is to operate satisfactorily under a wide range of ambient conditions and power demands. Under some combinations of temperature, altitude, and load, the mass rate at which liquid water is recovered by the fuel cell system is less than the mass rate of water required to humidify the membranes. Unless significant liquid water reserves are carried not an attractive design option then the membranes will become dry, with potential catastrophic results. In this study, an analysis is shown which allows the water discharge rate to be calculated as a function of ambient conditions and operating parameters such as overall stoichiometry, operating pressure and exhaust temperature. The analysis is design-independent, in that specific design choices only affect the inputs to the model such as air fuel stoichiometry and exhaust temperature and pressure parameters. The condition of xiv

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zero net water discharge is emphasized, since that corresponds to the boundary between sufficient water and the catastrophic dry-out process. Results indicate that moderate-to-high altitude operation will most likely require pressurization of the fuel cell stack. The operating parameters of non-ideal components and subsystems change under varying operating conditions, which imposes additional limitations on achieving water balance. The effect of these limitations associated with the air delivery sub-system and water recovery components has been studied by considering certain specific design and equipment choices and analyzing their effect on water balance under varied ambient and operating conditions. The results of this portion of study indicate that the efficiency of the water recovery subsystem, in addition to ambient and operating parameters, affects the water balance of the fuel cell system. The magnitude of this effect is however design dependent and should be taken into account when considering a specific arrangement. The effect of using a non-ideal air handling subsystem such as a centrifugal compressor is that the water discharge rate reduces when the fuel cell operates at part load conditions; however the effect is more profound for lower fractions of design load. xv

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CHAPTER 1 INTRODUCTION With a growing emphasis on the preservation of our environment, air pollution has become a focus of concern. Significant contributors to air pollution are the conventional vehicles that operate on petroleum. In the United States, they are responsible for over 60 percent of the carbon monoxide emissions and about 20 percent of greenhouse gas emissions. A conscious effort has been made over the past few decades to develop an alternate fuel for transport applications. Use of hydrogen to operate a fuel cell promises to be a clean and efficient solution to the problem. Fuel cell based vehicles have the potential of producing lower emission than their petroleum based counterparts. However fuel cell technology is still in its development stages and there are certain design issues that need to addressed in order to ensure reliable and efficient operation under varied operating conditions. 1.1 Fuel Cells Basics Fuel cells produce electricity by utilizing the chemical energy released when hydrogen combines with oxygen to form water. The overall reaction is as follows: H 2 + 12 O 2 H 2 O 1-1 Hydrogen is supplied to the anode where it splits into H + ions and electrons in the presence of a catalyst. The electrons travel via the external circuit towards the cathode. The charge that is transferred across the external circuit, for each mole of diatomic 1

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2 hydrogen oxidized, is the product of the number of electrons transferred in the electrochemical reaction, and the Faraday constant. The H + ions migrate to the cathode via the electrolyte where they combine with the oxidant and the electrons to form water. Based on the Nernst equation, 1 the potential generated by a fuel cell operating on hydrogen is given by the following equation: 2221/2HOHOp.pRTEElnnFp 1-2 where E is the EMF of the cell under standard conditions and its value is 1.229 V when the product of the reaction is liquid water and 1.18 V when the product is gaseous water. 2 The remaining part of equation 1-2 takes into account the change in the cell voltage from its standard value due to changes in temperature of the reaction or change in partial pressures of the reactants or the products. R is the universal gas constant, T is the temperature of the reaction, n is the number of electrons transferred for each mole of fuel utilized, F is the Faraday constant and p H2 p O2 and p H2O are the partial pressures of hydrogen, oxygen and water respectively. Based on this expression and Equation 1-2, one would expect the value of voltage developed by the fuel cell for different values of current to be constant at constant operating pressure and temperature. However, the actual value of cell potential decreases due to certain irreversible losses. These losses originate primarily from three sources: (1) activation polarization (2) ohmic polarization, and (3) concentration polarization. 3 Activation polarization is predominant at low current densities and is related to the rate of the electrochemical reaction. Ohmic polarization losses take place due to the resistance offered by the electrolyte to the flow of ions and the resistance to the flow of electrons

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3 through the electrode material. Its value increases with the increase in current, mainly because the resistance of the cell remains more or less constant over the entire range of current. Concentration polarization is caused due to a concentration gradient that develops near the electrode when the reactant material is consumed and the surroundings are unable to maintain the initial concentration. It mainly results from the slow transport of reactants/products to/from the electrochemical reaction site and has a more pronounced effect at higher values of current. The above-mentioned losses affect the voltage versus current characteristics, defined as polarization curve, of a fuel cell. Figure 1-1 shows a typical polarization curve of a fuel cell. Figure1-1. Cell voltage v/s current density for a general fuel cell. 3 (Source: EG & G Services Parson Inc., Fuel Cell Handbook, 5 th edition, U.S. Department of Energy, National Energy Technology Laboratory, 2000) 1.2 Type of Fuel Cells Different types of fuel cells are available as a potential source of clean and efficient energy. Amongst the more common ones are alkaline fuel cell (AFC), phosphoric acid fuel cells (PAFC), molten carbonate fuel cell (MCFC), solid oxide fuel cells (SOFC) and proton exchange membrane cells (PEMFC). This section discusses in brief the above

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4 mentioned fuel cell types with a greater emphasis on PEM based fuel cells. It also gives the rationale behind the popularity of PEM based fuel cell in automotive applications. 1.2.1 Phosphoric Acid Fuel Cells (PAFC) Phosphoric acid fuel cells, as the name suggests, use phosphoric acid (H 3 PO 4 ) as an electrolyte. These fuel cells operate at a temperature of around 200C. PAFCs, in general, are not very suitable for low to medium power automobiles because of their low power to weight ratio and high operating temperatures which result in longer system startup times. Moreover, the presence of a liquid electrolyte in the fuel cell increases the chances of acid spillage and poses a limitation on the orientation of the cell. However the electrolyte does not need humidification to maintain its conductivity. These cells are generally used in stationary power applications and sometimes in large vehicles such as buses where size and weight are not major limitations. 1.2.2 Alkaline Fuel Cells (AFC) These fuel cells use an alkaline solution as an electrolyte, generally potassium hydroxide (KOH) or sodium hydroxide (NaOH) with a concentration of 85 wt%. The normal operating temperature of these fuel cells is around 250C. The main drawback of AFCs is that hydrogen and oxygen have to be supplied to the cell in pure form. Another option is to supply scrubbed fuel and oxidizer (air) to the anode and cathode respectively. 5 This requirement makes the auxiliaries of the fuel cell more complex and high in weight and volume. A high operating temperature means slower system startup, costlier material of construction and complex manifolds and bends that are added to the system due to the requirement of an active cooling system. Moreover, as in case of PAFC, the liquid form of the electrolyte poses a limitation on the

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5 orientation of the cell. The liquid electrolyte on the positive side does not need humidification for efficient operation. 1.2.3 Molten Carbonate Fuel Cells (MCFC) These cells use a mixture of molten alkali carbonates as an electrolyte. The electrolyte is retained in a ceramic matrix of lithium aluminum oxide (LiAlO 2 ). These fuel cells normally operate at a high temperature of around 600 to 700 C. From a commercial applications point of view, MCFCs have an efficiency approaching 60% which is considerably higher than the efficiency of PAFCs. The conductivity of the membranes of MCFCs is not dependent on the humidity of the membranes. Moreover, these cells can directly use a high density hydrocarbon fuel. However, very high operating temperatures make them unfavorable for use in automotive applications like cars. These cells are more suited for stationary applications. When the waste heat of these cells is utilized by a power plant to generated additional electricity, the overall efficiency of the system reaches close to 85%. 1.2.4 Solid Oxide Fuel Cells (SOFC) Solid oxide fuel cells use a non-porous ceramic compound, generally yttria-stabilized zirconia (YSZ) as an electrolyte. These cells normally operate at a very high temperature of about 1000 C. A high operating temperature gives these fuel cells the capability to internally reform a hydrocarbon fuel to hydrogen. SOFCs like the fuel cell types discussed above do not require water to maintain the conductivity of the membranes. Hence, overall water balance of the fuel cell system does not affect its performance. Moreover, these fuel cells are more resistant to impurities than any other fuel cell. The disadvantages of operating close to 1000 C are high thermal stresses that impose limitations on the construction

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6 material and the design of its auxiliaries, slow system startup, heavier and costly insulation and higher chances of material corrosion. 1.2.5 Proton Exchange Membrane Fuel Cells (PEMFC) These fuel cells use a solid proton conducting membrane, generally made of sulphonated fluro-polymers, as an electrolyte. One such commercially available product is Nafion (DuPont). The electrolyte is sandwiched between two electrodes that are made of platinum impregnated porous carbon. Platinum dispersed in the electrodes acts as a catalyst and aids the electrochemical reaction. The back of the electrodes are generally coated with a hydrophobic compound such as PTFE. The hydrophobic coating on the porous electrodes removes water from the catalyst sites and aids the reactant gases to diffuse onto the catalyst. The normal operating temperature of PEM fuel cells is around 80C. Increasing the fuel cell temperature shifts the polarization curve to higher values of voltage and thus increases the cell performance. However, high operating temperatures dehydrates the electrolyte and reduces its conductivity. Therefore PEM fuel cells are operated at a temperature 20C less than the boiling point of water corresponding to the cell operating pressure. Increasing the fuel cell pressure increases its reversible potential. However, high operating pressures require higher compressor power. The use of a solid electrolyte reduces the ohmic loses in the fuel cell and makes the cell more compact. As a result PEM fuel cells have a high power to weight and power to volume ratio. Moreover a solid electrolyte does not place a limitation on the orientation of the fuel cell as there is no problem of electrolyte spillage. The operating temperature of these fuel cells is much lower than the normal temperature of other fuel cell types. As a result the heat removal system is much lighter and less complex in PEM fuel cell systems

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7 than in other fuel cell types. It also reduces component wear and increases the available range of materials for construction. This again decreases the size and cost of the system. A lower operating temperature in comparison to other fuel cells results in comparatively fast system startup time. Moreover these cells are able to sustain operation at high current densities. All these advantages make PEM fuel cells more favorable for automotive applications than other fuel cells. Despite its advantages, PEM fuel cells have certain drawbacks that impose limitations on the design of the overall system. Platinum, which is used as a catalyst, is sensitive to CO poisoning. Carbon monoxide strongly bonds to platinum at temperatures less than 150C and makes them unavailable as catalysts. Hydrogen reformed from hydrocarbons generally contains greater than one percent carbon monoxide, whereas, a concentration of greater than 10 ppm of CO is able to poison the catalyst. 5 Hence an additional reactor to reduce the amount of CO in the fuel gas is required if hydrogen is produced by an on-board fuel reformer. Another drawback specific to automotive applications is fuel storage. Hydrogen if stored on-board an automobile as pure compressed gas, must be carried along in large volumes in order to achieve a reasonable travel distance. This is because of the low density of hydrogen. Use of high density hydrocarbons, such as methanol, as fuel decreases the storage volume but increases the cost and maintenance requirements of installing an additional reformer. Moreover, adding a reformer increases the overall weight of the fuel cell system. Hence a proper design choice must be made when deciding on the mode of fuel supply.

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8 Last but not the least, and probably the one of the more important drawbacks related to PEM fuel cells, is maintaining water balance. This issue will be discussed in depth in the following section. 1.3 Water Balance in PEM Fuel Cells The conductivity of the proton exchange membrane is directly proportional to the amount of water present in it. Absence of water in the membranes causes what is known as membrane dry out, where the electrolyte stops conducting protons. On the other extreme, too much water in the membranes causes flooding, where the pores in the electrodes are blocked by water. Flooding of the electrode pores prevents the reactant gases from coming in contact with the catalyst and hence inhibits the rate of the electrochemical reaction. The total water present in the fuel cell does not indicate the local condition of the membranes. Even though sufficient water may be present in the fuel cell to humidify the membranes, some parts of the membrane may be flooded while others may be deficient or even dry. There are multiple reasons for this effect, of which the most common one is the inability of the water generated at the cathode to diffuse towards the anode. This makes the portion of the membranes near the cathode wet and the one near the anode dry. Another reason is due to electro-osmotic drag where the H + ions moving from the anode towards the cathode pull water molecules along with them, making the anode dry. In general, a drop in the quantity of water in the fuel cell stack indicates loss of water content of the membranes. This condition should be avoided in all cases to prevent membrane dry-out. Water enters the fuel cell in the form of vapor as a part of the moist air supplied to the cathode and sometimes along with the hydrogen, which may be humidified depending

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9 upon the overall system design. Water is constantly generated, due to the electrochemical reaction, at a rate which depends upon the amount of fuel used. The air leaving the fuel cell entrains liquid water along with it and at times, depending upon the operating temperature and pressure, evaporates water present in the membranes. Water is also lost due to leakage in different components present in the overall system. The net water present in the fuel cell and in the membranes thus depends on ambient conditions and operating parameters such as air fuel stoichiometry and operating temperature and pressure. Careful control of the governing parameters of water present in fuel cell is imperative as excess or dearth of water hampers the stack performance. This study examines the sensitivity of the controlling parameters of water content of the overall fuel cell system. It also takes into account the effect of the non-ideal nature of some of the auxiliaries of the fuel cell system such as the air delivery sub-system and water recovery components on the controlling parameters of water balance. The limitations imposed on the design of fuel cell systems due to uneven distribution of water in the membranes or due to membrane flooding have not been considered in this study. It is assumed that the fuel cell system is capable of getting rid of the additional water that may be present throughout the membranes or in parts of it. 1.4 General Arrangement of PEM Fuel Cell and Auxiliary Systems Figure 1-2 represents the most general arrangement of PEM fuel cell and its auxiliaries from a broad perspective without going into the specifics of each component. As shown, the hydrogen management system supplies hydrogen to the fuel cell stack. It utilizes hydrogen either directly from compressed hydrogen cylinders or from the exit of a reformer that reforms hydrocarbons like methanol. The rate at which hydrogen is consumed by the stack depends on the current drawn from it, which in turn depends on

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10 the load requirement. The main function of the hydrogen management system is to ensure adequate supply of hydrogen to the stack and, depending upon the overall system design, re-circulate the unused hydrogen, if any, back to the stack. The supply of hydrogen is typically controlled using flow metering and regulating devices. The hydrogen management system, depending upon the stack design, also humidifies hydrogen before supplying it to the stack. Water for this purpose is supplied either by an external source or as shown in Figure 1-2 from the Water Management System. Figure 1-2. General arrangement of PEM fuel cell and auxiliaries Figure 1-2 also shows air being supplied to the stack by the Air Handling System. The main function of the Air Handling System is to supply adequate, air for complete oxidation of hydrogen in the stack. The air, before being supplied to the stack, may be humidified, either by an external water source or with the help of the water management system. In addition, the Air Handling System may pressurize the stack. Typical equipment options for achieving this function include blowers, fans, compressors, or ejectors.

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11 The main function of the Water Management System is to recover liquid water from the humid air leaving the stack that is depleted in oxygen, and supply part of it back to the stack to maintain the humidity of the membranes, discharging the excess or storing it. One way of achieving this function is by using a water collection device (e.g. a knockout) that separates liquid water from the depleted air leaving the stack. An alternative component is a humidity exchanger, which uses the depleted air leaving the stack to humidify the air entering the stack via a semi-permeable membrane. The membrane transfers water from its region of higher concentration (usually depleted air leaving the stack) to the region of lower concentration (usually ambient air). In a humidity exchanger, the excess water that could not be transferred to the air entering the stack is either stored or is discharged to the ambient along with the air leaving the stack. The humidified air that enters the stack via the humidity exchanger helps in maintaining the humidity of the membranes. Thus the net result of using a water separator or a humidity exchanger is the same. A portion of the collected water, depending upon the overall design, is supplied to other auxiliaries like the Hydrogen Management System, Air Handling System and the Cooling System to aid their purpose. The air leaving the stack is generally at higher pressure than ambient and is partially depleted of oxygen. Once water is separated from this depleted air, its pressure is reduced to ambient in an expansion device such as a valve or turbine. This device is referred to as an expander in Figure 1-2. Lastly, the Cooling System cools the air leaving the stack and, depending upon the design choice, cools the stack itself, hence controlling the amount of water entering the

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12 water management system in liquid form. This is typically achieved by using either a passive cooling system or a separate refrigeration device.

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CHAPTER 2 LITERATURE REVIEW This chapter reviews literature relevant to the water balance issue in PEM fuel cells. It also reviews some of the literature that, though not directly related to the water balance issue, helped in building a water balance model, which is the focus of this study. 2.1 Water Balance in PEM Fuel Cells As mentioned earlier, the net rate at which water is generated or depleted in the fuel cell can be controlled by changing the various operating parameters like operating temperature and pressure, and air stoichiometry. Research efforts focused on improving the overall performance of the fuel cell system have also tried to determine either the mass of water present in the membranes at any point of time, or rate at which excess water is discharged from the fuel cell system. Yu et al. 6 developed a two phase model to analyze the effect of membrane humidification on the overall performance of the stack. Air (moist or dry) and hydrogen were assumed to follow ideal gas law at all times. The flow of water through the membranes was considered as the sum of the electro-osmotic drag flux that is caused by hydrogen ion drag, diffusion flux that is caused by water concentration gradient between anode and cathode and convection flux that is caused by pressure gradient. The inputs to the model included general parameters like operating temperature and pressure and air fuel stoichiometry, and some membrane specific parameters like membrane charge concentration and membrane permeability of water. The water content in the membranes was calculated for different cases of inlet humidification and was provided as an input to 13

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14 the overall model to calculate the effect on the polarization curve and stack temperature of a Ballard Mark V stack both at steady state as well as at transient conditions. The model developed to calculate the water content in the membranes, however, did not consider those operating and ambient conditions that lead to progressive loss of water from the membranes. Moreover the results of the model were specific to a particular model of fuel cell stack. Haraldsson and Alvfors 7 used the ADVISOR software developed by National Renewable Energy Laboratory to develop an overall model for the fuel cell system. The model considered a specific arrangement of the stack and its auxiliaries that was assumed to run a mid-size automobile. The overall system included a condenser that supplied water to a storage device by condensing water from the air leaving the stack. The ADVISOR software was able to calculate the amount of water condensed at various ambient and operating conditions by using models developed for each system. The stack was assumed to be pressurized using a twin screw compressor. The study analyzed the effect of varying load conditions on water balance by calculating the change in the water quantity of the storage device when the fuel cell based automobile was assumed to run through the standard New European Drive Cycle (NEDC) at different altitudes and ambient temperatures. The ambient conditions were supplied as inputs to the various component models. The operating parameters were governed by the load conditions and the choice of equipment, both of which were pre-decided. The result of the analysis indicated that the quantity of water in the storage device increased over the drive cycle. This result was, however, specific to the case when a particular design of the fuel cell system and its auxiliaries was operated at the load conditions determined by NEDC. The

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15 model did not consider continuous operation at those ambient conditions where water balance could not be achieved. Moreover it did not focus on design parameters where water balance would be achieved at all ambient conditions. Markel et al. 8 later calculated the variation in the quantity of water in the storage device for a similar arrangement of the fuel cell systems, when the fuel cell based automobile would operate at two other drive cycles, UDSS (Urban Dynamometer Driving Schedule) and US06 (the high-speed, high-acceleration-rate driving profile).The results of this model indicated that water balance was not achieved, both at cold start and hot start conditions, when the automobile operated on the US06 drive cycle. This analysis, however, like the previous one, focused on a specific arrangement of the fuel cell system. Moreover the results were specific to certain load cycle and were un-able to determine the sensitivity of various design parameters on water balance. Stumper et al. 9 calculated the mass of water present in the membranes from the membrane ohmic resistance using known relationship between proton conductivity and water content developed by Kreuer et al. 10 The membrane resistance was calculated for known values of stack current and overall resistance offered by the fuel cell and its components, other than the membranes, like electrodes and plates. Resistance of a fuel cell was measured for a particular fuel cell system using the membrane resistance and electrode diffusivity (MRED) method, for several operating conditions. The membrane wetness calculated by this method was specific to a fuel cell stack and its internals. Moreover, the ohmic resistance of the cell internals changes over a period of time; hence its value must be periodically measured to estimate the water quantity in the membranes.

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16 It has been seen that various studies, including the ones discussed above, that focus on the condition of the membrane, calculate either the mass of water present in the membranes at any point of time, or rate at which excess water is discharged from the fuel cell system, when particular designs of the fuel cell stack and its auxiliaries operate under specific ambient and operating conditions. None of them have made an attempt to determine the minimum system design requirements that can achieve water balance. The current study achieves this end by keeping the water balance analysis independent of the design of the fuel cell system. 2.2 Configuration of Fuel Cell Stack and Its Auxiliaries This section contains a review of the literature on configurations of the fuel cell auxiliaries that affect water balance. Figure 2-1 shows the general arrangement of the fuel cell system considered by Haraldsson and Alvfors 7 in their analysis. The ambient air is pressurized before being supplied to the stack. In order to prevent localized dry-out and in general maintain the water content of the membranes, both the reactants, air and hydrogen, are humidified from a water reservoir before being supplied to the stack. The water reservoir also supplies water to cool the stack. Water that is used as coolant is in turn cooled by a radiator, similar to the one used in conventional automobiles. Water is supplied to the reservoir from a condenser that condenses liquid water from the air leaving the stack. The current arrangement ensures that the membranes remain moist, provided that the water reservoir always contains liquid. Gelfi et al. 12 and Cunningham 13 considered a general arrangement, similar to the one described above, for their respective studies. Figure 2-2 shows the system configuration considered by Hussain et al. 14 The arrangement is similar to the one described above except that a separate coolant (other

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17 than water) is used to cool the stack. The coolant in turn rejects heat to the ambient with the help of a radiator. Cooling the stack, in general, helps condense liquid water from the air leaving the stack. This condensed liquid water is used to humidify the reactants and also heat the air entering the stack. Figure 2-1 General arrangement of fuel cell systems used by Haraldsson and Alvfors 7 in their analysis Hussain et al. 14 carried out exergy analysis of the overall system described above to predict the gross and net power developed by the fuel cell system at various ambient and operating conditions. The voltage developed by the stack was predicted using the model developed by Baschuk and Li. 15 The 1.2 kW Nexa fuel cell system developed by Ballard systems does not use a pressurized stack. Water recovery from the air leaving the stack is achieved by a humidity exchanger instead of a condenser or water separator. A humidity exchanger uses a semi-permeable membrane to transfer water from its region of higher

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18 concentration (usually depleted air leaving the stack) to the region of lower concentration (usually ambient air). The ambient air, in turn, helps in maintaining the water content of the membranes. Figure 2-2 General arrangement of fuel cell systems used by Hussain et al. 14 in their analysis A change in the operating pressure of the fuel cell stack varies the saturation pressure of the moist air leaving the stack. The saturation pressure of the exhaust air determines the rate at which liquid water leaves the fuel cell and affects the water balance of the overall system. Thus a change in operating pressure of the stack affects the water balance of the fuel cell system. The pressure ratio (or the operating pressure of the stack) and the power consumption of a pressurizer vary with the change in load conditions. As these performance characteristics vary with the type and model of equipment, selection of

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19 the pressurization equipment is critical to the overall performance of the fuel cell in general and water balance in particular. Kulp 16 compared the effect of using a centrifugal compressor as opposed to a twin screw compressor, on the performance of a 60 kW PEM fuel cell stack. Actual compressor maps were used to model the performance of each compression device under varying operating conditions. A specific voltage equation that relates stack voltage to current density, average stack temperature and average partial pressure of oxygen in the stack was used to develop polarization curves of the stack. The study concluded that the centrifugal compressor is more efficient than the screw compressor when a expander (a turbine that supplies power to the compressor) is used in conjunction with the compression device. Cunningham 13 used the performance characteristics of an Allied Signal centrifugal compressor to develop a model for simulating the performance of the air supply system used in fuel cell vehicle. The compressor map of an Allied Signal compressor was also used by Peng et al. 17 to develop a control oriented model of the fuel cell system. The stack was modeled using polarization data of 75 kW fuel cell stack. The fuel cell auxiliaries other than the compressor were modeled using conservation laws. The current study also uses the performance characteristics of the same Allied Signal compressor model to demonstrate the effect of using a non-ideal compressor on water balance. 2.3 Different Models to Predict Properties of Moist Air at Elevated Temperature and Pressure The air leaving the stack is generally at an elevated temperature and pressure and is partially depleted of oxygen. Ji et al. 18 compared the properties of moist air calculated from different models with the experimental data. The results of this analysis concluded

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20 that the accuracy of the ideal gas model decreases with the increase in pressure. Thus the ideal gas law is not accurate enough to calculate the properties of moist air leaving a high pressure stack and real gas models have to be used. The real gas models studied by Ji et al. 18 included the ideal mixing model that considered moist air as an ideal mixture of two real gases, vapor and dry air. This model was found accurate enough to calculate the properties of saturated vapor at pressures less than 10 bar and temperatures above 280 K. Other real gas models studied by Ji et al. are The model developed by Luks et al. 18 that is accurate in a temperature range of 200 K to 600 K for pressures as high as 200 atmospheres. Hyland and Wexler model 18 accurate in temperature range of 173.15 K to 473.15 K for pressures as high as 50 atmospheres. Model of Rabinovich and Beketov 18 which is accurate to a temperature of 400K and a pressure of 100 atmospheres. The results of the study determined the Hyland and Wexler model to be more accurate than the other models. Each of the above-mentioned models is based on the virial equation of real gases and aims towards calculating the virial coefficients and cross virial coefficients of the air vapor mixture. The equation of state developed by each of these models are applicable to standard air having a composition of 21% oxygen and is not applicable to moist air depleted in oxygen. Xiaoyan and Jinyue 19 used the ideal mixing model to calculate the properties of saturated moist air. Air and vapor were assumed to follow the modified Redlich-Kwong equation. Henrys Law was used to calculate the mole fraction of vapor in moist air. One of the inputs to the model was the total number of moles of moist air. This limited the

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21 model to calculate the properties of moist air flow only when its molar flow rate or total number of moles was known. When the quantity of moist air is unknown, the mole fraction of vapor in moist air can be calculated by using the ideal mixing model in conjunction with the Poynting effect. 20 This approach has followed in the current study to estimate the properties of depleted and pressurized moist air leaving the stack.

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CHAPTER 3 WATER BALANCE MODEL To analyze the effect of various operating parameters on the water balance of PEM fuel cells, a control volume analysis was carried out for steady state operation of the fuel cell system. As a part of the analysis, a control volume was defined for the most general arrangement of PEM fuel cell systems. As shown in Figure 3-1, the fuel cell stack and various systems, except the expander and storage device, are inside the control volume. Figure 3-1. Control volume defined for the general arrangement of PEM fuel cell and auxiliary systems Water enters the control volume in vapor state as a part of the atmospheric air at a mass flow rate of. Water is generated inside the fuel cell (and hence the control volume) as a result of the electro-chemical reaction where hydrogen reacts with oxygen present in the ambient air to form water. In this study, it is assumed that the net hydrogen (hydrogen supplied hydrogen re-circulated) entering the stack (and hence the control HO-in2m 22

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23 volume) is completely converted to water by supplying adequate air to facilitate the reaction. The net rate at which hydrogen enters the control volume depends on the current drawn from the stack, which in turn varies with the varying load requirement. Hence, the mass rate of water generation is a function of the current drawn from the stack. A portion of, depending upon the ambient and operating conditions, is entrained along with the air that leaves the stack. HO-gen2m HO-gen2m Figure 3-2. Different flow streams of water crossing the control volume boundary The water collection/separation device separates liquid water, if any, carried along with the air leaving the stack. Part of this liquid water is supplied back to the stack to maintain the humidity of the membranes. The remaining portion (referred to as excess water) leaves the control volume at a mass flow rate of and is either discharged to the ambient or stored in a storage device. HO-excess2m

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24 Water leaves the control volume in the form of vapor, at the rate of as a part of the air depleted in oxygen (referred to as depleted air) that leaves the control volume after exiting the stack and other components such as a water separator. The air leaving the control volume also carries along with it a portion of the liquid water, which could not be separated in the water separator/collector, at a mass flow rate of HO-out2m mliquidout For the current analysis, the control volume is assumed to be in steady state at all conditions. Water needs to be constantly supplied to the membranes to maintain their humidity level. From a global standpoint, the water used to humidify the membranes can only originate from the hydrogen oxidation reaction or from humidity in the inlet air. Hence, steady operation requires that the sum of those two sources be greater than the rate at which water is lost as a part of the exhaust, both in liquid and vapor form. Thus the mass flow rate of excess water should be greater than zero to achieve water balance at steady state and prevent membranes from progressively drying out. In order to determine the effect of various operating parameters on water balance, an expression for the mass flow rate of excess water is required in terms of ambient and design parameters. This expression would help in calculating the mass flow rate of excess water for known values of operating conditions, which in turn would determine whether water balance is achieved under those conditions. The sensitivity of the controlling parameters of water balance could also be determined from this expression. 3.1 Expression for the Mass Flow Rate of Excess Water The integral form of continuity equation for water inside the control volume is HO-gen222HOHO()mCVCSdVvdAt 3-1

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25 where 2HOCVdVt represents the rate of change of mass of water inside the control volume, represents the net rate at which water leaves the control volume and represents the rate at which mass is generated inside the control volume. As the control volume is at steady state, the first term is zero. The second term, based on the control volume shown in Figure 3-2, is 2HO(CSvdA ) HOgen2m 2HO()CSvdA = +HOoutliquidout2mm HOexcess2m HOin2m 3-2 The third term, the net rate at which water is generated inside the control volume, is. Thus Equation 3-1 can we written as HOgen2m HOexcess2m = + 3-3 HOin2m HOgen2m HO-out-2m-mliquidout As explained earlier, when the value of is negative, the membranes will eventually dry out. HOexcess2m The next step is to express the variables on the right hand side of Equation 3-3 in terms of ambient conditions and design parameters of the fuel cell. The mass flow rate at which water vapor enters the control volume as a part of ambient air, depends on the mass flow rate of ambient air supplied to the fuel cell which in turn depends on the requirement of oxygen for the electrochemical reaction. The overall reaction inside the fuel cell is as follows: HOin2m H 2 + 12 O 2 => H 2 O 3-4

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26 Each mole of diatomic hydrogen (H 2 ) supplied requires half a mole of oxygen (O 2 ) to form one mole of water. Let N H2 be the molar flow rate of diatomic hydrogen entering the control volume. For full utilization of the fuel, the minimum required molar flow rate of oxygen is N H2 /2. If y is the fraction of excess air supplied, then the actual molar flow rate of oxygen is (1+y) N H2 /2. If O2-dry is the mole fraction of oxygen in dry ambient air (often assumed to be 0.21) then the molar flow rate of dry ambient air entering the control volume is 22Hdry(1+)N2Oy Thus, the mass flow rate of water entering the control volume along with ambient air in vapor form is HOin2m = 222wHO-inHdryHO-in(1+)N2(1Oy 2) 3-5 where 2HO-in is the mole fraction of water in the ambient air and w is the molecular weight of water. The molar rate of oxygen consumption inside the fuel cell is N H2 /2 (assuming complete conversion of hydrogen to water). Hence the molar flow rate of dry depleted air leaving the control volume is 22dryHdry(1+)N2OOy 2

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27 and the mass flow rate of water leaving the control volume () is HOout2m HOout2m = 2222wHO-outdryHdryHO-out(1+)N2(1)OOy 2 3-6 where 2HO-out is the mole fraction of water in the depleted air. As can be seen from Equation 3-4, for each mole of diatomic hydrogen utilized one mole of water is produced. Thus the molar rate of water generation inside the control volume is N H2 and the mass rate of water production is HOgen2m = N w H2 3-7 Substituting the expressions derived in Equations 3-5, 3-6 and 3-7 in Equation 3-3, we find the mass flow rate of excess water produced as HOexcess2m = 2222222222HO-inHHO-outHwHdryHO-indryHO-out(1+)N(1+)NN + m 2(1-)2(1-)liquidoutOOOyy 3-8 The mass flow rate of excess water was expressed in non-dimensional terms by dividing Equation 3-8 by the mass rate of water produced () HOgen2m excessM = 22 2 2222HO-inHO-outdryHO-indryHO-out(1+)(1+)2(1-)2(1-)OOOyyliquidout 1 + [m/] 3-9 HOgen2m Here, is the non-dimensional form of the excess water rate and is equal to the mass flow rate of excess water per unit mass rate of water produced. The term /represents the non-dimensional form of the mass flow rate of liquid water carried along with the depleted air as it could not be separated or recovered. This term excessM mliquidout HOgen2m

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28 shall be represented by variable liquidoutM and shall be referred to as non-dimensional un-recovered liquid water. As explained earlier, when the value of is negative, the membranes will dry out eventually. It can be seen from Equations 3-8 and 3-9 a non-negative would mean a non-negative value of HOexcess2m HOexcess2m excessM as is always positive. Hence in order to achieve water balance under steady state conditions and prevent the membranes from drying out, the value of the non-dimensional term HOgen2m excessM should be always positive. The next section explains the procedure to calculate the value of excessM in order to determine whether water balance is achieved at steady state for a particular set of ambient and operating conditions. 3.2 Procedure to Calculate excessM Based on Equation 3-9, the inputs required to calculate the value of are excessM 2HO-in , 2dryO 2HO-out y and liquidoutM Of these variables, 2HO-in andgovern the amount of water and oxygen present in the ambient air respectively and their values depend on the ambient conditions. The other variables, 2dryO 2HO-out liquidoutM and y, are independent, and their values depend on the design conditions. Thus the value of excessM can be calculated at different ambient conditions and design choices. A Matlab code was developed that would calculate the value of excessM for various inputs. The value of was assumed to be 0.21 in the current analysis. For all terrestrial conditions, the properties of humid ambient air can be accurately calculated 2dryO

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29 using the ideal gas law. 18 Thus ambient air at the inlet to the control volume was modeled using the ideal gas law. Given this, 2HO-in can be equated to the ratio of partial pressure of water vapor to the total pressure i.e. 2HO-in = samb.pp 3-10 Here, the relative humidity of ambient air and the ambient pressure p amb depend on the atmospheric conditions and are inputs to the model. The saturation pressure of the vapor in the ambient air, p s was calculated using the Hyland and Wexler 18 equation for saturated vapor pressure which is given as follows: log(p s ) = (-0.58002206x10 4 /T a ) + 1.3914993 (0.048640239.T a ) + (0.41764768x10 -4 .T a 2 ) (0.14452093x10 -7 .T a 3 ) + (6.5459673.log (T a )) 3-11 The ambient temperature T a was an input to the model. The ambient air properties, namely pressure, temperature and relative humidity, define the humidity ratio of the ambient air, which governs the amount of water entering the control volume. However, ambient conditions are not commonly expressed in terms of its humidity ratio. Hence pressure, temperature and relative humidity, which more commonly represent the ambient air conditions, are used as inputs to the model. Any combination of the three inputs that give rise to a particular value of humidity ratio will give the same result. In order to calculate 2HO-out the properties of depleted air must be known. In the current model, it is assumed that depleted air leaving the control volume is saturated. Depleted air is usually at an elevated pressure and temperature. At explained earlier in Chapter 2, the accuracy of the ideal gas model decreases with increasing pressure. For the

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30 flow leaving the control volume, the current model uses the Redlich-Kwong (RK) 20 equation for real gases for each of its constituents: 0.5realrealrealrealrealrealRTap = -b)(+b)T 3-12 where p real is the pressure of a real gas, T real is its temperature and real its molar volume in. The symbols a, b and R are represent constants where R is the universal gas constant a = 0.42748 22.5ccRTP and b = 0.08664 ccRTP 3-13 T c and P c are the critical temperature and critical pressure, respectively, of the real gas. Xiaoyan and Jinyue 19 used the Redlich-Kwong equation to model the properties of pure vapor, nitrogen, oxygen and a mixture of all three gases for different mole fractions of each component. The results of the model were compared with experimental data and the accuracy of the model was found to be in the range of .45%. Thus the Redlich-Kwong equation is considered sufficiently accurate to calculate the properties of depleted air. In order to calculate the properties of the vapor in depleted air, the temperature and pressure of depleted air must be supplied to the model as an input. Let p t be the pressure of the depleted air at the exit of the control volume and p r (compression ratio) be the ratio of depleted air pressure to ambient pressure. Thus p r = p t /p amb 3-14 The saturation pressure of vapor in the depleted air is different than the saturation pressure of pure vapor at the same temperature due to the presence of non-condensable dry air along with the vapor. In order to calculate the saturation pressure of the vapor in the depleted air, the Poynting effect 20 was considered. Following the Poynting effect,

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31 pure water vapor is assumed to be in equilibrium with liquid water at the depleted air temperature. State 1 be the state of the water vapor and liquid water mixture at the depleted air temperature. The pressure of the vapor and the liquid at State 1 would thus be equal to the saturation pressure corresponding to the depleted air temperature. Dry air was now assumed to be added to the pure vapor at constant temperature until the total pressure of the air-vapor mixture equals the depleted air pressure, p t This would modify the partial pressure of vapor which is still in the saturated condition. State 2 be the state of the moist air and liquid water mixture after addition of non-condensable gases to water vapor. The pressure of the liquid water at State 2, which is in equilibrium with the air vapor mixture above it, would be equal to the depleted air pressure. The modified saturation vapor pressure is calculated by equating the change in Gibbs free energy at the liquid-vapor interface from State 1 to 2 when an infinitesimal quantity of non condensable gases is added to a pure liquid vapor mixture at a constant temperature. This gives the following equation: dg liquid = dg vapor 3-15 where g liquid and g vapor are the gibbs free energies of liquid and vapor respectively. As the temperature of liquid and vapor does not change between State 1 and 2, dg = .dp Thus Equation 3-15 can be written as (dp) liquid = (dp) vapor 3-16 Integrating between State 1 and 2, to calculate the total change in the gibbs free energy at the liquid-vapor interface, the following equation is obtained. 21ppdp = (p 2 2 ) (p 1 1 ) 21pd = liq (p t p 1 ) 3-17

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32 Here p 2 represents the modified saturation pressure of the vapor at State 2, when the total pressure of the air-vapor mixture is p t (depleted air pressure). The molar volume of liquid water, liq is assumed approximately constant between State 1 and 2, and its value is taken as 18.016x10 -6 m 3 /mole. As mentioned earlier the temperature T 1 (temperature of the depleted air) is an input to the model. The saturation pressure of pure vapor at the depleted air temperature (p 1 ) is calculated at temperature T 1 using the Hyland and Wexler equation. The molar volume of vapor at State 1 ( 1 ) is calculated by the R.K. equation with p 1 as the input. The modified saturation pressure (p 2 ) is expressed in terms of 2 using the R.K. equation and is also expressed in terms of 21pd 2 as 1 is known. As a result, Equation 3-17 takes the form 110.5-6t10.5RT.b)a (p. ) RT.ln -b)b)(+b)Tb)a ln(18.016x10)(p-p) b)bT 3-18 Except for 2 and p t all other variable in the above equation are known. The depleted air pressure p t is one of the parameters that is varied in order to observe its effect on the excess water produced and is hence an input to the equation. For a particular value of p t 2 is calculated iteratively by the code. The value of 2 is used to find the value of p 2 (modified saturation pressure of vapor in the depleted air) using the RK equation. For developing the model, the mixture of dry air and vapor is considered to be an ideal solution. Hence, the mole fraction of vapor in depleted air 2HO-out is equal to the

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33 ratio of the fugacity of the vapor at its partial pressure to the fugacity of the vapor at the total pressure of the mixture, 20 or 2HO-out = 21t1f(p,T)f(p,T) 3-19 In Equation 3-19, f(p 2 ,T 1 ) is the fugacity of vapor at pressure p 2 and temperature T 1 and f(p t ,T 1 ) is the fugacity at pressure p t and temperature T 1 Fugacity of a gas that follows Redlich-Kwong equation is given by 20 f = 1.5ba11exp lnln(b)b)b)TRTbR b 3-20 Equation 3-20 is used to calculate the value of f(p 2 ,T 1 ), as 2 and T 1 are already known. The value of p t is input in the R.K. equation to determine the value of t and the value of f(p t ,T 1 ) is determined using Equation 3-20. Consequently, 2HO-out can be calculated for different values of p t at a given value of T 1 From Equations 3-9, 3-10, and 3-19, can be calculated when ambient temperature (T excessM a ), ambient pressure (p amb ), ambient relative humidity (), fraction of excess air (y), depleted air temperature (T 1 ), and depleted air pressure (p liquidoutM t ) are provided as input. Of these inputs, y, T 1 and p liquidoutM t are design parameters, as their values can be varied using different equipment choices and operating conditions. 3.3 Model Validation In order to validate the accuracy of the water balance model developed above, the results of the model were compared with the values calculated by the Hyland and Wexler 18 model, which has been accepted to be more accurate in comparison to other real gas models for moist air. 18 As the Hyland and Wexler model was not applicable for

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34 depleted air, the water balance model was used to calculate the humidity ratio () of ambient air and its values were compared with those calculated by the Hyland and Wexler model for different ambient temperatures and pressures. Tables 3-1 and 3-2 show the comparison of different values of at sea level and 2250 meters. Figure 3-3 graphically represents the deviation of the values calculated using the model from the readings calculated by the Hyland and Wexler model. It can be seen that the current model based on R.K. equation, closely follows the Hyland and Wexler model and the deviation in the value of for different temperatures at two different elevations is less than %. Table 3-1. Comparison of different values of at sea level Sea level: 101.325 kPa (humidity ratio) Percent error Temperature (C) % RH Hyland and Wexler model Current model based on RK equation Current model v/s Hyland and Wexler readings 5 100 0.0054 0.0055 -1.59% 10 100 0.0076 0.0077 -1.15% 15 100 0.0107 0.0107 -0.28% 20 100 0.0147 0.0147 0.38% 25 100 0.0202 0.0199 1.42% 30 100 0.0273 0.0266 2.73% Table 3-2. Comparison of different values of at 2250 meters Altitude 2250 meters : 77.058 kPa (humidity ratio) Percent error Temperature (C) % RH Hyland and Wexler model Current model based on RK equation Current model v/s Hyland and Wexler readings 5 100 0.0072 0.0072 -0.16% 10 100 0.0102 0.0101 0.89% 15 100 0.0142 0.014 1.24% 20 100 0.0195 0.0192 1.50% 25 100 0.027 0.026 3.69% 27 100 0.0303 0.0293 3.60%

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35 Figure 3-3. Comparison of model predictions with Hyland and Wexler data

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CHAPTER 4 RESULTS AND DISCUSSION In order to achieve water balance at steady state, the value of the non-dimensional excess water term should be greater than zero. As seen previously in Chapter 3, the dimensionless form of excess water excessM excessM can be calculated when ambient temperature, pressure and relative humidity and design parameters pressure ratio, depleted air temperature, non-dimensional form of un-recovered liquid water and fraction of excess air are provided as inputs. Of these inputs, the ones that can be controlled are only the design parameters. liquidoutM The ambient conditions and stoichiometry govern the amount of water entering the control volume. For a given set of operating conditions, any increase in the humidity ratio of the ambient air would bring more water into the control volume and hence would increase the value of. excessM This can also be seen from Equation 3-9 in which an increase in 2HO-in (the mole fraction of water in ambient air) increases the value of excessM As ambient conditions cannot be controlled, the fuel cell must be designed for the worst operating conditions which, from a water balance point of view, would be ambient air with a relative humidity of zero. At completely dry ambient conditions, i.e., at =0, 2HO-in is zero for all ambient temperatures. Hence excessM is independent of ambient temperature at =0. 36

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37 In addition to being able to operate under dry ambient conditions, fuel cell-driven vehicles should be capable of operating at high altitudes (low ambient pressure). To consider the effect of low ambient pressure on water balance, a maximum altitude limit of 12,000 feet that corresponds to 64.539 kPa was considered in this study. An altitude of 12,000 feet is the more commonly accepted upper limit for high altitudes that is used by fuel cell automobile manufacturers. To analyze the variation of excessM for dry ambient conditions (=0), the Matlab code was used to plot 3D graphs of excessM versus y and p r at different depleted air temperatures and altitudes. For the initial part of the analysis, the value of was chosen to be zero. liquidoutM Figures 4-1 to 4-4 are the plots showing variation of excessM at four different depleted air temperatures at an ambient pressure of 101.325 kPa. Figures 4-5 to 4-8 are similar to Figures 4-1 to 4-4 except that the ambient pressure is 64.539 kPa, corresponding to an altitude of 12,000 feet, in all of these cases. Figures 4-1 to 4-8 indicate that for a given excess air fraction y, increases with the increase in pressure ratio. An increase in depleted air pressure for a given depleted air temperature decreases the humidity ratio of the depleted air and causes more water to condense. Hence less water leaves the control volume as a part of the depleted air and the excess water variable increases. This trend is seen at all ambient conditions. Mathematically, an increase in depleted air pressure decreases the humidity ratio of depleted air and hence the value of excessM 2HO-out This in turn decreases the value of 2HO-out22HO-out [(1+yo)2 o(1)] 2 and increases the value of excessM based on Equation 3-9. This is the same as mentioned before.

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38 A comparison of the values of excessM at different depleted air temperatures, in Figures 4-1 through 4-4 for sea level and Figures 4-5 through 4-8 for 12,000 feet, shows that a decrease in the depleted air temperature increases the value of A decrease in the depleted air temperature when all other parameters are kept constant, decreases the humidity ratio of the depleted air and causes more water to condense. Hence less water leaves the control volume as a part of the depleted air and the excess water variable increases. This trend is consistent under all ambient conditions. excessM An increase in the quantity of excess air for a given depleted air pressure decreases the value of for the ambient conditions under consideration. The incoming or ambient air is dry and takes in part of the water generated in the fuel cell to become saturated. An increase in the fraction of excess air increases the mass flow rate of the ambient air for a given water production rate. Thus more water is required to saturate the incoming air, which in turn implies that a greater portion of the water generated leaves the control volume as a part of the depleted air than as excess water. Consequently the rate of excess water produced decreases. This trend, however, is specific to the ambient conditions under consideration and changes completely for humid ambient cases. excessM It can be seen from Equation 3-9 that a change in the value of results in an equal change in the value of liquidoutM excessM The shape of a plot of excessM versus any of the controlling parameters, for a constant liquidoutM remains unaltered for all values of This effect is indicated in Figure 4-11, showing liquidoutM excessM versus pressure ratio for =0 and =0.1. The ambient temperature, pressure and relative humidity were assumed to be 298 K, 1 atmosphere and 0%, respectively, and the depleted air liquidoutM liquidoutM

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39 temperature was assumed to be 353 K. The values of liquidoutM were assumed to stay constant at 0 and 0.1 with the change in pressure, for both cases. It can be seen from Figure 4-11 that the trend of variation of does not change with a variation in the value of excessM liquidoutM The only effect, as mentioned before, is a drop in the value of by an amount equal to excessM liquidoutM An implication of this effect is that if is negative (water balance not achieved at steady state) for =0 under certain operating conditions, water balance will never be achieved at those conditions for all positive values of Thus analyzing the case of excessM liquidoutM liquidoutM liquidoutM =0 determines those values of design parameters where water balance cannot be achieved for all values of It should be noted that the value liquidoutM liquidoutM cannot be less than zero as it is the non-dimensional form of the amount of liquid water that could not be separated from depleted air. It can be seen from Figures 4-1, 4-2, 4-5 and 4-6 that, when operating at sea level and even at 12000 feet, a depleted air temperature of 298K would produce excess water even when the fraction of excess air is as high as 4, for liquidoutM =0. A value of >0.75 would drop liquidoutM excessM below zero and pressurization may be needed in those cases to achieve water balance. In general, pressurization of the fuel cell is not required even at 12,000 feet for a maximum value of y as high as 4 when <0.75. However, depleted air temperatures as low as 298K for a fuel cell that operates close to 353K is possible only when a refrigeration system cools the stack. liquidoutM Figure 4-3 shows that when the depleted air temperature is increased to 323K at sea level, water balance is not achieved at liquidoutM =0 for an un-pressurized stack when the

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40 fraction of excess air y increases beyond 2 In such cases, the fuel cell must be pressured for all values of to prevent membrane dry-out under continuous operation. An increase in altitude to 12000 feet at a depleted air temperature of 323K drastically affects the water balance as the system must be pressurized for excess air fraction beyond 1. liquidoutM When the depleted air temperatures are as high as 353K, the fuel cell must be pressured under all operating conditions to ensure production of excess water. Moreover at 12000 feet, excess water is produced only at very high depleted air pressures and low excess air fractions. Such operating conditions place significant constraints on system design. Figures 4-1 to 4-4 for sea level and Figures 4-5 to 4-8 for an altitude of 12,000 feet indicate that an increase in depleted air temperature moves the constant excess air lines on the versus pressure ratio plot closer to each other. This can be seen from Equation 3-9. As ambient relative humidity is zero, excessM 2HO-in =0 hence Equation 3-9 becomes excessM = 2222HO-outHO-out(1+)12(1-)OliquidoutOyM An increase in depleted air temperature at dry ambient conditions increases the saturation pressure of depleted air. Hence 2HO-out increases and 22HO-outHO-out/(1) decreases. As this term is the multiplying factor to the term 2(1+yo) any increase in y has a comparatively lesser impact on excessM for higher depleted air temperatures than for lower ones. Thus the constant excess air lines move closer to each other for higher temperatures

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41 at dry ambient conditions. As explained earlier, this trend would stay the same for all values of liquidoutM So far we have observed the trend of variation of excessM with respect to excess air y for dry ambient conditions. The trend is not always same when the ambient air has a relative humidity greater than zero. Figure 4-9 is again a plot of excessM with operating conditions the same as those in Figure 4-2 except that the relative humidity, is 0.5 instead of zero. Comparing Figure 4-2 with Figure 4-9 shows that the excess water produced at particular operating and ambient conditions is always greater for =0.5 than for =0. This is in confirmation to the result mentioned earlier that an increase in the ambient humidity ratio will increase the value of excessM As can be seen from Figure 4-9, the quantity of excess water decreases with the increase in excess air up to a pressure ratio of 2. Beyond a pressure ratio of 2, the pattern changes and the quantity of excess water decreases with excess air. This phenomenon becomes clearer when we examine Equation 3-9. Differentiating excessM with respect to y, assuming constant we obtain the following: liquidoutM 222HO-in2HO-inHO-out2HO-out//[2(1)]/[2(1excessdMdyoo 2)] 4-1 When the mole fraction of water in the depleted air is greater than that in the ambient air, the derivative of excessM with respective to y is negative and an increase in excess air decreases the quantity of excess water. The opposite effect is seen when 2HO-out is less than 2HO-in Physically, when 2HO-out is greater than 2HO-in some portion of the water generated inside the fuel cell is required to saturate a unit mass of depleted air. An increase in y increases the mass flow rate of excess air. Hence additional water

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42 would be required to saturate the flow of depleted air. Consequently the amount of excess water generated decreases. When 2HO-out is less than 2HO-in the amount of vapor present per unit mass of ambient air is more than what is required to saturate a unit mass of depleted air. Hence, upon pressurization, water is condensed from the air. An increase in y and hence an increase in the mass flow rate of air results in more water being removed from the depleted air. Hence the quantity of excess water increases. It should be noted that this trend is valid for all values of liquidoutM provided its value is independent of y. In order to determine the set of values of design parameters for which water balance is not achieved for all values of liquidoutM under the worst case of dry ambient conditions. Equation 3-9 (Section 3.1) was used. At liquidoutM =0, when =0, 2HO-in = 0, thus = excessM 2HO-out221(1)/yoo 2 Water balance is not achieved at steady state when <0, that is when excessM 22HO-out22HO-out1{(1)/2(1)yoo } < 0 4-2 For 2O = 0.21, the above inequality becomes 2HO-out0.42/(1.21)y 4-3 The above inequality indicates a relation between 2HO-out (which depends on the depleted air temperature and pressure) and excess air y. Figure 4-10 gives a plot of 2HO-out versus y in which the region above the curve represents the operating conditions under which excess water is not produced. Approximating depleted air to be an ideal gas

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43 2HO-out is the ratio of the partial pressure of vapor to the total pressure of depleted air ( 2HO-out =p 2 /p t ) Hence water balance is not achieved for all values of when liquidoutM 2/0.42/(1.21)t p p y 4-4 For a non-pressurized system operating at sea level (p t =1 atmosphere), when y=0, p 2 <0.347 atm which corresponds to a saturation temperature of 346 K. When y increases, the maximum limit of p 2 decreases and the corresponding saturation temperature decreases. Hence for a non-pressurized system operating at sea level, the maximum limit of depleted air temperature is approximately 346 K (73 C). Similarly, for an altitude of 12000 feet, p t = 0.6368 atm and the maximum limit of depleted air temperature is approximately 336 K. Using Equation 4-4 one can thus determine the approximate maximum limit of depleted air temperature for different operating and ambient pressure conditions. Figure 4-1. Excess water versus pressure ratio and fraction of excess air: sea level, very low depleted air temperature case

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44 Figure 4-2. Excess water versus pressure ratio and fraction of excess air: sea level, low depleted air temperature case Figure 4-3. Excess water versus pressure ratio and fraction of excess air: sea level, intermediate depleted air temperature case

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45 Figure 4-4. Excess water versus pressure ratio and fraction of excess air: sea level, high depleted air temperature case Figure 4-5. Excess water versus pressure ratio and fraction of excess air: high altitude, very low depleted air temperature case

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46 Figure 4-6. Excess water versus pressure ratio and fraction of excess air: high altitude, low depleted air temperature case Figure 4-7. Excess water versus pressure ratio and fraction of excess air: high altitude, intermediate depleted air temperature case

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47 Figure 4-8. Excess water versus pressure ratio and fraction of excess air: high altitude, high depleted air temperature case Figure 4-9. Excess water versus pressure ratio and fraction of excess air: sea level, low depleted air temperature, humid ambient air case

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48 Figure 4-10. Excess water versus pressure ratio and fraction of excess air: sea level, low depleted air temperature, humid ambient air case Figure 4-11. Excess water versus pressure ratio for liquidoutM =0 and =0.1: sea level, high depleted air temperature. liquidoutM

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CHAPTER 5 EFFECT OF CERTAIN NON-IDEAL COMPONENTS ON WATER BALANCE MODEL INPUTS As mentioned previously in chapter 3, excessM can be calculated from the water balance model when ambient conditions and design parameters are provided as inputs. The water balance model is independent of the choice of equipment. Any combination of equipment that leads to a same set of values of the design parameters yields the same result of from the water balance model, for constant ambient conditions. Thus the choice of equipment affects the inputs to the water balance model and not the model itself. excessM The non-ideal nature of various components and sub-systems affects the design parameters of the fuel cell system, and hence the inputs to the water balance model. The effects on model inputs under varying operating conditions, when non-ideal air delivery sub-system and water recovery components are a part of the PEM fuel cell system, have been studied in this chapter. 5.1 Effect of a Non-Ideal Air Handling System on Model Inputs The air handling system uses equipment like a blower or compressor to supply air for the electrochemical reaction and if required pressurize the stack. The non-ideal nature of the system varies certain operating parameters and hence affects the inputs to the water balance model. The changes in the model inputs due to the non-ideal behavior of the air-handling are as follows: 49

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50 Change in the depleted air pressure due to change in pressure ratio developed by a compression device under varying operating conditions. Change in the fraction of excess air at part load conditions due to the in-ability of the air supply device to reduce the mass flow rate of air below a certain limit. In ability of the air supply equipment to supply sufficient air quantity to all parts of the stack for lower mass flow rates of air. This forces the air handling system to maintain a minimum rate of air supply which results in an increase in the fraction of excess air at part load conditions. Each of the above-mentioned changes in the model inputs and the resulting impact on water balance has been discussed in the subsequent sections of this chapter. 5.1.1 Change in Pressure Ratio Developed by a Non-ideal Air Compressor and Its Effect on Water Balance For a pressurized stack, the depleted air pressure depends on the pressure ratio developed by the compression device. An ideal compressor would maintain a constant pressure ratio at all operating conditions. However for a non-ideal compressor, the pressure ratio and hence the depleted air pressure generally varies with the change in the mass flow rate of air through the compressor. Changing depleted air pressure, p t an input to the model, changes the value 2HO-out and hence the amount of excess water generated by the system. Thus the extent to which pressurization affects water balance depends on the pressure ratio achieved by the equipment at a particular rotational speed and air mass flow rate. These performance characteristics vary with the type of equipment used and its geometry. For the current analysis a centrifugal compressor developed by Allied Signal Aerospace 17 was considered. The change in pressure ratio and hence water balance of a PEM based fuel cell stack was analyzed, when this device used for pressurization operated at part load conditions. It was assumed that the pressure at a location just downstream of the compressor was equal to the pressure of the depleted air.

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51 5.1.1.1 Performance characteristics of an Allied Signal compressor at part load conditions The performance characteristics of a centrifugal compressor are generally represented in terms of a compressor map which is a plot of pressure ratio versus corrected mass flow rate at various corrected rotational speeds. Corrected mass flow rate, is correctm 21/()am and corrected rotational speed, is correctN N/ where am and N are the actual mass flow rate of air and actual rotational speed of the compressor respectively. The parameter is the ratio of inlet air temperature to reference temperature. The variable is the ratio of inlet air pressure to reference pressure and 1 is the ratio of dimensional parameters. The value of 1 is useful for comparing two different dimensionally similar compressors. When the performance characteristic of a particular compressor is analyzed, the value of 1 is 1. Figure 5-1 shows the compressor map of the centrifugal compressor used in the current analysis. The reference temperature and pressure for this Allied Signal compressor are 298K and 101.32 kPa. The red markings on the plot are the actual operating points at different rotational speeds and the blue lines are curefits to the data, generated by Jensen and Kristensen nonlinear curve fitting method. 24 These lines are constant corrected speed lines and represent the variation of pressure ratio with corrected mass flow rate for a particular rotational speed. The green colored line on the left hand side of the map is the surge limit of the compressor and the one on the right hand side indicates the stall limit. It is generally recommended that centrifugal compressors should operate in the region between their surge limit and the stall limit on the compressor map, which, in case of the Allied Signal

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52 compressor, is between the two green lines. Operating outside this region would lead to unsteady operation of the compressor. Figure 5-1. Compressor map of an Allied Signal compressor. (Source: Control-oriented modeling and analysis for automotive fuel cell systems, Pukrushpan J.T., Peng H., and Stefanopoulou A.G. Figure modified to represent the operating line on the compressor map) The actual points on the map along which the compressor operates at various speeds depend on the resistance offered by the system, (which in our analysis is a fuel cell stack and its connecting piping) to which it is supplying compressed air. However, the system resistance offered by a stack and its connecting piping can be varied by adding one or more valves anywhere in the system and varying the closure of each valve or by varying the pipe size. Hence an operating line on a compressor map defines the system resistance offered at various operating conditions but does not limit it to a particular stack. In other words, the analysis is independent of the design of the fuel cell stack.

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53 For the current analysis, the Allied Signal compressor is assumed to operate at a margin of 15% from the surge limit. This means that at a particular rotational speed, the mass flow rate of air through the compressor is 15% greater than the mass flow rate at the surge limit corresponding to that rotational speed. It can be seen from Figure 5-1 that when the operating point moves closer to the surge limit, higher pressure ratios can be achieved for the same rotational speed. However, operating close to the surge line involves the risk of the operating point crossing the surge limit, putting the compressor in the regime of unsteady operation. It is due to these factors that the compressor was assumed to operate at a 15% surge limit. The 15% surge limit line, which can also be referred to as the operating line of the compressor, has been indicated by a solid red line in Figure 5-1. As shown in Figure 5-1, the constant speed lines for the compressor are plotted at different corrected rotational speeds starting from 10 kRPM reaching up to 105 kRPM. The design point of operation of the compressor in the current analysis is the one that lies at the intersection of the operating line (15% surge limit line) and the 105 kRPM constant corrected speed line. The fuel cell was assumed to produce maximum/design current when the compressor operates at this point. For analyzing the effect of water balance when the Allied Signal compressor is used as a compression device, 10 different points along the operating line of the compressor were selected. These points also include the design point of the compressor. They are indicated in Figure 5-1 as blue squares. The first three columns in Table 5-1 indicate the values of various parameters like normalized air flow rate, pressure ratio and corrected speeds at each of these points.

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54 As mentioned earlier, the fuel cell is assumed to produce maximum current when the compressor operates at its design point. A drop in the speed of the compressor along the assumed operating line would reduce the mass flow rate and pressure of the air at the inlet of the fuel cell. This can be observed from parameters at various operating points depicted in Table 5-1. The current generated by the stack is directly proportional to the mass flow rate of air entering the stack. As the normalized mass flow rate of air at the 10 operating points are known, these points can be represented in terms of fraction of the design/ maximum stack current. The relation between stack current and normalized mass flow rate of air is explained below. Table 5-1. Values of different parameters at the 10 selected operating points of an Allied Signal compressor Normalized flow (kg/s) Pressure ratio Corrected speed (kRPM) Normalized flow/ Desi g n normalized flow 0.014 1.033 20 0.1759 0.017 1.104 30 0.2132 0.025 1.237 40 0.3034 0.031 1.420 50 0.3782 0.038 1.641 60 0.4661 0.046 1.900 70 0.5629 0.055 2.248 80 0.6684 0.066 2.712 90 0.8135 0.078 3.195 100 0.9577 0.082 3.374 105 (Design point) 1 5.1.1.2 Relation for fraction of design current The current generated in a PEM based fuel cell is given by the equation 11 I= 4F/ 5-1 2ON where F is the faraday constant, n is the number of fuel cells in the stack and is molar flow rate of oxygen in moles/sec that is effectively used by the fuel cell to produce water. It can be seen from Equation 3-4 that the number of moles of hydrogen required to 2ON

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55 produce water is twice the number of moles of oxygen. In other words N H2 =2. Hence Equation 5-1 can be written as 2ON I= 2F N H2 / 5-2 Based on Equation 3-5, the molar flow rate of air entering the control volume and eventually the fuel cell is equal to 2H(1+)N2oy 2 The molecular weight of ambient air for a standard composition of 21% mole fraction of oxygen and 78% mole fraction of nitrogen is 28.97. Hence the mass flow rate of air entering the compressor and eventually the fuel cell stack can be represented by the equation. am = 28.97 22H(1+)N2Oy 5-3 Comparing Equations 5-2 and 5-3 we can represent am in terms of I as follows. am = 28.97 2(1+).I.n.OyF 5-4 The value of n cell remains constant for a particular fuel cell stack and, F and are constants. Thus the ratio stack current to the design stack current can be represented by 2O designI/I = (1)(1)adesignadesignmyym 5-5 Here, I and y are mass flow rate of air, stack current and fraction of excess air respectively at any operating point of the compressor. Variables, I am adesignm design and designy are the mass flow rate, stack current and fraction of excess air corresponding to the design point of the compressor.

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56 The corrected mass flow rate is given by correctm 21/()am For constant ambient conditions, the values of and 1 remain constant for the Allied Signal compressor. Thus Equation 5-5 can be written as designI/I = (1)(1)correctdesigncorrectdesignmyym 5-6 correctdesignm is the corrected mass flow rate at the design point. Here y and y design are inputs to the water balance model. The values of the ratio at all the 10 operating points have been indicated in the fourth column of Table 5-1. Each of the 10 operating points can thus be indicated in terms of fraction of design current provided, the value of y at each of these points is known. The values of the pressure ratios at these operating points can be used to provide input to the model and the value of can be calculated for a given set ambient conditions and depleted temperatures (T /correctcorrectdesignmm excessM 1 ). Thus the variation of excessM when an Allied Signal compressor is used and the stack current and fraction of excess air (y) change from their design values, can be observed. As explained in section 3.2 for the case when an Allied Signal compressor is used as a compression device, can be plotted as a function of fraction of design stack current when y is known at all operating points and ambient conditions and depleted air temperature is provided as input. excessM

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57 5.1.1.3 Variation of with fraction of design current for part load operation of an Allied Signal compressor excessM As explained earlier, the performance characteristics of an Allied Signal compressor decide the values of depleted air pressure (an input to the model) when the compressor operates at part load conditions. When the value of y (another input to the model) is known at all operating points of the compressor, excessM can be plotted as a function of fraction of design current. For the current analysis, it was assumed that the value of y does not change from its design value at all operating points of the compressor. Figure 5-2 compares the plot of excessM versus fraction of design current for an Allied Signal compressor with that of an ideal compressor. The graphs are plotted for different values of design excess air fraction (y design ). The depleted air temperature (T 1 ) was assumed to be equal to 323K and the ambient conditions were assumed as follows: T a = 298K, =0, p amb =101325.16 Pa (sea level). The value of liquidoutM was assumed to be zero. Figure 5-3 is similar to Figure 5-2 except that plots correspond to a higher value of T 1 which is equal to 353K. Figures 5-4 and 5-5 are similar to Figures 5-2 and 5-3 respectively, except that the values of excessM were calculated assuming that the fuel cell operates at 12000 feet instead of sea level (i.e. p amb =64539 Pa). A few trends are common amongst all four figures. First one is that for an Allied Signal compressor, decreases along the constant excess air lines with the decrease in fraction of design current. From Equation 5-5, when the value of y remains constant at its design value, the stack current is directly proportional to the mass flow rate of air. A decrease in the fraction of design stack current decreases the mass flow rate of air through the stack. A drop in the value of mass flow rate of air through the compressor excessM

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58 along its operating line decreases the pressure ratio across the stack. This in turn drops the depleted air pressure. As explained in section 4.1, a drop in the depleted air pressure decreases the value of at all times. Thus excessM excessM decreases with the decrease in stack current. In comparison, the value of excessM for an ideal compressor stays constant, along the constant y lines, with the change in fraction of design current. This is because the pressure ratio developed by an ideal compressor stays constant at all mass flow rates. Another trend that is observed in Figures 5-2 through 5-5 is that an increase in the value of y design decreases the value of excessM both for an ideal and a non-ideal compressor. The variation of with excess air fraction is governed by Equation 4-1. For the case where =0, the value of always decreases with the increase in the fraction of excess air. excessM excessM A third trend common to all four figures is that the value of for the non-ideal compressor, drops more rapidly, with the decrease in the fraction of design current, for higher fractions of excess air than for lower ones. Moreover the difference between the constant fractions of excess air lines increases. A drop in the stack current results in a lower depleted air pressure and hence a drop in the rate at which excess water is produced for a unit mass of ambient air supplied. An increase in the value of y increases the mass flow rate of ambient air. As a result the drop in the rate of excess water production is magnified and the constant fraction of excess air lines tend to move farther away from each other. This can also be seen from Equation 3-9; a drop in the pressure ratio drops the value of excessM 2HO-out and hence excessM Now an increase in value y further magnifies this effect resulting in steeper lines of constant y. It should be noted that the trends described above

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59 do not change for all values of liquidoutM provided liquidoutM stays constant all operating points of the compressor. exit air temp = 323K, amb press = 1 atm, RH=0, -0.8-0.6-0.4-0.200.20.40.60.810.10.30.50.70.9fraction of design current/ design flow ratemass of excess water/ mass of water produced y=0:Allied compressor y=2:Allied compressor y=4:Allied compressor y=0:Ideal compressor y=2:Ideal compressor y=4:Ideal compressor =0 Figure 5-2. Excess water versus fraction of design current and fraction of excess air: sea level, intermediate depleted air temperature, liquidoutM =0 exit air temp = 353K, amb press = 1 atm, RH=0-10-8-6-4-2020.10.20.30.40.50.60.70.80.91fraction of design currentmass of excess water/ mass of wate r produced y=0:Allied compressor y=2:Allied compressor y=4:Allied compressor y=0:Ideal compressor y=2:Ideal compressor y=4:Ideal compressor =0 Figure 5-3. Excess water versus fraction of design current and fraction of excess air: sea level, high depleted air temperature, liquidoutM =0

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60 exit air temp = 323K, amb press = 64539 Pa, RH=0-2-1.5-1-0.500.511.50.10.30.50.70.9fraction of design currentmass of excess water/ mass of water produced y=0:Allied compressor y=2:Allied compressor y=4:Allied compressor y=0:Ideal compressor y=2:Ideal compressor y=4:Ideal compressor =0 Figure 5-4. Excess water versus fraction of design current and fraction of excess air: high elevation, intermediate depleted air temperature, liquidoutM =0 exit air temp = 353K, amb press = 64539 Pa, RH=0-30-25-20-15-10-5050.10.30.50.70.9fraction of design currentmass of excess water/ mass of water produced y=0:Allied compressor y=2:Allied compressor y=4:Allied compressor y=0:Ideal compressor y=2:Ideal compressor y=4:Ideal compressor =0 Figure 5-5. Excess water versus fraction of design current and fraction of excess air: high elevation, high depleted air temperature, liquidoutM =0

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61 5.1.2 Change in Fraction of Excess Air due to Compressor Limitations A drop in the mass flow rate of air through a non-ideal compressor decreases the pressure ratio developed by it. Thus one of the inputs to the model, the depleted air pressure, is governed by the characteristics of a compressor. This has also been seen in section 5.1.1 for the case of an Allied Signal compressor. Most compression devices are unable to maintain stable operation when the mass flow rate of air drops below a certain limit. Hence it is recommended that the mass flow rate of air through a compressor should not drop below a certain minimum value. This limits the ratio to a minimum value. If the fraction of excess air is maintained at its design value at all operating points of the compressor, the minimum mass flow rate of air through a compressor corresponds to a minimum value of fraction of design current. Based on Equation 5-6, if current must be dropped below this minimum value, y must be increased above its design value. As the fraction of design current decreases the value of y increases. Thus the value of y (another input to the model) under the condition of low current is governed by the minimum mass flow rate of air that a compressor can supply under stable operation. To summarize, the values of two of the inputs of the model namely depleted air pressure and fraction of excess air are dependent on the performance of the compressor. /correctcorrectdesignmm Figure 5-6 shows the variation of y with respect to the fraction of design current when an Allied Signal compressor is used to pressurize a stack. The minimum ratio of for stable operation of the Allied Signal compressor is 0.176 which corresponds to a pressure ratio of about 1. The value of y is assumed to stay constant at its design value of 0.8 until the ratio of drops to the minimum value of /correctcorrectdesignmm /correctcorrectdesignmm

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62 0.176. A constant value of y implies that the fraction of design current is equal to the ratio based on equation 5-6. For fractions of design current lower than this point, the mass flow rate of air stays constant and the value of y increases from its design value. Figure 5-6 shows that a drop in the fraction of design current below 0.176 results from an increase in the value of y. A zero current is never achieved in this case as it would correspond to a value of y reaching infinity. /correctcorrectdesignmm Figure 5-7 shows the variation of excessM versus fraction of design current. The ambient temperature, pressure and relative humidity were assumed to be 298 K, 1 atmosphere and 0% and the depleted air temperature was assumed to be 323 K. The value of was assumed to be zero in this case. It can be seen that for fractions of design current greater than 0.176, the value of liquidoutM excessM decreases due to a drop in pressure ratio. When the fraction of design current increases beyond 0.176, the pressure ratio stays constant at its minimum value of 1 and the value of y increases (as shown in Figure 5-6) An increase in y when ambient air relative humidity is zero, decreases the value of excessM as seen in Figure 5-7.

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63 Change in fraction of excess air due to compressor limitations0510152000.20.40.60.81Fraction of design currentFraction of excess air Figure 5-6. Change in fraction of excess air due to compressor limitations for lower fractions of design current. exit air temp = 323K, amb press = 1 atm, ambient RH=0-7-6-5-4-3-2-10100.10.20.30.40.50.60.70.80.91fraction of design current/ design flow ratemass of excess water/ mass of water produced Figure 5-7. Excess water versus fraction of design current: compressor limitation: sea level, intermediate depleted air temperature, liquidoutM =0

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64 5.1.3 Change in Fraction of Excess Air due to Air Distribution Limitations A conventional PEM fuel cell stack consists of a number of cells that are electrically connected together. In order to ensure adequate supply of air to all cells in the stack, a certain minimum flow of air should be supplied to the stack. This limits the value of the ratio and fraction of design current for constant value of y. The minimum flow of air supply required by the stack is generally higher than the minimum possible air that the compressor can supply. The effect of limiting the air supply to a minimum value, as discussed in section 5-1-2, is that the value of y must be increased beyond its design value to achieve lower fractions of current. Thus the value of one of the model inputs y is also governed by the air distribution limitations in the stack. /correctcorrectdesignmm Figure 5-8 shows the variation of y with the change in fraction of design current when an Allied Signal compressor is used to pressurize the stack. It was assumed that the minimum value of the ratio of corrected mass flow rate of air, required by the stack was 0.3. Here again, the value of y stayed constant for fractions of design current greater than 0.3. When, the value of the fraction of design current decreases below 0.3, the value of y increases. Figure 5-9 shows the variation of with fraction of stack current. The ambient conditions and design parameters like depleted air temperature, and y /correctcorrectdesignmm excessM liquidoutM design and were assumed to be same as in case of Figure 5-7. It can be seen from Figure 5-9 that excessM decreases with the decrease in fraction of design current due to the change in pressure ratio for greater than 0.3. Until this point, the fraction of design current is equal to The value of y must be increased beyond its design value for fractions of design current lower than 0.3. The /correctcorrectdesignmm /correctcorrectdesignmm

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65 result as shown in Figure 5-9 is that excessM progressively decreases with the increase in y. Figure 5-10 shows the plots in Figures 5-7 and 5-9 super-imposed on each other. It can be seen that the value of starts decreasing earlier due to stack limitations. This is because the minimum mass flow rate of air required by the stack is higher than the minimum mass flow rate of stable operation of the compressor in this case. Thus the value y starts decreasing earlier due to stack limitations, resulting in an earlier drop of excessM excessM Change in fraction of excess air due to air distribution limitations0510152000.20.40.60.81Fraction of design currentFraction of excess air Figure 5-8. Change in fraction of excess air due to air distribution limitations for lower fractions of design current.

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66 exit air temp = 323K, amb press = 1 atm, ambient RH=0-6-5-4-3-2-10100.10.20.30.40.50.60.70.80.91fraction of design current/ design flow ratemass of excess water/ mass of water produced Figure 5-9. Excess water versus fraction of design current: air distribution limitation: sea level, intermediate depleted air temperature, liquidoutM =0 exit air temp = 323K, amb press = 1 atm, RH=0-7-6-5-4-3-2-10100.20.40.60.81fraction of design current/ design flow ratemass of excess water/ mass of water produced compressor limitation air distribution limitation Figure 5-10. Excess water versus fraction of design current: comparison of air distribution limitation versus compressor limitation: sea level, intermediate depleted air temperature, liquidoutM =0

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67 5.2 Effect of Non-Ideal Water Separator on Water-Balance Model Inputs An ideal water separator, having an efficiency of 100%, would separate all the liquid water from the depleted air. Hence the mass flow rate of un-recovered liquid in this case would be zero. In other words, the value of liquidoutM for an ideal water separator would be zero for all operating and ambient conditions. However, the efficiency of a realistic water separator is less than 100% as some liquid water cannot be recovered from the depleted air. The value of liquidoutM in this case would be greater than zero. Thus the value of an input to the water balance model, depends on the efficiency of the water separator device. liquidoutM 5.2.1 Relation between and liquidoutM In order to find a relation between liquidoutM and a separate control volume was drawn just around the water separator device. As explained in chapter 3, part of the liquid water separated from the depleted air is supplied back to the stack to maintain the humidity of the membranes. Let represent the mass flow rate at which liquid water is supplied back to the stack. The remaining portion is either discharged to the ambient or stored in a storage device at a mass flow rate of The mass flow rate of liquid water that could not be separated in the water separator is represented by Figure 5-11 shows the control volume drawn around the water separator and also indicates the various flow streams of water entering and leaving the control volume. The mass flow rate of water leaving the water separator and also the control volume is memm HOexcess2m liquidoutm

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68 HOexcess2m ++. The control volume around the water separator is assumed to be at steady state for the current analysis. Consequently, the mass flow rate at which liquid water enters the control volume equals the mass flow rate at which it leaves. The mass flow rate at which liquid water enters the water separator and hence the control volume is thus equal to ++. This can also be seen from Figure 5-11. memm liquidoutm HOexcess2m memm liquidoutm Figure 5-11. Mass flow rate of water entering and leaving the water separator and the control volume The efficiency of the water separator device may be defined as liquid water separated by the water separatorliquid water entering the water separator 5-8 Based on Figure 5-11, can be written as = memHOexcess2memHOexcessliquidout2mmmmm 5-9 Dividing the numerator and denominator with we obtain the following: HO-gen2m

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69 = memHO-gen2memHO-gen2(m/m)(m/m)excessexcessliquidoutMMM 5-10 Let be defined as the non-dimensional membrane flow term, represented by the variable Rearranging Equation 5-10 we obtain the following: memHO-gen2(m/m) memM liquidoutM = mem())excessMM (15-11 Equation 5-11 relates the non-dimensional un-separated liquid water term to the water separator efficiency in terms of the non-dimensional membrane flow and excess flow terms. In order to show the effect of using a non-ideal water separator on water balance, specific design of the fuel cell system was considered and the value of and calculated for a certain set of operating and ambient conditions. liquidoutM excessM 5.2.2 Design Case The value of is related to the water separator efficiency by Equation 5-11. The value of is given by Equation 3-9 and its value can be calculated from the model for known values of Substituting Equation 3-9 in Equation 5-11 we obtain the following: liquidoutM excessM liquidoutM liquidoutM = (1) 222222HO-inHO-outHO-inHO-out(1+)(1+)1 + 2(1-)2(1-)OmemOOyyM 2 5-12 Here, the values of 2HO-in and 2HO-out can be calculated using a procedure similar to the one described in chapter 3 when ambient conditions and depleted air temperature and pressure are provided as input. The values of y and 2O are inputs as in case of the model

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70 developed to calculate The value of excessM memM varies with the operating conditions and the design of the fuel cell stack and its auxiliaries. The current analysis assumes that the overall system was designed such that the ambient air entering the stack first is pressurized and heated up to depleted air pressure and temperature respectively. The air then is humidified to 90% relative humidity after which it contacts the electrodes and participates in the electrochemical reaction. It was also assumed that humidifying the ambient air to 90% relative humidity at depleted air temperature and pressure ensures that the membranes reach a steady state and dont lose or gain any water. The mass flow rate at which water is supplied back to the stack () is equal to the mass flow rate of water required to humidify the ambient air to 90% relative humidity at depleted air temperature and pressure. The value of can be determined for a given set of ambient and operating conditions and can also be calculated. memm memM liquidoutM As can be seen from Equation 3-5, the mass flow rate of water entering the control volume in the form of vapor, as a part of the ambient air is HO-in22222wHO-inHHO-inm(1+y)N[2(1O )] where 2HO-in is the mole fraction of vapor present in the ambient air. Ambient air that is pressurized and heated to depleted air conditions and humidified up to 90% relative humidity shall be referred to as humidified air in the rest of the analysis. Let 2HO-90% represent the mole fraction of vapor present in the humidified air. As this process of humidification takes place before the electrochemical reaction, the mass flow rate of dry

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71 air remains the same before and after humidification. Based on Equation 3-5 the mass flow rate of water flowing through the stack as a part of the humidified air is 2humid2wHO-90%H2HO-90%(1+y)Nm2o(1) 5-13 The mass flow rate at which liquid water should be supplied to the stack, in order to humidify the ambient air (), is the difference between memm HOin2m and and is given by humidm memm = 2222HO-90%HO-inwH2HO-90%HO-in(1+y)N2o(1)(1) 5-14 From Equation 3-9 and 5-14 memM = 2222HO-90%HO-in2HO-90%HO-in(1+y)2o(1)(1) 5-15 The value of o 2 for ambient air is usually 0.21 and y is one of the inputs. The mole fraction of vapor in ambient air, 2HO-in as explained in section 3.1, is calculated from Equation 3-10. In order to calculate the value of 2HO-90% the modified saturation pressure of vapor in the humidified air (p 2 ) corresponding to depleted air temperature was calculated using the Poynting effect. The procedure to calculate p 2 is the same as explained in section 3.1. As the relative humidity of humidified air is 90%, the partial pressure of vapor present in the humidified air (denoted as p humid ) is 0.9 times p 2. p humid = 0.9 p 2 5-16

PAGE 87

72 As mentioned earlier in section 3.1, the mole fraction of vapor present in moist air is the ratio of the fugacity of the vapor at its partial pressure to the fugacity of the vapor at the total pressure of the mixture. Thus 2HO-90% = f(p humid ,T 1 )/f(p t ,T 1 ) The value of 2HO-90% was input in Equation 5-15 to calculate memM The value of was input in Equation 5-12 to calculate the value of for a given set of design and operating conditions. memM liquidoutM The value of calculated using the procedure described above indicates the drop in the non-dimensional excess water term from its ideal value for the current design case and can be used to calculate liquidoutM excessM using model developed earlier in chapter 3. 5.2.3 Variation of for the Design Case excessM As explained earlier, the value of liquidoutM can be calculated for a specific design case where the value of was assumed to be equal to the mass flow rate of water required to humidify the ambient air to 90% relative humidity at depleted air temperature and pressure. The value of memm liquidoutM can be provided as an input to the model and the value of can be calculated for different ambient and operating conditions. excessM Figure 5-12 shows the plot excessM versus pressure ratio for the design case and compares it with the plot of excessM versus pressure ratio for the case where stays constant at 0. The efficiency of the water separator was assumed to be 90% (=0.9) and the ambient temperature, pressure and relative humidity were assumed to be 298K, 64.539 kPa (0.637 atmosphere) and 0% RH respectively. The depleted air temperature liquidoutM

PAGE 88

73 was assumed to have a value of 353K which corresponds to the case of an un-cooled stack and the value of y was assumed to be 0. Figure 5-13 is similar to figure 5-12 except that the value of depleted air temperature was dropped to 298K from 353K. A trend that is common to both the figures is that the difference between excessM for the design case and for the case where excessM liquidoutM =0 (difference is equal to the value of for the design case) stays approximately constant with the increase in pressure ratio for a constant value of y, and pressure ratio varying from 1 to 3. This effect results from a combination of two different factors. As mentioned in section 4.1, an increase in the pressure ratio increases the value of liquidoutM excessM and also the fraction of excess water that was not separated in the water separator, This effect tends to increase the value of with the increase in pressure ratio. An increase in pressure ratio also reduces the mole fraction of water present in air at 90% relative humidity corresponding to depleted air temperature and pressure ( -mliquidout liquidoutM 2HO-90% ). This reduces the amount of water required to be supplied back to the stack ( memM ) and hence decreases based on Equation 5-15. The net effect is that the value of remains more or less constant with the increase in pressure for the design case. This effect however is specific to the design case considered in Section 3.3. liquidoutM liquidoutM

PAGE 89

74 12000 feet; ambient RH =0; exit air temp=353K-1.2-1-0.8-0.6-0.4-0.200.20.411.522.53Pressure ratiomass of excess water/mass of wate r generated M_excess: M_liquid-out=0 M_excess: design case Figure 5-12. Variation of the excess water term with pressure ratio for =0 and the design case: high elevation, high depleted air temperature liquidoutM 12000 feet; ambient RH =0; exit air temp=298K00.20.40.60.811.21.41.611.522.53Pressure ratiomass of excess water/mass of water generated M_excess: M_liquid-out=0 M_excess: design case Figure 5-13. Variation of the excess water term with pressure ratio for =0 and the design case: high elevation, low depleted air temperature liquidoutM

PAGE 90

CHAPTER 6 CONCLUSIONS To ensure adequate humidification of the membranes, a steady state condition must be achieved in which excess water is always generated. To find the quantity of excess water, a water balance analysis was carried out for a control volume that circumscribed the fuel cell stack and most of its auxiliaries. The results of the analysis may be summarized as follows: A water balance model was developed that was able to calculate the excess water quantity when ambient conditions and design parameters fraction of excess air, exhaust gas pressure and exhaust gas temperature were provided as input. The sensitivity to each model input determined. The model developed was independent of the design of the fuel cell system in the sense that any combination of equipment or sub-system choices that lead to the same set of values of design parameters would yield the same result. The model was used to calculate the values of excess water rate for different ambient and operating conditions. Based on the results of the model it can be concluded that Pressurizing the fuel cell stack or cooling the stack exhaust, or both, is recommended in order to achieve water balance in a PEM fuel cell operating at high altitudes when ambient air relative humidity is low. The rate at which excess water is produced increases with the increase in depleted air pressure for all ambient and design conditions. The rate of excess water increases with decreasing depleted air temperature for all ambient and design conditions An increase excess air decreases the rate of excess water production when ambient air relative humidity is zero. When the ambient relative humidity is greater than 75

PAGE 91

76 zero, the trend of excess water rate versus excess air depends on the relative humidity of ambient air and depleted air pressure. The non-ideal nature of various components and sub-systems affects the design parameters of the fuel cell system, and hence the inputs to the water balance model. To study the limitations imposed by a non-ideal air handling system on model inputs, the performance characteristics of an Allied Signal air compressor, typically chosen for fuel cell systems, were studied. Based on the study it was concluded that For a pressurized stack, the pressure ratio (and hence depleted air pressure) developed by a non-ideal compressor decreases with the decrease in the current generated by the stack. As a result, the rate at which excess water is produced decreases with the drop in stack current. Thus low-power and idle conditions represent the most difficult water balance challenge. Due to limitations imposed on the mass flow rate of air delivered by the compressor, the fraction of excess air must be increased in order to achieve a drop in stack current beyond a certain limit. The result is that the rate of excess water production decreases when the stack current falls beyond that limit, even though the depleted air pressure may remain the same. Therefore, low-power conditions would be even more challenging, using the design choice for stack pressurization. To summarize, a fuel cell stack operating at low power conditions may encounter water balance problems at near-dry ambient conditions. To study the effect of a non-ideal water separator on model inputs, a control volume analysis of the water separator was carried out. Based on the analysis it was determined that One of the inputs to the water balance model, the mass flow rate of liquid water that could not be recovered by the water separator, is directly proportional to the efficiency of the water separator. A decrease in the efficiency of the water separator decreases the rate at which excess water is produced, provided other operating parameters and design conditions are constant. Hence, it can be concluded that the efficiency of the water separator affects the water balance in the fuel cell system.

PAGE 92

CHAPTER 7 RECOMMENDATIONS Based on the water balance analysis and its results, the following recommendations are being made for future work pertinent to the current area of study. The water balance model discussed in this study was able to determine those operating conditions where water balance is not achieved. It is recommended that various options to improve water balance should be analyzed in order to determine the optimum choice for each set of operating conditions where water balance is not achieved. Here optimum choice refers to an option which results in maximum efficiency of the overall system. Once the optimum choices for various operating conditions have been determined, different control schemes for various drive cycles should be formulated. These control schemes should be designed in a manner such that for a given set of ambient parameters and load conditions, the controller would vary the operating parameters of various equipments to achieve water balance in the most efficient manner. The current study does not take into account the effect of flooding. It is recommended that a parametric study be carried out on various fuel cells to determine the maximum value of the excess water rate beyond which flooding becomes more prominent in PEM fuel cells. The current water balance model is independent of the design of the system. It is only limited to the hydrogen oxidation reaction that take place inside the fuel cells. With minor modifications, the model can be applied to other energy conversion processes that involve oxidation of hydrocarbons to produce water. It is recommended that such an exercise be carried determine the potential of these energy conversion cycles to produce potable water along with electricity. The excess water generated by the fuel cell system can be used to cool the stack and the water separator. A thermodynamic analysis of such an arrangement can be carried out to provide inputs to the water balance model in order to determine the operating conditions under which water balance is achieved at steady state. The effect of non-ideal nature of heat exchanger can also be considered in this study. 77

PAGE 93

LIST OF REFERENCES 1. Ebbing, D., General Chemistry, 3 rd edition, Houghton Mifflin, Boston, 1990. 2. Atkins, P.W., Physical Chemistry, 3 rd edition, W.H. Freeman and Company, New York, 1986. 3. EG & G Services Parson, Inc., Fuel Cell Handbook, 5 th edition, U.S. Department of Energy, National Energy Technology Laboratory, Morgantown, 2000. 4. Kordesch, K.V., Survey of Carbon and Its Role in Phosphoric Acid Fuel Cells, Report Prepared for Brookhaven National Laboratory, 1979, BNL 51418. 5. Betts, D., Modeling and Analysis of Fuel Cell Engines for Transport Applications, Masters Thesis, University of Florida, Gainesville, 2000. 6. Yu, X., Zhou, B. and Sobiesiak, A., Water and thermal management for ballard PEM fuel cell stack, Journal of Power Sources, in press, 2005. 7. Haraldsson, K. and Alvfors, P., Effects of ambient conditions on fuel cell vehicle performance, Journal of Power Sources, in press, 2004. 8. Markel, T., Haraldsson, K. and Wipke, K., An analysis of water management for a PEM fuel cell system in automotive drive cycles, http://www.ctts.nrel.gov/analysis/pdfs/asme_rit_fc_conf_403_water_mgmt_paper.pdf accessed Gainesville, July 2005. 9. Stumper, J., Lohr, M. and Hamada, S., Diagnostic tools for liquid water in PEM fuel cells, Journal of Power Sources, 143 (2005), 150. 10. Kreuer, K.D., Vielstich ,W., Lamm A. and Gasteiger, H., Handbook of Fuel Cells Fundamentals, Technology Applications, Vol. 3, Part 3, John Wiley & Sons, Chichester, 2003. 11. Larmine, J. and Dicks A., Fuel Cell Systems Explained, 2 nd edition, John Wiley & Sons, West Sussex, 2003. 12. Gelfi, S., Stefanopoulou, A.G., Pukrushpan, J. T. and Peng, H., Dynamics of low-pressure and high-pressure fuel cell air supply system, IEEE Proceedings of American Control Conference, Colorado, 2003, 2049-2054. 78

PAGE 94

79 13. Cunningham, J. M., Air System Management for Fuel Cell Vehicle Applications, Masters Thesis, University of California, Davis, 2001. 14. Hussain, M. M., Baschuka, J. J., Li, X. and Dincer, I., Thermodynamic analysis of a PEM fuel cell power system, Journal of Power Sources, 44 (2005), 903. 15. Baschuk, J. J. and Li, X., Mathematical model of a PEM fuel cell incorporating CO poisoning and O2 (air) bleeding, https://www.inderscience.com/browse/index.php?journalID=13 accessed Gainesville, May 2005. 16. Kulp, G. W., A Comparison of Two Air Compressors for PEM Fuel Cell Systems, Masters Thesis, Virginia Polytechnic Institute and State University, Blacksburg, 2001. 17. Stefanopoulou, A.G., Pukrushpan, J. T. and Peng, H., Control-oriented modeling and analysis for automotive fuel cell systems, Journal of Dynamic Systems, Measurement, and Control, 126 (2004), 14-25. 18. Ji, X., Lu, X. and Yan, J., Survey of experimental data and assessment of calculation methods of properties for the airwater mixture, Journal of Applied Thermal Engineering, 23 (2003), 2213. 19. Xiaoyan Jia and Jinyue Yana, Saturated thermodynamic properties for the airwater system at elevated temperatures and pressures, Journal of Chemical Engineering Science, 58 (2003), 5069. 20. Wark, K., and Richards, D.E., Advanced Thermodynamics for Engineers, 6 th edition, McGraw-Hill, New York, 1999. 21. Reynolds, W.C., Physical Properties of 40 Substances in SI, Stanford University Press, Stanford, 1979.

PAGE 95

BIOGRAPHICAL SKETCH Rohit Sharma was born in Ahmedabad, India, on the 30 th of April, 1980. Rohit completed his bachelors degree from Sardar Patel University, Gujarat, India, on July 2001 after which he joined Alstom Projects India Ltd. as a systems design engineer. Rohit worked with the organization for duration of two years after which he decided to pursue his masters degree in mechanical engineering. Rohit started working towards his masters at the University of Florida from the Fall of 2003. Later, he got the opportunity to be a part of the fuel cell lab under the guidance of Dr. W. E. Lear and Dr. James Fletcher. Upon completion of his masters in August 2003, Rohit plans to continue contributing to the energy industry and build on his knowledge and experience. 80


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WATER BALANCE CONSIDERATIONS IN MODELING OF PEM FUEL CELL
SYSTEMS
















By

ROHIT M. SHARMA


A THESIS PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE

UNIVERSITY OF FLORIDA


2005





























Copyright 2005

by

Rohit M. Sharma
































This document is dedicated to my parents who have supported me in all my endeavors















ACKNOWLEDGMENTS

First of all, I would like to thank Dr. William. E. Lear, the chairman of my graduate

committee, for providing me with an opportunity to work under his guidance as a part of

the fuel cell lab. Dr. Lear shared with me his extensive knowledge and always motivated

me to perform better. I would also like to thank Dr. James Fletcher, the co-chair of my

committee, for his efforts. It was fun working under his guidance as he shared a lot of his

experiences. I would also like to acknowledge Dr. Herbert Ingley for being a part of my

committee and for the time and support that he provided.

In addition, I would like to thank the members of the fuel cell lab and my friends

and colleagues for their support.

Above all I would like to express my gratitude to my parents for their unwavering

support and blessings.
















TABLE OF CONTENTS



A C K N O W L E D G M E N T S ................................................................................................. iv

LIST O F TA B LE S ......................................... ......... .. ........... ............ .. vii

LIST O F FIG U R E S .................. ............. ........................... ............... .. viii

N O M E N C L A T U R E .......................................................................................................... x i

ABSTRACT .............. .......................................... xiv

CHAPTER

1 IN TR OD U CTION ............................................... .. ......................... ..

1.1 F u el C ells B asics................................................. 1
1.2 T ype of Fuel C ells .......... ....... ............. ...... ........................ ............ ....... 3
1.2.1 Phosphoric A cid Fuel Cells (PA FC) ........................................ .................4
1.2.2 Alkaline Fuel Cells (AFC) ................................. ........................ ........ 4
1.2.3 Molten Carbonate Fuel Cells (MCFC)..................................................5
1.2.4 Solid O xide Fuel C ells (SO FC) ............................ .......... ....................5
1.2.5 Proton Exchange Membrane Fuel Cells (PEMFC) ....................................6
1.3 W after B balance in PE M Fuel C ells..........................................................................8
1.4 General Arrangement of PEM Fuel Cell and Auxiliary Systems...........................9

2 LITER A TU R E R EV IEW ......... ................. ..................................... ......................13

2.1 W after Balance in PEM Fuel Cells.................................. ......................... 13
2.2 Configuration of Fuel Cell Stack and Its Auxiliaries .......................................16
2.3 Different Models to Predict Properties of Moist Air at Elevated Temperature
and Pressure ............... ......... ....................... 19

3 WATER BALANCE MODEL ........... ..... ......... ................... 22

3.1 Expression for the Mass Flow Rate of Excess Water ........................... ........24
3.2 Procedure to Calculate M' 28
3.3 Model Validation ..............Calculate M .................................................................................... 3328
3.3 Model Validation......... ...... .. ........... ...............33

4 RESULTS AND DISCU SSION ........................................... .......................... 36



v









5 EFFECT OF CERTAIN NON-IDEAL COMPONENTS ON WATER BALANCE
M O D E L IN P U T S ............................................................................. ................ .. 4 9

5.1 Effect of a Non-Ideal Air Handling System on Model Inputs ............................49
5.1.1 Change in Pressure Ratio Developed by a Non-ideal Air Compressor
and Its Effect on W ater B balance ......................... ............. ............... .... 50
5.1.1.1 Performance characteristics of an Allied Signal compressor at
part load conditions............... .. ............................ 51
5.1.1.2 Relation for fraction of design current ..................... ..................54
5.1.1.3 Variation of M,,c, with fraction of design current for part load
operation of an Allied Signal compressor.................... .................... 57
5.1.2 Change in Fraction of Excess Air due to Compressor Limitations............61
5.1.3 Change in Fraction of Excess Air due to Air Distribution Limitations......64
5.2 Effect of Non-Ideal Water Separator on Water-Balance Model Inputs ...............67
5.2.1 Relation between M qud and r .......................... ..... ..................67
5.2 .2 D esign C ase ...................... ................................... ................................... 69
5.2.3 Variation of M 'xc. for the Design Case...............................................72

6 C O N C L U SIO N S ....................... .... .......................... ................ ...... ......... 75

7 RECOM M ENDATION S............................................................................ 77

LIST OF REFEREN CES ............................................................................. 78

BIO GRAPH ICAL SK ETCH .................................................. ............................... 80
















LIST OF TABLES


Table page

3-1 Comparison of different values of co at sea level .............................................. 34

3-2 Comparison of different values of co at 2250 meters......... ..................................34

5-1 Values of different parameters at the 10 selected operating points of an Allied
Signal com pressor .......................... ...... ...................... .. .. ... ... ...... ... 54
















LIST OF FIGURES


Figure p

1-1 Cell voltage v/s current density for a general fuel cell.3 .........................................3

1-2 General arrangement of PEM fuel cell and auxiliaries ................. ................10

2-1 General arrangement of fuel cell systems used by Haraldsson and Alvfors in
th eir an a ly sis ................................................................... 17

2-2 General arrangement of fuel cell systems used by Hussain et al.14 in their
a n a ly sis ................................................ ........... ................ 1 8

3-1 Control volume defined for the general arrangement of PEM fuel cell and
auxiliary systems .............. ..... ........... .. ....... .......... 22

3-2 Different flow streams of water crossing the control volume boundary ..................23

3-3 Comparison of model predictions with Hyland and Wexler data............................35

4-1 Excess water versus pressure ratio and fraction of excess air: sea level, very low
depleted air tem perature case ............................................................................43

4-2 Excess water versus pressure ratio and fraction of excess air: sea level, low
depleted air tem perature case ............................................................................44

4-3 Excess water versus pressure ratio and fraction of excess air: sea level,
interim ediate depleted air tem perature case ................................... .................44

4-4 Excess water versus pressure ratio and fraction of excess air: sea level, high
depleted air tem perature case ............................................................................45

4-5 Excess water versus pressure ratio and fraction of excess air: high altitude, very
low depleted air tem perature case ........................................ ........................ 45

4-6 Excess water versus pressure ratio and fraction of excess air: high altitude, low
depleted air tem perature case ...........................................................................46

4-7 Excess water versus pressure ratio and fraction of excess air: high altitude,
interim ediate depleted air tem perature case ................................... .................46









4-8 Excess water versus pressure ratio and fraction of excess air: high altitude, high
depleted air tem perature case .............................................................................47

4-9 Excess water versus pressure ratio and fraction of excess air: sea level, low
depleted air temperature, humid ambient air case................ ...............47

4-10 Excess water versus pressure ratio and fraction of excess air: sea level, low
depleted air temperature, humid ambient air case ...... ......................................... 48

4-11 Excess water versus pressure ratio for M',Iqd- =0 and M',d-ou =0.1: sea level,
high depleted air tem perature ....................................... ............... ............... 48

5-1 Compressor map of an Allied Signal compressor............................... ...............52

5-2 Excess water versus fraction of design current and fraction of excess air: sea
level, intermediate depleted air temperature, Mqudout =0 ...................... ........... 59

5-3 Excess water versus fraction of design current and fraction of excess air: sea
level, high depleted air temperature, M 'qudout =0 .............................. 59

5-4 Excess water versus fraction of design current and fraction of excess air: high
elevation, intermediate depleted air temperature, M' ,qdt =0..............................60

5-5 Excess water versus fraction of design current and fraction of excess air: high
elevation, high depleted air temperature, M quid out =0 ...........................................60

5-6 Change in fraction of excess air due to compressor limitations for lower
fractions of design current .......................... .................................. ............... 63

5-7 Excess water versus fraction of design current: compressor limitation: sea level,
intermediate depleted air temperature, M qudout =0 ...................................... ..... 63

5-8 Change in fraction of excess air due to air distribution limitations for lower
fractions of design current .......................................................................... .... ... 65

5-9 Excess water versus fraction of design current: air distribution limitation: sea
level, intermediate depleted air temperature, M' quidu=0 ...............................66

5-10 Excess water versus fraction of design current: comparison of air distribution
limitation versus compressor limitation: sea level, intermediate depleted air
tem perature, M d out = 0 ................................................................................... 66

5-11 Mass flow rate of water entering and leaving the water separator and the control
volume e ............. ...... ........................................ .......... ...... .. 68









5-12 Variation of the excess water term with pressure ratio for Mjqud out =0 and the
design case: high elevation, high depleted air temperature............................. 74

5-13 Variation of the excess water term with pressure ratio for MAquld out =0 and the
design case: high elevation, low depleted air temperature.............................. 74















KEY TO SYMBOLS
NOMENCLATURE




m mass flow rate of water

N molar flow rate

y fraction of excess air

M molecular weight

M' non-dimensional mass flow rate

p pressure

R gas constant

T temperature

a constant in Redlich-Kwong equation

b constant in Redlich-Kwong equation

g gibbs free energy

f fugacity

N rotational speed of a compressor

F faraday's constant

in number of cells in a fuel cell stack

n number of electrons transferred in an electrochemical reaction

I fuel cell stack current

v velocity










m mass flow rate of air

V Volume

A Area

Greek

0q relative humidity of ambient air

) specific volume

rl efficiency of water separator

o ratio of inlet air temperature to reference temperature in a compressor

6 ratio of inlet air pressure to reference pressure in a compressor

71 ratio of dimensional parameters of a compressor

x mole fraction

p density

Subscripts

H20-in water that enters the control volume

H20-out water that leaves the control volume

H20-gen water generated inside the control volume

H20-excess excess water leaving the control volume

mem water supplied back to the stack

liquid-out liquid water leaving the control volume along with exit air

design design point

excess excess water leaving the control volume

amb ambient

r ratio









t exit air properties

1 saturated exit air properties

2 modified saturated exit air properties

real real gas properties

liq liquid

c critical

correct corrected properties of gas

a actual properties of gas

humid properties of humidified air

H20 -90% properties of vapor present in 90% humidified air

dry dry conditions (relative humidity is zero)















Abstract of Thesis Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Master of Science

WATER BALANCE CONSIDERATIONS IN MODELING OF PEM FUEL CELL
SYSTEMS

By

Rohit M. Sharma

August 2005

Chair: W. E. Lear
Co-chair: J. Fletcher
Major Department: Mechanical and Aerospace Engineering.

In order for the potential of proton exchange membrane (PEM) fuel cells to be

realized for automotive applications, several important system-level issues must be

solved. One of the requirements placed on automobile engine operation is to operate

satisfactorily under a wide range of ambient conditions and power demands. Under some

combinations of temperature, altitude, and load, the mass rate at which liquid water is

recovered by the fuel cell system is less than the mass rate of water required to humidify

the membranes. Unless significant liquid water reserves are carried not an attractive

design option then the membranes will become dry, with potential catastrophic results.

In this study, an analysis is shown which allows the water discharge rate to be calculated

as a function of ambient conditions and operating parameters such as overall

stoichiometry, operating pressure and exhaust temperature. The analysis is design-

independent, in that specific design choices only affect the inputs to the model such as air

fuel stoichiometry and exhaust temperature and pressure parameters. The condition of









zero net water discharge is emphasized, since that corresponds to the boundary between

sufficient water and the catastrophic dry-out process. Results indicate that moderate-to-

high altitude operation will most likely require pressurization of the fuel cell stack.

The operating parameters of non-ideal components and subsystems change under

varying operating conditions, which imposes additional limitations on achieving water

balance. The effect of these limitations associated with the air delivery sub-system and

water recovery components has been studied by considering certain specific design and

equipment choices and analyzing their effect on water balance under varied ambient and

operating conditions. The results of this portion of study indicate that the efficiency of the

water recovery subsystem, in addition to ambient and operating parameters, affects the

water balance of the fuel cell system. The magnitude of this effect is however design

dependent and should be taken into account when considering a specific arrangement.

The effect of using a non-ideal air handling subsystem such as a centrifugal compressor is

that the water discharge rate reduces when the fuel cell operates at part load conditions;

however the effect is more profound for lower fractions of design load.















CHAPTER 1
INTRODUCTION

With a growing emphasis on the preservation of our environment, air pollution has

become a focus of concern. Significant contributors to air pollution are the conventional

vehicles that operate on petroleum. In the United States, they are responsible for over 60

percent of the carbon monoxide emissions and about 20 percent of greenhouse gas

emissions.

A conscious effort has been made over the past few decades to develop an alternate

fuel for transport applications. Use of hydrogen to operate a fuel cell promises to be a

clean and efficient solution to the problem. Fuel cell based vehicles have the potential of

producing lower emission than their petroleum based counterparts. However fuel cell

technology is still in its development stages and there are certain design issues that need

to addressed in order to ensure reliable and efficient operation under varied operating

conditions.

1.1 Fuel Cells Basics

Fuel cells produce electricity by utilizing the chemical energy released when

hydrogen combines with oxygen to form water. The overall reaction is as follows:

1
H2 + 02 H20 1-1
2

Hydrogen is supplied to the anode where it splits into H+ ions and electrons in the

presence of a catalyst. The electrons travel via the external circuit towards the cathode.

The charge that is transferred across the external circuit, for each mole of diatomic









hydrogen oxidized, is the product of the number of electrons transferred in the

electrochemical reaction, and the Faraday constant. The H ions migrate to the cathode

via the electrolyte where they combine with the oxidant and the electrons to form water.

Based on the Nernst equation,1 the potential generated by a fuel cell operating on

hydrogen is given by the following equation:

(2RT>lnr 1/2
E E R n PH2P 1-2
EnF) K PH O

where E is the EMF of the cell under standard conditions and its value is 1.229 V when

the product of the reaction is liquid water and 1.18 V when the product is gaseous water.2

The remaining part of equation 1-2 takes into account the change in the cell voltage from

its standard value due to changes in temperature of the reaction or change in partial

pressures of the reactants or the products. R is the universal gas constant, T is the

temperature of the reaction, n is the number of electrons transferred for each mole of fuel

utilized, F is the Faraday constant and PH2, po2 and PH2o are the partial pressures of

hydrogen, oxygen and water respectively.

Based on this expression and Equation 1-2, one would expect the value of voltage

developed by the fuel cell for different values of current to be constant at constant

operating pressure and temperature. However, the actual value of cell potential decreases

due to certain irreversible losses. These losses originate primarily from three sources: (1)

activation polarization (2) ohmic polarization, and (3) concentration polarization.3

Activation polarization is predominant at low current densities and is related to the rate of

the electrochemical reaction. Ohmic polarization losses take place due to the resistance

offered by the electrolyte to the flow of ions and the resistance to the flow of electrons










through the electrode material. Its value increases with the increase in current, mainly

because the resistance of the cell remains more or less constant over the entire range of

current. Concentration polarization is caused due to a concentration gradient that

develops near the electrode when the reactant material is consumed and the surroundings

are unable to maintain the initial concentration. It mainly results from the slow transport

of reactants/products to/from the electrochemical reaction site and has a more

pronounced effect at higher values of current.

The above-mentioned losses affect the voltage versus current characteristics,

defined as "polarization curve," of a fuel cell. Figure 1-1 shows a typical polarization

curve of a fuel cell.



Theoretical EMF or Ideal Voltage
Region of Activation Polarzation
(Reaction Rate Loss)
1.0- Total Loss

Conce-mrar.on Polanzarion
I I as Tranr t Loss)
Regior, c4.: O n-ric Polarzai.r,
0.5- IResstadr1 Loss'


Operation Voltage, V, Curve

Current Density (mA'cm2)
Figurel-1. Cell voltage v/s current density for a general fuel cell.3 (Source: EG & G
Services Parson Inc., Fuel Cell Handbook, 5th edition, U.S. Department of
Energy, National Energy Technology Laboratory, 2000)

1.2 Type of Fuel Cells

Different types of fuel cells are available as a potential source of clean and efficient

energy. Amongst the more common ones are alkaline fuel cell (AFC), phosphoric acid

fuel cells (PAFC), molten carbonate fuel cell (MCFC), solid oxide fuel cells (SOFC) and

proton exchange membrane cells (PEMFC). This section discusses in brief the above-









mentioned fuel cell types with a greater emphasis on PEM based fuel cells. It also gives

the rationale behind the popularity of PEM based fuel cell in automotive applications.

1.2.1 Phosphoric Acid Fuel Cells (PAFC)

Phosphoric acid fuel cells, as the name suggests, use phosphoric acid (H3P04) as an

electrolyte. These fuel cells operate at a temperature of around 2000C.

PAFCs, in general, are not very suitable for low to medium power automobiles

because of their low power to weight ratio and high operating temperatures which result

in longer system startup times. Moreover, the presence of a liquid electrolyte in the fuel

cell increases the chances of acid spillage and poses a limitation on the orientation of the

cell. However the electrolyte does not need humidification to maintain its conductivity.

These cells are generally used in stationary power applications and sometimes in large

vehicles such as buses where size and weight are not major limitations.

1.2.2 Alkaline Fuel Cells (AFC)

These fuel cells use an alkaline solution as an electrolyte, generally potassium

hydroxide (KOH) or sodium hydroxide (NaOH) with a concentration of 85 wt%. The

normal operating temperature of these fuel cells is around 2500C.

The main drawback of AFCs is that hydrogen and oxygen have to be supplied to

the cell in pure form. Another option is to supply "scrubbed fuel and oxidizer (air)" to the

anode and cathode respectively.5 This requirement makes the auxiliaries of the fuel cell

more complex and high in weight and volume. A high operating temperature means

slower system startup, costlier material of construction and complex manifolds and bends

that are added to the system due to the requirement of an active cooling system.

Moreover, as in case of PAFC, the liquid form of the electrolyte poses a limitation on the









orientation of the cell. The liquid electrolyte on the positive side does not need

humidification for efficient operation.

1.2.3 Molten Carbonate Fuel Cells (MCFC)

These cells use a mixture of molten alkali carbonates as an electrolyte. The

electrolyte is retained in a ceramic matrix of lithium aluminum oxide (LiAO02). These

fuel cells normally operate at a high temperature of around 600 to 700 OC.

From a commercial applications point of view, MCFCs have an efficiency

approaching 60% which is considerably higher than the efficiency of PAFCs. The

conductivity of the membranes of MCFCs is not dependent on the humidity of the

membranes. Moreover, these cells can directly use a high density hydrocarbon fuel.

However, very high operating temperatures make them unfavorable for use in automotive

applications like cars. These cells are more suited for stationary applications. When the

waste heat of these cells is utilized by a power plant to generated additional electricity,

the overall efficiency of the system reaches close to 85%.

1.2.4 Solid Oxide Fuel Cells (SOFC)

Solid oxide fuel cells use a non-porous ceramic compound, generally yttria-

stabilized zirconia (YSZ) as an electrolyte. These cells normally operate at a very high

temperature of about 1000 oC.

A high operating temperature gives these fuel cells the capability to internally

reform a hydrocarbon fuel to hydrogen. SOFCs like the fuel cell types discussed above

do not require water to maintain the conductivity of the membranes. Hence, overall water

balance of the fuel cell system does not affect its performance. Moreover, these fuel cells

are more resistant to impurities than any other fuel cell. The disadvantages of operating

close to 1000 OC are high thermal stresses that impose limitations on the construction









material and the design of its auxiliaries, slow system startup, heavier and costly

insulation and higher chances of material corrosion.

1.2.5 Proton Exchange Membrane Fuel Cells (PEMFC)

These fuel cells use a solid proton conducting membrane, generally made of

sulphonated fluro-polymers, as an electrolyte. One such commercially available product

is Nafion (DuPont). The electrolyte is sandwiched between two electrodes that are

made of platinum impregnated porous carbon. Platinum dispersed in the electrodes acts

as a catalyst and aids the electrochemical reaction. The back of the electrodes are

generally coated with a hydrophobic compound such as PTFE. The hydrophobic coating

on the porous electrodes removes water from the catalyst sites and aids the reactant gases

to diffuse onto the catalyst.

The normal operating temperature of PEM fuel cells is around 800C. Increasing the

fuel cell temperature shifts the polarization curve to higher values of voltage and thus

increases the cell performance. However, high operating temperatures dehydrates the

electrolyte and reduces its conductivity. Therefore PEM fuel cells are operated at a

temperature 200C less than the boiling point of water corresponding to the cell operating

pressure. Increasing the fuel cell pressure increases its reversible potential. However,

high operating pressures require higher compressor power.

The use of a solid electrolyte reduces the ohmic loses in the fuel cell and makes the

cell more compact. As a result PEM fuel cells have a high power to weight and power to

volume ratio. Moreover a solid electrolyte does not place a limitation on the orientation

of the fuel cell as there is no problem of electrolyte spillage. The operating temperature of

these fuel cells is much lower than the normal temperature of other fuel cell types. As a

result the heat removal system is much lighter and less complex in PEM fuel cell systems









than in other fuel cell types. It also reduces component wear and increases the available

range of materials for construction. This again decreases the size and cost of the system.

A lower operating temperature in comparison to other fuel cells results in comparatively

fast system startup time. Moreover these cells are able to sustain operation at high current

densities. All these advantages make PEM fuel cells more favorable for automotive

applications than other fuel cells.

Despite its advantages, PEM fuel cells have certain drawbacks that impose

limitations on the design of the overall system. Platinum, which is used as a catalyst, is

sensitive to CO poisoning. Carbon monoxide strongly bonds to platinum at temperatures

less than 1500C and makes them unavailable as catalysts. Hydrogen reformed from

hydrocarbons generally contains greater than one percent carbon monoxide, whereas, a

concentration of greater than 10 ppm of CO is able to poison the catalyst.5 Hence an

additional reactor to reduce the amount of CO in the fuel gas is required if hydrogen is

produced by an on-board fuel reformer.

Another drawback specific to automotive applications is fuel storage. Hydrogen if

stored on-board an automobile as pure compressed gas, must be carried along in large

volumes in order to achieve a reasonable travel distance. This is because of the low

density of hydrogen. Use of high density hydrocarbons, such as methanol, as fuel

decreases the storage volume but increases the cost and maintenance requirements of

installing an additional reformer. Moreover, adding a reformer increases the overall

weight of the fuel cell system. Hence a proper design choice must be made when

deciding on the mode of fuel supply.









Last but not the least, and probably the one of the more important drawbacks

related to PEM fuel cells, is maintaining water balance. This issue will be discussed in

depth in the following section.

1.3 Water Balance in PEM Fuel Cells

The conductivity of the proton exchange membrane is directly proportional to the

amount of water present in it. Absence of water in the membranes causes what is known

as 'membrane dry out', where the electrolyte stops conducting protons. On the other

extreme, too much water in the membranes causes flooding, where the pores in the

electrodes are blocked by water. Flooding of the electrode pores prevents the reactant

gases from coming in contact with the catalyst and hence inhibits the rate of the

electrochemical reaction.

The total water present in the fuel cell does not indicate the local condition of the

membranes. Even though sufficient water may be present in the fuel cell to humidify the

membranes, some parts of the membrane may be flooded while others may be deficient

or even dry. There are multiple reasons for this effect, of which the most common one is

the inability of the water generated at the cathode to diffuse towards the anode. This

makes the portion of the membranes near the cathode wet and the one near the anode dry.

Another reason is due to "electro-osmotic drag" where the H ions moving from the

anode towards the cathode pull water molecules along with them, making the anode dry.

In general, a drop in the quantity of water in the fuel cell stack indicates loss of water

content of the membranes. This condition should be avoided in all cases to prevent

membrane dry-out.

Water enters the fuel cell in the form of vapor as a part of the moist air supplied to

the cathode and sometimes along with the hydrogen, which may be humidified depending









upon the overall system design. Water is constantly generated, due to the electrochemical

reaction, at a rate which depends upon the amount of fuel used. The air leaving the fuel

cell entrains liquid water along with it and at times, depending upon the operating

temperature and pressure, evaporates water present in the membranes. Water is also lost

due to leakage in different components present in the overall system. The net water

present in the fuel cell and in the membranes thus depends on ambient conditions and

operating parameters such as air fuel stoichiometry and operating temperature and

pressure. Careful control of the governing parameters of water present in fuel cell is

imperative as excess or dearth of water hampers the stack performance.

This study examines the sensitivity of the controlling parameters of water content

of the overall fuel cell system. It also takes into account the effect of the non-ideal nature

of some of the auxiliaries of the fuel cell system such as the air delivery sub-system and

water recovery components on the controlling parameters of water balance. The

limitations imposed on the design of fuel cell systems due to uneven distribution of water

in the membranes or due to membrane flooding have not been considered in this study. It

is assumed that the fuel cell system is capable of getting rid of the additional water that

may be present throughout the membranes or in parts of it.

1.4 General Arrangement of PEM Fuel Cell and Auxiliary Systems

Figure 1-2 represents the most general arrangement of PEM fuel cell and its

auxiliaries from a broad perspective without going into the specifics of each component.

As shown, the hydrogen management system supplies hydrogen to the fuel cell stack. It

utilizes hydrogen either directly from compressed hydrogen cylinders or from the exit of

a reformer that reforms hydrocarbons like methanol. The rate at which hydrogen is

consumed by the stack depends on the current drawn from it, which in turn depends on










the load requirement. The main function of the hydrogen management system is to ensure

adequate supply of hydrogen to the stack and, depending upon the overall system design,

re-circulate the unused hydrogen, if any, back to the stack. The supply of hydrogen is

typically controlled using flow metering and regulating devices. The hydrogen

management system, depending upon the stack design, also humidifies hydrogen before

supplying it to the stack. Water for this purpose is supplied either by an external source or

as shown in Figure 1-2 from the Water Management System.




H20
re-circulated H2
YDROEN Depleted
H2 HYDROGEN H2 at-
2--- MANAGEMENT WATER
SYSTEM STACK H20 + air MANAGEMENT EXPANDER To ambient


HANDLING
SYSTEM
COOLING
SYSTEM
Excess
liquid water
STORAGE/
EXHAUST


Figure 1-2. General arrangement of PEM fuel cell and auxiliaries

Figure 1-2 also shows air being supplied to the stack by the Air Handling System.

The main function of the Air Handling System is to supply adequate, air for complete

oxidation of hydrogen in the stack. The air, before being supplied to the stack, may be

humidified, either by an external water source or with the help of the water management

system. In addition, the Air Handling System may pressurize the stack. Typical

equipment options for achieving this function include blowers, fans, compressors, or

ejectors.









The main function of the Water Management System is to recover liquid water

from the humid air leaving the stack that is depleted in oxygen, and supply part of it back

to the stack to maintain the humidity of the membranes, discharging the excess or storing

it. One way of achieving this function is by using a water collection device (e.g. a

knockout) that separates liquid water from the depleted air leaving the stack. An

alternative component is a humidity exchanger, which uses the depleted air leaving the

stack to humidify the air entering the stack via a semi-permeable membrane. The

membrane transfers water from its region of higher concentration (usually depleted air

leaving the stack) to the region of lower concentration (usually ambient air). In a

humidity exchanger, the excess water that could not be transferred to the air entering the

stack is either stored or is discharged to the ambient along with the air leaving the stack.

The humidified air that enters the stack via the humidity exchanger helps in maintaining

the humidity of the membranes. Thus the net result of using a water separator or a

humidity exchanger is the same.

A portion of the collected water, depending upon the overall design, is supplied to

other auxiliaries like the Hydrogen Management System, Air Handling System and the

Cooling System to aid their purpose.

The air leaving the stack is generally at higher pressure than ambient and is

partially depleted of oxygen. Once water is separated from this depleted air, its pressure

is reduced to ambient in an expansion device such as a valve or turbine. This device is

referred to as an expander in Figure 1-2.

Lastly, the Cooling System cools the air leaving the stack and, depending upon the

design choice, cools the stack itself, hence controlling the amount of water entering the






12


water management system in liquid form. This is typically achieved by using either a

passive cooling system or a separate refrigeration device.














CHAPTER 2
LITERATURE REVIEW

This chapter reviews literature relevant to the water balance issue in PEM fuel

cells. It also reviews some of the literature that, though not directly related to the water

balance issue, helped in building a water balance model, which is the focus of this study.

2.1 Water Balance in PEM Fuel Cells

As mentioned earlier, the net rate at which water is generated or depleted in the

fuel cell can be controlled by changing the various operating parameters like operating

temperature and pressure, and air stoichiometry. Research efforts focused on improving

the overall performance of the fuel cell system have also tried to determine either the

mass of water present in the membranes at any point of time, or rate at which excess

water is discharged from the fuel cell system.

Yu et al.6 developed a two phase model to analyze the effect of membrane

humidification on the overall performance of the stack. Air (moist or dry) and hydrogen

were assumed to follow ideal gas law at all times. The flow of water through the

membranes was considered as the sum of the electro-osmotic drag flux that is caused by

hydrogen ion drag, diffusion flux that is caused by water concentration gradient between

anode and cathode and convection flux that is caused by pressure gradient. The inputs to

the model included general parameters like operating temperature and pressure and air

fuel stoichiometry, and some membrane specific parameters like membrane charge

concentration and membrane permeability of water. The water content in the membranes

was calculated for different cases of inlet humidification and was provided as an input to









the overall model to calculate the effect on the polarization curve and stack temperature

of a Ballard Mark V stack both at steady state as well as at transient conditions. The

model developed to calculate the water content in the membranes, however, did not

consider those operating and ambient conditions that lead to progressive loss of water

from the membranes. Moreover the results of the model were specific to a particular

model of fuel cell stack.

Haraldsson and Alvfors7 used the ADVISOR software developed by National

Renewable Energy Laboratory to develop an overall model for the fuel cell system. The

model considered a specific arrangement of the stack and its auxiliaries that was assumed

to run a mid-size automobile. The overall system included a condenser that supplied

water to a storage device by condensing water from the air leaving the stack. The

ADVISOR software was able to calculate the amount of water condensed at various

ambient and operating conditions by using models developed for each system. The stack

was assumed to be pressurized using a twin screw compressor. The study analyzed the

effect of varying load conditions on water balance by calculating the change in the water

quantity of the storage device when the fuel cell based automobile was assumed to run

through the standard "New European Drive Cycle" (NEDC) at different altitudes and

ambient temperatures. The ambient conditions were supplied as inputs to the various

component models. The operating parameters were governed by the load conditions and

the choice of equipment, both of which were pre-decided. The result of the analysis

indicated that the quantity of water in the storage device increased over the drive cycle.

This result was, however, specific to the case when a particular design of the fuel cell

system and its auxiliaries was operated at the load conditions determined by NEDC. The









model did not consider continuous operation at those ambient conditions where water

balance could not be achieved. Moreover it did not focus on design parameters where

water balance would be achieved at all ambient conditions. Markel et al.8 later calculated

the variation in the quantity of water in the storage device for a similar arrangement of

the fuel cell systems, when the fuel cell based automobile would operate at two other

drive cycles, UDSS (Urban Dynamometer Driving Schedule) and US06 (the high-speed,

high-acceleration-rate driving profile).The results of this model indicated that water

balance was not achieved, both at cold start and hot start conditions, when the automobile

operated on the US06 drive cycle. This analysis, however, like the previous one, focused

on a specific arrangement of the fuel cell system. Moreover the results were specific to

certain load cycle and were un-able to determine the sensitivity of various design

parameters on water balance.

Stumper et al.9 calculated the mass of water present in the membranes from the

membrane ohmic resistance using known relationship between proton conductivity and

water content developed by Kreuer et al.10 The membrane resistance was calculated for

known values of stack current and overall resistance offered by the fuel cell and its

components, other than the membranes, like electrodes and plates. Resistance of a fuel

cell was measured for a particular fuel cell system using the membrane resistance and

electrode diffusivity (MRED) method, for several operating conditions. The membrane

wetness calculated by this method was specific to a fuel cell stack and its internals.

Moreover, the ohmic resistance of the cell internals changes over a period of time; hence

its value must be periodically measured to estimate the water quantity in the membranes.









It has been seen that various studies, including the ones discussed above, that focus

on the condition of the membrane, calculate either the mass of water present in the

membranes at any point of time, or rate at which excess water is discharged from the fuel

cell system, when particular designs of the fuel cell stack and its auxiliaries operate under

specific ambient and operating conditions. None of them have made an attempt to

determine the minimum system design requirements that can achieve water balance. The

current study achieves this end by keeping the water balance analysis independent of the

design of the fuel cell system.

2.2 Configuration of Fuel Cell Stack and Its Auxiliaries

This section contains a review of the literature on configurations of the fuel cell

auxiliaries that affect water balance. Figure 2-1 shows the general arrangement of the fuel

cell system considered by Haraldsson and Alvfors7 in their analysis. The ambient air is

pressurized before being supplied to the stack. In order to prevent localized dry-out and

in general maintain the water content of the membranes, both the reactants, air and

hydrogen, are humidified from a water reservoir before being supplied to the stack. The

water reservoir also supplies water to cool the stack. Water that is used as coolant is in

turn cooled by a radiator, similar to the one used in conventional automobiles. Water is

supplied to the reservoir from a condenser that condenses liquid water from the air

leaving the stack. The current arrangement ensures that the membranes remain moist,

provided that the water reservoir always contains liquid. Gelfi et al.12 and Cunningham13

considered a general arrangement, similar to the one described above, for their respective

studies.

Figure 2-2 shows the system configuration considered by Hussain et al.14 The

arrangement is similar to the one described above except that a separate coolant (other







17


than water) is used to cool the stack. The coolant in turn rejects heat to the ambient with

the help of a radiator. Cooling the stack, in general, helps condense liquid water from the

air leaving the stack. This condensed liquid water is used to humidify the reactants and

also heat the air entering the stack.



H: From Tanns Dome Loade Humidifier
Pressure
Air Intake Regulator


Air
L^""" W'~~" ^_ Water








Se Condenser


By-Pass
Fuel System
pg san t ------p d-eego--p b te- Theenrmal System
d b By-Pass and LiSse

Reservoir Cooling water
(de-ionozied)


Figure 2-1 General arrangement of fuel cell systems used by Haraldsson and Alvfors7 in
their analysis

Hussain et al.14 carried out exergy analysis of the overall system described above to

predict the gross and net power developed by the fuel cell system at various ambient and

operating conditions. The voltage developed by the stack was predicted using the model

developed by Baschuk and Li.15

The 1.2 kW Nexa fuel cell system developed by Ballard systems does not use a

pressurized stack. Water recovery from the air leaving the stack is achieved by a

humidity exchanger instead of a condenser or water separator. A humidity exchanger

uses a semi-permeable membrane to transfer water from its region of higher











concentration (usually depleted air leaving the stack) to the region of lower concentration


(usually ambient air). The ambient air, in turn, helps in maintaining the water content of


the membranes.


environment
C ntr ol vellm




( Humidifier







L---- ------------------------
Pressure tulaar I-






PEM
Fu--ell -------
17 k Electric wrk


0111on n ]Air

















Figure 2-2 General arrangement of fuel cell systems used by Hussain et al.14 in their
determines the rate at which liquid water leaves the fuel cell and affects the water balance
of the overall system. Thus a change in operating pressure of the stack affects the water
11 13 *






O"nviroarwnt 15 1
Car
-mdiaaoe -

L --^ r
to the environment


Figure 2-2 General arrangement of fuel cell systems used by Hussain et al.14 in their
analysis

A change in the operating pressure of the fuel cell stack varies the saturation


pressure of the moist air leaving the stack. The saturation pressure of the exhaust air


determines the rate at which liquid water leaves the fuel cell and affects the water balance


of the overall system. Thus a change in operating pressure of the stack affects the water


balance of the fuel cell system. The pressure ratio (or the operating pressure of the stack)


and the power consumption of a pressurizer vary with the change in load conditions. As


these performance characteristics vary with the type and model of equipment, selection of









the pressurization equipment is critical to the overall performance of the fuel cell in

general and water balance in particular.

Kulp16 compared the effect of using a centrifugal compressor as opposed to a twin

screw compressor, on the performance of a 60 kW PEM fuel cell stack. Actual

compressor maps were used to model the performance of each compression device under

varying operating conditions. A specific voltage equation that relates stack voltage to

current density, average stack temperature and average partial pressure of oxygen in the

stack was used to develop polarization curves of the stack. The study concluded that the

centrifugal compressor is more efficient than the screw compressor when a expander (a

turbine that supplies power to the compressor) is used in conjunction with the

compression device.

Cunningham13 used the performance characteristics of an Allied Signal centrifugal

compressor to develop a model for simulating the performance of the air supply system

used in fuel cell vehicle. The compressor map of an Allied Signal compressor was also

used by Peng et al.17 to develop a control oriented model of the fuel cell system. The

stack was modeled using polarization data of 75 kW fuel cell stack. The fuel cell

auxiliaries other than the compressor were modeled using conservation laws. The current

study also uses the performance characteristics of the same Allied Signal compressor

model to demonstrate the effect of using a non-ideal compressor on water balance.

2.3 Different Models to Predict Properties of Moist Air at Elevated Temperature
and Pressure

The air leaving the stack is generally at an elevated temperature and pressure and is

partially depleted of oxygen. Ji et al.18 compared the properties of moist air calculated

from different models with the experimental data. The results of this analysis concluded









that the accuracy of the ideal gas model decreases with the increase in pressure. Thus the

ideal gas law is not accurate enough to calculate the properties of moist air leaving a high

pressure stack and real gas models have to be used.

The real gas models studied by Ji et al.18 included the ideal mixing model that

considered moist air as an ideal mixture of two real gases, vapor and dry air. This model

was found accurate enough to calculate the properties of saturated vapor at pressures less

than 10 bar and temperatures above 280 K. Other real gas models studied by Ji et al. are

The model developed by Luks et al.18 that is accurate in a temperature range of

200 K to 600 K for pressures as high as 200 atmospheres.

Hyland and Wexler model18 accurate in temperature range of 173.15 K to

473.15 K for pressures as high as 50 atmospheres.

Model of Rabinovich and Beketov18 which is accurate to a temperature of 400K

and a pressure of 100 atmospheres.

The results of the study determined the Hyland and Wexler model to be more

accurate than the other models. Each of the above-mentioned models is based on the

virial equation of real gases and aims towards calculating the virial coefficients and cross

virial coefficients of the air vapor mixture. The equation of state developed by each of

these models are applicable to standard air having a composition of 21% oxygen and is

not applicable to moist air depleted in oxygen.

Xiaoyan and Jinyuel9 used the ideal mixing model to calculate the properties of

saturated moist air. Air and vapor were assumed to follow the modified Redlich-Kwong

equation. Henry's Law was used to calculate the mole fraction of vapor in moist air. One

of the inputs to the model was the total number of moles of moist air. This limited the






21


model to calculate the properties of moist air flow only when its molar flow rate or total

number of moles was known.

When the quantity of moist air is unknown, the mole fraction of vapor in moist air

can be calculated by using the ideal mixing model in conjunction with the Poynting

effect.20 This approach has followed in the current study to estimate the properties of

depleted and pressurized moist air leaving the stack.

















CHAPTER 3
WATER BALANCE MODEL

To analyze the effect of various operating parameters on the water balance of PEM


fuel cells, a control volume analysis was carried out for steady state operation of the fuel


cell system. As a part of the analysis, a control volume was defined for the most general


arrangement of PEM fuel cell systems. As shown in Figure 3-1, the fuel cell stack and


various systems, except the expander and storage device, are inside the control volume.

,--------------------------------------------

H20
re-circulated H2

H2a HYDROGEN
-- MANAGEMENT WATER Depleted
SYSTEM MANAGEMENT ar
STACK HO2 + air SYSTEM To ambient
I- EXPANDER
Air AIR Air
I HANDLING
SYSTEM
COOLING ----
SYSTEM -

Excess
liquid water
CONTROL VOLUME STORAGE/
EXHAUST


Figure 3-1. Control volume defined for the general arrangement of PEM fuel cell and
auxiliary systems

Water enters the control volume in vapor state as a part of the atmospheric air at a



mass flow rate ofmHo-n Water is generated inside the fuel cell (and hence the control


volume) as a result of the electro-chemical reaction where hydrogen reacts with oxygen


present in the ambient air to form water. In this study, it is assumed that the net hydrogen


(hydrogen supplied hydrogen re-circulated) entering the stack (and hence the control










volume) is completely converted to water by supplying adequate air to facilitate the

reaction. The net rate at which hydrogen enters the control volume depends on the current

drawn from the stack, which in turn varies with the varying load requirement. Hence, the


mass rate of water generation mH20-gg is a function of the current drawn from the stack. A


portion ofmH20-go depending upon the ambient and operating conditions, is entrained

along with the air that leaves the stack.


Inlet air 1 FUEL CELL STACK &

pressure)------
(Water supplied
back to the stack)
(Liquid water separated
from the outlet air stream)

To Storage Device
or exhaust
Control Vohllune
IIH20-excess


1xiHt0 +illiqnd-ct
Exit air


Figure 3-2. Different flow streams of water crossing the control volume boundary

The water collection/separation device separates liquid water, if any, carried along

with the air leaving the stack. Part of this liquid water is supplied back to the stack to

maintain the humidity of the membranes. The remaining portion (referred to as excess


water) leaves the control volume at a mass flow rate of mH2'-o.exc and is either discharged

to the ambient or stored in a storage device.










Water leaves the control volume in the form of vapor, at the rate of mH o.u,, as a

part of the air depleted in oxygen (referred to as depleted air) that leaves the control

volume after exiting the stack and other components such as a water separator. The air

leaving the control volume also carries along with it a portion of the liquid water, which


could not be separated in the water separator/collector, at a mass flow rate of m d-,t

For the current analysis, the control volume is assumed to be in steady state at all

conditions. Water needs to be constantly supplied to the membranes to maintain their

humidity level. From a global standpoint, the water used to humidify the membranes can

only originate from the hydrogen oxidation reaction or from humidity in the inlet air.

Hence, steady operation requires that the sum of those two sources be greater than the

rate at which water is lost as a part of the exhaust, both in liquid and vapor form. Thus the

mass flow rate of excess water should be greater than zero to achieve water balance at

steady state and prevent membranes from progressively drying out.

In order to determine the effect of various operating parameters on water balance,

an expression for the mass flow rate of excess water is required in terms of ambient and

design parameters. This expression would help in calculating the mass flow rate of excess

water for known values of operating conditions, which in turn would determine whether

water balance is achieved under those conditions. The sensitivity of the controlling

parameters of water balance could also be determined from this expression.

3.1 Expression for the Mass Flow Rate of Excess Water

The integral form of continuity equation for water inside the control volume is


t- PHOdV + jP (vdA) mO H2gen 3-1
CV CS










where pH20dV represents the rate of change of mass of water inside the control



volume, f PH20 (v d) represents the net rate at which water leaves the control volume
cs


and mH2 gen represents the rate at which mass is generated inside the control volume. As

the control volume is at steady state, the first term is zero. The second term, based on the

control volume shown in Figure 3-2, is

jpo (v dA)= m +m +m -m 3-2
SPH20 (vdA)= m H20-out h liquid out mH20-excess -H20-n 3-2
cs

The third term, the net rate at which water is generated inside the control volume,


is moH20g Thus Equation 3-1 can we written as


m H20-excess H20O-n H20-gen H20-out lquid-out 3-3


As explained earlier, when the value of m, H2oces is negative, the membranes will

eventually dry out.

The next step is to express the variables on the right hand side of Equation 3-3 in

terms of ambient conditions and design parameters of the fuel cell. The mass flow rate at


which water vapor enters the control volume as a part of ambient air, mH2-in depends on

the mass flow rate of ambient air supplied to the fuel cell which in turn depends on the

requirement of oxygen for the electrochemical reaction. The overall reaction inside the

fuel cell is as follows:

1
H2 + 02=> H20 3-4
2









Each mole of diatomic hydrogen (H2) supplied requires half a mole of oxygen (02) to

form one mole of water.

Let NH2 be the molar flow rate of diatomic hydrogen entering the control volume.

For full utilization of the fuel, the minimum required molar flow rate of oxygen is NH2/2.

Ify is the fraction of excess air supplied, then the actual molar flow rate of oxygen is

(1+y) NH2/2.

If XO2-dry is the mole fraction of oxygen in dry ambient air (often assumed to be

0.21) then the molar flow rate of dry ambient air entering the control volume is

(I+y)NH2
2Xo2-dry
Thus, the mass flow rate of water entering the control volume along with ambient

air in vapor form is

M H 20-n (I+y)NH2
mH20-n 3-5
H2- 2X -dry(1 ( H20-in


where H2-in is the mole fraction of water in the ambient air and Mw is the molecular

weight of water.

The molar rate of oxygen consumption inside the fuel cell is NH2/2 (assuming

complete conversion of hydrogen to water). Hence the molar flow rate of dry depleted air

leaving the control volume is

(l+y- XOdry)NH,
2XO,-dry









and the mass flow rate of water leaving the control volume (mH20 out ) is

S M XH20-out(l+y- X2 d)NH2
H2out 2X -dry ( H20-out 3-6

where ,Hz-out is the mole fraction of water in the depleted air.

As can be seen from Equation 3-4, for each mole of diatomic hydrogen utilized one

mole of water is produced. Thus the molar rate of water generation inside the control

volume is NH2 and the mass rate of water production is


mH20-e = M NH2 3-7

Substituting the expressions derived in Equations 3-5, 3-6 and 3-7 in Equation 3-3,

we find the mass flow rate of excess water produced as


+ {H, H2-L i (1+y)NH H20-out ( +y X02 )NH 3
mo-= N^ + Xo, -- (l--.,O--- ---~. mI ,d 3-8
mH20-ecess = M" NH2 2X, _dy ( >X2N 2XO2_ I-XH 2 lut Miquid-out 3-8


The mass flow rate of excess water was expressed in non-dimensional terms by

dividing Equation 3-8 by the mass rate of water produced (mH2o-gen


i H20-in (+Y) H20-out (' Y 02 )
So2 -dry (OH20-in) -2o2-dry (I H20-out) 3


Here, M'xcess is the non-dimensional form of the excess water rate and is equal to

the mass flow rate of excess water per unit mass rate of water produced. The term


mhqd-, mH20-gO represents the non-dimensional form of the mass flow rate of liquid water

carried along with the depleted air as it could not be separated or recovered. This term









shall be represented by variable M, qudout and shall be referred to as non-dimensional un-

recovered liquid water.


As explained earlier, when the value of mH2o, exe is negative, the membranes will


dry out eventually. It can be seen from Equations 3-8 and 3-9 a non-negative mH20-cess


would mean a non-negative value of Mx Ce as mH20- is always positive. Hence in order

to achieve water balance under steady state conditions and prevent the membranes from

drying out, the value of the non-dimensional term M'x... should be always positive. The

next section explains the procedure to calculate the value of M'.ess in order to determine

whether water balance is achieved at steady state for a particular set of ambient and

operating conditions.

3.2 Procedure to Calculate M'excess

Based on Equation 3-9, the inputs required to calculate the value of M'xc. are

H20n, Odry, XH20-out y and M'qrdout. Of these variables, XH20n and xz-, govern the

amount of water and oxygen present in the ambient air respectively and their values

depend on the ambient conditions. The other variables, XH0-out '1quid-out and y, are

independent, and their values depend on the design conditions. Thus the value of M'excess

can be calculated at different ambient conditions and design choices. A Matlab code

was developed that would calculate the value of M'xess for various inputs.

The value of x was assumed to be 0.21 in the current analysis. For all

terrestrial conditions, the properties of humid ambient air can be accurately calculated









using the ideal gas law."1 Thus ambient air at the inlet to the control volume was modeled

using the ideal gas law. Given this, XHo-in can be equated to the ratio of partial pressure

of water vapor to the total pressure i.e.


HO-m= 3-10
Pamb

Here, the relative humidity of ambient air 4 and the ambient pressure pamb depend

on the atmospheric conditions and are inputs to the model. The saturation pressure of the

vapor in the ambient air, ps was calculated using the Hyland and Wexler18 equation for

saturated vapor pressure which is given as follows:

log(ps) = (-0.58002206x104/Ta) + 1.3914993 (0.048640239.Ta) +

(0.41764768x10-4.Ta2) (0.14452093x10-7.Ta3) + (6.5459673.1og (Ta)) 3-11

The ambient temperature Ta was an input to the model. The ambient air properties,

namely pressure, temperature and relative humidity, define the humidity ratio of the

ambient air, which governs the amount of water entering the control volume. However,

ambient conditions are not commonly expressed in terms of its humidity ratio. Hence

pressure, temperature and relative humidity, which more commonly represent the

ambient air conditions, are used as inputs to the model. Any combination of the three

inputs that give rise to a particular value of humidity ratio will give the same result.

In order to calculate XH20-out, the properties of depleted air must be known. In the

current model, it is assumed that depleted air leaving the control volume is saturated.

Depleted air is usually at an elevated pressure and temperature. At explained earlier in

Chapter 2, the accuracy of the ideal gas model decreases with increasing pressure. For the









flow leaving the control volume, the current model uses the Redlich-Kwong (RK)20

equation for real gases for each of its constituents:

RTreal a
Real a 3-12
(Vreal-b) Vreal(Vreal+b)Tral

where real is the pressure of a real gas, Treal is its temperature and Vreal its molar volume

in. The symbols a, b and R are represent constants where R is the universal gas constant

R2T 25 RT
a = 0.42748 and b = 0.08664 3-13
P Pc

To and Pc are the critical temperature and critical pressure, respectively, of the real gas.

Xiaoyan and Jinyue19 used the Redlich-Kwong equation to model the properties of

pure vapor, nitrogen, oxygen and a mixture of all three gases for different mole fractions

of each component. The results of the model were compared with experimental data and

the accuracy of the model was found to be in the range of +0.45%. Thus the Redlich-

Kwong equation is considered sufficiently accurate to calculate the properties of depleted

air.

In order to calculate the properties of the vapor in depleted air, the temperature and

pressure of depleted air must be supplied to the model as an input.

Let ptbe the pressure of the depleted air at the exit of the control volume and pr

(compression ratio) be the ratio of depleted air pressure to ambient pressure. Thus

Pr = Pt/Pamb 3-14

The saturation pressure of vapor in the depleted air is different than the saturation

pressure of pure vapor at the same temperature due to the presence of non-condensable

dry air along with the vapor. In order to calculate the saturation pressure of the vapor in

the depleted air, the Poynting effect20 was considered. Following the Poynting effect,









pure water vapor is assumed to be in equilibrium with liquid water at the depleted air

temperature. State 1 be the state of the water vapor and liquid water mixture at the

depleted air temperature. The pressure of the vapor and the liquid at State 1 would thus

be equal to the saturation pressure corresponding to the depleted air temperature. Dry air

was now assumed to be added to the pure vapor at constant temperature until the total

pressure of the air-vapor mixture equals the depleted air pressure, pt. This would modify

the partial pressure of vapor which is still in the saturated condition. State 2 be the state

of the moist air and liquid water mixture after addition of non-condensable gases to water

vapor. The pressure of the liquid water at State 2, which is in equilibrium with the air

vapor mixture above it, would be equal to the depleted air pressure. The modified

saturation vapor pressure is calculated by equating the change in Gibbs free energy at the

liquid-vapor interface from State 1 to 2 when an infinitesimal quantity of non

condensable gases is added to a pure liquid vapor mixture at a constant temperature. This

gives the following equation:

dgliquid = dgvapor 3-15

where liquid and gvapor are the gibbs free energies of liquid and vapor respectively. As the

temperature of liquid and vapor does not change between State 1 and 2, dg = u.dp

Thus Equation 3-15 can be written as

(v dp)liquid = (v dp)vapor 3-16

Integrating between State 1 and 2, to calculate the total change in the gibbs free

energy at the liquid-vapor interface, the following equation is obtained.


vdp = (P2. V2) (P V 1)- fpdv = Vliq(Pt P) 3-17
p v 1









Here p2 represents the modified saturation pressure of the vapor at State 2, when the total

pressure of the air-vapor mixture is pt (depleted air pressure). The molar volume of liquid

water, v liq, is assumed approximately constant between State 1 and 2, and its value is

taken as 18.016x10-6 m3/mole.

As mentioned earlier the temperature T1 (temperature of the depleted air) is an

input to the model. The saturation pressure of pure vapor at the depleted air temperature

(pi) is calculated at temperature T1 using the Hyland and Wexler equation. The molar

volume of vapor at State 1 (v 1) is calculated by the R.K. equation with pi as the input.

The modified saturation pressure (p2) is expressed in terms of v2 using the R.K. equation

v2
and J pdv is also expressed in terms of V2, as V1 is known. As a result, Equation 3-17


takes the form

RT.v2 a-(v, b)R
RT.v2 a (p. v) RT.In v2 -b)
(v2 -b) (v2 +b)T' L (v b)
3-18
-r--bT052In/V2 b = (18.016xl 0-6)(Pl) 3-18
bT V2 (v, + b)

Except for V2 and pt all other variable in the above equation are known. The

depleted air pressure pt is one of the parameters that is varied in order to observe its effect

on the excess water produced and is hence an input to the equation.

For a particular value of pt, V2 is calculated iteratively by the code. The value of v2

is used to find the value of p2 (modified saturation pressure of vapor in the depleted air)

using the RK equation.

For developing the model, the mixture of dry air and vapor is considered to be an

ideal solution. Hence, the mole fraction of vapor in depleted air zH2o-ou is equal to the









ratio of the fugacity of the vapor at its partial pressure to the fugacity of the vapor at the

total pressure of the mixture,2 or

f(p,T,) 3-19
XH20-out f(pt,T1)
f(pt,T,)

In Equation 3-19, f(p2,Ti) is the fugacity of vapor at pressure p2 and temperature Ti

and f(pt,Ti) is the fugacity at pressure pt and temperature Ti. Fugacity of a gas that

follows Redlich-Kwong equation is given by20

Sb RT a ( 1 1 lnv+b3Y
S (v- b) (v -b) R (v + b) b v3-20

Equation 3-20 is used to calculate the value of f(p2,Ti), as v2 and T1 are already

known. The value of pt is input in the R.K. equation to determine the value of vt and the

value of f(pt,Ti) is determined using Equation 3-20. Consequently, XH20-out can be

calculated for different values of pt at a given value of Ti. From Equations 3-9, 3-10, and

3-19, M' x,, can be calculated when ambient temperature (Ta), ambient pressure (pamb),

ambient relative humidity (0), fraction of excess air (y), depleted air temperature (Ti),

M'iquid-out and depleted air pressure (pt) are provided as input. Of these inputs, y, T1,

M' ,quid-o and pt are design parameters, as their values can be varied using different

equipment choices and operating conditions.

3.3 Model Validation

In order to validate the accuracy of the water balance model developed above, the

results of the model were compared with the values calculated by the Hyland and

Wexler18 model, which has been accepted to be more accurate in comparison to other real

gas models for moist air.18 As the Hyland and Wexler model was not applicable for









depleted air, the water balance model was used to calculate the humidity ratio (co) of

ambient air and its values were compared with those calculated by the Hyland and

Wexler model for different ambient temperatures and pressures. Tables 3-1 and 3-2 show

the comparison of different values of co at sea level and 2250 meters. Figure 3-3

graphically represents the deviation of the values calculated using the model from the

readings calculated by the Hyland and Wexler model. It can be seen that the current

model based on R.K. equation, closely follows the Hyland and Wexler model and the

deviation in the value of co for different temperatures at two different elevations is less

than +5%.

Table 3-1. Comparison of different values of co at sea level
Sea level: 101.325 kPa
co (humidity ratio) Percent error
Temperature Current model v/s
temperature % RH Hyland and Current model based Current model v/s
(0C) yland and
Wexler model on RK equation Hyland and
Wexler readings
5 100 0.0054 0.0055 -1.59%
10 100 0.0076 0.0077 -1.15%
15 100 0.0107 0.0107 -0.28%
20 100 0.0147 0.0147 0.38%
25 100 0.0202 0.0199 1.42%
30 100 0.0273 0.0266 2.73%

Table 3-2. Comparison of different values of co at 2250 meters
Altitude 2250 meters : 77.058 kPa
co (humidity ratio) Percent error
Temperature Current model v/s
temperature %RH Hyland and Current model based Current model v/s
(0C) yland and
Wexler model on RK equation Hyland and
Wexler readings
5 100 0.0072 0.0072 -0.16%
10 100 0.0102 0.0101 0.89%
15 100 0.0142 0.014 1.24%
20 100 0.0195 0.0192 1.50%
25 100 0.027 0.026 3.69%
27 100 0.0303 0.0293 3.60%












Model Predictions versus Test Data for 100% Relative Humidity
and Nominal Ambient Pressures at Sea-Level and 2250 m


0.04
E

0.03


0.02


S0.01


5 10 15 23
Temperature (C)


25 30 35


Figure 3-3. Comparison of model predictions with Hyland and Wexler data


-*- Hyland-Wexler Data (Sea Level) -- Model Predictions (Sea Level)
Hyland-Wexler Data (2250 m) Model Prediction (2250 m)















CHAPTER 4
RESULTS AND DISCUSSION

In order to achieve water balance at steady state, the value of the non-dimensional

excess water term M'cx should be greater than zero. As seen previously in Chapter 3, the

dimensionless form of excess water M.ces, can be calculated when ambient temperature,

pressure and relative humidity and design parameters pressure ratio, depleted air

temperature, non-dimensional form of un-recovered liquid water M ,quid out and fraction

of excess air are provided as inputs. Of these inputs, the ones that can be controlled are

only the design parameters.

The ambient conditions and stoichiometry govern the amount of water entering the

control volume. For a given set of operating conditions, any increase in the humidity ratio

of the ambient air would bring more water into the control volume and hence would

increase the value ofM'ces,,. This can also be seen from Equation 3-9 in which an increase

in XH2O-n (the mole fraction of water in ambient air) increases the value ofM',,, As

ambient conditions cannot be controlled, the fuel cell must be designed for the worst

operating conditions which, from a water balance point of view, would be ambient air

with a relative humidity of zero. At completely dry ambient conditions, i.e., at 0=0,

SH20-n is zero for all ambient temperatures. Hence M n is independent of ambient

temperature at 0=0.









In addition to being able to operate under dry ambient conditions, fuel cell-driven

vehicles should be capable of operating at high altitudes (low ambient pressure). To

consider the effect of low ambient pressure on water balance, a maximum altitude limit

of 12,000 feet that corresponds to 64.539 kPa was considered in this study. An altitude of

12,000 feet is the more commonly accepted upper limit for high altitudes that is used by

fuel cell automobile manufacturers.

To analyze the variation of MAxce for dry ambient conditions (0=0), the Matlab

code was used to plot 3D graphs of MAxce. versus y and pr at different depleted air

temperatures and altitudes. For the initial part of the analysis, the value of Ml'qu,,dout was

chosen to be zero.

Figures 4-1 to 4-4 are the plots showing variation of M ~o,, at four different

depleted air temperatures at an ambient pressure of 101.325 kPa. Figures 4-5 to 4-8 are

similar to Figures 4-1 to 4-4 except that the ambient pressure is 64.539 kPa,

corresponding to an altitude of 12,000 feet, in all of these cases.

Figures 4-1 to 4-8 indicate that for a given excess air fraction, M'Xcss increases

with the increase in pressure ratio. An increase in depleted air pressure for a given

depleted air temperature decreases the humidity ratio of the depleted air and causes more

water to condense. Hence less water leaves the control volume as a part of the depleted

air and the excess water variable increases. This trend is seen at all ambient conditions.

Mathematically, an increase in depleted air pressure decreases the humidity ratio of

depleted air and hence the value of XH2o-out This in turn decreases the value of

[zXH2Oout(l+y- XO2)/2 xo2(1- Ho2ut)] and increases the value of M'CS, based on Equation 3-

9. This is the same as mentioned before.









A comparison of the values of MHx,, at different depleted air temperatures, in

Figures 4-1 through 4-4 for sea level and Figures 4-5 through 4-8 for 12,000 feet, shows

that a decrease in the depleted air temperature increases the value of MA A decrease in

the depleted air temperature when all other parameters are kept constant, decreases the

humidity ratio of the depleted air and causes more water to condense. Hence less water

leaves the control volume as a part of the depleted air and the excess water variable

increases. This trend is consistent under all ambient conditions.

An increase in the quantity of excess air for a given depleted air pressure decreases

the value of MA,, for the ambient conditions under consideration. The incoming or

ambient air is dry and takes in part of the water generated in the fuel cell to become

saturated. An increase in the fraction of excess air increases the mass flow rate of the

ambient air for a given water production rate. Thus more water is required to saturate the

incoming air, which in turn implies that a greater portion of the water generated leaves

the control volume as a part of the depleted air than as excess water. Consequently the

rate of excess water produced decreases. This trend, however, is specific to the ambient

conditions under consideration and changes completely for humid ambient cases.

It can be seen from Equation 3-9 that a change in the value of MI~ udout results in an

equal change in the value of MAc.ss The shape of a plot of M c,, versus any of the

controlling parameters, for a constant M, qud-out, remains unaltered for all values of

M',q dout This effect is indicated in Figure 4-11, showing Annx, versus pressure ratio for

MJqu,,d-o =0 and Miqud-out =0.1. The ambient temperature, pressure and relative humidity

were assumed to be 298 K, 1 atmosphere and 0%, respectively, and the depleted air









temperature was assumed to be 353 K. The values of Mq,,4out were assumed to stay

constant at 0 and 0.1 with the change in pressure, for both cases.

It can be seen from Figure 4-11 that the trend of variation of M .x,, does not change

with a variation in the value of Mquou The only effect, as mentioned before, is a drop

in the value of M'ce by an amount equal to M' ,quou An implication of this effect is that

if M' is negative (water balance not achieved at steady state) for M',qdout =0 under

certain operating conditions, water balance will never be achieved at those conditions for

all positive values of M'udou Thus analyzing the case of M' udou =0 determines those

values of design parameters where water balance cannot be achieved for all values of

M' udou It should be noted that the value M',uout cannot be less than zero as it is the

non-dimensional form of the amount of liquid water that could not be separated from

depleted air.

It can be seen from Figures 4-1, 4-2, 4-5 and 4-6 that, when operating at sea level

and even at 12000 feet, a depleted air temperature of 298K would produce excess water

even when the fraction of excess air is as high as 4, for M',qudout =0. A value of


M'qu d-out >0.75 would drop M'ces, below zero and pressurization may be needed in those

cases to achieve water balance. In general, pressurization of the fuel cell is not required

even at 12,000 feet for a maximum value ofy as high as 4 when M qudout <0.75. However,

depleted air temperatures as low as 298K for a fuel cell that operates close to 353K is

possible only when a refrigeration system cools the stack.

Figure 4-3 shows that when the depleted air temperature is increased to 323K at sea

level, water balance is not achieved at M,'qudou, =0 for an un-pressurized stack when the









fraction of excess airy increases beyond 2 In such cases, the fuel cell must be pressured

for all values of Mi, ,uIdout, to prevent membrane dry-out under continuous operation. An

increase in altitude to 12000 feet at a depleted air temperature of 323K drastically affects

the water balance as the system must be pressurized for excess air fraction beyond 1.

When the depleted air temperatures are as high as 353K, the fuel cell must be

pressured under all operating conditions to ensure production of excess water. Moreover

at 12000 feet, excess water is produced only at very high depleted air pressures and low

excess air fractions. Such operating conditions place significant constraints on system

design.

Figures 4-1 to 4-4 for sea level and Figures 4-5 to 4-8 for an altitude of 12,000 feet

indicate that an increase in depleted air temperature moves the constant excess air lines

on the M'xc versus pressure ratio plot closer to each other. This can be seen from

Equation 3-9. As ambient relative humidity is zero, XH20-n =0 hence Equation 3-9

becomes


M P 1 -L H20-out( l YX2)
excess l0 1 \ quid-out
2Xo2 (1 -H20-out ) ] qdout

An increase in depleted air temperature at dry ambient conditions increases the saturation

pressure of depleted air. Hence XH20-out increases and H20-out /(1 H20out) decreases. As

this term is the multiplying factor to the term (l+y- Xo2), any increase iny has a

comparatively lesser impact on M'xco for higher depleted air temperatures than for lower

ones. Thus the constant excess air lines move closer to each other for higher temperatures









at dry ambient conditions. As explained earlier, this trend would stay the same for all

values of Mi, qidou

So far we have observed the trend of variation of MAxces with respect to excess airy

for dry ambient conditions. The trend is not always same when the ambient air has a

relative humidity greater than zero. Figure 4-9 is again a plot of MAces, with operating

conditions the same as those in Figure 4-2 except that the relative humidity, D is 0.5

instead of zero. Comparing Figure 4-2 with Figure 4-9 shows that the excess water

produced at particular operating and ambient conditions is always greater for D=0.5 than

for D=0. This is in confirmation to the result mentioned earlier that an increase in the

ambient humidity ratio will increase the value of M'ss. As can be seen from Figure 4-9,

the quantity of excess water decreases with the increase in excess air up to a pressure

ratio of 2. Beyond a pressure ratio of 2, the pattern changes and the quantity of excess

water decreases with excess air. This phenomenon becomes clearer when we examine

Equation 3-9. Differentiating AM',, with respect toy, assuming constant M' iud-out we

obtain the following:

dM'ces / dy = ZH0-m /[2X02 (1 -H20- )] XH2-out /[2o2 (1 XH2out)] 4-1

When the mole fraction of water in the depleted air is greater than that in the

ambient air, the derivative of MAces, with respective toy is negative and an increase in

excess air decreases the quantity of excess water. The opposite effect is seen when

XH20-out is less than XH20-O Physically, when XH20-out is greater than XH20- some portion

of the water generated inside the fuel cell is required to saturate a unit mass of depleted

air. An increase iny increases the mass flow rate of excess air. Hence additional water









would be required to saturate the flow of depleted air. Consequently the amount of excess

water generated decreases.

When %H,0-out is less than H2o-ln, the amount of vapor present per unit mass of

ambient air is more than what is required to saturate a unit mass of depleted air. Hence,

upon pressurization, water is condensed from the air. An increase iny and hence an

increase in the mass flow rate of air results in more water being removed from the

depleted air. Hence the quantity of excess water increases. It should be noted that this

trend is valid for all values of Ml,, _o,,, provided its value is independent ofy.

In order to determine the set of values of design parameters for which water

balance is not achieved for all values of Ml,, o, under the worst case of dry ambient

conditions. Equation 3-9 (Section 3.1) was used. At MI,,,o,,=0, when D=0, %,2O,, = 0,

thus M, =1 zHO-out(+ y OZO) / 2 Water balance is not achieved at steady state

when M' <0, that is when

1 {ZH2O-out(l+Y 02)/2o,2(1- XH2-out)} < 0 4-2

For Z, = 0.21, the above inequality becomes


ZHo-out > 0.42/(1.21+ y) 4-3

The above inequality indicates a relation between H20o-ot (which depends on the

depleted air temperature and pressure) and excess airy. Figure 4-10 gives a plot of H20-out

versus y in which the region above the curve represents the operating conditions under

which excess water is not produced. Approximating depleted air to be an ideal gas











ZHzO-out is the ratio of the partial pressure of vapor to the total pressure of depleted air


( H2-out =P2/Pt). Hence water balance is not achieved for all values of Ml,, Iqu out when


P2/Pt > 0.42/(1.21+y) 4-4

For a non-pressurized system operating at sea level (pt=l atmosphere), when y=0,

p2<0.347 atm which corresponds to a saturation temperature of 346 K. When y increases,

the maximum limit of p2 decreases and the corresponding saturation temperature

decreases. Hence for a non-pressurized system operating at sea level, the maximum limit

of depleted air temperature is approximately 346 K (73 C). Similarly, for an altitude of

12000 feet, pt= 0.6368 atm and the maximum limit of depleted air temperature is

approximately 336 K.

Using Equation 4-4 one can thus determine the approximate maximum limit of

depleted air temperature for different operating and ambient pressure conditions.




Tamb (Kelvin):298 Inlet RH (fractions):O Exit air temp (Kelvin):283 Pamb (Pascals):101325.16
Pressure ratio varies from 1 to 3 and Excess air(fraction): varies from 0 to 4



,


0.956.-

E "Excess alr(fraction) 0.
Excess air(fraction) 0.
0 2 P Excess alr(fraction) 20
6" 09 -- Excess alr(fraction) 1 2


S -- Excess air(fraction) 3.
2 2.6 Excess air(fraction)43.6
15 21 --- 15 2 25 3
Excess air in fraction 0 1 Pressure ratio Pressure ratio


Figure 4-1. Excess water versus pressure ratio and fraction of excess air: sea level, very
low depleted air temperature case

















Tamb (Kelvin):298 Inlet RH (fractions):0 Exit air temp (Kelvin):298 Panmb (Pascals):101325.16
Pressure ratio varies from 1 to 3 and Excess air(fraction): varies from 0 to 4


35







352
8

72

65. "




2
1
ir infracion


0.
0
0.1
0


0
0


Excess


Pressure ratio


Pressure ratio


Figure 4-2. Excess water versus pressure ratio and fraction of excess air: sea level, low

depleted air temperature case


Tamb (Kelvin):298 Inlet RH (fractions):0 Exit air temp (Kelvin):323 Painb (Pascals):101325.16
Pressure ratio varies from 1 to 3 and Excess air(fraction): varies from 0 to 4


Excess air in fraction


Pressure ratio


2
Pressure ratio


Figure 4-3. Excess water versus pressure ratio and fraction of excess air: sea level,

intermediate depleted air temperature case


11 Ill II IIU


::
















Tamb (Kelvin):298 Inlet RH (fractions):0 Exit air temp (Kelvin):353 Pamb (Pascals):101325.16
Pressure ratio varies from 1 to 3 and Excess air(fraction): varies from 0 to 4


Excess air in fraction


Pressure ratio


Pressure ratio


Figure 4-4. Excess water versus pressure ratio and fraction of excess air: sea level, high

depleted air temperature case


Tamb (Kelvin):298 Inlet RH (fractions):0 Exit air temp (Kelvin):283 Pamb (Pascals):64539
Pressure ratio varies from 1 to 3 and Excess air(fraction): varies from 0 to 4


Excess air in fraction


15 2
Pressure ratio


Figure 4-5. Excess water versus pressure ratio and fraction of excess air: high altitude,

very low depleted air temperature case


095


09





08
s 08
E


0Pr ure ratio
Pressure ratio









46





Tamb (Kelvin):298 Inlet RH (fractions):O Exit air temp (Kelvin):298 Pamb (Pascals):64539
Pressure ratio varies from 1 to 3 and Excess air(fraction): varies from 0 to 4











07 Excess air(fraction) O
E0,07
S6 Excess air(fraction) 0.4
S-Excess air(fraction).0 8
0 --- -- ----- 06---- Excess air(fraction) 1.2
06 Excess air(fraction) 1.
0 4 0 Excess air(fraction) 2
~0 5 - -- -
Excess air(fraction) 2.4
4 Excess air(fraction) 2.8
E 3 04 ------------------------ Excess alr(fraction) 3.2
3 3 E Excess alr(fraction) 3.6
2 2 Excess air(fraction) 4
1 15 1 15 2 25 3
Excess air in fraction 1 Pressure ratio Pressure ratio





Figure 4-6. Excess water versus pressure ratio and fraction of excess air: high altitude,

low depleted air temperature case




Tamb (Kelvin):298 Inlet RH (fractions):0 Exit air temp (Kelvin):323 Pamb (Pascals):64539
Pressure ratio varies from 1 to 3 and Excess air(fraction): varies from 0 to 4









P I -I- F--I
0,


Excess alr(fraction) 0
5 Excess air(fraction) O 4
-1 Excess air(fraction)0 81
Excess air(fraction) 12
-1 --1 .. Excess air(fraction) 21 6
Excess air(fraction) 2
I I^Y '-'-*-."'"' ''-.---"'''"-- ,--^3 -I--'------i-- ----------- -- arfacon32
-2 Excess air(fraction) 2
4 -- --- Excess alr(fraction) 2
S____- Excess air(fraction) 3
2 2 6 Excess alr(fraction) 3 6
2 2 Excess air(fraction) 4
5 1 15 2 25 3
Excess air in fraction 1 Pressure ratio Pressure ratio





Figure 4-7. Excess water versus pressure ratio and fraction of excess air: high altitude,

intermediate depleted air temperature case
















Tamb (Kelvin):298 Inlet RH (fractions):0 Exit air temp (Kelvin):353 Pamb (Pascals):64539
Pressure ratio varies from 1 to 3 and Excess air(fraction): varies from 0 to 4


0,







Z
-40,
4

2 a c
1 "15
air in frrtin 0 1


7,^n


- Excess air(fraction).0
- Excess air(fraction) 0 4
- Excess air(fraction) 0 8
Excess air(fraction) 1 2
Excess air(fraction) 1 6
Excess air(fraction) 2
Excess alr(fraction) 2 4
- Excess air(fraction) 2 8
- Excess air(fraction).3.2
Excess air(fraction) 3 6
Excess air(fraction) 4


1 15 2
Pressure ratio


Pressure ratio


Figure 4-8. Excess water versus pressure ratio and fraction of excess air: high altitude,

high depleted air temperature case


Tamb (Kelvin):298 Inlet RH (fractions):0.5 Exit air temp (Kelvin):298 Pamb (Pascals):101325.16
Pressure ratio varies from 1 to 3 and Excess air(fraction): varies from 0 to 4


I 11 -




S 1
S105

E


Pressure ratio


----------

---- --- ,------ ---





1.5 2
Pressure ratio


Figure 4-9. Excess water versus pressure ratio and fraction of excess air: sea level, low

depleted air temperature, humid ambient air case


Excess


I 1.15.

1 1
1.05

E
095
0.96


I 08
f 0.85 ,





S21.5

o,.- ,, s.-, 0 1


-------


"' "' "~~""'


Excess air(fraction) 0
Excess air(fraction).0.4
Excess alr(fraction) 0.8
Excess air(fraction) 1.2
Excess air(fraction). 1.6
Excess alr(fraction) 2
Excess alr(fraction) 2.4 .......................
Excess air(fraction).2.8
Excess air(fraction) 3.2
E .- ...r .,-.' r :...
_ __ --_=. ..,,,,,, -_-t------


0 95


-1"


Excess air in ac in


E












xw-out versus y


0 05 1 1.5 2 2.5
y => fraction of excess air


Figure 4-10. Excess water versus pressure ratio and fraction of excess air: sea level, low
depleted air temperature, humid ambient air case


Figure 4-11. Excess water versus pressure ratio for MI', udou =0 and MI',q,,ido =0.1: sea

level, high depleted air temperature.


sea level: ambient RH =C: exit air temp=353K: y=0

0.8

0.6 -

0 0.4
C:
S 0.2
|: I '------ +---0

S1 2 3
a -0.2 M- n =0 1

a:
-0.4

0.6

S-0.8

-1
Pressure ralio















CHAPTER 5
EFFECT OF CERTAIN NON-IDEAL COMPONENTS ON WATER BALANCE
MODEL INPUTS

As mentioned previously in chapter 3, Mcen can be calculated from the water

balance model when ambient conditions and design parameters are provided as inputs.

The water balance model is independent of the choice of equipment. Any combination of

equipment that leads to a same set of values of the design parameters yields the same

result of Mc',, from the water balance model, for constant ambient conditions. Thus the

choice of equipment affects the inputs to the water balance model and not the model

itself.

The non-ideal nature of various components and sub-systems affects the design

parameters of the fuel cell system, and hence the inputs to the water balance model. The

effects on model inputs under varying operating conditions, when non-ideal air delivery

sub-system and water recovery components are a part of the PEM fuel cell system, have

been studied in this chapter.

5.1 Effect of a Non-Ideal Air Handling System on Model Inputs

The air handling system uses equipment like a blower or compressor to supply air

for the electrochemical reaction and if required pressurize the stack. The non-ideal nature

of the system varies certain operating parameters and hence affects the inputs to the water

balance model. The changes in the model inputs due to the non-ideal behavior of the air-

handling are as follows:









* Change in the depleted air pressure due to change in pressure ratio developed by a
compression device under varying operating conditions.

* Change in the fraction of excess air at part load conditions due to the in-ability of
the air supply device to reduce the mass flow rate of air below a certain limit.

* In ability of the air supply equipment to supply sufficient air quantity to all parts of
the stack for lower mass flow rates of air. This forces the air handling system to
maintain a minimum rate of air supply which results in an increase in the fraction
of excess air at part load conditions.

Each of the above-mentioned changes in the model inputs and the resulting impact

on water balance has been discussed in the subsequent sections of this chapter.

5.1.1 Change in Pressure Ratio Developed by a Non-ideal Air Compressor and Its
Effect on Water Balance

For a pressurized stack, the depleted air pressure depends on the pressure ratio

developed by the compression device. An ideal compressor would maintain a constant

pressure ratio at all operating conditions. However for a non-ideal compressor, the

pressure ratio and hence the depleted air pressure generally varies with the change in the

mass flow rate of air through the compressor. Changing depleted air pressure, pt, an input

to the model, changes the value X H2o-ou and hence the amount of excess water generated

by the system. Thus the extent to which pressurization affects water balance depends on

the pressure ratio achieved by the equipment at a particular rotational speed and air mass

flow rate. These performance characteristics vary with the type of equipment used and its

geometry. For the current analysis a centrifugal compressor developed by Allied Signal

Aerospace17 was considered. The change in pressure ratio and hence water balance of a

PEM based fuel cell stack was analyzed, when this device used for pressurization

operated at part load conditions. It was assumed that the pressure at a location just

downstream of the compressor was equal to the pressure of the depleted air.









5.1.1.1 Performance characteristics of an Allied Signal compressor at part load
conditions

The performance characteristics of a centrifugal compressor are generally

represented in terms of a compressor map which is a plot of pressure ratio versus

corrected mass flow rate at various corrected rotational speeds. Corrected mass flow

rate, morrc, is m'f-/(57j) and corrected rotational speed, Ncorrc, is N/ / where m' and

N are the actual mass flow rate of air and actual rotational speed of the compressor

respectively. The parameter e is the ratio of inlet air temperature to reference

temperature. The variable a is the ratio of inlet air pressure to reference pressure and 7, is

the ratio of dimensional parameters. The value of 7, is useful for comparing two different

dimensionally similar compressors. When the performance characteristic of a particular

compressor is analyzed, the value of 7, is 1.

Figure 5-1 shows the compressor map of the centrifugal compressor used in the

current analysis. The reference temperature and pressure for this Allied Signal

compressor are 298K and 101.32 kPa. The red markings on the plot are the actual

operating points at different rotational speeds and the blue lines are curefits to the data,

generated by Jensen and Kristensen nonlinear curve fitting method.24 These lines are

constant corrected speed lines and represent the variation of pressure ratio with corrected

mass flow rate for a particular rotational speed.

The green colored line on the left hand side of the map is the surge limit of the

compressor and the one on the right hand side indicates the stall limit. It is generally

recommended that centrifugal compressors should operate in the region between their

surge limit and the stall limit on the compressor map, which, in case of the Allied Signal










compressor, is between the two green lines. Operating outside this region would lead to

unsteady operation of the compressor.

4-







06 kRPM
2.5





1.5



10 kRM 100 kR Cone cted speeds
0.5 I I I I I
0 O1 0.02 003 004 0.05 0.06 007 0.08 009 0.1
Corrected flow (kg/sec)

Figure 5-1. Compressor map of an Allied Signal compressor. (Source: Control-oriented
modeling and analysis for automotive fuel cell systems, Pukrushpan J.T., Peng
H., and Stefanopoulou A.G. Figure modified to represent the operating line on
the compressor map)

The actual points on the map along which the compressor operates at various

speeds depend on the resistance offered by the system, (which in our analysis is a fuel

cell stack and its connecting piping) to which it is supplying compressed air. However,

the system resistance offered by a stack and its connecting piping can be varied by adding

one or more valves anywhere in the system and varying the closure of each valve or by

varying the pipe size. Hence an operating line on a compressor map defines the system

resistance offered at various operating conditions but does not limit it to a particular

stack. In other words, the analysis is independent of the design of the fuel cell stack.









For the current analysis, the Allied Signal compressor is assumed to operate at a

margin of 15% from the surge limit. This means that at a particular rotational speed, the

mass flow rate of air through the compressor is 15% greater than the mass flow rate at the

surge limit corresponding to that rotational speed. It can be seen from Figure 5-1 that

when the operating point moves closer to the surge limit, higher pressure ratios can be

achieved for the same rotational speed. However, operating close to the surge line

involves the risk of the operating point crossing the surge limit, putting the compressor in

the regime of unsteady operation. It is due to these factors that the compressor was

assumed to operate at a 15% surge limit. The 15% surge limit line, which can also be

referred to as the operating line of the compressor, has been indicated by a solid red line

in Figure 5-1.

As shown in Figure 5-1, the constant speed lines for the compressor are plotted at

different corrected rotational speeds starting from 10 kRPM reaching up to 105 kRPM.

The design point of operation of the compressor in the current analysis is the one that lies

at the intersection of the operating line (15% surge limit line) and the 105 kRPM constant

corrected speed line. The fuel cell was assumed to produce maximum/design current

when the compressor operates at this point. For analyzing the effect of water balance

when the Allied Signal compressor is used as a compression device, 10 different points

along the operating line of the compressor were selected. These points also include the

design point of the compressor. They are indicated in Figure 5-1 as blue squares. The first

three columns in Table 5-1 indicate the values of various parameters like normalized air

flow rate, pressure ratio and corrected speeds at each of these points.









As mentioned earlier, the fuel cell is assumed to produce maximum current when

the compressor operates at its design point. A drop in the speed of the compressor along

the assumed operating line would reduce the mass flow rate and pressure of the air at the

inlet of the fuel cell. This can be observed from parameters at various operating points

depicted in Table 5-1. The current generated by the stack is directly proportional to the

mass flow rate of air entering the stack. As the normalized mass flow rate of air at the 10

operating points are known, these points can be represented in terms of fraction of the

design/ maximum stack current. The relation between stack current and normalized mass

flow rate of air is explained below.

Table 5-1. Values of different parameters at the 10 selected operating points of an Allied
Signal com ressor
Normalized flow Pressure ratio Corrected speed Normalized flow/ Design
(kg/s) (kRPM) normalized flow
0.014 1.033 20 0.1759
0.017 1.104 30 0.2132
0.025 1.237 40 0.3034
0.031 1.420 50 0.3782
0.038 1.641 60 0.4661
0.046 1.900 70 0.5629
0.055 2.248 80 0.6684
0.066 2.712 90 0.8135
0.078 3.195 100 0.9577
0.082 3.374 105 (Design point) 1

5.1.1.2 Relation for fraction of design current

The current generated in a PEM based fuel cell is given by the equation1

I= 4F No / f 5-1

where F is the faraday constant, n is the number of fuel cells in the stack and No, is molar

flow rate of oxygen in moles/sec that is effectively used by the fuel cell to produce water.

It can be seen from Equation 3-4 that the number of moles of hydrogen required to









produce water is twice the number of moles of oxygen. In other words NH2=2 N2 Hence

Equation 5-1 can be written as

I= 2F NH2 / i 5-2

Based on Equation 3-5, the molar flow rate of air entering the control volume and

eventually the fuel cell is equal to (+y)NH2 /2xo2. The molecular weight of ambient air

for a standard composition of 21% mole fraction of oxygen and 78% mole fraction of

nitrogen is 28.97. Hence the mass flow rate of air entering the compressor and eventually

the fuel cell stack can be represented by the equation.

(1+y)NH,
ma = 28.97 5-3
2Xo,

Comparing Equations 5-2 and 5-3 we can represent m' in terms of I as follows.

(l+y).I.n
ma = 28.97 y)5-4
4.F.Xo2

The value of ncell remains constant for a particular fuel cell stack and, F and Z,2 are

constants. Thus the ratio stack current to the design stack current can be represented by


ma (1 + yde~sgr,)
I/I 5-5
design 5-5
(1+ y) ma-des,g


Here, m,, I andy are mass flow rate of air, stack current and fraction of excess air


respectively at any operating point of the compressor. Variables m ade,,, Idesign and yde,

are the mass flow rate, stack current and fraction of excess air corresponding to the

design point of the compressor.










The corrected mass flow rate correct is given by m, -[ /(l67) For constant ambient

conditions, the values of o, 8 and 71 remain constant for the Allied Signal compressor.

Thus Equation 5-5 can be written as


correct (1 + degn)
I/Ie 5-6
I/Idesign 5-6
(1 + y) correct design


mcorrect-dei is the corrected mass flow rate at the design point.

Here y and Ydesign are inputs to the water balance model. The values of the ratio


mn correct /m correc,- ,d at all the 10 operating points have been indicated in the fourth column of

Table 5-1. Each of the 10 operating points can thus be indicated in terms of fraction of

design current provided, the value ofy at each of these points is known. The values of the

pressure ratios at these operating points can be used to provide input to the model and the

value of M'xl can be calculated for a given set ambient conditions and depleted

temperatures (Ti). Thus the variation of M' ,ss, when an Allied Signal compressor is used

and the stack current and fraction of excess air (y) change from their design values, can

be observed.

As explained in section 3.2 for the case when an Allied Signal compressor is used

as a compression device, M cess can be plotted as a function of fraction of design stack

current when y is known at all operating points and ambient conditions and depleted air

temperature is provided as input.









5.1.1.3 Variation of MA,,, with fraction of design current for part load operation of
an Allied Signal compressor

As explained earlier, the performance characteristics of an Allied Signal

compressor decide the values of depleted air pressure (an input to the model) when the

compressor operates at part load conditions. When the value ofy (another input to the

model) is known at all operating points of the compressor, MH,, can be plotted as a

function of fraction of design current. For the current analysis, it was assumed that the

value ofy does not change from its design value at all operating points of the compressor.

Figure 5-2 compares the plot of MH',, versus fraction of design current for an

Allied Signal compressor with that of an ideal compressor. The graphs are plotted for

different values of design excess air fraction designgn. The depleted air temperature (Ti)

was assumed to be equal to 323K and the ambient conditions were assumed as follows:

Ta = 298K, D=0, pamb=101325.16 Pa (sea level). The value of M'qud -out was assumed to

be zero. Figure 5-3 is similar to Figure 5-2 except that plots correspond to a higher value

ofT1 which is equal to 353K. Figures 5-4 and 5-5 are similar to Figures 5-2 and 5-3

respectively, except that the values of MA' were calculated assuming that the fuel cell

operates at 12000 feet instead of sea level (i.e. pamb=64539 Pa).

A few trends are common amongst all four figures. First one is that for an Allied

Signal compressor, M,, decreases along the constant excess air lines with the decrease

in fraction of design current. From Equation 5-5, when the value ofy remains constant at

its design value, the stack current is directly proportional to the mass flow rate of air. A

decrease in the fraction of design stack current decreases the mass flow rate of air

through the stack. A drop in the value of mass flow rate of air through the compressor









along its operating line decreases the pressure ratio across the stack. This in turn drops

the depleted air pressure. As explained in section 4.1, a drop in the depleted air pressure

decreases the value of HMx...o at all times. Thus HMce_ decreases with the decrease in stack

current. In comparison, the value of MH',,, for an ideal compressor stays constant, along

the constant lines, with the change in fraction of design current. This is because the

pressure ratio developed by an ideal compressor stays constant at all mass flow rates.

Another trend that is observed in Figures 5-2 through 5-5 is that an increase in the

value of design decreases the value of MA',c, both for an ideal and a non-ideal compressor.

The variation of MAl', with excess air fraction is governed by Equation 4-1. For the case

where D=0, the value of Mnen~ always decreases with the increase in the fraction of excess

air.

A third trend common to all four figures is that the value of Ml'xe, for the non-ideal

compressor, drops more rapidly, with the decrease in the fraction of design current, for

higher fractions of excess air than for lower ones. Moreover the difference between the

constant 'fractions of excess air' lines increases. A drop in the stack current results in a

lower depleted air pressure and hence a drop in the rate at which excess water is produced

for a unit mass of ambient air supplied. An increase in the value ofy increases the mass

flow rate of ambient air. As a result the drop in the rate of excess water production is

magnified and the constant fraction of excess air lines tend to move farther away from

each other. This can also be seen from Equation 3-9; a drop in the pressure ratio drops the

value of X H20out and henceM A' Now an increase in value y further magnifies this effect

resulting in steeper lines of constant. It should be noted that the trends described above







59


do not change for all values of M'quo, provided M ,iqudout stays constant all operating


points of the compressor.


exit air temp = 323K, amb press = 1 atm, RH=0, M'9_.t =0



1 .08
S-*-y=0:Allied compressor
S 06
) -A-y=2:Allied compressor
M 04 --W- y=4:Allied compressor
S2 -*- y=0:Ideal compressor
S- y=2:Ideal compressor
S0 ---y=4:ldeal compressor


fraction of design current/ design flow rate


Figure 5-2. Excess water versus fraction of design current and fraction of excess air: sea
level, intermediate depleted air temperature, M'quidout =0


exit air temp = 353K, amb press = 1 atm, RH=0 M'-,. =0


-*-y=0:Allied compressor
---y=2:Allied compressor
---y=4:Allied compressor
--y=0:ldeal compressor
---y=2:ldeal compressor
-- y=4:ldeal compressor


fraction of design current


Figure 5-3. Excess water versus fraction of design current and fraction of excess air: sea
level, high depleted air temperature, M qudout =0













exit air temp = 323K, amb press = 64539 Pa, RH=0 1 -t


-*-y=0:Allied compressor
-A-y=2:Allied compressor
---y=4:Allied compressor
--y=0:ldeal compressor
---y=2:ldeal compressor
--y=4:ldeal compressor


fraction of design current


Figure 5-4. Excess water versus fraction of design current and fraction of excess air: high
elevation, intermediate depleted air temperature, M'qud-out =0


exit air temp = 353K, amb press = 64539 Pa, RH=0 -MAI%-~ t


--y=0:Allied compressor
-A-y=2:Allied compressor
---y=4:Allied compressor
--y=0:ldeal compressor
---y=2:ldeal compressor
--y=4:ldeal compressor


fraction of design current


Figure 5-5. Excess water versus fraction of design current and fraction of excess air: high
elevation, high depleted air temperature, M'qud-out =0


0

-5

S-10
0-
-15

-20

-25









5.1.2 Change in Fraction of Excess Air due to Compressor Limitations

A drop in the mass flow rate of air through a non-ideal compressor decreases the

pressure ratio developed by it. Thus one of the inputs to the model, the depleted air

pressure, is governed by the characteristics of a compressor. This has also been seen in

section 5.1.1 for the case of an Allied Signal compressor. Most compression devices are

unable to maintain stable operation when the mass flow rate of air drops below a certain

limit. Hence it is recommended that the mass flow rate of air through a compressor


should not drop below a certain minimum value. This limits the ratio incorrectim correct- des, to a

minimum value. If the fraction of excess air is maintained at its design value at all

operating points of the compressor, the minimum mass flow rate of air through a

compressor corresponds to a minimum value of fraction of design current. Based on

Equation 5-6, if current must be dropped below this minimum value, y must be increased

above its design value. As the fraction of design current decreases the value ofy

increases. Thus the value ofy (another input to the model) under the condition of low

current is governed by the minimum mass flow rate of air that a compressor can supply

under stable operation. To summarize, the values of two of the inputs of the model

namely depleted air pressure and fraction of excess air are dependent on the performance

of the compressor.

Figure 5-6 shows the variation ofy with respect to the fraction of design current

when an Allied Signal compressor is used to pressurize a stack. The minimum ratio of


m correct/m ncorrect- des, for stable operation of the Allied Signal compressor is 0.176 which

corresponds to a pressure ratio of about 1. The value ofy is assumed to stay constant at

its design value of 0.8 until the ratio of m correct /mcorrect-de,,, drops to the minimum value of









0.176. A constant value ofy implies that the fraction of design current is equal to the ratio


m ectlm mco.ect- de,, based on equation 5-6. For fractions of design current lower than this

point, the mass flow rate of air stays constant and the value ofy increases from its design

value. Figure 5-6 shows that a drop in the fraction of design current below 0.176 results

from an increase in the value ofy. A zero current is never achieved in this case as it

would correspond to a value ofy reaching infinity.

Figure 5-7 shows the variation of Mc',, versus fraction of design current. The

ambient temperature, pressure and relative humidity were assumed to be 298 K, 1

atmosphere and 0% and the depleted air temperature was assumed to be 323 K. The value

of M'qudout was assumed to be zero in this case. It can be seen that for fractions of design

current greater than 0.176, the value of MAc'_ decreases due to a drop in pressure ratio.

When the fraction of design current increases beyond 0.176, the pressure ratio stays

constant at its minimum value of 1 and the value ofy increases (as shown in Figure 5-6)

An increase iny when ambient air relative humidity is zero, decreases the value ofMess

as seen in Figure 5-7.







63



Change in fraction of excess air due to compressor limitations


0 0.2 0.4 0.6 0.8


Fraction of design current



Figure 5-6. Change in fraction of excess air due to compressor limitations for lower
fractions of design current.



exit air temp = 323K, amb press = 1 atm, ambient RH=0



0 0
S01 02 03 04 05 06 07 08 09
2













E
U) 1









fraction of design current/design flow rate



Figure 5-7. Excess water versus fraction of design current: compressor limitation: sea
level, intermediate depleted air temperature, M'quid-out =0
level ie da depleted ---------air-----temperature,----qd out0









5.1.3 Change in Fraction of Excess Air due to Air Distribution Limitations

A conventional PEM fuel cell stack consists of a number of cells that are

electrically connected together. In order to ensure adequate supply of air to all cells in the

stack, a certain minimum flow of air should be supplied to the stack. This limits the value


of the ratio m ...orre/m ,orretdei,, and fraction of design current for constant value ofy. The

minimum flow of air supply required by the stack is generally higher than the minimum

possible air that the compressor can supply. The effect of limiting the air supply to a

minimum value, as discussed in section 5-1-2, is that the value ofy must be increased

beyond its design value to achieve lower fractions of current. Thus the value of one of the

model inputs y is also governed by the air distribution limitations in the stack.

Figure 5-8 shows the variation ofy with the change in fraction of design current

when an Allied Signal compressor is used to pressurize the stack. It was assumed that the


minimum value of the ratio of corrected mass flow rate of air, m orrect /m correc-des,,d, required

by the stack was 0.3. Here again, the value ofy stayed constant for fractions of design

current greater than 0.3. When, the value of the fraction of design current decreases

below 0.3, the value ofy increases. Figure 5-9 shows the variation of M,,A with fraction

of stack current. The ambient conditions and design parameters like depleted air

temperature, M qudout and design and were assumed to be same as in case of Figure 5-7.

It can be seen from Figure 5-9 that Mc,,, decreases with the decrease in fraction of design


current due to the change in pressure ratio for m correct/m dorrec-d, greater than 0.3. Until this


point, the fraction of design current is equal to m correct /m ,correc-,,d. The value ofy must be

increased beyond its design value for fractions of design current lower than 0.3. The









result as shown in Figure 5-9 is that Mxc,, progressively decreases with the increase iny.

Figure 5-10 shows the plots in Figures 5-7 and 5-9 super-imposed on each other. It can be

seen that the value of MAl,. starts decreasing earlier due to stack limitations. This is

because the minimum mass flow rate of air required by the stack is higher than the

minimum mass flow rate of stable operation of the compressor in this case. Thus the

value y starts decreasing earlier due to stack limitations, resulting in an earlier drop of


Change in fraction of excess air due to air distribution limitations

Change in fraction of excess air due to air distribution limitations


0 0.2 0.4 0.6 0.8
Fraction of design current


Figure 5-8. Change in fraction of excess air due to air distribution limitations for lower
fractions of design current.







66



exit air temp = 323K, amb press = 1 atm, ambient RH=0


fraction of design current/ design flow rate


Figure 5-9. Excess water versus fraction of design current: air distribution limitation: sea
level, intermediate depleted air temperature, Mqudout =0




exit air temp = 323K, amb press = 1 atm, RH=0



I 7 ----------- -------
M 0
// 02 04 06 08
00


-3

compressor limitation
S 4 air distribution limitation


fraction of design current/ design flow rate


Figure 5-10. Excess water versus fraction of design current: comparison of air
distribution limitation versus compressor limitation: sea level, intermediate
depleted air temperature, M'qudout =0










5.2 Effect of Non-Ideal Water Separator on Water-Balance Model Inputs

An ideal water separator, having an efficiency of 100%, would separate all the

liquid water from the depleted air. Hence the mass flow rate of un-recovered liquid in this

case would be zero. In other words, the value of M'qldout for an ideal water separator

would be zero for all operating and ambient conditions. However, the efficiency of a

realistic water separator is less than 100% as some liquid water cannot be recovered from

the depleted air. The value of M'qud ou in this case would be greater than zero. Thus the

value of M' quidout, an input to the water balance model, depends on the efficiency of the

water separator device.

5.2.1 Relation between M'qudout and 11

In order to find a relation between M' qud and l, a separate control volume was

drawn just around the water separator device. As explained in chapter 3, part of the liquid

water separated from the depleted air is supplied back to the stack to maintain the


humidity of the membranes. Let mmem represent the mass flow rate at which liquid water

is supplied back to the stack. The remaining portion is either discharged to the ambient or


stored in a storage device at a mass flow rate of mH2o- exe The mass flow rate of liquid


water that could not be separated in the water separator is represented by mqu, out. Figure

5-11 shows the control volume drawn around the water separator and also indicates the

various flow streams of water entering and leaving the control volume. The mass flow

rate of water leaving the water separator and also the control volume is







68



mH2o-cess + mmem + mqudout The control volume around the water separator is assumed to be

at steady state for the current analysis. Consequently, the mass flow rate at which liquid

water enters the control volume equals the mass flow rate at which it leaves. The mass

flow rate at which liquid water enters the water separator and hence the control volume is


thus equal to mH20-oece +mmem +miquid out This can also be seen from Figure 5-11.



---------------------1

Liquid water that could not get
separated in the laiockout
Liquid water entering knockout
S WATER -
SEPARATOR
IlH20-excess + 111liquid-out + 11lmem 11 liqud-out



Liquid water separated by
the knockout ControT Volume

11lHO-excess + lllmem



Figure 5-11. Mass flow rate of water entering and leaving the water separator and the
control volume

The efficiency of the water separator device ir may be defined as

liquid water separated by the water separator
r= 5-8
liquid water entering the water separator

Based on Figure 5-11, ir can be written as


m m.- + mH20excess 59
Il= 5-9

m m H20-excess liquid-out


Dividing the numerator and denominator with m' we obtain the following:
H20-gen











(mme /mH2oge )+M;.x. C 5-10
(m mem /mH2o-gen )+ excess + liquid-out


Let (mm, /mH2o-g, )be defined as the non-dimensional membrane flow term, represented

by the variable M' Rearranging Equation 5-10 we obtain the following:

M' m_ em + xcss)(1-) 5-11
lhquid-out


Equation 5-11 relates the non-dimensional un-separated liquid water term to the

water separator efficiency in terms of the non-dimensional membrane flow and excess

flow terms.

In order to show the effect of using a non-ideal water separator on water balance,

specific design of the fuel cell system was considered and the value of MZ quidout and


excess calculated for a certain set of operating and ambient conditions.

5.2.2 Design Case

The value of Mfqudout is related to the water separator efficiency by Equation 5-11. The

value of M' s. is given by Equation 3-9 and its value can be calculated from the model

for known values of M qudout Substituting Equation 3-9 in Equation 5-11 we obtain the

following:


M u- (1- t ) M +1 + XH20-in(Y) H205-12
2XI 02Xo2 H20-in ) 2Xo2 (1 H20-out) IJ


Here, the values of H20-in and XH20-ot can be calculated using a procedure similar to the

one described in chapter 3 when ambient conditions and depleted air temperature and

pressure are provided as input. The values ofy and X0 are inputs as in case of the model









developed to calculate M'. The value of Mm varies with the operating conditions

and the design of the fuel cell stack and its auxiliaries.

The current analysis assumes that the overall system was designed such that the

ambient air entering the stack first is pressurized and heated up to depleted air pressure

and temperature respectively. The air then is humidified to 90% relative humidity after

which it contacts the electrodes and participates in the electrochemical reaction. It was

also assumed that humidifying the ambient air to 90% relative humidity at depleted air

temperature and pressure ensures that the membranes reach a steady state and don't lose


or gain any water. The mass flow rate at which water is supplied back to the stack (mmem)

is equal to the mass flow rate of water required to humidify the ambient air to 90%

relative humidity at depleted air temperature and pressure. The value of Mmem can be

determined for a given set of ambient and operating conditions and Mqd-out can also be

calculated.

As can be seen from Equation 3-5, the mass flow rate of water entering the control

volume in the form of vapor, as a part of the ambient air is


mH20O-n = MH2,O-in (l+y)NH /[2Xo2 (1- XH,0-in)]
where XHo-in is the mole fraction of vapor present in the ambient air. Ambient air that is

pressurized and heated to depleted air conditions and humidified up to 90% relative

humidity shall be referred to as humidified air in the rest of the analysis. Let XH20-90%

represent the mole fraction of vapor present in the humidified air. As this process of

humidification takes place before the electrochemical reaction, the mass flow rate of dry









air remains the same before and after humidification. Based on Equation 3-5 the mass

flow rate of water flowing through the stack as a part of the humidified air is

Mw ZH20-90/o (1+y)NH
mhum,-d 5-13
2Xo2 (1- ZH20-90%) 5

The mass flow rate at which liquid water should be supplied to the stack, in order to


humidify the ambient air (mmem), is the difference between mH2-,- and m and is given

by


m m MW (l+y)NH H,20-90% H20-.n 5-1
mem 2xo2, (1- H20-90% ) 1 H20-in 5-14

From Equation 3-9 and 5-14


(1+y) H 20-90%o XH 20-mn
Mmem 2X02 (1- XH2090O ) (l_ 5-15


The value of X02 for ambient air is usually 0.21 and y is one of the inputs. The mole

fraction of vapor in ambient air, ,H2Om, as explained in section 3.1, is calculated from

Equation 3-10.

In order to calculate the value of xH-90%, the modified saturation pressure of vapor

in the humidified air (p2) corresponding to depleted air temperature was calculated using

the Poynting effect. The procedure to calculate p2 is the same as explained in section 3.1.

As the relative humidity of humidified air is 90%, the partial pressure of vapor present in

the humidified air (denoted as phumid) is 0.9 times p2.

humid = 0.9 p2 5-16









As mentioned earlier in section 3.1, the mole fraction of vapor present in moist air

is the ratio of the fugacity of the vapor at its partial pressure to the fugacity of the vapor

at the total pressure of the mixture. Thus

XH0z-90% = f(Phumid,Ti)/f(pt,T1)

The value of zHO-90% was input in Equation 5-15 to calculate Mmem.

The value of Mmem was input in Equation 5-12 to calculate the value of M ,qud-out for a

given set of design and operating conditions.

The value of M'qout calculated using the procedure described above indicates the

drop in the non-dimensional excess water term from its ideal value for the current design

case and can be used to calculate M'xces using model developed earlier in chapter 3.

5.2.3 Variation of M'xce for the Design Case

As explained earlier, the value of M _qud out can be calculated for a specific design


case where the value of mmem was assumed to be equal to the mass flow rate of water

required to humidify the ambient air to 90% relative humidity at depleted air temperature

and pressure. The value of M',qudout can be provided as an input to the model and the

value of M'ces can be calculated for different ambient and operating conditions.

Figure 5-12 shows the plot Mx ces versus pressure ratio for the design case and

compares it with the plot of M'ce versus pressure ratio for the case where Mqudout stays

constant at 0. The efficiency of the water separator was assumed to be 90% (rl=0.9) and

the ambient temperature, pressure and relative humidity were assumed to be 298K,

64.539 kPa (0.637 atmosphere) and 0% RH respectively. The depleted air temperature









was assumed to have a value of 353K which corresponds to the case of an un-cooled

stack and the value ofy was assumed to be 0.

Figure 5-13 is similar to figure 5-12 except that the value of depleted air

temperature was dropped to 298K from 353K.

A trend that is common to both the figures is that the difference between Mce for

the design case and HM',, for the case where Mqqud =out0 (difference is equal to the value

of Ml',qudouto for the design case) stays approximately constant with the increase in

pressure ratio for a constant value of y, and pressure ratio varying from 1 to 3. This effect

results from a combination of two different factors. As mentioned in section 4.1, an

increase in the pressure ratio increases the value of M' x- and also the fraction of excess


water that was not separated in the water separator, mihud-out. This effect tends to increase

the value of Mhq,,dt with the increase in pressure ratio. An increase in pressure ratio

also reduces the mole fraction of water present in air at 90% relative humidity

corresponding to depleted air temperature and pressure ( H,-90O% ). This reduces the

amount of water required to be supplied back to the stack (Mmem) and hence decreases

Mquid-out based on Equation 5-15. The net effect is that the value of M'quidout remains

more or less constant with the increase in pressure for the design case. This effect

however is specific to the design case considered in Section 3.3.







74



12000 feet; ambient RH =0; exit air temp=353K


- M_excess: M_liquid-out=0

-- M_excess: design case


Pressure ratio



Figure 5-12. Variation of the excess water term with pressure ratio for Mqud out =0 and

the design case: high elevation, high depleted air temperature



12000 feet; ambient RH =0; exit air temp=298K


1 1.5


-- M_excess: Mliquid-out=0

-A- M_excess: design case


2
Pressure ratio


Figure 5-13. Variation of the excess water term with pressure ratio for M _quidout =0 and

the design case: high elevation, low depleted air temperature


0.4

0.2

0

-0.2

-0.4

-0.6

-0.8

-1

-1.2


1.5 2.5


A A. A.














CHAPTER 6
CONCLUSIONS

To ensure adequate humidification of the membranes, a steady state condition must

be achieved in which excess water is always generated. To find the quantity of excess

water, a water balance analysis was carried out for a control volume that circumscribed

the fuel cell stack and most of its auxiliaries. The results of the analysis may be

summarized as follows:

* A water balance model was developed that was able to calculate the excess water
quantity when ambient conditions and design parameters fraction of excess air,
exhaust gas pressure and exhaust gas temperature were provided as input.

* The sensitivity to each model input determined.

* The model developed was independent of the design of the fuel cell system in the
sense that any combination of equipment or sub-system choices that lead to the
same set of values of design parameters would yield the same result.

The model was used to calculate the values of excess water rate for different

ambient and operating conditions. Based on the results of the model it can be concluded

that

* Pressurizing the fuel cell stack or cooling the stack exhaust, or both, is
recommended in order to achieve water balance in a PEM fuel cell operating at
high altitudes when ambient air relative humidity is low.

* The rate at which excess water is produced increases with the increase in depleted
air pressure for all ambient and design conditions.

* The rate of excess water increases with decreasing depleted air temperature for all
ambient and design conditions

* An increase excess air decreases the rate of excess water production when ambient
air relative humidity is zero. When the ambient relative humidity is greater than









zero, the trend of excess water rate versus excess air depends on the relative
humidity of ambient air and depleted air pressure.

The non-ideal nature of various components and sub-systems affects the design

parameters of the fuel cell system, and hence the inputs to the water balance model. To

study the limitations imposed by a non-ideal air handling system on model inputs, the

performance characteristics of an Allied Signal air compressor, typically chosen for fuel

cell systems, were studied. Based on the study it was concluded that

* For a pressurized stack, the pressure ratio (and hence depleted air pressure)
developed by a non-ideal compressor decreases with the decrease in the current
generated by the stack. As a result, the rate at which excess water is produced
decreases with the drop in stack current. Thus low-power and idle conditions
represent the most difficult water balance challenge.

* Due to limitations imposed on the mass flow rate of air delivered by the
compressor, the fraction of excess air must be increased in order to achieve a drop
in stack current beyond a certain limit. The result is that the rate of excess water
production decreases when the stack current falls beyond that limit, even though
the depleted air pressure may remain the same. Therefore, low-power conditions
would be even more challenging, using the design choice for stack pressurization.

To summarize, a fuel cell stack operating at low power conditions may encounter

water balance problems at near-dry ambient conditions.

To study the effect of a non-ideal water separator on model inputs, a control

volume analysis of the water separator was carried out. Based on the analysis it was

determined that

* One of the inputs to the water balance model, the mass flow rate of liquid water
that could not be recovered by the water separator, is directly proportional to the
efficiency of the water separator.

* A decrease in the efficiency of the water separator decreases the rate at which
excess water is produced, provided other operating parameters and design
conditions are constant.

Hence, it can be concluded that the efficiency of the water separator affects the

water balance in the fuel cell system.














CHAPTER 7
RECOMMENDATIONS

Based on the water balance analysis and its results, the following recommendations

are being made for future work pertinent to the current area of study.

The water balance model discussed in this study was able to determine those
operating conditions where water balance is not achieved. It is recommended that
various options to improve water balance should be analyzed in order to
determine the optimum choice for each set of operating conditions where water
balance is not achieved. Here optimum choice refers to an option which results in
maximum efficiency of the overall system.

Once the optimum choices for various operating conditions have been
determined, different control schemes for various drive cycles should be
formulated. These control schemes should be designed in a manner such that for a
given set of ambient parameters and load conditions, the controller would vary the
operating parameters of various equipment to achieve water balance in the most
efficient manner.

* The current study does not take into account the effect of flooding. It is
recommended that a parametric study be carried out on various fuel cells to
determine the maximum value of the excess water rate beyond which flooding
becomes more prominent in PEM fuel cells.

* The current water balance model is independent of the design of the system. It is
only limited to the hydrogen oxidation reaction that take place inside the fuel cells.
With minor modifications, the model can be applied to other energy conversion
processes that involve oxidation of hydrocarbons to produce water. It is
recommended that such an exercise be carried determine the potential of these
energy conversion cycles to produce potable water along with electricity.

* The excess water generated by the fuel cell system can be used to cool the stack
and the water separator. A thermodynamic analysis of such an arrangement can be
carried out to provide inputs to the water balance model in order to determine the
operating conditions under which water balance is achieved at steady state. The
effect of non-ideal nature of heat exchanger can also be considered in this study.















LIST OF REFERENCES


1. Ebbing, D., General Chemistry, 3rd edition, Houghton Mifflin, Boston, 1990.

2. Atkins, P.W., Physical Chemistry, 3rd edition, W.H. Freeman and Company, New
York, 1986.

3. EG & G Services Parson, Inc., Fuel Cell Handbook, 5th edition, U.S. Department of
Energy, National Energy Technology Laboratory, Morgantown, 2000.

4. Kordesch, K.V., Survey of Carbon and Its Role in Phosphoric Acid Fuel Cells,
Report Prepared for Brookhaven National Laboratory, 1979, BNL 51418.

5. Betts, D., Modeling and Analysis of Fuel Cell Engines for Transport Applications,
Master's Thesis, University of Florida, Gainesville, 2000.

6. Yu, X., Zhou, B. and Sobiesiak, A., Water and thermal management for ballard
PEM fuel cell stack, Journal of Power Sources, in press, 2005.

7. Haraldsson, K. and Alvfors, P., Effects of ambient conditions on fuel cell vehicle
performance, Journal of Power Sources, in press, 2004.

8. Markel, T., Haraldsson, K. and Wipke, K., An analysis of water management for a
PEM fuel cell system in automotive drive cycles,
http://www.ctts.nrel.gov/analysis/pdfs/asme ritfc conf 403 water mgmtpaper.p
df, accessed Gainesville, July 2005.

9. Stumper, J., L"ohr, M. and Hamada, S., Diagnostic tools for liquid water in PEM
fuel cells, Journal of Power Sources, 143 (2005), 150-157.

10. Kreuer, K.D., Vielstich ,W., Lamm A. and Gasteiger, H., Handbook of Fuel Cells -
Fundamentals, Technology Applications, Vol. 3, Part 3, John Wiley & Sons,
Chichester, 2003.

11. Larmine, J. and Dicks A., Fuel Cell Systems Explained, 2nd edition, John Wiley &
Sons, West Sussex, 2003.

12. Gelfi, S., Stefanopoulou, A.G., Pukrushpan, J. T. and Peng, H., Dynamics of low-
pressure and high-pressure fuel cell air supply system, IEEE Proceedings of
American Control Conference, Colorado, 2003, 2049-2054.









13. Cunningham, J. M., Air System Management for Fuel Cell Vehicle Applications,
Master's Thesis, University of California, Davis, 2001.

14. Hussain, M. M., Baschuka, J. J., Li, X. and Dincer, I., Thermodynamic analysis of
a PEM fuel cell power system, Journal of Power Sources, 44 (2005), 903-911.

15. Baschuk, J. J. and Li, X., Mathematical model of a PEM fuel cell incorporating CO
poisoning and 02 (air) bleeding,
https://www.inderscience.com/browse/index.php?journallD=13, accessed
Gainesville, May 2005.

16. Kulp, G. W., A Comparison of Two Air Compressors for PEM Fuel Cell Systems,
Master's Thesis, Virginia Polytechnic Institute and State University, Blacksburg,
2001.

17. Stefanopoulou, A.G., Pukrushpan, J. T. and Peng, H., Control-oriented modeling
and analysis for automotive fuel cell systems, Journal of Dynamic Systems,
Measurement, and Control, 126 (2004), 14-25.

18. Ji, X., Lu, X. and Yan, J., Survey of experimental data and assessment of
calculation methods of properties for the air-water mixture, Journal of Applied
Thermal Engineering, 23 (2003), 2213-2228.

19. Xiaoyan Jia and Jinyue Yana, Saturated thermodynamic properties for the air-
water system at elevated temperatures and pressures, Journal of Chemical
Engineering Science, 58 (2003), 5069-5077.

20. Wark, K., and Richards, D.E., Advanced Thermodynamics for Engineers, 6th
edition, McGraw-Hill, New York, 1999.

21. Reynolds, W.C., Physical Properties of 40 Substances in SI, Stanford University
Press, Stanford, 1979.















BIOGRAPHICAL SKETCH

Rohit Sharma was born in Ahmedabad, India, on the 30th of April, 1980. Rohit

completed his bachelor's degree from Sardar Patel University, Gujarat, India, on July

2001 after which he joined Alstom Projects India Ltd. as a systems design engineer.

Rohit worked with the organization for duration of two years after which he decided to

pursue his master's degree in mechanical engineering.

Rohit started working towards his master's at the University of Florida from the

Fall of 2003. Later, he got the opportunity to be a part of the fuel cell lab under the

guidance of Dr. W. E. Lear and Dr. James Fletcher. Upon completion of his master's in

August 2003, Rohit plans to continue contributing to the energy industry and build on his

knowledge and experience.