Modeling and Simulation of a PEM Fuel Cell Humidification System

Transcription

1 Modelg and Simulation of a EM Fuel Cell Humidification System Dongmei Cen Huei eng Department of Mecanical Engeerg University of Micigan, Ann Arbor, MI Abstract Matag proper fuel cell membrane umidification is a key callenge acievg optimal fuel cell performance. For automotive applications, te load and environment conditions are constantly cangg. erefore, te membrane umidity needs to be properly controlled durg transient. A umidifier system usg water vapor excange membrane is modeled and analyzed tis paper. e 4-state umidifier model is tegrated wit a fuel cell stack. Feedback and feed-forward control algoritms are developed so tat te fuel cell matas its igest membrane water content under a wide range of operation conditions wit floodg. I. INRODUCION olymer electrolyte membrane fuel cells (EMFC) ave drawn muc attention recent years. ey offer a igly efficient and environmentally friendly option for energy conversion []. ey are actively studied for commercial stationary power generation, residential applications and transportation tecnologies, especially ground veicle applications. EMFCs commonly employ ydrated Nafion films or oter ydrated perfluorated ionomeric materials as te electrolyte membrane [2]. ese membranes need to be properly ydrated order to acieve maximum performance and extended life. artial deydration of te membrane decreases te protonic conductivity and lead to creased resistive loss, decreased net power, and local ot spots tat may dramatically reduce te life of te membrane. On te oter and, if excessive water is present te membrane and/or te gas diffusion layer, a situation tat generally referred as floodg, te fuel cell performance will also be adversely affected due to te water blockage of te flow cannels, porous electrodes and backg layers [2]. erefore, water management was recognized as a critical issue for EMFCs performance. In addition, EMFCs for automotive applications operate a dynamic environment, were te power required from te fuel cells is constantly cangg because of te road conditions and te drivers beavior. e membrane umidity as to be controlled durg transient. ere were many papers te literature discussg te Correspondg autor, Associate rofessor, Department of Mecanical Engeerg, University of Micigan, Ann Arbor, MI , , peng@umic.edu fuel cell water management issues. A number of experimental studies were conducted to understand te water transport penomena and to caracterize te factors tat affect te membrane water content [3-6]. Innovative cannel designs ave been proposed to better mata te umidity [7, 8]. A number of matematic models ave been developed to optimize te fuel cell design to mata ig umidity [2, 9-4]. In addition, several types of umidifiers ave been designed and analyzed to enance te stack umidity [5-8]. All of tese works aimed to mata proper membrane water content for improved performance. However, te ma purpose of tese works is eiter to understand te system or to size te components. Few dynamic models tat are suitable for control purposes exist. Furtermore, te component and cannel sizg analysis results a design optimized around one stack current value, or te average of te wole fuel cell current range. is type of steady state analysis enables te fuel cell to acieve its peak performance wen it operates around te pots were te design is optimized. It does guarantee a good performance, owever, under oter operation conditions or durg transients. revious researc as found tat te membrane umidity is a function of water diffusion coefficient, electro-osmotic drag coefficient, water sorption isoterms, membrane conductivity and tickness [3, 2, 3, 9]. e membrane umidity is also affected by te fuel cell current, te temperature rise side te fuel cell, and te let gas umidity condition [2, 9, 2, 20, 2]. Wen te fuel cell is runng, te fuel cell current and steady-state temperature are determed by te stack power and te operation of auxiliary devices (e.g., coolg system). In addition, stack temperature significantly fluences te efficiency of te membrane and tus sould be tigtly regulated. e most feasible parameter tat can be used to control te membrane umidity is te let gas relative umidity, wic can be manipulated troug an let gas umidifier. is paper is focused on te development of a dynamic umidifier model, and te application of wic for fuel cell umidity control. e model presented tis paper captures te fluid flow dynamics, water excange troug te membrane, and te temperature dynamics of te umidifier. Unlike conventional umidifier analysis tat assumes steady state condition, tis model cludes te time varyg aspect of gas flow, temperature, pressure and gaseous and membrane RH. Simulations of te umidifier

2 are conducted to predict te beavior of te umidifier under transient conditions, especially wen tere is a sudden cange air flow, correspondg to variation of fuel cell stack current. A feedback control algoritm is developed to reject te effect of te disturbance. e umidifier model is subsequently tegrated wit a fuel cell system model. A feed-forward control algoritm is developed to compensate te current variation. Simulation results of te tegrated umidifier and fuel cell system sow tat a properly controlled umidifier could elp te fuel cell to acieve te best membrane umidity wit mimum floodg. II. ANALYSIS OF HUMIDIFICAION SYSEM ere exist several umidification mecanisms for EMFC applications. A simple metod tat as been widely adopted volves usg a spray nozzle to atomize coolant water tat leaves te power production section of te stack. e droplets are sprayed uniformly onto a clot or wire mes substrate. As te let air passes troug tese wet surfaces, it becomes more umid. If te air is not preeated, owever, te amount of water absorbed is let temperature dependent. Due to te fact tat te air temperature decreases as te water droplet vaporizes to te air, te effectiveness of subsequent layers decreases. erefore, te RH drops as te air enters te fuel cell stack and reaces te stack operatg temperature. Anoter simple tecnique commonly used for smaller stacks is to bubble te reactant gas streams troug eated bottles of water. Aga, te RH acieved is temperature dependent. Furtermore, a considerable pressure drop across te umidifier is common, wic requires iger let pressure. erefore, tis tecnique may not be suitable for low pressure fuel cells. In addition, bot of te above umidifiers are burdens te fuel cell system wit respect to weigt, complexity, cost and parasitic loss [8]. eir existence lowers te overall veicle efficiency. is is especially a big concern for ground transportation applications. In te effort to overcome te above sortages, An Entalpy Weel concept was developed [22]. It reuses te fuel cell exaust gas to umidify te dry let gas. Anoter umidification mecanism also recycles te exaust energy is te membrane umidification. is umidification metod was studied several previous works [6-8]. is paper will use fuel cell coolg water to umidify and crease te temperature of te dry gas. In tis approac, water diffuses from one side of te membrane to te oter side, were te gases flow parallel to te wet membrane. e water transfer is predomately determed by te water and gases flow rates (convective drivg force), membrane pressure differential (diffusive drivg force), membrane tickness, and te fluid temperatures. A umidifier cell is sown Fig.. ere are tree cannels eac umidifier unit: te umidification cannel marked wit A, a eat transfer cannel marked wit B, and a water cannel marked wit C, were te fuel cell coolg water passes troug. e dry let gas can be directed to go troug eiter cannel A or cannel B. Wen te let gas passes troug cannel A, bot eat and water vapor excanges wit cannel C will occur. On te contrary, wen te gas passes troug cannel B, only eat excange will appen. Dependg on te position of te slidg plate, te gas will be directed to go troug eiter cannel A to be umidified, or cannel B to be eated only. volume Grapite walls Water molecule Fuel cell coolg water B A C Slidg plate Membrane Dry gas Fig. : Structure of a umidifier cell Grapite wall volume 2 Based on te size and load of a fuel cell stack, te size and number of umidifier units can be calculated. Assumg tere are N umidifier units, te number of units designated as type A can be any number between 0 and N, dependg on te desired relative umidity of te exitg air. For example, if te desired umidifier let air relative umidity is 00%, te slidg plates are moved so tat all te gas goes troug te A cannels. Similarly, if te desired relative umidity is 0%, all te A cannels will be closed. In general, te number of cannel A will be 0 n N, and is calculated based on te fuel cell stack current, te desired relative umidity and te let air relative umidity and temperature. It sould be noted tat te autority of te umidifier reducg umidity is limited (or non-existent, if eat excange effect is ignores). For example, wen te let air as a non-zero relative umidity, we will not be able to get 0% relative umidity at te let even troug no cannel A is used. III. CONROL VOLUMES DEFINIION AND MODELING ASSUMIONS o derive te governg termodynamic equations, we first need to defe te control volumes of te umidifier system. For te umidifier design presented above, two control volumes are defed as sown Fig. 2. Volume cludes eiter Cannel A or Cannel B. Volume 2 cludes Cannel C. For Volume, te dry gas let mass flow rate, pressure, temperature, and relative umidity (RH) are denoted as M,,,,,, and Φ,, respectively. e gas let mass flow rate, pressure, temperature, and RH are denoted as

3 M,,,,,, and Φ,, respectively. If Volume cludes Cannel A, bot vapor transfer M tr and eat transfer Q occur. If Volume cludes Cannel B, only eat transfer Q occurs. For Volume 2, te water let mass flow rate, pressure, and temperature are denoted as M 2,, 2,, and 2,, respectively. e water let mass flow rate, pressure, and temperature are denoted as M 2,, 2,, and 2,, respectively. Water molecule volume M Φ M,,,, 2, 2, 2, M Φ,,,, Membrane M v, tr Q M 2, 2, 2, Fig. 2: volumes of one unit umidifier volume 2 e model assumptions are: ) e flows bot control volumes are fully developed lamar flows; 2) All gases follow te ideal gas law; 3) e umidifier units are well sulated from its surroundgs tus eat transfer only occurs across te membrane, between cannel A and C or B and C (wic are assumed to ave te same eat conductivity); 4) e ketic and potential energies of te gas molecules are neglected; 5) No external work is done to te system; 6) e flow specific eats are constant; 7) e overall convection eat transfer coefficient is constant; 8) e membrane water transfer is a function of water concentration and temperature gradients; 9) e nomal fuel cell coolg water temperature is assumed to be 80ºC; 0) Water is compressible; ) e followg let gas properties are te puts to te dynamic system: M,,,,,, Φ,, 2,, 2,, and 2,.. IV. HUMIDIFIER MODELING Apply te st law of termodynamics to Volume, te energy equation is [23] ma, ua, + m + m u + m tr u k, = Cvk, a, ua, + m u = Q+ ma, mem ma, a, m + m a, k, k 2 Cp = k mem, k 2 tr = Cpv were Cv a, Cv v, Cp a, Cp v are te specific eats of te air and vapor. Subscript k = a or represents air or vapor, represents Volume, tr represents membrane transfer, = or, representg let and let, respectively. It is also assumed tat mem equals 2,. () Apply te st law of termodynamics to Volume 2, te energy equation is m w,2cpw 2, Q+ m2, w, m2, w, m tr = (2) were w, k 2 Cp = w. Cp 2, k 2 w is te specific eat of water. Subscript w represents water, and 2 represents Volume 2. m a, and m are calculated from te mass contuity equation as m a, ma, ma, mem = (3) m m + m tr m = (4) m, k 2 = ma, k 2 + m k 2 (5) M ω v, = (6) M air a, ma, k 2 = mk 2, (7) + ω, k 2 Assumg te flow restriction between te umidifier let and te fuel cell let is described by a nozzle equation, m, can be calculated from m, = Cr, fc, were fc, is te fuel cell let pressure, and Cr is a constant wic canges wit orifice size and te gas density and can be obtaed troug experiments. m w, 2 can be calculated as m w,2 m2, m tr m2, (8) = (9) A vapor mass transfer m& vtr, occurs between te two control volumes and is calculated from [4, 20] C (246( )) 2 C m 303 w tr = Dw M v A Dw = Dλ e (0) tm were D w is te membrane coefficient of diffusion. C 2 and C are water concentrations Volume 2 and Volume, and are defed Eq. (2). t m is te membrane tickness. w is te membrane temperature Kel M v is te vapor molar mass. A is te mass transfer area (i.e., te membrane area). e coefficient D λ is determed empirically and as a piecewise-lear form [4, 20] 6 0 λ < ( + 2( λ 2)) 2 λ 3 D λ = () 0 6 (3.67( λ 3)) 3 < λ < λ *0

4 e water concentrations te water cannel and te gas cannel are ρm, dry C k3 = λ M k3 (2) m, dry were ρ m, dry is te membrane dry density and M m, dry is te membrane dry equivalent weigt. e subscript k 3 is eiter or 2, wic represent Volume and 2. Water content λ and λ2 are calculated from [4, 20] 2 3 v, λ = ( a 39.85a a ) a = sat, λ2 = 4 were. sat, (3) is te vapor partial pressure of Volume is te saturation pressure of Volume, and is determed by [4, 20] 2 5 2, ) log 0 ( sat = a, a, (4) a, 2.8 e vapor partial pressure of Volume is obtaed from te ideal gas law. v,v c = R v m v, a,v c = R a m a,, = + a, (5-7) were R a and R v are te air and vapor gas constant, V c is te volume of Volume, a, = a,, = v,. e eat transfer rate between te two control volumes can be calculated as [24] Q (8) = A 2 /η 0 were A is te eat transfer area, η 0 is te eat transfer efficiency, is te eat transfer coefficient defed as knud = (9) D were k is te membrane termal conductivity, N ud Nusselt number and D is te cannel ydraulic diameter. 2/ is te temperature difference between te water and te gas. For counter flow, ( w, g, ) ( w, g, ) 2 / = ln(( w, g, ) /( w, g, ) )) (20) e model, based on te equations listed above, is summarized as follows. e states are: x = m a m v,,, 2,. ossible measurements clude: y = Q m tr m,, Φ, m2,. e control put is: u = [ n]. e performance variable is: = mv tr N is z,, and te external disturbances clude: w = m,,, Φ, 2, 2, V. SIMULAION RESULS AND ANALYSIS Simulations are performed wit te assumption tat all te air goes troug A cannels. e results of cangg te let air condition are sown Fig. 3 and Fig. 4. Fig. 3 sows tat wen tere is a step crease te airflow rate, order to compensate te air flow crease, te membrane vapor transfer rate and te eat transfer rate bot crease wit some transient fluctuations. is transient effect adds more water to te let, and may cause floodg te fuel cell. Fig. 4 sows tat wen tere is a step decrease of te let air temperature, te eat transfer rate creases and te membrane vapor transfer rate decreases. e decrease and te transient fluctuations may cause te fuel cell to become deydrated. ese issues need to be addressed to mata fuel cell performance and life. 2, Fig. 3: System responses under step crease of te let airflow rate Fig. 4: System responses under step decrease of te let air temperature A simple proportional feedback control strategy is used ere to control n, te number of umidifyg cells, and te results are sown Fig. 5 and Fig. 6. Fig. 5 sows tat te large transient deviation vapor transfer rate is elimated by te feedback control strategy. Fig. 6 confirms tat te temperature disturbance does not affect te put variable under te feedback control.

5 fact more water is generated at catode at iger stack current, wile te catode let gas is (improperly) mataed at 00% RH. Obviously, proper control of te RH of catode let gas is necessary to prevent floodg. Fig. 5: System response wit and wit feed back control under step crease of te let airflow rate Fig. 7: Membrane water content under 4 let umidification conditions Fig. 6: System response wit and wit feed back control under step decrease of te let temperature VI. HUMIDIFIER AND FUEL CELL INEGRAION e umidifier model is tegrated wit te dynamic fuel cell model developed [2], wic was based on te Ford 2000 experimental veicle. e fuel cell membrane water content is described by te followg equation [4, 20] a m 39.85a m a m 0 < a m λ m= (2) 4 +.4( a m ) < a m 3 were a ca + a a an m =, a ca and an 2 a are catode and anode RH respectively. Sce te membrane water content is a function of te RH of te anode and catode gases, teir relationsip is studied. Fig. 7 sows tat tere is a significant improvement membrane water content if catode is amply umidified. e improvement is small if anode let gas is also completely umidified. In addition, it is known tat anode umidifier is not easy to implement because cange ydrogen temperature creates large variation RH. erefore, tis paper is focused on addg a umidifier at te fuel cell catode let. Fig. 8 sows te result of te fuel cell wit 00% RH at te catode let, under varyg fuel cell stack current. e fuel cell membrane water content creases from 0A to 60A, ten decreases after 60A despite te fact more water is generated at te catode. is is caused by decreasg anode RH after 60A, due to proton osmotic drag. From Eq. (2), one can see tat te membrane water content is proportional to te anode and catode RH. Wen te anode RH decreased, te membrane water content reduces accordgly. Anoter observation is tat te catode floodg is creased after 60A. is is maly due to te Fig. 8: Membrane water content, anode and catode RH and water liquid collected at anode and catode under 00% catode let RH An optimization searc is conducted to fd te desired catode let gas RH to mata ig fuel cell membrane water content wit mimum floodg. e result is sown Fig. 9. Sce more water is generated wen current creases, te fuel cell requires less water from its let gas. e desired catode let gas RH will be te desired put of te umidifier. H R t e le d o a t c current (A) Fig. 9: Desired catode let air RH vs. EMFC current Based on tis result, a feed-forward control map is developed and implemented te tegrated system. e tegrated system block diagram is sown Fig. 0. e simulation result of tis tegrated system is sown Fig., wic reveals tat a properly controlled catode let RH will mata te igest fuel cell membrane water content wit mimum floodg.

6 Feed forward Map ler Desired RH Disturbance (let air flow rate, emp) umidifier Catode Inlet RH Compressor Voltage Disturbance (current) EMFC Figure 0: Integrated fuel cell and umidifier system Catode RH Stack Voltage Fig. : Fuel cell membrane water content and floodg condition under controlled and non-controlled catode let air RH VII. CONCLUSIONS A membrane umidifier for automotive fuel cell systems is modeled and analyzed tis paper based on basic termodynamic laws. is lumped model describes te transient beavior of te umidification penomena and captures te time varyg aspect of te flow rate, temperature, pressure and relative umidity. e umidifier model is subsequently tegrated wit a fuel cell model. By controllg te number of umidification cell units, we can actively control te fuel cell let air to mata proper membrane umidification for te fuel cell stack. A simple proportional feedback control algoritm is developed to regulate te let air relative umidity. e umidifier simulation results sow tat te feed back control algoritm works well under many uncertaties, suc as let air flow rate cange and te let air temperature variation. A feed forward algoritm is developed to compensate te fuel cell current cange. Simulation results on te tegrated umidifier and fuel cell system sow tat te fuel cell membrane water content is umidified wit mimum floodg. ACKNOWLEDGMEN e autors wis to acknowledge te support from te University of Micigan Rackam Graduate Scool Fellowsip, and te valuable puts from Jay ukruspan, Joe L, Sangseok Yu and rof. Claus Borgnakke. REFERENCES [] M. Ciureanu and R. Roberge, Electrocemical Impedance Study of EM Fuel Cells, Experimental Diagnostics and Modelg of Air Catodes, Journal of ys. and Cem., v.05, pp , 200. [2].E. Sprger,.A. Zawodzski and S. 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