ÃCorresponding author.Tel.:+1-860-486-5911;fax:+1-860-486-5088.
E-mail address:jtang@engr.uconn.edu(J.Tang).
0960-1481/$-e front matter#2004Elvier Ltd.All rights rerved. doi:10.2004.05.001
Nomenclature
C capacitance in(F)
C O
2concentration of dissolved oxygen
C p;H
2
specific heat of hydrogen at constant pressure(J/kg K) C p;N
2幼儿情绪管理
specific heat of nitrogen at constant pressure(J/kg K) C p;O
2
specific heat of oxygen at constant pressure(J/kg K) C p,s average specific heat of fuel cell(J/kg K)
E reversible cell voltage(V)
E Nernst Nernst potential(V)
E an total internal energy in the anode volume(J)
E ca total internal energy in the cathode volume
E s internal energy of the lumped fuel cell body
F Faraday’s constant(C/mol)
h H
2;diff
specific enthalpy of diffud hydrogen(J/kg)
h H
2;in
inlet specific enthalpy hydrogen(J/kg)
h H
2;out
outlet specific enthalpy hydrogen(J/kg)
h O
2;diff
specific enthalpy of diffud oxygen(J/kg)
h O
2;in
inlet specific enthalpy of oxygen(J/kg)
h O
2;out
outlet specific enthalpy oxygen(J/kg)
D H R,T lower heating value(energy content of1kg of hydrogen reacting with
hydrogen reacting with oxygen to form water)(J/kg)
I current(A)
k an,d downstream nozzle coefficient of anode channel(kg/atm)
k an,s convection heat transfer coefficient between body and anode channel (W/k)
k an,u upstream nozzle coefficient of anode channel(kg/atm)
k ca,d downstream nozzle coefficient of cathode channel(kg/atm)
k ca,s convection heat transfer coefficient between body and cathode chan-nel(W/k)
k ca,u upstream nozzle coefficient of cathode channel(kg/atm)
举的词语k room,s convection heat transfer coefficient between body and surrounding environment(W/k)
_m air massflow rate of air(kg/s)
_m air;in inlet massflow rate of air(kg/s)
怎么委婉的辞职_m air;out outlet massflow rate of air(kg/s)
m s mass of fuel cell(kg)
萝卜干的制作m H
2hydrogen mass in the anode control volume(kg)
_m H
2massflow rate of hydrogen(kg/s)
_m H
2;diff
massflow rate of diffud hydrogen(kg/s)
_m H
2;in
inlet massflow rate of hydrogen(kg/s)
_m H
2;out
out let massflow rate of hydrogen(kg/s)
m H
2O;gen
mass of water generated by electrochemical reaction(kg) P.R.Pathapati et al./Renewable Energy30(2005)1–22
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1.Introduction
Rearch and development of fuel cell systems for various applications has dra-matically been incread in the past few years.Proton exchange membrane fuel cell (PEMFC)system emerges as one of the most promising candidates for both m N 2nitrogen mass in the anode control volume (kg)m O 2oxygen mass in the anode control volume (kg)_m O 2mass flow rate of oxygen (kg/s)_m
O 2;diff mass flow rate of diffud oxygen (kg/s)_m
O 2;in inlet mass flow rate of oxygen (kg/s)_m
O 2;out mass flow rate of oxygen (kg/s)M H 2molecular mass of hydrogen (kg/kmol)M N 2molecular mass of nitrogen (kg/kmol)M O 2molecular mass of oxygen (kg/kmol)N number of cells
P an,d downstream hydrogen pressure of anode channel (atm)
P an ;u upstream hydrogen pressure of anode channel (atm)
P ca,d
downstream air pressure of cathode channel (atm)P ca,u upstream air pressure of cathode channel (atm)
综合素质考试大纲
P H 2effective pressure of hydrogen (atm)P O 2effective pressure of oxygen (atm)R a
activation resistance in ohms R H 2gas constant of hydrogen (N m/kg K)R N 2gas constant of nitrogen (N m/kg K)R O 2gas constant of oxygen (N m/kg K)R int ,R ohm internal resistance in ohms
T fuel cell temperature (K)
T an lumped gas temperature in the anode control volume (K)
T an,in upstream hydrogen temperature of anode channel (K)
T an,out downstream hydrogen temperature of anode channel (K)
T ca lumped gas temperature in the cathode control volume (K)
T ca,in upstream hydrogen temperature of cathode channel (K)
T ca,out downstream hydrogen temperature of cathode channel (K)
T s lumped fuel cell body temperature (K)
V cell fuel cell output voltage (V)
V an volume of the anode channel (m 3)
V ca volume of the cathode channel (m 3)
g act over voltage due to activation (V)
g ohmic over voltage due to ohmic loss (V)
n 1,n 2,n 3,n 4empirical coefficients of activation over voltage
n 5,n 6,n 7empirical coefficients of internal resistance
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P.R.Pathapati et al./Renewable Energy 30(2005)1–22
stationary and automotive applications as a substitute of traditional systems such as internal combustion engines.The PEMFC offers a relatively high electrical efficiency,who average stack efficiency is higher than that of a comparably sized internal combustion engine [1].The PEMFC is especially attractive for automotive applications due to its higher power density (power per fuel cell active area)and lower operating temperature (stack exit temperature of reaction products)compared to other types of fuel cells.
In order to utilize the systems in an effective way,mathematical models of the fuel cell stack are necessary so that the system behavior can be analyzed at the design stage by means of computer simulations in different conditions of load cur-rent,pressure of reactant gas,temperature,stack voltage,etc.[1].The capability of predicting transient dynamics will also prove uful when attempting to develop a control strategy.Membrane-electrode asmbly (MEA)modeling is the kernel of the entire PEMFC system modeling.It describes mathematically the entire physical environment of electrochemical reaction;the transport phenomena of gas (hydro-gen,oxygen,gas water,etc.),water,pr
oton and current;and the relationships among fuel cell voltage,current,temperature,material (electrode,catalyst and membrane)properties and transport parameters.Traditional MEA modeling is bad upon mechanistic relation [2–6].Several aspects are involved in this model-ing,which include multi-species diffusion through substrate and diffusion layer of electrode,reaction kinetics in active layer (catalyst)and proton and water transport through the membrane.Bernardi and Verbrugge [2,3]developed a comprehensive mechanistic MEA model by taking a partially hydrated membrane into account.Springer et al.[4]improved upon this model by incorporating empirical results.Rowe and Li [5]investigated the effect of design and operating conditions on the cell performance,thermal respon and water management.In general,mechanistic MEA model facilitates the understanding of the physical process and mechan-isms,and can deal with multi-dimensional problem,but in-situ measurements of the required model parameters,such as the diffusion coefficient of species,the effec-tive electric conductivity,etc.,are very difficult to ascertain.Empirical modeling,by mapping the fuel cell voltage as a function of various contributing variables,has certain advantages in practical applications [6].The limitation of this kind of mod-eling is that the applicable range is small due to its phenomenological nature and the models cannot reflect the actual physical process involved in electrochemical reactions.Amphlett et al.[7,8]attempted combining the advantage of both approaches by integrating together the mechanistic model and empirical relation.The system-level m
odeling of fuel cell,as compared to MEA modeling,is even more complicated.So far most of the models in the literature are bad upon steady-state condition [9–12].Barbir and co-workers [9,10]have studied air supply–stack interactions and highlighted veral effects that will be helpful in optimizing fuel cell stack performance.Geyer and Ahluwalia have developed a computer simulation tool,GC tool,which can be ud for fuel cell system design and analy-sis [11].Their PEMFC system model is primarily an empirical one where the volt-age is modeled as a function of current,cell temperature and the partial pressure of oxygen at the cathode inlet.Fronk et al.[12]addresd veral issues regarding
P.R.Pathapati et al./Renewable Energy 30(2005)1–22
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PEM fuel cell systems for transportation applications.They demonstrated the importance of thermal management while trying to maximize the performance of the systems.Despite large number of publications on fuel cell modeling,models suitable for studying transient phenomena are still lacking.The existent limited number of papers in this regard are mostly developed to address specific transient behaviors [13–15].Temperature dynamics is the focus of Wohr et al.[13]and Amphlett et al.[
14].Though Pukrushpan et al.[15]propod a fuel cell system-level dynamic model by incorporating the dynamic property of fluid flow (pressure)through anode and cathode channels,all the models discusd above have neglec-ted the effects of charge double layer capacitance [17].Iqbal [16]propod a hybrid fuel cell—wind turbine dynamic model bad on the capacitor effect of double charge layer but experimental and theoretical verification of this model with the open literature is yet to be established.
唐伯虎的桃花庵Although the dynamic behavior of various properties has not been included sim-ultaneously in the above modeling studies,the studies established a good basis for understanding the transient phenomena in the fuel cell.Building on the mod-eling studies,a complete fuel cell system-level dynamic model capable of character-izing transient phenomena is propod in this paper which incorporates simultaneously three prominent dynamic aspects,the temperature changes of fuel cell,fluid flow changes through channels,and capacitor effect of charge double lay-ers.The propod model is implemented in SIMULINK [21].A ries of numerical studies are then carried out to compare with published benchmark data [14,20].Correlation with experimental investigation is also performed.All comparisons show good agreement between the predicted results and benchmark/experimental results.This model will be very uful for the optimal design and real-time control of PEM fuel cell systems.
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2.Dynamic modeling approach
Fuel cell is a fluid–solid–heat–electrochemistry coupled complex system.There are macroscopic level fluid flow as well as microscopic level mass diffusion and transportation,which provide fuel for the electrochemical reaction to occur.The humidification level of the MEA is also a key factor that affects mass diffusion and proton transportation.On one hand,too much water leads to the flooding of MEA,which in turn blocks the mass diffusion and proton transportation;on the other hand,if the humidification level of the MEA is too low,the proton transpor-tation through the membrane will become difficult,and this will lead to higher internal resistance thereby increasing ohmic overvoltage.To keepthe op timum humidification level of the MEA,one possible approach is to humidify the inlet fuel and air.But the final humidification level is dependent on the fuel cell temperature.The fuel cell temperature change is dependent on veral ,heat produced by electrochemical reaction,the convection heat transfer to the surrounding atmosphere through the fuel cell surface,the convection heat transfer between fuel cell and anode/cathode channel.Bad on the above obrvation,one 5
P.R.Pathapati et al./Renewable Energy 30(2005)1–22
can clearly e that fuel/air flow and temperature are the two important dynamic properties of the fuel cell.Any disturbances on surrounding operating conditions and more often load changes will lead to the state changes of the dynamic properties.It will be demonstrated in this paper that the current drawn,cell tem-perature,H 2pressure,and O 2pressure will significantly affect the fuel cell voltage.The PEMFC modeling process can be divided into the following five parts.
2.1.Electrochemical model
This ction discuss in detail the physical structure and the operating principle of a PEMFC,and prents a model for characterizing the electrochemical property of MEA that is the kernel of the system.The MEA consists of a cathode electrode and an anode electrode with a proton conducting membrane as the electrolyte sandwiched in between.A schematic reprentation of a fuel cell with the reactant/product gas and the ion conduction flow directions through the cell is shown in Fig.1.Air is fed to the cathodic compartment,and hydrogen is fed to the anodic one and the electrolyte performs both the functions of transferring H +from the anode to the cathode and reactant paration.The electrochemical
reactions
跨年度Fig.1.A typical PEM fuel cell.P.R.Pathapati et al./Renewable Energy 30(2005)1–22
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