Visualization of Temperature Distribution and Clarification of Heat and

Journal of Thermal Science and Technology

Vol. 4, No. 4, 2009

Visualization of Temperature Distribution and Clarification of Heat and Mass Transfer Mechanism in a Single Cell of PEFC* Akira NISHIMURA**, Kenichi SHIBUYA**, Masayuki TAKEUCHI**, Masafumi HIROTA**, Seizo KATO**, Yoshihiro NAKAMURA***, Hironari TACHI*** and Masahiko NARITA*** **Mie University, 1577 Kurimamachiya-cho, Tsu, Mie Pref., 514-8507, Japan E-mail: [email protected] ***Toho Gas Co., LTD., 507-2 Shinpo-machi, Tokai, Aichi Pref., 476-8501, Japan

Abstract Polymer electrolyte fuel cell (PEFC) has been developing as clean power generation technology. However, there are some subjects to spread PEFC among industries and homes in the world. The one of such subjects is drop in power generation performance and durability caused by heat and mass distribution in a single cell of PEFC. The purpose of this study is to point out the dominant factor of heat and mass transfer phenomena and clarify the reason for heat and mass distribution in a single cell. With the aid of observation window, the in-plane temperature distribution in single cell under power generation was measured by thermograph. The influence of operation conditions on temperature distribution was investigated. Moreover, to clarify the heat and mass transfer mechanism theoretically, the simulations to investigate the factor needed for the ideal reaction and evaluate the influence of separator structure on heat and mass distribution were carried out. Key words: PEFC, Visualization by Thermograph, Temperature Distribution, Heat and Mass Transfer, Simulation

1. Introduction

*Received 25 Feb., 2009 (No. 09-0083) [DOI: 10.1299/jtst.4.438]

Global warming and fossil fuel depletion have been serious global environmental problems due to mass consumption of fossil fuels. In order to solve these problems, new energy technologies which are more efficient, convenient and cleaner than the present technologies should be developed. Fuel cell is thought to be a promising device for clean energy generation. There are several types of fuel cells that generate electrical power for various applications. Especially, PEFC is expected to become a power source of vehicles and homes in the near future since PEFC has the advantages such as small size, operation under comparative lower temperature and high power density. However, there are many subjects to be solved from the viewpoint of spreading widely. The performances of current PEFC are as follows (1); The power generation efficiency is about 30 %. The durability time is about 20,000 hours. The operation temperature is usually set from 343 K to 353 K. On the other hand, the target performances after 10 - 20 years are as follows (1); The power generation efficiency is more than 40 %. The durability time is about 90,000 hours (about 10 years). The operation temperature is desired in the range from 363 K to 373 K. To clear

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this target, there are many subjects that should be overcome on the technological side. As one of the subjects, it can be pointed out that the distribution of temperature and mass (gas and water) in a single cell of PEFC are not uniform. It is thought that the decrease in the voltage of PEFC and deterioration of the cell materials are caused by the behavior of condensed water and the local temperature rise (2-4). The distributions of temperature, gas and water in a single cell of PEFC influence on the durability and performance of reaction and power generation strongly (4-9). However, the mechanism of distribution of them is not clarified well. The aim of this study is pointing out the dominant factor of transfer phenomena and the main reason for distribution on heat and mass in a single cell of PEFC. We carried out experiments with changing supply gas flow rate of H2 and O2, considering the operation temperature and the cell voltage as well as mass balance of inlet and outlet gas flow rate. In addition, in order to investigate the temperature distributions in the single cell of PEFC under power generation, we made an observation window in PEFC. With the aid of the observation window, the in-plane temperature distributions in the single cell of PEFC under power generation were measured by using the thermograph. In the experiment, the temperature distribution according to the separator structure and the gas supply condition was obtained. The effects of gas flow rates of anode and cathode side on the heat and mass transfer in the single cell was confirmed. Moreover, for the purpose of clarifying the heat and mass transport phenomena and proposing the operation conditions for the high efficiency power generation, the one-dimensional simple model to the through-plane direction in the single cell was simulated by using CFD software. We clarified operation condition which was required for the ideal reaction and the essential phenomena in the single cell. In the next step, the simulation by using the two-dimensional model was carried out in order to analyze the influence of the gas flow channel structure on the gas flow distribution to the through-plane direction. The relationship between the gas flow distribution on the reaction surface in two-dimensional model and the performance of ideal reaction model obtained by calculation result of one-dimensional simple model was investigated.

Nomenclature aij' aij" B Di Dj F h hi hS i iF iS I0,j IT IT,j Ji M Mi N NG

normalized stoichiometric coefficients of the reactants, normalized stoichiometric coefficients of the products, body force vector, N/(m・s2) effective mass diffusion coefficient of i-th species, m2/s effective mass diffusion coefficient of j-th species, m2/s Faraday constant, C/mol enthalpy of mixture, J/kg enthalpy of i-th species, J/kg enthalpy of solid, J/kg net current density, A/m2 transfer current in fluid region, A/m2 transfer current in solid region, A/m2 reference current density in j-th reaction step, A/m2 net transfer current due to electrochemical reaction, A/m2 net transfer current due to electrochemical reaction of j-th step, A/m2 diffusion flux of i-th species, kg/(m2・s) mixture molecular weight, kg/kmol mixture molecular weight of i-th species, kg/kmol total number of reacting species, total number of gas species, -

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Nsteps number of calculation step, p absolute pressure, Pa q heat flux, W/m2 R universal gas constant (= 8314), J/(kmol・K) ． enthalpy source due to phase change, W/m3 Sh effective ratio of catalyst surface to catalyst volume, m2/m3 (S/V)eff t lapse time, s T bulk temperature, T U fluid velocity vector, m/s V catalyst volume, m3 Yi mass fraction of i-th species, mass fraction of j-th species, Yj YP,i mass fraction of i-th species in pore region, Greek symbols αa,j anodic Tafel constant for j-th reaction step, αc,j cathodic Tafel constant for j-th reaction step, αk,j concentration exponent of the k-th species for j-th reaction step, δ average pore size, m ε porosity, η electrode overpotential, V κ permeability, m2 λ effective thermal conductivity, W/(m・K) λF thermal conductivity of fluid (or pore) in porous region, W/(m・K) λS thermal conductivity of solid in porous region, W/(m・K) [Λk] average molar concentration of the k-th species on interface, kmo/m3 [Λk,ref] reference molar concentration of the k-th species on interface, kmo/m3 µ dynamic viscosity, Pa・s ρ mass density of mixture, kg/m3 ρS mass density of solid, kg/m3 σ electrical conductivity, 1/(Ω・m) σF electrical conductivity of fluid (or pore) in porous region, 1/(Ω・m) σS electrical conductivity of solid in porous region, 1/(Ω・m) τ shear stress tensor, N/m2 φF electrical potential of fluid (or pore) in porous region, V φ． electrical potential of solid in porous region, V S ωi production rate of i-th species in gas phase, kg/(m3・s)

2. Experiment and Simulation Procedure 2.1 Experimental Apparatus and Procedure In this study, the single cell of PEFC (Micro Cell Technologies; MC-25-SC-NH) which has the serpentine gas flow channel was used. The channel number of separator was 5. The width and depth of the channel was 1 mm and 1 mm, respectively. The observation window was made by holing for the end block, the electricity collector and the hot water passage plate on the cathode side of the single cell. Although we wanted to observe the interface between catalyst layer of cathode side and polymer electrolyte membrane as the reaction surface, the gas leak and change of power generation performance were terrible. Then, we decided to observe the back of cathode separator. Considering the heat transfer from the reaction surface to the back of cathode separator, the effect of thermal conduction through-plane direction is very small. According to the estimation on one-dimensional thermal conduction between the reaction surface and the back of cathode separator, the

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temperature difference is below 0.0001 K. In this estimation, the thermal conductivity of separator made of carbon graphite, Gas Diffusion Layers (GDL) made of carbon paper, catalyst consisting of platinum and carbon, and polymer electrolyte membrane is set at 25, 1.7, 1.7, and 0.195 W/(m・K), respectively, by referring to parts catalog. The thickness of separator, GDL, catalyst, and polymer electrolyte membrane is set at 2.00, 0.17, 0.010, and 0.13 mm, respectively, by referring to parts catalog. From the result of this estimation, the in-plane temperature distribution in observation area is thought as the in-plane temperature distribution on reaction surface including the influence of convection heat transfer by gas flow in the gas channel of separator. The width and height of the observation window, which was equal to those of the electrode, was 50 mm and 50 mm, respectively. To prevent gas leak, the width and height of hole made in hot water passage plate was set at 40 mm and 50 mm, respectively. Figures 1 and 2 illustrate the single cell structure with observation window and the experimental set-up, respectively. The temperature distribution on the back of the cathode separator was measured through the observation window by using the thermograph (Thermotracer TH9100WL, NEC Avio Infrared Rays Technology). The emissivity of the separator in this experimental condition was measured by the pre-experiment, resulting that it was set at 0.76 in the case of temperature measurement by thermograph. The decrease in power generation output due to the observation window was not recognized. The single cell was heated for start-up by the silicon rubber heater which was set around the end block. The cell excluding observation window side and the opposite side was covered by thermal insulator. The temperature in the cell before starting each experiment was kept at 343 K. To measure the temperature distribution caused by reaction heat accurately, the single cell was operated under higher load current of 20 A. Under this condition, the temperature of the single cell was able to maintain at 343 K without cooling by coolant and heating by silicon rubber heater before measurement by thermograph. Hot Water Hot Water Passage Plate Coolant PassageSeparator Plate Separator Separator Coolant Separator

Cathode

Anode

Observation Window

Anode End Block

1m

Electricity Collector MEA&GDL Current Collector

Fig. 1

Thermograph Thermography

Cathode End Block

Structure of single cell of PEFC with observation window

Mass Flow Controller

Mass Flow Meter

Dew Point Meter

H2

Discharge Fuel Cell Drier (Silica Gel)

Humidifier

Electronic Load Equipment

N2 Mass Flow Controller

Dew Point Meter

Drier (Silica Gel)

O2

Discharge PC Humidifier

Mass Flow Meter Thermography Thermograph

Fig. 2

Experimental set-up

The effect of operation conditions such as flow rate of supply gas on the temperature distribution was investigated. Humidified H2 and O2 were used for the supply gas. The humidity of them was controlled by the humidifier and the dew point meter. The gas flow rate was controlled by the mass flow controller. The current was controlled by the electric load device. Flow rate of supply was such as H2 and O2 was changed from 0.199 NL/min to

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Journal of Thermal Science and Technology

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0.319 NL/min, from 0.070 NL/min to 0.279 NL/min, respectively. The voltage value corresponding to the load current, the temperature measured by thermocouples, the humidity and the gas flow rate at inlet and outlet were obtained as well as the temperature distribution measured by thermograph. With comparing these data, the heat and mass transfer phenomena in the single cell were investigated. Tables 1 and 2 list experimental conditions. Experiment I is the standard operation condition under the load current of 20A. We compared the results of experiment II - IV with the result of experiment I. In experiment II, gas flow rates of the anode and the cathode were set higher than the standard operation conditions, that is, the excess gas was supplied into the single cell of PEFC. In experiment III, the same amount of O2 as the standard operation condition and the amount of H2 which was the stoichiometric ratio of one were set as the inlet gas flow rate. In experiment IV, the same amount of H2 as the standard operation condition and the amount of O2 which was the stoichiometric ratio of one were set as the inlet gas flow rate. In each experiment, the difference of the voltage value from no observation window operation was not recognized. Table 1 Experimental condition Opearation Temperature [K]

343

Load Current [A]

20 2

0.80

Current Density [A/cm ] Anode

Cathode

Supply Gas

H2

O2 341

Supply Gas Temperature [K]

341

Humidification Temperature of Supply Gas [K]

338

338

Inlet Gas Flow Rate [NL/min]

Parameter

Parameter

Table 2 Inlet gas flow condition

Anode Cathode

Experiment Inlet Gas Flow Rate [NL/min] Stoichiometric Ratio [-] Inlet Gas Flow Rate [NL/min] Stoichiometric Ratio [-]

I 0.199 1.43 0.174 2.50

II 0.199 - 0.319 1.43 - 2.33 0.174 - 0.279 2.50 - 4.00

III 0.140 1.00 0.174 2.50

IV 0.199 1.43 0.070 1.00

2.2 Simulation Model and Calculation Condition For the purpose of clarifying the heat and mass transfer phenomena and proposing the operation condition for the high-efficiency power generation, the simple model to through-plane direction in the single cell was simulated by using CFD software (CFD-ACE+, Wave Front). This CFD software has the simulation code for PEFC which is composed of the equations shown below. The validation of simulation way using these equations has been already proved well (10-14). As the first step, the one-dimensional simple model to the through-plane direction shown in Fig.3 was simulated under an ideal reaction condition. In this study, we define "ideal" as the condition where there is no gas flow distribution to the x-axis direction and no excess gas for the requested power generation. With using this model, the optimum gas supply condition was clarified when the platinum is used as the catalyst for PEFC. One-dimensional model means that heat, mass and electricity are transferred to through-plane direction only though the simulation is carried out under two dimension. As shown in Fig.3, H2 and O2 supplies from top and bottom of the model, respectively. GDL of anode and cathode side are located between these inlets of gas supply and Membrane Electrode Assembly (MEA). MEA consists of a polymer electrolyte membrane and thin catalyst layers located on both surfaces of the membrane. In this model, the following phenomena are assumed. (1) The gas diffuses uniformly. (2) The gas penetrates from the gas flow channel to the polymer electrolyte membrane vertically. (3)

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The inflow gas reacts perfectly without excess and deficiency. In this calculation, we clarified operation condition which was required for the ideal reaction and the essential phenomena in the single cell. In the next step, the simulation by using the two-dimensional simple model was carried out in order to analyze the influence of gas flow channel structure on gas flow distribution. This simulation model is also shown in Fig.3. With using this model, the gas flow distribution near the interface between the gas flow channel and rib part was examined. In addition, the relationship between the gas flow distribution on the reaction surface and the performance of ideal reaction model was investigated. In this paper, the simulation result can not be compared with the experimental result directly since the simulation is carried out under ideal condition from the viewpoint of selecting the optimum operation condition of PEFC and checking the effect of gas flow channel structure on gas flow distribution simply. In the near future, we are going to simulate by the three-dimensional model which can be compared with the experimental result. 86µm

43µm

H2

H2

43µm Separator Rib

150 µm

GDL

150 µm

GDL

10 µm

Catalyst Layer

10 µm

Catalyst Layer

100 µm

Membrane

100 µm

Membrane

10 µm

Catalyst Layer

10 µm

Catalyst Layer

150 µm

GDL

150 µm

GDL

O2

Fig. 3

O2

Separator Rib

One-dimensional and two-dimensional simple model of a single cell (left: one-dimensional, right: two-dimensional)

The conservation equations of mass, momentum, energy, current, and species transport on a computational grid using finite-volume are solved in this study. There are following three key elements to construct a fuel cell model. (1) transport through porous media, (2) heterogeneous reactions within porous electrodes, and (3) coupling among mass transport, electrochemical reactions, and current transport. In this calculation, the volume-averaged conservation equations of mass and momentum in a porous media are as follows (15-17):

∂ (ερ ) + ∇ ⋅ (ερU ) = 0 ∂t

(1)

2 ∂ (ερU ) + ∇ ⋅ (ερUU ) = −ε∇p + ∇ ⋅ (ετ ) + εB − ε µU ∂t κ

(2)

The last term in Eq. (2) represents Darcy's drag force imposed by the pore walls on the fluid within the pores. This force usually causes significant pressure drop across the porous medium (15, 16). The conservation equation for energy is written as (18, 19):

∂ {(1 − ε )ρ S hS + ερh} + ∇ ⋅ (ερUh ) ∂t ⋅ i ⋅i dp = ∇ ⋅ q + ετ∇U + ε − ITη + + Sh dt σ

(3)

The heat flux q is comprised of thermal conduction and diffusion of species, and is

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written as (20): NG

q = λ∇T + ∑ J i hi

i =1 The effective thermal conductivity of the fluid and solid region is written as (16):

λ = −2λ S +

1

(4)

(5)

ε

1− ε + 2λ S + λ F 3λ S

The mass conservation equations for the individual gas phase species is written as: ⋅ ∂ (ερYi ) + ∇ ⋅ (ερUYi ) = ∇ ⋅ J i + ωi (6)

∂t

The species diffusion flux is written as (17):

ρYi

J i = ρDi ∇Yi +

M

Di ∇M − ρM ∑ D j ∇Y j − ρ∇M ∑ D j Y j j

(7)

j

The Ji represents Fickian diffusion driven by concentration gradients. The last three terms in right side are correction terms which are necessary to satisfy the effective mass diffusion coefficients of species systems. Di is the effective mass diffusion coefficient of species i within the porous medium, and depends on the porosity and tortuosity factor of the medium. This is called Bruggeman model (16). Electrochemical reactions occur at the inner surfaces of the pores, where the fluid comes in contact with catalyst clusters. Reactants flowing through the pores arrive at the solid catalyst surface by diffusion. The diffusion flux is balanced by the reaction as follows (21) : N steps

∑ M (a j =1

i

" ij

− aij'

) IF

T,j

= ρDi

Yi − Y p ,i

δ

(8)

where aij' and aij" is the normalized stoichiometric coefficient of the products and reactants, respectively. In this study, these numbers were set 0.5. F is Faraday constant (=964500 C/mol). The transfer current IT is obtained from the Butler-Volmer equation (22, 23), and is written in the following most general form:

IT =

I 0, j

[

N

]

Π Λk , ref α k , j

α k, j   α a, j F   α c. j F  N η  exp − η  Π [Λk ] (9) exp RT   RT     i =1

i =1 where αa,j and αc,j is the kinetic constant of anode and cathode reaction determined from Tafel plots obtained experimentally, respectively. The species sources in each cell of the catalyst layer can be computed by the following equation (10, 11): ⋅ Yi − Y p , i  S  ω i = ρDi (10)   V δ  V  eff The transfer current within the material under electroneutral conditions could be conserved. When the material is a porous electrode, the current is split into two parts; one flows through the pores denoted by iF and the other flows denoted by iS through the solid parts of the porous material. ∇ ⋅ i F + ∇ ⋅ iS = 0 (11) During electrochemical reactions within a porous solid, electrons are transferred (expressed by the transfer current) from the pores to the solid material. This equation can be

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rewritten by the following equation: N steps − ∇ ⋅ i F = ∇ ⋅ iS = I T = ∑ I T , j j =1

(12)

This equation is defined under a valid assumption since the current is carried by irons in the pore phase, whereas it is carried by electrons in the solid phase. There can be no interaction between these two current components unless a heterogeneous chemical reaction occurs on the pore-solid interface. Under this assumption, application of Ohm's law to Eq.(12) yields: ∇ ⋅ (σ F ∇φ F ) = −∇ ⋅ (σ S ∇φ S ) = IT (13) The solution of conservation equation was performed by using a finite volume scheme on arbitrary unstructured mesh topology within the framework of the commercial CFD code CFD-ACE+. In this study, the governing equations are derived on the basis of the following assumptions (10, 11): 1. The volume of condensed water is ignored and the water moves with gas. 2. The reduction of the reaction area caused by flooding of electrode is ignored and diffusion prevention caused by water condensation is ignored. 3. Cell voltage is uniform and constant. 4. The effective porosity and the permeability of porous media are isotropic. 5. Heat transfer between gas and solid phase of porous media is ignored. 6. Fluid is incompressible Newtonian fluid and ideal gas. Flow condition is laminar flow. 7. The inlet gas flow rate in each side is uniform. 8. The temperature on interface between separator and GDL is constant. 9. In a polymer electrolyte membrane, ionic conductivity, the electro-osmosis coefficient and the water effective diffusion coefficient that depend on humidity are disregarded. 10. The gas cross over through polymer electrolyte membrane is disregarded.

3. Results and Discussion 3.1 Experiment I (Standard Operation Condition) Figure 4 shows the trend graph of experiment I under power generation. In this figure, the lapse time is shown on the horizontal axis. The values of inlet and outlet gas flow rate are followed by the left vertical axis. Total voltage value is followed by the right vertical axis. The image of temperature distribution under OCV (Open Circuit Voltage) operation is shown in Fig.5. The image shown in Fig. 5 was taken under heating by silicon rubber heater since the power generation could not be carried out under OCV operation. Since the around of cell was heated by silicon rubber heater, the center part of image is seen lower that the other region of image. Figure 6 shows the images of temperature distribution taken by every 30 seconds by the thermograph. In this Fig.6, the number of images corresponds to the number shown in Fig.4. Inlet gas flow rate of anode s ide

Inlet gas flow rate of chasode side

Outlet gas flow rate of chasode s ide

Total voltage

Outlet gas flow rate of anode s ide

1.20

0.35

1.00

0.30

Normal operation starts. 1

0.25

2

3

4

0.80

0.20

0.60

0.15

0.40

0.10

Total voltage, V Total voltage [V]

GasGas flow flowrate rate, [NL/min] NL/min

0.40

0.20

0.05

0 0.00

0.00 0 0

100

200

300

400

500

600

700

800

Time, s ec

Lapse time [s]

Fig. 4

Trend graph of gas flow rate and total voltage (Experiment I)

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343.2 70.0 [K] °C

342.7 69.5 342.2 69.0 341.7 68.5 341.2 68.0 340.7 67.5 340.2 67.0 339.7 66.5 339.2 66.0

Fig. 5

Temperature distribution in observation area under OCV operation

1

2

3

70.0 343.2[K

4

°C

69.8 343.0 69.5 342.7 69.3 342.5 69.0 342.2 68.8 342.0 68.5 341.7 68.3 341.5 68.0 341.2

Fig. 6

Temperature distribution in observation area under Experiment I (taken every 30 seconds)

According to Fig.6, the tendency of temperature rise from the gas inlet region toward the gas outlet region can be confirmed. Compared Fig.6 with Fig.5, the temperature distribution by power generation can be observed from Fig.6. It can be seen from Fig.4 that the voltage value is constant during the acquisition of temperature distribution data. Moreover, it is indicated that outlet gas flow rates of anode and cathode side are also almost steady. Therefore, the steady power generation is carried out under this condition. 3.2 Experiment II (Excess Gas Supply Condition) In experiment II, the inlet gas flow rates of anode and cathode side were increased at almost constant rate every five minutes. Figure 7 shows the trend graph of experiment II under power generation. Images of temperature distribution for each gas flow rate condition, which are taken at the time numbered in Fig.7, are shown in Fig.8. Inlet gas flow rate of chasode side

Outlet gas flow rate of chasode side

Total voltage

1

0.35

2

3

4

Outlet gas flow rate of anode side

5

6

7

1.20 1.00 0.80

0.25 0.20

0.60

0.15

0.40

Total voltage, V

0.30

Total voltage [V]

Gas flow rate, NL/min

Gas flow rate [NL/min]

0.40

Inlet gas flow rate of anode side

0.10 0.20

0.05

0

0 0.00

0.00 0

200

400

600

800

1000

1200

1400

1600

1800

Time, sec Lapse time [s]

Fig. 7

Trend graph of gas flow rate and total voltage (Experiment II)

According to Fig.8, it is confirmed that the temperature of the total observation area, especially gas inlet region, is descending with increasing inlet gas flow rate gradually. On the other hand, according to Fig.7, there is no change in the voltage value though the inlet gas flow rate is changed. From Fig.7, the outlet gas flow rate increases when the inlet gas flow rate increases. It is known that the amount of gas consumed for reaction does not change, resulting that the excess gas flows in the single cell. Therefore, it can be thought that the excess gas cools the reaction surface, resulting in temperature decrease of the total observation area and gas inlet region.

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1 (Normal operation)

2

3

4

H2：0.199NL/min (1.43) O2：0.174NL/min (2.50)

H2：0.219NL/min (1.56) O2：0.192NL/min (2.78)

H2：0.239NL/min (1.72) O2：0.209NL/min (3.03)

H2：0.259NL/min (1.89) O2：0.227NL/min (3.23)

6

7

5

70.0 70.0℃ 343.2[K] °C 69.8 69.8 343.0 69.5 69.5 342.7 69.3 69.3 342.5 69.0 69.0 342.2 68.8 68.8 342.0 68.5 68.5 341.7

H2：0.279NL/min (2.04) O2：0.244NL/min (3.45)

Fig. 8

H2：0.299NL/min (2.17) O2：0.261NL/min (3.70)

H2：0.319NL/min (2.33) O2：0.279NL/min (4.00)

68.3 68.3 341.5 68.0 68.0 341.2

Temperature distribution in observation area at each gas flow rate under experiment II

3.3 Experiment III (The Stoichiometric Ratio of Inlet Gas Flow Rate of H2 is One.) In experiment III, the inlet gas flow rate of H2 was set at 0.140 NL/min. The stoichiometric ratio of this inlet gas flow rate is one, resulting in no outlet gas of anode side. Figure 9 shows the images of temperature distribution taken several times in this experiment. Compared Fig.9 with Fig.6, the change in temperature distribution is not recognized well. In addition, the descent of voltage value was not confirmed in this experiment. From these results, it is obvious that the temperature distribution change and the descent of voltage value are not caused even though the outlet gas flow rate of H2 is decreased to 0. Anode reaction can be carried out well even under the borderline gas flow rate condition due to high diffusivity of H2 as well as no necessity of produced water discharge comparing with cathode.

Normal operation

1

2

3

343.2[K] 70.0 70.0℃ °C 343.0 69.869.8

342.7

69.569.5

342.5 69.369.3 69.0 342.2 69.0 68.8 68.8 342.0

68.568.5

341.7

68.368.3

341.5

68.068.0

341.2

Fig. 9

Temperature distribution in observation area under experiment III

3.4 Experiment IV (The Stoichiometric Ratio of Inlet Gas Flow Rate of O2 is One.) In experiment IV, the inlet gas flow rate of O2 was set as 0.070 NL/min. The stoichiometric ratio of this inlet gas flow rate is one, resulting in no outlet gas of cathode side. Figure 10 shows the temporal change of temperature distribution after the gas flow rate is changed from 2.50 NL/min to 0.070 NL/min in this experiment. According to Fig.10, it can be known that the temperatures in the region around the inlet of gas flow become higher compared with the other regions when the outlet gas flow rate of O2 is decreased. In addition, the temperatures in the region around the inlet of gas flow become higher compared with that obtained under experiment I by 1K - 2K. Moreover, it was confirmed that the in-plane temperature distribution returns to the state in the standard operation condition when the outlet gas flow rate of O2 was increased after this

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experiment. From these results, it is thought that the change in the gas flow rate of O2 in the cathode side is one of the dominant factors influencing on in-plane temperature distribution in a single cell of PEFC. When the inlet gas flow rate of O2 is excessive, the cooling effect by convention heat transfer of inlet gas is confirmed as shown in Fig.8. On the other hand, when the inlet gas flow rate of O2 is not excessive, the cooling effect by convection heat transfer of inlet gas is small. In addition, it can be thought that the overpotential by gas diffusion shortage causes the temperature decrease in the region around the outlet of gas flow. Therefore, it can be said that the in-plane temperature distribution brought by reaction heat is obtained under the condition of experiment IV. 1

2

3

4

5

6

343.2[K] 70.0℃ 70.0 °C

343.0 69.8 69.8 342.7 69.5 69.5 69.3 342.5 69.3 69.0 69.0 342.2

68.8 68.8 342.0 68.5 68.5 341.7 68.3

68.3 341.5

68.0 68.0

341.2

Fig. 10

Temperature distribution in observation area under experiment IV

3.5 One-dimensional Simple Model Calculation The calculation condition is listed in Table 3. In order to clarify the effect of inlet gas pressure, the inlet gas pressure was changed from 0.10 MPa to 0.51 MPa. The calculation results are listed in Tables 4 and 5. Table 3 Calculation condition Establishment Condition

Value

Thickness of GDL

150 µm

Thickness of Catalyst Layer

10 µm

Thickness of Polymer Electrolyte Membrane Width of Model

100 µm 8.6E-2 mm

Inlet Flow Rate of Anode Side

6.74E-8 kmol/s

Inlet Flow Rate of Cathode Side

3.37E-8 kmol/s

Inlet Gas Pressure at Anode and Cathode Side

0.10 MPa - 0.51 MPa 2

Permeability of GDL and Catalyst Layer

8.69E-12 m

Permeability of Polymer Electrolyte Membrane

1.00E-18 m

2

Porosity of GDL and Catalyst Layer

0.78

Porosity of Polymer Electrolyte Membrane

0.28

Tortuosity Factor of GDL and Catalyst Layer

1.5

Tortuosity Factor of Polymer Electrolyte Membrane

5.0 3

Exchange Current Density (Anode)

9.23E+8 A/m

Exchange Current Density (Cathode)

1.05E+6 A/m

Electrical Conductivity of Polymer Electrolyte Membrane

3

1.0E+20 1/(Ω・m)

Electrical Conductivity of GDL and Catalyst Layer

53 1/(Ω・m)

Thermal Conductivity of GDL and Catalyst Layer

1.3 W/(m・K)

Thermal Conductivity of Polymer Electrolyte Membrane

0.195 W/(m・K)

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Table 4 Relationship between inlet gas pressure and mole flux of unreacted gas Inlet Gas Pressure [MPa] 0.10

Unreacted Mole Flux of H2 [kmol/(m・s)]

Unreacted Mole Flux of O2 [kmol/(m・s)]

5.270E-08

1.475E-08

0.20

2.660E-08

2.250E-08

0.30 0.41

8.900E-09 2.000E-10

5.200E-09 6.500E-10

0.51

4.990E-08

7.650E-09

Table 5 Evaluation of the ratio of unreacted gas Inlet Gas Mole Flux [kmol/(m・s)]

Unreacted Gas Mole Flux [kmol/(m・s)]

The Ratio of Unreacted Gas [%]

H2

4.090E-07

2.000E-10

0.05

O2

2.050E-07

6.500E-10

0.32

Table 4 shows the relationship between the inlet gas pressure and the mole flux of unreacted gas. It is known that the unreacted gas is the minimum at inlet gas pressure of 0.41 MPa. Moreover, the ratio of mole flux of unreacted gas to that of inlet gas is less than 1 % at inlet gas pressure of 0.41 MPa as shown in Table 5. Consequently, it can be said that the optimum inlet gas pressure is 0.41 MPa for the reaction of all gases without excess. We decide to name the simulation under this condition as an ideal one-dimensional model. Figure 11 shows the through-plane temperature distribution at the horizontal center under the calculation condition of the inlet gas pressure of 0.41 MPa. It is understood that the highest temperature is obtained in cathode catalyst layer. The temperature difference by 3.4 K from the cathode catalyst layer to the interface between GDL and separator is found. In addition, it can be seen that the temperature is decreased remarkably in GDL of cathode side. In this temperature region such as 353 K - 358 K, the relative humidity of gas changes drastically. Therefore, this temperature difference is important to clarify the phenomena in the single cell of PEFC. Anode catalyst

Cathode catalyst

Anode GDL Membrane

Cathode GDL

Temperature [K]

356.5 356.0

3.4 K

355.5 355.0 354.5 354.0 353.5 353.0

0

5E-5 1.0E-4 1.5E-4 2.0E-4 2.5E-4 3.0E-4 3.5E-4 4.0E-4 4.5E-4

Position thickness direction [m][m] Position totothethethrough-plane direction

Fig. 11

Through-plane temperature distribution obtained by one-dimensional model

3.6 Two-dimensional Simple Model Calculation It is thought that the gas flow distribution on the reaction surface affects the cell performance and durability of materials composing PEFC. In the last section, the ideal one-dimensional model was constructed and obtained the relationship between the through-plane temperature distribution and the cell performance of PEFC. In two-dimensional simple model calculation, the influence of the gas flow channel structure on the gas flow to through-plane direction was considered. The gas flow distribution near the interface between the gas flow channel and rib part was examined. In addition, the relationship between the gas flow distribution on the reaction surface and the performance

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of ideal reaction model was investigated. The calculation condition is already listed in Table 4 except for inlet gas pressure. In this calculation, inlet gas pressures of anode and cathode sides are set 0.41 MPa which is the optimum inlet gas pressure according to the results of one-dimensional model. Figure 12 shows the obtained result on distribution of mole flux of each gas. From this figure, it is seen that gas flow distribution at the interface between GDL and catalyst layer is not recognized. In this study, the permeability and porosity of GDL are set as isotropic. It might be thought that uniform gas flow is obtained by the isotropic of GDL properties. Compared the through-plane temperature distribution at the horizontal center of two-dimensional model with that of ideal one-dimensional model, it becomes clear that there is no difference between these two results. Therefore, it can be said that the uniform reaction as same as ideal reaction model is occurred when the length of gas flow channel and rib part is set short, respectively. To prove the uniform reaction obtained by two-dimensional model more, the cell performance of power generation was investigated. As a result, the voltage is 0.63 V when the load current is 12.7 A. Compared with one-dimensional model, the difference of the cell performance of power generation between one-dimensional model and two-dimensional model is not recognized. H2 [kmol/(m･s)]

[kmol/(m･s)]

[kmol/(m･s)]

O2 Fig. 12

Distribution of mole flux of each gas obtained by two-dimensional model

According to the former results of this study, heat and mass transport phenomena were strongly related with each other. The excess gas flow takes heat produced by reaction to the outlet of the gas flow. Therefore, the excess gas flow has the effect of cooling the reaction surface. However, the reaction of H2 and O2 is taken place around the inlet of the gas flow in the single cell since a lot of reactive gases diffuse and penetrate through GDL to the catalyst layer. Around the inlet region of the gas flow in the single cell, H2 and O2 react actively due to high concentration and pressure of each supply gas. Since there is no distribution of gas flow at the interface between GDL and catalyst layer, the uniform reaction performance of the single cell is kept.

4. Conclusion (i)

Due to cooling the reaction surface by the excess gas, the temperature in the total observation area becomes lower as the supply gas is increased. (ii) The descent of inlet gas flow rate of H2 does not affect the cell performance as well as the in-plane temperature distribution in observation area. (iii) The temperatures in the region around the inlet of gas flow become higher compared with the other regions when the inlet (also outlet) gas flow rate of O2 is decreased.

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(iv) When the gas flow rate of O2 is set at the stoichiometric ratio of one, the in-plane temperature distribution brought by reaction heat can be obtained. (v) From the results of one-dimensional model, the optimum inlet gas pressure is 0.41 MPa for the reaction of all gases without excess. The temperature difference by 3.4 K from the cathode catalyst layer to the interface between GDL and separator is found. The temperature is decreased remarkably in GDL of cathode side. (vi) From the result of two-dimensional model, the gas flow distribution at the interface between GDL and catalyst layer is not recognized when the porosity and permeability of GDL are set as isotropic. The through-plane temperature distribution in PEFC is not different from one-dimensional model.

Acknowledgements This work was supported by Mie prefecture industrial research institute. This work was also financially supported by Tokai Science Encouragement Association and Okasan Kato Culture Promotion Foundation. We would like to thank these organizations.

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