Three-dimensional numerical study of SOFe temperature field: Polarization heat source effect

Slimane Saighi Department of mechanical. Faculty of technology.

University Hadj Lakhder Batna slimsofc@yahoo.fr

Abstract-This study represents the fields and the temperature profiles in a single cell of an anode supported planar a SOFC fuel cell under the influence of various polarization resistance sources; The Ohm polarization resistance type is at the anode, electrolyte, cathode and interconnector. The activation polarization resistance type at the electrodes (anode and cathode). The study is done at 3-D. The numerical simulation is performed by a FORTRAN program. The results are shown in the vertical plane passing through the channel center and parallel to the gas flow direction.

Keywords: SOFC, 3-D, heat sources, Ohm, activation,

polarization, FORTRAN.

I. INTRODUCTION

The fuel cell is an electrochemical device that converts chemical energy of a reaction directly into electrical energy and heat. It is the total energy of the water reaction formation that is converted into electricity and heat. The heat generated by the stack components is evacuated through the gas flowing in the channels. This heat quantity is mainly for the heated gases input the channels and for the best function of the fuel cell. The production of this heat is under the influence of several parameters: geometry (thickness of components, cell length, and width), gas velocities (fuel, air) and under the effect of different over-potentials (Ohm, activation ... ).

This study is based on the influence of heat sources due to Ohm and activation polarizations on the temperature distribution within SOFC cell.

II. ELECTROCHEMICAL MODELING

The overall reaction in a SOFC cell is written in the form:

The change in Gibbs free energy in the SOFC cell is a function of temperature and pressure:

[p pOS

] t.G=t.Go (T)-RT.ln H,' O2 =-2FE PH,o

(1)

Bariza Zitouni *,1, Rocine Ben Moussa 2 1 Department of food Technology. Institute of veterinary

sciences and agricultural sciences and lor 1.2 Department of mechanical. Faculty of technology.

University Hadj Lakhder Batna zitounibariza@yahoo.fr, H2S0FC@gmail.com

Or t.Go(T) the standard Gibbs free energy variation (p = 01 bar) is also a function of temperature, is then given as the polynomial temperature:

t.G (T) _ 0 =1.273-2.7645xlO-4.T

2F (2)

And E is the Nernst reversible potential of a single cell. According to equation (1), the Nemst reversible potential is given by the expression:

E=- t.G =_ t.Go(T) + RT .In[PH,.pg;]

2F 2F 2F PH,o (3)

When the current flowing through the cell is non-zero, the cell voltage is lower than the ideal voltage E. This is mainly due to over-potentials; Ohm, activation and concentration. So the voltage of the cell is given by the following expression:

U cell = E -llohm -llact -llcon (4)

According to Ohm's law, the Ohm losses are given by the following expression:

llohm = Rohm .i (5)

With

(6)

Activation losses in the electrodes are expressed by Tafel approach as follows:

- RT In[_i J llact( an,cat) -azF i oean,cat) a and z are constants that takes 0,5 and 2 values

such as

. - ( PH2 J ( PH20 J (Eact,an J lOan -Yan' - ,

--

,exp ---

Pref Pref RT

(7)

(8)

978-1-4673-6374-7/13/$31.00 ©2013 IEEE

. 0, Eact,cat (p JO.25 ( J 10cat =Ycat· - . exp -

--

Pref RT

III. SOFe PHYSIC MODEL

,

Cell stud ied , ,

,

L'"

z ,

, x ' ,

,

, ,

'

0 ,

Figure I. SOFC Physic model

IV. THERMO-ELECTRIC MODELING

The momentum equations

The continuity equation

3(pu) 3(pv) 3(pw) -- + -- + -- = 0

ax ay 3z

The energy equation

or aT aT puc -+pvc -+pwc -= Pax Pay Paz

� (AaT )+� [Aor J+� (AaT )+s Ox Ox ay ay az az T

V. RESULTS AND DISCUSSION

(9)

(10)

(11)

(12)

We start in the present work by the potential (Ucell) and the electric power (P) supplied by the cell as a function of the current density imposed under a mean operating temperature of the SOFe anode supported (1069.05 K) [Fig.2] and also we present the different over-potentials: Ohm and activation as a function of current density and temperature [Fig.3] and thereafter it is the goal of our work, we present the fields and temperature profiles under effect of a different polarizations heat sources: Ohm and activation for three current densities imposed.

Our study is based on two polarizations: Ohm and activation because the concentration polarization is very low compared to other over-potentials whatever the temperature and the current density imposed as shown in the curves (l1-i) and (l1-T) [Fig.3].

To quantify the amount of heat in the SOFe cell under effect of different heat sources: Ohm and activation we will draw the Table.IV. This table contains the maximum temperatures according to the current density imposed for two heat sources [Fig.5, Fig.6 and Fig.7], and then draw a curve representing the maximum temperature according to the current density.

We note from the curves of Fig. 8 where the current density is relatively low, the heat generated between two heat sources: Ohm and activation are nigh but the Ohm source is still important to compared the activation source [Fig .5], when it increases the current density the heat generated between the two sources it diverges [Fig.6, Fig.7]. This means that the increase in temperature is very high in the case of Ohm source relatively to the activation source. This reasoning is remarkable in curves [Fig.3-(a)], as both losses: Ohm and activation are almost very high at little low current densities, against the two curves of losses are diverges with increasing current density and superior Ohm losse.

As it can be seen in the contours of the Ohm heat source shown in Figures [Fig.5-(a), Fig.6-(a), Fig.7-(a)], the temperature increases successively at input of cell to exit, but cons in the contours of activation heat source shown in Figures [Fig.5-(b) Fig.6-(b), Fig.7-(b)] the temperature rises to half of cell then remains almost stable until the output of cell, this reasoning is clear in fig [Fig.3-(b)] as the Ohm loss is always higher then activation loss whatever the temperature that's why the cell inlet the temperature is relatively low, the activation loss increases with decreasing temperature so the source is considerable subsequently the cell it releases a heat quantity, while the cell is heated so the activation loss is reduced with the heating of cell and then the heat is low in the second half of cell [Fig.9]. But at high current density the activation source is important [Fig.7-(b)], [Fig.9-(c)].

TABLE I. THE THERMO-PHYSICAL AND GEOMETRIC PROPERTIES [02], [03], [04], [05], [06], [10], [13] AND [15]

Property [unit] Value

inlet temperature [K] 873

inlet pressure [Pal 1.013 105

anode thikness [11m] 100

electrolyte thikness [11m] 20

cathode thikness [11m] 75

interconnector thikness [mm] 2.5

hydrogen inlet mass fraction ['Yo] 0.97

water vapor inlet mass fraction ['Yo] 0.03

oxygen inlet mass fraction ['Yo] 0.21

cell width [mm] 3.4

cell length [mm] 100

air inlet velocity [m/s] 6.3

fuel inlet velocity [m/s] 0.8

Property [unit) Value

air density [kglm3) 0.58

fuel density [kglm3) 0.2

permeability of electrodes porous [m2] 10.12

anode thermal conductivity [w/m.k] 6.2

electrolyte thermal conductivity [w/m.k] 2.7

cathode thermal conductivity [w/m.k] 9.6

fuel thermal conductivity [w/m.k] 0.2

air thermal conductivity [w/m.k] 0.047

anode specific heat [J/kg.k] 595

electrolyte specific heat [J/kg.k] 606

cathode specific heat [J/kg.k] 573

anodic activation energy [J/mole] 105

cathodic activation energy [J/mole] 1.2 105

universal gas constant [J/mole.k] 8.3145

Faraday constant [C/mole] 96495

anodic pre-exponential factor [Alm2] 1.334 1010

cathodic pre-exponential factor [Alm2] 2.051 109

TABLE 11. VARIOUS COMPONENTS ELECTRICAL CONDUCTIVITIES [04]

Component Expression

9.5x107 ( -1150 ) anode .exp -T-T

electrolyte 3.34xI04.exp ( -1�00 ) 4.2xl07 (-1200 )

cathode .exp -T-T

9.3x106 (-1100 ) interconnector .exp ---T T

TABLE TIT. SOURCE TERMS [ I I]

Source terms

Momentum Energy Uj = 0 · 2 I

interconnector ST =

--

Su = 0 crjnt /lr 'Uj

· 2 anode S =--- ST = _1_ + 11an .i 1I Kan cran Dan

Uj = 0 · 2 I electrolyte

Su = 0 ST =

--

cre1e

Source terms

Momentum Energy

/la .Uj · 2

cathode S =--- ST =

_1_ + 11eat .i u Keat creat Dcat

anodic channel Su = 0 ST = 0

cathodic Su = 0 ST = 0 channel

1.2 26000

1.1 24000 1.0

�og 22000 " I T=1069,05 K I � v '"

<.> 20000 ;; =>. 0.8 (ij !!! �O.7 !l!.

18000 -? (5 " c. =0.6

16000 ! '" t.> 0.5

0.4 14000

0.3 12000 10000 15000 20000 25000 30000 35000 40000 45000 50000 55000

Current Density, i (AIm')

0.50

0.45

0.40

� 0.35 "'" 0.30

(ij � 0.25 '" "0 c. 0.20 Q; <3 0.15

0.10

Figure 2. Electrochemical performance of SOFC

0.05

]������������:�:::::-, 0.00 10000 15000 20000 25000 30000 35000 40000 45000 50000 55000

0.9

0.8

0,7

� 0.6

I=" 0,5 '" :;:; � 0,4 "0 a. di: 0,3 <3

0.2

i [AIm'] (a)

I i=25000 Alm' l

950 1000 1050 1100 1150 1200 1250 1300 1350 1400 1450 T[OK]

(b)

Figure 3. (a) Over-potentials a function of i, (b) a function of T

0.01

0.00

75 X

0.005 rniiImnlmm;;;;;liII;;;;;;;;; 0.00

25

Figure 4. Velocity fields

0.01

X 0.005

002 0.04 0.06 0.08 Z

0.01

X 0.005

002 004 006 008 Z

96816

903616

839072

77.528

709984 64544 580896

516352

.51808

387264

32272

258176

193632

129088

064544

1054.18 1039.4 1024.61 1009.83 995.045 980.26 965.475 950.691 935.906 921.121 906.336 891.551 876.767 861.982 847.197

1044.2 1030.04 1015.89 1001.73 987.572 973.415 959.257 945.1 930.943 916.785 902.628 888.47 874.313 860.156 845.998

Figure 5. Temperature field under heat source effect: (a) Ohm, (b) Act at a current density i=20000

0.01 1065.92 1050.4 1034.87 1019.35

X 1003.83 988.303 0 005 972.78

957256 941.732 926208 910.685 895.161 879.637 864.113 848.589

0.01

X 0.005 ==��_""'======='"----____ I

002 0.04 0.06 0.08 z

Figure 6. Temperature field under heat source effect: (a) Ohm, (b) Act at a current density i=25000

0.01 1095.19 1077.76 1060.33 1042.9 1025.47 1008.04 990.605 973.174 955.744 938.313 920.882 903.452 886.021 868.59 851.16

0.01

X 0.005 1::����_=========""

1058.89 1043.81 1028.73 1013.65 998.574 983.494 968.414 953.334 938.254 923.173 908.093 893.013 877.933 862.853 847.773

002 004 006 Z

008

Figure 7. Temperature field under heat source effect: (a) Ohm, (b) Act at a current density i=30000

TABLE TV. MAXIMUM TEMPERATURES [K]

Table Head Maximum temperature

i=20000 A/m2

Ohm source

Act source

1120

1110

� 1100 V> � ::J ro 1090 Q; a. E <1> 1080 t-E ::J

E 1070 'x OJ

:2 1060

1050

i=25000 i=30000 1068.9 1081.45 1112.62

\058.36 1065.92 1073.97

• -.- Ohm Source -e- Act. SOlu'ce

.�.�. ---------------. e

20000 22000 24000 26000

i [Aim'] 28000 30000

Figure 8. Maximum temperatures under heat source effect

1060

1040 � 1020 l� '� r'YY...

J .,... � 1000 r 980 ..... 960

g 940 h ..... t- 920 ,.:�.

900 f -- air, Ohm Source -880 1 -- air, Act Source

} ----A-- fuel, Ohm Source -860

, .I ----T- fuel, Act Source -

840 ... 820

-0.01 0.00 0.01 0,02 0,03 0.04 0.05 0.06 0,07 0.08 0.09 0.10 0.11

Z[m] (a)

1100

1050

1000

g 950 I-

900

850

800

�

I�

I �,

r""

...:

Ii ¥"

� � -.. ...-

� II'"" �

--- air. Ohm Source -- air, Act Source -� fuel, Ohm Source ----T- fuel, Act Source

·0,01 0,00 0,01 0,02 0,03 0,04 0.05 0,06 0,07 0,08 0,09 0,10 0,11

1150

1100

1050

1000

g I- 950

900

850

800

I

�

� �

l& 1/r-

I

Z[m[ (b)

.--� � �

t::--,---- air, Ohm Source ----- air, Act Source r----� fuel, Ohm Source ----T- fu el, Act Source

·0,01 0,00 0,01 0,02 0,03 0,04 0,05 0,06 0,07 0,08 0,09 0,10 0,11

Z[m] (c)

Figure 9. Fuel temperature profil at x=1.5mm, y= I.7mm and air temperature at x=3.695mm, y=l. 7mm under heat sources effect: Ohm and Act for three

current densities: (a) i=20000, (b) i=25000, (c) i=30000

CONCLUSION

In this study, we have presented a SOFC cell modeling. Our model is based on a coupling of three models (electrochemical, fluid and thermal). Thermal phenomena is due to overpotentials, Ohmic and activation are taken into account in the modeling, for studying the effect of polarizations heat sources at the temperature distribution in an SOFC single cell.

Our results are two types: the first one are about to all over­potential as function of a current density and all over-potential as function of a temperature, the second results are about to temperature fields at a plan passed by a channels middle and with the gas flow under effect of the over-potential heat sources at the different current densities and temperature profiles of the gases (air and fuel) at a channels center line along the cell.

We have remark than the over-potential activation and over-potential ohmic values converges for low current densities, but the over-potential activation and over-potential ohmic values are diverges at high current densities.

In another hand, at low temperature values; the over­potential ohmic is upper to over-potential activation and with high temperature the two over-potentials are negligible.

The temperature elevation is always important in presence of ohmic heat source, but at low inlet temperature gases, the over-potential activation and over-potential ohmic heat sources effect are different.

The increasing temperature is important at high current density for both heat sources.

NOMENCLATURE

Parameter [unitl Meaning

cp [J/kg.k] specific heat at constant pressure

E [V] cell reversible potential

Eact,k [J/mole] activation energy at anode, at cathode

F [C/mole] Faraday constant

G [J/mole] Gibbs free energy

R [JIk.mole] universal gas constant

T [k] temperature

P [Pal pressure

Pi [Pal partial pressure of specie i

Pref [Pa] reference pressure

Rohm [Q.m2] cell ohmic resistance

Ucell [V] cell voltage

u,v, w [m/s] velocities along the three axes x, y, z

i [Alm2] current density

iO (an, cat) [Alm2] Exchange current density anodic, cathodic

K (an, cat) [m2] anodic and cathodic permeability

Su [kglm2.s2] Darcy's term

ST [w/m3] heat source

GREEK LETTERS

A [w/m.K] thermal conductivity

11 [kglm.s] dynamic viscosity

o [l1m] i th component thickness

T] [V] ovepotential

cr [S/m] electrical conductivity

p [kglm3] density

y [Alm2] pre-exponential factor anodic, cathodic

L'> variation

SUBSCRIPTS AND SUPERSCRIPTS

air con concentration

f fuel an anode, anodic

Ohm ohmic ele electrolyte

Act activation cat cathode, cathodic

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