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A CFD model to simulate power performance of a solid oxide fuel cell

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A CFD model to simulate power performance of a solid oxide fuel cell

B. Laoun * and M. Belhamel

Centre de Développement des Energies Renouvelables, CDER B.P. 62, Route de l’Observatoire, Bouzareah, 16340, Algiers, Algeria

Abstract - Many of today’s industries, including automotive manufacturers, are investing considerable resources in finding and implementing new technologies to replace traditional power production methods in order to stay competitive in future markets. One of these newly emerging technologies is based on hydrogen and fuel cells. The solid oxide fuel cell is one of the most attractive types of fuel cells. Based on numerical simulations, the polarization curve and the electrical power for high temperature solid oxide fuel cells (SOFC) are presented. With the aid of a well knows semiphysical equation, that describes gas flow and mass transport flow, the partial differential equations are solved with a CFD COMSOL code. As a result we quantify the performance of a planar SOFC in various pressures and temperatures.

Keywords: Hydrogen, Butler-Volmer equation, Computer Simulation, Electrochemical model, Overpotential.

1. INTRODUCTION

The attractive potential for the solid oxide fuel cells (SOFC) has been the application in transportation, in vehicular auxiliary power units (APU), and in the stationary power generation with outputs from 100 W to 2 MW. This potential is inherent to the higher efficiency of SOFC, and also to the fact that at higher operating temperature, combination with heat engine energy recovery devices or combined heat and power further increases overall fuel efficiency [1], this enables SOFC to utilize hydrocarbons without upstream fuel processing.

A planar single cell of solid oxide fuel, shown in Fig. 1, is made up of: an activated catalyst cathode, where the electrochemical reduction of oxygen gas into oxygen ion occurs, this ion can then diffuse through the solid oxide electrolyte to the anode where they can electrochemically oxidize the fuel. The byproduct of this operation is water as well as two electrons. These electrons then flow through an external circuit where they can do work. The cycle then repeats as those electrons enter the cathode material again.

Fig. 1: Schematic of single cell of solid oxide fuel       

* b.laoun@cder.fr , m.belhamel@cder.dz

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198

SOFC can have multiple geometries. The planar fuel cell design geometry is the typical sandwich type geometry, employed by most types of fuel cells, where the electrolyte is sandwiched in between the electrodes, Fig.1. Tubular geometries, where either air or fuel is passed through the inside of the tube, the other gas is passed along the outside of the tube.

The criteria to the wide deployment of SOFC, is based on obtained a higher efficiency, thus identify the physical and chemical parameters that optimize the all operation. In this present work, a modeling method, based on semi physical approach solved by a CFD technique, is utilized to visualize the power output on a defined single SOFC, under a variety of pressures and temperatures.

2. MODEL DEVELOPMENT The model is based on the following assumptions:

1. The SOFC operates under steady state conditions using H2 as a fuel and air as oxidizer.

2. The reactant gases are taken as ideal gases.

3. The gas flow is laminar and compressible.

4. The gas diffusion layers, catalyst layers and membrane are treated as isotropic porous media.

5. The electrochemical reactions are considered heterogeneous at the electrode/electrolyte interfaces.

6. The model is assumed to be isothermal.

7. Ohmic and reaction heating are not taken into account.

3. MODEL GEOMETRY AND COMPUTATIONAL DOMAIN SOFC geometry can be planar or tubular, currently, better performance is observed of the planar geometry than the tubular design [1, 2], because the planar design has a lower resistance comparatively. The geometry presented here is a 3D planar SOFC, Fig.2. The 2D computational domain, is made of the anode and cathode current collectors, flow channels, the gas diffusion layers, the anode and the cathode catalyst layers, and the electrolyte layers.

Fig. 2: The planar SOFC with 2D computational domain and 3D representation 3.1 Modeling equations

3.1.1 Gas flow equation in the open channels

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The flow in the open channels is modelled by a Weakly compressible Navies-Stokes equations, the continuity equation is:

0 ) u (ρ =

(1)

The W.N.S. is:

) u 3( ) 2 )T u ( u ( p

) u u

(

⎥⎦

⎢⎣µ× +

+

=

×

ρ (2)

u is the gas velocity vector (m/s).

3.1.2 Gas flow equation in the gas diffusion layer

The governing equation of the flow, in porous media of the GDE (Gas diffusion layer), is the Brinkman equation:

⎥⎦

⎢⎣µ× +

+

× ε

=

+ κ

ε µ ( u))

3 T 2 ) u ( u ( p

m u

S (3)

Sm ) u (ρ =

(4)

ε and κ denote, respectively, the porosity and permeability (m2) of the medium, and Sm is the mass source term, defined as follows:

×× ×

= k

Sa k F

n Mk k , Jct Sm

k ,

Jct - The charge transfer current density, (A/m2); Sa- The specific surface area, (m2/m3); Mk- Molar mass of species k, (kg/mol), with Mk = ρk×

(

R×T p

)

; mk- Mass of the specie k, (kg); ρk- Density of species k (kg/m3); R- Ideal gas constant, (J/mol K); T- Temperature, (K); p- Pressure (atm); F- Faraday’s constant, (C/mol);

nk- Number of electrons transferred per pole of species of interest.

Both the air and fuel flows were considered as ideal gas mixtures with the density given by:

×

= ×

ρ

k Mk mk T

R p

3.1.3 Special transport equations

The approach used to solve the mass transport in the porous medium is the Maxwell- Stefan’s equation for diffusion and convection [3]:

rk 1

k p

) p k xk M (

M k k k

M M Dˆkm u k

k =

= ⎟⎟

⎜⎜

+ ω

ω +ω ω

ρ

ρ ω

(7)

ωk is the weight fraction of species k. Dˆkm is the Maxwell-Stefan diffusivities (m2/s), described by the following empirical equations:

2 / 1 Mm

1 Mk

1 3 2 / 1m 3 / 1 p k

75 . T1 10 8

16 . km 3

Dˆ

+

ς +ς

×

= (8)

ςkis the molar diffusion volume of species k (m3/mol), given in Table 1 [4].

rk- reaction source term for species k (kg/m3s).

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200

Table 1: Molar diffusion volume

Species Molar diffusion volume (m3/mol) H2

O2 H2O N2

6 × 10-6 16.6 × 10-6 12.7 × 10-6 17.9 × 10-6

F k nk

Mk k , Jct

rk ν

×

= × (9)

υk the stoichiometric coefficient and nk is the number of electrons in the reaction.

Both the anode and cathode are assumed to be made of porous materials providing electronic and ionic conductivity, then for the diffusion in porous medium, the porosity and the tortuous nature of the path through porous bodies, is taken into account by the approach proposed by Bruggemann [3, 5]:

τ ε

×

= D

Deff (10)

ε, the porosity of the medium, τ, the tortuosity of the porous medium 3.1.4 Current conservation equation

The electronic charge balance in the anode and cathode current is solved for the current conservation equation:

(

σelectronic×φelectronic

)

= 0

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electronic

σ , the electronic conductivity of the current feeder, (S/m); φelectronic, the electronic potential of the current feeder, (V).

The ionic charge balance, valid in the ionic conductor is:

(

σionic×φionic

)

= 0

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ionic

σ , the ionic conductivity of the current feeder, (S/m); φionic, the electronic potential of the current feeder, (V).

In, GDE the governing equations for the charge balance are as follows:

(

σelectronic×φelectronic

)

=Sm×Jct

(13)

(

σionic×φionic

)

= Sm×Jct

(14)

The density current coupled with overpotential provided a solution to the local potential losses in the electrolyte, electrodes and interconnects [1, 6]. The relation between the current density and the potential of the electrodes are described using the well knows approach of Butler and Volmer, the global equation is:

⎟⎟

⎜⎜

× η

×

× ν

α

⎟⎟

⎜⎜

× η

×

× ν

× α

= R T

F c e exp c

T R

F a e exp a J0

J (15)

ηa, ηc, the anodic and cathodic overpotential

νe, the stoichiometric coefficient of the reaction considered

αa, αcthe anodic and the cathodic charge transfer coefficients, αa= 0.5, αc= 1.

J0, the exchange current density expressed for the anode and the cathode as Arrhenius’s equation like [1]:

The anodic current density is expressed as:

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×

×

×

×

×

×

=

T R

103 exp 100

Pref O PH Pref PH 108 5 . a 5

J0 2 2 (16)

The cathodic current density is expressed as:

×

×

×

×

×

= R T

103 exp 120

25 . 0 Pref PO 108 0 . c 7

J0 2 (17)

R, universal gas constant, R = 8.3×145 (J mol-1K-1); Pref , reference pressure = 1 atm.

The electric conductivities for the different medium composing the SOFC, for our case the material used is based on the YSZ electrolyte material [1]

× ⎛ −

=

σ T

exp 1150 T

106 95

anode (18)

× ⎛ −

=

σ T

exp 1200 T

106 42

cathode (19)

× ⎛ −

×

=

σ T

10300 4 exp

10 34 . e 3

electrolyt (20)

The overpotential of the SOFC is computed as:

Vref ionic electronic φ φ

=

η (21)

Vref, the reference potential of the electrode defined for the anode and the cathode.

=

cathode the oc in

V

anode the in 0

Vref (22)

⎪⎩

φ φ

φ

= φ

η electronic ionic Voc inthecathode anode the ionic in

electronic

(23) Where Voc represents the open circuit voltage.

The reversible cell potential Erev can be found from well-known thermodynamic data [5]:

c) , pO ln 5 . a 0 , pH ln 5 ( 10 3080 . 4 ) 15 . 298 T 4 ( 10 4517 . 8 2291 . rev 1

E = × × + × × 2 + 2 (24)

a H ,

p 2 , partial pressure of hydrogen in the anode side, (atm); pO ,a

2 , partial pressure of oxygen in cathode side, (atm).

3.2 Boundary conditions

The boundary conditions are defined as follows:

ƒ At the inlets, anode side and cathode side, the boundary type is mass-flow-inlet.

ƒ At the outlets, anode side and cathode side, the boundary type is pressure-outlet.

ƒ A zero flux boundary condition for the membrane phase potential, in addition the electric potential at the top of the anode side interconnect is presumed constant, while at the bottom of the cathode side interconnect, a constant current density is prescribed at the base of the interconnect.

ƒ A zero flux boundary condition for the solid phase.

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202

3.3 Model geometric and computational domain

The electrolyte considered for this study is based on the Y2O3-stabilized ZrO2 (YSZ) ceramic material. The cathode is made of Sr-doped LaMnO3 strontium-doped lanthanum and the anode is made of nickel/yttria-stabilized zirconia (Ni/YSZ) cermet.

The physical properties for the different material used can be found in the work of [7-9].

The planar SOFC geometry, as shown in Fig. 2, is considered as the basic configuration, with the information given in Table 2 and Table 3. The computational domain is solved in the commercial CFD software COMSOL that is based on the finite element method (FEM), the direct linear solver PARDISO, integrated in COMSOL code, is used to solve the coupled equations.

Table 2: The planar SOFC dimensions

Element Size (mm)

Anode thickness, da Cathode thickness, dc Electrolyte thickness, de Unit cell width, d Cell width, dcell Cell length, L Rib width, drib

Interconnect height, dint Channel height, dch Channel width, tch

400 × 10-3 10 × 10-3 10 × 10-3 1 10 10 0.25 0.5 0.4 0.5

Table 3: Specific surface area of the SOFC elements

Description Value

Anode specific surface area Cathode specific surface area Porosity

1 × 10-9 (l/m) 1 × 10-9 (l/m) 0.4

4. RESULTS AND DISCUSSION

The performance of SOFC is evaluated from the polarization curves the current vs.

voltage and the current vs. the power delivered, at different temperatures and pressures.

For this purpose the inlet hydrogen mass fraction is fixed to 50 % and the values for temperature are fixed to 800 °C and 900 °C, and the values for pressure are 1, 5, 7 et 10 atm.

The polarization curves, power density are shown from Fig. 3 to Fig. 8. We noticed that the performance of SOFC increases with increasing pressure and temperature. With increasing temperature the activation losses are reduced and mass transfer is enhanced, resulting in a reduction in cell resistance and increase performance [3].

There is also the displacement of the polarization curve towards higher current densities by increasing the temperature; this is due to the increase of the conductivity of the membrane with increasing temperature.

The graph for the power density vs. current density shows that the maximum power density shifts to higher current densities with increasing temperature as a result of reduced ohmic losses [1, 3, 6].

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Fig. 3: Polarization curve vs. pressure at 800°C

Fig. 4: Power density vs. pressure at 800°C

Fig. 5: Polarization curve vs. pressure at 900°C

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204

Fig. 6: Power density vs. pressure at 900°C

Fig. 7: Polarization curve vs. temperature at 5 atm

Fig. 8: Power density vs. temperature at 5 atm

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In addition, Fig. 3 to Fig. 8 shows that the performance of the SOFC is improving with increasing pressure; this can be explained by the Nernst equation. All the polarization curves shift positively with increasing pressure. Another reason for the improved performance is the increase of partial pressure of reactive gas with increasing operating pressure.

The maximum power density evolves positively with increasing pressure as the rate of chemical reaction is proportional to the partial pressure of hydrogen and oxygen.

Indeed, higher pressures can forces hydrogen and oxygen to be in close contact with the electrolyte.

5. CONCLUSION

The model for estimating SOFC electrical power output, is based on the description and modeling the governing equation for gas flow in the anode and cathode channel, also the governing equation of the electrical potential in the different area that compose a single solid oxide cell.

The observations are consistent with the fact that the performance of the PEMFC is improving with increasing pressure, and all the curves of polarization varies positively.

The maximum power density evolves positively with increasing pressure because as the rate of chemical reaction is proportional to the partial pressure of hydrogen and oxygen.

It is interesting to note that the increase of temperature promote the electronic and the ionic conductivity of the electrode and the electrolyte respectively. The increase of the pressure, promote the efficient mass transport of the chemical species

REFERENCES

[1] A. Chaisantikulwat, C. Diaz-Goano and E.S. Meadows, ‘Dynamic Modelling and Control of Planar Anode-Supported Solid Oxide Fuel Cell’, Computers and Chemical Engineering, Vol.

32, N°10, pp. 2365 – 2381, 2008.

[2] B.A. Haberman and J.B. Young, ‘Three-Dimensional Simulation of Chemically Reacting Gas Flows in the Porous Support Structure of an Integrated-Planar Solid Oxide Fuel Cell’, International Journal of Heat and Mass Transfer, Vol. 47, N°17-18, pp. 3617 - 3629, 2004.

[3] S. Kakaç, A. Pramuanjaroenkij and Xiang Yang Zhou, ‘A Review of Numerical Modeling of Solid Oxide Fuel Cells’, Review Article, International Journal of Hydrogen Energy, Vol. 32, N°7, pp. 761 - 786, 2007.

[4] R. Bird, W. Stewart, and E. Lightfoot, ‘Transport Phenomena’, 2nd Ed., John Wiley & Sons, 2002.

[5] J.H. Koh, H.K. Seo, Y.S. Yoo and H.C. Lim, ‘Consideration of Numerical Simulation Parameters and Heat Transfer Models for a Molten Carbonate Fuel Cell Stack’, Chemical Engineering Journal, Vol. 87, N°3, pp. 367 – 379, 2002.

[6] K. Sudaprasert, R.P. Travis and R.F. Martinez-Botas, ‘A Computational Fluid Dynamics Model of a Solid Oxide Fuel Cell’, Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power and Energy, Vol. 219, pp. 159 - 167, 2005.

[7] Y. Wang, F. Yoshiba, T. Watanabe and S. Weng, ‘Numerical Analysis of Electrochemical Characteristics and Heat / Species Transport for Planar Porous Electrode-Supported SOFC’, Journal of Power Sources, Vol. 170, N°1, pp. 101 - 110, 2007.

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[8] R. Perry and D. Green, ‘Perry’s Chemical Engineering Handbook’, 7th Ed., McGraw-Hill, 1997.

[9] Z. Qu, P.V. Aravind, S.Z. Boksteen, N.J.J. Dekker, A.H.H. Janssen, N. Woudstra and A.H.M.

Verkooijen, ‘Three-Dimensional Computational Fluid Dynamics Modeling of Anode- Supported Planar SOFC’, International Journal of Hydrogen Energy, Vol. 36, N°16, pp.

10209 – 10220, 2011.

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