Species and Temperature Distribution in Cathode of a PEMFC Munir Ahmed Khan
Presentation Layout • Brief introduction to PEM fuel cells (Construction and Working) • Types of Fuel Cells and WHY PEMFCs? • Electrodes and Electrode Strucuture • Governing Equations • Agglomerate Modeling • Schematic of Porous Electrode • Model Assumptions • Catalyst Layer Modeling • Source Terms based on Agglomerate Model • Boundary Conditions and Properties • Approach for Thermal Distribution • Results
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PEM Fuel Cells
Reaction at Anode
2H 2 → 4H + + 4e − LTH, Division of Heat Transfer
Reaction at Cathode
O 2 + 4e − + 4H + → 2H 2 O
Working of PEM Fuel Cell
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Types of Fuel Cells and Why PEMFCs
• Alkaline (AFC)
•
Proton Exchange Membrane (PEMFC)
• Direct Methanol (DMFC)
•
Phosphoric Acid (PAFC)
• Molten Carbonate (MCFC)
•
Solid Oxide (SOFC)
Working domain of different types of FCs (Fuel Cell Systems Explained, 2nd Edition)
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Electrodes and Electrode Structure • The best catalyst for both the anode and cathode is platinum. • The structure of both electrodes is the same. • The platinum catalyst formed into very small particles on the surface of somewhat larger particles of finely divided powder.
Catalyst Agglomerate
TEM image of agglomerate, 18400X
Freeze cut cross section MEA
D. Harvy, J. Power Sources, 179(2008)209-219
(N.P.Siegel, J. Power Sources, 115(2003) 81-89)
(N.P.Siegel, J. Power Sources, 115(2003) 81-89)
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Schematic of Porous Electrode
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Governing Equations • Continuity Equation ∇ ( ρ u Darcy ) = S1 • Momentum Equation
ρ f u ⋅ ∇u = −∇ p + ∇ ⋅ (μ∇u ) + S 2 • Species Transport
∇ ⋅ (ρ uYi ) = −∇ ⋅ J i + S3 • Temperature Distribution
(ρ c ) u ⋅ ∇T p f
f
= ∇ ⋅ (k f ,eff ∇T f ) + S 4
0 = ∇ ⋅ (k s ,eff ∇Ts ) + S 5 LTH, Division of Heat Transfer
Modeling of Electrodes • Three different type of modeling techniques have been used so far of simulating the electrode of PEMFC. • The thin-film model • The discrete-volume model • The agglomerate model • Among the three approaches, the agglomerate model is considered the most theoretically detailed as it attempts to include effects due to the catalyst layer physical structure.
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Model Assumptions • The fuel cell is operating at steady conditions • Inlet mixture is modeled as ideal, laminar and incompressible • All the thermal properties of both mixture and module material are considered constant • The gas diffusion layer is composed of void spaces and carbon fiber • The catalyst layer is composed of agglomerates made of platinum particles supported on carbon and ionomer electrolyte • The inlet and rib temperatures are uniform and same • Water exits as gas only (no phase change).
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Catalyst Layer Model • Agglomerate Model • Revised form of Butler-Volmer equation has been used to model the catalyst layer, given as; ptotYO2 ⎛ ( ragg + δ )δ 1 ⎜ + i = 4F H O2 − N ⎜⎝ Er kc (1 − εC ) aagg ragg DO2 − N Er = ΦL =
1 ⎛ 1 1 ⎞ ⎜⎜ ⎟⎟ − ΦL ⎝ tanh (3ΦL ) 3ΦL ⎠ ragg 3
kc Deff
1.5 Deff = DΦagg
⎛ ⎞⎛⎜ io aPteff ⎜ ⎟⎟ reff kc = ⎜ ⎜ ⎝ 4 F (1 − ε C ) ⎠⎝ CO2 LTH, Division of Heat Transfer
⎞ ⎟ ⎟ ⎠
−1
⎛ E io = ioreff exp ⎜⎜ − act R ⎝ a Ptref = ε L a Pt a Pt =
3 m Pt rPt ρ Pt t cat
⎞⎛ ⎟⎜ exp⎛⎜ − α c F η act ⎞⎟ − exp⎛⎜ (1 − α c )F η act ⎞⎟ ⎞⎟ ⎟ ⎟⎜⎝ ⎝ RT ⎠ ⎝ RT ⎠⎠ ⎠
⎛ 1 1 ⎞⎞ ⎜⎜ − ⎟⎟ ⎟ ⎟ ⎝ T To ⎠ ⎠
Source Terms Based on Agglomerate Model Diffusion Layer
Catalyst Layer
Continuity Equation
0
⎛ Mw ⎞ ⎛ Mw ⎞ i⎟ + ⎜ i⎟ −⎜ ⎝ 4 F ⎠ O2 ⎝ 2 F ⎠ H 2O
Momentum Equation
μ − ui κD
Species Transport
0
Temperature (Fluid)
hv (T f − Ts )
Temperature (Solid)
hv (Ts − T f )
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−
μ ui κC
⎛ Mw ⎞ ⎜⎜ i ⎟⎟ z F ⎝ m ⎠
ηi 0
Boundary Conditions • Inlet
CO2 = 0.98 C H 2O = 0.02 T f = 300 K k s ,eff
∂Ts = hs (Ts − T f ) ∂x
• Rib Structure
Ts = 300 K k f ,eff
∂T f ∂x
= hs (Ts − T f )
∂ ∂ (CO2 ) = (C H 2O ) = 0 ∂x ∂x u=v=0
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Boundary Conditions • Outlet
k s ,eff
∂Ts = hs (Ts − T f ) ∂x
∂ (T f ) = 0 ∂x ∂ ∂ (CO2 ) = (C H 2O ) = 0 ∂x ∂x • Upper and lower boundaries are treated as symmetric boundary conditions • The interface between the catalyst layer and membrane considered as adiabatic wall assuming the same heat is being generated at anode of the fuel cell
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Properties Thermo- Physical Properties
Geometric Properties
Agglomerate Properties
Density (solid)
1100 kg·m-3
Density (fluid)
1.13 kg·m-3
Thermal conductivity (solid)
1.71 W·m-2·K-1
Thermal conductivity (fluid)
0.051 W·m-2·K-1
Viscosity
1.5863×10-5 m2·s-1
Interstitial heat transfer coefficient
103-108 W·m-3·K-1
GDL Porosity
48%
CL Porosity
42%
CL Viscous Resistance
9.775×1011 m-2
GDL Viscous Resistance
6.537×1011 m-2
Surface to volume ratio
1000 m-1
Platinum loading
4 g·m-3
Platinum radius
1.5 nm
Agglomerate radius
1 µm
Effective agglomerate area
3.6×105 m2·m-3
Reference exchange current density
3.85×10-4 A·cm-2
Activation energy
76.5×103 J·mol-1
Charge transfer
1
Reference O2 Concentration
3.6551 mol·m-3
Henry’s Constant
2685×108 Pa·m3·mol-1
Effective Pt surface ratio
0.75
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Numerical Methods • All simulations have been carried out in Fluent and grid was generated in GAMBIT. • 3rd order of discretization for all equations • PRESTO method was used for pressure interpolation • Pressure-velocity coupling was handled by SIMPLEC algorithm • Residual convergence was limited to 10-6 for all variables. • Grid independency was achieved at 200×500 (X×Y) uniform grid. • Each simulation took about 50 minutes.
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Velocity Distribution
Velocity distribution inside PEMFC domain (Magnitude, ms-1)
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Species Distribution
Depletion of O2 during the operation of PEMFC
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Increase in the concentration of H20
LTNE and LTE Approach for Temperature Distribution • The criteria selection of LTE (Local Thermal Equilibrium) or LTNE (Local Thermal Non Equilibrium) is
ΔTloc ΔTsys
≈1 LTNE
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