Modeling methods for designing fuel cell flow field

A modeling method for designing a flow field of a fuel cell including a membrane electrode assembly including a catalyst layer and an electrolyte membrane, a gas diffusion layer, a flow field, and a bipolar plate, the modeling method comprising:

• modeling using a numerical model derived from a governing equation including a mass conservation equation of species, a fluid momentum in a porous media, and a modified Butler-Volmer's equation;
• and
• outputting an oxygen diffusion characteristic in a catalyst layer from the modeling result;
• wherein the fluid momentum in the porous media is expressed by the following Equations (6) and (7):
• 1
• ε
• p
• ⁢
• ρ
• ⁡
• (
• u
• ·
• ∇
• )
• ⁢
• u
• ⁢
• 1
• ε
• p
• =
• ∇
• ·
• [
• -
• pI
• +
• K
• ]
• -
• (
• μ
• ⁢
• k
• -
• 1
• +
• β
• ⁢
• ϵ
• p
• ⁢
• ❘
• "\[LeftBracketingBar]"
• u
• ❘
• "\[RightBracketingBar]"
• +
• Q
• m
• ε
• p
• 2
• )
• ⁢
• u
• +
• F
• (
• 6
• )
• wherein ε is a porosity of the porous media, p is a pressure, I is a unit matrix, K is a distribution coefficient, μ is a kinematic coefficient of viscosity, κ is a permeability of a porous media, β is a Forchheimer drag coefficient, Q is a mass source term, and F is a Faraday constant;
• ∇·(ρu)=Qm (7)

A modeling method for designing a flow field of a fuel cell including a membrane electrode assembly including a catalyst layer and an electrolyte membrane, a gas diffusion layer, a flow field, and a bipolar plate, the modeling method comprising:

• modeling using a numerical model derived from a governing equation including a mass conservation equation of species, a fluid momentum in a porous media, and a modified Butler-Volmer's equation;
• and
• outputting an oxygen diffusion characteristic in a catalyst layer from the modeling result;
• wherein the modified Butler-Volmer's equation is expressed by the following Equations (8) to (10):
• i
• =
• i
• 0
• (
• exp
• ⁡
• (
• α
• 0
• RT
• ⁢
• F
• ⁢
• η
• c
• )
• -
• (
• C
• O
• 2
• C
• O
• 2
• ⁢
• ref
• )
• ⁢
• exp
• ⁡
• (
• -
• α
• c
• RT
• ⁢
• F
• ⁢
• η
• c
• )
• )
• (
• 8
• )
• wherein i0 is an exchange current density, αa is an anode transmission coefficient, αc is a cathode transmission coefficient, R is a gas constant, CO2 is an oxygen concentration in a catalyst layer, CO2,ref is a reference oxygen concentration in the catalyst layer, and ηc is a cathode overpotential;
• ηc=Ecell−(EOCV+R0×iloc)=Ecell−ET (9)
• wherein Ecell is a voltage of a unit cell, EOCV is an open circuit voltage of a unit cell, R0 is a collective effective resistance, i is a current, and ET is a theoretical voltage of a fuel cell;
• i0=nFCOf1e−Δg11/RT (10)
• wherein n is a number of electrons (n=2) moving through the electrochemical reaction, F is a Faraday constant, f is a decay rate to a product, Δg1‡ is a size of a positive reaction active barrier, R is a gas constant, and T is a cell temperature.

A modeling method for designing a flow field of a fuel cell including a membrane electrode assembly including a catalyst layer and an electrolyte membrane, a gas diffusion layer, a flow field, and a bipolar plate, the modeling method comprising:

• modeling using a numerical model derived from a governing equation including a mass conservation equation of species, a fluid momentum in a porous media, and a modified Butler-Volmer's equation;
• and
• outputting an oxygen diffusion characteristic in a catalyst layer from the modeling result;
• wherein in the outputting of an oxygen diffusion characteristic, at least one of an oxygen distribution and a water distribution in the catalyst layer and an oxygen concentration in the catalyst layer is output.

A modeling method for designing a flow field of a fuel cell including a membrane electrode assembly including a catalyst layer and an electrolyte membrane, a gas diffusion layer, a flow field, and a bipolar plate, the modeling method comprising:

• modeling using a numerical model derived from a governing equation including a mass conservation equation of species, a fluid momentum in a porous media, and a modified Butler-Volmer's equation;
• and
• outputting an oxygen diffusion characteristic in a catalyst layer from the modeling result;
• wherein the modeling further includes
• validating an accuracy of the numerical model,
• and the validating includes:
• estimating an oxygen concentration in the catalyst layer using the numerical model;
• estimating an exchange current density based on the oxygen concentration from the following Equation (11);
• j0=nFcR*f1e−ΔG1‡/(RT) (11)
• wherein j0 is the exchange current density, n is a number of electrons (n=2) moving through the electrochemical reaction, F is a Faraday constant, c*R is the oxygen concentration, f is a decay rate to a product, Δg1‡ is a size of a positive reaction active barrier, R is a gas constant, and T is a cell temperature;
• calculating a current density based on the oxygen concentration and an exchange current density using the following Equation (12);
• and
• j
• =
• j
• 0
• (
• exp
• ⁡
• (
• α
• a
• RT
• ⁢
• F
• ⁢
• η
• c
• )
• -
• (
• c
• R
• *
• c
• R
• ,
• ref
• 0
• )
• ⁢
• exp
• ⁡
• (
• -
• α
• c
• RT
• ⁢
• F
• ⁢
• η
• c
• )
• )
• (
• 12
• )
• estimating parameters j0, αa, and αc by matching between the current density and experimental data.