US 12,614,743 B2 · Discretization modeling method for electro-osmotic drag effect of water conservation in a fuel cell

Abstract

The present disclosure provides a discretization modeling method for electro-osmotic drag effect of water conservation in a fuel cell, comprising: establishing a conservation equation of membrane water in the fuel cell, performing a discretization for a complete electro-osmotic drag effect, obtaining a discretization simulation model of the complete electro-osmotic drag effect based on results of the discretization, solving the conservation equation of membrane water to establish a discretization simulation model of electro-osmotic drag effect of water conservation in the fuel cell. The discretization modeling method for the electro-osmotic drag effect of water conservation in a fuel cell in the present disclosure can perform a discretization and a numerical calculation for a complete electro-osmotic drag effect, the discretization comprising a water conservation portion caused by a membrane water content gradient and a water conservation portion caused by a proton transport flux gradient.

A discretization modeling method for electro-osmotic drag effect of water conservation in a fuel cell, wherein the fuel cell includes an anode catalytic layer, a proton exchange membrane, and a cathode catalytic laver, and the discretization modeling method comprises:

S1, establishing a conservation equation of membrane water in the fuel cell;
S2, performing a discretization for a complete electro-osmotic drag effect;
S3, obtaining a discretization simulation model of the complete electro-osmotic drag effect based on results of the discretization in S2;
S4, solving the conservation equation of membrane water to establish a discretization simulation model of an electro-osmotic drag effect of water conservation in the fuel cell;
S5, obtaining, based on the discretization simulation model of the electro-osmotic drag effect of water conservation in the fuel cell, an electro-osmotic drag effect of the anode catalytic layer, an electro-osmotic drag effect of the proton exchange membrane, and an electro-osmotic drag effect of the cathode catalytic layer to characterize the electro-osmotic drag effects of the anode catalytic layer, the proton exchange membrane, and the cathode catalytic layer of the fuel cell in operation;
performing the discretization for the complete electro-osmotic drag effect comprising:
performing a discretization for a water conservation portion caused by a membrane water content gradient and performing a discretization for a water conservation portion caused by a proton transport flux gradient;
for the water conservation portion caused by the membrane water content gradient, calculation expressions are as follows:
{
1
F
⁢
(
J
ion
⁢
∂
n
d
∂
x
)
❘
"\[RightBracketingBar]"
CLa
=
2.5
22
⁢
F
(
J
ion
CLa
⁢
λ
2
-
λ
1
δ
CLa
)
1
F
⁢
(
J
ion
⁢
∂
n
d
∂
x
)
❘
"\[RightBracketingBar]"
MEM
=
2.5
22
⁢
F
(
J
ion
MEM
⁢
λ
3
-
λ
2
δ
MEM
)
1
F
⁢
(
J
ion
⁢
∂
n
d
∂
x
)
❘
"\[RightBracketingBar]"
CLc
=
2.5
22
⁢
F
(
J
ion
CLc
⁢
λ
4
-
λ
3
δ
CLc
)
(
8
)
where F is the Faraday's constant;
1
F
⁢
(
J
ion
⁢
∂
n
d
∂
x
)
❘
"\[RightBracketingBar]"
CLa
,
1
F
⁢
(
J
ion
⁢
∂
n
d
∂
x
)
❘
"\[RightBracketingBar]"
MEM
,
and
1
F
⁢
(
J
ion
⁢
∂
n
d
∂
x
)
❘
"\[RightBracketingBar]"
CLc
are the water conservation portions caused by the membrane water content gradient in the anode catalytic layer, the proton exchange membrane, and the cathode catalytic layer, respectively;
J
ion
CLa
,
J
ion
MEM
,
J
ion
CLc
are the proton transport flux in the anode catalytic layer, the proton exchange membrane, and the cathode catalytic layer, respectively;
δCLa, δMEM, δCLc are thickness of the anode catalytic layer, the proton exchange membrane, and the cathode catalytic layer, respectively;
λ1, λ2, λ3, λ4 are the membrane water content at the left boundary of the anode catalytic layer, at the interface between the anode catalytic layer and the proton exchange membrane, at the interface between the proton exchange membrane and the cathode catalytic layer, and at the right boundary of the cathode catalytic layer;
calculation expressions of the proton transport flux in the anode catalytic layer, the proton exchange membrane, and the cathode catalytic layer are as follows:
{
J
ion
CLa
=
J
1
+
J
2
2
J
ion
MEM
=
J
2
+
J
3
2
J
ion
CLc
=
J
3
+
J
4
2
(
9
)
where, J1, J2, J3, J4 are the proton transport flux at the left boundary of the anode catalytic layer, at the interface between the anode catalytic layer and the proton exchange membrane, at the interface between the proton exchange membrane and the cathode catalytic layer, and at the right boundary of the cathode catalytic layer;
for the proton transport flux at the interface between the anode catalytic layer and the proton exchange membrane and at the interface between the proton exchange membrane and the cathode catalytic layer, the expressions are as follows:
{
J
1
,
J
4
=
0
J
2
,
J
3
=
I
(
10
)
where I is current density;
for the water conservation portion caused by the proton transport flux gradient, calculation expressions are as follows:
{
1
F
⁢
(
n
d
⁢
∂
J
ion
∂
x
)
❘
CLa
=
2.5
22
⁢
F
(
λ
CLa
⁢
J
2
-
J
1
δ
CLa
)
1
F
⁢
(
n
d
⁢
∂
J
ion
∂
x
)
❘
MEM
=
2.5
22
⁢
F
(
λ
MEM
⁢
J
3
-
J
2
δ
MEM
)
1
F
⁢
(
n
d
⁢
∂
J
ion
∂
x
)
❘
CLc
=
2.5
22
⁢
F
(
λ
CLc
⁢
J
4
-
J
3
δ
CLc
)
(
11
)
where
⁢
⁢
1
F
⁢
(
n
d
⁢
∂
J
ion
∂
x
)
❘
CLa
,
1
F
⁢
(
n
d
⁢
∂
J
ion
∂
x
)
❘
MEM
and
⁢
1
F
⁢
(
n
d
⁢
∂
J
ion
∂
x
)
❘
CLc
are the water conservation portions caused by the proton transport flux gradient in the anode catalytic layer, the proton exchange membrane, and the cathode catalytic layer, respectively;
λCLa, λMEM, λCLc are the membrane water content at the center of the anode catalytic layer, the proton exchange membrane, and the cathode catalytic layer, respectively.

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Discretization modeling method for electro-osmotic drag effect of water conservation in a fuel cell

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Discretization modeling method for electro-osmotic drag effect of water conservation in a fuel cell

Life of this patent

Abstract

Claims5