PRECISION DESIGN OF PROTON EXCHANGE MEMBRANE FUEL CELL FLOW FIELD BASED ON WATER AND HEAT TRANSFER MECHANISM

Xiangrong, Liao; Su, Jianbin; Photong, Chonlatee

doi:10.21577/0100-4042.20240047

Liao Xiangrong

Fujian Polytechnic of Information Technology, Fujian, 350003 China

Jianbin Su

Fuzhou Polytechnic, Fujian, 350108 China

Chonlatee Photong ^**e-mail: 13609517160@163.com

Faculty of Engineering, Mahasarakham University, 44160 Maha Sarakham, Thailand

https://orcid.org/0009-0002-4424-1132

*e-mail: 13609517160@163.com

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Figure 1
The calculated area

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Figure 2
Test verification: (a) schematic diagram of experiment device; (b) comparison of experiment and simulation results

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Figure 3
Comparison of PEMFC polarization curves of flow fields with different precision

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Figure 4
Concentration difference overpotential of different precision flow fields of PEMFC

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Figure 5
Analysis of oxygen inhomogeneity on the surface of cathode GDL of different precision flow field PEMFC

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Figure 6
Molar fraction of oxygen on the cathode GDL of PEMFC with different precision flow fields (cell voltage = 0.4 V): (a) 1 mm × 1 mm; (b) 0.7 mm × 0.7 mm; (c) 0.5 mm × 0.5 mm

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Figure 7
Current density inhomogeneity on the surface of the cathode CL of flow field

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Figure 8
Current density distribution of PEMFC cathode CL surfaces with different precision flow fields (cell voltage = 0.4 V): (a) 1 mm × 1 mm; (b) 0.7 mm × 0.7 mm; (c) 0.5 mm × 0.5 mm

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Figure 9
Mass transfer velocity of PEMFC with different precision flow fields (cell voltage = 0.4 V): (a) 1 mm × 1 mm; (b) 0.7 mm × 0.7 mm; (c) 0.5 mm × 0.5 mm

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Figure 10
Distribution of GDL liquid water in different precision flow field PEMFC (equal scale amplification, same size of MEA in the three figures): (a) 1 mm × 1 mm; (b) 0.7 mm × 0.7 mm; (c) 0.5 mm × 0.5 mm

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Figure 11
Hydration water distribution of adjacent flow fields of the different precision flow field (equal scale amplification, same size of MEA in the three figures): (a) 1 mm × 1 mm; (b) 0.7 mm × 0.7 mm; (c) 0.5 mm × 0.5 mm

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Table 1
Parameters

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Table 2
Conditional parameters of the experimental PEMFC

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Parameter	Value
Cell voltage	1 V
Reference pressure	1.0133 × 10⁵ Pa
Anode equilibrium potential	0.030549 V
Anode power viscosity	2.46 × 10^-5 Pa s
Anode stoichiometry ratio	2.5
Anode transfer coefficient	0.5
Cathode equilibrium potential	1.2069 V
Cathode power viscosity	1.19 × 10^-5 Pa s
Cathode stoichiometric ratio	1.5
Cathode transfer coefficient	0.5
Cell length	2 mm
Channel height	0.05 mm
Channel width	0.5 mm
CL conductivity	25 S m^-1
CL porosity	0.3
CL thickness	18 µm
Density of liquid water	1000 kg m^-3
Diffusivity of hydrogen in the ionomers	2 × 10^-9 m² s^-1
Dissociation polymer density	2000 kg m^-3
Electrode volume fractions, CL	0.4
Electrolyte liquid phase volume fraction	0.3
Exchange current density, hydrogen oxidation	100 A m^-2
Exchange current density, oxygen reduction	0.01 A m^-2
Exchange membrane with wet molar volume	1.8 × 10^-4 m³ mol 1
Exchange the membrane for a dry molar volume	5.5 × 10^-4 m³ mol 1
Gas constant	8.314 J mol^-1 K^-1
GDL conductivity	100 S m^-1
GDL permeability	6.2 × 10^-12 m²
GDL porosity	0.5
GDL thickness	215 µm
Hydrogen gas reference diffusion coefficient	1.24 × 10-⁴ m² s¹
Hydrogen molar mass	2 g mol^-1
Hydrogen-water vapor binary diffusion coefficient	9.15 × 10^-5 m² s¹
Initial humidity of the anode	100%
Initial humidity of the cathode	100%
Isomeric equivalents	1.1 kg mol^-1
Liquid water density	1000 kg m^-3
Liquid water viscosity	3.7 × 10-⁴ Pa s
Mixed gas viscosity	2.46 × 10^-5 Pa s
Nitrogen molar mass	28 g mol^-1
Nitrogen-water vapor binary diffusion coefficient	2.56 × 10^-5 m² s¹
Number of integrals of the ionomer	0.2
Oxygen molar mass	32 g mol^-1
Oxygen reference diffusion coefficient	2.8 × 10^-5 m² s-¹
Oxygen-nitrogen gas binary diffusion coefficient	2.2 × 10^-5 m² s-¹
Oxygen-water vapor binary-dependent diffusion coefficient	2.82 × 10^-5 m² s¹
Porous electrode permeability	1.24 × 10^-12 m²
Proton exchange membrane with an equivalent molar volume	5.17 × 10^-4 m³ mol 1
Proton-exchange membrane thickness	15 µm
Reference diffusion coefficient of water in the anode	1.24 × 10-⁴ m² s¹
Reference diffusion coefficient of water in the cathode	3.6 × 10⁵ m² s-¹
Reference temperature	353.15 K
Rib width	1 mm
Solid-phase volume fraction, GDL	0.4
Water molar mass	18 g mol^-1
Water vapor viscosity	2.1 × 10⁵ Pa s

Parameter / unit	Value
GDL porosity	0.4
GDL thickness / mm	0.215
CL thickness / mm	0.018
CL porosity	0.5
Platinum load / mg cm^-2	0.5
Flow field type	Three snake-shaped flow field
Effective area / cm²	25
Air flow rate / (mL min^-1)	680
Hydrogen flow rate / (mL min^-1)	340
Cell temperature / °C	70
Gas temperature / °C	70

i_{0, a} = i_{0, a}^{r e f} (1 - s_{i c e} - s_{l}) {(\frac{c_{H}_{_{2}}}{c_{H_{2}}^{r e f}})}^{0.5} \times \exp (- 1400 (\frac{1}{T} - \frac{1}{298.15}))

i_{0, a} = i_{0, a}^{r e f} (1 - s_{i c e} - s_{l}) {(\frac{c_{H_{2}}}{c_{H_{2}}^{r e f}})}^{0.5} \times \exp (- 7900 (\frac{1}{T} - \frac{1}{298.15}))

I_{D, a} = \frac{2 F c_{H_{2}}}{\frac{δ_{C L, a}}{2 D_{H_{2}, C L}^{e f f}} + \frac{δ_{G D L}}{D_{H_{2}, G D L}^{e f f}}}

I_{D, c} = \frac{4 F c_{O_{2}}}{\frac{δ_{C L, c}}{2 D_{O_{2}, C L}^{e f f}} + \frac{δ_{G D L}}{D_{O_{2}, G D L}^{e f f}}}

η_{o h m i c} = - (\frac{δ_{G D L}}{σ_{s, G D L}} + \frac{δ_{C L}}{σ_{s, C L}} + \frac{δ_{M E M}}{σ_{M E M}})

\frac{\partial}{\partial t} (\frac{ρ_{g} {\vec{u}}_{g}}{ε (1 - s_{l})}) + \nabla (\frac{ρ_{g} {\vec{u}}_{g} {\vec{u}}_{g}}{ε^{2} {(1 - s_{l})}^{2}}) = - \nabla p_{g} + μ_{g} \nabla (\nabla (\frac{{\vec{u}}_{g}}{ε (1 - s_{l})}) + \nabla (\frac{{\vec{u}}_{g}^{T}}{ε (1 - s_{l})})) - \frac{2}{3} μ_{g} \nabla (\nabla (\frac{{\vec{u}}_{g}}{ε (1 - s_{l})})) + S_{u}

ψ_{μ i j} = \frac{{[1 + {(\frac{μ_{i}}{μ_{j}})}^{0.5} {(\frac{M_{i}}{M_{j}})}^{0.25}]}^{0.5}}{{[8 (1 + \frac{M_{i}}{M_{j}})]}^{0.5}}

J (s) = {\begin{matrix} 1.417 (1 - s_{l}) - 2.120 {(1 - s_{l})}^{2} + 1.263 {(1 - s_{l})}^{3} & , θ < 90 ° \\ 1.417 s_{l} - 2.120 s_{l}^{2} + 1.263 s_{l}^{3} & θ \geq 90 ° \end{matrix}

\frac{ρ_{m e m}}{E W} \frac{\partial (ω λ_{n f})}{\partial t} - \frac{ρ_{m e m}}{E W} \nabla (ω^{1.5} D_{n m w} \nabla λ_{n f}) = S_{n m w}

D_{n m w} = {\begin{matrix} 3.1 \times 10^{- 7} λ_{n f} (\exp (0.28 λ_{n f}) - 1) \exp (\frac{- 2346}{T}) & , 0 < λ_{n f} < 3 \\ 4.17 \times 10^{- 8} λ_{n f} (161 \exp (- λ_{n f}) + 1) \exp (\frac{- 2346}{T}) & 3 \leq λ_{n f} < 17 \end{matrix}

\frac{\partial}{\partial t} ({(ρ C_{p})}_{f l, s l}^{e f f} T) + \nabla {(ρ C_{p})}_{f l}^{e f f} {\vec{u}}_{g} T - \nabla κ_{f l . s l}^{e f f} \nabla T = S_{T}

{(ρ C_{p})}_{f l, s l}^{e f f} = ε [s_{l} ρ_{l} {(C_{p})}_{l} + (1 - s_{l}) ρ_{g} {(C_{p})}_{g}] + (1 - ε - ω) ρ_{s l d} {(C_{p})}_{s l d} + ω ρ_{m e m} {(C_{p})}_{m e m}

ψ_{k i j} = \frac{{[1 + {(\frac{k_{i}}{k_{j}})}^{0.5} {(\frac{M_{i}}{M_{j}})}^{0.25}]}^{0.5}}{{[8 (1 + \frac{M_{i}}{M_{j}})]}^{0.5}}

S_{v - l} = {\begin{matrix} γ_{c o n d} ε (1 - s_{l}) \frac{(p_{v p} - p_{s a t}) M_{H_{2} O}}{R T} & if & p_{v p} \geq p_{s a t} \\ γ_{e v a p} ε s_{l} \frac{(p_{v p} - p_{s a t}) M_{H_{2} O}}{R T} & if & p_{v p} < p_{s a t} \end{matrix}

\log_{10} (\frac{p_{s a t}}{101325}) = - 2.1794 + 0.02953 (T - 273.15) - 9.1837 \times 10^{- 5} {(T - 273.15)}^{2} + 1.4454 \times 10^{- 7} {(T - 273.15)}^{3}

S_{n - v} = {\begin{matrix} ζ_{n - v} \frac{ρ_{m e m}}{E W} (λ_{n f} - λ_{e q}) (1 - s_{l}) if λ_{n f} \geq λ_{e q} \\ ζ_{n - v} \frac{ρ_{m e m}}{E W} (λ_{e q} - λ_{n f}) (1 - s_{l}) if λ_{n f} < λ_{e q} \end{matrix}

λ_{e q} = {\begin{matrix} 0.043 + 17.81 a - 39.85 a^{2} + 36.0 a^{3} & if & 0 \leq a \leq 1 \\ 14.0 + 1.4 (a - 1) & 1 < a \leq 3 \end{matrix}

S_{H_{2}} = {\begin{matrix} - \frac{j_{a}}{2 F} M_{H_{2}} & in & \begin{matrix} anode & CL \end{matrix} \\ 0 & \begin{matrix} other \end{matrix} \end{matrix}

S_{O_{2}} = {\begin{matrix} - \frac{j_{c}}{4 F} M_{O_{2}} & in & \begin{matrix} cathode & CL \end{matrix} \\ 0 & \begin{matrix} other \end{matrix} \end{matrix}

S_{u} = {\begin{matrix} - \frac{μ_{g}}{K_{g}} {\vec{u}}_{g} & in & CL & and & GDL \\ 0 & other \end{matrix}

S_{n m w} = {\begin{matrix} 0 & membrane \\ \frac{j_{c}}{2 F} - S_{n - v} + S_{E O D} & \begin{matrix} cathode & CL \end{matrix} \\ - S_{n - v} + S_{E O D} & \begin{matrix} anode & CL \end{matrix} \end{matrix}

j_{a} = (1 - s_{l}) j_{0, a}^{r e f} {(\frac{c_{H_{2}}}{c_{H_{2}}^{r e f}})}^{0.5} \times [\exp (\frac{2 α_{a} F}{R T} η_{a c t, a}) - \exp (- \frac{2 α_{c} F}{R T} η_{a c t, a})]

j_{c} = (1 - s_{l}) j_{0, c}^{r e f} (\frac{c_{O_{2}}}{c_{O_{2}}^{r e f}}) \times [- \exp (\frac{4 α_{a} F}{R T} η_{a c t, c}) + \exp (- \frac{2 α_{c} F}{R T} η_{a c t, c})]

S_{T} = {\begin{matrix} j_{a} | η_{a c t} | + {‖ \nabla ϕ_{e l e} ‖}^{2} κ_{e l e}^{e f f} + {‖ \nabla ϕ_{i o n} ‖}^{2} κ_{i o n}^{e f f} + S_{p c} & anode CL \\ - \frac{j_{c} T Δ S}{2 F} + j_{c} | η_{a c t} | + {‖ \nabla ϕ_{e l e} ‖}^{2} κ_{e l e}^{e f f} + {‖ \nabla ϕ_{i o n} ‖}^{2} κ_{i o n}^{e f f} + S_{p c} & cathode CL \\ {‖ \nabla ϕ_{e l e} ‖}^{2} κ_{e l e}^{e f f} + S_{p c} & GDL (69) \\ {‖ \nabla ϕ_{e l e} ‖}^{2} κ_{e l e}^{e f f} & BP \\ {‖ \nabla ϕ_{i o n} ‖}^{2} κ_{i o n}^{e f f} + S_{p c} & membrane \\ 0 & other \end{matrix}

S_{p c} = {\begin{matrix} h_{c o n d} S_{v - l} & GDL \\ h_{c o n d} (S_{v - l} - S_{n - v} M_{H_{2} O}) & CL \\ 0 & other \end{matrix}

\begin{matrix} C_{v} = \frac{s d}{m e a n} \\ s d = \sqrt{\sum \frac{{(x_{i} - \bar{x})}^{2}}{n}} \\ m e a n = \frac{\sum x_{i}}{n} \end{matrix}

[1] *e-mail: 13609517160@163.com

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PRECISION DESIGN OF PROTON EXCHANGE MEMBRANE FUEL CELL FLOW FIELD BASED ON WATER AND HEAT TRANSFER MECHANISM