Numerical Investigation on Cathode Gas Diffusion Layer with Conical Frustum Grooves for Enhancing Performance of Proton Exchange Membrane Fuel Cell

Abstract

To address performance limitations in proton exchange membrane fuel cells (PEMFCs), this work proposes and numerically investigates a cathode gas diffusion layer (GDL) with conical frustum grooves. A systematic comparison is performed across three GDL configurations: a baseline structure without grooves, a design with cylindrical grooves, and the proposed conical frustum grooves. The results demonstrate that the conical frustum grooves effectively enhance liquid water removal, oxygen mass transport, membrane current density, and peak power density. This improvement arises as the grooves expand transport pathways for both liquid water and oxygen, facilitating more robust electrochemical reactions. A parametric analysis is further conducted to evaluate the effects of groove spacing, depth, top radius, and bottom radius. Reduced groove spacing, together with increased groove depth, top radius, and bottom radius, consistently improves water management and oxygen delivery. However, membrane current density and power density do not vary monotonically with groove depth and bottom radius. The optimal values for these two parameters are identified as 0.3 mm and 0.5 mm, respectively.

1. Introduction

Recently, countries around the world have faced increasingly severe challenges from climate change and reducing carbon emissions has become the main goal of governments [1,2]. Applications of zero/low carbon power sources are the key solution for reducing carbon emissions and promoting sustainable social development [3,4]. Proton exchange membrane fuel cells (PEMFCs) exhibit significant promise as power sources for vehicles, ships, and unmanned aerial vehicles [5,6], owing to their inherent advantages of zero emissions, rapid startup, and high-power density [7,8,9]. However, the widespread adoption of PEMFCs remains hindered by persistent challenges in performance enhancement [10,11].

To address these limitations, optimizing the PEMFC flow field is a widely adopted strategy [12,13]. The cathode region involves multiple complex processes, including oxygen supply, gas–liquid transport, and water drainage. Characterized by high mass transfer resistance and significant flooding issues, it represents a critical bottleneck limiting improvements in output performance of PEMFCs. Therefore, optimizing the design of the cathode flow channels and gas diffusion layer is of great practical significance for improving internal mass transfer characteristics, mitigating flooding, and enhancing fuel cell performance [14,15,16]. Traditional channel designs, such as parallel, single-serpentine, and multi-serpentine configurations, have been proposed for bipolar plate engineering to enhance gas transport and liquid water removal, ultimately improving the electrical performance of PEMFCs [17,18]. Based on the channel layout, modifying the channel cross section is a popular way. A tapered channel [19], wave channel [20] and baffled channel [21,22] are widely used. Beyond the above conventional design, bionic design offers us a more creative design approach. The bionic leaf vein channel [23,24], biomimetic droplet flow-blocking channel [25], shark dermal denticle blocking channel [26], and bionic fish scale porous channel [27] are also applied.

However, compared to bipolar plate flow field optimization, gas diffusion layer (GDL) modification represents a more challenging yet highly effective approach. Gerteisen et al. [28] modified the GDL via laser perforation and experimentally evaluated the performance of laser-treated GDLs. The PEMFCs integrated with perforated GDLs demonstrated superior dynamic and overall performance relative to those equipped with unmodified GDLs. Iglesia et al. [29] employed a picosecond laser to fabricate periodic grooves on the GDL surface. The results indicated that power density was doubled at a periodic groove depth of 20 μm. Wang et al. [30] investigated the effects of perforation diameter and spacing on water transport. Results showed that the water transport was the best at the perforation diameter of 100 μm and the perforation pitch of 2 mm. Niu et al. [31] explored the influence of perforation depth and diameter on liquid water transport in perforated GDLs. Results showed that the GDL with a perforation diameter and depth of 100 μm exhibited the optimal performance. Yin et al. [32] punched elliptical grooves in GDLs of PEMFCs. Results showed that the elliptical groove could greatly enhance the reactant and product transport.

To summarize, introducing patterned grooves into the cathode GDL is a viable and effective strategy for improving PEMFC performance. Unlike previous studies, this work proposes conical frustum grooves on the cathode GDL, whose performance is compared with both unmodified and cylindrical-grooved GDL. Subsequently, effects of key geometric parameters of the conical frustum grooves, including spacing, depth, top radius, and bottom radius, on PEMFC performance are systematically investigated. This study aims to elucidate the performance enhancement mechanism of patterned conical frustum grooves in the cathode GDL.

2. Methodology

2.1. Geometrical and Physical Model

In this work, conical frustum grooves are uniformly patterned on the cathode GDL of the PEMFC, as illustrated in Figure 1. This structure can be fabricated by precise laser ablation or micro-CNC milling. Laser ablation ensures high precision of conical microstructures, while micro-CNC milling enables reliable control over depth and radius. The geometric dimensions and operating parameters of the PEMFC are presented in

Table 1. Dimensions of PEMFC with conventional GDL.

Dimensions	Values (mm)
Channel length	20.0
Membrane thickness	0.1
CL thickness	0.05
Channel width	0.7874
GDL thickness	0.38
Rib width	0.90932
Channel height	1.0

and

Table 2. Operation parameters.

Parameter	Value	Ref.
Working temperature (K)	343.15	[33]
Reference temperature (K)	453.15	[20]
Pressure (Pa)	101,325	[20]
Hydrogen stoichiometric ratio	1.2	[33]
Air stoichiometric ratio	2	[33]
Membrane permeability (m2)	1.80 × 10−11	[20]
Cathodic charge transfer coefficient	1	[33]
Membrane ionic conductivity (S·m−1)	9.825	[20]
H2 mole fraction	0.96268	[20]
O2 mole fraction	0.20216	[20]
H2O mole fraction	0.037319	[20]
Open-circuit voltage (V)	0.95	[20]
Surface-to-volume ratio (m−1)	1.00 × 107	[20]
GDL porosity	0.4	[20]
GDL electrical conductivity (S·m−1)	222	[20]
GDL permeability (m2)	2.36 × 10−12	[20]

, respectively. To reveal the performance enhancement mechanism of conical frustum grooves, the effects of groove spacing (d), depth (h), top radius (r₁), and bottom radius (r₂) are analyzed, with corresponding cases detailed in

Table 3. Geometrical parameters of cases.

Case No.	Top Radius (r1) /mm	Bottom Radius (r2) /mm	Depth (h) /mm	Spacing (d) /mm
Case 1	-	-	-	-
Case 2	0.25	0.25	0.25	2
Case 3	0.25	0.5	0.25	2
Case 4	0.25	0.5	0.25	3.6
Case 5	0.25	0.5	0.25	3
Case 6	0.25	0.5	0.25	1.5
Case 7	0.25	0.5	0.25	1.2
Case 8	0.25	0.5	0.1	2
Case 9	0.25	0.5	0.2	2
Case 10	0.25	0.5	0.3	2
Case 11	0.25	0.5	0.35	2
Case 12	0.1	0.5	0.25	2
Case 13	0.2	0.5	0.25	2
Case 14	0.3	0.5	0.25	2
Case 15	0.35	0.5	0.25	2
Case 16	0.25	0.3	0.25	2
Case 17	0.25	0.4	0.25	2
Case 18	0.25	0.6	0.25	2
Case 19	0.25	0.7	0.25	2
Case 20	0.35	0.5	0.3	1.2

.

2.2. Governing Equations

Prior to constructing the mathematical model of the PEMFC, the following assumptions are adopted [34]: (a) steady operation; (b) incompressible and laminar flow in channel; (c) gravitational effects and interfacial contact resistance are neglected; (d) isotropic and homogeneous porous medium; and (e) the membrane is impermeable to electrons and gases. The corresponding mass, momentum, energy, species, and charge conservation equations are described as follows [35,36,37,38,39]:

Mass conservation:

$$\nabla \cdot \left(\rho \overrightarrow{u}\right)=S_m,$$

(1)

$$S_m=\left\{\begin{array}{c}-M_{H_2}{\displaystyle \frac{j_a}{2F}} \mathrm{A}\mathrm{n}\mathrm{o}\mathrm{d}\mathrm{e}\\ M_{H_{2}O}{\displaystyle \frac{j_c}{2F}}-{M_O}_2{\displaystyle \frac{j_c}{4F}} \mathrm{C}\mathrm{a}\mathrm{t}\mathrm{h}\mathrm{o}\mathrm{d}\mathrm{e}\end{array}\right.,$$

(2)

where ρ denotes the fluid density, $\overrightarrow{u}$ the velocity vector, and Sm the mass source term. $M_{H_2}$, ${M_O}_2$ and $M_{H_{2}O}$ represent the molar masses of hydrogen, oxygen and water, respectively. j_a and j_c refer to the exchange current densities of the anode and cathode catalytic layers, respectively, and F represents the Faraday constant (F = 96,485 C·mol⁻¹).

Momentum conservation:

$${\displaystyle \frac{1}{{\epsilon }^2}}\nabla \cdot \left(\rho \overrightarrow{u}\overrightarrow{u}\right)=-\nabla p+{\displaystyle \frac{1}{\epsilon }}\nabla \cdot \left(\mu \nabla \overrightarrow{u}\right)+S_u,$$

(3)

$$S_u=\left\{\begin{array}{c}-{\displaystyle \frac{{\epsilon }^2\mu }{K_p}}\overrightarrow{u} \mathrm{CL} \mathrm{and} \mathrm{GDL}\\ 0 \mathrm{Other} \mathrm{regions}\end{array}\right.,$$

(4)

where ɛ represents the porosity, p represents the pressure, µ represents the dynamic viscosity, and Su represents the momentum source term, and Kp represents the permeability of porous media.

Energy conservation:

$$\nabla \cdot \left(\rho c_p\overrightarrow{u}T\right)=\nabla \cdot \left(k_{\mathrm{eff}}\nabla T\right)+S_T,$$

(5)

$$k_{\mathrm{e}\mathrm{f}\mathrm{f}}=\epsilon k_f+\left(1-\epsilon \right)k_s,$$

(6)

$$S_T=h_{\mathrm{react}}-j_{\mathrm{a}/c}{\eta }_{\mathrm{a}/c}+I^2{R}_{\mathrm{ohm}}+h_{\mathrm{phase}} \mathrm{All} \mathrm{domain},$$

(7)

where c_p represents the constant-pressure specific heat capacity, T represents the operating temperature, and k_eff represents the effective thermal conductivity. k_f and k_s represent the thermal conductivity of fluid and solid phases, respectively, and h_react represents the net enthalpy change associated with the electrochemical reaction, while ƞ_a/c is the activation overpotential within the anode or cathode catalyst layer, and I denotes the area-specific surface current density, R_ohm the ohmic resistance, and h_phase the enthalpy change from water condensation or vaporization.

Species conservation:

$${\displaystyle \frac{\partial \left(\epsilon c_i\right)}{\partial t}}+\nabla \left(\epsilon \overrightarrow{u}{c}_i\right)=\nabla \cdot \left({D_i}^{\mathrm{eff}}\nabla c_i\right)+S_i,$$

(8)

$${D_i}^{\mathrm{eff}}={\epsilon }^{1.5}{\left(1-s\right)}^{2.5}{D_i}^0\left({\displaystyle \frac{p_0}{p}}\right){\left({\displaystyle \frac{T}{T_0}}\right)}^{1.5},$$

(9)

$$S_i=\left\{\begin{array}{c}-{\displaystyle \frac{j_a}{2F}}{M}_{H_2} \mathrm{CL}\\ -{\displaystyle \frac{j_c}{4F}}{M}_{O_2} \mathrm{CL}\\ -{\displaystyle \frac{j_c}{2F}}{M}_{H_{2}O }\mathrm{CL}\end{array}\right.$$

(10)

where c_i represents the molar concentration of species, S_i represents the source term of species, Di^eff represents the effective diffusivity of species, s represents the water saturation, and Di⁰ represents the mass diffusion coefficient at T₀ and p₀.

Charge conservation:

$$\left\{\begin{array}{c}\nabla \cdot \left({\sigma }_s\nabla {\varphi }_s\right)+R_s=0\\ \nabla \cdot \left({\sigma }_{\mathrm{m}\mathrm{e}\mathrm{m}}\nabla {\varphi }_{\mathrm{m}\mathrm{e}\mathrm{m}}\right)+R_{\mathrm{m}\mathrm{e}\mathrm{m}}=0\end{array}\right.,$$

(11)

$${\sigma }_{\mathrm{mem}}=\left(0.514\lambda -0.326\right)e^{1268\left({\displaystyle \frac{1}{303}}-{\displaystyle \frac{1}{T}}\right)},$$

(12)

$$\left\{\begin{array}{c}{R}_{\mathrm{m}\mathrm{e}\mathrm{m}}=-R_s=j_a \mathrm{Anode} \mathrm{CL}\\ R_s=-R_{\mathrm{m}\mathrm{e}\mathrm{m}}=j_c \mathrm{Cathode} \mathrm{CL}\end{array}\right.,$$

(13)

where σ_s and σ_mem represent the electrical conductivity of the solid phase and membrane, respectively, ϕ_s and ϕ_mem refer to their corresponding potentials. R_s and R_mem represent the volumetric transfer current densities in the solid and membrane phases, respectively, and λ represents the membrane water content.

Additionally, as the catalytic layer involves a variety of electrochemical reactions, the Butler–Volmer equation is adopted to describe the relationship between current and activation polarization loss:

$$j=\left\{\begin{array}{c}{A}_v\cdot i_{0,a}{\left({\displaystyle \frac{c_{H_2}}{c_{H_2,\mathrm{ref}}}}\right)}^{{\gamma }_a}\left[\mathit{exp}\left({\displaystyle \frac{{\alpha }_{a}F{\eta }_a}{RT}}\right)-\mathit{exp}\left(-{\displaystyle \frac{{\alpha }_{c}F{\eta }_a}{RT}}\right)\right]\mathrm{A}\mathrm{n}\mathrm{o}\mathrm{d}\mathrm{e}\\ A_v\cdot {i{\left({\displaystyle \frac{c_{O_2}}{c_{O_2,\mathrm{ref}}}}\right)}^{{\gamma }_c}\left[\mathit{exp}\left({\displaystyle \frac{{\alpha }_{c}F{\eta }_c}{RT}}\right)-\mathit{exp}\left(-{\displaystyle \frac{{\alpha }_{a}F{\eta }_c}{RT}}\right)\right]\mathrm{Cathode}}_{0,c}\end{array}\right.,$$

(14)

where A_v represents the specific surface-to-volume ratio of the catalyst layer, γ_a and γ_c denote the concentration exponents for the anode and cathode reactions, with γa = 0.5 and γ_c = 1. i_0,a and i_0,c refer to the exchange current densities of the anode and cathode, respectively, and α_a and α_c are the anodic and cathode charge transfer coefficients. R is the universal gas constant, with R = 8.314 J·mol⁻¹·K⁻¹.

The equations about the above parameters are expressed as follows, respectively:

$$i_0=\left\{\begin{array}{c}{i}_{0,\mathrm{r}\mathrm{e}\mathrm{f},\mathrm{a}}\mathit{exp}\left[-{\displaystyle \frac{E_{\mathrm{a},\mathrm{a}\mathrm{c}\mathrm{t}}}{RT}}\left(1-{\displaystyle \frac{T}{T_{\mathrm{r}\mathrm{e}\mathrm{f},\mathrm{a}}}}\right)\right] \mathrm{Anode}\\ i_{0,\mathrm{r}\mathrm{e}\mathrm{f},c}\mathit{exp}\left[-{\displaystyle \frac{E_{\mathrm{c},\mathrm{a}\mathrm{c}\mathrm{t}}}{RT}}\left(1-{\displaystyle \frac{T}{T_{\mathrm{r}\mathrm{e}\mathrm{f},c}}}\right)\right] \mathrm{Cathode}\end{array}\right.,$$

(15)

$$\eta =\left\{\begin{array}{c}{\phi }_s-{\phi }_{\mathrm{mem}} \mathrm{A}\mathrm{n}\mathrm{o}\mathrm{d}\mathrm{e}\\ {\phi }_s-{\phi }_{\mathrm{mem}}-E_0 \mathrm{C}\mathrm{a}\mathrm{t}\mathrm{h}\mathrm{o}\mathrm{d}\mathrm{e}\end{array},\right.$$

(16)

$$E_0=1.23-0.9\times 10^{-3}\left(T-298\right),$$

(17)

where E_a,act and E_c,act represent the anodic and cathodic activation energy, respectively, T_ref,a and T_ref,c represent the reference temperature of anode and cathode, respectively, i_0,ref,a and i_0,ref,c represent the reference exchange current density of the anode and cathode at the specified reference temperature, respectively, and E₀ represents the open-circuit voltage.

Dissolved water exists in the catalyst layer and the PEM, and its generation and transport are described as follows:

$$\nabla \cdot \left(I_{\mathrm{i}\mathrm{o}\mathrm{n}}{\displaystyle \frac{2.5}{22F}}\lambda M_{H_{2}O}\right)=\nabla \cdot \left(M_{H_{2}O}{D}_{\lambda }\nabla \lambda \right)+S_w+S_{\mathrm{v}\mathrm{l}-\mathrm{d}},$$

(18)

where I_ion represents the ionic current density, S_w represents the source term for dissolved water, S_vl−d represents the mass change rate between dissolved water and liquid or vapor water, and D_λ is the water diffusivity in the membrane; λ represents balance moisture content.

The equations about the above parameters are expressed as follows, respectively:

$$S_w=\left\{\begin{array}{c}{\displaystyle \frac{M_{H_{2}O}}{2F}}{j}_c C\mathrm{a}\mathrm{t}\mathrm{h}\mathrm{o}\mathrm{d}\mathrm{e} \mathrm{C}\mathrm{L}\\ 0 \mathrm{PEM} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{a}\mathrm{n}\mathrm{o}\mathrm{d}\mathrm{e} \mathrm{C}\mathrm{L}\end{array}\right.,$$

(19)

$$S_{\mathrm{v}\mathrm{l}-\mathrm{d}}=\left\{\begin{array}{c}\left(1-s\right){\gamma }_{\mathrm{v}\mathrm{d}}{\displaystyle \frac{{\rho }_{\mathrm{m}\mathrm{e}\mathrm{m}}}{EW}}\left({\lambda }_{\mathrm{e}\mathrm{q}}-\lambda \right)\\ s{\gamma }_{\mathrm{l}\mathrm{d}}{\displaystyle \frac{{\rho }_{\mathrm{m}\mathrm{e}\mathrm{m}}}{EW}}\left({\lambda }_{\mathrm{e}\mathrm{q}}-\lambda \right)\end{array}\right.,$$

(20)

$$D_{\lambda }=\left\{\begin{array}{c}3.1\times 10^{-7}\lambda \left(e^{0.28\lambda }-1\right)e^{\left(-2346/T\right)}\left(0<\lambda \le 3\right)\\ 4.17\times 10^{-8}\lambda \left(\lambda +161e^{-\lambda }\right)e^{\left(-2346/T\right)}\left(\lambda >3\right)\end{array}\right.,$$

(21)

where E_W represents the equivalent weight of the membrane, λ_eq represents the equilibrium water content, ρ_mem represents the density of the membrane, and γ_vd and γ_ld represent the mass change rates of water vapor to dissolved water and liquid water to dissolved water.

The transport of liquid water in porous medium is driven by capillary forces:

$$\nabla \cdot \left({\displaystyle \frac{{\rho }_{l}K{K}_r}{{\mu }_l}}\nabla \left(p_c+p\right)\right)+S_{\mathrm{v}-\mathrm{l}}=0,$$

(22)

$$p_c=\left\{\begin{array}{c}{\displaystyle \frac{\sigma \mathit{cos}{\theta }_c}{{\left(K/\epsilon \right)}^{0.5}}}\left[1.417\left(1-s\right)-2.12{\left(1-s\right)}^2+1.263{\left(1-s\right)}^3\right]{\theta }_c<90°\\ {\displaystyle \frac{\sigma \mathit{cos}{\theta }_c}{{\left(K/\epsilon \right)}^{0.5}}}\left[1.417s-2.12s^2+1.263s^3\right]{\theta }_c>90°\end{array}\right.,$$

(23)

where K and K_r represent the absolute permeability and relative permeability, respectively, p_c represents the capillary pressure, θ_c represents the contact angle, and S_v−l refers to the phase change between liquid and vapor water, which is expressed as follows:

$$S_{\mathrm{v}-\mathrm{l}}=\left\{\begin{array}{c}{\gamma }_e\epsilon s{\displaystyle \frac{M_{H_{2}O}}{RT}}p\mathit{ln}\left({\displaystyle \frac{p-p_{\mathrm{sat}}}{p-p_{\mathrm{wv}}}}\right)p_{\mathrm{wv}}\le p_{\mathrm{sat}}\\ {\gamma }_e\epsilon \left(1-s\right){\displaystyle \frac{M_{H_{2}O}}{RT}}p\mathit{ln}\left({\displaystyle \frac{p-p_{\mathrm{sat}}}{p-p_{\mathrm{wv}}}}\right)p_{\mathrm{wv}}>p_{\mathrm{sat}}\end{array}\right.,$$

(24)

where γ_e represents the geometric correction factor for droplet size, and p_wv and p_sat represent the vapor pressure of water and saturated water, respectively.

The transport of liquid water in the channel is described by:

$$\nabla \cdot \left({\rho }_l\overrightarrow{u}s\right)=\nabla \cdot \left(D_l\nabla s\right),$$

(25)

where D_l represents the diffusion coefficient of liquid water.

2.3. Boundary Conditions

A symmetry boundary condition is employed at the outer surfaces of the GDL and CL, while zero fluxes and a non-slip boundary condition is used at all other surfaces excluding the channel inlet and outlet. Reference potentials are specified at the channel–GDL interfaces of the anode and cathode. Specifically, the anode and cathode voltage is 0 V and the open-circuit voltage, respectively [40]. In the numerical investigations, the cathode voltage is changed from 0.9 V to 0.35 V in steps of 0.05 V [41].

2.4. Grid Independence Study

To select an appropriate grid size for balancing numerical accuracy and computational time, five mesh models of Case 3 are generated, and the software COMSOL Multiphysics 6.0 is used to compute the above numerical model. As shown in Figure 2a, the polarization curves gradually converge as the grid number increases. When the grid count reaches 138,906 and 195,296, the polarization curves are basically overlapped. Meanwhile, as illustrated in the distribution profiles of oxygen mass fraction (Figure 2b) and liquid water mass fraction (Figure 2c) along the flow channel for different grid numbers, the simulated two-phase transport characteristics exhibit no significant variations with further mesh refinement once the grid number reaches 138,906. This means that the grid number of 138,906 is enough for capturing the performance characteristics of the PEMFC. And the overall computational cost is within a reasonable range. Therefore, the mesh model with the grid number of 138,906 is adopted in the subsequent studies.

2.5. Model Validation

To validate the above numerical model, the polarization curve results are compared with experimental data from the literature [42,43]. To ensure the objectivity of model validation, all parameters in the numerical model are kept identical to those used in the experiments. As observed in Figure 3, under operating conditions of 1.7 atm and 433 K, the numerical results agree well with the experimental data at high current densities, while a larger relative error is observed at low current densities. When the operating pressure and temperature are 1.0 atm and 453 K, respectively, the numerical results show good agreement with the experimental data at low current densities, but the relative error increases at high current densities. Therefore, with the above experiment validation, the above numerical model is considered to be reliable and accurate, and it can be used for subsequent simulations.

3. Results

3.1. Effects of Groove Structure

Liquid water accumulation hinders oxygen transport and exacerbates concentration polarization. This severely impairs the electrochemical reaction at the cathode GDL-CL interface and further reduces power density. Figure 4 illustrates the effects of groove structure on the liquid water and oxygen distributions at the cathode GDL-CL interface under 0.5 V. It is observed that the mass fraction of liquid water gradually increases along the flow direction, while the mass fraction of oxygen gradually decreases. This occurs because water is generated and oxygen is consumed as the electrochemical reaction proceeds. Moreover, when pouching grooves in the cathode GDL, the mass fraction variation curves of liquid water and oxygen around the grooves fluctuate. Liquid water is discharged into the channel by capillary pressure. The oxygen transfer distance to the CL surface is shortened by the reduction in GDL thickness at the grooves. This allows oxygen to more easily penetrate the GDL and reach the CL surface. Finally, Case 3 exhibits the lowest liquid water mass fraction and the highest oxygen mass fraction. This indicates that Case 3 has superior water removal and oxygen transport performance compared to Case 1 and Case 2. This is due to gas diffusion being the main driving force of gas entering into the GDL when no grooves pouch in the cathode GDL. However, when grooves are patterned, the water removal and oxygen transport pathways are widened. Especially, the bottom radius of conical frustum grooves is larger than that of cylindrical grooves, significantly improving the y-direction gas velocity of the cathode channel, as observed in Figure 5.

A higher and more uniform membrane current density is beneficial for achieving good PEMFC performance. Figure 6 illustrates the effects of groove structure on the membrane current density at 0.5 V. The results show that Case 2 has a higher average membrane current density and a larger standard deviation than Case 1. This suggests that pouching cylindrical grooves in the cathode GDL can improve the membrane current density but its uniformity becomes poor. Additionally, Case 3 exhibits the highest average membrane current density and the lowest standard deviation. This suggests that compared with pouching cylindrical grooves in the cathode GDL, pouching conical frustum grooves are more effective at achieving a higher and more uniform membrane current density.

Figure 7 shows the effects of groove structure on the electrical performance. It can be seen that at low current densities, the polarization and power density curves of all cases are nearly identical. However, at high current densities, Case 3 achieves the highest power density. Specifically, when the voltage is 0.5 V, the maximum power density of Case 3 is 0.7% higher than that of Case 2, and 1.8% higher than that of Case 1. This suggests that pouching conical frustum grooves in the cathode GDL is more effective for improving electrical performance.

3.2. Effects of Conical Frustum Groove Spacing

Figure 8 illustrates the effects of conical frustum groove spacing on liquid water and oxygen distribution at the cathode GDL-CL interface at 0.5 V. The results show that both the fluctuation amplitude and period of the mass fraction profiles for liquid water and oxygen decrease as groove spacing is shortened. Additionally, the average mass fraction of liquid water decreases while the average mass fraction of oxygen increases with smaller groove spacing. This indicates that smaller groove spacing yields better water removal and oxygen transport performance. This is because a smaller spacing allows more grooves to be patterned, which widens the pathways for water removal and oxygen transport.

Figure 9 illustrates the effects of conical frustum groove spacing on the membrane current density at 0.5 V. It can be seen that the average membrane current density gradually increases as the groove spacing decreases. The standard deviation of the current density also gradually reduces. This indicates that the smaller groove spacing leads to a higher and more uniform membrane current density. This is because a reduced spacing allows more grooves to be patterned. This expands the pathways for water removal and oxygen transport, leading to more intense electrochemical reactions.

Figure 10 presents the effects of conical frustum groove spacing on electrical performance. The results show that at low current densities, the polarization and power density curves for all cases are nearly identical. However, at high current densities, power density increases as the groove spacing is reduced. Specifically, when the voltage is 0.5 V, the maximum power density rises from 0.559 W/cm² to 0.567 W/cm² as the groove spacing decreases from 3.6 mm to 1.2 mm.

3.3. Effects of Conical Frustum Groove Depth

Figure 11 illustrates the effects of conical frustum groove depth on liquid water and oxygen distribution at the cathode GDL-CL interface at 0.5 V. The results show that the fluctuation amplitude of the mass fraction profiles for both liquid water and oxygen increases with greater groove depth. Additionally, the average mass fraction of liquid water decreases while the average mass fraction of oxygen increases as the groove depth increases. This indicates that deeper grooves yield better water removal and oxygen transport performance. This is because deeper grooves reduce the local GDL thickness, which diminishes the water removal and oxygen transport resistance.

Figure 12 illustrates how conical frustum groove depth affects membrane current density at 0.5 V. The average membrane current density initially rises with increasing depth, peaks at 0.3 mm, and then decreases as depth continues to grow. However, the standard deviation of membrane current density gradually declines with greater groove depth. When the groove depth is increased from 0.3 mm to 0.35 mm, the change in standard deviation is negligible. This suggests that a higher and more uniform membrane current density is obtained at 0.3 mm. This is because the deeper the groove the thinner the GDL thickness, which diminishes the water removal and oxygen transport resistance, leading to a more intense electrochemical reaction. However, a deeper groove not only decreases the mechanical strength of the GDL but also increases the electron conduction resistance.

Figure 13 describes the influence of conical frustum groove depth on cell performance. The results show that at low current densities, the polarization and power density curves for all cases are nearly indistinguishable. At high current densities, however, power density first increases with groove depth, reaches its maximum at 0.3 mm, and then decreases as the depth further increases. Specifically, at 0.5 V, the maximum power density reaches 0.563 W/cm² when the groove depth is 0.3 mm.

3.4. Effects of Top Radius of Conical Frustum Groove

Figure 14 illustrates how the top radius of conical frustum grooves affects liquid water and oxygen distributions at the cathode GDL-CL interface at 0.5 V. The results show that the fluctuation amplitude of the mass fraction profiles for both liquid water and oxygen increases as the top radius grows. The average mass fraction of liquid water decreases while the average mass fraction of oxygen rises with a lager top radius. This indicates that a larger top radius improves water removal and oxygen transport performance. This is because a wider transport pathway is created as the top radius increases, which facilitates more efficient water and oxygen transport.

Figure 15 illustrates the influence of the top radius on membrane current density at 0.5 V. The average membrane current density gradually increases with the top radius. Meanwhile, the standard deviation of membrane current density decreases. This suggests that a larger top radius yields a higher and more uniform membrane current density. This is because the wider transport pathways enhance water removal and oxygen transport, which in turn promotes more intense electrochemical reactions.

Figure 16 shows the effects of the top radius on cell performance. At low current densities, the polarization and power density curves for all cases are nearly indistinguishable. At high current densities, however, power density increases as the top radius grows. Specifically, when the voltage is 0.5 V, the maximum power density rises from 0.559 W/cm² to 0.567 W/cm² as the top radius increases from 0.1 mm to 0.35 mm.

3.5. Effects of Bottom Radius of Conical Frustum Groove

Figure 17 illustrates how the bottom radius of conical frustum grooves affects liquid water and oxygen distributions at the cathode GDL-CL interface at 0.5 V. The results show that the fluctuation amplitude of the mass fraction profiles for both liquid water and oxygen increases as the bottom radius grows. The average mass fraction of liquid water decreases while the average mass fraction of oxygen rises with a larger bottom radius. This indicates that a larger bottom radius improves water removal and oxygen transport performance. This is because the transport pathways for water and oxygen are widened with increasing bottom radius, which facilitates more efficient water removal and oxygen transport.

Figure 18 illustrates the influence of the bottom radius on membrane current density at 0.5 V. The average membrane current density initially rises with increasing bottom radius, peaks at 0.5 mm, and then decreases as the radius continues to grow. Meanwhile, the standard deviation of membrane current density gradually declines with a larger bottom radius. The results show that a bottom radius of 0.5 mm yields the highest and most uniform membrane current density. This is because wider transport pathways promote more intense electrochemical reactions. However, a larger bottom radius not only decreases the mechanical strength of the GDL but also increases the electron conduction resistance.

Figure 19 shows the influence of the bottom radius on cell performance. The results show that at low current densities, the polarization and power density curves for all cases are nearly indistinguishable. At high current densities, however, power density first rises with increasing bottom radius, peaks at 0.5 mm, and then decreases as the radius continues to grow. Specifically, at 0.5 V, the maximum power density reaches 0.563 W/cm² when the bottom radius is set to 0.5 mm.

4. Conclusions

In this work, conical frustum grooves are introduced into the cathode GDL of a PEMFC, and compared with no grooves and pouching cylindrical grooves. The effects of spacing, depth, top radius and bottom radius on cell performance are systematically analyzed and discussed. The main findings are summarized as follows:

(1)

Compared with no grooves and pouching cylindrical grooves, the conical frustum grooves deliver improved water removal and oxygen transport performance. They also yield a higher and more uniform membrane current density, as well as a higher power density. This is due to the grooves widening the transport pathways, which facilitates more intense electrochemical reactions.

(2)

Reducing groove spacing improves water removal and oxygen transport performance. It also leads to a higher and more uniform membrane current density, as well as increased power density.

(3)

With the increment of groove depth, better liquid water removal and oxygen transport ability is obtained. However, the optimal groove depth of 0.3 mm yields the highest and most uniform membrane current density, as well as the peak power density.

(4)

Increasing the top radius improves water removal and oxygen transport performance. It also leads to a higher and more uniform membrane current density, as well as an increased power density.

(5)

With the increase of the bottom radius, the liquid water removal and oxygen transport ability is gradually improved. However, the optimal bottom radius of 0.5 mm yields the highest and most uniform membrane current density, as well as the peak power density.

Overall, with conical frustum grooves in the cathode GDL, the PEMFC can achieve better oxygen transport and liquid water removal, higher and more uniform membrane current density, and higher power density. However, there are also some challenges in manufacturing feasibility and cost. In future work, more factors such as temperature, humidity, pressure and load will be considered. Additionally, response surface methodology (RSM), non-dominated sorting genetic algorithm II (NSGA-II) and technique for order preference by similarity to an ideal solution (TOPSIS) are combined to obtain the optimal design project for practical engineering applications.