Optimizing Performance in PEM Fuel Cells: A Simulation Study of T-Junction Fractal Flow Field Plate

The application area of fuel cells (FCs) is rapidly expanding due to their ability to directly convert chemical energy into electrical energy with high efficiency and minimal environmental impact. Among various FC types, proton exchange membrane fuel cells (PEMFCs) have gained significant attention due to their wide range of applications, high energy density, and silent operation. PEMFCs are composed of several key components, including Bipolar Plates (BPs) with flow-field channels, membrane electrode assemblies (MEA) with catalyst layers (CL), and Gas Diffusion Layers (GDLs), as shown in Figure 1 [1-5]. These components play crucial roles in ensuring efficient electrochemical reactions and overall system performance.

Among these components, the design and material selection of the flow field plates (FFPs) have garnered increased interest from researchers, as they directly impact the FC’s efficiency, durability, and cost-effectiveness. FFPs serve multiple functions, such as distributing reactant gases evenly across the MEA, facilitating product water removal, and assisting in thermal and electrical management. In fact, FFPs contribute approximately 60% of the overall FC weight and nearly 30% of the manufacturing cost [6, 7]. Therefore, optimizing FFP designs is crucial for improving PEMFC performance and achieving cost-effective commercialization [8-10]. Bio-inspired FFPs designs have emerged as promising alternatives to traditional configurations. These designs draw inspiration from natural structures that have evolved to optimize fluid distribution, such as tree branches, lung airways, and vascular networks. Fractal designs, as shown in Figure 2, in particular, have demonstrated superior gas distribution properties compared to conventional serpentine and parallel designs. By mimicking naturally efficient flow patterns, these bio-inspired structures can enhance PEMFC performance by ensuring uniform reactant distribution and reducing pressure losses. However, despite these advantages, fractal designs face challenges related to manufacturing complexity and water management, which can limit their practical implementation [11-13].

The present computational fluid dynamics (CFD) study addresses two key limitations of existing fractal FFP concepts: the manufacturing complexity and thickness of previously proposed tree-like plates, and the insufficient control of water management at high generations of fractal branching. To this end, a developed T-junction fractal FFP is designed for the cathode side of a 25 cm² PEMFC, based on Murray’s law and an entropy-minimizing diameter scaling parameter. The proposed plate features a reduced thickness compared to reported fractal designs, thereby simplifying fabrication while preserving the uniform distribution network.

Anode: $\mathrm{H}_2 \rightarrow 2 \mathrm{H}^{+}+2 \mathrm{e}^{-}$

Cathode: $\frac{1}{2} \mathrm{O}_2+2 \mathrm{H}_{\mathrm{G}}^{+}+2 \mathrm{e}^{-} \rightarrow \mathrm{H}_2 \mathrm{O}$               (1)

Figure 1. Schematic diagram showing the components of a single proton exchange membrane fuel cell (PEMFC) [5]

Based on the simulated water transport behaviour, two conceptual design modifications are also proposed: repositioning outlets to enhance drainage of liquid water and integrating microgrooves to promote capillary-driven removal from the GDL and channels. These propositions are intended as practical guidelines for future experimental implementation.

1.1 Flow-field design evaluation criteria

The evaluation of FFP designs in PEMFC involves several crucial criteria, including pressure drop, reaction uniformity, water management, and manufacturing complexity, as presented in Table 1. A minimized pressure drop is also essential to enhance energy efficiency by reducing the operational strain on pumps and compressors. Equally important is the uniform distribution of reactants across the catalytic surfaces to avoid gradual cell degradation. Effective water management within the FC is vital to maintain membrane hydration for optimal ionic conductivity while also preventing flooding that can impede GDL and MEA [14]. Lastly, the complexity of manufacturing FFPs significantly affects both the scalability and cost of the cell. All those influencing the operational stability and functionality of FC.

Figure 2. Bipolar plate designs in proton exchange membrane fuel cell (PEMFC)

Table 1. Evaluation of existing bio-inspired design of FFP; (+) are advantages, (-) are limitations, (n/a) are not mentioned

1.2 Theory of bio-inspired designs

The bio-inspired designs are mostly based on Murray’s law, which was discovered on the bifurcations of arterial blood vessels and airways in animals and humans [34, 35]. Later, it was detected in the construction of the fluid flow passages in plants [36], sponges, and fish [37]. The law states that the diameters of the parent branch d₀ and its daughter branches d₁, d₂, …, d_n satisfy the relationship.

$\mathrm{d}_0^\gamma=\mathrm{d}_1^\gamma+\mathrm{d}_2^\gamma+\cdots+\mathrm{d}_{\mathrm{n}}^\gamma$             (2)

where, γ = 3 for laminar flows, and γ = 7/3 for turbulent flows [38].

In this study, the fractal T-junction design of the FFP is considered based on (2) and on the impact of the total entropy production in the FFP. The value of 0.794 for the dimensionless diameter scaling parameter provided the lowest total entropy production for the FFP geometry [39].

1.3 Fractal design of flow field plate in PEMFC

Fractal binary tree patterns represent innovative design approaches for FFP, which are based on human lungs or vein networks of plant leaves. Sauermoser et al. [28] investigated the T-junction fractal FFP. The study focused on the development and testing of a new FFP design with varying width-scaling parameters, aiming to achieve a uniform distribution of reactants and improve the performance of PEMFCs. The tree-like FFP designs were CNC milled on high-quality graphite plates, and three designs with different width-scaling parameters were employed in the experimental investigations. It was noted that the RH had no significant impact on the FC performance and electrochemical impedance spectroscopy test of the classical serpentine FFP, indicating proper membrane hydration. However, for the tree-like FFP, higher charge transfer resistances and Warburg diffusion impedances were observed at even low RH, indicating problems caused by poor water management.

Bethapudi et al. [40] used fractal FFP of a novel method of 3D flow field by using 2D planar printed circuit board plates with a layer-wise assembly approach. This design emulates the efficient, scalable air transport inside the lungs, a n-generation hierarchical fractal structure, with the airflow occurring from a single inlet to 2n-1 outlets.

Table 2. Summary of T-junction fractal FFPs

Despite the progress achieved in recent fractal-based PEMFC flow fields, important limitations remain. The work of Sauermoser et al. [28] demonstrated that channel width-scaling strongly affects performance, yet the optimal scaling factor and nominal number of fractal generations required for balanced reactant distribution and water removal were not fully established. Conversely, the multilayer fractal configuration proposed by Bethapudi et al. [40] enabled high outlet multiplicity and efficient transport, but its printed-circuit architecture increases fabrication complexity and is less compatible with low-cost industrial plate manufacturing. achieving a fractal flow field that combines optimal geometric scaling, controlled outlet generation, and practical manufacturability, while simultaneously improving water management. To address this, the present work introduces a reduced-thickness T-junction fractal FFP, designed using an entropy-informed scaling parameter and evaluated across multiple humidity conditions. The comparison in Table 2 summarizes how the proposed design positions itself relative to existing approaches in terms of generation count, scaling factor, thickness, and outlet configuration.

The performance of the proposed PEMFC with the fractal FFP was evaluated and compared to the conventional serpentine design under identical operating conditions. The parameters used for both configurations are listed in Tables 5 and 6 across varying RH levels. The main results are summarized as follows.

3.1 Model validation

The numerical model was referenced to the experimental study of Sauermoser et al. [28], who reported that fractal PEMFCs operate most stably in the range of 60–70% relative humidity (RH). Figure 5 illustrates the measured voltage–time curves at RH = 50%, 60% and 70%, demonstrating that 70% RH provides the most stable output with minimal voltage decay over time. Based on this trend, RH = 70% was selected as the reference operating condition for validating the numerical setup and for subsequent performance comparison.

Figure 5. Operating voltage at RH = 50% (a), 60% (b), 70% (c) of fractal FFP [28]

3.2 Concentration of oxygen

The amount of current generation in a PEMFC is directly influenced by the oxygen concentration at the CL on the cathode side. Figure 6 shows the molar concentration contours of O₂ at the GDL/CL interface for both configurations: (a) the fractal FFP and (b) the serpentine FFP.

As illustrated in Figure 6(a), the fractal flow field provides more uniform and higher oxygen concentrations across the entire active area, with values reaching up to 2.16  × 10⁻² kmol/m³ from the inlet to the outlet. This uniformity is due to the symmetrical and distributed branching structure of the fractal channels, which promotes balanced oxidant delivery throughout the electrode surface. In contrast, Figure 6(b) reveals that the serpentine FFP exhibits non-uniform oxygen distribution, with a maximum concentration of only 1.37  ×  10⁻² kmol/m³ near the inlet, followed by a gradual decline toward the outlet at 1.45 ×  10⁻² kmol/m³. This leads to reactant starvation at downstream sections, resulting in localized current density variations and potentially non-uniform electrochemical reactions and thermal gradients, which can accelerate membrane degradation. These findings confirm the superior reactant distribution performance of the proposed fractal FFP and align with trends reported in prior numerical studies [17, 19-23].

Figure 6. Molar concentration of O₂ at the cathode GDL/CL interface in the fractal (a) and serpentine (b) FFPs

3.3 Current density

The contours of current density and heat generation at the cathode CL interface are shown in Figures 7 and 8, based on CFD results under identical operating conditions. These distributions are crucial for evaluating the electrochemical performance and thermal management of the FC.

Figure 7. Current density at 0.6 V at the cathode GDL/CL interface of fractal (a) and serpentine (b) FFPs

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Figure 8. Heat source reaction 0.6 V at the cathode GDL/CL interface of (a) fractal, (b) serpentine

Figure 7 presents the current density distribution. In the case of the fractal FFP (Figure 7(a)), the current density reaches up to 1.31 × 10⁴ A/m², especially concentrated at the outlets of the fractal branches, where oxygen is effectively delivered. The distribution is more uniform across the active area, reflecting improved oxygen availability and reactant utilization. In contrast, the serpentine FFP (Figure 7(b)) exhibits a lower peak current density of approximately 7.07 × 10³ A/m², with weaker activity toward the outlet, indicating oxygen depletion and less efficient electrochemical performance.

Figure 8 presents the associated heat source distribution, which is primarily governed by the rate of electrochemical reaction. The fractal FFP (Figure 8(a)) shows a smoother and more balanced heat profile, consistent with the uniform current generation. Meanwhile, the serpentine FFP (Figure 8(b)) exhibits a highly non-uniform heat source pattern with concentrated hot spots, especially near the inlet, where reactant delivery is strongest. These differences imply that the serpentine FFP leads to higher local energy dissipation and entropy generation, potentially causing thermal stress and long-term degradation of the membrane. In contrast, the fractal design enhances thermal uniformity, which supports better durability and performance stability, as also supported by previous studies [13, 28, 38].

The higher heat generation observed near the inlet region in the serpentine plate is associated with local reactant availability and higher current density, which increases activation losses and ohmic heating. In contrast, the fractal configuration distributes oxygen more evenly across the cathode surface, leading to a more uniform reaction rate and lower localized heat peaks. This mitigates thermal gradients within the MEA, reducing the risk of membrane drying near the inlet and water condensation downstream.

3.4 Water mass fraction and water content

The distributions of water mass fraction and water activity at the cathode GDL/CL interface for the fractal FFP at Vcell = 0.6 V are illustrated in Figure 9(a) and (b).

The water mass fraction (Figure 9(a)) exhibits a gradual increase from the inlet toward the outlet, indicating effective water transport along the flow channels. The maximum water mass fraction reaches 6.56 × 10⁻², while maintaining a relatively balanced distribution across the active area. This uniformity is essential for mitigating localized flooding and ensuring stable reactant transport.

Figure 9. Water content (a) and water activity, (b) at the cathode GDL/CL interface

The water activity (Figure 9(b)) shows consistent hydration across most of the active area, with values ranging from 3.2 × 10⁻¹ near the inlet to 9.4 × 10⁻¹ near the outlet. However, a notable observation is the higher water activity at the corner opposite the outlet, which suggests a tendency for localized water accumulation in this region. This could lead to flooding under high-humidity operating conditions, potentially hindering reactant transport and reducing performance.

3.5 Performance and power curves

Figure 10 presents the power density curves for the fractal FFP under varying humidity levels: RH = 50%, 55%, 60%, 70% and 80%. The results indicate that the highest performance is achieved at 70% humidity when the maximum power density was 0.584 W/m², while a humidity level of RH = 80% marks the onset of performance decline. Figure 11 depicts a comparative analysis between the fractal and serpentine FFPs. The results demonstrate that the fractal design outperforms the serpentine design, showing an enhanced performance of 8%.

Figure 10. The power-current density curves in the case of fractal FFP at different RH

Figure 11. The comparison power density of the proposed fractal and standard serpentine FFP

The comparison across different operating humidities (50–80% RH) indicates a clear performance trend: power density increases with membrane hydration up to 70% RH, beyond which excess liquid water accumulation hinders oxygen transport and reduces cell output. These results confirm that 70% RH represents the optimal balance between proton conductivity and liquid water removal for the present fractal configuration.

3.6 Recommendations and propositions

3.6.1 Water management

Based on the obtained results (Figure 9), the current design leads to inefficient removal of excess water, which potentially results in flooding of the FFP channels. This section outlines two proposed design modifications aimed at addressing this issue.

The first proposition (Figure 12) is redesigning the water outlet position. An enhanced removal of excess water can be achieved by placing these outlets at the lowest points of the cell, which is consistent with recent studies highlighting the importance of outlet positioning in mitigating flooding [44]. The proposition (a) shows two outlets, while the proposition (b) suggests positioning a central outlet along the parallel channels for more efficient design.

Figure 12. Proposed water outlet designs with one outlet, and two (a) or one (b) outlets for fractal PEMFC

The second proposition (Figure 13) is the integration of microgrooves in the flow channels, which is an innovative approach to improve water management in PEMFC, in line with recent findings that emphasize the synergy between flow field geometries and microporous structures for efficient liquid water removal [45]. The challenge of this proposition requires high precision, which means an increase in the cost and time of production of the FC [46]. Similar conclusions have been drawn in recent works, where structured flow field modifications showed potential for enhanced drainage but also raised concerns of increased design complexity [47].

Figure 13. Proposed microgrooves for water removal from the FFP and GDL [46]

3.6.2 Uniform distribution of reactants

Fractal design generally promotes uniform reactant distribution through multi-branching; however, simulation results show that the 7th-generation configuration exhibits maldistribution near the terminal outlets, where channels become closely spaced due to the applied scaling factor. This reduced spacing decreases local pressure gradients and creates preferential flow pathways, preventing homogeneous access to end branches and lowering overall distribution uniformity.

To address this limitation, a 6-generation fractal architecture is recommended. Reducing one branching level restores more uniform outlet spacing and equalizes hydraulic resistance across branches (Figure 14), improving flow allocation while also reducing geometric complexity and fabrication effort. This confirms that increasing generations beyond an optimal point, especially under a narrower scaling factor, does not enhance uniformity, and an intermediate order provides a more balanced transport network for PEMFC operation.

Figure 14. Distribution uniformity proposition