RETRACTED: Bio-Aerodynamic Flow Field Optimization in PEM Fuel Cells: A Peregrine Falcon-Inspired Flow Field Approach

Abstract

To simultaneously improve mass transfer and minimize pressure drop in proton exchange membrane fuel cells (PEMFCs), this study proposes a novel bionic flow field inspired by the streamlined abdominal structure of the peregrine falcon. A three-dimensional channel geometry is developed from this biological prototype and integrated into a single-channel PEMFC model for numerical simulation. A series of computational fluid dynamics (CFD) analyses compare the new design against conventional straight, trapezoidal, and sinusoidal flow fields. The results demonstrate that the falcon-inspired configuration enhances oxygen delivery, optimizes water management, and achieves a more uniform current density distribution. Remarkably, the design delivers a 9.45% increase in peak power density while significantly reducing pressure drop compared to the straight channel. These findings confirm that biologically optimized aerodynamic structures can provide tangible benefits in PEMFC flow field design by boosting electrochemical performance and lowering parasitic losses. Beyond fuel cells, this bio-inspired approach offers a transferable methodology for advanced energy conversion systems where efficient fluid transport is essential.

1. Introduction

Amid growing energy crises and environmental challenges, hydrogen energy technologies are increasingly recognized as essential solutions for sustainable energy transition and environmental protection. Among these, the proton exchange membrane fuel cell (PEMFC) has attracted significant attention due to its high efficiency and zero emissions, making it a promising option for applications such as power generation, electric vehicle charging, and distributed energy systems. Despite its potential, the widespread deployment of PEMFCs remains limited by high production and maintenance costs [1,2,3,4]. A critical component of PEMFCs is the bipolar plate, which ensures electron conduction and mass transport. Beyond material development, research has focused heavily on flow field design, as it directly impacts performance. Two common configurations dominate current studies: parallel flow fields, which are simple, easy to fabricate, and have low pressure drops but suffer from poor reactant distribution and water removal; and serpentine flow fields, which, through their meandering design, significantly improve gas–water management and overall efficiency. Recent work has explored optimizing serpentine channels by adjusting their number, geometry, and obstacle placement to further enhance performance [5].

Computational Fluid Dynamics (CFD) simulation is indispensable in the development and optimization of non-isothermal PEMFC [6]. Researchers have systematically analyzed the effects of various flow channel designs, including parallel [7,8,9], serpentine [10,11,12], and interdigitated flow channels [13]. Conventional and modified serpentine patterns are recognized as leading designs at both low- and high-temperature operation [14,15,16]. The serpentine pattern ensures uniform gas distribution around the GDL, promotes good under-rib convection in the GDL, and facilitates smooth temperature distribution. Klika et al. [17] developed a thermodynamic model to study water absorption in Nafion membranes, while Fan et al. [18] employed a 3D multiphase numerical model to investigate the performance of PEM fuel cells at low external humidification levels, finding that high current densities can reduce reliance on external humidification. Jiang et al. [19], using Monte Carlo simulations, identified that membrane thickness and volume fractions play a significant role in determining PEMFC performance. Similarly, Carcadea et al. [20] used CFD modeling to investigate the impact of catalyst layer microstructure, concluding that a higher ionomer volume fraction enhances fuel cell performance. Research on the simulation and modeling of non-isothermal PEMFC has been discussed in several papers. For example, Berning et al. [21] investigated the impact of temperature gradients on cell performance and water management in PEMFCs, highlighting the importance of thermal management in improving overall efficiency. Furthermore, Wu et al. [22] presented a study on non-isothermal transient modeling of water transport in PEMFCs.

For instance, Soong et al. [23] simulated the effect of adding blocks to flow channels and found that increasing the number of blocks significantly improved oxygen flux in the catalyst layer, thereby enhancing overall fuel cell performance. Similarly, Liu et al. [24] reported that higher gas flow rates, induced by block structures, led to better fuel cell efficiency. Dong et al. [25] compared five block geometries and demonstrated that the elliptical block design outperformed others, increasing output power by 15.77% compared to a straight channel. Ghanbarian et al. [26] examined three different cross-sectional block shapes and concluded that the sawtooth configuration delivered the best performance, boosting net power output by 26.75% over the straight flow channel.

Optimizing the flow channel structure can improve reactant gas transport efficiency and reduce energy losses, significantly enhancing the energy conversion efficiency of fuel cells and lowering the costs associated with hydrogen energy utilization [27,28,29]. Further optimization studies have highlighted the importance of block geometry. Perng et al. [30] found that a trapezoidal block with a 60° angle and 1.125 mm height was optimal for performance enhancement, while Heidary et al. [31] emphasized the role of block distribution within parallel flow fields. Xia et al. [32] introduced a bionic streamline block, showing improved current density uniformity, better gas distribution, and an 8.475% increase in output power compared to serpentine channels. Expanding on these concepts, three-dimensional mesh-like architectures—such as those employed in Toyota’s Mirai vehicle—have demonstrated effective gas–liquid separation and enhanced mass transfer. Bao et al. [33] reconstructed this design and confirmed that three-dimensional blocks improved gas transport capacity. In experimental work, Dhahad et al. [34] tested five flow plate geometries, showing that single-serpentine channels provided the most uniform velocity distribution (ϕ = 0.0271) but at the expense of higher pressure drop, while U-type channels reduced pressure drop but suffered from poor uniformity. For methanol-based systems, Vasu et al. [35] designed spiral-patterned anode flow fields in direct methanol fuel cells (DMFCs), mitigating CO₂ bubble accumulation, lowering pressure loss, and achieving a peak power density of 12.6 mW/cm². A 3D numerical simulation was performed by Ahmadi et al. [36] to assess the impact of adding obstacles in the flow channels on a PEMFC performance. Moayedi [37] numerically investigated the impact of installing a porous layer of a specific thickness near the PEMFC anode channel outlet on the reduction of fuel consumption.

An efficient flow field structure, complemented by baffles in flow channels, has proven effective in enhancing the performance of PEMFC [38,39]. Numerous simulations and experiments have explored various baffle configurations to improve reactant gas transport to the electrodes [40]. Although extensive research has been conducted on block-type and bio-inspired flow fields, few studies have addressed aerodynamic shaping as a strategy to simultaneously balance pressure drop and mass transfer. In particular, very recent PEMFC CFD studies, such as Bashiri et al. [41], Wang et al. [42], and Dong et al. [43], reported relative prediction errors as low as 0.1%. These works demonstrate the rapid advancement of simulation techniques in accurately reproducing experimental behavior. Compared to these state-of-the-art studies, the present work contributes by introducing a new aerodynamic biomimetic flow field, but we acknowledge that further refinement and experimental validation are necessary to achieve the same error margins.

Orthogonal testing is an effective multi-factor experimental method that utilizes orthogonal tables to identify representative experimental combinations, enabling the determination of optimal parameter values with fewer experiments [44]. Recently, this method has been extensively used for optimizing fuel cell structural parameters and improving overall performance [45,46].

Drawing inspiration from naturally streamlined geometries in high-speed species, this study proposes a drag-reducing bionic flow field based on the abdominal contour of a peregrine falcon. A comprehensive CFD model was developed to compare its performance with conventional straight, trapezoidal, and sinusoidal channels. Results show that the falcon-inspired flow field improves oxygen distribution, enhances gas transport, reduces pressure drop, and increases peak power density by 9.45%. These findings confirm the feasibility of applying bio-aerodynamic principles to PEMFC optimization and highlight a practical design pathway for achieving high-performance, low-loss systems. This work provides a valuable contribution for researchers and engineers focused on energy system modeling and advanced PEMFC performance enhancement.

2. Model Establishment and Verification

2.1. Physical Geometry

As illustrated in Figure 1a, the peregrine falcon—the fastest animal in the world—can reach flight speeds of up to 389 km/h, far exceeding those of most aircraft. Its aerodynamic body structure, evolved for high-speed flight, represents an optimal form for drag reduction. Notably, the fuselage design of the U.S. B-2 bomber was inspired by the falcon’s streamlined shape, as shown in Figure 1b.

To capture this streamlined structure, the abdominal profile of the peregrine falcon was scanned and reconstructed to generate a fitted curve for scaling. The key structural features of the optimized curve are presented in Figure 1c: s represents the spacing of the pseudo-falcon structure, while the ratios of the structural height h to the horizontal lengths of the two arc segments (l1 and l2) are 1:3 and 1:5, respectively.

Using this geometry, a three-dimensional block model was developed, from which a 3D flow channel configuration was constructed. In this model, the distance between adjacent falcon-inspired units is set to 0 mm; increasing this distance would make the geometry behave similarly to a straight channel, thus negating the enhanced mass transfer effect. The resulting structure is shown in Figure 1d.

Because oxygen diffuses much more slowly than hydrogen, its distribution within the cathode tends to be non-uniform, leading to several performance issues. In particular, the accumulation of liquid water can obstruct the electrochemical reaction. To address this challenge and enhance both the accuracy and efficiency of fuel cell simulations, this study introduces a falcon-inspired flow channel design on the cathode side of a single-channel fuel cell, while retaining a conventional straight channel at the anode. The corresponding fuel cell model and operating parameters are presented in Figure 2 and

Table 1. Structural Geometry and size parameters of the falcon-inspired single-channel fuel cell.

Parameters	Value
Proton exchange membrane thickness	0.025 mm
Catalyst layer thickness	0.01 mm
Gas diffusion layer thickness	0.2 mm
Number of unit structures imitating peregrine falcon	20
Structural height of mock peregrine falcon unit	0.6 mm
Unit structural length of imitation peregrine falcon	4.8 mm
Flow channel width and height	1 mm
The length of each component	96 mm
Plate width, height	2 mm
Number of horizontal cells	0.5

.

2.2. Mathematical Model

2.2.1. Model Assumptions

To ensure computational feasibility while maintaining physical accuracy, the PEMFC model was developed under several widely adopted simplifying assumptions. The fuel cell was simulated under steady-state conditions, with the fluid flow considered laminar, reflecting the low pressure and flow rates typical of PEMFC operation. Reactant gases were treated as ideal gases, enabling simplified equations of state for density and pressure calculations. The gas diffusion layers (GDLs) were modeled as isotropic and homogeneous, ensuring uniform transport properties without accounting for microstructural variability. The polymer electrolyte membrane was assumed impermeable to reactant gases, allowing only proton conduction, consistent with its real-world function. In addition, the effects of gravity and surface tension were neglected to reduce computational complexity.

These assumptions provided a balanced framework that simplified the numerical model while capturing the essential electrochemical, transport, and thermal behaviors of the PEMFC, ensuring both computational efficiency and physical relevance.

2.2.2. Governing Equations

In this study, a three-dimensional, two-phase non-isothermal PEMFC model is constructed based on ANSYS Fluent (version R2), and the numerical simulation of the proton exchange membrane fuel cell is achieved by coupling the interfaces of the hydrogen fuel cell, the free and porous media flow, the solid heat transfer, the dilute species transport, and the porous media phase transfer. Among them, the hydrogen fuel cell module solves the electrolyte/solid potential field and reactant concentration distribution; the free and porous media flow module calculates the fluid velocity and pressure fields; the solid heat transfer module resolves the temperature field evolution; the dilute species transport module characterizes the membrane water transport process; and the porous media phase transfer module quantifies the phase change behavior of water within the electrodes.

The numerical solution strictly adheres to the mass conservation equation, momentum conservation equation, energy conservation equation, species conservation equation, electrochemical equation, and water transport equation as shown in

Table 2. PEMFC control equations [14,47].

Equation	Scope	Formulation
Mass conservation	O2/H2/gaseous H2O transport in GCs/GDLs/CLs	${\displaystyle \frac{\partial }{\partial t}}\left({\epsilon }^{eff}{\rho }_g\right)+𝛻·\left({\rho }_g{\overrightarrow{v}}_g\right)=S_m$	(1)
Momentum conservation	H2/O2 mixture flow in GCs/GDLs/CLs	$\begin{array}{c}{\displaystyle \frac{\partial }{\partial t}}\left[{\displaystyle \frac{{\rho }_g{\overrightarrow{v}}_g}{{\epsilon }^{eff}\left(1-s\right)}}\right]+𝛻·\left[{\displaystyle \frac{{\rho }_g{\overrightarrow{v}}_g·{\overrightarrow{v}}_g}{{{\epsilon }^{eff}}^2}}\right]=\\ -𝛻P_g+{\displaystyle \frac{{\mu }_g}{{\epsilon }^{eff}}}𝛻·\left\{𝛻{\overrightarrow{v}}_g+𝛻{{\overrightarrow{(v}}_g)}^T-{\displaystyle \frac{2}{3}}\left(𝛻·{\overrightarrow{v}}_g\right)\right\}\\ -\left({\displaystyle \frac{{\mu }_g}{{\kappa }_0{\kappa }_{rg}}}+{\displaystyle \frac{S_m}{{\left({\epsilon }^{eff}\right)}^2}}\right){\overrightarrow{v}}_g\end{array}$	(2)
Gas species	H2/O2 mixture mass transfer in GCs/GDLs/CLs	${\displaystyle \frac{\partial c_i}{\partial t}}+𝛻\left(-D_i^{eff}𝛻c_i\right)+{\overrightarrow{v}}_g𝛻c_i=S_i$	(3)
Liquid water	Liquid H2O transport in GDLs/CLs	${\displaystyle \frac{\partial }{\partial t}}\left({\rho }_l{\epsilon }_0\right)+𝛻\left({\rho }_l{\overrightarrow{v}}_l\right)=S_{vl}$	(4)
Membrane water	H2O transport in CLs/PEM	$\begin{array}{c}{\displaystyle \frac{{\rho }_{mem}}{EW}}{\displaystyle \frac{\partial }{\partial t}}\left(\omega \lambda \right)+𝛻·\left({\displaystyle \frac{{2.5i}_{mem}}{22F}}\lambda \right)=\\ {\displaystyle \frac{{\rho }_{mem}}{EW}}𝛻\left(D_{mw}^{eff}𝛻\lambda \right)+S_{mw}\end{array}$	(5)
Energy conservation	Heat transfer in all zones	$\begin{array}{c}{\displaystyle \frac{\partial }{\partial t}}\left({\displaystyle \sum _{j=g,l,s}}\left({{\epsilon }_j\rho }_j{C}_{P,j}\right)T+{\displaystyle \sum _{j=g,l,s}}\left({{\epsilon }_j\rho }_j{C}_{P,j}\right)u_j𝛻T\right)=\\ 𝛻·\left(K^{eff}𝛻T\right)+S_T\end{array}$	(6)
Charge conservation	Proton/electron transport in CLs/GDLs	$𝛻·\left({\sigma }_m^{eff}𝛻{\mathsf{\Phi }}_m\right)=S_{ion}$	(7)
		$𝛻·\left({\sigma }_s^{eff}𝛻{\mathsf{\Phi }}_s\right)=S_e$	(8)

. The source terms of the governing equations in different computational domains are listed in

Table 3. Source terms of the control equation [47].

Source	Formulation		Unit
$S_m:$ Mass conservation	$\left\{\begin{array}{c}\hfill \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} \hspace{1em}-S_{vl}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} \mathrm{AGC}\hfill \\ \hfill \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} {-S}_{vl} \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} \mathrm{AGDL}\hfill \\ \hspace{1em}\hspace{1em} -J_a{M}_{H_2}/2F{-S}_{vl}-S_{mw}\hspace{1em}\hspace{1em}\hspace{1em} \mathrm{ACL}\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}0 \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} \mathrm{PEM}\\ {-J}_c{M}_{O_2}/4F+J_c{M}_{H_{2}O}/2F{-S}_{vl}-S_{mw}\hspace{1em}\mathrm{CCL}\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} {-S}_{vl}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\mathrm{CGDL}\\ {\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} -S}_{vl} \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\mathrm{CGC}\end{array}\right.$		$\mathrm{m}\mathrm{o}\mathrm{l}/{\mathrm{m}}^3\mathrm{s}$
$S_i:$ Gas species	$\left\{\begin{array}{c}{\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}-S}_{vl}/M_{H_{2}O}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\mathrm{AGC}\\ {\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}-S}_{vl}/M_{H_{2}O}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\mathrm{AGDL}\\ \hspace{1em}\hspace{1em}-J_a/2F{{-S}_{v-l}/M_{H_{2}O}-S}_{mw}/M_{H_{2}O} \hspace{1em}\mathrm{ACL}\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}0 \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} \mathrm{PEM}\\ -J_c/4F+J_c/2F-S_{vl}/M_{H_{2}O}-S_{mw}/M_{H_{2}O}\hspace{1em}\mathrm{CCL}\\ {\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}-S}_{vl}/M_{H_{2}O} \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\mathrm{CGDL}\\ {\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}-S}_{vl}/M_{H_{2}O}\hspace{1em} \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\mathrm{CGC}\\ \end{array}\right.$		$\mathrm{m}\mathrm{o}\mathrm{l}/{\mathrm{m}}^3\mathrm{s}$
$S_{vl}:$ Liquid water	$\left\{\begin{array}{c}{k}_c{\epsilon }_0\left(1-s\right)\left(x_{H_{2}O}{P}_g-P_{sat}\right)M_{H_{2}O}/RT,{\mathrm{x}}_{{\mathrm{H}}_2\mathrm{O}}{\mathrm{P}}_{\mathrm{g}}\ge {\mathrm{P}}_{\mathrm{s}\mathrm{a}\mathrm{t}}\\ k_e{\epsilon }_{0}s\left(x_{H_{2}O}{P}_g-P_{sat}\right)M_{H_{2}O}/RT,{\mathrm{x}}_{{\mathrm{H}}_2\mathrm{O}}{\mathrm{P}}_{\mathrm{g}}<{\mathrm{P}}_{\mathrm{s}\mathrm{a}\mathrm{t}}\end{array}\right.$		$\mathrm{m}\mathrm{o}\mathrm{l}/{\mathrm{m}}^3\mathrm{s}$
$S_T:$ Energy conservation	$\left\{\begin{array}{c}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}{\displaystyle \frac{{i_{op}}^2}{{\sigma }_{rib}}} \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\mathrm{Ribs}\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}h{S}_{vl}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} \mathrm{AGC}\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}{\displaystyle \frac{{i_{Ioc}}^2}{{\sigma }_{GDL}}}+h{S}_{vl}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\mathrm{AGDL}\\ \hspace{1em}\left|{\mathrm{R}}_{\mathrm{a}}\right|\left|{\eta }_a\right|+{\displaystyle \frac{{{\mathrm{R}}_{v,\mathrm{a}}}^2}{{\sigma }_s}}+{\displaystyle \frac{{{\mathrm{R}}_{\mathrm{v},\mathrm{a}}}^2}{{\sigma }_m}}+h{S}_{vl}\hspace{1em}\mathrm{ACL}\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}{\displaystyle \frac{{i_{Ioc}}^2}{{\sigma }_m}}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\mathrm{PEM}\\ \left|{\mathrm{R}}_{\mathrm{c}}\right|\left|{\eta }_c\right|-T\left({\displaystyle \frac{{dE}_{eq}}{dT}}\right){\displaystyle \frac{{R_c}^2}{{\sigma }_s}}+{\displaystyle \frac{{R_c}^2}{{\sigma }_m}}+h\hspace{1em}\mathrm{CGDL}\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}{\displaystyle \frac{{i_{Ioc}}^2}{{\sigma }_{GDL}}}+h{S}_{vl}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\mathrm{CCL}\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}h{S}_{vl}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\mathrm{CGC}\end{array}\right.$		$\mathrm{W}/{\mathrm{m}}^3$
Charge conservation	$\left\{\begin{array}{c}\pm R_a\hspace{1em}\mathrm{ACL} \\ \pm R_c \hspace{1em}\mathrm{CCL}\end{array}\right.$		$\mathrm{A}/{\mathrm{m}}^3$
$S_{mw}:$ Membrane water	$S_w^{vd}-S_w^{dl}$	$S_w^{vd}=k_{vd}{\displaystyle \frac{\lambda V_w}{\lambda V_w+V_{mw}}},c_w^{eq}>c_w^d$	$\mathrm{m}\mathrm{o}\mathrm{l}/{\mathrm{m}}^3\mathrm{s}$
		$S_w^{dl}=k_{dl}{\displaystyle \frac{\lambda V_w}{\lambda V_w+V_{mw}}},c_w^{eq}\le c_w^d$

. In addition, the physical and transport parameters involved in the governing equations and source terms are provided in

Table 4. Physical parameters and transmission equations of PEMFC.

Parameter	Relation
Effective porosity ${\epsilon }^{eff}$	${\epsilon }^{eff}={\epsilon }_0\left(1-s\right)$	(9)
Relative permeability of gas phase ${\kappa }_{rg}$ (m2)	${\kappa }_{rg}={\kappa }_0{\left(1-s\right)}^3$	(10)
Dynamic viscosity of gas mixture ${\mu }_g$ (Pa·s)	${\mu }_g={\displaystyle \sum _i}{\displaystyle \frac{x_i{\mu }_i}{{\sum }_k{x}_k{\Phi }_{ik}}}$	(11)
Mole fraction $x_i$	$x_i={\displaystyle \frac{c_i}{\sum c_i}}$	(12)
Effective gas mixture diffusion coefficient $D_i^{eff}$ (m2/s)	$D_i^{eff}=D_0{\left({\epsilon }^{eff}\right)}^{1.5}$	(13)
Binary diffusion coefficient of oxygen $D_{0,O}$	$D_{0,O}=2.82\times {10}^{-5}{\left({\displaystyle \frac{T}{307.1}}\right)}^{1.5}$	(14)
Binary diffusion coefficient of hydrogen $D_{0,H}$	$D_{0,H}=9.15\times {10}^{-5}{\left({\displaystyle \frac{T}{307.1}}\right)}^{1.5}$	(15)
Liquid water velocity ${\overrightarrow{v}}_l$ (m/s)	${\overrightarrow{v}}_l=-{\displaystyle \frac{{\kappa }_{rl}}{{\mu }_l}}𝛻P_l$	(16)
Dynamic viscosity of liquid water ${\mu }_l$ (Pa$·$s)	${\mu }_l=2.414\times {10}^{-5}\times {10}^{{\displaystyle \frac{247.8}{T-140.0}}}$	(17)
Relative permeability of liquid phase (m2)	${\kappa }_{rl}={\kappa }_0{s}^3$	(18)
Capillary pressure $P_c$ (Pa)	$P_c=\sigma \cos {\theta \left({\displaystyle \frac{{\epsilon }_0}{{\kappa }_0{\kappa }_{rl}}}\right)}^1\left\{\begin{array}{c}1.42\left(1-s\right)-2.12{\left(1-s\right)}^2+1.26{\left(1-s\right)}^3 \theta <90°\\ 1.42s-2.12s^2+1.26s^3 \theta >90°\end{array}\right.$	(19)
Capillary diffusion coefficient $D_c$	$D_c={\displaystyle \frac{{\sigma \mathit{cos}\left(\theta \right)\kappa }_{rl}}{{\mu }_l}}{\left({\kappa }_0{\epsilon }_0\right)}^{0.5}{\displaystyle \frac{dJ\left(s\right)}{ds}}$	(20)
Saturation vapor pressure $P_{sat}$ (Pa)	${\mathit{log}}_{10}\left({\displaystyle \frac{P_{sat}}{101325}}\right)=-2.1794+0.02953\left(T-273.15\right)-9.1837\times {10}^{-5}{\left(T-273.15\right)}^2$ $+1.4454\times {10}^{-7}{\left(T-273.15\right)}^3$	(21)
Effective membrane water diffusion coefficient	$D_{mw}^{eff}=\left\{\begin{array}{c}3.1\times {10}^{-7}\lambda \left(\mathit{exp}\left(0.28\lambda \right)-1\right)\mathit{exp}\left({\displaystyle \frac{-2346}{T}}\right)0<\lambda <3\\ 3.1\times {10}^{-7}\lambda \left(\mathit{exp}\left(0.28\lambda \right)-1\right)\mathit{exp}\left({\displaystyle \frac{-2346}{T}}\right)0<\lambda <3\hspace{1em}\\ 4.1\times {10}^{-10}{\left({\displaystyle \frac{\lambda }{25}}\right)}^{0.15}\left(1+\mathit{tanh}\left({\displaystyle \frac{\lambda -5}{1.4}}\right)\right) \lambda \ge 17\end{array}\right.$	(22)
Membrane water concentration $c_w^d$ (mol/m3)	$c_w^d={\displaystyle \frac{{\rho }_{mem}}{EW}}{\displaystyle \frac{\lambda }{1+k_s\lambda }}$	(23)
Water content $\lambda$	$\lambda =\left\{\begin{array}{c}0.43+17.81a-39.85a^2+36.0a^3 \left(0\le a\le 1\right)\\ 14.0+1.4\left(a-1\right) \left(1<a<3\right)\end{array}\right.$	(24)
Water activity $a$	$a={\displaystyle \frac{P_w}{P_{sat}}}+2s$
Anode/cathode electrochemical reaction rate (A/cm2)	$R_a={A_{V}J}_{0,a}^{ref}{\left({\displaystyle \frac{C_{H_2}}{C_{H_2}^{ref}}}\right)}^{0.5}\left[exp\left({\displaystyle \frac{F{\alpha }_a}{RT}}{\eta }_a\right)-exp\left(-{\displaystyle \frac{F{\alpha }_o}{RT}}{\eta }_a\right)\right]$	(25)
	$R_c=A_V{J}_{0,c}^{ref}{\left({\displaystyle \frac{C_{O_2}}{C_{O_2}^{ref}}}\right)}^1\left[\left(\mathrm{e}\mathrm{x}\mathrm{p}({\displaystyle \frac{F{\alpha }_a}{RT}}{\eta }_c\right)-exp\left(-{\displaystyle \frac{F\left(1-{\alpha }_o\right)}{RT}}{\eta }_c\right)\right]$	(26)
Equilibrium potential $E_{eq}$ (V)	$E_{eq}=1.23-9\times {10}^{-4}\left(T-298.15\right)$	(27)

.

2.3. Boundary Conditions

By employing a user-defined function (UDF) in Ansys Fluent, the governing equations of the fuel cell can be solved. To achieve this, it is necessary to define appropriate initial and boundary conditions at both the cathode and anode. These include specifying the inlet gas mass flow rate, the concentration ratio of each gas component, the outlet pressure, and the operating temperature.

For the cathode, the initial conditions require the specification of the reactant species concentrations and the inlet gas mass flow rate. For the anode, the initial gas mass flow rate and the concentration ratio of its components must be defined. Establishing these parameters ensures that the simulation produces accurate and reliable results.

In this study, the boundary conditions for the anode and cathode inlets are defined as mass flow inlet, with the corresponding gas mass flow, species mass fractions, temperature, and pressure set accordingly. The gas mass flow is determined using the following expression [27]:

$$v_{a,in}={\displaystyle \frac{{\xi }^a{I}^{ref}{A}_{act}^a}{2F{C}_{H_2}{A}_{in}^a}}, C_{H_2}={\displaystyle \frac{P_{g,in}^a-R{H}_a{p}^{sat}}{RT}},$$

(28)

$$v_{c,in}={\displaystyle \frac{{\xi }^c{I}^{ref}{A}_{act}^c}{4F{C}_{O_2}{A}_{in}^a}}, C_{O_2}={\displaystyle \frac{0.21\left(P_{g,in}^c-R{H}_c{p}^{sat}\right)}{RT}}$$

(29)

2.4. Grid Independence Verification and Model Validation

Figure 3a illustrates the mesh structure of the branched serpentine flow field. During the meshing process, the cathode and anode flow channels are meshed first. These channels are divided into straight sections and bend regions: structured hexahedral meshes are applied to the straight sections, while unstructured meshes are used for the bend regions to accommodate the geometric transition. Subsequently, due to their regular structures, both the catalyst layers and the proton exchange membrane are meshed using structured grids. Finally, considering the structural differences between the flow channels and the catalyst layers, the gas diffusion layers are meshed with unstructured grids to address this variation. After meshing is completed, the current density is compared across different mesh densities (340,531; 320,535; 305,962; 274,620; 154,620; 135,634; 116,514 cells), as shown in Figure 3b. The results in Figure 3b indicate that the variation in current density becomes negligible once the mesh density reaches 274,620 cells. Therefore, to balance computational accuracy and efficiency, the mesh with 274,620 cells is ultimately selected.

Mesh and Single-Cell Performance Assessment

Mesh independence was established by progressively refining the grid and monitoring the local current density distribution as the principal sensitive field for the coupled electrochemical/transport problem (see Figure 3b). Once the mesh reached approximately 274,620 cells, further refinement produced only negligible changes in the spatial current density profile and did not affect global outputs (average cell voltage, peak power density, and pressure drop) within the solver’s numerical tolerance. The final mesh uses structured hexahedral elements in straight regions and locally refined unstructured elements in geometric transition zones to capture steep gradients efficiently.

Regarding single-unit cell performance, the model directly computes the local reaction current density in the catalyst layer by solving the coupled species, momentum, energy and charge conservation equations with electrochemical source terms (thermodynamic Nernst potential, activation/kinetic and concentration overpotentials as formulated in Table 2, Table 3 and Table 4). The average current density is obtained by integrating the local current density over the catalyst active area, and the cell voltage at each operating point is derived from the computed solid-phase potentials (which include activation, ohmic and concentration losses).

$$\overline{i}=\left(1/A_{CL}\right){\int }_{A_{CL}}{i}_{loc} \mathrm{d}A$$

(30)

To ensure the physical reliability of these single-cell outputs, we validated the complete multiphysics model against experimental polarization and power density data from Barati et al. [48]; the simulated polarization curve reproduces the experimental trend with a maximum deviation below 4%. This combined approach—mesh convergence on the most sensitive field, full multiphysics electrochemical coupling, and literature benchmarking—provides confidence that the single-unit cell performance reported in this work is numerically robust and physically meaningful.

To ensure the accuracy of the data obtained from the established three-dimensional, two-phase, non-isothermal computational model of the PEMFC, the model must be validated for reasonableness before conducting actual numerical simulations. As shown in Figure 4, comparison is presented between the simulation data and the experimental data from reference [48]. Figure 4 indicates that the polarization curves and power density curves from both sources show good agreement, with a maximum relative error not exceeding 4%. This demonstrates that the three-dimensional, two-phase PEMFC model established in this study can accurately simulate the operating state of the PEMFC.

To ensure that the comparison with reference [48] is meaningful, particular attention was given to maintaining consistency between our model parameters and the experimental setup. Both studies adopted a channel width and height of 1 mm, which guarantees equivalence in the flow field geometry. For the membrane electrode assembly (MEA), the gas diffusion layer (GDL) porosity in our simulation was set to 0.6, consistent with the experimental configuration, while the catalyst layer thickness (0.01 mm) and membrane thickness (0.025 mm) also match the reported values. Furthermore, the operating temperature (343 K), inlet stoichiometric ratios (1.2 at the anode and 2.0 at the cathode), and operating pressure (1 atm) were kept identical to those in [48]. By ensuring these correspondences, the validation goes beyond simple curve alignment and instead reflects a physically consistent basis for comparison. As shown in Figure 4, the polarization and power density curves obtained from our CFD model closely match the experimental data, with a maximum deviation below 4%, thereby confirming the robustness and accuracy of the proposed numerical framework.

3. Results and Discussions

To evaluate and compare the performance of the falcon-inspired flow channel, two additional fuel cell blocks were designed based on a single-channel conventional straight flow channel. One of these is a wave-shaped block defined by the sinusoidal equation y = 0.6 sin(Pi/2.x). To eliminate the influence of structural dimensions on fuel cell performance, all three blocks have a uniform height of 0.6 mm and a spacing of 0 mm, while the remaining structural parameters are consistent with those listed in Table 4 and

Table 5. Proton exchange membrane fuel cell operating parameters [48].

Parameters	Symbol	Unit	Value
Contact angle (GDL, CL)	$\theta$	°	120, 95
Dry film density	${\rho }_{mem}$	kg/m3	1900
Electrolyte volume fraction (CL, PEM)	$\omega$	-	0.4, 1
Equivalent weight of film	$EW$	kg/mol	1100
Inlet mole fraction (H2/H2O/O2/N2)	$W_i$	-	0.697/0.303/0.146/0.55
Inlet temperature	$T$	K	343
Operating pressure	$P$	atm	Anode:1.0, Cathode:1.0
Operating temperature	$T$	K	343 K
Permeability (GDL, CL, PEM)	${\kappa }_0$	m2	1 × 10−12, 1 × 10−13, 1 × 10−18
Porosity (GDL, CL)	${\epsilon }_0$	-	0.6, 0.3
Reference volumetric current density	$I^{ref}$	A/m3	Anode: 3000, Cathode: 0.012
Relative humidity of gas	$RH$	-	Anode: 1.0, Cathode:1.0
Solid conductivity (GDL, CL)	$\sigma$	S/m	2500
Stoichiometric ratio	$\xi$	-	Anode: 1.2, Cathode:2.0
Thermal conductivity (GDL, CL, PEM)	$K$	W/(m$·$K)	1.6, 0.8, 0.45
Transfer coefficient	$\alpha$	-	${\alpha }_a=0.1,{\alpha }_c=0.5$

. The four fuel cell models are illustrated in Figure 5.

3.1. Molar Concentration Distribution of Oxygen

Figure 6 illustrates the spatial distribution of oxygen molar concentration in the cathode catalytic layer for four different fuel cell flow channel designs: straight, trapezoidal block, sinusoidal block, and bionic peregrine falcon block channels. The color map indicates oxygen concentration, with red representing high concentrations and blue representing low concentrations. In the straight flow channel, oxygen distribution is highly non-uniform, with high concentrations near the inlet that rapidly decrease along the channel, highlighting poor oxygen transport and significant mass transfer limitations due to reliance on diffusion alone. Both trapezoidal and sinusoidal block channels show improved uniformity, with less steep concentration gradients, as the block structures generate secondary flows that disrupt stagnant zones and enhance mass transfer. The bionic peregrine falcon block channel exhibits the most uniform distribution, maintaining high oxygen levels further along the channel. This design effectively directs gas flow both vertically and horizontally, reducing transport resistance and minimizing concentration polarization. Overall, the results indicate that introducing structured blocks markedly improves oxygen delivery to the catalyst layer, with the falcon-inspired design offering superior mass transfer, higher oxygen availability, and more uniform distribution. These improvements are expected to enhance fuel cell performance by mitigating local starvation, increasing reaction rates, and reducing concentration overpotentials, confirming the significant benefits of bio-inspired flow channel designs in PEMFC applications.

3.2. Water Mass Fraction Distribution

In addition to maintaining the proper operation of the moistened film electrode, excess water within the flow channel can hinder oxygen participation in the electrochemical reaction, thereby reducing reaction efficiency. Large accumulations of liquid water may lead to the “flooding” phenomenon, which can damage the membrane electrode and shorten the fuel cell’s lifespan. Consequently, the distribution of water mass within the cathode catalytic layer is a crucial performance indicator for assessing flow field designs.

Figure 7 shows the water mass fraction distribution at the interface between the catalytic layer and the gas diffusion layer for four fuel cell designs. At the channel inlet, water mass fractions are relatively low due to gas purging, with the Peregrine Falcon structure demonstrating the best water management and the straight flow channel the poorest. As oxygen consumption generates more water along the channel, the efficiency of water removal structures decreases. While differences in water mass fraction among the designs become minimal in the latter half of the channel, the first half clearly highlights the Peregrine Falcon structure’s superior water removal and enhanced mass transfer capabilities.

The observation that the Peregrine Falcon-inspired structure shows clear superiority in water removal in the first half of the channel but reduced differences in the second half can be explained by the reaction kinetics and local oxygen availability. In the upstream region, oxygen concentration is relatively high, and electrochemical reactions proceed more actively, generating liquid water at a higher rate. Under these conditions, the enhanced convective transport induced by the biomimetic geometry efficiently removes excess water, resulting in marked improvement compared to straight or block-type designs. In the downstream region, however, oxygen concentration decreases due to prior consumption, leading to reduced reaction rates and consequently lower water production. With less liquid water generated, the removal burden becomes smaller, and therefore, the difference in water mass fraction among the four designs diminishes in the latter part of the channel. This explains why the performance gap is most evident at the channel entrance and gradually narrows towards the outlet.

3.3. Velocity Distribution

Figure 8 illustrates the gas flow velocity distribution in the cathode flow channels of four fuel cell designs. Gas velocity serves as a direct indicator of the flow channel’s mass transfer performance. In the straight flow channel, the linear and vertical geometry allows the gas to flow undisturbed, relying solely on diffusion, which results in relatively low velocities. By contrast, in the channels with block structures, the protrusions into the flow path accelerate the gas and alter its direction, creating vertical velocity components corresponding to the shape of each block. According to the field synergy principle, these vertical components enhance gas diffusion within the membrane electrode, promoting greater reactant transport and improving fuel cell performance. Among the designs studied, the falcon-inspired structure has the most pronounced effect on gas velocity, confirming that it outperforms other block structures in enhancing mass transfer.

3.4. Pressure Distribution

Simulation and theoretical analysis show that incorporating a block structure in the flow channel significantly enhances its mass transfer capability. However, this improvement comes at the cost of increased pressure drop, which leads to higher parasitic power losses and can negatively affect both the performance and lifespan of the fuel cell. Figure 9 presents the pressure profiles at the interface between the cathode channel and the diffusion layer for four fuel cell designs. The figure clearly illustrates that while block structures improve mass transfer, they also induce higher pressure drops. Therefore, it is crucial to retain the block structure to enhance mass transfer while minimizing the associated pressure penalty. Among the designs, the peregrine falcon-inspired structure exhibits the smallest pressure drop, whereas the trapezoidal block shows the largest. This difference arises because the trapezoidal design has the poorest drag reduction capability, while the sinusoidal and falcon-inspired structures feature more streamlined geometries that reduce flow resistance. The falcon-inspired design, in particular, demonstrates superior drag reduction, combining enhanced mass transfer with minimal pressure loss.

In addition to improving mass transfer and water management, an effective flow field design must also minimize parasitic energy losses caused by excessive pressure drop. Figure 9 presents the pressure distribution along the cathode flow channels for the four designs under study. The results clearly show that the introduction of block-type structures increases the local pressure loss compared to the straight channel, as the flow is periodically accelerated and redirected around the obstacles. Among the conventional geometries, the trapezoidal block generates the highest pressure drop because of its abrupt edges, which intensify flow separation and vortex formation. The sinusoidal design provides a smoother pressure profile due to its wavy curvature, but still results in moderate pressure losses. By contrast, the Peregrine Falcon-inspired structure demonstrates the lowest pressure drop among the block-type channels. Its biologically streamlined contour reduces drag, allowing the gas to accelerate around the structure without significant separation zones. This confirms that the bio-inspired design successfully combines enhanced mass transfer with drag reduction, ensuring a more energy-efficient operation compared to other block geometries.

3.5. Polarization and Power Density Curves

Compared to the traditional straight flow channel, incorporating a three-dimensional block structure significantly enhances the peak power density of the fuel cell, as illustrated in Figure 10. The block structure has a notable impact on performance, exceeding that of trapezoidal and sinusoidal designs, with peak power density increases of 9.45%, 8.7%, and 7.89%, respectively. It is important to note that blocks with the same structural height exert a smaller effect on fuel cell performance. This is because the block improves performance primarily by directing gas toward the membrane electrode, increasing the molar concentration of reactants in the catalyst layer, and thereby enhancing the efficiency of the electrochemical reaction. Consequently, the block height has a greater influence on peak power density than its shape.

At low current densities, the polarization curves for all four channels are nearly identical. However, as current density rises, the effect of the block structure becomes more pronounced. The forced convection induced by the block enhances fuel concentration within the membrane electrode, reducing concentration polarization. Simultaneously, the increased gas velocity improves liquid water removal, effectively preventing flooding and enhancing water management, which together contribute to the overall improvement in fuel cell performance.

The lifting effect of different block structures also varies. While the sinusoidal (wavy) structure provides superior drag reduction compared to the trapezoidal design, the trapezoid maintains higher oxygen concentration at the membrane electrode due to its larger contact area, resulting in slightly better fuel cell performance. The falcon-inspired structure, however, exhibits a significantly stronger lifting effect, attributed to its biologically inspired drag reduction, which promotes a more uniform fuel concentration distribution and further reduces concentration polarization losses. This superior drag reduction compensates for differences in contact area between the falcon-inspired and trapezoidal designs.

Notably, at high current densities, fuel cells with trapezoidal blocks become unstable, with simulations failing to converge and preventing normal operation. In contrast, the falcon-inspired and sinusoidal structures maintain stable performance, thanks to their enhanced drag reduction, which ensures uniform oxygen distribution and reduces concentration polarization.

In conclusion, the falcon-inspired structure effectively enhances mass transfer, minimizes polarization losses, reduces system power losses through superior drag reduction, and ultimately boosts fuel cell power output. These combined effects make it the most promising design for improving overall fuel cell performance.

Finally, it should be emphasized that while the present study thoroughly analyzes oxygen distribution, water removal, velocity profiles, and pressure drop, it does not include explicit current density and temperature distribution maps. This decision was made to maintain the focus on aerodynamic optimization and fluid transport phenomena, while keeping the model computationally tractable. Future work will extend this analysis by incorporating full electrochemical current density distributions and thermal management studies for the biomimetic flow field. These results are planned to be presented in a separate article as a direct continuation of the present research.

4. Conclusions

This study presents a numerical investigation of a bionic three-dimensional flow field for a proton exchange membrane fuel cell (PEMFC), inspired by the abdominal contour of a peregrine falcon. The primary objective is to enhance reactant transport and water removal, reduce pressure drop, and improve overall fuel cell efficiency. The key findings are summarized as follows:

• Compared to the conventional straight channel, the bionic flow field significantly improves oxygen distribution and flow uniformity in the cathode by promoting aerodynamic acceleration and minimizing stagnant zones.
• The falcon-inspired structure increases peak power density by 9.45% while simultaneously reducing pressure drop, demonstrating enhanced electrochemical performance with lower parasitic losses.
• Analysis of velocity streamlines and oxygen mass fraction contours shows that the bionic geometry enhances convective transport and facilitates effective water removal, particularly near the outlet region.
• The optimized flow field reduces local pressure variations, ensuring more uniform reactant delivery and mitigating concentration polarization, especially at high current densities.
• This design maintains system stability while requiring less pumping power, highlighting its practical potential for integration into low-loss, high-performance PEMFC systems.
• Overall, the proposed bionic flow field, leveraging aerodynamic optimization, provides a feasible and scalable structural strategy for next-generation PEMFC design.