The Effect of Flow Field Design Parameters on the Performance of PEMFC: A Review

Abstract

Proton exchange membrane fuel cell is essentially utilized to generate energy with zero emission. There are many drawbacks in PEMFC, such as the mal-distribution of reactants, water management between the catalyst layer and the GDL, and the mass transport issue of reactants. Flow field design parameters can overcome these problems to improve cell performance. Where the flow field is an essential element of the fuel cell, and it is designed to provide the required amount of both hydrogen and oxygen with the lowest possible pressure drop on the anode and cathode sides, respectively. In this paper, the cell performance with different flow field design parameters, such as conventional flow field configuration, nature-inspired flow field configuration, and geometric parameters, as well as their modifications, is reviewed in detail. It has been demonstrated through the current review paper that the flow field design parameters can significantly affect the overall behavior of PEMFC, and each design parameter has advantages and disadvantages that make the flow fields suitable for specific applications.

1. Introduction

Because of the rising demand for energy sources and worldwide concerns about using fossil fuels due to their effect on global warming and climate change, clean energy generation becomes the only solution to these problems and an urgent requirement. Fuel cells are one of the most appropriate options for producing clean energy [1]. The working principle of a fuel cell is similar to that of a battery, except that it does not require recharging [2]. A fuel cell system can be utilized for converting the hydrogen that has been stored into electrical power [3]. Fuel cells are of several types, but the proton exchange membrane fuel cell (PEMFC) is the most preferred among all types because it has a simple design and high electrical efficiency [4]. A PEMFC is an electrochemical conversion apparatus that converts the chemical energy of fuel and an oxidizing agent (often hydrogen and oxygen, respectively) into electrical energy through redox reactions without undergoing intermediate stages and produces heat and water [5]. Water and heat management issues of PEMFC are essential issues that affect cell performance. There are several parameters that influence water management and PEMFC performance, but the flow field is one of the most essential parameters of PEMFC because it acts on several tasks, such as distributing oxygen (oxidant) and hydrogen fuel on the reactive sites, removing the products of the reaction (heat and water), and collecting the current produced from PEMFC [6]. So it must be developed and designed to provide an acceptable collection of current that is produced, uniform distribution, and good heat and water management, as well as provide low-pressure drop [7]. The water generated on the cathode side should remain at an optimum level to prevent hotspots, dehydration, flooding, and reduction in cell performance, which are generally affected by the design of the flow field [8]. A lot of configurations and modifications of the flow field have been employed in fuel cells to reach the optimum design and improve cell performance, such as serpentine, interdigitated, straight-parallel, and parallel wavy [9]. Accordingly, the current paper will review the studies that dealt with the design characteristics of flow fields of PEMFCs and divide flow fields design parameters into several types depending on configuration and geometric parameters to facilitate their study and understand their effect on water and heat management and performance of PEM fuel cells.

2. Flow Field Design Parameters

The flow field is an essential element of a fuel cell, and it is designed to provide the required amount of hydrogen and oxygen with the lowest possible pressure drop on the anode and cathode sides, respectively. Flow field materials should have high mechanical strength, high thermal and electric conductivities, ease of machinability, water resistance, and non-toxicity. Graphite materials are commonly used for this purpose. An optimal flow field design should have an acceptable collection of produced current that has a uniform distribution and good heat and water management and provide a low-pressure drop. According to extant research, flow field design depends on the configuration and geometric parameter of the flow field, as shown in Figure 1.

3. Flow Field Configuration

The configuration of a flow field is divided into two groups of designs; the first one is a conventional flow field configuration, and the second one is a bio-inspired flow field configuration.

3.1. Conventional Flow Field

Conventional flow fields are of various types, including straight, serpentine, parallel, spiral, pin, radial, cylindrical, interdigitated, and their modifications.

3.1.1. Straight Flow Field

The straight flow field (STFF) is designed by utilizing a single channel with a straight direction. The square or rectangle cross-section for the channel is uniform along the path. The two types of straight flow fields are the close-channeled flow field (ducted) and open-channeled flow field (ribbed), as shown in Figure 2. The ribbed design is open to the atmosphere on the cathode side. P. Manoj Kumar and Ajit Kumar Kolar compared ribbed and ducted designs at horizontal and vertical orientations [10].

Compared with the ducted design, the ribbed design’s vertical orientation allows for better water elimination by gravitational effects and better breathing, leading to improved performance.

Straight Flow Field Modification

The straight configuration has some modifications, such as blockages and traps, which affect cell performance. The most recent shape of the trap in the flow channel (Figure 3) was developed [11]. The channel trap (8 mm long) provided a uniform distribution of water and oxygen over CL and delivered higher current densities than other traps.

The blockages in the straight configuration have different shapes, such as regular wave, M, and bio-inspired wave shapes. The regular wave shape has been modified by employing a bio-inspired wave shape in the channels; this modification was inspired by a cuttlefish fin (Figure 4) [12]. Compared with the performance of a straight channel, the performance of a wavy channel is generally improved due to low resistance to reactant flow. Furthermore, a bio-inspired wave channel has higher efficiency and lower flow resistance compared with a regular wave channel. The optimized size of the wave channel that can improve power density by 2.2% is 3.52 wave cycles and 3.05 × 10⁻⁵ m central amplitude.

Wavy channels have been further enhanced by utilizing M-shape flow channels (Figure 5), which generate low entropy at the same pumping energy and high power density (21.3%) [13]. In M-shaped channels, the obstacle height and blockage thickness augment the reactant flow in the wall direction with high heat and mass transfer rates.

3.1.2. Serpentine Flow Field

The serpentine configuration (SFF) is a long channel that extends in form like the movement of a snake (serpent), where the flow path starts from the inlet and ends at the outlet continuously, as shown in Figure 6. In SFF, the reactant pressure drop increases. SFF is commonly used in PEMFCs because the distribution of reactants throughout the effective area is efficient. SFF has better performance than a straight flow field [14].

Serpentine Flow Field Modifications

The serpentine configuration has some modifications, such as multi-pass, zigzag designs, wavy, and porous material insertion in the ribs of SFF. The single path (1-SFF) in SFF is modified by increasing the number of passes or splitting the total length into many segments with an individual in/out for each segment. Previous research has investigated 1-SFF, symmetric single path, cyclic single path, and two passes (2-SFF) (Figure 7) [15]. The performance of 2-SFF is higher than that of other designs at high humidity. While the symmetric single path and cyclic single path demonstrate better performance and lower pressure drop at low humidity compared with the other designs.

Compared with 2-pass, 3-pass, and 4-pass SFFs, 3-pass SFF performs better at the same rib and channel size [16]. PEMFCs with 26, 13, 6, and 3 flow channels and a complex SFF with 26-flow channels (Figure 8) have also been investigated to study the influence of the number of passes and length of the channel path [17]. Compared with a long path, a short channel path delivers uniform distributions of current and decreases flooding and condensed water. Furthermore, the performance of the 13-channel serpentine configuration is better than that of the 26-channel configuration due to the differences in membrane hydration. The essential metric for PEM fuel cells is pressure drop across channels because the type of blowers and compressors are selected depending accordingly, as well as the pressure drop influence on the cell electrochemistry. Figure 9 reveals that water content and pressure drop growth by increasing channel path length while increasing the channels number leads to decreases in the pressure drop.

The performance of several SFF shapes (Z, 2Z, 3Z, S, 2S, W, and novel W-SFF) has been compared [18]. The performance of the novel W-SFF design (Figure 10) is better than that of the other designs because the most active surface is covered, leading to uniform current.

The sinusoidal wavy configuration of SFF shown in Figure 11 was also compared with the conventional configuration [19]. Three different amplitudes for sinusoidal wavy design (0.25, 0.5, and 0.75) mm with the same wavelength (6.28 mm) were used. The results of the sinusoidal wavy configuration (0.25 mm amplitude) were better than those of the conventional configuration by 20.15%. The former has good performance and augments both diffusion and flow rates.

In other studies, porous carbon inserts (PCI) were inserted among the ribs of the cathode in staggered (zigzag type) and uniform (pin type) arrangements (Figure 12), which enhanced the liquid water management and PEMFC performance of SFF [20,21]. The PCI absorbed the water between the ribs and interfacial area of GDL and delivered it to channels through the lateral sides. Compared with SFF, the zigzag type of PCI inserted among the ribs of the flow field on the cathode side improved the performance by 11.56%. Notably, the cubical PCI was made of Vulcan carbon. The efficient distribution in the cathode channel for reactants led to increasing the rate of water generation, as shown in Figure 13. Consequently, the zigzag and uniform type of PCI decreases the water accumulation in the channel and improves.

The types of flow channel designs used were conventional serpentine, pin type with uniform porous inserts, and pin type with zigzag porous inserts [22]). The analysis focused on the influence of decreasing the flooding between the ribs and GDL and the carbon inserts’ porosity on cell performance. The performance of zigzag and uniform pattern types was better than that of the conventional serpentine type. However, the performance of the zigzag pattern type was higher than that of the uniform pattern type by 2.98% due to the increase in water absorption by the capillary action of the cubical porous inserts in the zigzag pattern type. The effect of porosity was marginal.

3.1.3. Parallel Flow Field

The parallel flow field (PFF) configuration is simple and easy to fabricate. It involves longitudinal straight channels placed in parallel to one another, as shown in Figure 14. Conventional PFF has a single inlet and outlet.

Parallel Flow Field Modification

The parallel configuration has some modifications, such as changing the positions of the inlet and outlet, PFF with single and double in/out, PFF with baffles, PFF with a micro distributor, and PFF with zigzag wavy channels. On the basis of the position of the inlet and outlet, PFFs can be divided into many types, such as Z-type, multi-Z-type, U-type, 2U-type, 4U-type, and mixed (U and Z) type (Figure 15). Although the reactant pressure drop of PFF was lower than that of SFF, the flow maldistribution makes some channels almost empty of reactant. The design parameters, such as the dimensions of ribs, channels, and header, are the primary cause of the maldistribution. Figure 16 reveals that the U-type has an extreme maldistribution of flow with a non-uniformity index of 0.70, while the 2U type enhances the flow distribution with a non-uniformity index of 0.30. The best improvement of a non-uniformity index was for 4U-type by 0.16. In Z-type, the increase in Z-number leads to a decreased flow non-uniformity index and increases the pressure drop, as shown in Figure 17. Therefore, the Z-type has a greatly lower pressure drop with a fairly high non-uniformity index, while the 5Z-type has the lowest non-uniformity index with the highest pressure drop. Furthermore, the flow distribution for the U-Z type was better than that for the conventional PFF [23,24]. The pressure drop of these cases is listed in

Table 1. Flow distribution parameters for various design [24].

Configurations	Flow Non Uniformity Index (F1)	∆P (Pa)
1-U	0.70	66.75
2-U	0.30	76.51
4-U	0.16	78.22
1-Z	0.48	73.75
2-Z	0.27	170.79
4-Z	0.15	554.62
5-Z	0.12	842.71

. Where it notices that the relative increase of pressure drops by 20% led to a considerable enhancement in flow distribution.

In another study, the parallel configuration was modified based on the number of outlets and inlets. Single and double in/out and various channel widths of 1–3 mm were added to PFF, as shown in Figure 18. The channel width from the entrance to the middle was reduced, and the channel width from the middle to the end was increased to distribute the reactants evenly [25]. The single in/out PFF had a uniform distribution of reactants more than that of conventional PFF because it had an equal channel length. Thus, the performance of single in/out PFF was better than that of conventional PFF. Additionally, the uniform distribution of reactants for the single in/out PFF design led to the uniform current, which in turn reduced the hotspots in the catalyst layer [26]. Figure 19 reveals that a high-pressure drop decreases the cathode flooding as well as the uniform distribution of pressure improves the distribution of liquid water.

Meanwhile, A. Ghanbarian and M.J. Kermani [27] used baffles (blockages) of different shapes in PFF, and the adopted materials had high porosity. The different shapes of baffles placed along the channel of the cathode were square, semicircular, and trapezoidal. Along 80 mm of the cathode channel were six indentations spaced 10 mm apart. The amounts of current and reactants at CL were increased because of the presence of the indentations, leading to a synergy effect generated by diffusion and advection mechanisms. The variety of rib sizes, dent positions (staggered and parallel), and dent height influenced the power, which was augmented by 25%. Additionally, the performance of the trapezoidal shape of indentation was better than that of the other indentation shapes. In another work [28], plain nickel foam and small rectangular baffles were placed in PFF channels, as shown in Figure 20. In this modification, the rib and channels on the cathode were completely replaced, and the nickel metal foam with a porosity of 80% was utilized as a flow distribution layer. The addition of the metal foam and baffle plates augmented the concentrations of oxygen and current density. Additionally, the current density was improved by using high-porosity metal foam and reducing the depth of the channel. In addition, the plain nickel foam has the highest pressure drop, while the conventional parallel flow field has the lowest pressure drop, as shown in Figure 21. However, the pressure drop of plain nickel foam is considered comparatively high compared with that of SFF. Finally, the cell performance of PFF has been enhanced by utilizing plain nickel foam and rectangular baffles.

Abouzar Azarafza et al. [29] reported that the use of nickel foam with a permeability of 10⁻⁸ m² and porosity of 90% in PFF increases the power density, which is higher than that in SFF by 10% and that in PFF by 50% at high and medium values of humidity; it is also higher than that in IFF. It is worth mentioning that the effect of relative humidity on the pressure drop is very small (negligible) for all the designs. According to the ideal gas law, the increasing temperature led to an increased pressure drop slightly for all types of flow fields, as shown in Figure 22. Another study used four trapezoidal plates with slope angles of 45° and height of 0.8 mm instead of rectangular-shape blockages and placed them along the channels of PFF in staggered and parallel arrangements, namely, (PFF:2) and (PFF:1), respectively [30]. The pressure drop of (PFF:2) was lower than that of (PFF:1), and the water removal rate of (PFF:2) was better than that of (PFF:1). Furthermore, the net power of (PFF:2) was higher than that of PFF and (PFF:1) by 6.39% and 2.54%, respectively. The pressure drop of the baffle plate flow fields was higher than that of conventional PFF due to the high flow resistance. A micro distributor with a cross-sectional area of 0.2 × 0.2 mm² at the inlet of each channel was investigated to reveal the influence of the presence of a micro distributor in PFF on performance [31]. Figure 23 shows the PFF modified by the micro distributor. The performance of the micro-distributor PFF was higher than that of the conventional PFF by 22.8% and similar to the performance of SFF. Decreasing the micro distributor size led to increased performance and pressure drop, as shown in Figure 24. Moreover, by increasing the pressure drop between the inlet and outlet of the main channels, the irregular supply of oxygen in the interfacial region of CL and GDL was reduced.

Bipolar plates have separate channels for cooling that are present in large-sized PEMFCs. In [32], an analysis was performed on a cooling plate that had new zigzag wavy channels with a channel width and pitch length of 2 and 4 mm, respectively (Figure 25). The performance was estimated in terms of uniformity index, the temperature difference on the surface, and the maximum surface temperature; in comparison with the straight channels, the zigzag channels improved performance by 8%, 23%, and 5%, respectively. The zigzag channels enhanced the thermal performance of the PEMFCs. Figure 26 reveals that the maximum pressure drop of PFF with zigzag channels is higher than that of PFF with straight channels by 10 times due to the bends arrangement in zigzag channels. However, compared to SFF, the pressure drop of the zigzag type is relatively small.

3.1.4. Interdigitated Flow Field

The interdigitated flow field (IFF) design was proposed by Nguyen [33]. The channels in IFF are dead-ended. In this configuration, the mechanism of reactant transmission to and from the catalyst layer is by forced convection instead of diffusion transfer [34]. The electrochemical reactions are considerably improved at the CL of IFF because the convection process is fast compared with the diffusion process. Additionally, the shear force of the reactants removes the water trapped inside the electrodes.

Interdigitated Flow Field Modification

The performance and design parameters of IFF can be adjusted by adding baffles. Blockages were used to convert PFF into IFF, which was placed at the end and end/mid of the channel path (Types I and II, respectively), as shown in Figure 27 [35]. The presence of channel blockage improved the transit of reactants and cell performance. Additionally, using oxygen rather than air on the cathode side produced highly satisfactory results. Another study [36] reported that when air is used on the cathode side, the power output of the mid/end-blockage IIF (Type II) is higher than that of conventional IFF by 1.3 times. The mid-blockage IFF improves the power density by about 24% by increasing the back pressure from 1 bar to 2 bar.

The different positions of rectangular parallelepipeds and their numbers (1, 3, 5, 7, 8, and 9) in the channel inlet and outlet of IFF were analyzed [37]). An increase in the number of rectangular parallelepipeds led to enhanced performance. Moreover, the increase in the number of rectangular parallelepipeds led to increased pressure drop, but it reduced at N more than 8, as shown in Figure 28. The outlet channels with rectangular parallelepipeds enhanced the power by 26% compared with the smooth-walled channel. SFF and IFF have been merged into one flow field to produce a novel flow field called hybrid serpentine interdigitated (HSIFF) or (FF:14), as shown in Figure 29. Three types of HSIFF have been investigated and compared with SFF having one channel (1S); the first type has one inlet and one outlet (1-IO), the second one has two inlets and two outlets (2-IO), and the third one has one inlet and two outlets (1I-2O) [38]. The advantages of IFF and SFF designs are evident in the novel design (HSIFF). (2-IO) HSI achieves a uniform current, temperature, and gas distribution, leading to improved performance relative to the two other types of HSI and 1S flow fields. In general, the decreasing number of channels leads to a highly increased pressure drop; therefore, the pressure losses of the 1S design were much higher than his, as shown in Figure 30. Finally, the pressure losses of the 2-IO design decreased by 95% and 90% in the anode and cathode, respectively.

A novel configuration has also been designed, and it can transform between IFF and PFF [39]. This novel flow field design has two paths of flow (with the inlet and outlet being separate from each other) and a set of valves, as shown in Figure 31. The mechanism of changing the flow field between IFF and PFF occurs by closing and opening the valves. At a low voltage and peak current density, IFF provided high power and high current density.

3.1.5. Spiral Flow Field

The spiral flow field (SPFF) (Figure 32) has been analyzed with different paths (i.e., 8, 6, 4, 3, 2, and 1) and concentric spiral channels [40]. The better performance of the spiral flow field is obtained by employing four and three channels, but the use of eight and six channels results in poor performance. The four-channel design of the spiral flow field was the best configuration because of the good distribution of reactants. In addition, the increasing number of spirals increases the pressure drop, as shown in Figure 33. Therefore, the 1-spiral design gave the biggest pressure loss because the reactants must travel through a longer channel than required by the other design channels.

The spiral configuration with five outlets and five inlets of flow channels by a 28.2 mm radius (Figure 34) was analyzed and compared with SFF [41]. Secondary vortices were generated at the spiral flow field, so the performance exceeded that of SFF. The water flooding on the catalyst layer was enhanced because the outlets of channels were smaller than the inlets.

3.1.6. Radial Flow Fields

The radial flow field (RFF) design for PEMFCs (Figure 35) was investigated and compared with PFF and SFF [42]. The RFF design replaced conventional rectangular channels with ring channels. The ring channels allowed for better use of the active area and provided a better distribution of reactants. The mass transport and water removal capacity of the RFF design were better than those of SFF and PFF. The RFF design achieved better performance with half of the pressure drop compared with SFF.

Three types of RFF have been investigated; they are 4-channel, 8-channel, and 12-channel, arranged in a radial symmetrical path, as shown in Figure 36. Four-channel RFF shows better performance compared with other RFFs because it produces the least pressure drop and the highest current density [43].

3.1.7. Pin Flow Field

The pin or mesh flow field design (PIFF) is shaped like a net, as shown in Figure 37. The main advantage of the pin-type design is its low pressure, and the disadvantages are the maldistribution of reactants and stagnant areas [44].

The optimized configurations of the pin flow field (Figure 38) have been investigated [46]. The modified pin flow field has better performance than the conventional pin flow field design because the modified pin design achieves a more uniform distribution and lower pressure.

3.1.8. Cylindrical Flow Field

The cylindrical type (CYFF) of PEMFC can be distinguished from the planar type because of its high-power density (gravimetric and volumetric). Furthermore, planar bipolar plates increase the cell dead weight and are expensive. Removing the cathode water generated in planar flow channels is also difficult [47]. Tubular (cylindrical) plate designs were analyzed [48]. Three types of cylindrical configurations (Figure 39) were used, and these were straight, interdigitated, and serpentine. The results demonstrated that the performance of the cylindrical serpentine type is higher than that of other cylindrical designs. The angle of the flow path in the cylindrical serpentine type exhibits gradual decline and twisting, leading to the augmentation of oxygen concentration at CL, effortless water removal at GDL, and reduction in pressure drop.

3.2. Nature-Inspired (Biomimetic) Design of Flow Fields

Design in nature is an emerging and spontaneously developing phenomenon. Design occurs everywhere continuously, and it is not a result of a specified mechanism but a representation of physics laws, such as the thermodynamics law. Hence, nature design from inanimate to animate, such as rivers and vascular tissues, is a scientific field based on the physics law of development and design [49]. In recent years, researchers have begun to employ nature designs in flow fields to achieve the best possible overall performance of fuel cells because the above-mentioned conventional flow field designs may have drawbacks, such as fairly high-pressure drops or non-uniform distributions. The first researchers who utilized a bionics flow field with PEMFCs were Mellor and Chapman [50]. Afterward, other researchers increasingly investigated the different configurations of the bionics flow field in PEMFCs. This section presents nature-inspired designs of flow fields and sorts them by configuration type. In accordance with the available literature, the nature-inspired flow field designs are divided into the following two primary types: fractal and biologically inspired designs.

3.2.1. Fractal Designs

The first work on employing fractal designs as a flow field was conducted 18 years ago by Tüber et al. [51]. The researchers created fractal structures with a multi-ramified network of flow channels in PEMFCs, as shown in Figure 40. A computer algorithm was developed to achieve the lowest pressure drop and a uniform fluid distribution. The novel fractal configuration was investigated and compared with serpentine and parallel configurations. The results revealed that the fractal configuration of flow fields has a performance that is almost identical to that of the parallel configuration, but the serpentine configuration provides the highest and most stable power output. Figure 41 presents the influence of airflow on pressure loss in fractal design and compares it with conventional designs. Compared to both serpentine design and parallel design, the fractal design achieves the lowest reduction in the pressure drop.

The fractal configurations of the bipolar plate (current collector) for fuel cells have also been studied [52]. Various designs of conventional and fractal bipolar plates have been tested, including conventional circular, fractal circular, conventional rectangular, and fractal rectangular (Figure 42). The performance of fuel cells is influenced more by the use of a cathode bipolar plate than by the use of an anode bipolar plate.

Jing-Yi Chang et al. [53] studied other fractal designs of the bipolar plate by using Hilbert fractal curves in the DM fuel cell. The current collectors were fabricated in different orders of Hilbert fractal curves (first, second, and third), as shown in Figure 43. The tests that were conducted involved electrochemical impedance spectroscopy. The results of the power and polarization curves revealed that the third order design of the fractal curve achieves the best performance. Furthermore, the third order curve of the fractal design has the lowest impedance.

3.2.2. Biologically Inspired Design

Murray’s law must be employed when dealing with configurations inspired by biological structures; many researchers have utilized it to calculate the flow channel widths of various branches. The optimum diameters in biological-inspired design are obtained by Murray’s law. It provides a good representation of several plants’ circulatory, vascular, and pulmonary systems [54]. Murray’s law states that the cube of the main branch’s radius must match the sum of the cube of the sub-branches’ radii. It is expressed in the following mathematical form:

$${\mathrm{r}}_{\mathrm{p}}^3={ \mathrm{r}}_{\mathrm{d}1}^3+{ \mathrm{r}}_{\mathrm{d}2}^3+\dots +{ \mathrm{r}}_{\mathrm{dn}}^3$$

(1)

where r_p and r_d are the main channel radius and sub-channels’ radius, respectively. Notably, a special case exists where a non-circular cross-section must utilize the hydraulic diameter. In this section, the biologically inspired design is divided into different types, namely, leaf, tree, lung, and unconventional shape designs. The leaf shape configuration often utilizes Murray’s law to design the width of the channel.

Leaf-Shape Flow Field

Leaves are commonly found in ordinary life. The distribution of the water content in leaves occurs by transferring the water from the main vein to the different branches. Hence, leaf-shaped channels for flow fields have been designed by researchers depending on the structure of the leaf vein [55,56,57]. Some researchers improved the performance of PEMFCs by directly designing the flow channel as a leaf shape. Leaf-shape flow fields are of two types. The first one is symmetric. Leaf-shape flow channels (Figure 44) were studied and compared with interdigitated and serpentine flow channels [57]. The leaf-shape flow field decreased the pressure drop, which was 47.4% and 59.8% lower than the values for interdigitated and serpentine flow channels, respectively. A 30% increase in the peak power density of PEMFC was also observed.

The novel leaf-shape flow field design shown in Figure 45 was analyzed [55]. The results revealed that the concentrations of oxygen, pressure, and velocity distributions were more uniform. In addition, 26% and 56% increments in current density were observed compared with the serpentine and parallel flow fields, respectively.

The two designs of leaf-shape flow fields (ginkgo and net leaf) shown in Figure 46 were examined [58], and their effect on the performance of PEMFC was studied. The maximum power density provided by the ginkgo-shaped and net leaf-shaped flow channel designs was 40% and 24% higher than that for PFF, respectively. The ginkgo-shaped flow channel required 3% of the air-feeding power in SFF. Furthermore, the water removal capacity of the ginkgo-shaped design was higher than that of PFF. Thus, the ginkgo-shaped configuration was concluded to be the best among the designs of flow channels.

The effect of the bio-inspired design on cell performance was investigated [59]. The proposed flow field had a leaf vein shape and was compared with the single-serpentine and tree-shape designs. The results revealed that the performance of the leaf-vein flow field configuration is 3.75% better than that of the tree-shape configuration and 5.12% better than that of the single-serpentine configuration. The worst configuration is the single-serpentine design (basic design). Another study conducted a visual test by employing a clear Lexan plate rather than a graphite plate and revealed that the leaf-shaped design has a better capacity for water management compared with other designs [60]. Two leaf-shape flow field designs were studied; the first one was interdigitated, and the second one was non-interdigitated (Figure 47) [61]. The experimental and numerical results revealed that applying Murray’s law to determine the channel width improves fuel cell performance by 20–25% when the interdigitated design of the leaf-shape flow field is used.

A different pinnate vein-shaped design of a flow field (Figure 48) was proposed [56]. The novel design depends on Murray’s law when selecting the width of the main channel, sub-channels, and third channels. Compared with conventional SFF and PFF designs, the bio-inspired design has better output power, better water management capacity, and more uniform reactant distribution.

Different configurations of bio-inspired flow channels (leaf shape) (Figure 49) were studied and compared with one another [62,63]. The results revealed that the many branches, specifically the first branches of the bio-inspired flow field, lead to a uniform velocity distribution and smooth streamlining under various operating parameters.

Another type of flow channel with a leaf configuration is the asymmetric flow field. A new asymmetric bio-inspired flow field was analyzed and compared with PFF [64], as shown in Figure 50. The results revealed that the pressure loss between the inlet and outlet in the asymmetrical leaf design is smaller than that in PPF. In this novel asymmetric design, the reactant gas can be distributed to each channel branch uniformly, leading to improved current density and enhanced PEMFC performance. In addition, employing the asymmetrical bionic configuration prevents the flooding of water on the cathode side.

The influence of the bionic configuration on the performance of fuel cells under gravity was studied [65]. Asymmetrical and symmetrical bionic flow channels were used in the visualization and simulation, as shown in Figure 51. The results of the visualization and simulation experiments revealed that the performance of symmetric and asymmetric bionic flow channels presents notable differences. A fuel cell that has an asymmetric configuration of bionic flow channels demonstrates the best performance. Furthermore, the variation of pressure in the main asymmetric bionic channel is moderately smooth, while it fluctuated extensively in the main symmetrical bionic channel, as shown in Figure 52. It is worth mentioning that the difference between steady and fluctuation of pressure for the main channel of the two bionic designs leads to a disparity in drainage performance.

Tree-Shape Flow Field

In general, trees contain the primary stem and branches. The bifurcation angles and bifurcation number of branches are subject to a unique law of growth. Based on this tree configuration, various designs of tree-shaped flow fields were proposed by researchers, who also discovered that entropy production and pressure drop could be reduced by employing tree-shaped channels in the flow field [66,67,68]. Four shapes of tree-design flow fields were presented and compared [66]. The results showed that an increase in the number of branches leads to an increase in the current density of the cell and a reduction in entropy generation. At a bifurcation angle of 37° and with two levels of bifurcation (Figure 53), current density and water drainage are enhanced.

The effects of the micro-channel-nets flow field (tree-shaped) on cell performance were studied and compared with those of serpentine flow channels [67]). Compared with serpentine flow channels, tree-like channels produce a lower pressure drop at the same Reynolds number of the inlet and surface area. The coefficient of heat transfer is also greater. The influence of tree-shaped network flow channels (Figure 54) on cell performance was studied [68]. The effect of the mass flow rate of reactants was simulated, analyzed, and compared with that of PFF and SFF. The suggested tree-shape-inspired flow field has a lower power requirement for pumping and transporting reactants and a lower pressure drop compared with the others.

The use of tree-like channels (Figure 55) yielded a small entropy generation [69,70]. Peak power out was improved for the bio-inspired channels at a width scaling factor of 0.917 for the inlet and 0.925 for the outlet. Furthermore, Murray’s law was used by Dong and Liu [71] to determine the dimension of flow channels; they reported that the pressure loss was uniform in each channel and that the resistance of reactants was similar.

The impact of flow channel configuration (tree-shaped) on PEMFC performance was simulated [72]. The suggested flow fields were tree-shaped geometries with a radial design that connected the central flow entrance to the circumference of the plate, as shown in Figure 56. Three types of tree-shaped flow fields with various levels of bifurcation, namely, three levels of bifurcation, two levels of bifurcation, and one level of bifurcation, were used in the numerical simulation. Cell performance was examined by comparing the tree-shaped channels with parallel and serpentine flow channels through power and polarization curves. The results showed that the tree-shaped design decreases the pressure drop and achieves a uniform flow distribution. In addition, increasing the number of bifurcation levels leads to the use of a larger active area, which in turn results in higher current and power densities.

Lung-Shape Flow Field

The breathing process in living organisms is carried out through the lungs. The lungs contain a myriad of interconnected bronchioles that are connected to the main bronchus, as shown in Figure 57.

On the basis of the human lung configuration, researchers have designed a series of flow fields (bio-inspired). Initially, researchers studied flow channels that were directly designed from the shape of the lung. A novel configuration inspired by the shape of the lung (Figure 58) was investigated and compared with IFF and SFF [57]. The novel design has a more uniform distribution of velocity and a better polarization curve than IFF and SFF conventional designs.

The distributions of reactants, velocity, and pressure on the anode side of lung-inspired flow channels (Figure 59) were analyzed and compared with the parallel–serpentine design [74]. The use of the lung-inspired flow channel achieves a uniform distribution of reactants (hydrogen) with a proper fluid velocity and minimum pressure drop.

Given the absence of a mathematical definition, fractal theory, which is effective in explaining the self-similarity law that governs nature, is often utilized to enhance lung-inspired flow fields. A flow field inspired by the shape of the lung was utilized to solve the problem of non-uniformity of reactants and compared with SFF [75]. Fractal geometry was utilized as the model to design lung-like channels (Figure 60) with various branching generation numbers for reducing entropy production and achieving a uniform distribution of reactants. At 50% and 75% relative humidity, lung-like fractal flow channels with four branching generations (N = 4) performs better than the serpentine design and increases the current density. Furthermore, 30% and 20% augmentations in peak power density and performance, respectively, can be observed. Figure 60b illustrates the branching generations and their effect on current density.

A fractal cathode channel inspired by the shape of the lung was manufactured by utilizing printed circuit boards (PCB), as shown in Figure 61, and compared with the conventional serpentine design of flow channel [76]. The lung-like fractal flow pattern has better performance than the conventional serpentine design of the flow channels, and it is useful, especially when using air at low relative humidity. Furthermore, due to the homogenous distribution of the reactants, the lung-inspired design demonstrates a stable operation.

Unconventional-Shape Flow Fields

Aside from the bio-inspired flow fields discussed above, novel unconventional flow fields that are inspired by biology have been designed by researchers based on the structure of cuttlefish, blood vessels, and honeycomb.

Honeycomb-Inspired

The benefits of flow fields inspired by honeycomb structures include reduced fluid resistance and material savings [77,78]. Although honeycomb structures are rarely used in PEMFCs, they are commonly employed in fuel cells (solid oxide) [78,79,80,81,82]. A honeycomb-shaped flow field was constructed on the cathode side [83], as shown in Figure 62. The results revealed that the unconventional honeycomb design decreases the possibility of flooding and a number of hot spots and increases the rate of oxygen diffusion at the gas diffusion layer by 10 times. The uniformity indices of local current density, pressure, oxygen mass fraction, and temperature are 0.12, 0.1, 0.04, and 0.01, respectively.

The influence of the honeycomb-shaped flow field design (Figure 63) on the performance of PEMFCs was investigated [84]. Three configurations were used in a numerical simulation of honeycomb, serpentine, and parallel flow channels for comparison. The results revealed that the non-uniformity value for the honeycomb configuration (0.59 at 0.4 V) is lower than that for SFF and PFF, and the pressure loss of the honeycomb configuration is smaller than that of SFF by 6.9 times. The current density of PEMFC with the honeycomb configuration is 10.4% and 14.0% higher than that of PEMFC with serpentine and parallel configurations, respectively. Figure 64 shows a comparison of pressure drop and current density at 0.4 V for all types of flow fields.

Blood Vessel Inspired

A series of flow plates inspired by blood vessels (Figure 65) have been analyzed and compared with four flow field designs at various aspect ratios and Reynolds numbers to enhance cell performance [85,86]. The performance of the bio-inspired flow slab (BFF1) configuration is better than that of other configurations, where the flow distribution has been enhanced, which in turn leads to enhancing water management. Consequently, the drainage effect and oxygen transport are improved. Moreover, the current distribution and output power have been improved. The net power and pressure drop losses for SFF, PFF, and BFF1 at 0.27 V are given in

Table 2. Estimation of net power and pressure drop losses at 0.27 V [86].

Flow Field Type	∆P (Pa)	Wcell (W/m2)	WP (W/m2)	WNet (W/m2)
Parallel	248	3529	4.4	3524.6
Serpentine	5137	5583	91	5492
BFF1	2073	5593	37	5557

.

Cuttlefish Inspired

The above-mentioned study about the presence of wave shapes (baffles) in straight flow fields (Figure 4) are considered a modification and bio-inspired flow channels at the same time [12]. The wave shapes in the channels were inspired by cuttlefish fin. A wave-like surface flow field (Figure 66) was designed and compared with a conventional straight flow field [87,88]. The results revealed that the design of the wave-like surface flow field results in higher power density and output voltage than the conventional flow field. The use of the wave-inspired surface achieves better water management which leads to uniform temperature distribution, as well as improves the distribution of the reactant and increases the velocity of the gas.

Intersect-Flow Channels

The intersection tree-shaped structure was designed based on fractal theory and Murray’s law to obtain a novel design called intersect-flow channels, as shown in Figure 67 [89]. Three various configurations (serpentine, parallel, and intersect-flow channels) were investigated and compared in terms of pressure distribution, power density, current density, distribution of hydrogen mass fraction, and temperature distribution. The results showed that using an intersect-flow channel gave significant advantages, such as achieving a uniform distribution of gas reactants at both the cathode and anode side, which in turn produces a high current density. Moreover, the intersect-flow channel achieves high output power compared with other designs; consequently, the performance of the intersect-flow channel is higher than that of other conventional configurations under identical operational conditions.

The introduction should briefly place the study in a broad context and highlight why it is important. It should define the purpose of the work and its significance. The current state of the research field should be carefully reviewed, and key publications cited. Please highlight controversial and diverging hypotheses when necessary. Finally, briefly mention the main aim of the work and highlight the principal conclusions. As far as possible, please keep the introduction comprehensible to scientists outside your particular field of research. References should be numbered in order of appearance and indicated by a numeral or numerals in square brackets—e.g., [1] or [2,3], or [4,5,6]. See the end of the document for further details on references.

4. Effect of Geometric Parameters

4.1. Cross-Section Shape

The performance of PEMFCs is also affected by the flow channel shape (cross-section). Different shapes of cross-section channels (CCS), such as triangular, parallelogram, trapezoidal, rectangular, slanted, hemisphere, semi-circular, and stepped, have been designed and investigated. The parallelogram, trapezoidal, and rectangular shapes shown in Figure 68 were analyzed and compared [90]. The results showed that the rectangular channel shape achieves a higher voltage of the fuel cell compared with other shapes of channel cross-section. The rectangular case results in a large potential for the fuel cell. However, the trapezoidal cross-section achieves local distributions of current density and a uniform distribution of the reactant.

The square cross-section design was developed to achieve an optimal cross-section shape of straight flow channels [91]. With output power and power consumption as factual functions and the width of the top and bottom edges as variables, the optimal shape, namely, trapezoidal, was obtained. The trapezoidal design provided better distributions and more current density compared with the basic design. Hybrid stepped, trapezoidal, and square geometries (Figure 69) were analyzed to study the effect of the cross-section shape of the channel on the distribution of water [92]. The trapezoidal channel cross-section shape was identical to the stepped shape in all the particulars investigated, and the water management of both shapes was better than that of the rectangular cross-section. However, the rectangular design had a slightly higher current generation.

Fuel cells with a semicircle, trapezoid, and triangle shapes of the channel (Figure 70) were investigated and compared with the rectangular channel shape as a basic shape [93]. The performance of fuel cells under all cross-section shapes was found to be similar at high voltages. The performance at low voltages depended on the channel shape, and the performance of the triangle shape was better than that of the semicircle, trapezoid, and rectangular shapes. Oxygen utilization and water removal were enhanced under the semicircle, trapezoid, and triangle shapes due to the significant increase in reactant flow velocity.

The influence of changes in the cross-section configuration of the channel on the local transport phenomena, pressure drop, and power density of a single straight flow field was studied [94]. Thirty different cross-section shapes (Figure 71) were used; 25 shapes had novel, innovative designs, and 5 were available designs. At high and medium current densities, the shapes of the cross-sections significantly affected the power density. The reversed top trapezoidal design and bottom trapezoidal design of the cross-section showed the best performance. Meanwhile, the reversed bottom half elliptical design of the cross-section achieved the worst performance. The triangular cross-section design yielded the largest pressure drop, whereas the rectangular cross-section design achieved the smallest pressure drop. The wrong selection of the channel shape could lead to a 4.65% loss of power density.

To enhance water management, grooves slanted by 35° were placed on both the anode and cathode sides of a fuel cell (Figure 72) [95]. In comparison with a rectangular channel, the cathode side of the down-slanted anode channel had less water flowing out of it because of the hydration gradient generated from anode down-slanting that induced the back-diffusion of water into the anode and enhanced the hydration of the membrane and the conductivity, which in turn led to improved performance. At normal humidification, using the down-slanted anode channel rather than the rectangular channel improved the performance significantly. The high humidification reduced the performance because of the blocking of GDL that occurred via condensation. However, membrane dehydration occurred in the down-slanted cathode channel because the water drained away.

Various cross-section designs, namely, square, trapezium, reversed trapezium, and parallelogram, with an identical area were analyzed [96]. The square channel shape provided superior cell performance compared with the other shapes. Meanwhile, Nima Ahmadi et al. [97] analyzed the circular and elliptical shapes of cross-section channels for PEMFCs (Figure 73). The results demonstrated that by changing the circular shape of the channel into an elliptical shape while other conditions are fixed, the current density of the PEMFC can be reduced.

4.2. Bending in Channels

Investigations were conducted on the serpentine flow channel performance in large, small, and normal sectional areas with and without slope turns, as shown in Figure 74 [98] for different\cress sectional areas (Figure 74). The results demonstrated that to prevent the droplet from boomeranging from the flow channel bottom to the top surface (MEA), the angle of slope must be adequately large. A too-large slope angle led to an increase in pressure drop and a decrease in water removal capacity. The water removal was improved at 120° and 160° slope and contact angles, respectively, under the same condition.

The influence of curved bends, 180° bend, and single sharp bend of serpentine flow channels were analyzed [99]. The curvature ratios used were 0, 1.41, 2.82, and 5.66. The essential factor of PEMFC efficiency was pressure loss. The modification of the channel dimension, such as gap, width, and height, enhanced the management of water and the performance of the fuel cell by achieving the desired pressure drop. To obtain optimal channel dimensions, the influence of the curve, length, and width of the flow channel was investigated [100]. The investigation included SFF with various numbers of channels (1, 2, 3, 4, 5, and 6) and channel curvatures (Figure 75). According to the gas distribution, the sharp curve was the best curvature of the channel, and the six-flow channels were the best flow field; their performance was better than that of the four-flow channels by 25% because of their larger gas flow area and higher velocity.

The effect of bend sizes in the serpentine flow channel of PEMFC was studied [101]. The used flow channel was serpentine with three different sizes (0.8, 1, and 1.2 mm) of the square bend, as shown in Figure 76. The results revealed that an increase in bend size achieved a uniform distribution because of the increase in the surface contact area at the square bends. The performance of the 1.2 mm bend size was better than that of the other bend sizes. The boundary layer thickness increased with increasing bend size. For the same reason, the temperature distribution was the most uniform under the 1.2 mm bend size. Furthermore, the improvement in power and current densities at 1.2 mm square bends decreased the pressure drop.

4.3. Channel and Rib Dimensions

4.3.1. Width of the Channel and Ribs

The influences of channel and rib widths, which are considered important geometrical parameters of the flow channel, have been analyzed by many researchers [102,103,104,105,106]. These investigations have indicated that the values of channel and rib widths affect a number of operational characteristics of PEMFCs, and, subsequently, their performance. They reached the conclusion that these dimensions have a great impact under low operation potentials, and there is an optimal design of the flow channel to achieve the maximum performance of the fuel cell.

The performance of a serpentine flow channel with various channel/rib width ratios (0.7/1, 1/0.7, and 0.9/0.9) and a fixed height of 0.55 mm was examined [107], as shown in Figure 77. Under stationary conditions, good performance and adequate heat transfer were achieved with a wide rib and a narrow channel. A reduction in the channel area resulted in an increase in pressure drop. The uniformity of distributions was identical for all channel/rib width ratios.

Parallel, serpentine, and interdigitated flow channels with six-channel/rib width ratios (η) (Figure 78) were analyzed [108]. The width of the rib changed in contrast to the width of the channel to keep the channel number and area constant. Generally, width ratios and geometric configurations have a slight effect on performance at high voltages, but these parameters significantly affect performance at low voltages. The reduction in the channel/rib width ratio from 2.66 to 0.25 increased the cell performance by 23%, 45%, and 120% for parallel, interdigitated, and serpentine flow channels, respectively. Furthermore, a reduction in the width ratio increased the pressure drop and the speed of the reactants, which yielded high homogenous local transport; as a result, the power density was improved.

The influence of the landing-to-channel width (L:C) ratio in flow channels on the performance of PEMFCs was analyzed [109]. Four L:C ratios (2:2, 1.5:1.5, 1:1, and 0.5:0.5 in mm) and a constant channel length of 20 mm were used, as shown in Figure 79. The results revealed that the 0.5:0.5 mm L:C ratio resulted in a power density and current density higher than those for the other L:C ratios. Furthermore, having a small width for both channels and landing was acceptable to water management. The most suitable L:C ratio was 2:1 compared with 0.5:1 and 1:1 for the serpentine flow channel [110].

4.3.2. Height and Width of the Channel

The ratio of width to height (width/height) is called the aspect ratio, which has a direct impact on the performance of PEMFCs. Hence, many researchers have tested different aspect ratios to obtain the optimal value of this ratio (138, 142, 143). Six various aspect ratios (Figure 80) were studied and compared [111]. The employed aspect ratios in the experiments were 3.16/2.53, 2.53/3.16, 2.5/2, 2/2.5, 1.58/1.26, and 1.26/1.58 on the cathode side. The results demonstrated that improved performance of the flow field was obtained by using an increased aspect ratio. However, the performance was unaffected by the flow area in a substantial manner. The area with a high current density showed the impact of mass transfer loss. Two aspect ratios (1.25 and 0.8) with different cross-sectional areas (8, 5, and 2 mm) were analyzed [112]. The aspect ratio was directly proportional to fuel cell performance, and the cross-sectional area was inversely proportional to performance. The concentrations of molar oxygen increased with decreasing rib area.

The effect of aspect ratio (height/width) in a serpentine flow channel on PEMFC performance was analyzed [113]. Various aspect ratios in the flow channel were examined, and they varied from 15 to 0.07 with constant effective and cross-section areas, as shown in Figure 81. At low voltages, the performance was unaffected by the aspect ratio. At high voltages, an increase in aspect ratio enhanced the uniform distributions of current density and improved the cell performance. The polarization curve showed that the aspect ratios of 12/05 and 10/06 yielded the most satisfactory combination of variables.

Kap-Seung Choi et al. [114] analyzed various channel widths and heights of serpentine flow channels (Figure 82) and compared them with a basic design whose height and width were 0.34 and 1 mm, respectively. The increase in channel height led to decreases in the total pressure drop and accumulated water at the cathode and anode outlets. The reason for water accumulation in the anode was back diffusion. Channel width expansion decreased the pressure drop and accelerated the rate of water removal. Channel width expansion had a more significant impact on water removal than the increase in channel height.

4.3.3. Depth of Channel

Most researchers have focused on the geometric parameters of flow channels, such as the height and width of the channel and ribs, but only a few studies have been conducted on the influence of channel depth on PEMFC performance. Three angles of flow channel inclination (Figure 83), namely, 0°, 0.5°, and 0.75° were investigated [115]. The results demonstrated that the 0.75° inclination of the flow channel significantly increased the power and current densities by 8% and 9.5%, respectively. The major drawback of using non-uniform channels (tapered channels) was the increase in pressure drop, which was increased by 3.5 times for the 0.75° inclination and by 2 times for the 0.5° inclination.

A single serpentine flow field with five channels, which used various heights from channel 2 (H₁) to channel 5 (H₄), as shown in Figure 84, was adopted to optimize the flow field [116]. The results revealed that the flow in the main channel was improved, and the rate of oxygen transport and current density were increased. Compared with straight channels, the suggested design of serpentine flow channels increased the power density of the fuel cell by 11.9%. Furthermore, a diverging final channel was adopted to reduce the leakage of reactants to the outlet as much as possible.

A serpentine flow channel with modified lengths or heights of the channel outlet (Figure 85) was developed to enhance water removal and reactant utilization in PEMFCs [117]. The decrements in the flow channel outlet increased the reactant velocities, which in turn led to enhanced water removal, reactant utilization, and reactant transport, thus improving cell performance compared with the basic serpentine design. Moreover, the increase in the length of the reduced area and the decrease in the outlet area improved cell performance. The optimal length and height contraction ratio that yielded the optimal performance was 0.4.

The narrowing of the channel in a stream-wise direction (Figure 86) accelerates the reactant gas, enhances the electrochemical reaction, and forces the reactant into the GDL, thus improving the cell performance [118]. The contraction of the flow area along the channel (tapered channel) enhances fuel utilization and water removal capability and increases the gas velocity [119]. In addition, decreasing the ratio of taper height and increasing the ratio of taper width improve the cell performance.

5. Comparison of Flow Fields Performance

The performance analysis for the straight channel, Trap channel, ribbed channel, ducted channel, M-channel, Wave-channel, and bio-inspired channel is shown in Figure 87. The maximum power density of the trap channel is higher than that of the straight channel, where the value of power density for the trap channel and straight channel by 0.82 W/cm² and 0.7 W/cm², respectively, as shown in Figure 87a. The influence of cell orientation for ribbed channel and Duct channel is shown in Figure 72 and Figure 87c. The performance analysis reveals that the maximum power density for ducted cathode and ribbed cathode is 205 mW/cm² and 232 mW/cm², respectively. The increment of maximum power density for the bio-inspired channel (wave shape) was 2.2% compared with the straight channel, as shown in Figure 87d. Compared to wave-shape channel, it was revealed that the M-shape channel produces an augmentation power density of 21.3%, as shown in Figure 87e.

The performance evaluation for the serpentine channel, multi-pass channel, modified channel-w, and the wavy channel is shown in Figure 88. The maximum power density of the 2-pass design, 3-pass design, and 4-pass design is 0.4633 w/cm², 0.4640 w/cm², and 0.4634 w/cm², respectively, as shown in Figure 88a. Thus, the best performance is produced by the 3-pass design. Figure 88b demonstrates a comparison of modified serpentine -w, serpentine -w, serpentine -s, and serpentine-z. The highest peak power is produced by the modified Serpentine-W type by 4 W at 2 A, while the influence of the serpentine wavy channel of performance depends on amplitude. Figure 88c shows the power curve for different amplitudes of 0.25, 0.5, and 0.75. compared to the serpentine channel, the peak power is increased by 20.15% by using a 0.25 amplitude.

The performance analysis for the parallel design, metal foam in a parallel design, trapezoid baffle plate, and micro distributor is shown in Figure 89. The staggered metal foam in the parallel flow channel design achieves augmentation in maximum power density 50% higher than that of the basic parallel design, as shown in Figure 89a. The reason for enhancing performance is due to the lower water saturation resulting from the design of metal foam, which in turn permits more reactants to contact the catalyst layer. While peak power improvement of the staggered trapezoid baffle plate is 2.54% and 6.39% compared with the parallel trapezoid baffle plate and basic parallel flow field, respectively, as shown in Figure 89b. Furthermore, the increase in relative humidity improves cell performance (Figure 89c). The parallel flow field modified by a micro distributor increases the performance by 22.8% compared with the parallel flow field, while it decreases the performance by 10.3% compared with the serpentine flow field, as shown in Figure 89d. Where the peak power density of serpentine design, parallel design, and micro distributor is 0.78 W/cm², 0.57 W/cm², and 0.70 W/cm², respectively.

The performance evaluation for the interdigitated design, rectangular parallelepiped baffles, and hybrid serpentine interdigitated transformer design (IFF and PFF) is shown in Figure 90. The power curve (Figure 90a) for interdigitated and parallel flow field reveal that interdigitated design is better than parallel design by 100% at similar flow and operating conditions. The reason for augmentation is that oxygen transportation occurs by convection into the porous structures. In addition, the performance of modified interdigitated design by rectangular parallelepiped baffles increased with an increase in the number of baffles, as shown in Figure 90b, where the improvement in maximum out power is 26%. The reactants are forced to flow into GDL and CL to improve chemical reactions. The hybrid serpentine interdigitated flow field with two inlets and two outlets improves the maximum out power more than serpentine by 6%, as shown in Figure 90c. Furthermore, the transformer design (IFF and PFF) improves the maximum output power by 6.7% and the current density by 33% compared with the parallel flow field, as shown in Figure 90d. Where the parallel design produces a maximum power of 298 mW at 0.6 A/cm², and the interdigitated design produces a maximum power of 318 at 0.8 A/cm².

The power curve of multiple concentric spiral flow fields with 8, 6, 4, 3, 2, and 1 channel is shown in Figure 91a. The comparison of the power curves reveals that using spiral flow fields with 4-channel produces the biggest output power, while the employing same flow field with 8-channel produces the worst output power. Where the percentage difference of maximum generated power between spiral 4-channel design and spiral 8-channel design is 15%. Figure 91b reveals the power curve of the cylindrical flow field with interdigitated, serpentine, and straight channels. It is noticed that the generated power of the three configurations was equal at the normal operating condition. Furthermore, the performance of the parallel channel configuration is slightly more than the other configurations due to the individual gas supply in each channel.

The cell performance analysis for bio-inspired flow channels such as leaf-shape, tree-shaped, lung-shaped, honeycomb-shaped, and blood vessel inspired is shown in Figure 92. The maximum out power comparison between the conventional shape (serpentine and parallel) and leaf shape is shown in Figure 92a. The power curve reveals that the bio-inspired design improves cell efficiency. Compared to serpentine design and parallel design, the leaf-shape achieved higher peak power density by 26% and 56%. Although the actual peak power generated is lower than that mentioned due to ignoring major and minor losses, a higher efficiency can be obtained by using the leaf shape. Figure 92b shows the power curve for serpentine configuration, parallel configuration, and tree shaped. The best cell performance is the result of employing a serpentine configuration, but it produces the highest pressure drop. The peak power density of the serpentine configuration is higher than that of the tree configuration by 33.5%and higher than that of the parallel configuration. The power curve of lung-shape and serpentine configuration is shown in Figure 92c. The lung shape flow channel enhances the performance by 14%, 12%, and 41% for 100%RH, 70%RH, and 40%RH, respectively. The reason for the superiority of the lung flow channel design over the serpentine design is raising the operating temperature in the lung design between 2 and 3 °C. Figure 92d offers the power curve of the PEM fuel cell for parallel design, serpentine design, and honeycomb-inspired flow channel. The power curve reveals that the honeycomb shape demonstrated the best cell performance, and the parallel design demonstrated the worst cell performance among them. Where the maximum power densities of parallel design, serpentine design, and honeycomb shape are 2818.64 W/m², 2910.68 W/m², and 3213.96 W/m², respectively. Furthermore, the current densities of parallel design, serpentine design, and honeycomb shapes are 7046.6 A/m², 7276.7 A/m², and 8034.9 A/m², respectively.

The cell performance evaluation of various channel cross-sections is shown in Figure 93. The power curve for the rectangular channel, trapezoidal channel, and stepped channel are shown in Figure 93a. The maximum output power of a rectangular channel is higher than that in other cross sections. Furthermore, the polarization curve reveals that the rectangular channel improves the current density by 8.2% higher than the stepped and trapezoidal channels. While other investigations reveal that the triangle channel gave the best performance, followed by a semicircle, trapezoid, and rectangular, as shown in Figure 93b, where the increase in current densities for the trapezoid channel, semicircle channel, and triangle channel are 5.8%, 8.4%, and 19.4%. The maximum output power for various channel cross-sections of the flow field with different temperatures and pressures were tabulated in

Table 3. Power densities of different cross sections [96].

Shape of the Cross Section	Power Density (mW/cm2)
	Pressure 1 bar			Pressure 2 bar			Pressure 3 bar
	Temp 333k	Temp 343	Temp 353	Temp 333k	Temp 343	Temp 353	Temp 333k	Temp 343	Temp 353
Square	525.69	338.7	275.26	948.85	879.89	522.33	1133.75	1044.26	971.75
Triangle	530.72	339.04	275.31	948.93	878.62	524.15	1132.77	1042.78	970.46
Parallelogram 140	526.26	338.73	275.28	948.83	879.66	522.64	1132.49	1044.58	972.09
Parallelogram 260	528.76	338.85	275.35	948.86	879.15	523.62	1132.53	1044.25	971.19
Trapezium	518.82	337.20	272.95	937.21	874.68	519.08	1116.70	1035.66	969.99
Inverted Trapezium	512.51	336.96	272.75	938.90	876.46	515.69	1117.34	1036.27	973.64

.

Despite the absence of essential information in many pieces of cited research, the available information about the flow field geometric variables and fuel cell operating parameters in this review are summarized in

Table 4. Flow field design and operating parameters.

Type of Flow Field Design	Active Area (cm2)	Channel Width (mm)	Rib Width (mm)	Channel Height (mm)	Number of Channel (Nch)	Operating Conditions	Type of Study	Reference
Straight configuration (ribbed and ducted)	1.8	2	1	6	1	1 bar/293 k	Numerical	[10]
Straight configuration (with trap)	1	1	1	1	1	3 bar/353 k	Numerical	[11]
Straight configuration with bio inspired wave	0.6	1	1	1	1	1 bar/343.15 k	Numerical	[12]
Straight configuration with m-channel	-	1	1	1	1	1 bar/343 k	Numerical	[13]
Serpentine configuration	0.2	1	0.5	1	1	3 bar/353 k	Numerical	[14]
Serpentine configuration with single and multi passes	10	0.8	0.8	1	1, 2, 5, 5	1 bar/343 k	Numerical	[15]
Serpentine configuration with multi passes	3, 4.5, 6	0.8	0.7	0.8	2, 3, 4	1 bar	Numerical	[16]
Serpentine configuration with multi passes	200	0.9	0.9	0.55	3, 6, 13, 26	1 bar/343 k	Numerical	[17]
W-shape flow channel	-	1.1	-	0.4	3	0.7 bar/313 k	Experimental	[18]
Wavy serpentine configuration	25	1	1	1	1	298 k, 313 k, 333 k	Experimental	[19]
Serpentine with PCI (uniform and zigzag)	25	2	2	2	1	1 bar/(323–333) k	Experimental	[20]
Serpentine with PCI (uniform and zigzag)	25 and 70	2	2	2	1	1 bar/323 k	Experimental	[21]
Pin configuration (uniform and zigzag)	25	2	2	2	1	1 bar/323 k	Numerical	[22]
Parallel configuration with single and double (in/out)	(12.9 × 30.5)	3–1	1	1	65	1 bar	Numerical	[25]
Parallel configuration with single and double (in/out)	393.45	1	1	0.8	65	1 bar/353 k	Numerical	[26]
Parallel configuration with dents (square, semicircular, and trapezoidal)	1.2	0.5	1	0.6	1	1 bar/333 k	Numerical	[27]
Parallel configuration with metal foam	-	1	1	1	-	1 bar/353 k	Numerical	[28]
Parallel configuration with rectangular blockage	-	1	1	1	4	3 bar/353 k	Numerical	[29]
Parallel configuration with baffle plate	26.95	1	-	1	2	348.15 k	Experimental & numerical	[30]
Parallel configuration with micro-distributor	5.1 × 5.1	1	1	1	25	1 bar/353 k	Numerical	[31]
Parallel configuration with zigzag wavy channel	225	2	2	2	37	333 k	Numerical	[32]
Interdigitated and parallel configuration	198.81	0.8, 1, 1.2	1.2, 1, 1	1	69	0.97272 bar/323 k	Experimental	[35]
Interdigitated configuration with mid-baffled	7.1 × 7.1	1	1	1	1	1 bar, 2 bar/353 k	Experimental	[36]
Modified interdigitated configuration	25	H/h1 = 1.5, h2/h1 = 0.5, h3/h1 = 0.6	-	-	1	1 bar/313 k, 333 k, 353 k	Numerical	[37]
Hybrid interdigitated -serpentine configuration	48.067	0.8	0.8	0.8	1,2	1 bar/333 k	Numerical	[38]
Interdigitated -parallel configuration	30.5	1	1	1	7	-	Experimental	[39]
Concentric-spirals configuration	16.6	0.8	1.5	1	1, 2, 3, 4, 6, 8	2 bar/343 k	Numerical	[40]
Spiral configuration	25	1	1	1	5	343 k	Experimental and numerical	[41]
Radial configuration	10.54	Inlet = 0.3930 Outlet = 3.5340	-	10	4	1 bar/300 k	Numerical	[43]
		Inlet = 0.1963 outlet = 1.7671			8
		Inlet = 0.1309 Outlet = 1.1781			12
Pin-type configuration	1 × 1 5 × 5	1.5	-	1	-	1 bar/353 k	Numerical	[44]
Cylindrical configuration	5	0.8	0.8	-	1	2 bar/343 k	Numerical	[48]
Fractal configuration	109.5	Increase from 1 mm	-	1.5	-	323 k	Experimental	[51]
Hilbert curve fractal current collectors	1225	For 1st order 2.2	6.55	-	-	328 k	Experimental	[53]
		For 2nd order 2.2	2.18
		For 3rd order 1.1	1.09
Bio-inspired configuration	24.6	2	1	1	-	1 bar/323 k	Numerical	[55]
Leaf-shape flow field	7.2	-	1	1	-	1 bar/353 k	Numerical	[56]
Lung flow pattern	-	0.7874	0.8	1.016	-	1 bar/348 k	Numerical	[57]
Net leaf configuration	46.2	-	-	-	251	1 bar/353 k	Experimental	[58]
Leaf vein flow channel	9.84	Variable	Variable	0.4	-	0.7 bar/313 k	Experimental	[59]
Leaf-inspired configuration	50 × 50	-	-	2	-	1 bar/343 k	Experimental and numerical	[60]
Bio-inspired flow field design with varying channel width	5 × 5	Right and left branches 1st 2.51 2nd 1.23 3rd 1.00 Middle branches 1st 1.78 2nd 1.14 3rd 1.00	-	1.5	-	Bar/348 k	Numerical	[61]
Bionic flow field	2 × 2	Primary channel = 1	-	1	-	1 bar/353 k	Numerical	[62]
Bionic flow field	27.54	Primary channel = 1	-	1	-	1 bar/353.15 k	Numerical	[63]
Asymmetric leaf flow field	27.54	Primary channel = 2 Secondary channel = 0.5	0.5	0.5	Secondary channels = 64	1 bar/353 k	Numerical	[64]
Tree-like flow field channels	9	Primary channel = 1	-	1	-	2 bar/343 k	Numerical	[66]
Tree-like flow field patterns	25	Inlet = 0.917, 0.917, 1 Outlet = 0.925, 1, 1	-	Inlet = 1 Outlet 0.8	136	0.5 bar/353 k	Experimental	[70]
Lung-inspired configuration	7.5 × 7.5	2	-	2	8 main channels 34 branches	1 bar/338 k	Numerical	[74]
Lung-inspired configuration (PCB)	6.25	0.5	-	1	4 generation with (1-inlet, 256-outlet	318 k	Experimental	[76]
Honeycomb configuration	8.5, 17	Square flow channel = 5.3 × 5.3	1	-	9	1123 k	Experimental	[80]
Honeycomb configuration	19.2, 9.6	Square flow channel = 6	0.5	-	9	1123 k	Experimental and Numerical	[82]
Biophysical flow slab design	24.6	1.2	1	1	-	323 k	Numerical	[86]
Wave-like flow channel	-	0.5	-	0.5	-	1 bar/323 k, 333 k, 343 k	Numerical	[88]
Single straight channel	0.5076	0.8	0.4	1	1	1 bar/343 k	Numerical	[90]
		0.9	0.35
		0.8	0.4
Single straight channel	40	Basic design = 1	1	1	1	1 bar/343.14 k	Numerical	[91]
		Longer base of optimal design = 1.2874
Single serpentine channel	5	0.8	0.65	0.8	1	1 bar/353 k	Numerical	[92]
		Longer base of the trapezoid = 1.05	Longer base of the trapezoid = 0.4
Parallel flow channel	14 × 14	1	1	1	12	1 bar	Numerical	[93]
Single straight channel	-	0.8	0.8	-	1	1 bar/343 k	Numerical	[94]
Parallel flow channel	150	1.5	1	1	7	353 k	Experimental	[95]
Single straight channel	1.25	1	1	1	1	1 bar, 2 bar, 3 bar/333 k, 343 k, 353 k	Numerical	[96]
Serpentine configuration with slop turn	-	1	1	1	1	-	Numerical	[98]
Serpentine configuration	60	2	2	0.72	1	-	Numerical	[99]
Serpentine flow fields	100	1	1	1	1, 2, 3, 4, 5, 6	1 bar/323 k	Numerical	[100]
Serpentine flow channel	0.2	1	1	1	1	3 bar/353 k	Numerical	[101]
Parallel channels	-	Half channel width = 0.5	Half channel land width = 0.5	-	-	1.5 bar/353 k	Numerical	[103]
Parallel channels	50	2, 2, 1	3, 2, 1	-	-	343 k	Experimental	[106]
Serpentine flow channel	25, 200	0.9,	0.9	0.55	3	1 bar/343k	Numerical	[107]
Parallel, erpentine, and interdigitated channels	26.01	0.4, 0.6, 0.8, 1, 1.2, 1.4	1.6, 1.4, 1.2, 1, 0.8, 0.6	1	1	1 bar/323 k	Numerical	[108]
Single straight channel	0.3, 0.6, 0.9, 1.2	0.5, 1, 1.5, 2	0.5, 1, 1.5, 2	0.5, 1, 1.5, 2	1	1.5 bar/323 k	Numerical	[109]
Serpentine configuration	25	2, 1, 0.5	1	variable	1	1.21 bar/323 k	Experimental and Numerical	[110]
Parallel-serpentine configuration	100	3.16, 2.53, 2.5, 2, 1.58, 1.26	-	2.53, 3.16, 2, 2.5, 1.26, 1.58	20, 25, 40	1 bar/298 k	Experimental	[111]
Parallel flow channels	100	1.26	1.26	1.58	40	1 bar/348 k	Numerical	[112]
		1.58	0.94	1.26	40
		2	2	2.5	25
		2.5	1.5	2	25
		2.53	2.53	3.16	20
		3.16	1.9	2.53	20
Serpentine flow channel	8 × 32	1.33	Constant	0.8	1	1 bar/343 k	Numerical	[113]
	8.8 × 29.1	1.6		0.67
	10 × 25.6	2		0.53
	12 × 21.33	2.66		0.4
	16 × 16	4		0.27
	6.4 × 40	0.8		1.33
	6 × 42.67	0.67		1.6
	5.6 × 45.72	0.53		2
	5.2 × 49.23	0.4		2.66
	4.8 × 53.33	0.27		4
Serpentine flow channels	25	1	1	0.34	5-passes	1 bar/348 k	Numerical	[114]
		1	1	0.5
		1	1	0.67
		1	1	0.83
		1.25	0.75	0.34
		1.5	0.5	0.34
		1.75	0.25	0.34
Straight configuration tapered in height	-	1	-	-	1	1 bar/353 k	Numerical	[115]
Serpentine flow channels	0.81	1	1	1	5	323 k	Numerical	[116]
Serpentine channel with outlet contraction	5.29	1	1	1	4	323 k	Numerical	[117]
Straight configuration tapered in height	-	-	-	0.762	1	1 bar/353 k	Numerical	[118]
Straight configuration tapered in width or height	-	1	-	1	3	1 bar/323 k	Numerical	[119]

to clarify the conclusion that will be present throughout this work.

Figure 94 shows the power curve of two different models of channel dimensions. The first model has four cases of variable height and 1 mm width, where the height of case 1, case 2, case 3, and case 4 are 0.34 mm, 0.5 mm, 0.67 mm, and 0.83 mm, respectively. The power curve indicates that the output power decrease with increased channel height, as shown in Figure 94a. Although the performance differences were minimal, case 1 gave the best performance among the four cases. The second model has four cases of variable width and 0.34 mm height, where the width of case 1, case 5, case 6, and case 7 are 1 mm, 1.25 mm, 1.5 mm, and 1.75 mm, respectively. The power curve indicates that the output power decrease with increased channel width, as shown in Figure 94b, where the power density respectively decreases to 0.293 W/cm² and 0.341 W/cm² for case 7 and case 1. The overall percentage decrease in performance for case 7 was 16.38%.

6. Conclusions

There are many drawbacks in PEMFC, such as the mal-distribution of reactants, water management between the catalyst layer and the GDL, and the mass transport issue of reactants. Flow field design parameters can overcome these problems to improve cell performance. Where the flow field is an essential element of the fuel cell, and it is designed to provide the required amount of hydrogen and oxygen with the lowest possible pressure drop on the anode and cathode sides, respectively. It has been demonstrated through the current review paper that the flow field design parameters can significantly affect the overall behavior of PEMFC. Each design parameter has advantages and disadvantages that make the flow fields suitable for specific applications. The following crucial points are subtracted from the extensive literature.

6.1. Conventional Flow Field Configuration

• The performance of STPP can be improved by employing blockages in straight configurations;
• The serpentine configuration increases the reactant pressure drop. Several modifications can be conducted on SFF have been to improve the performance, such as using the sinusoidal channels, wavy channels, PCI inserted among the ribs of the cathode, three-pass channels, and short length of the channel path;
• The parallel configuration has a lower pressure drop of reactants compared with the serpentine configuration, but channels are often empty of reactants. The distribution of reactants can be improved by employing baffles, zigzag wavy channels, a micro distributor for the channels, changing the position of the inlet and outlet, and changing the number of outlets and inlets of the flow field;
• Although the interdigitated design’s performance is better than that of the serpentine design, the reactant pressure drop is very high. The performance can be enhanced by using oxygen rather than air. Mid-blockage, hybrid serpentine interdigitated, and increasing the number of rectangular parallelepipeds;
• The spiral configuration with four-path channels achieves the ideal distribution of reactants and decreases water flooding;
• Compared to SFF and PFF, the four-channel radial configuration produces the least pressure drop, higher current density, and better water removal capacity;
• The primary advantage of the pin-type design is low pressure, and its disadvantage is the maldistribution of reactants and stagnant areas;
• The cylindrical serpentine configuration demonstrates better performance than the spiral, radial, and cylindrical configurations. However, the fabrication and design of cylindrical flow fields are complex.

6.2. Nature-Inspired Flow Field Configuration

• The use of the third-order design of Hilbert fractal curves gives the best performance;
• Biologically inspired flow channels reduce the pressure drop, control the water removal, distribute the reactant gases uniformly, and increase the power density compared with interdigitated, parallel, and serpentine configurations.

6.3. Geometric Parameter

• The most widely utilized cross-section shape is rectangular;
• An increase in bend size achieves a highly uniform distribution;
• Wide ribs and narrow channels result in an optimal rib width;
• Increasing the aspect ratio (width/height) enhances performance;
• Tapered channels increase the reactant velocities, leading to enhanced water removal, reactant utilization, and reactant transport and increased cell performance.

6.4. Future Flow Fields

Although employing the biological-inspired configuration entails several disadvantages, such as water deficiency of the membrane under high temperatures and flooding resulting from increased relative humidity, unlike traditional designs, the bio-inspired design could have an important role in the flow fields design in fuel cells in the future because it reduces the pressure drop, control the water removal, distribute the reactant gases uniformly, and increase the power density compared with conventional designs. So, it may be possible to combine bio-inspired designs with each other or with conventional designs to obtain more efficient hybrid designs in the future.