Effect of Baffle Dimensionless Size Factor on the Performance of Proton Exchange Membrane Fuel Cell

Abstract

In this paper, the model of a proton exchange membrane fuel cell (PEMFC) with single straight channel is established to investigate the effect of dimensionless size factor of baffles on PEMFC performance. The influence of dimensionless length and height of baffles is discussed. Results show that adding baffles could dramatically optimize the mass transfer in PEMFC. The dimensionless length and height of the baffle have much influence on PEMFC performance.

1. Introduction

With the advantages of high performance, environment-friendly, and energy-saving, PEMFC is popular in lots of fields, such as vehicles, aerospace, and portable electricity supply. However, high-output power density and long duration of vehicular PEMFCs often lead to reactant starvation and water flood. Researchers have studied the factors influencing PEMFC performance under high current density [1,2,3,4,5,6,7]. A major challenge in the commercialization of PEMFC is to improve its mass transfer.

Water accumulation in cathodes is one major issue which needs to be solved. Some researchers used the visualization method and studied the droplet and water transfer in the channel [8,9,10,11]. Chen et al. analyzed motions of liquid water droplets considering inertial force impact [12].

Researchers also found that the optimization of the channel structure could improve the mass transfer [13,14,15,16,17,18,19]. Anyanwu et al. [20] proposed a sinusoidal channel to increase the droplet removal rate. Lei et al. [21] found that cathode channels with tapered slope structures could enhance the turbulence of airflow and improve oxygen concentration in the cathode. Baz et al. [22] designed a new serpentine flow field to optimize reactant transfer and reduce the liquid water saturation.

There are also many researchers focusing on novel flow fields [23,24]. Fahruddin et al. [25] proposed a leaf flow-field with different baffles inserted into the mother channel and found that the beam-shaped baffles could improve the performance. Liu et al. [26] studied the symmetric and asymmetric leaf veins flow channel and found that PEMFC with asymmetric bionic channels performs better. Kang et al. [27] investigated leaf-like flow fields. Results showed that the ginkgo pattern performs better. Chen et al. [28] found that large amplitude and short wavelength in the wave parallel flow fields can improve the PEMFC output power.

Some researchers find that setting baffles in the channel could enhance mass transfer due to the generation of a nozzle-type effect [29]. The size, shape, number, location, and arrangement of baffles are studied to increase the performance and durability of the PEMFC [30,31,32,33]. Wang et al. [34] proposed a novel dot matrix flow-field which could increase the PEMFC performance. Yin et al. [35] and He et al. [36] found that flow fields with baffles increase PEMFC performance. Guo et al. [37] compared the water managements in channels with different baffles and found that baffles in the channel help to remove liquid water more efficiently.

Researchers have found that the size of baffles has a great effect on PEMFC performance. However, most works focus on the actual physical size of baffles. In previous research on baffle shapes [36], it has been revealed that the dimensionless length and height of the baffle could explore the mass transfer enhancement mechanism more specifically than the actual physical size of baffles could. This study aims to explore the effect of dimensionless size of baffle on PEMFC performance and make baffle design quicker and more proper. In this paper, conclusions of relationship between dimensionless size and cell performance are put forward. Experiments are also carried out to validate conclusions.

2. Numerical Models

Figure 1 shows the schematic of one of the computational models studied. However, the number of baffles changes with the change of dimensionless length of baffles. Geometric parameters of the computational model are shown in

Table 1. Geometric parameters of the computational model.

Parameter	Value
Current collector length	50 mm
Current collector width	2 mm
Rib area width	1 mm
Flow channel width	1 mm
Flow channel height	0.85 mm
Flow channel length	50 mm
Gas diffusion layer (GDL) height	0.15 mm
Catalyst layer (CL) height	0.01 mm
Membrane height	0.025 mm

. The cross-section shape of baffles investigated is set to rectangle.

Cathode inlet direction and anode inlet direction are opposite. Operating conditions are shown in

Table 2. Operating conditions.

Parameter	Valve
Operation temperature	353.15 K
Reference current density	1 Acm−2
Anode/cathode pressure	101,325 Pa
Faraday constant	96,487 Cmol−1
Gas constant	8314 Jkmol−1 K−1
Electron number for anode reaction	2
Electron number for cathode reaction	4
Mass flow rate (cathode)	1 × 10−6 kg s−1
Mass flow rate (anode)	1 × 10−7 kg s−1
Relative humidity (cathode)	90%
Relative humidity (anode)	50%
Porosity (gas diffusion layer)	0.6
Porosity (catalyst layer)	0.2

. Computational governing equations are shown as below [38,39]:

$$\frac{\partial \left(\epsilon \rho \right)}{\partial \mathrm{t}}+\nabla ·\left(\epsilon \rho \overrightarrow{v}\right)=S_m$$

(1)

where $\epsilon$, $\rho$, $S_m$, and $\overrightarrow{v}$ stand for porosity, density, mass source, and velocity vector.

$$\frac{\partial }{\partial t}\left(\epsilon \rho \overrightarrow{v}\right)+\nabla ·\left(\epsilon \rho \overrightarrow{v}\overrightarrow{v}\right)=-\epsilon \nabla p+\nabla \left(\epsilon \mu \nabla \overrightarrow{v}\right)+S_v$$

(2)

where $S_v$, $\mu$, and $p$ are momentum source, dynamic viscosity, and pressure.

$$\frac{\partial }{\partial t}\left(\epsilon \rho c_{p}T\right)+\nabla \left(\epsilon \rho c_p\overrightarrow{v}T\right)=\nabla ·\left(k^{eff}\nabla T\right)+S_Q$$

(3)

where $T$, $c_p$, $S_Q$, and $k^{eff}$ are temperature, specific heat capacity, energy source, and effective thermal conductivity.

$$\frac{\partial \left(\epsilon c_k\right)}{\partial \mathrm{t}}+\nabla ·\left(\epsilon \overrightarrow{u}{c}_k\right)=\nabla ·\left(D_k^{eff}\nabla c_k\right)+S_k$$

(4)

where $D_k^{eff}$, $c_k$, $S_k$, and $\epsilon$ are species effective diffusion coefficient, species concentration, species code, and species source.

$$S_a=j_{a,ref}{\left(\frac{C_{H_2}}{C_{H_{2,ref}}}\right)}^{{\gamma }_a}\left(e^{\frac{{\alpha }_{a}F}{RT}{\eta }_a}-e^{-\frac{{\alpha }_{c}F}{RT}{\eta }_a}\right)$$

(5)

$$S_c=j_{c,ref}{\left(\frac{C_{O_2}}{C_{O_{2,ref}}}\right)}^{{\gamma }_c}\left(-e^{\frac{{\alpha }_{a}F}{RT}{\eta }_a}+e^{-\frac{{\alpha }_{c}F}{RT}{\eta }_c}\right)$$

(6)

where $C_i$, $\eta$, $j_{ref}$,$C_{i,ref}$, γ, and α are local molar concentration for specie $i$, over potential, reference volumetric exchange current density, reference molar concentration for specie $i$, concentration index, and transfer coefficient.

$$\nabla ·\left({\sigma }_e\nabla {\varphi }_e\right)+S_e=0$$

(7)

$$\nabla ·\left({\sigma }_m\nabla {\varphi }_m\right)+S_m=0$$

(8)

where Ф, σ, S, and subscripts m and e are local potential, electric conductivity, current source, membrane, and electron.

Computational flow dynamic software has been used and verified by many works [40,41]. Figure 2 shows the grid independence result for the simulations, and the grid number is set to about 120,000.

3. Experimental Procedure

To further verify the results, PEMFC single cells are designed and tested. The PEMFC single cell test bench is shown in Figure 3. Detailed parameters of PEMFC single cells are shown in

Table 3. Detailed parameters of PEMFC single cell.

Component	Length × Width × Height (mm)	Material
Flow field	100 × 100 × 18	Graphite
Current collector	100 × 100 × 2	Brass H80
End plate	100 × 100 × 12	Aluminum alloy 6061
Insulating plate	100 × 100 × 10	Epoxy resin
Sealant	100 × 100 × 0.15	PTFE
Gas diffusion layer	54 × 54 × 0.19	Toray TGP-H-060
Membrane	50 × 50 × 0.025	Nafion®112

.

4. Results and Discussion

The baseline case is conventional straight channel without baffle. Cases with different dimensionless heights and length of the baffles are discussed below.

4.1. Dimensionless Height of the Baffle

Detailed parameters of different cases are shown in

Table 4. Cases under different dimensionless heights of baffles.

Case	1	2	3	4	5
The ratio of the baffle height to the channel height	0	50%	70%	90%	94%
The ratio of the baffle total length to the channel length	0	21.6%	21.6%	21.6%	21.6%
The ratio of the single baffle length to the channel length	0	3.6%	3.6%	3.6%	3.6%

. Case 1 stands for the conventional straight channel without baffle and is considered as reference case. Case 2 to Case 5 stand for models with height of the baffles set to 50%, 70%, 90%, and 94% of the channel height, respectively.

Figure 4a shows polarization curves and gross power curves of different cases. It can be seen that difference of performance among cases is unobvious when current density is below 1.4 A·cm⁻². With the increase of the current density, difference of performance becomes apparent when the current density is greater than 1.4 A·cm⁻². It is obvious that performance of PEMFC increases with the increase of the dimensionless height of the baffle.

Case 1 obtains the maximum power density when current density is about 1.7 A·cm⁻². The current densities under the maximum power density of Case 2 to Case 5 gradually increase from about 1.75 A·cm⁻² to about 2.0 A·cm⁻². It can be found that increasing the dimensionless height of the baffle in the cathode channel could increase the effective operating current density range and obtain a higher maximum current density of PEMFC.

Figure 4b shows the partially enlarged polarization curves of different cases. The activation and ohmic loss of all cases differ a little. However, the concentration polarizations of all cases differ a lot. Cases with baffles could enhance the mass transfer, thus reducing the concentration polarization. The higher the dimensionless height of the baffle, the lower the concentration polarization.

Figure 4c shows the average oxygen molar concentrations between gas diffusion layer (GDL) and catalyst layer (CL) under the different current densities of all cases. The oxygen concentration decreases with the increase of the current density due to the increase of oxygen consumption along the increase of current density. However, the molar concentration raises with the increase of the dimensionless height of the baffle. The raise is more obvious under a higher current density. The concentration difference increases dramatically when the dimensionless height of the baffle is greater than 90%. Baffles in the channel help to improve the pressure inside the channel and speed the mass transfer from channel to GDL, thus enhancing mass transfer in GDL under ribs.

Figure 4d shows contours of oxygen molar concentration between GDL and CL of all cases at the current density set to 1.9 A∙cm⁻². It can be seen that the concentration difference is apparent. With the dimensionless height of the baffle increasing, the oxygen molar concentration increases and distributes more evenly both along the channel and normal to the channel direction. It can be found that increasing the dimensionless height of the baffle could optimize the mass transfer of oxygen inside the channel and GDL, especially areas under ribs. The higher the dimensionless height of the baffle is, the more the mass transfer is improved.

It can be concluded that adding baffles could dramatically enhance the mass transfer inside the channel, GDL and CL, and the oxygen could be replenished in time. Adding baffles could alleviate the concentration polarization to some extent.

Figure 4e shows contours of the current density distribution in the middle of GDL of all cases at the current density set to 1.9 A∙cm⁻². It is apparent that the gradient of the current density in Case 1 varies more greatly than cases with baffles. The gradient difference of the current density distribution decreases with the increase of the dimensionless height of the baffle since higher baffles lead to higher pressure and more even oxygen distribution in the channel.

Figure 4f shows net power densities of different cases.

Table 5. Cases performance under different dimensionless heights of baffles.

Case	1	2	3	4	5
The ratio of the baffle height to the channel height	0	50%	70%	90%	94%
Gross power density (W/cm2)	0.7916	0.8128	0.8219	0.8375	0.8537
Percentage increase in gross power density		2.67%	3.83%	5.79%	7.96%
Pumping power density (W/cm2)	0.0002	0.0003	0.0004	0.0041	0.0228
Net power density (W/cm2)	0.7914	0.8124	0.8215	0.8331	0.8319
Percentage increase in net power density		2.66%	3.81%	5.27%	5.12%

shows power densities at the current density set to 1.9 A cm⁻² of all cases and percentage increase compared with Case 1. It can be seen that compared with Case 1, gross power density increases with the dimensionless height of the baffle, while the net power density shows the different trend when the dimensionless height of the baffle height is more than 90% of channel height because of the excessive pumping power. Though the gross power density of Case 5 is higher than other cases, net power density of Case 4 is the highest of the cases. That is, the result of pumping power in Case 5 is excessive compared with other cases. The net power enhancement ratio reaches the maximum value 5.24% when the height of the baffle is 90% of the channel.

4.2. Dimensionless Length of the Baffle

4.2.1. Total Dimensionless Length of Baffles

The ratio of the total length of all baffles inside the channel to the length of channel is discussed as the total dimensionless length of baffles. Case 1 stands for the conventional straight channel without baffles and is considered as reference case. Case 6 to Case 10 stand for models with the total length of the baffle set to 10.8%, 21.6%, 32.4%, 37.8%, and 43.2% of the channel length, respectively. Detailed parameters of different cases are shown in

Table 6. Cases under different total dimensionless lengths of baffles.

Case	1	6	7	8	9	10
The ratio of the baffle height to the channel height	0	90%	90%	90%	90%	90%
The ratio of the baffle total length to the channel length	0	10.8%	21.6%	32.4%	37.8%	43.2%
The ratio of the single baffle length to the channel length	0	5.4%	5.4%	5.4%	5.4%	5.4%

.

Figure 5a shows that the performance of PEMFC increases with the increase of the total dimensionless length of baffles. It also can be found that increasing the total dimensionless length of baffles in the cathode channel would raise the effective operating current density range and obtain a higher maximum current density of PEMFC. Figure 5b shows the partially enlarged polarization curves of different cases. The activation and ohmic loss of all cases differ a little. However, the concentration polarizations of cases with baffles also differ a little. Figure 5c shows the average oxygen molar concentration between GDL and CL under different current densities of all cases. The oxygen concentration decreases when the current density increases due to the increasing of oxygen consumption at a higher current density. Increasing the total dimensionless length of baffles could dramatically increase the average oxygen molar concentration.

Figure 5c shows that with the increase of total dimensionless length of baffles, the oxygen distributes more evenly both along the channel and normal to the channel direction. Figure 5d shows contours of the current density distribution in the middle of GDL of all cases at the current density set to 1.9 A∙cm⁻². Compared to Case 1, cases with baffles obtain more even current density distribution. The distribution difference among cases become unobvious when the total dimensionless length of baffles is greater than 21.6%. Figure 5e shows net power densities of cases with different total length of baffles.

Table 7. Cases performance under different total dimensionless lengths of baffles.

Case	1	6	7	8	9	10
The ratio of the baffle total length to the channel length	0	10.8%	21.6%	32.4%	37.8%	43.2%
Gross power density (W/cm2)	0.7916	0.8155	0.8375	0.8396	0.8419	0.8445
Percentage increase in gross power density		3.01%	5.79%	6.06%	6.36%	6.68%
Pumping power density (W/cm2)	0.0002	0.0021	0.0041	0.0048	0.0052	0.0055
Net power density (W/cm2)	0.7914	0.8134	0.8331	0.8348	0.8367	0.8390
Percentage increase in net power density		2.79%	5.27%	5.48%	5.73%	6.01%

shows the influence of the total dimensionless length of baffles on the power density at the current density set to 1.9 A∙cm⁻². It can be seen that the pumping power density increases with the total length of baffles, and the net power density shows the same trend. Enhancement of net power density increases more slowly with the increase of total length of the baffle compared with gross power density. The net power enhancement ratio reaches the maximum value of 6.01% when the total length of baffles is 43.2% of the channel.

4.2.2. Dimensionless Length of the Single Baffle

The ratio of the length of a single baffle inside the channel to the length of the channel is discussed as the dimensionless length of the single baffle to further study the impact of the dimensionless length of baffles.

The dimensionless length of the single baffle is set to 3.6% and 7.2% in Case 11 and Case 12, respectively, while the total length of baffles and height of the baffle are set to 43.2% and 90% according to the discussion above. Detailed parameters of different cases are shown in

Table 8. Cases under different dimensionless lengths of the single baffle.

Case	1	11	10	12
The ratio of the baffle height to the channel height	0	90%	90%	90%
The ratio of the baffle total length to the channel length	0	43.2%	43.2%	43.2%
The ratio of the single baffle length to the channel length	0	3.6%	5.4%	7.2%

.

Figure 6a shows polarization curves and gross power curves of different cases. It can be seen that adding baffles could dramatically increase PEMFC performance when current density is high. However, the dimensionless length change of the single baffle has a little impact on PEMFC performance. Figure 6b shows the partially enlarged polarization curves of different cases. The activation and ohmic loss of all cases differ a little. However, the concentration polarizations of cases with baffles differ a little. Figure 6c shows the average oxygen molar concentration between GDL and CL under different current densities of all cases. It can be seen that adding baffles could greatly improve the mass transfer of oxygen. Although the smallest dimensionless length of the single baffle obtains the best performance, the concentration difference among the cases is tiny.

Figure 6d,e show contours of oxygen molar concentration between GDL and CL and the current density distribution in the middle of the GDL of all cases at the current density set to 1.9 A∙cm⁻². Similar to the trend above, the smallest dimensionless length of the single baffle obtains the most even current density distribution, but the oxygen concentration difference among the cases is not obvious. Figure 6f shows the net power densities of cases with different length of the single baffle.

Table 9. Cases performance under different dimensionless lengths of the single baffle.

Case	1	11	10	12
The ratio of the single baffle length to the channel length	0	3.6%	5.4%	7.2%
Gross power density (W/cm2)	0.7916	0.8471	0.8445	0.8421
Percentage increase in gross power density		7.01%	6.68%	6.38%
Pumping power density (W/cm2)	0.0002	0.0060	0.0055	0.0052
Net power density (W/cm2)	0.7914	0.8411	0.8390	0.8368
Percentage increase in net power density		6.29%	6.01%	5.74%

summarizes the influence of the dimensionless length of the single baffle on the power density at the current density set to 1.9 A∙cm⁻². Although pumping power decreases along the length of the single baffle, it can be seen that the net power density shows the same trend as gross power. However, the difference between different cases with different dimensionless lengths of the single baffle is not obvious. When the length of the single baffle is set to 3.6% of the channel, the PEMFC net power density could be increased by 6.29%, which is higher than a previous study [37].

4.3. Experimental Validation

Experiments are also carried out to verify the conclusion that baffles in the cathode channel could enhance the performance of the cell. PEMFC single cells are designed and tested. The dimensionless height of the baffle, total dimensionless length of baffles, and dimensionless length of the single baffle are set to 90%, 21.6%, and 3.6%, respectively.

Figure 7 shows polarization curves of tested cases. It can be seen the maximum net power density of PEMFC without baffles is about 0.624 W·cm⁻² when the current density is about 1.2 A∙cm⁻². The improvement of the maximum net power density is about 3.85%. The conclusion that baffles in the channel could enhance the performance of cell is verified.

5. Conclusions

In this paper, effects of dimensionless height of the baffle, total dimensionless length of baffles, and dimensionless length of the single baffle on PEMFC performance are investigated. However, the effect of baffle shape and baffle design criterion would be studied in the future. The main conclusions are as follows:

(1)

Adding baffles inside cathode channels could help replenish the oxygen in time, enhance the mass transfer inside the channel, GDL and CL, especially in the area under ribs, and improve PEMFC performance. The dimensionless sizes of baffles have a great impact on PEMFC performance.

(2)

The mass transfer and PEMFC performance increase with the increase of dimensionless height and total dimensionless length of baffles while decrease with the increase of dimensionless length of the single baffle. However, excessive dimensionless height of the baffle would weaken PEMFC performance due to the extraordinary higher parasitic power.

(3)

PEMFC net power density could be increased by 6.29% when the length of the single baffle, the total length of baffles, and height of the baffle are set to 3.6%, 43.2%, and 90%, respectively.