Leakage Analysis of PEMFC Sealing System Considering Temperature Cycling

Abstract

Addressing the leakage rate prediction problem of the PEMFC sealing system is of great importance for its stable operation. The leakage calculation method of the PEMFC sealing system is proposed based on thermal coupling. The parallel plate leakage model is improved to make it applicable to the leakage rate calculation with a variable channel cross-section height. The interface macroscopic contact pressure is solved using a finite element simulation for solid mechanics analysis. The Greenwood–Williamson model is used for contact mechanics analysis to solve for the average height of the leakage channel. The effects of the ambient temperature, compression ratio, bipolar plate misalignment, and gasket size on the cell sealing effect were studied numerically. The data indicated that as the ambient temperature, compression ratio, and gasket size became larger, the volume leakage rate began to be reduced. The leakage rate as a parameter to characterize the sealing performance, considering the influence of gasket size, operating conditions, and other factors on the cell sealing effect, is more meaningful for the durability study and failure analysis of PEMFC.

1. Introduction

Environmental pollution problems are becoming more and more serious due to the significant growth in the number of vehicles [1]. Resolving the conflict between environmental pollution and travel convenience requires the whole society to consider it collectively [2]. Developing fuel cell technology is an effective way to resolve conflicts [3]. PEMFC converts chemical energy into electrical energy by employing a reaction between an oxidizer and a fuel [4]. Because of its high current density, simple structure, and fast response during operation, it is well-suited for portable power sources and vehicles [5]. A sealing groove is opened and a seal is placed on the bipolar plate [6]. Applying certain compressive stress on both sides of the end plate deforms the seal and achieves a reliable seal [7]. The parts in a PEMFC need to be strong enough to withstand loads even under temperature variations [8]. The gasket is compressed between the bipolar plate and the membrane electrode frame to prevent gas from escaping from the boundary of the cell [9]. During the cell operation, the temperature cycling causes the contact pressure between the sealing surfaces to change, thus affecting the gas tightness [10]. Therefore, it is necessary to study the gas tightness of PEMFC under temperature cycling conditions [11].

The structural construction of the fuel cell stack is of great significance to improve the gas tightness and service life [12]. Numerous studies have been carried out on temperature distribution and leakage in sealed systems of PEMFC [13]. Qiu et al. [14] considered the unevenness of the gas pressure and the pressure on the contact surface of the sealing structure and established a numerical analysis method to calculate the gas leakage rate of the cell. Zhang et al. [15] analyzed the mechanical response and contact behavior of the PEMFC during assembly and operation, considering the thermal effects due to the redox reactions during the operation of the PEMFC. Xu et al. [16] proposed a theoretical model for a leakage rate calculation combining various numerical methods such as a rough surface generation technique and finite element simulation, and analyzed the flow characteristics of gas in the contact interface gap. Huang et al. [17] solved the problem of predicting the leakage rate of PEMFC over a long period, established a numerical model of the leakage rate of the sealing structure, and analyzed the quantitative effects of various factors on the leakage rate. Zhang et al. [18] established a model for PEMFC and investigated the leakage rate of single- and multi-cell structural seal systems at three different operating temperatures. Cui et al. [19] showed that the temperature dependence of polymer rubber materials leads to stress relaxation and creep, and discussed the development of liquid silicone rubber compressive stress between two clamped metal plates under the effect of temperature cycling. Liang et al. [20] discussed the influence of the geometry and material parameters of the seal structure on the component damage and assessed the risk of the failure of the seal structure. Cui et al. [21] investigated the sealing force of PEMFC rubber sealing material under temperature change and discussed the stress failure and thermal stress of silicone rubber under temperature differences. Chang et al. [22] studied the breakdown of silicone rubber of different stiffnesses under temperature changes.

Li et al. [23] controlled the temperature variation of PEMFC, it was found that the cell inevitably generates a certain amount of heat during operation, and the fuel cell only has good performance in a certain temperature range. Ghasemi et al. [24] performed modeling of the PEMFC at different cooling temperatures and simulations showing the temperature variation in the cell. Sun et al. [25] used a coolant to control the temperature change of the fuel cell, a geometric model of the cooling channel was developed, and the temperature conditions under operating conditions were simulated using simulation software. Song et al. [26] found the combined effects of assembly stress and operating temperature cause uneven contact pressure distribution between components and strain the structure. Khan et al. [27] proposed a variable temperature model for the PEMFC system and developed an algorithm to detect load variations and transient temperature changes in the PEMFC. Buchet et al. [28] studied the assembly stresses on the gasket and MEA and the development of the gasket inside the fuel cell stack and developed two- and three-dimensional models to explore the ideal behavior of the coupled MEA/gasket. Martemianov et al. [29] conducted an experimental and theoretical study of the mechanical effects in fuel cell operation by applying heat and humidity fields.

Previous scholars found that thermal expenditure is the main factor affecting the sealing pressure of temperature cycling gaskets, and tested the mechanical properties of rubber gaskets for PEMFC at high temperatures [30]. However, there is no quantitative analysis of the leakage rate of mass PEMFC under temperature cycling [31]. In this paper, the parallel flat plate leakage model is improved and the Greenwood–Williamson model is used for the finite element analysis of single rough body contact mechanics, and a numerical simulation method for the leakage rate of the sealing structure of PEMFC considering temperature cycling is proposed [32]. Based on numerical simulations, the laws of compression rate, misalignment, and gasket size on the gas tightness of sealing gaskets were investigated.

2. Model and Methodology

As shown in Figure 1 [18], taking into account the symmetry of the sealing structure of the PEMFC, one side was selected to build a finite element simulation model in ABAQUS software to solve for the macroscopic contact pressure between the contact surfaces for mechanical and thermal analysis. The sealing system consisted of a bipolar plate, a sealing gasket, and a PEM frame [33]. The surface morphology of the contact interface of the sealing system was numerically simulated using the Greenwood–Williamson statistical theory. The law of influence of the two-dimensional flow channel height variation at the interface on gas leakage is described based on the Hertzian contact theory.

2.1. Numerical Simulation Model

In this paper, the indentation test process of rubber gaskets is simulated using finite elements (Figure 2), and

Table 1. Structural dimensions of the assembled body.

Component Name	Materials	Modulus of Elasticity (/MPa)	Poisson’s Ratio (/°C)	Density (kg/m3)	Coefficient of Thermal Expansion	Conductivity W/(m × K)
Framework	Nylon	10,000	0.3	1330	0.0002	0.24
Sealing Gasket	Silicone Rubber	-	-	1000	0.00069	0.3
Bipolar Plate	Stainless Steel	210,000	0.267	7850	-	-
End Plate	Aluminum Alloy	137,800	0.33	2850	-	-

lists the material parameters of the sealing system parts. During the manufacturing process of the membrane electrode assembly, the catalyst layer is coated on both sides of the gas diffusion layer. Nonetheless, due to the low strength of PEM and GDL, these components need to be encapsulated by frames. The frame increases the strength of the cell stack assembly and makes the structure of the stack more stable. It seals the battery stack as well to prevent gas and coolant leakage and to protect the battery assembly from large compressive loads. The framework consists of two parts, the base layer and the adhesive layer, which serve to increase the resistance to deformation and to fix the lens coating film, respectively, and the two parts of the structure are usually bonded together by AL. The sealing gaskets extrude the membrane electrode frame in the assembly position, and materials including polyethylene terephthalate, glass fiber, composites, and rubber can be used as frames. Among them, nylon has good stiffness and excellent chemical resistance, so it is chosen as the material for the frame in this paper. The following assumptions were made for the sealing system:

(1)

The end plate will not change shape and is set to be rigid.

(2)

The material of the MEA framework is defined as an elastic and isotropic polymer.

(3)

The strain of the gasket is the same in both tension and compression.

(4)

The volume change of rubber is not affected by the material properties.

The Mooney–Rivlin model is suitable for describing the deformation of rubber materials at lower strains. Therefore, the Mooney–Rivlin model can be applied to describe the dynamic properties of rubber gaskets [17].

$$W=C_{10}\left(I_1-3\right)+C_{01}\left(I_2-3\right)$$

(1)

W is the strain potential energy of the specimen. $C_{10}$ and $C_{01}$ are the Mooney–Rivlin material coefficients. $C_{10}=1.87$ MPa and $C_{01}=0.47$ MPa in this paper. $I_1$ and $I_2$ are the primary and secondary strain tensor invariants.

The microcontact model for rough surfaces proposed by Greenwood and Williamson is particularly widely used, and it estimates the relationship between the contact area and loading force assuming that the rough surface is composed of spherical bumps with a uniform radius of curvature and Gaussian distributed height. The contact is set up as a surface-to-surface type. The bottom surface of the end plate is defined as a fixed restraint. The load is applied vertically to the rigid body to simulate the bolt-tightening process. According to the Greenwood–Williamson contact model, the microstructure of the gasket surface is assumed to be semicircular projections of different heights. Considering the incompressibility of the rubber and the contact problem, the cell property is set as a bilinear planar stress quadrilateral cell CPS4R. The quality of the mesh division in the finite element simulation has a great impact on the convergence of the calculation results, the contact position of the outer ring of the seal gasket will have a large deformation during compression, so the outer ring mesh is appropriately encrypted to ensure convergence. The final seed spacing was defined as 10 μm for the gasket, 100 μm for the bipolar plate, 700 μm for the end plate, and 35 μm for the proton exchange membrane frame members, using a progression algorithm and using mapping grids where appropriate. The boundary conditions are set in

Table 2. Boundary condition settings.

Objects/Boundaries	Mode/Value
Load mode	Displacement load
Bottom of the substrate	Fully fixed
Normal friction coefficient	Lagrange method
Tangential friction coefficient	0.068
Contact method	surface to surface
Sliding method	Limited slip

.

For the consideration of the effect of temperature on the sealing system, a full thermodynamic coupling analysis was performed in ABAQUS. The thermal load size and location of action were first obtained by considering the temperature change based on the results of the initial load loading calculation. Define the material properties of the part in ABAQUS, including thermal conductivity, and the coefficient of expansion with the temperature. Set the ambient temperature, apply the surface heat flux, conduct the temperature displacement coupling analysis, and finally find the seal system stress–strain state to complete the thermal coupling analysis.

2.2. Effective Height Determination

The Greenwood–Williamson contact model is a commonly used statistical model that is widely used in contact studies of rough surfaces. The height of the gap h at the contact interface of the sealing system varies with the sealing force and microscopic contact dynamics performed on the sealing surface, showing that the temperature affects the magnitude of the forces. At a set compressive load force F, the effective height h of the seal channel contact interface can be determined by microcontact dynamics analysis. As shown in Figure 2, part of the convex surface is deformed under the action of the sealing load F, causing a small displacement of the sealing surface $\delta$, and a reduced effective height between the contact surfaces from $h_0$ to $h$. By determining the connection among the load F and the little displaced $\delta$, the gap height $h$ ($h=h_0-\delta$), corresponding to a set compressive force, can be calculated.

According to the Hertzian contact model, the relationship between the compressive displacement $\delta$ and the vertical load is [17]:

$$\delta ={(\frac{9F^2}{16R{E}^{\prime 2}})}^{1/3}$$

(2)

where $E^{\prime }$ is the modulus of elasticity determined by the combination of two materials, the bipolar plate (subscript b) and the rubber gasket (subscript s)

$$\frac{1}{E^{\prime }}=\frac{1-v_b^2}{E_b}+\frac{1-v_s^2}{E_s}$$

(3)

where $v_b$ and $v_s$ is the Poisson’s ratio of the two structural materials, bipolar plates, and rubber gaskets, separately.

$$\frac{\delta }{R}=(\frac{9S_G^2}{16E^{\prime 2}})1/3$$

(4)

where $S_G$ is the average value of the contact surface stress, the value of the compression force F, and the ratio of the gasket surface path length L.

The practical significance of the initial gap height $h_0$ is equivalent to the peak radius of the contact surface R. In this paper, $R=h_0=3\sigma$ is defined. The dimensionless mean contact stress $S_G^{*}$ is defined as:

$$S_G^{\ast }=S_G/E$$

(5)

$$S_G=F/L$$

(6)

It follows that the dimension-free height $h^{*}\left(h^{*}=h/h_0\right)$ is a double feature of the dimensionless mean contact stress $S_G^{*}$ and the temperature t, namely:

$$h^{\ast }=f\left(S_G^{\ast },t\right)$$

(7)

The above equation can be obtained from finite element simulations to obtain the effective gap height at the contact interface.

The interaction is set to Universal Contact. Edit the contact properties to define the normal and tangential behavior, set the friction coefficient to 0.068 for the tangential behavior, and define the normal behavior as a “hard” contact. Set the upper and lower end plates as rigid bodies in the constraint manager, and bind them to the upper and lower bipolar plates, respectively. The linear stress is loaded on the end plate to emulate the bolt pre-load during the actual assembly, the loading method is compression, and the magnitude of the applied load is 0.1 MPa, and the boundary condition type is to set the bottom surface of the lower end plate to be completely fixed. The simulation is executed in explicit mode. The overall count of nodes and units is 736 and 510, and the cell types are CPS3, CPS4R, and RNODE2D.

The stresses at 0.1 MPa, 0.15 MPa, and 0.2 MPa were simulated and the results obtained from the numerical analysis of the microcontact mechanics of the individual gaskets were collected into two dimensionless quantities of dependence. It means that the dimensionless temperature is t and the dimensionless separation distance is $h^{*}=h/h_0$. The results for the different temperatures fell on the same $t-h^{*}$ curve, which was fitted accurately to the data points. Figure 3 shows that under the same $S_G^{*}$, $h^{*}$ depends only on t. When the stress is 0.1 MPa, the resultant expression is:

$$h^{\ast }=-4.27\times {10}^{-4}t+0.606$$

(8)

From Equation (12), it can be seen that for a given temperature t corresponding to the gap length h, the average compressive stress can be calculated from the micromechanics of the seal structure.

2.3. Leakage Mechanism Model

At present, there are models for calculating the leakage rate of static seals, such as the parallel plate model, Roth model, average flow model, porous media model, grid leakage model, single hub leakage model, etc., but there are few studies on the leakage model for the calculation of leakage rate of rubber O-ring seals. The gas flow in the rough interface gap can maintain the basic characteristics of the gas flow in the parallel plate, so the leakage rate is analyzed numerically using the parallel plate.

The laminar flow assumption can be applied to the gas flow within the rough interface gap. When the gas pressure difference between the inside and outside of the sealing system is kept constant, changes in effective height and surface roughness can lead to significant changes in the airflow in the interfacial gap. As the clearance height decreases, the low-velocity zone at the rough location increases, indicating that the resistance to gas flow in the channel becomes greater. The leakage rate is defined in terms of the roughness flow factor ${\varnothing }_{\sigma }$ and the height flow factor ${\varnothing }_h$. The numerical model of channel leakage can be expressed as follows [17]:

$$Q={\varnothing }_{\sigma }•{\varnothing }_h•Q_p$$

(9)

$Q$ is the channel leakage volume and $Q_p$ is the gas flow in the smooth channel at the original channel height. It can be figured out from the gas flow equation of the parallel plate leakage model as follows:

$$Q_p=\frac{B{h}^3}{12\mu L}\times \frac{p_1^2-p_2^2}{2p_1}$$

(10)

where $h$ is the height of the interface gap; $B$ is the leak passage width; $L$ is the leak passage length; $\mu$ is gas kinetic tack; $p_1$ and $p_2$ are the inner and outer strain of PEMFC. The roughness coefficient is calculated by the following equation:

$${\varnothing }_{\sigma }=\frac{Q_0}{Q_p}$$

(11)

$Q_0$ is the gas flow rate corresponding to the gap surface channel with an initial path height of $h_0$. ${\varnothing }_{\sigma }$ is a feature of the measureless thickness factor ${\sigma }^{*}$, and ${\sigma }^{*}$ is calculated by the following equation:

$${\sigma }^{\ast }=\frac{\sigma }{T}$$

(12)

$\sigma$ and $T$ describe the static values of the rough contact areas, the roughness and the autocorrelation length, respectively. From the fitting profile of the simulation outcome, it is obtained that:

$${\varnothing }_{\sigma }=0.9257{\sigma }^{\ast -1.505}$$

(13)

The high traffic coefficient ${\varnothing }_h$ reflects the effect of the gap height on the gas flow and is defined as follows:

$${\varnothing }_h=\frac{Q}{Q_0}$$

(14)

where Q is the rate of gas flow against the actual channel height h. ${\varnothing }_h$ is related to the infinitesimal elevation $h^{*}$, defined as:

$$h^{\ast }=h/h_0$$

(15)

The functions are as follows:

$${\varnothing }_h=0.009165h^{\ast 2.905}$$

(16)

Therefore, the leakage rate is calculated by the equation:

$$Q=0.00035{(\frac{\sigma }{T})}^{-1.505}\cdot {(\frac{h}{h_0})}^{2.905}\cdot \frac{B{h}^3(p_1^2-p_2^2)}{\mu L{p}_1}$$

(17)

2.4. Thermodynamic Coupling Model

The thermal stress value is related to several factors such as temperature change, the coefficient of thermal expansion, and material stiffness. In the actual working process, PEMFC has three working states of starting, running, and shutting down, and the temperature in each state remains constant, and each temperature cycle is composed of these three states, Simulate the temperature of the battery stack under different operating conditions, 90° is the simulated cell temperature in the operating condition and −10° indicates the night-time shutdown temperature. When the car is out of operation, the PEMFC is turned off. Some areas generally have lower temperatures in winter, defining the temperature at which the battery stops running at −10°. The minimum compression force occurs at low-temperature operating conditions and determines the performance of the seal and the service life of its sealing components. Leaks can also occur at operating temperatures if the sealing stress is lower than the working pressure of the cell channel.

In the paper, a thermodynamic coupling simulation model of the PEMFC sealing system is established through the mutual coupling of the sealing leakage mechanism, contact mechanics, and thermodynamics. Figure 4 shows the specific computational flow of the developed numerical simulation model.

The primary stages are listed below:

(1)

Input the basic parameters of the PEMFC and use the FEM software ABAQUS for contact mechanics analysis to obtain the static contact pressure and effective height.

(2)

Define the gasket surface roughness parameters, initial height, gas pressure, and temperature in working conditions, and combine the FEM simulation results to calculate the exposed stress.

(3)

Update the effective clearance height of the sealing channel according to the compression deformation of the gasket.

(4)

Output the leakage rate and other sealing performance parameters.

Based on the proposed model, a parametric study of leakage was conducted based on the temperature-effective gap height relationship. The influencing factors studied include compression ratio, misalignment error, and gasket size.

3. Results and Analysis

We used the Greenwood–Williamson model for contact mechanics analysis and to solve for the average height of the leakage channel. The influence of ambient temperature, compression ratio, bipolar plate misalignment, and gasket size on the sealing performance of PEMFC was studied.

3.1. Model Validation

To confirm the accuracy of the presented numerical model, the calculated battery leakage rate results are compared with the experimental data. A single fuel cell finite element model was developed and the predicted results of leakage rate at different temperatures were obtained by numerical calculations. As shown in Figure 5, the calculated and experimental values remained similar in magnitude and trend, which verified the precision of the numerical model. The results of the experiment are from Wu’s [34] actual study. As shown in

Table 3. Leakage rate numerical calculation parameters.

Experimental Parameters	Parameter Value
Surface roughness	1.85 μm
Initial clearance height	0.7 mm
Flow channel width	3 mm
Hydrogen pressure	170 KPa
Air pressure	150 KPa
Hydrogen dynamic viscosity	0.10969 Pa$·$s

, the parameters used for the prediction were the same as those used in the experimental study.

The initial compression rate is defined as 15% and the gasket is set to the same operating temperature as the proton exchange membrane frame. The end plate is moved downward during the simulation to simulate the pre-compression, and the magnitude of the pre-compression rate is controlled according to the applied load. The temperature cycling curve of the cell is shown in Figure 6. Three operating temperatures are set and the corresponding temperature fields are applied, and the material generates thermal expansion and contraction during the temperature change, and the strain of the valid clearance altitudes of the sealing paths is considered at different operating temperatures.

In different operating conditions, the leakage is kept in line with the temperature variation, i.e., the leakage rate drops with higher temperatures. The cooler the temperature, the more rapidly the leakage rate decreases, and at higher temperatures, the leakage rate gradually stabilizes in the operating condition. The magnitude of the stress change is obvious at lower temperatures, and the leakage rate becomes lower as the stress increases. However, when working at high temperatures, the compression load has almost no effect on the leakage rate. Changing other parameters did not affect the trend of leakage ratio with temperature, but this can have a significant effect on the value of the leakage rate.

3.2. Compression Ratio

The strain level has a remarkable impact on the leakage rate, and Figure 7 shows the leakage rate relative to the temperature for different strain levels. The effects of the spill ratio decreasing as the temperate rises are obvious at low temperatures. However, when the temperature increases to a certain level, its effect on the leakage rate starts to diminish. Figure 8 shows the surface contact pressure at different loads, with the contact pressure increases continuously with increasing load, causing the leakage rate to start decreasing.

The strain state of sealing structures under different stress loads is shown in Figure 9, pressure is applied to the end plates during assembly to achieve self-sealing of the system. The deformation of the rubber ring shown in Figure 9 increases as the pressure rate rises and the effective clearance height of the sealing path decreases. The higher the compression ratio, the larger the sealed route, and the smaller the effective clearance height, the better the self-sealing of the seal. When designing a PEMFC, determining the size of the compression ratio to seal the system and prevent leakage is required.

3.3. Bipolar Plate Misalignment

During the PEMFC assembly process, it is not easy to ensure that the gasket is fixed in the sealing groove without moving, and misalignment may occur causing the seal to slip out. Deviations generally come from two sources: misalignment of the BPP positions caused by the assembly process and deformation errors caused by thermal stresses during metal BPP welding. In actual working conditions, the existence of BPP misalignment and contact surface tangential force will lead to a frictional heat generation between the gasket and the proton exchange membrane frame, causing a local temperature rise at the contact position and increasing the deformation of the gasket and frame.

As shown in Figure 10, the larger the bit error difference is, the more pronounced the deformation is.

Table 4. The maximum stress of different dislocations of the bipolar plate under the working state.

Component Name	Stress (ε = 0)/MPa	Stress (ε = 0.1)/MPa	Stress (ε = 0.2)/MPa	Stress (ε = 0.3)/MPa	Stress (ε = 0.4)/MPa
Upper gasket	4.13	4.13	4.03	3.84	3.61
Lower washer	4.07	4.04	3.96	3.73	3.37
Frame	9.64	8.72	7.94	7.32	7.29

shows the maximum stress values for each component structure of the sealing system at different dislocations. High strain zones appear in the interface area between the MEA frames and the sealing gasket. The range of the high strain zone increases with the misalignment error and the seal structure is prone to failure. When ε is 0.4, the strain discrepancy between the MEA frame and the gasket is the greatest.

As shown in Figure 11, excessive misalignment errors lead to changes in the forces on the sealing system, the contact surface path length and the pressure decrease with an increasing misalignment error. The inhomogeneity of the forces on the membrane electrode frame leads to an increase in the deformation and a change in the contact stress transfer path. At the same operating temperature field, the maximum strain decreases with an increasing bit error difference. The strain in the membrane electrode frame is greater than the strain in the two rubber seals, and the strain in the lower seal is the smallest.

As shown in Figure 12, the failure rate of the sealing structure increases with the misalignment error. A misalignment deviation has a large impact on the effective height variation of the sealing structure, which can easily cause the performance failure of the frame and cell. Consequently, dimensional deviations must be controlled during manufacturing and assembly to ensure the accuracy of connections between the components and to reduce the misalignment errors of parts.

3.4. Seal Ring Size

The strain distribution of the seal at different sizes is shown in Figure 13.

Table 5. Maximum stress of different dislocations of the bipolar plate with different gasket sizes.

Component Name	Stress (H = 0.6)/MPa	Stress (H = 0.7)/MPa	Stress (H = 0.8)/MPa	Stress (H = 0.9)/MPa
Upper gasket	4.97	4.97	4.96	4.98
Lower washer	4.83	4.83	4.82	4.84
Frame	8.92	9.01	8.95	9.02

shows the maximum stress values for each component of the sealing system for different sizes of gaskets. The strain range of the sealing structure is concentrated between the gasket and the membrane electrode structure. On the other hand, the strain distribution at different sizes is similar. The strain in the gasket increases with H. The presence of high-strain regions within the cross-section can lead to a structural failure.

The leakage rates for various sizes of seal structures are presented in Figure 14. The seal path length and strain increase with an increasing size for the same compression ratio. The effective clearance height difference of the sealed path becomes larger as the size increases, and the strain change of the gasket becomes more pronounced as the seal size increases. The effect of the rubber seal size on the strain decreases at higher temperature fields.

The influence of seal size on PEMFC leakage rate occurs mainly at the assembly stage, where an increase in size can lead to an increase in sealing performance and stress. The thickness of the shim is more susceptible to deformation, as long as a small stress can bring it to the same level of strain. The elevated height of the PEMFC can lead to fuel cell seal failure, so involving the seal gasket size is one of the ways to extend the PEMFC life and reduce the fuel cell failure.

The leakage rate of the sealing system during temperature cycling at different compression ratios, different misalignment deviations, and different sealing gasket sizes is shown in

Table 6. Leakage rate of sealing system with temperature at different parameters.

Temp (°C)	Leakage Rate (μg/s)
	Compression Ratio (%)					Dislocation (mm)					Size (μm)
	8	10	12	14	16	0	0.1	0.2	0.3	0.4	0.6	0.7	0.8	0.9
−10	73.85	49.21	32.74	19.93	11.23	17.86	43.57	72.14	98.57	119	30	52.86	78.57	100
20	53.59	33.54	20.65	10.89	3.35	5.71	27.71	52.14	78.14	95.14	16.29	34.29	56	74.29
90	47	28.51	16.19	8.49	1.06	2.86	26.43	48.57	72.86	87.29	15	34.14	50	67.14

.

4. Conclusions

The leakage of a liquid or gas due to gasket failure during operation is considered critical to the durability of a PEMFC. This paper presents a numerical procedure for calculating the leakage rate of PEMFC sealing structures under temperature cycling. The method takes into account the changes in temperature during the cell operation. Under all operating conditions, the leakage rate increases with time, with an initial fast change in growth followed by leveling off, a trend that corresponds to the effect of temperature on the effective gap height.

(1)

The temperature will have a significant impact on the stress–strain of the sealing structure; the higher the temperature, the lower the effective height of the leakage channel, making the leakage rate decrease. The leakage rate of the PEMFC single-cell sealing system in different temperature fields is different, and the effect on the leakage rate becomes smaller as the temperature continues to increase.

(2)

As the compression ratio and seal size increase, the increased deformation of the gasket and the increased pressure at the contact interface result in better sealing performance. An assembly misalignment has the most serious effect on the leakage of the sealing structure, resulting in high-strain areas within the cross-section of the sealing gasket, which can easily cause the sealing failure of the fuel cell in the long term.

(3)

According to the numerical method proposed in the article, the optimization of design parameters such as surface roughness, gasket size, strain level, and bipolar plate misalignment error can reduce the probability of failure of the sealing structure during operation.