A method for predicting the optimal flow channel width in a proton exchange membrane fuel cell

Abstract

This invention discloses a method for predicting the optimal flow channel width of a proton exchange membrane fuel cell (PEMFC), comprising the following steps: discretizing the PEMFC along the channel direction, solving for the mass transfer of oxygen and water vapor segment by segment, then using boundary conditions to correlate the segments, establishing a coupled flow and mass transfer model to obtain the oxygen and water vapor mass transfer conditions at various points in the fuel cell, and calculating the limiting current density of the fuel cell based on the oxygen mass transfer. Finally, using the limiting current density as the evaluation criterion, combined with optimization methods, the optimal flow channel width of the PEMFC is rapidly predicted. The prediction method described in this invention can quickly obtain the optimal flow channel width of a PEMFC, and has advantages such as short optimization time, good optimization effect, and simple implementation.

Description

Technical Field

[0001] This invention relates to the field of fuel cells, and more specifically to a method for predicting the optimal flow channel width of a proton exchange membrane fuel cell. Background Technology

[0002] Fuel cells have shown great development potential due to their advantages such as being green and pollution-free, having high specific energy density, low noise, and a wide range of fuels. Among them, proton exchange membrane fuel cells (PEMFCs) are considered the most competitive next-generation power source due to their low operating temperature and fast start-stop response. The flow field of the bipolar plate in a PEMFC affects the transport of reactants, electron conduction, and heat diffusion within the cell, thus determining the output performance and lifespan of the PEMFC. Designing a suitable PEMFC flow field structure is one of the important ways to improve PEMFC performance. Parallel channels are simple to fabricate and have low pump power loss, making them widely used in commercial PEMFCs. Parallel channels are composed of multiple single channels, and many scholars have studied single-channel structures in order to obtain the optimal PEMFC output performance.

[0003] Research on PEMFCs mainly employs two methods: experimentation and numerical simulation. Experiments can directly and accurately determine fuel cell performance; however, traditional experiments often rely on trial-and-error methods, requiring multiple sets of experiments, which is time-consuming, labor-intensive, costly, and time-consuming. Numerical simulation can effectively reproduce the complex physicochemical phenomena within PEMFCs, but it requires significant computing resources and time. When studying the optimal flow channel width of a single-channel PEMFC, it is often necessary to repeatedly adjust the PEMFC flow channel width and perform performance evaluations, consuming substantial computational resources and time. Therefore, developing an efficient, accurate, and comprehensive method for predicting the optimal flow channel width of proton exchange membrane fuel cells is essential.

[0004] Pan et al. (Pan WT, Chen XL, Wang FC, Dai G. Mass transfer enhancement of PEM fuel cells with optimized flow channel dimensions[J]. International Journal of Hydrogen Energy, 2020, 46(57):29541-29555.) proposed a series resistance model, analyzed the rate control steps of PEMFCs under various voltages, theoretically derived the relationship between the optimal flow channel width and flow rate of a single-channel PEMFC, and verified the reliability of the method using computational fluid dynamics. The results show that the greater the deviation of the channel width from the optimal value, the worse the performance of the cell. However, this method ignores the diffusion mass transfer in the flow channel and the influence of parameters such as fin width and flow channel length on the optimal flow channel width. Currently, there is still a lack of an efficient, accurate, and comprehensive method for predicting the optimal flow channel width of proton exchange membrane fuel cells. Summary of the Invention

[0005] The purpose of this invention is to provide a method for predicting the optimal flow channel width of a proton exchange membrane fuel cell that is simple in process, has a short optimization cycle, and is highly reliable, and can quickly determine the optimal flow channel width.

[0006] The present invention is achieved by at least one of the following technical solutions.

[0007] A method for predicting the optimal flow channel width in a proton exchange membrane fuel cell includes the following steps:

[0008] S01. Obtain the initial structural and operating parameters of the proton exchange membrane fuel cell;

[0009] S02. Divide the proton exchange membrane fuel cell into N parts along the channel direction. Considering that the battery is in the limit current operating state, calculate the theoretical maximum oxygen mass transfer flux of the first part based on the oxygen molar concentration at the inlet of the flow channel.

[0010] S03. Calculate the molar concentration of water in the flow channel and catalyst layer at the outlet of the first part and the molar concentration of oxygen in the flow channel at the outlet of the first part.

[0011] S04. Use the gas composition and flow rate at the outlet of the first part of the flow channel as the initial conditions at the inlet of the next part of the flow channel, and calculate in this way to determine the theoretical maximum oxygen mass transfer flux of each part.

[0012] S05. Based on the theoretical maximum oxygen transfer mass of each part, calculate the theoretical limiting current density of the battery with the current flow channel width.

[0013] S06. Based on the theoretical limiting current density, adjust the flow channel width using optimization methods, return to step S02, and repeat steps S02 to S05 until the limiting current density no longer increases. At this point, the flow channel width corresponding to the maximum value of the limiting current density is the optimal flow channel width for the proton exchange membrane fuel cell.

[0014] Furthermore, in step S01, the initial structural parameters of the battery include the flow channel width, rib width, flow channel height, bipolar plate thickness, gas diffusion layer thickness, catalyst layer thickness, proton exchange membrane thickness, gas diffusion layer porosity, and catalyst layer porosity; the operating parameters include operating temperature, operating pressure, anode and cathode inlet gas humidity, and anode and cathode inlet gas flow rate.

[0015] Furthermore, in step S02, the battery is divided into N parts along the channel direction, where N can take any integer value greater than 0, and the length of each part can be the same or different.

[0016] Furthermore, in step S02, Taylor dispersion is used to describe the convective and diffusion mass transfer of oxygen in the flow channel when calculating the theoretical maximum oxygen mass transfer flux; Fick's law is used to describe the diffusion mass transfer of oxygen in the gas diffusion layer. The formula for calculating the theoretical maximum oxygen mass transfer flux is as follows:

[0017]

[0018] Among them, R c δ is the mass transfer flux of oxygen; h is the channel height; K is the oxygen dispersion; GDL The thickness of the gas diffusion layer; The molar concentration of oxygen in the cathode channel; Where is the effective diffusion coefficient of oxygen; A is the mass transfer area;

[0019] General formula for solving oxygen diffusion K:

[0020]

[0021] Among them, D c is the oxygen diffusion coefficient; Pe is the Peckle number, used to measure the relative importance of gas diffusion and convection in the flow channel; v is the oxygen flow velocity in the flow channel;

[0022] The effective diffusion coefficient of oxygen is obtained by the following formula:

[0023]

[0024] Where ε is the porosity of the diffusion layer; P0 and T0 are the reference pressure and reference temperature, respectively; and P and T are the operating pressure and operating temperature of the battery, respectively.

[0025] Furthermore, in step S03, when calculating the water vapor concentration in the catalyst layer and flow channel at the first part of the outlet, a conservation equation is established based on the mass conservation of water vapor to establish the relationship between the water diffusion transport flux, the water vapor diffusion flux, and the water generation flux:

[0026] N g +N d -N diff -N c =0;

[0027] N g -N c -N a =0;

[0028]

[0029] Where, N g N is the water generation flux. d For the electrochemical drag mass transfer flux of water; N diff For the reverse diffusion flux of water; N c N represents the diffusion flux of water vapor in the cathode gas diffusion layer. a This represents the diffusion flux of water vapor in the anode gas diffusion layer. The molar concentration of water vapor at the anode channel; q represents the molar concentration of water vapor at the cathode channel. a q represents the total gas flow rate in the anode channel. c This represents the total gas flow rate in the cathode channel; i+1 refers to the inlet of the (i+1)th part, which is also the outlet of the ith part.

[0030] Considering both electrochemical drag and reverse diffusion mechanisms of water diffusion in the membrane, the electrochemical drag mass transfer flux N of water was calculated. d The reverse diffusion flux N of water diff Calculate using the following formulas respectively:

[0031]

[0032] Where, n d ρ is the electric drag coefficient; F is the Faraday constant; I is the transfer current density; m M is the dry film density; m D is the equivalent mass of the membrane. l λ is the water diffusion coefficient in the membrane; λ is the water content in the membrane. For gradient operators;

[0033] The transfer current density I is obtained by the following formula:

[0034] I = 4FR c ;

[0035] Fick's law is used to describe the diffusion mass transfer of water vapor in a gas diffusion layer:

[0036]

[0037] in, The molar concentration of water vapor at the cathode and anode channels; The molar concentration of water vapor in the cathode catalyst layer and cathode flow channel; δ GDL The thickness of the gas diffusion layer; is the effective diffusion coefficient of water vapor in the gas diffusion layer;

[0038] The water vapor generation flux is calculated based on the chemical reaction conservation equation, using the following formula:

[0039] N g =2R c ;

[0040] Among them, R c This refers to the mass flux of oxygen.

[0041] The gas flow rate at the inlet of the (i+1)th part can be obtained by the following formula:

[0042]

[0043] Where, N c (i) represents the diffusion flux of water vapor in the i-th cathode gas diffusion layer; N a (i) represents the diffusion flux of water vapor in the i-th part of the anode gas diffusion layer; R c (i) represents the mass transfer flux of oxygen in the i-th part; P and T are the operating pressure and operating temperature of the battery, respectively; R a (i) represents the hydrogen consumption in the i-th part of the anode channel, which is obtained by the following formula:

[0044] R a (i)=2R c (i).

[0045] Further, in step S03, the oxygen molar concentration in the flow channel at the outlet of the first part is calculated using the following formula.

[0046]

[0047] in, and q represents the oxygen concentration at the inlet of the cathode channel in the (i+1)th part and the i-th part, respectively; c (i+1) and q c (i) represents the total gas flow rate at the inlet of the cathode channel in the (i+1)th part and the (i)th part, respectively.

[0048] Furthermore, in step S04, the initial conditions at the inlet of the next part of the flow channel include the flow rates of the cathode side and the anode side, the mole fraction of water vapor in the cathode side and the anode side, and the mole fraction of oxygen in the cathode side.

[0049] Furthermore, in step S04, considering two adjacent battery sections, the gas composition and flow rate at the outlet of the i-th section are used as the initial conditions at the inlet of the i+1-th section. Based on these initial conditions, the theoretical maximum oxygen mass transfer flux of the latter section and the molar concentrations of water and oxygen at the outlet of the channel can be calculated. By solving in this progressive manner, the theoretical maximum oxygen mass transfer flux of each section can be obtained from N sections.

[0050] Furthermore, in step S05, the theoretical limiting current density I m The relationship between the theoretical maximum oxygen transfer mass of each part is shown in the following formula:

[0051]

[0052] Where A act It is the activated area of ​​the battery, R t It is the sum of the theoretical maximum oxygen mass transfer flux of each part, and the formula is:

[0053]

[0054] Where R c (i) represents the mass transfer flux of oxygen in the i-th part.

[0055] Furthermore, in step S06, the optimization method is a single-parameter optimization method, including but not limited to traversal method, quadratic interpolation method, and Newton's iteration method.

[0056] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0057] 1. Short optimization time. Compared with conventional numerical methods, the method proposed in this invention considers the operating state of the limiting current density, which effectively reduces the number of equations required for calculation. At the same time, the proposed method solves algebraic equations, which significantly reduces the complexity of calculation and shortens the calculation time.

[0058] 2. Excellent optimization results. The mass transfer model employed in this invention couples one-dimensional flow and one-dimensional mass transfer, improving the prediction accuracy of the limiting current density while ensuring computational efficiency. During the optimization process, the performance of different PEMFC structures can be evaluated more accurately. This invention combines the mass transfer model with the optimization method to obtain optimization results with good performance.

[0059] 3. Simple to implement. The prediction method provided by this invention includes two key technical steps in its implementation: first, calculating the limiting current density using a mass transfer model; and second, optimizing the target variable using a single-parameter optimization method to obtain the optimal target variable. Attached Figure Description

[0060] Figure 1 This is a schematic diagram of single-channel PEMFC partitioning in an embodiment of the present invention.

[0061] Figure 2 This is the curve showing the change in current density with channel width in Embodiment 1 of the present invention.

[0062] Figure 3 This is the curve showing the change in current density with channel width in Embodiment 2 of the present invention.

[0063] Figure 4 This is the curve showing the change in current density with channel width in Embodiment 3 of the present invention. Detailed Implementation

[0064] The present invention will be further described in detail below with reference to the embodiments and accompanying drawings, but the embodiments of the present invention are not limited thereto.

[0065] This embodiment of a method for predicting the optimal flow channel width of a proton exchange membrane fuel cell uses the flow channel width as the optimization variable and the limiting current density as the index to characterize the performance of a single-channel PEMFC. The optimal flow channel width is determined using an ergodic method. The detailed operation includes the following steps:

[0066] Step S01: Determine the initial structural and operating parameters of the PEMFC. The initial structural parameters of the battery include the flow channel width, fin width, flow channel height, bipolar plate thickness, gas diffusion layer thickness, catalyst layer thickness, proton exchange membrane thickness, gas diffusion layer porosity, and catalyst layer porosity; the operating parameters include the operating temperature, operating pressure, anode and cathode inlet gas humidity, and anode and cathode inlet gas flow rate.

[0067] The single-channel PEMFC architecture considered in this implementation case is as follows: Figure 1 As shown in Table 1, the PEMFC consists of an anode bipolar plate a, an anode gas diffusion layer b, an anode catalyst layer c, a proton exchange membrane d, a cathode catalyst layer e, a cathode gas diffusion layer f, and a cathode bipolar plate g. The structural parameters of the PEMFC are shown in Table 1.

[0068] Table 1 PEMFC Geometric Parameters

[0069]

[0070] To solve the model, boundary conditions and operating parameters also need to be specified. The key operations and design parameters for the calculation using the method of this invention are shown in Table 2.

[0071] Table 2 Key Operation and Running Parameters of the Simulation

[0072]

[0073]

[0074] Step S02: Divide the PEMFC and calculate the theoretical maximum oxygen mass transfer flux for the first part. This invention divides the proton exchange membrane fuel cell into N parts along the channel direction. Considering the cell is operating at its limiting current, the theoretical maximum oxygen mass transfer flux for the first part is calculated based on the oxygen molar concentration at the channel inlet. N can take any integer value greater than 0, and the length of each part can be the same or different.

[0075] As one example, such as Figure 1 As shown, the single-channel PEMFC is divided into 9 equal parts along the channel direction, each part being 5mm in length.

[0076] Taylor dispersion is used to describe the convective and diffusion mass transfer of oxygen in the flow channel when calculating the theoretical maximum oxygen mass transfer flux; Fick's law is used to describe the diffusion mass transfer of oxygen in the gas diffusion layer. The formula for calculating the theoretical maximum oxygen mass transfer flux is as follows:

[0077]

[0078] Among them, R c δ is the mass transfer flux of oxygen; h is the channel height; K is the oxygen dispersion; GDL The thickness of the gas diffusion layer; The molar concentration of oxygen in the cathode channel; denoted as α, where α is the effective diffusion coefficient of oxygen; and A is the mass transfer area.

[0079] General formula for solving oxygen diffusion K:

[0080]

[0081] Among them, D c is the oxygen diffusion coefficient; Pe is the Peckle number, used to measure the relative importance of gas diffusion and convection in the flow channel; v is the oxygen velocity in the flow channel.

[0082] The effective diffusion coefficient of oxygen is obtained by the following formula:

[0083]

[0084] Where ε is the porosity of the diffusion layer; P0 and T0 are the reference pressure and reference temperature, respectively; and P and T are the operating pressure and operating temperature of the battery, respectively.

[0085] Step S03: Calculate the molar concentration of water in the first part of the outlet channel and the catalyst layer, and the molar concentration of oxygen in the first part of the outlet channel.

[0086] Based on the mass conservation of water vapor, a conservation equation is established to determine the relationship between the water diffusion flux, the water vapor diffusion flux, and the water generation flux. Solving the conservation equation yields the molar concentration of water in the cathode channel, cathode catalyst layer, anode channel, and anode catalyst layer at the first part of the outlet.

[0087] N g +N d -N diff -N c =0;

[0088] N g -N c -N a =0;

[0089]

[0090] Where, N g N is the water generation flux. d For the electrochemical drag mass transfer flux of water; N diff For the reverse diffusion flux of water; N c N represents the diffusion flux of water vapor in the cathode gas diffusion layer. a This represents the diffusion flux of water vapor in the anode gas diffusion layer. The molar concentration of water vapor at the anode channel; q represents the molar concentration of water vapor at the cathode channel. a q represents the total gas flow rate in the anode channel. c The total gas flow rate in the cathode channel is denoted as i+1; i+1 refers to the inlet of the i+1th part, which is also the outlet of the ith part.

[0091] Considering both electrochemical drag and reverse diffusion mechanisms of water diffusion in the membrane, the electrochemical drag mass transfer flux N of water was calculated. d The reverse diffusion flux N of water diff Calculate using the following formulas respectively:

[0092]

[0093] Where, n d ρ is the electric drag coefficient; F is the Faraday constant; I is the transfer current density; m M is the dry film density; m D is the equivalent mass of the membrane. l λ is the water diffusion coefficient in the membrane; λ is the water content in the membrane. This is the gradient operator.

[0094] The transfer current density I is obtained by the following formula:

[0095] I = 4FR c ;

[0096] Fick's law is used to describe the diffusion mass transfer of water vapor in a gas diffusion layer:

[0097]

[0098] in, The molar concentration of water vapor at the cathode and anode channels; The molar concentration of water vapor in the cathode catalyst layer and cathode flow channel; δ GDL The thickness of the gas diffusion layer; is the effective diffusion coefficient of water vapor in the gas diffusion layer.

[0099] The water vapor generation flux is calculated based on the chemical reaction conservation equation, using the following formula:

[0100] N g =2R c ;

[0101] Among them, R c This represents the mass transfer flux of oxygen.

[0102] The gas flow rate at the inlet of the (i+1)th part can be obtained by the following formula:

[0103]

[0104] Where, N c (i) represents the diffusion flux of water vapor in the i-th cathode gas diffusion layer; N a (i) represents the diffusion flux of water vapor in the i-th part of the anode gas diffusion layer; R c (i) represents the mass transfer flux of oxygen in the i-th part; P and T are the operating pressure and operating temperature of the battery, respectively; R a (i) represents the hydrogen consumption in the i-th part of the anode channel, which is obtained by the following formula:

[0105] R a (i)=2R c (i);

[0106] Calculate the molar concentration of oxygen in the flow channel at the outlet of the first section. Based on the law of conservation of mass, the molar concentration of oxygen in the flow channel at the outlet of the first section is:

[0107]

[0108] in, and q represents the oxygen concentration at the inlet of the cathode channel in the (i+1)th part and the i-th part, respectively;c (i+1) and q c (i) represents the total gas flow rate at the inlet of the cathode channel in the (i+1)th part and the (i)th part, respectively.

[0109] Step S04: Progressive calculation to determine the theoretical maximum oxygen mass transfer flux for each part.

[0110] The gas composition and flow rate at the outlet of the i-th part of the flow channel are used as the initial conditions for the i+1-th part. The initial conditions include the flow rates of the cathode side and anode side of the flow channel, the mole fraction of water vapor in the cathode side and anode side of the flow channel, and the mole fraction of oxygen in the cathode side of the flow channel.

[0111] Based on the initial conditions, the theoretical maximum oxygen mass transfer flux of the (i+1)th part and the molar concentrations of water and oxygen at the outlet of the flow channel can be calculated. By solving in this progressive manner, the theoretical maximum oxygen mass transfer flux of each part can be obtained.

[0112] Step S05: Based on the theoretical maximum oxygen transfer mass of each part, calculate the theoretical limiting current density of the battery under the width of the flow channel.

[0113] Theoretical limiting current density I m The relationship between the theoretical maximum oxygen transfer mass of each part is shown in the following formula:

[0114]

[0115] Among them, R t It is the sum of the theoretical maximum oxygen mass transfer flux of each part; A act It is the activated area of ​​the battery.

[0116]

[0117] Step S06: Based on the theoretical limiting current density, adjust the flow channel width using an optimization method, return to step S02, and repeat steps S02 to S05 until the limiting current density no longer increases. At this point, the flow channel width corresponding to the maximum value of the limiting current density is the optimal flow channel width for the proton exchange membrane fuel cell. As an example, the optimization method is a single-parameter optimization method, including but not limited to ergodic methods, quadratic interpolation methods, Newton's iteration method, etc.

[0118] This embodiment uses the traversal method, traversing the channel width [0.1mm, 3mm], and solves the equation using MATLAB 2023a. The entire optimization cycle is 6.5 seconds. Figure 2 Figure (a) shows the curve of the limiting current density as a function of the channel width calculated by the method of the invention. As shown in the figure, the limiting current density first increases and then decreases with the increase of the channel width. The limiting current density reaches its maximum when the channel width is 1.3 mm, and the PEMFC performance is optimal. Therefore, the optimal channel width is determined to be 1.3 mm.

[0119] To verify the accuracy of the invention method, a three-dimensional PEMFC model was used to calculate the output current density of the PEMFC for different channel widths. Figure 2 Figure (b) shows the curve of PEMFC output current density versus channel width at a voltage of 0.3V. As shown in the figure, the output current density first increases and then decreases with the increase of channel width, reaching its maximum of 2.65A / cm when the channel width is 1.3mm. 2 The greater the deviation of the flow channel width from 1.3 mm, the lower the current density of the PEMFC and the worse the battery output performance. Under this PEMFC structure and flow rate, the single-channel PEMFC performs best when the flow channel width is 1.3 mm, which proves the reliability of the invented method.

[0120] In another embodiment, the fixed rib width is 1mm, and the rest is the same as in embodiment 1. Figure 3 Figure (a) shows the curve of the limiting current density as a function of the channel width calculated by the method of the invention. As shown in the figure, the limiting current density first increases and then decreases with the increase of the channel width. The limiting current density reaches its maximum when the channel width is 1.1 mm, and the PEMFC performance is optimal. Therefore, the optimal channel width is determined to be 1.1 mm. Figure 3 Figure (b) shows the curve of single-channel PEMFC output current density versus channel width when the terminal voltage is 0.3V. As shown in the figure, the output current density first increases and then decreases with the increase of channel width, reaching its maximum of 3.26A / cm when the channel width is 1.1mm. 2 The greater the deviation of the flow channel width from 1.1 mm, the lower the current density of the PEMFC and the worse the battery output performance. Under this PEMFC structure and flow rate, the single-channel PEMFC performs best when the flow channel width is 1.1 mm, which proves the reliability of the invented method.

[0121] In another embodiment, the fixed flow channel length is 70mm, and the rest is the same as in embodiment 1. Figure 4 Figure (a) shows the curve of the limiting current density as a function of the channel width calculated by the method of the invention. As shown in the figure, the limiting current density first increases and then decreases with the increase of the channel width. The limiting current density reaches its maximum when the channel width is 1.1 mm, and the PEMFC performance is optimal. Therefore, the optimal channel width is determined to be 1.1 mm. Figure 4 Figure (b) shows the curve of single-channel PEMFC output current density as a function of channel width when the terminal voltage is 0.3V. As shown in the figure, the output current density first increases and then decreases with the increase of channel width, reaching its maximum of 2.15A / cm when the channel width is 1.1mm. 2The greater the deviation of the flow channel width from 1.1 mm, the lower the current density of the PEMFC and the worse the battery output performance. Under this PEMFC structure and flow rate, the single-channel PEMFC performs best when the flow channel width is 1.1 mm, which proves the reliability of the invented method.

[0122] The above description is merely a representative embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope disclosed in the present invention, based on the technical solution and inventive concept of the present invention, shall fall within the scope of protection of the present invention.

Claims

1. A method for predicting an optimal flow channel width of a proton exchange membrane fuel cell, characterized by, The method comprises the following steps: S01, obtaining initial structural parameters and operating parameters of the proton exchange membrane fuel cell; S02, dividing the proton exchange membrane fuel cell into N The first part of the theoretical oxygen maximum mass transfer flux is calculated according to the oxygen molar concentration at the inlet of the flow channel, considering that the cell is in an extreme current working state, and the calculation formula is as follows: ； wherein, is the mass transfer flux of oxygen; is the channel height; is the oxygen diffusivity; is the gas diffusion layer thickness; is the molar concentration of oxygen in the cathode channel; is the effective diffusion coefficient of oxygen; A is the mass transfer area; Oxygen diffusivity Solving the general formula: ； wherein, D is the oxygen diffusion coefficient; Pe Pe is the Peclet number, which measures the relative importance of gas diffusion and convection in the flow channel; Vo is the oxygen flow rate in the flow channel; The effective oxygen diffusion coefficient is obtained by the following formula: ； wherein, is the porosity of the diffusion layer; P 0 and T 0 are the reference pressure and the reference temperature, respectively; P and T are the working pressure and the working temperature of the battery, respectively. S03. Calculate the molar concentration of water in the flow channel at the outlet of the first section and the molar concentration of oxygen in the flow channel at the outlet of the first section; calculate the molar concentration of oxygen in the flow channel at the outlet of the first section using the following equation : ； wherein, and represent the first i +1 section and the second i section cathode flow channel inlet oxygen concentration, respectively; and represent the first i +1 section and the second i section cathode flow channel inlet total gas flow, respectively, is the mass transfer flux of oxygen in the first i section. S04, taking the gas composition and flow rate at the outlet of the first part of the flow channel as the initial conditions at the inlet of the next part of the flow channel, and iteratively calculating to determine the maximum theoretical oxygen mass transfer flux of each part; S05, calculating the theoretical limiting current density of the current flow channel width based on the maximum theoretical oxygen mass transfer flux of each part; S06, adjusting the flow channel width based on the theoretical limiting current density, returning to step S02, and repeating steps S02 to S05 until the limiting current density no longer increases, at which time the flow channel width corresponding to the maximum limiting current density is the optimal flow channel width of the proton exchange membrane fuel cell.

2. The method of claim 1, wherein the optimal flow channel width is determined by the following equation: ###0001### where, L is the optimal flow channel width, h is the height of the flow channel, and w is the width of the flow channel. In step S01, the initial structural parameters of the cell include the flow channel width, rib width, flow channel height, bipolar plate thickness, gas diffusion layer thickness, catalyst layer thickness, and proton exchange membrane thickness, gas diffusion layer porosity, and catalyst layer porosity; the operating parameters include operating temperature, operating pressure, anode and cathode inlet gas humidity, and anode and cathode inlet gas flow rate.

3. The method of claim 1, wherein the optimal flow channel width is determined by the following equation: ###0001### where, L is the optimal flow channel width, h is the height of the flow channel, and w is the width of the flow channel. In step S02, the battery is divided into N parts in the passage direction N Any integer value greater than 0 can be taken, and the length of each part can be the same or different.

4. The method of claim 1, wherein the optimal flow channel width is determined by the following equation: ###0001### where, L is the optimal flow channel width, h is the height of the flow channel, and w is the width of the flow channel. In step S03, when calculating the water vapor concentration at the outlet of the first part and in the flow channel, the relationship between the water film transport flux, the water vapor diffusion flux, and the water generation flux is established based on the mass conservation of water vapor: ； ； ； ； wherein, is the production flux of water; is the electrochemical drag mass transfer flux of water; is the back-diffusion flux of water; is the diffusion flux of water vapor in the cathode gas diffusion layer; is the diffusion flux of water vapor in the anode gas diffusion layer; is the molar concentration of water vapor at the anode flow channel; is the molar concentration of water vapor at the cathode flow channel; q a is the total gas flow rate in the anode flow channel; q c is the total gas flow rate in the cathode flow channel; refers to the first part inlet, which is also the first part outlet; The electrochemical drag and back-diffusion of water in the membrane are considered, and the electrochemical drag mass transfer flux of water and the back-diffusion flux of water are calculated by the following equations, respectively: ； ； wherein, is the electrical drag coefficient; is the Faraday constant; I is the transference current density; is the dry film density; is the equivalent weight of the membrane; is the water diffusion coefficient in the membrane; is the water content of the membrane; is the gradient operator; transfer current density I is obtained from the equation: ； The Fick's law is used to describe the diffusion mass transfer of water vapor in the gas diffusion layer: ； ； wherein, , is the water vapor molar concentration at the cathode flow channel and the anode flow channel; , is the water vapor molar concentration at the cathode catalyst layer and the cathode flow channel; is the gas diffusion layer thickness; is the effective diffusion coefficient of water vapor in the gas diffusion layer; The water vapor generation flux is obtained based on the chemical reaction conservation formula: ； wherein, J as the mass transfer flux of oxygen; Part The gas flow rate at the partial inlet can be found from the equation: ； ； wherein, is the first i fraction of the water vapor diffusion flux in the cathode gas diffusion layer; is the first i fraction of the water vapor diffusion flux in the anode gas diffusion layer; is the first i fraction of the oxygen mass transfer flux; P and T are the operating pressure and the operating temperature of the cell, respectively; is the first i fraction of the hydrogen consumption in the anode flow channel, obtained from the following equation: 。 5. The method of claim 1, wherein the optimal flow channel width is determined by the following equation: ###0001### where, L is the optimal flow channel width, h is the height of the flow channel, and w is the width of the flow channel. In step S04, the initial conditions at the inlet of the next part of the flow channel include the flow rate of the cathode side and anode side flow channels, the water vapor mole fraction of the cathode side and anode side flow channels, and the oxygen mole fraction of the cathode side flow channel.

6. The method of claim 1, wherein, In step S04, considering two adjacent cell sections, the first i The gas composition and flow rate at the outlet of the section stream channel are taken as the initial conditions for the next section i +1 section stream channel inlet, from which the theoretical maximum oxygen mass transfer flux and the molar concentrations of water and oxygen at the outlet of the stream channel can be calculated, and so on, until the N section, the theoretical maximum oxygen mass transfer flux of each section.

7. The method of claim 1, wherein the optimal flow channel width is determined by the following equation: ###0001### where, L is the optimal flow channel width, h is the height of the flow channel, and w is the width of the flow channel. In step S05, the theoretical limiting current density The relationship between each portion of the theoretical maximum oxygen transfer capacity is shown by the following equation: ； wherein is the Faraday constant, A act is the active area of the battery, is the sum of the maximum oxygen mass transfer fluxes of each part, which is given by ； wherein is the first i mass transfer flux of oxygen.

8. The method of claim 1, wherein the optimal flow channel width is determined by the following equation: ###0001### where, L is the optimal flow channel width, h is the height of the flow channel, and w is the width of the flow channel. In step S06, the optimization method is a single-parameter optimization method, including but not limited to the exhaustive method, the quadratic interpolation method, and the Newton iteration method.

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