CN115882016A - Estimation method for water content distribution of proton exchange membrane fuel cell membrane - Google Patents

Abstract

The invention discloses a method for estimating the water content distribution of a proton exchange membrane fuel cell membrane, comprising the following steps: Step 1, connecting experimental equipment: a single-chip fuel cell, a multi-sensor PCB board with temperature and current density measurements required, and fuel cell testing The platforms are connected together through connecting wires; step 2, preheating the fuel cell: preheating the fuel cell to the temperature required for the test; the present invention analyzes the different dimensions of the measured data of the PCB board by recording voltage, current, current density and temperature data, and adopts The interpolation algorithm expands the measured data to the same data dimension, so that the data at the same position in the plane corresponds to each other; calculate the ohmic loss at each position in the plane according to the relationship between each loss of the fuel cell output voltage expression and the temperature and current density, And the distribution characteristics of the water content in the plane of the fuel cell are obtained through the relationship expression between it and the water content of the membrane.

Description

Estimation Method of Water Content Distribution in Proton Exchange Membrane Fuel Cells

Technical Field

The invention relates to the field of proton exchange membrane fuel cells, in particular to a method for estimating water content distribution of a proton exchange membrane fuel cell membrane.

Background Art

As an energy conversion device, proton exchange membrane fuel cells produce water through the electrochemical reaction of hydrogen and oxygen, converting chemical energy into electrical energy and thermal energy. Proton exchange membrane fuel cells are a nonlinear complex system coupled with multiple physical fields. Their operation process involves multiple physical field coupling phenomena such as heat, electricity, and fluid (gas, liquid). Their output performance is comprehensively affected by parameters such as load current, operating temperature, reaction gas flow, and membrane water content. Water inside the fuel cell is not only a product, it can also be used to humidify the reaction gas and proton exchange membrane. During the operation of the proton exchange membrane fuel cell, an appropriate amount of water can reduce the internal resistance of the membrane and thus improve the output performance. Excessive water will occupy the pores of the gas diffusion layer, block the flow channel, etc., thereby hindering the transmission of the reaction gas and reducing the output performance. A small amount of water will make it difficult to wet the proton exchange membrane. The increase in membrane resistance reduces the output performance. During the operation of the fuel cell, water management failures are closely related to the internal water content. Water flooding and membrane drying are the most common types of failures. The causes are related to the operating current level, the humidity of the reaction gas, temperature, gas flow, drainage cycle, etc., which are manifested as a decrease in fuel cell output performance and voltage fluctuations. In addition, serious water management failures will cause irreversible output performance degradation and internal structural damage, reducing the remaining service life. Therefore, in the actual operation of the proton exchange membrane fuel cell system, it is very important to quickly and accurately evaluate the internal water content and operate it in the appropriate water content range to maintain stability, enhance durability and extend the operating life. In the commercialization process in recent years, proton exchange membrane fuel cells have achieved rapid development in large size and high power characteristics. For large-size fuel cells, the distribution and local characteristics of water content in the plane will affect its output performance and service life. Therefore, it is of great significance to explore the distribution of membrane water content in the fuel cell plane to avoid local water management failures during operation.

Among the existing fuel cell water content assessment methods, model-based methods are very common. This method establishes a one-dimensional mechanism model or a semi-empirical and semi-mechanistic model of a proton exchange membrane fuel cell, and verifies the accuracy of the model through experimental data such as output voltage and impedance spectrum; based on the relationship between the model and the membrane water content, the voltage response or impedance spectrum is used to reflect the changes in the membrane water content inside the fuel cell during operation. In addition, a two-dimensional/three-dimensional fuel cell mechanism model is established with the help of simulation software to simulate the distribution characteristics of the water content inside the fuel cell, and a real-time simulation is constructed to evaluate the changes in the internal water content and the transmission process of liquid water. The experimental detection method is also applied to the water content assessment of the fuel cell. During operation, the changes in the inlet and outlet pressure drops of the fuel cell reaction gas can reflect the internal water content characteristics in real time, and mainly reflect the water content in the flow field. Visualization experiments such as neutron imaging, direct imaging, nuclear magnetic resonance imaging and X-ray scanning imaging can observe the distribution characteristics of the water content in the plane.

However, the traditional method for estimating the water content distribution of fuel cell membranes has the following disadvantages:

(1) The method based on the one-dimensional model only estimates the water content characteristics perpendicular to the plane, and does not consider the distribution of water content at different positions in the fuel cell plane; the multi-dimensional model has the disadvantages of long simulation time, high requirements for computing equipment, and difficulty in experimental verification.

(2) The experimental method of pressure drop has difficulties in characterizing the distribution of water content in a plane; for visualization experiments, experimental testing is expensive, technically demanding, and costly.

Summary of the invention

The purpose of the present invention is to provide a method for estimating the water content distribution of a proton exchange membrane fuel cell membrane, so as to solve the problem that the method based on a one-dimensional model proposed in the above background technology only estimates the water content characteristics perpendicular to the plane, and does not consider the water content distribution at different positions in the fuel cell plane; the multi-dimensional model has the disadvantages of long simulation time, high requirements for computing equipment and difficulty in experimental verification, and the experimental method of pressure drop is difficult to characterize the water content distribution in the plane; for visualization experiments, the experimental test is expensive, the technical requirements are high and the cost is high.

To achieve the above object, the present invention provides the following technical solution: A method for estimating the water content distribution of a proton exchange membrane fuel cell membrane, comprising the following steps:

Step 1: Connect the experimental equipment: the monolithic fuel cell, the multi-sensor PCB board required for temperature and current density measurement, and the fuel cell test platform are connected together through connecting wires;

Step 2: Preheat the fuel cell: preheat the fuel cell to the temperature required for the test;

Step 3, loading current: Load current to perform steady-state performance test until the output voltage of the fuel cell drops sharply or even reaches 0, then stop loading;

Step 4: Record voltage and current: Record the output voltage and total output current of the fuel cell, and record the current density and temperature data of each sensor through the data acquisition device of the PCB board for subsequent analysis;

Step 5: Current density and temperature data analysis: The data collected by the PCB board during the fuel cell operation test is expressed in sequence in the form of a data matrix. The expressions of current density and temperature distribution data are:

为使插值后的温度分布数据尽量维持原始数据的分布特性，采用数据标准差量化分别量化插值前后的温度分布均匀性，并根据该值作为反馈调整插值算法，以选出更好的插值算法，测量温度数据的标准差为：

插值计算后温度数据的标准差为：Step 6: Use interpolation algorithm to expand the data dimension: Use interpolation algorithm to expand the data dimension, and perform interpolation calculation on the temperature distribution data by piecewise cubic Hermite interpolation, including inward interpolation and outward interpolation. The expanded temperature distribution expression is:

In order to make the interpolated temperature distribution data maintain the distribution characteristics of the original data as much as possible, the data standard deviation is used to quantify the uniformity of the temperature distribution before and after interpolation, and the interpolation algorithm is adjusted based on this value as feedback to select a better interpolation algorithm. The standard deviation of the measured temperature data is:

The standard deviation of the temperature data after interpolation is:

Step 7. One-to-one correspondence of data: The local current density and temperature data correspond one-to-one. After interpolation calculation, the temperature distribution data matrix is expanded to have the same dimension as the current density distribution data matrix. A position function f is set to represent the current density and temperature at the position. Its expression is:

f(a,b)=(i _a,b ,t _a,b ),1≤a≤m,1≤b≤n(6);

阳极、阴极的活化损耗表达式为：

欧姆损耗的经验表达式为：

浓差损耗的表达式为：Step 8: Construct a semi-empirical model: Construct a semi-empirical model of the fuel cell output voltage. The output voltage is expressed as: U = E _rev -η _act -η _ohm -η _conc (7). The thermodynamic reversible voltage is expressed by the Nernst equation:

The activation loss expressions of anode and cathode are:

The empirical expression for ohmic loss is:

The expression of concentration loss is:

式中，ξ为水含量，j为电流密度，T为温度，δ_mem为膜厚度，A为膜电极活性面积，η_ohm为活化损耗；对于燃料电池而言，平面内各位置输出电压相同。根据步骤五中不同位置处电流密度、温度分布，结合步骤六中输出电压模型中与电流密度、温度相关的表达式，可以将不同位置处的电压表示为：U＝U(a,b)＝E_rev(a,b)-η_act,a(a,b)-η_act,c(a,b)-η_ohm(a,b)-η_conc(a,b)(13)，由步骤六中式(10)可知，水含量与欧姆损耗相关，于是测量位置处的欧姆损耗可以表示为：η_ohm(a,b)＝E_rev(a,b)-U-η_act,a(a,b)-η_act,c(a,b)-η_conc(a,b)(14)，由此可知，不同位置处的欧姆损耗在电流密度、温度分布不均匀的情况下并不相同，因此，平面内各位置处的膜水含量存在差异，则式(12)可改写为：ξ(a,b)＝g(η(a,b),f(a,b))(15)，将步骤五中式(6)的电流密度、温度分布数据f(a,b)代入涉及步骤六、步骤七的式(8-15)中，计算出PCB板测量燃料电池平面内不同位置处的水含量数据，从而得到内部水含量的分布特征。Step 9: Reverse the water content: Rewrite the water content into an expression of ohmic loss, and reverse the distribution of water content in the plane. Rewrite equation (10) in step 6 as:

Where ξ is the water content, j is the current density, T is the temperature, δ _mem is the membrane thickness, A is the membrane electrode active area, and η _ohm is the activation loss. For fuel cells, the output voltage at each position in the plane is the same. According to the current density and temperature distribution at different positions in step 5, combined with the expressions related to current density and temperature in the output voltage model in step 6, the voltage at different positions can be expressed as: U = U (a, b) = E _rev (a, b) - η _{act, a} (a, b) - _{η act, c} (a, b) - _{η ohm} (a, b) - _{η conc} (a, b) (13). From equation (10) in step 6, it can be seen that the water content is related to the ohmic loss, so the ohmic loss at the measurement position can be expressed as: η _ohm (a, b) = E _rev (a, b) - U - η _{act, a} (a, b) - _{η act, c} (a, b) - _{η conc} (a, b)(14), it can be seen that the ohmic loss at different positions is not the same when the current density and temperature distribution are not uniform. Therefore, there are differences in the membrane water content at various positions in the plane. Then equation (12) can be rewritten as: ξ(a, b) = g(η(a, b), f(a, b))(15), the current density and temperature distribution data f(a, b) of equation (6) in step 5 are substituted into equations (8-15) involving steps 6 and 7, and the water content data at different positions in the plane of the fuel cell measured by the PCB board are calculated, thereby obtaining the distribution characteristics of the internal water content.

As a preferred technical solution of the present invention, the increment of current loading in step three is 50 mA/cm ² or 100 mA/cm ² .

As a preferred technical solution of the present invention, in the formulas (1) and (2) in step 5, m, n, j, l in the following table represent the positions of the corresponding sensors, k represents the test time sequence, i represents the current density (unit mA/cm ² ), and T, t represent the temperature (unit ° C).

As a preferred technical solution of the present invention, in the formulas (4) and (5) in step six, s is the standard deviation describing the uniformity of distribution, E represents the average value of the distribution data, the subscripts real and interp represent the actual measured data and the data after interpolation calculation, respectively, and the subscripts a and b represent the sampling positions of the local temperature in the distribution data.

As a preferred technical solution of the present invention, in formula (6) in step seven, a and b represent position coordinates, and i and t represent current density and temperature values at the position.

As a preferred technical solution of the present invention, in formula (7) in step eight, U is the output voltage of the single fuel cell, and E _rev , η _act , η _ohm , and η _conc are reversible voltage, activation loss, ohmic loss, and concentration loss, respectively.

Compared with the prior art, the present invention has the following beneficial effects:

1. By recording the voltage, current, current density and temperature data, we analyze the different dimensions of the PCB board measurement data, and use the interpolation algorithm to expand the measurement data to the same data dimension, so that the data at the same position in the plane correspond one to one;

2. Calculate the ohmic loss at each position in the plane based on the relationship between each loss and temperature and current density in the fuel cell output voltage expression, and obtain the distribution characteristics of the water content in the fuel cell plane through the expression of its relationship with the membrane water content;

3. The voltage at each position in the plane of the fuel cell is equal. Combine it with the one-dimensional fuel cell output voltage model, substitute the distribution data of current density and temperature to calculate the ohmic loss at different positions; calculate the water content corresponding to each position through the relationship between ohmic loss and membrane water content, and reversely infer the distribution characteristics of membrane water content in the plane, so as to estimate the membrane water content in the plane and solve the problem of its difficulty in observation.

BRIEF DESCRIPTION OF THE DRAWINGS

Fig. 1 is a flow chart of the present invention;

FIG2 is a diagram showing the positions of the fuel cell assembly and the PCB board of the present invention;

FIG3 is a schematic diagram of a test system of the present invention;

FIG4 is a graph showing the performance test of a fuel cell according to the present invention;

FIG5 is a temperature distribution diagram before and after interpolation calculation of the present invention;

FIG6 is a thermal diagram of current density and temperature distribution according to the present invention;

FIG. 7 is a diagram showing the distribution of water content in the plane of the fuel cell of the present invention.

DETAILED DESCRIPTION

The following will be combined with the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

Referring to FIGS. 1-7 , the present invention provides a method for estimating the water content distribution of a proton exchange membrane fuel cell membrane, comprising the following steps:

Step 1: Connect the experimental equipment: the monolithic fuel cell, the multi-sensor PCB board required for temperature and current density measurement, and the fuel cell test platform are connected together through connecting wires;

Step 2: Preheat the fuel cell: preheat the fuel cell to the temperature required for the test;

Step 3, loading current: Load current to perform steady-state performance test until the output voltage of the fuel cell drops sharply or even reaches 0, then stop loading;

Step 4: Record voltage and current: Record the output voltage and total output current of the fuel cell, and record the current density and temperature data of each sensor through the data acquisition device of the PCB board for subsequent analysis;

Step 5: Current density and temperature data analysis: The data collected by the PCB board during the fuel cell operation test is expressed in sequence in the form of a data matrix. The expressions of current density and temperature distribution data are:

为使插值后的温度分布数据尽量维持原始数据的分布特性，采用数据标准差量化分别量化插值前后的温度分布均匀性，并根据该值作为反馈调整插值算法，以选出更好的插值算法，测量温度数据的标准差为：

插值计算后温度数据的标准差为：Step 6: Use interpolation algorithm to expand the data dimension: Use interpolation algorithm to expand the data dimension, and perform interpolation calculation on the temperature distribution data by piecewise cubic Hermite interpolation, including inward interpolation and outward interpolation. The expanded temperature distribution expression is:

In order to make the interpolated temperature distribution data maintain the distribution characteristics of the original data as much as possible, the data standard deviation is used to quantify the uniformity of the temperature distribution before and after interpolation, and the interpolation algorithm is adjusted based on this value as feedback to select a better interpolation algorithm. The standard deviation of the measured temperature data is:

The standard deviation of the temperature data after interpolation is:

Step 7. One-to-one correspondence of data: The local current density and temperature data correspond one-to-one. After interpolation calculation, the temperature distribution data matrix is expanded to have the same dimension as the current density distribution data matrix. A position function f is set to represent the current density and temperature at the position. Its expression is:

f(a,b)=(i _a,b ,t _a,b ),1≤a≤m,1≤b≤n(6);

阳极、阴极的活化损耗表达式为：

欧姆损耗的经验表达式为：

浓差损耗的表达式为：Step 8: Construct a semi-empirical model: Construct a semi-empirical model of the fuel cell output voltage. The output voltage is expressed as: U = E _rev -η _act -η _ohm -η _conc (7). The thermodynamic reversible voltage is expressed by the Nernst equation:

The activation loss expressions of anode and cathode are:

The empirical expression for ohmic loss is:

The expression of concentration loss is:

Step 9: Reverse the water content: Rewrite the water content into an expression of ohmic loss, and reverse the distribution of water content in the plane. Rewrite equation (10) in step 6 as:

式中，ξ为水含量，j为电流密度，T为温度，δ_mem为膜厚度，A为膜电极活性面积，η_ohm为活化损耗；对于燃料电池而言，平面内各位置输出电压相同。根据步骤五中不同位置处电流密度、温度分布，结合步骤六中输出电压模型中与电流密度、温度相关的表达式，可以将不同位置处的电压表示为：U＝U(a,b)＝E_rev(a,b)-η_act,a(a,b)-η_act,c(a,b)-η_ohm(a,b)-η_conc(a,b)(13)，由步骤六中式(10)可知，水含量与欧姆损耗相关，于是测量位置处的欧姆损耗可以表示为：η_ohm(a,b)＝E_rev(a,b)-U-η_act,a(a,b)-η_act,c(a,b)-η_conc(a,b)(14)，由此可知，不同位置处的欧姆损耗在电流密度、温度分布不均匀的情况下并不相同，因此，平面内各位置处的膜水含量存在差异，则式(12)可改写为：ξ(a,b)＝g(η(a,b),f(a,b))(15)，将步骤五中式(6)的电流密度、温度分布数据f(a,b)代入涉及步骤六、步骤七的式(8-15)中，计算出PCB板测量燃料电池平面内不同位置处的水含量数据，从而得到内部水含量的分布特征。

Where ξ is the water content, j is the current density, T is the temperature, δ _mem is the membrane thickness, A is the membrane electrode active area, and η _ohm is the activation loss. For fuel cells, the output voltage at each position in the plane is the same. According to the current density and temperature distribution at different positions in step 5, combined with the expressions related to current density and temperature in the output voltage model in step 6, the voltage at different positions can be expressed as: U = U (a, b) = E _rev (a, b) - η _{act, a} (a, b) - _{η act, c} (a, b) - _{η ohm} (a, b) - _{η conc} (a, b) (13). From equation (10) in step 6, it can be seen that the water content is related to the ohmic loss, so the ohmic loss at the measurement position can be expressed as: η _ohm (a, b) = E _rev (a, b) - U - η _{act, a} (a, b) - _{η act, c} (a, b) - _{η conc} (a, b)(14), it can be seen that the ohmic loss at different positions is not the same when the current density and temperature distribution are not uniform. Therefore, there are differences in the membrane water content at various positions in the plane. Then equation (12) can be rewritten as: ξ(a, b) = g(η(a, b), f(a, b))(15), the current density and temperature distribution data f(a, b) of equation (6) in step 5 are substituted into equations (8-15) involving steps 6 and 7, and the water content data at different positions in the plane of the fuel cell measured by the PCB board are calculated, thereby obtaining the distribution characteristics of the internal water content.

The increment of current loading in step 3 is 50 mA/cm ² or 100 mA/cm ² .

In step 5, in equations (1) and (2), m, n, j, and l in the following table represent the positions of the corresponding sensors, k represents the test time sequence, i represents the current density (unit: mA/cm ² ), and T and t represent the temperature (unit: ° C).

In step 6, in equations (4) and (5), s is the standard deviation describing the uniformity of the distribution, E represents the average value of the distribution data, subscripts real and interp represent the actual measured data and the data after interpolation calculation, respectively, and subscripts a and b represent the sampling positions of the local temperature in the distribution data.

In step 7, in formula (6), a and b represent the position coordinates, and i and t represent the current density and temperature values at the position.

In step eight, in formula (7), U is the output voltage of the single fuel cell, and E _rev , η _act , η _ohm , and η _conc are the reversible voltage, activation loss, ohmic loss, and concentration loss, respectively.

采用插值算法对数据维度进行扩展，分段三次Hermite插值对温度分布数据进行插值计算，包括向内插值与向外插值，扩展后的温度分布表达式为：

为使插值后的温度分布数据尽量维持原始数据的分布特性，采用数据标准差量化分别量化插值前后的温度分布均匀性，并根据该值作为反馈调整插值算法，以选出更好的插值算法，测量温度数据的标准差为：

插值计算后温度数据的标准差为：

局部电流密度、温度数据一一对应，插值计算后，温度分布数据矩阵扩展为与电流密度分布数据矩阵具有相同的维度，设置一个位置函数f表示该位置处的电流密度、温度，其表达式为：f(a,b)＝(i_a,b,t_a,b),1≤a≤m,1≤b≤n(6)，构建燃料电池输出电压的半经验模型，输出电压的表达式为：U＝E_rev-η_act-η_ohm-η_conc(7)，热力学可逆电压通过能斯特方程表示：

(8)，阳极、阴极的活化损耗表达式为：

欧姆损耗的经验表达式为：

浓差损耗的表达式为：

水含量改写为欧姆损耗的表达式，反推平面内水含量分布，将式(10)改写为：

式中，ξ为水含量，j为电流密度，T为温度，δ_mem为膜厚度，A为膜电极活性面积，η_ohm为活化损耗；对于燃料电池而言，平面内各位置输出电压相同。根据步骤五中不同位置处电流密度、温度分布，结合输出电压模型中与电流密度、温度相关的表达式，可以将不同位置处的电压表示为：U＝U(a,b)＝E_rev(a,b)-η_act,a(a,b)-η_act,c(a,b)-η_ohm(a,b)-η_conc(a,b)(13)，由式(10)可知，水含量与欧姆损耗相关，于是测量位置处的欧姆损耗可以表示为：η_ohm(a,b)＝E_rev(a,b)-U-η_act,a(a,b)-η_act,c(a,b)-η_conc(a,b)(14)，由此可知，不同位置处的欧姆损耗在电流密度、温度分布不均匀的情况下并不相同，因此，平面内各位置处的膜水含量存在差异，则式(12)可改写为：ξ(a,b)＝g(η(a,b),f(a,b))(15)，将(6)的电流密度、温度分布数据f(a,b)代入式(8-15)中，计算出PCB板测量燃料电池平面内不同位置处的水含量数据，从而得到内部水含量的分布特征。When the present invention is used: a monolithic fuel cell, a multi-sensor PCB board with temperature and current density measurement and a fuel cell test platform are connected together through a connecting line, and the PCB board is located between the flow field plate and the current acquisition board. Before the test, the fuel cell is preheated to the temperature required for the test; then the current is loaded to perform a steady-state performance test, i.e., a polarization curve test. The increment of current loading is selected to be a suitable value, usually 50mA/ ^cm2 or 100mA/ ^cm2 , until the output voltage of the fuel cell drops sharply or even reaches 0, then the loading is stopped, the test is ended, the output voltage and total output current of the fuel cell are recorded, and the current density and temperature data of each sensor are recorded through the data acquisition device of the PCB board for subsequent analysis. The data collected by the PCB board during the fuel cell operation test is sequentially represented in the form of a data matrix, and the expressions of the current density and temperature distribution data are respectively:

The interpolation algorithm is used to expand the data dimension, and the temperature distribution data is interpolated by piecewise cubic Hermite interpolation, including inward interpolation and outward interpolation. The expanded temperature distribution expression is:

In order to make the interpolated temperature distribution data maintain the distribution characteristics of the original data as much as possible, the data standard deviation is used to quantify the uniformity of the temperature distribution before and after interpolation, and the interpolation algorithm is adjusted based on this value as feedback to select a better interpolation algorithm. The standard deviation of the measured temperature data is:

The standard deviation of the temperature data after interpolation is:

The local current density and temperature data correspond one to one. After interpolation calculation, the temperature distribution data matrix is expanded to have the same dimension as the current density distribution data matrix. A position function f is set to represent the current density and temperature at the position. Its expression is: f(a,b)＝(i _a,b ,t _a,b ),1≤a≤m,1≤b≤n(6). A semi-empirical model of the fuel cell output voltage is constructed. The expression of the output voltage is: U＝E _rev -η _act -η _ohm -η _conc (7). The thermodynamic reversible voltage is expressed by the Nernst equation:

(8), the activation loss expressions of anode and cathode are:

The empirical expression for ohmic loss is:

The expression of concentration loss is:

The water content is rewritten as an expression of ohmic loss, and the distribution of water content in the plane is reversed, and equation (10) is rewritten as:

Where ξ is the water content, j is the current density, T is the temperature, δ _mem is the membrane thickness, A is the membrane electrode active area, and η _ohm is the activation loss. For fuel cells, the output voltage at each position in the plane is the same. According to the current density and temperature distribution at different positions in step 5, combined with the expressions related to current density and temperature in the output voltage model, the voltage at different positions can be expressed as: U = U (a, b) = E _rev (a, b) - η _{act, a} (a, b) _{- η act, c} (a, b) - _{η ohm} (a, b) - _{η conc} (a, b) (13). From formula (10), it can be seen that the water content is related to the ohmic loss, so the ohmic loss at the measurement position can be expressed as: η _ohm (a, b) = E _rev (a, b) - U - η _{act, a} (a, b) - _{η act, c} (a, b) - η _conc (a, b)(14), it can be seen that the ohmic loss at different positions is not the same when the current density and temperature distribution are not uniform. Therefore, there are differences in the membrane water content at different positions in the plane. Then equation (12) can be rewritten as: ξ(a, b) = g(η(a, b), f(a, b))(15), substituting the current density and temperature distribution data f(a, b) in (6) into equation (8-15), the water content data at different positions in the plane of the fuel cell measured by the PCB board are calculated, and the distribution characteristics of the internal water content are obtained.

Although the present invention has been described in detail with reference to the aforementioned embodiments, it is still possible for those skilled in the art to modify the technical solutions described in the aforementioned embodiments, or to make equivalent substitutions for some of the technical features therein. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims (6)

1. A method for estimating the water content distribution of a proton exchange membrane fuel cell membrane, characterized in that it comprises the following steps: Step 1: Connect the experimental equipment: the monolithic fuel cell, the multi-sensor PCB board required for temperature and current density measurement, and the fuel cell test platform are connected together through connecting wires; Step 2: Preheat the fuel cell: preheat the fuel cell to the temperature required for the test; Step 3, loading current: Load current to perform steady-state performance test until the output voltage of the fuel cell drops sharply or even reaches 0, then stop loading; Step 4: Record voltage and current: Record the output voltage and total output current of the fuel cell, and record the current density and temperature data of each sensor through the data acquisition device of the PCB board for subsequent analysis; Step 5: Current density and temperature data analysis: The data collected by the PCB board during the fuel cell operation test is expressed in sequence in the form of a data matrix. The expressions of current density and temperature distribution data are:

Step 6: Use interpolation algorithm to expand the data dimension: Use interpolation algorithm to expand the data dimension, and perform interpolation calculation on the temperature distribution data by piecewise cubic Hermite interpolation, including inward interpolation and outward interpolation. The expanded temperature distribution expression is:

In order to make the interpolated temperature distribution data maintain the distribution characteristics of the original data as much as possible, the data standard deviation is used to quantify the uniformity of the temperature distribution before and after interpolation, and the interpolation algorithm is adjusted based on this value as feedback to select a better interpolation algorithm. The standard deviation of the measured temperature data is:

The standard deviation of the temperature data after interpolation is:

Step 7, one-to-one correspondence of data: The local current density and temperature data are one-to-one correspondence. After interpolation calculation, the temperature distribution data matrix is expanded to have the same dimension as the current density distribution data matrix. A position function f is set to represent the current density and temperature at the position. Its expression is: f(a,b)＝(i _a,b ,t _a,b ),1≤a≤m,1≤b≤n(6); Step 8: Construct a semi-empirical model: Construct a semi-empirical model of the fuel cell output voltage. The output voltage is expressed as: U = E _rev -η _act -η _ohm -η _conc (7). The thermodynamic reversible voltage is expressed by the Nernst equation:

The activation loss expressions of anode and cathode are:

The empirical expression for ohmic loss is:

The expression of concentration loss is:

Step 9: Reverse the water content: Rewrite the water content into an expression of ohmic loss, and reverse the distribution of water content in the plane. Rewrite equation (10) in step 6 as:

Wherein, ξ is the water content, j is the current density, T is the temperature, δ _mem is the membrane thickness, A is the membrane electrode active area, and η _ohm is the activation loss. For a fuel cell, the output voltage at each position in the plane is the same. According to the current density and temperature distribution at different positions in step 5, combined with the expressions related to current density and temperature in the output voltage model in step 6, the voltage at different positions can be expressed as: U = U (a, b) = E _rev (a, b) - η _{act, a} (a, b) - _{η act, c} (a, b) - _{η ohm} (a, b) _{- η conc} (a, b) (13). It can be seen from formula (10) in step 6 that the water content is related to the ohmic loss, so the ohmic loss at the measurement position can be expressed as: η _ohm (a, b) = E _rev (a, b) - U - η _{act, a} (a, b) - _{η act, c} (a, b) - _{η conc} (a, b)(14), it can be seen that the ohmic loss at different positions is not the same when the current density and temperature distribution are not uniform. Therefore, there are differences in the membrane water content at various positions in the plane, and equation (12) can be rewritten as: ξ(a, b) = g(η(a, b), f(a, b))(15), the current density and temperature distribution data f(a, b) of equation (6) in step 5 are substituted into equations (8-15) involving steps 6 and 7, and the water content data at different positions in the plane of the fuel cell measured by the PCB board are calculated, thereby obtaining the distribution characteristics of the internal water content. 2 . The method for estimating membrane water content distribution of a proton exchange membrane fuel cell according to claim 1 , wherein the increment of current loading in step 3 is 50 mA/cm ² or 100 mA/cm ² . 3 . 3. The method for estimating the membrane water content distribution of a proton exchange membrane fuel cell according to claim 1, characterized in that: in the formulas (1) and (2) in step 5, m, n, j, l in the following table represent the positions of the corresponding sensors, k represents the test time series, i represents the current density (unit mA/ ^cm2 ), and T, t represent the temperature (unit °C). 4. The method for estimating the water content distribution of a proton exchange membrane fuel cell according to claim 1 is characterized in that: in the formulas (4) and (5) in step 6, s is the standard deviation describing the uniformity of the distribution, E represents the average value of the distribution data, the subscripts real and interp represent the actual measured data and the data after interpolation calculation, respectively, and the subscripts a and b represent the sampling positions of the local temperature in the distribution data. 5. The method for estimating the water content distribution of a proton exchange membrane fuel cell according to claim 1, characterized in that: in the formula (6) in step seven, a and b represent position coordinates, and i and t represent the current density and temperature values at the position. 6. The method for estimating the membrane water content distribution of a proton exchange membrane fuel cell according to claim 1, characterized in that: in the formula (7) in step eight, U is the output voltage of the monolithic fuel cell, and E _rev , η _act , η _ohm , and η _conc are the reversible voltage, activation loss, ohmic loss, and concentration loss, respectively.

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