Electric drag coefficient measuring device and method

Abstract

The invention relates to an electric drag coefficient measuring device and method. The device is applied to a to-be-tested membrane electrode and comprises a clamping unit, a dew-point instrument, a heating unit, an anode ventilation pipeline and a cathode ventilation pipeline, and the to-be-tested membrane electrode is mounted in the clamping unit; the anode ventilation pipeline and the cathode ventilation pipeline penetrate through the clamping unit, and the areas, located in the clamping unit, of the two ventilation pipelines are straight flow channels and are tightly attached to the surfaces of the two sides of the membrane electrode to be detected respectively. The dew-point instruments are arranged at the air inlet end and the air outlet end of the anode ventilation pipeline and the air inlet end of the cathode ventilation pipeline; and the heating unit wraps the outer wall of the ventilation pipeline between the dew-point instrument and the clamping unit. Compared with the prior art, the method has the advantages that the electric drag coefficient of the proton exchange membrane under different working temperatures and humidity can be quickly and accurately measured, and the like.

Description

Technical Field

[0001] The present invention relates to the field of proton exchange membrane fuel cells, and particularly to a device and method for measuring the electroosmotic drag coefficient. Background Art

[0002] A fuel cell can convert the chemical energy in fuel into electrical energy through an electrochemical reaction, and is an important device for realizing the efficient utilization of hydrogen energy. As the core component of a fuel cell, a membrane electrode is mainly composed of laminated materials with different functions such as a gas diffusion layer, a catalytic layer, and a proton exchange membrane. Its water content plays a crucial role in the performance of the fuel cell. When the water content in the membrane electrode is too high, a flooding phenomenon will occur in the flow channel, thereby reducing the performance of a single cell; when the water content in the membrane electrode is too low, the resistance of the proton exchange membrane will increase, thereby reducing the performance of a single cell. The distribution of water in the membrane electrode is mainly affected by the electroosmotic drag performance, diffusion performance of the proton exchange membrane on water molecules, and the pressure difference between the anode and cathode sides. Among them, the electroosmotic drag performance of the proton exchange membrane on water molecules needs to be tested under discharge conditions. Since the amount of water migration obtained during the measurement not only comes from the electroosmotic drag process, but may also come from the diffusion process, the pressure difference process, etc., how to use a reasonable test device and test conditions to quickly and accurately measure the electroosmotic drag coefficient of the proton exchange membrane at different working temperatures and humidities has become a problem to be solved in this field. Summary of the Invention

[0003] The purpose of the present invention is to provide a device and method for measuring the electroosmotic drag coefficient to overcome the defects of long measurement time and inaccurate measurement results of the electroosmotic drag coefficient of the proton exchange membrane existing in the above prior art.

[0004] The purpose of the present invention can be achieved by the following technical solutions:

[0005] According to a first aspect of the present invention, there is provided a device for measuring the electroosmotic drag coefficient, which is applied to a membrane electrode to be tested. The device includes a clamping unit, and the membrane electrode to be tested is installed inside the clamping unit. The device further includes a dew point meter, a heating unit, an anode ventilation pipeline, and a cathode ventilation pipeline.

[0006] The anode ventilation pipeline and the cathode ventilation pipeline penetrate through the clamping unit. The regions of the two ventilation pipelines inside the clamping unit are both straight channels and are respectively closely attached to the two side surfaces of the membrane electrode to be tested.

[0007] The dew point meter is arranged at the inlet end and the outlet end of the anode ventilation pipeline, and the inlet end of the cathode ventilation pipeline.

[0008] The heating unit is wrapped around the outer wall of the ventilation pipeline between the dew point meter and the clamping unit.

[0009] As a preferred technical solution, the membrane electrode to be measured includes a first half membrane electrode, a proton exchange membrane, and a second half membrane electrode that are tightly attached to each other from top to bottom in sequence.

[0010] As a preferred technical solution, the gas flow field of the clamping unit is a parallel direct current field.

[0011] As a preferred technical solution, the straight-line length of the direct current field is 0.5 cm to 2 cm.

[0012] As a preferred technical solution, the heating unit includes a heating jacket and a heat preservation jacket.

[0013] As a preferred technical solution, a dew point meter is provided at the gas outlet end of the cathode ventilation pipeline.

[0014] As a preferred technical solution, the lengths of the contact areas of the anode ventilation pipeline and the cathode ventilation pipeline with the membrane electrode to be measured are both less than or equal to the length of the membrane electrode to be measured.

[0015] According to the second aspect of the present invention, there is provided a method for measuring the electroosmotic drag coefficient. The method is implemented by using the device, and includes the following steps:

[0016] S1, introducing hydrogen into the anode ventilation pipeline and introducing air into the cathode ventilation pipeline;

[0017] S2, heating the anode ventilation pipeline and the cathode ventilation pipeline to a preset temperature;

[0018] S3, discharging the membrane electrode to be measured at a fixed working current density, and controlling the dew point value and inlet air pressure value of the inlet end of the anode ventilation pipeline to be consistent with the dew point value and inlet air pressure value of the inlet end of the cathode ventilation pipeline, recording the readings of the dew point meters at the inlet end and outlet end of the anode ventilation pipeline, and obtaining the dry gas inlet gas pressure, dry gas inlet flow rate, moisture partial pressure in the inlet gas, and moisture partial pressure in the outlet gas;

[0019] S4, calculating the electroosmotic drag coefficient of the membrane electrode to be measured according to the dry gas inlet gas pressure, the dry gas inlet flow rate, the moisture partial pressure in the inlet gas, and the moisture partial pressure in the outlet gas.

[0020] As a preferred technical solution, the process of controlling the dew point value and inlet air pressure value of the inlet end of the anode ventilation pipeline to be consistent with the dew point value and inlet air pressure value of the inlet end of the cathode ventilation pipeline is achieved through a thermocouple, a heating jacket, a heat preservation jacket, a pressure sensor, and a back pressure valve, and the dry gas inlet flow rate is obtained through a mass flow controller.

[0021] As a preferred technical solution, the calculation formula for the electroosmotic drag coefficient is:

[0022]

[0023] In the formula, n T,RH represents the electro-osmotic drag coefficient, F is the Faraday constant, J is the operating current density of the fuel cell, A is the surface area of the membrane electrode catalyst layer, R is the ideal gas constant, T is the operating temperature, and P dry is the dry gas inlet pressure; Q An,in is the dry gas inlet flow rate; P An,in is the saturation vapor pressure of water obtained by looking up the table according to the reading of the dew point meter at the anode inlet end, that is, the water partial pressure in the inlet gas; P An,out is the saturation vapor pressure of water obtained by looking up the table according to the reading of the dew point meter at the anode outlet end, that is, the water partial pressure in the outlet gas.

[0024] Compared with the prior art, the present invention has the following beneficial effects:

[0025] 1. By setting a heating unit wrapped around the outer wall of the ventilation pipeline between the dew point meter and the clamping unit, the present invention can evaporate the liquid water, and obtain the water partial pressure by looking up the table according to the dew point meter reading, that is, obtain the change value of the water content, which can effectively shorten the measurement time of the electro-osmotic drag coefficient and quickly measure the electro-osmotic drag coefficient at different operating temperatures and humidities;

[0026] 2. Both the anode ventilation pipeline and the cathode ventilation pipeline adopted in the present invention are straight channels. Using the small area of the straight channel for battery testing significantly reduces the measurement error caused by uneven water distribution in the proton exchange membrane and improves the measurement accuracy of the electro-osmotic drag coefficient at different operating temperatures and humidities. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 is a schematic structural diagram of the device in Embodiment 1 of the present invention;

[0028] Figure 2 is a partial structural diagram of the clamping unit in Embodiment 1 of the present invention;

[0029] Figure 3 is a schematic diagram of the parallel direct current field in the clamping unit in Embodiment 1 of the present invention;

[0030] Figure 4 is an external contour diagram of the clamping unit and the ventilation pipeline in Embodiment 2 of the present invention;

[0031] Figure 5 is a partial structural diagram of the clamping unit and the ventilation pipeline in Embodiment 2 of the present invention;

[0032] Figure 6 is a cross-sectional view of the clamping unit and the ventilation pipeline structure in Embodiment 2 of the present invention;

[0033] Figure 7Schematic diagram of a partial structure of the clamping unit and the ventilation pipeline in Embodiment 3 of the present invention;

[0034] Figure 8 Cross-sectional view of the structure of the clamping unit and the ventilation pipeline in Embodiment 3 of the present invention;

[0035] Figure 9 Schematic flow chart of the method in Embodiment 4 of the present invention;

[0036] Wherein: 1, membrane electrode to be measured; 11, first half membrane electrode; 12, proton exchange membrane; 13, second half membrane electrode; 2, clamping unit; 31, first dew point meter; 32, second dew point meter; 33, third dew point meter; 41, first heating unit; 42, second heating unit; 43, third heating unit; 5, anode ventilation pipeline; 6, cathode ventilation pipeline. Detailed implementation manners

[0037] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. This embodiment is implemented on the premise of the technical solution of the present invention, and gives detailed implementation manners and specific operation processes, but the protection scope of the present invention is not limited to the following embodiments.

[0038] Embodiment 1

[0039] As Figure 1 shown, this embodiment provides an electro-drag coefficient measurement device, which is applied to the membrane electrode 1 to be measured, and can effectively obtain the electro-drag coefficient values of the proton exchange membrane at different working temperatures and humidities. The device includes a clamping unit 2, a first dew point meter 31, a second dew point meter 32, a third dew point meter 33, a first heating unit 41, a second heating unit 42, a third heating unit 43, an anode ventilation pipeline 5 and a cathode ventilation pipeline 6.

[0040] The membrane electrode 1 to be measured includes a first half membrane electrode 11, a proton exchange membrane 12 and a second half membrane electrode 13 that are tightly attached to each other from top to bottom in sequence. At this time, the complete membrane electrode 1 to be measured is pre-assembled. In some other embodiments, a sample of the membrane electrode 1 to be measured with a suitable size can be directly cut according to the specifications of the clamping unit 2. By adopting any one of the preparation methods, the prepared membrane electrode 1 to be measured can be installed inside the clamping unit 2.

[0041] The clamping unit 2 includes upper and lower parts, and the membrane electrode 1 to be measured is clamped between the two parts for use in the electro-drag coefficient measurement experiment. Figure 1 One of the structures of the clamping unit 2 is shown, and the areas of the two ventilation pipelines inside the clamping unit 2 are both straight channels; Figure 2 One part of the clamping unit 2 under this structure is shown. At this time, the inlet ends and outlet ends of the anode ventilation pipeline 5 and the cathode ventilation pipeline 6 are parallel to the plane where the parallel straight channels inside the clamping unit 2 are located. AsFigure 3 As shown, in this structure, the gas flow field in the clamping unit 2 is a parallel direct current field, and the straight-line length of the flow field is 0.5 cm to 2 cm.

[0042] Specifically, as Figure 1 shown, the anode gas supply pipe 5 and the cathode gas supply pipe 6 respectively penetrate through the upper and lower parts of the clamping unit 2. The anode gas supply pipe 5 is closely attached to the anode-side surface of the membrane electrode 1 to be measured, and the cathode gas supply pipe 6 is closely attached to the cathode-side surface of the membrane electrode 1 to be measured. Figure 1 The lengths of the contact areas between the anode gas supply pipe 5 and the cathode gas supply pipe 6 and the membrane electrode 1 to be measured shown are both less than the length of the membrane electrode 1 to be measured. In some other embodiments, the entire section of the gas supply pipe located inside the clamping unit 2 can be in contact with the membrane electrode 1 to be measured, that is, the length of the contact area between the gas supply pipe and the membrane electrode 1 to be measured is equal to the length of the membrane electrode 1 to be measured. In addition, pressure sensors and backpressure valves can be provided at the inlet ends of the anode gas supply pipe 5 and the cathode gas supply pipe 6 to measure and control the gas pressure at the inlet ends.

[0043] As Figure 1 shown, the first dew point meter 31 is arranged at the inlet end of the anode gas supply pipe 5, the second dew point meter 32 is arranged at the outlet end of the anode gas supply pipe 5, the third dew point meter 33 is arranged at the inlet end of the cathode gas supply pipe 6, and the dew point meters are effectively connected to the corresponding gas supply pipes.

[0044] As Figure 1 shown, the first heating unit 41 is wrapped around the outer wall of the inlet end of the anode gas supply pipe 5 between the first dew point meter 31 and the clamping unit 2, the second heating unit 42 is wrapped around the outer wall of the outlet end of the anode gas supply pipe 5 between the second dew point meter 32 and the clamping unit 2, and the third heating unit 43 is wrapped around the outer wall of the inlet end of the cathode gas supply pipe 6 between the third dew point meter 33 and the clamping unit 2. Each heating unit can adopt a heating sleeve and a heat preservation sleeve. In some other embodiments, the heating unit can also be connected to a temperature measurement unit, such as a thermocouple, to monitor the temperature change in real time, so as to facilitate timely regulation of the temperature at the inlet and outlet ends of the gas supply pipe. A dew point meter can also be arranged at the outlet end of the cathode gas supply pipe 6 to directly read the water partial pressure at this outlet end; if not arranged, as Figure 1 shown, the water partial pressure at this outlet end can be calculated from the data of the other three inlet and outlet ends.

[0045] Embodiment 2

[0046] This embodiment provides an electro-drag coefficient measuring device. The difference between this device and the measuring device provided in Embodiment 1 lies in the different structures of the clamping unit and the gas supply pipe. Figure 4The external contours of the clamping unit and the ventilation duct in the device are shown. It can be seen that the air inlet and outlet ends of the two ventilation ducts are perpendicular to the plane where the internal flow channel is located. The clamping unit includes two parts, the upper and lower parts, and the internal structure of one part is as follows Figure 5 As shown in FIG. 1 , the interior of the clamping unit is still a parallel straight flow path, and the anode ventilation duct and the cathode ventilation duct in the area inside the clamping unit are still straight flow paths. Figure 4 The plane where AA' is located is used to obtain the cross-sectional view of the clamping unit and the ventilation duct structure, such as Figure 6 As shown. It can be seen that the internal flow channels of the upper and lower parts of the clamping unit overlap in the projection area of ​​the membrane electrode surface to be measured. The rest of the structure of the entire electric drag coefficient measurement device is basically the same as that in Example 1, and will not be repeated here.

[0047] Example 3

[0048] This embodiment provides an electric drag coefficient measuring device, which is different from the measuring devices provided in Embodiment 1 and Embodiment 2 in that the structures of the clamping unit and the ventilation duct are different. The outer contours of the clamping unit and the ventilation duct in this device are the same as those in Embodiment 2, that is, the air inlet and outlet ends of the two ventilation ducts are still perpendicular to the plane where the internal flow channel is located. Figure 7 The internal structure of a part of the clamping unit at this time is shown, which is still a parallel straight flow channel, and under this structure, the area of ​​the anode ventilation pipe and the cathode ventilation pipe inside the clamping unit is also a straight flow channel. However, at this time, the internal flow channels of the upper and lower parts of the clamping unit do not completely overlap in the projected area of ​​the membrane electrode surface to be tested, including both overlapping areas and non-overlapping areas. The cross-sectional view of the clamping unit and the ventilation pipe structure along the plane where AA' is located is shown as follows Figure 8 The rest of the structure of the entire electric drag coefficient measuring device is basically the same as that in Example 1, and will not be described again.

[0049] Example 4

[0050] This embodiment provides a method for measuring an electric drag coefficient, which can be implemented using any device in Embodiments 1 to 3. Figure 9 As shown, the method comprises the following steps:

[0051] Step S1, installing the prepared membrane electrode to be tested in a clamping unit, introducing hydrogen into the anode ventilation pipe, and introducing air into the cathode ventilation pipe.

[0052] Step S2, heating the anode ventilation duct and the cathode ventilation duct to a preset temperature, the heating temperature of the heating jackets at the air inlet ends of the two ventilation ducts is the reading of the dew point meter at the air inlet end + (0~10℃), and the heating temperature of the heating jacket at the air outlet end of the anode ventilation duct is fixed at 105℃~110℃. The temperature data of the heating jacket can be measured by a temperature measurement unit, for example, by thermocouple measurement.

[0053] Step S3, discharge the membrane electrode to be tested at a fixed working current density of 50-200 mA / cm 2 , and control the dew point value and air pressure value of the anode ventilation pipeline at the inlet end to be consistent with the dew point value and air pressure value of the cathode ventilation pipeline at the inlet end, record the dew point meter readings at the inlet and outlet ends of the anode ventilation pipeline, record the gas flow at the inlet end, the gas flow rate is more than 5 times the metering ratio, and obtain the dry gas inlet gas pressure P dry , dry gas intake flow Q An,in 、Water partial pressure in intake air P An,in and the water partial pressure P in the outlet gas An,out . Among them, for the process of controlling the dew point value and air pressure value at the inlet end of the anode ventilation duct to be consistent with the dew point value and air pressure value at the inlet end of the cathode ventilation duct, the dew point value at the inlet end of the anode and cathode ventilation ducts can be controlled to be consistent, which can be achieved by real-time monitoring and adjustment through thermocouples, heating sleeves and insulation sleeves, and the air pressure value at the inlet end of the anode and cathode ventilation ducts can be controlled to be consistent, which can be achieved by real-time monitoring and adjustment through the pressure sensor and back pressure valve provided by the test bench. The consistency of these two parameters is controlled, on the one hand, to achieve the test conditions of specific temperature and specific humidity, and on the other hand, to avoid water flux caused by pressure difference and water concentration difference, so as to improve the accuracy of the measurement results. In addition, the dry gas intake flow rate can be obtained through a mass flow controller.

[0054] Step S4, according to the dry gas intake gas pressure P dry , dry gas intake flow Q An,in 、Water partial pressure in intake air P An,in and the water partial pressure P in the outlet gas An,out , calculate the electrical drag coefficient of the membrane electrode to be tested, that is, the electrical drag coefficient n of the proton exchange membrane at the battery operating temperature and humidity T,RH , n T,RH The calculation formula is:

[0055]

[0056] In formula (1), F is the Faraday constant, J is the operating current density of the fuel cell, A is the surface area of ​​the membrane electrode catalyst layer, R is the ideal gas constant, T is the operating temperature, and P is dry is the dry gas intake pressure, Q An,in is the dry gas intake flow rate; P An,in is the saturated vapor pressure of water obtained by looking up the table according to the reading of the dew point meter at the anode inlet end, that is, the partial pressure of water in the inlet air; P An,out is the saturated vapor pressure of water obtained by looking up the table based on the reading of the dew point meter at the anode outlet, that is, the partial pressure of water in the outlet gas. Among them, F, J, A, and R are all known quantities; T, P dry and QAn,in All of them are controlled quantities. Through the control of the experimenter, the electric drag coefficient can be tested under specific operating temperature, current density, relative humidity and gas flow rate; P An,in and P An,out is a measured quantity used to accurately calculate the electric drag coefficient. The derivation process of formula (1) is as follows:

[0057] (1) According to the definition of electric drag coefficient, we have:

[0058]

[0059] Where F is the Faraday constant, J is the operating current density of the fuel cell, A is the surface area of ​​the membrane electrode catalyst layer, and J*A represents the total current; Q e is the water flux generated by water transport across the membrane caused by ion transfer;

[0060] (2) According to the water transmission process at the anode inlet and outlet, we have:

[0061] Q An,water,in =Q e +Q An,water,out (3)

[0062] In the formula, Q An,water,in is the water flux at the anode inlet end, Q An,water,out is the water flux at the anode outlet;

[0063] (3) According to the law of partial pressure, we have:

[0064]

[0065] Right now:

[0066]

[0067] In the formula, Q dry is the dry gas intake flow rate, Q water is the increase in flow rate after all liquid water is converted into gaseous water, P dry is the dry gas intake pressure, P water is the partial pressure of gaseous water in the gas;

[0068] (4) Therefore:

[0069]

[0070] In the formula, Q An,in is the dry gas intake flow rate, P An,in is the partial pressure of water in the intake air, P dry,in is the intake dry gas partial pressure;

[0071] (5)Also:

[0072]

[0073] In the formula, Q An,out is the dry gas flow rate in the outlet gas, P An,out is the water partial pressure in the outlet gas, P dry,out is the partial pressure of dry gas in the outlet gas;

[0074] (6) According to the conservation of inlet and outlet gas of the anode extreme dry gas and the state equation of ideal gas, we have:

[0075]

[0076] (7) According to formula (7) and formula (8), we have:

[0077]

[0078] Substituting equation (9) and equation (6) into equation (3), we get:

[0079]

[0080] (8) Substituting equation (10) into equation (2), and according to the setting conditions of the measurement experiment, we can obtain:

[0081] P dry,out ≈P dry,in =P dry (11)

[0082] So we have:

[0083]

[0084] The preferred specific embodiments of the present invention are described in detail above. It should be understood that a person skilled in the art can make many modifications and changes based on the concept of the present invention without creative work. Therefore, any technical solution that can be obtained by a person skilled in the art through logical analysis, reasoning or limited experiments based on the concept of the present invention on the basis of the prior art should be within the scope of protection determined by the claims.

Claims

1. An electric drag coefficient measurement device is applied to a membrane electrode to be measured. The device includes a clamping unit, and the membrane electrode to be measured is installed inside the clamping unit. Characterized in that, The device further includes a dew point meter, a heating unit, an anode gas supply pipeline, and a cathode gas supply pipeline. The anode gas supply pipeline and the cathode gas supply pipeline penetrate through the clamping unit. The regions of the two gas supply pipelines inside the clamping unit are both straight channels and are respectively closely attached to the two side surfaces of the membrane electrode to be measured. The dew point meter is arranged at the inlet end and the outlet end of the anode gas supply pipeline, and the inlet end of the cathode gas supply pipeline. The heating unit is wrapped around the outer wall of the gas supply pipeline between the dew point meter and the clamping unit.

2. The electric drag coefficient measurement device according to claim 1, Characterized in that, The membrane electrode to be measured includes a first half membrane electrode, a proton exchange membrane, and a second half membrane electrode that are tightly attached to each other from top to bottom in sequence.

3. The electric drag coefficient measurement device according to claim 1, Characterized in that, The gas flow field of the clamping unit is a parallel straight flow field.

4. The electric drag coefficient measurement device according to claim 3, Characterized in that, The straight line length of the straight flow field is 0.5 cm to 2 cm.

5. The electric drag coefficient measurement device according to claim 1, Characterized in that, The heating unit includes a heating sleeve and a heat preservation sleeve.

6. The electric drag coefficient measurement device according to claim 1, Characterized in that, A dew point meter is arranged at the outlet end of the cathode gas supply pipeline.

7. The electric drag coefficient measurement device according to claim 1, Characterized in that, The lengths of the contact regions of the anode gas supply pipeline and the cathode gas supply pipeline with the membrane electrode to be measured are both less than or equal to the length of the membrane electrode to be measured.

8. An electric drag coefficient measurement method, Characterized in that, It is realized by using the device according to any one of claims 1-7, and includes the following steps: S1, introduce hydrogen into the anode gas supply pipeline and introduce air into the cathode gas supply pipeline. S2, heat the anode gas supply pipeline and the cathode gas supply pipeline to a preset temperature. S3, make the membrane electrode to be measured discharge at a fixed working current density, and control the dew point value and the inlet air pressure value of the inlet end of the anode gas supply pipeline to be the same as the dew point value and the inlet air pressure value of the inlet end of the cathode gas supply pipeline, record the readings of the dew point meters at the inlet end and the outlet end of the anode gas supply pipeline, and obtain the dry gas inlet gas pressure, the dry gas inlet flow rate, the moisture partial pressure in the inlet gas, and the moisture partial pressure in the outlet gas. S4, calculate the electric drag coefficient of the membrane electrode to be measured according to the dry gas inlet gas pressure, the dry gas inlet flow rate, the moisture partial pressure in the inlet gas, and the moisture partial pressure in the outlet gas.

9. The electric drag coefficient measurement method according to claim 8, Characterized in that, The process of controlling the dew point value and the inlet air pressure value of the inlet end of the anode gas supply pipeline to be the same as the dew point value and the inlet air pressure value of the inlet end of the cathode gas supply pipeline is realized by a thermocouple, a heating sleeve, a heat preservation sleeve, a pressure sensor, and a back pressure valve, and the dry gas inlet flow rate is obtained by a mass flow controller.

10. The electric drag coefficient measurement method according to claim 8, Characterized in that, The calculation formula of the electric drag coefficient is: Where n T,RH represents the electro-drag coefficient, F is the Faraday constant, J is the operating current density of the fuel cell, A is the surface area of the membrane electrode catalyst layer, R is the ideal gas constant, T is the operating temperature, P dry is the dry gas inlet gas pressure; Q An,in is the dry gas inlet flow rate; P An,in is the saturated vapor pressure of water obtained by looking up the table according to the reading of the dew point meter at the anode inlet end, that is, the moisture partial pressure in the inlet gas; P An,out is the saturated vapor pressure of water obtained by looking up the table according to the reading of the dew point meter at the anode outlet end, that is, the moisture partial pressure in the outlet gas.

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