Method, system and device for estimating gas partial pressure and relative humidity in fuel cell

Abstract

A method, system, and apparatus for estimating gas partial pressure and relative humidity in a fuel cell are presented. The method may include: setting a control volume in a fuel cell based on a physical characteristic of a gas; determining a residence period of the gas within the control volume based on the flow rate of the gas, where the residence period corresponds to a time at which the gas resides within the control volume; determining moles and molar mobility of the gas within the control volume based on the residence time period; estimating a partial pressure and a relative humidity of the gas within the control volume based on the determined number of moles and molar mobility; and controlling an operating parameter of the fuel cell based on the estimated partial pressure and relative humidity of the gas within the control volume.

Description

[0001] Cross-references to related applications

[0002] This application claims the benefit of priority to Korean Patent Application No. 10-2024-0118815, filed with the Korean Intellectual Property Office on September 2, 2024, the entire contents of which are incorporated herein by reference. Technical Field

[0003] This disclosure relates to a method for estimating the partial pressure and relative humidity of a gas, even for open systems with airflow. Background Technology

[0004] The descriptions in this background section are intended only to enhance the understanding of the background of this disclosure and should not be construed as an admission that they correspond to prior art known to those skilled in the art.

[0005] A fuel cell is a device that receives hydrogen and air from the outside and generates electricity and water inside the stack. Hydrogen is supplied to the anode, where an oxidation reaction occurs to produce hydrogen ions (protons) and electrons. The resulting hydrogen ions and electrons flow to the cathode through an electrolyte membrane and a separator, respectively. At the cathode, the hydrogen ions and electrons flowing from the anode, along with oxygen from the air, undergo an electrochemical reaction to produce water, and electricity is generated from the electron flow.

[0006] Water generated in a fuel cell undergoes phase changes depending on real-time operating conditions (such as temperature and pressure), transforming into forms such as water vapor or saturated liquid. This can also affect the gas and electron transport characteristics through the stack's separation channels, gas diffusion layers, catalyst layers, membranes, etc. Specifically, excessive water generation in a fuel cell can lead to "overflow," while insufficient generation can result in "drying out," both of which can negatively impact fuel cell performance and durability. Therefore, relative humidity sensors and condensate level sensors are sometimes installed in fuel cells. However, the installation of these sensors increases fuel cell manufacturing and maintenance costs, or reduces control reliability due to sensor malfunction. Furthermore, the relative humidity measured and / or estimated by these sensors can be estimated as 0 when there is no gas flow in the fuel cell, making it unsuitable for open systems.

[0007] Furthermore, the performance of a fuel cell varies depending on its internal hydrogen concentration, and various methods are considered to estimate the hydrogen concentration within the fuel cell, particularly when hydrogen emissions need to be controlled due to regulations. Some methods can utilize the ideal gas equation of state to perform these estimations. However, using only the ideal gas equation of state, especially in open-system fuel cell stacks, may fail to account for the dynamic effects of gas flow within the system, potentially leading to incomplete control and suboptimal operation of the fuel cell.

[0008] Therefore, research and development of methods are being considered to estimate the partial pressure and relative humidity of gases such as hydrogen and oxygen even in open systems with airflow. Summary of the Invention

[0009] This disclosure has been made to address the aforementioned issues.

[0010] According to this disclosure, a method executed by an apparatus for estimating the partial pressure and relative humidity of a gas in a fuel cell coupled to the apparatus, the method comprising: setting a control volume in the fuel cell based on the physical properties of the gas; determining a residence time period of the gas within the control volume based on the gas flow rate, wherein the residence time period corresponds to the amount of time the gas resides within the control volume in the fuel cell; determining the number of moles and molar mobility of the gas within the control volume based on the residence time period of the gas within the control volume; estimating the partial pressure and relative humidity of the gas within the control volume based on the determined number of moles and molar mobility; and controlling the operating parameters of the fuel cell based on the estimated partial pressure and relative humidity of the gas within the control volume.

[0011] The configuration may include setting the compression section, cathode inlet, manifold section, cathode section, and cathode outlet to control volumes respectively.

[0012] Determining the molar number and molar mobility may include: for the gas in the cathode, calculating the molar number of the gas in the cathode, the molar mobility of the diffused gas, and the molar mobility of the gas that permeates due to the current reaction.

[0013] The residence time of the gas is proportional to the length of the control volume and inversely proportional to the gas flow rate.

[0014] Determining the number of moles and molar mobility can include: calculating the number of moles of gas and the molar mobility of gas within a control volume based on a non-flowing gas, or calculating the molar mobility of gas within a control volume per unit time and the number of moles of gas within a control volume based on a flowing gas.

[0015] Calculating the number of moles of gas based on a non-flowing gas can include integrating the net inflow rate of gas diffusing into the control volume with respect to the residence time of the gas in the control volume.

[0016] The net inflow rate of gas is calculated based on the molar mobility of the gas.

[0017] The molar mobility of a gas is proportional to the gas diffusion coefficient, the area of ​​the control volume, and the pressure difference across the control volume, and inversely proportional to the gas constant, the temperature within the control volume, and the length of the control volume.

[0018] Based on the flowing gas, the molar mobility of the gas within the control volume is calculated per unit time based on the molar mobility of the dry gas, which is calculated based on the molar mobility of the gas, the molar mass of the dry gas, the pressure of the vapor within the control volume, the pressure within the control volume, and the molar mass of the vapor.

[0019] Gases can include hydrogen, nitrogen, oxygen, and vapor.

[0020] In this method, estimating relative humidity may include calculating relative humidity (RH) based on the following: the residence time of steam in the control volume, the number of moles of steam introduced into the control volume per unit time, the number of moles of steam generated, the temperature in the control volume, the pressure of saturated steam at that temperature in the saturated steam content curve, the gas constant, and the total volume of the control volume.

[0021] The method may further include: determining the amount of condensate produced based on the estimated relative humidity value being greater than 1, according to the number of moles of steam in the control volume and the number of moles of saturated steam in the control volume.

[0022] The method may further include: determining the amount of condensate generated within the control volume; calculating the cumulative sum of the determined amounts of condensate generated; and adjusting the operating conditions of the fuel cell based on the calculated cumulative sum.

[0023] According to this disclosure, a system may include: a fuel cell configured to generate electricity from gas in the fuel cell; a sensor configured to detect the flow rate of the gas; and a processor configured to: set a control volume in the fuel cell based on the physical properties of the gas; determine a residence time period of the gas within the control volume based on the gas flow rate, wherein the residence time period corresponds to the amount of time the gas resides within the control volume in the fuel cell; determine the number of moles and molar mobility of the gas within the control volume based on the residence time period of the gas within the control volume; estimate the partial pressure and relative humidity of the gas within the control volume based on the determined number of moles and molar mobility; and control the operating parameters of the fuel cell based on the estimated partial pressure and relative humidity of the gas within the control volume.

[0024] According to this disclosure, an apparatus for estimating the partial pressure and relative humidity of a gas in a fuel cell is provided. The apparatus may include: a sensor configured to sense the gas flow rate; a processor; and a memory storing instructions configured, when executed by the processor, to cause the apparatus to: set a control volume in the fuel cell based on the physical properties of the gas; determine a residence time period of the gas within the control volume based on the gas flow rate, wherein the residence time period corresponds to the amount of time the gas resides within the control volume in the fuel cell; determine the number of moles and molar mobility of the gas within the control volume based on the residence time period; estimate the partial pressure and relative humidity of the gas within the control volume based on the determined number of moles and molar mobility; and control the operating parameters of the fuel cell based on the estimated partial pressure and relative humidity of the gas within the control volume.

[0025] In this device, the instruction, when executed by the processor, is also configured to cause the device to set the compression section, cathode inlet, manifold section, cathode section, and cathode outlet to control volumes, respectively.

[0026] In this device, the instruction, when executed by the processor, is also configured to cause the device to: calculate, for the gas in the cathode section, the molar mobility of the diffused gas, and the molar mobility of the gas that permeates due to the current reaction.

[0027] In this device, the residence time of the gas is proportional to the length of the control volume and inversely proportional to the gas flow rate.

[0028] In this device, the instruction, when executed by the processor, is also configured to cause the device to calculate the relative humidity (RH) based on the following: the residence time of steam in the control volume, the number of moles of steam introduced into the control volume per unit time, the number of moles of steam generated, the temperature in the control volume, the pressure of saturated steam at that temperature in the saturated steam content curve, the gas constant, and the total volume of the control volume.

[0029] In this device, the instruction, when executed by the processor, is also configured to cause the device to: determine the amount of condensate produced based on the estimated relative humidity value being greater than 1, according to the number of moles of steam in the control volume and the number of moles of saturated steam in the control volume. Attached Figure Description

[0030] The above and other objects, features, and advantages of this disclosure will become more apparent from the following detailed description taken in conjunction with the accompanying drawings:

[0031] Figure 1 An example of gas flow in a fuel cell is shown in an example of setup operation according to the present disclosure, for example, when the pretreatment section, compression section, cathode inlet, manifold section, cathode section and cathode outlet are respectively set as control volumes in the fuel cell. Detailed Implementation

[0032] <Methods for estimating gas partial pressure and relative humidity in fuel cells>

[0033] According to this disclosure, a method for estimating the partial pressure and relative humidity of a gas in a fuel cell includes: setting a control volume, a first calculation operation for calculating the residence time of the gas, a second calculation operation for calculating the number of moles and molar mobility of the gas within the control volume, and a third calculation operation for estimating the partial pressure and relative humidity of the gas within the control volume.

[0034] In addition, the ideal gas law is used in the second and third calculation operations.

[0035] According to this disclosure, as described above, by setting a control volume in the fuel cell stack based on the physical properties of the gas, applying the ideal gas law to the control volume, and using different partial pressure estimation methods depending on whether the gas is flowing, the partial pressure and relative humidity of the gas in this open system, the fuel cell, can be estimated more accurately. Therefore, this disclosure can increase energy efficiency while meeting hydrogen emission regulation requirements, and can improve the durability of the fuel cell by preventing stack overflow and / or dry-out phenomena.

[0036] For the purposes of this application and claims, the exemplary phrases “at least one: A; B; or C” or “at least one of A; B; C” are used, which means any combination of “at least one A, or at least one B, or at least one C, or at least one A, at least one B, and at least one C”. Furthermore, exemplary phrases such as “A, B, and C”, “A, B, or C”, “at least one of A, B, and C”, “at least one of A, B, or C”, etc., as used herein, may refer to each listed item or all possible combinations of listed items. For example, “at least one of A or B” may refer to (1) at least one A; (2) at least one B; or (3) at least one A and at least one B.

[0037] Settings

[0038] In this operation, the control volume is set according to the physical properties of the gas in the fuel cell.

[0039] The physical properties of the gas in a fuel cell (such as pressure, humidification, and components produced by the reaction) change in various parts. In this disclosure, by taking into account the changes in the physical properties of the gas and setting the control volume based on the physical properties of the gas in the fuel cell, the accuracy of the estimated gas partial pressure and relative humidity is also improved.

[0040] More accurate estimations of the partial pressure and relative humidity of the gas within a fuel cell are useful for improving its performance and efficiency. For example, by dividing the fuel cell into control volumes, parameters such as gas residence time, molar number, and molar mobility can be estimated based on the conditions within each volume. These estimates provide real-time insight into the gas conditions inside the fuel cell, enabling dynamic adjustments to operating parameters such as gas flow rate, humidification level, or purging operations. Such control helps prevent problems such as membrane drying or overflow, ensuring reliable and efficient fuel cell operation and enhanced durability.

[0041] Specifically, in this operation, the compression section, cathode inlet, manifold section, cathode section, and cathode outlet can be set to control volumes respectively.

[0042] For example, the gas in the compression section has high-pressure characteristics due to compression by the compressor, while the gas in the cathode inlet section has humidified gas characteristics due to steam injection, and dry gas characteristics due to introduction from the compression section. Furthermore, the gas in the manifold section may have gas characteristics resulting from mass exchange between the gas in the cathode section and / or the gas in the cathode inlet. Additionally, the gas in the cathode section may have gas characteristics resulting from electrochemical reactions, anode permeation, and mass exchange with the gas in the manifold section and / or the cathode outlet. Furthermore, the gas in the cathode outlet section may have gas characteristics resulting from mass exchange with the gas in the cathode section and the gas connected to the atmospheric pressure section.

[0043] As another example, in this operation, the pretreatment section, compression section, cathode inlet, manifold section, cathode section, and cathode outlet can each be set to a controlled volume (see [reference]). Figure 1 The gas in the pretreatment section can have the characteristics of atmospheric gas flowing into the fuel cell.

[0044] Gases can include hydrogen, nitrogen, oxygen, and vapor.

[0045] First calculation operation

[0046] In this operation, the residence time of the gas within the control volume is calculated based on the gas flow rate. The residence time corresponds to the amount of time the gas resides within the control volume of the fuel cell.

[0047] For example, in this operation, the residence time of the gas can be calculated using the following Equation 1:

[0048] [Equation 1]

[0049]

[0050] In equation 1,

[0051] t dur_CV Indicates the residence time of the gas within the control volume.

[0052] L CV This indicates the length of the control volume, and

[0053] v gas This indicates the gas flow rate.

[0054] For example, v gas This can represent a value measured by sensors installed in the fuel cell stack. As another example, v gas It can represent the flow rate of gas injected into the fuel cell stack.

[0055] Second calculation operation

[0056] In this operation, the number of moles and molar mobility of the gas in the control volume are calculated based on the residence time of the gas in the control volume.

[0057] For example, in this operation, different characteristics of the gas within the control volume can be calculated based on whether the gas flows in the fuel cell. Specifically, in this operation, depending on whether the gas flows in the fuel cell, if the gas does not flow, the number of moles and molar mobility of the gas within the control volume can be calculated; and if the gas flows, the molar mobility per unit time of the gas within the control volume and the number of moles of the gas can be calculated.

[0058] When the gas is not flowing

[0059] In this operation, if the gas does not flow in the fuel cell, the number of moles of gas and the molar mobility of the gas within the control volume can be calculated.

[0060] Specifically, if the gas does not flow, the number of moles of gas can be obtained by integrating the net inflow rate of gas diffusing into the control volume with the residence time of the gas in the control volume.

[0061] In this case, the net inflow rate of the gas can be calculated based on the molar mobility of the gas obtained by using the diffusion equation. For example, the molar mobility of the gas obtained by using the diffusion equation. It can be calculated using Equation 2 below.

[0062] [Equation 2]

[0063]

[0064] In equation 2,

[0065] D AB The diffusion coefficient of a gas (mol / m³) 2 ·s),

[0066] "A" indicates the area of ​​the controlled volume (m²) 2 ),

[0067] “R” represents the gas constant (e.g., 8.314 J / mol·K).

[0068] "T" indicates the temperature (K) within the control volume.

[0069] ΔP represents the pressure difference (kPa), and

[0070] Δx represents the length (m) of the control volume.

[0071] Then, ΔP (pressure difference) can represent the pressure difference between the inlet and outlet of the control volume, or it can represent the value measured by the sensor or calculated by estimation.

[0072] Furthermore, the temperature (T) within the control volume can be a value measured by a sensor or a value calculated through estimation.

[0073] For example, the gas in the compression section may include steam, nitrogen, oxygen, and hydrogen.

[0074] For example, the number of moles of each gas in the control volume can be calculated by using the molar mobility of each gas, and the partial pressure of each gas can be estimated based on the calculated number of moles of each gas.

[0075] Specifically, the number of moles of steam in the compression section (m Vap_Comp The value can be obtained by integrating the molar mobility of the steam in the compression section based on the residence time of the steam in the compression section, and more specifically, it can be calculated in the following equation 7.

[0076] [Equation 7]

[0077]

[0078] In Equation 7, "t" represents time. dur_comp This indicates the residence time of the gas in the compression section, and This indicates the molar mobility of the gas in the compression section.

[0079] molar mobility of steam It can be calculated in Equation 2.

[0080] For example, the net inflow rate of oxygen or hydrogen in the compression section can be obtained by subtracting the amount of oxygen or hydrogen diffusing back to the pretreatment section from the amount of oxygen or hydrogen diffusing into the compression section from the amount of oxygen or hydrogen diffusing into the compression section. Then, the pretreatment section is the previous treatment section, and the compression section is the current treatment section. Furthermore, when calculating other control volumes, the "pretreatment section" can be interpreted, modified, and applied as the treatment section of the previous operation, and the "compression section" can be interpreted, modified, and applied as the treatment section of the current operation.

[0081] Specifically, the number of moles of oxygen or hydrogen in the compression section can be calculated in the following equation 8.

[0082] [Equation 8]

[0083]

[0084] In equation 8, This represents the molar mobility (mol / s) of oxygen or hydrogen diffusing from the pretreatment section to the compression section, and This indicates the molar mobility (mol / s) of oxygen or hydrogen diffusing from the compression section to the pretreatment section.

[0085] and It can be calculated using the ideal gas law, specifically in Equation 2.

[0086] In addition, the number of moles of nitrogen in the compression section (m N2_Comp This can be achieved by subtracting the number of oxygen moles (m) from the total number of moles of gas introduced into the compression section. O2_Comp ), number of moles of hydrogen (m) H2_Comp ) and the number of moles of steam (m Vap_Comp The value obtained is as follows: The number of moles of nitrogen in the compression section can be calculated using Equation 9 below. In Equation 9, "m" is the total number of moles of gas introduced into the compression section, which can be calculated by applying the ideal gas law or measured by a gas flow sensor.

[0087] [Equation 9]

[0088] m N2_Comp =mm Vap_Comp -m O2_Comp -m H2_Comp

[0089] Furthermore, the number of moles of nitrogen, oxygen, hydrogen, and vapor in the cathode inlet, manifold, and cathode outlet can be calculated in the same way as the number of moles of each gas in the compression section described above.

[0090] When gas flows

[0091] In this operation, if the gas flows in the fuel cell, the molar mobility of each gas per unit time and the number of moles of each gas can be calculated within the control volume.

[0092] Specifically, the molar mobility of each gas per unit time within the control volume can be obtained by using the molar mobility of the dry gas calculated in Equation 3 below. To calculate.

[0093] [Equation 3]

[0094]

[0095] In equation 3,

[0096] The molar mobility of a gas (mol / s)

[0097] The molar mobility of steam (mol / s) is expressed in Equation 4 below, and

[0098] M gas It is the molar mass (g / mol) of the dry gas.

[0099] [Equation 4]

[0100]

[0101] In equation 4,

[0102] The molar mobility of a gas (mol / s)

[0103] P vap_CV This indicates the pressure (kPa) of the steam within the control volume.

[0104] P CV It controls the pressure (kPa) within the volume, and

[0105] M vap It is the molar mass of steam (g / mol).

[0106] It can represent values ​​measured by sensors and can represent the molar mobility of a mixture of gases including hydrogen, nitrogen, oxygen, and vapor.

[0107] P vap_CV This can represent the pressure of steam within a control volume, which is estimated using a saturated steam content curve. Specifically, P vap_CV It can be the pressure (P) of the saturated steam at the temperature (K) within the control volume in the saturated steam content curve. sat_CV 30% of ).

[0108] For example, the molar mobility per unit time of each gas (specifically, hydrogen, nitrogen, and oxygen) in the compression section can be the same as that of the gas in the pretreatment section. That is, the molar mobility per unit time of hydrogen in both the compression and pretreatment sections can be 0 mol / s.

[0109] In addition, the molar mobility of nitrogen per unit time in the pretreatment section Molar mobility per unit time of oxygen The molar mobility of the dry gas can be calculated based on Equation 3. For example, by using the composition of the mixed gas flowing into the fuel cell and The molar mobility per unit time of each gas (specifically, hydrogen, nitrogen, and oxygen) in the compression section can be calculated. It can be 79%, and It can be 21%.

[0110] For example, the number of moles of each gas within a controlled volume can be calculated using the molar mobility of each gas per unit time and the molar ratio of each gas, and the partial pressure of each gas can be calculated based on the calculated number of moles of each gas.

[0111] Specifically, the number of moles of steam in the compression section (m Vap_Comp It can be calculated in Equation 10 below.

[0112] [Equation 10]

[0113]

[0114] In equation 10,

[0115] m sat-vap_comp The number of moles of saturated steam in the compression section is indicated, and can be estimated using the temperature in the compression section and the saturated steam profile. The temperature in the compression section can then be a value measured by a sensor.

[0116] P vap_amb This represents the pressure (kPa) of the steam in the compression section, and can be, for example, the pressure (P) of the saturated steam at the temperature (K) in the compression section as shown in the saturated steam content curve described above. sat_amb 30% of ).

[0117] P total_amb It is the pressure (kPa) inside the compression section, and can be a value measured or estimated by, for example, a sensor.

[0118] In addition, the number of moles (m) of each gas (e.g., oxygen, nitrogen, or hydrogen) in the compression section gas_comp It can be calculated using the following equation 11.

[0119] [Equation 11]

[0120]

[0121] In equation 11,

[0122] “m” represents the total number of moles of gas introduced into the compression section, and can be a value measured by a flow rate sensor or estimated using a method for estimating the number of moles of compressed gas.

[0123] m Vap_Comp This represents the number of moles of steam in the compression section, and can be calculated in Equation 10.

[0124] This represents the molar mobility (mol / s) of the gas in the compression section, and can be calculated, for example, using the ideal gas law, and specifically, in Equation 2.

[0125] and This represents the molar mobility (mol / s) of oxygen and nitrogen in the compression section, and can be calculated, for example, using the ideal gas law, and specifically, in Equation 2.

[0126] This represents the molar mobility of hydrogen in the compression section, and can be, for example, 0 mol / s.

[0127] Furthermore, the molar mobilities (mol / s) of oxygen and nitrogen in the cathode inlet, manifold, and cathode outlet can be the same as those in the compression section as described above. For example, the molar mobilities (mol / s) of oxygen and nitrogen in the cathode inlet, manifold, and cathode outlet can be calculated using Equation 2 above. That is, and They can be the same, and and They can be the same.

[0128] Furthermore, the molar mobility of hydrogen in the cathode inlet can be the same as that of hydrogen in the compression section as described above. That is, and They can be the same; for example, it can be 0 mol / s.

[0129] Molar mobility of hydrogen in the manifold This can be the same as the molar mobility of hydrogen calculated at the cathode inlet. That is, Can be with The same, for example, could be 0 mol / s.

[0130] In addition, the molar mobility (m) of hydrogen in the cathode outlet H2_Ca-Out () can be the molar mobility of hydrogen in the cathode. and the molar mobility of hydrogen gas through purging flow The sum of . Then, The value can be estimated or calculated using conventionally known methods.

[0131] The number of moles of nitrogen, oxygen, and hydrogen in the cathode inlet, manifold, and cathode outlet can be calculated in the same way as the number of moles of each gas in the compression section. Specifically, the number of moles of nitrogen, oxygen, and hydrogen in the cathode inlet, manifold, and cathode outlet can be calculated in Equation 11 above.

[0132] The molar mobility (mol / s) of the steam at the cathode inlet can be obtained by multiplying the sum of the molar mobility of the steam introduced from the compressor and the molar mobility of the steam introduced through the humidifier by the efficiency of the humidifier. Specifically, the molar mobility of the steam at the cathode inlet... It can be calculated in Equation 12 below.

[0133] [Equation 12]

[0134]

[0135] In equation 12,

[0136] This represents the molar mobility (mol / s) of the steam in the compression section per unit time, and specifically, it can be calculated in Equation 10.

[0137] It represents the molar mobility (mol / s) of the vapor discharged from the humidifier and flowing into the cathode inlet per unit time, and can be measured using a sensor in the humidifier.

[0138] η is the efficiency of the humidifier.

[0139] In addition, the molar mobility of steam in the manifold The molar mobility of the vapor in the cathode inlet can be compared with that of the cathode inlet. Same. Specifically, It can be calculated in Equation 12 above.

[0140] molar mobility of steam at cathode outlet The molar mobility of the vapor in the cathode inlet can be compared with that of the cathode inlet. Same. Specifically, It can be calculated in Equation 12 above.

[0141] (Cathode section)

[0142] In this operation, for the cathode section, the number of moles of each gas, the molar mobility of each gas, the molar mobility of each gas that has been crossed over due to the current reaction (current flow), and the molar mobility of each gas in the cathode section can be calculated.

[0143] Specifically, the molar mobility of nitrogen gas in the cathode section This can be determined by the molar migration rate of nitrogen gas from the manifold. Subtract the molar mobility of nitrogen gas that permeates due to the electric current reaction. And the value obtained. Then, It can be calculated in Equation 13 below.

[0144] [Equation 13]

[0145]

[0146] In equation 13,

[0147] D XO The diffusion coefficient of the gas due to osmosis (mol / m) 2 ·s),

[0148] "A" indicates the area of ​​the controlled volume (m²) 2 ),

[0149] “R” represents the gas constant (e.g., 8.314 J / mol·K).

[0150] "T" indicates the temperature (K) within the control volume.

[0151] ΔP represents the pressure difference (kPa), and

[0152] Δx represents the length (m) of the control volume.

[0153] Then, ΔP (pressure difference) can represent the pressure difference between the inlet and outlet of the control volume, and can be a value measured by a sensor or calculated by estimation.

[0154] Furthermore, the temperature (T) within the control volume can be a value measured by a sensor or a value calculated through estimation.

[0155] molar mobility of oxygen in the cathode It can be calculated in the following equation 14.

[0156] [Equation 14]

[0157]

[0158] In equation 14,

[0159] “N” represents the number of units.

[0160] “I” represents the current in the pile (A).

[0161] “F” represents the Faraday constant (C / mol).

[0162] This indicates the molar mobility (mol / s) of oxygen in the manifold.

[0163] This represents the molar mobility (mol / s) of oxygen diffusing from the manifold to the cathode.

[0164] This represents the molar mobility (mol / s) of oxygen diffusing from the cathode to the cathode outlet, and

[0165] This represents the molar mobility (mol / s) of oxygen permeated through the current reaction.

[0166] and It can be calculated in Equation 2, and, It can be calculated in Equation 13 above.

[0167] molar mobility of vapor in the cathode section It can be calculated in the following equation 15.

[0168] [Equation 15]

[0169]

[0170] In equation 15,

[0171] This indicates the molar mobility (mol / s) of steam in the manifold.

[0172] “N” represents the number of units.

[0173] “I” represents the current in the pile (A).

[0174] And "F" represents the Faraday constant (C / mol).

[0175] molar mobility of hydrogen in the cathode It can be calculated in the following equation 16.

[0176] [Equation 16]

[0177]

[0178] In equation 16,

[0179] This indicates the molar mobility (mol / s) of hydrogen gas in the manifold.

[0180] This represents the molar mobility (mol / s) of hydrogen gas diffusing from the manifold to the cathode.

[0181] This represents the molar mobility (mol / s) of hydrogen gas diffusing from the cathode to the cathode outlet, and

[0182] This represents the molar mobility (mol / s) of hydrogen gas that permeates due to the electric current reaction.

[0183] and It can be calculated in Equation 2, and, It can be calculated in Equation 13 above.

[0184] For example, the number of moles of gas in the cathode section can be calculated using the molar mobility of the gas, and the partial pressure of the gas can be estimated based on the calculated number of moles of gas.

[0185] Specifically, the number of moles of vapor, oxygen, and hydrogen in the cathode section can be obtained by integrating the molar mobility of vapor, oxygen, or hydrogen in the cathode section over the residence time of vapor, oxygen, or hydrogen in the cathode section, and more specifically, it can be calculated in Equation 7 above. Then, the residence time of the gas in the cathode section can be calculated in Equation 1 above.

[0186] In addition, the number of moles of nitrogen in the cathode (m N2_Ca This can be achieved by subtracting the number of moles of oxygen (m) from the total number of moles of gas introduced into the cathode. O2_Ca ), number of moles of hydrogen (m) H2_Ca ) and the number of moles of steam (m Vap_Ca The value obtained is as follows: That is, the number of moles of nitrogen in the compression section can be calculated using Equation 9 above. Then, the total number of moles of gas introduced into the cathode section (m, mol) can be calculated using the ideal gas law or measured using a flow sensor. Furthermore, if the total number of moles of gas introduced into the cathode section (m, mol) is calculated using the ideal gas law, the temperature can be the average of the values ​​measured by the cooling water sensors at the reactor inlet / outlet, and the pressure can be the average of the values ​​measured by the pressure sensors at the reactor inlet / outlet.

[0187] Third calculation operation

[0188] In this operation, the partial pressure and relative humidity of the gas within the control volume are estimated by using the calculated number of moles and molar mobility of the gas.

[0189] The partial pressure of a gas can be estimated and / or calculated based on the number of moles of the gas, which is estimated and / or calculated as described above.

[0190] In addition, relative humidity (RH) can be calculated using the following equation 5.

[0191] [Equation 5]

[0192]

[0193] In equation 5,

[0194] t dur_CV This represents the residence time of steam within the control volume, and can be calculated using Equation 1 above. Specifically, t dur_CV This can be the residence time of the steam in the cathode section.

[0195] This indicates the number of moles of steam flowing into the control volume per unit time, and specifically, the number of moles of steam flowing into the cathode per unit time.

[0196] This indicates the number of moles of steam produced.

[0197] “T” indicates the temperature (K) within the control volume, and specifically, it can be the temperature in the cathode section.

[0198] P sat_T This represents the pressure (kPa) of saturated steam at that temperature "T" in the saturated steam content curve, and specifically, it can be the pressure of saturated steam at the temperature in the cathode section of the saturated steam content curve.

[0199] “R” represents the gas constant, and “V” represents the volume (m³) within the control volume. 3 ).

[0200] Then, if the estimated relative humidity in this operation is greater than 1, the amount of condensate produced can be calculated in Equation 6 below.

[0201] [Equation 6]

[0202] n vap_condensed =n vap_CV -n vap_sat

[0203] In equation 6,

[0204] n vap_condensed This indicates the number of moles of condensate produced within the controlled volume.

[0205] n vap_CV It controls the number of moles of vapor within the volume, and

[0206] n vap_sat It controls the number of moles of saturated vapor within the volume.

[0207] Meanwhile, if the estimated relative humidity in this operation is 1 or less, the amount of condensate produced (n) vap_condensed () could be 0.

[0208] After this, the cumulative sum of the calculated values ​​of the amount of condensate produced (n) can be calculated. water_acc It may also include operations that utilize it to adjust the operating conditions of the fuel cell.

[0209] Then, the cumulative sum of the calculated values ​​of the amount of condensate produced can be obtained by subtracting the number of moles of condensate discharged from the number of moles of condensate produced calculated in Equation 6 above, and then integrating this value with the residence time of steam in the control volume.

[0210] The durability of a fuel cell can be improved by using n calculated as described above. water_acc Improvement is achieved by preventing overflow and / or drying out of the pile.

[0211]

[0212] Examples of this disclosure provide a method for estimating the partial pressure and relative humidity of gases (such as hydrogen and oxygen) even in open systems with airflow.

[0213] The technical problems to be solved by this disclosure are not limited to those described above, and any other technical problems not mentioned herein will be clearly understood by those skilled in the art from the following description.

[0214] According to an example of this disclosure, a method for estimating gas partial pressure and relative humidity in a fuel cell includes: a setting operation to set a control volume based on the physical properties of the gas in the fuel cell; a first calculation operation to calculate the residence time of the gas within the control volume based on the gas flow rate; a second calculation operation to calculate the number of moles and molar mobility of the gas within the control volume based on the residence time of the gas within the control volume; and a third calculation operation to estimate the gas partial pressure and relative humidity within the control volume by using the calculated number of moles and molar mobility of the gas, wherein in the second and third calculation operations, an ideal gas law and a system for performing these operations are used.

[0215] According to another example of this disclosure, a system is provided for estimating the partial pressure and relative humidity of a gas in a fuel cell by performing an estimation method.

[0216] Furthermore, this disclosure provides a system for estimating the partial pressure and relative humidity of a gas in a fuel cell by performing the estimation method described above.

[0217] The system can be a system used for general estimation and / or calculation of physical performance, and can be a system that can implement the methods described above.

[0218] The method for estimating the partial pressure and relative humidity of gases in a fuel cell according to this disclosure can estimate the partial pressure of hydrogen even in an open system with gas flow, thereby meeting hydrogen emission regulations and improving fuel cell performance. Furthermore, the estimation method allows for the estimation of relative humidity, preventing degradation of fuel cell performance and durability due to overflow and dry-out phenomena. Additionally, the estimation method allows for the estimation of oxygen partial pressure, thereby improving flow limiting functionality, preventing problems such as cell suction, and thus improving fuel cell operating performance. Moreover, because the estimation method can even be applied to open systems, it is feasible to expand the design and / or application of fuel cells with minimal additional experimentation and tuning changes.

Claims

1. A method performed by a device for estimating a partial pressure of a gas and a relative humidity of the gas in a fuel cell coupled to the device, the method comprising: setting a control volume in the fuel cell based on a physical property of the gas; determining a residence time period of the gas within the control volume based on a flow rate of the gas, wherein the residence time period corresponds to an amount of time the gas resides within the control volume in the fuel cell; determining a number of moles and a molar transference of the gas within the control volume based on the residence time period of the gas within the control volume; estimating the partial pressure of the gas and the relative humidity of the gas within the control volume based on the determined number of moles and molar transference; and controlling an operating parameter of the fuel cell based on the estimated partial pressure of the gas and the relative humidity of the gas within the control volume.

2. The method of claim 1, wherein, setting includes: setting a compression section, a cathode inlet, a manifold section, a cathode section, and a cathode outlet as the control volume, respectively.

3. The method of claim 2, wherein, determining the number of moles and the molar transference includes calculating, for the gas in the cathode section: a number of moles of the gas in the cathode section; a molar transference of the diffused gas; and a molar transference of the gas permeated by a current reaction.

4. The method of claim 1, wherein, the residence time period of the gas is proportional to a length of the control volume and inversely proportional to the flow rate of the gas.

5. The method of claim 1, wherein, determining the number of moles and the molar transference includes: calculating, based on the gas not flowing, a number of moles of the gas within the control volume and a molar transference of the gas, or calculating, based on the gas flowing, a molar transference per unit time of the gas within the control volume and a number of moles of the gas within the control volume.

6. The method of claim 5, wherein, calculating, based on the gas not flowing, a number of moles of the gas includes integrating a net influx rate of the gas diffused into the control volume over the residence time period of the gas within the control volume.

7. The method of claim 6, wherein, the net influx rate of the gas is calculated from the molar transference of the gas.

8. The method of claim 7, wherein, the molar transference of the gas: is proportional to a diffusion coefficient of the gas, an area of the control volume, and a pressure difference across the control volume; and is inversely proportional to a gas constant, a temperature within the control volume, and a length of the control volume.

9. The method of claim 5, wherein, based on the gas flowing, the molar transference of the gas within the control volume is calculated per unit time based on a molar transference of a dry gas, wherein the molar transference of the dry gas is calculated based on: the molar transference of the gas; a molar mass of the dry gas; a pressure of steam within the control volume; a pressure within the control volume; and a molar mass of the steam.

10. The method of claim 1, wherein, the gas includes hydrogen, nitrogen, oxygen, and steam.

11. The method of claim 1, wherein, estimating the relative humidity includes calculating the relative humidity based on: a residence time period of steam within the control volume; a temperature within the control volume; a pressure of saturated steam at the temperature in a saturated steam content curve; a gas constant; and a molar mass of the steam. a total volume of the control volume.

12. The method of claim 1, wherein, estimating the relative humidity includes: a residence time period of the vapor within the control volume; a number of moles of the vapor introduced into the control volume per unit time; a number of moles of the vapor produced; a temperature within the control volume; a pressure of the saturated vapor at the temperature in a saturated vapor content curve; a gas constant; and a total volume of the control volume.

13. The method of claim 1, further comprising, based on a value of the estimated relative humidity being greater than 1: determining an amount of condensate produced from a number of moles of the vapor within the control volume and a number of moles of the saturated vapor within the control volume.

14. The method of claim 1, further comprising: determining a value of the amount of condensate produced within the control volume; calculating a cumulative sum of the determined value of the amount of condensate produced; and based on the calculated cumulative sum, adjusting an operating condition of the fuel cell.

15. A system for estimating a partial pressure of a gas and a relative humidity of the gas in a fuel cell, the system comprising: a fuel cell configured to produce electricity from the gas in the fuel cell; a sensor configured to detect a flow rate of the gas; and a processor configured to: set a control volume in the fuel cell based on physical properties of the gas; determine a residence time period of the gas within the control volume based on the flow rate of the gas, wherein the residence time period corresponds to an amount of time the gas resides within the control volume in the fuel cell; determine a number of moles and a molar transference of the gas within the control volume based on the residence time period of the gas within the control volume; estimate a partial pressure of the gas and a relative humidity of the gas within the control volume based on the determined number of moles and the molar transference; and control an operating parameter of the fuel cell based on the estimated partial pressure of the gas and the relative humidity of the gas within the control volume.

16. An apparatus for estimating a partial pressure of a gas and a relative humidity of the gas in a fuel cell, the apparatus comprising: a sensor configured to sense a flow rate of the gas; a processor; and a memory storing instructions that, when executed by the processor, are configured to cause the apparatus to: set a control volume in the fuel cell based on physical properties of the gas; determine a residence time period of the gas within the control volume based on the flow rate of the gas, wherein the residence time period corresponds to an amount of time the gas resides within the control volume in the fuel cell; determine a number of moles and a molar transference of the gas within the control volume based on the residence time period of the gas within the control volume; estimate a partial pressure of the gas and a relative humidity of the gas within the control volume based on the determined number of moles and the molar transference; and control an operating parameter of the fuel cell based on the estimated partial pressure of the gas and the relative humidity of the gas within the control volume. ​ ​ ​ 17. The apparatus of claim 16, wherein, The instructions, when executed by the processor, are further configured to cause the apparatus to provide a compression section, a cathode inlet, a manifold section, a cathode section, and a cathode outlet as the control volume, respectively.

18. The apparatus of claim 17, wherein, The instructions, when executed by the processor, are further configured to cause the apparatus to calculate, for the gas in the cathode section: a number of moles of the gas in the cathode section; a molar diffusivity of the diffusing gas; and a molar permeation of the gas caused by the current reaction.

19. The apparatus of claim 16, wherein, The residence time period of the gas is proportional to the length of the control volume and inversely proportional to the flow rate of the gas.

20. The apparatus of claim 16, wherein, The instructions, when executed by the processor, are further configured to cause the apparatus to calculate the relative humidity based on: a residence time period of the vapor within the control volume; a number of moles of vapor introduced into the control volume per unit time; a number of moles of vapor produced; a temperature within the control volume; a pressure of the saturated vapor at the temperature in a saturated vapor content curve; a gas constant; and a total volume of the control volume.

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