A method for evaluating fuel cell stack fluid distribution uniformity
By arranging pressure sensors and porous media models in the fuel cell stack, and combining experiments and simulations, the accuracy problem of fluid distribution consistency assessment in fuel cell stacks was solved, achieving efficient assessment of fluid distribution consistency and improving stack performance and lifespan.
Patent Information
- Application Number
- CN202211188049.5
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2022-09-28
- Publication Date
- 2026-02-03
- Estimated Expiration
- 2042-09-28
AI Technical Summary
Existing technologies struggle to accurately assess the consistency of fluid distribution within a fuel cell stack, which impacts stack performance and lifespan.
By fabricating special single cells and arranging pressure sensors in the stack, combined with experimental testing and simulation models, the flow resistance of the plates is simulated using a porous media model. By adjusting the viscosity and inertial drag coefficients, the consistency of fluid distribution can be evaluated.
An accurate and simple method is provided to evaluate the consistency of fluid distribution in the three chambers of a fuel cell stack, improving the accuracy of the evaluation and the reliability of the method.
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Figure CN115911467B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of fuel cell technology, and in particular to a method for evaluating the consistency of fluid distribution in a fuel cell stack. Background Technology
[0002] Proton exchange membrane fuel cells (PEMFCs) are attracting increasing market attention as a pollution-free, high-efficiency, and low-noise energy conversion device. Fuel cell stacks typically consist of hundreds of individual cells stacked together to meet market design requirements for total stack power.
[0003] For fuel cell stacks with a common U-shaped flow field configuration, the flow rate is higher in individual cells near the water / gas (i.e., cooling water and reactant gas) interfaces, while the flow rate is lower at the blind ends. Increasing the number of individual cells to improve the total power of the stack can lead to a decrease in the consistency of fluid distribution within the stack, which in turn affects the overall performance and lifespan of the stack. Due to the compact structure of the fuel cell stack core, the narrow inlet and outlet channels of the common manifold, and the high sealing requirements, measuring the flow rate of each individual cell within the stack is extremely difficult. Therefore, effectively assessing the consistency of fluid distribution within the fuel cell stack is crucial.
[0004] In existing technologies, the evaluation of fluid consistency within a fuel cell stack is mostly conducted experimentally. One approach is to control the supply of reactant gas and external load, and indirectly determine the consistency of fluid distribution by measuring the consistency of current or voltage detected in each cell. See CN105789660A and CN111063920A for details. Another approach is to use a measuring device inserted into the inlet and outlet of each cell in the common manifold to measure the pressure or dynamic pressure value, and then calculate the fluid distribution of each cell through theoretical calculations to obtain the result of the stack flow distribution consistency. See CN109638319A for details.
[0005] The first approach, which involves detecting the consistency of current or voltage, is an indirect approach. However, this approach is influenced by many factors, making it difficult to guarantee that the consistency of current or voltage is caused by the consistency of fluid distribution. The second approach, which involves detecting the pressure values at the inlet and outlet of a single cell and then calculating the flow rate of that single cell, is a direct approach. However, the detection device can also cause changes in the flow field inside the stack, resulting in large measurement errors. Furthermore, theoretical calculations cannot accurately reflect the actual flow field distribution inside the stack. Summary of the Invention
[0006] The purpose of this invention is to overcome the shortcomings of the existing technology by providing a method for evaluating the consistency of fluid distribution in a fuel cell stack. Based on the established evaluation conditions, the effectiveness of the simulation model and the consistency of fluid distribution in the stack are judged, thus solving the problem that the consistency of fluid distribution in the three chambers of a fuel cell stack cannot be accurately evaluated at present.
[0007] The objective of this invention can be achieved through the following technical solutions:
[0008] The purpose of this invention is to provide a method for evaluating the consistency of fluid distribution in a fuel cell stack, comprising the following steps:
[0009] S1: Fabricate a special single cell and design its number of cells; assemble and test the experimental stack; output data through experimental testing: the total inlet and outlet pressure difference ΔP of the three chambers at different current points. Exp Common manifold pressure value P at the target current point Exp ;
[0010] S2: Establish a simplified three-cavity flow field model, mesh the model, adjust the porous medium resistance coefficient, perform simulation calculations, and output data from the simulation model: the pressure difference ΔP between the inlet and outlet of the three cavities at different current points. Num Common manifold pressure value P at the target current point Num ;
[0011] S3: Verify the effectiveness of the simulation model by comparing experimental data and simulation data, i.e., whether it simultaneously satisfies:
[0012] |ΔP Num -ΔP Exp | / ΔP Exp ≤A (1)
[0013] |P Num -P Exp | / P Exp ≤B (2);
[0014] S4: Calculate the flow rate Q on each chip pool using simulation software post-processing. Num This includes the average flow rate per pool. Minimum flow rate per pool
[0015] S5: Verify whether the fluid distribution within the fuel cell stack meets the above requirements by setting fluid distribution consistency evaluation conditions.
[0016]
[0017] Among them, A, B, and C are all preset thresholds.
[0018] Furthermore, a fuel cell stack consists of n or more individual cells stacked sequentially. The stack circuitry is connected in series, while the three chambers (air, hydrogen, and cooling water) are connected in parallel. Hydrogen gas is introduced into the anode inlet of the fuel cell stack, air is introduced into the cathode inlet, and coolant is introduced into the coolant inlet. For ease of piping connection, a U-shaped fluid configuration is commonly used for the three chambers of the stack: that is, the inlet and outlet are on the same side of the stack core.
[0019] Furthermore, A, B, and C are all 5%.
[0020] Furthermore, in S1, during the preparation of the special single cell, a pressure sensor is installed at the common manifold of the special single cell, and the pressure sensor is insulated from the stack core by an insulating sleeve.
[0021] Furthermore, in S1, during the assembly and testing of the experimental fuel cell stack, special single cells are respectively located at the front end of the stack core near the water and gas inlet / outlet sides, as well as at the blind end and inside the stack core.
[0022] Furthermore, several of the aforementioned special single cells can be inserted into the core, and they can be distributed uniformly or non-uniformly. Figure 3 As shown, three special single cells are uniformly inserted into the core.
[0023] Furthermore, the pressure value P at different pressure measuring points within the three-lumen common manifold is measured using a pressure sensor. in and P out , where P in P is the pressure value inside the common manifold on the inlet side. out This is the pressure value inside the common manifold on the outgoing side.
[0024] Furthermore, and The pressure values at the inlet and outlet of the first single cell (i.e., measuring points 1 and 1'); and The pressure values are at the inlet and outlet of the last single cell (i.e., measuring points 2 and 2'). and This represents the pressure value at the inlet and outlet of the nth single-cell module. Figure 3 The pressure values at measuring points 3, 3′, 4, 4′, and 5, 5′ are shown, corresponding to the n1, n2, and n3 single cells, respectively.
[0025] Furthermore, it can be calculated The voltage drop ΔP at the inlet and outlet of the nth single cell is obtained. n .
[0026] Furthermore, it can be calculated and The pressure drop ΔP in the inlet common manifold was obtained separately. in and the pressure drop ΔP of the common manifold on the output side out .
[0027] Furthermore, since the fuel cell stack is connected to the test bench via a connecting manifold, and the connecting manifold has a certain flow resistance, the total inlet and outlet pressure difference ΔP of the three chambers is... Exp Higher than the pressure difference ΔP between the inlet and outlet of each individual pool section n .
[0028] like Figure 5 ΔP ExpThe total inlet and outlet pressure difference of the fuel cell stack measured by the test bench at different current points is shown as a square dot.
[0029] like Figure 6 P Exp This indicates the pressure values at different measuring points on the common manifold of the experimental fuel cell stack at a certain current point. The square points in the figure represent the pressure in the outlet common manifold. It should be noted that this only shows the pressure inside the outlet common manifold of the fuel cell stack; similarly, the pressure inside the inlet common manifold of the fuel cell stack can also be obtained.
[0030] Furthermore, in S2, the simplified three-cavity flow field model includes the connecting manifold fluid domain, the inlet and outlet common manifold fluid domain, and the electrode fluid domain, and the electrode flow field does not include the actual electrode flow field structure.
[0031] Furthermore, in S2, in the simplified three-cavity flow field model, a porous medium model is set in the fluid domain of the electrode plate. The porous medium model simulates the flow resistance inside the electrode plate by setting the viscous drag coefficient C1 and the inertial drag coefficient C2.
[0032] Furthermore, in S2, the porous medium is simplified in the modeling process as a momentum source term appended to the standard flow equation. The momentum source term includes two parts: a viscous loss term and an inertial loss term, specifically:
[0033]
[0034] Where S i Let C1 represent the momentum source term in the i-th direction (x,y,z), C2 be the viscous drag coefficient, μ be the medium viscosity, and v be the fluid velocity. Rough estimates of C1 and C2 can be obtained by fitting the following equation:
[0035]
[0036] Wherein, ΔP Exp and v Exp Given the total inlet and outlet pressure difference and inlet flow velocity of the experimental stack at different current points, we have:
[0037] a=C1μΔn (6)
[0038]
[0039] Where Δn is the thickness of the porous medium region.
[0040] Furthermore, in S2, the simulation calculations are performed using the commercial fluid simulation software Fluent.
[0041] Furthermore, in S3, if the effectiveness index formulas (1) and (2) are not satisfied simultaneously, the porous medium resistance coefficients C1 and C2 are readjusted.
[0042] Furthermore, in S5, if the fluid distribution consistency index of equation (3) is not satisfied, the number of single cell cells is redesigned.
[0043] Compared with the prior art, the present invention has the following technical advantages:
[0044] This invention provides a method for evaluating the consistency of fluid distribution in fuel cell stacks by combining experiments and simulations. It can accurately evaluate the consistency of fluid distribution in the three chambers of fuel cell stacks for different structural forms. The method is simple and highly accurate. Attached Figure Description
[0045] The accompanying drawings used in the embodiments will be briefly described below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation of the scope. For those skilled in the art, other related drawings can be obtained from these drawings without creative effort.
[0046] Figure 1 This is a flowchart of the fuel cell stack fluid distribution consistency evaluation method combining experiment and simulation in an embodiment of the present invention.
[0047] Figure 2 This is a schematic diagram of a special single battery in an embodiment of the present invention.
[0048] Figure 3 This is a schematic diagram of a fuel cell stack for fluid distribution consistency experiments in an embodiment of the present invention.
[0049] Figure 4 This is a schematic diagram of a simulation model of fluid distribution consistency in a fuel cell stack according to an embodiment of the present invention.
[0050] Figure 5 This is a schematic diagram of the experimental and simulation results of fluid distribution consistency in a fuel cell stack according to an embodiment of the present invention.
[0051] Figure 6 This is a schematic diagram of the experimental and simulation results of fluid distribution consistency in a fuel cell stack according to an embodiment of the present invention.
[0052] Figure 7 This is a schematic diagram of the simulation results of the fluid distribution consistency of the fuel cell stack in an embodiment of the present invention. Detailed Implementation
[0053] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. Any structural / module names, control modes, algorithms, processes, or composition ratios not explicitly described in this technical solution are considered common technical features disclosed in the prior art.
[0054] This embodiment presents a fuel cell stack fluid distribution consistency evaluation method that combines experimentation and simulation. Based on established evaluation conditions, it judges the effectiveness of the simulation model and the consistency of fluid distribution in the fuel cell stack, solving the current problem of inaccurately evaluating the three-chamber fluid distribution consistency of fuel cell stacks. See also... Figure 1 The flowchart of the fuel cell stack fluid distribution consistency evaluation method combining experiment and simulation in this technical solution includes the following steps:
[0055] Step 1-a: Prepare a special single cell. Place a pressure sensor at the common manifold of the special single cell. The pressure sensor is insulated from the stack core by an insulating sleeve.
[0056] Step 1-b: Assemble and test the experimental fuel cell stack. The aforementioned special single cells need to be arranged separately at the front end of the core (near the water and gas inlet / outlet side), the blind end, and inside the core.
[0057] Step 1-c: Output data through experimental testing: 1. Total inlet and outlet pressure difference ΔP of the three chambers at different current points. Exp 2. The common manifold pressure value P at a certain current point. Exp .
[0058] Step 2-a: Establish a simplified three-cavity flow field model and mesh it. This simplified model includes a connecting manifold fluid domain, a common inlet and outlet manifold fluid domain, and an electrode fluid domain. The electrode flow field does not need to include the actual flow field structure of the electrode. A porous medium model is set for the electrode fluid domain. This model simulates the flow resistance inside the electrode by setting the viscous drag coefficient C1 and the inertial drag coefficient C2.
[0059] Step 2-b: Adjust the resistance coefficient of the porous medium and perform simulation calculations. The simulation calculations were completed using the commercial fluid simulation software Fluent.
[0060] Step 2-c: Output data through simulation model: 1. Pressure difference ΔP between the inlet and outlet of the three chambers at different current points. Num 2. The common manifold pressure value P at a certain current point. Num .
[0061] Step 3: Verify the effectiveness of the simulation model by comparing experimental and simulation data. This verification is completed by setting evaluation criteria for the effectiveness of the simulation modeling:
[0062] |ΔP Num -ΔP Exp | / ΔP Exp ≤5% (1)
[0063] |P Num -P Exp | / P Exp ≤5% (2)
[0064] Wherein, ΔP Exp P Exp These are the pressure difference between the inlet and outlet of the three chambers and the pressure value at the measuring point of the common manifold, respectively, measured experimentally in step 1-c; ΔP Num P Num These are the pressure difference between the inlet and outlet of the three chambers and the internal pressure value of the common manifold obtained from the simulation model in step 2-c, respectively. If the above validity indicators are not met, return to step 2-b, that is, adjust the porous media resistance coefficients C1 and C2.
[0065] Step 4: Output single-pool flow rate Q Num The flow rate Q on each chip's individual pool is calculated using simulation software post-processing. Num This includes the average flow rate per pool. Minimum flow rate per pool
[0066] Step 5: Verify the fluid distribution within the fuel cell stack by setting fluid distribution consistency evaluation conditions:
[0067]
[0068] in, The average flow rate of a single pool obtained from the simulation model in step 4 is divided into the average flow rate of the single pool. Minimum flow rate per pool If the above fluid distribution consistency criteria are not met, the number of individual cells needs to be redesigned.
[0069] In practice:
[0070] A fuel cell stack consists of n or more individual cells stacked sequentially. The stack circuitry is connected in series, and the three chambers (air, hydrogen, and cooling water) are connected in parallel. Hydrogen gas is introduced into the anode inlet of the fuel cell stack, air is introduced into the cathode inlet, and coolant is introduced into the coolant inlet. For ease of piping connection, a U-shaped fluid configuration is commonly used for the three chambers of the stack: that is, the inlet and outlet are on the same side of the stack core.
[0071] See Figure 2 The diagram shows a special single cell in the battery, where a pressure sensor is placed at the common manifold, and the pressure sensor is insulated from the battery stack core by an insulating sleeve.
[0072] Special single-cell three-chamber system (hydrogen, air, and cooling water) can be applied. Figure 2 The pressure sensor is arranged at the common manifold as shown.
[0073] The special single cell has cathode and anode flow fields on both sides, and cooling water flow field in the middle.
[0074] The special single cell on the inlet / outlet side and the blind side has only a cathode or anode flow field, while the middle part is a cooling water flow field.
[0075] See Figure 3 A schematic diagram of a fuel cell stack for fluid distribution consistency experiment, in which special single cells need to be arranged separately at the front end of the stack core (near the water and gas inlet / outlet side), the blind end, and inside the stack core.
[0076] Several of the aforementioned special single cells can be inserted into the core, and they can be distributed uniformly or non-uniformly. Figure 3 As shown, three special single cells are evenly inserted into the core.
[0077] The pressure value P at different pressure measuring points in the three-lumen common manifold is measured using a pressure sensor. in and P out , where P in P is the pressure value inside the common manifold on the inlet side. out This is the pressure value inside the common manifold on the outgoing side.
[0078] and The pressure values at the inlet and outlet of the first single cell (i.e., measuring points 1 and 1'); and The pressure values are at the inlet and outlet of the last single cell (i.e., measuring points 2 and 2'). and This represents the pressure value at the inlet and outlet of the nth single-cell module. Figure 3 The pressure values at measuring points 3, 3′, 4, 4′, and 5, 5′ are shown, corresponding to the n1, n2, and n3 single cells, respectively.
[0079] It can be calculated The voltage drop ΔP at the inlet and outlet of the nth single cell is obtained. n .
[0080] It can be calculated and The pressure drop ΔP in the inlet common manifold was obtained separately. in and the pressure drop ΔP of the common manifold on the output side out .
[0081] The total inlet and outlet pressure difference ΔP of the three chambers can be obtained through experimental measurement. Exp Pressure values P at different measuring points within the common manifold Exp .
[0082] Figure 4 A schematic diagram of a simulation model for consistent fluid distribution in a fuel cell stack is shown. This model includes a connecting manifold fluid domain, a common manifold fluid domain for the inlet and outlet sides, and a plate fluid domain. The plate flow field does not need to include the actual plate flow field structure.
[0083] The structure of the connecting manifold and common manifold should be designed according to the actual fuel cell stack.
[0084] A porous medium model is set up in the fluid domain of the electrode plate. This model simulates the flow resistance inside the electrode plate by setting the viscous drag coefficient C1 and the inertial drag coefficient C2.
[0085] In modeling porous media, a momentum source term is simplified to be added to the standard flow equations. This source term comprises two parts: a viscous loss term and an inertial loss term. The simplified form of the equation is as follows:
[0086]
[0087] Where S i Let C1 represent the momentum source term in the i-th direction (x,y,z), C2 be the viscous drag coefficient, C1 be the inertial drag coefficient, μ be the medium viscosity, and v be the fluid velocity. Rough estimates of C1 and C2 can be obtained by fitting the following equation.
[0088]
[0089] Wherein, ΔP Exp and v Exp for Figure 3 The total inlet and outlet pressure difference and inlet flow velocity of the experimental fuel cell stack at different current points are given.
[0090] a=C1μΔn (6)
[0091]
[0092] Where Δn is the thickness of the porous medium region.
[0093] It should be noted that the C1 and C2 values calculated by formulas (5-7) are not yet accurate enough to reflect the actual resistance of the fuel cell plate. The C1 and C2 values need to be further adjusted in conjunction with the effectiveness indicators of the simulation model (i.e., equations (1) and (2)).
[0094] The total inlet and outlet pressure difference ΔP of the three chambers can be obtained through simulation model. Num Public manifold pressure value P Num Each chip's single pool flow Q Num Average flow rate per pool Minimum flow rate per pool
[0095] See Figure 5 , 6 This is a schematic diagram of the experimental and simulation results of fluid distribution consistency in a fuel cell stack, where ΔP Exp This represents the total inlet and outlet pressure difference of the fuel cell stack measured by the test bench at different current points, such as... Figure 5 As shown by the square point; ΔP Num This represents the total inlet and outlet pressure difference of the fuel cell stack calculated by the simulation model at different current points, such as... Figure 5As shown by the middle dot; P Exp This represents the pressure values at different measuring points on the common manifold of the experimental fuel cell stack at a certain current point, such as... Figure 6 The square dot indicates the pressure in the common manifold on the outgoing side; P Num This represents the pressure values at different locations within the common manifold of the simulation model at a certain current point, such as... Figure 6 The center dot indicates the pressure in the output common manifold. It should be noted that this only shows the pressure inside the output common manifold of the fuel cell stack; similarly, the pressure inside the input common manifold of the fuel cell stack can also be derived.
[0096] The effectiveness of the simulation model is verified by setting evaluation criteria for the effectiveness of the simulation modeling:
[0097] |ΔP Num -ΔP Exp | / ΔP Exp ≤5% (1)
[0098] |P Num -P Exp | / P Exp ≤5% (2)
[0099] Wherein, ΔP Exp P Exp These are the pressure difference between the total inlet and outlet of the three chambers and the pressure value at the measuring point of the common manifold, as measured in the example; ΔP Num P Num These represent the pressure difference between the inlet and outlet of the three chambers and the internal pressure value of the common manifold obtained from the simulation model in the embodiment. If the above-mentioned simulation modeling effectiveness evaluation conditions are not met, the porous media resistance coefficients C1 and C2 need to be adjusted.
[0100] See Figure 7 This is a schematic diagram of the simulation results for the consistency of fluid distribution in a fuel cell stack, where Q... Num The solid line represents the average flow rate of each individual pool obtained from the simulation model in this embodiment. The dashed line represents the minimum flow rate of a single pool calculated by the simulation model.
[0101] The fluid distribution within the aforementioned fuel cell stack is examined by setting fluid distribution consistency evaluation conditions.
[0102]
[0103] in, The average flow rate of a single pool obtained from simulation in the examples is divided into... Minimum flow rate per pool If the above fluid distribution consistency criteria are not met, the number of individual cells needs to be redesigned.
[0104] The above description of the embodiments is provided to enable those skilled in the art to understand and use the invention. It will be apparent to those skilled in the art that various modifications can be made to these embodiments, and the general principles described herein can be applied to other embodiments without inventive effort. Therefore, the present invention is not limited to the above embodiments, and any improvements and modifications made by those skilled in the art based on the disclosure of the present invention without departing from the scope of the invention should be within the protection scope of the present invention.
Claims
1. A method for evaluating the consistency of fluid distribution in a fuel cell stack, characterized in that, Includes the following steps: S1: Fabricate a special single cell and design its number of cells; assemble and test the experimental stack; output data through experimental testing: total inlet and outlet pressure difference of the three chambers at different current points. Common manifold pressure value at the target current point ; S2: Establish a simplified three-cavity flow field model, mesh the model, adjust the porous medium resistance coefficient, perform simulation calculations, and output data from the simulation model: the pressure difference between the inlet and outlet of the three cavities at different current points. Common manifold pressure value at the target current point ; S3: Verify the effectiveness of the simulation model by comparing experimental data and simulation data, i.e., whether it simultaneously satisfies: (1) (2); S4: Calculate the flow rate on each chip pool using simulation software post-processing. This includes the average flow rate per pool. Minimum flow rate per pool ; S5: Verify whether the fluid distribution within the fuel cell stack meets the above requirements by setting fluid distribution consistency evaluation conditions. (3); Among them, A, B, and C are all preset thresholds; In S1, during the preparation of the special single cell, a pressure sensor is installed at the common manifold of the special single cell. The pressure sensor is insulated from the stack core by an insulating sleeve. In S1, during the assembly and testing of the experimental fuel cell stack, special single cells are respectively placed at the front end of the stack core near the water and gas inlet / outlet sides, as well as at the blind end and inside the stack core.
2. The method for evaluating the consistency of fluid distribution in a fuel cell stack according to claim 1, characterized in that, A, B, and C are all 5%.
3. The method for evaluating the consistency of fluid distribution in a fuel cell stack according to claim 1, characterized in that, In S2, the simplified three-cavity flow field model includes the connecting manifold fluid domain, the inlet and outlet common manifold fluid domain, and the electrode fluid domain, and the electrode flow field does not include the actual electrode flow field structure.
4. The method for evaluating the consistency of fluid distribution in a fuel cell stack according to claim 3, characterized in that, In S2, the simplified three-cavity flow field model includes a porous medium model within the electrode fluid domain. This porous medium model is defined by setting a viscous drag coefficient. and inertial drag coefficient To simulate the flow resistance inside the electrode plate.
5. The method for evaluating the consistency of fluid distribution in a fuel cell stack according to claim 4, characterized in that, In S2, porous media are simplified as a momentum source term appended to the standard flow equation during modeling. The momentum source term comprises two parts: a viscous loss term and an inertial loss term, specifically: (4) in Indicates the first Towards Momentum source term, It is the viscous drag coefficient. It is the inertial drag coefficient. It is the viscosity of the medium. It is the fluid velocity. and A rough estimate can be obtained by fitting the following equation: (5) in, and Given the total inlet and outlet pressure difference and inlet flow velocity of the experimental stack at different current points, we have: (6) (7) in, The thickness of the porous medium region.
6. The method for evaluating the consistency of fluid distribution in a fuel cell stack according to claim 1, characterized in that, In S2, the simulation calculations are performed using the commercial fluid simulation software Fluent.
7. The method for evaluating the consistency of fluid distribution in a fuel cell stack according to claim 4, characterized in that, In S3, if the effectiveness index equations (1) and (2) are not satisfied simultaneously, the porous medium resistance coefficient should be readjusted. and .
8. The method for evaluating the consistency of fluid distribution in a fuel cell stack according to claim 1, characterized in that, In S5, if the fluid distribution consistency index of equation (3) is not satisfied, the number of single cell cells should be redesigned.
Citation Information
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