Machine learning technology-based auxiliary electrolytic bath runner optimization design method

Through machine learning-based technical solutions, the alkaline electrolytic cell flow channel design is optimized, and the problems of flow dead zones and local excessive flow rates are solved, the discharge efficiency of hydrogen and oxygen is improved, and the cost of hydrogen production is reduced.

CN119885908AActive Publication Date: 2025-04-25ZHEJIANG UNIV +1
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Patent Information

Application Number
CN202510363593.6
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2025-03-26
Publication Date
2025-04-25
Estimated Expiration
2045-03-26

AI Technical Summary

Technical Problem

The existing alkaline electrolytic cell flow channel design has dead flow zones and locally excessive flow velocities, and lacks a systematic optimization design method, which affects the discharge efficiency of hydrogen and oxygen.

Method used

Using a machine learning-based technical solution, by constructing a flow field model of the runner, key variables of the runner geometric parameters are screened, and the runner structure is optimized using genetic algorithms to obtain the optimized combination of key variables to improve the runner design.

Benefits of technology

By optimizing the flow channel design, the flow dead zone and local excessive flow rate are reduced, the discharge efficiency of hydrogen and oxygen is improved, and the operating cost of electrolytic hydrogen production is reduced.

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Abstract

The invention relates to a machine learning technology-based auxiliary electrolytic bath flow channel optimization design method, and belongs to the technical field of water electrolysis hydrogen production, and the method comprises the following steps: S1, based on the influence of gas-liquid mixed flow in an alkaline water electrolysis hydrogen production electrolytic bath on electrochemical performance, selecting a flow channel flow field model, and constructing a flow channel optimization simulation basic model; s2, screening key variables of geometric parameters of the runner by adopting a regression method; and S3, optimizing the flow field model by using the key variable and a genetic algorithm to obtain parameters of the optimized key variable. According to the method, the gas-liquid two-phase flow behavior in the electrolytic cell serves as a key index of the performance of the flow channel of the electrolytic cell, the finally obtained flow channel design scheme is optimized, iteration updating is conducted on the combination of key variables according to the flow uniformity coefficient, the too high flow speed of a flow dead zone or a local area is reduced, and the hydrogen and oxygen discharging efficiency is improved.
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Description

Technical Field

[0001] The present invention belongs to the technical field of hydrogen production by electrolysis of water, and specifically relates to a method for optimizing the flow channel of an electrolyzer assisted by machine learning technology. Background Art

[0002] Hydrogen energy is an important part of the future energy system. Hydrogen has the advantage of high energy density and can effectively store a large amount of energy, making it suitable for use in large-scale energy storage and transportation. In addition, hydrogen does not produce harmful pollutants during use and is a completely clean energy source. Producing hydrogen by electrolysis of water is a green, zero-carbon emission method of hydrogen production. Different water electrolysis hydrogen production technologies have their own advantages and disadvantages, and alkaline water electrolysis has the advantages of mature technology and relatively low cost, and is currently one of the fastest commercialized hydrogen production technologies.

[0003] Alkaline electrolyzer is the core equipment of alkaline water electrolysis hydrogen production technology, which directly affects the efficiency and cost of hydrogen production. In the research of alkaline water electrolysis hydrogen production, the flow channel structure design on the plate is one of the key factors affecting the performance of alkaline electrolyzer. The optimization goal of the flow channel design is mainly to improve the flow uniformity of the electrolyte and promote the smooth discharge of gas products, thereby effectively reducing the voltage loss of the electrolyzer.

[0004] At present, there are still some problems that need to be improved in the flow channel design of alkaline electrolyzers. First, there are dead zones or excessively high flow velocities in local areas of the electrolyte in the flow channel, which leads to uneven distribution of the electrolyte, which directly affects the discharge efficiency of hydrogen and oxygen. Secondly, the current flow channel design focuses more on the analysis of the flow characteristics of the electrolyte, and optimizes the electrolyzer flow channel structure based on experience based on the flow characteristics. The existing research on the optimization design of the alkaline electrolyzer flow channel is still in its preliminary stage and lacks a systematic optimization design method. It is urgent to develop an efficient electrolyzer flow channel design optimization method to improve the performance of the electrolyzer and reduce the operating cost of hydrogen production by electrolysis. Summary of the invention

[0005] The purpose of the present invention is to provide an electrolytic cell flow channel optimization design method assisted by machine learning technology to solve the problems of existing alkaline electrolytic cell flow channel design, such as flow dead zones or excessively high flow velocities in local areas, and lack of a systematic optimization design method.

[0006] In order to achieve the above object, the technical solution of the present invention is as follows: The present invention relates to a method for optimizing the design of an electrolytic cell flow channel based on machine learning technology, which comprises the following steps: S1. Based on the influence of gas-liquid mixed flow in the alkaline water electrolysis hydrogen production electrolyzer on the electrochemical performance, a flow field model of the flow channel is constructed as the basic model for flow channel optimization simulation; S2. Use regression method to screen key variables of flow channel geometry parameters; S3. Utilize key variables and optimize the flow field model of the flow channel through genetic algorithms to obtain the optimized combination of key variables, and then screen and optimize the flow channel structure.

[0007] Preferably, the specific steps of constructing the flow field model in S1 include: S1.1. Construct the mass conservation formula of the fluid. The mass conservation formula is expressed as: (1), in, f g is the volume fraction of the gas phase, u g is the flow rate of the gas phase, u l is the flow rate of the liquid phase, m dc is the mass flux from liquid to gas, r l is the liquid density, r g is the gas phase density; S1.2. The Navier-Stokes equation is used to describe the momentum change of the fluid in the electrolytic cell flow channel. The formula is: (2), (3), Among them, ∇ p is the fluid pressure gradient, t l and t g are the stress tensors of the liquid and gas phases, respectively, F m,l is the momentum transferred from the liquid phase to the gas phase, F m,g is the momentum transferred from the gas phase to the liquid phase, u int is the flow velocity of the fluid inside the microelement; S1.3. The k-ε equation is used to describe the gas-liquid two-phase turbulent flow behavior, and the formula is: (4), (5), in, e is the turbulence dissipation ratio, k is the turbulent kinetic energy, u mix is the fluid flow rate, r is the fluid density, T is the ambient temperature of the reaction, m T is the fluid dynamic viscosity,P k is the turbulent flow energy term, s k ,s ε 、C ε,1 、C ε,2 They are k- e Parameters of the turbulence model; In formula (4) and formula (5), (6), (7), in, C u Also k- e Parameters of the turbulence model.

[0008] Preferably, in the flow field model constructed in S1, the mass flux from the liquid phase to the gas phase on the anode side and the cathode side of the electrolytic cell flow channel follows the following formula: (8), in, M g is the molar mass of the gas, n is the amount of charge transferred by the reaction, F is the Faraday constant, i ν is the reaction current of the microelement, and the gas mass flux of the microelement is calibrated by the reaction current of the electrochemical reaction m g .

[0009] Preferably, the specific steps of using regression method to screen key variables of flow channel geometric parameters in S2 are: S2.1. Establish an initial electrolytic cell flow channel design, and select several electrolytic cell convex point spacing parameters as initial variables based on the differences in the behavior of the flow field in the flow channel; S2.2. Establish several electrolytic cell flow channel convex points of different shapes, and select several initial variables of flow channel shape geometric parameters according to the difference in the influence of different shape convex points on the flow field; S2.3. Use multiple regression models to score each initial variable respectively, and normalize the scoring data to obtain the final score for each initial variable; S2.4. Set a scoring threshold and select variables whose final scores are greater than the scoring threshold as key variables.

[0010] Preferably, in S2.3, three regression models, namely, regression tree, gradient boosting regression and extra tree regression, are used to score each initial variable respectively, wherein the flow channel result feature of the regression method is called data dimension, and the normalization process uses the following formula to calculate the final score: (9), in, X norm To normalize the data, X The raw data for the regression model scoring results, X min is the minimum value of each dimension in the original data. X max is the maximum value of each dimension in the original data.

[0011] Preferably, the specific steps of S3 utilizing key variables and optimizing the flow field model of the flow channel through a genetic algorithm include: S3.1. Randomly combine the selected key variables to form several key variable combinations, and the key variable combinations are used as the initial population of the genetic algorithm to generate individuals, and the total number of iterations of the genetic algorithm is set; S3.2. Perform alkaline water electrolysis hydrogen production electrolyzer flow field simulation on the flow channel structure corresponding to each individual, calculate the corresponding flow uniformity coefficient as the fitness of the individual, and calculate the total fitness value; S3.3. Set the threshold of the next generation population size, take the quotient of the individual fitness and the total fitness value as the probability of random selection, randomly select a pair of individuals, and select the individual with higher fitness between the two and put it into the next generation population, repeat this step until the number of individuals in the next generation population reaches the threshold of the next generation population size, and the number of iterations increases by 1; S3.4. Determine whether the number of iterations reaches the set total number of iterations. If not, generate new individuals through crossover method and / or mutation method and add them to the population, and return to S3.2 for the next round of iterations; if reached, stop iteration, output the optimized individuals, and then obtain the optimized combination of key variables.

[0012] Preferably, the calculation formula of the flow uniformity coefficient in S3.2 is: (10), in, U v is the flow uniformity coefficient of the electrolyte, u i For the i The flow velocity of a microelement of the flow channel is u a is the weighted mean of the velocity of the entire flow field, A i For the iThe area of ​​a flow channel element, n is the total number of flow channel elements; The calculation method of the weighted mean of the flow velocity of the entire flow field is: (11).

[0013] Compared with the prior art, the technical solution provided by the present invention has the following beneficial effects: 1. The method for optimizing the flow path of an electrolyzer assisted by machine learning technology involved in the present invention optimizes the flow path morphology of the electrolyzer under the flow model through a genetic algorithm based on the fluid flow field model in the alkaline water electrolysis hydrogen production electrolyzer, obtains a combination of optimized key variables, obtains an optimized design scheme, and optimizes the flow path design scheme finally obtained.

[0014] 2. The machine learning technology-assisted electrolytic cell flow channel optimization design involved in the present invention iteratively updates the combination of key variables based on the flow uniformity coefficient during the process of optimizing the flow field model of the flow channel through a genetic algorithm, thereby obtaining the optimal combination of key variables, thereby reducing the dead zone of flow or the excessively high flow velocity in the local area, and promoting the discharge efficiency of hydrogen and oxygen. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 It is a schematic flow chart of the method of the present invention; Figure 2 Schematic diagram of the electrolytic cell flow channel partitioning method in the embodiment; Figure 3 Schematic diagram of the geometrical dimension parameters of the flow channel spoiler unit distribution in the embodiment; Figure 4 is an importance score diagram of the regression method of the geometric parameters of the spoiler unit geometric structure after data normalization in the embodiment; Figure 5 is a schematic diagram of the genetic algorithm optimization flow channel structure design process in the embodiment; Figure 6 is a data diagram of a genetic algorithm optimization process for optimizing the electrolytic cell flow channel based on machine learning technology in an embodiment; Figure 7 It is the optimal flow channel structure and flow field velocity distribution diagram of the electrolytic cell flow channel optimization design assisted by machine learning technology in the embodiment.

[0016] Figure 8 It is a data graph of the optimized flow uniformity coefficient based on the machine learning technology-assisted electrolytic cell flow channel optimization design in the embodiment. DETAILED DESCRIPTION

[0017] In order to further understand the content of the present invention, the present invention is described in detail in conjunction with examples. The following examples are used to illustrate the present invention but are not used to limit the scope of the present invention.

[0018] See attached Figure 1 As shown, the present invention relates to a method for optimizing the flow channel of an electrolytic cell based on machine learning technology, which comprises the following steps: S1. Based on the influence of gas-liquid mixed flow in the alkaline water electrolysis hydrogen production electrolyzer on the electrochemical performance, by partially simplifying the non-critical factors of the model, focusing on the core contradictions of the optimization process, and constructing the fluid flow field model in the flow channel as the basic model for flow channel optimization simulation; Among them, non-critical factors include the following assumptions: (1) The water inside the electrolytic cell is always in liquid state, and the evaporation of liquid water is ignored; (2) All gases in the electrolyzer are ideal gases and incompressible; (3) There is no significant contact resistance between the layers of the electrolytic cell; (4) The cross-permeation of hydrogen and oxygen in the membrane can be ignored.

[0019] The above-mentioned flow field model uses the Euler-Eulerian-Reynolds-Averaged Navier-Stokes k-ε turbulence model to calculate the flow velocity of the fluid and the volume ratio of the gas in the electrolytic cell flow channel, and improves the simulation accuracy of the model in terms of rotational flow by adding viscosity terms to the large-scale motion to reflect the influence of small-scale motion. At the same time, the simulation accuracy of the flow conditions in turbulence, laminar flow and laminar-turbulent transition zone in the flow field model is improved; the specific steps of the method for constructing the flow field model include: S1.1. Construct the mass conservation formula of the fluid. The mass conservation formula is expressed as: (1), in, f g is the volume fraction of the gas phase, u g is the flow rate of the gas phase, u l is the flow rate of the liquid phase, m dc is the mass flux from liquid to gas, r l is the liquid density, r g is the gas phase density; S1.2. To describe the flow behavior of the fluid, the Navier-Stokes equation is used to describe the momentum change of the fluid in the electrolytic cell flow channel. The formula is: (2), (3), Among them, ∇ p is the fluid pressure gradient, t l and t g are the stress tensors of the liquid and gas phases, respectively, F m,l is the momentum transferred from the liquid phase to the gas phase, F m,g is the momentum transferred from the gas phase to the liquid phase, u int is the flow velocity of the fluid inside the microelement; S1.3. The k-ε equation is used to describe the gas-liquid two-phase turbulent flow behavior, and the formula is: (4), (5), in, e is the turbulence dissipation ratio, k is the turbulent kinetic energy, u mix is the fluid flow rate, r is the fluid density, T is the ambient temperature of the reaction, m T is the fluid dynamic viscosity, P k is the turbulent flow energy term, s k ,s ε 、C ε,1 、C ε,2 They are k- e Parameters of the turbulence model; In formula (4) and formula (5), (6), (7), in, C u Also k- e Parameters of the turbulence model; In addition, on the anode and cathode sides of the electrolyzer flow channel, the mass flux from the liquid phase to the gas phase follows the following formula: (8), in, M g is the molar mass of the gas, n is the amount of charge transferred by the reaction,F is the Faraday constant, i ν is the reaction current of the microelement, and the gas mass flux of the microelement is calibrated by the reaction current of the electrochemical reaction m g .

[0020] S2. Use regression method to screen key variables of flow channel geometry parameters. The specific steps are as follows: S2.1. Establish the initial electrolytic cell flow channel design and partition it according to the differences in the flow field behavior in the flow channel. The partition results are as follows: Figure 2 As shown; the geometric structure of the flow channel around the unit in the partition is classified and numbered, such as Figure 3 As shown in the figure, the bump spacing parameters of 16 electrolytic cells are selected as the initial variables of the flow channel structure parameters; S2.2. Establish several electrolytic cell flow channel convex points of different shapes, and select several initial variables of flow channel shape geometric parameters according to the difference in the influence of different shape convex points on the flow field; S2.3. Use multiple regression models to score each initial variable (including the initial variables of the flow channel structure parameters and the initial variables of the flow channel shape geometry parameters). This embodiment uses three regression methods, namely regression tree, gradient boosting regression and additional tree regression, to screen key variables. By numerically normalizing the evaluation results of the three regression methods, a comprehensive evaluation is obtained to avoid the deviation that may be caused by a single regression model. The above three regression methods are conventional technical means in this field and do not belong to the content to be protected by this application. The scoring data is normalized, and the final score for each initial variable is calculated as the importance score. The flow channel result feature of the regression method is called the data dimension, and the calculation formula is as follows: (20), in, X norm To normalize the data, X The raw data for the regression model scoring results, X min is the minimum value of each dimension in the original data. X max is the maximum value of each dimension in the original data.

[0021] S2.4. Set a scoring threshold and select variables whose final scores are greater than the scoring threshold as key variables.

[0022] After S2, we get Figure 4The importance scores of the flow channel structure parameters shown in the figure select the flow channel structure parameters exceeding the score threshold as the key variables. The embodiment selects 6 flow channel structure parameters as the key variables. Similarly, several flow channel shape geometric parameters can be selected as the key variables, and the sum of the two key variables is all the selected key variables.

[0023] S3. Utilize key variables and optimize the flow field model of the flow channel through genetic algorithm to obtain the optimized combination of key variables, and then screen and optimize the flow channel structure. The specific steps are as follows: Figure 5 As shown, including: S3.1. Randomly combine the selected key variables to form several key variable combinations, and the key variable combinations are used as the initial population of the genetic algorithm to generate individuals, and the total number of iterations of the genetic algorithm is set; S3.2. Perform alkaline water electrolysis hydrogen production electrolyzer flow field simulation on the flow channel structure corresponding to each individual, calculate the corresponding flow uniformity coefficient as the fitness of the individual, and calculate the total fitness value. The calculation formula of the flow uniformity coefficient of each individual is: (twenty one), in, U v is the flow uniformity coefficient of the electrolyte, u i For the i The flow velocity of a microelement of the flow channel is u a is the weighted mean of the velocity of the entire flow field, A i For the i The area of ​​a flow channel element, n is the total number of flow channel elements; The calculation method of the weighted mean of the flow velocity of the entire flow field is: (twenty two).

[0024] S3.3. Set the threshold of the next generation population size, take the quotient of individual fitness and total fitness as the probability of random selection, randomly select a pair of individuals, and select the individual with higher fitness between the two and put it into the next generation population. Repeat this step until the number of individuals in the next generation population reaches the threshold of the next generation population size, and increase the number of iterations by 1. The chance of retaining individuals with high fitness is increased through the selection method. S3.4. Determine whether the number of iterations reaches the set total number of iterations. If not, generate new individuals through crossover and / or mutation methods and add them to the population. Introduce new configuration combinations through crossover and mutation methods to increase population diversity. Specifically, the crossover method is to exchange the spacing parameter values ​​of corresponding positions in two individuals, and the mutation method is to randomly select several spacing parameters in individuals with a small probability, and randomly generate a spacing parameter to replace the original spacing parameter value of the individual, and return to S3.2 for the next round of iteration; if it is reached, stop the iteration, output the optimized individual, and then obtain the optimized combination of key variables. The optimization results in this embodiment are as follows: Figure 6 shown.

[0025] Effect analysis: After genetic algorithm optimization, the optimization process converged after the 38th generation, and the flow uniformity coefficient reached the minimum value and tended to be stable, indicating that the flow channel structure has the best flow uniformity at this time. The geometric structure results of the flow channel and the electrolyte flow velocity distribution are shown in Figure 7 As shown in the figure, the flow uniformity coefficients of various flow channels before optimization in four characteristic flow channel sections are compared. Figure 8 As shown in the figure, the flow uniformity coefficient of the optimal flow channel structure is 0.6920, which is 1.97% higher than that of Model_3.4, 9.09% higher than that of DFC and 13.80% higher than that of CCSFC. Moreover, this flow uniformity coefficient is significantly higher than the results of single factor analysis of all unoptimized initial flow channel parameters.

[0026] The present invention is described in detail above in combination with the embodiments, but the contents described are only preferred embodiments of the present invention and cannot be considered to limit the scope of implementation of the present invention. All equivalent changes and improvements made according to the scope of application of the present invention should still fall within the scope of the patent coverage of the present invention.

Claims

1. A method for optimizing the flow channel design of an electrolytic cell based on machine learning technology, characterized in that: It includes the following steps: S1. Based on the influence of gas-liquid mixed flow in the alkaline water electrolysis hydrogen production electrolyzer on the electrochemical performance, a flow field model of the flow channel is constructed as the basic model for flow channel optimization simulation; S2. Use regression method to screen key variables of flow channel geometry parameters; S3. Utilize key variables and optimize the flow field model of the flow channel through genetic algorithms to obtain the optimized combination of key variables, and then screen and optimize the flow channel structure.

2. The method for optimizing the flow channel of an electrolytic cell based on machine learning technology according to claim 1, characterized in that: The specific steps of constructing the flow field model in S1 include: S1.

1. Construct the mass conservation formula of the fluid. The mass conservation formula is expressed as: (1), in, φ g is the volume fraction of the gas phase, u g is the flow rate of the gas phase, u l is the flow rate of the liquid phase, m dc is the mass flux from liquid to gas, ρ l is the liquid density, ρ g is the gas phase density; S1.

2. The Navier-Stokes equation is used to describe the momentum change of the fluid in the electrolytic cell flow channel. The formula is: (2), (3), Among them, ∇ p is the fluid pressure gradient, τ l and τ g are the stress tensors of the liquid and gas phases, respectively, F m,l is the momentum transferred from the liquid phase to the gas phase, F m,g is the momentum transferred from the gas phase to the liquid phase, u int is the flow velocity of the fluid inside the microelement; S1.

3. The k-ε equation is used to describe the gas-liquid two-phase turbulent flow behavior, and the formula is: (4), (5), in, ε is the turbulence dissipation ratio, k is the turbulent kinetic energy, u mix is the fluid flow rate, ρ is the fluid density, T is the ambient temperature of the reaction, μ T is the fluid dynamic viscosity, P k is the turbulent flow energy term, σ k , σ ε 、C ε,1 、C ε,2 They are k- ε Parameters of the turbulence model; In formula (4) and formula (5), (6), (7), in, C u Also k- ε Parameters of the turbulence model.

3. The method for optimizing the flow channel of an electrolytic cell based on machine learning technology according to claim 2, characterized in that: In the flow field model constructed in S1, the mass flux from the liquid phase to the gas phase on the anode side and the cathode side of the electrolytic cell flow channel follows the following formula: (8), in, M g is the molar mass of the gas, n is the amount of charge transferred by the reaction, F is the Faraday constant, i ν is the reaction current of the microelement, and the gas mass flux of the microelement is calibrated by the reaction current of the electrochemical reaction m g .

4. The method for optimizing the flow channel of an electrolytic cell based on machine learning technology according to claim 1, characterized in that: The specific steps of using regression method to screen key variables of flow channel geometry parameters in S2 are: S2.

1. Establish an initial electrolytic cell flow channel design, and select several electrolytic cell convex point spacing parameters as initial variables of the flow channel structure parameters according to the differences in the behavior of the flow field in the flow channel; S2.

2. Establish several electrolytic cell flow channel convex points of different shapes, and select several initial variables of flow channel shape geometric parameters according to the difference in the influence of different shape convex points on the flow field; S2.

3. Use multiple regression models to score each initial variable respectively, and normalize the scoring data to obtain the final score for each initial variable; S2.

4. Set a scoring threshold and select variables whose final scores are greater than the scoring threshold as key variables.

5. The method for optimizing the flow channel of an electrolytic cell based on machine learning technology according to claim 4 is characterized in that: In S2.3, three regression models, namely regression tree, gradient boosting regression and extra tree regression, are used to score each initial variable respectively, wherein the flow channel result feature of the regression method is called data dimension, and the normalization process uses the following formula to calculate the final score: (9), in, X norm To normalize the data, X The raw data for the regression model scoring results, X min is the minimum value of each dimension in the original data. X max is the maximum value of each dimension in the original data.

6. The method for optimizing the flow channel of an electrolytic cell based on machine learning technology according to claim 1, characterized in that: The specific steps of S3 utilizing key variables and optimizing the flow field model of the flow channel through a genetic algorithm include: S3.

1. Randomly combine the selected key variables to form several key variable combinations, and the key variable combinations are used as the initial population of the genetic algorithm to generate individuals, and the total number of iterations of the genetic algorithm is set; S3.

2. Perform alkaline water electrolysis hydrogen production electrolyzer flow field simulation on the flow channel structure corresponding to each individual, calculate the corresponding flow uniformity coefficient as the fitness of the individual, and calculate the total fitness value; S3.

3. Set the threshold of the next generation population size, take the quotient of the individual fitness and the total fitness value as the probability of random selection, randomly select a pair of individuals, and select the individual with higher fitness between the two and put it into the next generation population, repeat this step until the number of individuals in the next generation population reaches the threshold of the next generation population size, and the number of iterations increases by 1; S3.

4. Determine whether the number of iterations reaches the set total number of iterations. If not, generate new individuals through crossover method and / or mutation method and add them to the population, and return to S3.2 for the next round of iterations; if reached, stop iteration, output the optimized individuals, and then obtain the optimized combination of key variables.

7. The method for optimizing the flow channel of an electrolytic cell based on machine learning technology according to claim 6, characterized in that: The calculation formula of the flow uniformity coefficient in S3.2 is: (10), in, U v is the flow uniformity coefficient of the electrolyte, u i For the i The flow velocity of a microelement of the flow channel is u a is the weighted mean of the velocity of the entire flow field, A i For the i The area of ​​a flow channel element, n is the total number of flow channel elements; The calculation method of the weighted mean of the flow velocity of the entire flow field is: (11)。

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