Simulation Method for Reverse Electrodialysis Power Generation Process in Real-Size Grid Channel

Abstract

This invention discloses a simulation method for a real-size mesh channel reverse electrodialysis power generation process, comprising the following steps: S1, simplifying the real mesh channel into a two-dimensional zigzag circular mesh using the flow resistance method, and calculating the equivalent radius of the two-dimensional mesh according to the area equivalence principle; S2, selecting the smallest periodic unit membrane pair for modeling on the x-y plane, dividing the mesh, and setting membrane and solution properties, operating parameters, and boundary conditions; S3, extending the multiphysics field changes to the entire membrane pair height using the boundary coupling method; S4, calculating the membrane-side diffusion boundary layer thickness and potential abrupt change, solving for the resistance of each part of the system, and evaluating the impact of concentration polarization and ion short-circuit current on the output power. The real-size mesh channel reverse electrodialysis power generation process simulation method disclosed in this invention achieves the continuity of multiphysics field changes in the entire flow channel from the membrane pair inlet to the outlet through the boundary coupling method.

Description

Technical Field

[0001] This invention belongs to the technical field of simulation methods for reverse electrodialysis power generation processes, and relates to a simulation method for reverse electrodialysis power generation processes using a real-size grid channel. Background Technology

[0002] Salinity gradient energy possesses significant advantages in terms of cleanliness, greenness, and sustainability, and has broad prospects for development and utilization. Reverse electrodialysis power generation utilizes alternating ion-exchange membranes separated by meshes to separate concentrated and dilute solutions. The chemical potential difference of the solutions drives the transport of ions from the concentrated solution through the membrane to the dilute solution, thus converting salinity gradient chemical energy into electrical energy. In traditional reverse electrodialysis systems, the meshes are typically made of non-conductive materials that do not allow ions to pass through, covering part of the membrane area and hindering the horizontal ion transport across the membrane, causing a mesh shadowing effect, increasing system resistance, and reducing output power. However, in the direction perpendicular to ion transmembrane flow, the periodic structure of the meshes causes the solution to flow periodically from the inlet to the outlet, and the high convection / diffusion ratio within the flow channel results in a high Péclet number for the solution. As the solution flows along the transmembrane and flow channel directions, the different ion migration rates in the solution and within the membrane cause ion depletion near the concentrate membrane and ion aggregation near the dilute membrane, resulting in concentration polarization. The potential difference of the diffusion boundary layer formed by the ion aggregation and depletion regions drives ions to flow laterally along the salt bridge in the concentrate or dilute chamber, forming ion short-circuit current and reverse voltage drop, further reducing the system output power.

[0003] Existing simulation studies of reverse electrodialysis power generation processes mainly focus on the fluid flow and ion transport characteristics within a single periodic mesh or membrane-membrane unit region. These studies neglect the variations in multi-physics fields such as concentration, velocity, and current density throughout the entire flow channel from inlet to outlet in a real-scale mesh channel. Although a few models have simulated the fluid dynamics and mass transport within the entire flow channel, they are limited to modeling empty mesh channels due to the difficulty in considering the mesh shadowing effect and the resulting fluid mixing. Therefore, existing research has not yet been able to effectively simulate the power generation process of a real-scale mesh channel reverse electrodialysis system. Summary of the Invention

[0004] The purpose of this invention is to provide a simulation method for the reverse electrodialysis power generation process in a real-size mesh channel, which realizes the continuity of the multi-physics field changes in the entire flow channel from the inlet to the outlet of the membrane through the boundary coupling method.

[0005] The technical solution adopted in this invention is a simulation method for the reverse electrodialysis power generation process in a real-size grid channel, comprising the following steps:

[0006] S1, the real mesh channel is simplified into a two-dimensional "Z"-shaped circular mesh using the flow resistance method, the porosity is measured by the drainage method, and the equivalent radius of the two-dimensional mesh is calculated according to the principle of area equivalence. S2, for a two-dimensional mesh structure, select the smallest periodic unit membrane to model the xy plane, divide the mesh, and set the membrane and solution properties, operating parameters and boundary conditions; S3, coupled solution of the flow field, concentration field and electric field of the model, extends the multi-physics field variation to the height of the entire film pair through the boundary coupling method, ensuring the continuity of the variation; S4. Based on the solution results, calculate the thickness of the diffusion boundary layer on the membrane side and the potential change, solve the resistance of each part of the system, and evaluate the impact of concentration polarization and ion short-circuit current on the output power.

[0007] The technical solution of this invention is also characterized by, The expression for calculating the equivalent radius of the two-dimensional structural mesh in S1 using the principle of area equivalence is as follows: (1) In the formula, The porosity of the mesh. The width of the compartment. For the height of the minimum periodic unit membrane pair, The radius of the mesh is [value].

[0008] The membrane properties in S2 include the concentration of fixed ions, electrolyte volume fraction, and tortuosity within the anion and cation exchange membranes; the solution properties include the diffusion coefficients and activity coefficients of anions and cations, the inlet concentration, density, and dynamic viscosity of the concentrated and dilute solutions; the operating parameters are the pressure in the concentrated and dilute chambers and the potential difference between the membrane and the external sides; and the boundary conditions include the flow field, concentration field, and electric field. The flow field boundary conditions are set with pressure periodic boundary conditions at the inlet (HI, JK) and outlet (BC, DE) of the compartment, as follows: (2) In the formula, For pressure, subscript and Indicates the exit and the entrance; The boundaries of the ion exchange membrane and the compartment boundaries (BH, CI, DJ, EK) are provided with non-slip boundary strips, represented as follows: In the formula, It is a velocity vector; The concentration field and electric field boundary conditions are as follows, and the flux due to ion diffusion at the compartment outlets (BC, DE) is neglected: (3) In the formula, For the boundary normal vector, This refers to the ion concentration. For ion types, The ion diffusion coefficient; The flux periodic boundary condition is set at the outermost cation exchange membrane boundary (AG, FL) of the smallest periodic unit membrane pair, as follows: (4) In the formula, , These are the source boundary and target boundary normal vectors, respectively. This refers to ion flux; The electric field applied by the periodic conditional electrodes at the outer boundaries (AG, FL) is expressed as: (5) In the formula, This represents the electrolyte potential.

[0009] The specific steps of S3 are as follows: Simultaneously solve the fluid dynamics equations and the Nernst-Planck equations, and combine them with the electrical neutrality constraint to couple and solve the flow field, concentration field, and electric field within the smallest periodic unit membrane pair; use the generalized stretching operator to map the outlet position of the previous unit membrane pair to the inlet position of the next unit membrane pair; and extend the position information and multiphysics field changes calculated within the smallest periodic unit membrane pair to the entire height of the membrane pair through the boundary coupling method, thereby achieving the continuity of multiphysics field changes.

[0010] In S3, the fluid dynamics equations, Nernst-Planck equations, and charge neutrality conditions are coupled to solve for the flow field, concentration field, and electric field distribution within the minimum periodic unit membrane pair. The specific steps are as follows: within the minimum periodic unit membrane pair, the fluid mass and momentum conservation equations are combined to solve for the pressure and velocity distribution, and the Nernst-Planck equations and charge neutrality conditions are coupled to calculate the ion concentration and potential distribution. The fluid dynamics equations, including the fluid mass and momentum conservation equations, are as follows: (6) (7) In the formula, The density of the solution, For pressure, This represents the dynamic viscosity of the solution.

[0011] The Nernst-Planck equations and the electroneutrality condition are as follows: (8) (9) (10) In the formula, It is an ionic oxidation state. It is Faraday's constant. For ion mobility, To fix the concentration of charged groups in ion exchange membranes, To fix the valence of charged groups in ion exchange membranes; The Nernst-Planck equation requires the ion flux to be expressed using the ion mass conservation equation, while the Nernst-Einstein equation calculates ion mobility as follows: (11) (12) In the formula, This is the universal gas constant.

[0012] In S3, the calculated position information and multiphysics changes within the minimum periodic unit membrane pair are extended to the entire height of the membrane pair using the boundary coupling method to achieve continuity of multiphysics changes. The specific steps are as follows: Based on the fluid dynamics equations, the Nernst-Planck equations, and the electroneutrality condition, the velocity, concentration, potential, and current density distributions within the minimum periodic unit membrane pair are solved. Then, a generalized stretching operator is used to map the outlet position of the previous unit membrane pair to the inlet position of the next unit membrane pair, expressed as: (13) In the formula, For the next unit membrane pair outlet position, This refers to the outlet position of the membrane in the previous unit. By using boundary ordinary differential equations and differential algebraic equations, the velocity and concentration at the outlet of the previous membrane pair are mapped as the inlet conditions for the next membrane pair: (14) (15) (16) (17) in, Number the units for the entire membrane from the inlet to the outlet.

[0013] The specific steps of S4 are as follows: Based on the solution results of the minimum periodic unit membrane pair in S3, the thickness of the diffusion boundary layer on both sides of the membrane is calculated by the Leveque equation. Combined with the Donnan potential correction theory, the potential change on both sides of the membrane caused by the change in ion concentration in the diffusion boundary layer is solved. The system bulk resistance, salt bridge resistance and diffusion boundary layer resistance are calculated by the hierarchical equivalent circuit model. The characteristic ratio coefficient method is used to evaluate the impact of concentration polarization and ion short-circuit current on the system output power.

[0014] In S4, the expression for calculating the diffusion boundary layer thickness on both sides of the membrane within the minimum periodic unit membrane pair using the Leveque equation is as follows: (18) In the formula, For the thickness of the diffusion boundary layer, The average velocity of the solution in the compartment. This represents the harmonic average of the diffusion coefficients of anions and cations in the compartment solution; Represented as: (19) The abrupt change in membrane potential caused by the change in ion concentration within the diffusion boundary layer, calculated in S4 based on the Donnan potential correction theory, is expressed as follows: (20) In the formula, For the Tangnan electric potential, , These are the solution-side and ion-exchange membrane-side potentials. For ambient temperature, , Ion activity on the solution side and ion exchange membrane side; The solution process is repeated until the calculation of the last unit at the outlet is completed, thereby obtaining the multiphysics field with a high continuous distribution across the entire membrane.

[0015] In S4, the expressions for calculating the system bulk resistance, salt bridge resistance, and diffusion boundary layer resistance using a hierarchical equivalent circuit model are as follows: (twenty one) (twenty two) (twenty three) In the formula, For the system's own resistance, For the resistance of the cation exchange membrane, For the resistance of anion exchange membrane, For the resistance of the dilute chamber, For the concentration chamber resistance, For salt bridge resistors, For the diffuse boundary layer resistance, The conductivity of the solution, The effective area of ​​the membrane; The resistances of the concentrate and dilute chambers are calculated using equation (24): (twenty four).

[0016] In S4, the characteristic ratio coefficient method is used to evaluate the impact of concentration polarization and ion short-circuit current on the system output power. Specifically, this is achieved by introducing a dimensionless parameter. , Establish a functional relationship between the system output power and this parameter, and evaluate the impact of concentration polarization and ion short-circuit current on the system output power.

[0017] The beneficial effects of this invention are: This invention provides a simulation method for the real-size mesh channel reverse electrodialysis power generation process. It simplifies the real mesh channel into a two-dimensional zigzag circular mesh using the flow resistance method, and inversely calculates its equivalent radius based on porosity. The flow field, concentration field, and electric field within the smallest periodic unit membrane pair are solved through coupling. The multi-physics field changes of the smallest periodic unit membrane pair are continuously extended to the entire height of the membrane pair using the boundary coupling method. Based on Donald potential theory, the potential abrupt change across the membrane caused by ion concentration changes within the diffusion boundary layer is calculated. A hierarchical equivalent circuit model and the characteristic ratio coefficient method are used to evaluate the impact of concentration polarization and ion short-circuit current on the system output power. This provides a feasible solution for the study of fluid flow and ion transport in reverse electrodialysis systems.

[0018] (1) In traditional reverse electrodialysis systems, the mesh is usually made of a non-conductive material that does not allow ions to pass through. Therefore, the mesh covers part of the membrane area, thus hindering the horizontal ion transport across the membrane from the flow channel solution to the membrane, causing the mesh shadowing effect. Since the ion current path through the mesh is tortuous, the mesh shadowing effect increases the system resistance and reduces the output power. This invention uses the flow resistance method to simplify the real-size mesh channel into a two-dimensional structure with a zigzag circular mesh. The porosity of the mesh is measured by introducing the drainage method, and the equivalent radius of the two-dimensional structure mesh is calculated based on the area equivalence principle. Finally, the shadowing effect of the three-dimensional real-size mesh is simulated to an equivalent two-dimensional structure.

[0019] (2) When two salt solutions of different concentrations are introduced into a small curved channel from their respective inlets during the reverse electrodialysis power generation process to achieve sufficient mixing at the outlet, the periodic structure of the mesh in the perpendicular ion transmembrane direction causes the channel solution to flow periodically from the inlet to the outlet. The high convection / diffusion ratio in the solution results in a very high Péclet number in the channel, which means that the upstream solution will not be affected by the downstream solution. This invention aims to achieve coupled solution of the flow field, concentration field and electric field for the smallest periodic unit membrane pair in the reverse electrodialysis system. It uses a generalized stretching operator to map the position at the outlet of the previous unit membrane pair in the channel to the position at the inlet of the next unit membrane pair. Based on the boundary coupling method, the calculated position information and multiphysics field changes within the smallest periodic unit membrane pair are extended to the entire height of the membrane pair, realizing the continuity of the multiphysics field changes in the entire flow domain from the inlet to the outlet of the membrane pair.

[0020] (3) When ions are transported across the membrane from the concentrated chamber to the dilute chamber, the different ion migration rates in the solution and within the membrane cause ion depletion near the concentrated chamber membrane and ion aggregation near the dilute chamber membrane, resulting in concentration polarization. The potential difference of the diffusion boundary layer formed by ion aggregation and depletion drives ions to flow laterally along the salt bridge in the concentrated or dilute chamber, forming ion short-circuit current and reverse voltage drop, which reduces the system output power. This invention uses the Leveque equation to calculate the thickness of the diffusion boundary layer on both sides of the membrane within the smallest periodic unit membrane pair, and calculates the potential change on both sides of the membrane caused by the change in ion concentration within the diffusion boundary layer based on the Donnan potential correction theory, thereby simulating the concentration polarization phenomenon. The system body resistance, salt bridge resistance, and diffusion boundary layer resistance are calculated through a hierarchical equivalent circuit model, and the influence of concentration polarization and ion short-circuit current on the system output power is evaluated based on the characteristic ratio coefficient method. Attached Figure Description

[0021] Figure 1 A schematic flowchart illustrating the simulation method for the reverse electrodialysis power generation process in a real-size grid channel provided by this invention.

[0022] Figure 2 This is a schematic diagram of the two-dimensional structure of the membrane pair with the mesh channel at the actual size of the present invention.

[0023] Figure 3 This is a schematic diagram of the geometric model of the smallest periodic unit of the reverse electrodialysis membrane pair of the present invention.

[0024] Figure 4 This is a schematic diagram illustrating how the multiphysics calculation results of the smallest periodic unit are extended to the height of the entire film pair using the boundary coupling method of this invention.

[0025] Figure 5 This is a flow velocity distribution cloud map of the simulation results in Embodiment 6 of the present invention.

[0026] Figure 6 The simulation results in Embodiment 6 of the present invention Concentration distribution cloud map of the solution.

[0027] Figure 7 This is a current density distribution cloud map of the simulation results in Embodiment 6 of the present invention. Detailed Implementation

[0028] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0029] Example 1 This invention provides a simulation method for a real-size grid-connected reverse electrodialysis power generation process, such as... Figure 1 As shown, the specific implementation steps are as follows: S1, the real mesh channel is simplified into a two-dimensional "Z"-shaped circular mesh using the flow resistance method, the porosity is measured based on the drainage method, and the equivalent radius of the two-dimensional structure mesh is calculated through the area equivalence principle; In S2, ions in the concentrated chamber migrate to the dilute chamber along the transmembrane (x) direction driven by the concentration gradient. Under the condition of continuous supply of solution at the inlet of the compartment, the pressure gradient causes convection to mainly occur along the height (y) direction. Since the fluid is almost stationary along the thickness (z) direction and the multiphysics changes are similar, the influence of this direction on ion transport can be ignored. For the two-dimensional structure mesh of S1, this invention models the minimum periodic unit membrane with a height of 1 mm in the xy plane, then divides the mesh, and sets the membrane and solution properties, system operating parameters, and boundary conditions; S3, coupled solution of the flow field, concentration field and electric field of the model, extends the multi-physics field variation to the height of the entire film pair through the boundary coupling method, ensuring the continuity of the distribution; S4. Based on the solution results, calculate the thickness of the diffusion boundary layer on the membrane side and the potential change, solve the resistance of each part of the system, and evaluate the impact of concentration polarization and ion short-circuit current on the output power.

[0030] Example 2 Based on Example 1, S1 specifically involves the following: In a real reverse electrodialysis system, since the mesh completely fills the solution compartments, directly reproducing its true geometry in a two-dimensional model would lead to fluid channel blockage. To address this issue, a simplified two-dimensional non-blocking configuration is used to replace the actual mesh structure. The pressure drop from the inlet to the outlet of the solution is calculated using the Darcy-Weisbach equation, and the flow resistance method is used to simplify the actual mesh channels into a zigzag circular mesh in a two-dimensional structure. To preserve the structural characteristics of the actual mesh in the model, porosity is introduced to describe the volume fraction of the mesh pores. This parameter is related to the shadowing effect produced by the mesh on the membrane surface and directly affects the effective area for ion transport. Based on the mesh porosity measured by the drainage method, the equivalent radius of the two-dimensional mesh structure is calculated using the area equivalence principle, ultimately achieving an equivalent simulation of the shadowing effect of the three-dimensional mesh to a two-dimensional structure.

[0031] Darcy-Weisbach formula: , In the formula, The coefficient of friction, For the length of the pipe, The hydraulic diameter, It is the Reynolds number.

[0032] The formula for measuring the porosity of a mesh using the drainage method is as follows: In the formula, The porosity of the mesh. This represents the change in volume before and after the mesh is placed inside. The area of ​​the mesh is This refers to the thickness of the mesh.

[0033] In S1, the equivalent radius of the two-dimensional structural mesh calculated using the area equivalence principle is expressed as follows: (1) In the formula, The porosity of the mesh. The width of the compartment. For the height of the minimum periodic unit membrane pair, The radius of the mesh is [value].

[0034] Example 3 Based on Example 2, S2 specifically involves: discretizing the reverse electrodialysis system into multiple repeating membrane pairs along its width, according to the periodicity of the system, such as... Figure 2 As shown, each membrane pair consists of two outer half-cation exchange membranes, a middle anion exchange membrane, and a concentration chamber and a dilute chamber between them. Assuming the fluid within the chamber is an incompressible, laminar Newtonian fluid, ions in the concentration chamber migrate to the dilute chamber along the transmembrane (x) direction driven by the concentration gradient. Under continuous supply of solution at the chamber inlet, the pressure gradient causes convection to occur primarily along the height (y) direction. Since the fluid is almost stationary along the thickness (z) direction and the multiphysics changes are similar, the influence of this direction on ion transport can be ignored. Therefore, for the aforementioned zigzag circular mesh, the membrane pair is divided into 120 units along the height, and the units are numbered accordingly. This invention models the xy plane of the smallest periodic unit membrane with a height of 1 mm, such as... Figure 3 As shown.

[0035] Example 4 Based on Example 3, for the established two-dimensional geometric model of the minimum periodic unit membrane pair, a user-controlled triangular mesh type was adopted for the entire computational domain in COMSOL, and the mesh of the compartment and membrane-solution boundary region was refined. To meet the mesh independence requirement, a total of 48,650 meshes were selected, with the minimum mesh mass being greater than 0.04 and the average mesh mass being greater than 0.9.

[0036] The membrane properties that need to be set in S2 include the concentration of fixed ions in the anion and cation exchange membranes, the volume fraction of electrolytes, and tortuosity; solution properties include the diffusion coefficients and activity coefficients of anions and cations, the inlet concentration, density, and dynamic viscosity; and operating parameters include the pressure in the concentrate and dilute chambers and the potential difference between the membrane and the external sides. Boundary conditions include the flow field, concentration field, and electric field.

[0037] The flow field boundary conditions are as follows: pressure periodic boundary conditions are set at the inlet (HI, JK) and outlet (BC, DE) of the compartment. (2) In the formula, For pressure, subscript and Indicates the exit and the entrance; No-slip boundary conditions are set for the boundaries of ion exchange membranes and compartments (BH, CI, DJ, EK): ;in, This is the velocity vector.

[0038] The concentration field and electric field boundary conditions are as follows, and the flux due to ion diffusion at the compartment outlets (BC, DE) is neglected: (3) In the formula, For the boundary normal vector, This refers to the ion concentration. For ion types, The ion diffusion coefficient; The flux periodic boundary condition is set at the outermost cation exchange membrane boundary (AG, FL) of the smallest periodic unit membrane pair, as follows: (4) In the formula, , These are the source boundary and target boundary normal vectors, respectively. This refers to ion flux; The electric field applied by the electrodes is simulated by applying periodic conditions at the outer boundaries (AG, FL): (5) in, This represents the electrolyte potential.

[0039] Example 5 Based on Example 4, S3 specifically involves: simultaneously solving the fluid dynamics equations and the Nernst-Planck equations, combined with the electroneutrality constraint, to couple and solve the flow field, concentration field, and electric field within the smallest periodic unit membrane pair; using a generalized stretching operator to map the outlet position of the previous unit membrane pair to the inlet position of the next unit membrane pair; and extending the position information and multiphysics changes calculated within the smallest periodic unit membrane pair to the entire membrane pair height through boundary coupling, thereby achieving continuity of multiphysics changes, such as... Figure 4 As shown.

[0040] The equations of fluid dynamics include the equations of conservation of fluid mass and momentum: (6) (7) In the formula, The density of the solution, For pressure, This represents the dynamic viscosity of the solution.

[0041] The Nernst-Planck equations and the electroneutrality condition are as follows: (8) (9) (10) In the formula, It is an ionic oxidation state. It is Faraday's constant. For ion mobility, To fix the concentration of charged groups in ion exchange membranes, To fix the valence of charged groups in ion exchange membranes.

[0042] The Nernst-Planck equation requires the ion flux to be expressed using the ion mass conservation equation, while the Nernst-Einstein equation calculates ion mobility. (11) (12) In the formula, This is the universal gas constant.

[0043] In S3, the calculated position information and multiphysics changes within the minimum periodic unit membrane pair are extended to the entire height of the membrane pair using the boundary coupling method to achieve continuity of multiphysics changes. The specific steps are as follows: Based on the fluid dynamics equations, the Nernst-Planck equations, and the electroneutrality condition, the velocity, concentration, potential, and current density distributions within the minimum periodic unit membrane pair are solved. Then, a generalized stretching operator is used to map the outlet position of the previous unit membrane pair to the inlet position of the next unit membrane pair, expressed as: (13) In the formula, For the next unit membrane pair outlet position, This refers to the outlet position of the membrane in the previous unit. By using boundary ordinary differential equations and differential algebraic equations, the velocity and concentration at the outlet of the previous membrane pair are mapped as the inlet conditions for the next membrane pair: (14) (15) (16) (17) in, Number the units for the entire membrane from the inlet to the outlet.

[0044] Example 6 Based on Example 5, the specific steps of S4 are as follows: Based on the solution results of the minimum periodic unit membrane pair in S3, the thickness of the diffusion boundary layer on both sides of the membrane is calculated using the Leveque equation. Combined with the Donnan potential correction theory, the potential abrupt change on both sides of the membrane caused by the change in ion concentration within the diffusion boundary layer is solved. The system bulk resistance, salt bridge resistance, and diffusion boundary layer resistance are calculated using a hierarchical equivalent circuit model. The characteristic ratio coefficient method is used to evaluate the impact of concentration polarization and ion short-circuit current on the system output power. In S4, the Leveque equation is used to calculate the thickness of the diffusion boundary layer on both sides of the membrane within the minimum periodic unit membrane pair. The expression is: (18) In the formula, For the thickness of the diffusion boundary layer, The average velocity of the solution in the compartment. This is the harmonic average value of the diffusion coefficients of anions and cations in the compartment solution.

[0045] (19) The abrupt change in membrane potential caused by the change in ion concentration within the diffusion boundary layer, calculated in S4 based on the Donnan potential correction theory, is expressed as follows: (20) In the formula, For the Tangnan electric potential, , These are the solution-side and ion-exchange membrane-side potentials. For ambient temperature, , This represents the ion activity on the solution side and the ion exchange membrane side.

[0046] This embodiment calculates the ion activity coefficients on the solution side using the Pitzer model, assuming that the activity coefficients of the two ions in the solution are equal:

[0047] The ion diffusion coefficient and activity coefficient within the membrane were corrected using Manning's counterion condensation theory:

[0048]

[0049]

[0050]

[0051]

[0052]

[0053]

[0054]

[0055] In the formula, , These are the diffusion coefficients of co-ions and counter-ions within the ion exchange membrane, respectively. , The valence of the co-ion and counterion is [value missing]. , This represents the number of co-ions and counterions in a single electrolyte molecule. The water volume fraction of the membrane. The tortuosity of the membrane, The degree of swelling of the membrane. This represents the intramembrane coion concentration. The dimensionless charge density of the polymer, This represents the ratio of the concentration of the co-ion to the concentration of the fixed charged groups. This represents the density of immobilized groups within the membrane.

[0056] Repeat the above solution process until the calculation of the last unit at the exit is completed, thereby obtaining the multiphysics field of the entire membrane with continuously varying height.

[0057] Based on the above boundary coupling method solution process, this invention selects typical operating conditions of reverse electrodialysis technology for simulation verification, setting the flow rate to 20. The concentrations for the concentrated and dilute chambers were 513 and 17.1, respectively. of The solution has 5 membrane pairs. Figure 5 , Figure 6 , Figure 7 The internal flow velocity of the minimum periodic unit membrane obtained by the boundary coupling method is respectively... Solution concentration and current density distribution cloud maps (analysis of units 1, 60, and 120). As shown in the figures, after expansion using the boundary coupling method, the flow field, concentration field, and electric field exhibit good continuity along the membrane pair height direction, without significant discontinuities or abrupt changes. This verifies the rationality and effectiveness of extending the multi-physics field of the smallest periodic unit membrane pair to the entire membrane pair height. Further calculation of the system's maximum power density under this condition and comparison with experimental test data under the same condition show good agreement, thus confirming the accuracy of the simulation model established in this invention and providing a feasible solution for the study of fluid flow and ion transport in reverse electrodialysis systems.

[0058] Example 7 Based on Example 6, the system body resistance, salt bridge resistance and diffusion boundary layer resistance are calculated in S4 using a hierarchical equivalent circuit model. Specifically, when ions are transported across the membrane from the concentration chamber to the dilute chamber, the different ion migration rates in the solution and the membrane cause ion depletion near the concentration chamber membrane and ion aggregation near the dilute chamber membrane, resulting in concentration polarization. The potential difference of the diffusion boundary layer formed by the ion aggregation and depletion regions drives ions to flow laterally along the salt bridge in the concentration or dilute chamber, forming ion short-circuit current and reverse voltage drop, which reduces the system output power.

[0059] The expressions for the system bulk resistance, salt bridge resistance, and diffusion boundary layer resistance, calculated using a hierarchical equivalent circuit model, are as follows: (twenty one) (twenty two) (twenty three) In the formula, For the system's own resistance, For the resistance of the cation exchange membrane, For the resistance of anion exchange membrane, For the resistance of the dilute chamber, For the concentration chamber resistance, For salt bridge resistors, For the diffuse boundary layer resistance, The conductivity of the solution, This represents the effective area of ​​the membrane.

[0060] The resistance of the concentrate or dilute compartment is calculated using the following formula: (twenty four) The current and voltage of each branch are calculated based on Kirchhoff's laws and Ohm's law: (25) (26) in, The current flowing into this node, For the current flowing out of this node, The voltage across the branch is... For each branch resistance.

[0061] By introducing two dimensionless parameters and The system output power is expressed as a function of dimensionless parameters and the membrane logarithm, which allows for direct comparison of the system output power with different geometries, membrane materials, and solution properties.

[0062] (27) in, This refers to the system output power.

[0063] By comparing the output power of different membrane materials, system sizes, and membrane logarithmic conditions, it was found that... When the resistance is relatively low, the salt bridge resistance is relatively low, and the ion short-circuit current has a significant impact, resulting in lower output power. When the concentration polarization is large, the enhanced concentration polarization leads to a larger boundary layer resistance, making it difficult for the main current to be diverted to the salt bridge. This effectively suppresses the ion short-circuit current, resulting in higher system output power. The characteristic ratio coefficient method is used to evaluate the impact of concentration polarization and ion short-circuit current on the system output power, providing a theoretical basis for the design optimization of reverse electrodialysis systems.

Claims

1. A simulation method for reverse electrodialysis power generation process in a real-size grid channel, characterized in that, Includes the following steps: S1. The real mesh channel is simplified into a two-dimensional "Z"-shaped circular mesh using the flow resistance method. The porosity is measured by the drainage method, and the equivalent radius of the two-dimensional mesh is calculated according to the principle of area equivalence. S2, for a two-dimensional mesh structure, select the smallest periodic unit membrane to model the xy plane, divide the mesh, and set the membrane and solution properties, operating parameters and boundary conditions; S3, coupled solution of the flow field, concentration field and electric field of the model, extends the multi-physics field variation to the height of the entire film pair through the boundary coupling method, ensuring the continuity of the distribution; S4. Based on the solution results, calculate the thickness of the diffusion boundary layer on the membrane side and the potential change, solve the resistance of each part of the system, and evaluate the impact of concentration polarization and ion short-circuit current on the output power.

2. The simulation method for reverse electrodialysis power generation process using a real-size grid channel according to claim 1, characterized in that, The expression for calculating the equivalent radius of the two-dimensional structural mesh using the area equivalence principle, as described in S1, is as follows: （1） In the formula, The porosity of the mesh. The width of the compartment. For the height of the minimum periodic unit membrane pair, The radius of the mesh is [value].

3. The simulation method for reverse electrodialysis power generation process using a real-size grid channel according to claim 1, characterized in that, The membrane properties described in S2 include the concentration of fixed ions, electrolyte volume fraction, and tortuosity within the anion and cation exchange membranes; the solution properties include the diffusion coefficients and activity coefficients of anions and cations, the inlet concentration, density, and dynamic viscosity of the concentrated and dilute solutions; the operating parameters are the pressure in the concentrated and dilute chambers and the potential difference between the membrane and the external sides; and the boundary conditions include the flow field, concentration field, and electric field. The flow field boundary conditions are set with pressure periodic boundary conditions at the inlet (HI, JK) and outlet (BC, DE) of the compartment, as follows: （2） In the formula, For pressure, subscript and Indicates the exit and the entrance; The boundaries of the ion exchange membrane and the compartment boundaries (BH, CI, DJ, EK) are provided with non-slip boundary strips, represented as follows: In the formula, It is a velocity vector; The concentration field and electric field boundary conditions are as follows, and the flux due to ion diffusion at the compartment outlets (BC, DE) is neglected: （3） In the formula, For the boundary normal vector, This refers to the ion concentration. For ion types, The ion diffusion coefficient; The flux periodic boundary condition is set at the outermost cation exchange membrane boundary (AG, FL) of the smallest periodic unit membrane pair, as follows: （4） In the formula, , These are the source boundary and target boundary normal vectors, respectively. This refers to ion flux; The electric field applied by the periodic conditional electrodes at the outer boundaries (AG, FL) is expressed as: （5） In the formula, This represents the electrolyte potential.

4. The simulation method for reverse electrodialysis power generation process using a real-size grid channel according to claim 1, characterized in that, The specific steps of S3 are as follows: Simultaneously solve the fluid dynamics equations and the Nernst-Planck equations, and combine them with the electrical neutrality constraint to couple and solve the flow field, concentration field, and electric field within the smallest periodic unit membrane pair; use the generalized stretching operator to map the outlet position of the previous unit membrane pair to the inlet position of the next unit membrane pair; and extend the position information and multiphysics field changes calculated within the smallest periodic unit membrane pair to the entire height of the membrane pair through the boundary coupling method, thereby achieving the continuity of multiphysics field changes.

5. The simulation method for reverse electrodialysis power generation process using a real-size grid channel according to claim 1, characterized in that, The steps described in S3 for solving the flow field, concentration field, and electric field distribution within the smallest periodic unit membrane pair by simultaneously solving the fluid dynamics equations, Nernst-Planck equations, and electroneutrality conditions are as follows: Within the smallest periodic unit membrane pair, solve the pressure and velocity distribution by simultaneously solving the fluid mass and momentum conservation equations, and then calculate the ion concentration and potential distribution by coupling the Nernst-Planck equations and electroneutrality conditions. The fluid dynamics equations include the fluid mass and momentum conservation equations as follows: （6） （7） In the formula, The density of the solution, For pressure, The dynamic viscosity of the solution; The Nernst-Planck equations and the electroneutrality condition are as follows: （8） （9） （10） In the formula, It is an ionic oxidation state. It is Faraday's constant. For ion mobility, To fix the concentration of charged groups in ion exchange membranes, To fix the valence of charged groups in ion exchange membranes; The Nernst-Planck equation requires the ion flux to be expressed using the ion mass conservation equation, while the Nernst-Einstein equation calculates ion mobility as follows: （11） （12） In the formula, This is the universal gas constant.

6. The simulation method for reverse electrodialysis power generation process using a real-size grid channel according to claim 5, characterized in that, In S3, the calculated position information and multiphysics changes within the minimum periodic unit membrane pair are extended to the entire height of the membrane pair using the boundary coupling method to achieve continuity of multiphysics changes. The specific steps are as follows: Based on the fluid dynamics equations, the Nernst-Planck equations, and the electroneutrality condition, the velocity, concentration, potential, and current density distributions within the minimum periodic unit membrane pair are solved. Then, a generalized stretching operator is used to map the outlet position of the previous unit membrane pair to the inlet position of the next unit membrane pair, expressed as: （13） In the formula, For the next unit membrane pair outlet position, This refers to the outlet position of the membrane in the previous unit. By using boundary ordinary differential equations and differential algebraic equations, the velocity and concentration at the outlet of the previous membrane pair are mapped as the inlet conditions for the next membrane pair: （14） （15） （16） （17） in, Number the units for the entire membrane from the inlet to the outlet.

7. The simulation method for reverse electrodialysis power generation process using a real-size grid channel according to claim 6, characterized in that, The specific steps of S4 are as follows: Based on the solution results of the minimum periodic unit membrane pair in S3, the thickness of the diffusion boundary layer on both sides of the membrane is calculated by the Leveque equation. Combined with the Donnan potential correction theory, the potential change on both sides of the membrane caused by the change in ion concentration in the diffusion boundary layer is solved. The system bulk resistance, salt bridge resistance and diffusion boundary layer resistance are calculated by the hierarchical equivalent circuit model. The characteristic ratio coefficient method is used to evaluate the impact of concentration polarization and ion short-circuit current on the system output power.

8. The simulation method for reverse electrodialysis power generation process using a real-size grid channel according to claim 7, characterized in that, The expression for calculating the diffusion boundary layer thickness on both sides of the membrane using the Leveque equation in S4 is as follows: （18） In the formula, For the thickness of the diffusion boundary layer, The average velocity of the solution in the compartment. This represents the harmonic average of the diffusion coefficients of anions and cations in the compartment solution; Represented as: （19） The abrupt change in membrane potential caused by the change in ion concentration within the diffusion boundary layer, calculated in S4 based on the Donnan potential correction theory, is expressed as follows: （20） In the formula, For the Tangnan electric potential, , These are the solution-side and ion-exchange membrane-side potentials. For ambient temperature, , Ion activity on the solution side and ion exchange membrane side; The solution process is repeated until the calculation of the last unit at the exit is completed, thus obtaining the multiphysics field of the entire membrane with continuously varying height.

9. The simulation method for reverse electrodialysis power generation process using a real-size grid channel according to claim 8, characterized in that, In S4, the expressions for calculating the system bulk resistance, salt bridge resistance, and diffusion boundary layer resistance using a hierarchical equivalent circuit model are as follows: （21） （22） （23） In the formula, For the system's own resistance, For the resistance of the cation exchange membrane, For the resistance of anion exchange membrane, For the resistance of the dilute chamber, For the concentration chamber resistance, For salt bridge resistors, For the diffuse boundary layer resistance, The conductivity of the solution, The effective area of ​​the membrane; The resistances of the concentrate and dilute chambers are calculated using equation (24): （24）。 10. The simulation method for reverse electrodialysis power generation process using a real-size grid channel according to claim 9, characterized in that, In S4, the characteristic ratio coefficient method is used to evaluate the impact of concentration polarization and ion short-circuit current on the system output power. Specifically, this is achieved by introducing a dimensionless parameter. , Establish a functional relationship between the system output power and this parameter, and evaluate the impact of concentration polarization and ion short-circuit current on the system output power.

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