Fractal theory-based deep-eutectic solvent flow battery flow channel electrode design method

Abstract

The invention provides a fractal theory-based deep-eutectic solvent flow battery flow channel electrode design method. The method comprises the following steps: establishing a three-dimensional flow battery positive / negative electrode model with a porous electrode domain, an inlet domain and an outlet domain; determining physical and chemical characteristic parameters of an electrolyte and a porous electrode in the model and determining boundary conditions; coupling a topological optimization algorithm based on a variable density method on the model; adding a volume force Fb in the porous electrode domain, and describing a relationship between the reversible permeability and a design variable in the porous electrode domain; establishing a three-dimensional flow battery positive electrode / negative electrode topological optimization model based on fluid flow electrochemical reaction; according to the optimization model, a three-dimensional topological optimization solution program is selected for analysis and solution; carrying out convergence judgment, and outputting a flow channel electrode integrated structure based on fluid flow electrochemical reaction topological optimization; and the hierarchical structure form of the flow channel in the electrode is simplified, and the regular tree-shaped flow channel electrode integrated structure easy to process and manufacture is obtained.

Description

Technical Field

[0001] The present invention relates to the technical field of liquid flow batteries in electrochemical energy storage, and in particular to a method for designing flow channel electrodes for low eutectic solvent liquid flow batteries based on fractal theory. Background Art

[0002] Among the numerous energy storage systems, flow batteries are regarded as a reliable energy storage technology due to their flexible capacity design, good safety, high energy efficiency, and environmental friendliness. They have broad application prospects in large-scale energy storage technologies. Existing flow batteries can be divided into aqueous flow batteries and non-aqueous flow batteries according to the type of electrolyte solvent. Compared with aqueous flow batteries, non-aqueous flow batteries have a wider electrochemical window and higher current density, which improves the energy density of the entire energy storage system. The basic components of a typical flow battery include bipolar plates with flow channel structures, positive and negative porous electrodes, positive and negative electrolytes, and ion exchange membranes. The bipolar plates with flow channel structures act on the distribution of electrolytes in porous electrodes, which directly affects the performance and pressure drop of flow batteries; porous electrodes provide active sites for redox reactions, are the places where the charge and discharge reactions of flow battery energy storage systems occur, and determine the transmission performance of electrolytes and ions.

[0003] Researchers have conducted many studies on the flow channel structure and porous electrodes of liquid flow batteries. However, it is difficult to ensure that the performance of the two can reach the optimal level under the synergistic effect by studying the flow channel structure and porous electrodes separately. Therefore, the integrated design of flow channel electrodes for liquid flow batteries is proposed. The integrated design of flow channel electrodes for liquid flow batteries has many advantages, which are specifically reflected in: reducing the thickness of single cells to reduce ohmic resistance and improve the volume power density of the battery stack; using conductive plastics as bipolar plate materials to reduce system costs and increase the durability of the battery stack; reducing the flow volume of reactants and increasing the flow velocity in the electrode, thereby reducing transmission losses. The traditional flow channel structures of liquid flow batteries mainly include parallel flow channels, finger-shaped flow channels and serpentine flow channels. It is difficult to ensure the geometric parameters of the flow channels when the battery performance is optimal by directly etching these three flow channel structures on the porous electrodes. It relies on empirical design, which is time-consuming and labor-intensive. This makes the design of flow channel electrode integration still difficult. In order to overcome this problem, numerical optimization can be used as a promising strategy to automatically generate flow channel structures in porous electrodes.

[0004] Topology optimization is a reliable numerical optimization design technology. It is a numerical method that optimizes the material distribution in a given area according to given boundary conditions, loads and constraints. It has the advantages of high design freedom and no size and shape restrictions. It is widely used in the design of flow channel structures in the field of heat and mass transfer.

[0005] Similar topology optimization methods are used in the currently published patent documents. For example, patent CN 118094790A proposes a multi-heat source cold plate flow channel optimization method based on topology optimization, which optimizes the heat dissipation performance of the liquid cold plate and has the advantages of efficient heat dissipation and good temperature uniformity. Patent CN 116053505A proposes a method for preparing a porous electrode with strong mass transfer of a bionic composite structure. The electrode material prepared by this method has controllable porosity, large specific surface area, excellent mass transfer performance, good chemical stability, long service life, and can adapt to a variety of electrochemical reaction systems. Patent CN 118095008A proposes a battery cold plate flow channel topology optimization method considering size constraints. This method realizes the optimal design of the battery cold plate flow channel structure, while improving the heat dissipation effect of the battery cold plate, optimizing the working environment of the battery, and improving the cycle performance and life of the battery system. Patent CN117638156A proposes a topology optimization construction method for the proton exchange membrane fuel cell flow field plate. The constructed topological flow field structure effectively improves the performance of the fuel cell. However, the above topology optimization methods are all optimized designs of the flow channel structure in terms of heat dissipation or mass transfer, without combining the flow channel with the porous electrode for collaborative design, which makes it difficult to ensure the best performance of the flow battery under the synergistic effect of the two. In particular, for flow batteries with high flow resistance and low eutectic solvent as electrolyte, the electrolyte pump power loss during operation greatly reduces the battery operation efficiency. Therefore, it is urgent to use topology optimization methods to design flow channel-electrode integrated structures to synergistically improve the electrolyte flow transmission and electrochemical reaction energy efficiency. In addition, the above studies only optimize the flow channel structure at the numerical calculation level, and do not mention its processing and manufacturing. The flow channel electrode integrated structure obtained by topology optimization is often a very complex irregular structure, which is difficult to produce by simple mechanical processing. However, processing methods such as 3D printing are expensive and not suitable for large-scale production, thereby reducing the feasibility of the optimization results. Based on this, the present invention provides a method for simplifying the flow channel electrode integrated topology optimization structure, converting the irregular flow channel electrode integrated topology optimization structure into a regular flow channel electrode integrated structure that is easy to design, thereby improving the feasibility of the optimization results. Summary of the invention

[0006] An embodiment of the present invention provides a method for designing flow channel electrodes for low eutectic solvent flow batteries based on fractal theory, which combines a topology optimization algorithm with the integrated design of flow channel electrodes for flow batteries, generates an optimized flow channel structure in a porous electrode, and synergistically improves the performance of the flow battery. The fractal characteristics of the flow channel structure after topology optimization are calculated based on fractal theory, and regular fractal flow channels are designed based on these fractal characteristics for processing and manufacturing.

[0007] An embodiment of the present invention provides a method for designing flow channel electrodes for a deep eutectic solvent flow battery based on fractal theory, comprising the following steps:

[0008] Establish a three-dimensional liquid flow battery positive / negative electrode model with porous electrode domains, inlet domains, and outlet domains, and couple the electrochemical reaction and flow mass transfer reaction control equations in the three-dimensional liquid flow battery positive / negative electrode model;

[0009] Determine the physical and chemical properties of the electrolyte and porous electrodes in the three-dimensional flow battery positive / negative electrode model and determine the boundary conditions;

[0010] A topology optimization algorithm based on the variable density method is coupled to the positive / negative electrode model of a three-dimensional liquid flow battery to determine the topology optimization parameters and design domain, initialize the design variables of the topology optimization, and divide the design domain and non-design domain into grids of different densities;

[0011] Adding volume force F to the porous electrode domain b , the Darcy interpolation function model is used to describe the relationship between the reversible permeability α and the design variable γ in the porous electrode domain;

[0012] Based on the relationship between the reversible permeability α and the design variable γ, a three-dimensional liquid flow battery positive / negative electrode topology optimization model based on fluid flow electrochemical reaction was established with the maximum output current when the liquid flow battery was discharged as the optimization goal under the condition of fixed output voltage.

[0013] According to the three-dimensional liquid flow battery positive / negative electrode topology optimization model, a three-dimensional topology optimization solver is selected for analysis and solution;

[0014] Convergence judgment is performed, and when the objective function meets the convergence condition, the calculation is stopped, and the flow channel electrode integrated structure based on the topological optimization of the fluid flow electrochemical reaction is output;

[0015] The topology optimization algorithm is described based on fractal theory, which simplifies the hierarchical structure of the flow channel in the electrode and obtains a regular tree-like flow channel electrode integrated structure that is easy to process and manufacture.

[0016] Among them, based on fractal theory, the hierarchical structural morphology of the flow channel in the electrode formed by topology optimization calculation is simplified, and a regular tree-like flow channel electrode integrated structure is designed that has fractal similarity to the topology optimization structure and is easy to process and manufacture.

[0017] Preferably, the physicochemical parameters of the electrolyte include dynamic viscosity μ, density ρ, ion diffusion coefficient D and state charge SOC, and the physicochemical parameters of the porous electrode include porosity ε, permeability K and specific surface area a;

[0018] Set pressure boundary conditions and concentration boundary conditions at the inlet:

[0019] P in =c1

[0020] c R=c0·(1-SOC)

[0021] c O =c0·SOC

[0022] Among them, P in is the inlet pressure, c1 represents the inlet pressure value, which is a constant; c0 is the initial concentration, c R is the concentration of reducing substances, c O is the oxide concentration, SOC is the state of charge;

[0023] Set the pressure to zero boundary condition and the concentration diffusion flux to zero boundary condition at the outlet:

[0024] P out =0

[0025]

[0026] Among them, P out is the outlet pressure, i represents the type of active substance, represents the effective diffusion coefficient of active substance i, c i represents the concentration of active substance i, and n represents the vector direction;

[0027] Apply no-slip conditions and zero active species diffusion flux conditions to the external boundaries except at the inlet and outlet:

[0028]

[0029] Where P represents pressure, i represents the type of active substance, represents the effective diffusion coefficient of active substance i, c i represents the concentration of active substance i;

[0030] During the discharge / charge process, potential boundary conditions are applied to the positive / negative electrode plate side, and electrolyte potential boundary conditions are applied to the positive / negative electrode membrane side:

[0031] Positive / negative electrode plate side: φ s =V1

[0032] Positive / negative electrode membrane side: φ l =V2

[0033] Among them, φ s represents the potential applied to the positive / negative electrode plate side, φ l represents the electrolyte potential applied on the membrane side of the positive / negative electrode, V1 and V2 represent the potential values ​​on the plate side and membrane side, respectively, and both are constants.

[0034] Preferably, a Darcy interpolation function model is used to describe the relationship between the reversible permeability α and the continuous variable γ in the porous electrode domain, and the definition of the Darcy interpolation function is as follows:

[0035]

[0036] Among them, q is the penalty factor, which is used to adjust the convexity penalty parameter of the reversible permeability α;

[0037] Use Darcy interpolation function to calculate the volume force F b Punishment is performed to obtain the volume force F b The relationship between F and the design variable γ is b ∝α, so it is expressed by reversible permeability α, and its expression is as follows:

[0038]

[0039] Among them, γ is the design variable of topology optimization, α is the reversible permeability, and α s and α l are the reversible permeabilities of solid and liquid, respectively, s Related to the dynamic viscosity and permeability of the electrolyte;

[0040] where α s The definition is as follows:

[0041]

[0042] Where μ is the dynamic viscosity of the electrolyte and K is the permeability of the porous electrode.

[0043] Preferably, under the condition of fixed output voltage, the maximum output current of the flow battery during discharge is taken as the optimization target, the objective function is L, and the expression is as follows:

[0044]

[0045] Where γ is the design variable for topology optimization, F is the Faraday constant, and c R is the concentration of reducing substances, c O is the oxide concentration, R is the universal gas constant, T is the temperature at which the flow battery is running, k is the positive electrode standard rate constant, α a is the anode transfer coefficient, ΔE is the difference between the electrode potential and the standard potential, V is the initial volume of the porous electrode, and a represents the specific surface area of ​​the porous electrode;

[0046] The specific surface area a of the porous electrode is defined as follows:

[0047]

[0048] Where, ε represents the porosity of the porous electrode, df represents the porous electrode fiber diameter;

[0049] Based on the topology optimization method, mass transfer of materials, electrochemical reactions and fluid flow control equations, a topology optimization model for the positive / negative electrodes of flow batteries was established.

[0050] The electrolyte flows through the flow field and satisfies the continuity equation and Navier-Stokes equation:

[0051]

[0052] Among them, ρ and u represent the density and velocity of the electrolyte, respectively, μ represents the dynamic viscosity of the electrolyte, and P represents the pressure;

[0053] The penetration of electrolyte into the porous electrode is governed by Darcy's law:

[0054]

[0055] Where P represents pressure, ρ and u represent the density and velocity of the electrolyte, μ represents the dynamic viscosity of the electrolyte, and K represents the permeability of the porous electrode;

[0056] The permeability K of the porous electrode is calculated by the following formula:

[0057]

[0058] Among them, K CK is the Carman-Kozeny constant used to describe the fiber properties, ε represents the porosity of the porous electrode, and d f represents the porous electrode fiber diameter;

[0059] The Navier-Stokes equation and Darcy's law are combined to describe the flow of electrolytes in porous media mixtures. The expression equation is as follows:

[0060]

[0061] Where P represents pressure, ρ and u represent the density and velocity of the electrolyte respectively, μ represents the dynamic viscosity of the electrolyte, and F b is the body force, and its expression is:

[0062] F b =-αu

[0063] Where the negative sign indicates that the direction of the force is opposite to the direction of the local velocity, α is the reversible permeability, and u represents the velocity of the electrolyte;

[0064] The steady-state convection-diffusion equation is used to describe the mass transfer process of active substances in the porous electrode, and its expression is as follows:

[0065]

[0066] Among them, c i is the concentration of active material i in the porous electrode, S i is the source term of the electrochemical reaction in the porous electrode to produce substance i, u represents the velocity of the electrolyte, represents the effective diffusion coefficient of active species i;

[0067] Effective diffusion coefficient of active species i Calculation is done using the Bruggeman equation:

[0068]

[0069] Where ε represents the porosity of the porous electrode, D i is the diffusion coefficient of active species i;

[0070] The electrode reaction kinetics in the porous electrode is described by the concentration-dependent Butler-Volmer equation, which gives the relationship between the substance concentration, the difference between the electrode potential and the standard potential, and the transfer current density. The expression is as follows:

[0071]

[0072] Among them, j i represents the transfer current density; F represents the Faraday constant, c R is the concentration of reducing substances, c O is the oxide concentration, R is the universal gas constant, T is the temperature at which the flow battery is running, k is the positive electrode standard rate constant, α a is the anode transfer coefficient, and ΔE is the difference between the electrode potential and the standard potential.

[0073] Preferably, according to the topology optimization model, a three-dimensional solver is selected for analytical solution, the adjoint algorithm is used for sensitivity calculation, and the design variable γ is updated by a moving asymptote optimization algorithm.

[0074] Preferably, the convergence condition of the topology optimization algorithm result is set as:

[0075]

[0076] in, is the objective function value obtained in the current iteration, is the objective function value obtained by the previous iteration, and E is the allowable error of the objective function value.

[0077] After the iteration is completed, the integrated structure of the flow channel and electrode based on the topology optimization of the fluid flow electrochemical reaction is output.

[0078] Based on the fractal theory, the topology optimization algorithm is described, the hierarchical structure of the flow channel in the electrode is simplified, and a regular tree-like flow channel electrode integrated structure that is easy to process and manufacture is obtained. Specifically, based on the fractal theory, the hierarchical structure of the flow channel in the electrode formed by the topology optimization calculation is simplified, and a regular tree-like flow channel electrode integrated structure that has fractal similarity to the topology optimization structure and is easy to process and manufacture is designed, including the following steps:

[0079] Measure the average length and average width of the first-stage flow channel on the inlet / outlet side, denoted as l 入0 / l 出0 and d 入0 / d 出0 ; Measure the average width of the second-stage flow channel on the inlet / outlet side, recorded as d 入1 / d 出1 ; Measure the average height of the flow channel, recorded as h; Record the number of first-stage and second-stage flow channels on the inlet / outlet side, recorded as N 入0 / N 入1 / N 出0 / N 出1 ; record the bifurcation angle of the flow channel, denoted as θ 入 / θ 出 ;

[0080] Calculate the area S of the topology optimized flow channel structure T , construct regular tree-like channels according to the principle of a certain area;

[0081] The total area of ​​the first-stage flow channel on the inlet / outlet side is denoted as S 入0 / S 出0 , the total area of ​​the second-stage flow channel on the inlet / outlet side is recorded as S 入1 / S 出1 , in satisfying S 入0 +S 出0 +S 入1 +S 出1 =S T Under the condition of , calculate the average length of the second-stage flow channel on the inlet / outlet side, denoted as l 入1 / l 出1 ;

[0082] The simplified fractal features of the topology optimization results are obtained according to the length and width of each level, and a regular tree-structured channel is drawn based on the fractal features;

[0083] Preferably, the average length / average width of the first-stage flow channel is calculated by measuring the N(N 入0 / N 出0 ) lengths / widths of the N branch flow channels, and find the average value of these N branch flow channels, which is the average length / average width of the primary flow channel.

[0084] Preferably, the area S of the topologically optimized flow channel structure is calculated according to the ratio of the flow channel to the entire porous electrode. T , the calculation formula is as follows:

[0085]

[0086] Among them, S 电极 is the plane area of ​​the porous electrode, CR is the flow channel ratio, h e is the thickness of the porous electrode, and h is the average height of the topology optimized flow channel.

[0087] Preferably, the length and width of each level of the flow channel branches of the regular tree structure are calculated by the following formula:

[0088] S 入0 =N 入0 × 入0 ×d 入0

[0089] S 入1 =N 入1 × 入1 ×d 入1

[0090] S 出0 =N 出0 × 出0 ×d 出0

[0091] S 出1 =N 出1 × 出1 ×d 出1

[0092] Among them, S 入0 / S 出0 is the total area of ​​the first-stage flow channel on the inlet / outlet side, S 入1 / S 出1 is the total area of ​​the second-stage flow channel on the inlet / outlet side; l 入0 / l 出0 and d 入0 / d 出0 are the average length and average width of the first-stage flow channel at the inlet / outlet side, respectively; d 入1 / d 出1 is the average width of the second-stage flow channel at the inlet / outlet side; N 入0 / N 入1 / N 出0 / N 出1 is the number of first-stage and second-stage flow channels on the inlet / outlet side; l 入1 / l 出1 is the average length of the second-stage flow channel at the inlet / outlet side; l 入1 × 出1= constant value, l 入1 and l 出1 The value of is selected according to the actual application.

[0093] Compared with the prior art, the technical solution of the embodiment of the present invention has beneficial effects.

[0094] For example, the present invention provides a flow channel electrode design method for a low eutectic solvent liquid flow battery based on fractal theory. The topology optimization of the integrated structure of the flow channel electrode of the liquid flow battery simultaneously considers the mass transfer problem of the active material and the electrochemical reaction kinetics under constant pressure conditions, and effectively solves the phenomenon of the dead zone of the active material in the porous electrode; the fractal theory is used to simplify the topological optimization structure to make it a regular fractal tree structure, which is easy to process and manufacture; the integrated structure of the flow channel electrode of the liquid flow battery has different proportions of the flow channel and the electrode in the direction perpendicular to the membrane. Since the closer to the membrane side, the greater the overpotential of the electrode, the closer to the membrane side, the greater the proportion of the porous electrode, and the smaller the proportion of the flow channel, the porous electrode proportion is increased and the conductivity is increased; the integrated structure of the flow channel electrode directly reduces the use of bipolar plates, reduces the thickness of the single cell and thus reduces the ohmic resistance. The distribution of the reduced flow channel proportion on the membrane side improves the flow of the electrolyte, the mass transfer of the components and the uniformity of the distribution in the electrode, so as to reduce the flow resistance of the electrolyte, strengthen the mass transfer of the active components, reduce the overpotential loss and the transmission loss, and finally improve the overall performance of the low eutectic solvent liquid flow battery.

[0095] For another example, the method for designing flow channel electrodes for low eutectic solvent flow batteries based on fractal theory provided by the present invention can reduce the thickness of the bipolar plate, reduce the thickness of the single battery, and thus reduce the system cost and ohmic resistance; the requirements for the mechanical properties of the bipolar plate are reduced, so conductive plastics can be used as bipolar plate materials, which not only reduces costs but also reduces battery weight; it has a wide range of applications in the fields of heat and mass transfer, and the reduction in the inlet cross-section of the branch flow channel not only has the effect of increasing the flow rate but also helps the electrolyte to penetrate into the porous electrode to replenish the reactants in time, thereby reducing electrochemical polarization; its thickness changes accordingly with the changes in electrochemical parameters and physicochemical parameters, generally accounting for 30% to 50% of the thickness of the porous electrode, ensuring a trade-off between the supply of active substances and the conductivity of the battery, improving the flow distribution uniformity of the electrolyte in the porous electrode, and improving the utilization rate of the electrolyte; it is beneficial to reduce the cost of processing and manufacturing. BRIEF DESCRIPTION OF THE DRAWINGS

[0096] Figure 1 This is a flow chart of a method for designing flow channel electrodes for a deep eutectic solvent flow battery based on fractal theory according to an embodiment of the present invention;

[0097] Figure 2 This is a schematic diagram of the structure of a positive electrode model of a three-dimensional liquid flow battery according to an embodiment of the present invention;

[0098] Figure 3 (a)-(b) are schematic diagrams comparing the flow channel electrode integrated structure of an embodiment of the present invention with the existing bipolar plate flow channel structure. Figure 3 (a) is a schematic diagram of an existing electrode plate without flow channels and a corresponding bipolar plate; Figure 3 (b) is a schematic diagram of the flow channel electrode integrated structure and the corresponding bipolar plate of the embodiment;

[0099] Figures 4(a)-(c) are schematic diagrams of the integrated topological structure of the flow channel electrode simulated by the finite element method according to the flow channel electrode design method of the deep eutectic solvent flow battery based on fractal theory according to an embodiment of the present invention, wherein Figure 4(a) is a schematic diagram of the structure, Figure 4(b) is a front view, and Figure 4(c) is a side view;

[0100] Figure 5 It is a two-dimensional schematic diagram of a tree-like flow channel electrode integration simplified based on the flow channel electrode integration topology optimization structure according to an embodiment of the present invention;

[0101] FIG6 is a schematic diagram showing a comparison between the integrated structure of the flow channel electrode with the tree-like flow channel implemented in the present invention and the integrated structure of the flow channel electrode with the existing serpentine flow channel, finger-shaped flow channel and parallel flow channel; FIG6(a) is a schematic diagram showing the integrated structure of the flow channel electrode with the tree-like flow channel, FIG6(b) is a schematic diagram showing the integrated structure of the serpentine flow channel electrode, FIG6(c) is a schematic diagram showing the integrated structure of the finger-shaped flow channel electrode, and FIG6(d) is a schematic diagram showing the integrated structure of the parallel flow channel electrode;

[0102] Figure 7 It is a comparison diagram of battery discharge output current under constant voltage conditions of the flow channel electrode integration structure with tree-shaped flow channels according to an embodiment of the present invention and the flow channel electrode integration structure with existing serpentine flow channels, finger-shaped flow channels and parallel flow channels. DETAILED DESCRIPTION

[0103] In order to make the purpose, features and beneficial effects of the present invention more obvious and understandable, the specific embodiments of the present invention are described in detail below in conjunction with the accompanying drawings. It is understood that the specific embodiments described below are only used to explain the present invention, rather than to limit the present invention. In addition, the same or similar reference numerals may be used in the figures to refer to the same or similar elements in different embodiments, and the description of the same or similar elements in different embodiments and the description of the prior art elements, features, effects, etc. may be omitted.

[0104] Reference Figures 1 to 7 , an embodiment of the present invention provides a method for designing flow channel electrodes for a low eutectic solvent flow battery based on fractal theory.

[0105] Specifically, the method for designing flow channel electrodes for a deep eutectic solvent flow battery based on fractal theory provided in an embodiment of the present invention comprises the following steps:

[0106] S1: Establish a three-dimensional liquid flow battery positive / negative electrode model with porous electrode domains, inlet domains and outlet domains, and couple the electrochemical reaction and flow mass transfer reaction equations in the three-dimensional liquid flow battery positive / negative electrode model;

[0107] In the specific embodiment, a deep eutectic solvent iron-vanadium liquid flow battery is taken as an example. The deep eutectic solvent iron-vanadium liquid flow battery has an integrated structure of flow channel electrodes obtained by a deep eutectic solvent liquid flow battery flow channel electrode design method based on fractal theory.

[0108] like Figure 2 As shown, in a specific embodiment, the length, width and height of the three-dimensional liquid flow battery positive / negative electrode model are 10mm, 10mm, and 1mm respectively; the inlet and outlet three-dimensional model sizes are the same, and their length, width and height are 1mm, 1mm, and 1mm respectively. Add a physical field that couples electrochemical reactions and mass transfer to the three-dimensional model, check the porous electrode module, add a fluid flow physical field, and add a volume force module, an inlet module, and an outlet module to the physical field.

[0109] like Figure 3 As shown in , when the existing electrode plate without flow channels is used, it is necessary to carve flow channels on the bipolar plate corresponding to it, such as Figure 3 (a); and the flow channel electrode integrated structure of the present invention, as shown Figure 3 As shown in (b), the flow channel is arranged on the electrode plate, and there is no need to carve the flow channel on the corresponding bipolar plate, which reduces the mechanical property requirements of the bipolar plate. The thickness of the bipolar plate can be reduced, and conductive plastic can be used as the bipolar plate material to reduce the cost and reduce the weight of the battery.

[0110] S2: Determine the physicochemical parameters of the electrolyte and porous electrodes in the three-dimensional flow battery positive / negative electrode model and determine the boundary conditions;

[0111] The physicochemical parameters of the electrolyte include dynamic viscosity μ, density ρ, ion diffusion coefficient and state of charge SOC, the physicochemical parameters of the porous electrode include porosity ε, permeability K and specific surface area a;

[0112] Set pressure boundary conditions and concentration boundary conditions at the inlet:

[0113] P in =20kPa (1)

[0114]

[0115] Among them, P in is the inlet pressure, c0 is the initial total iron concentration, is the inlet concentration of ferrous ions, is the inlet concentration of iron ions, is the chloride ion inlet concentration, SOC is the state charge;

[0116] Set the pressure to zero boundary condition and the concentration diffusion flux to zero boundary condition at the outlet:

[0117] P out =0 (5)

[0118]

[0119] Among them, P out is the outlet pressure, i represents the type of active substance (Fe 3+ , Fe 2+ , Cl - ), represents the effective diffusion coefficient of active substance i, c i represents the concentration of active substance i, and n represents the vector direction;

[0120] Apply no-slip conditions and zero active species diffusion flux conditions to the external boundaries except at the inlet and outlet:

[0121]

[0122] Where P is the pressure, i represents the type of active substance, represents the effective diffusion coefficient of active substance i, c i represents the concentration of active substance i, and n represents the vector direction;

[0123] During the discharge process, the potential boundary condition is applied to the positive electrode plate side, and the electrolyte potential boundary condition is applied to the positive electrode membrane side:

[0124] Positive plate side: φ s =U=0.7V (9)

[0125] Positive electrode film side: φ l =0 (10)

[0126] Among them, φ s represents the potential applied to the positive electrode side, which is 0.7V; φ l Represents the electrolyte potential applied on the positive electrode membrane side, which is 0V

[0127] S3: Add the variable density method module in the topology optimization method to the three-dimensional liquid flow battery positive electrode model, determine the topology optimization parameters and design domain, initialize the design variable γ of the topology optimization, and divide the design domain and non-design domain into grids of different densities;

[0128] Add a variable density method module to the topology optimization module, select the Darcy interpolation model, determine the Darcy penalty function in the Darcy interpolation model, that is, the penalty factor q = 0.04, and determine the initial value of the control variable γ = 1; determine the porous electrode as the design domain, divide it into free triangular meshes, the maximum unit size of the mesh is 0.15mm, and then sweep the mesh, the maximum unit size of the mesh is 0.1mm, the inlet domain and the outlet domain are non-design domains, and the mesh is swept directly.

[0129] S4: Adding volume force F to the porous electrode domain b , the Darcy interpolation function model is used to describe the relationship between the reversible permeability α and the design variable γ in the porous electrode domain. γ = 1 means that the porous electrode domain adopts a flow channel structure, and γ = 0 means that the porous electrode domain adopts a porous electrode structure;

[0130] The Darcy interpolation function model is used to describe the relationship between the reversible permeability α and the continuous variable γ in the porous electrode domain. The definition of the Darcy interpolation function is as follows:

[0131]

[0132] Among them, q is the penalty factor, which is used to adjust the convexity penalty parameter of the reversible permeability α;

[0133] Use Darcy interpolation function to calculate the volume force F b Punishment is performed to obtain the volume force F b The relationship between F and the design variable γ is b ∝α, so it is expressed by reversible permeability α, and its expression is as follows:

[0134]

[0135] Among them, γ is the design variable of topology optimization, α is the reversible permeability, and α s and α l are the reversible permeabilities of solid and liquid, respectively, s Related to the dynamic viscosity and permeability of the electrolyte;

[0136] where α s The definition is as follows:

[0137]

[0138] Wherein, μ is the dynamic viscosity of the electrolyte, K is the permeability of the porous electrode;

[0139] α f With α sCompared with approaching 0, when the penalty factor q is too large, the penalty for the reversible permeability α interpolation will not be enough, which will lead to more meaningless porous areas; if the penalty factor q is too small, the calculation speed will be very slow and an unreasonable structure may be obtained.

[0140] S5: Based on the relationship between the reversible permeability α and the design variable γ, a three-dimensional liquid flow battery positive electrode topology optimization model based on fluid flow electrochemical reaction is established with the maximum output current of the low eutectic solvent iron-vanadium liquid flow battery during discharge as the optimization target under the condition of fixed output voltage, in which the electrochemical reaction only occurs in the porous electrode domain, that is, the area of ​​the design variable;

[0141] Under the condition of fixed output voltage, the maximum output current of the low eutectic solvent iron-vanadium liquid flow battery during discharge is taken as the optimization goal, and the topology optimization objective function L is constructed, and its expression is as follows:

[0142]

[0143] Among them, γ is the design variable for topology optimization, and F is the Faraday constant, which is 96485C mol -1 , Fe 3+ concentration, Fe 2+ concentration, R is the universal gas constant, which is 8.3145 Jmol -1 K -1 , T is the temperature at which the flow battery is running, which is 293.15K, and k is the standard rate constant of the positive electrode, which is 6.35×10 -8 ms -1 , α a is the anode transfer coefficient, which is 0.419, ΔE is the difference between the electrode potential and the standard potential, and V is the initial volume of the porous electrode, which is 100 mm -3 , a represents the specific surface area of ​​the porous electrode;

[0144] The specific surface area a of the porous electrode is defined as follows:

[0145]

[0146] Where ε represents the porosity of the porous electrode, which is 0.85, and d f Indicates the diameter of the porous electrode fiber, which is 15um;

[0147] Based on the topology optimization method, mass transfer of materials, electrochemical reactions and fluid flow control equations, a topology optimization model for the positive / negative electrodes of flow batteries was established.

[0148] The electrolyte flows through the flow field and satisfies the continuity equation and Navier-Stokes equation:

[0149]

[0150] Where ρ represents the density of the electrolyte, which is 1242.74 kg m -3 , u represents the velocity of the electrolyte, μ represents the dynamic viscosity of the electrolyte, and P represents the pressure;

[0151] The penetration of electrolyte into the porous electrode is governed by Darcy's law:

[0152]

[0153] Where ρ represents the density of the electrolyte, which is 1242.74 kg m -3 , u represents the velocity of the electrolyte, μ represents the dynamic viscosity of the electrolyte, P represents the pressure; K represents the permeability of the porous electrode, which is calculated by the following formula:

[0154]

[0155] Among them, K CK is the Carman-Kozeny constant used to describe the fiber properties, which is 5.5, ε represents the porosity of the porous electrode, which is 0.85, and d f Indicates the diameter of the porous electrode fiber, which is 15um;

[0156] The Navier-Stokes equation and Darcy's law are combined to describe the electrolyte flow in porous media mixtures. The expression equation is as follows:

[0157]

[0158] Where ρ represents the density of the electrolyte, which is 1242.74 kg m -3 , u represents the velocity of the electrolyte, μ represents the dynamic viscosity of the electrolyte, and P represents the pressure; F b is the physical field volume force, and its expression is:

[0159] F b = -αu (21)

[0160] Here, the negative sign indicates that the direction of the force is opposite to the direction of the local velocity, and α is the reversible permeability;

[0161] The larger the reversible permeability α is, the greater the obstruction of the porous medium to the fluid is, and the weaker the fluid permeation in the porous medium is. The reversible permeability α is Darcy interpolation in topology optimization.

[0162] The steady-state convection-diffusion equation is used to describe the mass transfer process of active substances in the porous electrode, and its expression is as follows:

[0163]

[0164] Among them, c i is the concentration of active material i in the porous electrode, S i is the source term of the electrochemical reaction in the porous electrode to produce substance i, u represents the velocity of the electrolyte, represents the effective diffusion coefficient of active species i;

[0165] Effective diffusion coefficient of active species i Calculation is done using the Bruggeman equation:

[0166]

[0167] Where ε represents the porosity of the porous electrode, D i is the diffusion coefficient of active species i;

[0168] The electrode reaction kinetics in the porous electrode is described by the concentration-dependent Butler-Volmer equation, which gives the relationship between the substance concentration, the difference between the electrode potential and the standard potential, and the transfer current density. The expression is as follows:

[0169]

[0170] Among them, j i represents the transfer current density; F represents the Faraday constant, which is 96485C mol -1 , Fe 3+ concentration, Fe 2+ concentration, R is the universal gas constant, which is 8.3145 J mol -1 K -1 , T is the temperature at which the flow battery is running, which is 293.15K, and k is the standard rate constant of the positive electrode, which is 6.35×10 -8 ms -1 , α a is the anode transfer coefficient, which is 0.419, and ΔE is the difference between the electrode potential and the standard potential.

[0171] S6: According to the three-dimensional liquid flow battery positive electrode topology optimization model, a three-dimensional topology optimization solver is selected for analysis and solution;

[0172] According to the topology optimization model, a three-dimensional solver is selected for analysis and solution. The adjoint algorithm is used for sensitivity calculation. The design variable γ is updated by the moving asymptote optimization algorithm (MMA). The maximum number of iterations is set to 100, and the convergence accuracy is set to 0.0001.

[0173] S7: Convergence judgment is performed. When the objective function meets the convergence condition, the calculation is stopped and the flow channel electrode integrated structure based on the topological optimization of the fluid flow electrochemical reaction is output;

[0174] The convergence condition of the topology optimization algorithm results is set as:

[0175]

[0176] in, is the objective function value obtained in the current iteration, is the objective function value obtained from the previous iteration, and E is the allowable error of the objective function value, which is 0.0001.

[0177] After the iteration is completed, the integrated structure of the flow channel and electrode based on the topology optimization of the fluid flow electrochemical reaction is output, as shown in Figure 4.

[0178] The flow channel structure obtained by topological optimization is relatively complex, difficult to process, and has high manufacturing costs. The flow channel structure needs to be optimized to form regular channels. It can be directly processed on commercial electrodes through CNC (Computerized Numerical Control) or laser etching, which is easy to process and conducive to large-scale low-cost production.

[0179] S8: Based on fractal theory, describe and simplify the hierarchical structure of topologically optimized flow channels, and form a flow channel-electrode integrated structure that is easy to process and manufacture. The tree-like flow channel is as follows: Figure 5 As shown;

[0180] Measure the average length and average width of the first-stage flow channel on the inlet / outlet side, denoted as l 入0 / l 出0 and d 入0 / d 出0 ; Measure the average width of the second-stage flow channel on the inlet / outlet side, recorded as d 入1 / d 出1 ; Measure the average height of the flow channel, recorded as h; Record the number of first-stage and second-stage flow channels on the inlet / outlet side, recorded as N 入0 / N 入1 / N 出0 / N 出1 ; record the bifurcation angle of the flow channel, denoted as θ 入 / θ 出 ;

[0181] Calculate the area S of the topology optimized flow channel structure T , construct regular tree-like channels according to the principle of a certain area;

[0182] The total area of ​​the first-stage flow channel on the inlet / outlet side is denoted as S 入0 / S出0 , the total area of ​​the second-stage flow channel on the inlet / outlet side is recorded as S 入1 / S 出1 , in satisfying S 入0 +S 出0 +S 入1 +S 出1 =S T Under the condition of , calculate the average length of the second-stage flow channel on the inlet / outlet side, denoted as l 入1 / l 出1 ;

[0183] Draw a regular tree-structured channel according to the length and width of each level;

[0184] The average length / average width of the first-stage flow channel is calculated by measuring the length / width of the N branch flow channels of this stage and finding these N (including (N 入0 / N 出0 )) The average value of the branch flow channels is the average length / average width of the primary flow channel.

[0185] The area S of the topologically optimized channel structure is calculated based on the ratio of the channel to the entire porous electrode. T , the calculation formula is as follows:

[0186]

[0187] Among them, S 电极 is the plane area of ​​the porous electrode, CR is the flow channel ratio, h e is the thickness of the porous electrode, and h is the average height of the topology optimized flow channel.

[0188] The length and width of each level of flow channel branches are calculated by the following formula:

[0189] S 入0 =N 入0 × 入0 ×d 入0 (27)

[0190] S 入1 =N 入1 × 入1 ×d 入1 (28)

[0191] S 出0 =N 出0 × 出0 ×d 出0 (29)

[0192] S 出1 =N 出1 × 出1 ×d 出1 (30)

[0193] Among them, S 入0 / S 出0 is the total area of ​​the first-stage flow channel on the inlet / outlet side, S 入1 / S 出1 is the total area of ​​the second-stage flow channel on the inlet / outlet side; l 入0 / l 出0 and d 入0 / d 出0 are the average length and average width of the first-stage flow channel at the inlet / outlet side, respectively; d 入1 / d 出1 is the average width of the second-stage flow channel at the inlet / outlet side; N 入0 / N 入1 / N 出0 / N 出1 is the number of first-stage and second-stage flow channels on the inlet / outlet side; l 入1 / l 出1 is the average length of the second-stage flow channel at the inlet / outlet side; l 入1 × 出1 = constant value, l 入1 and l 出1 The value of is selected according to the actual application.

[0194] The calculated parameters are as follows: 入0 =5mm, l 出0 =2mm,d 入0 =0.6mm,d 出0 =0.6mm, l 入1 =3mm, l 出0 =2mm,d 入1 =0.36mm,d 出1 =0.36mm, h=0.35mm, N 入0 =3, N 入1 =7,N 出0 =2,N 出1 =4,θ 入 =45°,θ 出 =60°.

[0195] FIG6 is a schematic diagram showing a comparison between the integrated structure of the flow channel electrode with tree-shaped flow channels implemented in the present invention and the flow channel electrode with existing serpentine flow channels, finger-shaped flow channels and parallel flow channels.

[0196] When the operating parameters and physicochemical parameters are kept the same as those of the tree-like flow channel, the finite element method is used for numerical calculation. The length and depth of the conventional serpentine / finger-shaped / parallel flow channel inlet are 0.5 mm and 0.35 mm, respectively, and the flow channel height of the conventional serpentine / finger-shaped / parallel flow channel is consistent with that of the tree-like flow channel.

[0197] The simulation results are as follows Figure 7 As shown, the output current performance of the non-aqueous iron-vanadium flow battery under the conditions of tree-like flow channel, serpentine flow channel, finger-shaped flow channel and parallel flow channel structure is 46.6mA, 9.05mA, 9.32mA and 9.06mA respectively. The output current of the non-aqueous iron-vanadium flow battery under the condition of tree-like flow channel electrode integration structure is the highest, which is 415%, 400% and 414% higher than the conventional serpentine / finger-shaped / parallel flow channel electrode integration structure.

[0198] Although specific embodiments have been described above, these embodiments are not intended to limit the scope of the present disclosure, even when only a single embodiment is described with respect to specific features. The feature examples provided in the present disclosure are intended to be illustrative rather than limiting, unless otherwise stated. In specific implementations, the technical features of one or more dependent claims may be combined with the technical features of the independent claim, based on actual needs and where technically feasible, and may be derived from the technical features of the corresponding independent claim in any appropriate manner rather than simply through the specific combination listed in the claims.

[0199] Although the present invention is disclosed as above, the present invention is not limited thereto. Any person skilled in the art can make various changes and modifications without departing from the spirit and scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the scope defined by the claims.

Claims

1. A method for designing flow channel electrodes for deep eutectic solvent flow batteries based on fractal theory, characterized in that: The steps include: Establish a three-dimensional liquid flow battery positive / negative electrode model with porous electrode domains, inlet domains, and outlet domains, and couple the electrochemical reaction and flow mass transfer reaction control equations in the three-dimensional liquid flow battery positive / negative electrode model; Determine the physical and chemical properties of the electrolyte and porous electrodes in the three-dimensional flow battery positive / negative electrode model and determine the boundary conditions; A topology optimization algorithm based on the variable density method is coupled to the positive / negative electrode model of a three-dimensional liquid flow battery to determine the topology optimization parameters and design domain, initialize the design variable γ of the topology optimization, and divide the design domain and non-design domain into grids of different densities; Adding volume force F to the porous electrode domain b , the Darcy interpolation function model is used to describe the relationship between the reversible permeability α and the design variable γ in the porous electrode domain; Based on the relationship between the reversible permeability α and the design variable γ, a three-dimensional liquid flow battery positive / negative electrode topology optimization model based on fluid flow electrochemical reaction was established with the maximum output current during discharge of the liquid flow battery as the optimization goal under the condition of fixed output voltage. According to the three-dimensional liquid flow battery positive / negative electrode topology optimization model, a three-dimensional topology optimization solver is selected for analysis and solution; Convergence judgment is performed, and when the objective function meets the convergence condition, the calculation is stopped, and the flow channel electrode integrated structure based on the topological optimization of the fluid flow electrochemical reaction is output; The topology optimization algorithm is described based on fractal theory, which simplifies the hierarchical structure of the flow channel in the electrode and obtains a regular tree-like flow channel electrode integrated structure that is easy to process and manufacture.

2. The method for designing flow channel electrodes for deep eutectic solvent flow batteries based on fractal theory according to claim 1, characterized in that: The physicochemical parameters of the electrolyte include dynamic viscosity μ, density ρ, ion diffusion coefficient D and state charge SOC, and the physicochemical parameters of the porous electrode include porosity ε, permeability K and specific surface area a; Set pressure boundary conditions and concentration boundary conditions at the inlet: P in =C1 c R =c0·(1-SOC) c O =c0·SOC Among them, P in is the inlet pressure, c1 represents the inlet pressure value, which is a constant; c0 is the initial concentration, c R is the concentration of reducing substances, c O is the oxide concentration, SOC is the state of charge; Set the pressure to zero boundary condition and the concentration diffusion flux to zero boundary condition at the outlet: P out ＝0 Among them, P out is the outlet pressure, i represents the type of active substance, represents the effective diffusion coefficient of active substance i, c i represents the concentration of active substance i, and n represents the vector direction; Apply no-slip conditions and zero active species diffusion flux conditions to the external boundaries except at the inlet and outlet: Where P represents pressure, i represents the type of active substance, represents the effective diffusion coefficient of active substance i, c i represents the concentration of active substance i; During the discharge / charge process, potential boundary conditions are applied to the positive / negative electrode plate side, and electrolyte potential boundary conditions are applied to the positive / negative electrode membrane side: Positive / negative electrode plate side: φ s =V1 Positive / negative electrode membrane side: φ l =V2 Among them, φ s represents the potential applied to the positive / negative electrode plate side, φ l represents the electrolyte potential applied on the membrane side of the positive / negative electrode, V1 and V2 represent the potential values ​​on the plate side and membrane side, respectively, and both are constants.

3. The method for designing flow channel electrodes for deep eutectic solvent flow batteries based on fractal theory according to claim 1, characterized in that: The Darcy interpolation function model is used to describe the relationship between the reversible permeability α and the continuous variable γ in the porous electrode domain. The definition of the Darcy interpolation function is as follows: Among them, q is the penalty factor, which is used to adjust the convexity penalty parameter of the reversible permeability α; Use Darcy interpolation function to calculate the volume force F b Punishment is performed to obtain the volume force F b The relationship between F and the design variable γ is b ∝α, so the reversible permeability α is used to express the relationship with the design variable γ, and its expression is as follows: Among them, γ is the design variable of topology optimization, α is the reversible permeability, and α s and α l are the reversible permeabilities of solid and liquid, respectively, s Related to the dynamic viscosity and permeability of the electrolyte; where α s The definition is as follows: Where μ is the dynamic viscosity of the electrolyte and K is the permeability of the porous electrode.

4. The method for designing flow channel electrodes for deep eutectic solvent flow batteries based on fractal theory according to claim 1, characterized in that: Under the condition of fixed output voltage, the optimization goal is to maximize the output current when the flow battery is discharged. The objective function is L, and the expression is as follows: Where γ is the design variable for topology optimization, F is the Faraday constant, and c R is the concentration of reducing substances, c O is the oxide concentration, R is the universal gas constant, T is the temperature at which the flow battery is running, k is the positive electrode standard rate constant, α a is the anode transfer coefficient, ΔE is the difference between the electrode potential and the standard potential, V is the initial volume of the porous electrode, and a represents the specific surface area of ​​the porous electrode; The specific surface area a of the porous electrode is defined as follows: Where, ε represents the porosity of the porous electrode, d f represents the porous electrode fiber diameter; Based on the topology optimization method, mass transfer of materials, electrochemical reactions and fluid flow control equations, a topology optimization model for the positive / negative electrodes of flow batteries was established. The electrolyte flows through the flow field and satisfies the continuity equation and Navier-Stokes equation: Among them, ρ and u represent the density and velocity of the electrolyte, respectively, μ represents the dynamic viscosity of the electrolyte, and P represents the pressure; The penetration of electrolyte into the porous electrode is governed by Darcy's law: Where P represents pressure, ρ and u represent the density and velocity of the electrolyte, μ represents the dynamic viscosity of the electrolyte, and K represents the permeability of the porous electrode; The permeability K of the porous electrode is calculated by the following formula: Among them, K CK is the Carman-Kozeny constant used to describe the fiber properties, ε represents the porosity of the porous electrode, and d f represents the porous electrode fiber diameter; The NaVier-Stokes equation and Darcy's law are combined to describe the electrolyte flow in porous media mixtures. The expression equation is as follows: Where P represents pressure, ρ and u represent the density and velocity of the electrolyte respectively, μ represents the dynamic viscosity of the electrolyte, and F b is the body force, and its expression is: F b =-αu Where the negative sign indicates that the direction of the force is opposite to the direction of the local velocity, α is the reversible permeability, and u represents the velocity of the electrolyte; The steady-state convection-diffusion equation is used to describe the mass transfer process of active substances in the porous electrode, and its expression is as follows: Among them, c i is the concentration of active material i in the porous electrode, S i is the source term of the electrochemical reaction in the porous electrode to produce substance i, u represents the velocity of the electrolyte, represents the effective diffusion coefficient of active species i; Effective diffusion coefficient of active species i Calculation is done using the Bruggeman equation: Where, τ represents the porosity of the porous electrode, D i is the diffusion coefficient of active substance i; The electrode reaction kinetics in the porous electrode is described by the concentration-dependent Butler-Volmer equation, which gives the relationship between the substance concentration, the difference between the electrode potential and the standard potential, and the transfer current density. The expression is as follows: Among them, j i represents the transfer current density; F represents the Faraday constant, c R is the concentration of reducing substances, c O is the oxide concentration, R is the universal gas constant, T is the temperature at which the flow battery is running, k is the positive electrode standard rate constant, α a is the anode transfer coefficient, and ΔE is the difference between the electrode potential and the standard potential.

5. The method for designing flow channel electrodes for deep eutectic solvent flow batteries based on fractal theory according to claim 1, characterized in that: According to the topology optimization model, a three-dimensional solver is selected for analysis and solution, the adjoint algorithm is used for sensitivity calculation, and the design variable γ is updated by the moving asymptote optimization algorithm.

6. The method for designing flow channel electrodes for deep eutectic solvent flow batteries based on fractal theory according to claim 1, characterized in that: The convergence condition of the topology optimization algorithm results is set as: in, is the objective function value obtained in the current iteration, is the objective function value obtained by the previous iteration, and E is the allowable error of the objective function value. After the iteration is completed, the integrated structure of the flow channel and electrode based on the topology optimization of the fluid flow electrochemical reaction is output.

7. The method for designing flow channel electrodes for deep eutectic solvent flow batteries based on fractal theory according to claim 1, characterized in that: Based on the fractal theory, the topology optimization algorithm is described to simplify the hierarchical structure of the flow channel in the electrode, and a regular tree-like flow channel electrode integrated structure that is easy to process and manufacture is obtained, including the following steps: Measure the average length and average width of the first-stage flow channel on the inlet / outlet side, denoted as l 入0 / l 出0 and d 入0 / d 出0 ; Measure the average width of the second-stage flow channel on the inlet / outlet side, recorded as d 入1 / d 出1 ; Measure the average height of the flow channel, recorded as h; Record the number of first-stage and second-stage flow channels on the inlet / outlet side, recorded as N 入0 / N 入1 / N 出0 / N 出1 ; record the bifurcation angle of the flow channel, denoted as θ 入 / θ 出 ; Calculate the area S of the topology optimized flow channel structure T , construct regular tree-like channels according to the principle of a certain area; The total area of ​​the first-stage flow channel on the inlet / outlet side is denoted as S 入0 / S 出0 , the total area of ​​the second-stage flow channel on the inlet / outlet side is recorded as S 入1 / S 出1 , in satisfying S 入0 +S 出0 +S 入1 +S 出1 =S T Under the condition of , calculate the average length of the second-stage flow channel on the inlet / outlet side, denoted as l 入1 / l 出1 ; The simplified fractal characteristics of the topology optimization results are obtained according to the length and width of each level, and a regular tree-structured channel is drawn based on the fractal characteristics.

8. The method for designing flow channel electrodes for deep eutectic solvent flow batteries based on fractal theory according to claim 7, characterized in that: The average length / average width of the first-stage flow channel is calculated by measuring the N(N 入0 / N 出0 ) lengths / widths of the N branch flow channels, and find the average value of these N branch flow channels, which is the average length / average width of the primary flow channel.

9. The method for designing flow channel electrodes for deep eutectic solvent flow batteries based on fractal theory according to claim 7, characterized in that: The area S of the topologically optimized channel structure is calculated based on the ratio of the channel to the entire porous electrode. T , the calculation formula is as follows: Among them, S 电极 is the plane area of ​​the porous electrode, CR is the flow channel ratio, h e is the thickness of the porous electrode, and h is the average height of the topology optimized flow channel.

10. The method for designing flow channel electrodes for deep eutectic solvent flow batteries based on fractal theory according to claim 7, characterized in that: The length and width of each level of the regular tree structure flow channel branch are calculated by the following formula: S 入0 =N 入0 ×l 入0 ×d 入0 S 入1 =N 入1 ×l 入1 ×d 入1 S 出0 =N 出0 ×l 出0 ×d 出0 S 出1 =N 出1 ×l 出1 ×d 出1 Among them, S 入0 / S 出0 is the total area of ​​the first-stage flow channel on the inlet / outlet side, S 入1 / S 出1 is the total area of ​​the second-stage flow channel on the inlet / outlet side; l 入0 / l 出0 and d 入0 / d 出0 are the average length and average width of the first-stage flow channel at the inlet / outlet side, respectively; d 入1 / d 出1 is the average width of the second-stage flow channel on the inlet / outlet side; N 入0 / N 入1 / N 出0 / N 出1 is the number of first-stage and second-stage flow channels on the inlet / outlet side; l 入1 / l 出1 is the average length of the second-stage flow channel at the inlet / outlet side; l 入1 × 出1 = constant value, l 入1 and l 出1 The value of is selected according to the actual application.

Images