Simulation method for morphology evolution of zinc dendrite on porous electrode in zinc-based flow battery

Abstract

This invention discloses a simulation method for the evolution of zinc dendrite morphology on porous electrodes in zinc-based flow batteries, belonging to the field of electrochemical energy storage. The method includes: constructing a geometric model containing the solid-phase framework of the porous electrode, and establishing a multiphysics model coupling phase-field order parameter evolution, zinc ion transport, electrolyte flow, and potential distribution. This enables mesoscale dynamic simulation of zinc deposition and dendrite growth processes within the porous electrode. This method can realistically reflect the non-uniform current distribution and localized mass transfer differences caused by the pore structure, significantly improving the physical realism and predictive ability of the simulation. It provides an effective numerical analysis tool and theoretical basis for optimizing electrode structure and suppressing dendrite growth.

Description

Technical Field

[0001] This invention belongs to the field of electrochemical energy storage, and in particular relates to a simulation method for the evolution of zinc dendrite morphology on porous electrodes in zinc-based flow batteries. Background Technology

[0002] Aqueous zinc-based flow batteries (such as zinc-bromine and zinc-iron batteries) have shown broad application prospects in large-scale energy storage due to their high safety, low cost, and environmental friendliness. However, the zinc anode is prone to dendrite formation during charge and discharge, which severely restricts the cycle life and safety of the battery. To reveal the dendrite growth mechanism, the phase-field method, as a numerical method that can intuitively describe the solid-liquid phase transition process, has been widely used in the simulation study of zinc electrodeposition. In existing technologies, studies have successfully revealed the influence of factors such as overpotential and anisotropy intensity on dendritic fractal structure through phase-field models, or elucidated the deposition kinetic competition mechanism driven by ion concentration gradient through multi-scale coupling methods.

[0003] Nevertheless, existing phase-field simulations are generally based on the assumption of ideal planar electrodes, while practical zinc-based flow batteries typically employ porous electrodes with complex pore network structures to improve reaction efficiency. The non-uniform current distribution, localized mass transfer differences, and solid-liquid interface constraints within porous electrodes lead to fundamentally different zinc deposition behavior compared to planar electrodes. Currently, research on zinc dendrite growth behavior within porous electrodes mainly relies on experimental observation, lacking a dedicated simulation method that can realistically reflect its complex structural features and multi-physics coupling effects at the mesoscale. This has become a key technical bottleneck in optimizing electrode structure and suppressing dendrite growth in this field. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention provides a simulation method for the evolution of zinc dendrite morphology on porous electrodes in zinc-based flow batteries, comprising: A geometric model containing a porous electrode solid-phase structure was constructed, and a multi-physics field coupling simulation model of phase field-electrochemical-fluid dynamics was established based on the geometric model. In the coupled simulation model, the interface evolution process between the zinc metal phase and the electrolyte phase is described by the phase field sequence parameter equation, the diffusion and convection behavior of zinc ions in the electrolyte is described by the mass transfer equation, the flow state of the electrolyte in the porous structure is described by the fluid dynamics equation, and the potential distribution in the electrode and electrolyte regions is described by the potential control equation. The initial conditions and boundary conditions of each physical field in the coupled simulation model are set. The initial conditions include setting initial nucleation sites at the electrode interface to trigger the zinc deposition process. Based on the initial and boundary conditions, the coupled simulation model is solved transiently to obtain the deposition morphology of zinc in the porous electrode and the dendrite growth evolution process.

[0005] Optionally, the construction of the geometric model includes: A two-dimensional computational domain is established in the finite element simulation software, and multiple circular or near-circular hole structures are arranged in the computational domain. The hole structures correspond to the solid phase skeleton in the porous electrode, and the remaining area is defined as the electrolyte region.

[0006] Optionally, establishing the coupled simulation model includes: The phase field order parameter equation is coupled with the electrochemical reaction kinetics, wherein the driving force of phase field evolution is determined by a function reflecting the electrochemical reaction rate and a dimensionless zinc ion concentration, which is calculated based on the ratio of the local zinc ion concentration to the initial zinc ion concentration and the applied overpotential.

[0007] Optionally, the mass transfer equation is the Nernst-Planck equation, which includes convection, diffusion, and electrochemical reaction consumption terms, wherein the effective diffusion coefficient of zinc ions transitions between the electrode phase diffusion coefficient and the electrolyte phase diffusion coefficient through an interpolation function based on the phase field variable.

[0008] Optionally, the fluid dynamics equation is the Navier-Stokes equation, in which the dynamic viscosity of the electrolyte is calculated as a function of the phase field variables to distinguish the electrolyte phase, the electrode solid phase, and the interface region between them.

[0009] Optionally, the potential control equation is a Poisson equation containing source terms, used to characterize the current density conservation under electrically neutral conditions, wherein the effective conductivity transitions between electrode conductivity and electrolyte conductivity through an interpolation function based on phase field variables.

[0010] Optionally, the initial conditions include: Initialize the phase field order parameters in the computational domain to the state of the electrolyte phase; Initial nucleation sites are introduced at predetermined locations on the surface of the electrode skeleton structure; The zinc ion concentration field is initialized to a uniform distribution; The electric potential field is initially set to zero potential.

[0011] Optionally, the set boundary conditions include: Set inflow and outflow boundaries for the concentration field, and apply periodic boundary conditions to the remaining boundaries; Define the flow inlet and pressure outlet boundaries for the fluid dynamics field; Apply fixed overpotential and zero potential boundaries to the potential field.

[0012] On the other hand, the present invention also provides an electronic device including a memory, a processor, and a computing program stored in the memory and executable on the processor, wherein the processor implements the method when executing the computing program.

[0013] On the other hand, the present invention also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the method.

[0014] Compared with the prior art, the present invention has the following advantages and technical effects: The simulation method proposed in this invention effectively overcomes the technical limitations of existing planar electrode models. By coupling the phase-field model with multiphysics equations describing ion transport, electrolyte flow, and potential distribution, and directly constructing the geometry of the porous electrode within the computational domain, the simulation process can fully consider the non-uniformity of current distribution, differences in local mass transfer conditions, and steric hindrance effects caused by the porous network. This method can continuously and dynamically simulate the deposition morphology and dendrite evolution of zinc within the porous electrode at the mesoscale, accurately reflecting the spatial differences in dendrite growth position, direction, and rate, significantly improving the physical realism and predictive ability of the simulation results. Therefore, it provides crucial theoretical basis and efficient numerical analysis tools for the structural design of porous electrodes, porosity optimization, and control of battery operating parameters without requiring extensive and time-consuming experiments, possessing significant engineering application value. Attached Figure Description

[0015] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. In the drawings: Figure 1 This is a schematic diagram of the computational domain according to an embodiment of the present invention; Figure 2 This is a schematic diagram of the deposition morphology in an embodiment of the present invention.

[0016] Figure 3 This is a schematic diagram of the zinc ion concentration distribution and electrolyte flow direction in an embodiment of the present invention; Figure 4 This is a potential gradient distribution diagram according to an embodiment of the present invention; Figure 5 This is a flowchart of an embodiment of the present invention. Detailed Implementation

[0017] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0018] It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although a logical order is shown in the flowchart, in some cases the steps shown or described may be executed in a different order than that shown here.

[0019] Example 1 like Figure 5 As shown, this embodiment provides a simulation method for the evolution of zinc dendrite morphology on porous electrodes in a zinc-based flow battery, including: A geometric model containing a porous electrode solid-phase structure was constructed, and a multi-physics field coupling simulation model of phase field-electrochemical-fluid dynamics was established based on the geometric model. In the coupled simulation model, the interface evolution process between the zinc metal phase and the electrolyte phase is described by the phase field sequence parameter equation, the diffusion and convection behavior of zinc ions in the electrolyte is described by the mass transfer equation, the flow state of the electrolyte in the porous structure is described by the fluid dynamics equation, and the potential distribution in the electrode and electrolyte regions is described by the potential control equation. The initial conditions and boundary conditions of each physical field in the coupled simulation model are set. The initial conditions include setting initial nucleation sites at the electrode interface to trigger the zinc deposition process. Based on the initial and boundary conditions, the coupled simulation model is solved transiently to obtain the deposition morphology of zinc in the porous electrode and the dendrite growth evolution process.

[0020] The specific process includes: Step 1: Construct a two-dimensional porous electrode geometric model. In the finite element simulation software, establish a square computational domain and uniformly arrange multiple circular hole structures within the computational domain to simulate the solid-phase interface formed by fibers or skeletons in the porous electrode. The hole region is set as a solid-phase region that cannot participate in electrochemical reactions, and the remaining regions are electrolyte regions.

[0021] Step 2: Based on the geometric model, establish a multiphysics coupled phase-field simulation model. This model uses order parameter equations to describe the interface evolution between the zinc metal phase and the electrolyte phase. The phase-field variable ξ is a non-conservative order parameter that evolves with the deposition process. The electrode phase and electrolyte phase are defined as 1 and 0, respectively, with 0 < ξ < 1 indicating a transition interface. The evolution equation of the order parameter ξ over time in the phase-field model is: ; in Indicates the interface migration rate. Represents the electrochemical reaction constant, double-well function W represents the potential barrier height for the phase transition. The gradient coefficient, which characterizes the irregularity of the electrode-electrolyte interface, is defined as follows: ,in For the anisotropy intensity, The angle between the vertical direction of the interface and the defined direction. This represents the gradient surface energy constant. The driving force directly reflects the strength of the electrochemical reaction kinetics, where... It is an interpolation function, and its expression is: α, F, n, R and T represent the charge transfer coefficient, Faraday constant, number of transferred electrons, ideal gas constant and temperature, respectively. The dimensionless zinc ion concentration is expressed as: ,in and These represent the ratios of the initial zinc ion concentration and the local zinc ion concentration in the electrolyte, respectively. This indicates the applied overpotential.

[0022] The diffusion and convection behavior of zinc ions in the electrolyte are described using the dilute mass transfer equation, and the transport behavior of ions in the electrolyte is described by combining the Nernst-Planck equation: ; in, The value represents the electrolyte flow rate, and z represents the number of charges transferred by zinc ions. The effective diffusion coefficient is represented by an interpolation function, which expresses the different diffusion coefficients in the electrolyte phase and the electrode phase. The expression is: , and These represent the diffusion coefficients of zinc ions in the electrode and the electrolyte, respectively. The source term on the right indicates the amount of zinc ions consumed during the electrochemical reaction when zinc ions are converted into zinc metal. This indicates the molar ratio of zinc metal.

[0023] The Navier-Stokes equations are used to describe the flow state of the electrolyte in the porous structure, assuming that the electrolyte is an incompressible viscous fluid. The specific equations are as follows: ; in The density of the electrolyte. Electrolyte flow rate For pressure, For the action force, This represents the dynamic viscosity of the electrolyte. To characterize the evolution of the phase field, dynamic viscosity is expressed using phase field variables. The function is calculated, and its expression is: It is used to identify fluids, solids, and fluid-solid interfaces. In the presence of a flowing electrolyte, viscosity changes with the phase. Viscosity increases significantly when flowing through a solid interface, while it remains at a normal electrolyte viscosity value in the liquid phase.

[0024] The Poisson equation, including the source term, calculates the potential distribution in the electrode and electrolyte regions, describing the conservation of current density during the charging process of an electrically neutral system. The equation is as follows: ; The effective conductivity can be expressed as: , and These are the electrode conductivity and the electrolyte conductivity, respectively.

[0025] Step 3: Set the initial conditions for each physical field. Initialize the order parameters in the computational domain to the electrolyte phase state, and introduce initial nucleation sites at the electrode interface to trigger the zinc deposition process. The initial nucleation sites are represented by a step function, and initial nucleation sites are set at the four positions (top, bottom, left, and right) of all circular electrode fibers. The zinc ion concentration is set to a uniform initial distribution, and the computational domain except for the initial nucleation sites uses the initial zinc ion concentration value. The initial value of the electric potential field is set to zero potential.

[0026] Step 4: Set the boundary conditions for each physical field. All order parameter boundary conditions are set to zero flux. In the concentration field, the left boundary is set as the inflow boundary with the initial zinc ion concentration fixed, the right boundary as the outflow boundary, and the remaining boundaries are set as periodic boundary conditions. In the laminar flow field, the left boundary is set as the flow inlet with a set velocity, the right boundary as the flow outlet, and pressure boundary conditions are set. The remaining boundary conditions have zero flux. The electric potential boundary conditions are set to a fixed overpotential at the upper boundary. The lower boundary is fixed as a zero potential boundary, and the other boundaries are periodic boundary conditions.

[0027] Step 5: Collect mass transfer parameters (including but not limited to electrolyte flow rate, diffusion coefficient, interface mobility, density, viscosity, etc.) and reaction kinetic parameters (including but not limited to reaction rate constant, gradient energy coefficient, energy barrier height, etc.) during zinc dendrite growth. Input the various parameters and variable expressions, as well as the various equations and boundary conditions into the finite element simulation software and perform mesh generation. Determine the calculation time and calculation step size.

[0028] Step 6: Under the above conditions, the zinc deposition behavior during the charging process is solved transiently to obtain the deposition morphology of zinc at different locations inside the porous electrode and the dendrite growth evolution process, thereby realizing the numerical simulation and analysis of the zinc dendrite growth behavior under the porous electrode structure.

[0029] Example 2 This embodiment provides a simulation method for the evolution of zinc dendrite morphology on porous electrodes in a zinc-based flow battery, including: Taking the zinc dendrite phase field dynamics model as an example, a method and system for predicting the growth morphology of zinc dendrites on porous electrodes are developed. In this embodiment, a two-dimensional porous electrode geometric model is first constructed, such as... Figure 1 As shown, a square computational domain with a side length of 200 micrometers was established in the computational software. Nine circular perforated structures were uniformly arranged within this domain to simulate the solid-phase interface formed by fibers or a framework in a porous electrode. The top layer of fiber perforations represents the electrode near the membrane side, the middle layer represents the electrode in the middle region, and the bottom layer represents the electrode near the current collector. The perforated region was designated as a solid-phase region that could not participate in the electrochemical reaction, while the remaining regions were electrolyte regions.

[0030] Subsequently, a multiphysics coupled phase-field simulation model was established based on the aforementioned geometric model. This model uses order parameter equations to describe the interface evolution between the zinc metal phase and the electrolyte phase. The phase-field variable ξ is a non-conservative order parameter that evolves with the deposition process. The electrode phase and electrolyte phase are defined as 1 and 0, respectively, with 0 < ξ < 1 indicating a transition interface. The equation for the evolution of the order parameter ξ over time in the phase-field model is as follows: ; in Indicates the interface migration rate. Represents the electrochemical reaction constant, double-well function W represents the potential barrier height for the phase transition. The gradient coefficient, which characterizes the irregularity of the electrode-electrolyte interface, is defined as follows: ,in For the anisotropy intensity, The angle between the vertical direction of the interface and the defined direction. This represents the gradient surface energy constant. The driving force directly reflects the strength of the electrochemical reaction kinetics, where... It is an interpolation function, and its expression is: α, F, n, R and T represent the charge transfer coefficient, Faraday constant, number of transferred electrons, ideal gas constant and temperature, respectively. The dimensionless zinc ion concentration is expressed as: ,in and These represent the ratios of the initial zinc ion concentration and the local zinc ion concentration in the electrolyte, respectively. This indicates the applied overpotential.

[0031] The diffusion and convection behavior of zinc ions in the electrolyte are described using the dilute mass transfer equation, and the transport behavior of ions in the electrolyte is described by combining the Nernst-Planck equation. ; in, The value represents the electrolyte flow rate, and z represents the number of charges transferred by zinc ions. The effective diffusion coefficient is represented by an interpolation function, which expresses the different diffusion coefficients in the electrolyte phase and the electrode phase. The expression is: , and These represent the diffusion coefficients of zinc ions in the electrode and the electrolyte, respectively. The source term on the right indicates the amount of zinc ions consumed during the electrochemical reaction when zinc ions are converted into zinc metal. This indicates the molar ratio of zinc metal.

[0032] The Navier-Stokes equations are used to describe the flow state of the electrolyte in the porous structure, assuming that the electrolyte is an incompressible viscous fluid. The specific equations are as follows: ; in The density of the electrolyte. Electrolyte flow rate For pressure, For the action force, This represents the dynamic viscosity of the electrolyte. To characterize the evolution of the phase field, dynamic viscosity is expressed using phase field variables. The function is calculated, and its expression is: It is used to identify fluids, solids, and fluid-solid interfaces. In the presence of a flowing electrolyte, viscosity changes with the phase. Viscosity increases significantly when flowing through a solid interface, while it remains at a normal electrolyte viscosity value in the liquid phase.

[0033] The Poisson equation, including the source term, calculates the potential distribution in the electrode and electrolyte regions, describing the conservation of current density during the charging process of an electrically neutral system. The equation is as follows: ; The effective conductivity can be expressed as: , and These are the electrode conductivity and the electrolyte conductivity, respectively.

[0034] In terms of initial conditions, the order parameters within the computational domain were initialized to the electrolyte phase state, and initial nucleation sites were introduced at the electrode interface to trigger the zinc deposition process. A step function was used to set the initial nucleation sites, which were located at the four positions (top, bottom, left, and right) of the nine electrode fibers as shown in the figure. The zinc ion concentration was set to a uniform initial distribution, and the computational domain, except for the initial nucleation sites, had an initial zinc ion concentration of c0 = 2000 mol / m³. The initial potential field was set to zero. Regarding boundary conditions, all order parameter boundary conditions were set to zero flux boundaries. In the concentration field, the left boundary was set as the inflow boundary with a fixed ion concentration of the initial zinc ion concentration, and the right boundary was set as the outflow boundary. In the laminar flow field, the left boundary was set as the flow inlet with a velocity of 0.026 m / s, and the right boundary was set as the flow outlet with pressure boundary conditions. The electric potential field boundary condition is set as a fixed overpotential at the upper boundary. The lower boundary is fixed as a zero potential boundary.

[0035] Mass transfer parameters (including but not limited to electrolyte flow rate, diffusion coefficient, interface mobility, density, viscosity, etc.) and reaction kinetic parameters (including but not limited to reaction rate constant, gradient energy coefficient, energy barrier height, etc.) during zinc dendrite growth were collected from existing technologies. The expressions for these parameters and variables, along with the equations and boundary conditions, were input into finite element simulation software, and meshing was performed. The maximum mesh size was 0.75 micrometers, the charging time was 200 s, and the calculation step size was 1 s. Under these conditions, the transient solution for zinc deposition behavior during the charging process was obtained. Figure 2 The image shows the morphology of zinc dendrites after 200 seconds of deposition. It can be seen that zinc dendrite growth is most obvious and has more branches in the region near the film side, while the zinc dendrite growth is relatively smooth in the region near the current collector. Figure 3 The graph shows the zinc ion concentration distribution after 200 seconds of deposition. It can be seen that the zinc ion concentration in the zinc deposition area is almost zero, indicating that the zinc ions in this area have successfully converted into zinc metal. Furthermore, the ion concentration also decreases drastically between dendrite branches. This is because ion diffusion is reduced in the tiny regions between branches, causing ions to migrate to surrounding active sites and react, resulting in localized concentration depletion zones between branches. Figure 4 The results also show that the potential gradient is mainly concentrated at the tips of the top row of dendrites. This concentration of gradient further leads to zinc deposition at the tips, i.e., the tip effect. This result is consistent with the conclusions obtained in the experiments, proving the accuracy and reliability of the model.

[0036] On the other hand, this embodiment also provides a simulation system for the evolution of zinc dendrite morphology on porous electrodes in zinc-based flow batteries, characterized in that it includes: The geometric modeling module is used to construct a computational domain geometric model that includes a porous electrode solid-phase structure. The physics modeling module is used to establish a multiphysics coupled simulation model of phase field-electrochemistry-fluid dynamics based on the geometric model. The condition setting module is used to set the initial conditions and boundary conditions of each physical field in the coupled simulation model; The solution and analysis module is used to perform transient solutions on the coupled simulation model based on the initial and boundary conditions, and output visualization results of zinc deposition morphology and dendrite evolution process.

[0037] On the other hand, this embodiment also provides an electronic device, including a memory, a processor, and a computing program stored in the memory and executable on the processor, wherein the processor implements the method when executing the computing program.

[0038] On the other hand, this embodiment also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the method.

[0039] The above are merely preferred embodiments of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A simulation method for the evolution of zinc dendrite morphology on porous electrodes in a zinc-based flow battery, characterized in that, include: A geometric model containing a porous electrode solid-phase structure was constructed, and a multi-physics field coupling simulation model of phase field-electrochemical-fluid dynamics was established based on the geometric model. In the coupled simulation model, the interface evolution process between the zinc metal phase and the electrolyte phase is described by the phase field sequence parameter equation, the diffusion and convection behavior of zinc ions in the electrolyte is described by the mass transfer equation, the flow state of the electrolyte in the porous structure is described by the fluid dynamics equation, and the potential distribution in the electrode and electrolyte regions is described by the potential control equation. The initial conditions and boundary conditions of each physical field in the coupled simulation model are set. The initial conditions include setting initial nucleation sites at the electrode interface to trigger the zinc deposition process. Based on the initial and boundary conditions, the coupled simulation model is solved transiently to obtain the deposition morphology of zinc in the porous electrode and the dendrite growth evolution process.

2. The method according to claim 1, characterized in that, The constructed geometric model includes: A two-dimensional computational domain is established in the finite element simulation software, and multiple circular or near-circular hole structures are arranged in the computational domain. The hole structures correspond to the solid phase skeleton in the porous electrode, and the remaining area is defined as the electrolyte region.

3. The method according to claim 2, characterized in that, The establishment of the coupled simulation model includes: The phase field order parameter equation is coupled with the electrochemical reaction kinetics, wherein the driving force of phase field evolution is determined by a function reflecting the electrochemical reaction rate and a dimensionless zinc ion concentration, which is calculated based on the ratio of the local zinc ion concentration to the initial zinc ion concentration and the applied overpotential.

4. The method according to claim 1, characterized in that, The mass transfer equation is the Nernst-Planck equation, which includes convection, diffusion, and electrochemical reaction consumption terms. The effective diffusion coefficient of zinc ions is interpolated between the electrode phase diffusion coefficient and the electrolyte phase diffusion coefficient based on the phase field variable through an interpolation function.

5. The method according to claim 1, characterized in that, The fluid dynamics equation is the Navier-Stokes equation, in which the dynamic viscosity of the electrolyte is calculated as a function of the phase field variables to distinguish the electrolyte phase, the electrode solid phase, and the interface region between the two.

6. The method according to claim 1, characterized in that, The potential control equation is a Poisson equation containing a source term, used to characterize the conservation of current density under electrically neutral conditions. The effective conductivity transitions between electrode conductivity and electrolyte conductivity through an interpolation function based on the phase field variable.

7. The method according to claim 1, characterized in that, The initial conditions include: Initialize the phase field order parameters in the computational domain to the state of the electrolyte phase; Initial nucleation sites are introduced at predetermined locations on the surface of the electrode skeleton structure; The zinc ion concentration field is initialized to a uniform distribution; The electric potential field is initially set to zero potential.

8. The method according to claim 1, characterized in that, The defined boundary conditions include: Set inflow and outflow boundaries for the concentration field, and apply periodic boundary conditions to the remaining boundaries; Define the flow inlet and pressure outlet boundaries for the fluid dynamics field; Apply fixed overpotential and zero potential boundaries to the potential field.

9. An electronic device comprising a memory, a processor, and a computing program stored in the memory and executable on the processor, characterized in that, When the processor executes the computing program, it implements the method of any one of claims 1-8.

10. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it implements the method of any one of claims 1-8.

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