Simulation method and device for salt ion migration during ice-water phase transition

Abstract

This application discloses a method and apparatus for simulating salt ion migration during ice-water phase transitions. The method includes determining the basic physical parameters of salt ions, including melting temperature, solute equilibrium distribution coefficient, diffusion coefficient in unfrozen solution, diffusion coefficient in ice, thermal diffusivity of unfrozen solution and ice, specific heat capacity, latent heat of phase transition, and latent heat of salt crystallization; constructing a phase field model represented by coupled differential equations based on these basic physical parameters; and solving the coupled differential equations to obtain phase field distribution results, concentration distribution results, and temperature distribution results. In this method, phase field values ​​are introduced to distinguish between the different thermodynamic states of the solid and liquid phases, establishing a phase field model for phase transition that couples the phase field, concentration field, and temperature fields. The model parameters of the phase field model consider the contribution of salt crystallization and the influence of the ion precipitation process in ice under freezing conditions, thereby improving the simulation results of ion migration in salt solutions during freezing.

Description

Technical Field

[0001] The present application relates to the technical field of ice-water phase transition data processing, and in particular to a method and device for simulating salt ion migration during ice-water phase transition. Background Art

[0002] During the freezing process of a saline solution, the formation of ice crystals causes ions to be continuously repelled, concentrating in the unfrozen solution near the freezing interface. This phenomenon of solute ice exclusion is quite common in physical and geochemical systems. For example, rivers, lakes, and seawater in high-latitude regions exhibit significant solute exclusion due to seasonal freezing. Generally speaking, the solubility of ice is only in the micromolar range or even lower, making salt ions almost insoluble in ice. However, in actual freezing processes, it is common to observe solute residues in the ice layer, especially when the solute diffusion rate is lower than the growth rate of ice crystals. The solute will exist in the ice in the form of bubbles of high-concentration salt solution.

[0003] In related technologies, in the process of exploring that the free interface of ice-water phase transition under freezing conditions will change constantly with freezing temperature and time, although most studies have explored the growth law of ice crystals during the phase transition, the accuracy of the simulation of salt ion migration needs to be improved. Summary of the Invention

[0004] In view of this, the present application provides a method and device for simulating salt ion migration during ice-water phase transition, which can accurately simulate the results of salt ion migration.

[0005] In a first aspect, the present application provides a method for simulating salt ion migration during ice-water phase transition, comprising:

[0006] determining basic physical parameters of salt ions, including melting temperature, solute equilibrium distribution coefficient, diffusion coefficient of salt ions in unfrozen solution, diffusion coefficient of salt ions in ice, thermal diffusivity of unfrozen solution and ice, specific heat capacity, latent heat of phase change, and latent heat of salt crystallization;

[0007] constructing a phase field model represented by coupled differential equations based on the basic physical parameters, the coupled differential equations including a phase field governing equation with phase field values ​​as dependent variables and time as independent variables, a concentration field governing equation with concentration as dependent variable and time as independent variables, and a temperature field governing equation with temperature as dependent variable and time as independent variables, wherein the phase field values ​​are used to characterize the degree of ice crystallization;

[0008] By solving the coupled differential equations, phase field distribution results, concentration distribution results and temperature distribution results are obtained.

[0009] Optionally, the phase field control equation is implemented as expressed by the following formula:

[0010]

[0011] h(φ)=φ 3 (10-15φ+6φ 2 );

[0012] g(φ)=φ 2 (1-φ) 2 ;

[0013]

[0014] In the above formula, M is the phase field mobility; φ is the phase field value, t is the time; ε(θ) is the phase field gradient coefficient related to the interface anisotropy, θ is the angle between the x-axis and the reference coordinate, ε'(θ) is the derivative of ε(θ); h(φ) is the derivative of h'(φ), h(φ) is the interpolation function that changes monotonically from h(φ) = 0 to h(φ) = 1; T is the temperature, R is the ideal gas constant, V m is the molar volume, c S is the equilibrium concentration of ice, c L is the equilibrium concentration of the unfrozen solution, Δc S is the salt crystal concentration at equilibrium, ω is the double potential well height, g'(φ) is the derivative of g(φ), g(φ) is the double potential well function related to the phase field value, k e is the solute equilibrium distribution coefficient, c is the concentration of the unfrozen solution, μ k is the interface dynamic coefficient, m e is the liquidus slope, σ is the interfacial energy, and the superscript e indicates the equilibrium state.

[0015] Optionally, the temperature field control equation is executed as expressed by the following formula:

[0016]

[0017] Where T is temperature, φ is phase field value, t is time, α L is the thermal diffusivity of the unfrozen solution, c p is the specific heat capacity, L s is the latent heat of salt crystallization, L i is the latent heat of ice crystallization, c is the concentration of the unfrozen solution, h(φ) is the derivative of h'(φ), h(φ) is the interpolation function that changes monotonically from h(φ) = 0 to h(φ) = 1, μ is the solid-liquid phase thermal diffusion coefficient, α S is the thermal diffusivity of ice.

[0018] Optionally, the concentration field control equation is implemented as expressed by the following formula:

[0019]

[0020] D(φ)=h(φ)D S +[1-h(φ)]D L ;

[0021] In the above formula, c is the concentration; t is the time, φ is the phase field value, h(φ) is the derivative of h'(φ), h(φ) is the interpolation function that changes monotonically from h(φ) = 0 to h(φ) = 1, c S is the equilibrium concentration of ice, c L is the equilibrium concentration of the unfrozen solution, Δc S is the salt crystal concentration at equilibrium, T is the temperature, y represents the y-axis direction, β is the ion precipitation rate coefficient in the solution bubble, κ is the ion formation coefficient in the solution bubble, D(φ) is the solute diffusion coefficient that depends on the phase field, D S is the solute diffusion coefficient in ice, D L is the solute diffusion coefficient in the unfrozen solution.

[0022] Optionally, the interface energy σ is determined by the following formula,

[0023]

[0024] In the above formula, ε(θ) is the phase field gradient coefficient related to the interface anisotropy, θ is the angle between the x-axis and the reference coordinate, and ω is the height of the double potential well;

[0025] The phase field gradient coefficient ε(θ) related to the interface anisotropy is determined by the following formula:

[0026] ε(θ)=ε0[1+ηcosk(θ-θ0)];

[0027]

[0028] In the above formula, θ is the angle between the x-axis and the reference coordinate, ε0 is the initial parameter of the interface anisotropy, η is the intensity of the anisotropy, k is the modulus of the anisotropy, θ0 is the angle between the x-axis and the reference coordinate, φ y is the partial derivative of φ about the y-axis, φ x is the partial derivative of φ with respect to x.

[0029] Optionally, the phase field governing equation satisfies the following conditions:

[0030]

[0031] In the above formula, φ i+1 is the phase field value after phase field perturbation at time i+1, φ iis the phase field value before the phase field perturbation at time i, r is a random number between -1 and +1; υ is the time-dependent perturbation intensity factor, g(φ) is the double-well potential function related to the phase field value, and χ is the forced perturbation parameter.

[0032] Optionally, the concentration field control equation satisfies the following conditions:

[0033]

[0034] In the above formula, c i+1 is the concentration after phase field perturbation at time i+1, c i is the concentration before the phase field perturbation at time i, r is a random number between -1 and +1; υ is the time-dependent perturbation intensity factor, g(φ) is the double-well potential function related to the phase field value, and χ is the forced perturbation parameter.

[0035] In a second aspect, the present application provides a device for simulating salt ion migration during ice-water phase transition, comprising:

[0036] a determination module for determining basic physical parameters of salt ions, wherein the basic physical parameters include melting temperature, solute equilibrium distribution coefficient, diffusion coefficient of salt ions in unfrozen solution, diffusion coefficient of salt ions in ice, thermal diffusivity of unfrozen solution and ice, specific heat capacity, latent heat of phase change, and latent heat of salt crystallization;

[0037] a construction module for constructing a phase field model represented by coupled differential equations based on the basic physical parameters, the coupled differential equations including a phase field governing equation with phase field values ​​as dependent variables and time as independent variables, a concentration field governing equation with concentration as dependent variable and time as independent variables, and a temperature field governing equation with temperature as dependent variable and time as independent variables, wherein the phase field values ​​are used to characterize the degree of ice crystallization;

[0038] The acquisition module is used to obtain phase field distribution results, concentration distribution results and temperature distribution results by solving the coupled differential equations.

[0039] In a third aspect, the present application provides an execution device, comprising a processor and a memory, wherein the processor is coupled to the memory;

[0040] The memory is used to store programs;

[0041] The processor is configured to execute the program in the memory, so that the execution device executes the above method.

[0042] In the method disclosed in the present application, by introducing phase field values ​​to distinguish the different thermodynamic states of the solid phase and the liquid phase, a phase field model of the ice-water phase transition of the salt solution is established by coupling the phase field, concentration field and temperature field. The contribution of salt crystallization and the influence of the ion precipitation process in ice under freezing conditions are considered in the model parameters of the phase field model, thereby improving the simulation results of ion migration in the salt solution during the freezing process. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] The following detailed description of the specific embodiments of the present application in conjunction with the accompanying drawings will make the technical solutions and other beneficial effects of the present application apparent.

[0044] Figure 1 An operational flow chart of a method for simulating salt ion migration during ice-water phase transition provided by an exemplary embodiment is shown.

[0045] Figure 2 The phase field, temperature field and concentration field simulation results of the free growth of a single crystal nucleus at different times provided by an exemplary embodiment are shown.

[0046] Figure 3 The phase field parameters, temperature and concentration distribution simulation results of the transverse cross section (Y=250) and the longitudinal cross section (X=250) during the free growth of a single crystal nucleus provided by an exemplary embodiment are shown.

[0047] Figure 4 The concentration field simulation results of the free growth of a single crystal nucleus under different ion conditions provided by an exemplary embodiment are shown.

[0048] Figure 5 The figure shows a phase field model provided by an exemplary embodiment to simulate the precipitation rules of different ions during the ice-water phase transition.

[0049] Figure 6 A block diagram of a device for simulating salt ion migration during ice-water phase transition provided by an exemplary embodiment is shown.

[0050] Figure 7 A block diagram of an execution device provided by an exemplary embodiment is shown. DETAILED DESCRIPTION

[0051] To make the above-mentioned objects, features, and advantages of the present application more clearly understood, the specific embodiments of the present application are described in detail below with reference to the accompanying drawings. The following description sets forth many specific details to facilitate a full understanding of the present application. However, the present application can be implemented in many other ways than those described herein, and those skilled in the art can make similar improvements without violating the scope of the present application. Therefore, the present application is not limited to the specific embodiments disclosed below.

[0052] The terms "first", "second", etc. in the specification and claims of this application and the above-mentioned drawings are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that the data used in this way can be interchangeable where appropriate so that the embodiments described herein can be implemented in a sequence other than that illustrated or described herein. In addition, the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusions. For example, a process, method, system, product or device that includes a series of steps or modules is not necessarily limited to those steps or modules clearly listed, but may include other steps or modules that are not clearly listed or that are inherent to these processes, methods, products or devices. The naming or numbering of steps in this application does not mean that the steps in the method flow must be executed in the time / logical sequence indicated by the naming or numbering. The process steps that have been named or numbered can be changed in the execution order according to the technical purpose to be achieved, as long as the same or similar technical effects can be achieved. The division of units in this application is a logical division. In actual application, there may be other division methods. For example, multiple units can be combined or integrated into another system, or some features can be ignored or not executed. In addition, the coupling or direct coupling or communication connection between each other shown or discussed can be through some interfaces, and the indirect coupling or communication connection between units can be electrical or other similar forms, which are not limited in this application. Moreover, the units or sub-units described as separate components may or may not be physically separated, may or may not be physical units, or may be distributed into multiple circuit units. Some or all of the units can be selected according to actual needs to achieve the purpose of the solution of this application.

[0053] Please refer to Figure 1 ,in Figure 1 A flow chart of a method for simulating salt ion migration during ice-water phase transition provided by an exemplary embodiment is shown. The method is implemented through steps 101-103.

[0054] In step 101, basic physical parameters of salt ions are determined, including melting temperature, solute equilibrium distribution coefficient, diffusion coefficient of salt ions in unfrozen solution, diffusion coefficient of salt ions in ice, thermal diffusion coefficient of unfrozen solution and ice, specific heat capacity, latent heat of phase change and latent heat of salt crystallization.

[0055] It is implicitly disclosed that the ice-water phase transition process herein is directed to a saline solution, which includes but is not limited to a NaCl solution, a KCl solution, a CaCl2 solution, a MgCl2 solution, a NaHCO3 solution, and a Na2SO4 solution.

[0056] As a demonstration of actual operation, the basic physical parameters of salt ions can be determined based on the critical conditions for salt crystallization during the ice-water phase transition of salt solutions, so as to collect and determine the basic physical parameters of different ions.

[0057] The selection of these specific types of fundamental physical parameters is based on the applicant's unexpected discovery that when a solution undergoes an ice-water phase transition, diffusion migration caused by solute repulsion and the latent heat of crystallization released by ice crystal growth will alter the concentration and temperature gradients in the solution. These two factors not only influence each other but also form a feedback mechanism with the nucleation, crystallization, and growth of ice crystals. Furthermore, under freezing conditions, the free interface of the ice-water phase transition will constantly change with freezing temperature and time.

[0058] Among them, the eutectic temperature of common binary water-salt systems and the resulting salt crystal forms are shown in Table 1.

[0059] Table 1 Phase equilibrium data of common binary water-salt systems

[0060]

[0061] The basic physical parameters of different ions include melting temperature T m , solute equilibrium distribution coefficient k e , the diffusion coefficient D of different ions in unfrozen solution L-ion , the diffusion coefficient D of different ions in ice S-ion , thermal diffusion coefficient α of unfrozen solution and ice, specific heat capacity c p , latent heat of phase change L i , latent heat of salt crystallization L S , the specific values ​​are shown in Table 2.

[0062] Table 2 Basic physical parameters of different ions

[0063]

[0064] In step 102, a phase field model represented by coupled differential equations is constructed based on the basic physical parameters. The coupled differential equations include a phase field control equation with phase field value as a dependent variable and time as an independent variable, a concentration field control equation with concentration as a dependent variable and time as an independent variable, and a temperature field control equation with temperature as a dependent variable and time as an independent variable. The phase field value is used to characterize the degree of ice crystallization.

[0065] Regarding "phase field values ​​are used to characterize the degree of ice crystallization", it should be added that the phase field value is used to distinguish the different thermodynamic states of ice and unfrozen solution. It can be understood as a measure of the degree of ice crystallization, and the phase field value φ can be defined as a continuous variable between ice (φ = 1) and unfrozen solution (φ = 0).

[0066] In this context, "coupled differential equations" refer to differential equations in which two or more unknown functions interact with each other, and these functions involve at least one or more independent variables. Solving coupled differential equations involves determining the functional relationship between the unknown functions.

[0067] As a preferred example, the phase field governing equation can be determined based on the Helmholtz free energy functional, specifically, by the following formula:

[0068]

[0069] h(φ)=φ 3 (10-15φ+6φ 2 );

[0070] g(φ)=φ 2 (1-φ) 2 ;

[0071]

[0072] In the above formula, M is the phase field mobility; φ is the phase field value (as mentioned above, it can be specified as 0≤φ≤1), t is the time; ε(θ) is the phase field gradient coefficient related to the interface anisotropy, θ is the angle between the x-axis and the reference coordinate, ε'(θ) is the derivative of ε(θ); h(φ) is the derivative of h'(φ), h(φ) is the interpolation function that changes monotonically from h(φ) = 0 to h(φ) = 1; T is the temperature, R is the ideal gas constant (taken as 8.31 J·K -1 ·mol -1 ), V m is the molar volume, c S is the equilibrium concentration of ice, c L is the equilibrium concentration of the unfrozen solution, Δc S is the salt crystal concentration at equilibrium, ω is the double potential well height, g'(φ) is the derivative of g(φ), g(φ) is the double potential well function related to the phase field value, k e is the solute equilibrium distribution coefficient, c is the concentration of the unfrozen solution, μ k is the interface dynamic coefficient, m e is the liquidus slope, σ is the interfacial energy, and the superscript e indicates the equilibrium state.

[0073] It is worth noting that, as a more common demonstration form, the equilibrium concentration k of ice and unfrozen solution is e , can be determined by the following formula,

[0074]

[0075] Among the above, The concentration of salt crystals at equilibrium is is the equilibrium concentration of ice, is the equilibrium concentration of the unfrozen solution.

[0076] Specifically, the interface energy σ is determined by the following formula:

[0077]

[0078] In the above formula, ε(θ) is the phase field gradient coefficient related to the interface anisotropy, θ is the angle between the x-axis and the reference coordinate, and ω is the height of the double potential well.

[0079] In order to determine the double potential well height ω, it can be determined by the following formula,

[0080]

[0081] In the above formula, ε(θ) is the phase field gradient coefficient related to the interface anisotropy, θ is the angle between the x-axis and the reference coordinate, λ is the interface thickness, and α is a constant that can be taken as 2.2.

[0082] Specifically, the phase field gradient coefficient ε(θ) related to the interface anisotropy is determined by the following formula:

[0083] ε(θ)=ε0[1+ηcosk(θ-θ0)];

[0084]

[0085] In the above formula, θ is the angle between the x-axis and the reference coordinate, ε0 is the initial parameter of the interface anisotropy (for example, ε0 = 0.01), η is the intensity of the anisotropy (for example, η = 0.03), k is the modulus of the anisotropy (for example, k = 6), θ0 is the angle between the x-axis and the reference coordinate (for example, θ0 = π / 2), φ y is the partial derivative of φ about the y-axis, φ x is the partial derivative of φ with respect to x.

[0086] For the above phase field governing equation, considering the phase field perturbation, it satisfies the following conditions:

[0087]

[0088] In the above formula, φ i+1 is the phase field value after phase field perturbation at time i+1, φ i is the phase field value before the phase field perturbation at time i, r is a random number between -1 and +1; υ is the time-dependent perturbation intensity factor, g(φ) is the double-well potential function related to the phase field value, and χ is the forced perturbation parameter.

[0089] Here, it can be added that the role of χg(φ) is to introduce a forced perturbation at the ice-water phase transition interface. When φ = 0.5, the maximum perturbation will occur at the ice-water phase transition interface, and the perturbation will decrease rapidly as it moves away from the interface.

[0090] As a preferred example, the temperature field control equation can be determined according to the law of conservation of energy. Specifically, it can be expressed as follows:

[0091]

[0092] Where T is temperature, φ is phase field value, t is time, α L is the thermal diffusivity of the unfrozen solution, c p is the specific heat capacity, L s is the latent heat of salt crystallization, L i is the latent heat of ice crystallization, c is the concentration of the unfrozen solution, h(φ) is the derivative of h'(φ), h(φ) is the interpolation function that changes monotonically from h(φ) = 0 to h(φ) = 1, μ is the solid-liquid phase thermal diffusion coefficient, α S is the thermal diffusivity of ice.

[0093] As a preferred example, the concentration field control equation can be determined according to Fick's diffusion law. Specifically, it can be expressed as follows:

[0094]

[0095] D(φ)=h(φ)D S +[1-h(φ)]D L ;

[0096] In the above formula, c is the concentration; t is the time, φ is the phase field value, h(φ) is the derivative of h'(φ), h(φ) is the interpolation function that changes monotonically from h(φ) = 0 to h(φ) = 1, c S is the equilibrium concentration of ice, c L is the equilibrium concentration of the unfrozen solution, Δc S is the salt crystal concentration at equilibrium, T is the temperature, y represents the y-axis direction, β is the ion precipitation rate coefficient in the solution bubble (for example, β = 0.05), κ is the ion formation coefficient in the solution bubble (for example, κ = 0.05), D(φ) is the solute diffusion coefficient that depends on the phase field, D S is the solute diffusion coefficient in ice, D L is the solute diffusion coefficient in the unfrozen solution.

[0097] For the above concentration field control equation, considering the concentration field disturbance, it satisfies the following conditions:

[0098]

[0099] In the above formula, c i+1 is the concentration after phase field perturbation at time i+1, c i is the concentration before the phase field perturbation at time i, r is a random number between -1 and +1; υ is the time-dependent perturbation intensity factor, g(φ) is the double-well potential function related to the phase field value, and χ is the forced perturbation parameter.

[0100] In step 103, the phase field distribution result, the concentration distribution result and the temperature distribution result are obtained by solving the coupled differential equation.

[0101] Here, the coupled differential equations can be solved by numerical solution, series expansion, variational method, etc., which are well known in the art. The above-mentioned solution process can be implemented with the aid of finite element software.

[0102] The actual operation of solving the problem using finite element software includes the following steps:

[0103] Step 1031: Determine the geometric dimensions of the simulation area and the calculation method of the time step of the phase field model, perform grid division, and define parameters;

[0104] Specifically, the geometry of the simulation area is set to 30 × 30 μm, and the grid division of the simulation area is 500 × 500 nodes, with a distance between each node of 6 × 10 -8 m.

[0105] The time step in this step is calculated by the formula:

[0106]

[0107] Where Δx is the spatial step length; D L-ion is the solute diffusion coefficient of different ions in unfrozen solution.

[0108] Step 1032, determine the initial conditions and simulation boundary conditions of the phase field model;

[0109] The initial conditions in this step include initial temperature, initial concentration, initial crystal nucleus size and position;

[0110] In this example, the salt solution is assumed to uniformly fill the entire computational domain. There is an initial nucleus with a radius of r0 at the center of the computational domain. 17 grids (r0 = 17Δx) are selected as the initial nucleus radius to simulate the free growth process of a single nucleus. The initial conditions are set as follows:

[0111] When x 2 +y 2 When ≥r0, φ=0 (unfrozen solution), c=c0=0.01mol·L -1, T=T f ;

[0112] When x 2 +y 2 When ≤r0, φ=1(ice), c=c0=0.01mol·L -1 , T=T f ;

[0113] Where x and y represent the horizontal and vertical coordinates of the computational domain node, respectively; φ is the phase field parameter; c represents the concentration of the salt solution in the computational domain; c0 is the initial concentration of the salt solution; T represents the temperature in the computational domain; T f is the freezing temperature of the salt solution, which is calculated by the following formula;

[0114]

[0115] Where c is the concentration of salt solution (mol·L -1 ), N m is the number of ions dissociated from the salt, and z is the valence of the salt.

[0116] In this step 1032 , at the boundary of the computational domain, the phase field, the temperature field, and the concentration field are all set to zero flux boundary conditions to achieve a free growth process of a single crystal nucleus.

[0117] Step 1033: Execute the solution of the custom partial differential equation (PDEs) module;

[0118] Specifically, the phase field, concentration field, and temperature field governing equations were solved using a custom partial differential equation (PDE) module within the COMSOL Multiphysics finite element software. During the numerical solution process, the governing PDEs were created, a step function for the phase field value φ was inserted, the geometry and material properties were imported, and after meshing, different initial parameters, initial conditions, and boundary conditions were set. The governing equations for the phase field, concentration field, and temperature fields were then coupled and calculated. Iterations were repeated based on the simulation results, and the concentration and temperature distributions within the computational domain were updated. These simulation results were used to refresh the phase field parameters, and new iterative calculations were then initiated until all calculations were completed within the set time.

[0119] It should be understood that the phase field distribution result here is the change of the phase field value over time, the concentration distribution result is the change of the concentration over time, and the temperature distribution result is the change of the temperature over time.

[0120] In order to visualize the phase field distribution results, concentration distribution results and temperature distribution results, similar tools such as but not limited to Origin software can be used to visualize the results, and the phase field morphology, temperature distribution, concentration distribution diagram of the free growth of single crystal nuclei during the ice-water phase transition, as well as the phase field parameters, temperature and concentration distribution simulation results at different cross sections can be obtained.

[0121] Through the above phase field morphology, temperature distribution and concentration distribution results, the process of dendrite growth, temperature distribution and solute distribution during the ice-water phase transition of the salt solution can be presented ( Figure 2 ), as well as the simulation results of the phase field parameters, temperature and concentration distribution at different times of the transverse section (Y = 250) and the longitudinal section (X = 250) during the free growth of a single crystal nucleus ( Figure 3 ), thus, the coupling and mutual feedback relationship in the phase field model solution process can be determined.

[0122] Among them, ice-water phase transition, heat transfer and mass transfer will occur simultaneously during the free growth of a single crystal nucleus. The diffusion coefficient D in the solid phase ice is S and the diffusion coefficient D in the unfrozen solution L The mass transfer process between ice and unfrozen solution is dominated by . Therefore, the free growth of a single crystal nucleus was simulated under different ionic conditions, and the concentration field distribution results were as follows: Figure 4 shown.

[0123] Using the concentration field simulation results of the free growth of a single crystal nucleus under different ionic conditions, we further sorted out the precipitation amounts of different ions in the cross section and determined the precipitation rules of ions during the ice-water phase transition simulation using the phase field model. The results are as follows: Figure 5 Finally, the migration law and precipitation amount of salt ions during the ice-water phase transition can be obtained.

[0124] It can be seen that the present invention can simulate the migration of salt ions during the ice-water phase transition process, and can study the precipitation amount of different salt ions by changing the diffusion coefficient of ions in unfrozen solutions and ice. On this basis, the microscopic mechanism affecting heat and mass transfer during the ice-water phase transition process is explored.

[0125] It should be emphasized that this simulation method has the following advantages:

[0126] 1. In this method, the contribution of salt crystallization and the influence of ion precipitation in ice under freezing conditions are considered in the construction of the phase field model of ion migration during the ice-water phase transition. In this process, the complex physical processes of the ice-water phase transition interface are clarified, including the position and morphology of the phase transition interface, local heat conduction and release of latent heat of crystallization, ion precipitation and ion diffusion migration during the ice-water phase transition, and the interaction between phase transition interface changes, temperature, and concentration. These interactions can be described by the coupling between the phase field, concentration field, and temperature field, and the mutual influence between phase change crystallization, heat transfer, and ion migration are revealed from a microscopic perspective, which can more realistically simulate the phase change crystallization process.

[0127] 2. In this method, the phase field model is established based on the binary water-salt system. During the ice-water phase transition, the relationship between the phase transition crystallization temperature and the eutectic temperature needs to be considered, that is, whether salt crystallization occurs. When the actual temperature of the system is higher than the eutectic temperature of the salt solution, only water undergoes phase transition during freezing. At this time, L in the phase field governing equation and the temperature field governing equation S =0, and the temperature control equation (Formula 7) in Δc S = 0. When the actual temperature of the system reaches or is lower than the eutectic temperature of the salt solution, the concentration and latent heat of crystallization generated by the salt crystallization cannot be ignored.

[0128] Please refer to Figure 6 , which shows a block diagram of the device for simulating salt ion migration during ice-water phase transition provided by the present application. The device 200 includes:

[0129] Determination module 201 is used to determine basic physical parameters of salt ions, wherein the basic physical parameters include melting temperature, solute equilibrium distribution coefficient, diffusion coefficient of salt ions in unfrozen solution, diffusion coefficient of salt ions in ice, thermal diffusion coefficient of unfrozen solution and ice, specific heat capacity, latent heat of phase change, and latent heat of salt crystallization;

[0130] A construction module 202 is configured to construct a phase field model represented by coupled differential equations based on the basic physical parameters, wherein the coupled differential equations include a phase field governing equation with phase field values ​​as a dependent variable and time as an independent variable, a concentration field governing equation with concentration as a dependent variable and time as an independent variable, and a temperature field governing equation with temperature as a dependent variable and time as an independent variable, wherein the phase field values ​​are used to characterize the degree of ice crystallization;

[0131] The acquisition module 203 is used to obtain phase field distribution results, concentration distribution results and temperature distribution results by solving the coupled differential equations.

[0132] Since the above methods have been discussed in detail, the specific implementation of the above modules will not be repeated here.

[0133] Next, we will introduce an execution device provided by the embodiment of the present application. Figure 7 , Figure 7 This is a schematic diagram of the structure of the execution device provided in the embodiment of the present application. The execution device 300 can be specifically manifested as an autonomous driving vehicle, a mobile phone, a tablet, a laptop computer, a desktop computer, a monitoring data processing device, etc., which is not limited here. Figure 1 The execution device 300 includes a receiver 301, a transmitter 302, a processor 303, and a memory 304 (the number of processors 303 in the execution device 300 can be one or more, Figure 7 (taking one processor as an example), the processor 303 may include an application processor 3031 and a communication processor 3032. In some embodiments of the present application, the receiver 301, the transmitter 302, the processor 303 and the memory 304 may be connected via a bus or other means.

[0134] Memory 304 may include read-only memory and random access memory, and provides instructions and data to processor 303. A portion of memory 304 may also include non-volatile random access memory (NVRAM). Memory 304 stores processor and operation instructions, executable modules, or data structures, or subsets or extended sets thereof. Operation instructions may include various operation instructions for implementing various operations.

[0135] Processor 303 controls the operation of the execution device. In specific applications, the various components of the execution device are coupled together via a bus system. In addition to a data bus, the bus system may also include a power bus, a control bus, and a status signal bus. However, for clarity, all of these buses are referred to as a bus system in the figure.

[0136] The methods disclosed in the above embodiments of the present application can be applied to the processor 303 or implemented by the processor 303. The processor 303 can be an integrated circuit chip with signal processing capabilities. During implementation, each step of the above method can be completed by the hardware integrated logic circuit in the processor 303 or by instructions in the form of software. The above processor 303 can be a general-purpose processor, a digital signal processor (DSP), a microprocessor or a microcontroller, and can further include an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA) or other programmable logic device, discrete gate or transistor logic device, discrete hardware components. The processor 303 can implement or execute the various methods, steps and logic block diagrams disclosed in the embodiments of the present application. The general-purpose processor can be a microprocessor or the processor can also be any conventional processor, etc. The steps of the method disclosed in the embodiments of the present application can be directly embodied as being executed by a hardware decoding processor, or can be executed by a combination of hardware and software modules in the decoding processor. The software module can be located in a storage medium well-known in the art, such as random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, registers, etc. The storage medium is located in memory 304, and processor 303 reads the information in memory 304 and performs the steps of the above method in conjunction with its hardware.

[0137] Receiver 301 can be used to receive input digital or character information and generate signal input related to executing device-related settings and function control. Transmitter 302 can be used to output digital or character information through the first interface. Transmitter 302 can also be used to send instructions to the disk pack through the first interface to modify data in the disk pack. Transmitter 302 can also include a display device such as a display screen.

[0138] In the embodiment of the present application, the processor 303 is used to execute Figure 1 The specific manner in which the application processor 3031 in the processor 303 performs the above steps is the same as that in the present application. Figure 1 The corresponding method embodiments are based on the same concept, and the technical effects they bring are the same as those in this application. Figure 1 The corresponding method embodiments are the same. For specific contents, please refer to the description in the method embodiments shown above in this application, which will not be repeated here.

[0139] The above is only a preferred specific implementation method of the present application, but the scope of protection of the present application is not limited thereto. Any changes or replacements that can be easily thought of by any technician familiar with this technical field within the technical scope disclosed in this application should be covered by the scope of protection of the present application.

Claims

1. A method for simulating salt ion migration during ice-water phase transition, characterized in that: include: determining basic physical parameters of salt ions, including melting temperature, solute equilibrium distribution coefficient, diffusion coefficient of salt ions in unfrozen solution, diffusion coefficient of salt ions in ice, thermal diffusivity of unfrozen solution and ice, specific heat capacity, latent heat of phase change, and latent heat of salt crystallization; constructing a phase field model represented by coupled differential equations based on the basic physical parameters, the coupled differential equations including a phase field governing equation with phase field values ​​as dependent variables and time as independent variables, a concentration field governing equation with concentration as dependent variable and time as independent variables, and a temperature field governing equation with temperature as dependent variable and time as independent variables, wherein the phase field values ​​are used to characterize the degree of ice crystallization; The phase field control equation is expressed as follows: h(φ)=φ 3 (10-15φ+6φ 2 ); g(φ)=φ 2 (1-φ) 2 ; In the above formula, M is the phase field mobility; φ is the phase field value, t is the time; ε(θ) is the phase field gradient coefficient related to the interface anisotropy, θ is the angle between the x-axis and the reference coordinate, ε'(θ) is the derivative of ε(θ); h(φ) is the derivative of h'(φ), h(φ) is the interpolation function that changes monotonically from h(φ) = 0 to h(φ) = 1; T is the temperature, R is the ideal gas constant, V m is the molar volume, c S is the equilibrium concentration of ice, c L is the equilibrium concentration of the unfrozen solution, Δc S is the salt crystal concentration at equilibrium, ω is the double potential well height, g'(φ) is the derivative of g(φ), g(φ) is the double potential well function related to the phase field value, k e is the solute equilibrium distribution coefficient, c is the concentration of the unfrozen solution, μ k is the interface dynamic coefficient, m e is the liquidus slope, σ is the interfacial energy, and the superscript e indicates the equilibrium state; By solving the coupled differential equations, phase field distribution results, concentration distribution results and temperature distribution results are obtained.

2. The method according to claim 1, characterized in that The temperature field control equation is implemented as follows: Where T is temperature, φ is phase field value, t is time, α L is the thermal diffusivity of the unfrozen solution, c p is the specific heat capacity, L s is the latent heat of salt crystallization, L i is the latent heat of ice crystallization, c is the concentration of the unfrozen solution, h(φ) is the derivative of h'(φ), h(φ) is the interpolation function that changes monotonically from h(φ) = 0 to h(φ) = 1, μ is the solid-liquid phase thermal diffusion coefficient, α S is the thermal diffusivity of ice.

3. The method according to claim 1, characterized in that The concentration field control equation is implemented as follows: D(φ)=h(φ)D S +[1-h(φ)]D L ; In the above formula, c is the concentration; t is the time, φ is the phase field value, h(φ) is the derivative of h'(φ), h(φ) is the interpolation function that changes monotonically from h(φ) = 0 to h(φ) = 1, c S is the equilibrium concentration of ice, c L is the equilibrium concentration of the unfrozen solution, Δc S is the salt crystal concentration at equilibrium, T is the temperature, y represents the y-axis direction, β is the ion precipitation rate coefficient in the solution bubble, κ is the ion formation coefficient in the solution bubble, D(φ) is the solute diffusion coefficient that depends on the phase field, D S is the solute diffusion coefficient in ice, D L is the solute diffusion coefficient in the unfrozen solution.

4. The method according to claim 1, wherein The interfacial energy σ is determined by the following formula, In the above formula, ε(θ) is the phase field gradient coefficient related to the interface anisotropy, θ is the angle between the x-axis and the reference coordinate, and ω is the height of the double potential well; The phase field gradient coefficient ε(θ) related to the interface anisotropy is determined by the following formula: ε(θ)=ε0[1+ηcosk(θ-θ0)]; In the above formula, θ is the angle between the x-axis and the reference coordinate, ε0 is the initial parameter of the interface anisotropy, η is the intensity of the anisotropy, k is the modulus of the anisotropy, θ0 is the angle between the x-axis and the reference coordinate, φ y is the partial derivative of φ about the y-axis, φ x is the partial derivative of φ with respect to x.

5. The method according to claim 1, characterized in that The phase field governing equation satisfies the following conditions: In the above formula, φ i+1 is the phase field value after phase field perturbation at time i+1, φ i is the phase field value before the phase field disturbance at time i, r is a random number between –1 and +1; υ is the time-dependent perturbation intensity factor, g(φ) is the double-well function related to the phase field value, and χ is the forced perturbation parameter.

6. The method according to claim 3, characterized in that The concentration field control equation satisfies the following conditions: In the above formula, c i+1 is the concentration after phase field perturbation at time i+1, c i is the concentration before the phase field perturbation at time i, r is a random number between –1 and +1; υ is the time-dependent perturbation intensity factor, g(φ) is the double-well potential function related to the phase field value, and χ is the forced perturbation parameter.

7. A device for simulating salt ion migration during ice-water phase transition, characterized in that: include: a determination module for determining basic physical parameters of salt ions, wherein the basic physical parameters include melting temperature, solute equilibrium distribution coefficient, diffusion coefficient of salt ions in unfrozen solution, diffusion coefficient of salt ions in ice, thermal diffusivity of unfrozen solution and ice, specific heat capacity, latent heat of phase change, and latent heat of salt crystallization; a construction module for constructing a phase field model represented by coupled differential equations based on the basic physical parameters, the coupled differential equations including a phase field governing equation with phase field values ​​as dependent variables and time as independent variables, a concentration field governing equation with concentration as dependent variable and time as independent variables, and a temperature field governing equation with temperature as dependent variable and time as independent variables, wherein the phase field values ​​are used to characterize the degree of ice crystallization; The phase field control equation is expressed as follows: h(φ)=φ 3 (10-15φ+6φ 2 ); g(φ)=φ 2 (1-φ) 2 ; In the above formula, M is the phase field mobility; φ is the phase field value, t is the time; ε(θ) is the phase field gradient coefficient related to the interface anisotropy, θ is the angle between the x-axis and the reference coordinate, ε'(θ) is the derivative of ε(θ); h(φ) is the derivative of h'(φ), h(φ) is the interpolation function that changes monotonically from h(φ) = 0 to h(φ) = 1; T is the temperature, R is the ideal gas constant, V m is the molar volume, c S is the equilibrium concentration of ice, c L is the equilibrium concentration of the unfrozen solution, Δc S is the salt crystal concentration at equilibrium, ω is the double potential well height, g'(φ) is the derivative of g(φ), g(φ) is the double potential well function related to the phase field value, k e is the solute equilibrium distribution coefficient, c is the concentration of the unfrozen solution, μ k is the interface dynamic coefficient, m e is the liquidus slope, σ is the interfacial energy, and the superscript e indicates the equilibrium state; The acquisition module is used to obtain phase field distribution results, concentration distribution results and temperature distribution results by solving the coupled differential equations.

8. An execution device, characterized in that: comprising a processor and a memory, wherein the processor is coupled to the memory; The memory is used to store programs; The processor is configured to execute the program in the memory, so that the execution device executes the method according to any one of claims 1 to 6.

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