Two-phase interface area calculation method and system for phase-field model simulation of two-phase flow

Abstract

The present disclosure relates to a two-phase interface area calculation method and system for simulating two-phase flow by a phase field model, the method comprising the following steps: S1, extracting the order parameter value at each lattice point from the phase field model simulation result, and calculating the order parameter gradient value at each lattice point; S2, calculating the bulk free energy density and the interface free energy density of each point in the two-phase system according to the order parameter value and the order parameter gradient value; S3, volume-integrating the calculated bulk free energy density and the interface free energy density to obtain the system free energy F(φ); S4, calculating the surface tension value σ of the two-phase system according to the parameter setting of the phase field model; and S5, calculating the interface surface area A according to the system free energy F(φ) and the surface tension value σ F The method of the present disclosure avoids the complex interface discretization process, thus avoiding the complex grid discretization algorithm and data structure storage mode related thereto, and the method is easy to implement parallel computing and can further improve the calculation efficiency.

Description

TECHNICAL FIELD

[0001] The present disclosure relates to the technical field of two-phase fluid mechanics, and particularly relates to a two-phase interface area calculation method and system for simulating two-phase flow by using a phase field model. BACKGROUND

[0002] Two-phase flow is widely present in nature and industrial processes, such as wave breaking, chemical reactions, etc. With the continuous improvement of computer performance and the development of algorithms, numerical simulation has become an important way to study such problems. The phase field model has a natural advantage in solving two-phase flow problems due to its physical basis.

[0003] However, the existing Sharp Interface method needs to discretize the curved surface. In order to handle complex curved surfaces or achieve higher precision, finer surface elements need to be used. Generating and processing a large number of polygonal meshes requires a large amount of computing resources and time, and puts high requirements on memory and storage devices. Moreover, the existing method is mainly integrated into CFD post-processing software, and its code logic is complex. The discretization process is extremely complex, involving computer graphics, data structures, etc. In particular, it is difficult to implement parallel operation and to write code for integration into self-developed computing programs. SUMMARY

[0004] In order to solve the problems existing in the prior art, the present disclosure aims to provide a two-phase interface area calculation method and system for simulating two-phase flow by using a phase field model. The two-phase interface area calculation method for simulating two-phase flow by using a phase field model avoids the complex interface discretization process, and thus avoids the complex grid discretization algorithm and data structure storage method related thereto. Moreover, since the calculation process is based on simple mathematical operations (such as gradient calculation, integration, etc.), the code logic is clearer and the calculation process is relatively simple, making the method easy to implement parallel computing to further improve the calculation efficiency. Furthermore, the method is directly based on the thermodynamic basis of the phase field model, and compared with the commonly used Sharp Interface method, it can be more consistent with the physical basis of the phase field model and can more accurately describe the interface behavior.

[0005] The two-phase interface area calculation method for simulating two-phase flow by using a phase field model according to the present disclosure comprises the following steps:

[0006] S1, extracting the order parameter values at each grid point from the simulation results of the phase field model, and calculating the order parameter gradient values at each grid point;

[0007] S2, calculating the bulk free energy density and the interface free energy density of each point in the two-phase system according to the order parameter values and the order parameter gradient values;

[0008] S3, volume-integrating the calculated bulk free energy density and the interface free energy density to obtain a system free energy F(φ);

[0009] S4, calculating a surface tension value σ of the two-phase system according to parameter settings of the phase field model;

[0010] S5, calculating an interface surface area A according to the system free energy F(φ) and the surface tension value σ F .

[0011] Preferably, the step S1 specifically comprises:

[0012] reading a result file of the phase field model simulation, and extracting a sequence parameter value φ on each grid point in the file;

[0013] calculating a sequence parameter gradient according to the sequence parameter value φ The calculation method is as follows:

[0014] For points inside the flow field or at the periodic boundary, a high-order difference method is constructed by using a central difference method:

[0015]

[0016] For points at the boundary, a high-order one-sided interpolation method is constructed by using a one-sided difference method:

[0017]

[0018] wherein i represents an x coordinate of the point.

[0019] Preferably, the step S2 specifically comprises:

[0020] calculating the bulk free energy density ψ(φ) according to a function of the sequence parameter value φ, and performing calculation according to a double-potential well model:

[0021] ψ(φ) = β(φ - φ A ) 2 (φ - φ B ) 2

[0022] calculating the interface free energy density according to the sequence parameter gradient The interface free energy density is:

[0023]

[0024] wherein φ A and φ Bare order parameters of two-phase fluid; k is used to control the interface thickness, when k tends to 0, it represents a sharp interface, and at the same time, it represents the relative size of the interface free energy; β is a coefficient of the double potential well model, representing the relative size of the bulk free energy.

[0025] Preferably, in the step S3, the system free energy F(φ) is calculated according to the following formula:

[0026]

[0027] wherein ψ(φ) is the bulk free energy density; is the interface free energy density.

[0028] Preferably, the step S4 specifically comprises:

[0029] According to the parameter setting of the phase field model, the surface tension value σ of the two-phase system is calculated according to the following formula:

[0030]

[0031] wherein φ A and φ B are order parameters of two-phase fluid, and satisfy φ A > φ B ; W is a parameter of the two-phase interface thickness; k is used to control the interface thickness, when k tends to 0, it represents a sharp interface, and at the same time, it represents the relative size of the interface free energy; β is a coefficient of the double potential well model, representing the relative size of the bulk free energy.

[0032] Preferably, in the step S5, the interface surface area A F is calculated according to the following formula:

[0033] A F = F(φ) / σ

[0034] wherein F(φ) is the system free energy; σ is the surface tension value.

[0035] A system for calculating the two-phase interface area of two-phase flow simulated by a phase field model, comprising:

[0036] at least one memory;

[0037] at least one processor;

[0038] at least one program;

[0039] The program is stored in the memory, and the processor executes at least one of the programs to implement the method for calculating the two-phase interface area of two-phase flow simulated by a phase field model according to any one of the above.

[0040] The two-phase interface area calculation method and system for phase field model simulation of two-phase flow has the advantages that:

[0041] 1. The two-phase interface area calculation method for phase field model simulation of two-phase flow comprises the following steps: S1, extracting the order parameter value at each lattice point from the phase field model simulation result, and calculating the order parameter gradient value of each lattice point; S2, calculating the bulk free energy density and interface free energy density of each point of the two-phase system according to the order parameter value and the order parameter gradient value; S3, performing volume integration on the calculated bulk free energy density and interface free energy density to obtain the system free energy F(φ); S4, calculating the surface tension value σ of the two-phase system according to the parameter setting of the phase field model; and S5, calculating the interface surface area A according to the system free energy F(φ) and the surface tension value σ F . The above method directly uses the order parameter and gradient of the phase field model for calculation, without additional surface discretization, avoiding the need for additional discretization of the surface in the traditional discrete grid method, reducing the requirements for memory and storage devices; the above method avoids the complex interface discretization process, and thus avoids the complex grid discretization algorithm and data structure storage method related thereto, and since the calculation process is based on simple mathematical operations (such as gradient calculation and integration), the code logic is clearer and the calculation process is relatively simple, making the method easy to implement parallel computing to further improve the calculation efficiency; and the above method is directly based on the thermodynamic basis of the phase field model, and compared with the commonly used Sharp Interface method, can be more consistent with the physical basis of the phase field model and can more accurately describe the interface behavior.

[0042] 2. The two-phase interface area calculation system for phase field model simulation of two-phase flow comprises at least one memory, at least one processor, and at least one program; the program is stored in the memory, and the processor executes the at least one program to implement the two-phase interface area calculation method for phase field model simulation of two-phase flow as described in any one of the above. The system implements the two-phase interface area calculation method for phase field model simulation of two-phase flow, and since the calculation process mainly relies on the order parameter value at the lattice point, the system can easily implement parallel computing, which not only can further improve the calculation speed, but also can better utilize the multi-core processor resources of the computer; and by using the above two-phase interface area calculation method for phase field model simulation of two-phase flow, the complex interface discretization process in the traditional method can be avoided, thereby reducing the requirements for memory and storage devices, which is particularly important for processing large-scale two-phase flow simulation problems. BRIEF DESCRIPTION OF DRAWINGS

[0043] Figure 1 is a flowchart of the two-phase interface area calculation method for phase field model simulation of two-phase flow described in the present disclosure;

[0044] Figure 2 is a schematic diagram of the theoretical relationship between the dimensionless surface area and the dimensionless interface thickness of a spherical droplet obtained by the two-phase interface area calculation method for simulating two-phase flow by a phase field model according to the present disclosure;

[0045] Figure 3 is a schematic diagram of the evolution of the correlation coefficient between the dimensionless surface area and the bulk free energy and the interfacial free energy of a stationary droplet over time according to the two-phase interface area calculation method for simulating two-phase flow by a phase field model according to the present disclosure. DETAILED DESCRIPTION

[0046] As shown in Figure 1 - Figure 3 The two-phase interface area calculation method for simulating two-phase flow by a phase field model according to the present disclosure comprises the following steps:

[0047] S1, extracting the order parameter values at each lattice point from the phase field model simulation results and calculating the order parameter gradient values at each lattice point;

[0048] S2, calculating the bulk free energy density and the interfacial free energy density at each point of the two-phase system according to the order parameter values and the order parameter gradient values;

[0049] S3, volume integrating the calculated bulk free energy density and interfacial free energy density to obtain the system free energy F(φ);

[0050] S4, calculating the surface tension value σ of the two-phase system according to the parameter settings of the phase field model;

[0051] S5, calculating the interface surface area A F according to the system free energy F(φ) and the surface tension value σ.

[0052] The above method directly utilizes the order parameter and gradient of the phase field model for calculation without additional discretization, avoiding the need for additional discretization of the curved surface in the traditional discrete grid method, reducing the requirements for memory and storage devices; the above method avoids the complex interface discretization process, thus avoiding the complex grid discretization algorithm and data structure storage method related thereto, and since the calculation process is based on simple mathematical operations (such as gradient calculation, integration, etc.), the code logic is clearer and the calculation process is relatively simple, making the method easy to implement parallel computing to further improve the calculation efficiency; and the above method is directly based on the thermodynamic basis of the phase field model, which can be more consistent with the physical basis of the phase field model and can more accurately describe the interface behavior compared to the commonly used Sharp Interface method.

[0053] Further, in the present embodiment, step S1 specifically comprises:

[0054] Reading the result file of the phase field model simulation, extracting the order parameter value φ of each grid point in the file;

[0055] According to the order parameter value φ, the order parameter gradient The order parameter gradient The calculation method is as follows:

[0056] For points inside the flow field or at the periodic boundary, a central difference method is used to construct a high-order difference method:

[0057]

[0058] For points at the boundary, a one-sided difference method is used to construct a high-order one-sided interpolation method:

[0059]

[0060] Where i represents the x-coordinate of the point;

[0061] The above calculation method is calculated in the x direction of the uniform grid.

[0062] Further, in the embodiment, step S2 specifically comprises:

[0063] According to the function of the order parameter value, the bulk free energy density ψ(φ) is calculated, and the calculation is performed according to the double potential well model:

[0064] ψ(φ) = β(φ - φ A ) 2 (φ - φ B ) 2

[0065] According to the order parameter gradient The interfacial free energy density is calculated, and the interfacial free energy density is:

[0066]

[0067] Where φ A and φ B are the order parameters of the two-phase fluid; k is used to control the interface thickness, when k tends to 0, it represents a sharp interface, and at the same time, it represents the relative size of the interfacial free energy; β is the coefficient of the double potential well model, representing the relative size of the bulk free energy.

[0068] Further, in the embodiment, in step S3, the system free energy F(φ) is calculated according to the following formula:

[0069]

[0070] Where ψ(φ) is the bulk free energy density; is the interfacial free energy density.

[0071] Further, in the embodiment, step S4 specifically comprises:

[0072] According to the parameter setting of the phase field model, the surface tension value σ of the two-phase system is calculated according to the following formula:

[0073]

[0074] Wherein, φ A and φ B are the order parameters of the two-phase fluid, and satisfy φ A > φ B ; W is the parameter of the two-phase interface thickness; k is used to control the interface thickness, when k tends to 0, it represents a sharp interface, and at the same time represents the relative size of the interface free energy; β is the coefficient of the double potential well model, representing the relative size of the bulk free energy.

[0075] Further, in the embodiment, in step S5, the interface surface area A F is calculated according to the following formula:

[0076]

[0077] Wherein, F(φ) is the system free energy; σ is the surface tension value;

[0078] In combination with the above content, the principle of the two-phase interface area calculation method for simulating two-phase flow by using the phase field model is further analyzed, and the derivation process of the above interface surface area A F calculation method is described in combination with the principle:

[0079] The phase field model is a commonly used Diffuse Interface model for solving interface flow problems. In the phase field model, the free energy functional of the two-phase flow includes bulk free energy and interface free energy, which can be expressed as:

[0080]

[0081] Wherein, Ψ(φ) is a double potential well form: Ψ(φ) = β(φ-φ A ) 2 (φ-φ B ) 2 , wherein φ A and φ B are the order parameters of the two-phase fluid (φ A > φ B ) ;

[0082] In the understanding of the Diffuse Interface model, φ B < φ < φ AThe region of the two phases can be considered as a two-phase interface, and if the Sharp Interface model is used, the two-phase interface can be defined as the equivalent surface of

[0083] Ψ(φ) is the bulk free energy density, as the bulk free energy density of the hydrophobic effect, indicating the bulk region separating the two phases into a single phase;

[0084] is the interfacial free energy density, as the hydrophilic effect, more inclined to make the two phases mixed;

[0085] The positive constants k and β represent the relative size of the interfacial free energy and the bulk free energy, respectively, and the first variation of the free energy F with respect to the order parameter φ gives the chemical potential μ φ That is:

[0086]

[0087] For a flat interface in equilibrium state, The plane solution of φ at this time can be obtained:

[0088]

[0089] Where ζ represents the distance in the vertical direction of the interface; is a parameter representing the thickness of the two-phase interface; the surface tension between the two phases is

[0090] First, from the simplest flat interface, for the flat interface perpendicular to the x direction, the surface tension can be calculated by the following integral:

[0091]

[0092] The free energy of this flat interface system is calculated, and since the bulk free energy density and the interfacial free energy density are equal, we have:

[0093]

[0094] Where A φ is the equivalent surface area at ;

[0095] In the gradient calculation, in order to ensure its accuracy, the central difference method is used for the internal points of the fluid. For periodic boundary conditions, it is easy to construct the central difference, and for no-slip walls, a second-order difference format is constructed; and the difference method can be used as appropriate First-order difference or second-order higher-order difference method;

[0096] This formula shows that for a flat interface in equilibrium state, the interfacial area can be calculated using .

[0097] For a two-dimensional or three-dimensional static droplet (radius R0), the surface tension is calculated as follows:

[0098]

[0099] In the result, Ch is the Cahn number (Ch = W / R0). When the Ch number is much smaller than 1 (which is usually required in the phase field simulation), the result can be simplified to the surface tension of the flat interface

[0100] For the free energy of a two-dimensional static droplet, it can be calculated as follows:

[0101]

[0102] When Ch is small, the above formula is expanded as:

[0103]

[0104] where α = exp(-4 / Ch) < 1, so F(φ) 2D Relative to A 2D The deviation of σ = 2πR0 can be estimated by the error term From Table 1 below, when Ch is small, the error term is very small;

[0105] Table 1 Error term of two-dimensional and three-dimensional static droplets

[0106] Ch 0.1 0.5 1.0 1.5 2.0 Err 2D ]]> 0.0000 0.0000 0.0001 0.0024 0.0104 Error 3D ]] 0.0008 0.0202 0.0806 0.0806 0.3167

[0107] For a three-dimensional static droplet, the free energy calculation method is the same as that of the two-dimensional case, and the result is:

[0108]

[0109] Similarly, when Ch is small, the two-dimensional droplet is expanded as:

[0110]

[0111] Here, the error term can be used to estimate F(φ) 3D and A 3D The deviation of σ = 4πR0; from Table 1 above, when Ch < 1, the result has a good performance, and compared with the two-dimensional result, the error term of the three-dimensional result contains the Ch quadratic term without α, so there will be greater error in the three-dimensional case;

[0112] Figure 2The relationship between the dimensionless surface area and the interfacial thickness Ch of the illustrated stationary droplet example (the green dashed line has a constant size of 1), where E0 represents the free energy calculated using the surface area A (since it is a stationary droplet, its size does not change, and it can be accurately calculated) and the surface tension σ, and F(φ) is the free energy calculated using its definition;

[0113] F(φ) / E0 can be expressed as that is, the dimensionless surface area, when this value tends to 1, it indicates that the surface area can be accurately calculated using the present method, and from the figure, it can be seen that for the two-dimensional example, the surface area calculated using the present method agrees with the theoretical surface area, and even when the Ch number is large, it has good accuracy;

[0114] For the three-dimensional example, when the Ch number is small, the present method can accurately calculate the interfacial surface area, and Table 1 shows the specific error term values, when the Ch number is equal to 0.5, the relative error of this result is 2%, which is within an acceptable range, and when initializing, the Ch number is generally set to 0.1, so the surface area of the stationary droplet calculated using the present method is sufficiently accurate;

[0115] If A φ (A φ represents the surface area calculated using the traditional method) is taken as the standard value of the area, then a correction coefficient can be determined according to the Ch number, and then A F is corrected based on A φ ;

[0116] If the droplet undergoes complex changes, such as large deformation or breaks into multiple sub-droplets of different sizes, etc., then Ch will change greatly and is not unique throughout the field, so it needs to be considered for correction in a statistical sense according to the interfacial curvature, droplet size, number of droplets, etc., which is relatively cumbersome. Generally speaking, at this time, a large Ch will appear, so A F is slightly larger than A φ ; In fact, since the phase field model is based on the Diffuse Interface model, it can be considered that A F is the true interfacial area, and no correction is needed;

[0117] Figure 3 The figure shows the evolution of the dimensionless surface area of the stationary droplet and the correlation coefficient between the bulk free energy and the interfacial free energy with time (the green dashed line in the figure has a constant size of 1, and the pink dashed line is a constant 1.0007, which is the analytical solution of A F / A0 and A F / A φ ), where A0 represents the surface area of the droplet calculated using the traditional method at the initial time, and A Fdenotes the surface area calculated using the present method, A φ denotes the surface area calculated using the conventional method, is the adopted dimensionless time;

[0118] Since the used interfacial order parameter distribution satisfies hyperbolic tangent, the bulk free energy density and the interfacial free energy density have the same value, so the theoretical values of the dimensionless surface area and the correlation coefficient of the bulk free energy density and the interfacial free energy density of the conventional method and the present method should both be 1;

[0119] At the initial time, the relative surface areas (A F / A0and A φ / A0) calculated using the conventional method and the present method are 1.0007 and 0.9998 respectively, and the correlation coefficient of the bulk free energy density and the interfacial free energy density is 1, which are very close to the theoretical values. With the time evolution, due to the shortcomings of the phase field model, the droplet will gradually become smaller because of the mass loss, resulting in the decrease of the droplet volume and the surface area;

[0120] When the evolution reaches t * = 39.1, the dimensionless surface area calculated using the present method is 0.9973, and that calculated using the conventional method is 0.9942, the present method is closer to the theoretical value;

[0121] At the same time, the correlation coefficient of the bulk free energy density and the interfacial free energy density is 0.9987, which is very close to the theoretical value 1, which means that the two free energy densities always maintain a strong correlation during the static evolution of the droplet, which verifies that the bulk free energy is equal to the interfacial free energy in the angle of the whole field and in the case of time variation;

[0122] In summary, the free energy of the static droplet can be approximately expressed as (Ch << 1):

[0123] F(φ)≈A φ σ

[0124] Based on the results of the planar interface and the two-dimensional and three-dimensional static droplets, the interface area calculation method for the phase field model simulation of two-phase flow is obtained:

[0125]

[0126] Here, A F is the interface area calculated using the present method. According to the above derivation process, it can be obviously obtained that for the planar interface in the equilibrium state, A F = A φ ; and for the static droplet, when Ch << 1, A F ≈ A φ ; for the two-dimensional droplet, A F and A φVery close, if the given relative error is not more than 1%, then Ch<1.96; and for three-dimensional droplets, it is more demanding, if A F and A φ The relative error is not more than 1%, then Ch<0.36, which is easy to achieve using the phase field model;

[0127] Therefore, the interface area A F More in line with the Diffuse Interface model used in the phase field model, its essence represents the free energy of the system, and it is more convenient for programming and data post-processing.

[0128] The system for calculating the two-phase interface area of the two-phase flow simulated by the phase field model comprises:

[0129] At least one memory;

[0130] At least one processor;

[0131] At least one program;

[0132] The program is stored in the memory, and the processor executes the at least one program to implement the method for calculating the two-phase interface area of the two-phase flow simulated by the phase field model as claimed in any one of the above;

[0133] The system implements the method for calculating the two-phase interface area of the two-phase flow simulated by the phase field model, and since the calculation process mainly depends on the order parameter value on the lattice point, the system can easily implement parallel computing, which not only can further improve the calculation speed, but also can better utilize the multi-core processor resources of the computer; and by using the above method for calculating the two-phase interface area of the two-phase flow simulated by the phase field model, the complex interface discretization processing in the traditional method can be avoided, thereby reducing the demand for memory and storage devices, which is particularly important for processing large-scale two-phase flow simulation problems.

[0134] In the description of the present disclosure, it should be understood that the orientation words such as "front, rear, upper, lower, left, right", "transverse, vertical, horizontal" and "top, bottom" and the like indicate the orientation or positional relationship shown in the drawings, which are only for the convenience of describing the present disclosure and simplifying the description, and in the absence of contrary indications, these orientation words do not indicate and imply that the indicated devices or elements must have a particular orientation or be constructed and operated in a particular orientation, and therefore cannot be understood as a limitation on the protection scope of the present disclosure.

[0135] For those skilled in the art, other various corresponding changes and modifications can be made according to the above described technical solutions and concepts, and all of these changes and modifications should belong to the protection scope of the claims of the present disclosure.

Claims

1. A method for calculating the interface area of ​​two-phase flows in a phase-field model, characterized in that, Includes the following steps: S1. Extract the order parameter values ​​at each grid point from the phase field model simulation results, and calculate the order parameter gradient values ​​at each grid point. S2. Calculate the volume free energy density and interface free energy density at each point of the two-phase system based on the order parameter value and the order parameter gradient value. S3. Based on the Diffuse Interface model, define The region is a two-phase interface, in which and For two-phase fluids, the order parameter is... This represents the order parameter of any grid point within the two-phase interface region; when using the SharpInterface model, the two-phase interface is defined as... The isosurface of the system is used. The volume free energy density considers hydrophobic effects, while the interface free energy density considers hydrophilic effects. The two phases are mixed at the interface. The calculated volume free energy density and interface free energy density are then divided by volume to obtain the system free energy F(…). ); S4. Calculate the surface tension value σ of the two-phase system based on the parameter settings of the phase field model; S5. Based on the system free energy F ( The interfacial surface area A is calculated from the surface tension value σ. F .

2. The method for calculating the two-phase interface area for simulating two-phase flow using a phase-field model according to claim 1, characterized in that, Step S1 specifically includes: Read the result file of the phase-field model simulation and extract the order parameter values ​​at each grid point in the file. ; According to the order parameter value Calculate the gradient of the order parameter ∇ The order parameter gradient ∇ The calculation method is as follows: For points inside the flow field or at periodic boundaries, a higher-order difference method is constructed using the central difference approach: ， For points at the boundary, a higher-order one-sided interpolation method is constructed using one-sided difference: ， ， Where i represents the x-coordinate of the point.

3. The method for calculating the two-phase interface area for simulating two-phase flow using a phase-field model according to claim 2, characterized in that, Step S2 specifically includes: Based on the order parameter value The function calculates the volume free energy density. ( The calculation is performed according to the double-well model: ， According to the order parameter gradient ∇ Calculate the interface free energy density, which is: ， in, A and B All are order parameters for two-phase fluids; k is used to control the interface thickness, and when k approaches 0, it indicates a sharp interface, and also indicates the relative magnitude of the interface free energy; β is a coefficient of the double potential well model, representing the relative magnitude of the volume free energy.

4. The method for calculating the two-phase interface area for simulating two-phase flow using a phase-field model according to claim 3, characterized in that, In step S3, the system free energy F ( Calculate according to the following formula: ， in, ( ) represents the volume free energy density; Let be the interfacial free energy density.

5. The method for calculating the two-phase interface area for simulating two-phase flow using a phase-field model according to claim 4, characterized in that, Step S4 specifically includes: Based on the parameter settings of the phase field model, the surface tension value σ of the two-phase system is calculated according to the following formula: ， ， in, and All are order parameters of two-phase fluids, and satisfy... W is the parameter for the thickness of the two-phase interface; k is used to control the interface thickness. When k approaches 0, it indicates a sharp interface and also represents the relative magnitude of the interface free energy; β is the coefficient of the double potential well model, representing the relative magnitude of the volume free energy.

6. The method for calculating the two-phase interface area for simulating two-phase flow using a phase-field model according to claim 5, characterized in that, In step S5, the interface surface area A F Calculate using the following formula: ， Among them, F ( ) represents the system free energy; σ represents the surface tension value.

7. A system for calculating the interface area of ​​two-phase flows in a phase-field model, characterized in that, include: At least one memory; At least one processor; At least one program; The program is stored in the memory, and the processor executes at least one of the programs to implement the method for calculating the two-phase interface area for simulating two-phase flow using a phase-field model as described in any one of claims 1-6.

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