Universal two-phase flow phase field model mesoscopic design method, device, equipment and medium

Abstract

The invention relates to a universal two-phase flow phase field model mesoscopic design method, device and equipment and a storage medium. The method comprises the steps that a two-phase flow control equation based on a phase field model is established; presetting an equilibrium state of the Boltzmann distribution function, calculating a low-order moment, and associating the low-order moment to a macroscopic quantity; performing analysis by using Chapman-Enskog to obtain an integral constraint condition required by a source item; utilizing a Hermite expansion method to obtain an expression of a source item; and outputting a mesoscopic design result. According to the universal two-phase flow phase field model mesoscopic design method provided by the invention, when the phase field model is used for two-phase flow simulation in the future, a mesoscopic format can be quickly obtained even if a new phase field equation is encountered, so that the mesoscopic method can be directly used for simulating the two-phase flow, and mesoscopic design does not need to be carried out again.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of computer simulation, and in particular to a general two-phase flow phase field model mesoscopic design method, device, equipment and storage medium. BACKGROUND

[0002] Two-phase flow exists everywhere in nature and is widely used in industry. Numerical simulation of two-phase flow is an important frontier topic in the field of fluid mechanics. Numerical simulation methods of fluid mechanics can be divided into two categories: traditional methods of numerically solving Navier-Stokes (N-S) equations and mesoscopic methods of numerically solving Boltzmann equations. As a multi-scale multiphase flow, the mesoscopic method is more consistent with the physical mechanism of multiphase flow in terms of multi-scale effects. Common numerical simulation methods for two-phase flow include phase field model method, volume of fluid method, and level set method. Compared with the latter two methods, the phase field model does not require a complex interface reconstruction process, but only needs a sequence parameter that satisfies the convection-diffusion equation, and the intermediate isosurface of the sequence parameter can be used as the two-phase interface. Therefore, the phase field model is more convenient for complex interface changes. Therefore, the mesoscopic method combined with the phase field model is an important numerical simulation method for two-phase flow.

[0003] Solving two-phase flow equations based on the phase field model using the mesoscopic method actually involves constructing specific expressions for the equilibrium state and source term of the mesoscopic distribution function based on the Boltzmann equation set, so that the integral of the Boltzmann equation set can restore the mass equation, momentum equation, and phase field equation. This construction process can be referred to as mesoscopic design. The expression of the phase field equation is not unique, and common models include the Allen-Cahn (AC) equation and the Cahn-Hilliard (CH) equation. For specific equations, there are specific mesoscopic design expressions, which can be found in previous research results.

[0004] However, a single specific macroscopic model requires a corresponding mesoscopic design, and a mesoscopic design is often only applicable to one model, resulting in a narrow range of application. Changing to a different model requires a new mesoscopic design. There are at least two types of phase field equations, AC and CH, and people may propose other equations to modify the method. New mesoscopic designs are required for new equations, which is time-consuming and labor-intensive. Existing methods sometimes have complex designs, and some unnecessary terms may be calculated, which increases the simulation time and has little effect on the simulation results. For specific macroscopic equation sets, there are countless corresponding mesoscopic designs, and the simplest and most practical one is the best. No one has proposed a general mesoscopic design method in two-phase flow models. Some previous results are even pieced together, which is one of the reasons for the aforementioned "complex design". SUMMARY

[0005] To overcome the deficiencies of the prior art, according to a first aspect of the present application, there is provided a universal two-phase flow phase field model mesoscopic design method, comprising the following steps:

[0006] establishing a two-phase flow control equation based on a phase field model;

[0007] presetting an equilibrium state of a Boltzmann distribution function, calculating low-order moments, and correlating to macroscopic quantities;

[0008] obtaining integral constraint conditions required by a source term by using Chapman-Enskog analysis;

[0009] obtaining an expression of the source term by using a Hermite expansion method;

[0010] outputting a mesoscopic design result.

[0011] In one embodiment, the two-phase flow control equation comprises a mass conservation equation, a momentum conservation equation, and a phase field equation, wherein

[0012]

[0013] wherein φ represents a field order parameter, t represents fluid motion time, u represents fluid motion velocity, μ represents fluid dynamic viscosity, γ represents a constant, ρ represents fluid density, p represents pressure, F represents force, J represents a driving force of a two-phase flow interface, φ A and φ B respectively represent order parameters of two-phase fluids.

[0014] In another embodiment, the fluid density ρ is associated with the order parameters φ A and φ B , and the constant γ is associated with the fluid density ρ and the order parameters φ A and φ0

[0015]

[0016] wherein ρ A and ρ B are densities of two-phase flows.

[0017] In still another embodiment, the Boltzmann distribution function is:

[0018]

[0019] wherein f represents a distribution function of pressure / velocity, g represents a distribution function of an order parameter, eq represents an equilibrium state, ξ represents a discrete particle velocity of mesoscopic, τ represents a relaxation time, and S represents a source term.

[0020] In still another embodiment, the equilibrium state is:

[0021]

[0022]

[0023] where w represents a weight coefficient corresponding to the particle velocity, c s represents the sound speed in the mesoscopic model.

[0024] In still another embodiment, the expression of the source term is:

[0025]

[0026] In still another embodiment, the expression of the macroscopic quantity is:

[0027] p = ∫fdξ (13)

[0028]

[0029] φ = ∫gdξ (15)

[0030]

[0031] According to a second aspect of the present application, there is provided a universal two-phase flow phase field model mesoscopic design device, comprising:

[0032] A creation module is configured to establish two-phase flow control equations based on a phase field model;

[0033] A calculation module is configured to preset an equilibrium state of a Boltzmann distribution function, calculate low-order moments, and associate to macroscopic quantities;

[0034] An analysis module is configured to obtain integral constraint conditions required by a source term by using Chapman-Enskog analysis;

[0035] An expansion module is configured to obtain an expression of the source term by using a Hermite expansion method;

[0036] An output module is configured to output mesoscopic design results.

[0037] According to a third aspect of the present application, there is provided a computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the universal two-phase flow phase field model mesoscopic design method according to the first aspect of the present application when executing the program.

[0038] According to a fourth aspect of the present application, there is provided a non-transitory computer readable storage medium, having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the universal two-phase flow phase field model mesoscopic design method according to the first aspect of the present application.

[0039] The universal two-phase flow phase field model mesoscopic design method provided by the application can quickly obtain a mesoscopic format even if a new phase field equation is encountered when a phase field model is used to simulate two-phase flow in the future, so that the two-phase flow can be directly simulated by using a mesoscopic method without re-designing the mesoscopic design. No matter whether a sequence parameter satisfies an AC equation, a CH equation or a newly proposed equation for some effect, the function J in the application can be changed and substituted into the formula of the application to directly obtain a mesoscopic design result. BRIEF DESCRIPTION OF DRAWINGS

[0040] The specific embodiments of the application will be further described in detail below with reference to the accompanying drawings, in which:

[0041] Figure 1 A flow chart of the universal two-phase flow phase field model mesoscopic design method according to an embodiment of the application is shown;

[0042] Figure 2 A schematic diagram of the universal two-phase flow phase field model mesoscopic design device according to an embodiment of the application is shown;

[0043] Figure 3 A schematic diagram of the computer device according to an embodiment of the application is shown. DETAILED DESCRIPTION

[0044] The application will be described in detail below with reference to the accompanying drawings and specific embodiments. The illustrative embodiments and descriptions are used to explain the application, but are not intended to limit the application.

[0045] The phase field model is a commonly used model for solving two-phase flow problems. In the phase field model, the free energy functional of two-phase flow includes a bulk free energy and an interface free energy, which can be expressed as:

[0046]

[0047] where Γ(φ) is a double potential well form Γ(φ) = β(φ-φ A ) 2 (φ-φ B ) 2 . Here, φ A and φ B are the order parameters of the two-phase fluid (φ A < φ B ). The two-phase interface can be defined as the isosurface composed of all points whose values of the order parameters are . Γ(φ) is the bulk free energy density as a hydrophobic effect, which indicates the separation of two phases into a bulk region of a single phase. is the interface free energy density as a hydrophilic effect, which tends to mix the two phases. The normal numbers κ and β reflect the relative sizes of the interface free energy and the bulk free energy. The free energy The first variation of the order parameter φ gives the chemical potential μ φ i.e.

[0048]

[0049] For a planar interface in equilibrium, The planar solution of φ at this time can be obtained

[0050]

[0051] Where ζ represents the distance in the vertical direction of the interface. The parameter represents the thickness of the two-phase interface, and the surface tension between the two phases is

[0052] Referring to Figure 1 , a flow chart of a general two-phase flow phase field model mesoscopic design method according to an embodiment of the present application is shown. The general two-phase flow phase field model mesoscopic design method of the present application comprises the following steps:

[0053] S1- establishing two-phase flow control equations based on a phase field model;

[0054] S2- presetting an equilibrium state of a Boltzmann distribution function, calculating low-order moments, and correlating to macroscopic quantities;

[0055] S3- obtaining integral constraint conditions required by a source term by using Chapman-Enskog analysis;

[0056] S4- obtaining an expression of the source term by using a Hermite expansion method;

[0057] S5- outputting a mesoscopic design result.

[0058] In step S1, there are mainly two kinds of commonly used order parameter φ evolution equations of the phase field model, one is the conservative form AC equation, as follows:

[0059]

[0060] The other is the CH equation, as follows:

[0061]

[0062] Where θ is a function of the equal value surface of the two-phase flow and the thickness W of the two-phase interface, and n is a unit vector perpendicular to the equal value surface of φ, and the expression is:

[0063]

[0064] Where M AC and M CH are the mobilities of the AC equation and the CH equation, respectively.

[0065] The two-phase flow control equations in the phase-field model can be expressed as

[0066]

[0067] where t represents the fluid motion time, u represents the fluid motion velocity, μ represents the fluid dynamic viscosity, γ represents a constant, ρ represents the fluid density, p represents the pressure, F represents the force, J represents the driving force of the two-phase flow interface, and φ A and φ B respectively represent the order parameters of the two-phase fluid.

[0068] Equation (5) describes the mass conservation, also known as the continuity equation; equation (6) describes the momentum conservation, i.e., the N-S equation. Here, the temperature field is not considered, and it is simply assumed to be isothermal flow, so the energy equation is not considered. Thus, for single-phase flow, equations (5) and (6) are already satisfied. However, for two-phase flow, the interface equation also needs to be described, i.e., equation (7) is the equation for describing the change of the two-phase interface in the phase-field model.

[0069] It is worth noting that, due to the existence of the two-phase interface, both equations (5) and (6) are affected, which is different from the case of single-phase flow. Specifically, in equation (5), the driving force J is brought by the phase-field equation; in equation (6), the force F contains the influence of the surface tension.

[0070] The density is a linear function of the order parameter:

[0071]

[0072] The constant parameter:

[0073]

[0074] The dynamic viscosity is a single-valued function of the order parameter:

[0075] μ = μ(φ) (10)

[0076] where ρ A and ρ B are the densities of the two-phase flow.

[0077] The force on the fluid can be decomposed into the interface force and other volume forces:

[0078] F = F s + F b (11)

[0079] For the wide applicability of the equations, the inventors do not continue to give the specific expressions of the dynamic viscosity and the stress. Meanwhile, the right-hand side term J of the phase-field model has stronger selectivity. If it is a conservative equation, then

[0080]

[0081] When the vector J takes different functions, this expression contains the conservative AC equation and the CH equation, and also contains a wider range of conservative evolution equations. J can also take a non-conservative form, and then the order parameter satisfies a non-conservative evolution equation.

[0082] In step S2, the mesoscopic equation set is the double-Boltzmann equation, that is:

[0083]

[0084] where f represents the distribution function of pressure / velocity, g represents the distribution function of the order parameter, eq represents the equilibrium state, ξ represents the discrete particle velocity of the mesoscopic, τ represents the relaxation time, and S represents the source term.

[0085] In order to reduce the degrees of freedom and facilitate mesoscopic design, the equilibrium state is first given. There are various choices for the equilibrium state, and a simple form is selected as follows:

[0086]

[0087] where w represents the weight coefficient corresponding to the particle velocity, c s represents the sound speed in the mesoscopic model.

[0088] In order to restore the macroscopic control equation set of two-phase flow, the 0th to 3rd moments of f eq and the 0th to 2nd moments of g eq are needed. With the help of the selection of the equilibrium state, the moments can be derived as follows:

[0089] ∫f eq dξ=p=∫fdξ(18)

[0090]

[0091] ∫g eq dξ=φ=∫gdξ(22)

[0092] ∫g eq ξdξ=φu(23)

[0093]

[0094] From the moments of the equilibrium state, the expressions of the macroscopic quantities are as follows:

[0095] p=∫fdξ(25)

[0096]

[0097] φ = ∫ g dξ (27)

[0098] In step S3, the condition that the source term S needs to satisfy can be derived:

[0099] First, for the continuity equation, the zeroth moment of the Boltzmann equation with respect to f is taken,

[0100]

[0101] and the moments of f in the second step are substituted into to obtain:

[0102]

[0103] In comparison with the continuity equation, the condition that the zeroth moment of S, f ∫ S dξ needs to satisfy can be obtained. f

[0104] Specifically, there can be several different expressions,

[0105]

[0106] It should be noted that formulas (30)-(33) are theoretically equivalent, but due to numerical errors, they can be different numerically.

[0107] In order to restore the momentum equation, the first moment of the Boltzmann equation with respect to f is taken, and the following is obtained:

[0108]

[0109] Substituting the moments of f, the following is obtained:

[0110]

[0111] The last term can be expanded by Chapman-Enskog, and the following is obtained:

[0112]

[0113] In which, the time derivative term of the macroscopic quantity is:

[0114]

[0115] The high-order term in the above formula has been ignored. In addition, the spatial derivative term can be split into:

[0116]

[0117] ​So far, the first moment of Boltzmann equation can be compared with momentum equation, and we have

[0118]

[0119] The divergence terms can be collected together, and a more compact design is

[0120]

[0121] At this point, S f all the integral constraints (i.e. 0 to 2nd moment) have been obtained. Next, the phase field equation, i.e. the evolution equation of order parameter, will be recovered.

[0122] To this end, the zeroth moment of Boltzmann equation with respect to g is taken, as follows:

[0123]

[0124] Substitute the moments of g and perform Chapman-Enskog expansion, we have

[0125]

[0126] Comparing with the phase field equation, we have

[0127]

[0128] For a general J, the integral constraint of the source term can be chosen as:

[0129] ∫S g dξ=J(45)

[0130]

[0131] And for the more common conservative form, the integral constraint can also be chosen as:

[0132] ∫S g dξ=0(47)

[0133]

[0134] The above are all the integral constraints that the source term S g needs to satisfy in different cases.

[0135] In step S4, the Hermite expansion of the integral result of the source term is performed, and the expression of the source term is obtained.

[0136] Specifically, for the source term S f , the 0th moment is chosen as formula (4), and combined with the above 1st and 2nd moments, S f can be designed as:

[0137]

[0138] And for the source term S g , assuming the order parameter satisfies the more common conservation-type equation, the source term can be designed as:

[0139]

[0140] The specific expression of the source term is derived.

[0141] In step S5, the equilibrium distribution function is respectively:

[0142]

[0143]

[0144] The source term is respectively:

[0145]

[0146] At the same time, the macroscopic quantity can be expressed as:

[0147] p = ∫fdξ (55)

[0148]

[0149] φ = ∫gdξ (57)

[0150] The above general two-phase flow phase field model mesoscopic design method can be applied to biomass boiler, waste incinerator and traditional coal-fired boiler two-phase flow heat exchanger, pharmaceutical and fine chemical reactor, building heating two-phase flow heat transfer technology and other scenes, so as to simulate the two-phase flow in the heat exchanger / reactor.

[0151] Figure 2 A schematic diagram of a general two-phase flow phase field model mesoscopic design device according to an embodiment of the application is shown, as Figure 2 shown, the device comprises a creation module 101, a calculation module 102, an analysis module 103, an expansion module 104, and an output module 105, wherein:

[0152] The creation module 101 is used to establish two-phase flow control equations based on the phase field model;

[0153] The calculation module 102 presets the equilibrium state of the Boltzmann distribution function, calculates the low-order moment, and is associated with the macroscopic quantity;

[0154] The analysis module 103 uses Chapman-Enskog analysis to obtain the integral constraint condition required by the source term;

[0155] The expansion module 104 obtains the expression of the source term by using a Hermite expansion method;

[0156] The output module 105 is configured to output the mesoscopic design result.

[0157] Figure 3 A schematic diagram of a computer device according to an embodiment of the present application is shown in FIG. 1. Figure 3 As shown in FIG. 1, the computer device can include a processor 201 and a memory 202. The processor 201 can invoke logic instructions stored in the memory 202 and executable on the processor 201 to perform the general two-phase flow phase field model mesoscopic design method provided by the above-mentioned method embodiments, which includes: establishing a two-phase flow control equation based on a phase field model; presetting an equilibrium state of a Boltzmann distribution function, calculating low-order moments, and correlating to macroscopic quantities; obtaining integral constraint conditions required for a source term by using Chapman-Enskog analysis; obtaining an expression of the source term by using a Hermite expansion method; and outputting a mesoscopic design result.

[0158] The processor 201 in the electronic device provided by the embodiments of the present application can invoke logic instructions in the memory 202, the implementation of which is consistent with the implementation of the general two-phase flow phase field model mesoscopic design method provided by the present application, and the same beneficial effects can be achieved, which will not be described here.

[0159] In another aspect, the embodiments of the present application further provide a non-transitory computer readable storage medium having a computer program stored thereon, which is executed by a processor to implement the general two-phase flow phase field model mesoscopic design method provided by the above-mentioned embodiments, which includes: establishing a two-phase flow control equation based on a phase field model; presetting an equilibrium state of a Boltzmann distribution function, calculating low-order moments, and correlating to macroscopic quantities; obtaining integral constraint conditions required for a source term by using Chapman-Enskog analysis; obtaining an expression of the source term by using a Hermite expansion method; and outputting a mesoscopic design result.

[0160] The computer program stored on the non-transitory computer readable storage medium provided by the embodiments of the present application is executed to implement the general two-phase flow phase field model mesoscopic design method, the specific implementation of which is consistent with the implementation described in the above-mentioned method embodiments, and the same beneficial effects can be achieved, which will not be described here.

[0161] The device embodiments described above are merely illustrative, wherein the units described as separate components can or can not be physically separate, and the components displayed as units can or can not be physical units, i.e., can be located in one place, or can be distributed to multiple network units. Part or all of the modules can be selected to achieve the purposes of the embodiments according to actual needs. Those skilled in the art can understand and implement without creative labor.

[0162] Through the description of the above embodiments, those skilled in the art can clearly understand that the embodiments can be realized by means of software and necessary universal hardware platforms, and of course can also be realized by hardware. Based on such understanding, the above technical solutions can be embodied in the form of software products, and the computer software products can be stored in a computer readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and include a plurality of instructions to make a computer device (which can be a personal computer, a server, or a network device, etc.) execute the methods described in each embodiment or some parts of the embodiments.

[0163] The above describes the technical solutions provided by the embodiments of the present application in detail, and the principles and implementation manners of the embodiments of the present application are described by applying specific examples. The above embodiment descriptions are only applicable to help understand the principles of the embodiments of the present application; meanwhile, for those skilled in the art, according to the embodiments of the present application, the specific implementation manners and application ranges will be changed, and the above description should not be understood as limiting the present application.

Claims

1. A general-purpose two-phase flow phase-field model meso-design method, characterized in that, The method comprises the following steps: establishing two-phase flow control equations based on a phase field model; presetting an equilibrium state of a Boltzmann distribution function, calculating low-order moments, and correlating to macroscopic quantities; obtaining integral constraint conditions required by source terms by using Chapman-Enskog analysis; obtaining expressions of the source terms by using a Hermite expansion method; outputting a mesoscopic design result.

2. The universal two-phase flow phase-field mesoscopic design method according to claim 1, wherein, The two-phase flow control equations comprise a mass conservation equation, a momentum conservation equation, and a phase field equation, wherein wherein φ represents a total field order parameter, t represents a fluid motion time, u represents a fluid motion velocity, μ represents a fluid dynamic viscosity, γ represents a constant, ρ represents a fluid density, p represents a pressure, F represents a force, J represents a driving force of a two-phase flow interface, φ A and φ B respectively represent order parameters of two-phase fluids.

3. The universal two-phase flow phase-field mesoscopic design method of claim 2, wherein, The fluid density p is associated with the order parameter f A and f B The constant g is associated with the fluid density p and the order parameter f A and f B ​ where p A and p B are the densities of the two phases, respectively.

4. The universal two-phase flow phase-field mesoscopic design method of claim 3, wherein, the Boltzmann distribution function is: wherein f represents a distribution function of pressure / velocity, g represents a distribution function of an order parameter, eq represents an equilibrium state, ξ represents a discrete particle velocity of mesoscopic, τ represents a relaxation time, and S represents the source term.

5. The universal two-phase flow phase-field mesoscopic design method of claim 4, wherein, The equilibrium state is: where w represents a weight coefficient corresponding to the particle velocity, c s denotes the speed of sound in the mesoscopic model.

6. The universal two-phase flow phase-field mesoscopic design method of claim 5, wherein, The expression of the source term is:

7. The universal two-phase flow phase-field mesoscopic design method of claim 6, wherein, The expression of the macroscopic quantity is: p = ∫ f dξ (13) φ = ∫ g dξ (15) 8. A general-purpose two-phase flow phase field model meso-design device, characterized in that, The method comprises: a creating module for establishing two-phase flow control equations based on a phase field model; a calculating module for presetting an equilibrium state of a Boltzmann distribution function, calculating low-order moments, and correlating to macroscopic quantities; an analysis module for obtaining integral constraint conditions required by source terms by using Chapman-Enskog analysis; an expansion module for obtaining expressions of the source terms by using a Hermite expansion method; an output module for outputting a mesoscopic design result.

9. A computer device comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, The processor executes the program to implement the general two-phase flow phase field model mesoscopic design method according to any one of claims 1 to 7.

10. A non-transitory computer-readable storage medium having stored thereon a computer program, characterized in that, The computer program is executed by the processor to implement the general two-phase flow phase field model mesoscopic design method according to any one of claims 1 to 7.

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