Lattice Boltzmann Numerical Simulation Method for Spontaneous Nucleation of Three-Phase Flow Droplet Boiling

Abstract

The present invention relates to the technical field of multiphase flow microchannel heat sinks, in particular to a lattice Boltzmann numerical simulation method for spontaneous nucleation of three-phase flow droplet boiling. It can be used for the numerical simulation of spontaneous nucleation boiling of three-phase flow droplets in a microchannel heat sink to obtain the precise three-phase distribution and the evolution process of bubble motion in the microchannel heat sink. The method described in this application combines an improved phase change model and a mechanism of spontaneous nucleation, and can effectively simulate the three-phase flow boiling process under a large density ratio, overcoming the numerical instability of traditional models under complex conditions; at the same time, by introducing new source terms and control equations, it can accurately capture the interaction between three-phase fluids and the bubble dynamics behavior.

Description

Technical Field

[0001] The present invention relates to the technical field of multiphase flow microchannel heat sinks, and particularly to a numerical simulation method for spontaneous nucleation of three-phase flow droplet boiling based on a lattice Boltzmann flux solver. Background Art

[0002] Multiphase flow boiling of two-phase flow (vapor-water) and three-component (vapor-water-oil / petroleum-natural gas-water) widely exists in related fields such as petrochemical industry, energy power, cryogenic refrigeration, and heat dissipation of electronic devices. The significant phase change ability and rapid detachment of bubbles during multiphase flow boiling can effectively improve the heat dissipation performance, promote heat transfer and diffusion, which is the basic principle for improving the cooling capacity of multiphase flow microchannel heat sinks. Dielectric fluids such as fluorocarbon fluids (FC-72, FC-87, and PF-5060) and hydrofluoroethers (HFE-7000, HFE-7100, HFE-7300) are widely used in the heat dissipation of wide-bandgap semiconductor chips due to their excellent heat dissipation performance. Such dielectric fluids usually exhibit a three-phase state during the microchannel boiling phase change process, and their boiling nucleation mechanism and bubble evolution process are different from those of traditional multiphase flows. The research on the spontaneous nucleation mechanism during three-phase flow boiling and the accurate directional characterization of bubble dynamics behavior are crucial for the successful application of these fields.

[0003] A large number of achievements have been made in the related research on the nucleation mechanism and behavior of three-phase flow boiling in both experiments and numerical simulations. However, the existing visualization experiments are only limited to the study of macroscopic boiling phenomena and cannot characterize the processes at the microscale. Traditional multiphase flow numerical simulation methods, such as the Level Set method and the Volume of Fluid (VOF) method, etc., cannot complete the simulation of the spontaneous nucleation process of bubbles. The lattice Boltzmann method (LBM) has developed rapidly in the study of multiphase flow problems due to its characteristics of automatically capturing the phase interface and spontaneously realizing boiling bubble nucleation. However, the existing multiphase LBM models have relatively low numerical stability and cannot simulate the nucleation phase change problem of three-phase flow with a large density ratio.

[0004] The lattice Boltzmann flux solver (LBFS) has become an effective solution for solving the numerical simulation of three-phase flow with a large density ratio. LBFS can effectively simulate incompressible multiphase flows with low and high density ratios. Extending LBFS to three-component fluids can effectively simulate the isothermal three-component fluid flow, but the numerical stability is very poor. As a result, the existing research is only limited to isothermal two-phase or three-phase flow problems, without considering heat transfer problems and not involving boiling phase change.

[0005] In summary, the existing research mainly focuses on two-phase or three-phase flow problems under isothermal conditions, and there are problems with poor numerical stability in the simulation of three-phase flow boiling processes with a large density ratio or high viscosity ratio. Summary of the Invention

[0006] The object of the present invention is to overcome the above-mentioned defects existing in the prior art, and propose a lattice Boltzmann numerical simulation method for spontaneous nucleation of three-phase flow droplet boiling, which can be used for numerical simulation of three-phase flow droplet flow boiling in a microchannel heat sink, and obtain the precise three-phase distribution and the evolution process of bubble movement in the microchannel heat sink. The method described in this application combines an improved phase change model and a mechanism of spontaneous nucleation, and can effectively simulate the three-phase flow boiling process under a large density ratio, overcoming the numerical instability of traditional models under complex conditions; at the same time, by introducing new source terms and control equations, the interaction between three-phase fluids and bubble dynamics behavior can be accurately captured.

[0007] The technical solution of the present invention is: a lattice Boltzmann numerical simulation method for spontaneous nucleation of three-phase flow droplet boiling, which includes the following steps:

[0008] S1. Establish a physical model and determine the computational domain; initialize the physical parameters at the center point of each grid cell at the boundary of the computational domain, and perform an initialization calculation of the physical parameters on the unit interface of the entire computational domain through linear interpolation;

[0009] S2. Calculate the density distribution function 、the temperature distribution function 、the phase distribution function ;

[0010] S3. Calculate the chemical potential function and obtain the potential function values of the three-phase fluids 、 、 ;

[0011] S4. Use LBFS-TPFB to calculate the interface macroscopic flux and the newly added source terms;

[0012] S5. Use the fourth-order Runge-Kutta method to obtain the total flux ,and calculate the physical parameters at the k-th grid cell, including , , , , T ; use the equation to calculate and obtain the physical parameters , , ,thus completing an iterative calculation of the physical parameters on the unit interface of the computational domain;

[0013] S6. Repeat the iterative calculation process of steps S2 to S5 until the cycle of a droplet nucleating to a bubble detaching and rising evolution process ends.

[0014] In the present invention, in step S1, a physical model is established according to the actual physical characteristics of the chip microchannel heat sink;

[0015] Select the cross-section within the specified area of the microchannel. The upper boundary is an open boundary condition, the left and right boundaries are both periodic boundaries, and the center of the lower boundary is the heating core boundary, and the other areas of the lower boundary are set as adiabatic wall boundary conditions.

[0016] In step S2, the density distribution function , the phase distribution function and the temperature distribution function are obtained based on the equilibrium distribution function , , at the current moment and the distribution functions , , at the previous moment.

[0017] The density equilibrium distribution function at the current moment is:

[0018] ;

[0019] Among them, represents the position at the current moment, represents the current moment, represents the particle direction at the current moment, represents the weight factor, represents the pressure, represents the mass density of the fluid at a specific position and time, represents the lattice sound speed, represents the discrete velocity of the lattice, represents the velocity of the fluid at a specific position and time;

[0020] The temperature equilibrium distribution function at the current moment is:

[0021] ;

[0022] Among them, T represents the macroscopic thermodynamic temperature at the current position and moment;

[0023] The phase equilibrium distribution function at the current moment is:

[0024] ;

[0025] Among them, represents the volume fraction of the j th phase fluid, represents the jThe potential function value of the immiscible fluid denotes the j thermal diffusivity of the phase immiscible fluid j and represents the relaxation time related to the diffusion rate of the phase immiscible fluid;

[0026] The density distribution function at the previous moment is:

[0027] ;

[0028] wherein, denotes the time step, and represents the previous moment;

[0029] The temperature distribution function at the previous moment is:

[0030] ;

[0031] The phase distribution function at the previous moment is:

[0032] ;

[0033] The calculation formula of the density distribution function is:

[0034] ;

[0035] wherein, denotes the relaxation time related to the kinematic viscosity of the j phase immiscible fluid;

[0036] The calculation formula of the temperature distribution function is:

[0037] ;

[0038] wherein, denotes the relaxation time related to the thermal diffusivity of the j phase immiscible fluid;

[0039] The calculation formula of the phase distribution function is:

[0040] .

[0041] In step S3, the specific calculation process of the potential function value of the three-phase immiscible fluid is as follows:

[0042] The simplified formula of the bulk free energy is:

[0043] ;

[0044] Among them, represents the volume fraction of the j -phase fluid; represents the surface tension of the j -phase fluid;

[0045] ;

[0046] Among them, W represents the interface thickness;

[0047] represents the weighted average of the surface tensions of the three-phase fluid, and its calculation formula is:

[0048] ;

[0049] represents the functional relationship satisfied by the volume fraction of the j -phase fluid, and its calculation formula is:

[0050] ;

[0051] The surface tension between the two-phase interfaces is calculated as:

[0052] ;

[0053] The body force in the entire computational domain is calculated as:

[0054] ;

[0055] Among them, represents the high density, represents the low density, represents the acceleration due to gravity.

[0056] In step S4, the evolution equation of LBFS-TPFB is:

[0057] ;

[0058] Among them, represents the total flux; represents the flux parallel to the x-axis; represents the flux parallel to the y-axis; represents the volume of the size-adjustable control element; represents the enclosed area of the k-th grid cell; represents the source term; , represents the unit vector related to the spatial direction;

[0059] Total flux The calculation formula is as follows:

[0060] ;

[0061] Among them, represents density, represents the vector velocity in the x direction, represents the vector velocity in the y direction, represents the volume fraction of the first phase in the mixture, represents the volume fraction of the second phase in the mixture;

[0062] The flux parallel to the x-axis The calculation formula is as follows:

[0063] ;

[0064] Among them, represents the component of the discrete velocity of the lattice in the x axis direction; represents the component of the discrete velocity of the lattice in the y axis direction;

[0065] The flux parallel to the y-axis The calculation formula is as follows:

[0066] ;

[0067] The calculation formula is as follows:

[0068] ;

[0069] Among them, represents the component of the surface tension in the x-axis direction, represents the component of the surface tension in the y-axis direction, represents the component of the body force in the x-axis direction, represents the component of the body force in the y-axis direction;

[0070] Phase change source term The calculation formula is as follows:

[0071]

[0072] Among them, represents the thermal conductivity, represents the ambient temperature, represents the thermal diffusivity, represents the phase volume fraction;

[0073] The phase field equation is modified to:

[0074] ;

[0075] Among them, M represents the thermal diffusivity;

[0076] The temperature equation is modified to:

[0077] ;

[0078] Among them, and both represent constants determined by latent heat.

[0079] In step S5, the fourth-order Runge-Kutta method is used to calculate the equation

[0080] ;

[0081] The total flux ;

[0082] The pressure The calculation formula is:

[0083] ;

[0084] The fluid velocity The calculation formula is:

[0085] ;

[0086] Through the j Volume fraction of the phase fluid, the volume fraction of the first phase and the volume fraction of the second phase are obtained:

[0087] ;

[0088] The temperature The calculation formula is:

[0089] .

[0090] Using the calculated volume fraction of the first phase and the volume fraction of the second phase , the volume fraction of the third phase is determined by the following formula:

[0091] ;

[0092] Density The calculation formula is:

[0093] ;

[0094] Viscosity The calculation formula is:

[0095] ;

[0096] So far, an iteration process is completed.

[0097] The period of a bubble evolution process includes a cycle from the spontaneous nucleation boiling of the droplet morphology, detachment and rise until leaving the entire physical model calculation domain;

[0098] An iterative calculation process of physical parameters on the unit interface of the physical model calculation domain is completed within one time step. The above iterative process is continuously repeated. When the period of a bubble evolution process ends, the iteration ends, and thus the simulation target is obtained.

[0099] The beneficial effects of the present invention are:

[0100] This application is based on the method of the lattice Boltzmann flux solver, namely LBFS-TPFB, to complete the spontaneous nucleation phenomenon of droplet boiling in a three-phase flow microchannel heat sink. By using the numerical simulation method, the cost of manual intervention can be greatly reduced and the influence of uncontrollable factors such as experiments can be reduced, improving the reliability and repeatability of the results;

[0101] Compared with traditional multiphase flow numerical simulation methods such as the level set method and the volume of fluid (VOF) method, the LBFS-TPFB method can effectively complete the spontaneous nucleation process of boiling bubbles and can simulate the three-phase flow boiling phase change evolution process in a nano-micro cross-scale microchannel heat sink, and can have a deeper understanding of the mechanism of the three-phase flow boiling spontaneous nucleation process from the mesoscopic level;

[0102] The advantage of the LBFS-TPFB method compared with the general multiphase flow LBM model is that it can simulate the three-phase flow phase change boiling nucleation process with a large density ratio, and has high numerical stability. A newly proposed phase change model for spontaneous nucleation can easily solve the newly added source term without modifying the entire evolution equation;

[0103] This application can better simulate and present the distribution of the three-phase flow in the three-phase flow microchannel heat sink and reproduce the process of the three-phase interface evolution.

[0104] In summary, the method described in the present invention can provide a theoretical basis for the design and optimization of microchannel heat exchangers, especially in improving the heat transfer efficiency and suppressing the boiling instability in microchannels, and has broad application potential. Brief Description of the Drawings

[0105] Figure 1 is a schematic flow chart of the method of the present invention;

[0106] Figure 2 is a schematic diagram of the physical model provided by the present invention;

[0107] Figure 3 is a schematic diagram of the three-phase density distribution during the spontaneous nucleation evolution process of a single three-phase droplet boiling in a three-phase flow microchannel of the present invention;

[0108] Figure 4 is a schematic diagram of the bubble shapes of LBFS-TPFB provided by the present application for different Eotvos numbers;

[0109] Figure 5 is a schematic diagram of the bubble shapes of the LBM model proposed by Yi for different Eotvos numbers;

[0110] Figure 6 is a schematic diagram of the bubble shapes of the LBM model proposed by Takada for different Eotvos numbers;

[0111] Figure 7 is for the present application verification diagram of spontaneous nucleation of a single three-phase droplet boiling under;

[0112] Figure 8 is for the present application verification diagram of spontaneous nucleation of a single three-phase droplet boiling under;

[0113] Figure 9 is for the present application verification diagram of spontaneous nucleation of a single three-phase droplet boiling under. Detailed Description of the Preferred Embodiments

[0114] In order to make the above objects, features, and advantages of the present invention more obvious and understandable, the following detailed description of the specific embodiments of the present invention will be given with reference to the accompanying drawings.

[0115] In the following description, specific details are set forth in order to provide a thorough understanding of the present invention. However, the present invention can be implemented in many other ways different from those described herein, and those skilled in the art can make similar extensions without departing from the connotation of the present invention. Therefore, the present invention is not limited by the specific embodiments disclosed below.

[0116] The following will be combined with Figure 1 to introduce in detail the specific steps of a numerical simulation method for spontaneous nucleation of three-phase flow droplet boiling based on a lattice Boltzmann flux solver described in the present application.

[0117] First step: Establish a physical model based on the actual physical characteristics of the chip microchannel heat sink to determine the computational domain.

[0118] The computational domain of the physical model selected in this application is as Figure 2 shown. A cross-section within a certain area range in the microchannel is selected. The upper boundary is an open boundary condition, and the left and right boundaries are both periodic boundaries. The computational domain of the physical model in this embodiment is selected as 150×150 lattice units. The center of the lower boundary is the heating core boundary with a certain degree of superheat, and the other areas of the lower boundary are set as adiabatic wall boundaries. In this embodiment, there is a heating core boundary of 3 lattice units at the center of the lower boundary.

[0119] The initial fluoride droplet is the second phase and is placed at the center of the lower boundary of the entire computational domain. The initial droplet diameter is set to 60 lattice units; the other areas are all in the liquid water phase, and the liquid water phase is the first phase; the fluoride droplet vapor bubbles generated by the boiling of the initial fluoride droplet due to heating are denoted as the third phase.

[0120] Second step: According to the actual situation, set the initialization conditions at the center of the unit and the physical parameters at the boundary. That is to say, directly initialize the physical parameters such as density, velocity, and temperature at the center point of each grid cell at the boundary. These parameters also need to be specially processed at the boundary conditions to ensure compliance with the physical actual situation, such as boundary conditions at the flow inlet, outlet, and solid wall.

[0121] In this application, the initial temperature of the first phase, i.e., the liquid water phase, is the saturation temperature of water, which is usually 100°C under normal temperature and pressure. The temperature of the second phase, i.e., the fluoride droplet, is the saturation temperature of fluoride, which is usually 61°C under normal temperature and pressure. The temperature at the heating core is between the saturation temperature of fluoride and the saturation temperature of liquid water. Therefore, the fluoride droplet boils while the liquid water does not boil, and a three-phase region will be generated in the entire physical model after heating, namely the first phase of liquid water, the second phase of the initial fluoride droplet, and the third phase of the fluoride vapor generated by heating and boiling, as shown in the appendix Figure 5 shown. In the figure, the green area represents the first phase, i.e., the liquid water phase; the red area represents the second phase, i.e., the initial fluoride droplet; the blue area represents the third phase, i.e., the fluoride vapor generated by heating and boiling.

[0122] Third step: Through linear interpolation, perform initialization calculations on the physical parameters at the unit interfaces in the computational domain of the entire physical model.

[0123] Dynamically calculate the physical parameters at the interfaces of the grid cells in the computational domain of the entire physical model through linear interpolation to determine the initial physical parameters at the interfaces of the grid cells, that is, at the junctions between the grid cells. The purpose is to more smoothly transition physical quantities during the numerical calculation process, thereby improving the accuracy and stability of the simulation.

[0124] Initialization at the center of the unit and setting of boundary conditions are usually important steps at the beginning of the simulation to ensure that the simulation starts from a reasonable initial state. The linear interpolation of physical parameters at the unit interface is a continuous process involved in each time step to ensure the rationality and accuracy of the transfer of physical quantities between different units when calculating the flow field.

[0125] Step 4: Calculate the density distribution function , the temperature distribution function , and the phase distribution function .

[0126] The density distribution function of the current node , the phase distribution function , and the temperature distribution function are approximately obtained based on the equilibrium distribution function , , at the current moment, and the distribution function , , at the previous moment.

[0127] and mainly describe the density distribution and temperature distribution of the fluid respectively, which are derived based on the fluid velocity u and corresponding physical quantities such as pressure, temperature, etc. describes the distribution of the phase field, chemical potential, etc., and is used for the capture of the three-phase interface and the acquisition of the three-phase distribution.

[0128] The density equilibrium distribution function at the current moment is:

[0129] ;

[0130] The above function represents the value of the distribution function of particles along the direction i at the position x and time t when reaching local thermodynamic equilibrium. represents the position at the current moment. represents the current moment. represents the weight factor. represents the pressure. represents the mass density of the fluid at a specific position and time. represents the lattice sound speed. represents the discrete velocity of the lattice. represents the velocity of the fluid at a specific position and time.

[0131] The temperature equilibrium distribution function at the current moment is:

[0132] ;

[0133] Among them, T represents the macroscopic thermodynamic temperature at the current position and time.

[0134] The phase equilibrium distribution function at the current moment is:

[0135] ;

[0136] Among them, represents the volume fraction of the j th phase fluid, j represents the potential function value of the th j phase fluid, represents the thermal diffusivity of the j th phase fluid, j is a constant, a factor related to the

[0137] phase fluid, used to correct or adjust the physical effects of the distribution function. The density distribution function at the previous moment

[0138] ;

[0139] Among them, represents the time step, represents the previous moment.

[0140] The temperature distribution function at the previous moment is:

[0141] ;

[0142] The phase distribution function at the previous moment is:

[0143] ;

[0144] Therefore, the calculation formula for the density distribution function is:

[0145] ;

[0146] Among them, represents the relaxation time related to the kinematic viscosity of the j th

[0147] The temperature distribution function is calculated as:

[0148] ;

[0149] Among them, represents the relaxation time related to the thermal diffusivity of the j -th phase fluid.

[0150] The phase distribution function has the following calculation formula:

[0151] .

[0152] Step 5: Calculate the chemical potential function and obtain the potential function value .

[0153] In multiphase flow simulation, in order to accurately describe the interface information of two-phase flow, in addition to the flow equation, an interface capture equation also needs to be introduced. In the diffuse interface method, the Cahn-Hilliard (CH) equation is an important tool widely used to calculate and capture the phase interface.

[0154] Simplify the bulk free energy formula to the following form:

[0155] ;

[0156] Among them, represents the volume fraction of the j -th phase fluid; represents the surface tension of the j -th phase fluid.

[0157] ;

[0158] Among them, W represents the interface thickness, represents the weighted average of the surface tensions of the three-phase fluid, and its calculation formula is:

[0159] ;

[0160] Among them, represents the functional relationship satisfied by the volume fraction of the j -th phase fluid in the mixture, and its calculation formula is:

[0161] .

[0162] The surface tension between the two-phase interfaces has the following calculation formula:

[0163] ;

[0164] The body force in the entire computational domain has the following calculation formula:

[0165] ;

[0166] Among them, represents high density, represents low density, represents the acceleration of gravity.

[0167] When one of the phases disappears and its order parameter is 0, such as = 0, the phase field equations of the three phases become the classical two-phase CH equations, satisfying .

[0168] Step 6: Use the improved LBFS-TPFB to calculate the interfacial macroscopic flux and the newly added source term.

[0169] In this step, the lattice Boltzmann flux solver (abbreviated as LBFS-TPFB, the same below) is used as the LBM flux solver for three-phase flow boiling to solve the governing equations of three-phase fluid boiling. Compared with LBM, LBFS can easily solve the newly added source terms, such as and , without modifying the entire evolution equation. The evolution equation of LBFS-TPFB in this application can be written as:

[0170] ;

[0171] Among them, represents the total flux; represents the flux parallel to the x-axis; represents the flux parallel to the y-axis; represents the volume of the size-adjustable control element; represents the enclosed area of the k-th grid cell; represents the source term; , represents the unit vector related to the spatial direction.

[0172] The total flux is calculated as:

[0173] ;

[0174] Among them, represents the density, represents the vector velocity in the x direction, represents the vector velocity in the y direction, represents the volume fraction of the first phase in the mixture, represents the volume fraction of the second phase in the mixture.

[0175] The flux parallel to the x-axis is calculated as:

[0176] ;

[0177] Among them, represents the component of the discrete velocity of the lattice in the x axis direction; represents the component of the discrete velocity of the lattice in the y axis direction.

[0178] The flux parallel to the y-axis is calculated as follows:

[0179] ;

[0180] The source term is calculated as follows:

[0181] ;

[0182] Among them, represents the component of the surface tension in the x-axis direction, represents the component of the surface tension in the y-axis direction, represents the component of the body force in the x-axis direction, represents the component of the body force in the y-axis direction.

[0183] The core idea of LBFS-TPFB is to apply LBM to the magnetic flux at the interface between two control units.

[0184] In many previous studies, the phase-field LBM model has been successfully applied to the study of various phase transition processes, and its governing equation is obtained by adding a phase transition source term to the CH equation. However, the existing original phase transition model cannot perform spontaneous nucleation calculations and can only simulate the phase changes in the interface region. Based on such problems, the present invention proposes a new phase transition source term , as follows:

[0185] ;

[0186] Among them, represents the thermal conductivity, represents the ambient temperature; represents the thermal diffusivity, represents the phase volume fraction.

[0187] In addition, the phase-field equation can be modified as:

[0188] ;

[0189] Among them, M represents the thermal diffusivity.

[0190] The temperature equation can be modified to:

[0191] ;

[0192] where, and both represent constants determined by latent heat.

[0193] Step 7: Use the fourth-order Runge-Kutta method to calculate the total flux to obtain the physical parameters , , , , T .

[0194] Use the fourth-order Runge-Kutta method to calculate the equation to obtain the total flux and use the following equations to define and obtain the flux physical parameters, including: pressure , fluid velocity , the volume fraction of the first phase , the volume fraction of the second phase , and temperature .

[0195] The calculation formula for pressure is:

[0196] ;

[0197] The calculation formula for fluid velocity is:

[0198] ;

[0199] The volume fraction j of the -th phase fluid is calculated as:

[0200] ;

[0201] The calculation formula for temperature is:

[0202] .

[0203] Step 8: Continue the calculation using the equation and obtain the physical parameters , , .

[0204] Using the physical parameters calculated in Step 7 and , the volume fraction of the third phase is determined by the following formula :[[]]

[0205] ;

[0206] The calculation formula for density is as follows:

[0207] ;

[0208] The calculation formula for viscosity is as follows:

[0209] ;

[0210] Thus, an iteration process is completed.

[0211] In the ninth step, repeat steps three to eight. Each time the processing process of steps three to eight is completed, an iteration of the physical parameters on the unit interface of the physical model calculation domain is completed. Continuously repeat the above iteration process until the end of a cycle of the evolution process from droplet nucleation to bubble detachment and rise, and the iteration ends, thereby obtaining the simulation target.

[0212] In this application, a cycle of the bubble evolution process includes a cycle from the spontaneous nucleation boiling of the droplet morphology, detachment and rise until leaving the entire physical model calculation domain.

[0213] As Figure 3 shown, its evolution process can be divided into three stages, namely, the initial stage of droplet boiling where the liquid film has not fallen off in the first stage, the stage from the liquid film falling off to the bubble just starting to detach in the second stage, and the process of the bubble rising from detachment in the third stage. Among them, the red area represents the initial droplet phase, the blue area represents the vapor bubble phase after boiling nucleation, the green area represents the third phase, and the yellow area represents the liquid film that has not fallen off during the boiling phase change process. The parameter t in the figure represents the iteration step number.

[0214] Figures 4 to 6 Shows the comparison of the bubble shapes for different Eotvos numbers using the LBFS-TPFB of this application and the LBM model of other researchers. The top set of figures is the result of this application's research Figure 5 and Figure 6 are the results of other researchers. It can be observed that as the Eotvos number increases, the bubble shape changes from circular to ellipsoidal and finally forms a mushroom shape. At small Eotvos numbers, the degree of bubble deformation is similar to that of previous researchers, basically verifying the accuracy of the LBFS-TPFB described in this application for the spontaneous nucleation evolution process of three-phase flow boiling.

[0215] Figures 7 to 9 Shown is a schematic diagram of the nucleation process of three-phase flow droplet boiling under different density ratios in this application. For the simulation of the nucleation process of three-phase flow droplets boiling under different density ratios, the density ratio that this application can simulate and achieve reaches 1000, and the maximum density ratio can reach 2000. Through Figures 7 to 9 The evolution results shown can illustrate the feasibility of the method described in this application in simulating the spontaneous nucleation of three-phase flow droplets boiling and the evolution of the three-phase interface at a large density ratio.

[0216] The above has introduced in detail the lattice Boltzmann numerical simulation method for the spontaneous nucleation of three-phase flow droplet boiling provided by the present invention. Specific examples are used in this article to elaborate on the principle and implementation manner of the present invention. The description of the above embodiments is only used to help understand the method of the present invention and its core idea. It should be pointed out that for those of ordinary skill in the art in this technical field, without departing from the principle of the present invention, several improvements and modifications can be made to the present invention, and these improvements and modifications also fall within the protection scope of the claims of the present invention. The above description of the disclosed embodiments enables those skilled in the art to implement or use the present invention. Various modifications to these embodiments will be obvious to those skilled in the art, and the general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to these embodiments shown herein, but will conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A lattice Boltzmann numerical simulation method for spontaneous nucleation of three-phase flow droplet boiling, characterized in that: The following steps are involved: S1. Establish a physical model and determine the computational domain; initialize the physical parameters at the center point of each grid cell at the boundary of the computational domain, and perform initialization calculations on the physical parameters on the cell interface of the entire computational domain through linear interpolation; S2. Calculate density distribution function , temperature distribution function , phase distribution function ; S3. Calculate the chemical potential function and obtain the potential function value of the three-phase fluid , , ; S4. Calculate the interface macro flux and the newly added source term using LBFS-TPFB; The evolution equation of LBFS-TPFB is: ； in, represents the total flux; represents the flux parallel to the x-axis; represents the flux parallel to the y-axis; Indicates the volume of a control element whose size can be adjusted; represents the enclosed area of ​​the kth grid cell; represents the source term; , represents a unit vector associated with a spatial direction; Total flux The calculation formula is: ； in, represents density, represents the vector velocity in the x direction, represents the vector velocity in the y direction, represents the volume fraction of the first phase in the mixture, represents the volume fraction of the second phase in the mixture; Flux parallel to the x-axis The calculation formula is: ； in, The discrete velocity of the lattice is x Component in the axial direction; The discrete velocity of the lattice is y Component in the axial direction; Flux parallel to the y-axis The calculation formula is: ； The calculation formula is: ； in, represents the component of surface tension in the x-axis direction, represents the component of surface tension in the y-axis direction, represents the component of the body force in the x-axis direction, represents the component of body force in the y-axis direction; Phase change source The calculation formula is: ； in, represents the thermal conductivity, Indicates the ambient temperature, is the thermal diffusion coefficient, represents the phase volume fraction; The phase field equation is modified as follows: ； Where M represents the thermal diffusivity; The temperature equation is modified to: ； in, and All represent constants determined by latent heat; S5. Use the fourth-order Runge-Kutta method to obtain the total flux , and calculate the physical parameters at the kth grid unit, including , , , , T ; Use the equation to calculate and obtain the physical parameters , , , so far the iterative calculation of the physical parameters on the interface of the computational domain unit is completed; in, Indicates pressure, represents the mass density of the fluid at a specific location and time, represents the velocity of the fluid at a specific position and time, T represents the macroscopic thermodynamic temperature at the current position and time, represents the volume fraction of the first phase, represents the volume fraction of the second phase, represents the volume fraction of the third phase, Indicates viscosity; S6. Repeat the iterative calculation process of steps S2 to S5 until a cycle of the evolution process from droplet nucleation to bubble detachment and ascent is completed.

2. The lattice Boltzmann numerical simulation method for spontaneous nucleation of three-phase flow droplet boiling according to claim 1 is characterized in that: In step S1, a physical model is established according to the actual physical characteristics of the chip microchannel heat sink; A cross section within the specified area of ​​the microchannel is selected, the upper boundary is an open boundary condition, the left and right boundaries are periodic boundaries, the center of the lower boundary is the heating core boundary, and the rest of the lower boundary is set as an adiabatic wall boundary.

3. The lattice Boltzmann numerical simulation method for spontaneous nucleation of three-phase flow droplet boiling according to claim 1 is characterized in that: In step S2, the density distribution function of the current node , phase distribution function and temperature distribution function is the equilibrium distribution function based on the current moment , , and the distribution function of the previous moment , , get.

4. The lattice Boltzmann numerical simulation method for spontaneous nucleation of three-phase flow droplet boiling according to claim 3 is characterized in that: Density equilibrium distribution function at the current moment for: ； in, Indicates the current position. Indicates the current moment, represents the grid direction of the particle at the current moment, represents the weight factor, Indicates pressure, represents the mass density of the fluid at a specific location and time, represents the lattice sound speed, represents the discrete velocity of the lattice, It expresses the velocity of a fluid at a specific location and time; Temperature equilibrium distribution function at the current moment for: ； Where T represents the macroscopic thermodynamic temperature at the current position; Phase balance distribution function at the current moment for: ； in, Indicates j The volume fraction of the phase fluid, Indicates j The potential function value of the phase fluid, Indicates j Thermal diffusivity of the phase fluid, Indicates j The relaxation time related to the diffusivity of the phase fluid, represents a constant; The density distribution function at the previous moment for: ； in, represents the time step, Indicates the previous moment; Temperature distribution function at the previous moment for: ； Phase distribution function at the previous moment for: ； Density distribution function The calculation formula is: ； in, Indicates j relaxation time related to the kinematic viscosity of the phase fluid; Temperature distribution function The calculation formula is: ； in, Indicates j relaxation time related to the thermal diffusivity of the phase fluid; Phase distribution function The calculation formula is: 。 5. The lattice Boltzmann numerical simulation method for spontaneous nucleation of three-phase flow droplet boiling according to claim 1, characterized in that: In step S3, the specific calculation process of the potential function value of the three-phase fluid is as follows: The simplified body free energy formula is: ； in, Indicates j Volume fraction of phase fluid; Indicates j Surface tension of the phase fluid; ； Where W represents the interface thickness; It represents the weighted average value of the surface tension of the three-phase fluid, and its calculation formula is: ； Indicates j The volume fraction of the phase fluid satisfies the functional relationship, and its calculation formula is: ； Surface tension between two phases The calculation formula is: ； Body force in the entire computational domain The calculation formula is: ； in, Indicates high density, Indicates low density, Represents the acceleration due to gravity.

6. The lattice Boltzmann numerical simulation method for spontaneous nucleation of three-phase flow droplet boiling according to claim 1, characterized in that: In step S5, the fourth-order Runge-Kutta method is used to calculate the equation: ； Get total flux ; pressure The calculation formula is: ； Fluid velocity The calculation formula is: ； Through the j Volume fraction of phase fluid The volume fraction of the first phase is obtained by the calculation formula , volume fraction of the second phase : ； temperature The calculation formula is: 。 7. The lattice Boltzmann numerical simulation method for spontaneous nucleation of three-phase flow droplet boiling according to claim 6, characterized in that: Using the calculated first phase volume fraction and the second phase volume fraction , the volume fraction of the third phase is determined by the following formula : ； density The calculation formula is: ； Viscosity The calculation formula is: ； At this point, an iterative process is completed.

8. The lattice Boltzmann numerical simulation method for spontaneous nucleation of three-phase flow droplet boiling according to claim 1, characterized in that: A cycle of bubble evolution process includes a cycle from spontaneous nucleation boiling in droplet form, detachment and rise until leaving the calculation domain of the entire physical model; The iterative calculation process of the physical parameters on the unit interface of the physical model calculation domain is completed once within one time step. The above iterative process is repeated continuously. When a cycle of the bubble evolution process is completed, the iteration ends, and the simulation target is obtained.

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