A fragmentation simulation method for the interaction between melt and coolant based on the fully explicit particle method
By combining the improved explicit particle method with the melt fragmentation discrimination model and the fluid-solid coupling model, the problems of calculation accuracy and stability of the fragmentation process in the interaction between the melt and the coolant are solved, and high-precision simulation of the fragmentation bed and cooling effect analysis are achieved.
Patent Information
- Application Number
- CN202411513136.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2024-10-28
- Publication Date
- 2025-09-30
- Estimated Expiration
- 2044-10-28
AI Technical Summary
Traditional grid methods have problems with calculation accuracy and stability when simulating the interaction between melt and coolant, especially the fragmentation process. It is difficult to accurately describe the dynamic evolution of the melt fragmenting into small particles and free surfaces in the coolant.
An improved explicit particle method is used in combination with the melt fragmentation discrimination model, fluid-solid coupling model and discrete element method. Through the explicit pressure equation of state and heat transfer model, the interaction process between the melt and the coolant is simulated to accurately capture the fragmentation behavior and the fragment bed formation process.
It achieves high-precision simulation of the melt fragmentation process in the coolant, solves the computational instability problem in traditional methods, and can accurately describe the structure of the fragment bed and the cooling effect.
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Figure CN119724658B_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of research on the fragmentation behavior of melts in nuclear power plant cores under interaction with coolants in severe accidents, and in particular to a numerical simulation method of the fragmentation process of melts and coolants under interaction based on a particle method. Background Art
[0002] Fuel-coolant interaction (FCI) is a critical issue in nuclear reactor safety analysis. In particular, in severe accident scenarios, strong interactions can occur when the melt contacts the coolant, leading to rapid coolant evaporation, pressure surges, and even explosive steam explosions. This complex physical process has a significant impact on nuclear power plant safety, making accurate simulation and analysis of FCI a crucial research topic in nuclear engineering. Traditional FCI numerical simulation methods, such as the finite difference method (FDM), finite element method (FEM), and finite volume method (FVM), are mostly based on meshing of the computational domain. However, during the melt-coolant interaction process, the drastic interface deformation and complex phase interfaces can cause mesh deformation or distortion, compromising computational accuracy and stability. When the melt fragments, the resulting fine particles and free surfaces cannot be accurately described using a fixed mesh, making simulation of the fragmentation process difficult. To overcome the limitations of meshing methods, particle methods, as a meshless numerical approach, have garnered widespread attention.
[0003] The particle method uses discrete particles to represent continuous media, eliminating the need for a fixed grid. It is suitable for simulating complex problems involving free surfaces and multiphase flows. It can flexibly adapt to the resolution requirements of different regions by adjusting the particle density, thereby providing high-precision simulations in critical areas. Currently, the particle method has been applied to several complex fields. A particle-based method for analyzing the evolution characteristics of a nuclear reactor core material melt pool (CN112102894A) studies the flow, heat transfer, mass transfer, phase change, and chemical reactions of various substances in the nuclear reactor core material melt pool, revealing possible mechanisms within the melt pool. A method for analyzing severe nuclear reactor accidents based on an advanced particle method (CN115062525A) analyzes key phenomena associated with severe nuclear reactor accidents, such as core heating transients, core melting, melt migration, debris bed behavior, and core melt retention. The explicit moving particle method (EMPS) is widely used in the simulation of various complex fluid mechanics problems due to its advantages such as simple algorithm and high computational efficiency. However, it still faces many challenges in describing the physical mechanism of the fragmentation of the melt by interaction with the coolant. In particular, in the simulation of the fragmentation process, how to accurately capture the dynamic evolution of the melt rapidly cooling, solidifying and eventually forming small fragments in the coolant remains a difficult point. In addition, the traditional explicit moving particle method (EMPS) has numerical instability problems such as high-frequency oscillation and discontinuous pressure distribution. Summary of the Invention
[0004] In order to solve the above problems, the present invention proposes a numerical simulation method for the fragmentation process of the interaction between the melt and the coolant based on the particle method. The improved explicit pressure state equation is combined with the melt fragmentation discrimination model, the fluid-solid coupling model (PMS) and the discrete element method (DEM) to accurately simulate the fragmentation behavior in the process of interaction between the melt and the coolant. The interaction between the solid fragments of the melt and the interaction between the solid fragments and the coolant are studied, and the influence of the superheat of the melt and the supercooling of the coolant on the fragmentation of the melt and the formation of the fragment bed are analyzed.
[0005] The present invention is achieved through at least one of the following technical solutions.
[0006] The fragmentation simulation method of the melt and coolant based on the fully explicit particle method includes the following steps:
[0007] Step 1: Initialize the particle distribution of the melt and coolant and define the particle scope. The melt and coolant are discretized using the particle method. The material properties carried by each particle include density, temperature, and velocity.
[0008] Step 2: Establish a heat transfer model and phase change model between the melt and coolant particles. Describe the heat exchange process between particles by coupling differential equations, simulate the state evolution of particles in the thermodynamic process, analyze the change in internal energy of particles, the ratio of liquid to solid during the phase change process, and the heat distribution of particles during cooling or heating, and obtain the dynamic process of phase state, enthalpy and temperature change over time of the interaction between the melt and coolant;
[0009] Step 3: Obtain the gravity term, surface tension term, and viscosity term explicitly to estimate the temporary velocity and position of the particle;
[0010] Step 4: Obtain the pressure on the particle through the explicit pressure state equation, update the pressure field by solving the explicit pressure state equation, and correct the particle velocity and position by solving the pressure gradient term;
[0011] Step 5: Using the fragmentation and combination model, the molten particles that are close to each other are identified and judged, and the molten particles that are close to each other are combined to form new fragments;
[0012] Step 6: After the solid fragments of the melt are identified, the state of the solid fragments is initialized using the fluid-solid coupling model PMS based on conservation of angular momentum to obtain the center of gravity position, velocity, and angular velocity of the solid fragments:
[0013] Step 7: When solids collide with each other, the discrete element method (DEM) is used to obtain the contact force generated when updating the velocity and position of solid particles. This contact force only occurs between two particles belonging to different solids. The temporary velocity and position of the DEM are updated using the contact force. The center of gravity position, velocity, and angular velocity of the solid fragments after the DEM action are calculated based on the temporary velocity and position of the particles. The position and velocity of the particles are updated through the translation and rotation of the solid fragments.
[0014] Step 8. By looping the calculations of steps (2) to (7), the position, velocity, temperature, and pressure of the solid fragments after the melt is fragmented at different times are obtained as a function of time. Finally, the structure, porosity, and particle morphology of the fragment bed formed by the accumulation of solid fragments are obtained. The heat exchange performance and cooling effect of the fragment bed in the coolant are analyzed. By simulating and calculating the temperature field distribution and heat conduction behavior inside the fragment bed, the cooling efficiency of the fragment bed under different cooling conditions is evaluated.
[0015] Furthermore, the particle temperature is:
[0016]
[0017] Where: T represents the particle temperature, T m represents the melting point of the particle, h represents the particle enthalpy value, h0 represents the particle solidus enthalpy value, h1 represents the particle liquidus enthalpy value, ρs represents the density of the particle in the solid state, ρ l represents the density of the particle in liquid state, C p,s represents the constant pressure specific heat capacity of the particle in the solid state, C p,l It represents the specific heat capacity at constant pressure when the particle is in liquid state;
[0018] The liquid phase fraction during the particle phase transition is:
[0019]
[0020] Where: α represents the liquid phase fraction of the particle, h represents the particle enthalpy value, h0 represents the particle solidus enthalpy value, and h1 represents the particle liquidus enthalpy value.
[0021] Furthermore, the surface tension is obtained using a continuous surface tension model based on contour lines:
[0022]
[0023] Where: F t represents the surface tension of the particle, σ represents the surface tension coefficient, and κ i represents the interface curvature, C i represents the color function, Represents the color function C i The gradient of , where the color function is used to mark particles in different phases:
[0024]
[0025] The interface curvature is shown in formula (5):
[0026]
[0027] Where: κ i represents the interface curvature, f x,i represents the first-order partial derivative of f(x,y) with respect to x, f y,i represents the first-order partial derivative of f(x,y) with respect to y, f xx,i represents the second-order partial derivative of f(x,y) with respect to x, f xy,i represents the second-order mixed partial derivative of f(x,y) with respect to x and y, f yy,i represents the second-order partial derivative of f(x,y) with respect to y;
[0028] The viscosity term is calculated using the multiphase viscosity model, as shown in formula (6):
[0029]
[0030] Where: represents the value of the viscous diffusion term at particle i, represents the gradient, μ represents the dynamic viscosity coefficient, μ ij represents the interaction dynamic viscosity coefficient between particles i and j, u represents the velocity of the particles, and u i 、u j represents the speed of particles i and j, d represents the spatial dimension, r e Represents the effective radius of the particle, r i 、r j represents the radius of particles i and j, n G i represents the Gaussian particle number density, G(||r j -r i ||,r e ) represents the Gaussian kernel function.
[0031] Furthermore, the color function is smoothed:
[0032]
[0033] Where: f(x,y) represents the smooth color function, (x,y) represents the spatial position of the particle, x j 、y j represents the spatial position of particle j, C j represents the color function, G(||r j -r i ||,r s ) represents the Gaussian function, ||r j -r i || represents the distance between particles i and j, r s Indicates the smoothing radius.
[0034] Furthermore, the explicit pressure state equation is:
[0035]
[0036] Where: P k represents the pressure on the particle at the current moment, u represents the velocity of the particle, K represents the artificial bulk modulus, Δt represents the time step, and n i * Indicates the temporary particle number density at the current moment, n 0 represents the initial particle number density.
[0037] Furthermore, step 5 includes:
[0038] First, the action range of the particles is defined. The necessary conditions for the combination of droplet particles and fragments within the action range are: the liquid phase fraction of the particles participating in the combination must be lower than a specific threshold β, and at least one particle must be in a molten state; the combination of droplet particles and fragments must meet the requirement that the distance between the two is less than ξl0:
[0039] r ij ≤ξl0 formula (9)
[0040] Where: r ij represents the distance between particles i and j, ξ represents the adjustable parameter of the fragmentation binding model, and l0 represents the initial particle distance m;
[0041] Then, the particles judged as solid fragments are divided into different rigid particle groups. For a solid fragment, a list of particle groups belonging to the fragment is established, and the particle IDs belonging to the same particle group are saved. If a particle i judged to be in a solidified state at time t is already in a solidified state and belongs to a rigid particle group at time t-Δt, then the particle i still belongs to the same particle group at time t. If a particle i is in a molten state at time t-Δt but solidifies at time t, and there is a solid particle j that satisfies formula (9), then particle i and particle j belong to the same rigid particle group. Particles that have participated in fragment identification and have been merged into a rigid particle group will no longer participate in subsequent identification.
[0042] During the discrimination process, if the distance between the melt particle i and the coolant particle j satisfies the condition of formula (9), or there are coolant particles in the particle group that has been judged as solid fragments, or the coolant particles are attached to the solid fragments, then these coolant particles will not be classified into the same rigid body particle group.
[0043] Furthermore, in step 6, the center of gravity position, velocity and angular velocity of the solid fragments are calculated as:
[0044]
[0045] Where: N represents the number of particles contained in the solid fragments, r i n represents the position of particle i at the current moment, r ii n+1 represents the position of solid fragment ii at the next moment, u i * represents the temporary velocity of particle i, u ii n+1 represents the velocity of solid fragment ii at the next moment, m i represents the mass of particle i, I ii n+1 represents the moment of inertia of solid fragment ii at the next moment, ω ii n+1 represents the angular velocity of solid fragment ii at the next moment.
[0046] Furthermore, according to the center of gravity position, velocity and angular velocity of the molten solid fragments, the position and velocity of particle i in the molten solid fragments are corrected using formulas (11) and (12):
[0047]
[0048] Where r i n+1 represents the position of particle i at the next moment, represents the velocity of particle i at the next moment;
[0049] Among them, the transformation matrix M is expressed as:
[0050]
[0051] Furthermore, when solids collide with each other, the overlap between two particles is calculated according to formula (13):
[0052]
[0053] Where: δ n represents the overlap distance between two particles of different solid fragments, r eq represents the equilibrium distance of the particle, r ij represents the distance between particle i and particle j.
[0054] Furthermore, the contact force f between different solid fragments ij Calculate using formula (14):
[0055]
[0056] Where: k n represents the normal elastic stiffness, η n represents the normal damping coefficient, n ij =(r j -r i ) / r ij , r i 、r j represents the radius of particles i and j, u i 、u j represents the speed of particles i and j.
[0057] Compared with the existing technology, the calculation method proposed in this invention has the following advantages:
[0058] This method, based on the particle method, employs a modified explicit pressure equation of state. It describes the relationship between pressure and fluid density through changes in the velocity field and particle number density field, thereby achieving a stable pressure and a smoother pressure field. By coupling the explicit particle method with a melt fragmentation discriminant model, a fluid-structure interaction model (PMS), and a discrete element method (DEM), it accurately captures the fragmentation of the melt into small particles in the coolant, the subsequent collision of solid fragments, and the ultimate formation of the fragment bed. BRIEF DESCRIPTION OF THE DRAWINGS
[0059] Figure 1 It is a calculation flow chart for simulating the fragmentation process of the interaction between the melt and the coolant;
[0060] Figure 2 It is a schematic diagram of the melt fragmentation and bonding model;
[0061] Figure 3 It is a schematic diagram of modeling the initial state of the melt and coolant;
[0062] Figure 4a is a schematic diagram of the simulation of the contact between the melt jet and the coolant;
[0063] Figure 4b It is a schematic diagram of the molten droplet particles combining to form solid fragments;
[0064] Figure 4c It is a schematic diagram of the shape of a debris bed formed by accumulation of solid debris. DETAILED DESCRIPTION
[0065] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.
[0066] The fragmentation simulation method of the melt and coolant based on the fully explicit particle method of this embodiment is as follows: Figure 1 As shown, the following steps are included:
[0067] Step 1: Initialize the particle distribution of the melt and coolant and define the particle scope. The melt and coolant are discretized using the particle method.
[0068] As an example, each particle carries its material properties, including density, temperature, velocity, etc.
[0069] Step 2: Establish a heat transfer model and phase change model between the melt and the coolant particles. The heat exchange process between the particles is described by coupled differential equations. The particle temperature is shown in formula (1), and the liquid phase fraction during the particle phase change process is shown in formula (2):
[0070]
[0071] Where: T represents the particle temperature, unit K, Tm represents the melting point of the particle, unit K, h represents the enthalpy value of the particle, unit J / Kg, h0 represents the solidus enthalpy value of the particle, unit J / Kg, h1 represents the liquidus enthalpy value of the particle, unit J / Kg, ρ s Indicates the density of the particle in solid state, unit Kg / m 3 ,ρ l Indicates the density of the particle in liquid state, unit Kg / m 3 , C p,s Indicates the specific heat capacity of the particle at constant pressure when it is in solid state, unit is J / (Kg·K), C p,l It represents the specific heat capacity at constant pressure when the particle is in liquid state, with the unit of J / (Kg·K).
[0072]
[0073] Where: α represents the liquid phase fraction of the particle, h represents the particle enthalpy value, unit is J / Kg, h0 represents the particle solid phase enthalpy value, unit is J / Kg, h1 represents the particle liquid phase enthalpy value, unit is J / Kg.
[0074] Through the calculation in step 2, the state evolution of particles in the thermodynamic process can be simulated, the changes in the internal energy of particles, the ratio of liquid to solid particles during phase change, and the thermal distribution of particles during cooling or heating can be analyzed, and the dynamic process of the phase state, enthalpy and temperature changes over time of the interaction between the melt and the coolant can be obtained.
[0075] Step 3: Explicitly calculate the gravity term, surface tension term, and viscosity term to estimate the temporary velocity and position of the particle;
[0076] The surface tension is obtained using a continuous surface tension model based on contour lines, as shown in formula (3), where the color function is used to mark particles in different phases, as shown in formula (4), and the interface curvature is calculated as shown in formula (6).
[0077]
[0078] Where: F t represents the surface tension of the particle, in N, σ represents the surface tension coefficient, κ i represents the interface curvature, C i represents the color function, Represents the color function C i gradient;
[0079] As an embodiment, the color function can be smoothed using formula (5),
[0080]
[0081] Where: f(x,y) represents the smooth color function, (x,y) represents the spatial position of the particle, C j represents the color function, G(||r j -r i ||,r s ) represents the Gaussian function, ||r j -r i || represents the distance m, r between particles i and j s Indicates the smoothing radius, in meters.
[0082]
[0083] Where: f x,i represents the first-order partial derivative of f(x,y) with respect to x, f y,i represents the first-order partial derivative of f(x,y) with respect to y, f xx,i represents the second-order partial derivative of f(x,y) with respect to x, f xy,i represents the second-order mixed partial derivative of f(x,y) with respect to x and y, f yy,i represents the second-order partial derivative of f(x,y) with respect to y.
[0084] The viscosity term is calculated using the multiphase viscosity model, as shown in formula (7):
[0085]
[0086] Where: represents the value of the viscous diffusion term at particle i, and μ represents the dynamic viscosity coefficient (N·s / m) 2 , μ ij The interaction dynamic viscosity coefficient between particles i and j is N·s / m 2 , u represents the particle speed m / s, d represents the spatial dimension, r e Indicates the effective radius of the particle m, n G i represents the Gaussian particle number density, G(||r j -r i ||,r s ) represents the Gaussian kernel function.
[0087] Step 4: The pressure on the particle is calculated using the explicit pressure state equation, as shown in formula (8):
[0088]
[0089] Where: P k represents the pressure Pa on the particle at the current moment, u represents the velocity of the particle in m / s, K represents the artificial bulk modulus, Δt represents the time step in s, and n i *Indicates the temporary particle number density at the current moment, n 0 represents the initial particle number density.
[0090] The pressure field is updated by solving the explicit pressure equation of state, and the particle velocities and positions are corrected by solving the pressure gradient terms.
[0091] Step 5: Using the fragmentation and combination model, the molten particles that are close to each other are identified and judged, and they are combined to form a new fragment;
[0092] The action range of the particles is defined. The necessary conditions for the combination of droplet particles and fragments within the action range are: the liquid phase fraction of the particles participating in the combination must be lower than a specific threshold β, and at least one particle is in a molten state; the combination of droplet particles and fragments requires that the distance between them is less than ξl0, as shown in formula (9):
[0093] r ij ≤ξl0 formula (9)
[0094] Where: r ij represents the distance between particles i and j, in m, ξ represents the adjustable parameter of the fragmentation binding model, and l0 represents the initial particle distance, in m.
[0095] The particles judged as solid fragments in the above steps are divided into different rigid particle groups. For a solid fragment, a list of particle groups belonging to the fragment is established, and the particle IDs belonging to the same particle group are saved. If a particle i judged to be in a solidified state at time t is already in a solidified state and belongs to a rigid particle group at time t-Δt, it still belongs to the same particle group at time t. If a particle i is in a molten state at time t-Δt but solidifies at time t, and there is a solid particle j that satisfies formula (9), then particle i and particle j belong to the same rigid particle group. Particles that have participated in fragment identification and have been merged into a rigid particle group will no longer participate in subsequent identification.
[0096] During the discrimination process, if the distance between the melt particle i and the coolant particle j satisfies the condition of formula (9), or there are coolant particles in the particle group that has been judged as solid fragments, or the coolant particles are attached to the solid fragments, then these coolant particles will not be classified into the same rigid body particle group.
[0097] Figure 2 The particle distribution and interaction process based on the fragmentation binding model are shown. eWithin the action range, the particles will combine together to form solid fragments if the distance between them satisfies the condition of formula (9), which is reflected by the closely arranged particle groups in the figure. It shows how the particles combine together through interaction within the action range to eventually form a stable solid fragment structure, and the melt particles attached to the solid fragments will not be classified into the same rigid body particle group.
[0098] Step 6: After the solid fragments of the melt are identified, the state of the solid fragments is initialized using the fluid-solid coupling model PMS based on conservation of angular momentum to obtain the center of gravity position, velocity, and angular velocity of the solid fragments:
[0099]
[0100] Where: N represents the number of particles contained in the solid fragments, r i n represents the position of particle i at the current moment, r ii n+1 represents the position of solid fragment ii at the next moment, u i * Indicates the temporary velocity of particle i, in m / s, u ii n+1 Indicates the velocity of solid fragment ii at the next moment, in m / s, m i Indicates the mass of particle i, in kg, I ii n+1 Represents the moment of inertia of solid fragment ii at the next moment, unit Kg·m 2 ,ω ii n+1 It represents the angular velocity of solid fragment ii at the next moment, in rad / s.
[0101] According to the center of gravity position, velocity and angular velocity of the molten solid fragments, the position and velocity of particle i in the molten solid fragments are corrected using formulas (11) and (12):
[0102]
[0103] Where r i n+1 represents the position of particle i at the next moment, represents the velocity of particle i at the next moment;
[0104] The transformation matrix M is expressed as:
[0105]
[0106] Step 7. When solids collide with each other, PMS alone cannot fully guarantee the rigidity of the solids, and particle overlap may occur, causing numerical instability. At this time, DEM is used to calculate the contact force generated when updating the velocity and position of the solid particles. It only occurs between two particles belonging to different solids. The overlap distance between the two particles is:
[0107]
[0108] Where: δ n Represents the overlap distance between two particles of different solid fragments, in m, r eq Represents the equilibrium distance of the particle, in m, r ij Represents the distance between particles i and j, in meters.
[0109] Contact forces between different solid fragments:
[0110]
[0111] Where k n represents the normal elastic stiffness, η n represents the normal damping coefficient, n ij =(r j -r i ) / r ij .
[0112] The temporary velocity and position of the DEM are updated using the required contact force. The center of gravity position, velocity and angular velocity of the solid fragments after the action of the DEM are calculated based on the temporary velocity and position of the particles. The position and velocity of the particles are updated through the translation and rotation of the solid fragments.
[0113] Step 8. By looping through the calculations of steps (2) to (7), the position, velocity, temperature, and pressure of the solid fragments after the melt is fragmented are obtained over time at different times, and ultimately the structure, porosity, and particle morphology of the fragment bed formed by the accumulation of solid fragments are obtained. On this basis, the heat exchange performance and cooling effect of the fragment bed in the coolant can be further analyzed. By simulating the temperature field distribution and heat conduction behavior within the fragment bed, the cooling efficiency of the fragment bed under different cooling conditions can be evaluated.
[0114] The model used in the present invention is that a stationary molten liquid column falls to the coolant area below under the action of gravity, such as Figure 3 As shown in the figure, the coolant is contained in a container with walls and virtual walls to simulate the actual boundary conditions and physical environment; the walls are used to constrain the movement of the coolant and the melt, ensuring that the melt liquid column will not be disturbed by the external environment when it is injected into the coolant; the initial uniformly arranged particles have a spacing of 0.001m, and the total number of particles is 13746.
[0115] Figure 4a 、 Figure 4b 、 Figure 4c The process from the melt jet contacting the coolant surface to the melt fragmentation into solid fragments and finally accumulation into a fragment bed is shown. Figure 4a In the process, when the molten material jet contacts the coolant surface, the surface cools down rapidly due to the temperature difference, and the initial fragmentation phenomenon begins to appear; as time goes by, Figure 4b The melt is further fragmented in the coolant, and the melt jet gradually breaks into smaller solid fragments, which cool rapidly in the coolant and lose their liquid properties; finally, Figure 4c It is shown that these solid fragments accumulate at the bottom of the coolant, forming a fragment bed with a specific porosity and particle morphology.
[0116] The preferred embodiments of the present invention disclosed above are intended only to help illustrate the present invention. These preferred embodiments do not exhaustively describe all details, nor do they limit the present invention to the specific embodiments described. Obviously, numerous modifications and variations are possible based on the contents of this specification. These embodiments are selected and described in detail in this specification to better explain the principles and practical applications of the present invention, so that those skilled in the art can better understand and utilize the present invention.
Claims
1. A method for simulating the fragmentation of melt and coolant based on a fully explicit particle method, characterized in that: The following steps are involved: Step 1: Initialize the particle distribution of the melt and coolant and define the particle scope. The melt and coolant are discretized using the particle method. The material properties carried by each particle include density, temperature, and velocity. Step 2: Establish a heat transfer model and phase change model between the melt and coolant particles. Describe the heat exchange process between particles by coupling differential equations, simulate the state evolution of particles in the thermodynamic process, analyze the change in internal energy of particles, the ratio of liquid to solid during the phase change process, and the heat distribution of particles during cooling or heating, and obtain the dynamic process of phase state, enthalpy and temperature change over time of the interaction between the melt and coolant; Step 3: Obtain the gravity term, surface tension term, and viscosity term explicitly to estimate the temporary velocity and position of the particle; Step 4: Obtain the pressure on the particle through the explicit pressure state equation. Update the pressure field by solving the explicit pressure state equation. The particle velocity and position are corrected by solving the pressure gradient term. The explicit pressure state equation is: Where: P k represents the pressure on the particle at the current moment, u represents the velocity of the particle, K represents the artificial bulk modulus, Δt represents the time step, Indicates the temporary particle number density at the current moment, n 0 represents the initial particle number density; Step 5: Using the fragmentation and combination model, the molten particles that are close to each other are identified and judged, and the molten particles that are close to each other are combined to form new fragments; Step 6: After the solid fragments of the melt are identified, the state of the solid fragments is initialized using the fluid-solid coupling model PMS based on conservation of angular momentum to obtain the center of gravity position, velocity, and angular velocity of the solid fragments: Step 7: When solids collide with each other, the discrete element method (DEM) is used to obtain the contact force generated when updating the velocity and position of solid particles. This contact force only occurs between two particles belonging to different solids. The temporary velocity and position of the DEM are updated using the contact force. The center of gravity position, velocity, and angular velocity of the solid fragments after the DEM action are calculated based on the temporary velocity and position of the particles. The position and velocity of the particles are updated through the translation and rotation of the solid fragments. Step 8. By looping the calculations of steps (2) to (7), the position, velocity, temperature, and pressure of the solid fragments after the melt is fragmented at different times are obtained as a function of time. Finally, the structure, porosity, and particle morphology of the fragment bed formed by the accumulation of solid fragments are obtained. The heat exchange performance and cooling effect of the fragment bed in the coolant are analyzed. By simulating and calculating the temperature field distribution and heat conduction behavior inside the fragment bed, the cooling efficiency of the fragment bed under different cooling conditions is evaluated.
2. The method for simulating the fragmentation of a melt and a coolant based on a fully explicit particle method according to claim 1, characterized in that: The particle temperature is: Where: T represents the particle temperature, T m represents the melting point of the particle, h represents the particle enthalpy value, h0 represents the particle solidus enthalpy value, h1 represents the particle liquidus enthalpy value, ρ s represents the density of the particle in the solid state, ρ l represents the density of the particle in liquid state, C p,s represents the constant pressure specific heat capacity of the particle in the solid state, C p,l It represents the specific heat capacity at constant pressure when the particle is in liquid state; The liquid phase fraction during the particle phase transition is: Where: α represents the liquid phase fraction of the particle, h represents the particle enthalpy value, h0 represents the particle solidus enthalpy value, and h1 represents the particle liquidus enthalpy value.
3. The method for simulating the fragmentation of melt and coolant based on the fully explicit particle method according to claim 1, characterized in that: Obtain the surface tension using a contour-based continuous surface tension model: Where: F t represents the surface tension of the particle, σ represents the surface tension coefficient, and κ i represents the interface curvature, C i represents the color function, Represents the color function C i The gradient of , where the color function is used to mark particles in different phases: The interface curvature is shown in formula (5): Where: κ i represents the interface curvature, f x,i represents the first-order partial derivative of f(x,y) with respect to x, f y,i represents the first-order partial derivative of f(x,y) with respect to y, f xx,i represents the second-order partial derivative of f(x,y) with respect to x, f xy,i represents the second-order mixed partial derivative of f(x,y) with respect to x and y, f yy,i represents the second-order partial derivative of f(x,y) with respect to y; The viscosity term is calculated using the multiphase viscosity model, as shown in formula (6): Where: represents the value of the viscous diffusion term at particle i, represents the gradient, μ represents the dynamic viscosity coefficient, μ ij represents the interaction dynamic viscosity coefficient between particles i and j, u represents the velocity of the particles, and u i 、u j represents the speed of particles i and j, d represents the spatial dimension, r e Represents the effective radius of the particle, r i 、r j represents the radius of particles i and j, n G i represents the Gaussian particle number density, G(||r j -r i ||,r e ) represents the Gaussian kernel function.
4. The method for simulating the fragmentation of a melt and a coolant based on a fully explicit particle method according to claim 3, characterized in that: Smooth the color function: Where: f(x,y) represents the smooth color function, (x,y) represents the spatial position of the particle, x j 、y j represents the spatial position of particle j, C j represents the color function, G(||r j -r i ||,r s ) represents the Gaussian function, ||r j -r i || represents the distance between particles i and j, r s Indicates the smoothing radius.
5. The method for simulating the fragmentation of melt and coolant based on the fully explicit particle method according to claim 1, characterized in that: Step 5 includes: First, the action range of the particles is defined. The necessary conditions for the combination of droplet particles and fragments within the action range are: the liquid phase fraction of the particles participating in the combination must be lower than a specific threshold β, and at least one particle must be in a molten state; the combination of droplet particles and fragments must meet the requirement that the distance between the two is less than ξl0: r ij ≤ξl0 formula (9) Where: r ij represents the distance between particles i and j, ξ represents the adjustable parameter of the fragmentation binding model, and l0 represents the initial particle distance m; Then, the particles judged as solid fragments are divided into different rigid particle groups. For a solid fragment, a list of particle groups belonging to the fragment is established, and the particle IDs belonging to the same particle group are saved. If a particle i judged to be in a solidified state at time t is already in a solidified state and belongs to a rigid particle group at time t-Δt, then the particle i still belongs to the same particle group at time t. If a particle i is in a molten state at time t-Δt but solidifies at time t, and there is a solid particle j that satisfies formula (9), then particle i and particle j belong to the same rigid particle group. Particles that have participated in fragment identification and have been merged into a rigid particle group will no longer participate in subsequent identification. During the discrimination process, if the distance between the melt particle i and the coolant particle j satisfies the condition of formula (9), or there are coolant particles in the particle group that has been judged as solid fragments, or the coolant particles are attached to the solid fragments, then these coolant particles will not be classified into the same rigid body particle group.
6. The method for simulating the fragmentation of melt and coolant based on the fully explicit particle method according to claim 1, characterized in that: In step 6, the center of gravity position, velocity, and angular velocity of the solid fragment are calculated as: Where: N represents the number of particles contained in the solid fragments, r i n represents the position of particle i at the current moment, r ii n+1 represents the position of solid fragment ii at the next moment, u i * represents the temporary velocity of particle i, u ii n+1 represents the velocity of solid fragment ii at the next moment, m i represents the mass of particle i, I ii n+1 represents the moment of inertia of solid fragment ii at the next moment, ω ii n+1 represents the angular velocity of solid fragment ii at the next moment.
7. The method for simulating the fragmentation of a melt and a coolant based on a fully explicit particle method according to claim 6, characterized in that: According to the center of gravity position, velocity and angular velocity of the molten solid fragments, the position and velocity of particle i in the molten solid fragments are corrected using formulas (11) and (12): Where r i n+1 represents the position of particle i at the next moment, represents the velocity of particle i at the next moment; Among them, the transformation matrix M is expressed as:
8. The method for simulating the fragmentation of melt and coolant based on the fully explicit particle method according to claim 1, characterized in that: When solids collide with each other, the overlap between the two particles is calculated according to formula (13): Where: δ n represents the overlap distance between two particles of different solid fragments, r eq represents the equilibrium distance of the particle, r ij represents the distance between particle i and particle j.
9. The method for simulating the fragmentation of a melt and a coolant based on a fully explicit particle method according to claim 8, characterized in that: The contact force f between different solid fragments ij Calculate using formula (14): Where: k n represents the normal elastic stiffness, η n represents the normal damping coefficient, n ij =(r j -r i ) / r ij , r i 、r j represents the radius of particles i and j, u i 、u j represents the speed of particles i and j.