Method, product and equipment for simulating pore defect forming process in alloy solidification process

Abstract

The invention discloses a method, a product and equipment for simulating a pore defect forming process in an alloy solidification process, and belongs to the technical field of alloy smelting. According to the method, three phase field variables of solid, liquid and gas are introduced, a solid-liquid-gas multi-phase field-lattice Boltzmann model is established, and simulation of dendritic crystal growth and movement, bubble dynamics and a solid-liquid-gas multi-phase coupling evolution process in the alloy solidification process is achieved. According to the method, the problem of complex evolution of multiphase coupling can be solved, especially dynamic evolution of dendritic crystals and bubbles and interaction among multiple phases can be solved, solution of multiphase coupling evolution is achieved, and theoretical guidance is provided for prediction of pore defects and optimization of technological parameters in the magnesium alloy solidification process.

Description

Technical Field

[0001] The present invention belongs to the technical field of alloy smelting, and particularly relates to a method, a product and a device for simulating the formation process of pore defects during the solidification process of an alloy. Background Art

[0002] For decades, the prediction and control of pore defects during the solidification process have been a research hotspot. As a mesoscale numerical simulation method based on the principles of thermodynamics, the phase field method has shown unique advantages in the simulation of solidification microstructures. By introducing phase field variables quantified by order parameters to characterize the multiphase system, establishing a dynamic evolution model with a finite interface thickness, and combining with the thermodynamic potential function, the numerical simulation of the evolution process of solidification microstructures is realized. It is a powerful research method for revealing the pore formation process.

[0003] The physical processes of solid-liquid-gas multiphase interactions include dendrite growth and movement, solute redistribution, bubble deformation, and gas-liquid two-phase flow, etc. Affected by the diffusion-curvature interaction and crystal anisotropy, the shape of the primary solid phase usually presents a dendritic structure, called dendrite. The solutes discharged from the solid phase during the solidification process are enriched near the interface. The uneven solute distribution leads to liquid convection around the dendrite, which will further change the solute transport. Due to the different densities of the solid and liquid phases, movement also occurs during the dendrite growth process, that is, it occurs simultaneously with the bubble movement process, resulting in an extremely complex solid-liquid-gas multiphase interaction process.

[0004] For the problem of solid-liquid-gas multiphase interactions, most of the existing phase field models are constructed based on the pure diffusion hypothesis, ignoring the solute transport problem and solid phase movement problem caused by melt convection, and mostly simplifying the bubble shape, such as only assuming the bubble shape to be circular and not considering the shape change caused by bubble deformation, resulting in a large difference between the simulation results and the actual situation.

[0005] Patent One (A simulation method for the microstructure morphology of magnesium alloy under forced convection based on the phase field method-lattice Boltzmann method and its application, Publication No.: CN116994683A) provides a simulation method for the microstructure morphology of magnesium alloy under forced convection based on the phase field method-lattice Boltzmann method. A lattice Boltzmann model is constructed to calculate the movement of the fluid in the solid-liquid two-phase region, the phase field model is discretely solved by the finite difference method, and the distribution function of the lattice Boltzmann model is solved by the D2Q9 model to simulate the change of dendrite morphology caused by solute flow. This invention focuses on solid-liquid phase change and lacks the consideration of gas phase problems.

[0006] Patent Two (A method for analyzing bubble dynamics in a liquid containing obstacles, Publication No.: CN115455855A) relates to the technical field of fluid mechanics, specifically to a method for analyzing bubble dynamics in a liquid containing obstacles. By setting various types of obstacles in a microchannel containing liquid, and obtaining the evolution of the flow field and the change of the gas-liquid interface in the microchannel, then quantifying the evolution of the bubble shape according to the morphological parameters, and further realizing the quantitative analysis of bubble dynamics based on the evolution of the flow field, the change of the gas-liquid interface and the bubble shape, and finally realizing the quantitative analysis of bubble dynamics in a liquid containing obstacles. This invention focuses on bubble dynamics, does not consider the evolution of the solid phase, and lacks the consideration of the problem of solid-liquid-gas multiphase interaction.

[0007] Currently, these above methods cannot well solve the problems simultaneously involving dendrite growth and movement, bubble dynamics, and solid-liquid-gas multiphase coupled evolution. The existing defects include:

[0008] 1. Insufficient accuracy of dynamic evolution: The traditional phase field model is based on the assumption of pure diffusive solute transport, ignores the melt convection effect and the movement of the solid phase, and simplifies the bubble shape, making it difficult to accurately simulate the simultaneous growth and movement of the solid phase, the movement and deformation of the bubble, etc.

[0009] 2. Difficulty in multiphase coupling: The existing methods cannot well solve the complex problems of dendrite growth movement and movement, bubble dynamics, and solid-liquid-gas multiphase coupled evolution, resulting in a deviation between the simulation of the formation process of pore defects and the actual process. Summary of the Invention

[0010] The present invention aims to solve at least one of the technical problems in the above related technologies to a certain extent.

[0011] To this end, the purpose of the present invention is to provide a method, product and equipment for simulating the formation process of pore defects in the alloy solidification process, which can solve the complex evolution problems of multiphase coupling, especially involving the dynamic evolution of dendrites and bubbles and the interaction between multiple phases, realize the solution of multiphase coupled evolution, and provide theoretical guidance for the prediction of pore defects and the optimization of process parameters in the magnesium alloy solidification process.

[0012] In order to solve the above technical problems, the present invention is implemented as follows:

[0013] The embodiment of the present invention provides a method for simulating the formation process of pore defects in the alloy solidification process. By introducing three phase field variables of solid-liquid-gas, a solid-liquid-gas multiphase field - lattice Boltzmann model is established to realize the simulation of the dendrite growth and movement, bubble dynamics, and solid-liquid-gas multiphase coupled evolution process in the alloy solidification process.

[0014] In addition, the method for simulating the formation process of pore defects during the solidification process of an alloy according to the present invention may further have the following additional technical features:

[0015] In some embodiments, the steps of the method include:

[0016] S1. Update the solid-liquid-gas phase field, including:

[0017] Introduce three phase field variables of solid-liquid-gas to simulate the coupling effect of solid-liquid-gas multiphase; control the phase field variables through equations to make them smoothly change from 0 to 1 at the two-phase interface; the sum of the three phase field variables always remains 1;

[0018] S2. Update the flow field, including:

[0019] Use the lattice Boltzmann method to solve the gas-liquid two-phase flow, and use the two-dimensional nine-speed model to calculate the particle distribution function;

[0020] S3. Update the solid motion, including:

[0021] Follow Newton's laws of motion to update the centroid position of the dendrite;

[0022] Calculate the total force and total torque acting on the moving dendrite;

[0023] Combine translation and rotation to update the solid velocity;

[0024] S4. Perform parameter settings, including:

[0025] Set the initial positions of the solid-phase crystal nuclei and bubbles;

[0026] Set boundary conditions for the phase field, flow field, and solute field;

[0027] S5. Perform visualization processing on the evolution process of the interaction between dendrites and bubbles.

[0028] In some embodiments, the content of step S1 further includes:

[0029] Set a mobility function to adjust the difference between the crystallization kinetics and the bubble expansion evolution rate;

[0030] Make the evolution of the alloy solute concentration follow Fick's second law and consider the convective flux.

[0031] In some embodiments, during the multiphase coupling effect simulation process, consider the phase change driving force at the solid-liquid interface and the liquid-gas interface, and characterize the solid-gas interface interaction by setting boundary conditions at the solid phase boundary.

[0032] In some of these embodiments, in step S1, the phase field variables are controlled by minimizing the free energy functional.

[0033] In some of these embodiments, when calculating the flow velocity in step S2, the solid-liquid interface dissipation resistance, the buoyancy caused by the solute concentration difference, the buoyancy of the bubble, and the surface tension of the bubble boundary are considered.

[0034] In some of these embodiments, in step S4, the phase field and the solute field are both set to the Neumann boundary condition, and the flow field is set to the no-slip boundary condition.

[0035] In some of these embodiments, during the simulation, the shape of the bubble is not simplified, and the deformation and movement process of the bubble are simulated.

[0036] The embodiment of the present invention also provides a computer program product, including a computer program, which when executed by a processor, implements the content of the method for simulating the formation process of pore defects during alloy solidification as described in any one of the above.

[0037] The embodiment of the present invention also provides a computer device, including: a memory, a processor, and a computer program stored on the memory and executable on the processor, where the processor executes the computer program to implement the content of the method for simulating the formation process of pore defects during alloy solidification as described in any one of the above.

[0038] Compared with the prior art, the present invention has at least the following beneficial effects:

[0039] In the embodiment of the present invention, the method for simulating the formation process of pore defects during alloy solidification provided, through a numerical model that couples the multi-phase field method (Phase Field Method, PFM) and the lattice Boltzmann method (Lattice Boltzmann Method, LBM), is used to simulate the dynamic evolution of pore defects during the solidification process of magnesium alloys; by introducing three phase field variables of solid-liquid-gas, a solid-liquid-gas multi-phase field-lattice Boltzmann model is established to realize the simulation of dendrite growth and movement, bubble dynamics, and solid-liquid-gas multi-phase coupling evolution process during alloy solidification, providing a basis for the dynamic prediction of pore defects during alloy solidification and the optimization of process parameters.

[0040] The additional aspects and advantages of the present invention will be partially given in the following description, partially become obvious from the following description, or be understood through the practice of the present invention. Description of the Drawings

[0041] Figure 1 It is a flowchart of the method for simulating the formation process of pore defects during alloy solidification disclosed in an embodiment of the present invention;

[0042] Figure 2 The simulation result diagram of the method for simulating the formation process of pore defects during the solidification process of an alloy disclosed in an embodiment of the present invention. Specific embodiments

[0043] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all of the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0044] Next, the embodiments of the present invention will be described in detail through specific embodiments and their application scenarios in conjunction with the accompanying drawings.

[0045] Please refer to Figure 1 As shown, in some embodiments of the present invention, a method for simulating the formation process of pore defects during the solidification process of an alloy is provided. The steps of the method include:

[0046] Step 1: Update the solid-liquid-gas phase field

[0047] In some embodiments of the present invention, in order to simulate the coupling effect of the solid-liquid-gas multiphase, three parameters, namely φ s , φ l and φ g , are introduced to represent the solid phase, liquid phase, and gas phase. The phase field variable φ i (i = s, l, g) smoothly changes from 0 to 1 at the interface of the two phases, and the sum of φ i remains 1 at any position. By minimizing the free energy functional, φ i is controlled by the following equation.

[0048]

[0049] In the formula,

[0050]

[0051]

[0052] In the formula, τ i (i = s, l, g), v s , K i (i = s, l, g), σ, and h are the relaxation time, solid velocity, mobility function of the i-phase, gradient energy coefficient, and potential energy coefficient of the i-phase, respectively. Λ is the Lagrange multiplier that satisfies the constraint , Θ i and Θ mis the derivative of the bulk free energy, where the subscript m is introduced to avoid ambiguity caused by the subscripts i, j, k during the summation operation in the equation. a j and b j are two constants that regulate the energy barrier heights of the two-phase and three-phase coexistence regions in the free energy surface.

[0053] In some embodiments of the present invention, to adjust the difference in the evolution rates between crystallization kinetics and bubble expansion, K i is set to:

[0054]

[0055] where α is the migration coefficient, which is determined by making the mobility of the solid-liquid interface much greater than that of the liquid-gas interface. The phase transformation rate can be adjusted by selecting an appropriate α, and a larger α (or K i ) corresponds to a faster interface advancement rate.

[0056] In some embodiments of the present invention, the solid phase acts as the moving boundary of the gas phase in the model, so the driving force for the solid-gas phase transformation is zero. The phase transformation mainly occurs at the solid-liquid interface and the liquid-gas interface. The two driving forces for the liquid-gas phase transformation and the solid-liquid phase transformation are:

[0057] ΔG lg / h = p g - p l - γ lg / r g

[0058] ΔG ls / h = -8λ(θ + MC ∞ U) / 15

[0059] where p i is the pressure of the i-phase, γ lg is the gas-liquid interface energy, rg = (Sg / π) 1 / 2 is the equivalent bubble radius, S g is the two-dimensional bubble area, and λ, θ, M, C ∞ , U are the coupling constant, dimensionless temperature, dimensionless liquid slope, far-field solute concentration, and dimensionless solute concentration, respectively. The dimensionless supercooling is defined as Δ = -θ.

[0060] In some embodiments of the present invention, the evolution of the alloy solute concentration follows Fick's second law. Considering the convective flux, the equation governing the solute concentration is:

[0061]

[0062] where X represents the alloy solute and gas species, D Xis the diffusion rate of X, and R(X) represents the distribution of X at the solid-liquid interface.

[0063]

[0064] In the formula, n i (i = s, l) is a step function, that is, if n i = 1, otherwise n i = 0, and k X is the equilibrium distribution coefficient of X.

[0065] Step 2: Update the flow field

[0066] In some embodiments of the present invention, the gas-liquid two-phase flow is solved by LBM, where the liquid flow is assumed to be a repeated collision and migration operation of a group of pseudo-particles. In the single-relaxation-time LBM, the evolution of the particle distribution function satisfies:

[0067]

[0068] In the formula, f i (r, t) represents the particle probability density with velocity c i at position r and time t, τ LB is the relaxation time in LBM, and its relationship with the kinematic viscosity v kin is:

[0069] τ LB = 0.5 + 3v kin / (c 2 δt)

[0070] is the equilibrium distribution function, which is expressed as:

[0071]

[0072] In the formula, ρ is the kinematic viscosity, c = δx / δt is the lattice velocity, and δx and δt are the lattice spacing and time step in LBM. c i is the discrete velocity, w i is the weight coefficient on the Cartesian uniform lattice with additional diagonals. For the two-dimensional nine-speed (D2Q9) model adopted, w0 = 4 / 9, w 1.4 = 1 / 9, w 5-8 = 1 / 36, and the discrete velocities in the corresponding directions are:

[0073]

[0074] F i (r, t) is the discrete external force and can be expressed as:

[0075]

[0076] In the formula,

[0077] F = F d + F b + F g + F bs

[0078]

[0079] F b = -ρgβ c (C - C ∞ )f l

[0080] F g = -(ρ - ρ l )g

[0081]

[0082] In the formula, the force vector F includes four parts. F d is the dissipation resistance near the solid-liquid interface, which makes the flow velocity approach 0 when the liquid fraction f l approaches zero; h is a dimensionless constant with a value of 2.757; W0 is the width of the solid-liquid interface; F b represents the buoyancy force caused by the concentration difference in the liquid, g represents the acceleration due to gravity, and β c represents the solute expansion coefficient; F g represents the buoyancy force driving the bubble to rise, ρ l is the melt density; F bs represents the surface tension at the bubble boundary. μ g is the chemical potential determined by the gradient:

[0083]

[0084] Considering the above four forces, the flow velocity is calculated as:

[0085] v = ∑ i f i c i / ρ + δtF / (2ρ)

[0086] Step 3: Update the solid motion

[0087] In some embodiments of the present invention, the solid motion follows Newton's laws of motion. The prerequisite for solving the dendrite kinematics is to update the position of the center of mass.

[0088] r0 = ∑rρ s f s ΔV / Ms

[0089] In the formula, ρ s is the solid density, f s is the solid fraction, r0 is the centroid, and M s is the dendrite mass.

[0090] M s = ∑ρ s f s ΔV

[0091] In some embodiments of the present invention, the total force F s acting on the moving dendrite and the total torque T s are:

[0092] F s = M s (dv st / dt)

[0093] T s = I s (dω s / dt)

[0094] In the formula, v st is the translational velocity, ω s is the angular velocity, and I s is the moment of inertia.

[0095] I s = ∑ρ s f s |r - r0| 2 ΔV

[0096] F s and T s also satisfy:

[0097] F s = -∑(F d + (ρ s - ρ l )f s g)ΔV

[0098] T s = -∑(r - r0) × (F d + (ρ s - ρ l )f s g)ΔV

[0099] In the formula, ρ l is the liquid density.

[0100] Combining translation and rotation, the solid velocity is updated as:

[0101] v s= v st + ω s (r - r0)

[0102] Step 4: Parameter setting

[0103] In some embodiments of the present invention, during the simulation, an Mg-6wt.% Gd alloy is used for simulation. The positions of the solid-phase nuclei are initialized as (0.5X, 0.75Y), and the positions of the bubbles are initialized as (0.5X, 0.2Y), where X and Y are the width and height of the computational domain, respectively. For the boundaries of the computational domain, both the phase field and the solute field are set to the zero Neumann boundary condition, and the flow field is set to the no-slip boundary condition.

[0104] Step 5: Visualize the evolution process of the interaction between dendrites and bubbles.

[0105] Typical simulation results of the present invention are as Figure 2 shown. The magnesium alloy dendrites are initialized as circular and located in the upper part of the computational domain. Under the action of anisotropy, protrusions are generated on the circular surface, presenting a six-fold branching morphology (represented in black). During the falling process of the dendrites, due to the uneven solute distribution, the dendrite morphology is asymmetric up and down. The lower part of the dendrite is less developed than the upper part because it enriches more solutes, resulting in a lower local supercooling and a slower growth rate. Under the action of gravity, the magnesium dendrites grow and move downward, and local protrusions are generated on the main dendrite arms. The bubbles (represented in white) located in the lower part of the computational domain float upward under the action of buoyancy until they are blocked by the descending dendrites and stay at the dendrite roots in the lower part of the dendrites. When the bubbles are blocked by the dendrite arms, they also hinder the growth of the dendrites, causing local depressions on the adjacent dendrite surfaces. When the bubbles are wrapped by the solid-phase skeleton and cannot escape from the melt, porosity defects will be formed. If the liquid phase in the closed area of the dendrites and bubbles is not replenished in time during the late stage of solidification, the volume of the pores will further increase. This case is a specific implementation of the present invention for the formation process of porosity defects during the solidification of alloys, while realizing the growth and movement of dendrites, bubble dynamics, and the multi-phase coupling evolution process of solid-liquid-gas.

[0106] Compared with the prior art, the advantages of the present invention include:

[0107] 1. High accuracy in predicting porosity defects

[0108] For the gas-liquid two-phase flow (melt convection and bubble rise) problem, the present invention uses the kinetic lattice Boltzmann method (LBM) to handle the flow problem, and its boundary conditions are set flexibly and have excellent stability. The model of the present invention accurately simulates the migration and movement process of bubbles during the solidification of magnesium alloys.

[0109] 2. Predicting solid-phase movement

[0110] By introducing Newtonian mechanics, the multiphase model can accurately simulate the translational and rotational motions of dendrites, truly reflecting the motion process of dendrites during solidification.

[0111] 3. Predicting solid-liquid-gas interactions

[0112] By introducing three phase-field variables whose sum is 1 to characterize the solid phase, liquid phase, and gas phase respectively, multi-phase coupling simulation of solid-liquid-gas can be achieved, laying a foundation for predicting solid-liquid-gas interactions.

[0113] 4. Strong scalability

[0114] The model framework of the present invention is compatible with multi-component alloy systems and can be adapted to different materials by modifying the solute distribution coefficient and thermodynamic parameters. At the same time, the model also supports simulation expansion from two dimensions to three dimensions, and can efficiently simulate complex dendrite network structures and three-dimensional dynamic deformations of bubbles, meeting the research needs of multiple scenarios.

[0115] 5. Promoting green manufacturing and lightweight strategies

[0116] Through the collaborative optimization of numerical simulation and experiments, the present invention can effectively reduce the number of process trial-and-errors, reduce the energy consumption and raw material consumption generated during the experiment, and conform to the concept of green manufacturing.

[0117] For the parts not described in detail in the present invention, reference can be made to the prior art or the well-known technology in the art. This embodiment does not make any limitations in this regard and will not be described in detail here.

[0118] The embodiments of the present invention have been described above with reference to the drawings. However, the present invention is not limited to the above specific embodiments. The above specific embodiments are merely illustrative and not restrictive. Under the inspiration of the present invention, those of ordinary skill in the art can also make many forms without departing from the purpose of the present invention and the scope protected by the claims, and all belong to the protection scope of the present invention.

Claims

1. A method for simulating the formation process of pore defects during the solidification process of an alloy, characterized in that, The method realizes the simulation of dendrite growth and movement, bubble dynamics, and the coupled evolution process of solid-liquid-gas multiphase during alloy solidification by introducing three phase-field variables of solid-liquid-gas and establishing a solid-liquid-gas multiphase-field lattice Boltzmann model.

2. The method for simulating the formation process of porosity defects during the alloy solidification process according to claim 1, characterized in that, The steps of the method include: S1. Update the solid-liquid-gas phase field, including: Introduce three phase-field variables of solid-liquid-gas to simulate the coupled action of solid-liquid-gas multiphase; control the phase-field variables through equations to make them smoothly change from 0 to 1 at the two-phase interface; the sum of the three phase-field variables always remains 1; S2. Update the flow field, including: Use the lattice Boltzmann method to solve the gas-liquid two-phase flow and calculate the particle distribution function using a two-dimensional nine-speed model; S3. Update the solid movement, including: Follow Newton's laws of motion to update the centroid position of the dendrite; Calculate the total force and total torque acting on the moving dendrite; Update the solid velocity by combining translation and rotation; S4. Perform parameter settings, including: Set the initial positions of solid-phase nuclei and bubbles; Set boundary conditions for the phase field, flow field, and solute field; S5. Visualize the evolution process of the interaction between dendrites and bubbles.

3. The method for simulating the formation process of pore defects during alloy solidification according to claim 2, wherein The content of step S1 also includes: Set the mobility function to adjust the difference in crystallization kinetics and bubble expansion evolution rate; Make the evolution of the alloy solute concentration follow Fick's second law and consider the convective flux.

4. The method for simulating the formation process of pore defects during alloy solidification according to claim 2, characterized in that, During the simulation of the coupled multiphase action, consider the phase change driving force at the solid-liquid interface and liquid-gas interface, and characterize the solid-gas interface action by setting boundary conditions at the solid phase boundary.

5. The method for simulating the formation process of porosity defects during alloy solidification according to claim 2, characterized in that, In step S1, control the phase-field variables by minimizing the free energy functional.

6. The method for simulating the formation process of pore defects during the solidification process of an alloy according to claim 2, characterized in that, When calculating the flow velocity in step S2, consider the dissipation resistance at the solid-liquid interface, the buoyancy caused by the solute concentration difference, the bubble buoyancy, and the bubble boundary surface tension.

7. The method for simulating the formation process of pore defects during alloy solidification according to claim 2, characterized in that, In step S4, set both the phase field and the solute field to zero Neumann boundary conditions, and set the flow field to a no-slip boundary condition.

8. The method for simulating the formation process of porosity defects during alloy solidification according to claim 1, wherein During the simulation process, do not simplify the bubble shape and simulate the bubble deformation and movement process.

9. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by a processor, it realizes the content of the method for simulating the formation process of pore defects during alloy solidification described in any one of claims 1-8.

10. A computer device, comprising: A memory, a processor, and a computer program stored on the memory and executable on the processor, wherein the processor executes the computer program to realize the content of the method for simulating the formation process of pore defects during alloy solidification described in any one of claims 1-8.

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