Method for predicting pore capture behavior of directional solidification dendritic crystal front edge of alloy

Abstract

The invention discloses an alloy directional solidification dendritic crystal front pore capture behavior prediction method comprising the following steps: obtaining data, and obtaining a CA-FD-LB coupling model; updating the distribution state of fluid particles in the grid in real time, and marking or updating the gas phase according to the distribution state of the particles in the grid; the temperature gradient and the cooling speed are initialized, and meanwhile the temperature of the whole calculation area changes along with time; obtaining a liquid phase equilibrium component at a solid / liquid interface and a solid phase fraction increment of a solid / liquid grid in a time step, marking solid phase distribution in a calculation area, and calculating a concentration field and solute redistribution; calculating the fluid-solid interaction between the bubbles and the solid phase; judging whether a calculation ending condition is met or not, if yes, ending calculation, and performing data visualization processing; otherwise, returning to the step 2, and starting calculation of the next time step. According to the method, the microscopic structure evolution process can be observed in real time while the calculation efficiency is high, and information is quantified.

Description

Technical Field

[0001] The present invention belongs to the method for predicting pore capture, specifically a method for predicting the pore capture behavior at the dendrite front during the directional solidification of alloys. Background Art

[0002] During the material preparation process, the solidification process of molten metal is a key link in determining whether high-performance metal materials can be prepared. The evolution of the solidification microstructure, the formation of pore defects, and their interaction are crucial for the final microstructure morphology and mechanical properties of the material. Micropore defects are typical solidification microstructure defects, and their morphology and distribution will directly affect the macroscopic mechanical properties of the material, ultimately seriously affecting the service performance of the casting, subsequent processing, and the service life of the product. Currently, due to the high melting point and opacity of metals, high requirements are imposed on experimental equipment, the experimental cost is high, the resolution of the photos is still limited, and it is difficult to obtain quantitative data on the evolution of the solute field during solidification. Therefore, it is difficult to observe the evolution process of the solidification microstructure and its interaction with micropores in real time during the experiment, and the complex interaction between the solid phase with irregular morphology and the fluid phase at the gas / liquid / solid triple-phase interface during the solidification process greatly increases the difficulty of studying the problem. Using numerical simulation means can make up for the deficiencies in measurement accuracy, variable control, etc. in the experiment and is conducive to reducing the experimental cost.

[0003] Through the numerical simulation method of a computer, the co-evolution process of the interaction between dendrites and bubbles during the directional solidification of alloys can be reproduced in real time. Commonly used numerical simulation methods for solidification microstructure and fluid-solid interaction include phase field, cellular automaton, and lattice Boltzmann methods. So far, in the existing simulation and experimental studies on alloy directional solidification dendrites and bubbles, either the research stays on the morphological evolution of dendrites and bubbles and it is impossible to obtain the distribution evolution of the solute field in real time; or there are also significant differences in the materials and solidification conditions selected in the simulation and experiment, and it is still impossible to directly compare and quantitatively analyze the simulation and experimental results while taking into account the computational efficiency. Summary of the Invention

[0004] Object of the Invention: In order to overcome the deficiencies existing in the prior art, the object of the present invention is to provide a prediction method for the pore capture behavior at the dendrite front during the directional solidification of alloys that has both computational efficiency and can observe the evolution process of the microstructure and quantitative information in real time.

[0005] Technical Solution: A prediction method for the pore capture behavior at the dendrite front during the directional solidification of alloys according to the present invention includes the following steps:

[0006] Step 1: Initialize simulation parameters including grid size, calculation area size, temperature field, concentration field, preferred orientation of dendritic growth, bubble position and size, flow-flow interaction coefficient, and flow-solid interaction coefficient. Couple the CA-FD model describing dendritic growth with the two-dimensional nine-velocity multi-relaxation LB model describing pore behavior to obtain the CA-FD-LB coupling model;

[0007] Step 2: Use the LB model to update the distribution state of fluid particles in the grid in real time. Before entering the calculation of the next time step, mark or update the gas phase according to the particle distribution state in the grid;

[0008] Step 3: Initialize the temperature gradient and cooling rate, and at the same time, the temperature change of the entire calculation area over time;

[0009] Step 4: Obtain the liquid-phase equilibrium composition at the solid / liquid interface, the solid-phase fraction increment of the grid at the solid / liquid interface within one time step, and mark the solid-phase distribution in the calculation area through the CA-FD model. Calculate the concentration field and solute redistribution through the CA-FD model;

[0010] Step 5: Calculate the flow-solid interaction between the bubble and the solid phase through the LB model;

[0011] Step 6: Determine whether the calculation end condition is met. If it is met, the calculation ends and data visualization processing is performed; otherwise, return to Step 2 and start the calculation of the next time step.

[0012] Furthermore, the governing equation of the two-dimensional nine-velocity multi-relaxation LB model is:

[0013]

[0014] where f i (x,t) and are the gas particle distribution function and the particle equilibrium distribution function in the i direction, respectively; x, t, and Δt represent position, time, and time step, respectively; M is an orthogonal transformation matrix used to transform the particle distribution function from the velocity space to the moment space; M -1 is its inverse matrix; F i ′ is the external force term; e i is the discrete velocity of the particle, which is related to the geometric format of the LB model; Λ is the particle collision diagonal matrix, which contains different relaxation times; through the transformation matrix M, the particle distribution function and the equilibrium distribution function are projected from the velocity space to the moment space to obtain the particle distribution function and the equilibrium distribution function in the moment space.

[0015] Furthermore, in the LBM model, the expression of the equilibrium distribution function m eq in the moment space is:

[0016]

[0017] In the formula, ρ is the macroscopic density of the fluid, calculated by ρ = ∑ i fi; u = [u x , u y , u z T is the macroscopic velocity of the fluid, calculated by ρu = ∑ i e i f i + FΔt / 2, where F is the total force acting on the fluid particles, and F is the sum of the fluid-fluid force (F c ) and the fluid-solid force (F ads ). Further, in step four, the difference between the equilibrium liquid phase composition and the actual liquid phase composition at the solid / liquid interface is the increment of the solid phase fraction in the solid / liquid interface grid within one time step, which serves as the driving force for dendrite growth. Its calculation formula is

[0018]

[0019] In the formula, g is the shape factor; δ k is the kinetic anisotropy coefficient of the dendrite; is the angle between the normal direction of the solid / liquid interface and the horizontal direction, calculated by the formula ; θ0 is the angle between the preferred growth direction of the dendrite and the horizontal direction; is the equilibrium liquid phase composition at the solid / liquid interface; is the actual liquid phase composition; k p is the solute distribution coefficient.

[0020] Further, the calculation formula for the shape factor g is:

[0021]

[0022] In the formula, is the state parameter of the m-th of the 4 nearest neighbor cells of the interface (i, j) grid in the two-dimensional calculation region, is the state parameter of the m-th of the 4 next-nearest neighbor cells of the interface (i, j) grid in the two-dimensional calculation region.

[0023] Further, and take values according to the states of the neighboring positions as

[0024]

[0025] In the formula, f s is the solid phase fraction in a single grid.

[0026] Further, the equilibrium liquid phase composition ​The calculation formula is as follows:

[0027]

[0028] In the formula, C0 is the initial alloy composition; T * is the actual interface temperature; is the equilibrium liquidus temperature of the alloy with the initial composition, which is calculated by the formula T m is the melting point temperature of the pure metal; m l is the liquidus slope; is the average Gibbs-Thomson coefficient; is the interface energy anisotropy function. For the primary α phase of the SCN-ACE alloy with a four-fold symmetry of the anisotropic interface energy, its calculation formula is ε is the interface energy anisotropy coefficient; K is the interface curvature.

[0029] Furthermore, the calculation formula of the interface curvature K is:

[0030]

[0031] Furthermore, the actual liquid composition is obtained by solving the solute diffusion equation by the FD method. The solute diffusion equation in the simulation region is:

[0032]

[0033] In the formula, X represents the solute atom; the subscript i represents the solid phase (s) or the liquid phase (l); C i (X) is the solute concentration; D i (X) is the solute diffusion coefficient; R i (X) is the source term, which is related to the solute redistribution of the solute atoms at the solid / liquid interface.

[0034] Furthermore, the calculation formula of R i (X) within a time step is:

[0035]

[0036] In the formula, is the actual solute concentration in the liquid phase at the solid / liquid interface; is the actual solid composition in the newly formed solid phase in the interface cell, which is calculated by the formula The non-diffusion boundary condition is adopted at the boundary of the calculation region.

[0037] Advantages: Compared with the prior art, the present invention has the following remarkable features: while having high computational efficiency, it can observe the evolution process of the microstructure in real time, realize the evolution solution of the behavior of capturing pores at the dendrite front, quantify the influence of the interaction between pores and dendrites on the evolution of the solute field, etc., predict the possible occurrence of microporous microdefects and dendrite morphology characteristics, and provide scientific theoretical guidance for the actual solidification microstructure control. Brief Description of the Drawings

[0038] Figure 1 is a flowchart of the present invention;

[0039] Figure 2 is a schematic diagram of the calculation region in Example 1 of the present invention;

[0040] Figure 3 is a schematic diagram of the simulation and experimental states of small-sized pores captured by the dendrite tip at different solidification times. Among them, (a) is the simulation at t a seconds, (b) is the simulation at t a +8 seconds, (c) is the simulation at t a +16 seconds, (d) is the experiment at t d seconds, (e) is the experiment at t d +6 seconds, (f) is the experiment at t d +12 seconds;

[0041] Figure 4 is a schematic diagram of the simulation and experimental states of large-sized pores captured by the dendrite tip at different solidification times. Among them, (a) is the simulation at t a seconds, (b) is the simulation at t a +7 seconds, (c) is the simulation at t a +21 seconds, (d) is the simulation at t a +33 seconds, (e) is the experiment at t e seconds, (f) is the experiment at t e +8 seconds, (g) is the experiment at t e +30 seconds, (h) is the experiment at t e +58 seconds;

[0042] Figure 5 is a schematic diagram of the simulation and experimental states of small-sized pores captured by the dendrite side branches at different solidification times. Among them, (a) is the simulation at t a seconds, (b) is the simulation at t a +4 seconds, (c) is the simulation at t a +12 seconds, (d) is the simulation at t a +19 seconds, (e) is a partial enlarged view at the simulation at t a +19 seconds, (f) is the experimentally observed morphology;

[0043] Figure 6Schematic diagrams of the simulation and experimental states of dendrite side branches capturing inter-dendritic pores with different solidification times in the present invention. Among them, (a) is the simulation at t a seconds, (b) is the simulation at t a + 2 seconds, (c) is the simulation at t a + 9 seconds, (d) is the experiment at t a seconds, (e) is the experiment at t a + 2 seconds, (f) is the experiment at t a + 9 seconds. Detailed implementation manners

[0044] In the following examples, materials, reagents, etc. used, unless otherwise specified, can be obtained from commercial channels. The experimental methods without specific conditions noted in the examples usually follow conventional conditions or the conditions recommended by the manufacturer.

[0045] Examples 1 and 2 aim to explore the evolution process of pores of different sizes being captured by dendrite tips.

[0046] Example 1

[0047] As Figure 1 shown, a prediction method for the pore capture behavior at the dendrite front during the directional solidification of an alloy includes the following steps:

[0048] S1. Initialize simulation parameters such as grid size, calculation region size, temperature field, concentration field, dendrite growth preferred orientation, bubble position and size, flow-flow interaction coefficient, and flow-solid interaction coefficient. By coupling the CA-FD model describing dendrite growth and the two-dimensional nine-velocity multi-relaxation LB model describing pore behavior, a CA-FD-LB coupling model is obtained.

[0049] S1.1. Establish a CA-FD model describing the directional solidification dendrite growth. Use the difference between the equilibrium liquid phase composition and the actual liquid phase composition at the solid / liquid interface as the driving force for dendrite growth. The solid phase increment (Δf s ) obtained by dendrite growth in a single grid per unit time is calculated by the formula:

[0050]

[0051] In the formula, δ k is the kinetic anisotropy coefficient of the dendrite; θ0 is the angle between the preferred dendrite growth direction and the horizontal direction; is the angle between the normal direction of the solid / liquid interface and the horizontal direction, calculated by the formula ; k p is the solute distribution coefficient; g is the shape factor, and its calculation formula is:

[0052]

[0053] In the formula, S Ⅰ and S Ⅱ are the state parameters of the 4 nearest-neighbor cells and the 4 next-nearest-neighbor cells of the interface (i, j) grid in the two-dimensional calculation region respectively. According to the states of the neighboring positions, and take values as follows:

[0054]

[0055] In the formula, f s is the solid-phase fraction in a single grid.

[0056] The equilibrium liquid-phase composition at the solid / liquid interface in formula (1) is calculated by the formula:

[0057]

[0058] In the formula, C0 is the initial alloy composition; T * is the actual interface temperature; is the equilibrium liquidus temperature of the alloy with the initial composition, which is calculated by the formula T m is the melting point temperature of the pure metal; m l is the liquidus slope; is the average Gibbs-Thomson coefficient; is the interface energy anisotropy function. For the primary α-phase of succinonitrile-acetone (SCN-ACE) with a four-fold symmetry of the anisotropic interface energy, its calculation formula is ε is the interface energy anisotropy coefficient; K is the interface curvature, and its calculation formula is:

[0059]

[0060] S1.2. The finite difference (FD) method is used to solve the solute diffusion equation to obtain the actual liquid-phase composition at the solid / liquid interface. The solute diffusion equation in the simulation region is:

[0061]

[0062] In the formula, X represents the solute atom; the subscript i represents the solid phase (s) or the liquid phase (l); C i (X) is the solute concentration; D i (X) is the solute diffusion coefficient. Ri(X) is the source term, which is related to the solute redistribution of the solute atom at the solid / liquid interface. Its calculation formula within a time step is:

[0063]

[0064] In the formula, is the actual solute concentration in the liquid phase at the solid / liquid interface; is the actual solid-phase composition in the newly formed solid phase in the interface cell, calculated by the formula . The boundary of the calculation region adopts a non-diffusion boundary condition. The temperature within the calculation region is cooled at a certain cooling rate by applying a constant temperature gradient.

[0065] S1.3. Couple the CA-FD model describing dendritic growth and the LB model describing pore behavior. Adopt a multi-relaxation LB model with two-dimensional nine velocities (D2Q9), and its governing equation is:

[0066]

[0067] In the formula, f i (x, t) and are the gas particle distribution function and the particle equilibrium distribution function in the i direction, respectively; x, t, and Δt represent position, time, and time step, respectively; M is an orthogonal transformation matrix used to transform the particle distribution function from the velocity space to the moment space; M -1 is its inverse matrix; F i ′ is the external force term; e i is the discrete velocity of the particle, which is related to the geometric format of the LB model; Λ is the particle collision diagonal matrix, containing different relaxation times.

[0068] The left side of formula (8) represents the migration of particles during the evolution process, and the right side represents the collision of particles. Particle migration and collision are carried out in the velocity space and the moment space, respectively. Through the transformation matrix M, the particle distribution function (f) and the equilibrium distribution function (f eq ) are projected from the velocity space to the moment space, that is, m = Mf, m eq = Mf eq , where m and m eq are the particle distribution function and the equilibrium distribution function in the moment space, respectively. For the D2Q9 format LBM model adopted, the expression of m eq is:

[0069]

[0070] In the formula, ρ is the macroscopic density of the fluid, calculated by ρ = ∑ i f i ; u = [u x , u y , u z T is the macroscopic velocity of the fluid, calculated by ρu = ∑ i e i f i ​Calculated by +FΔt / 2, where F is the total force acting on the fluid particles.

[0071] In the relaxation model, the total force F acting on the fluid particles is the sum of the fluid-fluid force (F c ) and the fluid-solid force (F ads ), that is, F = F c +F ads . F c and F ads The calculation formulas are as follows:

[0072]

[0073] In the formula, G c and G ads are the fluid-fluid interaction coefficient and the fluid-solid interaction coefficient respectively, which determine the force intensity between fluid particles and between fluid particles and the solid phase. s(x+e i Δt,t) is an indicator function, and its value is determined by the lattice state: the value of the solid-phase lattice is 1, and the value of the fluid-phase lattice is 0. ω i is the weight coefficient, and its value is: when i = 0, ω i = 4 / 9; when i = 1-4, ω i = 1 / 9; when i = 5-8, ω i = 1 / 36. ψ is the pseudo-potential function, which is determined by the formula , where G c takes the value of -1; c s is the lattice sound speed, and its value is

[0074] As described above, the collision evolution model of particles in the LB model is presented. The particle migration is completed in the velocity space, and the governing equation is:

[0075]

[0076] In the formula, f * = M -1 m * , transforms the particle distribution function in the moment space to the velocity space; E is the source term, which is related to the redistribution of gas-phase particles at the solid / liquid interface. In this model, it is set to 0, that is, there is no transport process of gas-phase particles at the solid / liquid interface.

[0077] S1.4, Figure 2 is a schematic diagram of the calculation area. The four sides of the area are periodic boundary 1. The area is filled with alloy solution 2. A number of dendritic nuclei 3 are initially set at the bottom of the area, and a single air hole 4 is initially preset in the area. The top of the area is set to a relatively high temperature (T hot ), and the bottom is at a relatively low temperature (T cold ), and a constant temperature gradient (T is formed in the entire calculation area along the y direction.G ) and cooled at a fixed cooling rate (CR). After the calculation starts, the temperature of the region decreases. When the supercooling degree (ΔT0) for dendritic nucleation is reached, the bottom nuclei are activated and start to grow upward along the temperature gradient in the form of columnar crystals. Set the calculation region to 800×1200, with each grid being 2 microns. A number of nuclei with the same preferred orientation are placed at the bottom of the calculation region, and the nucleus spacing is evenly distributed, with the adjacent dendrite spacing being ∼225 μm. A pore with a size radius of ∼50 μm is located at the tip of the primary dendrite trunk in the middle position.

[0078] S2. The distribution state of fluid particles in the grid is updated in real time through formula (8) in the LB model. Before entering the calculation of the next time step, the gas phase is marked or updated according to the particle distribution state in the grid (such as the macroscopic density ρ of the fluid).

[0079] S3. A fixed temperature gradient and cooling rate are preset in the model, where the temperature gradient is T G = 5 K / mm and the cooling rate is CR = 0.24 K / s. In addition, the initial supercooling degree ΔT0 for dendritic nucleation is preset to 0.4 K. In the calculation region, the temperature distribution along the temperature gradient direction is calculated by T * (y) = T cold + y×T G ; meanwhile, the change of the temperature in the entire calculation region with time is calculated by the formula T * = T * - CR×Δt.

[0080] S4. The liquid-phase equilibrium composition at the solid / liquid interface, the increment of the solid-phase fraction of the grid at the solid / liquid interface within one time step, and the solid-phase distribution in the calculation region are obtained through formulas (1)–(5) in the CA-FD model, and the concentration field and solute redistribution are calculated through formulas (6) and (7) in the CA-FD model.

[0081] S5. The fluid-solid interaction between the bubble and the solid is calculated through formulas (8)–(12) in the LB model.

[0082] S6. Determine whether the calculation end condition is met. If it is met, the calculation ends and data visualization processing is performed; otherwise, return to step two and start the calculation of the next time step.

[0083] The results of the visualization processing are as Figure 3 shown. Figure 3 (a), 3(b), and 3(c) are respectively the morphological evolution of columnar crystal growth and pore capture and the solute concentration contour maps at the simulated solidification times of t a seconds, t a + 8 seconds, and t a + 16 seconds. Figure 3(d), 3(e), and 3(f) are the morphological evolution diagrams of columnar crystal growth and pore capture at the moment of directional solidification of the SCN-ACE transparent alloy observed in the experiment at t d seconds, t d +6 seconds, and t d +12 seconds. It can be seen that under the drive of the temperature gradient, the dendrites grow upward and form a columnar dendrite array. When the dendrite tip encounters a pore, the dendrite will change its growth path, grow along the pore surface, and form a solid shell to completely wrap it. At the same time, due to interface instability, a new solid protrusion grows on the solid shell and grows radially. As the solidification process proceeds, the newly formed laterally growing small dendrites are hindered by adjacent primary dendrites and stop growing. Comparing Figure 3 (a), 3(b), 3(c) and Figure 3 (d), 3(e), 3(f), it can be seen that the simulation results are in good agreement with the experimental results. In addition, through the simulation results, it can be quantitatively seen that the solutes discharged by dendrite growth continuously accumulate in the liquid phase region between dendrite arms, causing the growth of newly formed small dendrites whose growth directions deviate from the temperature gradient direction to gradually stagnate. Only the small dendrites growing parallel to the temperature gradient direction can continue to grow and become the main trunk of new primary dendrites, and finally the average primary dendrite arm spacing remains unchanged.

[0084] Example 2

[0085] The remaining steps of this example are the same as those of Example 1, except that: the pore radius is changed and set to ~250 μm.

[0086] The visualization processing results are as shown in Figure 4 shown, Figure 4 (a), 4(b), 4(c), 4(d) are the morphological evolution and solute concentration nephograms of columnar crystal growth and pore capture at the moment of simulated solidification at t a seconds, t a +7 seconds, t a +21 seconds, and t a +33 seconds. Figure 4 (e), 4(f), 4(g), 4(h) are the morphological evolution diagrams of columnar crystal growth and pore capture at the moment of directional solidification of the SCN-ACE transparent alloy observed in the experiment at t e seconds, t e +8 seconds, t e +30 seconds, and t e +58 seconds. It can be seen that when the pore size increases significantly, multiple dendrites interact with the pores and capture the pores by growing along the pore surface until they are completely wrapped. Comparing Figure 4 (a), 4(b), 4(c), 4(d) and Figure 4(e), 4(f), 4(g), and 4(h) show that the simulation results are in good agreement with the experimental results. Different from the case of small and medium-sized pores: large-sized pores hinder the growth of multiple dendrites below, and a larger liquid channel area is formed at the front of the pore tip, which is conducive to more new small dendrites on the solid shell above the pore to grow into the liquid phase along the temperature gradient direction and develop into new primary dendrite trunks at the same time, that is, from the original 3 dendrites to 4 dendrites, which results in a decrease in the average primary dendrite arm spacing. Figure 3 Different from the case of small and medium-sized pores, large-sized pores hinder the growth of multiple dendrites below, and a larger liquid channel area is formed at the front of the pore tip, which is conducive to more new small dendrites on the solid shell above the pore to grow into the liquid phase along the temperature gradient direction and develop into new primary dendrite trunks at the same time, that is, from the original 3 dendrites to 4 dendrites, which results in a decrease in the average primary dendrite arm spacing.

[0087] Example 3 and Example 4 aim to explore the evolution process of pores at different relative positions being captured by the dendrite front.

[0088] Example 3

[0089] The remaining steps of this example are the same as those of Example 1, except that: before the calculation starts, the relative position of the pore and the dendrite array is changed. The center position of the bubble with a radius of ~70 μm is offset from the dendrite tip, and the primary dendrite arm spacing on the side where the bubble is located is ~360 μm.

[0090] The visualization processing results are as Figure 5 shown Figure 5 (a), 5(b), 5(c), and 5(d) are the morphology evolution and solute concentration contour maps of columnar crystal growth and pore capture at the solidification times of t a seconds, t a + 4 seconds, t a + 12 seconds, and t a + 19 seconds respectively. Figure 5 (e) is Figure 5 the local enlarged view in Figure 5 (d), Figure 3 (f) is the morphology map of dendrite capturing bubbles observed in the experiment. Comparing 5(e) and 5(f), it can be seen that the simulation results are in good agreement with the experimental results at the same spatial scale. In addition, it can be seen that the pore is captured by the nearest dendrite, and the dendrite tip and side branches change the solidification direction after touching the pore and gradually wrap the gas from the side. Different from the

[0091] Example 4

[0092] The remaining steps of this example are the same as those of Example 1, except that: the relative position of the pore and the dendrite array is changed, and the pore with a radius of ~70 μm is placed in the liquid channel between two dendrites.

[0093] The visualization processing results are asFigure 6 As shown Figure 6 (a), 6(b), and 6(c) are respectively the morphological evolution and solute concentration contour maps of columnar crystal growth and pore capture at the simulated solidification times of t a seconds, t a + 2 seconds, and t a + 9 seconds. Figure 6 (d), 6(e), and 6(f) are respectively the experimental observation morphology maps corresponding to different solidification times. By comparing the simulation and experimental results, it can be seen that the simulation results are in good agreement with the experimental results at the same spatial scale. In addition, it can be seen that the pores located between the dendrite channels are captured by the dendrite side branches; from Figure 6 (b), it is found that after the dendrite side branches on both sides of the pore touch the pore, they both grow along the surface of the pore to the top along both sides of the pore, combining to form a solid shell. Due to interface instability, several small dendrites germinate from the solid phase at the top of the pore. As the solidification process progresses, the small dendrites growing from the top of the pore will soon be submerged due to the obstruction of the upper side branches of adjacent dendrites and cannot develop into new primary dendrites, and will not affect the growth morphology of the subsequent dendrite array. From Figure 6 (c), it can be seen that solute enrichment occurs in the inter-dendrite channels, which is also one of the reasons for the inhibition of the growth of new dendrites.

Claims

1. A prediction method for the pore capture behavior at the dendrite front during directional solidification of an alloy, characterized in that, It includes the following steps: Step 1: Initialize simulation parameters such as grid size, calculation area size, temperature field, concentration field, preferred orientation of dendrite growth, bubble position and size, flow-flow interaction coefficient, and flow-solid interaction coefficient. Couple the CA-FD model for describing dendrite growth and the two-dimensional nine-velocity multi-relaxation LB model for describing pore behavior to obtain the CA-FD-LB coupled model; Step 2: Update the distribution state of fluid particles in the grid in real time through the LB model. Before entering the calculation of the next time step, mark or update the gas phase according to the particle distribution state in the grid; Step 3: Initialize the temperature gradient and cooling rate, and at the same time, the temperature change of the entire calculation area over time; Step 4: Obtain the liquid-phase equilibrium composition at the solid / liquid interface, the increment of the solid-phase fraction of the grid at the solid / liquid interface within one time step through the CA-FD model, and mark the solid-phase distribution in the calculation area. Calculate the concentration field and solute redistribution through the CA-FD model; Step 5: Calculate the flow-solid interaction between the bubble and the solid phase through the LB model; Step 6: Judge whether the calculation end condition is met. If it is met, the calculation ends and data visualization processing is performed; otherwise, return to Step 2 and start the calculation of the next time step.

2. The prediction method for the pore capture behavior at the dendrite front during the directional solidification of an alloy according to claim 1, wherein: The control equation of the two-dimensional nine-velocity multi-relaxation LB model is: i,j = 0,1,...,8 where f i (x,t) and f i eq are the gas particle distribution function and the particle equilibrium distribution function in the i direction, respectively; x, t, and Δt represent position, time, and time step, respectively; M is an orthogonal transformation matrix used to transform the particle distribution function from velocity space to moment space; M -1 is its inverse matrix; F i ′ is the external force term; e i is the discrete velocity of the particle, which is related to the geometric format of the LB model; Λ is the particle collision diagonal matrix, which contains different relaxation times; through the transformation matrix M, the particle distribution function and the equilibrium distribution function are projected from the velocity space to the moment space to obtain the particle distribution function and the equilibrium distribution function in the moment space.

3. The prediction method for the gas pore capture behavior at the dendrite front during the directional solidification of an alloy according to claim 1, characterized in that: In the LBM model, the equilibrium distribution function m in the moment space eq has the following expression: where ρ is the macroscopic density of the fluid, calculated by ρ = ∑ i f i ; u = [u x , u y , u z T is the macroscopic velocity of the fluid, calculated by ρu = ∑ i e i f i + FΔt / 2, where F is the total force acting on the fluid particles, and F is the sum of the fluid-fluid force (F c ) and the fluid-solid force (F ads ).​ 4. The prediction method for the pore capture behavior at the dendritic front during the directional solidification of an alloy according to claim 1, characterized in that: In the fourth step, the liquid-phase equilibrium composition at the solid / liquid interface and the actual liquid-phase composition The difference is used as the driving force for dendrite growth. Therefore, during dendrite growth, the calculation formula for the increment of the solid-phase fraction in the solid / liquid interface grid within one time step is where g is the shape factor; δ k is the kinetic anisotropy coefficient of the dendrite; is the angle between the normal direction of the solid / liquid interface and the horizontal direction, calculated by the formula ; θ0 is the angle between the preferred growth direction of the dendrite and the horizontal direction; is the equilibrium liquid-phase composition at the solid / liquid interface; is the actual liquid-phase composition; k p is the solute distribution coefficient.

5. The prediction method for the pore capture behavior at the dendrite front during directional solidification of an alloy according to claim 4, wherein: The calculation formula of the shape factor g is: wherein, is the state parameter of the m-th one among the 4 nearest neighbor cells of the interface (i, j) grid in the two-dimensional calculation region, is the state parameter of the m-th one among the 4 next nearest neighbor cells of the interface (i, j) grid in the two-dimensional calculation region.

6. The prediction method for the pore capture behavior at the dendrite front during the directional solidification of an alloy according to claim 5, wherein: The said and The value according to the state of the adjacent position is where f s is the solid fraction in a single grid.

7. A prediction method for the pore capture behavior at the dendrite front during the directional solidification of an alloy according to claim 4, characterized in that: The equilibrium liquid-phase composition at the solid / liquid interface is calculated by the formula: where, C0 is the initial alloy composition; T * is the actual interface temperature; is the equilibrium liquidus temperature of the alloy with the initial composition, calculated by the formula T m is the melting point temperature of the pure metal; m l is the liquidus slope; is the average Gibbs-Thomson coefficient; is the interface energy anisotropy function. For the primary α-phase of the succinonitrile-acetone (SCN-ACE) alloy with a four-fold symmetry of the anisotropic interface energy, its calculation formula is ε is the interface energy anisotropy coefficient; K is the interface curvature.

8. A prediction method for the pore capture behavior at the dendrite front during directional solidification of an alloy according to claim 7, characterized in that: The calculation formula of the interface curvature K is:

9. A prediction method for the pore capture behavior at the dendrite front during the directional solidification of an alloy according to claim 4, characterized in that: The actual liquid-phase composition is obtained by solving the solute diffusion equation through the FD method. The solute diffusion equation in the simulation area is: In the formula, X represents a solute atom; the subscript i represents the solid phase (s) or the liquid phase (l); C i (X) is the solute concentration; D i (X) is the solute diffusion coefficient; R i (X) is the source term, which is related to the solute redistribution of solute atoms at the solid / liquid interface.

10. The prediction method for the pore capture behavior at the dendrite front during the directional solidification of an alloy according to claim 9, characterized in that: Said R i (X) The calculation formula within one time step is as follows: wherein, is the actual solute concentration in the liquid phase at the solid / liquid interface; is the actual solid phase composition in the newly formed solid phase in the interface cell, which is calculated by the formula and the boundary of the calculation region adopts a non-diffusion boundary condition.

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