Rapid tracking and predicting method and system for involved bubble movement in casting and mold filling process

Abstract

The invention belongs to the technical field related to casting, and discloses a rapid tracking and predicting method and system for involved bubble movement in the casting and mold filling process. The method comprises the following steps: (1) carrying out grid division on a three-dimensional geometric model for casting and mold filling; (2) calculating the filling rate, the speed and the pressure intensity of each grid in a casting mold filling cavity at the moment i in the mold filling process; identifying bubbles in the cavity and grids contained in each bubble; and (3) repeating the step (2) until updating of the filling rates, the filling speeds and the pressure intensities of the grids in the bubbles at all moments is completed, so that tracking and prediction of bubble movement in the casting and mold filling process are realized. By means of the method, tracking and calculation of involved bubbles in the mold filling process are achieved, and the solving accuracy of casting numerical simulation software is enhanced.

Description

Technical Field

[0001] The present invention belongs to the technical field related to casting, and more specifically, relates to a method and system for quickly tracking and predicting the movement of entrained bubbles during the casting filling process. Background Technique

[0002] Porosity defects caused by entrained gas during the filling process are a common defect in the casting process and can have a great impact on the performance of the casting. During the filling process, liquid metal often exhibits phenomena such as jetting and splashing due to its high flow rate. In these cases, the jetted and splashed liquid metal will generate curling or convection, resulting in a large amount of gas in the cavity being entrained into the liquid metal and flowing along with the metal liquid. If the gas entrained by the metal liquid cannot be discharged in time, the gas will remain inside the metal, forming a gas entrainment defect. Gas entrainment defects will reduce the physical and mechanical properties of the casting, causing problems such as porosity on the machined surface, reduced density of the casting, air leakage during use, stress concentration, and even fracture. At the same time, the oxygen in the entrained gas can react with the liquid metal to form inclusions, and the entrained gas is the main source of oxygen required for the reaction.

[0003] Traditional single-phase flow casting filling simulation software does not consider the presence of air in the mold during the filling simulation calculation. It can only judge whether gas entrainment will occur based on the hydrodynamic development and changes on the liquid phase surface of the metal liquid during the filling process, and the predicted physical authenticity is low. For example, at a certain moment, if the front of the free surface of the metal liquid curls, the program will consider that gas entrainment has occurred at the curled part and consider the cavity part wrapped by the curled liquid to be a vacuum, and does not calculate the pressure and movement trend of the gas in the cavity part. Therefore, in subsequent calculations, the cavity formed by the gas entrained into the metal liquid will gradually disappear. After the calculation is completed, the single-phase flow numerical simulation software cannot give the defect distribution in the casting caused by the entrained gas. Therefore, a method for simulating gas movement during the filling process is needed. Summary of the Invention

[0004] Aiming at the above defects or improvement requirements of the prior art, the present invention provides a method and system for quickly tracking and predicting the movement of entrained bubbles during the casting filling process, which solves the problem of not considering the presence of air and gas movement in the casting simulation process.

[0005] To achieve the above object, according to one aspect of the present invention, a method for quickly tracking and predicting the movement of entrained bubbles during the casting filling process is provided. The method includes the following steps:

[0006] (1) Mesh the three-dimensional geometric model of the casting filling;

[0007] (2) Calculate the filling rate, velocity, and pressure of each grid in the casting filling cavity at any moment i during the filling process; identify the bubbles in the cavity and the grids contained in each bubble; update the filling rate, velocity, and pressure of the grids in the bubble at any moment i in the following manner:

[0008] Calculate the surface tension and inertial force of each bubble, and determine whether the bubble breaks according to the magnitude relationship between the surface tension and the inertial force. For the broken bubble, the filling rate is 1, and the velocity and pressure of the grids in the broken bubble are updated using the velocity and pressure of the surrounding liquid; for the unbroken bubble, determine whether the bubbles collide. For the non-colliding bubbles, the filling rate, velocity, and pressure are not updated;

[0009] For the colliding bubbles, calculate the filling rate of the grids in the bubble after the collision according to the volume change amount of the colliding bubbles, so as to update the filling rate; determine whether the updated filling rate is less than the preset threshold without liquid overflow. If there is no overflow, the velocity and pressure at the current moment are not updated. If there is an overflow, update the velocity and pressure of the grid at the current moment using the velocity and pressure of the adjacent grids;

[0010] (3) Let i = i + 1, and repeat step (2) until the filling rate, velocity, and pressure of the grids in the bubble at all moments are updated, so as to realize the tracking and prediction of the bubble movement during the casting filling process.

[0011] Further preferably, the calculation formula of the surface tension is as follows:

[0012]

[0013] Among them, is the divergence operator, σ is the surface tension coefficient, n is the surface normal vector, κ is the local surface curvature, ρ l is the liquid density, ρ g is the gas density.

[0014] Further preferably, the local surface curvature is calculated in the following manner:

[0015]

[0016] Among them, is the discrete error, is the grid filling rate under the interface cut with a slope of a, α i+l,j+m,k+n is the actual grid filling rate.

[0017] Further preferably, the calculation formula of the inertial force is as follows:

[0018] ∑F = F s - F p - Fd

[0019] Among them, F s is the surface tension on the bubble surface, F d is the viscous force on the bubble surface, F p is the pressure difference inside and outside the bubble.

[0020] Further preferably, it is determined whether the bubble breaks in the following manner:

[0021] When the surface tension is less than the inertial force, the bubble breaks; otherwise, the bubble does not break.

[0022] Further preferably, the update formula for the filling rate of the colliding bubbles is as follows:

[0023]

[0024] Among them, is the updated filling rate of the bubble grid, is the grid filling rate before update, is the calculated change in the grid filling rate.

[0025] Further preferably, the calculation formula for the change in the filling rate of each grid is as follows:

[0026]

[0027] Among them, is the constructed Lagrangian function, is the initial filling rate of the grid, is the target filling rate of the grid, is the change in the grid filling rate, N is the number of grids, λ is the Lagrange multiplier, Δα n is the sum of the changes in the filling rates of all grids.

[0028] Further preferably, the velocity and pressure of the grid at the current moment are updated using the velocities and pressures of adjacent grids according to the following formula:

[0029]

[0030] Among them, V x , V y , V z are the velocity values of the grid in the x, y, and z directions respectively, V x+1 , V x-1 , V y+1 , V y-1 , V z+1 , V z-1 are the velocity values of the grids adjacent to the grid in the x, y, and z directions respectively, P is the pressure value of the grid, Px+1 , P x-1 , P y+1 , P y-1 , P z+1 , P z-1 are the pressure values of the grids adjacent to the grid respectively.

[0031] Further preferably, the method for identifying the bubbles in the cavity and the grids included in each bubble adopts the air entrainment search method;

[0032] The coordinates L of the bubble numbered b at any moment are updated according to the following formula:

[0033]

[0034] where is the grid coordinate of the updated bubble b, L x , L y , L z is the grid coordinate of the bubble b before update, v x , v y , v z are the velocity components of the bubble grid in three directions, and Δt is the time step.

[0035] According to another aspect of the present invention, there is provided a fast tracking and prediction system for the movement of entrained bubbles during the casting filling process. The system includes an actuator, and the actuator is used to execute the above-mentioned fast tracking and prediction method for the movement of entrained bubbles during the casting filling process.

[0036] Generally speaking, compared with the prior art by the above technical solutions conceived by the present invention, the following beneficial effects are achieved:

[0037] 1. The method provided by the present invention considers the dynamic changes of bubbles during the casting process, and updates the filling rate, velocity and pressure of the bubble grids according to different situations of bubble breakage and collision during the bubble movement, dynamically analyzes the morphological evolution process of bubbles in the flow field, ensures the mass conservation of the molten metal in the computational domain, considers the existence of air and simulates the movement of gas, significantly improving the accuracy of casting numerical simulation.

[0038] 2. The present invention distinguishes and processes the situations such as bubble breakage, collision and whether there is overflow during the bubble movement process to improve the simulation accuracy and stability. The breakage of bubbles is mainly caused by the imbalance between inertial force and surface tension. The collision between bubbles will cause bubble coalescence, and the change of liquid pressure will cause the volume fluctuation of bubbles, which will further affect the distribution of the gas-liquid interface and the overflow situation. By constructing exclusive models for these different physical mechanisms respectively, the bubble behavior characteristics can be accurately captured, avoiding the distortion and simplification of complex bubble dynamics by a single model and improving the prediction accuracy.

[0039] 3. The present invention corrects the defect that the single-phase flow numerical simulation system can only simulate the liquid motion state but cannot simulate the gas motion, avoids using the two-phase flow calculation model, thereby greatly improving the calculation efficiency, and can obtain the numerical simulation results of the gas entrainment defect in the casting on the premise of ensuring a certain accuracy. Finally, it provides a new idea for the high-precision and rapid numerical simulation of the gas entrainment defect.

[0040] 4. The method provided by the present invention is applicable to the entire process of casting filling, and can accurately simulate the bubble behavior at different stages, including the generation, coalescence, breakup of bubbles and the formation of entrainment defects. This method can track the morphological evolution of bubbles in real time during the filling process, accurately depict the dynamic changes of the gas-liquid interface, and provide a scientific basis for the prediction of casting gas entrainment defects and process optimization. Brief Description of the Drawings

[0041] Figure 1 is a flowchart of a rapid tracking and prediction method for the movement of entrained bubbles during the casting filling process constructed according to the preferred embodiment of the present invention;

[0042] Figure 2 is a flowchart of a gas entrainment search algorithm constructed according to the preferred embodiment of the present invention;

[0043] Figure 3 is a schematic diagram of the force analysis of a single bubble constructed according to the preferred embodiment of the present invention;

[0044] Figure 4 is a schematic diagram of reconstructing the gas-liquid interface under a finite difference grid constructed according to the preferred embodiment of the present invention. Detailed Embodiments

[0045] In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0046] Refer to Figure 1 , the present invention provides a rapid tracking and prediction algorithm for the movement of entrained bubbles during the casting filling process. Refer to Figure 2 , quickly identify the bubbles in the molten metal. Refer to Figure 3 and Figure 4 , calculate the overall movement and morphological changes of the bubbles, realize the prediction of the bubble movement behavior, and ensure the global mass conservation. The method includes the following steps:

[0047] S1: Mesh the three-dimensional geometric model during the casting filling process to construct a discretized space suitable for numerical calculation. For the meshed geometric model, an initial filling state is assigned, where the filling rate α of all meshes without molten metal is initially set to 0, and specific parameter values α_Wall are set for the meshes corresponding to the mold wall to distinguish the cavity region from the mold wall region, thereby clarifying the boundary conditions of the filling region. Set the time step for calculating the flow field and input the physical properties of the molten metal, gravitational acceleration, filling speed, pressure conditions, and other casting process-related parameters.

[0048] S2: Update the filling rate, velocity value, and pressure value in the bubble mesh

[0049] A. Advance the time step according to the flow equation and calculate the filling rate, velocity, and pressure of each mesh in the casting filling cavity at any time i during the filling process. The calculation method can adopt the numerical solution method of the grid filling rate, velocity, and pressure mainly centered around the N-S equation. Generally, there are methods such as the SIMPLE method, SOLA-VOF method, and projection method. The above methods are all existing technical methods and will not be elaborated here.

[0050] B. Calculate the gas entrainment situation in the flow field file at this time step through the gas entrainment search algorithm. The main function of the gas entrainment search algorithm is to identify bubbles in the liquid of the three-dimensional geometric model, mainly including three basic operations: initialization, query, and merging.

[0051] (1) Initialization operation

[0052] Assume there are n meshes in the model. In the initial state, each mesh is regarded as an independent set, that is, before any merging operation, the n meshes correspond to n sets. Use an array named parent to record the parent node relationship of each element. Assume there are n elements numbered from 1 to n. Initially, set parent[i] to i, indicating that the parent node of the i-th element is itself.

[0053] (2) Query operation

[0054] Starting from the given mesh x, continuously trace upward along the parent pointer until a node y is found such that parent[y] = y, that is, y is the parent node of itself and no longer points to other nodes. The node y is the root node of the set where x is located.

[0055] (3) Merging operation

[0056] Before performing the union operation, first call the find operation to separately confirm the root nodes of the sets where x and y are located. For example, let root_x be the root node of the set where x is located, and root_y be the root node of the set where y is located. If root_x = root_y, it means that these two grids are already in the same set and no additional operations are required; if root_x != root_y, it means that x and y come from two different sets and these two sets need to be merged. The union operation only needs to point the parent pointer of one set's root node to the other root node. Assuming that the root node root_y of the set where y is located is merged under the root node root_x of the set where x is located, just execute parent[root_y] = root_x.

[0057] In this way, it is obtained how many bubbles are contained in the flow field, the grids contained in each bubble, and the coordinates corresponding to each grid, that is, the coordinates of the bubble grids.

[0058] The efficient bubble search algorithm based on the union-find set proposed by the present invention realizes the rapid identification and tracking of bubbles by constructing a dynamic connectivity data structure. This method can efficiently search for adjacent bubble grids in a complex flow field and accurately determine the merging, splitting, and movement of bubbles. Compared with the traditional algorithms based on seed filling or two-pass scanning, the time complexity of this method is close to linear, and the solution efficiency is significantly improved in large-scale calculations.

[0059] C. Update of Bubble Coordinates

[0060] Establish a force model of the bubble, calculate the overall movement of the bubble, consider the combined action of various forces exerted on the bubble in the molten metal, calculate the displacements of the bubble in three directions at this time step, and according to Newton's second law, the overall movement of the bubble can be solved by the formula:

[0061]

[0062] Among them, F g is the gravitational force, F b is the buoyancy force, F d is the viscous force, F B is the Basset force, F A is the added mass force.

[0063] Then the coordinates L of the bubble numbered b are updated to:

[0064]

[0065] Among them, is the grid coordinate of the updated bubble b, L x , L y , L z is the grid coordinate of the bubble b before update, vx , v y , v z are the velocity components of the bubble grid in three directions, and Δt is the time step.

[0066] D. Update of filling rate, velocity value and pressure value

[0067] (1) Calculate the surface tension of each bubble

[0068] Calculate the morphological evolution of the bubbles, including the merging and splitting behavior of the bubbles and the volume change of the bubbles. By calculating the surface tension acting on the bubbles, the merging and splitting behavior of the bubbles can be judged. The surface tension is calculated according to the following formula:

[0069]

[0070] where σ is the surface tension coefficient, n is the surface normal, κ is the local surface curvature, ρ l is the liquid density, and ρ g is the gas density.

[0071] The local surface curvature can be calculated by the following formula:

[0072]

[0073] The key to the calculation of the surface tension lies in the calculation of the surface normal vector n. In the framework of the finite difference grid and the VOF method, the calculation of the surface normal vector n requires smoothing the gas-liquid interface. An interface reconstruction algorithm based on the least squares method is used to smooth the gas-liquid interface. The possible slope a x in the x direction of the grid interface is calculated by the following formula:

[0074]

[0075] where a x,b , a x,c , a x,f are the possible slopes in the x direction respectively, and α i+l,j+m,k+n (l = -1, 0, 1; m = -1, 0, 1; n = -1, 0, 1) is the grid filling rate around the grid of this interface. The calculation formulas of the possible slopes in the y and z directions can be written analogously to the x direction.

[0076] After calculating the possible interface slopes, in order to determine the position distribution of the molten metal at the interface, it is necessary to accurately judge the direction of the interface normal n. The direction of the interface normal directly determines the distribution relationship between the molten metal and the gas in the cell. Only when the direction of the interface normal is consistent with the actual filling situation can it be used as an effective basis for the next geometric reconstruction. The directions of the interface normal in the x, y, and z components can be judged by the following formula:

[0077]

[0078] Among them, For all possible interface conditions, the intercept l is calculated by using forced grid volume conservation. The cutting unit grid is continuously moved along the plane determined by the interface slope until the volume of the cut grid is equal to the volume of the liquid in the grid, so as to determine the position of the gas-liquid interface in the grid. The volume of the grid after interface cutting can be calculated by the following formula:

[0079]

[0080] Among them, n is the interface normal vector, n x , n y , n z represent the components of the interface normal vector in three directions, Δx is the grid side length, l max = n x Δx + n y Δx + n z Δx, f n (s) is defined as:

[0081]

[0082] The optimal interface slope is determined by calculating and minimizing the discrete error. The minimization of the discrete error can be calculated by the following formula:

[0083]

[0084] Among them, is the discrete error, is the grid filling rate under the interface cutting with slope a, and α i+l,j+m,k+n is the actual grid filling rate.

[0085] (2) Calculate the inertial force on the bubble

[0086] Calculate the inertial force on the bubble. For a point O on the bubble surface, a force analysis is carried out. The bubble surface is jointly affected by the surface tension Fs, the viscous force Fd, and the pressure difference Fp between the inside and outside of the bubble. Among them, the direction of the surface tension is parallel to the tangent direction of the bubble surface, the pressure is along the normal direction of the bubble surface, and the direction of the viscous force is related to the fluid velocity gradient and is parallel to the fluid flow direction. The resultant inertial force on the bubble is:

[0087] ∑F = F s - F p - F d

[0088] (3) When the surface tension is less than the inertial force, the bubble breaks. The filling rate of the broken bubble is 1, and the velocity and pressure of the bubble are obtained by interpolating the velocity and pressure of the surrounding liquid;

[0089] (4) Determine whether the unbroken bubbles collide with other bubbles

[0090] When the grid clusters of two bubbles collide during the filling process, the bubbles will merge to form a larger bubble cluster. To accurately identify and handle the merging phenomenon of bubbles, first number all the detected bubbles to ensure that the grid clusters of different bubbles can be effectively distinguished during the calculation process.

[0091] For the bubble numbered j, all the grids it contains are traversed in turn to judge the bitmap identifier of each grid cell. If the bitmap value of this grid is 0, it means that this grid has not been occupied by other bubbles. At this time, the bitmap of this grid needs to be updated to 1, and the volume information of this grid is calculated and recorded; if the bitmap value of this grid is already 1, it indicates that this grid has been occupied by another bubble, meaning that a collision has occurred here. Do not update the bitmap, calculate the volume of this grid and record it. After completing the grid detection of the current bubble, continue to process the next bubble j + 1 until all bubbles have been detected, and finally obtain the updated distribution of the bubble grid clusters.

[0092] Volume change of a single bubble

[0093] P0(t)Vgas0(t) = P1(t)Vgas1(t)

[0094] According to this equation, first calculate the volume Vgas0(t) and internal pressure P0(t) of the bubble. Considering the action of the external pressure, solve the internal pressure P1(t) of the bubble after movement. According to this equation, the volume of the bubble after movement can be calculated The volume change of the bubble can be obtained by the following formula:

[0095] ΔVgas = Vgas1(t) - Vgas0(t)

[0096] For the bubbles involving volume changes, in order to ensure the conservation of the liquid metal volume at the previous and subsequent time steps, the liquid volume at the original bubble location is redistributed to the liquid flow front, and the updated filling rate data of each grid is obtained;

[0097] 1) Assume that the volume filling rate of each grid at the previous time step is α n-1 , after advancing one time step, the volume filling rate at the current moment is α n , after calculating the movement and morphological changes of the bubbles, the liquid metal volume change caused by the bubble volume change is Δα n .

[0098] 2) Solve for Δα n

[0099] For the volume change of the molten metal caused by bubbles at each step length, it will ultimately be reflected on the molten metal flow interface, that is, this part of the molten metal needs to be distributed to the front of the molten metal flow, and finally meet the constraint conditions of overall mass conservation. To ensure that the total mass of the distributed molten metal matches Δα n A quadratic optimization problem regarding the filling rate of the interface grid is established. By introducing Lagrange multipliers, the constraint conditions are incorporated into the objective function. Let the filling rate assigned to each grid at the current moment be The goal is to minimize the following error:

[0100]

[0101] where is the initial filling rate of the grid, is the target filling rate of the grid, and the constraint conditions are:

[0102]

[0103] Combining the objective function and the constraint conditions, the Lagrangian function is constructed:

[0104]

[0105] where λ is the Lagrange multiplier used to handle the constraint conditions.

[0106] Taking the partial derivative of in and setting the result to zero, we get:

[0107]

[0108] Then we can find Substituting it into the equation for λ and factoring out the sum of , after rearrangement, we get:

[0109]

[0110] Then we can find λ, and substituting it into the partial derivative equation of we can calculate the change in the filling rate of each interface grid Finally, update the filling rate of the interface grid:

[0111]

[0112] where is the updated filling rate of the interface grid.

[0113] (5) The liquid allocated to the new position may overflow into the empty grid, introducing inaccurate velocity and pressure values. To ensure the correctness of the velocity and pressure values of the liquid in the previous and subsequent time steps, the velocity and pressure values of the redistributed grid M are corrected, and the corrected velocity field data and pressure field data are obtained.

[0114] For the grid filling rate α updated in step (4), if it indicates that the grid does not overflow and no operation is performed. If it indicates that the grid overflows, and the velocity and pressure values of the new grid need to be corrected.

[0115] Read the velocity values of the liquid grids around this grid, and correct the data of the new grid M using the linear interpolation method:

[0116]

[0117]

[0118] In the formula: V x , V y , V z are the velocity values of grid M in the x, y, and z directions respectively, V x+1 , V x-1 , V y+1 , V y-1 , V z+1 , V z-1 are the velocity values of the grids adjacent to grid M in the x, y, and z directions respectively, P is the pressure value of grid M, P x+1 , P x-1 , P y+1 , P y-1 , P z+1 , P z-1 are the pressure values of the grids adjacent to grid M respectively.

[0119] S3 Repeat step S2 until the filling process is completed;

[0120] Output the calculation results, including the filling rate α of each grid in the bubble, the velocity values V in three directions, the grid pressure value P, and the bubble coordinates L.

[0121] Those skilled in the art can easily understand that the above is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent replacements, and improvements made within the spirit and principles of the present invention shall be included within the protection scope of the present invention.

Claims

1. A rapid tracking and prediction method for the movement of entrained bubbles during the casting filling process, characterized in that, The method includes the following steps: (1) Meshing the three-dimensional geometric model of the casting filling process; (2) Calculating the filling rate, velocity, and pressure of each grid in the casting filling cavity at any moment i during the filling process; identifying the bubbles in the cavity and the grids contained in each bubble; updating the filling rate, velocity, and pressure of the grids in the bubble at any moment i in the following manner: Calculating the surface tension and inertial force of each bubble, judging whether the bubble breaks according to the magnitude relationship between the surface tension and the inertial force. For the broken bubble, the filling rate is 1, and the velocity and pressure of the grids in the broken bubble are updated using the velocity and pressure of the surrounding liquid; for the unbroken bubble, judging whether the bubbles collide. If there is no collision, the filling rate, velocity, and pressure of the bubble are not updated; For the colliding bubbles, calculating the filling rate of the grids in the bubble after the collision according to the volume change amount of the colliding bubbles, so as to realize the update of the filling rate; judging whether the updated filling rate is less than the preset threshold without liquid overflow. If there is no overflow, the velocity and pressure at the current moment are not updated. If there is overflow, updating the velocity and pressure of the grid at the current moment using the velocity and pressure of the adjacent grids; (3) i = i + 1, repeating step (2) until the update of the filling rate, velocity, and pressure of the grids in the bubble at all moments is completed, so as to realize the tracking and prediction of the bubble movement during the casting filling process.

2. The rapid tracking and prediction method for the movement of entrained bubbles during the casting filling process according to claim 1, characterized in that, The calculation formula of the surface tension is as follows: Among them, is the divergence operator, σ is the surface tension coefficient, n is the surface normal vector, κ is the local surface curvature, ρ l is the liquid density, ρ g is the gas density.

3. A rapid tracking and prediction method for the movement of entrained bubbles during the casting filling process according to claim 2, characterized in that, The local surface curvature is calculated in the following manner: wherein, is the discrete error, is the grid filling rate under the cut of the interface with a slope of a, α i+l,j+m,k+n is the actual grid filling rate.

4. A rapid tracking and prediction method for the movement of entrained bubbles during the casting filling process according to claim 1 or 3, characterized in that, The calculation formula of the inertial force is as follows: ∑F = F s -F p -F d Among them, F s is the surface tension on the bubble surface, F d is the viscous force on the bubble surface, F p is the pressure difference inside and outside the bubble.

5. A rapid tracking and prediction method for the movement of entrained bubbles during the casting filling process according to claim 1 or 3, characterized in that, Judging whether the bubble breaks is carried out in the following manner: when the surface tension is less than the inertial force, the bubble breaks, otherwise, the bubble does not break.

6. A rapid tracking and prediction method for the movement of entrained bubbles during the casting filling process according to claim 1 or 3, characterized in that, The update formula of the filling rate of the colliding bubbles is as follows: Among them, is the updated bubble grid filling rate, is the grid filling rate before update, is the calculated change in grid filling rate.

7. A rapid tracking and prediction method for the movement of entrained bubbles during the casting filling process according to claim 6, characterized in that The change amount of the filling rate of each grid The calculation formula is as follows: Among them, is the constructed Lagrangian function, is the initial filling rate of the grid, is the target filling rate of the grid, is the change in the grid filling rate, N is the number of grids, λ is the Lagrange multiplier, and Δα n is the sum of the changes in the filling rates of all grids.

8. A rapid tracking and prediction method for the movement of entrained bubbles during the casting filling process according to claim 1 or 3, characterized in that Updating the velocity and pressure of the grid at the current moment using the velocity and pressure of the adjacent grids is carried out according to the following formula: Among them, V x , V y , V z are the velocity values of the grid in the x, y, and z directions respectively. V x+1 , V x-1 , V y+1 , V y-1 , V z+1 , V z-1 are the velocity values of the grids adjacent to the grid in the x, y, and z directions respectively. P is the pressure value of the grid. P x+1 , P x-1 , P y+1 , P y-1 , P z+1 , P z-1 are the pressure values of the grids adjacent to the grid respectively.

9. A rapid tracking and prediction method for the movement of entrained bubbles during the casting filling process according to claim 1, characterized in that, Identifying the bubbles in the cavity and the grids contained in each bubble adopts the air entrainment search method; The coordinates L of the bubble numbered b at any moment are updated according to the following formula: Among them, is the grid coordinate of the updated bubble b, L x , L y , L z is the grid coordinate of the bubble b before update, v x , v y , v z are the velocity components of the bubble grid in three directions, and Δt is the time step.

10. A rapid tracking and prediction system for the movement of entrained bubbles during the casting filling process, characterized in that, The system includes an actuator, which is used to execute a method for rapid tracking and prediction of the movement of the entrained bubbles during the casting filling process according to any one of claims 1-9.

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