Casting mold-filling multiphase flow field determination method and equipment based on unstructured grid, medium and product

Abstract

The invention discloses a casting mold-filling multiphase flow field determination method and device based on an unstructured grid, a medium and a product, and relates to the field of casting flow field determination, and the method comprises the following steps: establishing a mathematical model and a geometric model of a target casting mold-filling process; dividing the geometric model into unstructured grids, storing coordinates of all vertexes, calculating geometric information of grid units of the unstructured grids, discretizing the interface capture model, the fluid domain heat transfer control model and the multiphase flow model, and solving the discretized interface capture model by using a flux correction transmission algorithm to obtain a multi-phase flow model. The method comprises the following steps: dispersing a fluid domain heat transfer control model to obtain a volume fraction field of molten metal, solving the dispersed fluid domain heat transfer control model by using a linear algebraic solver to obtain a temperature field of the molten metal and air, and solving a dispersed multiphase flow model by using a pressure implicit operator splitting algorithm to obtain a velocity field and a pressure field of the molten metal. According to the method, the geometric model is fitted by adopting the unstructured grid, so that the calculation precision of the flow field is improved.

Description

Technical Field

[0001] The present application relates to the field of casting flow field determination, and in particular to a method, device, medium and product for determining a casting filling multiphase flow field based on an unstructured grid. Background Art

[0002] As casting structures become increasingly complex, the accuracy of solving casting flow fields depends, to a certain extent, on the choice of mathematical model and the accuracy of the mesh fit to the casting geometry. The filling process in most casting processes is a multiphase flow problem. In addition to the typical gas-liquid phase, it also involves solid-liquid phase transitions and the obstruction of the solidified metal phase relative to the unsolidified metal phase. Currently, most commercial casting simulation software only calculates the liquid phase during the filling process and cannot directly simulate air entrapment defects. Furthermore, their flow field calculations often use structured meshes fitted to the geometric model, which reduces the accuracy of the flow field solution. Summary of the Invention

[0003] The purpose of this application is to provide a method, equipment, medium and product for determining the multiphase flow field of casting filling based on unstructured grids, so as to improve the solution accuracy of the multiphase flow field of casting filling.

[0004] To achieve the above objectives, this application provides the following solutions:

[0005] In a first aspect, the present application provides a method for determining a casting filling multiphase flow field based on an unstructured grid, comprising:

[0006] Establishing a mathematical model and a geometric model of the target casting filling process; the mathematical model includes an interface capture model, a fluid domain heat transfer control model, and a multiphase flow model;

[0007] Dividing the geometric model into unstructured grids and storing all vertex coordinates and grid topological relationships;

[0008] Calculating geometric information of a grid cell of the unstructured grid based on all the vertex coordinates; the geometric information includes a grid cell volume, an area of ​​a grid cell face, and a face normal;

[0009] Based on the geometric information, the interface capture model, the fluid domain heat transfer control model, and the multiphase flow model are discretized to obtain a discretized interface capture model, a discretized fluid domain heat transfer control model, and a discretized multiphase flow model;

[0010] Solving the discretized interface capture model using a flux-corrected transport algorithm to obtain a volume fraction field of the molten metal during the target casting filling process;

[0011] Based on the volume fraction field, a linear algebra solver is used to solve the discretized fluid domain heat transfer control model to obtain the temperature fields of the molten metal and the air during the target casting filling process;

[0012] Based on the temperature fields of the molten metal and air, the discretized multiphase flow model is solved using a pressure implicit operator splitting algorithm to obtain the velocity field and pressure field of the molten metal during the target casting filling process.

[0013] Optionally, the process of establishing the interface capture model specifically includes:

[0014] Based on the volume fraction method, an artificial compression convection term is added to establish the interface capture model; the interface capture model is:

[0015]

[0016] Where α is the volume fraction field of the liquid metal in any grid unit; t is time; U is the velocity of the liquid metal and air; is the artificial compression convection term; c1 is the compression factor.

[0017] Optionally, the process of establishing the fluid domain heat transfer control model specifically includes:

[0018] Based on the law of energy conservation in the target casting filling process, the fluid domain heat transfer control model is established; the fluid domain heat transfer control model is:

[0019]

[0020] Where T is the temperature of the molten metal and air; t is time; U is the velocity of the molten metal and air; ρ is the local average density of the molten metal and air; λ is the local average thermal conductivity of the molten metal and air; c2 is the local average specific heat capacity of the molten metal and air; S T is the heat source term.

[0021] Optionally, the process of establishing the multiphase flow model specifically includes:

[0022] Based on the law of conservation of mass and momentum, combined with the surface tension of the gas-liquid interface during the casting filling process and the obstruction of the solidified metal liquid to the movement of the unsolidified metal liquid, the multiphase flow model is established; the multiphase flow model is:

[0023]

[0024] Where ρ is the local average density of the liquid metal and air; U is the velocity of the liquid metal and air; t is time; μ is the local average dynamic viscosity; p is the fluid pressure; S is the source term; U pull is the casting speed in the continuous casting process; fs is the current solid phase ratio in the molten metal paste zone; S up is the critical solid fraction.

[0025] Optionally, based on the volume fraction field, a linear algebra solver is used to solve the discretized fluid domain heat transfer control model to obtain the temperature fields of the molten metal and the air during the target casting filling process, specifically including:

[0026] According to the volume fraction field, locally averaging the physical property parameters in the discretized fluid domain heat transfer control model to obtain the local average density of the molten metal and the air, the local average thermal conductivity of the molten metal and the air, and the local average specific heat capacity of the molten metal and the air;

[0027] Based on the local average density of the molten metal and air, the local average thermal conductivity of the molten metal and air, and the local average specific heat capacity of the molten metal and air, a linear algebra solver is used to solve the discretized fluid domain heat transfer control model to obtain the temperature field of the molten metal and air during the target casting filling process.

[0028] Optionally, based on the temperature fields of the molten metal and air, a pressure implicit operator splitting algorithm is used to solve the discretized multiphase flow model to obtain the velocity field and pressure field of the molten metal during the target casting filling process, specifically including:

[0029] Calculate the current solid phase ratio in the molten metal mushy zone based on the temperature fields of the molten metal and air;

[0030] updating the local average dynamic viscosity and the drag coefficient of the molten metal in the discretized multiphase flow model according to the current solid phase ratio of the molten metal mushy region to obtain an updated multiphase flow model;

[0031] The updated multiphase flow model is solved using a pressure implicit operator splitting algorithm to obtain the velocity field and pressure field of the molten metal during the target casting filling process.

[0032] Optionally, the current solid phase ratio of the molten metal mushy zone is calculated based on the temperature fields of the molten metal and the air, specifically including:

[0033] Using formula f S =α(TT S ) / (T L -T S ) calculates the current solid phase ratio of the molten metal paste zone; where f s is the current solid phase ratio of the molten metal in the mushy zone; α is the volume fraction field of the molten metal in any grid unit; T is the temperature of the molten metal and air; T S is the solidus temperature of the molten metal; T L is the liquidus temperature of the molten metal.

[0034] In a second aspect, the present application provides 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 implement any one of the above-described methods for determining a multiphase flow field in a casting mold based on an unstructured grid.

[0035] In a third aspect, the present application provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements any of the above-mentioned methods for determining a casting filling multiphase flow field based on an unstructured grid.

[0036] In a fourth aspect, the present application provides a computer program product, comprising a computer program, which, when executed by a processor, implements any of the above-mentioned methods for determining a casting filling multiphase flow field based on an unstructured grid.

[0037] According to the specific embodiments provided in this application, this application has the following technical effects:

[0038] The present application provides a method, equipment, medium and product for determining the multiphase flow field of casting filling based on unstructured grids, and establishes a mathematical model and a geometric model of the target casting filling process; the mathematical model includes an interface capture model, a fluid domain heat transfer control model and a multiphase flow model; the geometric model is divided into an unstructured grid, and all vertex coordinates and grid topological relationships are stored; based on all vertex coordinates, the geometric information of the grid cells of the unstructured grid is calculated, and the interface capture model, the fluid domain heat transfer control model and the multiphase flow model are discretized to obtain the discretized interface capture model, the discretized fluid domain heat transfer control model and the discretized multiphase flow model; the discretized interface capture model is solved by a flux correction transmission algorithm to obtain the volume fraction field of the molten metal in the target casting filling process, the discretized fluid domain heat transfer control model is solved by a linear algebra solver to obtain the temperature field of the molten metal and the air in the target casting filling process, and the discretized multiphase flow model is solved by a pressure implicit operator splitting algorithm to obtain the velocity field and pressure field of the molten metal in the target casting filling process. This application uses an unstructured grid fitting geometric model to calculate the multiphase flow field of the target casting filling process, thereby improving the calculation accuracy of the flow field. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0040] Figure 1 A schematic flow chart of a method for determining a multiphase flow field in a casting mold filling process based on an unstructured grid according to an embodiment of the present application;

[0041] Figure 2 This is a flow chart of the numerical solution of the casting filling process in this embodiment;

[0042] Figure 3 Schematic diagram for calculating the area of ​​the grid cell surface;

[0043] Figure 4 Schematic diagram for grid cell volume calculation;

[0044] Figure 5 Schematic diagram of linear interpolation (central difference);

[0045] Figure 6 Schematic diagram of surface normal gradient calculation based on orthogonal grid;

[0046] Figure 7 Schematic diagram of surface normal gradient calculation based on non-orthogonal super-relaxation correction;

[0047] Figure 8 is a schematic diagram of the reverse diffusion flux;

[0048] Figure 9 Flowchart for solving the momentum conservation equation and continuity equation using the PISO algorithm;

[0049] Figure 10 A schematic diagram of the structure of a computer device provided in one embodiment of the present application. DETAILED DESCRIPTION

[0050] The following will be combined with the drawings in the embodiments of this application to clearly and completely describe the technical solutions in the embodiments of this application. Obviously, the embodiments described are only part of the embodiments of this application, not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of this application.

[0051] In order to make the above-mentioned purposes, features and advantages of the present application more obvious and easy to understand, the present application is further described in detail below with reference to the accompanying drawings and specific implementation methods.

[0052] In an exemplary embodiment, Figure 1 As shown, a method for determining a casting filling multiphase flow field based on an unstructured grid is provided, comprising the following steps:

[0053] S1: Establishing a mathematical model and a geometric model of the target casting filling process; the mathematical model includes an interface capture model, a fluid domain heat transfer control model, and a multiphase flow model.

[0054] like Figure 2 As shown in the figure, the numerical solution process is to analyze the problem to obtain the mathematical model and boundary conditions of the problem, then mesh the geometric model and store the mesh results, and then discretize the governing equations on the mesh. Different mesh formats will affect the specific discretization process, but have no effect on the determination of the mathematical model. After the equations are discretized, they are solved.

[0055] As an optional implementation method, the process of establishing the interface capture model specifically includes:

[0056] The interface capture model is established by adding an artificial compression convection term based on the VOF (Volume of Fluid) method; the interface capture model is:

[0057]

[0058] Where α is the volume fraction of the molten metal in any grid cell, α = 1 means that the grid cell is completely occupied by the molten metal, α = 0 means that the grid cell is completely occupied by air, and α = 0 to 1 means that the grid cell is a gas-liquid interface; t is time; U is the velocity of the molten metal and air; is the artificial compression convection term; c1 represents the compression factor, and the maximum value of c1 is 1.

[0059] The interface capture model established using the VOF method is solved to obtain α, which is the volume fraction field of the molten metal.

[0060] After the interface capture model is solved and the results are obtained, the results of the interface capture model are used to perform local averaging on the parameters in the heat transfer equation (fluid domain heat transfer control model).

[0061] As an optional implementation method, the process of establishing the fluid domain heat transfer control model specifically includes:

[0062] Based on the law of energy conservation in the target casting filling process, the fluid domain heat transfer control model is established; the fluid domain heat transfer control model is:

[0063]

[0064] Where T is the temperature of the molten metal and air, in °C; ρ is the local average density of the molten metal and air, in kg / m 3;λ is the local average thermal conductivity of the metal liquid and air, in W / m / K; c2 is the local average specific heat capacity of the metal liquid and air, in J / kg / K; S T is the heat source term. ρ, λ, and c2 are locally averaged using α obtained by the VOF method / interface capture model, as shown in Equations (3), (4), and (5).

[0065] λ=αλ l +(1-α)λ g (3)

[0066] ρ=αρ l +(1-α)ρ g (4)

[0067] c2=αc l +(1-α)c g (5)

[0068] Wherein, the subscripts l and g represent the metal liquid phase and the air phase respectively, λ l is the thermal conductivity of the molten metal, λ g is the thermal conductivity of air, ρ l is the density of the molten metal, ρ g is the density of air, c l is the specific heat capacity of the molten metal, c g is the specific heat capacity of air.

[0069] During the flow of molten metal, solidification will occur and latent heat will be released. The equivalent specific heat method and temperature rise method are used to deal with the latent heat release. Before solving the heat transfer equation, the equivalent specific heat method is used to correct the specific heat capacity c of the molten metal. l The latent heat of crystallization is converted into specific heat capacity and added to the actual specific heat of the molten metal to obtain the equivalent specific heat capacity of the molten metal. The calculation method is shown in formula (6).

[0070]

[0071] Among them, c el Indicates the equivalent specific heat capacity of the molten metal, in J / kg / K; T L Indicates the liquidus temperature of the molten metal (solidification begins when the actual temperature of the molten metal is lower than the liquidus temperature), in °C; T S It represents the solidus temperature of the molten metal (the molten metal is completely solidified when its actual temperature is lower than the solidus temperature), and its unit is ℃; L represents the latent heat of the alloy, and its unit is J / kg.

[0072] The temperature recovery method is used to solve the heat transfer equation. After obtaining the temperatures of the molten metal and the air, the temperature of the molten metal will be corrected. The processing can be summarized into the following six situations:

[0073] (1)T n >T L Cool down to T S ≤T n+1 ≤T L The temperature value obtained after calibration is:

[0074]

[0075] Among them, T n Indicates the temperature of the previous time step, in °C; T n+1 Indicates the temperature of the current time step, in °C; The temperature is obtained after correction, in °C.

[0076] (2)T S ≤T n ≤T L Cool down to T n+1 <T S The temperature value obtained after calibration is:

[0077]

[0078] (3)T n >T L Cool down to T n+1 <T S The temperature value obtained after calibration is:

[0079]

[0080] if A second calibration is required, and the temperature value obtained after two calibrations is

[0081]

[0082] in, The temperature is obtained by correcting twice, and the unit is ℃.

[0083] (4)T n <T S Heating to T S ≤T n+1 ≤T L The temperature value obtained after calibration is:

[0084]

[0085] (5)T S ≤T n ≤T L Heating to T n+1 >T L The temperature value obtained after calibration is:

[0086]

[0087] (6)T n <T S Heating to T n+1 >T L The temperature value obtained after calibration is:

[0088]

[0089] if A second calibration is required. The temperature values ​​obtained after two calibrations are:

[0090]

[0091] Finally, the correct temperature T of the molten metal and air can be obtained after correction by the temperature recovery method.

[0092] The solidification ratio of the molten metal (solid phase ratio of the molten metal) is calculated based on the temperature T of the molten metal and the air. The calculation method is shown in formula (15).

[0093] f S =α(TT S ) / (T L -T S )(15)

[0094] f S is the solidification ratio of the metal phase in the grid unit (the current solid phase ratio of the molten metal paste area), 1 means complete solidification, 0 means no solidification, T S Is the solidus temperature of the molten metal. Below this temperature, the molten metal will completely solidify. L It is the liquidus temperature of the molten metal, below which the molten metal begins to solidify.

[0095] Based on the solid phase fraction f S Considering the obstruction of the solidified molten metal to the movement of the unsolidified molten metal, there are three cases:

[0096] Case (1): When the solid phase ratio is low, the viscosity of the molten metal increases. The equivalent viscosity of the molten metal is calculated as shown in formula (16).

[0097]

[0098] Where μ el Indicates the equivalent dynamic viscosity of the molten metal, Pa·s; μ l is the initially defined dynamic viscosity of the molten metal, Pa·s; S up It represents the critical solid fraction from case (2) to case (3).

[0099] Case (2): When the solid fraction level is medium, calculate the equivalent viscosity of the molten metal and the drag coefficient of the solidified molten metal on the unsolidified molten metal.

[0100]

[0101] Where S down represents the critical solid fraction from case (1) to case (2); F φ Indicates the resistance coefficient of solidified molten metal to unsolidified molten metal; D drag Indicates a user-defined constant, s -1 , used to characterize the magnitude of resistance.

[0102] Case (3): When the solid phase fraction is high, the molten metal is almost completely solidified and stops flowing. At this time, the velocity of the molten metal is calculated as shown in formula (19).

[0103] U el =U pull (19)

[0104] Where U el Indicates the velocity of solidified molten metal in m / s; U pull It indicates the casting speed in continuous casting process, in m / s. For other casting processes, its value is 0.

[0105] As an optional implementation method, the process of establishing the multiphase flow model specifically includes:

[0106] Based on the laws of conservation of mass and momentum, combined with the surface tension of the gas-liquid interface during the casting filling process and the obstruction of the solidified molten metal on the movement of the unsolidified molten metal, the multiphase flow model (also known as the continuity equation and the momentum conservation equation, which together constitute the multiphase flow model) is established; the multiphase flow model is:

[0107]

[0108] Where μ is the local average dynamic viscosity, μ = αμ l +(1-α)μ g , unit is Pa·s; p is the fluid pressure, unit is Pa; S is the source term, as shown in formula (22).

[0109]

[0110] Where g is the acceleration due to gravity, in m / s 2 ; σ is the surface tension coefficient between the metal liquid and the air; κ is the interface curvature between the metal liquid and the air; D drag It is a user-defined coefficient that represents the resistance of the solidified molten metal to the unsolidified molten metal.

[0111] S2: Divide the geometric model into an unstructured mesh and store all vertex coordinates and mesh topology relationships. In practical applications, commercial software such as HyperMesh and Fluent Meshing is used to divide the geometric model into an unstructured mesh and store all vertex coordinates and mesh topology relationships.

[0112] S3: Calculating geometric information of the mesh cells of the unstructured mesh based on all the vertex coordinates; the geometric information includes mesh cell volume, mesh cell surface area, and surface normal.

[0113] In practical applications, the geometric information of the mesh cells (mesh cell volume, mesh cell surface area and surface normal, etc.) is calculated based on the mesh vertex coordinates.

[0114] (1) The area of ​​the grid cell surface.

[0115] For any polygon (i.e., mesh unit face), connect the non-adjacent vertices in the polygon, divide the polygon into multiple triangles, calculate the area of ​​each triangle and sum them up to get the area of ​​the polygon. The area of ​​the triangle is obtained by the result of vector cross product, such as Figure 3 As shown, for triangle No. 1, the area is calculated as:

[0116] S1=|(A2-A1)×(A3-A1) / |2 (23)

[0117] Among them, A1, A2, and A3 are the vertices of the grid unit surface, and S1 is the area of ​​triangle No. 1.

[0118] (2) Face normal.

[0119] The normal vector of the polygon is consistent with the normal vector of the decomposed triangle, so the face normal n can also be obtained by cross product:

[0120] n=(A2-A1)×(A3-A1) / |(A2-A1)×(A3-A1)| (24)

[0121] (3) Grid cell volume.

[0122] For any polyhedron, it can be decomposed into pyramids with polygonal bases, such as Figure 4 As shown, the volume of the polyhedron can be obtained by calculating the volume of each pyramid and summing them up. The volume of the pyramid is obtained by the result of the vector dot product:

[0123] V=(A2-A1)·S f / 3(25)

[0124] Among them, S f is the base area of ​​the pyramid.

[0125] S4: Based on the geometric information, the interface capture model, the fluid domain heat transfer control model and the multiphase flow model are discretized to obtain a discretized interface capture model, a discretized fluid domain heat transfer control model and a discretized multiphase flow model.

[0126] In practical applications, each item in the three mathematical models is discretized, and the geometric information of the grid cells is required in the discretization process.

[0127] Specifically, the transient term, convection term, diffusion term and source term in the three mathematical models are discretized.

[0128] (1) Transient term.

[0129] The transient term is discretized using first-order Euler backwards, and the discretization result is:

[0130]

[0131] Where φ is an arbitrary physical quantity; n+1 represents the new time step, n represents the current time step, Δt is the time step length, subscript C represents the current grid unit, V C Represents the volume of the current grid cell.

[0132] (2) Convection term.

[0133] For convex polyhedrons (tetrahedron, cube, cuboid, etc.), the surfaces of the control volume are planes, and the convection term is discretized using Gauss's theorem:

[0134]

[0135] Where v is an arbitrary vector; s is an arbitrary scalar; the subscript f represents the value at the center of the grid, φ f is the value of any physical quantity at the center of the control volume; U f is the value of the velocity at the center of the control body; S f is the surface normal of the control volume.

[0136] Since the physical quantities are stored at the center of the grid, φ f Through the surface S f It is represented by the body center value of the main grid cell and the adjacent grid cell, such as Figure 5 As shown, in the linear interpolation (central difference, CD) format, φ f It can be expressed as formula (30).

[0137] φ f =g f φ C +(1-g f )φ N (30)

[0138] Where, φ C is the physical quantity of the current grid cell; φ N is the physical quantity of the adjacent grid unit; g f is the surface coefficient calculated by linear interpolation format, which is calculated as follows:

[0139]

[0140] Among them, d Cf is the distance vector from the center of the current grid cell to the center of the surface; n f is the unit normal vector of the surface; d fN is the distance vector from the center of the face to the center of the neighboring grid cell.

[0141] g calculated by different discrete formats f Different, if the first-order upwind format is used for calculation, then g f The expression is:

[0142]

[0143] Where, F f is the velocity flux at the center of the surface, which is calculated as shown in formula (33):

[0144] F f =U f ·S f (33)

[0145] Similarly, for other discrete formats, the final φ f The expressions are all in the form of formula (30), so the final discrete format of the convection term is:

[0146]

[0147] (3) Diffusion term.

[0148] Using Gauss's theorem to discretize the diffusion term, we can obtain:

[0149]

[0150] Where, Γ is the diffusion coefficient; f is the value of the diffusion coefficient at the center of the surface; Represents the face normal gradient at the face center.

[0151] for Figure 6 The orthogonal grid shown, It can be calculated according to formula (36).

[0152]

[0153] Among them, d CN is the distance vector from the center of the current grid cell to the center of the adjacent grid cell.

[0154] However, as the non-orthogonality of the grid increases, the calculation of the surface normal gradient requires non-orthogonality correction, such as Figure 7 As shown, in order to improve the convergence of the discrete matrix, this embodiment adopts the non-orthogonal super-relaxation method to correct it. The non-orthogonal part t in the super-relaxation method f Perpendicular to the surface normal, then n f , t f and e f The relationship between the three is as follows:

[0155]

[0156] Among them, e f with d CN Same direction.

[0157] At this time, the surface normal gradient at the surface center is calculated as:

[0158]

[0159] Therefore, the final discretization format of the diffusion term is:

[0160]

[0161] Where, Use the physical quantity φ of the current time step n Construct and interpolate to the face center, The calculated result of is added as the source term to the right side of the final linear equation system.

[0162] (4) Source term.

[0163] The source term is known and can be discretized directly.

[0164] ∫ V S φ dV≈S φ V C (40)

[0165] Arranging equations (26), (34), (39) and (40) yields the final discrete form:

[0166]

[0167] Where, subscript C represents the current grid cell, subscript N represents the adjacent grid cell, and A C is the diagonal coefficient of the linear equation system; A N are the off-diagonal coefficients of the linear equations; B is the right-hand side term of the linear equations.

[0168] The purpose of discretization is to convert the partial differential form equations that cannot be solved directly into a solvable linear equation system. The linear equation system is used to solve the unknown quantity φ, similar to a quadratic equation.

[0169] S5: Solving the discretized interface capture model using a flux correction transmission algorithm to obtain the volume fraction field of the molten metal during the target casting filling process.

[0170] In practical applications, the FCT (Flux-Corrected Transport) algorithm is used to solve the discretized interface capture model to obtain the volume fraction field α of the molten metal.

[0171] Specifically, in the simulation of the casting filling process, the calculation of the volume fraction field needs to maintain two conditions: high precision and strict boundedness. For this reason, this embodiment applies the FCT method to solve the interface capture model.

[0172] When the artificial compression term and the right-hand side term in Equation (1) are not considered, the VOF equation (interface capture model) can be discretized into the form of Equation (42).

[0173]

[0174] Where, F f =α f U f ·S f The core idea of ​​the FCT method is to calculate the flux F f The basic process of processing is as follows:

[0175] Step 1: Calculate the flux using a low-order interpolation scheme Low-order interpolation formats are more stable and will not produce unphysical results, but they have large numerical spread.

[0176] Step 2: Calculate the flux using a high-order interpolation scheme Higher-order interpolation formats are more accurate but can produce unphysical overshoot or undershoot.

[0177] Step 3: Prediction step,

[0178] Step 4: Define the anti-diffusion flux

[0179] Step 5: Correction Among them C f Indicates the limit correction coefficient, 0<C f <1; A f is the back diffusion flux on the surface.

[0180] Cf The determination of depends on the inflow and reverse diffusion flux P on the grid cell + and the outflow counterdiffusion flux P - .like Figure 8 As shown, the reverse diffusion flux A on surface f f Flowing from grid unit 1 to grid unit 2, at this time A f The outflow counter-diffusion flux for grid cell 1 is generated Contribution, inflow anti-diffusion flux to grid cell 2 Taking grid cell 1 as the research object, after counting all its inflow / outflow anti-diffusion fluxes, the inflow / outflow restriction correction coefficient of grid cell 1 can be calculated according to formula (43).

[0181]

[0182] Where, and They represent the inflow restriction correction factor and the outflow restriction correction factor respectively, and represents the maximum inflow / outflow anti-diffusion flux. The FCT algorithm will and It is defined as the form of formula (44).

[0183]

[0184] Where, and are the maximum and minimum values ​​of α in all neighboring grid cells of grid cell 1 at the current moment, is the predicted step value of grid unit 1.

[0185] Similarly, the inflow / outflow restriction correction coefficient of grid unit 2 can be obtained: and Due to the back diffusion flux A on the surface f f Flow from grid unit 1 to grid unit 2, so the correction coefficient C is limited on surface f f To be less than or equal to and greater than or equal to At this time C f The final expression of is shown in formula (45).

[0186]

[0187] For the VOF equation shown in formula (1), this embodiment first uses the first-order upwind formula to calculate the predicted volume fraction field α * , then based on the current volume fraction field α n Constructing high-order surface flux fields using the Van Leer scheme and in Based on the integration of artificial compression items, the final Finally, calculate the limit correction coefficient of all surfaces to α * The correction is made, and the solution of the VOF equation is completed.

[0188] S6: Based on the volume fraction field, a linear algebra solver is used to solve the discretized fluid domain heat transfer control model to obtain the temperature fields of the molten metal and the air during the target casting filling process.

[0189] As an optional implementation, S6 specifically includes:

[0190] S61: Based on the volume fraction field, locally average the physical property parameters in the discretized fluid domain heat transfer control model to obtain the local average density of the molten metal and the air, the local average thermal conductivity of the molten metal and the air, and the local average specific heat capacity of the molten metal and the air.

[0191] S62: Based on the local average density of the molten metal and the air, the local average thermal conductivity of the molten metal and the air, and the local average specific heat capacity of the molten metal and the air, a linear algebra solver is used to solve the discretized fluid domain heat transfer control model to obtain the temperature field of the molten metal and the air during the target casting filling process.

[0192] In practical applications, the volume fraction field α of the molten metal obtained by solving the VOF equation is used to locally average the physical parameters in the heat transfer equation, and the temperatures of the molten metal and air are obtained by solving the discretized heat transfer equation.

[0193] Specifically, a linear equation system Ax=b is obtained by discretization, which can be solved using a linear algebra solver without any processing such as interface capture model and multiphase flow model.

[0194] S7: Based on the temperature fields of the molten metal and the air, the discretized multiphase flow model is solved using a pressure implicit operator splitting algorithm to obtain the velocity field and pressure field of the molten metal during the target casting filling process.

[0195] As an optional implementation, S7 specifically includes:

[0196] S71: Calculate the current solid phase ratio in the molten metal mushy zone based on the temperature fields of the molten metal and air, specifically including:

[0197] Using formula f S =α(TT S ) / (T L -T S ) calculates the current solid phase ratio of the molten metal paste zone; where f sis the current solid phase ratio of the molten metal in the mushy zone; α is the volume fraction field of the molten metal in any grid unit; T is the temperature of the molten metal and air; T S is the solidus temperature of the molten metal; T L is the liquidus temperature of the molten metal.

[0198] S72: updating the local average dynamic viscosity and the drag coefficient of the molten metal in the discretized multiphase flow model according to the current solid phase ratio of the molten metal mushy region to obtain an updated multiphase flow model.

[0199] S73: Solve the updated multiphase flow model using a pressure implicit operator splitting algorithm to obtain the velocity field and pressure field of the molten metal during the target casting filling process.

[0200] In practical applications, after solving the heat transfer equation to obtain the temperature field, the solid phase fraction of the liquid metal is calculated and the viscosity and resistance coefficient of the liquid metal in the multiphase flow model are updated based on the solid phase fraction. The PISO (Pressure-Implicit with Splitting of Operators) algorithm is used to solve the multiphase flow model to obtain the velocity field distribution and pressure field distribution of the geometric model. The velocity field distribution will affect the solution of the VOF equation at the next moment.

[0201] In the discretization process of the momentum conservation equation shown in Equation (21), the pressure gradient term can be discretized according to Equation (28). In addition, in order to ensure the accuracy of the solution, the convection term is discretized using a second-order upwind scheme. At this time, the interpolation calculation of the velocity at the center of the surface is shown in Equation (46).

[0202]

[0203] Where, Represents the gradient of the velocity at the center of the current grid cell, which can be obtained by using the known velocity field U at the current moment n Calculated, d Cf represents the distance vector from the center of the face to the center of the grid cell, The result of is added to the right-hand side of the discretized equations in the form of a source term.

[0204] Therefore, this application uses the PISO algorithm to solve the momentum conservation equation. The specific steps are as follows:

[0205] (1) Prediction step.

[0206] Initially, according to the pressure field p of the current time step n Solve the discrete equation of the momentum conservation equation to obtain the predicted velocity field U * , as shown in formula (47):

[0207]

[0208] (2) Correction step.

[0209] According to the predicted velocity field U * Construct equation (48).

[0210]

[0211] in, U′ C and p′ f is the correction amount, and by shifting the terms in equation (48), we can get:

[0212]

[0213] Substituting Equation (49) into the continuity equation can form the pressure Poisson equation shown in Equation (50).

[0214]

[0215] After solving equation (50) discretely, we can get p * , p * Substituting back into equation (49) we can obtain the equation that satisfies the continuity equation However, since Equation (48) ignores the influence of neighboring grid cells, the velocity correction value U′ of the neighboring grid is not considered. N , With p * does not strictly satisfy the momentum equation, so we use Reorganize the formula (50), refer to the H in the formula (50) here ** And solving the pressure Poisson equation can get the new pressure field p ** , and then according to formula (49) we get the new velocity field After a finite number of corrections at the current time step, the final and p n+1 The whole algorithm process is as follows Figure 9 shown.

[0216] After solving the multiphase flow model (continuity equation and momentum conservation equation), the velocity field and pressure field of the metal liquid and air can be obtained. The velocity field is used to substitute into the VOF equation at the next moment to solve the metal liquid integral fraction field α at the new moment. Then, the VOF equation, heat transfer equation and multiphase flow model are repeatedly solved until the set termination condition is reached.

[0217] In an exemplary embodiment, a computer device is provided, including a memory and a processor. The memory stores a computer program, and the processor implements the above-mentioned method for determining the casting filling multiphase flow field based on unstructured grid when executing the computer program.

[0218] In an exemplary embodiment, a computer-readable storage medium is provided, storing a computer program, which, when executed by a processor, implements the above-mentioned method for determining a casting filling multiphase flow field based on an unstructured grid.

[0219] In an exemplary embodiment, a computer program product is provided, including a computer program. When the computer program is executed by a processor, the computer program implements the above-mentioned method for determining a casting filling multiphase flow field based on an unstructured grid.

[0220] In an exemplary embodiment, a computer device is provided. The computer device may be a server or a terminal. The internal structure diagram thereof may be as follows: Figure 10 As shown. The computer device includes a processor, a memory, an input / output interface (Input / Output, abbreviated as I / O) and a communication interface. The processor, the memory and the input / output interface are connected through a system bus, and the communication interface is connected to the system bus through the input / output interface. The processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system, a computer program and a database. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The input / output interface of the computer device is used to exchange information between the processor and an external device. The communication interface of the computer device is used to communicate with an external terminal through a network connection. When the computer program is executed by the processor, a method for determining a casting filling multiphase flow field based on an unstructured grid is implemented.

[0221] Those skilled in the art will understand that Figure 10 The structure shown in the figure is only a block diagram of a part of the structure related to the solution of the present application, and does not constitute a limitation on the computer device to which the solution of the present application is applied. The specific computer device may include more or fewer components than shown in the figure, or combine certain components, or have a different component arrangement.

[0222] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, stored data, displayed data, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of relevant data must comply with relevant regulations.

[0223] Those skilled in the art will appreciate that all or part of the processes in the above-mentioned embodiment methods can be implemented by instructing the relevant hardware through a computer program, and the computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to memory, database or other media used in the embodiments provided in this application may include at least one of non-volatile and volatile memory. Non-volatile memory may include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory may include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM may be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM).

[0224] The databases involved in the various embodiments provided herein may include at least one of a relational database and a non-relational database. Non-relational databases may include, but are not limited to, distributed databases based on blockchains. The processors involved in the various embodiments provided herein may include, but are not limited to, general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic units, data processing logic units based on quantum computing, and the like.

[0225] The technical features of the above embodiments can be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0226] This document uses specific examples to illustrate the principles and implementation methods of this application. The description of the above examples is only intended to help understand the method and core concept of this application. At the same time, for those skilled in the art, based on the concept of this application, there may be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting this application.

Claims

1. A method for determining the multiphase flow field in casting filling based on unstructured grids, characterized in that: include: Establish mathematical and geometric models of target casting filling process; The mathematical model includes an interface capture model, a fluid domain heat transfer control model and a multiphase flow model; Dividing the geometric model into unstructured grids and storing all vertex coordinates and grid topological relationships; Calculating geometric information of a grid cell of the unstructured grid based on all the vertex coordinates; The geometric information includes the volume of the grid cell, the area of ​​the grid cell face and the face normal; Based on the geometric information, the interface capture model, the fluid domain heat transfer control model, and the multiphase flow model are discretized to obtain a discretized interface capture model, a discretized fluid domain heat transfer control model, and a discretized multiphase flow model; Solving the discretized interface capture model using a flux-corrected transport algorithm to obtain a volume fraction field of the molten metal during the target casting filling process; Based on the volume fraction field, a linear algebra solver is used to solve the discretized fluid domain heat transfer control model to obtain the temperature fields of the molten metal and the air during the target casting filling process; Based on the temperature fields of the molten metal and air, the discretized multiphase flow model is solved using a pressure implicit operator splitting algorithm to obtain the velocity field and pressure field of the molten metal during the target casting filling process.

2. The method for determining the casting filling multiphase flow field based on unstructured grid according to claim 1, characterized in that: The process of establishing the interface capture model includes: Based on the volume fraction method, an artificial compression convection term is added to establish the interface capture model; the interface capture model is: Where α is the volume fraction field of the liquid metal in any grid unit; t is time; U is the velocity of the liquid metal and air; is the artificial compression convection term; c1 is the compression factor.

3. The method for determining the casting filling multiphase flow field based on unstructured grid according to claim 1, characterized in that: The process of establishing the fluid domain heat transfer control model includes: Based on the law of energy conservation in the target casting filling process, the fluid domain heat transfer control model is established; the fluid domain heat transfer control model is: Where T is the temperature of the molten metal and air; t is time; U is the velocity of the molten metal and air; ρ is the local average density of the molten metal and air; λ is the local average thermal conductivity of the molten metal and air; c2 is the local average specific heat capacity of the molten metal and air; S T is the heat source term.

4. The method for determining the casting filling multiphase flow field based on unstructured grid according to claim 1, characterized in that: The process of establishing a multiphase flow model includes: Based on the law of conservation of mass and momentum, combined with the surface tension of the gas-liquid interface during the casting filling process and the obstruction of the solidified metal liquid to the movement of the unsolidified metal liquid, the multiphase flow model is established; the multiphase flow model is: Where ρ is the local average density of the liquid metal and air; U is the velocity of the liquid metal and air; t is time; μ is the local average dynamic viscosity; p is the fluid pressure; S is the source term; U pull is the casting speed in the continuous casting process; f s is the current solid phase ratio in the molten metal paste zone; S up is the critical solid fraction.

5. The method for determining the casting filling multiphase flow field based on unstructured grid according to claim 1, characterized in that: Based on the volume fraction field, a linear algebra solver is used to solve the discretized fluid domain heat transfer control model to obtain the temperature fields of the molten metal and air during the target casting filling process, specifically including: According to the volume fraction field, locally averaging the physical property parameters in the discretized fluid domain heat transfer control model to obtain the local average density of the molten metal and the air, the local average thermal conductivity of the molten metal and the air, and the local average specific heat capacity of the molten metal and the air; Based on the local average density of the molten metal and air, the local average thermal conductivity of the molten metal and air, and the local average specific heat capacity of the molten metal and air, a linear algebra solver is used to solve the discretized fluid domain heat transfer control model to obtain the temperature field of the molten metal and air during the target casting filling process.

6. The method for determining the casting filling multiphase flow field based on unstructured grid according to claim 1, characterized in that: Based on the temperature fields of the molten metal and air, the discretized multiphase flow model is solved using the pressure implicit operator splitting algorithm to obtain the velocity field and pressure field of the molten metal during the target casting filling process, specifically including: Calculate the current solid phase ratio in the molten metal mushy zone based on the temperature fields of the molten metal and air; updating the local average dynamic viscosity and the drag coefficient of the molten metal in the discretized multiphase flow model according to the current solid phase ratio of the molten metal mushy region to obtain an updated multiphase flow model; The updated multiphase flow model is solved using a pressure implicit operator splitting algorithm to obtain the velocity field and pressure field of the molten metal during the target casting filling process.

7. The method for determining the casting filling multiphase flow field based on unstructured grid according to claim 6, characterized in that: Based on the temperature fields of the molten metal and air, the current solid phase ratio in the mushy zone of the molten metal is calculated, including: Using formula f S =α(TT S ) / (T L -T S ) calculates the current solid phase ratio of the molten metal paste zone; where f s is the current solid phase ratio of the molten metal in the mushy zone; α is the volume fraction field of the molten metal in any grid unit; T is the temperature of the molten metal and air; T S is the solidus temperature of the molten metal; T L is the liquidus temperature of the molten metal.

8. A computer device comprising: A memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the method for determining the casting filling multiphase flow field based on unstructured grids according to any one of claims 1 to 7.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the method for determining a casting filling multiphase flow field based on an unstructured grid according to any one of claims 1 to 7 is implemented.

10. A computer program product comprising a computer program, characterized in that When the computer program is executed by a processor, the method for determining a casting filling multiphase flow field based on an unstructured grid according to any one of claims 1 to 7 is implemented.

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