Directional solidification heating device optimization design method based on multi-physics field coupling and related equipment
By using parametric modeling with multiphysics coupling and gradient-free optimization algorithms, the directional solidification heating device is automatically optimized, solving the problem of uneven heating and improving casting quality and design efficiency.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-01-13
- Publication Date
- 2026-03-13
AI Technical Summary
The fixed structure of the heating device in existing directional solidification equipment leads to uneven heating of the castings, which affects the metallurgical quality of the castings. In addition, the design relies on experience and is inefficient, lacking a systematic parametric design method.
By establishing a parametric model through multiphysics coupling and combining it with a gradient-free optimization algorithm, the shape and material parameters of the heating device are automatically optimized, a temperature uniformity index is established, and quantitative optimization of the heating device is achieved.
It improves the uniformity of the temperature field in castings, reduces the probability of solidification defects, shortens the design cycle, reduces costs, and improves design efficiency.
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Figure CN121659673A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of finite element simulation technology for metal casting, specifically to an optimization design method and related equipment for a directional solidification heating device based on multi-physics coupling. Background Technology
[0002] Directional solidification is a key process for manufacturing high-end components such as high-temperature alloy single-crystal turbine blades for aero-engines. This process establishes a steep temperature gradient along the axis of the casting (such as a blade mold), causing the melt to solidify in a single direction, thus obtaining a high-performance single-crystal microstructure. Currently, high-speed solidification (HRS) is a widely used directional solidification method in industry. Typical equipment usually includes an upper heating zone and a lower cooling zone. Under vacuum or low-pressure conditions, after the mold is preheated and poured in the heating zone, it moves downwards at a set pulling rate into the cooling zone, where the axial temperature gradient enables directional crystal growth.
[0003] In actual production, especially in cases involving multiple castings, such as multiple blade mold shells solidifying simultaneously, the rational design of the heating device is crucial. Due to the near-vacuum environment within the equipment, heat transfer between the heating zone and the casting, and between the casting and the cooling zone, primarily relies on radiative heat transfer. Currently, heating devices in HRS equipment are mostly fixed-structure ring heaters. When dealing with complex modules, such as multiple blade mold shells with complex internal cavities arranged in a ring or in a straight line, fixed heating devices struggle to provide uniform radiative heating to castings of different positions and shapes. Especially for castings on the inner side of the module, their heated surfaces may be obstructed by adjacent castings or parts of the module structure, forming radiation shadow areas, causing the heating efficiency in these areas to lag behind that of the outer areas. This heating non-uniformity directly leads to asymmetrical lateral temperature field distribution during solidification, and severe bending and tilting of the isotherms at the solid-liquid interface. The consequences include a decrease in local temperature gradient, an increase in the width of the mushy zone, and an increase in thermal undercooling, thereby increasing the probability of solidification defects such as freckles and impurities, affecting the integrity of the single-crystal structure and the final metallurgical quality of the casting.
[0004] To overcome these problems, researchers have recognized the necessity of targeted optimization design for heating devices. However, in current engineering practice, the design and improvement of heating devices still heavily rely on engineers' accumulated experience, analogy with existing designs, or trial-and-error methods. First, due to the lack of a systematic parametric design method, the quantitative relationship between key structural parameters such as the shape and position of the heating device and the final casting temperature field is unclear, making the optimization direction ambiguous. Second, even with the assistance of finite element simulation software, the entire design, simulation, evaluation, and modification process often requires repeated manual intervention, making it time-consuming and inefficient. Finally, this non-automated, experience-dependent iterative model results in long design cycles, high costs, and difficulty in quickly providing optimal heating solutions for modules with different casting shapes and arrangements. Summary of the Invention
[0005] To address the problems existing in the prior art, this invention provides an optimization design method and related equipment for a directional solidification heating device based on multi-physics field coupling. The purpose is to overcome the difficulties in uniformly radiating and heating castings of different positions and shapes in existing HRS equipment, which leads to uneven heating, high probability of solidification defects, and impact on the metallurgical quality of castings. It also addresses the shortcomings of existing heating devices, such as reliance on experience in design and improvement, lack of systematic parametric design methods, vague optimization direction, and time-consuming and inefficient design process. The invention enables the rapid provision of optimal heating solutions for modules with different casting shapes and arrangements.
[0006] To solve the above-mentioned technical problems, the present invention is achieved through the following technical solution: According to a first aspect of the present invention, a method for optimizing the design of a directional solidification heating device based on multiphysics coupling is provided, comprising: S1. Determine the assembly method and quantity of the castings, and select the set of parameters to be optimized that affect the heating effect. The set of parameters to be optimized shall include at least the structural parameters used to define the shape of the heating device. S2. Based on the set of parameters to be optimized, perform parametric modeling on the system including the heating device and the casting to generate a two-dimensional geometric model that can be automatically updated with the set of parameters to be optimized. S3. Based on the two-dimensional geometric model, establish a multiphysics simulation model that couples at least solid heat transfer and surface radiation heat transfer, and perform numerical solution to obtain the temperature field distribution of the casting. S4. Based on the temperature field distribution, calculate the average temperature difference at the casting boundary as a temperature uniformity index to set the optimization target. At the same time, set the set of parameters to be optimized as optimization variables in the optimization solver, and set geometric constraints and / or process constraints. S5. Under the premise of satisfying the constraints, the optimization solver is driven to iterate using a gradient-free optimization algorithm. The iteration process includes repeating steps S2 to S4 until the temperature uniformity index reaches an extreme value, thereby obtaining the optimized parameter set.
[0007] In one possible implementation of the first aspect, in step S1, the casting assembly method is a linear arrangement, with multiple castings arranged in one or more rows along the same straight line; the structural parameters include at least the coordinates of multiple control points used to control the outline shape of the heating device.
[0008] In one possible implementation of the first aspect, in step S2, the parametric modeling includes: using control points to construct interpolated line segment polygons or interpolated curve closed figures to form a two-dimensional geometric contour of the heating device, such that the shape of the contour can be automatically updated as the coordinate parameters of the control points change.
[0009] In one possible implementation of the first aspect, in step S4, the temperature uniformity index is the average temperature difference. U Calculate according to the following formula: At the preset evaluation time, for the first i The average temperature of the left and right boundaries of each casting is calculated based on the temperature field distribution. and Then the first i The average temperature difference between the two boundaries of the casting is For all N A casting, the average temperature difference .
[0010] In one possible implementation of the first aspect, in step S1, the set of parameters to be optimized further includes material parameters, the material parameters including the emissivity of the surface of the heating device; In step S4, the optimization variables include both the structural parameters and the material parameters.
[0011] In one possible implementation of the first aspect, in step S4, the constraints include one or more of the following: the shape profile of the heating device does not self-intersect, the heating device and the casting do not interfere geometrically, and the minimum heating rate of the casting is not lower than a specified threshold.
[0012] In one possible implementation of the first aspect, in step S5, the gradient-free optimization algorithm is one of a coordinate search algorithm, a Nelder-Mead algorithm, or a Monte Carlo algorithm.
[0013] In one possible implementation of the first aspect, the design methodology also includes: S6. Based on the optimized parameter set, construct a three-dimensional model of the heating device and perform directional solidification simulation including the dynamic pulling process to verify the improvement effect of the casting temperature field index before and after optimization. The temperature field indicators include at least one of temperature uniformity indicators, isotherm tilt angles, and temperature gradients.
[0014] According to a second aspect of the present invention, a computer device is provided, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the computer program, implements the aforementioned method for optimizing the design of a directional solidification heating device based on multiphysics coupling.
[0015] According to a third aspect of the present invention, a computer-readable storage medium is provided, the computer-readable storage medium storing a computer program, which, when executed by a processor, implements the aforementioned method for optimizing the design of a directional solidification heating device based on multiphysics coupling.
[0016] According to a fourth aspect of the present invention, a computer program product is provided, which, when executed by a processor, implements the aforementioned method for optimizing the design of a directional solidification heating device based on multiphysics coupling.
[0017] Compared with the prior art, the present invention has at least the following beneficial effects: This invention provides an optimization design method for directional solidification heating devices based on multiphysics coupling. Addressing the problem of uneven heating in castings caused by the fixed structure of the heating device during traditional directional solidification, this method establishes a multiphysics model coupling solid heat transfer and surface radiation. This allows for quantitative optimization of the heating device's structural parameters, thereby improving the uniformity of the casting's temperature field at the simulation level. It effectively suppresses the inclination of the solid-liquid interface caused by lateral temperature differences, helps reduce the width of the pasty region, and increases the local temperature gradient, thus reducing the probability of solidification defects such as freckles and impurities, and improving the metallurgical quality of single-crystal castings. Through parametric modeling, the shape and even material properties of the heating device are transformed into automatically adjustable design variables, constructing a two-dimensional geometric model that can be updated with parameter changes. This establishes a mathematical model foundation for the optimization process, reducing the workload of repeated manual modeling and effectively controlling the number of optimization variables, thus lowering the complexity of the optimization solution. This method employs a gradient-free optimization algorithm to drive iterative optimization, efficiently searching for the optimal parameter combination that maximizes temperature uniformity even with multiple variables and constraints, without requiring gradient calculations. This overcomes the limitations of traditional methods relying on trial and error or gradient optimization, which struggle to handle complex parameter relationships. This automates the design of heating devices, improving design efficiency. Ultimately, this approach forms a complete design process from parametric modeling and multiphysics simulation to automatic optimization. It can quickly provide customized heating device optimization schemes for different casting shapes and molding methods, shortening the design cycle and reducing the costs of traditional repeated trial production and testing. Attached Figure Description
[0018] To more clearly illustrate the technical solutions in the specific embodiments of the present invention, the drawings used in the description of the specific embodiments will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.
[0019] Figure 1 This is a flowchart of an optimized design method for a directional solidification heating device based on multi-physics coupling according to the present invention; Figure 2 This is a schematic diagram of the overall process of the optimized design method for a directional solidification heating device based on multi-physics field coupling according to the present invention. Figure 3 This is for the construction of the initial parameterized model in Embodiment 1 of the present invention; Figure 4 This is the optimization iterative process of the target value in Embodiment 1 of the present invention; Figure 5 This is a comparison of the temperature field distribution of the casting before and after optimization in Embodiment 1 of the present invention; Figure 6This is for the construction of the initial parameterized model in Embodiment 2 of the present invention; Figure 7 This is the optimization iterative process of the target value in Embodiment 2 of the present invention; Figure 8 This is a comparison of the temperature field distribution of the casting before and after optimization, and a comparison of the shape and surface radiant heat flux distribution of the heating device in Embodiment 2 of the present invention. Figure 9 This is for the construction of the initial parameterized model in Embodiment 3 of the present invention; Figure 10 This refers to the optimization and iterative process of the target value in Embodiment 3 of the present invention; Figure 11 This is a comparison of the temperature field distribution of the casting before and after optimization in Embodiment 3 of the present invention; Figure 12 This is a comparison of the temperature field distribution in the mushy region of the casting before and after optimization during the three-dimensional dynamic pulling process in Embodiment 3 of the present invention. Detailed Implementation
[0020] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0021] like Figure 1 and Figure 2 As shown, this invention provides an optimization design method for a directional solidification heating device based on multiphysics coupling. The aim is to address the problems in existing high-speed solidification equipment, such as uneven radiant heating in fixed heating devices leading to asymmetrical temperature field distribution in castings, increased solidification defects, and the reliance on experience and low efficiency in the design process. This method combines parametric modeling, multiphysics simulation, and automatic optimization iteration to achieve quantitative optimization of the heating device's shape and key parameters. The following provides a detailed description of each step of the method.
[0022] S1. Determine the assembly method and quantity of the castings, and select the set of parameters to be optimized that affect the heating effect. The set of parameters to be optimized shall include at least the structural parameters used to define the shape of the heating device.
[0023] Specifically, the assembly method and quantity of castings are determined based on the actual production process. In this embodiment, the castings are assembled in a linear arrangement, meaning multiple aero-engine blade castings (mold shells) are arranged sequentially along the same straight line, forming a row. Based on this module layout, a set of parameters requiring optimization is selected from the key factors affecting the heating effect. The set of parameters to be optimized mainly includes structural parameters and material parameters, as detailed below: Structural parameters are used to define the shape and position of the heating device. Specifically, they include at least the coordinates of multiple control points used to control the outline shape of the heating device, such as key points along the length and width of the heating device, and the spatial position parameters of the heating device relative to the casting module. By adjusting these control point coordinates, the two-dimensional outline shape of the heating device can be changed.
[0024] Material parameters include the emissivity of the surface material of the heating device, and optionally, the thermal conductivity of the material. Emissivity and / or thermal conductivity directly affect the radiative heat transfer efficiency.
[0025] S2. Based on the set of parameters to be optimized, perform parametric modeling on the system including the heating device and the casting to generate a two-dimensional geometric model that can be automatically updated with the set of parameters to be optimized.
[0026] In other words, based on the set of parameters to be optimized determined in step S1, parametric modeling is performed on the system including the heating device and the casting module. Preferably, the rarefied air inside the heating device cavity is considered during parametric modeling. For example, the modeling process is performed in CAE software or a modeling environment with parametric capabilities.
[0027] Specifically, using the control point coordinates defined in step S1, polygons are formed by constructing interpolated line segments, or closed figures are formed by constructing interpolated curves, thereby outlining the two-dimensional geometric contour of the heating device. Simultaneously, a simplified two-dimensional geometric model is established for the casting modules based on their linear arrangement and quantity. Through parameter correlation, the contour shape of the heating device can be automatically updated as the control point coordinates and other structural position parameters change, eliminating the need for manual redrawing of the geometry.
[0028] S3. Based on the two-dimensional geometric model, establish a multiphysics simulation model that couples at least solid heat transfer and surface radiation heat transfer, and perform numerical solution to obtain the temperature field distribution of the casting.
[0029] In other words, a multiphysics coupled simulation model is established based on the parameterized two-dimensional geometric model generated in step S2. The multiphysics coupled simulation model couples at least the solid heat transfer physical field and the surface radiation heat transfer physical field.
[0030] Among them, the solid heat transfer physical field is used to calculate the heat conduction process in solid domains such as heating devices and casting modules.
[0031] The surface radiation heat transfer physical field is used to calculate the radiation heat transfer process between the surface of the heating device and the surface of the casting in a near-vacuum environment. This process is the main way to simulate heat transfer in the heating zone.
[0032] Depending on the needs, fluid heat transfer physics (i.e., considering rarefied gas convection) or phase change physics can be selectively coupled to more accurately simulate actual conditions.
[0033] After establishing a multiphysics coupled simulation model, corresponding material properties, such as thermal conductivity and surface emissivity, are assigned to each part of the simulation model. Initial temperature conditions and boundary conditions are set, and mesh generation is performed. Subsequently, unsteady-state numerical solutions are performed to calculate the transient temperature field distribution of the casting module during the heating stage. The unsteady-state temperature field data is used to calculate the heating rate and to equivalently characterize the radiative heat flux density.
[0034] S4. Based on the temperature field distribution, calculate the average temperature difference at the casting boundary as a temperature uniformity index to set the optimization target. At the same time, set the set of parameters to be optimized as optimization variables in the optimization solver, and set geometric constraints and / or process constraints.
[0035] In other words, based on the temperature field distribution obtained in step S3, key information is extracted to set optimization objectives and constraints. The optimization objective is the temperature uniformity of the casting during heating. Specifically, the temperature uniformity index is the average temperature difference. U The calculation method is as follows: At a preset evaluation time, such as the moment when heating reaches a quasi-steady state, for the first... i For each casting, its left and right boundaries are selected as evaluation objects. Based on the temperature field distribution, the average temperature of the left boundary is calculated. and the average temperature of the right boundary ,in and Let these represent the distances from the left edge to the left side of the heating device and the distances from the right edge to the right side of the heating device, respectively. Then the... i The average temperature difference between the two boundaries of the casting is For all of the modules N Each casting, calculate all The average value, i.e., the average temperature difference, is obtained. The optimization objective is to minimize this average temperature difference. U .
[0036] The set of parameters to be optimized determined in step S1, including structural parameters that control the shape of the heating device and material parameters such as surface emissivity, are set as optimization variables.
[0037] Necessary constraints are set according to the actual engineering situation. These constraints include, but are not limited to, geometric constraints and process constraints. Geometric constraints specifically include that the shape and contour of the heating device cannot intersect each other, i.e., the contour lines cannot intersect; and the heating device and the casting cannot interfere geometrically. Process constraints stipulate that, to ensure heating efficiency, the minimum heating rate of the casting must not be lower than a certain specified threshold.
[0038] In the optimization solver, complete the setting of the optimization objective (minimizing U), optimization variables (parameter set), and constraints. It should be noted that the optimization solver can be the built-in optimization solution module of the multiphysics simulation software COMSOL Multiphysics.
[0039] S5. Under the premise of satisfying the constraints, the optimization solver is driven to perform iteration using a gradient-free optimization algorithm. The iteration process includes repeatedly executing steps S2 to S4 until the temperature uniformity index reaches an extreme value, thereby obtaining the optimized parameter set.
[0040] Preferably, gradient-free optimization algorithms suitable for this embodiment include, but are not limited to, coordinate search algorithms, Nelder-Mead algorithms, or Monte Carlo algorithms. These algorithms do not rely on the gradient information of the objective function with respect to the parameters and are suitable for handling problems where the relationship between the parameters and the objective is complex or difficult to differentiate.
[0041] Specifically, the optimization iteration process is as follows: Based on the current parameter values, the optimization solver automatically calls steps S2 to S4, namely, updating the two-dimensional geometric model according to the current parameters, performing multiphysics simulation to calculate the temperature field, and calculating the current average temperature difference. U Value. Then, the optimization algorithm is based on U Once the values and constraints are satisfied, a new set of parameter values is generated, and the above process is restarted. This process is repeated iteratively until the average temperature difference is reached. U Once the minimum value is reached, or the preset convergence condition is met, the optimized parameter set is obtained. This process achieves automatic quantitative optimization of the shape and parameters of the heating device.
[0042] S6. Based on the optimized parameter set, construct a three-dimensional model of the heating device and perform directional solidification simulation including a dynamic pulling process to verify the improvement effect of the casting temperature field index before and after optimization.
[0043] In detail, based on the optimized parameter set obtained in step S5, a corresponding 3D solid model of the heating device with actual dimensions is constructed in 3D modeling software. Simultaneously, a complete 3D model of the directional solidification equipment, including casting modules and cooling systems, is established.
[0044] The 3D model was imported into finite element analysis software to simulate the entire directional solidification process, including the dynamic pulling process. The simulation verified the effectiveness of the optimized heating device under actual dynamic process conditions. Key comparison indicators included before and after optimization were at least: temperature uniformity indicators, such as the average temperature difference U; the inclination angle of the isotherms at the solid-liquid interface of the casting; and the temperature gradient in key areas of the casting.
[0045] By comparison, the improvement effects of the optimization scheme on improving the lateral temperature uniformity of castings, reducing isotherm inclination, and increasing temperature gradient can be intuitively demonstrated, thereby verifying the effectiveness of this optimization design method and providing a design basis for final manufacturing.
[0046] In summary, the embodiments of the present invention, through the above steps, achieve a closed-loop design process encompassing parametric modeling, multiphysics simulation analysis, automated optimization iteration, and three-dimensional dynamic verification. This method can quickly and quantitatively provide the optimal heating device shape and parameter scheme for castings with different mold assembly methods, such as inline arrangement, reducing the workload of traditional experience-based trial and error, shortening the design cycle, lowering costs, and effectively improving the heating uniformity and metallurgical quality of the castings in the directional solidification process.
[0047] The implementation process of this method is described in detail below through three specific embodiments. Embodiment 1 shows the optimization process of basic shape parameters; Embodiment 2 further introduces the synergistic optimization of material parameters; Embodiment 3 optimizes for more complex shapes and finally verifies its substantial improvement on solidification quality through three-dimensional dynamic process simulation.
[0048] Example 1 This embodiment uses a simple module with five cylindrical casting test bars arranged in a straight line as an example to demonstrate how to improve the lateral temperature uniformity by optimizing the outline shape of the heating device.
[0049] Step S1: Determine the assembly method and quantity of the castings, and select the set of parameters to be optimized that affect the heating effect.
[0050] This embodiment focuses on a single-row module formed by arranging five cylindrical test bars sequentially along the same straight line. The shape parameters of the heating device are selected as the set of parameters to be optimized. Specifically, the coordinates of a set of control points are used to parameterize and define the contour of the heating device in a two-dimensional cross-section. The coordinates of these control points are the parameters to be optimized determined in this step.
[0051] Step S2: Based on the set of parameters to be optimized, perform parametric modeling on the system including the heating device and the casting to generate a two-dimensional geometric model that can be automatically updated with the set of parameters to be optimized.
[0052] In the geometry module of COMSOL Multiphysics, a parametric modeling platform built into the finite element simulation software, a simplified two-dimensional axisymmetric model is established, including the heating device, five castings, and the rarefied air inside the cavity. Figure 3 As shown, the outline of the heating device is formed by connecting a series of control points through interpolation curves to create a closed shape. Taking the outline in the first quadrant of the model as an example, seven control points are used, with coordinates (x0, y0), (x1, y1), (x2, y2), (x3, y3), (x4, y4), (x5, y5), and (x6, 0) respectively. Their initial coordinate values are shown in Table 1. By writing a parametric script, the geometric outline is dynamically associated with this set of coordinate parameters. When the optimization algorithm modifies these coordinate values in subsequent steps, the two-dimensional geometric model can automatically update its shape without manual reconstruction.
[0053] Step S3: Based on the two-dimensional geometric model, establish a multiphysics simulation model that couples at least solid heat transfer and surface radiation heat transfer, and perform numerical solution to obtain the temperature field distribution of the casting.
[0054] A simulation model coupling solid-state heat transfer and surface-to-surface radiation physical fields is established on the aforementioned two-dimensional geometric model. Material properties are set as follows: the casting material is copper, the heating device is a high-emissivity material, and the rarefied air within the cavity is set as a fluid domain with a pressure of 10. -3 The process was designed to simulate a near-vacuum environment. Boundary conditions were set as follows: the outer boundary temperature of the heating device was 1800 K, and the initial system temperature (i.e., the initial temperature of the casting and the air) was 293.15 K. Based on this, after meshing, a transient solver was used to calculate the temperature field distribution 50 seconds after the start of heating. The output of this step is detailed spatial temperature data for the casting region.
[0055] Step S4: Based on the temperature field distribution, calculate the average temperature difference at the casting boundary as a temperature uniformity index to set the optimization target. At the same time, in the optimization solver, set the set of parameters to be optimized as the optimization variable and set geometric constraints and / or process constraints.
[0056] Evaluation indicators are extracted from the temperature field obtained in step S3. This embodiment focuses on minimizing the average temperature difference. U To optimize the objective, the specific calculation method is as follows: for the ... i For each casting, calculate the average temperature at its left boundary. and the average temperature of the right boundary To obtain the temperature difference of a single piece The average temperature difference of the five castings .
[0057] The 12 coordinate parameters (6 Y-coordinates y0~y5 and 6 X-coordinates x0~x6) that define the contour of the heating device are set as optimization variables, i.e. To ensure the physical rationality of the optimization results, two types of constraints are applied: first, boundary constraints, with the range of parameter variations shown in Table 1; second, geometric and logical constraints, requiring the X-coordinate to satisfy... A strict incremental relationship is required to prevent the heating device contours from self-intersecting.
[0058] Step S5: Under the premise of satisfying the constraints, the optimization solver is driven to iterate using a gradient-free optimization algorithm. The iteration process includes repeating steps S2 to S4 until the temperature uniformity index reaches an extreme value, thereby obtaining the optimized parameter set.
[0059] In this embodiment, the coordinate search algorithm in gradient-free optimization algorithms is selected as the solver. The optimization process runs fully automatically, executing steps S2 to S4, without manual intervention during the loop. Figure 4 This shows the objective function during the optimization iteration process. U The process of the value continuously decreasing and eventually converging. After optimization, the output makes U The optimal set of parameters for minimizing the value is shown in the final value column in Table 1.
[0060] The comparison results of the temperature field before and after optimization are as follows: Figure 5 As shown, Figure 5 In the figure, (a) and (b) represent the temperature distribution before and after optimization, respectively. After optimization, the lateral temperature distribution of the casting is significantly more uniform. Quantitative data show that when using the heating device before optimization, the average temperature difference between the left and right boundaries of the casting is 0.77587°C; while when using the heating device after optimization, the average temperature difference between the left and right boundaries of the casting is 0.62649°C, a reduction of 19.3%, confirming the effectiveness of the optimization scheme.
[0061] Table 1
[0062] Example 2 This embodiment uses a module with two cylindrical casting test bars arranged in a straight line as the object to demonstrate how to further improve the temperature uniformity of the casting by simultaneously optimizing the shape parameters and material parameters (surface emissivity) of the heating device.
[0063] S1. Determine the molding method and quantity of the castings, and select the set of parameters to be optimized that affect the heating effect.
[0064] In this embodiment, the casting consists of two cylindrical test bars arranged in a single row along the same straight line. The shape parameters and material parameters of the heating device are selected as the key set of parameters to be optimized. Specifically, the shape parameters are the coordinates of the control points defining the contour of the heating device; the material parameters are the emissivity of different zones on the surface of the heating device.
[0065] S2. Based on the set of parameters to be optimized, perform parametric modeling on the system including the heating device and the casting to generate a two-dimensional geometric model that can be automatically updated with the set of parameters to be optimized.
[0066] like Figure 6 As shown, a simplified model is constructed in the parametric modeling environment, comprising a heating device, two heated castings, and rarefied air within the cavity. The outline of the heating device is formed by connecting five control points through interpolated line segments to create a polygon. Taking the first quadrant outline as an example, the initial coordinates of the control points are (0, y0), (50, y1), (100, y2), (150, y3), and (200, 0), where y0, y1, y2, and y3 are the shape parameters to be optimized. Simultaneously, the outline of the heating device is divided into four segments, and each segment is assigned an independent surface emissivity value, denoted as e1, e2, e3, and e4, respectively. These emissivity values are the material parameters to be optimized. Through parametric scripts, the geometry is bound to these coordinates and material parameters, enabling automatic updates.
[0067] S3. Based on the two-dimensional geometric model, establish a multiphysics simulation model that couples at least solid heat transfer and surface radiation heat transfer, and perform numerical solution to obtain the temperature field distribution of the casting.
[0068] A simulation model coupling solid-state heat transfer and surface-to-surface radiation physical field is established on the aforementioned two-dimensional geometric model. Material properties are set as follows: the casting material is copper; the surface emissivity of each zone of the heating device is set to e1 to e4 (initial value 0.8); the rarefied air inside the cavity is set as a fluid domain with a pressure of 10. -3 Pa. Boundary conditions were set as follows: the outer boundary temperature of the heating device was 1000 K, and the initial system temperature was 293.15 K. After meshing, a transient solver was used to calculate the temperature field distribution 100 seconds after the start of the radiative heating process.
[0069] S4. Based on the temperature field distribution, calculate the standard deviation of the casting boundary temperature as a temperature uniformity index to set the optimization target. At the same time, set the set of parameters to be optimized as optimization variables in the optimization solver, and set geometric constraints and / or process constraints.
[0070] From the temperature field distribution data obtained in step S3, a quantitative index for evaluating heating uniformity is extracted. In this embodiment, the standard deviation of the boundary temperature of each casting is selected. The optimization objective to be minimized is as follows: First, calculate the average temperature of the left and right boundaries of each casting. and A total of four boundary temperature values were obtained, and the average value of these four temperature values was calculated. Then, its standard deviation is obtained. :
[0071]
[0072] The four shape parameters (y0, y1, y2, y3) and four material parameters (e1, e2, e3, e4) defined in step S1, totaling eight parameters, are set as optimization variables. Boundary constraints are set for these variables, and the initial values, lower limits, and upper limits of each parameter are shown in Table 2.
[0073] S5. Under the premise of satisfying the constraints, the optimization solver is driven to perform iteration using a gradient-free optimization algorithm. The iteration process includes repeatedly executing steps S2 to S4 until the temperature uniformity index reaches an extreme value, thereby obtaining the optimized parameter set.
[0074] The coordinate search algorithm in gradient-free optimization is used as the optimization solver. The optimization process automatically executes steps S2 to S4 in a loop, which are: generating a new set of parameter values for the optimizer, automatically triggering step S2 to update the model shape and material properties, automatically calling step S3 to perform simulation calculations, and automatically executing step S4 to calculate the temperature standard deviation under the current parameters. The optimizer is based on The value is determined and the next set of trial parameters is generated. Figure 7 This shows the objective function value (temperature standard deviation) during the optimization iteration process. The process of decreasing with increasing iterations and eventually converging. After optimization stops, the output makes... The optimal set of parameters that minimizes the value is shown in the row of Table 2, which represents the optimized value.
[0075] Compare the simulation results before and after optimization, such as... Figure 8 As shown, the changes in the shape of the optimized heating device, the distribution of radiant heat flux, and the temperature distribution of the casting can be seen intuitively. Figure 8 In the figure, (a) and (b) represent the temperature distribution of the casting before and after optimization, respectively; (c) and (d) represent the emissivity distribution of the heating device before and after optimization, respectively. Quantitative comparison shows that when using the heating device before optimization, the standard deviation of the temperature at each boundary of the casting is 0.47154, while when using the optimized heating device, the standard deviation of the temperature at each boundary of the casting is 0.092758, a reduction of 80.33%, demonstrating that the synergistic optimization of shape and material can more significantly improve heating uniformity.
[0076] Table 2
[0077] Example 3 This embodiment uses a module with five cylindrical casting test bars arranged in a straight line as the object to demonstrate the effect of optimizing the shape of a complex heating device with more control points. Through three-dimensional dynamic pull-out simulation, it verifies the substantial improvement of the optimization scheme on the core quality indicators of the solidification process.
[0078] S1. Determine the molding method and quantity of the castings, and select the set of parameters to be optimized that affect the heating effect.
[0079] In this embodiment, the casting consists of five cylindrical test bars arranged in a single row along the same straight line. To describe a more complex heating device profile, the Y-coordinates of 12 control points are selected as the set of shape parameters to be optimized.
[0080] S2. Based on the set of parameters to be optimized, perform parametric modeling on the system including the heating device and the casting to generate a two-dimensional geometric model that can be automatically updated with the set of parameters to be optimized.
[0081] like Figure 9 As shown, a simplified model containing a heating device, five heated castings, and rarefied air within a cavity is constructed in a parametric modeling environment. The outline of the heating device is formed by connecting 13 control points (including endpoints) through interpolated line segments to create a polygon. Taking the first quadrant outline as an example, the coordinates of the control points are (0, y0), (10, y1), (20, y2), (30, y3), (40, y4), (50, y5), (60, y6), (70, y7), (80, y8), (90, y9), (100, y10), (110, y11), and (120, 0), where the 12 Y-coordinates from y0 to y11 are the shape parameters to be optimized. The model shape is automatically updated according to these parameters using a parametric script.
[0082] S3. Based on the two-dimensional geometric model, establish a multiphysics simulation model that couples at least solid heat transfer and surface radiation heat transfer, and perform numerical solution to obtain the temperature field distribution of the casting.
[0083] A simulation model coupling solid-state heat transfer and surface-to-surface radiation physical fields is established on the aforementioned two-dimensional geometric model. Material properties are set as follows: the casting material is copper, the surface emissivity of the heating device is set to a fixed value of 0.8, and the rarefied air inside the cavity is set as a fluid domain with a pressure of 10. -3 Pa. Boundary conditions were set as follows: the outer boundary temperature of the heating device was 1800 K, and the initial system temperature was 293.15 K. After meshing, a transient solver was used to calculate the temperature field distribution 50 seconds after the start of the radiative heating process.
[0084] S4. Based on the temperature field distribution, calculate the average temperature difference at the casting boundary as a temperature uniformity index to set the optimization target. At the same time, set the set of parameters to be optimized as optimization variables in the optimization solver and set geometric constraints.
[0085] Evaluation indicators are extracted from the temperature field distribution data obtained in step S3. This embodiment focuses on minimizing the average temperature difference. U To optimize the objective, the calculation method is the same as in Example 1. Twelve shape parameters (y0 to y11) are set as optimization variables. Boundary constraints are set for these variables, and the initial values, lower limits, and upper limits of each parameter are shown in Table 3.
[0086] S5. Under the premise of satisfying the constraints, the optimization solver is driven to perform iteration using a gradient-free optimization algorithm. The iteration process includes repeatedly executing steps S2 to S4 until the temperature uniformity index reaches an extreme value, thereby obtaining the optimized parameter set.
[0087] The coordinate search algorithm in gradient-free optimization is used as the optimization solver, and the optimization process is automatically repeated. Figure 10 This shows the objective function value (mean temperature difference) during the optimization iteration process. U The process of decreasing with increasing iterations and eventually converging. After optimization stops, the output makes... U The optimal set of parameters that minimizes the value is shown in the final value column of Table 3.
[0088] S6. Based on the optimized parameter set, construct a three-dimensional model of the heating device and perform directional solidification simulation including a dynamic pulling process to verify the improvement effect of the casting temperature field index before and after optimization.
[0089] Using the optimal parameter set obtained in step S5 as input, the optimized 3D solid model of the heating device is reconstructed in the 3D CAD software (Solidworks). The 3D models of the heating device before and after optimization are respectively placed into the multiphysics simulation software (COMSOL Multiphysics) to establish a complete directional solidification process model including the heating zone, cooling zone, heat insulation baffle, and dynamic pulling motion of the mold for casting simulation verification.
[0090] First, compare the static heating effect. For example... Figure 11 As shown, Figure 11 In the figure, (a) and (b) represent the temperature distribution before and after optimization, respectively. After optimization, the lateral temperature distribution of the casting is more uniform. Quantitative calculations show that when using the heating device before optimization, the average temperature difference at each boundary of the casting is 0.91855, while when using the heating device after optimization, the average temperature difference at each boundary of the casting is 0.677, which is a reduction of 26.30%.
[0091] Secondly, the solidification quality indicators during the dynamic pulling process were compared. Dynamic pulling simulations were performed on the models before and after optimization. Figure 12 The simulation demonstrates a comparison of the temperature field distribution in the mushy region of the casting at a specific moment during the drawing process. It is clearly observed that with the unoptimized heating device, the isotherms in the mushy region are significantly tilted; while with the optimized heating device, the isotherms are straighter and the tilt is reduced. Simultaneously, simulation data shows that the axial temperature gradient of the casting is also improved after optimization. The improvement in the mushy region morphology and the increase in the temperature gradient directly prove that this optimization scheme is beneficial for obtaining a straighter solidification interface and better single-crystal growth conditions.
[0092] Table 3
[0093] In summary, this invention solves the temperature field through multi-physics field coupling modeling, including solid heat transfer and surface-to-surface radiation, and uses temperature uniformity as the optimization objective. This enables quantitative optimization of key structural / material parameters of the heating device, thereby improving the temperature field asymmetry and heat transfer lag problems caused by traditional directional solidification heating devices, reducing the risk of defects such as freckles and impurities, and improving process stability and yield. By constructing an automatically updatable two-dimensional parametric geometric model by controlling the position of interpolation points, the shape of the heating device is represented by the coordinates of the interpolation points. Simultaneously, material parameters such as surface emissivity and thermal conductivity are introduced to achieve parametric modeling of the heating device, establishing a basic mathematical model for optimization design, and controlling the number of parameters to be optimized, thus reducing the difficulty of optimization. Iterative search using a gradient-free optimization algorithm seeks the optimal solution, effectively characterizing the structural / shape parameters of the heating device while avoiding the difficulty in accurately finding extreme values due to excessive parameters and complex models encountered with gradient algorithms. This provides a theoretical basis for device design, reduces the workload of manual model reconstruction and repeated calculations, and improves the efficiency of optimization iteration and effect verification. It also provides a more universal solution for designing heating devices for casting modules with different assembly methods and shapes, shortening the design cycle and reducing design costs. By characterizing the radiative heat flux density with the heating rate of a two-dimensional unsteady temperature field to simulate the heat flux changes during three-dimensional solidification, the computational workload of the optimization algorithm and radiative heat transfer is greatly simplified. After obtaining the optimal parameters, three-dimensional modeling and dynamic pulling / solidification process simulation verification are performed, outputting comparisons of key indicators such as temperature uniformity and isotherm tilt before and after optimization, improving the efficiency of design scheme verification, ensuring the reliability of the optimized scheme, and reducing the number of experiments and economic costs.
[0094] In another embodiment of the present invention, a computer device is provided, comprising a processor and a memory. The memory stores a computer program, which includes program instructions. The processor executes the program instructions stored in the computer storage medium. The processor may be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. It is the computing and control core of the terminal, suitable for implementing one or more instructions, specifically suitable for loading and executing one or more instructions in the computer storage medium to achieve a corresponding method flow or corresponding function. The processor described in this embodiment of the present invention can be used in the operation of an optimization design method for a directional solidification heating device based on multi-physics coupling.
[0095] In another embodiment of the present invention, a storage medium is provided, specifically a computer-readable storage medium (Memory), which is a memory device in a computer device used to store programs and data. It is understood that the computer-readable storage medium here can include both the built-in storage medium in the computer device and extended storage media supported by the computer device. The computer-readable storage medium provides storage space that stores the terminal's operating system. Furthermore, the storage space also stores one or more instructions suitable for loading and execution by a processor. These instructions can be one or more computer programs (including program code). It should be noted that the computer-readable storage medium here can be Random Access Memory (RAM) or non-volatile memory, such as at least one disk storage device. The processor can load and execute one or more instructions stored in the computer-readable storage medium to implement the corresponding steps of the above embodiment regarding the optimization design method of a directional solidification heating device based on multiphysics coupling.
[0096] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, optical storage, etc.) containing computer-usable program code.
[0097] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.
[0098] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.
[0099] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.
[0100] This invention also provides a computer program product, which is used to execute any of the above-described methods for optimizing the design of a directional solidification heating device based on multiphysics coupling. Since the computer program product provided by this invention and the above-described method for optimizing the design of a directional solidification heating device based on multiphysics coupling belong to the same inventive concept, the computer program product provided by this invention possesses all the advantages of the above-described method for optimizing the design of a directional solidification heating device based on multiphysics coupling. Therefore, the beneficial effects of the computer program product provided by this invention will not be elaborated upon here.
[0101] In this invention, the terms "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., refer to a specific feature, structure, material, or characteristic described in connection with that embodiment or example, which is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.
[0102] Finally, it should be noted that the above-described embodiments are merely specific implementations of the present invention, used to illustrate the technical solutions of the present invention, and not to limit them. The scope of protection of the present invention is not limited thereto. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that any person skilled in the art can still modify or easily conceive of changes to the technical solutions described in the foregoing embodiments within the scope of the technology disclosed in the present invention, or make equivalent substitutions for some of the technical features; and these modifications, changes, or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and should all be covered within the scope of protection of the present invention.
Claims
1. An optimization design method for a directional solidification heating device based on multiphysics coupling, characterized in that, include: S1. Determine the assembly method and quantity of the castings, and select the set of parameters to be optimized that affect the heating effect. The set of parameters to be optimized shall include at least the structural parameters used to define the shape of the heating device. S2. Based on the set of parameters to be optimized, perform parametric modeling on the system including the heating device and the casting to generate a two-dimensional geometric model that can be automatically updated with the set of parameters to be optimized. S3. Based on the two-dimensional geometric model, establish a multiphysics simulation model that couples at least solid heat transfer and surface radiation heat transfer, and perform numerical solution to obtain the temperature field distribution of the casting. S4. Based on the temperature field distribution, calculate the average temperature difference at the casting boundary as a temperature uniformity index to set the optimization target. At the same time, set the set of parameters to be optimized as optimization variables in the optimization solver, and set geometric constraints and / or process constraints. S5. Under the premise of satisfying the constraints, the optimization solver is driven to iterate using a gradient-free optimization algorithm. The iteration process includes repeating steps S2 to S4 until the temperature uniformity index reaches an extreme value, thereby obtaining the optimized parameter set.
2. The method for optimizing the design of a directional solidification heating device based on multiphysics coupling according to claim 1, characterized in that, In step S1, the casting assembly method is a linear arrangement, with multiple castings arranged in one or more rows along the same straight line; the structural parameters include at least the coordinates of multiple control points used to control the outline shape of the heating device.
3. The optimized design method for a directional solidification heating device based on multiphysics coupling according to claim 2, characterized in that, In step S2, the parametric modeling includes: using control points to construct interpolated line segment polygons or interpolated curve closed figures to form a two-dimensional geometric contour of the heating device, so that the shape of the contour can be automatically updated as the coordinate parameters of the control points change.
4. The optimization design method for a directional solidification heating device based on multiphysics coupling according to claim 1, characterized in that, In step S4, the temperature uniformity index is the average temperature difference. U Calculate according to the following formula: At the preset evaluation time, for the first i The average temperature of the left and right boundaries of each casting is calculated based on the temperature field distribution. and Then the first i The average temperature difference between the two boundaries of the casting is For all N A casting, the average temperature difference .
5. The optimized design method for a directional solidification heating device based on multiphysics coupling according to claim 1, characterized in that, In step S1, the set of parameters to be optimized also includes material parameters, which include the emissivity of the surface of the heating device; In step S4, the optimization variables include both the structural parameters and the material parameters.
6. The optimized design method for a directional solidification heating device based on multiphysics coupling according to claim 1, characterized in that, In step S4, the constraints include one or more of the following: the shape profile of the heating device does not self-intersect, the heating device and the casting do not interfere geometrically, and the minimum heating rate of the casting is not lower than a specified threshold.
7. The optimization design method for a directional solidification heating device based on multiphysics coupling according to claim 1, characterized in that, In step S5, the gradient-free optimization algorithm is one of the coordinate search algorithm, Nelder-Mead algorithm, or Monte Carlo algorithm.
8. The method for optimizing the design of a directional solidification heating device based on multiphysics coupling according to claim 1, characterized in that, The design methodology also includes: S6. Based on the optimized parameter set, construct a three-dimensional model of the heating device and perform directional solidification simulation including the dynamic pulling process to verify the improvement effect of the casting temperature field index before and after optimization. The temperature field indicators include at least one of temperature uniformity indicators, isotherm tilt angles, and temperature gradients.
9. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the optimization design method for a directional solidification heating device based on multiphysics coupling as described in any one of claims 1 to 8.
10. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements the optimization design method for a directional solidification heating device based on multiphysics coupling as described in any one of claims 1 to 8.