Phase field simulation analysis method and system for dendrite growth process under action of ultrasonic field

Abstract

The application relates to the technical field of computational simulation of material microstructure evolution, and discloses a phase field simulation analysis method and system for dendrite growth process under the action of an ultrasonic field. The method comprises the following steps: using a quantitative phase field method, a lattice Boltzmann method and a perfect matched layer method, correcting a basic quantitative phase field model based on ultrasonic field pressure, convection and mechanical effects, and obtaining an ultrasonic quantitative phase field model containing a multi-physical field coupling control equation; performing spatial and time discretization on the coupling control equation to obtain a discrete control equation; determining initial conditions and total boundary conditions based on solidification process working conditions; using a heterogeneous parallel algorithm to iteratively solve a definite equation group composed of the discrete control equation, the initial conditions and the total boundary conditions, and obtaining a numerical calculation result including global physical field data of dendrite evolution at each moment; calculating liquid undercooling degree distribution and extracting physical field parameters and solidification characteristic parameters of dendrite tips based on the numerical calculation result, and obtaining quantitative analysis results.

Description

Technical Field

[0001] This application relates to the field of computational simulation technology of material microstructure evolution, and also to the interdisciplinary fields of ultrasonic-assisted material processing, computational materials science and multiphysics field coupled numerical simulation. It relates to, but is not limited to, a phase field simulation analysis method and system for dendrite growth process under ultrasonic field. Background Technology

[0002] Advanced metallic materials and their efficient preparation technologies are crucial cornerstones for high-end equipment manufacturing in the national economy and defense sectors. Dendritic alloys, in particular, possess irreplaceable advantages in aerospace equipment and energy power due to their superior comprehensive properties, including corrosion resistance, high temperature resistance, oxidation resistance, and high strength and toughness. However, dendritic alloys are primarily alloyed by adding large amounts of refractory elements and rapidly prepared using high-temperature gradient methods such as arc melting, directional solidification, and additive manufacturing. This process often suffers from prominent problems such as multi-component solute segregation, crystal structure defects, extremely high residual stress, and lengthy and inefficient heat treatment.

[0003] High-energy ultrasound is a universally applicable external physical field for controlling the solidification process of metals. The nonlinear effects it generates near the solid-liquid interface, such as pressure, acoustic flow, and cavitation, have significant effects on suppressing macro- and micro-segregation, altering microstructure morphology, and improving mechanical properties. This has been verified in important dendritic materials such as aluminum alloys, magnesium alloys, copper alloys, stainless steel, nickel-based alloys, and high-entropy alloys. It represents a promising and promising frontier technology with broad applications in precision casting, high-efficiency welding, and additive manufacturing. Although scholars have gradually attempted to characterize the acoustic field and flow field of high-temperature molten metals and explore the ultrasonic solidification mechanism through macroscopic physical field simulation, high-temperature melt acoustic field sensing, and synchrotron radiation observation, limitations such as simulation scale, signal resolution, and sample material size still hinder a deep, quantitative, and fundamental understanding of the multi-physics coupling effect and its nonlinear characteristics near the solid-liquid interface. This severely restricts the quantitative research and theoretical establishment of the ultrasonic solidification mechanism of dendritic alloy materials, and impedes the large-scale application of ultrasonic solidification technology for molten metals / melt pools.

[0004] In fact, the key to simulating and predicting dendrite morphology in ultrasonic fields lies in the accurate calculation of diffusion and convection processes in the solid and liquid phases near complex solid-liquid interfaces. However, existing phase-field models cannot describe the mechanism by which ultrasonic forced convection affects dendrite growth, mainly due to the challenges posed by multiphysics and nonlinear problems in terms of models, algorithms, and computing power.

[0005] Given the current state of development of related ultrasonic solidification technologies, it is urgent to develop a phase-field simulation analysis method and system for dendrite growth under ultrasonic field. Summary of the Invention

[0006] In view of this, embodiments of this application provide a phase-field simulation analysis method and system for dendrite growth process under ultrasonic field action, which at least solves the problem that related phase-field models are difficult to accurately characterize the influence of the multi-effect coupling effect of ultrasonic field on dendrite growth behavior.

[0007] The technical solution of this application embodiment is implemented as follows: In a first aspect, embodiments of this application provide a phase-field simulation analysis method for dendrite growth under ultrasonic field, the method comprising: Using the quantitative phase-field method, the lattice Boltzmann method, and the perfectly matched layer method, based on the multi-physics coupling effect of the dendritic interface inside the alloy melt under the action of ultrasonic field, as well as the ultrasonic field pressure effect, ultrasonic field convection effect, and ultrasonic field mechanical effect, the basic quantitative phase-field model is modified to obtain an ultrasonic quantitative phase-field model that can characterize the dendrite growth law under the multi-effect coupling of ultrasonic field. The ultrasonic quantitative phase-field model includes the multi-physics coupling control equations of phase field, solute field, temperature field, and flow field, as well as the non-reflective boundary condition. The multiphysics coupling control equations are spatially and temporally discretized to obtain discrete control equations for each physics field. Initial conditions and overall boundary conditions are determined based on the solidification process of the alloy melt within the set simulation control parameters. The initial conditions are used to initialize the variables of each physics field across the entire domain. The overall boundary conditions include conventional boundary conditions and the non-reflection boundary conditions. Based on the set of boundary equations composed of the discrete control equations, the initial conditions, and the overall boundary conditions, iterative solutions are obtained using a heterogeneous parallel algorithm, an adaptive mesh refinement algorithm, a frame shifting algorithm, and a feedback control algorithm. The numerical calculation results of the ultrasonic quantitative phase-field model are obtained, including the target global physics field data corresponding to the dendrite evolution at each time step. Based on the numerical calculation results of the ultrasonic quantitative phase field model, the liquid phase undercooling distribution is calculated and the physical field parameters and solidification characteristic parameters of the dendrite tip are extracted to obtain the quantitative analysis results, so as to complete the quantitative analysis of dendrite growth.

[0008] Secondly, embodiments of this application provide a phase-field simulation analysis system for dendrite growth under ultrasonic field, the system comprising: The model building module is used to modify the basic quantitative phase field model using the quantitative phase field method, the lattice Boltzmann method, and the perfectly matched layer method. Based on the multi-physics coupling effect of the dendritic interface inside the alloy melt under the action of ultrasonic field, as well as the ultrasonic field pressure effect, ultrasonic field convection effect, and ultrasonic field mechanical effect, the model obtains an ultrasonic quantitative phase field model that can characterize the dendrite growth law under the multi-effect coupling of ultrasonic field. The ultrasonic quantitative phase field model includes the multi-physics coupling control equations of phase field, solute field, temperature field, and flow field, as well as the non-reflective boundary conditions. The numerical calculation module is used to spatially and temporally discretize the multiphysics coupling control equations to obtain discrete control equations for each physics field. Based on the solidification process of the alloy melt in the set simulation control parameters, initial conditions and overall boundary conditions are determined. The initial conditions are used to initialize the variables of each physics field in the global domain. The overall boundary conditions include conventional boundary conditions and the non-reflection boundary conditions. Based on the set of boundary equations composed of the discrete control equations, the initial conditions, and the overall boundary conditions, iterative solutions are obtained using heterogeneous parallel algorithms, adaptive mesh refinement algorithms, frame shifting algorithms, and feedback control algorithms to obtain the numerical calculation results of the ultrasonic quantitative phase-field model. The numerical calculation results include target global physics field data corresponding to dendrite evolution at each time step. The numerical analysis module is used to calculate the liquid phase undercooling distribution and extract the physical field parameters and solidification characteristic parameters of the dendrite tip based on the numerical calculation results of the ultrasonic quantitative phase field model, so as to obtain the quantitative analysis results and complete the quantitative analysis of dendrite growth.

[0009] The beneficial effects of the technical solutions provided in this application include at least the following: This application's embodiments, by integrating quantitative phase-field, lattice Boltzmann, and perfectly matched layer methods, and combining the multi-dimensional coupling effects of ultrasonic field pressure, convection, and mechanics to correct traditional phase-field models, effectively solve the problem that existing models cannot accurately characterize the mechanism of ultrasonic field action on dendrite growth. By constructing multi-physics field coupling control equations and non-reflective boundary conditions, coupled with a multi-algorithm collaborative iterative solution strategy, accurate numerical solutions for the entire process of alloy dendrite evolution under ultrasonic action are achieved. This enables complete acquisition of global physical field data at all times, ultimately completing a quantitative analysis of dendrite growth characteristics, significantly improving the overall integrity and accuracy of ultrasonic solidification dendrite simulation, and compensating for the insufficient quantitative analysis capabilities of traditional simulation methods. Attached Figure Description

[0010] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort, wherein: Figure 1 A schematic flowchart illustrating a phase-field simulation analysis method for dendrite growth under ultrasonic field action, provided in an embodiment of this application; Figure 2 This application provides a hardware system topology for numerical calculation of a phase-field model of dendrite growth process under ultrasonic field. Figure 3 A multiphysics field cloud map of the ultrasonic directional solidification dendrite growth process of a nickel-based alloy is provided in the embodiments of this application; Figure 4 A multiphysics field cloud map of the transformation process of columnar to equiaxed crystals in ultrasonic directional solidification of a nickel-based alloy is provided in the embodiments of this application. Figure 5 This is a schematic diagram of the composition and structure of a phase-field simulation analysis system for dendrite growth under ultrasonic field, provided in an embodiment of this application. Detailed Implementation

[0011] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. The following embodiments are used to illustrate this application, but are not intended to limit the scope of this application. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0012] In the following description, references are made to “some embodiments,” which describe a subset of all possible embodiments. However, it is understood that “some embodiments” may be the same subset or different subsets of all possible embodiments and may be combined with each other without conflict.

[0013] It should be noted that the terms "first, second, and third" used in the embodiments of this application are merely to distinguish similar objects and do not represent a specific ordering of objects. It is understood that "first, second, and third" can be interchanged in a specific order or sequence where permitted, so that the embodiments of this application described herein can be implemented in an order other than that illustrated or described herein.

[0014] It will be understood by those skilled in the art that, unless otherwise defined, all terms used herein (including technical and scientific terms) have the same meaning as commonly understood by one of ordinary skill in the art to which the embodiments of this application pertain. It should also be understood that terms such as those defined in general dictionaries should be understood to have a meaning consistent with their meaning in the context of the prior art, and should not be interpreted in an idealized or overly formal sense unless specifically defined as herein.

[0015] This application provides a phase-field simulation analysis method for dendrite growth under ultrasonic field, applicable to electronic devices. These electronic devices include, but are not limited to, mobile phones, laptops, tablets, handheld internet devices, multimedia devices, streaming media devices, mobile internet devices, wearable devices, or other types of electronic devices. The functions implemented by this method can be achieved by a processor in the electronic device calling program code. The program code can be stored in a computer storage medium; therefore, the electronic device includes at least a processor and a storage medium. The processor can be used to perform phase-field simulation analysis of the dendrite growth process under ultrasonic field, and the memory can be used to store the data required and generated during the phase-field simulation analysis of the dendrite growth process under ultrasonic field.

[0016] Figure 1 A schematic flowchart illustrating a phase-field simulation analysis method for dendrite growth under ultrasonic field provided in this application embodiment is shown below. Figure 1 As shown, the method includes at least the following steps: Step S110: Using the quantitative phase field method, the lattice Boltzmann method, and the perfect matching layer method, based on the multi-physics coupling effect of the dendritic interface inside the alloy melt under the action of ultrasonic field, as well as the ultrasonic field pressure effect, ultrasonic field convection effect, and ultrasonic field mechanical effect, the basic quantitative phase field model is modified to obtain an ultrasonic quantitative phase field model that can characterize the dendrite growth law under the multi-effect coupling of ultrasonic field. The ultrasonic quantitative phase field model includes the multi-physics coupling control equations of phase field, solute field, temperature field, and flow field, as well as the non-reflection boundary condition. Among them, a quantitative phase field model for the dendrite growth of binary alloys under ultrasonic field can be constructed based on quantitative phase field, lattice Boltzmann and perfect matching layer methods, taking into account ultrasonic pressure, acoustic flow and mechanical effects, so as to calculate the isothermal, directional, rapid and molten pool solidification process of dendritic alloy materials.

[0017] Step S120: The multiphysics coupling control equations are spatially and temporally discretized to obtain discrete control equations for each physics field; initial conditions and total boundary conditions are determined based on the solidification process of the alloy melt in the set simulation control parameters. The initial conditions are used to initialize the variables of each physics field in the whole domain, and the total boundary conditions include conventional boundary conditions and the non-reflection boundary conditions; based on the set of boundary equations composed of the discrete control equations, the initial conditions, and the total boundary conditions, iterative solutions are obtained using heterogeneous parallel algorithms, adaptive mesh refinement algorithms, frame shifting algorithms, and feedback control algorithms to obtain the numerical calculation results of the ultrasonic quantitative phase field model. The numerical calculation results include the target whole domain physics field data corresponding to the dendrite evolution at each time step. In this method, the control equations of the ultrasonic phase-field model are spatially and temporally discretized using numerical calculation methods. Initial and boundary conditions are determined based on the solidification process conditions. The numerical calculations are accelerated using high-performance heterogeneous parallel processing, adaptive mesh refinement, frame shifting, and feedback control algorithms. In some embodiments, the spatial discretization of the control equations can be based on the finite difference method, finite volume method, finite element method, or lattice Boltzmann method.

[0018] Step S130: Based on the numerical calculation results of the ultrasonic quantitative phase field model, calculate the liquid phase undercooling distribution and extract the physical field parameters and solidification characteristic parameters of the dendrite tip to obtain the quantitative analysis results, so as to complete the quantitative analysis of dendrite growth.

[0019] Among them, based on the numerical calculation results of the ultrasonic phase field model, the liquid phase undercooling distribution can be calculated, and physical field and solidification characteristic parameters such as dendrite tip pressure, flow rate, growth rate, kinetic undercooling, solute undercooling, curvature undercooling, and pressure undercooling can be extracted and quantitatively analyzed.

[0020] In the above embodiments, by integrating multiple methods such as quantitative phase field, lattice Boltzmann, and perfectly matched layers, and combining the multi-dimensional coupling effects of ultrasonic field pressure, convection, and mechanics to correct the traditional phase field model, the problem that existing models cannot accurately characterize the mechanism of ultrasonic field action on dendrite growth is effectively solved. By constructing multi-physics field coupling control equations and non-reflective boundary conditions, and combining them with a multi-algorithm collaborative iterative solution strategy, accurate numerical solutions for the entire process of alloy dendrite evolution under ultrasonic action are achieved. This enables the complete acquisition of global physical field data at each moment, and ultimately completes the quantitative analysis of dendrite growth characteristics, significantly improving the overall integrity and accuracy of ultrasonic solidification dendrite simulation, and making up for the shortcomings of traditional simulation methods in terms of quantitative analysis capabilities.

[0021] In some embodiments, the physical field includes a phase field, a temperature field, a solute field, and a flow field, and the basic quantitative phase field model includes basic quantitative phase field equations, basic solute field equations, basic temperature field equations, and basic flow field equations; step S110, "using the quantitative phase field method, the lattice Boltzmann method, and the perfectly matched layer method, based on the multi-physical field coupling effect of the dendritic interface inside the alloy melt under the action of the ultrasonic field, as well as the ultrasonic field pressure effect, ultrasonic field convection effect, and ultrasonic field mechanical effect, the basic quantitative phase field model is modified to obtain an ultrasonic quantitative phase field model that can characterize the dendrite growth law under the multi-effect coupling of the ultrasonic field," includes: Step S1101: Using the quantitative phase field method, based on the ultrasonic pressure effect, the pressure undercooling term is derived through the pressure state equation and the Clapeyron equation. The pressure undercooling term is then embedded into the basic quantitative phase field equation to obtain the phase field control equation, so as to characterize the driving law of ultrasonic pressure effect on dendrite growth. The phase field control equation can be expressed by formula (1): Formula (1); in, These are phase-field parameters, in the solid phase. In the liquid phase And in the solid-liquid diffusion interface region It changes smoothly between +1 and -1, and is used to distinguish between solid and liquid phases and characterize the interface position; Phase field parameters Regarding time The first-order partial derivative describes the rate of interface evolution over time; The phase field gradient characterizes the spatial gradient at the solid-liquid interface. | represents the magnitude of the phase field gradient; For the first-order partial differential operator with respect to x-space coordinates, = This represents the gradient components of the phase field parameters along the x-coordinate. For the first-order partial differential operator with respect to the y-space coordinates, = This represents the gradient components of the phase field parameters along the y-coordinate; The divergence operator describes the spatial divergence / convergence of flux; It represents the unit normal vector of the solid-liquid interface, characterizing the local normal orientation of the interface.

[0022] It represents the anisotropy of crystals and is a function of grain growth orientation; , These are the partial derivatives of the interface anisotropy function with respect to the gradient components of the phase field in the x and y directions, respectively. The reference kinetic relaxation time characterizes the characteristic time of atomic attachment / detachment at the solid-liquid interface, controlling the speed of interface evolution kinetics; The reference interface width corresponds to the characteristic thickness of the solid-liquid diffusion interface when there is no anisotropy.

[0023] It is a dimensionless temperature, in the formula It is the local temperature of the melt. The melt reference temperature, To balance the melting point, This refers to the pressure undercooling induced by ultrasound. To balance the solute partition coefficient, For the dimensionless undercooling of the conventional thermal / solute field, Let be the free energy function of the solid-liquid two-phase double potential well. Let be the first derivative of the free energy function of the solid-liquid two-phase double potential well with respect to the phase field. This is the temperature-phase field coupling potential function. This is the first derivative of the temperature-phase-field coupling potential function with respect to the phase field. This is the coupling strength coefficient.

[0024] To account for the pressure effect of ultrasound propagation in the liquid phase at the interface front, pressure undercooling is introduced into the dimensionless temperature. According to the Clapeyron equation, pressure undercooling... It can be expressed by formula (2): Formula (2); in, Liquidus temperature Local pressure, including static pressure generated by gravity and sound pressure generated by ultrasound. This is the reference pressure without ultrasonic action. For enthalpy of fusion, For local density, To correspond to pressure The reference density below. It can be expressed by formula (3): Formula (3); in, The average interfacial energy reference constant is For the fourth-order anisotropy intensity coefficient, ( ) is with <100> Aligned material coordinate system , Represents the x and y gradient components of the phase field in the material coordinate system. The phase field gradient in the material coordinate system. The gradient magnitude. and( The coordinate transformation relationship shown in formula (4) is satisfied: Formula (4); in, It is the i-th grain shaft and <100> The angle between orientations.

[0025] This process clarifies the complex coupling effects of multiple physical fields, such as phase field, orientation field, solute field, flow field, and temperature field, near the dendrite interface under ultrasonic field action, as well as nonlinear effects such as ultrasonic mechanics, sound pressure, acoustic flow, and cavitation. The cavitation effect can be considered as a severe sound pressure and acoustic flow effect. The phase field governing equation, including solute undercooling, considering the ultrasonic pressure effect, can be extended to a multiphase phase field model based on the double obstacle potential or double well potential. Considering the ultrasonic field pressure effect, the pressure state equation is solved, and the pressure undercooling term is introduced into the basic quantitative phase field equation according to the Clapeyron equation.

[0026] Step S1102: Using the lattice Boltzmann method, based on the ultrasonic field convection effect, the convection term including natural gravity convection and ultrasonic forced convection is embedded into the basic solute field equation and / or the basic temperature field equation to obtain the solute field control equation and / or the temperature field control equation. Among them, the solute field control equation and / or temperature field control equation, taking into account the ultrasonic solute and / or thermal convection effects, can be extended to multi-component alloy systems based on alloy thermodynamic data or calculation phase diagram methods; considering the ultrasonic field convection effect, the convection term is introduced into the basic solute field and / or basic temperature field equation, including natural convection generated by gravity and forced convection generated by ultrasound.

[0027] The solute field governing equation, considering the ultrasonic solute convection effect, is expressed by equation (5) in two dimensions: Formula (5); in, The flow field vector includes natural convection caused by gravity and forced convection caused by ultrasound. Represents the dimensionless solute field with respect to time The first-order partial derivative, For the spatial gradient of the solute field, For phase field parameters The solute diffusion coefficient is the independent variable, and the subscript is... Represents liquid phase, subscript Represents ultrasound field correction. Add solute flux to interface atoms. This refers to the macroscopic solute flux in the external field.

[0028] Step S1103: Using the lattice Boltzmann method, based on the ultrasonic field mechanical effect, the solid-liquid interface during the solidification process of the alloy melt is used as the dynamic internal boundary condition of the basic flow field equation and updated in real time to characterize the mechanical coupling between the solid dendrites and the liquid melt. Based on the equivalence principle of dynamic acceleration and gravitational acceleration, ultrasonic acceleration is embedded in the buoyancy term of the basic flow field equation so that the ultrasonic acceleration and the gravitational acceleration in the buoyancy term are vectored and superimposed to obtain the flow field control equation. The flow field control equations, considering the buoyancy effect caused by ultrasonic acceleration, can be described by the Navier-Stokes equations or the Lattice Boltzmann Method (LBM) equations. Considering the mechanical effect of the ultrasonic field, the solid-liquid interface during dendrite growth is used as the internal boundary condition of the flow field control equations and updated in real time to describe the mechanical coupling between the solid dendrites and the liquid melt. Considering the ultrasonic field application method, based on the equivalence principle of dynamic acceleration and gravitational acceleration, ultrasonic acceleration is introduced into the buoyancy term of the flow field control equations and vector-superimposed with gravitational acceleration.

[0029] Among them, the flow field equation, considering the buoyancy effect caused by ultrasonic acceleration, is expressed by formula (6) as the two-dimensional evolution equation of the flow field based on the Lattice Boltzmann Method (LBM): Formula (6); in, = (x, y) is a two-dimensional spatial position vector. Let be the lattice Boltzmann discrete velocity distribution function. Subscript Indicates the first The direction of motion of discrete particles Let be the equilibrium distribution function. Indicates the first A discrete lattice velocity vector, For lattice Boltzmann time steps, For particles The new spatial location after time convection migration For lattice Boltzmann relaxation time, Add a particle distribution correction term to the phase-field interface. The local density of the liquid fluid. For the first The weighting coefficients corresponding to each discrete velocity. This is the buoyancy vector. As shown in formula (7), the buoyancy is caused by the difference between the solute concentration and temperature and the reference value. It can be represented as: Formula (7); in, Let x be the vector of total equivalent buoyancy force per unit mass of liquid fluid at position x and time t in two-dimensional space. For reference density, It is the gravitational acceleration vector. It is a scalar of gravitational acceleration. It is the transpose symbol. Instantaneous solute concentration As the reference solute concentration, and These are the solute coefficient and the coefficient of thermal expansion, respectively. For simplicity, the embodiments in this application are omitted. . It is the local temperature of the melt. Since the melt reference temperature is used, ultrasonic forced convection and natural gravity convection are equivalent in terms of hydrodynamic effects. Therefore, ultrasound can be introduced into the buoyancy term as acceleration. In the embodiments of this application, It is the acceleration generated by the standing wave ultrasonic field, where , This refers to the ultrasonic amplitude. The frequency is the ultrasonic frequency.

[0030] Step S1104: Using the perfect matching layer method, a perfect matching layer is constructed on the non-physical boundary of the flow field computation domain to form a non-reflection boundary condition. The flow field computation domain is the solution space domain of the basic flow field equation. Among them, considering the boundary conditions of the non-reflective sound field, in order to avoid the reflection waves from contaminating the sound field and the flow field, a perfectly matched layer is constructed on the non-physical boundary of the flow field computational domain to achieve the non-reflective boundary conditions.

[0031] Boundary conditions are considered, including the ultrasonic mechanical effect at the solid-liquid interface, the ultrasonic field application method, and the no-reflection sound field condition. The ultrasonic field is applied by acceleration, and the no-reflection sound field condition is expressed by formula (8): Formula (8); in, The Perfectly Matched Layer (PML) absorbs and corrects source terms. For the actual absorption intensity, take , This represents the distance from the grid nodes within the absorption layer to the flow field-absorption layer boundary. The thickness of the absorption layer, As the reference absorption intensity, Take 0.08, For discrete lattice velocity components, Subscript Speed ​​number, subscript For spatial coordinate components, To perturb auxiliary storage variables, for In space Gradient of direction, for The derivative with respect to time t, Let be the disturbance equilibrium distribution function. Let be the local instantaneous macroscopic fluid velocity vector of the flow field. For the hypothetical far-field reference density, This represents the hypothetical far-field reference velocity.

[0032] Step S1105: Couple the phase field control equation, the solute field control equation, the temperature field control equation, the flow field control equation, and the non-reflective boundary condition to form an ultrasonic quantitative phase field model that can characterize the dendrite growth law under the multi-effect coupling of ultrasonic fields.

[0033] Among them, the non-reflective boundary condition considers the mechanical effect of the ultrasonic field at the solid-liquid interface, the ultrasonic field application method, and the non-reflective sound field condition. The ultrasonic field application method can be achieved by pressure, displacement, velocity, acceleration, etc.

[0034] In some embodiments, the establishment of the ultrasonic quantitative phase-field model considers any combination of crystal anisotropy, dynamic anisotropy, strain energy anisotropy, microjets and shock wave effects induced by cavitation bubbles or cavitation swarms.

[0035] In the above embodiments, targeted hierarchical correction and coupled modeling of the multiphysics field control equations were completed. Iterative optimization of the model was performed for the three core effects of ultrasonic pressure, convection, and mechanical processes. Simultaneously, a perfect matching layer method was introduced to construct reflection-free boundary conditions, completely solving the technical shortcomings of traditional phase-field models that neglect ultrasonic forced convection, solid-liquid interface mechanical coupling, and boundary acoustic wave reflection interference. This achieved deep coupled modeling of ultrasonic multi-effects and multiphysics fields, accurately reproducing the real physical mechanism of dendrite growth in alloy melts under ultrasonic fields, and fundamentally improving simulation accuracy and physical realism.

[0036] In some embodiments, the ultrasonic quantitative phase-field model is applicable to important dendritic structural materials such as aluminum alloys, magnesium alloys, copper alloys, stainless steel, nickel-based alloys, and high-entropy alloys, as well as processes such as isothermal solidification, rapid solidification, directional solidification, and molten pool solidification.

[0037] In some embodiments, the simulation control parameters include the total computational domain, the material parameters of the alloy melt, and simulation conditions, wherein the simulation conditions include the solidification process conditions; step S120, "based on the set of boundary equations composed of the discrete control equations, the initial conditions, and the total boundary conditions, iteratively solving the equations using heterogeneous parallel algorithms, adaptive mesh refinement algorithms, frame shifting algorithms, and feedback control algorithms to obtain the numerical calculation results of the ultrasonic quantitative phase-field model," includes: Step S1201: Based on the initial conditions, initialize and assign values ​​to each physical field variable in the global domain; configure the boundary conditions of each physical field based on the overall boundary conditions; Step S1202: The total computational domain is divided into grids using an adaptive mesh refinement algorithm to obtain a discrete grid; Among them, the heterogeneous parallel algorithm can be accelerated based on the adaptive mesh refinement algorithm.

[0038] Step S1203: Using a heterogeneous parallel algorithm, the following dendrite evolution iteration steps are repeatedly executed on the discrete grid until a preset calculation termination condition is met: The boundary conditions of the phase field, solute field, and flow field are configured sequentially and the corresponding discrete control equations are solved. The discrete control equations of the temperature field are updated and solved simultaneously to obtain the initial global physical field data. The initial global physical field data are processed and converted to output target global physical field data including phase field, solute field, temperature field, flow field and derived pressure field data. By using frame shifting algorithms and feedback control algorithms, frame shifting processing or feature parameter feedback control processing is performed based on the physical field data of the target global domain to correct the simulation control parameters.

[0039] In the above embodiments, by finely configuring initial and boundary conditions, combined with adaptive mesh refinement and heterogeneous parallel iterative solution strategies, accurate discretization and efficient solution of the simulation computational domain are achieved. By updating physical field data and correcting simulation control parameters in real time during the iteration process, the transient evolution characteristics of dendrite growth can be dynamically adapted, effectively solving the problems of poor mesh adaptability, fixed parameters, and low computational accuracy in traditional simulations. This ensures the stability and accuracy of the numerical solution throughout the process and meets the dynamic simulation requirements of dendrites under complex solidification conditions.

[0040] In some embodiments, the numerical calculation process includes nucleation model calculation and / or orientation field update to enable quantitative analysis of crystal nucleation and polycrystalline competition processes in an ultrasonic field.

[0041] In some embodiments, the numerical calculation process can perform computational analysis of arbitrary irregular computational domains in order to match the actual shape of the mold or component.

[0042] In some embodiments, the heterogeneous parallel algorithm in step S1203 achieves parallel computing in the dendrite evolution iteration step through total computing domain partitioning, multi-process parallelism, multi-CPU parallelism, multi-GPU parallelism, optimized communication protocols and hardware, parallel data file reading and writing, and device computing load balancing.

[0043] Discretizing the multiphysics coupling control equations in both spatial and temporal dimensions transforms them into a discrete numerical format suitable for parallel computing. Total computational domain partitioning involves decomposing the overall computational task into multiple independent sub-task blocks, achieving data parallelism. Multi-process parallelism employs a distributed memory programming model, launching multiple independent computational processes, each responsible for processing one or more computational sub-region blocks, with processes coordinating and exchanging data through message passing. Multi-CPU parallelism coordinates multiple CPUs for distributed computing, expanding the overall system processing capacity. Multi-GPU parallelism utilizes multiple GPUs for large-scale data parallelism, accelerating computationally intensive tasks. Optimized communication protocols and hardware ensure efficient and real-time data exchange between parallel units, achieving high-bandwidth, low-latency communication. Parallel data file reading and writing reduces I / O bottlenecks by having multiple processes simultaneously perform data file read and write operations. Device load balancing dynamically allocates computational tasks to CPUs and GPUs, maximizing the utilization of heterogeneous computing resources and avoiding device idleness or overload.

[0044] The above embodiments employ a multi-dimensional heterogeneous parallel computing architecture, integrating multiple optimization strategies such as computational domain partitioning, multi-process, multi-CPU and GPU collaborative computing, and load balancing. This significantly overcomes the bottlenecks of insufficient computing power and low computational efficiency in traditional serial computing. It effectively reduces data communication overhead and computation time in large-scale multiphysics simulations, solves the problems of large computational load and slow iterative convergence in ultrasonic coupled multiphysics simulations, and significantly improves the computational efficiency and computing power utilization of dendrite evolution numerical simulations, making it suitable for ultra-large-scale, high-precision simulation scenarios.

[0045] In some embodiments, the heterogeneous parallel algorithm can construct a two-dimensional or three-dimensional ultrasonic phase field model solver, and can be implemented through secondary development based on relevant commercial or open-source analysis software.

[0046] In some embodiments, the simulation conditions further include a simulated physical scenario, and the solidification process conditions include process parameters, ultrasonic parameters, and solidification parameters. Step S1203, "using a frame-shifting algorithm and a feedback control algorithm to perform frame-shifting processing or feature parameter feedback control processing based on the target global physical field data to correct the simulation control parameters," includes: Based on the simulated physical scenario and the solidification process conditions, a feedback control algorithm is used to perform feedback control on the simulation control parameters corresponding to specific detection positions in the dendrites and the alloy melt, based on the physical field data of the target global domain. The material parameters include alloy composition, alloy melting point, liquidus slope, and solute partition coefficient; the process parameters include pulling speed and temperature gradient; the ultrasonic parameters include amplitude, frequency, and phase; and the solidification parameters include solute concentration, growth rate, supercooling, flow rate, pressure, temperature, and curvature.

[0047] In the above embodiments, multi-dimensional simulation variables such as alloy material parameters, process parameters, ultrasonic parameters, and solidification parameters are refined and differentiated. A feedback control algorithm is introduced to correct and regulate key simulation parameters in real time, achieving precise matching between the simulation process and actual solidification conditions and ultrasonic loading scenarios. This effectively solves the problem of traditional simulation parameters being fixed and unable to adapt to dynamic conditions. It can accurately reproduce the differences in dendrite growth under different ultrasonic parameters and process conditions, significantly improving the adaptability and engineering versatility of the simulation model.

[0048] In some embodiments, step S130, "based on the numerical calculation results of the ultrasonic quantitative phase field model, calculating the liquid phase undercooling distribution and extracting the physical field parameters and solidification characteristic parameters of the dendrite tip to obtain quantitative analysis results, thereby completing the quantitative analysis of dendrite growth," includes: Step S1301: Based on the data file format of the numerical calculation results of the ultrasonic quantitative phase field model, parse out the target global physical field data corresponding to the dendrite evolution at each time step. Step S1302: Based on the physical field data of the target global domain, calculate auxiliary field variables including liquid phase undercooling distribution, physical field time mean and extreme values; Step S1303: Based on the auxiliary field variables, search and determine the target feature position corresponding to the dendrite tip; The target feature locations include the dendrite trunk, the secondary dendrite arm, and the tip of the tertiary dendrite arm.

[0049] Step S1304: Extract and calculate the solidification feature parameters corresponding to the target feature location; The solidification characteristic parameters include pressure, flow rate, growth rate, kinetic undercooling, solute undercooling, curvature undercooling, and pressure undercooling.

[0050] Step S1305: Based on the solidification characteristic parameters, quantitatively analyze the spatial distribution characteristics and temporal characteristics of the physical field to obtain quantitative analysis results; The spatial distribution characteristics and temporal characteristics include the spatial and temporal mean and maximum values ​​of the physical field, fluctuation period, phase delay, as well as the thickness and concentration of the solute boundary layer and the effective solute distribution coefficient of the alloying elements.

[0051] Step S1306: Save the quantitative analysis results.

[0052] The quantitative analysis results are saved for efficient visualization processing.

[0053] In the above embodiments, a fully closed-loop quantitative process was designed, from data parsing, auxiliary variable calculation, feature localization, parameter extraction to quantitative analysis. Strictly following a progressive data analysis logic, this process achieved accurate extraction of key characteristic parameters at the dendrite tip and quantitative characterization of the spatiotemporal features of the physical field. This overcomes the limitations of traditional simulations, which can only macroscopically observe and cannot accurately quantify the local growth characteristics of dendrites. It enables quantitative analysis of the growth law of ultrasonically solidified dendrites, providing precise data support for revealing the mechanism of ultrasonic-controlled dendrite growth.

[0054] In some embodiments, the method further includes: Step S141: Store the quantitative analysis results in a preset data file format; The quantitative analysis results may include the spatial and temporal mean and maximum values ​​of the physical field, fluctuation period, phase delay, as well as the thickness and concentration of the solute boundary layer and the effective solute distribution coefficient of the alloying elements.

[0055] Step S142: Using visualization software, the quantitative analysis results are displayed in the form of cloud maps, slices, and curves.

[0056] Among them, the results of the ultrasonic phase field model numerical calculation and analysis can be stored in a high-performance data file format, and the physical fields and solidification characteristic parameters such as phase field, solute field, pressure field, flow field, undercooling distribution, and orientation distribution can be visualized as cloud maps, slices, and curves through efficient visualization software.

[0057] In the above embodiments, based on precise numerical calculation and quantitative analysis, standardized data storage and multi-format visualization processes are added, achieving efficient retention and intuitive presentation of dendrite growth quantitative analysis results. Storing simulation results in a dedicated data format ensures data integrity and reusability; relying on diverse visualization formats such as cloud maps, slices, and curves, abstract physical field data and solidification characteristic parameters are transformed into intuitive and visual image data, facilitating technicians to quickly analyze the dendrite growth evolution law and greatly improving the readability, practicality, and engineering application value of the simulation results.

[0058] In some embodiments, step S141, "storing the quantitative analysis results in a preset data file format," includes: Step S1411: A block-based and layered data organization method is adopted to establish an independent storage channel for each physical field data of the target global domain and the solidification characteristic parameters, supporting fast selective reading; Step S1412: Add complete metadata to the quantitative analysis results. The metadata includes spatial grid information, time step, physical quantity units, coordinate system, and simulation parameters. Adding metadata ensures the self-descriptiveness and traceability of the data.

[0059] In some embodiments, the preset data file format includes: Supports reading and writing of structured data files; Supports parallel read / write and random access; Supports rapid data location and partial reading; Configure standardized, universal interfaces for cross-platform use; It has version compatibility and structural expansion capabilities; Supports access to operating system-level memory-mapped files.

[0060] The preset data file format supports reading and writing ultra-large structured data files, providing a 64-bit address space and single file per time step; it supports parallel reading and writing as well as random access, dividing large-scale datasets into fixed-size or variable-size data blocks for storage, with each data block capable of independent compression, encoding, and verification; it supports fast location and partial reading, employing a logically layered data organization architecture, with each layer stored and accessed independently; it features a standardized cross-platform interface, with the file structure independent of the operating system, hardware platform, and programming language, providing access from multiple environments; it supports version compatibility and expandable data areas, with the file header containing a format version identifier, supporting backward compatibility design, allowing the expansion of custom metadata or data areas while retaining the core structure; it supports operating system-level memory-mapped file access, directly mapping file content to the process address space, reducing data copy overhead, and achieving zero-copy, high-efficiency access. In some embodiments, the preset data file format may adopt a general data storage format.

[0061] The defined high-performance data file format boasts multiple advantages, including cross-platform compatibility, high compatibility, scalability, and zero-copy efficient access. It addresses the problems of poor compatibility, low read / write efficiency, inability to access data in parallel, and insufficient scalability associated with traditional simulation data formats. It can adapt to the calling needs of multiple systems and programming environments, supporting efficient read / write and memory-mapped access to ultra-large simulation datasets. While ensuring data storage security and format universality, it further improves simulation data access efficiency, providing a reliable guarantee for the long-term storage and reuse of large-scale ultrasonic dendrite simulation data.

[0062] Step S142, "using visualization software to display the quantitative analysis results in the form of cloud maps, slices, and curves," includes: Step S1421: Decode the quantitative analysis results to obtain the decoded dataset; Step S1422: Based on preset visualization requirements, perform data pruning, resampling, interpolation, or statistical calculations on the decoded dataset to generate a derived dataset suitable for rendering. Step S1423: Multi-resolution construction is performed on the derived dataset to generate detailed hierarchical structure data, supporting smooth zoom browsing from macro to micro. Step S1424: Visualize and render the detailed hierarchical structure data to obtain a visualized cloud map, a visualized slice, a visualized curve, a visualized physical field, and a visualized multi-physics field overlay and fusion map.

[0063] Among them, cloud map visualization renders scalar field data (such as supercooling and solute concentration) into a continuous color distribution cloud map in two-dimensional or three-dimensional space using color mapping technology; slice visualization supports the generation of data slices at any specified location and direction, projecting three-dimensional field data onto a two-dimensional plane for detailed observation; curve visualization extracts the changes of physical quantities at specific spatial points or along specific paths over time or space and plots them as two-dimensional curves for quantitative analysis; vector field visualization intuitively expresses vector field data (such as flow fields) using arrows, streamlines, or traces; and multi-physics field overlay and fusion visualization supports the overlay display of multiple physical fields in the same view, revealing the coupling relationship between fields through techniques such as transparency adjustment and hybrid rendering.

[0064] In the above embodiments, a dedicated data storage architecture with block-based and layered structures, coupled with a complete metadata embedding mechanism, is adopted to achieve classified storage, rapid location, and selective reading of simulation data, ensuring the integrity, orderliness, and traceability of massive simulation data. Simultaneously, through a visualization process of data preprocessing, multi-resolution construction, and layered rendering, seamless scaling and multi-field overlay analysis of simulation results from macro to micro levels are achieved. This solves the problems of poor data adaptability, insufficient detail display, and inability to perform multi-dimensional comparative analysis in traditional visualizations, significantly improving the level of precision in simulation post-processing.

[0065] Following visualization, the system also includes interactive and post-processing steps, providing a wealth of interactive tools that support viewpoint rotation, scaling, panning, animation playback (time series data), and dynamic adjustment of cross-sections; it integrates data query, measurement, statistics (such as maximum, minimum, average, and integral) and export functions; it supports outputting visualization results in various standard image or video formats and generating interactive web reports or 3D scene files.

[0066] In some embodiments, this application also provides a software and hardware system for implementing the phase-field simulation analysis method, including a software system and a hardware system, wherein: The software system includes: The core calculation module for phase field simulation is used to perform numerical solutions to the phase field control equations; The pre- and post-processing modules provide functions for geometric modeling, mesh generation, initial condition setting, result visualization, and analysis. The task management and scheduling module is responsible for task decomposition, resource allocation, and workflow control. The data management module is responsible for the input / output, storage, and efficient access of simulated data, and supports preset data file formats; The user interface module provides a graphical user interface, a command-line interface, and an application programming interface for user interaction and integration.

[0067] The hardware system includes: The computing unit cluster consists of multiple multi-core central processing unit nodes, providing distributed computing capabilities; Accelerator arrays integrate multiple graphics processors or dedicated computing accelerator cards to accelerate computationally intensive cores; A high-speed interconnect network, employing low-latency, high-bandwidth networking to connect all computing nodes and accelerators; The tiered storage system consists of a high-speed cache, a parallel file system, and a large-capacity archive storage, meeting the needs of high-speed reading, writing, and persistence of large-scale data. The system management node is responsible for resource monitoring, job scheduling, and system maintenance of the entire hardware cluster.

[0068] The software performs instruction set-level optimization and adaptation for the hardware, specifically in the following ways: Optimize instruction sets for specific CPU architectures and improve single-instruction multiple-data stream processing performance by utilizing instruction sets such as advanced vector extensions; Deep optimization of GPU kernel code, including thread block configuration, shared memory usage, and global memory access merging, to maximize GPU computing throughput; Hardware-aware communication optimization is employed to optimize inter-process communication patterns based on the interconnection network topology, thereby reducing latency and congestion. To optimize storage access, technologies such as data prefetching and non-contiguous access aggregation are used to adapt to the characteristics of tiered storage systems and hide I / O latency. It provides dynamic runtime tuning capabilities, adjusting the allocation strategy and parallel parameters of computing tasks between CPUs and accelerators in real time based on hardware load and performance feedback.

[0069] More preferably, the hardware and software system for implementing the phase-field simulation analysis method can be implemented based on workstations, servers, supercomputing platforms, cloud computing services, etc.

[0070] In some embodiments, the hardware and software system implementing the phase-field simulation analysis method comprises a software system written in C / C++ based on the MPI (Multi-Node Distributed Parallel) and CUDA (GPU Single Card Acceleration) libraries, with instruction set-level optimization and adaptation for the dual-node hardware platform. The core component topology of the dual-node hardware is as follows: Figure 2As shown, a single node includes a CPU (CPU1 and CPU2), a GPU (GPU1 to GPU8), a PCIe bus, an NVLink interconnect, an IB network card (i.e., the IB card in the diagram), a solid-state drive (SSD), and a hard disk drive (HDD). The PCIe bus is used to enable high-bandwidth communication between CPUs, between CPUs and GPUs, between CPUs and SSDs, between CPUs and HDDs, and between CPUs and IB network cards. The NVLink interconnect is used to enable high-bandwidth communication between GPUs. The IB network card is used to enable cross-node communication between CPU and GPU computing units. The SSD is used to implement high-speed parallel caching of numerical calculation results, and the HDD is used for large-capacity storage and access of numerical calculation results.

[0071] Multiphysics field cloud diagram of the ultrasonic directional solidification dendrite growth process of nickel-based alloys, as shown in the figure. Figure 3 As shown, the physical field comprises a pressure field, a flow field, a solute field, and a phase field, exhibiting a symmetrical distribution. Under the influence of gravity and ultrasound, a local low-pressure region appears on both sides of the dendrite tip; local convection occurs at the dendrite tip and on both sides, with the flow field intensity on both sides being higher than that at the dendrite tip; the solute field changes with the flow field, and the solute boundary layer is violently disturbed by the vortex flow field, resulting in an increase in the thickness of the solute boundary layer at the dendrite tip and a decrease in the thickness of the solute boundary layer on both sides of the dendrite tip; the change in the solute field causes a change in the supercooling at the solid-liquid interface during dendrite growth, leading to a deviation of the dendrite tip morphology from the parabolic shape under static conditions.

[0072] Multiphysics field cloud diagram of the columnar-equiaxed crystal transformation process in ultrasonic directional solidification of nickel-based alloys, as shown in the figure. Figure 4 As shown, the physical field includes the phase field, orientation field, pressure field, flow field, solute field, and undercooling distribution. The undercooling distribution is obtained from numerical calculation results. From the phase field and orientation field, it can be seen that along... <001> Preferred-oriented, statically growing dendrite clusters undergo extensive nucleation at the solid-liquid interface front after ultrasonication, generating randomly oriented equiaxed dendrites. The greater undercooling near the solid-liquid interface results in relatively larger equiaxed dendrites, while the smaller undercooling further away leads to relatively smaller equiaxed dendrites. Under ultrasonication, the pressure field interacts with the dendrites, causing local distortions in the pressure field that deviate from the oriented pressure gradient distribution. The flow field is stronger in regions with moderate solid fraction, primarily affecting the thickness and concentration of the solute boundary layer during dendrite growth, thus determining the undercooling distribution and enabling symmetrical and rapid growth of oriented solidified dendrites away from the interface.

[0073] The embodiments of this application include the following beneficial effects: To address the complex multi-physics coupling effects and nonlinear characteristics of dendrite growth under ultrasonic fields, a method for constructing a quantitative phase-field model of ultrasound is proposed, taking into account ultrasonic sound pressure, acoustic flow, and mechanical effects. By deeply integrating the advantages of quantitative phase field, lattice Boltzmann and perfect matching layer methods, a quantitative phase field model for dendrite growth of binary alloys under ultrasonic field is established. Based on a multi-node, multi-process, multi-GPU+CPU heterogeneous parallel algorithm, the parameters of the ultrasonic phase field model are set, the model is initialized, the control equations are solved, the boundary conditions are applied, and the calculation results are analyzed and output. Based on the numerical calculation results of the ultrasonic phase field model, the calculation of liquid phase undercooling distribution and the extraction and quantitative analysis of physical field and solidification characteristic parameters such as dendrite tip pressure, flow rate, growth rate, kinetic undercooling, solute undercooling, curvature undercooling, and pressure undercooling were realized. Based on a hardware system consisting of computing unit clusters, accelerator arrays, high-speed interconnect networks, and hierarchical storage, a phase-field simulation analysis method for dendrite growth under ultrasonic field action was realized, achieving efficient and accurate implementation. The establishment and implementation of a phase-field simulation analysis method for dendrite growth under ultrasonic field action lays the foundation for quantitative research and theoretical system establishment of ultrasonic solidification mechanism of dendritic alloy materials, and provides scientific guidance for the development of multi-component, multi-phase, and multi-physics phase-field models.

[0074] Based on the foregoing embodiments, this application provides a phase-field simulation analysis system for dendrite growth process under ultrasonic field. The system includes various modules and sub-modules, and each unit of each sub-module can be implemented by a processor in an electronic device; of course, it can also be implemented by specific logic circuits. In the implementation process, the processor can be a central processing unit (CPU), microprocessor (MPU), digital signal processor (DSP), or field programmable gate array (FPGA), etc.

[0075] Figure 5 This is a schematic diagram of the composition and structure of a phase-field simulation analysis system for dendrite growth under ultrasonic field provided in an embodiment of this application, as shown below. Figure 5 As shown, the system 500 includes: The model building module 51 is used to modify the basic quantitative phase field model by using the quantitative phase field method, the lattice Boltzmann method and the perfect matching layer method, based on the multi-physics coupling effect of the dendritic interface inside the alloy melt under the action of ultrasonic field, as well as the ultrasonic field pressure effect, ultrasonic field convection effect and ultrasonic field mechanical effect, to obtain an ultrasonic quantitative phase field model that can characterize the dendritic growth law under the multi-effect coupling of ultrasonic field. The ultrasonic quantitative phase field model includes the multi-physics coupling control equations of phase field, solute field, temperature field and flow field and the non-reflection boundary condition. The numerical calculation module 52 is used to spatially and temporally discretize the multiphysics coupling control equations to obtain discrete control equations for each physics field; determine initial conditions and total boundary conditions based on the solidification process of the alloy melt in the set simulation control parameters, wherein the initial conditions are used to initialize the variables of each physics field in the whole domain, and the total boundary conditions include conventional boundary conditions and the non-reflection boundary conditions; based on the set of boundary equations composed of the discrete control equations, the initial conditions, and the total boundary conditions, iteratively solve the equations using heterogeneous parallel algorithms, adaptive mesh refinement algorithms, frame shifting algorithms, and feedback control algorithms to obtain the numerical calculation results of the ultrasonic quantitative phase field model, wherein the numerical calculation results include the target whole domain physics field data corresponding to the dendrite evolution at each time step; The numerical analysis module 53 is used to calculate the liquid phase undercooling distribution and extract the physical field parameters and solidification characteristic parameters of the dendrite tip based on the numerical calculation results of the ultrasonic quantitative phase field model, so as to obtain the quantitative analysis results and complete the quantitative analysis of dendrite growth.

[0076] In some possible embodiments, the system further includes: The storage module is used to store the quantitative analysis results in a preset data file format; The display module is used to present the quantitative analysis results in the form of cloud maps, slices, and curves using visualization software.

[0077] In some possible embodiments, the physical field includes a phase field, a temperature field, a solute field, and a flow field; the basic quantitative phase field model includes basic quantitative phase field equations, basic solute field equations, basic temperature field equations, and basic flow field equations; the model construction module 51 includes: The first embedded submodule is used to derive the pressure undercooling term by using the quantitative phase field method based on the ultrasonic pressure effect through the pressure state equation and the Clapeyron equation, and embed the pressure undercooling term into the basic quantitative phase field equation to obtain the phase field control equation, so as to characterize the driving law of ultrasonic pressure effect on dendrite growth. The second embedding submodule is used to embed convection terms, which include natural gravity convection and ultrasonic forced convection, into the basic solute field equation and / or the basic temperature field equation based on the ultrasonic field convection effect using the lattice Boltzmann method, so as to obtain the solute field control equation and / or the temperature field control equation. The third embedded submodule is used to utilize the lattice Boltzmann method, based on the ultrasonic field mechanical effect, to take the solid-liquid interface of the alloy melt solidification process as the dynamic internal boundary condition of the basic flow field equation and update it in real time, characterizing the mechanical coupling between the solid dendrite and the liquid melt; based on the equivalence principle of dynamic acceleration and gravitational acceleration, ultrasonic acceleration is embedded in the buoyancy term of the basic flow field equation, so that the ultrasonic acceleration and the gravitational acceleration in the buoyancy term are vectoredly superimposed to obtain the flow field control equation; A construction submodule is used to construct a perfect matching layer on the non-physical boundary of the flow field computational domain using the perfect matching layer method, thereby forming a non-reflection boundary condition. The flow field computational domain is the solution space domain of the basic flow field equation. The coupling submodule is used to couple the phase field control equation, the solute field control equation, the temperature field control equation, the flow field control equation, and the non-reflective boundary conditions to form an ultrasonic quantitative phase field model that can characterize the dendrite growth law under the multi-effect coupling of ultrasonic fields.

[0078] In some possible embodiments, the simulation control parameters include the total computational domain, the material parameters of the alloy melt, and simulation conditions, the simulation conditions including the solidification process conditions; the numerical calculation module 52 includes: The assignment submodule is used to initialize and assign values ​​to each physical field variable in the global domain based on the initial conditions; and to configure the boundary conditions of each physical field based on the overall boundary conditions. The sub-module is used to divide the total computational domain into discrete grids using an adaptive mesh refinement algorithm. The iterative submodule is used to perform the following dendrite evolution iteration steps on the discrete grid using a heterogeneous parallel algorithm until a preset calculation termination condition is met: The solver submodule is used to configure the boundary conditions of the phase field, solute field, and flow field in sequence and solve the corresponding discrete control equations. It also updates and solves the discrete control equations of the temperature field simultaneously to obtain the initial global physical field data. The sorting submodule is used to sort and convert the initial global physical field data and output the target global physical field data, which includes phase field, solute field, temperature field, flow field and derived pressure field data. The feedback submodule is used to perform frame shifting or feature parameter feedback control processing based on the physical field data of the target global domain using frame shifting and feedback control algorithms to correct the simulation control parameters.

[0079] In some possible embodiments, the heterogeneous parallel algorithm is characterized by collaboratively achieving parallel computation in the dendrite evolution iteration step through total computation domain partitioning, multi-process parallelism, multi-CPU parallelism, multi-GPU parallelism, optimized communication protocols and hardware, parallel data file reading and writing, and device computational load balancing.

[0080] In some possible embodiments, the simulation conditions further include a simulated physical scenario, the solidification process conditions include process parameters, ultrasonic parameters, and solidification parameters, and the feedback submodule includes: The feedback unit is used to perform feedback control on the simulation control parameters corresponding to specific detection positions in the dendrites and the alloy melt based on the simulated physical scene and the solidification process conditions, using a feedback control algorithm and the physical field data of the target global domain. The material parameters include alloy composition, alloy melting point, liquidus slope, and solute partition coefficient; the process parameters include pulling speed and temperature gradient; the ultrasonic parameters include amplitude, frequency, and phase; and the solidification parameters include solute concentration, growth rate, supercooling, flow rate, pressure, temperature, and curvature.

[0081] In some possible embodiments, the numerical analysis module 53 includes: The parsing submodule is used to parse the target global physical field data corresponding to the dendrite evolution at each time step based on the data file format of the numerical calculation results of the ultrasonic quantitative phase field model. The first calculation submodule is used to calculate auxiliary field variables, including liquid phase undercooling distribution, physical field time mean and extreme value, based on the physical field data of the target global domain. The determination submodule is used to search and determine the target feature position corresponding to the dendrite tip based on the auxiliary field variable; An extraction submodule is used to extract and calculate the solidification feature parameters corresponding to the target feature location; The analysis submodule is used to quantitatively analyze the spatial distribution characteristics and temporal characteristics of the physical field based on the solidification characteristic parameters, and obtain quantitative analysis results. The storage submodule is used to store the quantitative analysis results.

[0082] In some possible embodiments, the storage module includes: A submodule is established to use a block-based and layered data organization method to create independent storage channels for each physical field data of the target global domain and the solidification characteristic parameters, supporting fast selective reading. Add a submodule to add complete metadata to the quantitative analysis results. The metadata includes spatial grid information, time step, physical quantity units, coordinate system, and simulation parameters. The display module includes: The decoding submodule is used to decode the quantitative analysis results to obtain the decoded dataset. The second calculation submodule is used to perform data pruning, resampling, interpolation or statistical calculation on the decoded dataset based on preset visualization requirements, and generate a derived dataset suitable for rendering. A submodule is built to construct the derived dataset at multiple resolutions, generating detailed hierarchical data that supports smooth zooming from macro to micro. The rendering submodule is used to perform visualization mapping and rendering on the detailed hierarchical structure data to obtain visualized cloud maps, visualized slices, visualized curves, visualized physical fields, and visualized multi-physics field overlay and fusion maps.

[0083] In some possible embodiments, the preset data file format includes: Supports reading and writing of structured data files; Supports parallel read / write and random access; Supports rapid data location and partial reading; Configure standardized, universal interfaces for cross-platform use; It has version compatibility and structural expansion capabilities; Supports access to operating system-level memory-mapped files.

[0084] It should be understood that the phrase "one embodiment" or "an embodiment" throughout the specification means that a specific feature, structure, or characteristic related to the embodiment is included in at least one embodiment of this application. Therefore, "in one embodiment" or "in an embodiment" appearing throughout the specification does not necessarily refer to the same embodiment. Furthermore, these specific features, structures, or characteristics can be combined in any suitable manner in one or more embodiments. It should be understood that in the various embodiments of this application, the sequence numbers of the above-described processes do not imply a sequential order of execution; the execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of this application. The sequence numbers of the above-described embodiments are merely descriptive and do not represent the superiority or inferiority of the embodiments.

[0085] It should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes that element.

[0086] In the several embodiments provided in this application, it should be understood that the disclosed devices and methods can be implemented in other ways. The device embodiments described above are merely illustrative. For example, the division of units is only a logical functional division, and in actual implementation, there may be other division methods, such as: multiple units or components can be combined, or integrated into another system, or some features can be ignored or not executed. In addition, the coupling, direct coupling, or communication connection between the various components shown or discussed can be through some interfaces, and the indirect coupling or communication connection between devices or units can be electrical, mechanical, or other forms.

[0087] The units described above as separate components may or may not be physically separate, and the components shown as units may or may not be physical units; they may be located in one place or distributed across multiple network units; some or all of the units may be selected to achieve the purpose of the embodiments of this application according to actual needs. In addition, each functional unit in the embodiments of this application may be fully integrated into one processing unit, or each unit may be a separate unit, or two or more units may be integrated into one unit; the integrated unit may be implemented in hardware or in the form of hardware plus software functional units.

[0088] Alternatively, if the integrated units described above are implemented as software functional modules and sold or used as independent products, they can also be stored in a computer-readable storage medium. Based on this understanding, the technical solutions of the embodiments of this application, or the parts that contribute to related technologies, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause the device automatic test line to execute all or part of the methods described in the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as mobile storage devices, ROMs, magnetic disks, or optical disks.

[0089] The methods disclosed in the several method embodiments provided in this application can be arbitrarily combined to obtain new method embodiments without conflict. The features disclosed in the several method or device embodiments provided in this application can be arbitrarily combined to obtain new method embodiments or device embodiments without conflict.

[0090] The above description is merely an embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A phase-field simulation analysis method for dendrite growth process under ultrasonic field, characterized in that, The method includes: Using the quantitative phase-field method, the lattice Boltzmann method, and the perfectly matched layer method, based on the multi-physics coupling effect of the dendritic interface inside the alloy melt under the action of ultrasonic field, as well as the ultrasonic field pressure effect, ultrasonic field convection effect, and ultrasonic field mechanical effect, the basic quantitative phase-field model is modified to obtain an ultrasonic quantitative phase-field model that can characterize the dendrite growth law under the multi-effect coupling of ultrasonic field. The ultrasonic quantitative phase-field model includes the multi-physics coupling control equations of phase field, solute field, temperature field, and flow field, as well as the non-reflective boundary condition. The multiphysics coupling control equations are spatially and temporally discretized to obtain discrete control equations for each physics field. Initial conditions and overall boundary conditions are determined based on the solidification process of the alloy melt within the set simulation control parameters. The initial conditions are used to initialize the variables of each physics field across the entire domain. The overall boundary conditions include conventional boundary conditions and the non-reflection boundary conditions. Based on the set of boundary equations composed of the discrete control equations, the initial conditions, and the overall boundary conditions, iterative solutions are obtained using a heterogeneous parallel algorithm, an adaptive mesh refinement algorithm, a frame shifting algorithm, and a feedback control algorithm. The numerical calculation results of the ultrasonic quantitative phase-field model are obtained, including the target global physics field data corresponding to the dendrite evolution at each time step. Based on the numerical calculation results of the ultrasonic quantitative phase field model, the liquid phase undercooling distribution is calculated and the physical field parameters and solidification characteristic parameters of the dendrite tip are extracted to obtain the quantitative analysis results, so as to complete the quantitative analysis of dendrite growth.

2. The method according to claim 1, characterized in that, The method further includes: The quantitative analysis results are stored in a preset data file format; The quantitative analysis results are displayed using visualization software in the form of cloud maps, slices, and curves.

3. The method according to claim 1, characterized in that, The physical fields include phase field, temperature field, solute field, and flow field. The basic quantitative phase field model includes basic quantitative phase field equations, basic solute field equations, basic temperature field equations, and basic flow field equations. The basic quantitative phase field model is modified using the quantitative phase field method, the lattice Boltzmann method, and the perfectly matched layer method. Based on the multi-physical field coupling effect of the dendritic interface inside the alloy melt under ultrasonic field action, as well as the ultrasonic field pressure effect, ultrasonic field convection effect, and ultrasonic field mechanical effect, the model is modified to obtain an ultrasonic quantitative phase field model capable of characterizing the dendrite growth law under the multi-effect coupling of ultrasonic fields, including: Using the quantitative phase-field method, based on the ultrasonic pressure effect, the pressure undercooling term is derived through the pressure state equation and the Clapeyron equation. The pressure undercooling term is then embedded into the basic quantitative phase-field equation to obtain the phase-field control equation, which characterizes the driving law of ultrasonic pressure effect on dendrite growth. Using the lattice Boltzmann method, based on the ultrasonic field convection effect, the convection term, which includes natural gravity convection and ultrasonic forced convection, is embedded into the basic solute field equation and / or the basic temperature field equation to obtain the solute field control equation and / or the temperature field control equation. Using the lattice Boltzmann method, based on the ultrasonic field mechanical effect, the solid-liquid interface during the solidification process of the alloy melt is used as the dynamic internal boundary condition of the basic flow field equation and updated in real time to characterize the mechanical coupling between the solid dendrites and the liquid melt. Based on the equivalence principle of dynamic acceleration and gravitational acceleration, ultrasonic acceleration is embedded in the buoyancy term of the basic flow field equation so that the ultrasonic acceleration and the gravitational acceleration in the buoyancy term are vectoredly superimposed to obtain the flow field control equation. Using the perfect matching layer method, a perfect matching layer is constructed on the non-physical boundary of the flow field computational domain to form a non-reflection boundary condition. The flow field computational domain is the solution space domain of the basic flow field equation. By coupling the phase field control equation, the solute field control equation, the temperature field control equation, the flow field control equation, and the non-reflective boundary condition, an ultrasonic quantitative phase field model is constructed that can characterize the dendrite growth law under the multi-effect coupling of ultrasonic fields.

4. The method according to claim 3, characterized in that, The simulation control parameters include the total computational domain, the material parameters of the alloy melt, and simulation conditions, wherein the simulation conditions include the solidification process conditions; the set of boundary equations based on the discrete control equations, the initial conditions, and the total boundary conditions is iteratively solved using a heterogeneous parallel algorithm, an adaptive mesh refinement algorithm, a frame shifting algorithm, and a feedback control algorithm to obtain the numerical calculation results of the ultrasonic quantitative phase-field model, including: Based on the initial conditions, the physical field variables of the entire domain are initialized and assigned values; the boundary conditions of each physical field are configured based on the overall boundary conditions. The total computational domain is divided into discrete grids using an adaptive mesh refinement algorithm. Using a heterogeneous parallel algorithm, the following dendrite evolution iteration steps are repeatedly executed on the discrete grid until a preset calculation termination condition is met: The boundary conditions of the phase field, solute field, and flow field are configured sequentially and the corresponding discrete control equations are solved. The discrete control equations of the temperature field are updated and solved simultaneously to obtain the initial global physical field data. The initial global physical field data are processed and converted to output target global physical field data including phase field, solute field, temperature field, flow field and derived pressure field data. By using frame shifting algorithms and feedback control algorithms, frame shifting processing or feature parameter feedback control processing is performed based on the physical field data of the target global domain to correct the simulation control parameters.

5. The method according to claim 4, characterized in that, The heterogeneous parallel algorithm achieves parallel computation in the dendrite evolution iteration step through total computation domain partitioning, multi-process parallelism, multi-CPU parallelism, multi-GPU parallelism, optimized communication protocols and hardware, parallel data file reading and writing, and device computational load balancing.

6. The method according to claim 4, characterized in that, The simulation conditions also include a simulated physical scenario. The solidification process conditions include process parameters, ultrasonic parameters, and solidification parameters. The step of using frame-shifting algorithms and feedback control algorithms to perform frame-shifting processing or feature parameter feedback control processing based on the physical field data of the target global domain to correct the simulation control parameters includes: Based on the simulated physical scenario and the solidification process conditions, a feedback control algorithm is used to perform feedback control on the simulation control parameters corresponding to specific detection positions in the dendrites and the alloy melt, based on the physical field data of the target global domain. The material parameters include alloy composition, alloy melting point, liquidus slope, and solute partition coefficient; the process parameters include pulling speed and temperature gradient; the ultrasonic parameters include amplitude, frequency, and phase; and the solidification parameters include solute concentration, growth rate, supercooling, flow rate, pressure, temperature, and curvature.

7. The method according to claim 1, characterized in that, The numerical calculation results based on the ultrasonic quantitative phase field model are used to calculate the liquid phase undercooling distribution and extract the physical field parameters and solidification characteristic parameters of the dendrite tip to obtain quantitative analysis results, thereby completing the quantitative analysis of dendrite growth, including: Based on the data file format of the numerical calculation results of the ultrasonic quantitative phase field model, the target global physical field data corresponding to the dendrite evolution at each time moment are parsed out. Based on the physical field data of the target global domain, auxiliary field variables including liquid phase undercooling distribution, physical field time mean and extreme value are calculated; Based on the auxiliary field variables, the target feature position corresponding to the dendrite tip is searched and determined. Extract and calculate the solidification feature parameters corresponding to the target feature location; Based on the solidification characteristic parameters, the spatial distribution characteristics and temporal characteristics of the physical field are quantitatively analyzed to obtain quantitative analysis results. Save the quantitative analysis results.

8. The method according to claim 2, characterized in that, The storage of the quantitative analysis results in a preset data file format includes: A block-based and layered data organization method is adopted to establish independent storage channels for each physical field data of the target global domain and the solidification characteristic parameters, supporting fast selective reading; Add complete metadata to the quantitative analysis results, including spatial grid information, time step, physical quantity units, coordinate system, and simulation parameters; The use of visualization software to display the quantitative analysis results in the form of cloud maps, slices, and curves includes: The quantitative analysis results are decoded to obtain the decoded dataset; Based on preset visualization requirements, data pruning, resampling, interpolation, or statistical calculations are performed on the decoded dataset to generate a derived dataset suitable for rendering. The derived dataset is constructed at multiple resolutions to generate detailed hierarchical data, supporting smooth zooming and browsing from macro to micro. The detailed hierarchical structure data is visualized, mapped, and rendered to obtain visualized cloud maps, visualized slices, visualized curves, visualized physical fields, and visualized multi-physics field overlay and fusion maps.

9. The method according to claim 2, characterized in that, The preset data file format includes: Supports read and write operations for structured data files; Supports parallel read / write and random access; Supports rapid data location and partial reading; Configure standardized, universal interfaces for cross-platform use; It has version compatibility and structural expansion capabilities; Supports access to operating system-level memory-mapped files.

10. A phase-field simulation and analysis system for dendrite growth under ultrasonic field, characterized in that, The system includes: The model building module is used to modify the basic quantitative phase field model using the quantitative phase field method, the lattice Boltzmann method, and the perfectly matched layer method. Based on the multi-physics coupling effect of the dendritic interface inside the alloy melt under the action of ultrasonic field, as well as the ultrasonic field pressure effect, ultrasonic field convection effect, and ultrasonic field mechanical effect, the model obtains an ultrasonic quantitative phase field model that can characterize the dendrite growth law under the multi-effect coupling of ultrasonic field. The ultrasonic quantitative phase field model includes the multi-physics coupling control equations of phase field, solute field, temperature field, and flow field, as well as the non-reflective boundary conditions. The numerical calculation module is used to spatially and temporally discretize the multiphysics coupling control equations to obtain discrete control equations for each physics field. Based on the solidification process of the alloy melt in the set simulation control parameters, initial conditions and overall boundary conditions are determined. The initial conditions are used to initialize the variables of each physics field in the global domain. The overall boundary conditions include conventional boundary conditions and the non-reflection boundary conditions. Based on the set of boundary equations composed of the discrete control equations, the initial conditions, and the overall boundary conditions, iterative solutions are obtained using heterogeneous parallel algorithms, adaptive mesh refinement algorithms, frame shifting algorithms, and feedback control algorithms to obtain the numerical calculation results of the ultrasonic quantitative phase-field model. The numerical calculation results include target global physics field data corresponding to dendrite evolution at each time step. The numerical analysis module is used to calculate the liquid phase undercooling distribution and extract the physical field parameters and solidification characteristic parameters of the dendrite tip based on the numerical calculation results of the ultrasonic quantitative phase field model, so as to obtain the quantitative analysis results and complete the quantitative analysis of dendrite growth.

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