A method for correcting the undercooling degree of alloy melt for electromagnetic suspension experiment

Abstract

The application discloses a kind of alloy melt supercooling degree correction methods for electromagnetic suspension experiment, belong to material science and solidification process measurement field.The method includes: in electromagnetic suspension device, alloy melt is carried out cooling solidification experiment, obtains experimental cooling curve;Establish multi-physics field simulation model, numerical simulation cooling process;With the section before metastable liquid phase transition occurs in experimental cooling curve as benchmark, adjust specific parameters in model, make simulation cooling curve and the section accurate match, and after the matching simulation cooling curve is extended to metastable liquid phase transition until the stage before recalescence phenomenon appears, to obtain corrected simulation cooling curve;According to recalescence temperature inflection point on experimental cooling curve, determine recalescence starting time;With the time as benchmark, calibrate corrected recalescence starting temperature on simulation cooling curve, and based on the temperature, corrected supercooling degree is obtained.The application can accurately obtain the real supercooling degree of alloy melt.

Description

Technical Field

[0001] This invention belongs to the field of materials science and solidification process measurement technology, specifically relating to a method for correcting the undercooling of alloy melts for electromagnetic levitation experiments. Background Technology

[0002] Electromagnetic levitation is an important containerless material handling technology that effectively avoids heterogeneous nucleation. It is often used to study the deep supercooling solidification behavior of alloy melts and to prepare metastable materials. In electromagnetic levitation experiments, a non-contact infrared thermometer is typically used to monitor the cooling curve of the alloy melt to obtain the key thermodynamic parameter of nucleation supercooling.

[0003] However, for alloys prone to metastable liquid phase transitions, such as peritectic metastable liquid-phase separation alloys, the melt decomposes into two liquid phases (L→L1+L2) upon cooling to a certain degree of undercooling. Due to differences in composition, structure, and surface condition between the two newly formed phases, the surface emissivity of the alloy undergoes a sudden change at the moment of liquid phase separation. The signal intensity detected by an infrared thermometer is directly related to the emissivity of the target surface, and the accuracy of its output temperature value depends on a preset constant emissivity parameter. Therefore, this sudden change in emissivity causes a false sharp drop in the temperature curve output by the infrared thermometer, severely distorting the true cooling curve. This results in a significant error in the nominal undercooling obtained directly from this curve, failing to reflect the true undercooling of the alloy and becoming a long-standing bottleneck in measurement technology in this field.

[0004] Currently, while maintaining the advantages of electromagnetic levitation technology, there is still no effective solution for how to conveniently and accurately correct emissivity abrupt changes to obtain true supercooling. Summary of the Invention

[0005] The technical problem to be solved: To avoid the shortcomings of existing technologies, this invention provides a method for correcting the undercooling of alloy melts for electromagnetic levitation experiments. This method uses a combination of experimental measurement and numerical simulation to effectively correct temperature measurement errors caused by sudden changes in emissivity, thereby accurately obtaining the true undercooling of the alloy melt.

[0006] The technical solution of this invention is: a method for correcting the undercooling of alloy melts in electromagnetic levitation experiments. This method is used to correct infrared thermometry distortion caused by a sudden change in surface emissivity due to a metastable liquid phase transition during the cooling process of the alloy melt. The specific steps are as follows: Step 1: Conduct a cooling and solidification experiment on the alloy melt in the electromagnetic levitation device. Set the emissivity parameters of the infrared thermometer according to the emissivity value at the alloy liquidus temperature, and synchronously collect the temperature change curve of the alloy melt over time through the infrared thermometer as the experimental cooling curve. Step 2: Based on the physical parameters of the electromagnetic levitation device and the thermal properties of the alloy melt, establish a multiphysics simulation model that couples the electromagnetic field, flow field, and temperature field for numerical simulation of the cooling process; Step 3: Using the section before the metastable liquid phase transition in the experimental cooling curve as a benchmark, adjust specific parameters in the multiphysics simulation model to make the cooling curve obtained by simulation calculation accurately match the section, and extend the matched simulated cooling curve to the stage after the metastable liquid phase transition until the reglow phenomenon occurs, thereby obtaining the corrected simulated cooling curve. Step 4: Determine the re-glow start time based on the re-glow temperature inflection point on the experimental cooling curve; use this time as a reference to calibrate the corrected re-glow start temperature on the simulated cooling curve, and calculate the corrected supercooling based on this temperature.

[0007] A further technical solution of the present invention is: the alloy is an alloy that undergoes a metastable liquid phase transformation during solidification, and the metastable liquid phase transformation includes metastable liquid phase separation.

[0008] A further technical solution of the present invention is: in step 2, the governing equations of the multiphysics simulation model include: The electromagnetic field control equations based on the high-frequency Maxwell's equations in the case of no free charge are used to calculate the magnetic induction intensity, induced current density, Lorentz force density and Joule thermal power density. The flow field control equations based on the continuity equation and the Navier-Stokes equations are used to describe the flow field of liquid alloys under the combined action of electromagnetic force and buoyancy. The energy conservation equation, which includes the Joule heat source term, is used to calculate the temperature field distribution of the alloy melt; And mixed boundary conditions that simultaneously include convective and radiative heat transfer.

[0009] A further technical solution of the present invention is: in step 3, the specific parameters adjusted include the input current intensity of the levitation coil. I Convective heat transfer coefficient of suspended sample h ; The quantitative standard for precise matching is as follows: within the target time interval before the metastable liquid phase transition occurs, the relative root mean square error between the simulated cooling curve and the experimental cooling curve is ≤0.3%, and the absolute value of the relative temperature deviation between the two at the same time point is ≤0.5%, wherein the relative error is based on the liquidus temperature.

[0010] A further technical solution of the present invention is: the method for adjusting the specific parameter employs a sequential quadratic programming optimization algorithm, aiming to minimize the relative root mean square error, and iteratively adjusts... I and / or hThis continues until the quantification criteria are met.

[0011] A further technical solution of the present invention is: in step 3, the specific operation of the extension is: keep the optimized specific parameters unchanged, continue the simulation time, no longer use the experimental cooling curve as the fitting target, and independently calculate the temperature evolution until the re-glow start time.

[0012] A further technical solution of the present invention is as follows: In step 4, the method for determining the re-glow start time is as follows: the experimental cooling curve is numerically differentiated, and when the cooling rate changes from a negative value to a positive value and the positive duration exceeds a preset threshold, the time corresponding to the transition point is the re-glow start time.

[0013] A further technical solution of the present invention is as follows: In step 4, the specific method for calibrating the corrected re-glow start temperature on the simulated cooling curve is as follows: the re-glow start time on the experimental cooling curve is directly mapped to the simulated cooling curve that has achieved time axis matching, and the temperature value corresponding to that time is obtained by linear interpolation as the corrected re-glow start temperature.

[0014] A further technical solution of the present invention is: in step 4, the corrected undercooling is: Δ T ' = T L - T N ',in, T L This is the liquidus temperature of the alloy. T N 'This is the corrected re-ignition starting temperature.'

[0015] A further technical solution of the present invention is: the method further includes determining whether an emissivity mutation has occurred: on the experimental cooling curve, if an abnormal temperature drop or curvature mutation occurs before or after the metastable liquid phase transition, and this abnormal phenomenon cannot be explained by changes in experimental conditions such as changes in cooling gas flow rate or fluctuations in induction heating power, and simultaneously, changes in surface morphology or phase distribution observed by high-speed imaging occur synchronously, then it is determined that an emissivity mutation has occurred and the method is applicable; otherwise, the supercooling is directly calculated using the reglow temperature on the experimental cooling curve.

[0016] Beneficial effects The beneficial effects of this invention are as follows: This invention optimizes the multiphysics simulation model using reliable experimental data before the metastable transition, and then predicts the actual temperature evolution from the metastable liquid phase transition to the re-glow stage through epitaxial calculations; through the synergy of experiment and simulation, it achieves physical modeling and numerical decoupling of the physical interference source of "emissivity mutation," thereby obtaining the true undercooling of the alloy melt. Specific effects are analyzed as follows: (1) This invention addresses the specific physical phenomenon of abrupt changes in surface emissivity caused by metastable liquid phase transitions during the solidification process of a class of alloys prone to metastable liquid phase transitions (such as peritectic metastable liquid phase separation alloys). It proposes a correction scheme that combines experimental measurement with multiphysics simulation. This method provides an effective technical approach to overcome the distortion of infrared thermography curves caused by this phenomenon and thus accurately obtain the true undercooling of the alloy.

[0017] (2) Compared with the traditional approach of changing the temperature measurement method or ignoring the error, the present invention completes the correction of the temperature measurement error at the numerical level without changing the existing electromagnetic levitation experimental device. Thus, while fully retaining the core advantages of electromagnetic levitation technology of containerless and deep supercooling, it provides a reliable means for accurate measurement of supercooling.

[0018] (3) This method establishes a clear and repeatable analysis process. The simulation correction method adopted provides a possible technical path for dealing with transient physical property interference problems in other measurements. Attached Figure Description

[0019] Figure 1 This is a flowchart illustrating the alloy melt undercooling correction method for electromagnetic levitation experiments in this embodiment of the invention. Figure 2 This is a schematic diagram of the electromagnetic levitation experiment in an embodiment of the present invention; Figure 3 Electromagnetic levitation Co in this embodiment of the invention 50 Fe 25 Cu 25 Schematic diagram of metastable liquid phase separation during rapid solidification of alloys; Figure 4 The original cooling curve (black line) obtained experimentally in this embodiment of the invention is used to directly calculate the experimental nominal supercooling Δ. T ; Figure 5 This is a schematic diagram comparing the original infrared temperature measurement data (black line) of curve ③ in this embodiment of the invention with the simulated temperature curve (red line) after correction by the method of this invention. Figure 6 The original experimental cooling curves (black lines) and the corrected simulated curves (red lines) for curves ①, ②, and ③, and the experimental nominal supercooling Δ T With the corrected undercooling Δ T A comparison diagram of '. Detailed Implementation The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain the invention, and should not be construed as limiting the invention.

[0020] Existing technologies have significant shortcomings in addressing the problem of abrupt changes in temperature curve curvature caused by changes in emissivity: First, some researchers misjudge this temperature anomaly as experimental interference (such as airflow fluctuations or power instability) or believe it reflects a true temperature drop, thus directly reading the nominal supercooling and resulting in severely overestimated measurement results; Second, a few researchers have attempted to use colorimetric infrared thermometers (such as CN113252863A) to reduce the impact of emissivity changes, but colorimetric thermometry can only correct for proportional errors caused by changes in the absolute value of emissivity and cannot handle abrupt changes in the ratio of emissivity between two wavelengths caused by metastable phase transitions. Moreover, colorimetric thermometry will also produce significant deviations at the moment of phase transition due to changes in spectral emission characteristics; Third, although replacing contact temperature measurement methods such as thermocouples (such as CN104889348A) can avoid emissivity problems, it will disrupt the containerless conditions of electromagnetic levitation, introduce heterogeneous nucleation, and fail to obtain the true deep supercooled state.

[0021] Based on the above problems, this invention proposes a method for correcting the undercooling of alloy melts for electromagnetic levitation experiments. The method is used to correct infrared thermometry distortion caused by the sudden change in surface emissivity due to the metastable liquid phase transition of the alloy melt during the cooling process.

[0022] For the alloy, the following criteria are used to determine whether the metastable liquid phase transition during solidification will lead to a significant abrupt change in surface emissivity: If an abnormally sharp drop in temperature (a sudden increase in the rate of temperature decrease) or a sudden change in the slope of the temperature curve occurs before and after the metastable liquid phase transition, and this abnormal phenomenon cannot be explained by changes in experimental conditions such as changes in cooling gas flow rate or fluctuations in induction heating power, and the changes in surface morphology or phase distribution observed by high-speed imaging occur simultaneously, then it is determined that there is a sudden change in emissivity; otherwise, this method is not applicable.

[0023] The above technical solution will be further analyzed below with reference to examples and accompanying figures: In one embodiment, refer to Figure 1 As shown, the specific steps of a method for correcting the undercooling of alloy melts for electromagnetic levitation experiments are as follows: Step 1, refer to Figure 2 As shown, a cooling and solidification experiment was conducted on the alloy melt in an electromagnetic levitation device. The emissivity parameters of the infrared thermometer were set according to the emissivity value at the alloy liquidus temperature. The temperature change curve of the alloy melt over time was synchronously collected by the infrared thermometer and used as the experimental cooling curve. Step 2: Based on the physical parameters of the electromagnetic levitation device and the thermal properties of the alloy melt, establish a multiphysics simulation model that couples the electromagnetic field, flow field, and temperature field for numerical simulation of the cooling process; Step 3: Using the section before the metastable liquid phase transition in the experimental cooling curve as a benchmark, adjust specific parameters in the multiphysics simulation model to make the cooling curve obtained by simulation calculation accurately match the section, and extend the matched simulated cooling curve to the stage after the metastable liquid phase transition until the reglow phenomenon occurs, thereby obtaining the corrected simulated cooling curve. Step 4: Determine the re-glow start time based on the re-glow temperature inflection point on the experimental cooling curve; use this time as a reference to calibrate the corrected re-glow start temperature on the simulated cooling curve, and calculate the corrected supercooling based on this temperature.

[0024] In one embodiment, in step 1, the temperature measurement method used is infrared thermometry, and the emissivity parameter of the infrared thermometer needs to be set to a fixed value according to the emissivity value at the alloy liquidus temperature.

[0025] In one embodiment, step 2 employs a multiphysics model coupling electromagnetic, flow, and temperature fields to simulate the cooling process of the alloy melt under electromagnetic levitation conditions. The governing equations of the multiphysics simulation model are as follows: The electromagnetic field control equations are based on the high-frequency Maxwell's equations under the condition of no free charges, and are used to solve for the high-frequency electromagnetic field distribution generated by the induction coil; then, based on the induced current density... J With magnetic induction intensity B Calculate the Lorentz force density acting on the alloy melt. F And based on the induced current density J With electric field strength E Calculate the Joule heat power density as a heat source. Q m The calculation formulas are as follows:

[0026]

[0027]

[0028]

[0029]

[0030]

[0031] in, H The magnetic field strength, E For electric field strength, B =µ0 µ r H It represents the magnetic flux density. D =ε0 e r E It is the electric displacement vector. J = s e E The induced current density is µ0 = 4π × 10⁻⁶. -7 H / m is the free magnetic permeability, ε0 ​​= 8.854 × 10⁻⁶ -12 F / m is the vacuum dielectric constant; µ r , e r and s e These are the relative permeability, relative permittivity, and conductivity of the material (or medium), respectively. F The density of the Lorentz force. Q m The Joule heat power density is used as the average value of one oscillation period when both are used in subsequent calculations of the flow field and temperature field.

[0032] The flow field control equations are based on the continuity equation and the Navier-Stokes equations, and are used to describe the flow field of the liquid alloy under the combined action of electromagnetic force and buoyancy. The calculation formulas are as follows:

[0033]

[0034] in, u Represents the velocity vector. r For density, p For pressure, I It is the identity matrix. or For kinetic viscosity, g This is the gravitational acceleration vector.

[0035] The temperature field control equation is based on a term that includes a Joule heat source. Q m The energy conservation equation, used to calculate the temperature field distribution of an alloy melt, is expressed as follows:

[0036] in, T For temperature, C PL and k These represent the specific heat capacity and thermal conductivity of the liquid alloy, respectively.

[0037] The boundary conditions of the energy conservation equation, used to describe the heat exchange on the surface of the alloy melt under helium cooling, employ a hybrid boundary condition that simultaneously includes convective and radiative heat transfer. Its expression is as follows:

[0038] in, T ∞ For ambient temperature, h and e L These represent the convective heat transfer coefficient and the surface emissivity of the alloy, σ SB This is the Stefan-Boltzmann constant, with a value of 5.67 × 10⁻⁶. 8 W m -2 K -4 .

[0039] In one embodiment, in step 3, the experimental cooling curve before metastable liquid phase separation is used as a reference, and the convective heat transfer coefficient in the multiphysics simulation model is adjusted. h This ensures that the cooling curve obtained from the simulation calculation accurately matches the section.

[0040] The quantitative standard for "precise matching" is: the relative root mean square error (in terms of liquidus temperature) between the simulated cooling curve and the experimental cooling curve within the time interval before metastable liquid phase separation occurs. T L (Based on) less than or equal to 0.3%, and the absolute value of the relative temperature difference between the two at the same time point (based on the liquidus temperature) is less than or equal to 0.3%. T L (Based on the standard) not exceeding 0.5%. The adjustment strategy is as follows: first, set the parameters according to the physical properties of the cooling gas (He) and the experimental conditions. h The initial value is determined; then, a sequential quadratic programming (SQP) optimization algorithm is used to minimize the relative root mean square error (i.e., RMSE) and... T L The ratio is used as the target, and iterative adjustments are made. h Until the above quantitative standards are met.

[0041] The specific simulation calculation process is as follows: An axisymmetric two-dimensional geometric model of the electromagnetic levitation experiment is established; the alloy melt and surrounding gas domain are divided into triangular meshes, with the mesh density refined near the melt surface; material parameters include the alloy density. r Specific heat capacity C PL Thermal conductivity k Electrical conductivity s e kinetic viscosity or and surface emissivity e L The parameters include the thermophysical properties of the protective atmosphere; the electromagnetic field excitation parameters include the input current of the levitation coil. I and frequency fThe boundary conditions are as follows: convective heat transfer, radiative heat transfer, and free surface boundary conditions are applied to the melt surface, and magnetic potential or vector boundary conditions are applied to the electromagnetic field boundary. The initial conditions are the initial temperature of the alloy melt (liquidothermal temperature + superheat 100 ~ 200 K) and zero flow velocity and zero pressure. The solution process adopts the finite element method to solve the electromagnetic field, flow field, and temperature field in a sequential coupled manner, with a time step of 0.001 s. The parameter adjustment and convergence criteria are as follows: the solution stops when the objective function changes by less than 0.1% in two consecutive iterations or when the maximum number of iterations of 50 is reached.

[0042] After obtaining a simulated cooling curve that matches the experimental cooling curve well in the section before metastable liquid phase separation, the simulation curve is then calculated again from the moment before metastable liquid phase separation, using the same physical model and optimized parameter values, up to the stage after the metastable liquid phase transition and before the reglow phenomenon, thus obtaining the corrected simulated cooling curve. The specific operation of this "extension" is: maintaining the optimized convective heat transfer coefficient. h The simulation time progression remains unchanged, continuing from step 3. Instead of using the experimental curve as the fitting target, the temperature evolution is calculated independently until the re-ignition start time.

[0043] In one embodiment, in step 4, the re-glow inflection point on the experimental cooling curve is used as a reference to determine the re-glow initiation time, and the corrected re-glow initiation temperature is calibrated on the simulated cooling curve. Specifically: the re-glow initiation time is determined based on the re-glow temperature inflection point (i.e., the turning point where the temperature changes from decreasing to rapidly increasing) on ​​the experimental cooling curve. t Since both the experiment and simulation start from the same initial state (the superheated melt begins to cool), and step 3 has already matched the simulation curve and the experimental curve of the pre-separation metastable liquid phase section on the time axis (the time coordinates can be directly correlated), therefore the experimental curve... t This is directly mapped to the same moment on the simulation curve. On the corrected simulated cooling curve obtained in step 3, the temperature value corresponding to that moment is obtained using a linear interpolation method. T N ', as the corrected re-glow initiation temperature; then based on the liquidus temperature of the alloy. T L Calculate the corrected undercooling Δ T ' = T L - T N '.

[0044] In one embodiment, Co is electromagnetically levitated 50 Fe 25 Cu 25 Taking a pericrystalline metastable liquid phase separation alloy as an example, the method of this invention is applied to correct its undercooling.

[0045] I. Experimental Materials and Preparation: 1.1 Alloy Composition and Master Alloy Preparation The alloy selected in this embodiment is Co. 50 Fe 25 Cu 25 (Atomic percentage) This alloy undergoes metastable liquid phase separation (L→L1+L2) during solidification, belonging to a typical peritectic metastable phase separation system. The master alloy uses Co, Fe, and Cu metal raw materials with a purity of not less than 99.95%. After being mixed according to the nominal composition, it is repeatedly melted twice in a vacuum arc melting furnace to ensure uniform composition. The alloy sample used for the electromagnetic levitation experiment has a mass of approximately 0.6g.

[0046] 1.2 Thermophysical parameters Co 50 Fe 25 Cu 25 Liquidus temperature of alloy T L = 1696 K, liquid density r = 7.63 × 10 3 kg / m 3 Specific heat capacity C PL = 50.95 J / (mol·K) (equivalent to approximately 859 J / (kg·K) in mass heat capacity), thermal conductivity k = 74.2 W / (m·K) (liquid), conductivity s e = 2.37 × 10 6 S / m, kinetic viscosity or = 2.98 × 10 -3 Pa·s (liquid), surface emissivity e L The value is approximately 0.25 near the liquidus temperature (measured value). The protective atmosphere is high-purity Ar gas, whose thermal conductivity is... k g = 0.018 W / (m·K).

[0047] II. Experimental Apparatus and Parameters: 2.1 Electromagnetic levitation device This experiment utilizes a self-developed high-frequency electromagnetic levitation system, which mainly includes: a high-frequency induction heating power supply (maximum power 6.6 kW, operating frequency 200–700 kHz), a copper levitation coil (inner diameter 4 mm), and a vacuum chamber (ultimate vacuum degree 1.0 × 10⁻⁶). -5The system includes a Pa, a gas flow control system (Ar gas protection, He gas cooling), an infrared temperature measurement system (M316 type, response time 10ms, temperature measurement range 400~2500 K, accuracy ±1.5 K), and a high-speed camera system (Photron FASTCAM MiniUX100, sampling frequency 30000fps).

[0048] 2.2 Experimental Parameter Setting First, evacuate the vacuum chamber to a vacuum level of 1.0 × 10⁻⁶. -5 Pa, then backfilled with high-purity Ar gas to 1.0 × 10⁻⁶ Pa. 5 Pa was used as the protective atmosphere; the high-frequency induction heating device was adjusted to suspend and completely melt the sample to a superheat of 100K to 200K (corresponding to an initial temperature of 1796K to 1896K); after heating was stopped, He gas was immediately blown into the vacuum chamber to achieve rapid cooling; an M316 infrared thermometer was used, and its emissivity parameter was set to 0.25 at the alloy liquidus temperature of 1696K and kept constant; the sampling frequency of the infrared thermometer was set to 60Hz, and the high-speed camera sampling frequency was 30000fps.

[0049] III. Experimental Procedure and Data Acquisition: 0.6g of Co 50 Fe 25 Cu 25 The alloy sample was placed on the support rod at the center of the levitation coil, and a vacuum of 1.0 × 10⁻⁶ was applied. -5 Pa, then backfilled with high-purity Ar gas to 1.0 × 10⁻⁶ Pa. 5 Pa was used as the protective atmosphere. The high-frequency induction heating device was adjusted to suspend the sample and heat it to a superheated state of 100K–200K. He gas was then blown into the vacuum chamber to achieve rapid cooling and solidification of the sample. During the experiment, the surface liquid phase separation process of the alloy was recorded using a Photron FASTCAM Mini UX100 high-speed camera, such as... Figure 3 As shown. An M316 infrared thermometer was used, and its emissivity parameter was set according to the emissivity value (0.25) at the alloy liquidus temperature. The temperature change curve of the melt over time was collected synchronously through the thermometer and used as the experimental cooling curve.

[0050] This embodiment yielded three experimental cooling curves, such as... Figure 4 As shown by the black curve in the middle. Where: Curve ①: No abnormal temperature drop was observed; the nominal subcooling Δ was directly measured. T = 96 K (based on the liquidus temperature) T L Based on 1696K, the re-glow temperature T N=1600K, Δ T =96K); Curve ②: A significant abnormal temperature drop occurs during the cooling process, and the nominal subcooling Δ is directly measured. T =240K (re-glow temperature) T N =1456 K); Curve ③: An abnormal temperature drop occurs, which is more significant than that of curve ②, and the nominal subcooling Δ is directly measured. T =455 K (Reignition Temperature) T N =1241 K).

[0051] To verify the effectiveness and universality of the method of this invention, numerical simulation corrections will be performed on all three curves. The correction process will be illustrated in detail below using curve ③ as an example.

[0052] IV. Construction of Multiphysics Simulation Model: 4.1 Geometric Model and Mesh Generation An axisymmetric two-dimensional geometric model was established for the electromagnetic levitation experiment: the levitation coil was simplified to a lower 7-turn circular ring used to heat the sample and provide levitation force, while the upper 2 turns were control coils with opposite current directions. The alloy melt was approximately spherical (about 5 mm in diameter), surrounded by a protective atmosphere (Ar gas) region (i.e., the fluid domain). A triangular mesh was used to divide the computational domain, with local refinement at the melt surface, melt-gas interface, and near the coils to accurately capture the gradient changes of the electromagnetic field, flow field, and temperature field. The minimum mesh size was 0.05 mm, and the total number of meshes was approximately 30,000.

[0053] 4.2 Governing Equations and Boundary Conditions (1) Electromagnetic field governing equations:

[0054]

[0055]

[0056]

[0057] in, H The magnetic field strength, E For electric field strength, B =µ0 µ r H It represents the magnetic flux density. D =ε0 e r E It is the electric displacement vector. J = s e E The induced current density is µ0 = 4π × 10⁻⁶. -7 H / m is the free magnetic permeability, ε0 ​​= 8.854 × 10⁻⁶ -12 F / m is the vacuum dielectric constant; µ r , e r and s e These represent the relative permeability, relative permittivity, and conductivity of the material (or medium), respectively. Under the high-frequency electromagnetic field conditions described in this embodiment, the calculated temperature range is above the Curie point of the alloy; therefore, the relative permeability of the alloy melt is... µ r Take 1; at the same time, since the displacement current in the molten metal is much smaller than the conduction current, its relative permittivity is 1. e r Take 1. The protective atmosphere argon is an insulating gas with a relative magnetic permeability of 1. µ r and relative permittivity e r All values ​​are set to 1, conductivity s e =0.

[0058] Based on the induced current density J With magnetic induction intensity B Calculate the Lorentz force density acting on the alloy melt. F :

[0059] Based on the induced current density J With electric field strength E Calculate the Joule heat power density as a heat source. Q m :

[0060] The above Lorentz force density F With Joule heat power density Q m In subsequent calculations of the flow field and temperature field, the average value of one oscillation period is taken.

[0061] (2) Control equations of the flow field:

[0062]

[0063] in, u Represents the velocity vector. r For density,p For pressure, I It is the identity matrix. or For kinetic viscosity, g This is the gravitational acceleration vector.

[0064] (3) Temperature field governing equations:

[0065] in, T For temperature, C PL and k These represent the specific heat capacity and thermal conductivity of the liquid alloy, respectively.

[0066] (4) Boundary conditions:

[0067] in, T ∞ =298 K is the ambient temperature. h and e L These represent the convective heat transfer coefficient and the surface emissivity of the alloy, σ SB This is the Stefan-Boltzmann constant, with a value of 5.67 × 10⁻⁶. 8 W m -2 K -4 .

[0068] (5) Initial conditions: initial temperature of the melt T 0 = Liquidus temperature T L + Superheat, in this embodiment, is taken as T 0 = 1696K + 150K = 1846K; Initial flow velocity u 0 = 0; Initial pressure p 0 = 0.

[0069] 4.3 Initial assignment of material parameters Liquid phase density r = 7.63×10 3 kg / m 3 Specific heat capacity C PL =859 J / (kg·K), liquid thermal conductivity k = 74.2 W / (m·K), conductivity s e = 2.37 × 10 6 S / m, kinetic viscosity or = 2.98 × 10 -3 Pa·s, surface emissivity eL =0.25, initial estimated value of convective heat transfer coefficient h = 1000 W / (m 2 •K) (further optimization). Density of the protective atmosphere (Ar). r g =1.78 kg / m 3 thermal conductivity k g = 0.018 W / (m·K), kinetic viscosity or g = 2.2×10 5 Pa·s.

[0070] 4.4 Electromagnetic field excitation parameters In the simulation model constructed in this embodiment, the input current of the levitation coil... I Set to 350 A, frequency f Set to 300kHz.

[0071] V. Parameter Adjustment and Matching: 5.1 Parameters to be adjusted and optimization Considering the deviation between the actual experimental conditions and the initial estimate, the convective heat transfer coefficient was selected. h As the parameter to be adjusted, the experimental data of curve ③ before metastable liquid phase separation occurs (i.e., before the temperature drop point, 0–3.14 s) are used as the benchmark. The objective function is defined as the relative root mean square error (based on the liquidus temperature). T L = 1696 K as the baseline):

[0072] Among them, the number of sampling points N =188 (time interval length 3.14 s, sampling frequency 60 Hz).

[0073] 5.2 Optimize Algorithm Settings Algorithm: Sequential Quadratic Programming (SQP) Variable range: h ∈ [500, 2000] W / (m 2 ·K) Initial value: h 0 = 1000 W / (m 2 ·K) Convergence criteria: The relative change in the objective function between two consecutive iterations is less than 0.1%, or the maximum number of iterations is 50. Simulation time step: 0.001s 5.3 Iteration Process and Results After 23 iterations, the objective function converged, decreasing from an initial 0.755% (corresponding to an absolute RMSE of 12.8 K) to 0.277% (corresponding to an absolute RMSE of 4.7 K), satisfying the matching criteria of relative root mean square error ≤ 0.3% and relative temperature deviation absolute value ≤ 0.5%. The optimal parameters are: h * = 1600W / (m 2 ·K) reflects the intensity of convective cooling under He gas blowing.

[0074] 5.4 Epitaxial Simulation Keep the optimized h *The simulation calculation remains unchanged until the re-ignition start time (3.14 s to 6.14 s), and the temperature evolution is calculated independently without using the experimental curve as the fitting target. The corrected simulated cooling curve is thus obtained, as shown by the red curve in Figure 5. In the section where the experimental curve experiences an abnormally sharp drop, the simulated curve maintains its original trend and smoothly decreases.

[0075] VI. Calculation of Subcooling Correction: 6.1 Determination of the Re-enhancing Start Time Experimental curve ③ in t At 6.14 s, the temperature changes from decreasing to rising sharply (the inflection point of reglow initiation). This moment corresponds to the start of growth of a large number of primary solid nuclei in the melt and the release of latent heat of crystallization.

[0076] 6.2 Mapping and Temperature Reading Since both the experiment and simulation started cooling from the same initial temperature (1846 K), and Part 5 (parameter adjustment and matching) has already ensured precise matching of the time axis within the 0–6.14 s range, the re-glow start time on the experimental curve is... t N Once the value is determined to be 6.14s, it can be directly mapped to the simulation curve. Through linear interpolation, the simulated temperature corresponding to that moment is obtained. T N '( t N = 1374 K.

[0077] 6.3 Calculation of Subcooling Liquidus temperature T L = 1696 K, then the corrected undercooling is: Δ T ' = T L T N = 1696K 1374K = 322K 6.4 Summary of Correction Results for the Three Curves Curves ① and ② were corrected using the same procedure, and the results are shown in the table below. A comparison graph is also available. Figure 6 .

[0078]

[0079] Curve ① shows minimal change before and after correction (3 K) since no abrupt change in emissivity occurred; the difference mainly stems from the computational accuracy of the simulation model. Curves ② and ③ show significant correction values, indicating that the original experimental curves deviate severely from the true temperature. This method effectively eliminates the temperature measurement error introduced by the abrupt change in emissivity caused by the metastable phase transition.

[0080] VII. Comparative Example (Traditional Method): 7.1 Scale settings To verify the superiority of this invention, a comparative example using a traditional method was set up: The experimental setup and procedures were identical to those of this invention, but in the data processing stage, multiphysics simulation correction was not performed. Instead, the original cooling curve measured by an infrared thermometer was directly used, and the re-glow temperature inflection point was read. T N Calculate the supercooling (i.e., the experimental nominal supercooling Δ). T The calculation formula is: Δ T = T L T N For curves showing abnormal temperature drops (such as curves ② and ③ in this embodiment), traditional methods cannot identify or correct the emissivity mutation error and can only accept the measured value.

[0081] 7.2 Comparison of Results The supercooling obtained by the traditional method (direct temperature measurement) and the method of this invention (simulation correction) are compared, and the results are shown in the table below. The supercooling measured by the traditional method is denoted as Δ. T The supercooling corrected by the method of the present invention is denoted as Δ. T '.

[0082]

[0083] 7.3 Conclusion of the Comparative Example When the alloy does not undergo a metastable phase transition that causes a sudden change in emissivity (curve ①), the results of the traditional method and the present invention are similar (96 K vs 93 K), and both are acceptable.

[0084] When a sudden change in emissivity occurs (curves ② and ③), the supercooling given by the traditional method is significantly higher, while the supercooling corrected by the method of this invention is significantly lower, indicating that this method effectively corrects the temperature measurement error introduced by the sudden change in emissivity.

[0085] The method of this invention can effectively identify and correct temperature measurement errors introduced by metastable phase transitions, significantly improve the accuracy of supercooling measurement, and can be achieved without changing the experimental setup, simply through numerical simulation post-processing.

[0086] VIII. Conclusion: This embodiment fully demonstrates the entire process from experimentation to simulation and calibration. For Co 50 Fe 25 Cu 25 For alloys, the corrected undercooling obtained using the method of this invention can effectively correct the measurement deviation introduced by the abrupt change in emissivity, while the undercooling given by the traditional direct temperature measurement method is significantly higher when metastable phase transitions occur. Therefore, the undercooling correction method based on the synergy of experiment and simulation proposed in this invention has significant advantages and practical value.

[0087] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention without departing from the principles and spirit of the present invention.

Claims

1. A method for correcting the undercooling of an alloy melt for electromagnetic levitation experiments, characterized in that, The method described above is used to correct infrared thermometry distortion caused by abrupt changes in surface emissivity due to metastable liquid phase transitions during the cooling process of the alloy melt. The specific steps are as follows: Step 1: Conduct a cooling and solidification experiment on the alloy melt in the electromagnetic levitation device. Set the emissivity parameters of the infrared thermometer according to the emissivity value at the alloy liquidus temperature, and synchronously collect the temperature change curve of the alloy melt over time through the infrared thermometer as the experimental cooling curve. Step 2: Based on the physical parameters of the electromagnetic levitation device and the thermal properties of the alloy melt, establish a multiphysics simulation model that couples the electromagnetic field, flow field, and temperature field for numerical simulation of the cooling process; Step 3: Using the section before the metastable liquid phase transition in the experimental cooling curve as a benchmark, adjust specific parameters in the multiphysics simulation model to make the cooling curve obtained by simulation calculation accurately match the section, and extend the matched simulated cooling curve to the stage after the metastable liquid phase transition until the reglow phenomenon occurs, thereby obtaining the corrected simulated cooling curve. Step 4: Determine the re-glow start time based on the re-glow temperature inflection point on the experimental cooling curve; use this time as a reference to calibrate the corrected re-glow start temperature on the simulated cooling curve, and calculate the corrected supercooling based on this temperature.

2. The method for correcting the undercooling of alloy melts for electromagnetic levitation experiments according to claim 1, characterized in that: The alloy is an alloy that undergoes a metastable liquid phase transformation during solidification.

3. The method for correcting the undercooling of alloy melt for electromagnetic levitation experiments according to claim 1, characterized in that: In step 2, the governing equations of the multiphysics simulation model include: The electromagnetic field control equations based on the high-frequency Maxwell's equations in the case of no free charge are used to calculate the magnetic induction intensity, induced current density, Lorentz force density and Joule thermal power density. The flow field control equations based on the continuity equation and the Navier-Stokes equations are used to describe the flow field of liquid alloys under the combined action of electromagnetic force and buoyancy. The energy conservation equation, which includes the Joule heat source term, is used to calculate the temperature field distribution of the alloy melt; And mixed boundary conditions that simultaneously include convective and radiative heat transfer.

4. The method for correcting the undercooling of alloy melt for electromagnetic levitation experiments according to claim 1, characterized in that: In step 3, the specific parameters adjusted include the input current intensity of the levitation coil. I Convection heat transfer coefficient of suspended sample h ; The quantitative standard for precise matching is as follows: within the target time interval before the metastable liquid phase transition occurs, the relative root mean square error between the simulated cooling curve and the experimental cooling curve is ≤0.3%, and the absolute value of the relative temperature deviation between the two at the same time point is ≤0.5%, wherein the relative error is based on the liquidus temperature.

5. The method for correcting the undercooling of alloy melt for electromagnetic levitation experiments according to claim 4, characterized in that: The adjustment method for the specific parameter employs a sequential quadratic programming optimization algorithm, aiming to minimize the relative root mean square error, and iteratively adjusts the parameter. I and / or h This continues until the quantification criteria are met.

6. The method for correcting the undercooling of alloy melt for electromagnetic levitation experiments according to claim 5, characterized in that: In step 3, the specific operation of the extension is as follows: keep the optimized specific parameters unchanged, continue the simulation time, no longer use the experimental cooling curve as the fitting target, and independently calculate the temperature evolution until the re-glow start time.

7. The method for correcting the undercooling of alloy melt for electromagnetic levitation experiments according to claim 1, characterized in that: In step 4, the method for determining the re-glow start time is as follows: perform numerical differentiation on the experimental cooling curve, and when the cooling rate changes from a negative value to a positive value and the positive duration exceeds a preset threshold, the time corresponding to this transition point is the re-glow start time.

8. The method for correcting the undercooling of alloy melt for electromagnetic levitation experiments according to claim 7, characterized in that: In step 4, the specific method for calibrating the corrected re-glow start temperature on the simulated cooling curve is as follows: the re-glow start time on the experimental cooling curve is directly mapped to the simulated cooling curve that has achieved time axis matching, and the temperature value corresponding to that time is obtained by linear interpolation, which is used as the corrected re-glow start temperature.

9. The method for correcting the undercooling of alloy melt for electromagnetic levitation experiments according to claim 8, characterized in that: In step 4, the corrected undercooling is: Δ T ' = T L - T N ',in, T L This is the liquidus temperature of the alloy. T N 'This is the corrected re-ignition starting temperature.' 10. A method for correcting the undercooling of an alloy melt for electromagnetic levitation experiments according to any one of claims 1-9, characterized in that: The method further includes determining whether an emissivity mutation has occurred: on the experimental cooling curve, if an abnormal temperature drop or curvature mutation occurs before or after the metastable liquid phase transition, and this abnormal phenomenon cannot be explained by changes in experimental conditions such as changes in cooling gas flow rate or fluctuations in induction heating power, and simultaneously occurs in conjunction with changes in surface morphology or phase distribution observed by high-speed imaging, then it is determined that an emissivity mutation has occurred and the method described in any one of claims 1-9 applies; otherwise, the supercooling is directly calculated using the reglow temperature on the experimental cooling curve.

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