A superconducting coil simulation method, system and computer storage medium

Abstract

The present application discloses a superconducting coil simulation method, system, and computer storage medium. The method is executed in parallel on a graphics processing unit and includes: establishing an electromagnetic response physical model of the full structure of the superconducting coil; determining the self-field; establishing a representative unit cell model; determining the magnetic field change rate of each turn of superconducting wire; calculating the current density distribution of the superconducting coil cross-section with the superconducting core filaments completely uncoupled using the FFT method; determining the heating power of the superconducting coil cross-section; determining the temperature field change of the superconducting coil cross-section; coupling the electromagnetic field and temperature field changes to determine the simulation data of the current density, magnetic field, and temperature over time; generating the result data of the electromagnetic response, hysteresis loss, and magnetic-thermal stability simulations. The present application realizes rapid simulation analysis of the electromagnetic response, hysteresis loss, and magnetic-thermal stability with the core filaments completely uncoupled in the two-dimensional problems of superconducting coils through 2D modeling, and has a lower calculation cost and higher efficiency compared to other methods of the same type.

Description

Technical Field

[0001] This application relates to the field of computer simulation technology, and particularly relates to a superconducting coil simulation method, system, and computer storage medium. Background Art

[0002] Driven by major demands such as the transformative development of future energy, advanced medical equipment, and large scientific installations, the requirement for the magnetic field strength of magnets is continuously increasing. Due to the strong current-carrying capacity of superconducting materials, high-field superconducting magnets have become the core technology for scientific instruments, medical treatment, industrial processing, power equipment, and national defense special equipment. In actual production, in order to obtain a higher magnetic field, superconducting materials are often made into multi-strand wire coils wound with multi-turn superconducting wires, and these multi-strand superconducting coils usually need to carry a transmission current in an external magnetic field. Considering performance stability and safety, the problems of magnetic hysteresis loss and magnetic-thermal stability are key issues in the design of these engineering structures. Especially when designing a coil, it is very important to be able to reliably simulate the electromagnetic response, loss, and magnetic-thermal stability of each turn of superconducting wire inside the coil. The structure of the superconducting coil is complex, and the number of internal superconducting core wires is uncertain, ranging from a dozen to tens of thousands, resulting in cumbersome development of actual superconducting coils. Compared with the actual long and arduous development cycle, it is more economical and efficient to conduct research on the electromagnetic response, loss, and magnetic-thermal stability of multi-strand superconducting coils with complex structures and develop an effective simulation method.

[0003] However, the simulation of the electromagnetic response, loss, and magnetic-thermal stability of a full-structure superconducting coil with a complex structure is still a challenge, mainly reflected in: (i) the electromagnetic constitutive of superconducting materials has the characteristic of strong non-linearity, numerical calculation is extremely difficult to converge, and the thermal loss has high requirements for accuracy; (ii) different from bulk superconductors, the structure of the superconducting coil is very complex, and usually the coil is composed of thousands of turns of superconducting wires. At present, due to the overly complex calculation object, the problem of magnetic-thermal stability cannot be directly simulated; (iii) superconductors are very sensitive to factors such as force, electricity, magnetism, and heat, and at the same time the magnet is exposed to a changing electromagnetic field, involving many physical quantities and mutual coupling, and there is an urgent need for a tool to analyze the magnetic-thermal stability of superconducting coils.

[0004] At present, some scholars have proposed solutions to the above requirements: using a 2D finite element program developed by MATLAB and COMSOL software packages to realize the simulation of the magnetic hysteresis loss and magnetic-thermal stability of a helical structure conductor. However, this method has a large amount of calculation and a long calculation time, and it is impossible to simulate the structure of a real multi-strand superconducting coil under the limitation of calculation cost. Summary of the Invention

[0005] An embodiment of the present application provides a superconducting coil simulation method, system and computer storage medium, which are used to solve the problems of large computational amount and long calculation time in the simulation of the hysteresis loss and magnetic-thermal stability of a helical structure conductor by a 2D finite element program developed using MATLAB and COMSOL software packages in the prior art.

[0006] On the one hand, an embodiment of the present application provides a superconducting coil simulation method, which is executed in parallel on a graphics processing unit. The method includes:

[0007] Establish an electromagnetic response physical model of the entire structure of the superconducting coil;

[0008] Apply an external current to the electromagnetic response physical model to determine the generated self-field;

[0009] Select a single-turn superconducting wire in the cross-section of the superconducting coil to establish a representative unit cell model;

[0010] Determine the magnetic field change rate of each turn of superconducting wire in the cross-section according to the three-dimensional background magnetic field and the self-field;

[0011] Calculate the current density distribution of the superconducting coil cross-section when the superconducting core wire is completely uncoupled on the representative unit cell model using the FFT method;

[0012] Iteratively calculate the electromagnetic field according to the magnetic field change rate, and determine the heating power of the superconducting coil cross-section according to the iterated electromagnetic field, the current density distribution and the temperature field distribution;

[0013] Combine the heat diffusion equation and the heating power to determine the temperature field change of the superconducting coil cross-section;

[0014] Couple the electromagnetic field and the temperature field change to determine the simulation data of the current density, magnetic field and temperature of the superconducting coil cross-section over time;

[0015] After obtaining the simulation data of each turn of superconducting wire in the superconducting coil, generate the result data of electromagnetic response, hysteresis loss and magnetic-thermal stability simulation.

[0016] On the other hand, an embodiment of the present application also provides a superconducting coil simulation system, which is deployed in parallel on a graphics processing unit. The system includes:

[0017] A physical model establishment module, configured to establish an electromagnetic response physical model of the entire structure of the superconducting coil;

[0018] A self-field determination module, configured to apply an external current to the electromagnetic response physical model to determine the generated self-field;

[0019] A unit cell model establishment module, configured to select a single-turn superconducting wire in the cross-section of the superconducting coil to establish a representative unit cell model;

[0020] A magnetic field change rate determination module, configured to determine the magnetic field change rate of each turn of superconducting wire on a cross-section according to a three-dimensional background magnetic field and a self-field;

[0021] A current density distribution determination module, configured to calculate the current density distribution of a superconducting coil cross-section in a case where superconducting core filaments are completely uncoupled on a representative unit cell model by using an FFT method;

[0022] A heat generation power determination module, configured to perform iterative calculation on an electromagnetic field according to the magnetic field change rate, and determine the heat generation power of a superconducting coil cross-section according to the iterated electromagnetic field, the current density distribution, and a temperature field distribution;

[0023] A temperature field determination module, configured to determine the change of the temperature field of a superconducting coil cross-section by combining a heat diffusion equation and the heat generation power;

[0024] A simulation data generation module, configured to couple the changes of the electromagnetic field and the temperature field to determine the simulation data of the current density, magnetic field, and temperature of a superconducting coil cross-section over time;

[0025] A post-processing module, configured to generate result data of electromagnetic response, hysteresis loss, and magnetic-thermal stability simulation after obtaining the simulation data of each turn of superconducting wire in a superconducting coil.

[0026] On the other hand, an embodiment of the present application further provides a computer storage medium, in which multiple computer instructions are stored, and the multiple computer instructions are used to cause a computer to execute the above method.

[0027] A superconducting coil simulation method, system, and computer storage medium in the present application have the following advantages:

[0028] By performing 2D modeling, rapid simulation analysis of the electromagnetic response, hysteresis loss, and magnetic-thermal stability of a superconducting coil in a two-dimensional problem with completely uncoupled superconducting core filaments is realized. Compared with other methods of the same type, the calculation cost is lower and it is more efficient. Description of the Drawings

[0029] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings required for use in the description of the embodiments or the prior art. Obviously, the following drawings are only some embodiments of the present application. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0030] Figure 1 It is a flowchart of a superconducting coil simulation method provided by an embodiment of the present application;

[0031] Figure 2Schematic diagram of the current density distribution of the non-coupled three-core superconducting wire H-φ method, H method and the method of the present application at different times provided by the embodiments of the present application;

[0032] Figure 3 Schematic diagram of the heat generation power comparison of the non-coupled three-core superconducting wire H-φ method, H method and the method of the present application provided by the embodiments of the present application;

[0033] Figure 4 Variation diagram of the cross-sectional temperature distribution of the full-structure superconducting coil with a 10×10 array structure provided by the embodiments of the present application under non-coupling. Detailed implementation manners

[0034] Next, the technical solutions in the embodiments of the present application will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present application.

[0035] Figure 1 Flowchart of a superconducting coil simulation method provided by the embodiments of the present application. The embodiments of the present application provide a superconducting coil simulation method, which is executed in parallel on a graphics processing unit. The method includes:

[0036] S100, establish an electromagnetic response physical model of the full structure of the superconducting coil.

[0037] Exemplarily, S100 specifically includes: obtaining the actual size of the full-structure superconducting coil; establishing an electromagnetic response physical model of the full-structure superconducting coil according to the actual size.

[0038] In the embodiments of the present application, the electromagnetic response physical model of the full-structure superconducting coil is a combined structure including multiple turns of superconducting wires.

[0039] S110, apply an external current to the electromagnetic response physical model and determine the generated self-field.

[0040] Exemplarily, the self-field is the magnetic field generated by the electromagnetic response physical model under the action of an external current. After applying an external current to the superconducting coil in the electromagnetic response physical model, it is considered that the self-field is uniform everywhere at the same superconducting wire, and the self-field value is the sum of the magnetic fields of all superconducting wires on the current superconducting wire at the same external current. The magnitude of the self-field caused by the current at each turn of the superconducting wire can be calculated using Ampere's circuital law.

[0041] S120, select a single turn of superconducting wire on the cross-section of the superconducting coil and establish a representative unit cell model.

[0042] Exemplarily, the established representative unit cell model includes composite structures such as multi-core wires, copper-based materials, and epoxy. When establishing the representative unit cell model, a single-turn superconducting wire can be selected from the cross-section of the superconducting coil according to the electromagnetic response physical model and actual size of the full-structure superconducting coil, and the representative unit cell model can be established. Taking the Nb3Sn superconducting wire as an example, its basic composition structure includes a copper matrix, Nb3Sn superconducting core wires, an epoxy impregnation layer, etc. Its effective current calculation domain is the calculation domain composed of the epoxy impregnation layer, copper matrix, and superconducting core wires, and its effective temperature calculation domain is the overall calculation domain.

[0043] S130. Determine the magnetic field change rate of each turn of superconducting wire on the cross-section according to the three-dimensional background magnetic field and self-field.

[0044] Exemplarily, when determining the magnetic field change rate, it is necessary to traverse each turn of superconducting wire to determine the magnetic field change rate of each turn of superconducting wire.

[0045] S140. Use the FFT method to calculate the current density distribution of the superconducting coil cross-section when the superconducting core wires are completely uncoupled on the representative unit cell model.

[0046] Exemplarily, FFT is the fast Fourier transform. After selecting a single-turn superconducting wire and establishing the representative unit cell model, numerical simulation can be carried out on this representative unit cell model to obtain the current density distribution on the cross-section of the superconducting wire.

[0047] S150. Perform iterative calculation on the electromagnetic field according to the magnetic field change rate, and determine the heat generation power of the superconducting coil cross-section according to the iterated electromagnetic field, the current density distribution, and the temperature field distribution.

[0048] Exemplarily, before the start of iteration, initial values of the temperature field and electromagnetic field need to be set. In the initial simulation, the heat generation power of the superconducting coil cross-section can be determined based on the initial values of the temperature field, electromagnetic field, and current density distribution. In the subsequent simulation process, iterative calculation needs to be carried out based on the initial values of the temperature field and electromagnetic field to determine the temperature field and electromagnetic field at the next moment, and based on this, determine the heat generation power at the next moment.

[0049] S160. Combine the heat diffusion equation and the heat generation power to determine the temperature field change of the superconducting coil cross-section.

[0050] Exemplarily, during the electromagnetic field iteration process, it can be based on the electromagnetic field change rate and the initial value of the electromagnetic field or the electromagnetic field at the previous moment. During the temperature field iteration process, after determining the temperature field change in S160, iterative calculation needs to be carried out based on the initial value of the temperature field or the temperature field at the previous moment according to the temperature field change to determine the temperature field at the next moment, as the input data for S150.

[0051] S170. Determine the simulated data of the current density, magnetic field, and temperature over time at the cross-section of the superconducting coil by coupling the changes in the electromagnetic field and temperature field.

[0052] S180. After obtaining the simulated data of each turn of superconducting wire in the superconducting coil, generate the result data of electromagnetic response, hysteresis loss, and magneto-thermal stability simulation.

[0053] Exemplarily, the result data includes results such as the current density distribution, heating power, and temperature distribution at each turn of superconducting wire. After completing the collection of the result data, corresponding charts are also generated. Since the result data includes results such as the current density distribution and temperature distribution, the generated charts also include charts such as the current density distribution chart, temperature distribution chart, and temperature change chart over time.

[0054] In S180, if the simulated data of each turn of superconducting wire in the superconducting coil is not fully obtained, it is necessary to return to S130 to re-perform the loop until the loop ends.

[0055] This application is executed in parallel on a graphics processing unit, i.e., GPU, and after optimizing the storage of memory data, the execution efficiency of the method can be further improved, the data processing speed of superconducting coil simulation can be enhanced, and the calculation cost can be reduced.

[0056] The embodiment of this application also provides a superconducting coil simulation system, which is deployed in parallel on a graphics processing unit. The system includes:

[0057] A physical model establishment module, used to establish an electromagnetic response physical model of the entire structure of the superconducting coil;

[0058] A self-field determination module, used to apply an external current to the electromagnetic response physical model to determine the generated self-field;

[0059] A unit cell model establishment module, used to select a single turn of superconducting wire at the cross-section of the superconducting coil to establish a representative unit cell model;

[0060] A magnetic field change rate determination module, used to determine the magnetic field change rate of each turn of superconducting wire at the cross-section according to the three-dimensional background magnetic field and the self-field;

[0061] A current density distribution determination module, used to calculate the current density distribution at the cross-section of the superconducting coil when the superconducting core wire is completely uncoupled by using the FFT method on the representative unit cell model;

[0062] A heating power determination module, used to perform iterative calculations on the electromagnetic field according to the magnetic field change rate, and determine the heating power at the cross-section of the superconducting coil according to the iterated electromagnetic field, the current density distribution, and the temperature field distribution;

[0063] A temperature field determination module, configured to determine the change of the temperature field of the superconducting coil cross-section by combining the heat diffusion equation and the heat generation power;

[0064] A simulation data generation module, configured to couple the electromagnetic field and the change of the temperature field to determine the simulation data of the current density, magnetic field, and temperature of the superconducting coil cross-section over time;

[0065] A post-processing module, configured to generate the result data of electromagnetic response, hysteresis loss, and magneto-thermal stability simulation after obtaining the simulation data of each turn of superconducting wire in the superconducting coil.

[0066] An embodiment of the present application also provides a computer storage medium, in which multiple computer instructions are stored, and the multiple computer instructions are used to cause a computer to execute the above method.

[0067] As Figure 2 shown, the calculation results of the present application method combined with the H-φ and H methods are used to compare and verify the current density distribution cloud diagrams of the three-core wire superconductor with completely uncoupled core wires at T / 4, T / 2, 3T / 4, and T moments under an alternating magnetic field. The consistent comparison results verify the accuracy and reliability of the method of the present application. As Figure 3 shown, the comparison results of the heat generation power of the non-coupled three-core wire superconducting wire based on the present application under the same loading environment in the current configuration are given to characterize the feasibility of the method of the present application. As Figure 4 shown, the temperature distribution diagram of the cross-section of the multi-strand wire superconducting coil based on the 10×10 array structure is given to characterize the feasibility of the method of the present application.

[0068] Although the preferred embodiments of the present application have been described, those skilled in the art can make additional changes and modifications once they learn the basic creative concepts. Therefore, the appended claims are intended to be construed to include the preferred embodiments and all changes and modifications falling within the scope of the present application.

[0069] Obviously, those skilled in the art can make various changes and modifications to the present application without departing from the spirit and scope of the present application. Thus, if these modifications and variations of the present application fall within the scope of the claims of the present application and their equivalent technologies, the present application is also intended to include these modifications and variations.

Claims

1. A superconducting coil simulation method, characterized in that, The method is executed in parallel on a graphics processing unit, and the method includes: Establishing an electromagnetic response physical model of the full structure of a superconducting coil; Applying an external current to the electromagnetic response physical model to determine the generated self-field; Selecting a single-turn superconducting wire in the cross-section of the superconducting coil to establish a representative unit cell model; the representative unit cell model includes a multi-core wire, a copper matrix, and an epoxy composite structure. When establishing the representative unit cell model, according to the electromagnetic response physical model and the actual size of the full-structure superconducting coil, select a single-turn superconducting wire in the cross-section of the superconducting coil to establish the representative unit cell model; Determining the magnetic field change rate of each turn of superconducting wire in the cross-section according to the three-dimensional background magnetic field and the self-field; Calculating the current density distribution of the superconducting coil cross-section with the superconducting core wires completely uncoupled on the representative unit cell model using the FFT method; Performing iterative calculations on the electromagnetic field according to the magnetic field change rate, and determining the heating power of the superconducting coil cross-section according to the iterated electromagnetic field, the current density distribution, and the temperature field distribution; Combining the heat diffusion equation and the heating power to determine the temperature field change of the superconducting coil cross-section; Coupling the electromagnetic field and the temperature field change to determine the simulation data of the current density, magnetic field, and temperature of the superconducting coil cross-section over time; After obtaining the simulation data of each turn of superconducting wire in the superconducting coil, generating the result data of electromagnetic response, hysteresis loss, and magneto-thermal stability simulation.

2. The superconducting coil simulation method according to claim 1, characterized in that, The establishing of the electromagnetic response physical model of the full structure of the superconducting coil includes: Obtaining the actual size of the full-structure superconducting coil; Establishing an electromagnetic response physical model of the full-structure superconducting coil according to the actual size.

3. A superconducting coil simulation method according to claim 1, characterized in that, After determining the temperature field change of the superconducting coil cross-section, performing iterative calculations on the temperature field based on the temperature field change.

4. A superconducting coil simulation method according to claim 1, characterized in that, It also includes: Generating a chart corresponding to the result data.

5. A superconducting coil simulation system, characterized in that, The system is deployed in parallel on a graphics processing unit, and the system includes: A physical model establishment module for establishing an electromagnetic response physical model of the full structure of a superconducting coil; A self-field determination module for applying an external current to the electromagnetic response physical model to determine the generated self-field; A unit cell model establishment module for selecting a single-turn superconducting wire in the cross-section of the superconducting coil to establish a representative unit cell model; the representative unit cell model includes a multi-core wire, a copper matrix, and an epoxy composite structure. When establishing the representative unit cell model, according to the electromagnetic response physical model and the actual size of the full-structure superconducting coil, select a single-turn superconducting wire in the cross-section of the superconducting coil to establish the representative unit cell model; A magnetic field change rate determination module for determining the magnetic field change rate of each turn of superconducting wire in the cross-section according to the three-dimensional background magnetic field and the self-field; A current density distribution determination module for calculating the current density distribution of the superconducting coil cross-section with the superconducting core wires completely uncoupled on the representative unit cell model using the FFT method; A heating power determination module for performing iterative calculations on the electromagnetic field according to the magnetic field change rate, and determining the heating power of the superconducting coil cross-section according to the iterated electromagnetic field, the current density distribution, and the temperature field distribution; A temperature field determination module, configured to determine the change of the temperature field of the superconducting coil cross-section by combining the heat diffusion equation and the heat generation power; A simulation data generation module, configured to couple the electromagnetic field and the change of the temperature field to determine the simulation data of the current density, magnetic field, and temperature of the superconducting coil cross-section over time; A post-processing module, configured to generate result data of electromagnetic response, hysteresis loss, and magneto-thermal stability simulation after obtaining the simulation data of each turn of superconducting wire in the superconducting coil.

6. A computer storage medium, characterized in that, Multiple computer instructions are stored in the computer storage medium, and the multiple computer instructions are used to cause the computer to execute the method according to any one of claims 1-4.

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