Method, system and computer storage medium for electromagnetic behavior simulation of multi-filament superconducting strands

Abstract

The application discloses a multi-core superconducting strand electromagnetic behavior simulation method and system and a computer storage medium. The method comprises the following steps: establishing a two-dimensional geometric model of a multi-core superconducting strand; determining a self / mutual inductance coefficient matrix of the multi-core superconducting strand and a self / mutual inductance coefficient matrix of each core wire by using the two-dimensional geometric model; determining a transport current caused by an applied current of the multi-core superconducting strand and an induced current caused by an applied magnetic field; determining a coupling current of each core wire and a magnetic field change rate caused by the coupling current according to the induced current; determining a total current of each core wire; determining a current distribution of the multi-core superconducting strand by coupling the transport current and the total current; and obtaining result data of electromagnetic behavior simulation after a loop ends. The application adopts a 2D modeling strategy based on an A-V method, has the advantages of small calculation amount, large calculation range and fast calculation speed, and can be used as an efficient auxiliary design tool to realize rapid simulation analysis on the electromagnetic behavior of partial coupling in a superconductor 3D problem.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of superconducting simulation, in particular to a multi-core superconducting strand electromagnetic behavior simulation method and system and a computer storage medium. BACKGROUND

[0002] In recent years, twisted multi-core superconducting strands have been applied in various engineering fields, including large magnets, levitation systems, motors, etc. These superconductors usually carry transmission current in an external magnetic field. Considering the performance stability and safety, the AC loss and magnetic thermal stability problem is a key problem in the design of these engineering structures. Especially in the design of superconducting magnets, it is very important to reliably simulate the electromagnetic behavior of the magnet wound by multi-core superconducting strands. Since the filaments of superconducting wires in superconducting magnets are generally twisted, there is different degree of coupling (i.e. complete coupling, uncoupling or partial coupling) between the multi-core superconductors under the action of an external magnetic field, which depends on the specific operating temperature and the size of the copper-based resistance. Studies have shown that the degree of coupling is related to the twisting degree of the multi-filament superconductor, the matrix material and the residual resistivity. Compared to the long and tedious development cycle, it is more economical and efficient to study the electromagnetic behavior of multi-core superconducting strands with different degrees of coupling and develop effective methods.

[0003] However, the calculation of millions or even tens of millions of degrees of freedom and the calculation difficulty of high nonlinearity seriously restrict the simulation calculation of superconductors. Although the existing three-dimensional (3D) simulation tools are accurate for the calculation results of partially coupled wires, they require huge computational cost and can only realize the simulation of double-filament and triple-filament superconductors. In fact, 3D simulation is extremely limited. For example, the NbTi superconducting wire contains at least 10,000 ultra-fine filaments. Based on the above 3D problem, the decision of 2D modeling can significantly save the calculation time. Even so, the current research on two-dimensional problems of partially coupled multi-core superconducting strands is still in the exploratory stage, and relatively few studies have been published. Even if there are already developed circuit models, they are specially customized for specific situations and are difficult to be universally applied in flexible superconducting magnet design.

[0004] Currently, some scholars have proposed three solutions to the above problems: (1) Based on the GetDP open source software, the H method equation of the magnetic field along the superconducting straight spiral distribution is solved to simulate the AC loss of the twisted filament. However, this method still solves the 3D model, and there are problems such as large calculation difficulty and unaffordable calculation cost. (2) In the spiral structure, the spiral surface structure is mapped into the coordinate system characterized by translation by using the symmetry of the field, and the 2D finite element program developed by MATLAB and COMSOL software package is used to simulate the self-field magnetic hysteresis loss of the spiral structure conductor. However, this method has great development difficulty, low flexibility, and is only suitable for the self-field magnetic hysteresis loss of the standard spiral symmetry model (only for the case of external current). (3) A two-dimensional (2D) method for coupling, partial coupling and non-coupling superconducting wires based on the H method finite element model is proposed. However, this method requires a large air calculation domain, which increases unnecessary calculation amount, and the selection of the resistivity of the air domain not only affects the calculation efficiency but also affects the accuracy of the calculation. SUMMARY

[0005] The embodiment of the present application provides a multi-core superconducting strand electromagnetic behavior simulation method, system and computer storage medium, which is mainly used for simulating the electromagnetic behavior of the superconductor under partial coupling and solving the problem of large calculation amount in the existing 3D and 2D simulation.

[0006] In one aspect, the embodiment of the present application provides a multi-core superconducting strand electromagnetic behavior simulation method, comprising:

[0007] Step one: establishing a two-dimensional geometric model of the multi-core superconducting strand;

[0008] Step two: determining the self / mutual inductance coefficient matrix of the multi-core superconducting strand and the self / mutual inductance coefficient matrix of each core under full coupling by using the two-dimensional geometric model;

[0009] Step three: initializing the self / mutual inductance coefficient matrix of the multi-core superconducting strand and the self / mutual inductance coefficient matrix of each core, and entering the loop body;

[0010] Step four: determining the transport current caused by the external current in the cross section of the multi-core superconducting strand and the induced current caused by the external magnetic field under full coupling;

[0011] Step five: determining the coupling current of each core and the magnetic field change rate caused by the coupling current according to the induced current;

[0012] Step six: determining the total current of each core;

[0013] Step seven: determining the current distribution of the cross section of the multi-core superconducting strand by coupling the transport current and the total current;

[0014] Step eight: after the loop ends, the result data of the electromagnetic behavior simulation is obtained.

[0015] In another aspect, the embodiment of the present application provides a multi-core superconducting strand electromagnetic behavior simulation system, comprising:

[0016] A model establishing module is configured to establish a two-dimensional geometric model of the multi-core superconducting strand.

[0017] A matrix determining module is configured to determine the self / mutual inductance coefficient matrix of the multi-core superconducting strand and the self / mutual inductance coefficient matrix of each core wire by using the two-dimensional geometric model.

[0018] A matrix initializing module is configured to initialize the self / mutual inductance coefficient matrix of the multi-core superconducting strand and the self / mutual inductance coefficient matrix of each core wire, and enter a loop body.

[0019] A first current determining module is configured to determine the transport current caused by the applied current in the cross section of the multi-core superconducting strand and the induced current caused by the applied magnetic field under full coupling.

[0020] A magnetic field determining module is configured to determine the coupling current of each core wire and the magnetic field change rate caused by the coupling current according to the induced current.

[0021] A second current determining module is configured to determine the total current of each core wire.

[0022] A third current determining module is configured to determine the current distribution of the cross section of the multi-core superconducting strand by coupling the transport current and the total current.

[0023] A result obtaining module is configured to obtain the result data of the electromagnetic behavior simulation after the loop ends.

[0024] In another aspect, the embodiment of the present application provides a computer storage medium, which stores a plurality of computer instructions for enabling a computer to execute the method of the above functional modules.

[0025] The multi-core superconducting strand electromagnetic behavior simulation method, system and computer storage medium in the present application have the following advantages:

[0026] The 2D modeling can realize fast simulation analysis of the electromagnetic behavior of partial coupling in the three-dimensional problem of superconductors, can provide an effective design tool for developing new superconductors to a certain extent, and has less calculation amount and is more efficient than other schemes of the same type. BRIEF DESCRIPTION OF DRAWINGS

[0027] 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 needed to be used in the embodiments or prior art description. Obviously, the drawings in the following description only constitute some embodiments of the present application, and for those skilled in the art, other drawings can also be obtained without creative labor based on these drawings.

[0028] Figure 1 A flow chart of the multi-core superconducting strand electromagnetic behavior simulation method provided by the embodiment of the present application;

[0029] Figure 2 A comparison diagram of the H-phi method, the H method and the A-V method of the present application for the three-core superconducting wire under uncoupling;

[0030] Figure 3 A current density distribution diagram of the three-core superconducting wire with coupling degrees of 0.2 and 0.5. DETAILED DESCRIPTION

[0031] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments only constitute some embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor are within the scope of protection of the present application.

[0032] Figure 1 A flow chart of the multi-core superconducting strand electromagnetic behavior simulation method provided by the embodiment of the present application. The embodiment of the present application provides a multi-core superconducting strand electromagnetic behavior simulation method, which comprises:

[0033] S100, a two-dimensional geometric model of the multi-core superconducting strand is established.

[0034] Exemplarily, the two-dimensional geometric model can be established according to the actual size of the multi-core superconducting strand.

[0035] In the embodiment of the present application, the two-dimensional geometric model is a composite structure containing multiple materials. Taking the Nb3Sn superconducting wire as an example, its basic component structure has a copper matrix, a Nb3Sn superconducting core wire, an epoxy resin impregnation layer and a glass fiber woven layer, and the effective calculation domain is the calculation domain composed of the copper matrix and the superconducting core wire.

[0036] S110, the self / mutual inductance coefficient matrix of the multi-core superconducting strand under full coupling and the self / mutual inductance coefficient matrix of each core wire are determined by using the two-dimensional geometric model.

[0037] Exemplarily, the step S110 specifically comprises: S111, acquiring material properties and electromagnetic loading parameters of the composite multi-core superconducting strand; and S112, determining the self / mutual inductance coefficient matrix of the multi-core superconducting strand under full coupling and the self / mutual inductance coefficient matrix of each core wire according to the set parameters and the two-dimensional geometric model.

[0038] In the embodiment of the application, the self / mutual inductance coefficient matrix of the multi-core superconducting strand under full coupling includes the influence of all calculation domains on the current point, and the calculation range of the self / mutual inductance coefficient matrix of each core wire only covers the area where the current core wire is located.

[0039] S120, initializing the self / mutual inductance coefficient matrix of the multi-core superconducting strand and the self / mutual inductance coefficient matrix of each core wire, and entering the loop body.

[0040] S130, determining the transport current caused by the applied current and the induced current caused by the applied magnetic field under full coupling in the cross section of the multi-core superconducting strand.

[0041] Exemplarily, the transport current I_Ia can be determined by solving the state equation of the A-V method, and in the solving process, the total current of each core wire calculated at the last time needs to be considered.

[0042] S140, determining the coupling current of each core wire and the magnetic field change rate caused by the coupling current according to the induced current.

[0043] Exemplarily, the step S140 specifically comprises: S141, determining the net current of each core wire according to the induced current; and S142, determining the coupling current of each core wire and the magnetic field change rate caused by the coupling current according to the net current and the coupling degree.

[0044] After completing the step S140, it further comprises: S143, determining the total magnetic field change rate and the magnetic vector potential change rate by considering the influence of the applied magnetic field.

[0045] In S141, the net current of each core wire is obtained by integrating the induced current caused by the magnetic field under full coupling. It is particularly noted that the magnetic field caused by the coupling current of the core wire in step S140 is obtained by simplifying the coupling current of the core wire into a current element placed at the geometric center of the core wire and using the Ampere loop theorem.

[0046] S150, determining the total current of each core wire.

[0047] Exemplarily, in the determination of the total current, the influence of the current applied needs to be considered. And in the solving process of steps S130 and S150, the synchronization of the magnetic field and the current in time needs to be noted.

[0048] S160, determining the current distribution of the cross section of the multi-core superconducting strand by coupling the transport current and the total current.

[0049] Exemplarily, the current distribution of the multi-core superconducting strand section is obtained by superimposing the transport current I_Ia and the total current of each core wire.

[0050] S170, after the loop ends, the result data of the electromagnetic behavior simulation is obtained.

[0051] Exemplarily, the result data includes current distribution, magnetic field distribution, and AC loss, etc.

[0052] After the collection of the result data is completed, it further includes: S171, generating a chart corresponding to the result data. Since the result data includes current distribution, magnetic field distribution, and AC loss, etc., the generated chart includes current distribution chart, magnetic field distribution chart, and AC loss table, etc.

[0053] In the embodiment of the application, the judgment of whether the loop ends is performed after the processing of step S160 is completed each time, if it is determined that the loop ends, the result data is collected, if the loop has not ended, the loop processing is continued until the loop ends.

[0054] As shown in Figure 2 The current distribution cloud map of the three-core superconductor at T / 4 and T / 2 moments under alternating magnetic field is verified by comparing the calculation results of the method of the application combined with H-phi and H method, and the consistent comparison results verify the accuracy and reliability of the method of the application. As shown in Figure 3 The calculation results of the three-core superconducting wire under the same loading environment based on the application about the partially coupled (coupling degree is 0.2 and 0.5) three-core superconducting wire under the current configuration are given, to represent the feasibility of the method of the application.

[0055] The embodiment of the application further provides a multi-core superconducting strand electromagnetic behavior simulation system, the system comprises:

[0056] The model establishing module is used to establish a two-dimensional geometric model of the multi-core superconducting strand.

[0057] The matrix determining module is used to determine the self / mutual inductance coefficient matrix of the multi-core superconducting strand and the self / mutual inductance coefficient matrix of each core wire by using the two-dimensional geometric model.

[0058] The matrix initialization module is used to initialize the self / mutual inductance coefficient matrix of the multi-core superconducting strand and the self / mutual inductance coefficient matrix of each core wire, and enter the loop body.

[0059] The first current determining module is used to determine the transport current caused by the applied current in the multi-core superconducting strand section and the induced current caused by the applied magnetic field under full coupling.

[0060] The magnetic field determination module is configured to determine the coupling current of each core wire and the rate of change of the magnetic field generated by the coupling current according to the induced current;

[0061] The second current determination module is configured to determine the total current of each core wire;

[0062] The third current determination module is configured to determine the current distribution of the multi-core superconducting strand cross section by coupling the transport current and the total current;

[0063] The result acquisition module is configured to obtain the result data of the electromagnetic behavior simulation after the loop ends.

[0064] The embodiment of the present application further provides a computer storage medium, which stores a plurality of computer instructions, and the computer instructions are used for enabling a computer to execute the method.

[0065] Although the preferred embodiments of the present application have been described, those skilled in the art can make additional changes and modifications to the embodiments once they know the basic inventive concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications falling within the scope of the present application.

[0066] Obviously, those skilled in the art can make various modifications and variations 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 equivalent technologies, the present application is also intended to include these modifications and variations.

Claims

1. A method for simulating the electromagnetic behavior of multi-core superconducting strands, characterized in that, The methods include: Step 1: Establish a two-dimensional geometric model of the multi-core superconducting strand; Step 2: Use the two-dimensional geometric model to determine the self / mutual inductance coefficient matrix of the fully coupled multi-core superconducting strand and the self / mutual inductance coefficient matrix of each core wire; Step 3: Initialize the self / mutual inductance coefficient matrix of the multi-core superconducting strand and the self / mutual inductance coefficient matrix of each core wire, and enter the loop body; Step 4: Determine the transport current caused by the applied current and the induced current caused by the applied magnetic field under full coupling in the cross section of the multi-core superconducting strand. Step 5: Determine the coupling current of each core wire and the rate of change of the magnetic field generated by the coupling current based on the induced current; Step Six: Determine the total current for each core wire; Step 7: Couple the transport current and the total current to determine the current distribution across the cross-section of the multi-core superconducting strand; Step 8: After the loop ends, obtain the result data of the electromagnetic behavior simulation; Step two includes: Obtain the material properties and electromagnetic loading rate parameters of composite multi-core superconducting strands; The self / mutual inductance coefficient matrix of the multi-core superconducting strand under full coupling and the self / mutual inductance coefficient matrix of each core wire are determined based on the set parameters and the two-dimensional geometric model. Step five includes: The net current of each core wire is determined based on the induced current; The coupling current of each core wire and the rate of change of the magnetic field generated by the coupling current are determined based on the net current and the coupling degree.

2. The method for simulating the electromagnetic behavior of multi-core superconducting strands according to claim 1, characterized in that, After determining the coupling current of each core wire and the rate of change of the magnetic field generated by the coupling current based on the induced current, the method further includes: The total rate of change of the magnetic field and the rate of change of the magnetic vector potential are determined by considering the influence of the applied magnetic field.

3. The method for simulating the electromagnetic behavior of multi-core superconducting strands according to claim 1, characterized in that, After obtaining the results data from the electromagnetic behavior simulation, the following is also included: Generate a chart corresponding to the resulting data.

4. A multi-core superconducting strand electromagnetic behavior simulation system, characterized in that, include: The model building module is used to build a two-dimensional geometric model of a multi-core superconducting strand. The matrix determination module is used to determine the self / mutual inductance coefficient matrix of the fully coupled multi-core superconducting strand and the self / mutual inductance coefficient matrix of each core wire using the two-dimensional geometric model; the matrix determination module obtains the material properties and electromagnetic loading rate parameters of the composite multi-core superconducting strand; and determines the self / mutual inductance coefficient matrix of the fully coupled multi-core superconducting strand and the self / mutual inductance coefficient matrix of each core wire according to the set parameters and the two-dimensional geometric model. The matrix initialization module is used to initialize the self / mutual inductance coefficient matrix of the multi-core superconducting strand and the self / mutual inductance coefficient matrix of each core wire, and then enter the loop body; The first current determination module is used to determine the transport current caused by the applied current and the induced current caused by the applied magnetic field under full coupling in the cross section of the multi-core superconducting strand. The magnetic field determination module is used to determine the coupling current of each core wire and the rate of change of the magnetic field generated by the coupling current based on the induced current. The magnetic field determination module determines the net current of each core wire based on the induced current; and determines the coupling current of each core wire and the rate of change of the magnetic field generated by the coupling current based on the net current and the coupling degree. The second current determination module is used to determine the total current of each core wire; The third current determination module is used to couple the transport current and the total current to determine the current distribution of the cross section of the multi-core superconducting strand. The results acquisition module is used to obtain the result data of the electromagnetic behavior simulation after the loop ends.

5. A computer storage medium, characterized in that, The computer storage medium stores a plurality of computer instructions, which are used to cause the computer to perform the method described in any one of claims 1-3.

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