Electromagnetic-thermal-field-circuit coupling simulation method and system for non-insulated superconducting magnet

Abstract

The present invention provides an electromagnetic-thermal-field-circuit coupling simulation method and system for an insulation-free superconducting magnet, including constructing a circuit network model, a magnetic field model, and a solid heat transfer model. The current distribution obtained from the circuit network model is imported into the magnetic field model and the solid heat transfer model; the magnetic field and temperature distributions update their critical current distribution parameters in real time. During iteration, healthy coils with a temperature rise lower than the threshold value construct a centralized circuit network model, and quenched coils exceeding the threshold value are dynamically switched to a distributed circuit network model. The present invention effectively improves the calculation accuracy in highly nonlinear regions by constructing a refined circuit mesh in the quenched area, and realizes the accurate simulation of electromagnetic and thermal indexes during the full working cycle of the insulation-free superconducting magnet; by adopting a centralized circuit network model and a sparse circuit mesh, while ensuring the calculation accuracy of the model, the number of variables to be solved is reduced, and the problem of excessive simulation burden of a ten-thousand-turn high-field insulation-free magnet is solved.

Description

Technical Field

[0001] The present invention relates to the field of superconducting electrical engineering modeling, and in particular to an electromagnetic thermal field circuit coupling simulation method and system for a non-insulated superconducting magnet. Background Art

[0002] Uninsulated superconducting magnets are a type of magnet made from second-generation high-temperature superconducting tapes. Their uniqueness lies in the removal of electrical insulation materials between turns while maintaining a good electrical path between adjacent turns. When a quench occurs in an uninsulated superconducting magnet, part of the current can bypass the quench hotspot and shunted to other areas with the help of radial inter-turn electrical contact, thereby effectively reducing the current density and heat generation in the quench area, and thus having higher quench self-protection performance. However, it is precisely because of the existence of this shunting mechanism that the internal current distribution of uninsulated magnets is complex during electromagnetic transients. Conventional finite element simulation methods make it difficult to quantitatively describe the radial shunting characteristics of uninsulated magnets, so a coupled circuit network model is required to simulate the current path inside the coil.

[0003] The centralized circuit network model is a traditional simulation method for uninsulated superconducting magnets. This model assumes that the annular current and radial shunt of the uninsulated superconducting coil are evenly distributed between the turns. Based on this, the uninsulated coil is simplified and constructed as a parallel circuit consisting of characteristic resistance, superconducting resistance and coil inductance, so as to calculate the equivalent annular current and radial shunt inside the coil. However, this model can only reflect the macroscopic characteristics of the uninsulated superconducting coil, and cannot analyze the complex electromagnetic thermal characteristics inside the coil under electromagnetic transient conditions. Moreover, when facing the overcurrent and overload conditions, its calculation error is large, and it is difficult to carry out accurate simulation analysis for the magnet fault conditions.

[0004] At present, the simulation of uninsulated superconducting magnets mostly adopts a distributed circuit network model based on equally divided units (such as Figure 5 ). This model is more sophisticated than the centralized circuit network model. It divides each turn of the uninsulated superconducting coil into several units evenly along the spiral direction. Adjacent spiral units are connected by radial contact resistance, thereby dividing the uninsulated coil into multiple small circuit meshes, thereby realizing accurate calculation of the distribution of electromagnetic thermal characteristics inside the coil. However, large uninsulated magnets have a large number of coils and turns, which greatly increases the number of spiral units, resulting in a sharp increase in the amount of calculation and complexity of the model, making this distributed model difficult to use for simulation of large high-field magnets. In addition, when simulating a small-scale local quench (the initial size of the hot spot is usually only at the millimeter to centimeter level), the resolution of the hot spot area may be insufficient because the spiral units are equally divided and fixed during the iterative calculation process, and the circuit mesh in the superconducting area is too dense, which not only affects the calculation accuracy, but also causes redundant calculations.

[0005] Through searching patent documents, it was found that the invention patent with application number CN202211248164.7 disclosed a superconducting magnet electromagnetic thermal multi-field coupling simulation modeling method and system, which includes: geometric modeling of superconducting magnets, adding corresponding physical properties to each material; simulating the cooling environment of superconducting magnets during operation according to the cooling method adopted by superconducting magnets; modeling electromagnetic fields, temperature fields, and mechanical fields respectively; using the critical current density of superconducting tapes affected by electromagnetic thermal multi-fields as a coupling link and combining the internal thermal expansion module to realize superconducting magnet multi-field coupling; meshing the established geometric model, and solving the model by setting a two-step solver. The simulation modeling method proposed in this patent is for insulating superconducting magnets, and can only analyze the annular current flowing along the winding direction of the tape, and does not include the optimization design of the model calculation efficiency.

[0006] The invention patent with application number CN202210589342.6 discloses a finite element-based simulation modeling method and system for the overall overcurrent quench of a superconducting coil. The method includes: constructing a geometric model of the superconducting coil and adding physical property functions to each layer; establishing a geometric model of the cooling medium and adding physical property functions; using the superconducting coil model as a heat source, setting the junction between the superconducting coil and the cooling medium as a heat flux boundary, and modeling the electromagnetic field of the superconducting coil through the H equation; using the temperature calculated under the current Joule heat generated by the heat source to calculate the current density of the electromagnetic field; obtaining the magnetic field strength under the new current density; obtaining the current density under the new magnetic field strength, and using it to calculate and update the Joule heat generated by the heat source; adding the boundary conditions of the electromagnetic field through point-by-point constraints, solving the multi-physical field coupling quench calculation model of the superconducting coil to be simulated, and obtaining the distribution of each physical field. The simulation modeling method and system proposed in this patent are oriented to the insulating superconducting coil, and only consider the annular current flowing along the winding direction of the strip; and do not involve the optimization of the model calculation amount; at the same time, this patent is only oriented to the overall overcurrent quenching condition of the superconducting coil.

[0007] The paper with DOI 10.1016 / j.supcon.2024.100140 discloses a simulation method for electromagnetic thermal field-circuit coupled quench of uninsulated coils. The method includes: establishing a distributed circuit network model, magnetic field model and solid heat transfer model of uninsulated coils; the circuit network model is used to calculate the current distribution inside the coil during the local quench; the current distribution calculated by the circuit network model is imported into the solid heat transfer model as a heat source, and the magnetic field model is imported at the same time to calculate the coil temperature rise and magnetic field distribution during the local quench respectively; the magnetic field distribution and temperature distribution will change the critical current distribution of the coil, thereby obtaining the internal current distribution under the new critical current. The distributed circuit model in the simulation modeling method proposed in this paper divides each turn of the uninsulated superconducting coil into several fine units along the spiral direction, resulting in a huge amount of calculation, which can only be used for the simulation of small uninsulated magnets.

[0008] The invention patent with application number CN202010993657.8 discloses a finite element analysis method for the quench process of a superconducting magnet. The method includes: obtaining the change of the current in the magnet coil over time during the quench process, and then establishing the electromagnetic field control equation and the heat conduction equation. By solving the two equations in turn, the eddy current density, electromagnetic force and temperature distribution at each moment in the magnet are obtained. The analysis method proposed in the patent is based on the curve of the current change over time after the magnet quench is directly collected, and does not involve the calculation of the current distribution inside the magnet.

[0009] The invention patent with application number CN201710023808.5 discloses a modeling method for nonlinear analysis of high-temperature superconducting magnets. The method includes: establishing a PDE model for electromagnetic thermal coupling analysis based on the actual model of the magnet, and calculating the dynamic inductance and resistance equivalent parameters based on the solution results of the PDE model, and obtaining key parameters such as the critical current and maximum temperature rise of the superconducting magnet; using a controlled current source to equivalent the magnet model based on the mathematical relationship between the inductance and resistance parameters and the voltage drop across the magnet, at any time in the simulation, the equivalent inductance, equivalent resistance and key parameters of the magnet are related to the current state of the magnet, and the nonlinear EJ characteristics of the superconducting magnet are fully considered. The analysis method proposed in this patent only analyzes the equivalent annular current of the magnet through a two-dimensional axisymmetric nonlinear PDE model, and cannot analyze the current spatial distribution along the spiral direction and the radial current distribution of the uninsulated magnet.

[0010] In summary, in view of the above-mentioned problems of the prior art, studying an electromagnetic thermal field circuit coupling simulation method and system for non-insulated superconducting magnets has become a key task that needs to be solved urgently. Summary of the invention

[0011] In view of the defects in the prior art, an object of the present invention is to provide an electromagnetic thermal field circuit coupling simulation method and system for a non-insulated superconducting magnet.

[0012] According to the present invention, a method for simulating electromagnetic thermal field circuit coupling of a non-insulated superconducting magnet is provided, comprising the following steps:

[0013] Step S1, constructing a circuit network model, the circuit network model includes a centralized circuit network model and a distributed circuit network model;

[0014] Step S2, constructing a magnetic field model based on the circuit network model;

[0015] Step S3, constructing a solid heat transfer model based on the circuit network model and the magnetic field model;

[0016] Step S4, constructing an electromagnetic thermal simulation model of a non-insulated magnet based on the circuit network model, the magnetic field model and the solid heat transfer model.

[0017] Preferably, in step S1, in the centralized circuit network model, the non-insulated coil is equivalent to a group of parallel loops, wherein R c is the characteristic resistance, R su is the equivalent superconducting resistance, L c is the coil inductance, and the centralized circuit network model equates the internal current of the uninsulated coil to the radial current flowing through the characteristic resistance. I r and the circular current flowing in the strip winding direction I s , and the radial current and tangential current are evenly distributed in each turn of the uninsulated coil. The control equation of the centralized circuit network model is:

[0018]

[0019] in, I op is the current source current that powers the coil, and the coil inductance is calculated according to the Biot-Savart law; the time constant of the uninsulated superconducting coil is measured by a rapid discharge test τ , calculate the characteristic resistance according to the following expression:

[0020] .

[0021] Preferably, in step S1, in the distributed circuit network model of the non-insulated superconducting coil based on unequally divided microelements, each turn is divided into a The length of the spiral unit of each turn is uneven. The closer the geometric position is to the quench region, the shorter the spiral unit length is. The number and length of the spiral unit are determined according to the geometric range of the quench region and the calculation accuracy requirements. In the radial direction, each pair of adjacent spiral units consists of 2 radial resistors. R r Each pair of adjacent spiral units and their connected pair of radial resistors form a unit circuit mesh, in which the current is decomposed into radial currents flowing through the radial resistors. j k and the circular current flowing into each spiral unit along the strip winding direction i k ， Each spiral element contains a unit impedance Z , the impedance is determined by the unit inductance M , Metal layer resistance R m and the equivalent superconducting layer resistance R su Therefore, the circular current flowing into each spiral unit ik is decomposed into the current flowing into the superconducting layer of the tape i su and the current flowing into the metal layer of the strip i m The quench region is defined as the region where there is a shunting phenomenon from the superconducting layer of the tape to the metal layer of the tape, that is, i m >0;

[0022] Applying Kirchhoff's current law to each circuit node yields the governing equation:

[0023]

[0024] Applying Kirchhoff's voltage law to each unit cell yields the governing equation:

[0025]

[0026] in, U s is the toroidal voltage on each spiral unit, U r is the radial voltage generated by the radial resistance, N is the total number of coil spiral units, unit inductance M According to the Biot-Savart law, the loop resistance R s According to the resistance of the metal layer of the superconducting tape R m and superconducting equivalent resistance R su The time constant of the uninsulated superconducting coil is obtained by fast discharge test. τ , the radial resistance is calculated according to the following expression R r :

[0027]

[0028] in, w is the superconducting tape width, l is the length of the spiral unit.

[0029] Preferably, step S2 comprises: based on TA The magnetic field model of the uninsulated superconducting magnet is constructed by using the formula. TA The governing equation of the formula is as follows:

[0030]

[0031] Among them, E is the electric field, B is the magnetic induction intensity, A is the magnetic potential, μ is the magnetic permeability and J is the current density, which are derived from the circuit network model.

[0032] Preferably, step S3 comprises: in a solid heat transfer model of a non-insulated superconducting magnet, calculating the temperature distribution in the magnet according to the following formula:

[0033]

[0034] in, d. C p , k are the density, specific heat capacity and thermal conductivity of the homogenized superconducting tape, T is the temperature, Q s is the toroidal loss inside the magnet, and the calculation equation is as follows:

[0035]

[0036] in ρ i is the equivalent hoop resistivity, J i is the annular current density, from the circuit network model, Q r is the radial loss inside the magnet and is described by the following formula:

[0037]

[0038] in J j is the radial current density, from the circuit network model, ρ r is the equivalent radial resistivity, calculated according to the following formula:

[0039] .

[0040] Preferably, step S4 includes the following sub-steps:

[0041] Step S4.1: construct a centralized circuit network model for all coils in the non-insulated magnet, couple the magnetic field model and the solid heat transfer model, construct an electromagnetic thermal simulation model for the non-insulated magnet, initialize the parameters, and set the temperature rise threshold. T max and iterative time series [ t 0 , t 1 , … , t imax ];

[0042] Step S4.2, iterative calculation: Based on the electromagnetic thermal simulation model of the uninsulated magnet constructed at the previous moment, at each time point t i, calculate the current of each coil {1, 2, …, n Temperature distribution of T n,ti , current distribution and magnetic field distribution; for t 0 At this moment, the electromagnetic thermal simulation model of the non-insulated magnet constructed in step S4.1 is used;

[0043] Step S4.3, for each coil {1, 2, …, n},judge t i Whether the coil temperature rise exceeds the threshold at the moment, that is, whether it satisfies | T n,ti - T n,0 |≥ T max ; to satisfy | T n,ti - T n,0 |≥ T max The coil constructs a distributed circuit network model based on unequally divided differential elements; for those that satisfy | T n,ti - T n,0 |< T max The coils are used to construct a centralized circuit network model, and a new circuit network model is obtained;

[0044] Step S4.4, coupling the new circuit network model with the magnetic field model and the solid heat transfer model to construct a new electromagnetic thermal simulation model of the non-insulated magnet;

[0045] Step S4.5, continue iterative solution, repeat steps S4.2 to S4.4, and when the iteration time reaches t imax Then terminate the calculation.

[0046] Preferably, in step S4.1 and step S4.4, the circuit network model and the magnetic field model are bidirectionally coupled, including: inputting the annular current distribution calculated by the circuit network model into the magnetic field model, and the magnetic field model calculates the spatial magnetic field distribution of the superconducting magnet; according to the magnetic field dependence and critical current anisotropy of the superconducting tape, the critical current of the superconducting magnet is changed by using the spatial magnetic field distribution, and the critical current changes the magnet voltage, and the circuit network model calculates the current distribution based on the voltage value updated in real time.

[0047] Preferably, in step S4.1 and step S4.4, the circuit network model is bidirectionally coupled with the solid heat transfer model, including: obtaining the radial loss distribution of the superconducting magnet according to the radial current distribution calculated by the circuit network model, and inputting the radial loss distribution of the superconducting magnet as a heat source into the solid heat transfer model, and the solid heat transfer model calculates the temperature distribution of the superconducting magnet; then, the temperature distribution changes the critical current of the superconducting magnet, the critical current changes the magnet voltage, and the circuit network model calculates the current distribution based on the voltage value updated in real time.

[0048] Preferably, in step S4.1 and step S4.4, the magnetic field model and the solid heat transfer model are unidirectionally coupled, including: the magnetization loss calculated by the magnetic field model is input into the solid heat transfer model as a heat source.

[0049] The present invention also provides an electromagnetic thermal field circuit coupling simulation system for a non-insulated superconducting magnet, comprising:

[0050] Module M1, constructing a circuit network model, the circuit network model includes a centralized circuit network model and a distributed circuit network model;

[0051] Module M2, constructs a magnetic field model based on the circuit network model;

[0052] Module M3, constructs a solid heat transfer model based on the circuit network model and magnetic field model;

[0053] Module M4 builds an electromagnetic thermal simulation model of an uninsulated magnet based on the circuit network model, magnetic field model and solid heat transfer model.

[0054] Compared with the prior art, the present invention has the following beneficial effects:

[0055] 1. The present invention is composed of a circuit network model, a magnetic field model and a solid heat transfer model coupled with each other, wherein the circuit network model of each coil in the magnet can be adaptively adjusted according to the coil temperature during the iterative calculation process.

[0056] 2. In a multi-coil magnet, a distributed circuit network model based on unequally divided units is used for coils whose temperature rise exceeds the threshold (i.e., quench coils). Furthermore, each turn of the coil is unevenly divided into several units along the spiral direction, with the spiral unit length in the local quench area being shorter and the spiral unit length in the superconducting area being longer. In this way, the circuit mesh in the quench area is dense and the circuit mesh in the superconducting state area is sparse. The refined circuit mesh in this local quench area can improve the calculation accuracy of highly nonlinear regions and help to achieve accurate simulation of electromagnetic thermal indicators in the full working cycle of the non-insulated superconducting magnet.

[0057] 3. In multi-coil magnets, a centralized circuit network model is used for coils with temperature rise below the threshold (i.e., healthy coils). This centralized circuit network model and the sparse circuit mesh in the healthy area of ​​the distributed circuit network model based on unequally divided units can significantly reduce the number of variables to be solved in the model while ensuring the calculation accuracy of the model, avoiding redundant calculations caused by subdividing the circuit mesh in the superconducting area, and solving the problem of excessive simulation burden of tens of thousands of turns of strong field non-insulated magnets. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Other features, objects and advantages of the present invention will become more apparent from the detailed description of non-limiting embodiments made with reference to the following drawings:

[0059] Figure 1 It is a centralized equivalent circuit network model of a non-insulated superconducting coil in an embodiment of the present invention;

[0060] Figure 2 It is a distributed equivalent circuit network model of a non-insulated superconducting coil based on unequally divided units in an embodiment of the present invention;

[0061] Figure 3 It is a simulation model iteration flow chart in an embodiment of the present invention;

[0062] Figure 4 Schematic diagram of an electromagnetic thermal coupling simulation method for a non-insulated superconducting magnet in an embodiment of the present invention;

[0063] Figure 5 The invention is a traditional non-insulated superconducting coil distributed equivalent circuit network model based on equally divided units in the background technology. DETAILED DESCRIPTION

[0064] The present invention is described in detail below in conjunction with specific embodiments. The following embodiments will help those skilled in the art to further understand the present invention, but are not intended to limit the present invention in any form. It should be noted that, for those of ordinary skill in the art, several changes and improvements can also be made without departing from the concept of the present invention. These all belong to the protection scope of the present invention.

[0065] Uninsulated superconducting magnets have special electromagnetic heat characteristics and shunting mechanisms. Previously, the centralized circuit network model simplified the uninsulated coil into a parallel circuit of a single superconducting resistor, coil inductance and characteristic resistor, and was unable to analyze the complex internal characteristics; the equally divided unit distributed circuit network model evenly divides each wire turn into several spiral units along the winding direction of the tape, realizing the accurate calculation of the electromagnetic heat distribution inside the uninsulated superconducting magnet, but it still has two major technical problems: (1) The model calculation amount is positively correlated with the number of spiral units, and increases significantly with the increase in the number of circuit solution variables. When the unit division is extremely fine, or when it is necessary to simulate a large-scale high-field magnet with multiple coils and a high number of turns, the model calculation amount will be too high, which is difficult for conventional computing equipment to bear; (2) When simulating local quench conditions, the equally divided spiral units may cause the circuit mesh in the resistive state area to be too sparse, making it difficult to accurately reflect the quench propagation process, resulting in insufficient calculation accuracy for local hot spots. At the same time, the circuit mesh in the superconducting state area is too dense, the calculation amount is redundant, and the model calculation efficiency is reduced.

[0066] The present invention provides an electromagnetic thermal field circuit coupling simulation method and system for an uninsulated superconducting magnet. The uninsulated superconducting magnet is formed by cascading uninsulated superconducting coils. The method includes a circuit network model, a magnetic field model and a solid heat transfer model that are coupled and calculated synchronously. In each sub-model, the current distribution required by the circuit network model is imported into the magnetic field model to calculate the magnetic field distribution of the magnet; the current distribution is simultaneously imported into the solid heat transfer model to calculate the temperature distribution; the magnetic field and temperature distribution update the critical current distribution parameters in the circuit network model in real time. In each iterative step, the circuit network model is adaptively adjusted, and a centralized circuit network model is constructed for healthy coils whose temperature rise in the magnet is lower than a threshold, which can reduce the overall calculation amount of the model; a distributed circuit network model based on unequally divided units is constructed for quenched coils whose temperature rise exceeds the threshold, wherein the length of a single spiral unit in the quench region is lower than that in the superconducting region. The circuit mesh in the quench region is dense and the superconducting region is sparse, which can improve the resolution of the quench region and eliminate the redundant calculation amount in the superconducting region. The present invention constructs a centralized circuit network model for the healthy coil and a sparse circuit mesh for the superconducting region of the quenched coil, which can greatly reduce the number of variables to be solved, thereby significantly reducing the amount of model calculation and realizing the simulation design of large-scale high-field non-insulated magnets; the high-density circuit mesh in the quenched region can effectively improve the calculation accuracy of the local hot spot area and realize the accurate simulation of the full working cycle of the non-insulated superconducting magnet.

[0067] Terminology explanation:

[0068] Quench: When any of the temperature, magnetic field, and current of a superconductor exceeds its critical value, the superconductor loses its superconducting properties and enters a resistive state from a superconducting state.

[0069] Uninsulated superconducting magnet: The present invention specifically refers to a magnet formed by cascading multiple uninsulated superconducting coils, wherein the uninsulated superconducting coils are pancake-shaped coils wound by second-generation high-temperature superconducting tapes without adding insulating materials between turns.

[0070] Embodiment 1:

[0071] This embodiment provides an electromagnetic thermal field circuit coupling simulation method for a non-insulated superconducting magnet, comprising the following steps:

[0072] Step S2, constructing a circuit network model 1, where the circuit network model 1 includes a centralized circuit network model and a distributed circuit network model.

[0073] Figure 1 This is a centralized equivalent circuit network model of a non-insulated superconducting coil in an embodiment of the present invention.

[0074] like Figure 1 As shown in the centralized circuit network model, the non-insulated coil is equivalent to a set of parallel loops, where R c is the characteristic resistor 101, R su is the equivalent superconducting resistance 102, L c is the coil inductance 103. The centralized circuit network model equates the internal current of the uninsulated coil to the radial current flowing through the characteristic resistance I r and the circular current flowing in the strip winding direction I s , and the radial current and tangential current are evenly distributed in each turn of the uninsulated coil. The control equation of the centralized circuit network model is:

[0075]

[0076] in, I op is the current source current supplying the coil, and the coil inductance 103 is calculated according to the Biot-Savart law; the time constant of the uninsulated superconducting coil is measured by the rapid discharge test τ , calculate the characteristic resistance 101 according to the following expression:

[0077]

[0078] Figure 2 It is a distributed equivalent circuit network model of a non-insulated superconducting coil based on unequally divided units in an embodiment of the present invention.

[0079] like Figure 2 As shown in the distributed circuit network model of non-insulated superconducting coils based on unequally divided microelements, each turn is divided intoa The length of the spiral unit 104 of each turn is uneven. The closer the geometric position is to the quench region 105, the shorter the spiral unit length is. The specific number and length of the units depend on the geometric range of the quench region 105 and the calculation accuracy requirements. In the radial direction, each pair of adjacent spiral units 104 consists of two radial resistors. R r Each pair of adjacent spiral units 104 and their connected pair of radial resistors 107 form a unit circuit mesh 106, in which the current is decomposed into radial currents flowing through the radial resistors 107. j k and the circular current flowing into each spiral unit 104 along the strip winding direction i k Each spiral unit 104 includes a unit impedance Z 108, the impedance is composed of the unit inductance M 109. Metal layer resistance R m 110 and equivalent superconducting layer resistance R su 111. Therefore, the circular current flowing into each spiral unit 104 i k is decomposed into the current flowing into the superconducting layer of the tape i su and the current flowing into the metal layer of the strip i m The quench region 105 is defined as a region where there is a shunting phenomenon from the superconducting layer of the strip to the metal layer of the strip, that is, i m >0.

[0080] Applying Kirchhoff's current law to each circuit node gives the governing equation:

[0081]

[0082] Applying Kirchhoff's voltage law to each unit cell 104, the control equation is:

[0083]

[0084] in, U s is the ring voltage on each spiral unit 104, U r is the radial voltage generated by the radial resistor 107, N is the total number of coil spiral units. Unit inductance M 109 According to the Biot-Savart law, the ring resistance is R sAccording to the resistance of the metal layer of the superconducting tape R m 110 and superconducting equivalent resistance R su 111. The time constant of the uninsulated superconducting coil is measured by the rapid discharge test τ , the radial resistance is calculated according to the following expression R r 107:

[0085]

[0086] in, w is the superconducting tape width, l is the length of the spiral unit.

[0087] It should be noted that Figure 1 and Figure 2 Only the physical structure of the uninsulated superconducting coil wound by a single superconducting tape is shown, and the circuit network model of the present invention is not limited to the specific number of superconducting tapes, geometric dimensions of the superconducting coil and geometric structure of the superconducting tape.

[0088] It should be noted that Figure 2 The number and length of the spiral unit divisions are only examples. The number and length of the units in the distributed circuit network model of the present invention are determined according to the range of the quench region and the calculation accuracy requirements.

[0089] Step S2, constructing a magnetic field model based on the circuit network model.

[0090] Specifically, based on TA Formula to construct magnetic field model of uninsulated superconducting magnet 2, TA The governing equation of the formula is as follows:

[0091]

[0092] Among them, E is the electric field, B is the magnetic induction intensity, A is the magnetic potential, μ is the magnetic permeability. J is the current density, which comes from the circuit network model 1.

[0093] Step S3, constructing a solid heat transfer model based on the circuit network model and the magnetic field model.

[0094] Specifically, in the solid heat transfer model 3 of the non-insulated superconducting magnet, the temperature distribution inside the magnet is calculated according to the following formula:

[0095]

[0096] in, d. C p , k are the density, specific heat capacity and thermal conductivity of the homogenized superconducting tape,T For temperature. Q s is the toroidal loss inside the magnet, and the calculation equation is as follows:

[0097]

[0098] in ρ i is the equivalent hoop resistivity. J i is the circular current density, from the circuit network model 1. Q r is the radial loss inside the magnet and is described by the following formula:

[0099]

[0100] in J j is the radial current density, from the circuit network model 1. ρ r is the equivalent radial resistivity, calculated according to the following formula:

[0101]

[0102] Step S4, constructing an electromagnetic thermal simulation model of a non-insulated magnet based on the circuit network model, the magnetic field model and the solid heat transfer model.

[0103] Figure 3 It is a simulation model iteration flow chart in an embodiment of the present invention.

[0104] like Figure 3 As shown, step S4 includes the following sub-steps:

[0105] Step S4.1: construct a centralized circuit network model for all coils in the non-insulated magnet, and couple the magnetic field model 2 and the solid heat transfer model 3 to construct an electromagnetic thermal simulation model of the non-insulated magnet, initialize the parameters, and set the temperature rise threshold. T max and iterative time series [ t 0 , t 1 , … , t imax ].

[0106] Figure 4 Schematic diagram of the electromagnetic thermal coupling simulation method of the non-insulated superconducting magnet in an embodiment of the present invention.

[0107] like Figure 4As shown, the circuit network model 1 is bidirectionally coupled with the magnetic field model 2, and the specific coupling method is: the annular current distribution calculated by the circuit network model 1 is input into the magnetic field model 2, and the magnetic field model 2 calculates the spatial magnetic field distribution of the superconducting magnet; according to the magnetic field dependence and critical current anisotropy of the superconducting tape, the spatial magnetic field distribution will change the critical current of the superconducting magnet, and the critical current will change the magnet voltage, and the circuit network model 1 calculates the current distribution based on the voltage value updated in real time.

[0108] The circuit network model 1 is bidirectionally coupled with the solid heat transfer model 3. The specific coupling method is as follows: based on the radial current distribution calculated by the circuit network model 1, the radial loss distribution of the superconducting magnet is obtained, and it is input into the solid heat transfer model 3 as a heat source. The solid heat transfer model 3 calculates the temperature distribution of the superconducting magnet; the temperature distribution will change the critical current of the superconducting magnet, and the critical current will change the magnet voltage. The circuit network model 1 calculates the current distribution based on the voltage value updated in real time.

[0109] The magnetic field model 2 is unidirectionally coupled with the solid heat transfer model 3. The specific coupling method is: the magnetization loss calculated by the magnetic field model 2 is input into the solid heat transfer model 3 as a heat source.

[0110] In each iteration, the calculation steps between the above models are performed synchronously, and the electrical, magnetic and thermal field parameters are updated in real time.

[0111] Step S4.2, iterative calculation: Based on the electromagnetic thermal simulation model of the uninsulated magnet constructed at the previous moment, at each time point t i (in i is the sequence number in the time series and i ≥0), calculate the current of each coil {1, 2, …, n Temperature distribution of T n,ti , current distribution and magnetic field distribution. In particular, for t 0 At this moment, the electromagnetic thermal simulation model of the non-insulated magnet constructed in step S4.1 is used;

[0112] Step S4.3, for each coil {1, 2, …, n},judge t i Whether the coil temperature rise exceeds the threshold at the moment, that is, whether it satisfies | T n,ti - T n,0 |≥ T max ; to satisfy | T n,ti - Tn,0 |≥ T max The coil is constructed based on the distributed circuit network model of unequally divided microelement. For satisfying | T n,ti - T n,0 |< T max A centralized circuit network model is constructed by using the coil to obtain a new circuit network model.

[0113] Step S4.4, coupling the new circuit network model 1 with the magnetic field model 2 and the solid heat transfer model 3 to construct a new electromagnetic thermal simulation model of an uninsulated magnet, and the coupling method is as above.

[0114] Step S4.5, continue iterative solution, repeat steps S4.2 to S4.4, and when the iteration time reaches t imax Then terminate the calculation.

[0115] The iterative process of the above non-insulated magnet electromagnetic thermal simulation model is not limited to specific non-insulated coils and magnet structures, and the temperature rise threshold and iterative time sequence are determined according to the magnet characteristics and calculation requirements.

[0116] Embodiment 2:

[0117] The present invention also provides an electromagnetic thermal field circuit coupling simulation system for a non-insulated superconducting magnet. The electromagnetic thermal field circuit coupling simulation system for a non-insulated superconducting magnet can be realized by executing the process steps of the electromagnetic thermal field circuit coupling simulation method for a non-insulated superconducting magnet, that is, those skilled in the art can understand the electromagnetic thermal field circuit coupling simulation method for a non-insulated superconducting magnet as a preferred implementation mode of the electromagnetic thermal field circuit coupling simulation system for a non-insulated superconducting magnet.

[0118] Electromagnetic thermal field circuit coupling simulation system, including:

[0119] Module M1, constructing a circuit network model, the circuit network model includes a centralized circuit network model and a distributed circuit network model;

[0120] Module M2, constructs a magnetic field model based on the circuit network model;

[0121] Module M3, constructs a solid heat transfer model based on the circuit network model and magnetic field model;

[0122] Module M4 builds an electromagnetic thermal simulation model of an uninsulated magnet based on the circuit network model, magnetic field model and solid heat transfer model.

[0123] Those skilled in the art know that, in addition to realizing the system and its various devices, modules, and units provided by the present invention in a purely computer-readable program code, it is entirely possible to realize the same functions in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers by logically programming the method steps. Therefore, the system and its various devices, modules, and units provided by the present invention can be considered as a hardware component, and the devices, modules, and units included therein for realizing various functions can also be regarded as structures within the hardware component; the devices, modules, and units for realizing various functions can also be regarded as both software modules for realizing the method and structures within the hardware component.

[0124] In the description of the present application, it should be understood that the terms "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside", etc., indicating orientations or positional relationships, are based on the orientations or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present application and simplifying the description, and do not indicate or imply that the referred device or element must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be understood as a limitation on the present application.

[0125] The above describes the specific embodiments of the present invention. It should be understood that the present invention is not limited to the above specific embodiments, and those skilled in the art can make various changes or modifications within the scope of the claims, which does not affect the essence of the present invention. In the absence of conflict, the embodiments of the present application and the features in the embodiments can be combined with each other arbitrarily.

Claims

1. A method for simulating electromagnetic thermal field circuit coupling of a non-insulated superconducting magnet, characterized in that: The steps include: Step S1, constructing a circuit network model, wherein the circuit network model includes a centralized circuit network model and a distributed circuit network model; Step S2, constructing a magnetic field model based on the circuit network model; Step S3, constructing a solid heat transfer model based on the circuit network model and the magnetic field model; Step S4, constructing an electromagnetic thermal simulation model of a non-insulated magnet based on the circuit network model, the magnetic field model and the solid heat transfer model; The step S4 includes the following sub-steps: Step S4.1, construct a centralized circuit network model for all coils in the non-insulated magnet, and couple the magnetic field model and the solid heat transfer model to construct an electromagnetic thermal simulation model of the non-insulated magnet, initialize parameters, and set the temperature rise threshold T max and iterative time series [ t 0, t 1, … , t imax ]; Step S4.2, iterative calculation: Based on the electromagnetic thermal simulation model of the uninsulated magnet constructed at the previous moment, at each time point t i , calculate the current of each coil {1, 2, …, n Temperature distribution of T n,ti , current distribution and magnetic field distribution; for t At time 0, the electromagnetic thermal simulation model of the non-insulated magnet constructed based on step S4.1; Step S4.3, for each coil {1, 2, …, n },judge t i Whether the coil temperature rise exceeds the threshold at the moment, that is, whether it satisfies | T n,ti - T n,0 |≥ T max ; to satisfy | T n,ti - T n,0 |≥ T max The coil constructs a distributed circuit network model based on unequally divided differential elements; for those that satisfy | T n,ti - T n,0 |< T max The coils are used to construct a centralized circuit network model, and a new circuit network model is obtained; Step S4.4, coupling the new circuit network model with the magnetic field model and the solid heat transfer model to construct a new electromagnetic thermal simulation model of a non-insulated magnet, wherein the current distribution required by the circuit network model is imported into the magnetic field model to calculate the magnetic field distribution of the magnet; the current distribution is simultaneously imported into the solid heat transfer model to calculate the temperature distribution; the magnetic field and temperature distributions update the critical current distribution parameters in the circuit network model in real time; Step S4.5, continue iterating and solving, repeating steps S4.2 to S4.4 until the iteration time reaches t imax Then terminate the calculation.

2. The electromagnetic thermal field circuit coupling simulation method of a non-insulated superconducting magnet according to claim 1, characterized in that: In step S1, in the centralized circuit network model, the non-insulated coil is equivalent to a group of parallel loops, wherein R c is the characteristic resistance, R su is the equivalent superconducting resistance, L c is the coil inductance, and the centralized circuit network model equates the internal current of the uninsulated coil to the radial current flowing through the characteristic resistance I r and the circular current flowing in the strip winding direction I s , and the radial current and the tangential current are evenly distributed in each turn of the uninsulated coil, the control equation of the centralized circuit network model is: in, I op is the current source current supplying the coil, t is the time, the coil inductance is calculated according to the Biot-Savart law; the time constant of the uninsulated superconducting coil is measured by the rapid discharge test τ , the characteristic resistance is calculated according to the following expression: 。 3. The electromagnetic thermal field circuit coupling simulation method of a non-insulated superconducting magnet according to claim 1, characterized in that: In step S1, in the distributed circuit network model of non-insulated superconducting coils based on unequally divided microelements, each turn is divided into a The length of the spiral unit of each turn is uneven. The closer the geometric position is to the quench region, the shorter the spiral unit length is. The number and length of the spiral unit are determined according to the geometric range of the quench region and the calculation accuracy requirements. In the radial direction, each pair of adjacent spiral units consists of 2 radial resistors. R r Each pair of adjacent spiral units and their connected pair of radial resistors form a unit circuit mesh, in which the current is decomposed into radial currents flowing through the radial resistors. j k and the circular current flowing into each spiral unit along the strip winding direction i k ， Each spiral element contains a unit impedance Z , the impedance is determined by the unit inductance M , Metal layer resistance R m and the equivalent superconducting layer resistance R su Therefore, the circular current flowing into each spiral unit i k is decomposed into the current flowing into the superconducting layer of the tape i su and the current flowing into the metal layer of the strip i m The quench region is defined as the region where there is a shunting phenomenon from the superconducting layer of the tape to the metal layer of the tape, that is, i m >0; Applying Kirchhoff's current law to each circuit node gives the governing equation: Applying Kirchhoff's voltage law to each unit cell gives the governing equation: in, U s is the toroidal voltage on each spiral unit, U r is the radial voltage generated by the radial resistance, N is the total number of coil spiral units, unit inductance M According to the Biot-Savart law, the loop resistance R s According to the resistance of the metal layer of the superconducting tape R m and superconducting equivalent resistance R su The time constant of the uninsulated superconducting coil is obtained by fast discharge test. τ , the radial resistance is calculated according to the following expression R r : in, w is the width of the superconducting tape, l is the length of the spiral unit.

4. The electromagnetic thermal field circuit coupling simulation method of a non-insulated superconducting magnet according to claim 1, characterized in that: The step S2 comprises: based on TA The magnetic field model of the uninsulated superconducting magnet is constructed by using the formula. TA The governing equation of the formula is as follows: Among them, E is the electric field, B is the magnetic induction intensity, T is the temperature, A is the magnetic potential, μ is the magnetic permeability and J is the current density, which are derived from the circuit network model.

5. The electromagnetic thermal field circuit coupling simulation method of a non-insulated superconducting magnet according to claim 1, characterized in that: The step S3 comprises: in a solid heat transfer model of a non-insulated superconducting magnet, calculating the temperature distribution in the magnet according to the following formula: in, d. C p , k are the density, specific heat capacity and thermal conductivity of the homogenized superconducting tape, T is the temperature, Q s is the toroidal loss inside the magnet, and the calculation equation is as follows: in ρ i is the equivalent hoop resistivity, J i is the circular current density, from the circuit network model, Q r is the radial loss inside the magnet and is described by the following formula: in J j is the radial current density, from the circuit network model, ρ r is the equivalent radial resistivity, calculated according to the following formula: 。 6. The electromagnetic thermal field circuit coupling simulation method of a non-insulated superconducting magnet according to claim 1, characterized in that: In step S4.1 and step S4.4, the circuit network model is bidirectionally coupled with the magnetic field model, including: inputting the annular current distribution calculated by the circuit network model into the magnetic field model, and the magnetic field model calculates the spatial magnetic field distribution of the superconducting magnet; according to the magnetic field dependence and critical current anisotropy of the superconducting tape, the critical current of the superconducting magnet is changed by using the spatial magnetic field distribution, and the critical current changes the magnet voltage, and the circuit network model calculates the current distribution based on the voltage value updated in real time.

7. The electromagnetic thermal field circuit coupling simulation method of a non-insulated superconducting magnet according to claim 1, characterized in that: In step S4.1 and step S4.4, the circuit network model is bidirectionally coupled with the solid heat transfer model, including: obtaining the radial loss distribution of the superconducting magnet according to the radial current distribution calculated by the circuit network model, and inputting the radial loss distribution of the superconducting magnet as a heat source into the solid heat transfer model, and the solid heat transfer model calculates the temperature distribution of the superconducting magnet; then, the temperature distribution changes the critical current of the superconducting magnet, the critical current changes the magnet voltage, and the circuit network model calculates the current distribution based on the voltage value updated in real time.

8. The electromagnetic thermal field circuit coupling simulation method of a non-insulated superconducting magnet according to claim 1, characterized in that: In step S4.1 and step S4.4, the magnetic field model and the solid heat transfer model are unidirectionally coupled, including: the magnetization loss calculated by the magnetic field model is input into the solid heat transfer model as a heat source.

9. An electromagnetic thermal field circuit coupling simulation system for a non-insulated superconducting magnet based on the method of claim 1, characterized in that: include: Module M1, constructing a circuit network model, wherein the circuit network model includes a centralized circuit network model and a distributed circuit network model; Module M2, constructing a magnetic field model based on the circuit network model; Module M3, constructing a solid heat transfer model based on the circuit network model and the magnetic field model; Module M4, based on the circuit network model, the magnetic field model and the solid heat transfer model, constructs an electromagnetic thermal simulation model of a non-insulated magnet. The module M4 includes the following sub-steps: Step S4.1, construct a centralized circuit network model for all coils in the non-insulated magnet, and couple the magnetic field model and the solid heat transfer model to construct an electromagnetic thermal simulation model of the non-insulated magnet, initialize parameters, and set the temperature rise threshold T max and iterative time series [ t 0, t 1, … , t imax ]; Step S4.2, iterative calculation: Based on the electromagnetic thermal simulation model of the uninsulated magnet constructed at the previous moment, at each time point t i , calculate the current of each coil {1, 2, …, n Temperature distribution of T n,ti , current distribution and magnetic field distribution; for t At time 0, the electromagnetic thermal simulation model of the non-insulated magnet constructed based on step S4.1; Step S4.3, for each coil {1, 2, …, n },judge t i Whether the coil temperature rise exceeds the threshold at the moment, that is, whether it satisfies | T n,ti - T n,0 |≥ T max ; to satisfy | T n,ti - T n,0 |≥ T max The coil constructs a distributed circuit network model based on unequally divided differential elements; for those that satisfy | T n,ti - T n,0 |< T max The coils are used to construct a centralized circuit network model, and a new circuit network model is obtained; Step S4.4, coupling the new circuit network model with the magnetic field model and the solid heat transfer model to construct a new electromagnetic thermal simulation model of a non-insulated magnet, wherein the current distribution required by the circuit network model is imported into the magnetic field model to calculate the magnetic field distribution of the magnet; the current distribution is simultaneously imported into the solid heat transfer model to calculate the temperature distribution; the magnetic field and temperature distributions update the critical current distribution parameters in the circuit network model in real time; Step S4.5, continue iterating and solving, repeating steps S4.2 to S4.4 until the iteration time reaches t imax Then terminate the calculation.

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