A method for analyzing quench failure of a type D high-temperature superconducting non-insulated coil
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- LANZHOU UNIV
- Filing Date
- 2026-02-13
- Publication Date
- 2026-05-26
Smart Images
Figure CN121706510B_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of superconductors, specifically a method for analyzing the quenching failure of a type D high-temperature superconducting non-insulated coil. Background Technology
[0002] High-temperature superconducting (HTS) non-insulated (NI) coils have significant application prospects in large magnet systems such as toroidal field (TF) coils in nuclear fusion devices (e.g., tokamak) due to their excellent self-protection characteristics and high magnetic field potential. Among them, the D-type coil, designed to adapt to the shape of the plasma chamber, has a composite geometry that combines circular and straight segments, and its electromagnetic and thermodynamic behavior is more complex than that of traditional circular or racetrack-shaped coils.
[0003] In existing technologies, simulation analysis of uninsulated coils is mostly focused on conventional small circular structures. The models used mainly include lumped circuit models, as well as axisymmetric models and distributed network models derived from them. Through coupling with two-dimensional heat conduction models, these methods can effectively simulate the current bypass and temperature evolution of coils under local thermal disturbances. However, these existing methods generally fail to systematically study the dynamic behavior of high-temperature superconducting uninsulated coils and cannot be applied to complex geometric structures such as D-type coils. Summary of the Invention
[0004] The purpose of this invention is to provide a method for analyzing the quench failure of a type D high-temperature superconducting uninsulated coil, so as to solve the problems mentioned in the background art.
[0005] To achieve the above objectives, the present invention provides the following technical solution: a method for quench analysis of a type D high-temperature superconducting uninsulated coil, comprising the following steps:
[0006] S1: Establish a distributed mesh model of the D-type coil; first, discretize each turn of the conductor of the D-type coil into multiple interrelated arc segment units and straight line segment units, and set radial resistance at the nodes of adjacent turns;
[0007] S2: Calculate the inductance of the D-type coil using the numerical integration method for the D-type coil distributed grid model obtained in step S1.
[0008] S3: Establish a system of equations for each circuit node and loop of the arc segment and straight line segment elements in the D-type coil distributed mesh model established in step S2. The equations include the first... Circulating current of each arc segment unit and straight segment unit Radial current Superconducting layer circumferential current Normal layer circumferential current and inter-turn contact resistance Superconducting layer resistance Normal layer resistance and node voltage The system of equations is as follows:
[0009] ;
[0010] Among them, the superconducting layer parameters adopt Power-law model: Construct, in the formula For electric field strength, The critical electric field strength, The value is an exponent. For current density, The critical current density, This indicates the number of segments in the corresponding arc segment or line segment element parameters. +1、 -1、 + , - These represent the first and second parameters, respectively. +1 paragraph, No. -1st paragraph, No. + , - The number of segments in an arc segment unit or a straight segment unit; based on Power-law model , , , This can be expressed by the following formula:
[0011] ;
[0012] In the formula: For the D-shaped coil Section and the Inductance between segments, when ≠ hour, For the D-shaped coil Section and the The inductance between segments is mutual inductance; when hour, For the D-shaped coil Section and the Between segments, For the first The circumferential current of the segment, For time, This represents the equivalent inter-turn contact resistivity of the coil. It is the temperature-dependent equivalent resistivity of the normal layer. and They are the first The surface area and length of each arc segment or straight segment unit; It is the cross-sectional area of the REBCO conductor. This refers to the critical circumferential current at the inter-segment circuit node. This can be expressed by the following relation:
[0013] ;
[0014] In the expression, the numerator is the temperature-dependent term, and the denominator is the term considering the anisotropy of the magnetic field, i.e., the parallel component of the magnetic field. Component perpendicular to the magnetic field The magnetic field contribution, of which This is the critical circumferential current at the initial moment of the D-type coil. This is the critical temperature of a D-type coil. Let m be the temperature of the m-th segment of the D-type coil at a certain moment. The initial temperature. , These are all coefficients describing the critical circumferential current model. In this invention, =0.0605, =0.7580, This is the critical magnetic field strength;
[0015] S4: Establish a two-dimensional finite element model of heat conduction. First, on the COMSOL Multiphysics platform, establish a two-dimensional planar model of the D-type coil and use the transient solver to solve the heat conduction equation to obtain the temperature distribution of the two-dimensional planar model of the D-type coil:
[0016] ;
[0017] In the formula, For density, For specific heat capacity, For the anisotropic thermal conductivity tensor, For temperature; and in the two-dimensional heat conduction finite element model, the heat sources include the resistance of the timeout current in the normal layer. Heat generated during inter-turn contact and externally generated local heat pulses And set the convective heat transfer boundary conditions between the surface of the D-type coil and the low-temperature cooling medium;
[0018] S5: Using the COMSOL with MATLAB co-simulation interface, calculate the normal layer circumferential current of each cell in the D-type coil distributed mesh model based on the electromagnetic coupling distribution. and radial current Import the two-dimensional heat conduction finite element model, map it to the corresponding position in the two-dimensional heat conduction finite element model, calculate and update the temperature. Heat generated during inter-turn contact Externally generated local heat pulse Specific heat capacity as a function of temperature in a two-dimensional finite element model of heat conduction and anisotropic thermal conductivity tensor ;
[0019] S6: Calculate the temperature of each element from the two-dimensional heat conduction finite element model in step S5. The data is fed back in real time to the D-type coil distributed mesh model via the COMSOL with MATLAB co-simulation interface, which is used to update the critical circumferential current of the superconducting layer of the corresponding element in the D-type coil distributed mesh model. Temperature-dependent equivalent resistivity of the normal layer and the equivalent inter-turn contact resistivity of the coil ;
[0020] S7: Within one time step, steps S5 and S6 are solved alternately until the solution results of steps S5 and S6 meet the convergence criterion, and then the process is advanced to the next time step to simulate the dynamic propagation process of quenching.
[0021] S8: Establish a three-dimensional finite element mechanical model of the D-type coil, based on the circumferential current calculated in step S3. and radial current and the temperature calculated in step S7 The temperature change and electromagnetic force generated by the coil during the quench period are calculated. The electromagnetic force is calculated using the Lorentz force calculation formula. Then, the temperature change and electromagnetic force are input into the three-dimensional finite element mechanical model of the D-type coil structure to solve the stress, strain and deformation of the D-type coil during the quench process and assess the risk of mechanical damage.
[0022] Furthermore, in step S2, when calculating the inductance of the D-type coil, the following method can also be used to calculate the inductance of any two segments of the D-type coil. , inductance At that time, set Duan You A straight line segment, A circular arc segment, Duan You A straight line segment, Each arc segment is calculated using the following formula:
[0023] ;
[0024] In the formula subscript The straight line segment representing the D-shaped coil. The arc segment representing the D-shaped coil For the first The nth straight segment and the nth Inductance between straight line segments For the first The nth straight segment and the nth Inductance between the arc segments For the first The arc segment and the first Inductance between straight line segments For the first The arc segment and the first Inductance between the arc segments and These are the integral volumes of the two D-shaped superconducting coils for the desired inductance; and These are the x-coordinates of the centers of the two arc segments of the D-shaped coil. and These are the ordinates of the centers of the two arc segments of the D-shaped coil, respectively. The permeability of free space, , These represent the thicknesses of the strip material for the two sections of the D-shaped inductor. , These represent the widths of the strip material for the two segments of the D-shaped inductor. and These are the angles between the two straight segments of the D-shaped coil inductance and the coordinate axes. These are the coordinates of the infinitesimal segment of the integral of the inductance between the two segments of the desired D-shaped coil. , Let be the angles between the arc elements of the two circular arc segments of the desired D-shaped coil inductance, and the angles between the centers of their respective arc segments. , These are the radii of the two circular arc segments of the desired D-shaped coil inductance. This method introduces a Neumann six-fold integral solution based on the Monte Carlo method. This method significantly reduces the curse of dimensionality and computational time of traditional numerical integration methods when calculating the inductance of coils with complex geometries through a random sampling strategy, and significantly improves the efficiency of electromagnetic parameter identification while ensuring accuracy.
[0025] Preferably, in step S8, the three-dimensional finite element mechanical model of the D-type coil is constructed in COMSOL. The three-dimensional finite element mechanical model includes a D-type uninsulated coil and a steel inner frame. The helical structure of the D-type coil is retained to avoid stress concentration at the current input and output. The contact between the mechanical components in the three-dimensional finite element mechanical model adopts the elastic thin-layer method, and a three-dimensional anisotropic spring is set in the contact layer between each turn to simulate the elastic contact phenomenon between the turns of the D-type coil.
[0026] Compared with the prior art, the beneficial effects of the present invention are:
[0027] This invention establishes a distributed circuit network model adapted to the complex geometry of a D-type coil, and combines an efficient Monte Carlo inductance integral algorithm with a two-dimensional thermal conduction finite element model to achieve a bidirectional strongly coupled iterative solution of the electromagnetic-thermal field. Ultimately, it can output spatiotemporal distribution cloud maps of key physical quantities such as current distribution, temperature evolution, stress, and strain of the D-type coil during the quench process. It effectively reveals the unique "current routing" and "thermo-electromagnetic delayed coupling" phenomena of large D-type uninsulated coils, clarifies the interaction between local stress, temperature rise, and electromagnetic force, and provides a complete numerical analysis tool and theoretical basis for the quench propagation mechanism analysis, thermo-mechanical stability assessment, and engineering safety design of D-type high-temperature superconducting uninsulated coils. Attached Figure Description
[0028] Figure 1 This is a diagram of a D-type coil distributed grid model provided in an embodiment of the present invention;
[0029] Figure 2 This is a charging experiment verification diagram of the D-type coil distributed grid model provided in the embodiment of the present invention;
[0030] Figure 3 This is a two-dimensional heat conduction finite element model diagram of a D-type coil provided in an embodiment of the present invention;
[0031] Figure 4 This is a three-dimensional finite element mechanical model diagram of a D-type coil provided in an embodiment of the present invention;
[0032] Figure 5 This is a current distribution cloud map during the quench period provided in an embodiment of the present invention;
[0033] Figure 6 This is a stress analysis diagram during the quench period provided in an embodiment of the present invention. Detailed Implementation
[0034] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0035] This invention provides a technical solution: a method for quench analysis of a type D high-temperature superconducting uninsulated coil, comprising the following steps:
[0036] S1: Establish a distributed grid model of the D-type coil; First, discretize each turn of the conductor of the D-type coil into multiple interconnected arc segment units and straight line segment units. Each unit node has the same electronic components and is regarded as a circuit branch containing a superconducting layer and a normal layer (such as silver or copper) connected in parallel; Consider the contact phenomenon of uninsulated coils at the nodes of adjacent turns and set radial resistance.
[0037] S2: Efficient Calculation of Inductance Parameters: Based on the Monte Carlo method, the Neumann six-fold integral solution method is used to calculate the inductance parameters of any two segments of the D-shaped coil in the distributed mesh model obtained in step S1. , inductance ,set up Duan You A straight line segment, A circular arc segment, Duan You A straight line segment, Each arc segment is calculated using the following formula:
[0038] ;
[0039] In the formula subscript The straight line segment representing the D-shaped coil. The arc segment representing the D-shaped coil, For the first The nth straight segment and the nth Inductance between straight line segments For the first The nth straight segment and the nth Inductance between the arc segments For the first The arc segment and the first Inductance between straight line segments For the first The arc segment and the first Inductance between the arc segments and Let be the integral volumes of the two D-shaped superconducting coils for the desired inductance, respectively. and These are the x-coordinates of the centers of the two arc segments of the D-shaped coil. and These are the ordinates of the centers of the two arc segments of the D-shaped coil, respectively. The permeability of free space, , These represent the thicknesses of the strip material for the two sections of the D-shaped inductor. , These represent the widths of the strip material for the two segments of the D-shaped inductor. and These are the angles between the two straight segments of the D-shaped coil inductance and the coordinate axes. These are the coordinates of the infinitesimal segment of the integral of the inductance between the two segments of the desired D-shaped coil. , Let be the angles between the arc elements of the two circular arc segments of the desired D-shaped coil inductance, and the angles between the centers of their respective arc segments. , These are the radii of the two circular arc segments of the desired D-shaped coil inductance. The inductance parameter calculation method of this invention introduces a Neumann six-fold integral solution method based on the Monte Carlo method. This method, through a random sampling strategy, significantly reduces the curse of dimensionality and computational time of traditional numerical integration methods when calculating the inductance of coils with complex geometries, and significantly improves the efficiency of electromagnetic parameter identification while ensuring accuracy.
[0040] Figure 2 This is a comparison chart of the magnetic induction intensity and voltage curves of the D-type coil mesh model established in step S2 with those of the actual D-type coil charging experiment. In the chart, the blue line represents the magnetic induction intensity curve of the D-type coil mesh model, and the □ point in the blue line represents the measured magnetic induction intensity data in the experiment. The red line represents the voltage curve of the D-type coil mesh model, and the △ point in the red line represents the measured voltage data in the experiment. As can be seen from the chart, the magnetic induction intensity and voltage of the D-type coil mesh model are basically consistent with those of the actual D-type coil charging experiment, proving the rationality of applying the D-type coil mesh model to the D-type coil for D-type coil simulation analysis.
[0041] S3: Establishing the governing equations: For each circuit node and loop of the arc segment and straight segment elements of the D-type coil distributed mesh model established in step S2, establish a set of equations, including the first... Circulating current of each arc segment unit and straight segment unit Radial current Superconducting layer circumferential current Normal layer circumferential electricity and inter-turn contact resistance Superconducting layer resistance Normal layer resistance and node voltage The system of equations is as follows:
[0042] ;
[0043] The first two equations of the above system are based on Kirchhoff's nodal current equation and loop voltage equation; in this invention, the superconducting layer and the normal layer of each segment of the coil are connected in parallel (e.g., Figure 1 As shown in the figure, the third equation indicates that the sum of the circumferential currents of the superconducting layer and the normal layer is the total circumferential current of the segment, and the fourth equation indicates that the voltages of the parallel superconducting layer and the normal layer are equal.
[0044] Among them, the superconducting layer parameters adopt Power-law model: Construct, in the formula For electric field strength, The critical electric field strength, The value is an exponent. For current density, The critical current density, This indicates the number of segments in the corresponding arc segment or line segment element parameters. +1、 -1、 + , - These represent the first and second parameters, respectively. +1 paragraph, No. -1st paragraph, No. + Section, No. - The number of segments in an arc segment unit or a straight segment unit; based on Power-law model , , , This can be expressed by the following formula:
[0045] ;
[0046] In the formula: For the D-shaped coil Section and the Inductance between segments, when ≠ hour, For the D-shaped coil Section and the The inductance between segments is mutual inductance; when hour, For the D-shaped coil Section and the Between segments, For the first The circumferential current of the segment, For time, This represents the equivalent inter-turn contact resistivity of the coil. It is the temperature-dependent equivalent resistivity of the normal layer. and They are the first The surface area and length of each arc segment or straight segment unit; It is the cross-sectional area of the REBCO conductor. This refers to the critical circumferential current at the inter-segment circuit node. This can be expressed by the following relation:
[0047] ;
[0048] In the expression, the numerator is the temperature-dependent term, and the denominator is the term considering the anisotropy of the magnetic field, i.e., the parallel component of the magnetic field. Component perpendicular to the magnetic field The magnetic field contribution, of which This is the critical circumferential current at the initial moment of the D-type coil. This is the critical temperature of a D-type coil. Let m be the temperature of the m-th segment of the D-type coil at a certain moment. The initial temperature. , These are all coefficients describing the critical circumferential current model. In this invention, =0.0605, =0.7580, The critical magnetic field strength is denoted as .
[0049] From the above equation, we obtain the first... Critical circumferential current at each node The relationship with temperature and magnetic field, substituted The specific magnitude of the superconducting layer resistance can be obtained from the expression; , , , By taking the circuit nodes and loops of the arc segment and straight segment elements of the established D-type coil distributed mesh model and establishing a set of equations, the governing equations of the distributed mesh model can be obtained. The final D-type coil distributed mesh model is as follows: Figure 1 As shown.
[0050] S4: Establish a two-dimensional finite element model of heat conduction, as shown in the model below. Figure 3As shown, firstly, a two-dimensional planar model of the D-type coil is established on the COMSOL Multiphysics platform, and the heat conduction equation is solved using a transient solver to obtain the temperature distribution of the two-dimensional planar model of the D-type coil:
[0051] ;
[0052] In the formula, For density, For specific heat capacity, For the anisotropic thermal conductivity tensor, For temperature; and in the two-dimensional heat conduction finite element model, the heat sources include the resistance of the timeout current in the normal layer. Heat generated during inter-turn contact and externally generated local heat pulses And set the convective heat transfer boundary conditions between the surface of the D-type coil and the low-temperature cooling medium;
[0053] After the above analytical model is established, a two-way strong coupling analysis of electromagnetic and thermal multiphysics fields can be performed, specifically including steps S5-S7:
[0054] S5: Electromagnetic → Thermal: Using the COMSOL with MATLAB co-simulation interface, due to the critical circumferential current in the superconducting term of the control equations of the distributed grid model in step S3. Since it is related to the magnetic field, meaning the magnetic field affects the current distribution, and the magnetic field can be calculated from the current using Biot-Savart's law, the calculation process in S3 is electromagnetically coupled. Based on the electromagnetic coupling distribution, the normal layer circumferential current of each cell calculated from the D-type coil distributed mesh model is... and radial current Import the two-dimensional heat conduction finite element model, map it to the corresponding position in the two-dimensional heat conduction finite element model, calculate and update the temperature. Heat generated during inter-turn contact Externally generated local heat pulse Specific heat capacity as a function of temperature in a two-dimensional finite element model of heat conduction and anisotropic thermal conductivity tensor ;
[0055] S6: Thermal → Electromagnetic: Calculate the temperature of each element from the two-dimensional heat conduction finite element model in step S5. The data is fed back in real time to the D-type coil distributed mesh model via the COMSOL with MATLAB co-simulation interface, which is used to update the critical circumferential current of the superconducting layer of the corresponding element in the D-type coil distributed mesh model. Temperature-dependent equivalent resistivity of the normal layer and the equivalent inter-turn contact resistivity of the coil ;
[0056] S7: Iterative solution: Within one time step, steps S5 and S6 are solved alternately until the solution results of steps S5 and S6 meet the convergence criterion, and then the process is advanced to the next time step, thereby simulating the dynamic propagation process of quench loss.
[0057] S8: Mechanical Analysis: A three-dimensional finite element mechanical model of a D-type coil is constructed in COMSOL. This model includes a D-shaped uninsulated coil and a steel inner frame. The helical structure of the D-type coil is retained to avoid stress concentration at current input and output. The contact between the coils in the three-dimensional finite element model employs an elastic thin-layer method, with three-dimensional anisotropic springs placed between each turn to simulate the elastic contact phenomenon between the turns of the D-type coil. The three-dimensional finite element mechanical model of the D-type coil established in this embodiment is as follows: Figure 4 As shown; based on the circumferential current calculated in step S3 and radial current and the temperature calculated in step S7 The temperature change and electromagnetic force generated by the coil during quench are calculated, with the electromagnetic force calculated using the Lorentz force formula. The temperature change and electromagnetic force are then input into a three-dimensional finite element mechanical model of the D-type coil structure to solve for the stress, strain, and deformation of the D-type coil during quench, thus assessing the risk of mechanical damage. Figure 5 This is the stress analysis result during the quench period in this embodiment.
[0058] During the implementation of this embodiment, such as Figure 6 As shown, Figure 6 The method calculates the circumferential current distribution cloud map at one time step during the quench process. It can be clearly seen that the circumferential current in the blue part in the middle of the coil is very small, while the circumferential current in the adjacent turns increases significantly. This shows that during the quench of the D-type coil, the current bypasses the hot spot of the coil. This characteristic of the current bypassing the quench region can prevent the temperature in the quench occurrence area from continuing to rise, thus improving the thermal stability of the coil and demonstrating the special electromagnetic characteristics of the uninsulated coil. The method of this invention can effectively reproduce the unique "current bypass" and "thermo-electromagnetic delayed coupling" phenomena of large D-type uninsulated coils, clarify the interaction relationship between local stress, temperature rise, and electromagnetic force, and provide a complete numerical analysis tool and theoretical basis for the quench propagation mechanism analysis, thermo-mechanical stability assessment, and engineering safety design of D-type high-temperature superconducting uninsulated coils.
[0059] Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.
Claims
1. A method for quench analysis of a type D high-temperature superconducting uninsulated coil, characterized in that, Includes the following steps: S1: Establish a distributed mesh model of a D-type coil in MATLAB; first, discretize each turn of the conductor of the D-type coil into multiple interconnected arc segment units and straight line segment units, and set radial resistance at the nodes of adjacent turns; S2: Calculate the inductance of the D-type coil using the numerical integration method for the D-type coil distributed grid model obtained in step S1. S3: Calculate each circuit node and loop of the arc segment and straight line segment elements of the D-type coil distributed mesh model established in step S2 in MATLAB; obtain the critical circumferential current of the D-type coil superconducting layer. Normal layer circumferential current of each unit Radial current of each unit Circular current of each unit Temperature-dependent equivalent resistivity of the normal layer and the equivalent inter-turn contact resistivity of the coil In the D-type coil distributed mesh model, each circuit node and loop of the arc segment and straight line segment elements is calculated by establishing the following system of equations: ； In the formula, For the first The circumferential current of each arc segment unit and straight segment unit, For radial current, For the superconducting layer circumferential current, For normal layer circumferential current, Inter-turn contact resistance, For superconducting layer resistance, For normal layer resistance, The term represents the inter-segment node voltage, where m represents the corresponding arc segment element parameter or the number of straight segment element parameters. +1、 -1、 + , - These represent the first and second parameters, respectively. +1 paragraph, No. -1st paragraph, No. + , - Number of segments in an arc segment unit or a straight segment unit; Among them, the superconducting layer parameters adopt Power-law model: Construct, in the formula For electric field strength, The critical electric field strength, The value is an exponent. For current density, For the critical current density, according to Power-law model , , , This can be expressed by the following formula: ； In the formula: For the D-shaped coil Section and the Inductance between segments, when ≠ hour, For the D-shaped coil Section and the The inductance between segments is mutual inductance; when hour, For the D-shaped coil Section and the Between segments, For the first The circumferential current of the segment, For time, This represents the equivalent inter-turn contact resistivity of the coil. It is the temperature-dependent equivalent resistivity of the normal layer. and They are the first The surface area and length of each arc segment or straight segment unit; It is the cross-sectional area of the REBCO conductor; The critical circumferential current of the superconducting layer at the inter-segment circuit node; S4: On the COMSOL Multiphysics platform, build a two-dimensional finite element model of the heat conduction of the D-type coil and calculate the temperature of each element in the two-dimensional planar model of the D-type coil. distributed; S5: Using the COMSOL with MATLAB co-simulation interface, calculate the normal layer circumferential current of each cell in the D-type coil distributed mesh model based on the electromagnetic coupling distribution. and radial current Import the two-dimensional heat conduction finite element model from step S4 and map it to the corresponding position in the two-dimensional heat conduction finite element model to update the temperature of each element in the two-dimensional planar model of the D-type coil. distributed; S6: Calculate the temperature of each unit as shown in step S5. The data is fed back in real time to the D-type coil distributed mesh model via the COMSOL with MATLAB co-simulation interface, which is used to update the critical circumferential current of the superconducting layer of the corresponding element in the D-type coil distributed mesh model. Temperature-dependent equivalent resistivity of the normal layer and the equivalent inter-turn contact resistivity of the coil ; S7: Within one time step, solve steps S5 and S6 alternately until the solution results of steps S5 and S6 meet the convergence criterion, and then proceed to the next time step. S8: Establish a three-dimensional finite element mechanical model of the D-type coil, based on the circumferential current calculated in step S3. and radial current and the temperature calculated in step S7 The temperature change and electromagnetic force generated by the coil during the quench period are calculated. The temperature change and electromagnetic force are input into the three-dimensional finite element mechanical model of the D-type coil structure to solve the stress, strain and deformation of the D-type coil during the quench process and assess the risk of mechanical damage.
2. The quench analysis method for a type D high-temperature superconducting uninsulated coil according to claim 1, characterized in that, In step S3, This can be represented by the following relationship: ； In the expression, the numerator is the temperature-dependent term, and the denominator is the term considering the anisotropy of the magnetic field, i.e., the parallel component of the magnetic field. Component perpendicular to the magnetic field The magnetic field contribution, of which This is the critical circumferential current at the initial moment of the D-type coil. This is the critical temperature of a D-type coil. Let m be the temperature of segment m of the D-type coil at a certain moment. The initial temperature. The coefficients are used to describe the critical circumferential current model. The critical magnetic field strength is denoted as .
3. The quench analysis method for a type D high-temperature superconducting uninsulated coil according to claim 1, characterized in that, In step S2, when calculating the inductance of the D-type coil, the following method is used to calculate the inductance of any two segments of the D-type coil. inductance At that time, set The segment has g straight line segments. A circular arc segment, Duan You A straight line segment, Each arc segment is calculated using the following formula: ； In the formula subscript The straight line segment representing the D-shaped coil. The arc segment representing the D-shaped coil For the first The nth straight segment and the nth Inductance between straight line segments For the first The nth straight segment and the nth Inductance between the arc segments For the first The arc segment and the first Inductance between straight line segments For the first The arc segment and the first Inductance between the arc segments Let be the integral volumes of the two D-shaped superconducting coils for the desired inductance, respectively. These are the x-coordinates of the centers of the two arc segments of the D-shaped coil. These are the ordinates of the centers of the two arc segments of the D-shaped coil, respectively. The permeability of free space, , These represent the thicknesses of the strip material for the two sections of the D-shaped inductor. , The widths of the strips for the two segments of the D-shaped inductor are respectively. These are the angles between the two straight segments of the D-shaped coil inductance and the coordinate axes. These are the coordinates of the infinitesimal segment of the integral of the inductance between the two segments of the desired D-shaped coil. Let be the angles between the arc elements of the two circular arc segments of the desired D-shaped coil inductance, and the positions of their respective arc center points. These are the radii of the two circular arc segments of the desired D-shaped coil inductance.
4. The quench analysis method for a type D high-temperature superconducting uninsulated coil according to claim 1, characterized in that, In step S4, after establishing a two-dimensional finite element model of the D-type coil's heat conduction, a transient solver is used to solve the heat conduction equation to obtain the temperature of the two-dimensional planar model of the D-type coil. distributed: ； In the formula, For density, For specific heat capacity, For the anisotropic thermal conductivity tensor, For temperature; and in the two-dimensional heat conduction finite element model, the heat sources include the resistance of the timeout current in the normal layer. Heat generated during inter-turn contact and externally generated local heat pulses Furthermore, convective heat transfer boundary conditions were set between the surface of the D-type coil and the low-temperature cooling medium.
5. The quench analysis method for a type D high-temperature superconducting uninsulated coil according to claim 3, characterized in that, In step S5, the temperature of each unit in the two-dimensional planar model of the D-type coil is updated. When distributing, the updated parameters include temperature. Heat generated during inter-turn contact Externally generated local heat pulse Specific heat capacity as a function of temperature in a two-dimensional finite element model of heat conduction and anisotropic thermal conductivity tensor .
6. The quench analysis method for a type D high-temperature superconducting uninsulated coil according to claim 1, characterized in that, In step S8, the three-dimensional finite element mechanical model of the D-type coil is constructed in COMSOL. The three-dimensional finite element mechanical model includes a D-type uninsulated coil and a steel inner frame. The helical structure of the D-type coil is retained to avoid stress concentration at the current input and output. The contact between the mechanical components in the three-dimensional finite element mechanical model adopts the elastic thin-layer method, and three-dimensional anisotropic springs are set in the contact layer between each turn to simulate the elastic contact phenomenon between the turns of the D-type coil.
7. The quench analysis method for a type D high-temperature superconducting uninsulated coil according to claim 2, characterized in that, In step S3 In the expression, The possible values are: =0.0605, 0.7580 8. The quench analysis method for a type D high-temperature superconducting uninsulated coil according to claim 1, characterized in that, In step S8, the electromagnetic force is calculated using the Lorentz force calculation formula.