CN-121980883-A - Multi-field coupling analysis method for superconducting cable under fusion working condition

CN121980883ACN 121980883 ACN121980883 ACN 121980883ACN-121980883-A

Abstract

The invention discloses a multi-field coupling analysis method of a high-temperature superconducting cable under a fusion working condition, which systematically realizes the whole process simulation of the multi-field behavior of the cable, integrates an electromagnetic field model, a heat transfer model and a mechanical model, realizes the multi-field synchronous transient solution through the mutual coupling relation among physical fields, and effectively reflects the complex multi-field coupling behavior of the high-temperature superconducting cable under the fusion working condition; by means of model post-processing, the method can systematically calculate key performance indexes such as alternating current loss, temperature field distribution, stress strain and the like of the high-temperature superconducting cable in the process of applying an external magnetic field, form a complete link from input conditions to performance response, and provide a complete numerical analysis method for performance evaluation, failure prediction and structure optimization of the high-temperature superconducting cable in an extreme fusion environment.

Inventors

LIU DONGHUI
SHI XUAN
Jia hang
YONG HUADONG

Assignees

兰州大学

Dates

Publication Date: 20260505
Application Date: 20260409

Claims (7)

1. The multi-field coupling analysis method for the high-temperature superconducting cable under the fusion working condition is characterized by comprising the following steps of: s1, constructing a three-dimensional multi-physical field finite element model in finite element software, wherein the method specifically comprises the following steps: Electromagnetic model control equation: In which, in the process, In order to achieve a specific electrical resistance of the material, In order for the magnetic field to be of a strength, Magnetic permeability, t is time; Heat transfer model control equation: In which, in the process, Is the density of the solid material which is to be treated, Is the actual temperature of the solid material and, Is the specific heat capacity of the material at temperature T, As the thermal conductivity of the material at temperature T, Heat source terms that are equations; Mechanical model control equation: In which, in the process, As a function of the stress tensor, Is a physical force vector; S2, constructing a coupling relation for a multi-physical field finite element model, wherein the method specifically comprises the following steps: s21, establishing a Maxwell equation set required in superconducting simulation calculation in an electromagnetic model and supplementing an electromagnetic constitutive relation, wherein the Maxwell equation set is as follows: In which, in the process, For the strength of the electric field, For the magnetic induction intensity, the magnetic flux is measured, The electromagnetic constitutive relation is as follows: ; s22, the electric field intensity of each unit of the superconducting material domain in the electromagnetic model And current density Performing point multiplication to obtain the instantaneous power of each unit, and substituting the instantaneous power as a heat source term into a control equation of the heat transfer model; s23, constructing stress tensors in the mechanical model And strain tensor Is a constitutive relation of (a): , In the formula, Establishing physical force vector of strong electromagnetic field in electromagnetic model to superconducting material The equation is calculated as follows: ; S3, detecting the resistivity of the material by consulting the material parameter data or adopting the prior method Magnetic permeability of Density of solid material Specific heat capacity of material at different temperatures T Thermal conductivity of materials at different temperatures T Elastic tensor Strain tensor Magnetic induction intensity Current density (Current Density) Substituting the parameters into a model established by finite element software, the parameters of alternating current loss, temperature change and stress strain for superconducting analysis can be calculated by using the finite element software.
2. The method for multi-field coupling analysis of high-temperature superconductive cable under fusion condition according to claim 1, wherein in step S3, in order to obtain resistivity of material conforming to fusion condition more accurately And ensuring the calculation efficiency, simplifying the layered structure of the material by calculating the engineering critical current density of the material by using a homogenization method, and obtaining the resistivity of the superconducting material by using a power law model The expression is as follows: , wherein, The critical electric field is as follows: , in order to achieve a critical current density, Is obtained by detection through the prior experimental method, The value is an index, the isotropy of the rest solid materials and the air domain is considered, and the resistivity of the corresponding materials is referred to and substituted into a control equation of the electromagnetic model for calculation.
3. The method for multi-field coupling analysis of superconducting cable under fusion condition according to claim 2, wherein, in order to further improve model calculation accuracy, more accurate critical current density is obtained by the following method The method comprises the following steps: s31, taking the change of critical current density of the superconductor along with the magnetic field into consideration in an electromagnetic model, and adopting the magnetic induction intensity Is decomposed into two components parallel to the surface of the material and perpendicular to the surface of the material, the two components are respectively of the size And To characterize the effect of anisotropy of the material, the specific expression is as follows: , wherein, For a critical current density that varies with the magnetic field, Is the critical current density of the material in the absence of an external magnetic field, Is the critical magnetic field of the material, 、 The method is obtained by the prior detection method, In order to fit the coefficients of the coefficients, , In order to fit the index(s), ; S32, considering the change of the critical current density of the superconducting material along with the temperature in the electromagnetic model, and defining the temperature dependence term of the critical current density of the superconducting material as And (3) with The effect of temperature on critical current density is corrected by multiplication as follows: Wherein, the method comprises the steps of, Is the critical temperature of the superconducting material, is obtained by the existing detection method, As a result of the initial temperature being set, Is the actual temperature; s33, the electromagnetic model also considers the critical current density of the superconducting material along with the axial strain Defining the strain-dependent term of critical current density of superconducting material as And (3) with The effect of axial strain on critical current density is corrected by multiplication as follows: ; S34 critical current density of superconducting material The final steps are as follows: , When the temperature does not reach the critical temperature of the superconducting material, and the axial strain of the superconducting material is not more than 0.67%, the critical current density of the superconducting material is expressed as: 。
4. The method for multi-field coupling analysis of high-temperature superconductive cable under fusion condition according to claim 3, wherein when density, specific heat capacity and thermal conductivity of the material are obtained, the solid material is considered to be isotropic, the superconductive material is in layered structure, and the density and specific heat capacity of each layer of material in the material are calculated by average according to the geometric dimension of the layered structure by using a homogenizing method, and the specific formula is as follows: Wherein Is the first The thickness of the layer is chosen to be the same, Is the first The specific heat capacity and density of the layer material, The specific heat capacity and the density of the section of the whole homogenized material are respectively calculated, the anisotropy of the material is considered, the thickness direction, the width direction and the length direction of the material are distinguished when the heat conductivity of the material is calculated, and the heat conductivity along the thickness direction, the width direction and the length direction is calculated according to the following formula: In the formula (I), in the formula (II), Is the first The thermal conductivity of the layer material, To homogenize, the superconducting material has a thermal conductivity in the thickness direction thereof, The thermal conductivity of the superconducting material along the width and length directions after homogenization.
5. The method for multi-field coupling analysis of superconductive cable under fusion condition according to claim 4, wherein physical force vector Calculated by the following formula: In which, in the process, Along the global coordinate system, respectively, the current density The projected size of the direction is chosen to be the same, Respectively, the magnetic induction intensity along the global coordinate system The projected size of the direction is chosen to be the same, Is a global coordinate system Unit basis vector of direction.
6. The method for multi-field coupling analysis of high-temperature superconductive cable under fusion condition according to claim 5, wherein the temperature change in the heat transfer model causes the cable to generate corresponding temperature strain, thereby changing stress strain state of each point in the material, when temperature change occurs When the thermal strain of the superconducting material occurs in the length direction, the width direction, and the thickness direction, it can be calculated by the following formula: wherein Thermal strain of the superconducting material occurs in the length direction, the width direction and the thickness direction thereof respectively, The coefficients of thermal expansion of the material along its length, width and thickness directions, respectively.
7. The method for multi-field coupling analysis of high-temperature superconducting cable under fusion condition according to claim 1, wherein in step S3, the ac loss calculation method is as follows: In the formula (I), in the formula (II), In the event of an ac loss, In order to be an integral region, Is the integral time domain.

Description

Multi-field coupling analysis method for superconducting cable under fusion working condition Technical Field The invention belongs to the technical field of high-temperature superconductivity, and particularly relates to a multi-field coupling analysis method for a high-temperature superconductivity cable under a fusion working condition. Background Under fusion working conditions, the electromagnetic thermal behaviors of the high-temperature superconducting cable are complex and changeable, strong electromagnetic force load is brought by strong current, strong magnetic field and high change rate of the strong magnetic field, meanwhile, large thermal strain is caused to the material due to rising of temperature, the force and thermal stability of the superconducting cable are obviously influenced, so that the superconducting performance and mechanical performance of the cable are damaged, meanwhile, critical current of the material is further influenced by temperature rise and strain, irreversible damage to the superconducting material is aggravated, however, the existing superconducting simulation is mostly single physical field solution analysis, or a multi-field joint solution method with extremely high complexity is adopted, the requirement on calculation resources is high, and the simulation efficiency is low. Disclosure of Invention The invention aims to provide a multi-field coupling analysis method for a high-temperature superconducting cable under a fusion working condition, so as to solve the problems of the background technology. In order to achieve the purpose, the invention provides the technical scheme that the multi-field coupling analysis method for the high-temperature superconducting cable under the fusion working condition comprises the following steps: s1, constructing a three-dimensional multi-physical field finite element model in finite element software, wherein the method specifically comprises the following steps: Electromagnetic model control equation: In which, in the process, In order to achieve a specific electrical resistance of the material,In order for the magnetic field to be of a strength,Magnetic permeability, t is time; Heat transfer model control equation: In which, in the process, Is the density of the solid material which is to be treated,Is the actual temperature of the solid material and,Is the specific heat capacity of the material at temperature T,As the thermal conductivity of the material at temperature T,Heat source terms that are equations; Mechanical model control equation: In which, in the process, As a function of the stress tensor,Is a physical force vector; S2, constructing a coupling relation for a multi-physical field finite element model, wherein the method specifically comprises the following steps: s21, establishing a Maxwell equation set required in superconducting simulation calculation in an electromagnetic model and supplementing an electromagnetic constitutive relation, wherein the Maxwell equation set is as follows: In which, in the process, For the strength of the electric field,For the magnetic induction intensity, the magnetic flux is measured,Is the current density; The electromagnetic constitutive relationship is as follows: ; s22, the electric field intensity of each unit of the superconducting material domain in the electromagnetic model And current densityPerforming dot product to obtain the instantaneous power of each unit, and substituting the instantaneous power as a heat source term into a control equation of the heat transfer model; s23, constructing stress tensors in the mechanical model And strain tensorIs a constitutive relation of (a): In which, in the process, Establishing physical force vector of strong electromagnetic field in electromagnetic model to superconducting materialThe equation is calculated as follows:; S3, detecting the resistivity of the material by consulting the material parameter data or adopting the prior method Magnetic permeability ofDensity of solid materialSpecific heat capacity of material at different temperatures TThermal conductivity of materials at different temperatures TElastic tensorStrain tensorMagnetic induction intensityCurrent density (Current Density)Substituting the parameters into a model established by finite element software, the parameters of alternating current loss, temperature change and stress strain for superconducting analysis can be calculated by using the finite element software. Further, in step S3, in order to obtain the resistivity of the material which meets the fusion condition more accuratelyAnd ensuring the calculation efficiency, simplifying the layered structure of the material by calculating the engineering critical current density of the material by using a homogenization method, and obtaining the resistivity of the superconducting material by using a power law modelThe expression is as follows: , wherein, The critical electric field is as follows:, in order to ac