WO2024077861A1 - 基于有限元的超导磁体电磁热力多场耦合仿真建模方法 - Google Patents

基于有限元的超导磁体电磁热力多场耦合仿真建模方法 Download PDF

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WO2024077861A1
WO2024077861A1 PCT/CN2023/081195 CN2023081195W WO2024077861A1 WO 2024077861 A1 WO2024077861 A1 WO 2024077861A1 CN 2023081195 W CN2023081195 W CN 2023081195W WO 2024077861 A1 WO2024077861 A1 WO 2024077861A1
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superconducting magnet
superconducting
field
electromagnetic
temperature
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PCT/CN2023/081195
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French (fr)
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杨志星
任丽
徐颖
石晶
蔡针铭
李敬东
唐跃进
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华中科技大学
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    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01F—MAGNETS; INDUCTANCES; TRANSFORMERS; SELECTION OF MATERIALS FOR THEIR MAGNETIC PROPERTIES
    • H01F6/00—Superconducting magnets; Superconducting coils
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01F—MAGNETS; INDUCTANCES; TRANSFORMERS; SELECTION OF MATERIALS FOR THEIR MAGNETIC PROPERTIES
    • H01F6/00—Superconducting magnets; Superconducting coils
    • H01F6/04—Cooling
    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01F—MAGNETS; INDUCTANCES; TRANSFORMERS; SELECTION OF MATERIALS FOR THEIR MAGNETIC PROPERTIES
    • H01F6/00—Superconducting magnets; Superconducting coils
    • H01F6/06—Coils, e.g. winding, insulating, terminating or casing arrangements therefor

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  • the present invention belongs to the technical field of superconducting electrical engineering modeling, and more specifically, relates to a finite element-based superconducting magnet electromagnetic thermal multi-field coupling simulation modeling method.
  • Superconducting power technology helps to achieve lightweight, miniaturized and low-power consumption of power devices, and can improve the stability, safety and power quality of power systems, and has broad application prospects.
  • superconducting magnets are the core components of superconducting power devices, and their stability is the most critical factor affecting the safe operation of superconducting power devices.
  • the central magnetic field and leakage magnetic field generated by superconducting magnets are important factors that need to be considered in the electromagnetic optimization design of superconducting magnets.
  • Thermal stability is a key factor affecting the safe operation of small and medium-sized superconducting magnets.
  • superconducting magnets will be subject to thermal stress caused by temperature differences and electromagnetic stress caused by current flow during operation.
  • the allowable strength of superconducting magnets and their supporting materials needs to be considered under stress, so the stress of superconducting magnets also needs to be analyzed. Therefore, in the design process of superconducting magnets, it is necessary to comprehensively consider the stability analysis and verification of multiple aspects of electromagnetic and thermal forces.
  • a superconducting magnet multi-physics field coupling calculation and analysis model is needed to analyze the magnetic field distribution, AC loss, and stress distribution during the operation of superconducting magnets.
  • the current technology has the following drawbacks:
  • the present invention provides a finite element-based superconducting magnet electromagnetic thermal multi-field coupling simulation modeling method and system, which aims to solve the technical problem that the prior art does not fully consider the multi-field coupling relationship of magnetic field, temperature and stress when performing stress verification, magnetic field verification and thermal stability analysis in the process of superconducting magnet design, and does not complete the stress verification, magnetic field verification and thermal stability analysis in the process of superconducting magnet design, which does not meet the actual operating conditions of the superconducting magnet.
  • the present invention provides a finite element-based superconducting magnet electromagnetic thermal multi-field coupling simulation modeling method, comprising:
  • Electromagnetic field-temperature field coupling the temperature calculated under the current Joule heat generated by the heat source is used to calculate the current density of the electromagnetic field; the magnetic field strength of the electromagnetic field under the new current density is obtained; the current density of the electromagnetic field under the new magnetic field strength is obtained, and it is used to calculate and update the Joule heat generated by the heat source;
  • Electromagnetic field-mechanical field coupling Use the magnetic field calculated from the current electromagnetic field to calculate the stress of the superconducting magnet; obtain the strain of the superconducting magnet under the new stress; obtain the current density of the superconducting tape under the new strain, and use it to calculate and update the magnetic field;
  • Temperature field-mechanical field coupling use the temperature calculated by the current temperature field to calculate stress; obtain new stress and strain; obtain the current density under the new stress and strain, calculate the heat loss under the new current density, and use the Joule heat currently generated by the heat source to calculate the real-time temperature of the superconducting magnet;
  • a contact thermal resistance is set between the superconducting magnet and the cold head of the refrigerator for conduction cooling connection, simulating the heat exchange between the superconducting magnet and the refrigerator during the actual cooling process.
  • the temperature field modeling process is specifically as follows: the established superconducting magnet device model is used as a solid heat source as a whole.
  • the cold head of the refrigerator is set to heat flux to simulate the actual cooling process: when the superconducting magnet adopts cooling medium to cool down, the junction between the superconducting magnet and the cooling medium is set to heat flux boundary, and the type of heat flux is convective heat flux.
  • the first solid mechanics module the superconducting coil and its supporting material are set as thermal expansion materials, so that the superconducting coil and its supporting material can simulate the thermal expansion and contraction effect of the material.
  • the reference temperature is the ambient temperature
  • the actual temperature is the normal operating temperature of the superconducting magnet, which is used to simulate the cooling effect of the superconducting magnet and calculate and analyze the thermal stress caused by the temperature difference during the cooling process of the superconducting magnet.
  • the reference temperature and the actual temperature are both set to the normal operating temperature of the superconducting magnet.
  • the initial prestress and prestrain in the second solid mechanics module are set to the stress and strain expressions calculated by the first solid module, which are used to simulate the normal operation process of the superconducting magnet and calculate the comprehensive stress during the normal operation of the superconducting magnet.
  • the superconducting coil is modeled by homogenization, the edge of the superconducting coil is modeled by refined geometry, and the material properties of the superconducting tape are modeled by equivalent composite modeling.
  • step S5 the superconducting coil part with regular geometry is mapped to obtain quadrilateral mesh units, and the other parts with irregular geometry are divided to obtain triangular mesh units.
  • fr is the unit volume force of the superconducting magnet along the radial direction
  • fz is the unit volume force along the height of the superconducting coil
  • Bz and Br are the magnetic induction intensities along the height and radius of the superconducting coil, respectively;
  • Jc (B,T, ⁇ ) Jc0 ⁇ f( ⁇ ) ⁇ f(T) ⁇ f(B);
  • Jc0 represents the self-field critical current density of the superconducting tape
  • ⁇ is strain
  • ⁇ , ⁇ p , ⁇ 0 , ⁇ are characteristic parameters fitted according to the influence of different stresses and strains on the tape
  • f(T) is the dependence of the critical current density of the superconducting tape on temperature
  • f(B) is the dependence of the critical current density of the superconducting tape on magnetic field;
  • the present invention utilizes the finite element simulation method to perform multi-physical field coupling modeling on the superconducting coil and its supporting structure, and the cooling environment, and can simultaneously calculate the current propagation, magnetic field distribution, magnet temperature rise, AC loss, and stress distribution during the operation of the superconducting magnet, and is used for stability analysis and verification of multiple aspects of electromagnetic and thermal forces during the design of the superconducting magnet.
  • the present invention reduces the modeling time, improves the efficiency of magnet design, can provide a theoretical basis for the design of superconducting magnets, and is of great significance for ensuring the stable operation of the superconducting magnet.
  • FIG1 is a flow chart of a superconducting magnet electromagnetic thermal multi-field coupling simulation modeling method
  • FIG2 is a diagram showing the electromagnetic and thermal multi-field coupling relationship of a superconducting magnet
  • FIG3 (a) is a result of calculating the magnetic field distribution using the electromagnetic thermal coupling model of the present invention
  • FIG3 (b) is a result of calculating the magnetic field distribution using the existing electromagnetic thermal coupling model
  • FIG4 (a) shows the current density distribution result calculated by the electromagnetic thermal coupling model of the present invention
  • FIG4 (b) shows the current density distribution result calculated by the existing electromagnetic thermal coupling model.
  • FIG. 5 (a) is a temperature rise distribution result calculated by the electromagnetic thermal coupling model of the present invention
  • FIG. 5 (b) is a temperature rise distribution result calculated by the existing electromagnetic thermal coupling model
  • FIG6 is a magnet stress distribution calculated by the method of the present invention.
  • FIG. 7 shows the AC loss of the magnet calculated by the method of the present invention.
  • an embodiment of the present invention provides a superconducting magnet electromagnetic thermal multi-field coupling simulation modeling method, comprising:
  • Superconducting magnet modeling Set the structural parameters of the superconducting magnet device to be simulated, establish the geometric model of the superconducting magnet device, set the superconducting magnet to be simulated and its supporting structure materials, add corresponding thermal, electromagnetic, and mechanical material property parameters to the geometric model, and complete the superconducting magnet modeling.
  • Jc 0 represents the self-field critical current density of the superconducting tape
  • f( ⁇ ) is the dependence of the critical current density of the superconducting tape on strain
  • f(T) is the dependence of the critical current density of the superconducting tape on temperature
  • f(B) is the dependence of the critical current density of the superconducting tape on magnetic field.
  • a contact thermal resistance is set between the superconducting magnet and the cold head of the refrigerator for conduction cooling connection.
  • the contact thermal resistance of the present invention fully considers the influence of the contact thermal resistance on the conduction cooling effect, simulates the heat exchange between the superconducting magnet and the refrigerator in the actual cooling process, and the calculation result is more accurate.
  • the present invention obtains the refrigeration power curve of the refrigerator through interpolation fitting, which is more in line with the actual operating state and the calculation result is more accurate.
  • the present invention When the superconducting magnet is cooled by a cooling medium, the present invention fully considers the convective heat exchange between the superconducting magnet and the external cooling medium domain in which it is immersed, so that a heat transfer coefficient function that changes with temperature is obtained by interpolation fitting, which has higher calculation accuracy.
  • Electromagnetic field modeling The electromagnetic field of the superconducting coil is modeled through the H equation, and the boundary conditions of the electromagnetic field are added through point-by-point constraints as the excitation conditions.
  • Temperature field modeling The established superconducting magnet device model is used as a solid heat source.
  • the cold head of the refrigerator is set to heat flux to simulate the actual cooling process: when the superconducting magnet is cooled by cooling medium, the junction between the superconducting magnet and the cooling medium is set to heat flux boundary, and the type of heat flux is convection heat flux.
  • the reference temperature is the ambient temperature
  • the actual temperature is the normal operating temperature of the superconducting magnet, which is used to simulate the cooling effect of the superconducting magnet.
  • the thermal stress caused by the temperature difference during the cooling process of the superconducting magnet can be calculated and analyzed.
  • both the reference temperature and the actual temperature are set to the normal operating temperature of the superconducting magnet.
  • the initial prestress and prestrain in the second solid mechanics module are added to the stress and strain expressions calculated by the first solid module to simulate the normal operation process of the superconducting magnet and calculate the comprehensive stress during the normal operation of the superconducting magnet;
  • the method of the present invention sets two solid mechanics modules, and the initial input parameters of the second solid mechanics module are the stress-strain results solved by the first solid mechanics module. This realizes the connection of the results of the two solid mechanics modules, and can realize thermal stress and comprehensive stress calculation, analysis and verification in one model, thereby reducing modeling costs.
  • Br is the magnetic induction intensity along the radial direction of the superconducting coil
  • Bz is the magnetic induction intensity along the height direction of the superconducting coil
  • k, B 0 , and ⁇ are characteristic parameters fitted according to the influence of the strip on different magnetic fields.
  • the multi-physics field coupling of the present invention is achieved by the following method:
  • Electromagnetic-thermal coupling
  • the temperature calculated under the current Joule heat generated by the heat source is used to calculate the current density of the electromagnetic field; the magnetic field strength of the electromagnetic field under the new current density is obtained; the current density of the electromagnetic field under the new magnetic field strength is obtained and used to calculate and update the Joule heat generated by the heat source. Electromagnetic-thermal coupling is achieved.
  • the Joule heat generated according to the heat conduction formula causes the temperature of the magnet to change.
  • the specific heat conduction formula is as follows:
  • ⁇ m , C p , k are material density, specific heat capacity and equivalent thermal conductivity respectively
  • N is the heat transfer direction vector
  • h(T) is the heat transfer convection coefficient of the cooling medium that changes with temperature.
  • Tc is the critical temperature of the superconducting tape
  • Tref is the actual operating temperature of the superconducting magnet, which causes the critical current density of the superconducting tape to change; after the critical current density of the superconducting tape changes, according to the superconducting EJ pow law relationship
  • the electric field strength also changes accordingly. Due to the electromagnetic interaction, the magnetic field strength Hz and Hr change; according to Ampere's law
  • Electromagnetic-mechanical coupling
  • the magnetic field calculated from the current electromagnetic field is used to calculate the stress of the superconducting magnet; the strain of the superconducting magnet under the new stress is obtained; the current density of the superconducting tape under the new strain is obtained and used to calculate and update the magnetic field to achieve electromagnetic-force coupling.
  • the magnetic field calculated from the current electromagnetic field is used to calculate the volume force of the superconducting magnet
  • E is the Young's modulus of the solid
  • u is the Poisson's ratio
  • ⁇ r , ⁇ z and ⁇ r , ⁇ z represents the strain and stress of the superconducting magnet along the radius, annular direction, and height direction respectively;
  • the temperature calculated from the current temperature field is used to calculate stress; new stress and strain are obtained; the current density under the new stress and strain is obtained, the heat loss under the new current density is calculated, and the Joule heat currently generated by the heat source is used to calculate the real-time temperature of the superconducting magnet, realizing thermal-mechanical coupling.
  • a thermal expansion submodule is set in the multiphysics module to realize the intrinsic coupling between the solid thermal module and solid mechanics.
  • the first step solver solves solid mechanics module 1 to simulate the calculation and analysis during the cooling process of the magnet.
  • the second step solver solves solid mechanics 2, where the initial input parameters in the second solid mechanics module are the stress-strain results obtained by solving the first solid mechanics module, so as to realize the connection of the results of the two solid mechanics modules and simulate the calculation and analysis during the stable operation of the magnet.
  • solver settings solve the electromagnetic thermal multi-physics field coupling calculation model of the superconducting magnet to be simulated to obtain the distribution of each physical field.
  • the present invention also uses mapping operation to divide the superconducting coil part, and uses free triangle mesh to divide other parts.
  • the mapping method is used to finely divide the mesh of the superconducting coil domain of the key research part, and the free triangle network is used to reduce the number of meshes for other non-key areas, reduce the calculation complexity, and improve the model simulation calculation speed.
  • Figure 3 (a) and (b) and Figure 4 (a) and (b) are comparison diagrams of the magnetic field distribution and current density distribution calculation results of the present invention method and the existing electromagnetic thermal coupling model. By comparison, it can be seen that the accuracy of the present invention method is verified.
  • Figure 5 (a) and (b) are A comparison diagram of the calculation results of the magnetic field distribution of magnets using the method of the present invention and the existing electromagnetic thermal coupling model.
  • FIG6 is the stress distribution of the magnet calculated by the method of the present invention.
  • FIG7 is the AC loss of the magnet calculated by the method of the present invention, in which the four double-pancake coils are double-pancake coils 1-4 from top to bottom.

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Abstract

本发明公开了一种超导磁体电磁热力多场耦合仿真建模方法和系统，属于超导电工学建模领域。方法包括：对超导磁体几何建模，为各材料添加对应物理属性；根据超导磁体采取的冷却方式模拟超导磁体运行过程中的冷却环境；对电磁场、温度场、力学场分别进行建模；通过受到电磁热力多场影响的超导带材临界电流密度作为耦合纽带、结合内部热膨胀模块实现超导磁体多场耦合；对所建立几何模型进行网格剖分，通过设置两步求解器进行模型求解。本发明能够同时计算得到超导磁体运行过程中的电流传播、磁场分布、磁体温升、交流损耗和应力分布，用于超导磁体设计中电磁热力多个方面的稳定性分析与校验，提升了建模效率，对保证超导磁体的稳定运行具有重要意义。

Description

基于有限元的超导磁体电磁热力多场耦合仿真建模方法 【技术领域】
本发明属于超导电工学建模技术领域，更具体地，涉及一种基于有限元的超导磁体电磁热力多场耦合仿真建模方法。
【背景技术】
超导电力技术有助于实现电力装置轻量化、小型化、低功耗，并且能提高电力系统的稳定性、安全性和电能质量，具有广阔的应用前景。其中，超导磁体是超导电力装置的核心部件，其稳定性问题是影响超导电力装置安全运行的最关键因素。
对于超导磁体产生的中心磁场与漏磁场是超导磁体电磁优化设计需要考虑的重要因素。热稳定性问题是影响中小型超导磁体安全运行的关键因素。此外，超导磁体在运行过程中会受到温差导致的热应力和通流导致的电磁应力，超导磁体及其支撑材料在应力作用下需要考虑其许用强度，因此也需要对超导磁体的应力进行分析。因此，超导磁体设计过程中需要综合考虑电磁热力多个方面的稳定性分析与校验，需要一种超导磁体多物理场耦合计算分析模型对超导磁体运行过程中的磁场分布、交流损耗、应力分布进行分析。
目前的技术存在以下缺陷：
现有技术多只考虑单一物理场或某几个物理场对超导磁体运行的影响，没有办法同时进行电磁热力多场耦合下超导磁体分析与校验。
现有技术中电磁热力多场之间为间接耦合或者解耦计算，未充分考虑多个物理场之间的耦合关系。
现在技术多只考虑温度与磁场对超导带材临界电流的衰退影响，未考虑所受应力对带材临界电流影响，且现有的电磁热模型无法满足超导磁体 设计应力校核，不利于装置的安全设计。
【发明内容】
针对现有技术的以上缺陷或改进需求，本发明提供了一种基于有限元的超导磁体电磁热力多场耦合仿真建模方法和系统，其目的在于解决现有技术进行超导磁体设计过程中的应力校核、磁场校核与热稳定性分析时，未充分考虑磁场、温度、应力多场耦合关系，完成超导磁体设计过程中的应力校核、磁场校核与热稳定性分析，不符合超导磁体实际运行工况的技术问题。
为实现上述目的，本发明提供了一种基于有限元的超导磁体电磁热力多场耦合仿真建模方法，包括：
S1.超导磁体建模：建立超导磁体装置的几何模型，并为几何模型添加对应的材料属性参数；
S2.超导磁体冷却环境建模：超导磁体采取传导冷却降温方式时，建立制冷机冷头结构；超导磁体采取冷却介质降温方式时，建立超导磁体装置所处冷却介质的几何模型，添加冷却介质的材料属性参数；
S3.分别对电磁场、温度场和力学场建模；
S4.电磁场-温度场耦合：将热源当前产生焦耳热下计算出的温度用于计算电磁场的电流密度；获取在新电流密度下电磁场的磁场强度；获取新磁场强度下电磁场的电流密度，将其用于计算并更新热源产生的焦耳热；
电磁场-力学场耦合：将当前电磁场计算出的磁场用于计算超导磁体应力；获取在新应力下的超导磁体应变；获取新应变下的超导带材电流密度，将其用于计算并更新磁场；
温度场-力学场耦合：将当前温度场计算出的温度用于计算应力；获取新的应力应变；获取在新应力应变下的电流密度，计算新电流密度下的热损耗，将热源当前产生焦耳热用于计算出超导磁体实时温度；
S5.求解待仿真超导磁体电磁热力多物理场耦合计算模型，得到各物理 场分布。
进一步地，超导磁体采取传导冷却降温时，超导磁体与制冷机冷头之间设置接触热阻进行导冷连接，模拟实际冷却过程中超导磁体与制冷机进行热交换。
进一步地，温度场建模过程具体为：将建立的超导磁体装置模型整体作为固体热源，当超导磁体采取传导冷却降温时，制冷机冷头处设置为热通量进行模拟实际降温过程：当超导磁体采取冷却介质降温时，将超导磁体与冷却介质交界处设置为热通量边界，所述热通量的类型为对流热通量。
进一步地，力学场的建模过程具体为：
设置两个固体力学模块，第一个固体力学模块中设置超导线圈及其支撑材料为热膨胀材料，使得超导线圈及其支撑材料可以模拟材料热胀冷缩效应，参考温度为环境温度，实际温度为超导磁体正常运行温度，用以模拟超导磁体冷却降温效果，计算分析超导磁体降温过程中温差导致的热应力；第二个固体力学模块中参考温度与实际温度均设置为超导磁体正常运行温度，同时将第二个固体力学模块中初始预应力与预应变设置为第一个固体模块计算得到的应力与应变表达式，用于模拟超导磁体正常运行过程，计算超导磁体正常运行过程中的综合应力。
进一步地，步骤S1超导磁体建模过程中，超导线圈采用均质化建模，超导线圈边缘精细化几何建模，超导带材材料属性采用等效复合建模。
进一步地，步骤S5求解前，对规整几何的超导线圈部分通过映射操作得到四边形网格单元，将非规整几何的其他部分剖分得到三角形网格单元。
进一步地，电磁场-力学场耦合的具体过程为，
根据计算超导磁体体积力；fr为超导磁体沿半径方向的单位体积力，fz为沿超导线圈高度的单位体积力，为环向电流密度，Bz、Br分别为沿超导线圈高度与沿半径方向的磁感应强度；
利用σ＝div f通过计算得到的体积力求解磁体所受应力；σ为应力，div 为散度矢量算子；
通过广义胡克定律求解新磁体应力下的应变结果；
根据Jc(B,T,ε)＝Jc0×f(ε)×f(T)×f(B)计算应变变化导致的超导带材临界电流密度变化；Jc0表示超导带材的自场临界电流密度，ε为应变，γ、εp、ε0、ζ为根据带材对不同应力应变影响拟合出的特征参数，f(T)为超导带材临界电流密度与温度的依赖关系式，f(B)为超导带材临界电流密度与磁场的依赖关系式；
利用超导E-J pow law关系得到新的磁场强度，Ec为临界失超判据，n为超导指数。
进一步地，温度场-力学场耦合具体过程为，
利用根据当前计算出的温度计算应变ε，其中，α为材料热膨胀系数；
计算应变变化导致的超导带材临界电流密度变化；
利用超导E-J pow law关系得到新的磁场强度。
总体而言，通过本发明所构思的以上技术方案与现有技术相比，能够取得下列有益效果。
本发明利用有限元仿真方法，分别对超导线圈及其支撑结构、冷却环境进行多物理场耦合建模，能够同时计算得到超导磁体运行过程中的电流传播、磁场分布、磁体温升、交流损耗、应力分布，用于超导磁体设计过程中电磁热力多个方面的稳定性分析与校验，相对于单一物理场计算，减少了建模时间，提升了磁体设计效率，可以为超导磁体设计提供理论依据，对保证超导磁体的稳定性运行具有重要意义。
【附图说明】
图1是超导磁体电磁热力多场耦合仿真建模方法流程图；
图2是超导磁体电磁热力多场耦合关系图；
图3中(a)为本发明电磁热力耦合模型计算磁场分布结果；图3中(b)为现有电磁热耦合模型计算磁场分布结果；
图4中(a)为本发明电磁热力耦合模型计算电流密度分布结果，图4中(b)为现有电磁热耦合模型计算电流密度分布结果
图5中(a)为本发明电磁热力耦合模型计算温升分布结果；图5中(b)为现有电磁热耦合模型计算温升分布结果；
图6为本发明方法计算得到的磁体应力分布；
图7为本发明方法计算得到的磁体交流损耗。
【具体实施方式】
为了使本发明的目的、技术方案及优点更加清楚明白，以下结合附图及实施例，对本发明进行进一步详细说明。应当理解，此处所描述的具体实施例仅仅用以解释本发明，并不用于限定本发明。此外，下面所描述的本发明各个实施方式中所涉及到的技术特征只要彼此之间未构成冲突就可以相互组合。
参考图1，本发明实施例提供的一种超导磁体电磁热力多场耦合仿真建模方法，包括：
S1.超导磁体建模：设置待仿真的超导磁体装置结构参数，建立超导磁体装置的几何模型，设置待仿真超导磁体及其支撑结构材料，为几何模型添加对应的热学、电磁学、力学材料属性参数，完成超导磁体建模。
优选地，为了在保证求解精度的同时，降低求解复杂度，提升计算速度，超导线圈采用均质化建模；将超导线圈边缘精细化几何建模；超导带材材料属性采用等效复合建模；超导线圈电磁电阻率根据超导E-J pow law 关系建立，超导E-J pow law关系为其中，Ec为临界失超判据，n为超导指数，J为电流密度，Jc(B,T,ε)是与温度、磁场、应力相关的带材临界电流密度；其中Jc(B,T,ε)＝Jc0×f(ε)×f(T)×f(B)
其中，Jc0为表示超导带材的自场临界电流密度，f(ε)为超导带材临界电流密度与应变的依赖关系式，f(T)为超导带材临界电流密度与温度的依赖关系式，f(B)为超导带材临界电流密度与磁场的依赖关系式。
S2.超导磁体冷却环境建模；超导磁体采取传导冷却降温方式时，建立制冷机冷头结构；超导磁体采取冷却介质降温方式时，建立超导磁体装置所处冷却介质的几何模型，获取冷却介质的电磁学、热学等材料属性参数。
优选地，超导磁体采取传导冷却降温时，超导磁体与制冷机冷头之间设置接触热阻进行导冷连接。本发明设置接触热阻充分考虑了接触热阻对导冷效果的影响，模拟实际冷却过程中超导磁体与制冷机进行热交换，计算结果更加准确。
超导磁体采取传导冷却降温时，由于实际制冷机制冷过程中，制冷功率并不是固定值，而是随温度降低而制冷功率降低的曲线，因此，本发明通过插值拟合获得制冷机制冷功率曲线，更加符合实际运行状态，计算结果更加准确。
在超导磁体采取冷却介质降温时，本发明充分考虑了超导磁体与其所浸泡的外部冷却介质域的对流换热，因此通过插值拟合方式获得随温度变化的传热系数函数，具有更高的计算精度。
S3.多物理场建模：
电磁场建模：通过H方程，对超导线圈的电磁场进行建模，通过逐点约束添加电磁场的边界条件，作为施加励磁条件
温度场建模：将建立的超导磁体装置模型整体作为固体热源，当超导 磁体采取传导冷却降温时，制冷机冷头处设置为热通量进行模拟实际降温过程：当超导磁体采取冷却介质降温时，将超导磁体与冷却介质交界处设置为热通量边界，所述热通量的类型为对流热通量。定义热源为超导磁体当前产生的焦耳热Q，Q＝E·J，E表示电场强度，J表示电流密度。因此在整个迭代求解过程中，温度会被反复的输入，实现热参数实时更新。
力学场建模：设置两个固体力学模块，以体积力的形式施加力学载荷，因此超导磁体沿半径方向的单位体积力fr可以通过计算得到，沿超导线圈高度的单位体积力fz可以通过计算得到，其中为环向电流密度，Bz、Br分别为沿超导线圈高度与沿半径方向的磁感应强度，将支撑结构设置固定，使得支撑材料不再具有任何方向运动的自由度，限制支撑材料所有位移。第一个固体力学模块中设置超导线圈及其支撑材料为热膨胀材料，使得超导线圈及其支撑材料可以模拟材料热胀冷缩效应，参考温度为环境温度，实际温度为超导磁体正常运行温度，用以模拟超导磁体冷却降温效果，可以计算分析超导磁体降温过程中温差导致的热应力。第二个固体力学模块中参考温度与实际温度均设置为超导磁体正常运行温度，同时添加第二个固体力学模块中初始预应力与预应变为第一个固体模块计算得到应力与应变表达式，用于模拟超导磁体正常运行过程，计算超导磁体正常运行过程中的综合应力；
现在技术只能通过修改励磁条件计算得到磁体降温过程的热应力，需要两个模型计算得到，而本发明方法通过设置两个固体力学模块，第二个固体力学模块初始输入参数为第一个固体力学模块求解得到的应力应变结果，实现两个固体力学模块结果承接，可以在一个模型中实现热应力与综合应力计算分析校验，减小建模成本。
S4.多物理场耦合：
更具体地，超导带材临界电流密度与磁场的依赖关系式为：
其中Br为沿超导线圈半径方向的磁感应强度，Bz为沿超导线圈高度方向的磁感应强度；k、B0、α为根据带材对不同磁场影响拟合出来的特征参数。
参考图2，本发明多物理场耦合通过以下方式实现耦合：
电磁-热耦合：
将热源当前产生焦耳热下计算出的温度用于计算电磁场的电流密度；获取在新电流密度下电磁场的磁场强度；获取新磁场强度下电磁场的电流密度，将其用于计算并更新热源产生的焦耳热。实现电磁-热耦合。
电磁-热耦合详细过程如下：
根据热传导公式产生的焦耳热导致磁体温度发生变化，具体地热传导公式如下：

其中，ρm,Cp,k分别是材料密度和比热容、等效热导率，N为传热方向向量，h(T)是冷却介质随温度变化的换热对流系数。
温度发生变化后，根据超导带材临界电流密度与温度的依赖关系式
其中，Tc为超导带材临界温度，Tref为超导磁体实际运行温度，导致超导带材临界电流密度发生变化；超导带材临界电流密度发生变化后，根据超导E-J pow law关系电场强度也随之变化，由于电磁相生关系，磁场强度Hz与Hr发生变化；根据安培定律
其中z为沿磁体高度方向，r为沿半径方向，得到新磁场 强度下电流密度；根据焦耳热Q＝E·J，更新此时热源产生的焦耳热。由此实现电磁-热耦合。
电磁-力耦合：
将当前电磁场计算出的磁场用于计算超导磁体应力；获取在新应力下的超导磁体应变；获取新应变下的超导带材电流密度，将其用于计算并更新磁场，实现电磁-力耦合。
电磁-力耦合详细过程如下：
根据将当前电磁场计算出的磁场用于计算超导磁体体积力；
根据体积力与应力之间的关系，应力σ＝div f，其中σ为应力，div为散度矢量算子，可以通过计算得到的体积力求解出磁体所受应力；
根据广义的胡克定律求解新磁体应力下的应变结果，
E是固体的杨氏模量，u是泊松比，εr、εz和σr、σz分别代表超导磁体沿半径、环向、沿高度方向上的应变和应力；
由于应变发生改变，根据超导带材临界电流密度与应力的依赖关系式
可知超导带材临界电流密度发生变化，其中，γ、εp、ε0、ζ为根据带材对不同应力应变影响拟合出的特征参数；
当超导带材临界电流密度发生变化，根据超导E-J pow law关系
得到新的磁场强度。实现电磁-力耦合。
热-力耦合：
将当前温度场计算出的温度用于计算应力；获取新的应力应变；获取在新应力应变下的电流密度，计算新电流密度下的热损耗，将热源当前产生焦耳热用于计算出超导磁体实时温度。实现热-力耦合。
热-力耦合详细过程如下：
根据其中，α为材料热膨胀系数，当前计算出的温度用于计算应变ε；由于应变发生变化，根据超导带材临界电流密度与应变的依赖关系式，超导带材临界电流密度发生变化，从而根据超导E-J pow law关系，得到新的电流密度；电流密度发生变化后，根据焦耳热Q＝E·J计算公式与热传导公式，计算得到超导磁体实时温度。实现热-力耦合。
在多物理场模块中设置热膨胀子模块实现固体热学模块与固体力学的内在耦合。
S5.求解设置与求解，设置两步求解器。第一步求解器求解固体力学模块1，用以模拟磁体降温过程中计算分析，第二步求解器求解固体力学2，其中第二个固体力学模块中初始输入参数为第一个固体力学模块求解得到的应力应变结果，实现两个固体力学模块结果承接，用以模拟磁体稳定运行过程中计算分析。完成求解器设置后，求解待仿真超导磁体电磁热力多物理场耦合计算模型，得到各物理场分布。
优选地，求解之前本发明还对超导线圈部分采用映射操作方式进行剖分，对其他部分采用自由三角形网格剖分。对重点研究部分超导线圈域采用映射方式精细剖分网格，对非重点其他区域采用自由三角形网络降低网格数量，减少计算复杂度，提升模型仿真计算速度。
下面以通入4个双饼240匝工作电流50A的超导磁体作为研究对象，验证本发明的建模方法。图3中(a)和(b)与图4中(a)和(b)为本发明方法与现有电磁热耦合模型磁体磁场分布、电流密度分布计算结果对比图，通过对比可知，验证了本发明方法的准确性。图5中(a)和(b)为 本发明方法与现有电磁热耦合模型磁体磁场分布计算结果对比图，由于本发明方法考虑了应力对超导带材临界电流的影响，计算结果更加贴近实际工况，仿真温升较大；图6为本发明方法计算得到的磁体应力分布；图7为本发明方法计算得到的磁体交流损耗，其中4个双饼线圈从上往下依次为①-④号双饼线圈。
本领域的技术人员容易理解，以上所述仅为本发明的较佳实施例而已，并不用以限制本发明，凡在本发明的精神和原则之内所作的任何修改、等同替换和改进等，均应包含在本发明的保护范围之内。

Claims (9)

  1. 一种基于有限元的超导磁体电磁热力多场耦合仿真建模方法，其特征在于，包括：
    S1.超导磁体建模：建立超导磁体装置的几何模型，并为几何模型添加对应的材料属性参数；
    S2.超导磁体冷却环境建模：超导磁体采取传导冷却降温方式时，建立制冷机冷头结构；超导磁体采取冷却介质降温方式时，建立超导磁体装置所处冷却介质的几何模型，添加冷却介质的材料属性参数；
    S3.分别对电磁场、温度场和力学场建模；
    S4.电磁场-温度场耦合：将热源当前产生焦耳热下计算出的温度用于计算电磁场的电流密度；获取在新电流密度下电磁场的磁场强度；获取新磁场强度下电磁场的电流密度，将其用于计算并更新热源产生的焦耳热；
    电磁场-力学场耦合：将当前电磁场计算出的磁场用于计算超导磁体应力；获取在新应力下的超导磁体应变；获取新应变下的超导带材电流密度，将其用于计算并更新磁场；
    温度场-力学场耦合：将当前温度场计算出的温度用于计算应力；获取新的应力应变；获取在新应力应变下的电流密度，计算新电流密度下的热损耗，将热源当前产生焦耳热用于计算出超导磁体实时温度；
    S5.求解待仿真超导磁体电磁热力多物理场耦合计算模型，得到各物理场分布。
  2. 根据权利要求1所述的一种基于有限元的超导磁体电磁热力多场耦合仿真建模方法，其特征在于，超导磁体采取传导冷却降温时，超导磁体与制冷机冷头之间设置接触热阻进行导冷连接，模拟实际冷却过程中超导磁体与制冷机进行热交换。
  3. 根据权利要求2所述的一种基于有限元的超导磁体电磁热力多场耦 合仿真建模方法，其特征在于，温度场建模过程具体为：将建立的超导磁体装置模型整体作为固体热源，当超导磁体采取传导冷却降温时，制冷机冷头处设置为热通量进行模拟实际降温过程：当超导磁体采取冷却介质降温时，将超导磁体与冷却介质交界处设置为热通量边界，所述热通量的类型为对流热通量。
  4. 根据权利要求3所述的一种基于有限元的超导磁体电磁热力多场耦合仿真建模方法，其特征在于，力学场的建模过程具体为：
    设置两个固体力学模块，第一个固体力学模块中设置超导线圈及其支撑材料为热膨胀材料，使得超导线圈及其支撑材料可以模拟材料热胀冷缩效应，参考温度为环境温度，实际温度为超导磁体正常运行温度，用以模拟超导磁体冷却降温效果，计算分析超导磁体降温过程中温差导致的热应力；第二个固体力学模块中参考温度与实际温度均设置为超导磁体正常运行温度，同时将第二个固体力学模块中初始预应力与预应变设置为第一个固体模块计算得到的应力与应变表达式，用于模拟超导磁体正常运行过程，计算超导磁体正常运行过程中的综合应力。
  5. 根据权利要求3所述的一种基于有限元的超导磁体电磁热力多场耦合仿真建模方法，其特征在于，步骤S1超导磁体建模过程中，超导线圈采用均质化建模，超导线圈边缘精细化几何建模，超导带材材料属性采用等效复合建模。
  6. 根据权利要求4所述的一种基于有限元的超导磁体电磁热力多场耦合仿真建模方法，其特征在于，步骤S5求解前，对规整几何的超导线圈部分通过映射操作得到四边形网格单元，将非规整几何的其他部分剖分得到三角形网格单元。
  7. 根据权利要求6所述的一种基于有限元的超导磁体电磁热力多场耦合仿真建模方法，其特征在于，电磁场-力学场耦合的具体过程为，
    根据计算超导磁体体积力；fr为超导磁体沿半径方 向的单位体积力，fz为沿超导线圈高度的单位体积力，为环向电流密度，Bz、Br分别为沿超导线圈高度与沿半径方向的磁感应强度；
    利用σ＝div f通过计算得到的体积力求解磁体所受应力；σ为应力，div为散度矢量算子；
    通过广义胡克定律求解新磁体应力下的应变结果；
    根据Jc(B,T,ε)＝Jc0×f(ε)×f(T)×f(B)计算应变变化导致的超导带材临界电流密度变化；Jc0表示超导带材的自场临界电流密度，ε为应变，γ、εp、ε0、ζ为根据带材对不同应力应变影响拟合出的特征参数，f(T)为超导带材临界电流密度与温度的依赖关系式，f(B)为超导带材临界电流密度与磁场的依赖关系式；
    利用超导E-J pow law关系得到新的磁场强度，Ec为临界失超判据，n为超导指数。
  8. 根据权利要求7所述的一种基于有限元的超导磁体电磁热力多场耦合仿真建模方法，其特征在于，温度场-力学场耦合具体过程为，
    利用根据当前计算出的温度计算应变ε，其中，α为材料热膨胀系数；
    计算应变变化导致的超导带材临界电流密度变化；
    利用超导E-J pow law关系得到新的磁场强度。
  9. 一种基于有限元的超导磁体电磁热力多场耦合仿真建模系统，其特征在于，包括：计算机可读存储介质和处理器；
    所述计算机可读存储介质用于存储可执行指令；
    所述处理器用于读取所述计算机可读存储介质中存储的可执行指令， 执行权利要求1至8任一项所述的基于有限元的超导磁体电磁热力多场耦合仿真建模方法。
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CN115565745A (zh) * 2022-10-12 2023-01-03 华中科技大学 基于有限元的超导磁体电磁热力多场耦合仿真建模方法
CN116432384B (zh) * 2023-02-14 2024-02-27 华中科技大学 一种二元电流引线电磁热耦合求解方法和系统
CN116432484B (zh) * 2023-03-23 2024-04-16 中国科学院高能物理研究所 无液氦超导腔降温失超过程的多物理场耦合数值仿真方法
CN117077473B (zh) * 2023-08-02 2024-04-30 哈尔滨工业大学 基于传输线法的二维轴对称电磁热力多场耦合计算方法
CN116956378B (zh) * 2023-09-20 2024-01-02 宁波健信超导科技股份有限公司 一种超导磁体传热分析方法、装置、设备及存储介质
CN117272762B (zh) * 2023-11-21 2024-02-06 中国科学院合肥物质科学研究院 水冷磁体线圈对流换热系数确定方法及系统
CN117709218A (zh) * 2023-12-12 2024-03-15 中国科学院近代物理研究所 超导磁铁冷却结构的热仿真方法、装置、设备和存储介质

Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US8855978B2 (en) * 2010-03-18 2014-10-07 Fujitsu Limited Method for simulating magnetic material
CN112001101A (zh) * 2020-07-20 2020-11-27 中国南方电网有限责任公司超高压输电公司广州局 基于有限元的gil电-磁-热-流-力多物理场耦合仿真建模方法
CN113657064A (zh) * 2021-08-20 2021-11-16 华中科技大学 一种功率半导体模块多物理场联合仿真方法
CN114254528A (zh) * 2020-09-21 2022-03-29 河海大学 一种超导磁体失超过程的有限元分析方法
CN114999595A (zh) * 2022-05-26 2022-09-02 华中科技大学 基于有限元的超导线圈整体过流失超仿真建模方法和系统
CN115565745A (zh) * 2022-10-12 2023-01-03 华中科技大学 基于有限元的超导磁体电磁热力多场耦合仿真建模方法

Patent Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US8855978B2 (en) * 2010-03-18 2014-10-07 Fujitsu Limited Method for simulating magnetic material
CN112001101A (zh) * 2020-07-20 2020-11-27 中国南方电网有限责任公司超高压输电公司广州局 基于有限元的gil电-磁-热-流-力多物理场耦合仿真建模方法
CN114254528A (zh) * 2020-09-21 2022-03-29 河海大学 一种超导磁体失超过程的有限元分析方法
CN113657064A (zh) * 2021-08-20 2021-11-16 华中科技大学 一种功率半导体模块多物理场联合仿真方法
CN114999595A (zh) * 2022-05-26 2022-09-02 华中科技大学 基于有限元的超导线圈整体过流失超仿真建模方法和系统
CN115565745A (zh) * 2022-10-12 2023-01-03 华中科技大学 基于有限元的超导磁体电磁热力多场耦合仿真建模方法

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