高温超导磁悬浮三维理论模型及其数值计算研究
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摘要
虽然高温超导磁悬浮的理论研究已突破二维或轴对称情形的局限,逐步向更接近实际情况的三维情形靠拢,但目前的三维理论模型或者忽略高温超导体的电磁各向异性或者对其作过多的简化处理,导致模型对高温超导体电磁特性的描述不够。因此,高温超导磁悬浮的理论研究还有待进一步完善。
本文从Maxwell方程组和高温超导体电阻率的各向异性出发,结合高温超导体的电磁本构关系,以矢量电位为状态变量,建立了考虑高温超导体电各向异性现象的三维电磁场控制方程。为研究运动状态下高温超导体的热磁耦合问题,给出了高温超导体的温度场控制方程。在数值实现方法上,分别采用Galerkin有限元和Crank-Nicolson-θ有限差分格式对控制方程进行空间离散和时间离散。此外,为模拟永磁轨道中相邻永磁体之间的缝隙引起的外场沿纵向的不均匀性,采用面电流模型建立了永磁轨道磁场的三维解析模型。
在对模型的验证方面,详细比较讨论了不同运动模式下的数值计算结果与实验测试结果,具体包括竖直运动下平移对称场中的零场冷、场冷悬浮与悬挂三种情形以及轴对称场中零场冷情形；横向运动下场冷悬浮、悬浮高度等于场冷高度与悬挂三种情形；纵向运动下悬浮力随运动时间的变化关系。结果表明本文提出的三维理论模型可以很好地反映高温超导体与外场的电磁作用力。在此基础上,理论研究了三维运动下高温超导块材的磁悬浮特性。
对于竖直运动,首先分析了工作条件、外场结构、材料性能与几何尺寸等影响因素对悬浮力的作用规律,接着讨论了悬浮力的弛豫特性及其影响因素的作用规律,得出提高块材的材料性能或降低温度,既可显著提高悬浮力,也能有效抑制甚至避免悬浮力弛豫衰减的结论,最后从理论上证实了预载可以有效地抑制悬浮力的弛豫衰减,是提高系统悬浮稳定性的一种有效手段。
对于横向运动,首先分析了工作条件、最大横向位移、材料性能与几何尺寸等影响因素对电磁力的作用规律,接着讨论了高温超导体的临界场冷高度问题,发现随着悬浮高度的增加、材料性能的提高或者温度的降低,临界场冷高度是逐渐降低的,随后提出了用于研究悬浮体横向可恢复特性的最小能量法,最后就连续横向运动过程中不同条件下悬浮力和导向力随横向运动次数的变化规律进行了深入分析,并从理论上证实预载能够有效地抑制横向运动引起的悬浮力衰减。
对于纵向运动,分为磁悬浮发射和磁悬浮轨道交通两种应用。就磁悬浮发射应用而言,研究的内容包括轨道缝隙、出口速度和温度对悬浮力的影响规律以及不同出口速度和温度下块材内最大温升的变化规律；就轨道交通应用而言,研究了不同场冷高度、悬浮高度、运动速度和温度下运动过程中悬浮力的变化规律,分析了运动速度和温度对块材内部最大温升的影响规律。研究结果表明,对于任何一种应用,降低块材的温度,都能起到抑制悬浮力衰减和减小温升的作用。此外,研究中还发现,悬浮体的阻浮比很小,这对高温超导磁悬浮技术应用于速度较高的领域是非常有利的。
Theoretical studies on high temperature superconducting (HTS) magnetic levitation (MagLev) are no longer limited to two-dimensional, axisymmetic, or three-dimensional (3D) cases, for which the latter one yields results that, are closer towards practical applications. The present 3D model neglects the electromagnetic (EM) anisotropy phenomena found present in high temperature superconductors (HTSC) and involves too many simplifications when taking this phenomena into account thereby lacking in the total understanding of the EM properties in HTSCs. Therefore, more effort should be done to further improve the theoretical studies of HTS MagLev.
In this thesis, a current vector potential was introduced to establish the 3D EM governing equations of the HTSC on the basis of Maxwell's equations and the anisotropy of the resistivity in the HTSC combined with the EM constitutive relations of the HTSC. In order to take the thermal-magnetic coupling problem into account, a thermal governing equation was also presented. To numerically solve the governing equations, finite element method via Galerkin's method and finite-difference method via Crank-Nicolson-θmethod were employed, respectively, to implement the study of space discretization and time discretization. Moreover, to simulate the aperture between adjacent permanent magnets composing the Permanent Magnet Guidway (PMG), a 3D analytical model of the PMG was also performed based on the surface current model.
To confirm the validity of the above-mentioned theoretical model, the numerical and experimental results under different movement types were discussed and compared in detail such as:Zero Field-Cooling (ZFC), Field-Cooling (FC) with levitation and suspension in translational symmetry and ZFC in axisymmetric applied fields under vertical movement; ZFC, identical Field-Cooling Height (FCH) and Levitation Height (LH) and suspension under transverse movement; and the relationship between levitation force (LF) and running time under longtitudinal movement, and the results indicated that the proposed 3D theorectical model is valid to describe the EM interaction between HTSC and applied field. Based on the above-mentioned analysis, the levitation performance of the HTS MagLev under 3D movement was theoretically investigated.
For movement along the vertical direction, the performance of LF under different operating conditions, applied field structures, material properties and geometries were firstly analyzed, and then the relaxation characterstic of LF and associated rules of the various influencing factors were discussed, and the conclusion that, LF can be improved and the force decay can be suppressed by enhancing the material property or lowering the operating temperature of the HTSC, were derived. In the end, it is theoretically proved that pre-loading is an effective approach to reduce the force decay during relaxation, and then the stability of the levitation system can be improved by this approach.
For movement along the transverse direction, the performance of the magnetic force under differenet operating conditions, maximum lateral diaplacements, material properties and geometries were firstly analyzed, and then the critical FCH problem of the HTSC was discussed, and we found that the critical FCH decreases with the increase of the LH, improvement of the material property as well as decrement of the the operating temperature. Subsequently, a minimum energy method to evaluate the restorable characteristics of a levitated body during transverse movement was proposed. Lastly, the changing trendency of the LF and guidance force under different operating conditions during continuous transverse movement was thoroughly studied. Furthermore, theoretical verification of pre-loading which is considered to be effective to reduce LF decay due to transverse movement was achieved.
For movement along the longitudinal direction, two different appliacable fields were considered, MagLev launch and MagLev rail transit. For the MagLev launch application, the main aspects studied included the influence of the aperture of the PMG, exit velocities and operating temperatures on the LF and the changing rule of Maximum Temperature Raise (MTR) under different exit velocities and operating temperatures. For the MagLev rail transit application, the changing tendency of the LF under different FCHs, LHs, velocities and operating temperatures was calculated, and the velocity and operating temperature dependence of the MTR in the HTSC were also monitored. The results showed that, for any application, lowering the operating temperature of the HTSC can suppress not only the LF decay but also the temperature raise during the longitudinal movement. In addition, we also found that, the drag-to-lift ratio of levitated body is small, and this is beneficial for the application the HTS MagLev in the high-speed field.
本文从Maxwell方程组和高温超导体电阻率的各向异性出发,结合高温超导体的电磁本构关系,以矢量电位为状态变量,建立了考虑高温超导体电各向异性现象的三维电磁场控制方程。为研究运动状态下高温超导体的热磁耦合问题,给出了高温超导体的温度场控制方程。在数值实现方法上,分别采用Galerkin有限元和Crank-Nicolson-θ有限差分格式对控制方程进行空间离散和时间离散。此外,为模拟永磁轨道中相邻永磁体之间的缝隙引起的外场沿纵向的不均匀性,采用面电流模型建立了永磁轨道磁场的三维解析模型。
在对模型的验证方面,详细比较讨论了不同运动模式下的数值计算结果与实验测试结果,具体包括竖直运动下平移对称场中的零场冷、场冷悬浮与悬挂三种情形以及轴对称场中零场冷情形；横向运动下场冷悬浮、悬浮高度等于场冷高度与悬挂三种情形；纵向运动下悬浮力随运动时间的变化关系。结果表明本文提出的三维理论模型可以很好地反映高温超导体与外场的电磁作用力。在此基础上,理论研究了三维运动下高温超导块材的磁悬浮特性。
对于竖直运动,首先分析了工作条件、外场结构、材料性能与几何尺寸等影响因素对悬浮力的作用规律,接着讨论了悬浮力的弛豫特性及其影响因素的作用规律,得出提高块材的材料性能或降低温度,既可显著提高悬浮力,也能有效抑制甚至避免悬浮力弛豫衰减的结论,最后从理论上证实了预载可以有效地抑制悬浮力的弛豫衰减,是提高系统悬浮稳定性的一种有效手段。
对于横向运动,首先分析了工作条件、最大横向位移、材料性能与几何尺寸等影响因素对电磁力的作用规律,接着讨论了高温超导体的临界场冷高度问题,发现随着悬浮高度的增加、材料性能的提高或者温度的降低,临界场冷高度是逐渐降低的,随后提出了用于研究悬浮体横向可恢复特性的最小能量法,最后就连续横向运动过程中不同条件下悬浮力和导向力随横向运动次数的变化规律进行了深入分析,并从理论上证实预载能够有效地抑制横向运动引起的悬浮力衰减。
对于纵向运动,分为磁悬浮发射和磁悬浮轨道交通两种应用。就磁悬浮发射应用而言,研究的内容包括轨道缝隙、出口速度和温度对悬浮力的影响规律以及不同出口速度和温度下块材内最大温升的变化规律；就轨道交通应用而言,研究了不同场冷高度、悬浮高度、运动速度和温度下运动过程中悬浮力的变化规律,分析了运动速度和温度对块材内部最大温升的影响规律。研究结果表明,对于任何一种应用,降低块材的温度,都能起到抑制悬浮力衰减和减小温升的作用。此外,研究中还发现,悬浮体的阻浮比很小,这对高温超导磁悬浮技术应用于速度较高的领域是非常有利的。
Theoretical studies on high temperature superconducting (HTS) magnetic levitation (MagLev) are no longer limited to two-dimensional, axisymmetic, or three-dimensional (3D) cases, for which the latter one yields results that, are closer towards practical applications. The present 3D model neglects the electromagnetic (EM) anisotropy phenomena found present in high temperature superconductors (HTSC) and involves too many simplifications when taking this phenomena into account thereby lacking in the total understanding of the EM properties in HTSCs. Therefore, more effort should be done to further improve the theoretical studies of HTS MagLev.
In this thesis, a current vector potential was introduced to establish the 3D EM governing equations of the HTSC on the basis of Maxwell's equations and the anisotropy of the resistivity in the HTSC combined with the EM constitutive relations of the HTSC. In order to take the thermal-magnetic coupling problem into account, a thermal governing equation was also presented. To numerically solve the governing equations, finite element method via Galerkin's method and finite-difference method via Crank-Nicolson-θmethod were employed, respectively, to implement the study of space discretization and time discretization. Moreover, to simulate the aperture between adjacent permanent magnets composing the Permanent Magnet Guidway (PMG), a 3D analytical model of the PMG was also performed based on the surface current model.
To confirm the validity of the above-mentioned theoretical model, the numerical and experimental results under different movement types were discussed and compared in detail such as:Zero Field-Cooling (ZFC), Field-Cooling (FC) with levitation and suspension in translational symmetry and ZFC in axisymmetric applied fields under vertical movement; ZFC, identical Field-Cooling Height (FCH) and Levitation Height (LH) and suspension under transverse movement; and the relationship between levitation force (LF) and running time under longtitudinal movement, and the results indicated that the proposed 3D theorectical model is valid to describe the EM interaction between HTSC and applied field. Based on the above-mentioned analysis, the levitation performance of the HTS MagLev under 3D movement was theoretically investigated.
For movement along the vertical direction, the performance of LF under different operating conditions, applied field structures, material properties and geometries were firstly analyzed, and then the relaxation characterstic of LF and associated rules of the various influencing factors were discussed, and the conclusion that, LF can be improved and the force decay can be suppressed by enhancing the material property or lowering the operating temperature of the HTSC, were derived. In the end, it is theoretically proved that pre-loading is an effective approach to reduce the force decay during relaxation, and then the stability of the levitation system can be improved by this approach.
For movement along the transverse direction, the performance of the magnetic force under differenet operating conditions, maximum lateral diaplacements, material properties and geometries were firstly analyzed, and then the critical FCH problem of the HTSC was discussed, and we found that the critical FCH decreases with the increase of the LH, improvement of the material property as well as decrement of the the operating temperature. Subsequently, a minimum energy method to evaluate the restorable characteristics of a levitated body during transverse movement was proposed. Lastly, the changing trendency of the LF and guidance force under different operating conditions during continuous transverse movement was thoroughly studied. Furthermore, theoretical verification of pre-loading which is considered to be effective to reduce LF decay due to transverse movement was achieved.
For movement along the longitudinal direction, two different appliacable fields were considered, MagLev launch and MagLev rail transit. For the MagLev launch application, the main aspects studied included the influence of the aperture of the PMG, exit velocities and operating temperatures on the LF and the changing rule of Maximum Temperature Raise (MTR) under different exit velocities and operating temperatures. For the MagLev rail transit application, the changing tendency of the LF under different FCHs, LHs, velocities and operating temperatures was calculated, and the velocity and operating temperature dependence of the MTR in the HTSC were also monitored. The results showed that, for any application, lowering the operating temperature of the HTSC can suppress not only the LF decay but also the temperature raise during the longitudinal movement. In addition, we also found that, the drag-to-lift ratio of levitated body is small, and this is beneficial for the application the HTS MagLev in the high-speed field.
引文
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