液氮中耦合复杂气泡动力学特性的三维瞬态电场数值计算方法研究

When the quench fault occurs in superconducting equipment, the nitrogen bubbles will be generated by heating the liquid nitrogen. For the special features of the nitrogen bubbles, such as large amount, multi-spatial-scale, movable, mutable and easy to coalesce, the insulation performance of the high-voltage superconducting equipment will be degraded. However, the 3D transient electric field distribution characteristics in liquid nitrogen, which contains a large sum of suspended nitrogen bubbles, are difficult to be calculated quickly and precisely. Therefore, by taking into account the dynamics characteristics of bubbles, the three-dimensional transient flow field-electric field coupling extended finite element method, which suitable for the complex mobile material interface conditions, is proposed in this project. In this method, the four-dimensional level set function will be adopted to describe the interface between bubble and liquid nitrogen. Meanwhile, by introducing the three-dimensional enrichment function which satisfies the interface conditions into the interpolation function, the discrete meshes would not be restricted by the material interface. By combining the dynamics characteristics of bubbles, the method for describing the distortion and movement of spatial material interface and the dynamic level set function can be established. With the help of this method, there is no need to refine the mesh for the tiny bubble, or re-mesh for the moving bubble. Besides, the amount of computation will be reduced. Hence, the three-dimensional transient flow field-electric field of liquid nitrogen which contains large amount, multi-scale, deformable nitrogen bubbles can be accurately calculated. Finally, the accuracy of the proposed method will be validated experimentally. Therefore, the results of the research will contribute to the development of the numerical analysis method, and have important theoretical significance and application value.

超导体失超发热产生的氮气泡具有数量多、空间尺度变化大、易移动、易形变和易融合等特点，降低了高压超导电力设备的绝缘性能，而传统的数值方法难以快速、精确地计算含大量悬移气泡时液氮的三维瞬态电场分布特性。据此，本项目耦合气泡动力学特性，提出适合复杂移动形变媒质分界面的三维瞬态流场-电场耦合扩展有限元法。该方法采用四维水平集函数描述气泡-液氮媒质分界面，通过在有限单元插值函数中引入满足媒质分界面条件的三维富集函数，使离散网格不再受限于媒质分界面；结合气泡动力学特性，建立空间媒质分界面形变和运动的动态水平集函数描述方法，微小尺寸气泡无需加密剖分，气泡移动形变不必多次剖分，计算量减少，从而实现了含大量、多尺度、悬移气泡的液氮内三维瞬态流场-电场的快速准确计算。最后通过实验验证仿真方法的准确性。本项目的研究成果将丰富数值分析的手段，具有重要的理论意义和应用价值。

超导体失超发热产生的氮气泡具有数量多、空间尺度变化大、易移动、易形变和易融合等特点，降低了高压超导电力设备的绝缘性能，而传统的数值方法难以快速、精确地计算含大量悬移气泡时液氮的三维瞬态电场分布特性。.据此，本项目耦合气泡动力学特性，提出适合复杂移动形变媒质分界面的三维瞬态流场-电场耦合扩展有限元法。该方法采用四维水平集函数描述气泡-液氮媒质分界面，通过在有限单元插值函数中引入满足媒质分界面条件的三维富集函数，使离散网格不再受限于媒质分界面；结合气泡动力学特性，建立空间媒质分界面形变和运动的动态水平集函数描述方法，微小尺寸气泡无需加密剖分，气泡移动形变不必多次剖分，计算量减少，从而实现了含大量、多尺度、悬移气泡的液氮内三维瞬态流场-电场的快速准确计算。最后搭建了用于测量含有气泡的液氮中电位的实验平台。.经过研究，发现气泡会导致液氮环境的电场产生畸变，气泡边界的电场畸变最为明显。将扩展有限元的电位计算结果与传统有限元进行比较，单个悬浮气泡的平均相对误差为0.57%，多气泡的平均相对误差0.94%，运动气泡所有时间点的平均相对误差为0.958%，所有情况的误差都较小。使用扩展有限元进行计算，大大减少了计算时间和节点单元个数，提高了计算效率。.本项目的研究成果丰富了数值分析的手段，具有重要的理论意义和应用价值。