A Lagrangian Approach to the Simulation of a Constricted Vacuum Arc in a Magnetic Field

The use of numerical simulations of vacuum arcs can be very useful in order to improve the performance of vacuum interrupters. Standard computational fluid dynamics methods based on the Eulerian approach have difficulties to deal with this kind of problem, so a new technique is proposed, based on a Lagrangian approach. In order to focus on the performance of the new approach and not on specific details of a full model, a simplified arc model is used to investigate the capabilities of a Lagrangian approach in the context of vacuum arc simulations. The focus of this initial study is on implementing the necessary ingredients, that is, the development of a compressible flow solver, the introduction of the relevant boundary conditions and the coupling with the current conservation equation for the electric current. In addition, the stability of such a numerical scheme is evaluated. Furthermore, comparisons with results obtained using commercial software are also provided to demonstrate the validity of the results obtained with the new methodology

Three‐dimensional immersed finite‐element method for anisotropic magnetostatic/electrostatic interface problems with nonhomogeneous flux jump

Anisotropic diffusion is important to many different types of common materials and media. Based on structured Cartesian meshes, we develop a three-dimensional (3D) nonhomogeneous immersed finite-element (IFE) method for the interface problem of anisotropic diffusion, which is characterized by an anisotropic elliptic equation with discontinuous tensor coefficient and nonhomogeneous flux jump. We first construct the 3D linear IFE space for the anisotropic nonhomogeneous jump conditions. Then we present the IFE Galerkin method for the anisotropic elliptic equation. Since this method can efficiently solve interface problems on structured Cartesian meshes, it provides a promising tool to solve the physical models with complex geometries of different materials, hence can serve as an efficient field solver in a simulation on Cartesian meshes for related problems, such as the particle-in-cell simulation. Numerical examples are provided to demonstrate the features of the proposed method

Anatomy of a laminar starting thermal plume at high Prandtl number

We present an experimental study of the dynamics of a plume generated from a small heat source in a high Prandtl number fluid with a strongly temperature-dependent viscosity. The velocity field was determined with particle image velocimetry, while the temperature field was measured using differential interferometry and thermochromic liquid crystals. The combination of these different techniques run simultaneously allows us to identify the different stages of plume development, and to compare the positions of key-features of the velocity field (centers of rotation, maximum vorticity locations, stagnation points) respective to the plume thermal anomaly, for Prandtl numbers greater than 103. We further show that the thermal structure of the plume stem is well predicted by the constant viscosity model of Batchelor (Q J R Met Soc 80: 339-358, 1954) for viscosity ratios up to 50. © 2010 Springer-Verlag