Numerical Modeling and Simulation of Electric Arcs

Abstract

This thesis is concerned with three aspects of numerical simulations of electric arcs: Part 1 extends a previous numerical scheme in 1D to 3D and non-constant timestepping for a plasma defined in an Euler-Maxwell framework. The main feature of the scheme is that it allows for the scaled Debye length as a modeling parameter to continuously blend between the full Maxwell system and the eddy current model; this feature is known as asymptotic preserving. The generalization to higher dimensions is involved because it requires a dual mesh strategy and interpolation of the electromagnetic field. The submodels of the newly designed scheme are validated with testcases; however, setting the scaled Debye length to zero unveiled that assuming a linear relation in Ohm's law prevents the new 3D scheme from being asymptotic preserving. Part 2 focuses on radiation modeling. It reviews the relevant modeling assumptions that reduce the radiative transfer equation to a computationally tractable model as it is found in applied numerical simulations. However, the main issue lies in the complex structure of the absorption coefficient. We consider the Elenbaas-Heller equation as the simplest model for a wall-stabilized arc and derive the linearized equation. A sensitivity analysis permits to analyze effects of uncertainties in the spectral absorption coefficient on the arc voltage and temperature profile. We also consider the line limited Planck mean and show that an appropriately chosen renormalization length permits to retrieve the correct temperature profile at minimal computational costs. Part 3 presents applied numerical simulations of electric arcs in circuit breakers. It is hard to find simulation suites that permit for a robust coupling of the numerous modeling aspects as required for applied thermal plasma simulations, which encompass gas dynamics, electromagnetism, and radiative heat transfer, rigid body motion, mesh morphing, and other modeling aspects. Our software choice enabled us to consider a low voltage circuit breaker and evaluate the contact arm motion with respect to mechanics, plasma pressure, and electromagnetic force. A second case analyzes a recent design of a high voltage direct current circuit breaker and shows results of the electric field and gas flow field complementing previous measurement. Combining a caloric estimate with the simulation results of radiative heat flux to the nozzle wall, we provide an argument for the experimental observation that wall ablation is measured only for sufficiently large currents.