Interactions between an arc and external fields are crucially important for the design and the optimization of modern plasma torches. Multiple studies have been conducted to help better understand the behavior of DC and AC current arcs exposed to external and ‘self-induced’ magnetic fields, but the theoretical foundations remain very poorly explored. An analytical investigation has therefore been carried out in order to study the general behavior of DC and AC arcs under the effect of random cross-fields.
A simple differential equation describing the general behavior of a planar DC or AC arc has been obtained. Several dimensionless numbers that depend primarily on arc and field parameters and the main arc characteristics (temperature, electric field strength) have also been determined. Their magnitude indicates the general tendency pattern of the arc evolution. The analytical results for many case studies have been validated using an MHD numerical model.
The main purpose of this investigation was deriving a practical analytical model for the electric arc, rendering possible its stabilization and control, and the enhancement of the plasma torch power.
Large-scale industrial plasma torches and processes use primarily high-current electric arcs. Therefore, their basic design must inevitably account for radiative transfer which becomes the prevailing heat loss mechanism at high currents. This heavily increases the complexity of the governing equations. Many approximate approaches have been proposed. The present work relies on the method of approximate average net emission coefficient (NEC) using the isothermal sphere approximation with a radius Rs to solve semi-analytically the Ellenbaas–Heller equation and compares it with exact calculations obtained using an iterative method. To our knowledge no study has provided yet a method to determine the most accurate value of Rs. In this paper, we present an optimal method for determining the best value of Rs that leads to the best agreement between the approximate and the exact methods. As a result, the complete electric characteristic has been obtained for hydrogen at 1 bar in a detailed case study.
The motion of the gliding DC electric arc under the effect of magnetic field is investigated. The temperature distribution in the inside and the outside of the moving arc is computed. The temperature distribution for the fixed-spot arc is also obtained. It appears that the gas relative velocity inside the arc gives rise to heat convection, which has an impact on the arc motion. A practical analytical solution is derived using magneto gas dynamic equations in order to investigate the heat transfer occurring in the arc and its vicinity, to determine its characteristics, and to estimate its velocity when it is exposed to external and electrode-induced magnetic fields. Two methods are suggested: one for the free-burning arc and the other for arc burning between close surrounding walls.
In this paper, we propose a simple and practical method for the modeling of the local and total magnetic force generated at the cathode. We prove that, if the current density profile obeys the same distribution along the axial-direction, the axial force depends only on the total current and the ratio of the arc spot radius to the radius of the arc column. We also provide an estimate for that the radial force. The power generated by Joules heating is also inserted as a term source in the energy balance equation. The use of source terms is very attractive for large scale industrial applications as it prevents from solving Maxwell’s equations that require fine meshing in the arc region and imprecise boundary conditions. It also helps to circumvent the extra complications in computation that are related to the cathode and anode falls. In the case of a mono-phase or 3-phase arc, if steady-state simulations are desired, a time-average is calculated.
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