Calculating the Arc Characteristics in Plasma Arc Furnaces Based on the Modified Mecker Arc Model

Abstract

The article presents a method for calculating the characteristics of heat transfer between the electric arc and gas jet in the plasma arc furnace melting space in the course of melting on the basis of modified G. Mecker’s arc column model. No engineering methods for modeling and calculating the electric and thermal characteristics of the melting plasma generator arc as a source of heating and nonlinear electric load that would be suitable for design purposes have so far been available. The concepts of the modern electric arc heating theory open the possibility to suggest — based on well-known G. Mecker’s electric arc convective model, and with attraction of the arc heat transfer model methods and the mathematical method of arc universal characteristics — a methodology for calculating the heat transfer characteristics and the related external electric and thermal characteristics of the arc produced by a plasma arc furnace melting plasma generator that is convenient for being used in design practice. The universal arc characteristics method developed for calculating the electric and thermal characteristics of Mecker’s arc column model cylindrical part enables the user to calculate the arc column characteristics at a distance away from the cathode by means of simple algebraic methods, thereby making Mecker’s mathematical model more specific. The arc model conservatism has been proven proceeding from the spatial layer with an increased volume viscosity that appears on the column surface. As a result, a boundary condition of the third kind can be applied to the arc column cylindrical part surface according to the concepts of the boundary layer theory. By using the universal arc characteristics method it is also possible to correlate the heat flux linear density boundary value on the column cylindrical part surface with the column temperature profile and, thereby, link the dependence of the plasma column electric, geometrical and thermal characteristics on the arc heat transfer conditions in the electric arc heated working space of the installation. By applying the proposed method, it is possible to identify Mecker’s heat transfer model using only the arc external volt-ampere characteristics and to calculate, by means of a simple algebraic method, the structure and values of the heat fluxes produced by the arc in the course of heat transfer to the plasma generator gas jet in the plasma arc furnace melting space. Examples of arc characteristics during operation with different gases for different stages of melting, namely, at the beginning of melting and in melting the furnace charge are given.