No abstract

A mathematical model describing heat and fluid flow in an electric arc has been developed and used to predict heat transfer from the arc to the steel bath in a DC Electric Arc Furnace. The arc model takes the separate contributions to the heat transfer from each involved mechanism into account, i.e. radiation, convection, condensation and energy transported by electrons. The model predicts heat transfer for different currents and arc lengths. Model predictions show that arc efficiency is higher for lower power input. The model also predicts shear stresses and current density distribution at the steel surface. This information can be used as boundary condition input to simulate the effect of heating with electrodes in a DC EAF on the heat and fluid flow in the steel bath.KEY WORDS: modeling; arc; heat transfer.model. More specifically these authors used three different methods to determine the Lorentz forces responsible for the fluid flow. These methods are i) The Laplace equation for electric potential ii) the magnetic diffusion equation, and iii) the complete magnetic transport equation. The first two methods, however, do not include the induced electric field term, vϫB, in the solution. Assuming that the magnetic Reynolds number is much less than unity, these methods give a good approximation of the Lorentz forces. However, this is not always the case for high-current arcs, as in the case of EAFs. The third method does include this term, but a disadvantage with this method is that the system of equations becomes more difficult to solve. In the present work, the Poisson equation for electric potential is used to overcome these problems since the induced electric field is included and the current in the system can be correctly described. Mathematical Model of a DC Electric ArcIn the model presented in this report the arc is treated as a fluid [1][2][3][4][5][6][7][8][9][10][11][12] with temperature-dependent thermodynamic properties. 15,16) The coupled conservation equations of energy, mass and momentum, which define plasma temperature, pressure and velocity, are solved together with Maxwell's equations. First the problem is stated and a description of the fluid-flow model is provided. Then source terms, boundary conditions and heat transfer mechanisms are discussed. Statement of the ProblemIn Fig. 1 a schematic representation of the region of integration of the DC arc model is given. The system consists of the cathode (graphite electrode), the arc column, and the anode (steel bath). The calculation domain is defined so as to allow for entrainment and general interaction with the surrounding gases. Mathematical Formulation of the FlowThe following assumptions are made in the statement of the mathematical model of a DC arc:• The arc is axis symmetric.• The operation of the arc is independent of time, i.e. steady state.• The arc is in local thermal equilibrium (LTE), 17) i.e. the electron and heavy-particle temperatures are very similar. This assumption has been shown to be valid throughout most of a gas tungsten ...

No abstract

During experiments on the MSL-1 (first microgravity science laboratory) mission of the space shuttle (STS-83 and STS-94, April and July 1997), a droplet of palladium-silicon alloy was electromagnetically levitated for viscosity measurements. For the nondeforming droplet, the resultant magnetohydrodynamic (MHD) flow inside the drop can be inferred from motion of impurity particulates on the surface. In the experiments, subsequent to melting, Joule heating produces a continuous reduction of viscosity of the fluid resulting in an acceleration of the flow with time. These observations indicate formation of a pair of co-rotating toroidal flow structures inside the spheroidal drop that undergo flow instabilities. As the fluid temperature rises, the amplitude of the secondary flow increases, and beyond a point, the tracers exhibit noncoherent chaotic motion signifying emergence of turbulence inside the drop. Assuming that the observed laminar-turbulent transition is shear-layer type, the internal structure of the toroidal loops is used to develop a semiempirical correlation for the onset of turbulence. Our calculations indicate that the suggested correlation is in modest agreement with the experimental data, with the transition occurring at a Reynolds number of 600.

No abstract