Modeling and simulation of anode melting pool flow under the action of high-current vacuum arc

In this paper, a transient magnetohydrodynamic (MHD) model of an anode melting pool (AMP) flow (AMPF) is established. Mass equation, momentum equations along axial, radial and azimuthal directions, energy equation, and current continuity equations are considered in the model. In the momentum equations, the influence of electromagnetic force, viscosity force and Marangoni force (anode surface shear stress) are included. Joule heating is also included in the energy equations. According to the MHD model of AMPF, the influence of different heat flux densities to melting pool flow velocities (including azimuthal, radial, and axial velocity), anode temperature, fraction of liquid, melting depth, melting radius, and anode vapor flux will be analyzed. In the AMP, the azimuthal velocity is dominant, whose value approximately approaches velocity magnitude, the radial velocity is much smaller than azimuthal velocity, and the axial velocity is the smallest one compared with radial and azimuthal velocity. According to simulation results, anode surface temperature, melting width, melting depth, and anode vapor flux are increased with the increase in heat flux densities, but the increase in azimuthal velocity is not significant. Simulation results also show that the maximum anode temperature appears near 6.5–7 ms (50 Hz), but the maximum velocity of AMPF appears near 8–10 ms, which is in agreement with the experimental observation. Simulation result of AMPF swirl velocity (about 0.4 m/s) is approximately close to experimental result (about 0.6 m/s) based on high-speed camera data. Simulation results also show that the influence of joule heating and radiation on anode temperature can be neglected. The influence of Marangoni force on AMPF is significant.