The Method of Majorant Functions for the Calculation of Arc Erosion

The mathematical model describing the dynamics of the arc erosion is presented. It is based on the axisymmetric Stefan problem for two zones, liquid metal pool under the arc spot, and the contact solid zone with boundary conditions on the interface of the phase transformation describing the contact melting. The arc heat flux entering the cathode is represented as the sum of components corresponding to cathode heating due to ion bombardment, radiation, the inverse electron emission and cathode cooling due to electron emission and evaporation. Similar conditions, corresponding to kinetic, potential and thermal components of the heat flux, are written for the anode. All parameters, such as the thermal and electric conductivities, thermal capacitance, density etc. are considered as functions of the temperature.The method of majorant functions is elaborated for the solution of this problem, and the algorithm of its numerical realization is described in details. This algorithm is based on the analytical expression for the contact temperature containing two components, corresponding to the heating due to the arc flux and due to Joule sources. It includes several consecutive iteration steps with successive calculation of overstated and understated values of the heat flux, isothermal surfaces and temperature and other parameters. The example of the numerical calculation is presented and compared with the experimental data.