A simple model is reported for copper electrode erosion in electric arc heaters as a result of electrode surface fusion by the action of the arc spot. In the analysis we substitute the real arc spot by an intensive moving surface heat source. The time evolution and the distribution of the electrode surface temperature within the arc spot is studied in coordinates coupled with the moving heat source. The electrode erosion is attributed in the model to the unbalance between the heat supply and the heat removal due to the development of an arc spot fusion zone. An erosion effective enthalpy is applied in the analysis, including all physical processes for the material transformation from the solid state into the plasma state under the action of the intensive heat flux. Formulae were obtained that enable one to calculate the electrode erosion as a function of arc velocity, electrode temperature, current, near-electrode thermal volt-equivalent, current density and electrode material properties. We show briefly that the theory agrees reasonably well with experimental results. The present model enables us to reveal the relative significance of the different parameters in the erosion process and to predict the erosion behaviour in copper electrode electric arc heaters.

Two important copper electrode parameters, namely, the volt-equivalent of the arc spot heat flux and the arc spot effective current density have been measured experimentally in magnetically driven arcs in air. The measurements were performed for currents in the range 0.025 - 1 kA, magnetic field strengths 0.133 - 0.95 T and air pressures 1 - 40 atm. The volt-equivalent of the arc spot heat flux is proposed to account for the total heat flux entering the electrode surface through the arc spot. An unsteady thermal method was applied in the measurements. To obtain the effective current density, the thermophysical experiment was combined with the application of equations of the erosion model presented in a previous companion paper. We show that the volt-equivalent of the cathode arc spot heat flux increases with increasing magnetic field. The sum of the cathode and the anode voltage drops is shown to be approximately equal to the sum of the corresponding volt-equivalents of the arc spot heat fluxes. Good agreement with the measurements of other authors is obtained. In particular, the effective arc spot current density allows one to confirm the thermophysical model for the erosion of copper electrodes indirectly.

Experimental results are presented on copper-cathode erosion for magnetically driven arcs in air, for currents in the range 0.025 - 1 kA, magnetic induction values 0.03 - 0.24 T, arc velocities 19.3 - 344 m and electrode surface temperatures 300 - 1073 K. From experimental data we obtained the important characteristic parameters for the copper-cathode's erosion process; namely the effective enthalpy of electrode material ablation in the arc spot, , and the specific microerosion value, . The experiments demonstrated that, just like the near-cathode thermal volt equivalent U, the arc spot current density j is also a monotonic ascending function of the magnetic field strength. We have shown a good agreement between the theory and the experimental data for a wide range of arc-heater operating regimes. A mathematical analysis and diagrams are provided for predicting the best conditions for an arc heater to work with the minimum erosion level. The minimum erosion is shown to depend on the temperature attained by the electrode and on the degree of influence of the gas velocity on the electrode temperature. It is predicted that the erosion decreases with increasing arc velocity, then stabilizes at a given minimum level and then increases as one increases the value of the arc velocity.

A new, more precise and simple semi-empirical formula has been obtained for the prediction of the rotational velocity of magnetically driven arcs in air and nitrogen. The formula is based on the balance between the motive Lorentz force and the aerodynamic drag force and takes into account changes in the gas density value due to the arc rotation and the axial gas velocity. The formula enables the calculation of the arc velocity in electric arc heaters as a function of current, magnetic field, axial gas velocity and gas density. Experimental results are presented for arcs in air and nitrogen, for currents in the range 100-1760 A, magnetic induction values of 0.005-3.9 T and axial gas velocities of 0.2-33 m s-1. The formula can be useful for the study of cold electrode erosion and engineering calculations of electric arc heaters.

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