Effect of Cathode-Plasma Coupling on Plasma Torch Operation Predicted by a 3D Two-Temperature Electric Arc Model

In a DC plasma spray torch, the plasma-forming gas is the most intensively heated and accelerated at the cathode arc attachment due to the very high electric current density at this location. A proper prediction of the cathode arc attachment is, therefore, essential for understanding the plasma jet formation and cathode operation. However, numerical studies of the cathode arc attachment mostly deal with transferred arcs or conventional plasma torches with tapered cathodes. In this study, a 3D time-dependent two-temperature model of electric arc combined with a cathode sheath model is applied to the commercial cascaded-anode plasma torch SinplexPro fitted with a wide single cathode. The model is used to investigate the effect of the cathode sheath model and bidirectional cathode-plasma coupling on the predicted cathode arc attachment and plasma flow. The model of the plasma-cathode interface takes into account the non-equilibrium space-charge sheath to establish the thermal and electric current balance at the interface. The radial profiles of cathode sheath parameters (voltage drop, electron temperature at the interface, Schottky reduction in the work function) were computed on the surface of the cathode tip and used at the cathode-plasma interface in the model of plasma torch operation. The latter is developed in the open-source CFD software Code_Saturne. It makes it possible to calculate the plasma flow fields inside and outside the plasma torch as well as the enthalpy and electromagnetic fields in the gas phase and electrodes. This study shows that the inclusion of the cathode sheath model in the two-temperature MHD model results in a higher constriction of the cathode arc attachment, more plausible cathode surface temperature distribution, more reliable prediction of the torch voltage and cooling loss, and more consistent thermal balance in the torch.