Numerical simulation of a multicomponent non-transferred constricted direct current arc with a supersonic plasma jet

Maximizing dissociated species transport in plasma assisted chemical vapor deposition (CVD) is important in many low-pressure plasma jet processes. To maximize atomic hydrogen transport to a substrate in the deposition of high quality diamond, a two-dimensional computational model of a supersonic contoured direct current (dc) torch anode nozzle and its subsequent high speed jet are examined. A multicomponent chemically reacting Ar-H{dollar}sb2{dollar} plasma is modeled from the species generation in the high temperature arc through the species transport in the low-pressure chamber. The joule heating source term is implicitly coupled with the compressible-viscous fluid equations with a novel source term algorithm. The effect of the electrode sheath region is introduced in an atypical type of phenomenological boundary condition that allows the voltage to slip at the cathode and anode spots. To examine the anode attachment a forced or drift diffusion model and a corresponding implicit algorithm is introduced. Both diffusive fluxes, those due to ordinary mass and ambipolar diffusion, and those due to the electric field body forces are included. Unique implicit schemes are introduced to solve these diffusive fluxes. The computation of the source terms and the diffusive fluxes, are integrated into a modified flux-vector splitting finite volume formulation. It is shown that such high-speed gas flows are far from chemical equilibrium and it is necessary to include finite rate chemistry to get an accurate description of the species transport. Calculations confirm that high velocities and low pressures work favorably in the transport of precursor species. The diamond shock structure in the overexpanded jet converts kinetic energy to internal energy helping to further maintain the unstable transport. To predict an anode arc attachment, it is essential to resolve the drift diffusion to drive the charged particles through the strong axial bulk flow. Resultant fields bracketing the real three-dimensional phenomena inside the torch are calculated for the cases of an axisymmetric arc with and without a distinct anode attachment ring. The subsequent supersonic torch exit conditions are then used to predict the relevant contours in the overexpanded low-pressure jet.