Multiscale Finite Element Modeling of Arc Dynamics in a DC Plasma Torch

Abstract

The dynamics of the electric arc inside a direct current non-transferred arc plasma torch are simulated using a three-dimensional, transient, equilibrium model. The fluid and electromagnetic equations are solved numerically in a fully coupled approach by a multiscale finite element method. Simulations of a torch operating with argon and argon-hydrogen under different operating conditions are presented. The model is able to predict the operation of the torch in steady and takeover modes without any further assumption on the reattachment process except for the use of an artificially high electrical conductivity near the electrodes, needed because of the equilibrium assumption. The results obtained indicate that the reattachment process in these operating modes may be driven by the movement of the arc rather than by a breakdown-like process. It is also found that, for a torch operating in these modes and using straight gas injection, the arc will tend to re-attach to the opposite side of its original attachment. This phenomenon seems to be produced by a net angular momentum on the arc due to the imbalance between magnetic and fluid drag forces.Keywords Thermal plasma · Torch · Modeling · Arc dynamics · Finite elements · Multiscale Notation A magnetic vector potential (T-m) A advective Jacobian A 0 transformation Jacobian from conservative to primitive variables B magnetic field (T) C p specific heat at constant pressure (J/kg-K) e elementary charge (C) E electric field (V/m) h enthalpy (J/kg) and convective heat transfer coefficient (W/m 2 -K) 558 Plasma Chem Plasma Process (2006) 26:557-575 I total current (A) j current density (A/m 2 ) k B Boltzmann constant (J/K) K diffusivity matrix K DCO discontinuity-capturing-operator diffusivity matrix n normal to the boundary N basis or interpolation function p pressure (Pa) q 0 , q 1 linearizations of specified diffusive fluxes Q volumetric flow rate (lpm) r radial coordinate (m) R total residual of the conservation equations R radius (m) S boundary of the computational domain S 0 , S 1 reactive terms (i.e., linearizations of a general source term S) t time (s) T temperature (K) u velocity (m/s) U average velocity (m/s) V computational domain X vector of spatial coordinates Y vector of unknowns x, y, z main coordinate axes (m) x,ŷ,ẑ unit vectors of the main axes Greek symbols α Polar coordinated angle (rad) ↔ δ identity tensor ε r net emission coefficient (W/m 3 -sr) φ electric potential (V) κ thermal conductivity (W/m-K) μ dynamic viscosity (kg/m-s) μ 0 permeability of free space (Wb/A-m) ρ density (kg/m 3 ) σ electrical conductivity (1/ -m) ↔ τ stress tensor (Pa) τ SGS matrix of time scales θ average inclination angle of the inlet flow with respect to the torch axis (rad)

Formation of self-organized anode patterns in arc discharge simulations

“…23 using the Variational Multiscale (VMS) FEM [44], which has been proven very successful in the solution of diverse transport problems, such as incompressible, compressible, reactive, laminar and turbulent flows [44][45][46], electron -hole transport in semiconductors [48], magnetohydrodynamics [47], and fully ionized plasmas [49,50]. Initial work in the application of VMS methods for LTE and NLTE thermal plasma flows is reported in [31,[51][52][53]. The VMS framework is also ideally suited for the modeling of turbulent flows with the same rationality of Large Eddy Simulation (LES) techniques (i.e., solution of the large-and modeling of the small-scales), but with the added advantages of a consistent and complete coarse-grained description of the flow, which is not the case for most traditional LES techniques [46].…”

“…This boundary condition is different from that used in [29], but is often adopted in arc plasma flow simulations, e.g., [31,21,72].…”

“…Section 3 describes the numerical method used based on the Variational Multiscale Finite Element Method [30,31], and implemented in a time-implicit second-order-accurate in time and space discretization approach. Section 4 describes the free-burning arc problem: the geometry of the spatial domain, the computational discretization, and the boundary conditions used.…”

Modelling of the in-flight synthesis of TaC nanoparticles from liquid precursor in thermal plasma jet

“…Similar distribution is assumed by Trelles et al (2006) for the density of current near the cathode's tip. The outcome of the computations is a set of ensembleaveraged (mean) steady-state fields of temperature, velocity, concentrations of argon and air, pressure and density.…”

“…The main difficulty was to find a correct description of the plasma torch structure and behaviour. Three different operation modes of the torch are usually distinguished (see Trelles et al 2006): steady mode, takeover mode and restrike mode, each corresponding to a particular pattern of arc movement. The numerical models found in the literature can relatively accurately predict the structure of the torch and the flow generated for the steady mode only.…”