Plasma Chemistry and Plasma Processing

, Volume 26, Issue 6, pp 557–575 | Cite as

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

  • Juan Pablo TrellesEmail author
  • Emil Pfender
  • Joachim Heberlein
Original Article


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.


Thermal plasma Torch Modeling Arc dynamics Finite elements Multiscale 



magnetic vector potential (T-m)

\({\boldsymbol A}\)

advective Jacobian


transformation Jacobian from conservative to primitive variables


magnetic field (T)


specific heat at constant pressure (J/kg-K)


elementary charge (C)


electric field (V/m)


enthalpy (J/kg) and convective heat transfer coefficient (W/m2-K)


total current (A)


current density (A/m2)


Boltzmann constant (J/K)

\({\boldsymbol K}\)

diffusivity matrix

\({\boldsymbol K}_{\rm DCO}\)

discontinuity-capturing-operator diffusivity matrix


normal to the boundary


basis or interpolation function


pressure (Pa)

\({{\boldsymbol q}}_{{\boldsymbol 0}}, {{\boldsymbol q}}_{{\boldsymbol 1}}\)

linearizations of specified diffusive fluxes


volumetric flow rate (lpm)


radial coordinate (m)


total residual of the conservation equations


radius (m)


boundary of the computational domain

\({{\boldsymbol S}}_{{\boldsymbol 0}}\), \({\boldsymbol S}_{{\boldsymbol 1}}\)

reactive terms (i.e., linearizations of a general source term S)


time (s)


temperature (K)


velocity (m/s)


average velocity (m/s)


computational domain


vector of spatial coordinates


vector of unknowns

x, y, z

main coordinate axes (m)

\(\hat{x},\ \hat {y},\ \hat {z}\)

unit vectors of the main axes

Greek symbols



Polar coordinated angle (rad)

\(\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\leftrightarrow$}}\over {\delta}}\)

identity tensor


net emission coefficient (W/m3-sr)


electric potential (V)


thermal conductivity (W/m-K)


dynamic viscosity (kg/m-s)


permeability of free space (Wb/A-m)


density (kg/m3)


electrical conductivity (1/Ω-m)

\(\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\leftrightarrow$}}\over {\tau}}\)

stress tensor (Pa)

\(\varvec{\tau}_{\rm SGS}\)

matrix of time scales


average inclination angle of the inlet flow with respect to the torch axis (rad)

Subscripts, superscripts


a, c

anode, cathode


inlet conditions


cooling water


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Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • Juan Pablo Trelles
    • 1
    Email author
  • Emil Pfender
    • 1
  • Joachim Heberlein
    • 1
  1. 1.Department of Mechanical EngineeringUniversity of MinnesotaMinneapolisUSA

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