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Modeling of RF plasma torch with a metallic tube inserted for reactant injection

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Abstract

Flow, temperature, and electromagnetic (EM) fields in a radio-frequency thermal plasma torch designed for the preparation of superconducting powders or films have been analysed by using a new two-dimensional modeling approach with the electric field intensity as the fundamental EM field variable. The insertion of a stainless steel injection tube into the torch leads to large induction currents in this tube. Although such large induction currents cause pronounced changes of the EM fields near the injection tube, flow and temperature fields are little affected. There exists only one large toroidal vortex in the upper part of the present torch, while the maximum temperature appears at an off-axis location within the coil region.

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Abbreviations

A,A 0 :

magnetic vector potential and its azimuthal component

B, Bx B r :

magnetic induction flux vector and its axial and radial component

C p :

specific heat at constant pressure

E(k I ):

elliptic integral of the second kind

E,E 0 :

electric field intensity vector and its azimuthal component

E 1,E 2 :

amplitudes of the in-phase and out-of-phase components of Eθ with respect to the excitation current

F L ,F Lr ,F Lx :

Lorentz force vector and its radial and axial components

g :

acceleration due to gravity

h :

specific enthalpy

H(k 1 ):

elliptic integral in Eq. (29)

I,I 0 :

excitation current in the coil and its amplitude

j,j θ :

current density and its azimuthal component

k :

thermal conductivity of the plasma

k :

argument of the elliptic integrals

k ij ,k n :

k 1 for induction current at position (i,j) and for excitation current at the nth turn

K(k 1 ):

elliptic integral of the first kind

L tube :

length of injection tube

Q 1,Q 2 :

How rates of the carrier gas and plasma/sheath gas radial coordinate

r :

radial accordance

r 2,r 3 :

radii shown in Fig. 2

R c :

radius of excitation coil; characteristic length

r tube :

radius of the current-carrying loop with currentI

R 0 :

radius of the inner surface of the quartz tube

t :

time

V,V c :

velocity vector and characteristic velocity

u,v,w :

axial, radial, and azimuthal components of the velocity

ø :

electrostatic potential

κ :

thermal conductivity of quartz tube

μ :

viscosity

ϱ :

density

σ :

electric conductivity

ω :

circular frequency

ω :

magnetic permeability

Overbar (−):

time-averaged value; effective value

1:

in-phase amplitude

2:

out-of-phase amplitude

B :

boundary

i,j :

ith inx-direction andjth inr-direction (control volume)

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Author notes

  1. Xi Chen

    Present address: Department of Engineering Mechanics, Tsinghua University, 100084, Beijing, China

Authors and Affiliations

  1. Department of Mechanical Engineering, University of Minnesota, 55455, Minneapolis, Minnesota

    Xi Chen & E. Pfender

Authors
  1. Xi Chen
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  2. E. Pfender
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Chen, X., Pfender, E. Modeling of RF plasma torch with a metallic tube inserted for reactant injection. Plasma Chem Plasma Process 11, 103–128 (1991). https://doi.org/10.1007/BF01447036

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  • DOI: https://doi.org/10.1007/BF01447036

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