R.F. Induction Plasma Spraying

Abstract

Radio Frequency (r.f.) Induction plasma spraying, or as more commonly known as Vacuum Induction Plasma Spraying (VIPS), has attracted increasing attention over the past three decades. While it is not a technology that is posed to replace any of the other thermal spray processes, it is commercially used in niche applications such as to perform cladding in the fiber optics industry, or X-ray target manufacturing, where the high purity and density of the deposit obtained are of critical importance. VIPS is characterized by the electrodeless nature of the discharge, which allows for high purity and greater flexibility with regard to the chemistry of the plasma gas, and the ease of axial injection of the powder into the center of the plasma jet. In this context, one of the fastest growing applications of induction plasma spraying is in the area of powder treatment for powder densification, purification, and/or spheroidization. The r.f. induction plasma torch is first presented with the basic concepts, its design and resulting temperature, fluid flow, and concentration fields. Then the discharge and the plasma–particle interactions modeling are discussed and typical results presented. At last vacuum induction plasma spraying (VIPS) with the torch operating conditions, the reactive, the suspension, and the supersonic spraying are described.

Nomenclature

$\overrightarrow{A}$ :

Magnetic vector potential ( )

c :

Speed of light in space c = 299,792,458 (m/s)

c _p :

Specific heat (J/K kg)

$\overrightarrow{D}$ :

Electric displacement (C/m²)

D _j :

The mass diffusivity of species j in the mixture ( )

E :

Electric field (V/m

$\overrightarrow{E}$ :

Electric field vector (V/m)

f :

Oscillator frequency (Hz)

F _r :

Radial component of Lorentz force (N)

F _z :

Radial component of Lorentz force (N)

h :

Total enthalpy of mixture (J/kg)

h _j :

The specific enthalpy of species j (J/kg)

$\overrightarrow{H}$ :

Magnetic field vector (T)

j :

Current density (A/m²)

I _c :

Coil current (A)

I _im :

Applied coil current (A)

I _in :

Induced current in the coil due to plasma electromagnetic fields (A)

$\overrightarrow{J}$ :

Magnetic flux density vector (W/m²)

J _jr :

Diffusion flux of species j in radial direction ( )

J _jz :

Diffusion flux of species j in axial direction ( )

k :

Molecular thermal conductivity (W/m K)

k _e :

Effective thermal conductivity (W/m K)

k _t :

Turbulent thermal conductivity (W/m K)

L _c :

Coil length (m)

M _i :

Molecular weight of species i (kg/mole)

n _c :

Coil number of turns

p :

Pressure (Pa)

P :

Local energy generation through ohmic heating, P = σ|E|² (W/m³)

P _v :

Viscous power dissipation, ${P}_v=-\nabla \cdot \left(\overrightarrow{\tau}\cdot \overrightarrow{V}\right)$ (W/m³)

r _c :

Internal radius of the induction coil (m)

r _n :

Radius of equivalent cylindrical load of discharge (m)

r _o :

Internal radius of the plasma confining tube (m)

R :

Local volumetric radiation heat losses (W/m³)

R _j :

Local volumetric radiation heat losses of species j (W/m³)

u :

Axial velocity component (m/s)

v :

Radial velocity component (m/s)

w :

Tangential velocity component (m/s)

δ _t :

Thickness of skin depth (m)

ε :

Dielectric constant (permittivity) of materials ε = ε ₀ ε _r (Farad/m)

ε ₀ :

Dielectric constant of free space (ε ₀ = 8.854 × 10¹²) (Farad/m)

ε _r :

Relative dielectric constant.

φ :

Free charge density (C/m³)

Ω _D :

Diffusion collision integral ( )

η _c :

Energy coupling efficiency

κ:

Coupling parameter, $\upkappa =\sqrt{2}.{r}_{\mathrm{n}}/{\delta}_{\mathrm{t}}$

μ _o :

Magnetic permeability of the medium (Hy/m)

μ :

Magnetic permeability of materials $\mu ={\mu}_0{\mu}_{\mathrm{r}}$ ( H/m)

μ _o :

Magnetic permeability of vacuum μ ₀ = 4π × 10⁷ (H/m)

${\mu}_{\mathrm{r}}$ :

Relative magnetic permeability

μ :

Molecular viscosity (Pa s)

μ _e :

Effective viscosity (Pa s)

μ _t :

Turbulent viscosity (Pa s)

σ _o :

Electrical conductivity of equivalent load (mho/m) or A/(V m)

ρ :

Mass density (kg/m³)