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Three-Dimension and Transient D.C. Plasma Flow Modeling

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Abstract

The behavior of plasma flow, generated by a D.C. plasma spraying gun, is simulated in a time-dependent 3 D. design. The high-temperature and high-velocity plasma plume is generated by a simple model based on Joule effect. The criterion of validation is the thermal efficiency while the only adjustment parameter is the length of the plasma column inside the anode. The transient plasma flow issuing in air atmosphere is reproduced. The plasma behavior is quite similar to that observed by fast-image video. Moreover, the centerline plasma plume properties are in agreement with experiment measurements, especially close to the torch exit and downstream the laminar-to-turbulent transition.

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Abbreviations

S ef :

Thermal source by Joule effect (W)

Q conv :

Losses by convection (W)

\( \ifmmode\expandafter\vec\else\expandafter\vec\fi{u} \) :

Velocity vector (m/s)

E:

Global energy (W)

k:

Thermal conductivity (W/m K)

\( \ifmmode\expandafter\vec\else\expandafter\vec\fi{J}_{j} \) :

Diffusion flux of the j specie (kg/m2 s)

ε:

Turbulent dissipation rate (m2/s3)

u i :

Velocity component along direction i (m/s)

G k :

Turbulent kinetic energy production source term

Prt :

Turbulent PRANDTL number

C1ε :

Constant for k–ε model

σ k :

Turbulent PRANDTL number for k

Cμ :

Constant for k–ε model

μ:

Dynamic viscosity (kg/m s)

U:

Average arc voltage (V)

L m :

Average plasma column length (m)

V1 :

First heating zone volume (m3)

P1 :

Electrical power generated in V1 volume (W)

l1 :

Constant length of the heating zone V1 (m)

γ:

Rotating angle of the V2 area (degree)

f :

Frequency of the arc voltage fluctuation (hz)

lmin :

Shortest global heating zone length (m)

p :

Pressure (Pa)

Q rad :

Losses by radiation (W)

ρ:

Density (kg/m3)

T :

Temperature (K)

h j :

Specific enthalpy of the j specie (J/kg)

\( \overline{\overline \tau } _{{eff}} \cdot \ifmmode\expandafter\vec\else\expandafter\vec\fi{u} \) :

Viscous dissipation term (W/m2)

κ:

Turbulent kinetic energy (m2/s3)

g i :

Gravitation vector component along the i direction

G b :

Turbulence production rate due to natural convection

β :

Volume dilatation coefficient (1/K)

C 2ε :

Constant for k-ε model

σ ε :

PRANDTL turbulent number for ε

μt :

Turbulent viscosity (kg/m s)

Pm :

Average input power (W)

I:

Arc current intensity (A)

η :

Thermal efficiency rate (%)

V2 :

Second heating zone volume (m3)

P2 :

Electrical power generated in V2 volume (W)

l2(t):

Time-dependent length of the heating zone V2 (m)

V(t):

Time-dependent arc voltage (V)

α :

Constant angle of the truncated cornet of the V2 area (degree)

lmax :

Longest global heating zone length (m)

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  1. CEA Le Ripault, B.P. 16, 37260, Monts, France

    E. Meillot, D. Guenadou & C. Bourgeois

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  1. E. Meillot
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  2. D. Guenadou
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  3. C. Bourgeois
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Meillot, E., Guenadou, D. & Bourgeois, C. Three-Dimension and Transient D.C. Plasma Flow Modeling. Plasma Chem Plasma Process 28, 69–84 (2008). https://doi.org/10.1007/s11090-007-9108-9

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  • DOI: https://doi.org/10.1007/s11090-007-9108-9

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