Modelling and diagnostics of multiple cathodes plasma torch system for plasma spraying

Abstract

Usage of a multiple-arcs system has significantly improved process stability and coating properties in air plasma spraying. However, there are still demands on understanding and controlling the physical process to determine process conditions for reproducible coating quality and homogeneity of coating microstructure. The main goal of this work is the application of numerical simulation for the prediction of the temperature profiles at the torch outlet for real process conditions. Behaviour of the gas flow and electric arcs were described in a three-dimensional numerical model. The calculated results showed the characteristic triangular temperature distribution at the torch nozzle outlet caused by three electric arcs. These results were compared with experimentally determined temperature distributions, which were obtained with specially developed computed tomography equipment for reconstructing the emissivity and temperature distribution of the plasma jet close to the torch exit. The calculated results related to temperature values and contours were verified for the most process parameters with experimental ones.

Key words： plasma spraying; electric arc; three-cathode plasma torch; numerical simulation; computed tomography

Acknowledgements

The authors gratefully acknowledge the financial support of the German Research Foundation (DFG) within the project “Homogenization of Coating Properties in Atmospheric Plasma Spraying” (Bo 1979/7-1 and Sche 428/6-1).

Notations
\overrightarrow{B}	magnetic flux density
cp	specific heat capacity by constant pressure
\overrightarrow{D}	electric displacement field
\overrightarrow{E}	electric field
{\overrightarrow{f}}_{\mathrm{L}}	Lorentz force density
f_{\mathrm{T}}	temperature distribution
f_{\mathrm{v}}	velocity distribution
\overrightarrow{g}	gravitation acceleration
\dot{m}	mass flow
\overrightarrow{H}	magnetic field
h	enthalpy density
\overrightarrow{j}	current density
p	pressure
r	radial coordinate
SJoule	joule heating rate density
SRad	radiation rate density
S_{\mathrm{N}\mathrm{e}\mathrm{t}}	net emission rate density
S_{\mathrm{A}\mathrm{b}\mathrm{s}}	reabsorbed radiation rate density
T	temperature
t	time
v	plasma velocity
{\dot{W}}_{\mathrm{e}\mathrm{f}\mathrm{f}}	effective power
\overrightarrow{u}	gas velocity
Greek letters
\lambda	thermal conductivity
\rho	gas density
\mathrm{\Theta }	angular coordinate
{\rho }_{\mathrm{f}}	charge density
\sigma	electric permeability
\overrightarrow{\tau }	stress tensor
{\mu }_{\mathrm{f}}	magnetic permeability

References

1 Pfender E. Thermal plasma technology: Where do we stand and where do we go. Plasma Chemistry and Plasma Processing, 1999, 19(1): 1–31

2 Fauchais P. Understanding plasma spraying. Journal of Physics. D, Applied Physics, 2004, 37(9): 86–108

3 Fauchais P, Fukumoto M, Vardelle A, Vardelle M. Knowledge concerning splat formation: An invited review. J Thermal Spray Technol, 2004, 13(3): 337–360

4 Dorier J L, Gindrat M, Hollenstein C, Salito A, Loch M, Barbezat G. Time-resolved imaging of anodic arc root behavior during fluctuations of a DC plasma spraying torch. IEEE Transactions on Plasma Science, 2001, 29(3): 494–501

5 Dzulko M, Forster G, Landes K D, Zierhut J, Nassenstein K. Plasma torch developments. In: Proc of the International Thermal Spray Conference, Basel, Switzerland, DVS Deutscher Verband für Schweißen, 2005

6 Fauchais P, Montavon P, Vardelle M, Cedelle J. Developments in direct current plasma spraying. Surface and Coatings Technology, 2006, 201(5): 1908–1921

7 Bobzin K, Ernst F, Richardt K, Sporer D, Fiala P. Tailor-made coatings for turbine applications using the triplex pro 200. In: Proc International Thermal Spray Conference, Maastricht, Netherlands, DVS Deutscher Verband für Schweißen, 2008

8 Schein J, Richter M, Landes K D, Forster G, Zierhut J, Dzulko M. Tomographic investigation of plasma jets produced by multielectrode plasma torches. J Thermal Spray Technol, 2008, 17(3): 338–343

9 Baudry C, Vardelle A, Mariaux G. Numerical modeling of a DC non-transferred plasma torch: Movement of the arc anode attachment and resulting anode erosion. High Tech Plasma Proc, 2005, 9(1): 1–15

10 Trelles J P, Chazelas C, Vardelle A, Heberlein J V R. Arc Plasma Torch Modeling. J Thermal Spray Technol, 2009, 18(5-6): 728–752

11 Felix A, Muggli F, Molz R J, McCullough R, Hawley D.Improvement of plasma gun performance using comprehensive fluid element modelling: Part I. J Thermal Spray Technol, 2007, 16(5-6): 677–683

12 Molz R, McCullough R, Hawley D, Muggli F. Improvement of plasma gun performance using comprehensive fluid element modelling: Part II. J Thermal Spray Technol, 2007, 16(5-6): 684–689

13 Speckhofer G. Der magnetisch ausgelenkte Argonhochdruck-lichtbogen: Experimentelle untersuchungen and 3D-Modellierung. Dissertation for the Doctoral Degree, TU München, 1995: 27–29 (in German)

14 Murphy A B, Arundelli C J. Transport coefficients of argon, nitrogen, oxygen, argon-nitrogen, and argon-oxygen plasmas. Plasma Chemistry and Plasma Processing, 1994, 14(4): 451–490

15 Marqués J L, Forster G, Schein J. Multi-electrode plasma torches: Motivation for development and current state-of-the-art. Open Plasma Phys J, 2009, 2(2): 89–98

16 Boulos M, Fauchais P, Pfender E. Thermal Plasmas. New York: Plenum Press, 1994