# Simulation of arc root fluctuation in a DC non-transferred plasma torch with three dimensional modeling

R. Huang, H. Fukanum, SaiWama/J, Y. Uesugi and Y. Tanaka, Kanazawa/Japan

## Abstract

It has been well known that the coating quality of plasma spraying is strongly influenced by instability of jets in plasma spray due to the arc root fluctuation. A three dimensional (3D) unsteady modeling was employed in the research to analyze the arc root fluctuation in a DC non-transferred plasma torch. Numerical calculations on the distribution of gas temperature and velocity in plasma torch were carried out using argon as plasma gas. The electrical current density and potential were also discussed. The results indicate that the fluctuation of arc inside the plasma torch is mainly induced by the movement of the arc root on the anode surface. The arc root moves downstream with the flow of gas, and the arc will wraped caused by the electromagnetic force simultaneously. While the arc wraped closed enough to anode boundary, a new arc root is formed somewhere upstream of the original attachment. This article represents nature of fluctuation of arc root, also in this paper we will present that the voltage-drop calculated is larger than that measured experimentally based on the hypothesis of local thermodynamic equilibrium.

## 1 Introduction

The plasma spraying is the injection of metal or ceramic powder into hot gas plasma which melts and projects the molten droplets at high velocity onto a substrate to form coatings. Gases such as argon or hydrogen are passed through as electric arc inside a torch [1]. Plasma spraying, one of the most widely used in industrial fields based on thermal plasmas, is commonly employed to provide coatings for protection of materials against wear, erosion, corrosion, and thermal loads. Despite its versatility, the limited reproducibility of the processes is a major limitation for its wider application. A major factor for this limited reproducibility is the lack of understanding and control of the dynamic behaviours of the arc inside the spraying torch and, the effect of erosion of the anode on the forcing of the plasma jet [2-6].

A conventional DC non-transferred plasma torch (more than 90% of industrial torches) with a stick type cathode is shown schematically in Fig. 1 [7-8]. After working gas enters into the torch, it is heated by an electric arc formed between a nozzle-shaped anode and a conical cathode, which is ejected as a jet. The arc inside the torch has been characterized experimentally [4, 6, 9] and numerically [1-3, 8]. Unfortunately, experiments have been limited by involvement of high cost equipments and lack of understanding of the results obtained.

Fortunately, the numerical calculation provides a validway to understand the arc behavior inside plasmatorch. The modelling of DC arc plasma torches is an extremely challenging task because the plasma flow ishighly nonlinear and presents strong propertygradients. It is characterized by a wide range of timeand length scales, and often includes chemical andthermodynamic non-equilibrium effects, especiallynear its boundaries [8]. Despite of the complexity ofthe subject, over the past few decades, many papersconcerning numerical studiesof the characteristics ofDC arc plasma torches have been published [2-3, 8,9-22]. At the initial stage, two-dimensional (2D)modeling method was employed in the research topredict the heat transfer and flow patterns inside theplasma torch [10-14]. The predicted arc voltage of thetorch in the turbulent regime is much higher than themeasured value; in addition the predicted axiallocation of the arc attachment at the anode surface isalso much farther downstream than that observed inexperiments [15]. With the rapid development ofcomputer technology, the calculation of heat transferand fluid flow for a 3D thermal plasma torch withaxisymmetrical geometries become feasible [2-3, 15-22]. The models most frequently used for simulation ofplasma spray torch rely on the LTE approximation,and regard the plasma flowas a property-varyingelectromagnetic reactive fluid in chemical equilibriumin which the internal energy of the fluid ischaracterized by a single parameter of gastemperature [2-3, 15-21]. Selvan et al. developed asteady 3D LTE model to describe the temperature andvelocity distributions inside a DC plasma torch.Moreover the arc length and radius were alsodiscussed. But the model overestimated the plasmagas temperature near the arc-root due to theassumption that all the electric current transferred tothe anode only through a fixed arc-root [3, 16]. KlingerL. et al. also developed a steady 3D LTE modelsimulation of the plasma arc inside a DC plasmatorch. However, the position of arc-root wasdetermined arbitrarily [17]. A. Vardelle and J. P.Trelles developed a time-dependent 3D LTE modelrepresenting the fluctuant of plasma arc [2, 18-21].The voltage drop for the LTE model was largercompared with the experimental ones due to the hypothesis of LTE, resulted in less estimation of theelectrical conductivity especially near the electrodeboundary. A non-equilibrium (NLTE) model wasdeveloped for the non-transferred arc plasma torch,which showed better agreement with the experimentalresults [22]. However, to solve the NLTE model isextremely difficult due to the fact that the two-temperature chemical equilibrium need to beconsidered compared with the LTE mode.

In this research, an 3D LTE model was developed tomimic the non-transferred DC plasma torch. Theplasma gas temperature and velocity distributionswere obtained with the LTE model. The fluctuation ofarc inside the torch was also presented.

## 2 Description of the Mathematical Model

### 2.1 Model Assumptions

The model developed in this study is base on thefollowing main assumptions for simulating the heattransfer and flow patterns inside a plasma torch.

(1) The continuum assumption is valid and theplasma can be considered as a compressible,perfect gas in Local Thermodynamic Equilibrium(LTE).

(2) The plasma is optically thin.

(3) Gravitational effect and viscous dissipation areconsidered negligible.

(4) The induced electric field is negligible incomparison with the applied electric field intensityin the plasma arc region.

(5) The transport properties of plasma gas were onlydetermined by the plasma gas temperature.

(6) Because of the lower electric conducitivity nearthe cold boundary of electrode, the vicinity ofanode, distance of 0.1 mm, is artificiallyconsidered as a high electrical conductivity of 104S/m, so that a new arc-root can be formed if thearc is closed enough to the inside surface ofanode.

### 2.2 Computational Domain and Boundary Conditions

Based on the forgoing assumptions, the governingequations for the 3D time-dependent for the arcplasma can be written as follows:

### 2.3 Governing Equations

The geometry used in the current study correspondsto the SG-100 plasma torch from Praxair. Thecomputational domain formed by the region inside thetorch limited by the cathode, the gas flow inlet, theanode and the outlet as shown inFig. 2. Thecomputational domain is meshed using 217600hexahedral cells with 224567 nodes. The governingequations are solved by theSIMPLE algorithm usingthe commercial CFD software of FLUENT 6.3.

As seen inFig. 2, the boundary of the computationaldomain is divided into 4 different faces to allow thespecification of boundary conditions. Table 1 showsthe boundary conditions used in the simulation, wherePinrepresents the inlet pressure equal to 111325 Pa(10 kPa overpressure),hwthe convective heat transfercoefficient at the anode wall equal to 1105W.m-2.K-1[19-22],Twa reference cooling water temperature of500 K. The current density of cathode was defined by:

Where r is radial distance from the torch axisand Jcath0 and nc are parameters that specify the shape of current density profile. The Rc is DVS 276 calculated to ensure that integration of j(r) over the cathode equals the total applied current. According to the reference 20 and 23, Jcath0 of 2.08×108 A/m2 , nc of 4 and Rc of 0.913 mm were used in this study for the applied electric current of 500 A.

Argon gas was employed as the plasma gas in this study. As the table 1 showed, the spray conditions is 500 A of current and 50 SLM of gas flow rate.

## 3 Results and Discussions

### 3.1 Flow fields inside the torch

The distribution of electric field strength inside plasmatorch calculated by the LTE model is shown in theFig.3. The maximum electric field strength is about 0.78105V/m near the anode boundary.Figure 4showsthe time-evolution of the electric current distributions.It reveals that the arc-root moved downstream for thetime of 858 μs to 868 μs. At the same time, a newelectric current ]path^ will beformed if the electric fieldstrength is strong enough to break down between thearc and anode boundary. Consequently, electriccurrent will go through the old arc-root and the newone simultaneously. With the time elapsed, the oldarc-root will be disappeared and only the new onemaintained as shown in the Fig. 4.

With the arc-root movement and transition, the arcshould be fluctuated. The time-evolution of gastemperature and velocity distributions inside plasmatorch are showed in theFig. 5. While the attachmentof arc to the anode at the underside surface at thetime of 858 μs as shown in the Fig. 4, the arc waswarped and deviated to the contrary side. Thedeviation of arc resulted to rise of the electric fieldstrength at the fringe of the arc so that a new arc-rootformed. As the old arc-root disappeared, the arc willdeviate to the other side too in order to generate thenext attachment as shown in the Fig. 5 (a). The gasvelocity distributions insideplasma torch show that the gas velocity inside plasma torch has also a significantfluctuation with the arc-root movement and transitionas shown in the Fig. 5 (b). The fluctuations of plasmagas temperature and velocity are the main reason tocaused the plasma jet fluctuated, consequentlyinfluencing on the reproductivity of coatings. Themaximum gas temperature more than 30000K andvelocity more than 1000 m/s are obtained under thecurrent spray conditions of argon gas, 500 A electriccurrent and 50 SLM gas flow rate.

Figure 6shows the gas temperature and velocity atdifferent cross sections inside plasma torch. It can beseen that the gas temperature and velocitydistributions are asymmetric even though thegeometry of plasma torch is axisymmetric due to thefluctuations of arc.

The electric potential distribution of plasma arc isshowed inFig. 7(a). The voltage drop of the arccolumn should be lower than the voltage of powersupply theoretically because the voltage drop ofsheath exists. However, the arbitrary higher electricconductivity nearby electrode and LET assumptionsresult to a lower accuracy for the electric potentialdistribution especially the vicinity of cathode.Therefore,the sheath voltage drop cannot beobserved and the voltage drop of the arc columncalculated is much higher than the voltage of powersupply measured experimentally. Figure 7 (b) showsthe time-evolution of average voltage on the cathode.It reveals the frequency of plasma arc fluctuation isabout 11 kHz.

### 3.2 Gas flow at the torch exit

The plasma jet are mainly determined by the gas flowat the torch exit. The parameters of plasma jet can bepredicted by the distributionsof gas temperature andvelocity of torch outlet. Therefore, it is extremelyimportant to mimic the outlet temperature and velocityof gas in order to understand the fluctuations of jet ofplasma spray. The calculated distributions of gastemperature and velocity atthe nozzle exit are showninFig. 8. The maximum temperature of about 14000K and velocity of about 1000 m/s are obtained at thenozzle exit. It can be foundedthat the value calculatedis well agree with the results measured experimentallyaccording to the references [25-27].

The gas temperature and velocity at the nozzle exitfluctuate with the time elapsed too as shown in the Fig.8. The fluctuations resultto the vibration of the gasflow rate of torch outlet around 50 SLM, the inlet gasflow rate, as shown in theFig. 9.

## 4 Conclusions

A LTE model has been developed and applied to thethree-dimensional and time-dependent simulation ofthe flow inside a DC arc plasma torch. This mode wellmimiced the arc fluctuation inside a plasma torch. Thetemperature and velocity distribution of arc gas insidethe torch were calculated. The electric current mainlyconducts through the arc-root to the anode. Theconcentration of electric current causes the warp ofarc resulting to the rise of electric field strength at the contrary side of arc-root. When the arc is closedenough to the anode boundary and the elecrricfield strength is strong enough, the old acr-root willtransfer to a new one. The movement andtransiation of arc-root result to the fluctuation ofplasma arc inside plasma torchwith the frequency of11 kHz. A gas temperature of about 14000K andvelocity of about 1000 m/s were obtained at the torchexit. A higher voltage drop of arc column was obtainedcompared to the one measured experimentally due tothe LTE assumption underestimated the electricconductivity of plasma gas inside the torch, especiallythe regions around the arc-root.

## 5 Literature

1. Miloshevsky G.V., Romanov G.S., Tolkach V.I.,Smurov I. Yu., Simulation of the Dynamics ofTwo-Phase Plasma Jet in the Atmosphere.Proceedings of III International Conference onPlasma Physics and Plasma Technology, Minsk,Belarus, September 18-22, 2000, p244-247

2. Juan Pablo Trelles, Emil Pfender, JoachimHeberlein, Multiscale Finite Element Modeling ofArc Dynamics in a DC Plasma Torch, PlasmaChem Plasma Process (2006) 26, p557`575

3. B. Selvan and K. Ramachandran, ComparisonsBetween Two Different Three-Dimensional ArcPlasma Torch Simulations, Journal of ThermalSpray Technology, Volume 18(5-6) Mid-December 2009, p846`857

4. Z. Duan and J. Heberlein, Arc Instabilities in aPlasma Spray Torch, Journal of Thermal SprayTechnology, Volume 11(1) March 2002, p44-51

5. D. Outcalt, M. Hallberg, G. Yang, J. Heberlein, E.Pfender, P. Strykowski , Instabilities in PlasmaSpray Jets, Proceedings of the 2006 InternationalThermal Spray Conference, May 15`18, 2006,Seattle, Washington, USA Copyright 2006 ASMInternational (In CD)

6. J. F. Coudert, M. P. Planche, P. Fauchais,Characterization of DC Plasma Torch VoltageFluctuations, Plasma Chemistry and PlasmaProcessing, Vol. 16, No. 1, 1996 (Supplement,211S~227s)

7. P Fauchais, Understanding plasma spraying, J.Phys. D: Appl. Phys. 37 (2004) R86`R108

8. J.P. Trelles, C. Chazelas, A. Vardelle, and J.V.R.Heberlein, Arc Plasma Torch Modeling, Journal ofThermal Spray Technology, Volume 18, Numbers5-6, p728-752

9. R. Ramasamy and V. Selvarajan, Current-voltagecharacteristics of a non-transferred plasma spraytorch, Eur. Phys. J. D 8, p125`129

10. R. Westhoff, A. H. Dilawari, J. Szekely, AMathematical Representation of TransportPhenomena Inside a Plasma Torch, J. Appl.Phys., 1991, 190, p213-219

11. Westhoff, R.; Szekely, J., A Model of Fluid, HeatFlow, and Electromagnetic Phenomena In aNontransferred Arc Plasma Torch, Journal ofApplied Physics, Volume 70, Issue 7, October 1,1991, p3455-3466

12. Han Peng, Yu lan, Chen Xi, Modeling of PlasmaJets with Computed Inlet Profiles, In: C.K. Wu,Editor, Proceedings of the 13th InternationalSymposium on Plasma Chemistry, PekingUniversity Press, Beijing (1997), p338`343

13. Scott, D. A.; Kovitya, P.; Haddad, G. N.,Temperatures in the Plume of a DC PlasmaTorch, Journal of Applied Physics, Volume 66,Issue 11, December 1, 1989, p5232-5239

14. Seungho Paik, P. C. Huang, J. Heberleinand andE. Pfender, Determination of the Arc-root Positionin a DC Plasma Torch, Plasma Chemistry andPlasma Processing, Volume 13, Number 3, p379-397

15. He-Ping Li and E. Pfender, Three DimensionalModeling of the Plasma Spray Process, Journalof Thermal Spray Technology, Volume 16(2)June 2007, p245`260

16. B. Selvan, K. Ramachandran, K. P. Sreekumar,T. K. Thiyagarajan2, P. V.Ananthapadmanabhan, Three-DimensionalNumerical Modeling of an Ar-N2 Plasma ArcInside a Non-Transferred Torch, Journal PlasmaScience and Technology, IssueVolume 11,Number 6, p679-687

17. Klinger L, Vos JB, Appert K, High-resolution CFDsimulation of a plasma torch in 3 dimensions,Centre de Recherches en Physique des Plasmas` Preprint Report, LRP 763,http://crppwww.epfl.ch/

18. C. Baudry, A. Vardelle, G. Mariaux, F C.Delalondre, Electricite De France, Chatou, E.Meillot, Commissariat al Energie Atomique,Monts, Three-dimensional and time-dependentmodel of the dynamic behavior of the arc in aplasma spray torch, Thermal Spray 2004:Advances in Technology and Applications (ASMInternational), p717 ` 723

19. E. Moreau, C. Chazelas, G. Mariaux and A.Vardelle, Modeling the Restrike Mode Operationof a DC Plasma Spray Torch, Journal of ThermalSpray Technology, Volume 15, Number 4, p524-530

20. J P Trelles, E Pfender and J V R Heberlein,Modelling of the arc reattachment process inplasma torches, Journal of Physics D: AppliedPhysics, Volume 40, Number 18, p5635

21. J. P. Trelles and J. V. R. Heberlein, Simulationresults of Arc Behavior in Different Plasma SprayTorches, Journal of Thermal Spray Technology,Volume 15, Number 4, p563-569

22. J P Trelles, J V R Heberlein and E Pfender, Non-equilibrium Modelling of Arc Plasma Torches,JournalJournal of Physics D: Applied Physics,Volume 40, Number 19, p5937

23. Maher I. Boulos, Pierre Fauchais, Emil Pfender,Thermal plasmas: fundamentals and applications,Springer, 1994

24. V. Colombo, E. Ghedini*, P. Sanibondi,Thermodynamic and transport properties in non-equilibrium argon, oxygen and nitrogen thermalplasmas, Progress in Nuclear Energy, V50(2008), p921`933

25. S.C. Snyder, G.D.Lassahn and J.D. Grandy,Direct determination ofgas velocity and gastemperature in an atmospheric-pressure argon`hydrogen plasma jet, Journal of QuantitativeSpectroscopy and Radiative Transfer, olume 107,Issue 2, September 2007, P217-225

26. M. P. Planche, J. F. Coudert and P. Fauchais,Velocity Measurements for Arc Jets Produced bya DC Plasma Spray Torch, Plasma Chemistryand Plasma Processing, Vol. 18, No. 2, 1998

27. J.-L. Dorier, Ch. Hollenstein, A. Salito, M. Lochand G. Barbezat, Diagnostics of Plasma TorchFluctuations, AG Sulzer Metco