IEEE Transactions on Plasma Science; Volume: 39, Issue: 10, p 1974 – 1982

An Improved Local Thermal Equilibrium Model of DC Arc Plasma
TorchR. Huang and H. Fukanuma, Plasma Giken Co., Ltd., Tokyo, JapanY. Uesugi and Y. Tanaka, Kanazawa University, Kanazawa City, Japan
Abstract
Most of the simulation models about arc plasma are based on the hypothesis of Local Thermal Equilibrium (LTE). The non-equilibrium
model is very complicated due to the calculation of electron temperature. In this study, an improved LTE model is developed andapplied to the three-dimensional simulation of the flow patterns inside a non-transferred DC arc plasma torch. Numerical calculations on
the distribution of gas temperature and velocity in the plasma torch were carried out using argon as the plasma gas. The electric current
density and potential are also discussed. The results indicate that the temperature and velocity distributions of arc are almost
axisymmetrical. The results of voltage drop agree well with the experiment observations. It seems that anode erosion is located on theinternal surface of the anode, where the largest number of electrons are injected.
Index Terms-plasma spraying, plasma torch, local thermal equilibrium, three-dimensional modeling.

ρ
V
t
𝑗
𝑐𝑝
𝐸
𝜆
∅
𝜇0
𝑇𝑒
𝑚𝑒
𝜆𝑒
𝑛ℎ

Gas mass density
Gas velocity
TimeElectric current density vector
Specific heat at constant pressure
Electric field
Gas thermal conductivity
Electric potential
Permeability of free space
Nominal electron temperature
Mass of electronFree path of electron
Number density of heavy particles

Nomenclature
𝐵
𝑃
𝜇
𝑆
T
𝑆𝑟
𝜎
𝐴
𝑅𝑔
𝑚ℎ
𝑒
𝑘
𝑛𝑒

I. INTRODUCTION
Plasma spraying is widely used in industrial fields to provide
coatings for protection of materials against wear, erosion,
corrosion and thermal loads based on a high heat source withtemperature over 10000K enough to melt any material atatmospheric pressure. Since the appearance of industrial DC arc
plasma spray torches in the 1960s, the research of this field
through both measurements and modeling has been extensively
conducted [1]. In recent years, although a number of robust, user
friendly particle diagnostic tools have become available forplasma spray processes to assess the in-flight particle
temperature, velocity, trajectory and particle diameter
distributions, it is still difficult to observe the complex propertiesof arc inside a plasma torch [2].
A conventional DC non-transferred plasma torch (representing
more than 90% of industrial torches) with a stick-type cathode isshown schematically in figure 1 [3-4]. After the working gas
enters the torch, it is heated by an electric arc formed between anozzle-shaped anode and a conical cathode, and ejected as a jet.
Particles to be plasma sprayed are fed into the particle inlet,
heated and accelerated within the plasma jet by the working gas
via the plasma arc. The experimental research performed on the

Magnetic induction vector
Gas pressure
Dynamic viscosity
Strain rate tensor
Gas temperature
Volumetric net radiation losses
Electric conductivity
Magnetic vector potential
Gas constant
Mass of heavy particle
Elementary charge
Boltzmann constant
Number density of electrons

plasma arc is mainly concentrated on the measurement of arc
voltage [3-6], arc behavior at the torch exit and observation of
the jet formed by the plasma torch [3]. S. Goutier et al. alsomeasured the particle temperature fluctuations [7]. Few of thereports about the arc behavior inside the torch present
experimental results, due to the equipment limitations.

Fig. 1. Schematic of a conventional DC arc torch

Fortunately, numerical calculation provides a valid way tounderstand arc behavior inside the plasma torch. The modelingof DC arc plasma torches is an extremely challenging task
because the plasma flow is highly nonlinear and presents strong
property gradients. It is characterized by a wide range of timeand length scales, and often includes chemical andIEEE Transactions on Plasma Science; Volume: 39, Issue: 10, p 1974 – 1982
thermodynamic non-equilibrium effects, especially near its
boundaries [8]. Despite of the complexity of the subject, over the
past few decades, many papers concerning numerical studies of
the characteristics of DC arc plasma torches have been published[8-23]. At the initial stage, two-dimensional (2D) modelingmethod was employed in the research to predict the heat transfer
and flow patterns inside the plasma torch [9-13]. The predictedarc voltage of the torch in the turbulent regime is much higher
than the measured value; in addition the predicted axial locationof the arc attachment at the anode surface is also much farther
downstream than that observed in experiments [14]. With therapid development of computer technology, the calculation ofheat transfer and fluid flow for a 3D thermal plasma torch withaxisymmetrical geometries become feasible [14-23]. The models
most frequently used for simulations of plasma spray torches relyon the LTE approximation, and regard the plasma flow as aproperty-varying electromagnetic reactive fluid in chemical
equilibrium state, in which the internal energy of the fluid ischaracterized by the single parameter of gas temperature [14-22].
Selvan et al. developed a steady 3D LTE model to describe thetemperature and velocity distributions inside a DC plasma torch.
Moreover the arc length and radius were also discussed. But themodel overestimated the plasma gas temperature near thearc-root due to the assumption that all the electric current
transferred to the anode only through a fixed arc-root [15-16].
Klinger L. et al. also developed a steady 3D LTE model
simulation of the plasma arc inside a DC plasma torch. However,the position of the arc-root was determined arbitrarily [17]. A.
Vardelle and J. P. Trelles developed a time-dependent 3D LTE
model representing the fluctuations of plasma arc [18-22]. The
voltage drop for the LTE model was larger compared with theexperimental ones due to the hypothesis of LTE. A
non-equilibrium (NLTE) model was developed for the
non-transferred arc plasma torch, which showed better agreementwith the experimental results [23]. However, to solve the NLTE
model is extremely difficult due to the fact that the
two-temperature chemical equilibrium needs to be considered
compared with the LTE mode.
Due to the LTE assumptions for the conventional LTE mode,the value of electron temperature is equal to heavy particles
temperature, which is low near the electrodes, especially near theanode surface. Hence the equilibrium electrical conductivity,
being a function of electron temperature, is extremely low, which
limits the flow of electrical current through the electrodes. To
alleviate this, some additional assumptions are necessary toachieve high electrical conductivity near the electrodes. In thecurrent study, a nominal electron temperature was proposed, thatwas derived from the plasma gas temperature and adjusted by theelectrical field strength, to amend the electrical conductivity ofplasma gas. Therefore, no more additional assumptions arenecessary to ensure the electrical current path between thecathode and anode if the electrical conductivity of plasma gas isdetermined by the nominal electron temperature instead of thegas temperature.
In order to differentiate from the conventional LTE model, themodel using this study was named “improved LTE model”. With
the improved LTE model, the plasma gas temperature andvelocity distributions inside a DC plasma torch were calculated,
and the distributions of electrical potential and current density

were investigated. The results show that the total voltage drop
and the location of anode erosion obtained by the improved LTE
model are well consistent with experimental observations.

II. DESCRIPTION OF THE MATHEMATICAL
MODEL
A. Model Assumptions
The model developed in this study is based on the following
main assumptions for simulating the heat transfer and flow
patterns inside a plasma torch.
(1) The continuum assumption is valid and the plasma can beconsidered as a compressible gas in the state of Local
Thermodynamic Equilibrium (LTE).
(2) The plasma is optically thin.
(3) Gravitational effect and viscous dissipation are considerednegligible.
(4) The induced electric field is negligible in comparison withthe applied electric field intensity in the plasma arc region.
(5) The variation of gas pressure inside the torch is so little thatthe effects of pressure on the thermodynamic and transport
properties of plasma are negligible. Based on the LTE
assumption, the thermodynamic and transport properties ofplasma gas (such as cp, 𝜇 and 𝜆) are determined by the gas
temperature excluding the electrical conductivity (𝜎) as
mentioned above. The electrical conductivity of plasma gas
is determined by the nominal electron temperature derived
from gas temperature, corrected by the electric field.
B. Governing Equations
Based on the forgoing assumptions, the governing equations
for a 3D time-dependent flow of arc plasma can be written as
follows:
Conservation of mass:
∂

ρ

∂

t

+

∇

(

∙

ρ

V

1

=

0	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
  
)

Conservation of momentum:𝜌 𝜕 𝑉 𝜕 𝑡 + 𝑉 . 𝛻 𝑉 = 𝑗 × 𝐵 − 𝛻 𝑃 + 2 3 𝜇 𝛻 ∙ 𝑉 + 2 𝛻 ∙ 𝜇 𝑆 	
   	
   	
   	
   ( 2 )Conservation of energy:
𝜌𝑐𝑝𝜕𝑇𝜕𝑡+𝑉.∇𝑇−𝐷𝑃𝐷𝑡=𝑗.𝐸−𝑆𝑟+∇∙𝜆∇𝑇	
   	
   	
   	
   	
   	
   	
   	
   (3)
Maxwell electromagnetism equations:∇∙−𝜎∇∅=0	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
  
(4)
𝐸=−∇∅	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
  
(5)
∆𝐴=−𝜇0𝑗	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
  
(6)
𝐵=∇×𝐴	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
  
(7)
Ohm law:
𝑗=𝜎𝐸	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
  
(8)

Density of plasma:𝜌=𝑃𝑅𝑔𝑇	
   	
   	
  

	
  

𝑤𝑖𝑡ℎ	
  

𝑅𝑔=𝑘(𝑛ℎ+𝑛𝑒𝑛ℎ𝑚ℎ+𝑛𝑒𝑚𝑒)	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
  

IEEE Transactions on Plasma Science; Volume: 39, Issue: 10, p 1974 – 1982
(9)
In order to determine the electrical conductivity of plasma gas,
the electron temperature must be calculated. It is difficult tosolve the electron energy conservation equation to get theelectron temperature because of strong nonlinearity. Therefore, anominal electron temperature was calculated from the equation
as follows [24]:𝑇𝑒−𝑇𝑇𝑒=3𝜋32𝑚ℎ𝑚𝑒𝑒𝜆𝑒𝐸32𝑘𝑇𝑒2	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
  
(10)
C. Computational Domain and Boundary Conditions
The geometry used in the current study corresponds to theSG-100 plasma torch from Praxair. The cross sectional
dimension of SG-100 torch used in this study is shown in figure
2 (a), and the 3D computational domain is shown in figure 2 (b).
The computational domain is meshed using 217600 structured
hexahedral cells with 224567 nodes as shown in the figure 2 (b).

(a) Cross section dimension of SG-100 torch

Argon gas was employed as the plasma gas in this study. The
conditions for simulation are shown in table 3.
Table 1. Boundary conditions
Inlet

CathodeAnodeOutletP

Pin

𝜕𝑃𝜕𝑛=0𝜕𝑃𝜕𝑛=0101325

V

Flow Rate

0

0

300

T(r)

𝑄𝑎=ℎ𝑤(𝑇−𝑇𝑤)

𝜕𝑉𝑖𝜕𝑛=0T∅𝜕∅𝜕𝑛=0j(r)0𝜕∅𝜕𝑛=0𝐴

0𝜕𝐴𝑖𝜕𝑛=0𝜕𝐴𝑖𝜕𝑛=0𝜕𝐴𝑖𝜕𝑛=0

𝜕𝑇𝜕𝑛=0

Table 2. The shape parameters of current density
Specified Current (A)Jcath0 (A/m2)

nc

Rc (mm)

600

2.5e8

4

0.912245

Table 3. The conditions for simulation
Gas type

Applied current (A)Gas flow rate (SLM)

Argon

600

50

The gas flow inside the plasma torch was calculated by
FLUENT, commercial CFD software, with the SIMPLE
algorithm. For gas flow calculations, the K-ε model is employedin this study.
Base on the assumption above, the electrical conductivity ofplasma gas depends on gas electron temperature. The calculated
method of electrical conductivity was presented in Ref. 23 and
25 to 27. The electrical conductivity of argon plasma gas inrelation to the electron temperature is shown in figure 3. The
other thermodynamic and transport properties of the plasma gasthat only rely on the gas temperature, such as heat specific,
thermal conductivity, viscosity and volumetric radiation, aretaken from Ref. 28.

(b) Mesh of computational domain
Fig. 2. Geometry of the computational domain

As seen in figure 2, the boundary of the computational domain
is divided into 4 different faces to allow the specification ofboundary conditions. Table 1 shows the boundary conditions
used in the simulation, where Pin represents the inlet pressure
equal to 111325 Pa (10 kPa overpressure), hw the convective heattransfer coefficient at the anode wall equal to 2×104 W.m-2.K-1[19-23], and Tw a reference cooling water temperature of 500 K.
The electrical current density and temperature of the cathode wasdefined by:
𝑗𝑟=𝐽𝑐𝑎𝑡ℎ0exp⁡−𝑟𝑅𝑐𝑛𝑐	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   (11)
𝑇𝑟=500+3000exp−𝑟2𝑅𝑐𝑛𝑐	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   	
   (12)where r is radial distance from the torch axis (𝑟2=𝑥2+𝑦2), andJcath0 and nc are parameters that specify the shape of the current
density profile. The Rc is calculated to ensure that integration ofj(r) over the cathode equals the total applied current. According
to references 20 and 23, the values of the shape parameters usedin the current study are shown in table 2.

Fig. 3. Electrical conductivity of argon plasma gas [23, 25 and 26]

III. RESULTS AND DISCUSSIONS
A. Nominal electron temperature
Based on equation 10, the calculated nominal electron
temperature of the argon gas in relation to different electric fieldstrengths at the pressure of 1 atm is shown in figure 4. It’s
revealed that the high electric field strength prevents theestablishment of an equilibrium state in which the gas
temperature is equal to the electron temperature. Therefore, thenominal electron temperature is much higher than the gas

IEEE Transactions on Plasma Science; Volume: 39, Issue: 10, p 1974 – 1982
temperature especially under the low gas temperature conditions
while the electric field strength is strong. In contrast, the nominal
electron temperature is similar to the gas temperature while theelectric field strength is low, due to few ionizations occurring.
When the gas temperature is high enough to obtain sufficientcollisions between the heavy particles and the electrons, thenominal electron temperature is also similar to the gas
temperature with little dependency on the electric field strength
as shown in the figure 4.

near 36500K at the current simulation conditions. The gas
temperature distribution changes slightly with the elapse of time.
Figure 7 shows the instantaneous velocity distribution inside thetorch. Similar to the temperature distribution, the distribution ofgas velocity is almost axisymmetrical. The maximum velocity of
inside the torch is near 1740 m/s and the variation of velocity
with the elapse of time is significant compared with the gas
temperature.

Fig. 4. The relationship between the nominal electron temperature andthe gas temperature under different electric field strength

B. Flow fields inside the torch
Figure 5 (a) shows the voltage drop of the plasma column
calculated by the improved LTE model. The amplitude ofvoltage is between 22 and 25 V with a fluctuation frequency of
13.9 kHz. An experiment was carried out to measure the plasma
system power source voltage under the same conditions used in
the current simulation, 600 A electrical current and 50 SLM gas
flow rate. Limited by the experimental equipment, only theaverage voltage of power source was obtained. The
experimentally observed voltage of the power source is 29.5 V.
There are two reasons that the voltage drop calculated is lower
than the experimental results. One is that the voltage drop of theplasma column should be less than voltage drop of plasma torch
because the sheath voltage drop of the electrode was not taken
into account in the simulation. The other is that the experimental
voltage of the power source should be higher than the voltage
drop of plasma torch owing to the voltage drop on the electricalcables. Figure 5 (b) shows the voltage drop of a SG-100 plasma
torch researched by Trelles et al under the conditions of 700A
electrical current and 60 SLM gas flow rate [23]. It seems thatthe experimental voltage drop in the reference 23 is a little lower
than the ones in this study in spite of the higher electrical current
applied. This is caused by the cable voltage drop in the current
study because the voltage in reference 23 is the voltage drop ofplasma torch instead of power source. The research reveals thatvoltage drop calculated with the LTE model is more than twicethat of the experimental results. It seems that the improved LTE
mode can obtain comparable accuracy to the NLTE mode.
The instantaneous temperature distributions inside the torch at
600 and 630µs, two representative times for observing theconditions at maximum and minimum voltage drop, arepresented in figure 6. It can be observed that the distributions arealmost axisymmetrical and the temperature of the plasma core is(a) Results in this study(b) Trelles’s results in reference 23
Fig. 5. Voltage drop of plasma

Figure 8 and 9 show the gas temperature and velocity
distributions of different axial cross sections inside the torch. It
reveals that the distribution of gas temperature and velocity arealmost axisymmetrical at all the axial cross sections.
The calculated nominal electron temperature distribution
inside the torch is presented in figure 10. Compared to the gas
temperature distribution in figure 6 (b), it is obviously higher
than the gas temperature with greatly varying degrees dependingIEEE Transactions on Plasma Science; Volume: 39, Issue: 10, p 1974 – 1982
on the regions. As figure 4 shows, in the high temperature region
near the plasma core, the nominal electron temperature is similar
to the gas temperature owing to sufficient collisions between
electrons and heavy particles under the condition of higher gas
temperature. However, a significant difference between thenominal electron temperature and gas temperature is observed in
the region far from the plasma core, especially the regions near
the corner of the anode internal surface, where the nominal
electron temperature is more than 10000 K. This is on account of
the insufficient collisions between the electrons and the heavy
particles in the lower gas temperature regions resulting in a great
temperature difference. Consequently, the electrical current canreach the anode in spite of the lower gas temperature near theanode boundary because of the higher electrical conductivity
determined by the nominal electron temperature. Therefore, theproblem of lower electric conductivity near the anode boundary
in the conventional LTE model can be solved in this study by
calculating nominal electron temperature. Using the improved
model, the simulation can be executed without making further
assumptions about the electric conductivity.

higher temperature and electric current density lead to a lower
sheath voltage drop [29-30]. Therefore, different electricalpotential is observed at the cathode boundary because of thedifferent sheath voltage drop.

(a) at 600 µs(b) at 630 µs
Fig. 7. Velocity distributions of a cross section inside the torch (unit:m/s)(a) at 600 µs(b) at 630 µs

Fig. 8. Temperature distribution inside the torch of different axial crosssections at 630 µs (unit: K)

Fig. 6. Temperature distributions of a cross section inside the torch (unit:
K)

Figure 11 shows the electric potential distribution inside thetorch. It seems that different electrical potential is obtained along
the cathode boundary although a uniform electric potential isloaded on the cathode. The minimum electrical potential of theplasma gas is observed at the cathode tip and the electricalpotential should decrease with the increase of distance from thecathode tip. The situation is caused by the sheath voltage of thecathode, not considered in the current study. Therefore, themagnitude of the gas electrical potential at the cathode boundary
should be the value of the plasma voltage subtracting the sheathvoltage drop. According to the studies of Benilov and Zhou,

Fig. 9. Velocity distribution inside the torch of different axial crosssections at 630 µs (unit: m/s)

IEEE Transactions on Plasma Science; Volume: 39, Issue: 10, p 1974 – 1982
C. Gas flow at the torch exit
Figure 12 and 13 show the respective gas temperature andvelocity distributions at the torch exit. The distributions oftemperature and velocity are both axisymmetrical, thetemperature at the symmetrical center of the torch exit is near
13000 K, and the velocity there is about 1000 m/s. It can be seenthat the gas temperature and velocity of the torch exit at the timeof 600 µs are a little higher than the ones at the time of 630 µs
owing to the higher voltage drop of arc column as shown in Fig.
5 (a) resulting in a higher plasma power. This is evidence that thearc length is longer at the time of 600 µs than that of 630 µs.

velocity fluctuation leads the gas flow rate at the torch exit tofluctuate around 50 SLM, the inlet flow rate, as shown in the
figure 14 (b).

Fig. 13. Velocity distributions at the torch exit (unit: m/s)

Fig. 10. Nominal electron temperature distribution of a cross section
inside the torch at 630 µs (unit: K)(a)Fig. 11. Electric potential distribution of a cross section inside the torch
at 630 µs (unit: V)(b)Fig. 12. Temperature distributions at the torch exit (unit: K)

Fig. 14. (a) symmetrical center velocity and (b) gas flow rate of the torch
exit

Figure 14 shows the velocity and gas flow rate at thesymmetrical center of the torch exit. It reveals that the gas
velocity of the symmetrical center at the torch exit fluctuatedperiodically from 650 to 1000 m/s. The fluctuation of gas
velocity at the symmetrical center of the torch exit is caused by
the plasma arc fluctuation because the frequency is 13.9 kHz,similar to the fluctuation frequency of plasma voltage. The gas

D. Erosion of the anodeAn anode erosion test was carried out to ascertain location oferosion. In order to accelerate the rate of erosion, the conditions
for the anode erosion test are somewhat different from thesimulation conditions, as shown in table 4. The applied electricalcurrent was increased to 750 A, and helium was mixed with

IEEE Transactions on Plasma Science; Volume: 39, Issue: 10, p 1974 – 1982
argon gas to raise the plasma voltage. Figure 15 shows two crosssections of used SG-100 torch’s anodes. In Fig. 15 (a), the anode
was used for 30 hours, and some slight erosion occurred at theanode internal surface. After extended usage, the anode wasseverely eroded as shown in figure 15 (b). It seems that anode
erosion always occurs at the location close to the corner of theanode internal surface. Extended usage only leads to a spread ofthe erosion range.

16 (a), the similar location in the internal surface of anode is
obtained, where the main electrical current passes through. It
seems that the location is well consistent with the place oferosion. Overlapping the electrical current density distribution
and the eroded anode reveals that the location of anode erosion iswhere the main electric current “path” passes through as shownin figure 16 (b).

Table 4. Spray conditions for anode erosion test
Argon flow rate (SLM)

50

Helium flow rate (SLM)

20Electrical current (A)750

Voltage (V)40

Cooling water flow rate (l/min)

22-24

(a)

(a) Slight erosion for a relatively short time usage(b)
Fig. 16. Electric current density distribution of a cross section inside thetorch (a) and overlapped with the eroded anode (b)(b) Severe erosion for a relatively long time usage
Fig. 15. Eroded anode

Figure 16 shows the electric current density distributions
inside the torch. It can be seen that the arc length at the time of
600 µs is longer than the one at the time of 630 µs. For a
non-transferred DC plasma torch, the arc length depends on thebalance of flow drag force and electromagnetic force. If the flow
drag force dominates over electromagnetic force, the arc length
becomes longer and the electromagnetic force increases. If the
opposite occurs, the arc length will become shorter (ref 20). The
arc length change leads to arc voltage fluctuation because alonger arc can gain high plasma voltage as shown in Fig 5 (a).
Even though the arc length changes with time as shown in Fig.

IV. CONCLUSIONSAn improved LTE model has been developed and applied tothe three-dimensional and time-dependent simulation of the flow
inside a DC arc plasma torch. The important change comparedwith the conventional LTE model is to adjust the electricalconductivity of plasma gas with a nominal electron temperature
instead of the gas temperature. The temperature and velocity
distribution of arc gas inside the torch were calculated, and theflow will fluctuate with the elapse of time. A gas temperature ofabout 13000K and velocity of about 1000 m/s were obtained at
the torch exit. The voltage drop of arc column calculated
matches well with the value measured. The location of anode
erosion can also be predicted correctly using this model by thecalculation of electric current density distribution.

IEEE Transactions on Plasma Science; Volume: 39, Issue: 10, p 1974 – 1982

REFERENCES[1] P Fauchais, Understanding plasma spraying, J. Phys. D:
Appl. Phys. 37 (2004) R86–R108[2] T. Streibl, A. Vaidya, M. Friis, V. Srinivasan and S.
Sampath, A critical assessment of particle temperature
distributions during plasma spraying: experimental resultsfor YSZ, Plasma Chemistry and Plasma Processing, Vol. 26,
No. 1, February 2006, p73–102[3] Z. Duan and J. Heberlein, Arc Instabilities in a Plasma
Spray Torch, Journal of Thermal Spray Technology,
Volume 11(1) March 2002, p44-51[4] D. Outcalt, M. Hallberg, G. Yang, J. Heberlein, E. Pfender,
P. Strykowski , Instabilities in Plasma Spray Jets,
Proceedings of the 2006 International Thermal Spray
Conference, May 15–18, 2006, Seattle, Washington, USA
Copyright 2006 ASM International (In CD)[5] J. F. Coudert, M. P. Planche, P. Fauchais, Characterizationof DC Plasma Torch Voltage Fluctuations, Plasma
Chemistry and Plasma Processing, Vol. 16, No. 1, 1996
(Supplement, 211S~227s)[6] R. Ramasamy and V. Selvarajan, Current-voltage
characteristics of a non-transferred plasma spray torch, Eur.
Phys. J. D 8, p125–129[7] S. Goutier, E. Nogues-Delbos, M. Vardelle, and P. Fauchais,
Particle temperature fluctuations in plasma spraying,
Journal of Thermal Spray Technology, Volume 17(5-6)
Mid-December 2008, p895-901[8] J.P. Trelles, C. Chazelas, A. Vardelle, and J.V.R. Heberlein,
Arc Plasma Torch Modeling, Journal of Thermal Spray
Technology, Volume 18, Numbers 5-6, p728-752[9] R. Westhoff, A. H. Dilawari, J. Szekely, A Mathematical
Representation of Transport Phenomena Inside a Plasma
Torch, J. Appl. Phys., 1991, 190, p213-219[10] Westhoff, R.; Szekely, J., A Model of Fluid, Heat Flow, andElectromagnetic Phenomena In a Nontransferred Arc
Plasma Torch, Journal of Applied Physics, Volume 70,
Issue 7, October 1, 1991, p3455-3466[11] Han Peng, Yu lan, Chen Xi, Modeling of Plasma Jets with
Computed Inlet Profiles, In: C.K. Wu, Editor, Proceedingsof the 13th International Symposium on Plasma Chemistry,
Peking University Press, Beijing (1997), p338–343[12] Scott, D. A.; Kovitya, P.; Haddad, G. N., Temperatures in
the Plume of a DC Plasma Torch, Journal of Applied
Physics, Volume 66, Issue 11, December 1, 1989,
p5232-5239[13] Seungho Paik, P. C. Huang, J. Heberleinand and E. Pfender,
Determination of the Arc-root Position in a DC Plasma
Torch, Plasma Chemistry and Plasma Processing, Volume
13, Number 3, p379-397[14] He-Ping Li and E. Pfender, Three Dimensional Modeling of
the Plasma Spray Process, Journal of Thermal Spray
Technology, Volume 16(2) June 2007, p245–260[15] B. Selvan and K. Ramachandran, Comparisons Between
Two Different Three-Dimensional Arc Plasma Torch
Simulations, Journal of Thermal Spray Technology,
Volume 18(5-6) Mid-December 2009, p 846–857[16] B. Selvan, K. Ramachandran, K. P. Sreekumar, T. K.

Thiyagarajan2,
P.
V.
Ananthapadmanabhan,
Three-Dimensional Numerical Modeling of an Ar-N2
Plasma Arc Inside a Non-Transferred Torch, Journal Plasma
Science and Technology, IssueVolume 11, Number 6,
p679-687[17] Klinger L, Vos JB, Appert K, High-resolution CFD
simulation of a plasma torch in 3 dimensions, Centre deRecherches en Physique des Plasmas – Preprint Report,
LRP 763, http://crppwww.epfl.ch/[18] C. Baudry, A. Vardelle, G. Mariaux, F C. Delalondre,
Chatou,E.
Meillot,Three-dimensional
andtime-dependent model of the dynamic behavior of the arc ina plasma spray torch, Thermal Spray 2004: Advances inTechnology and Applications (ASM International), p717 –
723[19] E. Moreau, C. Chazelas, G. Mariaux and A. Vardelle,
Modeling the Restrike Mode Operation of a DC Plasma
Spray Torch, Journal of Thermal Spray Technology,
Volume 15, Number 4, p524-530[20] J P Trelles, E Pfender and J V R Heberlein, Modelling of
the arc reattachment process in plasma torches, Journal of
Physics D: Applied Physics, Volume 40, Number 18, p5635[21] Juan Pablo Trelles, Emil Pfender, Joachim Heberlein,
Multiscale Finite Element Modeling of Arc Dynamics in a
DC Plasma Torch, Plasma Chem Plasma Process (2006)
V26, p557-575[22] J. P. Trelles and J. V. R. Heberlein, Simulation results of
Arc Behavior in Different Plasma Spray Torches, Journal of
Thermal Spray Technology, Volume 15, Number 4,
p563-569[23] J P Trelles, J V R Heberlein and E Pfender,Non-equilibrium Modelling of Arc Plasma Torches, Journalof Physics D: Applied Physics, Volume 40, Number 19,
p5937[24] M. F. Zhukov and I. M. Zasypkin, Thermal Plasma Torches:
Design, Characteristics, Application, Cambridge Int Science
Publishing, 2007, p3[25] V. Colombo, E. Ghedini, P. Sanibondi, Thermodynamic andtransport properties in non-equilibrium argon, oxygen andnitrogen thermal plasmas, Progress in Nuclear Energy, V50(2008), p921–933[26] V Rat, P Andre, J Aubreton, M F Elchinger, P Fauchais andD Vacher, Transport coefficients including diffusion in a
two-temperature argon plasma, J. Phys. D: Appl. Phys, 35(2002) , p981–991[27] V. Rat,P. Andre, J. Aubreton, M. F. Elchinger,P. Fauchaisand A. Lefort, Transport properties in a two-temperatureplasma: Theory and application, Physical Review E, V64,
026409[28] Maher I. Boulos, Pierre Fauchais, Emil Pfender, Thermal
plasmas: fundamentals and applications, Springer, 1994[29] M
S
Benilov,
Understanding
andmodelling
plasma-electrode interaction in high-pressure arc discharges:
a review, J. Phys. D: Appl. Phys. 41 (2008), p1-30[30] X Zhou and J Heberlein, Analysis of the arc-cathodeinteraction of free-burning arcs, Plasma Source Sci. Technol.
3 (1994), p564-574

IEEE Transactions on Plasma Science; Volume: 39, Issue: 10, p 1974 – 1982