Effects of inter-electrode insertion on the performance and thermal flow fields of a hollow-electrode plasma torch

In-Mok YANG, Jun-Seok NAM, Min-Kyu CHOI, Jun-Ho SEO,3and Shi-Young YANG

1 Department of Applied Plasma Engineering, Chonbuk National University, Jeonju 54896, Republic of Korea

2 Graduate School of Flexible & Printable Electronics, Chonbuk National University, Jeonju 54896,

Republic of Korea

Abstract The effects of inter-electrode insertion on the performance of a hollow-electrode plasma torch have been investigated by numerical analysis. Simulation results revealed that when inter-electrodes are inserted,the arc voltages and plasma powers increase due to the increase in the arc length.In addition,it was predicted that thermal efficiency can be improved with the increase in plasma power by injecting plasma gases through the gaps between inter-electrodes. These unique effects of inter-electrode insertion are a result of the plasma temperatures adjusting themselves to increase arc voltages when the arc column is contracted radially by increasing gas-flow rate or decreasing inter-electrode diameter.

Keywords: hollow-electrode plasma torch, inter-electrodes, numerical analysis, torch performance(Some figures may appear in colour only in the online journal)

1. Introduction

In recent decades, hollow-electrode plasma torches have been widely used as a high powered heat source in the thermal plasma treatment of various wastes, such as PCBs (polychlorinated biphenyls)containing oil[1,2],municipal solid waste[3,4],and low-level radioactive wastes [5, 6]. By producing ionized hot flames with high temperatures of ＞5000 K even in oxidizing gases[7],this type of plasma torch is advantageous for not only gasification of combustible wastes by pyrolysis or oxidation,but also vitrification of noncombustibles by plasma melting. These features of a hollow-electrode plasma torch that can work with oxidizing gases come from the cold-well type of cathode primarily made of copper or copper alloys [7, 8]. However, these relatively low melting-point metals require not only current limitation(＜1-2 kA)but also arc-root movement using a vortex gas injection [7, 8] in order to secure an electrode lifetime for practical applications. As a result, hollow-electrode plasma torches show the unique dynamic behaviors of arc voltages caused by the arc-root movement on the surface of the cold-well type cathode, resulting in the continuous fluctuation of the plasma flame. In addition, high gas flow rates for vortex gas injection often make it difficult to produce plasma flames with a specific enthalpy higher than 10 MJ kg?1[9].

In order to obtain stable plasma flames with high specific enthalpy, inter-electrodes (hereinafter referred to as IEs) can be inserted between the cold-well type cathode and the cylindrical anode of a conventional hollow-electrode plasma torch,as introduced in the patent of SKF Co.[10].First of all,the insertion of electrically insulated IEs can allow highvoltage operation of the torch by forcing the arc column to extend as long as the IE length.The high-voltage operation is advantageous for scaling up the operation power level under the current limitation (≤1-2 kA) of copper or copper-alloy electrodes, permitting the extension of electrode service lifetime. In addition, the elongated arc column can alsocontribute to increasing the specific enthalpy of the plasma flame by heating up the injected gases for a longer time before they exit the torch[10].Accordingly,the insertion of IEs can bring a high-voltage/high-power operation mode together with high thermal efficiency to the conventional hollowelectrode plasma torch, allowing it to have a long electrode lifetime as well as a high specific enthalpy plasma jet.Although these advantages were revealed in the patent of SKF Co. [10] in the 1980s, there have been few papers that show the effects of IE insertion through numerical simulations.

Table 1.Design parameters for numerical analysis of hollowelectrode plasma torches with IEs.

In this work, we present numerical results about these effects of IE insertion on the torch performance and thermal flow fields of a hollow-electrode plasma torch. By predicting the torch performance according to the IE insertion, our numerical work can be expected to help in designing and improving this type of plasma torch for actual applications,such as the thermal plasma treatment of hazardous wastes.

2. Numerical modeling

2.1. Torch geometry, numerical methods, and basic assumptions

Figures 1(a)and(b)show the electrode configuration and the computational domain of a hollow-electrode plasma torch with IEs employed in the numerical work.In these figures,the presented plasma torch has three IEs, designated as first IE,second IE, and third IE, between the hollow cathode and cylindrical anode. In order to investigate the effects of IE insertion, however, numerical analyses were conducted by changing the number of IEs from one to three.

In figure 1, the plasma-forming gases are injected into the plasma torch through the gaps between electrodes.Considering that the gaps are distributed with the addition of IEs, plasma-forming gases were labeled after the left electrode name of the gap. For example, in figure 1(a), cathode gas with a flow rate of Gc is introduced into the torch through the gap between the cathode and the first IE. In addition, the cathode, first IE, second IE, and third IE andanode are assumed to be electrically insulated from each other. By inserting these electrically insulated IEs, the arc column can be elongated forcibly as shown in figure 1(a),illustrating the electrical connections together with the arc column between the front anode and rear cathode. In the actual system, as indicated in this electrical connection, the first IE can be used as an intermediate electrode for easy ignition [10]. For example, the arc can ignite between the cathode and the first IE when the switch is closed in figure 1(a),and the arc jet can be formed.Depending on the arc current and gas injection conditions,the generated arc jet can touch the anode surface,allowing a small amount of arc current to flow through the anode. Then, for the two arc currents flowing through the first IE and anode, a power control system (not seen in figure 1(a)) can be designed to raise up the ratio of arc current through the anode by gradually opening the switch connected to the first IE. Finally,if the power supply opens the switch completely, the long arc column can be obtained between the rear cathode and front anode.

Table 2.Operation conditions for numerical analysis of hollowelectrode plasma torches with IEs.

The details of torch dimensions and operating conditions illustrated in figures 1(a) and (b) are summarized in tables 1 and 2, respectively. The computational domain was divided by rectangular grids. All governing equations are discretized by the finite-volume method (FVM) and calculated using the SIMPLE algorithm [11]. Finally, the following assumptions were used for the present numerical modeling work:

(1) Steady, 2D axisymmetric thermal plasma.

(2) Negligible displacement current in the plasma.

(3) Optically thin plasma.

(4) Local thermodynamic equilibrium (LTE).

(5) Incompressible nitrogen plasma at atmospheric pressure.

2.2. Governing equations

As a thermal fluid flow,arc plasma inside the hollow-electrode plasma torch can be described by the MHD (magnetohydrodynamic) equations combining the well-known conservation equations for mass, momentum, and energy with the electric potential equation inside the torch. In addition, the turbulent effects in the arc plasma can be included by selecting the appropriate turbulence model and adding the related equations to the MHD equation. In this work, we used a standard K-ε turbulence model, which was reported to produce reasonable results when simulating the arc plasma generated in the cylindrical electrodes [12]. These governing equations are expressed in the steady state, axisymmetric cylindrical coordinates as follows:

(1) Conservation of mass

(2) Conservation of momentum

· Axial component

· Radial component

· Azimuthal component

(1) Conservation of energy

(2) Electrical potential equation

(3) Standard K-ε turbulence model

In the above equations, u, v, and w are the axial, radial, and tangential components of the velocity vector of the arc plasma.The terms ofρ,p,and μ represent the mass density,pressure and viscosity, respectively. The body forces Fzand Frin the momentum conservation equations (equations (2) and (3))indicate the axial and radial components of the Lorentz force,respectively, which are exerted on the arc currents by the selfinduced magnetic field. Gravity is neglected in this work. In equation (5), k, Cp, and h indicate the thermal conductivity,specific heat at constant pressure,and specific enthalpy of the arc plasma,respectively.The Joule heating and volumetric radiation heat loss in equation (5) are represented in terms of P and R0,respectively, where the radiation loss term R0is taken into account by using the net emission coefficient for optically thin nitrogen plasma. Additionally, Poisson's equation for the electrostatic potential φ is used to find the arc current density vector, j, in the arc column. In equation (6), σ is the electrical conductivity, and the axial and radial components of j can be expressed as the derivative forms of the electrostatic potential φ as:

The self-induced magnetic field B by arc current is also obtained from Ampere's law, ?× B =μ0j.From the calculated results of the arc current and the magnetic field, the source terms associated with the Lorentz force and Joule heating can be obtained according to the following equations:

In equations (7) and (8) for the description of a standard K-ε turbulence model, the viscosity term is modified by adding the turbulent viscosity, μt, to the molecular one, μ, defined as follows:

The typical values are allocated to the turbulence constants as Cμ= 0.09, Ck= 1.00, Cε= 1.30, C1= 1.44, and C2= 1.92[13], and the turbulent generation term of G is expressed as:

The thermodynamic and transport properties of nitrogen used for the numerical calculations of these equations can be found in [14].

2.3. Boundary conditions

Table 3 summarizes the boundary conditions used in this work. In a suggested type of plasma torch, plasma-forming gases are normally injected with a swirl to stabilize the arc column along the centerline [10, 15].

In order to describe this swirling injection of plasmaforming gases, we used the swirl number, Sw, defined as the ratio of azimuthal velocity to the radial one, i.e., Sw= w v,/for the boundary conditions at gas inlets as shown in table 3.In this expression of swirl number,the radial velocity v can be calculated from the gas flow rates distributed to each gas inlet as listed in table 2. In addition, the turbulent variables at the gas inlets were calculated by using the following equations,which are widely employed for the numerical modelling of arc plasmas [12, 13].

Table 3 also shows that there is no radial change of velocity, temperature, and turbulent variables caused by the axial symmetry along the central axis(r = 0),whereas,at the torch exit, no axial gradients for those parameters exist,assuming that the arc plasma flow is fully developed. Along the inner surface of the electrodes including the IEs,a no-slip condition and the wall function were used for boundary conditions of flow parameters(u,v,w)and turbulent variables,respectively,together with the constant temperatures as listed in table 3.

For the boundary conditions of the electric potential equation, we used the usual assumptions widely employed in DC arc modeling [12, 15, 16]. For example, the arc current density jsis assumed to have the following exponential distribution at the cathode spot [15, 16].

Here, the exponential coefficient b is chosen to satisfy the

Table 3.Boundary conditions for temperatures, velocities, and turbulent variables.

following equation, indicating that

the arc current I0supplied from the power supply should be equal to the value obtained by integrating the current density jsover the cathode spot area, S. The location of the cathode spot was identified on the surface of the rear electrode as being 25 mm away from the closed end of the rear electrode by cold-gas analysis [16]. At the anode surface of the front electrode in figure 1,the electrostatic potential φ was assumed to be zero,taking into account that the electrical conductivity of the anode (normally Cu) is very high. In the modelling of the conventional DC plasma torch, the position of the anode spot has usually been determined by Steenbeck's minimum principle [16, 17]. As is well known, Steenbeck's minimum principle postulates that the arc length is determined naturally so as to minimize the arc voltage for a given current and boundary conditions. In this work dealing with the IE insertion,however,it is inappropriate to use Steenbeck's minimum principle to determine the anode spot position because the arc length is forced to be elongated by the electrically insulated IEs.Taking into account this difficulty in determining the arc lengths,we did not consider the formation of the electric spot on the anode surface in this work. In other words, Poisson's equation for φ(equation(6))can be solved with the boundary conditions at the anode for φ = 0 and the cathode for equation (15). According to equations (6) and (9), the calculated results for φ produce not only arc current density vector, j, but also the Joule heating, P, in the computational domain. From the computed Joule heating, plasma input power, P0(kW), can be calculated at a given arc current and other simulation conditions, such as gas flow rates and torch dimensions. In addition to plasma input power, design criteria, such as average specific enthalpy at torch exit, H0(kJ kg?1)and torch efficiency,η(%),can be also obtained.Here,H0and η are defined as the ratio of total enthalpy at torch exit to the mass flow rates of nitrogen and P0, respectively.Finally, no arc current flows through the gas inlets and the IEs, since they are electrically insulated.

3. Results and discussion

3.1. Effects of IE insertion

Figures 2(a)-(c)show the calculated temperature fields of N2arc plasma simulated in the plasma torches with three different lengths of IEs, L0= 250 mm, 370 mm and 490 mm,corresponding to the number of the inserted IEs, 1, 2 and 3,respectively. These numerical results were obtained for the operating conditions of I0= 600 A and the gas-flow rates listed in table 2 with Sw= 3.0. In this figure, first, hightemperature regions of ≥10 000 K were observed to extend in the axial direction proportional to the number of the cylindrical IE. Considering that the nitrogen is ionized in earnest higher than 10 000 K, the axial extension of the high-temperature regions can be regarded as an extension of the arc column, resulting in the elevation of arc voltages by the insertion of the IE. This increase of arc voltages can be confirmed in table 4, which presents the main numerical results for three hollow-electrode plasma torches used to obtain figure 4.From table 4,one can see that the arc voltages are increasing at the rate of ～1.4 V mm?1with the increase of the total IE length L0.Because of this increase of arc voltages,it can also be observed that the plasma powers are increasing proportionally to L0. With the increase of plasma powers, H0and η were calculated to be elevated, as presented in table 4.These improvements in thermal efficiency and average specific enthalpy at torch exit can be attributed to the additional N2injected through the gaps between the existing IEs and the newly inserted ones.

As presented in table 2 and figure 1,the total flow rate of plasma-forming gas was designed to be increased with the increase in the number of IEs by injecting additional N2through the gaps between the existing IEs and the newly inserted ones.Consequently,the raising of arc voltages by the insertion of IEs can be used to ionize this additionally injected N2, which increases not only the plasma power but also the efficient heating of plasma-forming gases shared by the gaps between IEs.

3.2. Effects of gas-flow rates

Figures 3(a)-(c)show the calculated temperature fields of N2arc plasmas inside the plasma torch with three IEs(L0= 490 mm)for three different gas flow rates of Gin= 750 slpm,900 slpm,and 1050 slpm with Sw= 3.0.Each value of Ginrepresents the summation of the flow rates of gas injected through the gaps between electrodes, as listed in table 2. In addition, table 5 shows the main numerical results for three cases of figures 3(a)-(c). From the comparison between figures 3(a)-(c), when Gin= 750 slpm, the temperature region of ≥10 000 K corresponding to arc column is diminished in the section of the third IE(0.1 m ≤ z ≤ 0.2 m).With the increase of total gas-flow rate Gin, however, the arc column was heating up to ≥10 000 K in the section of third IE,as shown in figures 3(b) and (c). This heating up and of arc column with the increase of Ginis to balance the generation and removal of not only heat but also charged particles in the arc column [18].

Table 4.Calculation results for three different IE lengths (L0) and gas-flow rates (Gin) at a fixed arc current I0 = 600 A and the swirl number of Sw = 3.0.The gas flow rate Gin depends on L0 because of the torch structure, as listed in table 2.

As explained by Pfender et al for example, if the gasflow rates of G1,G2,and G3are increased in figure 1,the arc column surface is cooled even more in the section of the third IE, increasing the loss of charged particles together with the heat loss toward the wall of the third IE. In order to compensate for these increasing losses of charged particles and energy, the ionization rate and heat generation in the arc column should be increased by raising the arc voltages [18, 19].

Figure 4 shows how the plasma temperatures adjust themselves to meet these requirements for increasing not only the ionization rate but also heat generation by raising the arc voltage. In this figure, which shows the radial temperature profiles of arc plasma simulated for Gin= 750 slpm and Gin= 1050 slpm, one can see that the high-temperature region of ≥8000 K is expanded widely for Gin= 750 slpm,producing a relatively gradual temperature gradient. However, for Gin= 1050 slpm, the same region of ≥8000 K is contracted toward the center line, where the central temperatures are increased, making the temperature gradient steeper. In other words, if the arc column is cooled down because of the increasing gas-flow rate,the arc column can be contracted, as shown in figure 4, and then the electrical resistance can be increased. Consequently, the arc voltages will be elevated as represented in table 5, increasing the ionization rate as well as the Joule heat generation in the contracted arc column. Thanks to the increase of the ionization rate, first, the loss of charged particles can be compensated for, keeping the self-sustaining discharge condition.Next, with the increase of Joule heat generation, the core of the arc column can be heated up to temperatures higher than 10 000 K, as shown in figures 3 and 4.

Table 5.Calculation results for three different gas-flow rates (Gin)with Sw = 3.0 at a fixed arc current of I0 = 600 A and an IE length of L0 = 490 mm.

Table 6.Calculation results for plasma torches with different IE diameters (D3 = 37 mm and 25 mm) at the fixed gas-flow rate and arc current of Gin = 1050 slpm with Sw = 3.0 and I0 = 600 A,respectively.

Combined with the contraction of the arc column, this increase of central temperatures brings a steep gradient to the temperature fields, allowing for the increase of radial heat transfer in accordance with the greater heat loss.Since the arc was optically thin,radiation heat loss hardly contributes to the radial heat transfer even if, above 8000 K, radiation may be strong. Thus, the radial heat transfer is dominated by the radial diffusion, i.e., the radial temperature gradient, which decreases due to the association of N atoms in the region below 8000 K [20, 21]. As a result, despite a relatively large increase of plasma power, the thermal efficiencyη is slightly changed within 1%for the gas flow rates of Ginbetween 750slpm and 1050 slpm,as listed in table 5,and then the average specific enthalpy at torch exit H0decreases proportionally to the increase in gas flow rate Gin.

Table 7.Calculation results for plasma torch with L0 = 490 mm obtained by varying the arc currents from 400 A to 600 A at a fixed gas-flow rate, Gin = 1050 slpm with Sw = 3.0.

3.3. Effects of IE diameters

Figure 5 compares the temperature fields of N2arc plasmas inside the plasma torch with two different diameters of the second and third IEs of D3= 25 mm and 37 mm. In these numerical results, the arc currents and total gas-flow rates were fixed at I0= 600 A and Gin= 1050 slpm with Sw= 3.0, respectively.

In figure 5, the temperature region of ≥8000 K is expanded more for D3= 37 mm than for D3= 25 mm,although the high-temperature region of ≥10 000 K is reduced. This change of temperature fields depending on IE diameter can also be explained by the behavior of plasma temperatures to balance generation and removal of not only heat but also charged particles in the arc column,as shown in figure 6.In this figure,comparing the radial profiles of plasma temperatures for D3= 37 mm and D3= 25 mm,for example,the central temperatures are decreasing but the temperature region of ≥7000 K is widely expanded with the increase of IE diameter from 25 mm to 37 mm.

By changing the radial profiles of plasma temperatures as shown in figure 6,the arc column can minimize losses of both heat and charged particles, then balance their generation and removal, corresponding to the increase of IE diameter. In addition, although the temperature is as low as 7000 K, the radial expansion of this high-temperature region certainly contributes to the decrease of arc resistance. As discussed in figure 4, accordingly, arc voltage is decreasing in the arc column for D3= 37 mm,and consequently the plasma power can be lowered compared with the one for D3= 25 mm as listed in table 6, in which it should be checked that thermal efficiency is decreasing for D3= 37 mm. As shown in figure 6, the plasma temperatures higher than 6000 K are rapidly falling to the coolant temperature of 300 K near the wall regardless of IE diameter.However,the internal surfaces in the second and third IE sections are increasing with the increase in IE diameter, D3. Accordingly, a relatively large portion of heat is transferred to the wall for D3= 37 mm,despite the decrease in plasma power,leading to the decrease in thermal efficiency.

3.4. Effects of arc current

Table 7 presents the numerical results obtained for a plasma torch with three IEs (L0= 490 mm) by varying the arc currents from 400 A to 600 A at a fixed gas-flow rate of Gin= 1050 slpm with Sw= 3.0. In addition, figures 7 and 8 show the temperature contours in the plasma torch and their radial profiles at z = 0.015 m,respectively,for arc currents of I0= 400 A and 600 A. In table 7, first, plasma power P0is observed to increase proportionally to arc current at the rate ofabout 0.655 kW A?1. Since plasma power P0can be expressed as P0=for plasma resistance Rp,this increase in P0proportionally to I0indicates that Rpis decreasing with the increase of I0. Normally, the electrical conductivity of N2plasma is improved as the plasma temperature is increased[14]. Accordingly, the decrease in Rpseems to be primarily caused by the increase in electrical conductivity because of the increase of plasma temperatures in the arc column, as shown in figures 7 and 8. With the increase of plasma temperature, however, thermal efficiency decreases because of radiation heat loss, as listed in table 7. Despite the reduction of thermal efficiency, however, specific enthalpy is increased because of the elevation of plasma power by the increasing arc current.

Table 8.Calculation results for plasma torch with first IE(L0 = 250)obtained by varying the swirl number from 0.0 to 3.0 at a fixed gasflow rate, Gin = 750 slpm.

3.5. Effects of swirling

Table 8 presents the main numerical results obtained for three different swirl numbers of Sw= 0.0,1.5 and 3.0,respectively,in the plasma torch only with the first IE. The simulated plasma torch corresponds to the one of figure 2(a) with the lengths of IEs, L0= 250 mm and the operating conditions,such as arc current I0and gas flow rates are the same with the values used for figure 2(a). Normally, the elevation of swirl number increases the radius and the electrical conductivity of the arc [22]. These effects can be confirmed in table 8, presenting the arc voltages and the plasma power decreasing with the increase in swirl number at the same operating conditions.However, the exit enthalpy is calculated to be increased with the increase in Sw,which leads to the improvement of thermal efficiency at the same operating condition. For example, the data in table 8 indicate that the swirling injection with Sw= 1.5 increases thermal efficiency by 23.5% despite the decrease of input power by about 2% in the designed plasma torch, as listed in table 5.

The effects of swirl on the radius and the electrical conductivity can also be found in figures 9(a)-(c), showing the temperature contours obtained for three different swirl numbers,Sw= 0.0, 1.5 and 3.0, respectively. From figure 9(a) for Sw= 0.0, for example, it is observed that a cold zone with temperatures lower than 1000 K is formed in the entrance region of the first IE by the radial injection of cold nitrogen gases without a swirl. With the decrease of temperatures in the arc column developed along the center line, however, the plasma gas injection with a swirl reduces this cold zone significantly by expanding the hot region of plasma radially, as shown in figures 9(b) and (c) representing the temperature fields for Sw= 1.5 and 3.0, respectively. As discussed previously, this radial expansion of the hot region brings the increase of electrical conductivity to the arc together with the decrease of maximum temperatures in the arc column,which contributes to lowering the arc voltage along the centerline.

Figures 10(a)-(c) show the contours of azimuthal component,w of arc plasma with different number of IEs and swirl number. For example, figure 10(a) is obtained from the calculation results at Sw= 1.5 for the plasma torch with the first IE while figures 10(b) and (c) illustrate the results computed at Sw= 1.5 and 3.0, respectively, for the plasma torch with first, second and third IE.

From the comparison between figures 10(a) and (b), the swirl velocity field spreads from the cathode gas inlet to the next electrodes along the surface of the first IE. However, it decays rapidly in the first IE,then disappears in the section of the second IE for the plasma torch with three IEs,as shown in figure 10(b). Since the swirl velocity field provides the stabilizing radial force against the kink instability in the arc[22],it is important to keep the swirl flow field along all sections of IEs when operating this type of plasma torch. Accordingly,the effect of swirl number needs to be investigated together with optimum gas flow rates injected through the gaps between electrodes. For example, figure 10(c) shows that the swirl velocity field can be kept along the surfaces of three IEs by increasing the swirl number up to 3.0.

4. Conclusions

In this work,we investigated the effects of IE insertion on the performance characteristics of a hollow-electrode plasma torch, such as arc voltage, plasma power, and thermal efficiency, by using numerical analysis. First, the numerical results demonstrated that arc voltage is elevated proportionally to the number of inserted IEs,resulting in the increase in plasma power at fixed arc current.In addition,when the gases are injected additionally through the gaps between IEs,it was found that thermal efficiency can be improved simultaneously with the increases in arc voltage and plasma power.

The numerical results for temperature fields inside the torch revealed that these unique performance characteristics primarily come from the structural advantages of IE insertion,which allows for the injection of additional gases through gaps between the IEs, together with the increase in arc voltages. For example, the additionally injected gases can cool down the arc column and contract it radially, increasing arc resistance.As a result,the arc voltage can be increased a little more to balance between the generation and the removal of heat and charged particles in the arc column, leading to the increase in not only plasma power but also thermal efficiency.However, the increases in only arc currents without the addition of plasma gases or IEs were calculated to cause no increase in arc voltages, and accordingly, the thermal efficiency decreased, as expected in the conventional hollowelectrode plasma torches. In addition, numerical results revealed that the increase in swirl number can also improve thermal efficiency by increasing exit enthalpy despite decreasing arc voltages at the fixed arc current and gas flow rate.

It should be noted that in long arcs with a length larger than the radius,such as the arc column formed in figure 1(a),deviations from LTE or LCE (locally chemical equilibrium)can be common rather than exceptional, meaning that the thermal flow fields of arcs can be different from those computed using the LTE model.As investigated by Wu et al[21],however,the non-LCE effects are negligible in the arc column with a temperature of ≥8000 K,where most of the arc voltage is calculated. Accordingly, the numerical results obtained from the LTE model can be used to estimate the effects of IE insertion on the torch performance, such as arc voltage and plasma power, despite the inability to describe the non-LCE effects.

By optimizing these performance characteristics according to the IEs'insertion,we expect that a hollow-electrode plasma torch with IEs can be applied to many practical applications requiring high power and high efficiency operation,such as the thermal plasma treatment of hazardous wastes.

Acknowledgments

This research was supported by the Technology Development Program to Solve Climate Changes of the National Research Foundation(NRF)funded by the Ministry of Science and ICT(NRF-2016M1A2A2940152).

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