Acta Polytechnica Acta Polytechnica 53(2):189–192, 2013 © Czech Technical University in Prague, 2013 available online at http://ctn.cvut.cz/ap/ ATMOSPHERIC ARGON FREE BURNING ARCS WITH A SIMPLIFIED UNIFIED MODEL USING CFD-ARC MODELING Won-Ho Leea, Jong-Chul Leeb,∗ a Graduate School of Automotive Engineering, Gangneung-Wonju National University, Republic of Korea b School of Mechanical and Automotive Engineering, Gangneung-Wonju National University, Republic of Korea ∗ corresponding author: jclee01@gwnu.ac.kr Abstract. Free burning arcs, where the work piece acts as an anode, are frequently used for a number of applications. Our investigation is exclusively concerned with a simplified unified model of arcs and their electrodes under steady state conditions at atmospheric pressure. The model is used to make predictions of arc and electrode temperatures and arc voltage for a 200 A arc in argon. The computed temperatures along the axis between the cathode tip and the anode surface compare well the measured data. Keywords: free burning arcs, thermal plasmas, arc modeling, arc-electrode interaction, computational fluid dynamics. 1. Introduction High pressure arcs (also known as thermal plas- mas) have been used for cutting, welding, spray- ing, coating, material heating and melting, lighting, current interruption, and, more recently, for waste disposal, production of fine particles, and thermal plasma vapor deposition [7, 10]. Two methods, one is a DC arc discharge and the other an inductively coupled discharge, are used for generating thermal plasmas, and the DC arc torches have been widely modified due to their simplicity for applications. There are two types of DC arc torches, transferred arc and non-transferred arc, by the configuration of elec- trodes. It has been studying on high-power DC arc torches for transferred arc (also known as free burn- ing arc) because the arc energy is directly deposited on the treated materials acting as anode with high heat transfer efficiency in free burning arc plasma systems [2]. Thermal plasmas are usually at atmospheric pres- sure or above. The very frequent collisions between particles of different species within the arc ensure the attainment of a single temperature for all species. For such a plasma, local thermodynamic equilibrium (LTE) usually holds, and computer simulation based on LTE can usually predict satisfactorily the bulk properties (i.e. the arc column) of the arc plasma. For understanding the basic physical processes oc- curring in free burning arcs there have been con- ducted several computations with comparing the re- sults to the temperature measurements of an arc col- umn successfully [4, 1]. However, the accuracy of com- putations is insufficient for the anode region because there is severe departure from LTE. It is very impor- tant to predict precisely the temperature of anode region in free burning arcs. The quality and the effi- ciency of a process depend on the energy flux going into the work piece which acts as anode. Our investigation is exclusively concerned with ar- gon free burning arcs under steady state conditions at atmospheric pressure by computational fluid dy- namics (CFD) analysis. We are also interested in the energy flux and temperature transferring to the an- ode work piece with a simplified unified model of arcs and their electrodes. In order to determine two thermodynamic quantities such as temperature and pressure and flow characteristics we have modified Navier–Stokes equations to take into account radia- tion transport, electrical power input and the elec- tromagnetic driving forces with the relevant Maxwell equations. From the simplified self-consistent solution the energy flux to the anode work piece can be derived. 2. Numerical methods In order to determine two thermodynamic quantities such as temperature and pressure and flow charac- teristics of the free burning arc under steady state we have modified Navier–Stokes equations to take into account radiation transport, electrical power input and the electromagnetic driving forces with the rele- vant Maxwell equations, 1 r ∂ ∂r [ rρvφ−rΓφ ∂φ ∂r ] + ∂ ∂z [ rρwφ−Γφ ∂φ ∂z i ] = Sφ, (1) 1 r ∂ ∂r ( rσ ∂ϕ ∂r ) + ∂ ∂z ( σ ∂ϕ ∂z ) = 0 , (2) where ρ is the gas density, Γφ the diffusion coeffi- cient, Sφ the source term, φ the dependent variables, µ the molecular viscosity, κ the thermal conductivity, ϕ the electrostatic potential and σ the electrical con- ductivity (Tab. 1). The subscript ‘l’ denotes the lami- nar part of the diffusion coefficient and ‘t’ the turbu- lent part. In the energy conservation equation, q repre- sents the net radiation loss per unit volume and time. 189 http://ctn.cvut.cz/ap/ Won-Ho Lee, Jong-Chul Lee Acta Polytechnica Equations φ Γφ Sφ Continuity 1 0 0 Axial w µl + µt −∂p/∂z + JrBθ momentum + viscous terms Radial v µl + µt −∂p/∂r + JzBθ momentum + viscous terms Enthalpy h (κl + κt)/cp σE2 − q + ∂p ∂r v + ∂p ∂z w + viscous dissipation Electrostatic ϕ σ 0 potential Table 1. Definitions of variable, diffusion coefficient, and source term for governing equations. v (m/s) w (m/s) T (K) Sφ DE ** ** 1000 ∂ϕ/∂z = j0/σ EJ 0 win 1123 ∂ϕ/∂z = 0 KG * * ∂h/∂n = 0 ∂ϕ/∂n = 0 GH BC 0 ∂w/∂r = 0 ∂h/∂r = 0 ∂ϕ/∂r = 0 CD ** ** ∂T/∂r = 0 ∂ϕ/∂r = 0 EF 0 0 --- --- FC BH 0 0 --- ϕ = const. HI ** ** 1000 --- AI Table 2. Boundary conditions for the temperature and the electric potential. The viscous terms in the momentum and energy equa- tions which are not included in the diffusion coefficient are treated as their respective source terms. Ohmic heating σE2 is providing heat source and Lorentz force J × B is providing momentum source. In addition, the current density and the magnetic field are calcu- lated from the electrostatic potential and Ampere’s law, respectively, and can be written as jr = σ ∂ϕ ∂r , jz = σ ∂ϕ ∂z , (3) 1 r ∂ ∂r (rBθ) = µ0jz , (4) where Bθ is the azimuthal component of the magnetic field and µ0 the permeability of free space. Thermodynamic and transport properties such as density, enthalpy, constant pressure specific heat, vis- cosity, electrical and thermal conductivities, and opti- cally thin radiation losses required for this calculation are strongly dependent on temperature and pressure. The data adopted in this study have been taken from Refs. [8, 9]. The boundary conditions required for the solution of Eqs. 1 and 2 are listed in Tab. 2. From Tab. 2, j0 is the total current divided by the uniform cross section of the cathode and ‘n’ denotes the normal di- rection to a surface. Symbol ‘*’ denotes the pressure is Figure 1. Schematic of a free-burning arc plasma system for experiments performed by Haddad and Farmer [3]. set at 0.1 MPa and symbol ‘**’ denotes the locations where velocities do not need to be specified. The given inlet flow conditions correspond to those investigated by Haddad and Farmer which is 0.5 l/min [3]. Sym- bol ‘---’ indicates that the solid surface temperature is calculated. Energy transport within the solid electrodes is gov- erned by conduction. The energy conservation equa- tion for steady state case can be written as −∇· (km∇Tm) , (5) where km and Tm are respectively the thermal con- ductivity and temperature of the electrode material. 3. Results and discussion The argon arc burns at atmospheric pressure in a 5 mm gap between a shaped cathode and a water-cooled copper anode as shown in Fig. 1 (commonly known as the point-plane arc), where the key locations in the computational domain are indicated by let- ters A to I. The tungsten cathode has a rod diameter of 3.2 mm and its tip has a full conical angle of 60◦ [3]. Temperature distribution in the arc can be predicted by including the electrodes in the solution domain without the inclusion of the non-LTE sheaths. The experimental arrangements and the experimen- tally measured arc temperature of Farmer and Had- dad [3] have become a benchmark for theoretical stud- ies of argon free burning arc. The argon gas with a temperature of 1000 K and a pressure of 0.1 MPa is fed in through an annular nozzle at a fixed flow rate of 0.5 l/min. The comparison between the simulation result and the experimental measurement was given for the arc current of 200 A. The two-dimensional temperature and axial veloc- ity fields are shown in Fig.2. The temperature in the arc region presents the typical bell shape of high intensity arcs. The present results for 200 A, com- pared with those of [3, 11] given in brackets, were maximum arc temperature 24 300 K (23 700 K), max- imum axial velocity 500 m/s (500 m/s) and arc volt- age 10.5 V (12.9 V). The temperature near the cath- ode is high because of contraction of arc column 190 vol. 53 no. 2/2013 Atmospheric Argon Free burning Arcs (a) Temperature (b) Axial velocity Figure 2. Temperature [unit: K] and axial velocity [unit: m/s] fields for a 200 A free burning argon arc at 1 atm under the experiment conditions of Haddad and Farmer [3]. near the cathode spot. The magnetic pinch effect induced by the arc current creates an over pressure near the cathode. Since the arc temperature is very high, a small pressure difference will accelerate the arc- ing gas to a high speed, typically a couple of hundred meters per second. There is a very thin, high ve- locity core (Fig. 2b) in the arc column. The half width of the radial profile of axial velocity, defined as the radial position at which the velocity is re- duced to 50 % of the axis velocity at the mid-gap (2.5 mm from the cathode tip), is 0.4 mm. Such a nar- row high velocity core is typical of laminar arc plasma flow for which viscous effects are negligible. The en- ergy transport is dominated by convection and radia- tion in the core region near the axis. However, the tur- bulent model is essential to predict flow characteristics near cathode and anode due to separation and stagna- tion, respectively [5]. According to the above compara- tive data, our simulation results match well with other measured and predicted data given by [3, 11]. Figure 3 shows the detailed comparisons with the temperatures along the axis. The experimental data of [3] for an arc under same conditions are also plotted in Fig. 3. The temperature near the cathode is higher than that near the anode because of contraction of arc column near the cathode spot. The differences between these two sets of results are not significant and there is good agreement. Figure 3. Comparison of the predicted temperature (solid lines) along the axis between the cathode tip and the anode surface with the experiment results (symbols) of Haddad and Farmer [3] for a 200 A argon arc at 1 atm. Figure 4. Temperature and isotherm lines for a 200 A argon arc at 1 atm. In anode, outer isotherm, 1400K, interval 25 K for the temperature range 1000 ÷ 1400 K, whereas interval 1000 K is for the temperature range 1000 ÷ 23 000 K in arc column. In Fig. 4 we now present the computed isotherm lines for the part of anode. The temperature reaches a maximum of 1365 K in the anode, which shows good agreement with the results by Lago et al. [6]. From this value, we can predict the presence of a liq- uid metal pool in the anode and the presence of metal vapours in the plasma because it is greater than the melting point of cooper (1357 K). Therefore, further investigation should include the modelling of Cu evaporation from anode and non-LTE situation near electrode for more realistic calculations. 4. Conclusions In this study, we have carried out computational inves- tigation of argon free burning arcs under steady state conditions at atmospheric pressure with a simplified unified model of arcs and their electrodes. It was found that the computed temperatures along the axis be- 191 Won-Ho Lee, Jong-Chul Lee Acta Polytechnica tween the cathode tip and the anode surface show good agreement with those measured by Haddad and Farmer [3]. For the maximum axial velocity, the predicted value of 750 m/s from our simulation results matches well with the predicted value given by Zhu et al. [11]. In addition to the arc column, the temperature distribution in the anode also shows good agreement with the results by Lago et al. [6]. This knowledge of free burning arc features can play a role in developing the atmospheric plasma systems, however, further investigation should include the mod- elling of Cu evaporation from anode and non-LTE sit- uation near electrodes for more realistic calculations. Acknowledgements This research was supported by Basic Science Research Program through the National Research Foundation of Ko- rea (NRF) funded by the Ministry of Education, Science and Technology (2012-0007808). References [1] R. Bibi, M. Monno, M. I. Boulos. Numerical and experimental study of transferred arcs in argon. J Phys D: Appl Phys 39(15):3253–3266, 2006. [2] W. H. Gauvin. Some characteristics of transferred-arc plasmas. Plasma Chem and Plasma Processing 9(1):65S–84S, 1989. [3] G. N. Haddad, A. J. D. Farmer. Temperature determinations in a free-burning arc. I. 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A comparison of treatments of diffusion in thermal plasmas. J Phys D: Appl Phys 29(7):1922–1932, 1996. [10] E. Pfender. Thermal plasma technology: Where do we stand and where are we going? Plasma Chem and Plasma Processing 19(1):1–31, 1999. [11] P. Zhu, J. J. Lowke, R. Morrow. A unified theory of free burning arcs, cathode sheaths and cathodes. J Phys D: Appl Phys 25(8):1221–1230, 1992. 192 Acta Polytechnica 53(2):189–192, 2013 1 Introduction 2 Numerical methods 3 Results and discussion 4 Conclusions Acknowledgements References