Numerical Modeling of Hybrid Stabilized Electric Arc ... - IEEE Xplore

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IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 32, NO. 2, APRIL 2004

Numerical Modeling of Hybrid Stabilized Electric Arc With Uniform Mixing of Gases Jiˇrí Jeniˇsta

Abstract—The paper is concerned with numerical modeling of an electric arc in the plasma torch with combined stabilization of arc by gas and water vortex. The axisymmetric model includes the arc discharge area between the outlet nozzle for argon and the outlet nozzle of the hybrid plasma torch. It is proved that the addition of argon increases the plasma velocity but does not influence substantially the plasma temperature. The outlet velocities exhibit the maximum difference up to 3000 ms 1 for 500 A, regarding a water-stabilized plasma torch. Transition to supersonic flow in the axial discharge region near the outlet occurs as a result of higher velocity and lower temperature for 500 A. The calculated velocities, temperature, and electron concentration profiles exhibit good agreement with experiments. Index Terms—Arc, hybrid torch, hybrid (water-vortex) stabilization, mass flow rate.

I. INTRODUCTION

A

TMOSPHERIC pressure thermal plasma jets are utilized in several plasma processing technologies like plasma spraying, waste treatment, plasma cutting, plasma synthesis, or decomposition of persistent chemical substances. In commonly used plasma torches, the arc is stabilized by gas flow along the arc column [1], [2]. An alternative to gas stabilization is stabilization of arc by water vortex, in which the stabilizing wall is formed by the inner surface of the water vortex which is created by tangential water injection in the arc chamber [3], [4]. Evaporation of water is induced by the absorption of a fraction of Joule power dissipated within the conducting arc core. Further heating and ionization of the steam are the principal processes which produce water plasma. The continuous inflow and heating lead to an overpressure and plasma is accelerated toward the nozzle exit. The arc properties are thus controlled by the radial energy transport from the arc core to the walls and by the processes influencing evaporation of the liquid wall. Water plasma torches exhibit higher input powers and lower mass flow rates ( 200 kW, 0.3 gs ) than gas stabilized arcs ( 50 kW, 3 gs ). This implicates special performance characteristics of water plasma torches; i.e., high-outlet velocities, temperatures, plasma enthalpy, and, namely, high-powder throughput, compared to gas-stabilized torches [5]. The arcing medium, water, is cheap and available in contrast to some gases used in gas torches like Ar, He, N or H . A relative disadvantage of water torches is that water plasma mixed with the ambient atmosphere creates a corrosive environment for some plasma apManuscript received August 31, 2003; revised November 27, 2003. This work was supported by the Grant Agency of the Czech Republic under Projects 202/02/1027 and 202/01/1563. The author is with the Institute of Plasma Physics of the Czech Academy of Sciences, 182 21 Prague, Czech Republic (e-mail: [email protected]). Digital Object Identifier 10.1109/TPS.2004.826143

plications. At the present time, the major industrial application of a water-stabilized arc is plasma spraying [6]–[10] using metallic or ceramic powders injected into the plasma jet. However, this kind of arc was successfully designed in for plasma cutting [11]. Waste treatment and chemical vapor deposition appear these days as perspective applications [12], [13]. Basic physical processes of water-stabilized arcs are similar to the processes in the arcs dominated by the ablation of solid wall, known from applications in circuit breakers or plasma sources of electrothermal launchers [14]–[22]. The arc region and the vapor sheath with ablation of material are treated separately in the two-zone model [14]–[19]. Advanced computational fluid dynamic codes [20]–[22] have been successfully applied to calculate complex flow phenomena, including ablation of the wall and arc turbulence. A two-dimensional axisymmetric model of the water-stabilized electric arc for the description of plasma inside and outside of the discharge chamber was elaborated by Kotalík [23], [24]. The model based on the combined finite elements and finite volume methods enabled us to calculate properties of the discharge and of the plasma jet, as well as the interaction of plasma with powder particles injected into the plasma jet and the nozzle shape optimization, regarding the outlet plasma temperature and velocity. The influence of a virtual anode position on arc parameters was studied in [25]. References [26]–[28], published previously by the author, describe the numerical model of the discharge region of a water-vortex stabilized electric arc. The results of the computer simulation presented here concern the thermal, fluid dynamic, and electrical characteristics for the currents 300–600 A. A combination of gas and vortex stabilization has been utilized in the so-called hybrid stabilized electric arc (Fig. 1). In the hybrid H O–Ar plasma torch, the arc chamber is divided into the short cathode part, where the arc is stabilized by tangential argon flow, and the longer part is water-vortex stabilized. This arrangement not only provides additional stabilization of the cathode region and protection of the cathode tip, it also offers the possibility of controlling plasma jet characteristics in a wider range than that of pure gas or liquid stabilized torches [29], [30]. The arc is attached to the external water-cooled rotating disc anode a few millimeters downstream of the torch orifice. Experiments made on this type of torch [29] showed that plasma mass flow rate, velocity, and momentum flux in the jet can be controlled by changing mass flow rate in the gas-stabilized section, while thermal characteristics are determined by processes in the water-stabilized section. This paper presents our first model dealing with calculation of characteristics of the arc with hybrid stabilization and originates from our previously published works [26]–[28]. It was

0093-3813/04$20.00 © 2004 IEEE

ˇ JENISTA: NUMERICAL MODELING OF HYBRID STABILIZED ELECTRIC ARC WITH UNIFORM MIXING

Fig. 1.

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Principle of hybrid plasma torch with combined gas (Ar) and vortex (water) stabilizations.

experimentally proved [31] that argon and water plasmas do not mix homogeneously, or uniformly, in the plasma jet and near the orifice, i.e., the ratio of mole fractions of different Ar to water species is not a constant within the discharge and the ratio also changes with arc current. It can be deduced that argon and water do not create a uniform mixture within the discharge chamber, too; nevertheless, in this simulation we neglect the effect of mixture nonuniformity. The domain for numerical calculation is shown in Fig. 1 by a dashed line and includes the discharge area between the outlet nozzle for argon and the outlet nozzle of the hybrid plasma torch. II. PHYSICAL MODEL

and argon gases. Since a relatively poor mixing of the argon and water plasma is observed in experiments, turbulent phenomena in the discharge chamber need not be very strong. Assumption 3) of a complete (uniform) mixing is a simplification of a reality, and in the future works it will be necessary to treat the argon and water vapor as separate gases. At this stage of the very first model of the hybrid torch, we intended to test the accuracy of this simple model to the experimental data rather than to present an advanced model of the hybrid torch. The set of governing two-dimensional equations in space is written for computer implementation in an axisymmetric cylindrical system of coordinates and can be expressed as follows. Continuity equation

A. Assumptions and the Set of Equations The following assumptions for the model are applied: 1) the model is two dimensional; 2) the plasma flow is laminar and compressible; 3) argon and water creates a uniform mixture in the arc chamber; 4) argon-water plasma itself is in local thermodynamic equilibrium; 5) gravity effects and viscous dissipation are negligible; 6) the magnetic field is generated only by the arc itself; 7) the net emission coefficient for radiation losses is employed. The model is two dimensional with an axisymmetric tangential velocity component . A swirl movement has little effect on time-averaged characteristics of the electric arc and power balance of the discharge but is important for the plasma jet stability [26], [32]. The introduction of argon increases axial velocity of the jet but will not influence the arc stability as far as the tangential velocity is high enough to ensure stable arc operation. The assumption of laminar flow 2) is based on experiments, showing the laminar structure of the plasma flowing from the discharge chamber. This result has been proved for currents up to 600 A. It is apparent from the present calculation that the Reynolds number based on the outlet diameter for 6 mm reaches in the axial region 13 000 and decreases to 300 near the radius of 3.3 mm for 500 A. The type of flow within the discharge chamber can be questionable due to mixing of water

(1) Momentum equations

(2)

(3)

(4)

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Energy equation

(5) Charge continuity equation (6) where and are the axial and radial coordinates, , , and are the axial, radial, and tangential components of the velocity, respectively, is the mass density, is the pressure, is the temperature, and are the axial and and radial components of the current density, are the axial and radial components of the electric field strength, is the electrical potential, is the Boltzmann constant, and is the elementary charge of the electron. The transport properties of atmospheric pressure argonwater plasma shown here are the thermal conductivity , the electrical conductivity , the dynamical viscosity , the thermodynamic properties are the mass density , and the specific heat under constant pressure . Radiation losses from the argon-water arc plasma are included through the , which is a function of local net emission coefficient temperature with optical thickness corresponding to the discharge radius of 3.3 mm. This radiation model has been applied, for example, in [26]. In the expected range of the Mach numbers 0.3–1, compressible effects are presented in the momentum equations by the terms

and in the energy equation by the compression work terms . Calculations carried out with the viscous dissipation term in the energy equation for 200, 350, and 500 A proved that the effect of viscous dissipation is negligible; the maximum differences in the outlet temperatures, velocities, electrical potentials are below 0.4%. For this reason, the viscous dissipation term in the energy equation was omitted. B. Properties of Argon-Water Plasma Mixture The transport and thermodynamic properties of argon and water plasma were calculated rigorously from the kinetic theory. For argon, the mass density , the specific heat under constant pressure , and the sonic velocity were taken from [33] and the thermal conductivity , the electrical conductivity , and the dynamical viscosity from [34]. For water plasma, the transport and thermodynamic properties are based on the results pubfor the relished in [35]. The net emission coefficients quired arc radius of 3.3 mm for both argon and water plasmas were interpolated from the values for the 2- and 5-mm-thick arc [36], [37].

For determination of the transport and thermodynamic properties and the net emission coefficient of the mixture argon-water, we applied linear mixing rules for nonreacting gases based either on mole or mass fractions of argon and water species. The electrical conductivity, thermal conductivity, and the net emission coefficient were mixed using mole fractions while the mass density, specific heat under constant pressure, enthalpy, and the sonic velocity were mixed using mass fractions [38]. The dynamical viscosity was calculated using Wilke’s approximation [39]. The impact of the assumption of a uniform (or complete) mixing on the arc performance should be evaluated from differences between argon and water properties. Thermal conductivity of water is much higher than that of argon. In the axial regions of the arc, where argon dominates, this assumption overestimates thermal conductivity. In arc fringes, where water plasma is abundant, thermal conductivity is underestimated. This results in lower plasma temperatures in the axial regions but higher temperatures in the outer regions of the arc. Net emission coefficient for agon, according to [36], is higher (lower) than that of water for temperatures below (above) 12 000 K. The consequence of this temperature dependence is an increase of radiation losses within the whole discharge and, of course, a decrease of temperature. Dynamical viscosities of argon and water are close enough so that averaging based on mole fractions using Wilke’s approximation provides a good estimate of the dynamical viscosity of a mixture. Electrical properties of the hybrid discharge should not depend on the assumption of a uniform/nonuniform mixing in a significant manner since the electrical conductivities of both gases are very close. From this qualitative consideration it comes out that the assumption of uniform mixing will underestimate temperature and velocity in the axial region. C. Boundary Conditions, Numerical Scheme, and Method of Calculation The calculation region and the corresponding boundary conditions are presented in Fig. 2. The dimensions of the two-dimensional cylindrical-symmetry region are, respectively, mm and mm for the radius and the length. These dimensions agree with the hybrid torch experimental are the axial, radial, and tangential setup. Here, , , and components of velocity. (a) Inlet surface (AB) is represented by the nozzle exit for argon. Along this surface, we assume no slip conditions for the radial and tangential velocity components, i.e., m s . Because of the lack of experimental data (no measurements of either temperature distribution or current density inside the discharge chamber are available in our group), we prescribe different forms of temperature profiles and magnitudes of the electric field strength. Numerical results showed a weak dependence of the form of the temperature profile on the overall solution (maximum a few per cent difference). That is why we decided to calculate the temperature profile and the electric field strength iteratively from the Elenbaas–Heller equation to obtain the prescribed level


Fig. 2.

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Discharge area geometry. Dimensions of the outlet nozzle are X = 6 mm (axial direction) and 0.3 mm (radial direction).

of the current, before the fluid-dynamic calculation itself. This approximation means that we assume the thermally fully developed region at AB. The inlet velocity profile for argon plasma is precalculated from the axial momentum equation under the assumption of fully developed flow. (b) Axis of symmetry (BC): The zero radial and tangential velocities and symmetry conditions are specified here. (c) Arc gas outlet plane (CD): The outlet velocity profile is determined approximately from the condition of conservation of the total mass flow; this is the standard procedure applied in the numerical code we are using. The zero electrical potential (the reference value) and zero axial derivatives of temperature, radial, and tangential velocities are also defined at CD. (d) Water vapor boundary and outlet nozzle (DA): Along this line, we specify the so-called “effective water vapor boundary” with a prescribed temperature of water vapor 773 K. This is our numerical simplification of the more complex physical reality assumed near the phase transition water-vapor in the discharge chamber. It was experimentally proved [32] that the water movement induces the fluctuations in the arc and in the plasma jet which are probably caused by small asymmetry of the vortex in the arc chamber. The shape of the phase transition can thus depend on the tangential coordinate and can be a function of time (fluctuation). The structure of the transition is also not known and it is not included in the physical model. Various irregularities in the transition such as splitting of the phase transition (i.e., transition: water vortex-vapor-water-vapor) or water drops in the vapor phase can increase complexity of the transition. So far, the structure of the transition was neglected and approximated by the line AD. The same temperature 773 K is ascribed to the outlet nozzle. Of course, the nozzle temperature can change depending on arc current because of different heat fluxes from plasma to the nozzle and the temperature is probably not uniform within the nozzle volume. Such calculations have been performed in [26]. Because of practically zero current density in cold vapor region (no current goes outside of the lateral domain edges), the radial component of the electric field V m at DA. The strength is put zero, i.e.,

Fig. 3. Axial values of temperature and velocity at the outlet (Fig. 2, point C) and the electrical potential drop in the discharge chamber for argon mass flow rate 22.5 sl/min. Outlet axial velocity for the water-stabilized torch is depicted by a dashed line.

magnitude of the radial inflow velocity is assumed to be nonuniform along the axial direction and it is calculated from conduction and radiation heat fluxes at the water vapor surface for the specified mass flow rate according to the procedure reported in [27]. The axial velocity of water vapor at DA is defined as zero, since the evaporation process is not included in the model and no information about axial velocity at this region is known. Nonzero axial velocity at this boundary should influence the results in a negligible manner, since it will be small at this radial position near the evaporation surface. Numerical experiments for 500 A show that differences in the outlet temperatures, velocities, and electrical potential drops are m/s), 0.52% (50 below 0.22% (axial velocity at m/s), and 1.48% (100 m/s) when comparing the case with zero axial velocity at AD. The magnitude of the tangential velocity is estimated from a simplified analytical expressions by Maecker [40] and it is set at 10 ms . The solution of (1)–(6) was carried out by a control volume method, using the both main and staggered grid lines approach, with the iteration procedure SIMPLER [41]. Pressure-density corrections were employed in the pressure and pressure-correc-

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tion equations in the original incompressible SIMPLER code to deal with a compressible flow properly. We elaborated on this compressible modification. Before the start of fluid-dynamic calculation, the generation of transport and thermodynamic properties for the mixture as well as determination of temperature and velocity profiles at AB have to be performed. At first, for a given current and mass flow rate of argon, we know the ratio of mass fractions of argon and water species. Thus, the transport and thermodynamic properties for the mixture can be calculated using a special subroutine. Second, the temperature profile and electric field strength at AB are solved from the Elenbaas–Heller equation for a prescribed current. Finally, the inlet velocity profile is calculated from the axial momentum equation based on the knowledge of the generated temperature profile and dynamical viscosity as a function of temperature. At the start of fluid-dynamic simulation, all these data and boundary conditions are executed. Since the pressure drop and the self-generated magnetic field change during iterations, the inlet velocity profile is reiterated several times in the fluid-dynamic simulation process. The final steady state was reached as a result of a time evolution of the initial state. A nonequidistant main grid with 61 41 points was employed for the axial and radial directions, respectively. III. RESULTS OF CALCULATION Calculations have been carried out for the currents 150, 200, 250, 300, 350, 400, and 500 A. The mass flow rate for the water-stabilized section of the discharge was taken for each current between 300 and 500 A from our previously published work [42], where it was determined iteratively as a minimum difference between numerical and experimental outlet quantities. The resulting values are 0.228 gs (300 A), 0.286 gs (350 A), 0.315 gs (400 A), and 0.329 gs (500 A). For currents lower than 300 A, the mass flow rates were obtained by numerical extrapolation from values for 300–600 A. The argon mass flow rate was varied in agreement with experiments in the interval from 7.5 to 27.5 sl/min, namely 7.5, 12.5, 17.5, 22.5, and 27.5 sl/min. It was proved in experiments that part of argon is taken away before it reaches the torch exit because it is mixed with vapor steam and removed to the water system of the torch. The amount of argon transferred in such a way from the discharge is approximately 50% for currents studied. Since the present model does not treat argon and water as separate gases and the mechanism of argon removal is not included in the model, we consider in the calculations that the argon mass flow rate present in the discharge equals 0.5 times the argon mass flow rate at the torch inlet according to flow-meter data. Axial values of temperature and velocity at the outlet (Fig. 2, point C), the electrical potential drop in the discharge area geometry (the discharge chamber) for the argon mass flow rate 22.5 sl/min, and different currents are shown in Fig. 3. The values of all quantities increase with current as can be expected. Outlet axial velocity for the water-stabilized torch is shown here by a dashed line. The hybrid-stabilized torch provides higher outlet velocities than the water-stabilized one; the differences range from 400 to 3000 ms . Comparison with available experimental data shows a relative difference below 10%.

Fig. 4. Outlet axial temperature, velocity, and the electrical potential drop in the discharge as a function of argon mass flow rate for 300 A.

Fig. 4 illustrates the outlet axial temperature, velocity, and the potential drop in the discharge chamber as a function of argon mass flow rate for 300 A. Since enthalpy of argon is of one order lower that that of hydrogen and oxygen, the outlet plasma temperature remains practically unchanged. The increase of the outlet velocity is obvious due to a higher mass flow rate of argon, while the decrease of the electrical potential can be attributed to power the increase of the arc efficiency (the arc efficiency losses/input power) for higher argon mass flow rates [30]. A comparison of radial profiles of electron density and plasma temperature for 300 A and argon mass flow rate 22.5 sl/min at the torch exit reveals good agreement between calculation and experiment (Fig. 5); a few percent of relative difference occurs in the axial region, but the two sets of numerical and experimental data nearly overlap in the outer arc regions. Electron densities for pure water (argon) plasma were taken from precalculated equilibrium compositions for atmospheric pressure. Electron density for a given mixture argon/water was calculated by mole, i.e.,

where denotes the argon mole fraction. This approach provides a good estimate of electron density for the case shown here. A comparison with the electron density profile obtained from the ADEP program by Pateyron [43] exhibits a good agreement with the present calculation based on the mole fractions. In experiment [31], the temperature was calculated from the ratios of various argon atomic to ionic line emission coefficients by using Saha equation and the measured electron number density. Concentrations of atomic species at the torch exit were determined from emission coefficients of various argon and oxygen line assuming the Boltzmann distribution atomic lines and of atomic level population. Fig. 6 presents input power and power losses from the arc discharge as a function of current. The term input power means the product of current and the potential drop in the discharge chamber. It increased more than five times for the 500 A arc ( 84 kW) with respect to the 150-A value. The power losses


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Fig. 5. Comparison of radial profiles of electron density and plasma temperature between calculation and experiment for 300 A and argon mass flow rate 22.5 sl/min at the torch exit. Electron density profile calculated by the program ADEP nearly overlaps with the present calculation.

Fig. 7. Contours of axial velocity for 200, 350, and 500 A and for argon mass flow rate 22.5 sl/min. 1000 ms corresponds to 1 in the plot.

Fig. 6. Input power and power losses from the arc discharge as a function of current. Power losses are due to the radial conduction and radiation which are two major processes responsible for power losses.

from the arc stand for the radial conduction power and radiation power leaving the discharge, which are considered the two principal processes responsible for power losses. The slope of the power losses practically follows the input power and increases with current. The ratio of the power losses to the input power is indicated as the power losses in a percent scale. For currents higher than 300 A, the amount of power losses is 50%, but as the current decreases the relative amount of losses increases. This behavior is addressed to a higher volume fraction of water species within the discharge for higher currents because of increased mass flow rates of water. Enthalpy of argon-water plasma increases with current and the amount of energy transferred axially increases, i.e., the power losses decreases. Figs. 7 and 8 comprise contours of the axial velocity and temperature for 200, 350, and 500 A and for the argon mass flow rate 22.5 sl/min. Orientation of the plot axes corresponds

to the domain shown in Fig. 2. The axial velocity component (Fig. 7) increases with axial position because of continuous inflow of cold water vapor. Higher velocity gradient at the outlet region is caused by the presence of the outlet nozzle. The temperature contours (Fig. 8) reveal a nearly thermally fully developed region in the central part of the discharge. In contrast to the 200 and 350 A cases, a slight axial temperature dependence is obvious for 500 A. Outlet axial values of the velocity and temperature are displayed at the right-hand side. The corresponding values for water torch are given in brackets below. One can see that relative changes in velocity between the hybrid and water torch are much higher than in the temperature which is in agreement with findings from the experiment. Figs. 9 and 10 depict contours of the Mach number ( ) and overpressure for the same coditions. Distribution of the Mach number in the discharge (Fig. 9) is in accord with the velocity and temperature fields and exhibits a steep decrease in the radial for 500 A in the axial freedirection. It can be seen that . Fig. 10 shows stream region near the outlet overpressure contours in the discharge chamber (overpressure with respect to atmospheric pressure). The reference pressure of 1 atm. is located at the grid point nearest to the nozzle surface at the outlet plane CD (Fig. 2), where the plasma velocity is close to zero. We can see, except for the 500 A case, a monotonous pressure increase from the outlet upstream; the highest pressure gradients occur near the position of the outlet nozzle edge. Distribution of the axial velocity, Mach number, overpressure, and temperature for 500 A reveal a supersonic flow in the axial discharge region near the outlet (Fig. 11). An overpressure minimum at the axial position of 48.6 mm is accompanied by the Mach number, axial velocity maxima, and a slight temperature minimum. This detects a beginning of compression and

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Fig. 8. Contours of temperature for 200, 350, and 500 A and for argon mass flow rate 22.5 sl/min. 10 000 K corresponds to 1 in the plot, contour increment = 1000 K.

Fig. 10. Contours of the pressure drop for 200, 350, and 500 A and for argon mass flow rate 22.5 sl/min. 10 000 Pa corresponds to 1 in the plot.

Fig. 11. Mach number, overpressure, axial velocity, and temperature along the axis for 500 A. Zero axial position corresponds to the inlet surface. Correlation among velocity, pressure, and temperature near the outlet detects transition to the supersonic regime. Fig. 9. Contours of the Mach number for 200, 350, and 500 A and for argon mass flow rate 22.5 sl/min. Mach = 1 corresponds to 1 in the plot.

expansion waves generation reported in papers dealing with supersonic plasma jets; see for example, [44]–[46]. Finally, contours of the electrical potential and vectors of the electric field strength for 500 A are presented in Fig. 12. The

nearly perpendicular contours of the electrical potential to the arc axis indicate that the electric current flows in the axial direction. The electric field strength is nearly constant in the disV m , except for the outlet region where charge the field increases as a consequence of an arc constriction due V m . Qualitatively, the same to the outlet nozzle results are also valid for 200 and 350 A.


Fig. 12. Contours of (a) electrical potential (100 V corresponds to 1 in the plot) and vectors of (b) electric field strength for 500 A and for argon mass flow rate 22.5 sl/min.

IV. CONCLUSION The numerical model for an electric arc in the plasma torch with the so-called hybrid stabilization, i.e., combined stabilization of arc by gas and water vortex, has been presented. Calculations have been carried out for the interval of currents 150–500 A and for argon mass flow rates between 7.5 and 27.5 sl/min. The presence of argon in the discharge chamber has a great impact on the plasma velocity but a minor impact on the plasma temperature. The outlet velocities are substantially higher than for the water-stabilized torch, for 500 A the difference is over 3000 ms . The power losses from the arc due to radial conduction and radiation steeply increase for currents lower than 300 A, but above this current level the losses reach approximately 50%. A 500-A transition to supersonic flow in the axial discharge region near the outlet is obvious from the distribution of the axial velocity, Mach number, overpressure, and temperature. A comparison of calculations with available experimental data shows good qualitative and quantitative agreement. ACKNOWLEDGMENT The author would like to thank the Academy of Sciences of the Czech Republic, the META Centrum Project, and the Information, Communication, Control and Computers (ICCC) Centre for granting their computational resources. REFERENCES [1] E. Pfender, M. Boulos, and P. Fauchais, Thermal Plasmas (Fundamentals and Applications). New York: Plenum, 1994, ch. 1. [2] O. P. Solonenko, Ed., Thermal Plasma Torches and Technologies. Cambridge, U.K.: Cambridge Int. Sci., 2001, vol. 1. [3] M. Hrabovský, M. Konrád, M. Kopecký, and V. Sember, “Processes and properties of electric arc stabilized by water vortex,” IEEE Trans. Plasma Sci., vol. 25, pp. 833–839, Oct. 1997. , “Properties of water stabilized plasma torches,” in Thermal [4] Plasma Torches and Technologies, O. P. Solonenko, Ed. Cambridge, U.K.: Cambridge Int. Sci., 1998, vol. 1, pp. 240–255. [5] P. Chráska and M. Hrabovsky, “An overview of water stabilized plasma guns and their applications,” in Proc. Int. Thermal Spray Conf. Exhibit., Orlando, FL, May 28–June 5 1992, pp. 81–85.

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ˇ Jiˇrí Jeniˇsta was born in Celadná, Czechoslovakia, in 1962. He received the Dipl.-Ing. degree in physical electronics from the Czech Technical University, Prague, in 1986, the M.Sc. degree in mechanical engineering from the University of Minnesota, Minneapolis, in 1995, and the Ph.D. (C.Sc.) degree in plasma physics from the Academy of Sciences, Prague, Czech Republic, in 2001. Since 1988, except for 1993 to 1995 when he studied in the United States, he has been associated with the Institute of Plasma Physics, Czech Academy of Sciences. His current research interests include physics and modeling of high-current electric arcs, namely liquid-stabilized plasma torches.