Plasma flow in a nozzle during plasma arc cutting

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Plasma flow in a nozzle during plasma arc cutting

This article has been downloaded from IOPscience. Please scroll down to see the full text article. 1998 J. Phys. D: Appl. Phys. 31 3102 (http://iopscience.iop.org/0022-3727/31/21/016) View the table of contents for this issue, or go to the journal homepage for more

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J. Phys. D: Appl. Phys. 31 (1998) 3102–3107. Printed in the UK

PII: S0022-3727(98)93650-6

Plasma flow in a nozzle during plasma arc cutting Valerian A Nemchinsky ESAB Welding and Cutting Products, PO Box 100545, Florence, SC 29501-0545, USA Received 27 April 1998, in final form 28 July 1998 Abstract. A simple model describing the plasma temperature, pressure and velocity distributions inside the nozzle during plasma arc cutting is developed. Temperature dependences of plasma properties are considered. Predicted and measured values of the plasma pressure inside the arc chamber are compared to validate the model. Calculations demonstrated that a substantial portion of the power dissipated inside the nozzle is radiated; the rest heats the plasma jet. The proportion of the power lost due to radiation increases with the arc current, length of the nozzle and gas-flow rate. The double-arcing phenomenon is hypothesized to result from the electrical breakdown of the gas at the nozzle’s exit. Calculations of the electrical field at the nozzle’s exit support this hypothesis.

1. Introduction Plasma arc cutting (PAC) is a process of metal cutting by a plasma jet. It is becoming increasingly popular because of its high productivity and ability to cut practically all metals [1–4]. In most cases the current-carrying plasma jet strikes between the cathode located inside the torch and the metal to be cut (the so-called transferred arc configuration). In order for the plasma jet to provide a fast and highquality cut, the jet emanating from the torch should be narrow and hot. Also, it has to exert enough force on the workpiece to remove the molten metal from the cut. This is made possible by a special nozzle inside the torch. The nozzle is an electrically neutral duct, through which the plasma is blown out of the torch. The nozzle creates a narrow, highly concentrated plasma flow. The narrowness of the nozzle causes a large voltage drop in the plasma inside the nozzle. Consequently, the resistance heating heats the plasma jet inside the nozzle very intensely. Also, the nozzle provides the high velocity of the arc jet and fast removal of the molten metal during cutting. Together with the electrode, the nozzle is one of the most vulnerable parts of the torch due to its exposure to extremely high heat fluxes. In contemporary systems, heat-flux densities above 103 W cm−2 are the rule rather than the exception. However, even minor melting of the orifice causes the cut’s quality to deteriorate and slows down the cutting process. What is worse, in some circumstances, the nozzle develops the so-called double-arcing phenomenon (figure 1), namely two arcs are created: one from the electrode to the nozzle and another from the nozzle to the workpiece. The nozzle becomes an electrical conduit connecting these two arcs. This catastrophically damages the nozzle and, in most cases, destroys the electrode as well. c 1998 IOP Publishing Ltd 0022-3727/98/213102+06$19.50

While designing a nozzle, it is necessary to satisfy a number of contradictory conditions. In order to provide a fast, constricted and hot jet, the nozzle should be long and narrow. To increase the force that the plasma exerts upon the workpiece, the gas pressure in the plenum chamber (see figure 1) should be high. On the other hand, the longer and the narrower the orifice the higher it is thermally loaded and the higher the risk of double arcing. Also, the higher the chamber pressure the higher the electrode-erosion rate. We see that designing a nozzle necessitates a series of trade-offs. Therefore, it would be desirable to develop a model allowing, if not precise calculations of plasma-flow parameters in the chamber and the nozzle, then at least an initial approximation to an at present mostly empirical endeavour. With the notable exception of two recent publications by Ramakrishnan et al [5, 6], there had been virtually no papers describing plasma flow during PAC. In their papers, Ramakrishnan et al measured the plenum chamber pressure and the diameter of the plasma jet emanating from the nozzle. The authors observed the shock-wave pattern in the jet indicating that the gas was moving at the speed of sound. In the theoretical part of [5, 6], Ramakrishnan et al modelled the plasma flow using the two-zone approximation. It was assumed that the main current flows in the hot plasma core, whereas the main mass flow is in the cold non-ionized envelope wrapping this plasma core. (This approximation has been developed in [7, 8] (see also review [9]) to describe plasma flow in plasma gas heaters and high-current switches.) By assuming that the plasma core’s temperature is equal to 26 000 K and that the envelope’s temperature is 6000 K, Ramakrishnan et al achieved a good agreement between calculated and observed plasma jet diameters. However, the

Plasma flow in a nozzle

Figure 2. The flow geometry. Empty arrows show cold gas flow; the filled arrow shows hot plasma flow.

nozzle by the equation

Figure 1. Normal operation (a) and double arcing (b) during plasma arc cutting: 1, electrode; 2, plenum chamber; 3, nozzle orifice; and 4, plasma jet.

plasma’s description in [5, 6] had substantial shortcomings: (i) both temperature values were picked rather arbitrarily, and (ii) all the plasma’s properties were assumed to be constant along the nozzle’s length. In this paper we attempt to take the next step in plasmaflow modelling. We do not use a two-zone approximation and will obtain the plasma’s temperature distribution by solving the heat-transfer equation in the moving medium.

2. The model Consider a plasma flow for a given gas-flow rate entering a metallic duct (nozzle), figure 2. The plasma channel is formed at the electrode’s surface and expands as the plasma moves from the electrode towards the nozzle. At the nozzle’s entrance the plasma flows through a central portion of the orifice; the cold gas enters the nozzle through the outer portion of the orifice. Inside the nozzle, Joule (resistance) heating heats the plasma. Some portion of this heat increases the plasma’s enthalpy flux, another portion of it is radiated and the rest is carried to the orifice’s surface by means of thermal conduction. Assuming cylindrical geometry, one can describe the gas temperature inside the

∂T 1 ∂ vρC = ∂z r ∂r



∂T rκ ∂r

 + σ E 2 − Wrad .

(1)

Here v is the plasma’s velocity, C is the heat capacity, κ is the thermal conductivity, ρ is the gas density, σ is the plasma’s conductivity and Wrad (T ) is the power radiated per unit volume. The current density j can be obtained from Ohm’s law: j (r, z) = σ [T (r, z)]E(z) where E is the electrical field such that Z R σ r dr. I = 2π E

(2)

(3)

0

Here I is the arc current. After introducing the heat potential Z T 2= κ(T ) dT equation (1) takes the form   v ∂2 1 ∂ ∂2 = r + j (r, z)E − Wrad (2) α(2) ∂z r ∂r ∂r

(4)

where α = κ/(ρC) is thermal diffusivity. We assume that the velocity v depends on the z coordinate and does not depend on the radial coordinate. This approximation, at least partially, is justified by the high Reynolds numbers of the flow and, therefore, by a relatively flat velocity profile. Also, we assume that the pressure depends on the z coordinate only; it has been 3103

V A Nemchinsky

shown in [8, 9] that the variation of the pressure across the nozzle’s cross section is negligible. Boundary conditions should be set for equation (4). We assume that the plasma temperature distribution at the nozzle’s entrance has a step-like shape: T (r < r0 ) = Tpl T (r0 < r < R) = T0 .

(5)

Here we introduce three unknown parameters: the plasma core’s temperature at the nozzle’s entrance Tpl , the plasma’s radius at the nozzle’s entrance, r0 , and the cold gas temperature at the nozzle’s entrance, T0 . The choice of these parameters will be discussed below. Solving the above equations allows us to calculate A(z), the area available for the cold gas flow. With the pressure and velocity constant over the nozzle’s cross section, the local gas-flow density (g s−1 cm−2 ) is inversely proportional to the local temperature. This means that gas does not flow through that portion of the nozzle where the temperature is high. Therefore, one can define A(z) as follows: R R r dr A(z) 0 T (r,z) = RR . (6) r dr A(z = 0) 0 T (r,z=0)

Now let us proceed to the gas dynamics of the cold gas flow. The cold gas flow is limited on one side by the hot plasma core, which acts as a wall, and on the other side by the nozzle’s orifice. The cross section of the cold gas flow decreases as it flows down the nozzle. One may say that cold gas flows in a converging nozzle. From continuity and momentum equations and from the ideal gas law we have ρvA = G dp + v dv = 0 ρ ρRg T /M = p.

(7) (8) (9)

Here G is the gas flow rate (g s−1 ), p is the pressure, ρ is the gas density, Rg is the gas constant and A(z) is the area occupied by the cold gas flow. For the gas temperature we use the simplest possible approximation: the cold gas has a constant temperature T0 which is equal to the envelope gas temperature at the nozzle’s entrance. Following Ramakrishnan et al [5, 6], we assume that the cold gas velocity at the nozzle’s exit is sonic, namely v(z = L) = (Rg T /M)1/2 for isotemperature flow. This condition allows us to express all the flow’s parameters at any given location in the nozzle as functions of those at the nozzle’s exit. For example, for the pressure we have    P 2 A2 1 P 1 − exit2 exit . (10) = exp Pexit 2 P A2 Obtaining A(z) from the plasma flow equations (1)–(6), we solved (10) for p(z) by an iterative process. It follows from this equation that, for a choked isotemperature flow (Aentrance → ∞, ventrance → 0), pentrance /pexit = 1.65. (Compare this value with 1.89 for isoentropic flow [12].) Calculations of plasma parameters and cold gas flow parameters are interconnected. The condition of constant 3104

pressure across the nozzle’s cross section implies that the gas density in the central core is negligible compared with the one on the periphery of the flow. Therefore, the flow pressure and velocity are determined by the gas dynamics of the cold envelope, whereas the envelope’s cross sectional area is determined by the plasma channel’s expansion during its travelling inside the nozzle. Also, since the radiation per unit volume depends on the pressure, the plasma’s energy balance is sensitive to the pressure, which is the parameter determined by the cold gas flow. 3. Results of calculations and comparison with experimental data Our calculations were performed for air. The following parameters of air were specified as functions of the temperature and pressure: the conductivity σ , thermal conductivity κ, diffusivity α and radiation per unit volume Wrad . We obtained the density, specific heat, thermal conductivity and electrical conductivity from [13–15]. The thermal conductivity and electrical conductivity were assumed to be pressure-independent quantities, while the specific heat and density were put directly proportional to the pressure. For Wrad , we used the formula for a nonreabsorbed recombination continuum suggested in [15], which describes well the experimental data from [16, 17]. Radiation losses were assumed to be proportional to the pressure squared. In section 2, we introduced three unknown parameters: the plasma core’s temperature at the nozzle’s entrance Tpl , the plasma’s radius at the nozzle’s entrance, r0 , and the cold gas temperature at the nozzle’s entrance, T0 . Ideally, all these parameters should be obtained from the solution of the equation, which describes the plasma in the gap between the electrode and the entrance of the nozzle. However, our computations showed that the resultant parameters (voltage, pressure and so on) are insensitive to Tpl , see table 1. The role of the plasma channel’s radius r0 demands special consideration. The arc plasma’s radius at z = 0 is determined by the following parameters: (i) the geometry of the chamber, (ii) the geometry of the electrode, (iii) its proximity to the nozzle’s entrance; and (iv) the gas-flow pattern inside the chamber (swirled or straight). If the electrode is far from the nozzle, so that its proximity does not influence the plasma’s parameters inside the nozzle, then the arc uses its own mechanism to regulate r0 . Namely, the arc assumes such an r0 as to provide the minimum possible voltage drop across the arc†. This principle was suggested by Steenbeck in the 1930s and since then has been applied very successfully to numerous † At first glance, it seems that the wider the plasma channel the lesser the current density, the lesser the electrical field and, therefore, the lower the total voltage. However, a wide plasma channel means a small area available for cold gas. With a fixed gas-flow rate, a small cross section demands a high pressure in the chamber and inside the nozzle. Since the power radiated per unit volume is proportional to the pressure squared, high pressure leads to large energy losses and, therefore, necessitates an increase in voltage to keep the plasma channel hot. Starting at a certain radius value, this effect of power loss completely offsets the advantageous decrease in voltage caused by lowering of the current density. From this point on, the voltage starts to rise.

Plasma flow in a nozzle Table 1. The voltage drop inside the nozzle, plasma temperature at the nozzle’s exit, plenum pressure, plasma jet’s radius, fraction of the power lost due to radiation and gas breakdown parameter at various Tpl .

Tpl (1000 K)

V (V)

Pressure (psi)

T (0, L) (1000 K)

r (L)/R

Qrad

Er /N (10−16 V cm2 )

11.9 14.9 17.8 21.2

62.7 60.5 55.8 53.6

41.1 43.5 47.0 50.8

28.2 28.0 27.7 27.2

0.842 0.849 0.858 0.867

0.296 0.349 0.420 0.495

1.6 1.5 1.4 1.4

Figure 3. The plenum pressure versus the arc current: line, calculations; and points, experimental data.

Figure 4. The plenum pressure versus the gas-flow rate. L = 0.8 cm and T0 = 1000 K.

plasma calculations [10, 11]. Under these circumstances, we performed calculations for various values of T0 in the wide range 1000–6000 K (see table 2). One can see that, so long as T0 is not too high, the plasma’s parameters are rather insensitive to T0 . In order to check our calculations, the plenum chamber pressure was measured. A small hole in the hose supplying plasma gas to the torch was connected to a pressure gauge. The comparison of the calculated and measured pressures at various arc currents is shown in figure 3. One can see that there is very good agreement. Figure 4 shows a comparison of calculated and measured plenum chamber pressures as functions of the gas-flow rate for two different arc currents

Figure 5. Radial distributions of the plasma temperature at the entrance (z = 0), mid-section (z = L/2) and exit (z = L) of the nozzle. 300 A, R = 1.52 mm, L = 0.8 cm, G = 1.27 g s−1 and T0 = 1000 K.

(200 and 385 A) and various nozzle diameters. Except for low gas-flow rates, the agreement is good. Most of our calculations were performed for the following conditions: the nozzle’s length is assumed to be 0.8 cm, the nozzle’s diameter 0.305 cm, the gas-flow rate 1.3 g s−1 and the cold gas temperature 1000 K. Let us consider plasma jet parameters for these conditions at 300 A. The radial distributions of the plasma temperature at the nozzle’s entrance, in the mid-section and at the nozzle’s exit are shown in figure 5. Note that, at the nozzle’s exit, the plasma channel is very close to the nozzle’s wall. Nonetheless, there still exists, although it is small, a layer of cold gas which separates the nozzle from the hot plasma. As a result, the heat flux to the nozzle due to thermal conduction is low. Even in the cases of long nozzles and low gas flow rates, for which the thermal conduction flux to the nozzle is maximal, it does not exceed 1% of the electrical power dissipated inside the nozzle. However, this does not preclude high local heat-flux densities and, consequently, some local temperature rise. According to our calculations, the heat flux due to thermal conduction is concentrated in a narrow (about 1 mm) ring-shaped portion of the orifice inside the surface close to the nozzle’s exit. Estimations showed that, in the worst-case scenario (long nozzles, low gas-flow rates), this heat flux can increase the local temperature by no more than 100 ◦ C. This increase is not important unless the local temperature is already close to the melting point. 3105

V A Nemchinsky Table 2. The same as table 1 but for various T0 .

T0 (1000 K)

V (V)

Pressure (psi)

T (0, L) (1000 K)

r (L)/R

Qrad

Er /N (10−16 V cm2 )

1 2 3 6

60.5 69.0 76.1 92.2

43.5 46.3 49.8 59.6

28.0 28.9 29.4 30.1

0.849 0.788 0.750 0.681

0.349 0.301 0.281 0.259

1.5 2.4 3.1 5.2

Figure 6. The ratio of the power spent on plasma jet heating to the total power dissipated inside the nozzle (the nozzle’s efficiency) versus the nozzle’s length. R = 1.52 mm, G = 1.27 g s−1 and T0 = 1000 K.

The total voltage drop inside the nozzle in the abovediscussed case (300 A) is 60 V; that is, the total power of 18 kW is dissipated inside the nozzle. A substantial portion of this power (about 35%) is radiated in the form of non-reabsorbed radiation. Plasma radiates isotropically and heats the nozzle, electrode and workpiece. The ratio of the nozzle-orifice length to the diameter is close to 2. Therefore, we can roughly estimate that approximately half of the radiated power (about 3 kW in our case) reaches the nozzle. Note that the metal surface of the orifice reflects back some fraction of the incident light, thus decreasing the heat load of the nozzle. Power losses in the nozzle are almost completely due to radiation. The rest of the dissipated power goes to plasma jet heating. One can define the nozzle’s efficiency as the ratio of the power spent on jet heating to the total dissipated power. In the above-considered case, the nozzle’s efficiency is 65%. Increasing the nozzle’s length causes the voltage to increase and the plasma jet power to rise. However, radiation loss increases even faster so that the nozzle’s efficiency falls, see figure 6. Our calculations showed that the nozzle’s efficiency falls as the gas flow increases and as the arc current increases. 4. Double-arcing conditions The potential difference between the metallic nozzle and the neutral plasma depends on the coordinate along the nozzle’s axis. At the nozzle’s entrance, this potential difference is slightly less than the floating potential. At the exit of the 3106

Figure 7. E /N in the cold gas envelope versus the nozzle’s length. E is the radial electrical field; N is the concentration of the neutral particles.

nozzle, the voltage between the plasma and the nozzle is close to the potential drop along the plasma channel inside the nozzle. In some regimes it could be as high as 100 V. In the cold gas envelope, the electron concentration is low. Therefore, the Debye length is large. This means that the radial electrical field penetrates deep inside the cold gas envelope. In this case, the radial electrical field is close to the ratio of the voltage drop across the envelope to the envelope’s width. The thickness of the envelope is small. This results in high values of Er /N, where Er is the radial electrical field and N is the concentration of neutral particles in the cold gas envelope†. Once Er /N exceeds a critical value, the Townsend avalanche develops and the cold insulating layer separating hot plasma from the nozzle breaks down. This leads to double arcing. The critical Er /N value for clean air at around atmospheric pressure is about (1–2) × 10−15 V cm2 [18]. In figure 7, the calculated Er /N parameter for various nozzle lengths is shown. One can see that the calculated Er /N is short of the critical value by a factor of five. We would like to emphasize that the critical Er /N parameter was obtained in experiments with clean polished electrodes, with cold and clean air. The conditions in the nozzle are quite different. The gas and the nozzle’s orifice are hot and are subjected to irradiation from the adjacent plasma. † In most cases the electron concentration in the cold envelope estimated according to the Saha equation is low so that the Debye length LD exceeds the envelope’s width. In these cases, the electrical field can be approximated as the ratio of the voltage drop to the envelope’s width. However, if, for some reason, the electron concentration rises so that the Debye length becomes shorter than the envelope’s width, then the electrical field in the vicinity of the nozzle rises to V /LD . This makes breakdown of the gas even more likely.

Plasma flow in a nozzle

Both the gas and the surface are not clean. The products of the electrode’s erosion, which have low workfunctions, are deposited inside the nozzle. All these factors decrease the critical field. Also, it is worthwhile to note that the electrical field was calculated assuming a perfectly central location of the plasma channel inside the nozzle. If, for any reason, the channel is shifted away from the central position, then the electrical field increases at one side, thus provoking gas breakdown. This happens, for example, when the electrode is worn out so that the arc attachment at the electrode shifts from the centre. Gas turbulence can cause this shift also. We, therefore, conclude that our calculations do not contradict the hypothesis of the Townsend-like breakdown of the cold gas envelope during double arcing. There is another consideration in favour of this hypothesis. It is known that double arcing occurs at lower currents when argon is used instead of air or nitrogen. This agrees with the fact that Ar has a critical E/N value substantially less than those for air and nitrogen. 5. Conclusion A physical model to describe plasma flow in the nozzle of a plasma arc cutting torch has been developed. It allows us to calculate a number of parameters of plasma flow, namely distributions of the temperature, pressure, voltage and velocity inside the nozzle. The model has been tested by comparing calculated and measured values of the arc chamber pressure for various arc currents, gas-flow rates and nozzle dimensions. Comparison showed that the agreement was good. It has been shown that a considerable portion of the total electrical power that is dissipated in the nozzle is radiated out. The rest of the power heats the plasma and is carried out from the nozzle by the plasma jet. Calculations showed that the nozzle’s efficiency (the percentage of the total electrical power that heats the jet) is about 60–80%. The nozzle’s efficiency is substantially lower for longer nozzles, higher currents and higher gas-flow rates. The heat transferred to the nozzle’s wall by thermal conductivity is small. However, local heat-flux densities may be considerable, especially at the nozzle’s exit. They can cause an additional local temperature rise of about 100 ◦ C. The calculations show that the thickness of the cold gas envelope wrapping the hot plasma channel and thus protecting the nozzle is very small. There is a high voltage

drop across the cold gas envelope at the nozzle’s exit. The calculated value of this drop is close to the electrical breakdown voltage. This is the mechanism we propose to explain the double-arcing phenomenon. References [1] Bykhovsky D G 1972 Plasmennaya rezka metalov (Plasma Metal Cutting) (Moscow: Mashgiz) (in Russian) [2] Anderson D G and Severance W S 1984 How plasma arc cutting gases affect productivity Weld. J. 63 35–9 [3] Fernicola R C 1998 A guide to manual plasma arc cutting Weld. J. 77 52–5 [4] Fernicola R C 1994 New oxygen plasma process rivals laser cutting method Weld. J. 73 65–9 [5] Ramakrishnan S, Gershenzon M, Polivka F, Kearny T N and Rogozinsky M R 1997 Plasma generation for plasma cutting process IEEE Trans. Plasma Sci. 25 937–46 [6] Ramakrishnan S and Rogozinsky M W 1997 Properties of electric arc plasma for metal cutting J. Phys. D: Appl. Phys. 30 636–44 [7] Hermann W, Kogelschatz U, Ragaller K and Schade E 1974 Investigation of a cylindrical, axially-blown, high-pressure arc J. Phys. D: Appl. Phys. 7 607–19 [8] Hermann W, Kogelschatz U, Niemeyer L, Ragaller K and Schade E 1974 Experimental and theoretical study of a stationary high-current arc in a supersonic nozzle flow J. Phys. D: Appl. Phys. 7 1703–22 [9] Pfender E 1978 Electric arcs and gas heaters Gaseous Electronics ed M N Hirsh and H J Oskam (New York: Academic) [10] Finkelnburg W and Maecker H 1956 Electric arcs and thermal plasma Encyclopedia of Physics vol 22 (Berlin: Springer) [11] Paik S, Huang P C, Heberlein J and Pfender E 1993 Determination of the arc-root position in a DC plasma torch Plasma Chem. Plasma Processing 13 379–97 [12] White F M 1991 Viscous Fluid Flow 2nd edn (New York: McGraw-Hill) [13] Dresvin S V (ed) 1977 Physics and Technology of Low-Temperature Plasma (Ames, IA: The Iowa State University Press) [14] Mitchener M and Kruger C H Jr 1973 Partially Ionized Gases (New York: Wiley) [15] Sobel’man I I 1972 Introduction to the Theory of Atomic Spectra (Oxford: Pergamon) [16] Krey V D and Morris J C 1970 Experimental total and total line radiation of nitrogen, oxygen and argon plasma Phys. Fluids 13 1438–7 [17] Evans D L and Tankin R C 1967 Measurement of emission and adsorption of radiation by an Ar plasma Phys. Fluids 10 1137–44 [18] Raizer Yu P 1991 Gas Discharge Physics (Berlin: Springer)

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