22nd International Symposium on Plasma Chemistry
July 5-10, 2015; Antwerp, Belgium
Effects of operating pressure on the cathode surface temperature and current
profile in a plasma arc cutting torch
E. Ghedini1 and A. Procacci2
1
Alma Mater Studiorum – Università di Bologna, Department of Industrial Engineering and Industrial Research
Centre for Advanced Mechanics and Materials, via Saragozza 8, Bologna, Italy
2
Alma Mater Studiorum – Università di Bologna, School of Engineering and Architecture, Bologna, Italy
Abstract: The effects of different operating pressures on the temperature and current
profile of a 150A plasma arc cutting torch are investigated using modelling in order to
provide useful information on the heat transfer mechanisms and on the position and
magnitude of the temperature peaks, with the final aim to provide some new insights on the
erosion mechanisms.
Keywords: plasma arc cutting, electrode erosion, modelling, thermionic emission
1. Introduction
Plasma arc cutting (PAC) is a well-established
industrial technology for high speed and high quality
cutting of metal sheets. The PAC process is characterized
by a transferred arc between an electrode placed inside a
cutting torch (cathode) and the workpiece to be cut
(anode) [1]. One of the main issues related to the
commercial exploitation of PAC is the limited life of the
plasma torch components and in particular of the cathode,
whose surface is exposed to the extremely high plasma
temperature and subject to continuum and cyclic erosion
[2].
The scope of this work is to understand via modelling
how operating pressure can affect the cathode surface
temperature distribution in order to provide useful
information on the heat transfer and thermionic emission
mechanisms. The final aim of this approach is to provide
means for the design of cathodes and operating conditions
that minimize the thermal stress of the cathode material.
Typical 150A PAC torch geometry with hafnium
cathode and oxygen as forming gas has been modelled,
including heat transfer on the electrode body. Results will
be presented for two different operating pressure values
with the same inlet swirl angle.
2. Model description
Plasma torch computational domain, main dimensions
and boundary conditions are sketched in Fig. 1a and 1b.
The plasma forming gas is oxygen and the arc current is
fixed at 150A. Details on the plasma fluid dynamic model
can be found in [3].
There is a general understanding on the physical
mechanisms of interaction between the plasma and the
cathode surface on refractory cathodes [1]: electrons flow
from the cathode surface by means of Schottky enhanced
thermionic emission while cathode is heated by ion
bombardment and cooled by thermal conduction and
emission cooling.
In this work, the thermionic cathode model proposed by
Lowke et al. in [4] has been implemented in the
cathode/plasma interface and coupled with the plasma
fluid dynamic model in order to predict the temperature,
current density and heat transfer on the cathode surface
taking into account the influence of the plasma flow field.
On the cathode surface the normal current component
will be the sum of the ionic and electronic currents, so
that:
|𝑗𝑧 | = |𝑗𝑖𝑖𝑖 | + |𝑗𝑒 |
where j e is the thermionic current evaluated using the
well-known Richardson formula
𝑗𝑅 = 𝐴𝑇 2 exp �−
Fig. 1. Torch internal geometry and main dimensions.
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𝑒𝑊𝑓
�
𝑘𝑘
with T the temperature of the cathode surface, A the
thermionic constant (106 A m-2 K-2 for Hf) and W f the
work function (3.9 V for Hf).
For each iteration step, the net electric current j on the
whole domain is firstly calculated using Poisson’s
equation, taking into account boundary imposed current
level. Following the above mentioned relations, j R is then
evaluated by means of the Richardson equation, using the
1
Fig. 2. Axial current density [A/m2] on the cathode
surface for 3.7 and 5 bar inlet pressures.
Fig. 3. Axial current density contributions [A/m2] on the
cathode surface for 5 bar inlet pressures.
surface temperature calculated by the heat transfer
equation. Finally, j ion can be evaluated simply by
|𝑗𝑖𝑖𝑖 | = |𝑗𝑧 | − |𝑗𝑒 |
with |𝑗𝑖𝑖𝑖 | = 0 if |𝑗𝑧 | < |𝑗𝑒 |.
Heat flux on the plasma/cathode interface can be
calculated for each iteration step using the following
relation, using the current values just evaluated:
𝑞𝑘 =
𝜆𝑝𝑝
𝑗𝑖𝑖𝑖 3
𝑗𝑒
� 𝑘𝑇 + 𝜖𝑖𝑖𝑖 − 𝑊𝑓 � − 𝑊𝑓 −
�𝑇 − 𝑇𝑝 �
𝑒 2 𝑝
𝑒
Δ𝑧 𝑐
4
4
− 𝜖𝜎𝑆 (𝑇𝑐 − 𝑇𝑎 )
with T p , T c e T a the cathode surface, plasma and ambient
temperatures, 𝜖𝑖𝑖𝑖 the oxygen ionization energy, 𝜆𝑝𝑝 the
thermal conductivity, Δ𝑧 the distance between cathode
surface and the first fluid control volume, 𝜖 the hafnium
emissivity and 𝜎𝑆 the Stefan-Boltzmann constant.
3. Results
Two different 150A cases at have been analysed with
inlet pressures of 3.7 and 5 bar, imposing an inlet swirl
angle of 45°. The calculated mass flow rates are 3.21·10-5
kg/s and 4.89·10-5 kg/s respectively and the voltage drops
between the cathode surface and the nozzle orifice 101 V
and 109 V.
Radial dependant current profiles in Fig. 2 show for both
pressures a net current emission from the cathode surface
with an off-axis peak located near the boundary of the
cathode insert. This phenomenon is especially evident for
the higher pressure 5 bar case, where the current is
restricted in an annular region from 0.30 to 0.55 mm and
drops down in the proximity of the axis. Electronic and
ionic current in Fig. 3 show a clear predominance of the
electronic with respect to the ionic contribution.
2
Fig. 4. Temperature [K] on the cathode surface for 3.7
and 5 bar inlet pressures.
Similar off-axis behaviour can be found for the radial
temperature profile shown in Fig. 4 on the cathode surface
and in the first fluid cells layer. While the maximum
temperature value seems the same for both pressures, the
higher pressure case shows a central temperature drop of
about 500 K.
Fig. 5 and Fig. 6 show the heat flux to the cathode
surface for the 5 bar and 3.7 bar cases respectively. These
figures show that the cathode is heated by conduction
between plasma and cathode and from the ion
recombination on the surface, while the electronic
emission contributes to cathode cooling. Radiation
emission from the cathode surface is negligible compared
to the other effects and not included in the plot. In the 5
bar case the heat flux is concentrated in an annular region
between 0.30 and 0.55 mm.
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Fig. 5. Heat flux to the cathode surface [W/m2] for 5 bar
inlet pressures: electronic q e , ionic q i , conduction q l and
total q tot .
Fig. 7. Temperature field [K] in the plasma chamber for
5 bar (left) and 3.7 bar (right) cases.
Fig. 6. Heat flux to the cathode surface [W/m2] for 3.7
bar inlet pressures: electronic q e , ionic q i , conduction q l
and total q tot .
Table 1. Heat fluxes on cathode surface.
qi
ql
qe
qr
q tot
5 bar
347 W
550 W
-483 W
-4.7 W
409 W
3.7 bar
321 W
527 W
-449 W
-4.4 W
395 W
Fig. 8. Swirl velocity field [m/s] in the plasma chamber
for 5 bar (left) and 3.7 bar (right) cases.
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3
The arising of such recirculation zone can be responsible
for the near-axis low temperature region and the annular
electric current emission.
Fig. 9. Velocity versors on the temperature field in the
near cathode region for the 5 bar (left) and 3.7 bar (right)
cases.
Table 1 summarizes the heat fluxes contributions on the
cathode surface for 3.7 and 5 bar cases. Results show that
an increase in operating pressure has only a very small
influence on the integrated heat fluxes values while the
main effect is on the heat flux profiles. The 5 bar case
shows more pronounced off-axis behaviour, being the
fluxes especially concentrated on an annular region
between 0.30 to 0.55 mm.
Temperature fields in the plasma chamber are shown in
Fig. 7, where an off-axis temperature peak near the
cathode surface is clearly visible for the 5 bar (left) case,
while the differences in the bulk of the plasma discharge
seem negligible. In Fig. 8 the comparison between the
swirl velocity fields shows that for the 5 bar case the
higher flow rate leads to a higher swirl velocity in the
plasma chamber with respect to the 3.7 bar case.
The effect of the increased flow rate on the flow pattern
in the near cathode region is shown in Fig. 9, where for
the 5 bar case a well-defined recirculation zone is formed.
4
4. Conclusions
The inclusion of the Richardson formula for the
prediction of the thermionic emission in plasma cutting
torch simulation can provide useful insights for the
understanding of the erosion mechanisms in PAC
cathodes. In particular, the effect of pressure increase on
the cathode temperature has been investigated showing
that the different flow pattern near the cathode surface,
with respect to the low pressure case, could be the cause
that leads to an enhanced annular current emission profile.
The axisymmetric model constraint ensures the stability
of an annular current emission configuration, by means of
a perfect forces balance on the axis. However in a realistic
three-dimensional environment the stability of this
configuration is highly questionable, due to the magnetic
constriction phenomena that tend to promote spot
attachments.
Future developments will investigate the influence of
other important parameters on the cathode surface
temperature distribution (e.g. material conductivity, insert
size) and the stability of the annular configuration in a full
three-dimensional environment.
5. References
[1] V.A. Nemchinsky and W.S. Severance, J. Phys. D:
Appl. Phys. 39 (2006)
[2] V.A. Nemchinsky, Plasma Chem. Plasma Process. 33
2 (2013)
[3] V. Colombo et al., Plasma Sources Sci. Technol. 20 3
(2011)
[4] J.J. Lowke, R. Morrow, J. Haidar, J. Phys. D: Appl.
Phys. 30 14 (1997)
[5] N.P. Long et al., J. Phys. D: Appl. Phys. 45 (2012)
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