st
21 International Symposium on Plasma Chemistry (ISPC 21)
Sunday 4 August – Friday 9 August 2013
Cairns Convention Centre, Queensland, Australia
Reduction of Heat Flux on the Hafnium Cathode Surface
by Changing the Cathode Holder Shape in Plasma Arc Cutting Torch
Nguyen Phi Long1, Y. Tanaka2, Y. Uesugi2, and Y. Yamaguchi3
1
Applied Laser Technology Institute, Japan Atomic Energy Agency
Division of Electrical Engineering and Computer Science, Kanazawa University
3
Komatsu Industries Corporation, Japan
2
Abstract: The aim of this work is to investigate the effects of cathode holder shape, not the
cathode insert, on hafnium (Hf) cathode evaporation by a developed two-dimensional
numerical model for oxygen arc plasma in a torch. Results showed that the heat flux on the
Hf cathode surface decreased markedly with the higher protrusion of the convex cathode
holder by a rapid clockwise rotation of gas flow.
Keywords: Plasma arc cutting, Hafnium evaporation, Shape of holder cathode.
C
4
Radial position [mm]
The plasma arc cutting (PAC) process is a technique
widely used for cutting different metals with high-speed
and high-accuracy in the industrial fields. Arc plasma is
established between the electrode in the plasma torch and
a work-piece. A summary of several investigations related
to plasma arc cutting processes can be found in topical
review [1]. During operation of a plasma arc cutting
torch, the molten material is ejected from the surface of
cathode insert. Thus, the shape of insert surface changes
rapidly until reaching the preferred concave shape at
steady state. As for the cathode with concave surface
insert used in a plasma arc torch, it has been shown in
patent literature [2, 3] that the curvature of this preferred
concave shape is a function of the current level of the
torch, and the diameter of the insert and the gas flow
pattern in the torch. Use of this concave insert reduces
deposition of the cathode material on the nozzle, and it
thereby reduces nozzle wear in the torch.
As discussed above, the geometry of the electrode
including cathode insert has a marked effect on the
characteristics of arc plasma. It is, however in general, too
much complicated to investigate the interaction between
thermal plasma and surface cathode insert shape such as
evaporation of the cathode material. Experimental
investigations of a plasma arc cutting torches with
different shapes of the Hf cathode insert are very difficult
because of the high running cost of plasma arc cutting.
Another approach for the geometry of the electrode is to
investigate the shape of a cathode holder, not a cathode
insert. This holder structure may affect the characteristics
of arc plasma, especially gas flow pattern. Thus, this can
also control the amount of cathode material evaporation.
The aim of this work is to investigate effects of cathode
holder shape on Hf cathode evaporation by a developed
two-dimensional numerical model for oxygen arc plasma.
This paper paid attention to steady state evaporation of
cathode material during arc cutting because it is also
important for long operation of PAC torch.
185 divide
inlet
O2gas D
3
Electrode
Swirl gas
20 divide
Cu-nozzle
F
2
Hf insert
O2 gas
E
Current
source
Cu
I
1
Hf
0
O
K
10 divide
G
L
Gas/plasma
0
H 2
68 divide
4
6
Axial position [mm]
B
Nozzle
outlet
A
8
Arc
Work-piece
plate
Fig.1 Schematic diagram of a plasma cutting torch
Radial position [mm]
1. Introduction
4
holder O
4
holder A
3
3
2
2
1
1
0
0
0
0
2
4
4
holder B
3
l=0.4 mm
2
l=0.5 mm
1
2
4
0
0
2
4
Axial position [mm]
Fig.2 Shape of the cathode holder
2. Mathematical model
2.1. Calculation space and assumptions
Fig.1 illustrates the schematic diagram of the arc model
and the calculation space of the DC plasma cutting arc
torch used in this work. The electrode is made of copper
with Hf tip insert of 1.27 mm in diameter. Oxygen is
used for plasma gas and is supplied from inlet by swirling
gas flow. Arc plasma is constricted by copper nozzle with
a nozzle outlet of 1.33 mm in diameter.
The calculation is performed for different the shapes of
the cathode holder shape, which are shown in Fig.2. In
this figure, holder O is the original flat surface holder,
which is usually used in the experiments. The holders A
and B indicate two of convex cathode holder, which has a
protruded. The shape of these holders is defined by a
distance (l) from the flat surface of the cathode and top of
the convex cathode holder at radial position of 1.6 mm.
The holder A has the distance l of 0.4 mm, while holder B
st
21 International Symposium on Plasma Chemistry (ISPC 21)
Sunday 4 August – Friday 9 August 2013
Cairns Convention Centre, Queensland, Australia
has distance l of 0.5 mm. The convex shape of holders A
and B are formed as a part of an arc of an ellipse.
the thermal conductivity of the solid/liquid, and
represents the electrical conductivity of the solid/liquid.
In this paper, the developed two dimensional numerical
model assumes the followings: the gas flow is laminar,
the plasma is in steady state and axisymmetric, the plasma
is in the local thermodynamic equilibrium and optically
thin, the effect of swirl gas flow is considered.
In this model, the following additional heat flux is
added to energy conservation equation for Hf:
(10)
2.2. Governing equations for gas and plasma
On the basis of assumptions described above, the gas
and arc plasma are governed by following equations:
The thermionic emission current density was given by the
Richardson-Dushmann equation with Schottky effect:
(11)
(1)
(12)
- Mass conservation:
(2)
(3)
(4)
- Energy conservation:
In these equations:
, heat flux between the surface
cathode and the plasma; , temperature of the plasma
contacting with the cathode; , temperature of the surface
cathode contacting with the plasma;
, ambient
temperature, here 300K as the wall temperature of nozzle;
e, elementary charge; k, Boltzmann’s constant;
,
Stefan–Boltzmann’s constant; A, thermionic emission
constant; , vacuum permittivity; , work function of
Hf and Cu;
, ionization energy of oxygen ion; , solid
emissivity; , material factor for thermionic emission; ,
thermionic emission current density of electron;
, ion
current density; , electric field at the cathode surface;
, thermal conductivity of the cathode; and , distance
between surface cathode and the centre of control volume.
(5)
2.4. Governing equations for evaporation flux
- Mass conservation for Hf vapor:
(6)
The mass production rate attributable to evaporation
is calculable approximately as
- Ohm's law:
(7)
- Ampere's law:
(8)
In these equations,
radiation loss;
, radial
coordinate; , electric field in the axial direction;
,
magnetic field in the azimuthal direction;
, mass
fraction of Hf vapour;
, effective diffusion
coefficient of Hf vapour in O2;
, latent heat for
evaporation;
, the mass production rate because of
evaporation; and I, the total electric current.
2.3. Governing equations for electrode
Inside the solid and liquid, the energy conservation
equation is established as follows:
(9)
where
signifies the enthalpy of the solid/liquid,
denotes the specific heat of the solid/liquid, stands for
(13)
Here,
is the effective mass of Hf vapour,
is the
mass flux of evaporated vapour,
is the mass flux of
redeposition,
is the surface of evaporated Hf and
is the volume of the control volume.
The mass flux of the evaporated vapour
was
calculated using the following Hertz–Knudsen relation as
(14)
where
is the saturation vapour pressure of hafnium
vapour. The saturation vapour pressure was evaluated
using the Clausius–Clapeyron. The mass flux of
redeposition vapour
was calculated as
(15)
The governing equations were used to obtain the
simulation results which have been set up in the previous
works [4, 5] in more detail.
st
21 International Symposium on Plasma Chemistry (ISPC 21)
Sunday 4 August – Friday 9 August 2013
Cairns Convention Centre, Queensland, Australia
Table 1. Thermodynamic properties of the solid material.
Solid
Cu
Hf
s
(kgm-3)
8930
13310
Cps
(Jkg-1K-1)
385.62
140
s
(Wm-1K-1)
381
23
Tmelt
(K)
1356
2506
Tboil
(K)
2855
4876
2.5. Thermodynamic and transport properties
Lv
(MJkg-1)
4.815
3.211
[K]
35000 K
25995 K
19306 K
14339 K
10650 K
10000
1
7909 K
5874 K
4363 K
0
3000
3240 K
2407 K
1787 K
1
1328 K
1000
986 K
732 K
3
544 K
holder B
2.6. Boundary conditions
404 K
300
300 K
0
2
4
6
Axial position [mm]
8
Fig.3 Temperature distributions of arc plasma
300
2
Heat flux [W/mm ]
holder O
250
holder A
200
holder B
150
100
50
0
0.0
0.1
0.2 0.3 0.4 0.5
Radial position [mm]
0.6
Fig.4 Heat flux on the Hf cathode surface
3. Results
3.1. Effects of heat flux on cathode surface by the convex
cathode holder
5.0
Temperature [kK]
Fig.3 portrays the temperature distributions of the arc
plasma with the shapes of the cathode holder of O and B.
The isothermal color fringe for temperature is indicated in
logarithm scale. The arc temperature profiles at axial
position z>3 mm are almost the same to the three shapes
of the cathode holder. On the other hand, it is apparent
that the arc root near the cathode has expanded in the
radial direction with the effect of the convex cathode
holder. The arc root behaviour tends to move to the
surface of the cathode holder with the higher protrusion of
the convex cathode holders A and B. Another noticeable
point is that the temperature inside the copper cathode
holder is decreased in cases of the convex holders
compared to the holder O.
Fig.4 shows the radial distribution of the heat flux on
cathode surface. In cases of the holder A and B, the heat
flux at the radial position r<0.4 mm is lower compared
with that for holder O. An increase in the protrusion of
33000
holder O
2
2
Fig. 1 also shows the computational domain used in this
work. On the axis OA, axial symmetry condition is
applied. Non-slip condition was considered on all the
boundary wall between solid and gas GH, HI, EI and BD.
The velocity inside the solid was fixed at 0 m/s. At copper
wall around inlet OD and CD, temperature was fixed at
300 K. At the outlet AB, the axial gradients of physical
parameters such as enthalpy and velocity were set to zero.
The oxygen gas is injected from the inlet ED with a swirl
component which can be expressed by the swirl gas angle.
The boundary shape is assumed not to change by melting
and evaporation. The SIMPLE method after Patankar [6]
was used for the calculation scheme to solve the
governing equations described in the previous section.
In this paper, the operating parameters are that the swirl
gas angle is fixed at 15 deg. The arc current of 100 A, and
gas flow rate of 20 slm are fixed in this calculation model.
Pressure at the inlet is also fixed at 0.9 MPa.
W
(eV)
4.65
3.53
3
Radial position [mm]
Table 1 shows the thermodynamic properties of solid
material for Hf and Cu. Thermodynamic and transport
properties of oxygen thermal plasma with Hf vapor were
calculated using the equilibrium composition and the
collision integrals between species. These transport
properties of Hf vapor were obtained by the first order
approximation of the Chapman-Enskog method.
Lm
(MJkg-1)
0.206
0.1347
holder O
4.5
holder A
4.0
3.5
holder B
3.0
2.5
2.0
1.5
0.0
0.1
0.2 0.3 0.4 0.5
Radial position [mm]
0.6
0.7
Fig.5 Radial temperature of Hf cathode surface
the convex cathode holder induces the expansion of the
arc root resulting in a low current density in the
immediate vicinity of the cathode, which decreases the
efficient heating of the cathode surface.
st
0.10
3
2
1
0
0
2
4
Axial position [mm]
0
2
4
Axial position [mm]
Fig.6 Distributions of gas flow field
-0.5 -0.3 -0.1 0.06 0.3
Radial position [mm]
W-redeposition
W/O-redeposition
Holder B
Holder O
0.4
0.6
0.8
Amount of mass loss [mg/s]
Radial position [mm]
21 International Symposium on Plasma Chemistry (ISPC 21)
Sunday 4 August – Friday 9 August 2013
Cairns Convention Centre, Queensland, Australia
6
0.08
0.06
0.04
0.02
1 [10 /s]
3
holder B
holder O
0.00
O
2
-0.5x10
1
0
0
2
4
Axial position [mm]
0
2
4
Axial position [mm]
Fig.7 Distributions of vorticity
The radial distribution of the surface temperature of the
Hf cathode for different the shapes of the cathode holder
is presented in Fig.5. The Hf cathode surface temperature
is decreased markedly around radial position r<0.4 mm
with the effect of convex cathode holder. The higher
protrusion of the convex cathode holder results in the
lower Hf surface temperature. This decrease in the surface
temperature is related mainly to arc behaviour, which
decreases the heat flux on the surface of the Hf cathode
by the effect plasma gas flow.
Furthermore, there is no significant change in the holder
surface temperature, which remains lower than the
melting temperature of copper even though the effect of
the convex cathode holder.
3.2. Gas flow pattern affected by convex cathode holder
Fig.6 depicts a comparison of gas flow fields obtained
with the shapes of the cathode holder of O and B. As a
result holder O, the gas flow in front of the Hf cathode
surface moves away from the cathode by effect of
swirling gas flow. In the holder B case, it is noteworthy
that a circular vortex appears in front of the Hf cathode in
which the flow direction is mainly toward the cathode and
moves in the direction against that of swirling gas flow.
Fig.7 presents the spatial distribution of vorticity. Near
the Hf cathode, the value of the vorticity is low for holder
O. It appears a clockwise rotation in the vicinity of the Hf
cathode with convex cathode holder B.
3.3. Effects of the convex cathode holder on evaporation
amount of hafnium cathode
Fig.8 shows the calculated total amount of mass loss of
the hafnium cathode different the shapes of the cathode
holder comparing with no redeposition of Hf vapour. The
effect of the convex holder cathode reduces the amount of
A
B
The shape of cathode holder
6
Fig.8 Amount of mass loss of Hf evaporation
mass loss of the Hf cathode evaporation. The higher
protrusion of the convex cathode holder induces the lower
amount of mass loss, although this progress decreases
slowly in comparison of convex cathode holder A and B.
The reason for a decrease in the amount of mass loss is
that the gas flow vortex close to the cathode surface is
present to move in the clockwise direction. This gas flow
vortex motion toward to the Hf cathode surface reduces
the probability of evaporated Hf escaping from the
cathode surface, and also facilitates the evaporated atoms
returning to cathode surface. In addition, the redeposition
of Hf vapour decreases the mass loss of Hf cathode.
4. Conclusions
Numerical simulations were performed to study the
influence of the shape of the cathode holder on Hf
cathode evaporation for oxygen plasma cutting arc torch
in this paper. The simulated results show that the convex
holder cathode not only reduces the gas flow velocity
from the cathode surface, but also makes a vortex in the
vicinity of the cathode surface moving in the opposite
direction. The heat flux on the Hf cathode surface
decreases markedly with the higher protrusion of the
convex cathode holder, resulting in a rapid clockwise
rotation of gas flow. In addition, the total amount of mass
loss of Hf cathode was predicted to decrease significantly
with the effect of convex cathode holder.
5. References
[1] V. A. Nemchinsky et al., J. Phys. D: Appl. Phys., 39,
R423-R438 (2006).
[2] L. Luo et al., Patent US 5,601,734 (1997).
[3] S. Sakuragi et al., Patent US 5,177,338 (1993).
[4] Nguyen Phi Long et al., J. Phys. D: Appl. Phys., 46,
224012 (2013).
[5] Nguyen Phi Long et al., J. Phys. D: Appl. Phys., 45,
435203 (2012).
[6] S. V. Patankar, Numerical Heat Transfer and fluid
flow, Hemisphere Publishing (1980).