24P023-O
Numerical Study on Eﬀect of Gas Pressure and Cathode Diameteron Evaporation of Hafnium Cathode in a Plasma Cutting Arc
Nguyen Phi Long, Yasunori Tanaka, and Yoshihiko Uesugi
Division of Electrical Engineering and Computer Science,Kanazawa University, Kakuma-machi, Kanazawa 920-1192, JapanThe eﬀects of the gas pressure and cathode diameter in plasma cutting arc torch were investigated using
a developed two-dimensional thermofluid model with considering hafnium cathode evaporation. The simulated results show that the temperature of the cathode surface is decreased at the center of cathode tip
with increasing cathode diameter. On the other hand, increasing gas pressure elevates the surface cathodetemperature in the range of 0.35 mm in radius of cathode tip. The net evaporation mass flux of hafnium
cathode was predicted to be enhanced with increasing gas pressure and cathode diameter.

1.

Introduction
The plasma arc cutting process is a widely usedtechnique for cutting diﬀerent metals with high speed
and high accuracy in industrial fields. An arc plasma isestablished between the electrode in the plasma torch
and a work-piece, which is molten by high-temperaturefrom the arc plasma and heated by oxidation reactions[1]. To enhance the performance and the lifetime ofplasma arc cutting device, understanding details of interactions between the electrode and the arc plasma
under diﬀerent operating conditions is necessary . This
report numerically studied the eﬀects of gas pressure
and cathode diameter on temperature field and the net
evaporated mass flux from hafnium (Hf) cathode in theplasma cutting arc torch.
2. Calculation model and boundary condition
Fig. 1 shows the arc model and calculation spaceused in this work. The copper electrode has a hafnium
tip insert at the cathode center. Oxygen, which is usedas the plasma gas, is supplied from the inlet by swirling
gas flow. The length from the cathode tip surface to thenozzle exit is approximately 8 mm. The arc plasma isconstricted by the copper nozzle with a nozzle outlet of
1.33 mm in diameter. The main simplifying assumptions on which the developed numerical models rely
are as follows: steady state, axis-symmetric, laminargas flow, local thermodynamic equilibrium, and optically thin plasma in a two dimensional space. Thismodel solves not only the mass, momentum, energy
conservation equation for plasma-gas, and mass conservation of Hf vapor evaporated from the cathode, butalso the energy conservation equation of the electrodeand the nozzle. The net mass flux from Hf cathodewas predicted considering the evaporation flux estimated using the saturation vapor pressure and the redeposition flux. The SIMPLE method after Patankar[3] was used for the calculation scheme to solve thegoverning equations described in our previous report[2]. The swirl gas angle is fixed at 15 deg. The arc
current of 100 A and gas flow rate of 20 slm are also
fixed for diﬀerent cathode diameters and gas pressures.

inletO2gas D
4.0]3.5 Em[m3.0I
Current niot 2.5
source is2.0
pol 1.5 Cu
iad1.0Nozzle
aR0.5 Hf H
0.0 O
G 2Work-piece
0Electrode
Hf insert
Swirl gas
O2 gasArcplateCCu-nozzle
Gas/plasma

46
Axial position [mm]outlet BA8Fig. 1: Arc model and calculation space43]2m[mno 1iit
so 0
pliad 1aR234[K]35000

1.3 mm

35000

25995
19306
14339
10650

10000

7909
5874
4363
3240

3000

2407
1787
1328
986

2.0 mm

1000

732
544
404

0246
Axial position [mm]

8300

300

Fig. 2: Temperature distribution of arc plasma with cathodediameter of 1.3 mm and 2.0 mm

3. Calculation Results
3.1. Eﬀect of cathode diameter
For purposes of studying the eﬀects of cathodediameter on behavior of hafnium cathode evaporation,
the cathode diameters are chosen with values of 1.3,1.6, and 2.0 mm. The gas pressure is fixed at 0.8 MPa.
Fig. 2 shows the temperature distribution of arc
plasma with cathode diameter of 1.3 mm and 2.0 mm.
This figure demonstrates that the arc root near the cathode surface is expanded in the radial direction with alarge cathode diameter and the maximum arc plasma

5.0] 4.5Kk[ 4.0er 3.5
ut 3.0rae
p 2.5
meT2.01.5
1.00.0dHf=2.0 mm
dHf=1.6 mm

dHf=1.3 mm

0.2 0.4 0.6 0.8
Radial position [mm]1.0Fig. 3: Radial distribution of surface temperature of Hfcathode for diﬀerent cathode diameters]) 0.55
2 s 0.50m(/ 0.45gk[ 0.40xu 0.35lf
ss 0.30
a 0.25m
no 0.20itar 0.15
op 0.10av
et 0.05
eN0.005.04.5]K4.0[ker 3.5
P=0.9 MPatua
P=0.8 MPa
re 3.0P=0.7 MPa
p 2.5m
P=0.6 MPa
eT2.01.5
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
Radial position [mm]Fig. 5: Radial distribution of surface temperature of Hfcathode for diﬀerent gas pressures
2dHf=2.0 mm
dHf=1.6 mmdHf=1.3 mm-0.05
0.0 0.1 0.2 0.3 0.4 0.5 0.6
Radial position [mm]]s) 0.45
P=0.9 MPa
0.40m/(g 0.35
P=0.8 MPak[xu 0.30
fls 0.25
sa
m0.20
no 0.15
tia
ro 0.10 P=0.7 MPa
pa
ve 0.05 P=0.6 MPa
te 0.00
N-0.050.0 0.1 0.2 0.3 0.4 0.5
Radial position [mm]Fig. 4: Radial distribution of net evaporated mass flux from Fig. 6: Radial distribution of net evaporated mass flux fromHf cathode for diﬀerent cathode diameters

Hf cathode for diﬀerent gas pressurestemperature reaches 33,000 K at the nozzle throat byconstriction of the nozzle.
The radial distribution of the surface temperatureof the Hf cathode for diﬀerent cathode diameters ispresented in Fig. 3. The temperature of the cathodesurface is decreased markedly at the center of cathodetip with increasing cathode diameter. The reason isthat the large cathode diameter allows a high densitypresence of hafnium evaporation on cathode surface
and increases the convective heat transfer.
Fig. 4 shows the net evaporation mass flux fromhafnium cathode tip for diﬀerent cathode diameters.
The net evaporation mass flux increases markedly andexpands in radial direction with increasing cathode diameter. This is explained by the fact that an increased
cathode diameter means a larger hafnium vapor in frontof cathode tip expanding in radial direction. However,the negative net evaporation flux appears around thefringe of the arc, where the evaporated atoms return tothe cathode surface.
3.2. Eﬀect of gas pressure
The similar calculations were made to investigate
the eﬀect of gas pressure on Hf cathode evaporation.
The gas pressures are chosen with values of 0.6, 0.7,0.8, and 0.9 MPa. The cathode diameter is fixed at 1.6
mm. Fig. 5 presents the radial distribution of surface
cathode temperature for diﬀerent gas pressures. Thisfigure shows that the surface cathode temperature in
the range of 0.35 mm in radius increases with gas pressure. As gas pressure increases, the arc root skrinks,
which allows a higher current density near the surface
cathode tip, causing a high temperature of Hf cathode.
Furthermore, the results from Fig. 6 indicated that thenet evaporation mass flux from Hf cathode increases
concomitantly with increasing gas pressure.
4. Conclusion
The numerical investigations of the influence of
cathode diameter and gas pressure in plasma cutting
arc torch are studied in this report. The calculation
results show that the surface cathode temperature at
the center of cathode tip decreases with an increasing
cathode diameter and a decreasing gas pressure.
In addition, the net evaporation mass flux fromhafnium cathode was enhanced with cathode diameterand gas pressure.
References[1] V. A. Nemchinsky, and W. S. Severance,: J. Phys. D:Appl. Phys. 39 (2006) 423-428.
[2] N. P. Long, Y. Tanaka, Y. Uesugi, and Y. Yamaguchi:
Proc. 20th Int. Symp. on Plasma Chem., Philadelphia,USA 2011.
[3] S. V. Patankar,: Numerical Heat Transfer and fluid
flow (Hemisphere Publishing Corp. New York) 1980.