The radial temperature distribution of

a constricted oxygen arc in plasma arc cutting

Sung Je KimHigh Temperature & Plasma Laboratory University of Minnesota

Rotating anode

Torch body

PowerSupply

Gas supply, O2

RHF Starter

2

Components of cutting system Cutting torch components

Plasma Arc Cutting

Elenbaas-Heller Equation

( ) ( ) ( ) 21 ETTdrdTrrk

drd

rσλ −=

( ) ( )∫∫ ⋅==RR

rdrrErdrrEI00

22 σπσπRr =

K [W/m.K]

0.00E+00

1.00E+00

2.00E+00

3.00E+00

4.00E+00

5.00E+00

6.00E+00

0 5000 10000 15000 20000 25000 30000

Temp [K]

sig [1/ohm.m]

0.00E+00

2.00E+03

4.00E+03

6.00E+03

8.00E+03

1.00E+04

1.20E+04

1.40E+04

1.60E+04

0 5000 10000 15000 20000 25000 30000

Temp [K]

( )Tσ ( )rk

( ) 0=Tλ KT o31040 ×≤≤

( ) ( )[ ] sec/12800/40001018512.1 3795.410 ⋅−×= cmergsTTλ KTK oo 33 1016104 ×≤≤×

( ) sec/108641.1 316 ⋅×= cmergsTλ KT o31016×>

Gauss-Siedel Method

2

1

21

21

1

21

211

iii

iiii

iiii

i

Edr

drTTkr

drTTkr

drd

rσλ −=

−−

− −−−

+++

∑=

iii

i drrIEσπ2

i=1 i=2 i=3 i=N-2 i=N-1 i=N

15000

17000

19000

21000

23000

25000

27000

29000

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Radius (mm)

Tem

pera

ture

(K)

0.5 mm1.5 mm2.5 mm4.0 mm

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

1.6

1.8

2

2.2

2.4

2.6

2.8

x 104

Radius [mm]

Tem

pera

ture

[K]

oxygen

Heat transfer to the anode

xEj σ= ∫∫ ==R

x

R

rdrEjrdrI00

22 σππ

)(203.3 wiie

eh

heB

wa jdxdT

KdxdT

KjTek

jq φεφ −−−−+=

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8x 109

radial distance [mm]

anod

e he

at fl

ux [W

/m2 ]

Differenct contribution to anode heat flux

total heat flux electron condensation electron enthalphy heavy particle conduction

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.91.8

1.9

2

2.1

2.2

2.3

2.4

2.5

2.6x 104

radial distance [mm]

tem

pera

ture

[K]