Calculation of the radiation emitted by isothermal arc plasmas in air and
air-metal mixtures.
Y. Cressault1, A. Gleizes1,2, G. Riquel3
1
Université de Toulouse, UPS, INPT, LAPLACE (Laboratoire Plasma et Conversion d'Energie), 118
route de Narbonne, F-31062 Toulouse Cedex 9, France
2
3
CNRS, LAPLACE, F-31062 Toulouse, France
EDF France, Les Renardières, 77818 Moret-Sur-Loing Cedex
Abstract: In order to evaluate the radiation received by workers located near
accidental high intensity arcs we have performed the calculation of the radiation
emitted along isothermal segments of air and air-metal thermal plasmas in seven
spectral intervals corresponding to the classical domains defined as visible,
infrared A to C and ultraviolet A to C. Two kinds of calculation have been
developed: local emission (i.e radiation emitted by a point and escaping the
segment) and total intensity integrated along the segment. The results show that
for pure air the relative contributions of the various intervals depend on the
temperature and that the absorption of radiation is almost negligible. In presence
of metallic vapors the contribution of the UV parts is enhanced but can be largely
attenuated by line self absorption.
Keywords: radiation, electric arc, air, air-metal
1. Introduction
The operators working on electrical installations of
low, medium and high voltages can be accidentally
exposed to short-circuit arcs ranging from a few kA
to several tens of kA. In order to protect them from
the thermal and glowing effects of these devices, the
protections have to be optimized so as to respect the
exposure limits. In order to do so, we need to
characterize more precisely the electric arc, to
consider it as a source of radiation and to evaluate
the radiated power in order to estimate the radiation
received by the workers and to limit the risks
(Erythema, cataract, conjunctivitis, retinal burn,
corneal burn, skin cancer).
The maximum permissible exposure (MPE) values
for the exposure of the human eye and skin to
incoherent optical radiation from artificial sources
are defined for seven wavelengths ranges : the UV
radiations UVA (315-400nm), UVB (280-315nm)
and UVC (100-280nm) that we have reduced to
(200-280nm) because the radiation before 200nm is
absorbed in ambient air; the visible radiations (380780nm) ; and the IR radiations IRA (780-1400nm),
IRB (1400-3000nm) and IRC (3000nm-1mm) that
we have limited to (3000nm-4500nm). These MPE
depend on the duration of exposure and on the
minimum angular subtense (visual angle subtended
by the apparent source at the eye of an observer).
The main objective is then to quantify, for
spectral ranges, the energy radiated by a plasma arc
of length between 0.1m and 2m and high intensity
(4kA < I < 40kA) in order to compare it to the
exposure limits. Three structures (EDF Renardieres,
GREMI of Orleans and LAPLACE of Toulouse)
have collaborated in this work. While EDF and
GREMI are characterizing experimentally the arc
and its environment (temperature, plasma
compositions, local emission, radiated power,
electrical parameters), LAPLACE is realizing a
numerical model of such a device. First, we have to
calculate the total radiation escaping from the
plasma to compare it to the measurements. This
work requires preliminary properties like the
emission coefficients in this interval:
λj
ε Δ (T , X ) = ∫ κ λ' (T ) ⋅ L0λ (T ) ⋅ exp (κ λ' (T ) X )dλ (1)
λi
With κ λ' the total absorption coefficient, L0λ the
black body intensity, and X the plasma's size.
This first calculation gives us two indications: the
spectral intervals where the radiation is the most
important; and its absorption through the plasma.
Then, we can simplify the calculation of the
radiative transfer by separating the non-absorbed and
absorbed radiations.
Figures 1 and 2 present the emission obtained for
pure air plasmas, different thicknesses, and the 7
spectral intervals defined earlier.
10
9
10
7
R p=10cm
R p=0m
R p=1mm
R p=5mm
R p=10mm
3
In this paper, we present one of the first
steps of this large study corresponding to the
calculation of required data which is the local
emission (and absorption). We applied these
calculations in the case of air plasmas at atmospheric
pressure, with or without metallic vapours
(Cu/Fe/Al), for temperatures between 300K and
30000K, for several thicknesses of plasma inferior to
10cm and the 7 spectral regions defined before. All
radiative processes were considered: the molecular
and atomic continua, lines and molecular bands of
O2, N2 and NO. For Air-Cu mixtures and for each
spectral interval, we present the net emission, the
contribution of each wavelength range on the total
radiation, and the influence of metallic vapours.
Finally, we present a first calculation of the intensity
L(X) obtained for pure air plasmas and for several
distances X from the luminous source.
Δ = λ j − λi is obtained by the sum of all the
εΣΔ ( W/m /sr)
temperature field, the local emission, the shape of
the arc and the concentration of the metallic vapours
issued from the erosion of the electrodes (iron,
copper or aluminium).
5
P = 1 atm
Pure Air
Total of spectral intervals
10
3
5
10
15
20
25
30
Tem perature (kK)
Figure 1. Net emission for air plasma and several thicknesses
(200nm < λ < 4.5μm)
3
To calculate the net emission, we first have to
estimate the different population number densities
(versus temperature) and the spectral distribution.
We then considered the radiation of the continuum
spectrum (atomic and molecular continuum), of the
molecular bands (O2, N2, NO) and of the atomic
lines (6267 lines for Oxygen, 9313 lines for
Nitrogen, 5180 lines for Copper and 95027 lines for
Iron). The lines broadenings were taken into account
but the influence of their overlapping on the
radiative transfer was neglected. More information is
available in a recent publication [1]. We calculated
the net emission for the 7 spectral intervals
according to the net emission coefficient (NEC).
This coefficient preserves the spectral dependence
(according to the wavelength) but simplifies the
geometrical dependence of the plasma. It is also
often used in the numerical models since it gives a
good estimation of the net radiation of the plasma
(by considering the absorption in the medium) in the
hottest regions and its use is very simple. For
homogeneous, isothermal and spherical plasmas
(radius Rp), the NEC for each spectral interval
10
εΔ ( W/m /sr)
2. Net emission by spectral intervals
10
9
10
7
10
5
10
3
ΣΔ
R p=0mm
P = 1 atm
Pure Air
IRC
10
UVA
UVB
UVC
Vis
IRA
IRB
IRC
Total
1
5
10
15
20
25
30
Temperature (kK)
Figure 2. Emission of the 7 spectral intervals for air plasma.
We observe that any wavelength range is negligible :
the Visible radiation is systematically a significant
10
3
Figure 3 shows the emission obtained for
optically thin Air-Cu plasmas. When a small
concentration of vapours (<1%) is added to the
plasma, this emission is strongly increased in Visible
and UV. This behaviour can be explained by the
presence of metallic resonance lines in these spectral
regions.
increases in the plasma, the Visible and IR
contributions are weaker than the UVC radiation as
shown in Figure 5. The same behaviour can be
observed for Air/Fe mixtures in Figure 6.
εΔ ( W/m /sr)
contribution to the total radiation, the IRA part plays
a role only for T<25kK (since the IRB and the IRC
intensities are always ten times inferior to the
maximum value); the UV part becomes more
important for high temperatures.
10
9
10
7
10
5
10
3
10
5
10
15
20
25
30
Temperature (kK)
3
Figure 4. Net emission for the 7 spectral intervals,
99%Air-1%Cu mixture ans Rp=1cm.
UVA
UVB
UVC
Vis
IRA
IRB
IRC
Total
5
IRC
Rp=0mm
P = 1 atm
99% Air - 1% Cu
Mass proportions
10
10
10
8
ΣΔ
1
5
10
15
20
25
30
3
10
1
ΣΔ
εΔ ( W/m /sr)
3
εΔ ( W/m /sr)
10
7
UVA
UVB
UVC
Vis
IRA
IRB
IRC
Total
R p=1cm
P = 1 atm
99% Air - 1% Cu
Mass proportions
IRC
9
10
10
ΣΔ
Compared to Figure 3 (Rp=0), Figure 4 (Rp=1cm)
shows that the total radiation of the 7 intervals is
mainly absorbed in the temperature range 3000K17000K. The emissions of the IR parts are lower
than the UVC part and are weakly absorbed. We also
observe that the behaviour of the UVB and UVA
emission is almost the same with a maximum
emission and absorption around 7000K but the
values are one order less than the UVC part. The
lines are strongly emissive and partially absorbed in
the UVC band which represents the major part of the
total emission at high temperature. This behaviour
was not remarked for pure air plasma and can be
explained by the radiation of the Iron lines and
specially the resonance lines which are more
intensive and localised in UV spectral range.
Consequently, the UVC part which does not play a
significant role in air plasma becomes very
important when iron, copper or alumina vapours
exist inside. When the proportion of metal vapours
10
6
10
4
10
UVA
UVB
UVC
Vis
IRA
IRB
IRC
Total
R p=1cm
P = 1 atm
90% Air - 10% Cu
Mass proportions
IRC
2
5
10
15
20
25
30
Temperature (kK)
Figure 5. Net emission for the 7 spectral intervals,
90%Air-10%Cu mixture and Rp=1cm
3
Figure 3. Emission for the 7 spectral intervals,
99%Air-1%Cu mixture and Rp=0mm.
εΔ ( W/m /sr)
Temperature (kK)
10
9
10
7
10
5
10
3
ΣΔ
IRC
10
UVA
UVB
UVC
Vis
IRA
IRB
IRC
Total
R p=1cm
P = 1 atm
99% Air - 1% Fe
Mass proportions
1
5
10
15
20
25
Temperature (kK)
Figure 6. Net emission for the 7 spectral intervals,
99%Air-1%Fe and Rp=1cm.
30
30
28
24
22
2
4
3. Intensity by spectral intervals
At a position x, the local emission is given by κ λ Lλ .
This emission is then absorbed along a distance (Xx), X being the length of the segment. For an
isothermal segment, at the exit X, the intensity is:
'
[
X
]
0
U VC
U VB
IRC
26
L(X) ( 10 W/m /sr)
Contrarily to Air/Cu and Air/Fe mixtures which
present a similar shape for the emission (higher
emission with iron), the results obtained with
aluminium vapours are slightly different.
without absorption
pure air
10000 K
20
18
16
without absorption
IRA
14
12
10
Vis
8
6
IRB
4
UVA
2
0
0
20
40
60
80
100
distance X (m m )
[
(
)]
Lλ ( X ) = ∫ L0λ Kλ' exp − ( X − x)Kλ' dx = L0λ 1 − exp − Kλ' X (2)
Figure 7. Influence of the distance X on the intensity L(X) for
pure air plasmas.
O
We can write this expression for a given spectral
interval Δ:
LΔ ( X ) =
λ2
∫λ
[
(
L0λ 1 − exp − K λ' X
)]
dλ (3)
1
In the introduction of this paper, we indicated that
the overlapping of the lines was neglected. The
radiative transfer of each line was then calculated by
the use of the escape factor defined by Drawin and
Emard [2]. This factor Λλ represents the ratio
between the radiation flux (including absorption)
escaping from the plasma and the radiation flux
escaping from the plasma without absorption.
Consequently, the escape factor allows us to
calculate the part of the radiation of a line which is
emitted at a point x and absorbed along a distance
(X-x). We can then write the expression (3) with the
use of the escape factor:
λ2
X
LΔ ( X ) = ∫ ε λ ∫ Λ λ ( x ) dx dλ
λ1
'
(4)
0
For each line, we must integrate the escape factor for
different distances X. This integration is not trivial
because it depends on the temperature and the
plasma’s size. We have tabulated this integration for
temperature between 300 and 30000K, distances
from 0 to 10 cm, and for several proportions of
metal vapours.
Figure 7 presents the intensity obtained for
pure air plasmas. The dashed curve is obtained
according to the relation (4) by considering the
absorption whereas the full curve represents this
intensity supposing any absorption in the plasma.
4. Conclusion
We showed that the emission of air plasma is weakly
absorbed whatever the spectral interval between
200nm and 4.5μm. Nevertheless, in presence of
metallic vapours, the emission increases in the
Visible and UV parts because of the metallic lines
and of the increase of the electron number density at
small temperatures. These lines are partially
absorbed. We showed that metallic vapours in the
plasma strongly modify the emission in the UVC
part which becomes dominant for high temperatures.
These results will be coupled with experimental
measurements and with the numerical modelling of
the arc. They will be used to estimate the radiative
transfer for a real arc in order to calculate the
radiative flux received by an observer positioned at
various distances from the arc (for each spectral
band UVC, UVB, UVA, Visible, IRA, IRB, IRC).
The results also constitute a database which can
either be used for the calculation of the radiative
transfer or be directly used in numerical modelling
to take into account the thermal properties of pure
Air, pure metallic vapours (copper, aluminium or
iron) or mixtures Air/vapours (for processes like arc
circuit breakers or arc welding for example).
This work has been supported by RTE-France
Company (EDF transport).
References
[1] Y. Cressault, R. Hannachi, Ph. Teulet, A. Gleizes, J.-P.
Gonnet, J.-Y. Battandier, Plasma Sources Sc. Technol. 17, 2008,
035016
[2] Drawin H.W., Emard F. Beitr Plasma Physik, 13, 143,
(1973)