used in an air-blast circuit breaker as the arc quenching medium, although it ..... (11) K.P.Huber and G.Herzbeg: Molecular Spectra and Molecular. Structure IV.
Paper
Thermodynamicand Transport Propertiesof N2/O2 Mixtures at Different Member
Yasunori
Member
Khokan
Member
Tadahiro
Admixture Tanaka
Ratios (Kanazawa University)
Chandra
Paul
Sakuta
(Kanazawa University) (Kanazawa University)
Thermodynamic and transport properties such as mass density, enthalpy, specific heat, electrical and thermal conductivities and radiation power of N2/02 mixture plasmas at different admixture ratios were calculated in pressure range from 0.1 to 2 MPa on the assumption of thermal equilibrium condition. The first order approximation of Chapman-Enskog method was adopted to derive the transport properties. The thermodynamic and the transport properties thus derived were used to predict the temperature distributions and electric field strength of wall-stabilized N2/02 arcs in steady state at a current of 20 Ad, in order to investigate fundamental feature of N2/02 mixture arcs before current zero. The calculation revealed that the temperature at the center of the arcs had a local minimum value of 8800 K at an admixture ratio around 80%N2-20% O2and whilst the conductance of the arc has a minimum at an admixture ratio of 100%N2 for pressure of 0.5 MPa in steady state. Keywords: bution
thermodynamic and transport properties, N2/O2 mixture plasma, admixture ratio, temperature distri
medium(3)-(7). These SF6 gas mixtures are expected to be used for the moment, however, the use of these mixtures is not an essential resolution of the environ mental issue. The atmosphere, that is air, is composed mainly of 78%-nitrogen and 22%-oxygen, which are, of course, environmental-friendly gases. The air has so far been used in an air-blast circuit breaker as the arc quenching medium, although it has much weaker arc quenching capability than SF6 gas. However, few engineers tried to find the optimum admixture ratio of N2/O2 for the purpose of arc interruption. The present research aims to find an N2/O2 admix ture ratio adequate to the arc quenching in a circuit breaker from the view point of thermodynamics. For this purpose, it is greatly required to obtain the ther modynamic and transport properties of N2/O2 mix tures. In this paper, therefore, numerical calculations were performed to derive thermodynamic and trans port properties such as mass density, enthalpy, specific heat, electrical and thermal conductivities and radiation power of N2/O2 mixture plasmas at different admixture ratios on the assumption of thermal equilibrium. First, equilibrium compositions of N2/O2 plasma at different admixture ratios were calculated. Secondly, their ther modynamic and transport properties were theoretically derived. Finally, using the properties thus derived, tem perature distributions of a wall-stabilized arc in steady state were predicted for different admixture ratios of N2/O2 in order to investigate fundamental feature of the arc before current zero.
1. Introduction In high-voltage circuit breakers, SF6 gas is widely adopted as the arc quenching medium since it has an attractive arc quenching capability. The capability is considered to arise not only from the electronegative properties of SF6 gas and its products, but also from the high thermal conductivity at low temperature around 2000 K (1). The use of SF6 gas as the arc quenching medium has led to the high interruption capability and the downsizingof a circuit breaker. Recently, however, emission of SF6 gas and its prod ucts to the atmosphere has been an environmental issue because of its remarkable greenhouse effect. In order to compare the greenhouse effect of different gases, a method has been developed of estimating their global warming potentials (GWP). The GWP is the cumula tive enhancement occurring between now and a chosen later time, in relation to a reference gas, CO2. Pure SF6 gas has an extremely high GWP of 23 900 over 100 years. Thereby, in the third Conference of Parties to the U.N. Framework Convention on Climate Change (COP3) held in Kyoto, Japan in 1997, developed coun tries were required to reduce the generation of six green house gases like CO2 as well as SF6 gas by on average 5.2 percent by the period 2008-2012(2). Much effort have been made to find out an alterna tive gas of SF6 gas for arc quenching medium until now. However, none of gases with small GWP and attractive arc quenching property has been able to be found yet. Gas mixtures such as SF6/N2, SF6/CF4 and SF6/C2F4 have been developed to utilize for the arc quenching 24
T. IEE Japan, Vol. 120-B, No. 1, 2000
Thermodynamic
Fig.1. Equilibriumcompositionof 80%N2-20% O2 plasma at a pressureof 0.1 MPa.
and Transport
Poroperties of N2/O2 Mixtures
Fig. 2. Mass density of N2/O2 plasma at a pres sure of 0.5 MPa.
2. Equilibrium composition of N2/O2 mixture In this calculation, we took account of the following 16 species: N2, O2, NO, N, O, N+2,O+2,NO+, N-2, N+, O+, N-, O-, N2+, O2+ and the electron. For these species, a system of equations was set up includ ing Saha's equations for ionization reactions, GulbergWaage's equations for dissociation reactions, the charge neutrality equation, the equation of state and the con servation equation of N2/O2 ratio, i.e.:
Fig. 3.
Dependence
plasma
on pressure.
3.
where XN2 and XO2 are the concentrations of nitrogen and oxygen, respectively, nj is the number density of species j. These equations were simultaneously solved using Newton-Raphson method in temperature range of T=300-30 000 K, for XN2 from 0 to 100% and pres sure P from 0.1 to 2 MPa. The case of XN2=78% cor responds to the pure dry air. Figure 1 indicates the equilibrium composition of N2/O2 plasma at an admixture ratio of 80%N2-20% O2 and at a pressure of 0.1 MPa as an example. As seen in Fig.1, N2 and O2 dissociate with temperature T to be N and O atoms. At the same time, N and O combine to produce NO. The molecule NO mainly emits electrons at temperatures up to 8000 K because of its lowest ion ization potential of 9.26 eV among all species in N2/O2 plasmas (11) 電 学 論B,
120巻1号,平
成12年
25
Thermodynamic
3.1
Mass
obtained
where of
mj
of
be
of
T.
300-4000 K,
8500 change
of
K.
to of
30
000
main
It
is
j.
K.
seen
O 2 to N2, O and to N, O lustrates the dependence
with of ƒÏ
of
in
in the
raises ƒÏ changes in
the
2 indicates
MPa in
XN2
These
particles
Figure
P=0.5
However, XN2
data
density ƒÏ
by
at
with
increasing
composition mass
species
plasmas
insignificantly
8500
the
section, calculated
mass
temperature
range
the
can
mixture
changes
from
Using
preceding
is the
N2/O2
tion
to
the
plasma
of 50% N2-50% O2
properties
density
in
mixture
ƒÏ
of mass density
as
this the
that ƒÏ
temperature
range while in ƒÏ mixture
a func
figure
from
4000
decreases ƒÏ are
due
from
to N2,
increasing T. Figure 3 il of 50% N2-50% O2 plasma
Fig. 4. Enthalpy of N2/O2 plasma at a pressure of 0.5 MPa. on pressure
P.
The
mass
density
p proves
to be almost
h of thermal
plasma
in proportion to pressure. 3.2 Enthalpy Enthalpy given
by the
where the
following
k is the internal
thalpy variations
in
tions
are
them
arises
of O02
and
3.3 cific sient
Boltzmann's
h
in
from N2,
Cp
plasma.
T
at
h around the
P=0.5 4200
energy
and •¢Hfj
are
standard
en
Figure
4
MPa.
Sharp
and
necessary
Zj the
7500 for
represents
K.
varia Each
of
dissociations
respectively.
Specific heat
and
respectively.
versus
found
constant, function
formation,
is
expression:
partition
of
Fig. 5. Specific heat at constant pressure of N2/O2 plasma at a pressure of 0.5 MPa.
heat is one The
at
of the value
constant
pressure
important
properties
Cp
can
be
computed
Spe for
tran
by
Fig. 6. Specific heat 50% N2-50% O2 plasma
Figure 5 shows Cp for N2/O2 plasma at P=0.5 MPa. We can notice two remarkable peaks in Cp, around T=4200 and 7500 K. They result from the requirement of energy for dissociating O2 and N2, respectively, as discussed in the previous section of h. The peak around T=17 200 K is due to ionizations of N and O. In Fig.6 pressure dependence of Cp is demonstrated for 50%N250% O2plasma. At higher pressure, the O2 and N2 dissociation peaks and the O and N ionization peaks are shifted to higher temperatures, and lowermaximum values are obtained. This is due to the fact that the fraction of dissociated and ionized particles in the gas decreases with rising pressure according to GuldbergWaage's and Saha's equations(8). 4.
Transport
into
momentum
cosity
cross
ticles
in
at constant pressure at different pressure,
transfer
cross
sections ƒÎƒ¶(2,2)ij
N2/O2
sections ƒÎƒ¶(1,l)ij between
plasma.
for
These
and
all data
couples
were
vis
of
par
obtained
as
follows: (i)
Neutral-neutral ƒÎƒ¶(1,1)ij a nd ƒÎƒ¶(2,2)ij
been
given
this
calculation.
(ii)
Ion-neutral
tween species were
by
Yos
species
NO+
N+, O+,
given
(9).
The
N2, O2,
These
by
N2
Yos(9).
the
other
were
For , O2,
cross
NO,
data
interaction.
neutral
ƒÎƒ¶(2,2 ) of
interaction. among
NO,
have used
in
interactions
and O, the
be
and
N2+
and O2+,
The
cross
sections ƒÎƒ¶(1,1)ij
were
assumed
couples
sections
and O
directly
the N
N
ionized
cross
sections and
to
b e equal
properties
to
4.1 Collision integrals The Chapman-Enskog formula for calculating electrical and thermal conduc tivities requires data on the collision integrals classified
the
(iii)
ones
26
neutral-neutral
Electron-neutral
tions ƒÎƒ¶(1,1)ij O
for
were
also
interaction.
and ƒÎƒ¶(2,2)ij derived
interactions.
by
of
The
electron-N2, O2,
cross NO,
sec N
and
Yos (9).
T. IEE Japan,
Vol. 120-B, No. 1 , 2000
Thermodynamic
(iv)
Interaction sections
by
between between
Gvosdover 4.2
cross
and
the
sections
Coulomb
of order
calculated
potential The
collision
enable
conductivity ƒÐ first
for
N2/O2
to plasma
the
in
of
on
derived
calculate
approximation
(9).
data
integrals
us
The
were
conductivity
compositions
the
particles.
particles
section
Electrical
previous
charged
charged
the
in
the
electrical
accordance
the
Properties of N2/O2 Mixtures
Fig. 8. Electrical conductivity of N2/O2 plasma at an admixture ratio of 50%.
Fig. 7. Electrical conductivity of N2/O2 plasma at 0.5MPa versus admixture ratio.
cross
and Transport
with
Chapman-Enskog
method:
where
e is the
stant
and ƒÃo
Figure noted
of
10%
at
is
45.6
S/m.
effect
sure
rise
than
12
500
K.
at
pressure K. This
the
from
a
95
to
on ƒÐ
reason
higher
Thermal
NO
by
should XN2
di
of ƒÐ
at
lower
in Fig.8.
the
other
temperatures of electron
Pres
hand
of
three
and
rising
10
includes
12 500 den
the
section
shifted
conduc
contributions:
the
and CPi
reaction
at
4200
the
peak
re
is
heat
to
the
the for
a
In
27
the
of
results
increase
this
the
elevating k,
in
15 which
number
found
7500 an
in K
are
increase
000-30 is
conductivity
electron
Figure
As
with
of
N2.
and
between
that
dissociation of
4200
whilst
means
on k. at
temperature
in
and
These
that
pressure
peaks
thermal
Radiation
account
two
higher
translational
by
effect
from
peak Rising
value,
K. from
K
mixtures the
remarked.
peak
7500
temperatures
rise
rising
7500
Cp
At
this
N2/O2
pure O2
be
originates
at
of
For can
around K
the of
of k
K in
peak
to tron
4200
decrease
pressure
ing
成12年
is
ratios.
about a
peak
5.
120巻1号,平
variations
another
O 2
k =Ktr+Kin+Kre...........(9)
電 学 論B,
the
pressure.
Thermal sum
9 shows
brings
the
rise.
the
i, •¢He
at
forms
collisions
than number
internal respectively,
species
admixture
centered
temperatures
frequent
translational,
of
different
XN2
seen
On
heat
Figure for
100%. be
are
conductivities,
reaction e.
lower
markedly
thermal
specific
XN2
has
and kre
actional
K, ƒÐ
with
which
species
conductivity
is expressed
where ktr, kint
It
T=5000
drastically
is more
pressure
con
around
at
can
pressures.
from
value
other
decline
The
MPa.
example,
enhances ƒÐ at higher is due to the augment
resulting
4.3
to
P=0.5
is because
than
XN2
at
drops
This
Boltzmann's of vacuum.
maximum For
of pressure
leads
occurring
tivity k
K.
100%.
with
The
a local
potential
minishes
XN2
Whereas, ƒÐ
to
ionization
sity
has
3000-8000
k the
constant
a versus
that ƒÐ
95
charge,
dielectric
7 plots
be
from
electronic the
000
in K,
ascribable of
the
elec
Prad
tak
density.
power
paper,
we of
calculated
contributions
radiation of
continuous
power
spectra
due
Fig. 9. Thermal conductivity of N2/O2 mixture at a pressure of 0.5 MPa.
Fig. 11. Radiation power of N2/O2 mixtures at a pressure of 0.5 MPa as a function of temperature. quantity Prad for pure N2 plasma at a pressure of 0.1 MPa derived in this paper was confirmed to have similar value to that calculated by Gleizes in the case that no self-absorption was taken into account (5). From Fig.11, we can find that Prad increases with XN2, in the tem perature range above 7000 K since emission coefficients of N and N+ spectral lines in the ultraviolet wavelength region, which are dominant components of Prad, rises with XN2. 6.
Temperature arc in steady
distribution state
in a wall-stabilized
For the purpose of investigating the arc interruption characteristics, it is useful to understand features of the wall-stabilized arcs. A wall-stabilized arc in steady state was assumed to be governed by the following relation ship: Fig. 10.
Thermal
plasma
versus
to bremsstrahlung tral
lines
lowing
c is
tion
of
tical of all were 0.5
the
from
weight, the the
adopted. MPa
hp
the
level, ă
lines
for
of
and
and that ions by using
of spec the fol
(9):
e, A
upper
atoms
velocity
species
of 50% N2-50% O2
and recombination,
emitted
expressions
where
conductivity
pressure.
N, Figure
different
of the
light,
Ze
Planck's
transition the N+, O
the
partition
probability, wavelength. and O+
11
is
constant,
illustrates
admixture
E For
on Prad ratios
func
g the
statis
the
energy
spectral
the
literature at
of
lines, (10)
a pressure N2/O2.
where E is the electric field strength, I is the current, r wallis the radius of the wall and G is the conductance for a 1-m long arc. The above equations were solved by iterative method to find the effect of admixture ratio of N2/O2 on the temperature distribution of a wall stabilized arc in steady state. The wall radius rwall and the temperature at the wall boundary were set to be 2.5mm and 300 K, respectively. The value of current I was fixed to 20 Adc,as an example, because it is im portant to investigate the important and fundamental characteristics of the arc at several micro-seconds be fore current zero in the high current interruption . In this calculation, any self-absorption was neglected for
of The
28
T. IEE Japan,
Vol. 120-B, No. 1, 2000
Thermodynamic
ferent
P
Fig.14 arc
and Transport
as
a function
(a) have
and
at
0.5
tio
80%
02,
T
the
at
radiation
seen
in
case
loss
of P=2.0
as
G
of
minimum
value
At
at
input
sustain
Adc,
N2 is better
7.
Thermodynamic
and
density,
thermal
mal
for
as
N2/O2
ratios.
The
port and
The
properties. transport
values
which
is almost
electric
field
0.5
and
arc
the Figure
conductance
12 plasmas
As
concentration
the
temperature
at
This
ductivity
at
effect
in
rise
thermal In ƒÐ at
to
arc
on
temperature high
Prad
of the
caused
the
can
be
the
the
by
in
the
of
trial
further
the
電 学 論B,
Fig.14
center
of
120巻1号,平
(a)(b)(c) the
and
arc 成12年
and
E
(d) as
of
us high
trans
thermodynamic the temperature
in steady
state
ratio was
on
found
of
were funda
that
the
have
local
80%
N2-20%
02
that
the
while at
min
XN2=100%. at a pressure
XN2=100%
for an
of
the
a current important
current
causes of
20
and arc
Adc. funda
around
cur
and
of
demonstrate as
G
was
partially
Industry Program
Technology
supported
Creative from
the
Development
Type New
by
the
Proposal
Technology Energy
Organization
and
R&D Indus
(NEDO)
of
received
April
5, 1999, revised
June
21, 1999)
References
(1)
Pressure shape
arc
study New
(Manuscript
distribution
well
arc
about
get
XN2=100% indicates
ther
Japan.
(2)
be high
(3)
conductivity. addition,
to
a maximum
of the
ad
the
approximation
and
result
give
on
con
dissociation
Fig.13.
the
ratio
were
region.
Promotion
is generally
plainer
center
state.
thermal
temperature seen
power
Acknowledgement
- Based
temperature
arc
the
results
It
composition,
V/mat
This
arc.
as and
different
based
using the derived,
admixture
such
at
of admixture
has
information zero
This
and
higher
distribution at
8.
of
in steady
direction
center
K
of pressure
makes of
the
T=4200
of a wall-stabilized
cause
increases, radial
is attributed
was
distributions MPa
of arc
temperature
under-estimated.
of 0.5
the
section
arc
temperature
of O2
shrinks
elevated.
O2. The
the
at a pressure
distribution the
G were
presents
N2/O2
the
pure
electrical
conductivity
air
is 4500
and
adopted
arc
effect
E
above
mental
previous
to
that
viewpoints
order
was
strength
conductance
The
rent
an the
MPa.
lowest
first
electrical
at
example,
of
Fig. 13. Temperature distribution of a wall-stabilized arc in 50% N2-50% O2 mixture at different pressures.
that
a
Fig.14
mixtures
radiation
was
of the
and
imum
For
the
characteristics
temperature
in the
the
as
In addition, properties thus
to find
mental
note
con has
in
imply
plasmas
of a wall-stabilized
calculated
derived
and
properties
well
mixture
method
distributions
Thereby,
whole
the
value of 0.0045 pure N2 requires
heat
calculation
equilibrium.
ChapmanEnskog
Prad
the XN2
N2/O2
from
as in
illustrated
might
specific
conductivities
mixture
and
However,
time,
transport
enthalpy,
computed
used.
air
P and
Conclusions
mass
directly
than
medium
with
except
with
other
result
ra
composition.
XN2
as
any
admixture
air
above.
same
This
S/m
conductivity
decreases
than
the
1240
decreases
G has a minimum This means that
arcs.
from of
interruption.
Fig. 12. Temperature distribution of a wall-stabilized arc in N2/O2 mixture at a pressure of 0.5 MPa.
simplicity
arc
with
the
and
of
the
the
XN2=100%
power
20
case
noted
center
K
thermal
increases
arc
For example, at 0.5 MPa.
more
of
be the
8800
mentioned
E
the
at
the
high
MPa.
ductance
in
center
(c),
should
is almost
from
Fig.14
It
of N2/O2 Mixtures
and ƒÐ
values
which
mainly
high
(d). S m
T
respectively,
N2-20%
resulting
that
minimum
MPa,
Further,
of XN2.
(b)
local
Properties
T, for
(4)
dif 29
H.M.Ryan and G,R.Jones: SF6 Switchgear, Peter Peregrinus Ltd., London, 1989, ch.2. M.Kuroda: J.IEE of Japan, 118, 697-700 (1998) (in Japanese). A.Gleizes, M.Razafinimanana and S.Vacquie: "Transport co efficients in arc plasma of SF6-N2 mixtures", J.Appl.Phys., 54, 3777-3787(1983) A.Gleizes, I.Sakalis, M.Razafinimanana and S.Vacquie: "De
cay of wall stabilized arcs in SF6-N2 mixtures", J.Appl.Phys., 61, 510-518(1987) (5) A.Gleizes, B.Rahmani, J.J.Gonzalez and B.Liani: "Calcula tion of net emission coefficient in N2, SF6 and SF6-N2 arc plasmas", J. Phys.D:Appl.Phys., 24, 1300-1309 (1991). (6) B.Chervy, H.Riad and A.Gleizes: Calculation of the In terruption Capability of SF6-CF4 and SF6-C2F6 MixturesPart I: Plasma Properties", IEEE Trans. Plasma Sci., 24, 198-209 (1996). (7) B.Chervy, J.J.Gonzalez and A.Gleizes: " Calculation of the Interruption Capability of SF6-CF4 and SF6-C2F6 MixturesPart II: Arc Decay Modeling", IEEE Trans. Plasma Sci., 24, 210-217 (1996). (8) M.I.Boulos, P.Fauchais and E.Pfender: Thermal Plasmas Fundamentals and Applications, Vol.1, p.160, Plenum Press (1994). (9) J.M.Yos: Transport Properties of Nigtrogen, Hydrogen, Oxy gen and Air to 30 000 K, AVCO Technical Memorandum, RAD-TM-63-7 (1963). (10) W.L.Wiese, M.W.Smith and B.M.Glennon: Atomic Transi tion Probabilities Vol.I Hydrogen Through Neon, NBS (1966) (11) K.P.Huber and G.Herzbeg: Molecular Spectra and Molecular Structure IV. Constants of Diatomic Molecules, Litton Edu cational (1979).
Yasunori
Tanaka
(Member)
(a) Temperature
was born in Mie on Novem
ber 19, 1970. He received the B.S., M.S. and Ph.D. degrees in electrical engineering from Nagoya University in 1993, 1995 and 1998, respectively. He is currently Research As sociate in the Department of Electrical and Computer Engineering, Kanazawa University. His reserch interests include the arc interrup tion phenomena and thermal plasma applica tions.
Khokan
Chandra
Paul
(Member)
was
born
on
July
(b) Electrical conductivity
1,
1965. He received the B.S. degree in 1990 from the Electrical and Electronic Engineer ing Department of Bangladesh Institute of Technology, Chittagong, Bangradesh, and the M.S. and Ph.D. degrees in 1995 and 1998, re spectively, from Kanazawa University, Japan. Presently, he has been working as a Japan Society for the Promotion of Science post doctoral fellow in Kanazawa University. His fields
of interest
include
RF-ICP's
and
circuit
breaker
arcs.
(c) Electric field strength Tadahiro
Sakuta
(Member)
was born on January 3, 1950.
He received the M.S. and Ph.D. degrees in electrical engineering from Nagoya University, in 1978 and 1981, respectively. In April 1980, he was appointed Research Associate in the Department of Electrical Engineering, Nagoya University. In April 1988, he became Asso ciate Professor in the Department of Electrical and Computer Engineering, Kanazawa Uni versity, gaged in studies thermal plasma breaker arcs.
and Professor
on the diagnosis and including inductively
in 1993.
He is mainly
en
application of high-pressure coupled plasmas and circuit
(d) Conductance
Fig. 14. Dependence of temperature, electrical conductivity at the center of the arc, electric field strength and conductance in N2/O2 arcs at differ ent pressures. The current is 20 Adc.
30
T. IEE Japan,
Vol. 120-B, No. 1, 2000
