Thermodynamic and Transport Properties of N2/O2 Mixtures - J-Stage

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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