AN ATTEMPT TO DESCRIBE VOLTAGE-CURRENT CHARACTERISTICS OF AN ARC WHEN UTILIZING EQUATIONS OF MAGNETOHYDRODYNAMICS

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Submitted on 1 Jan 1979

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AN ATTEMPT TO DESCRIBE VOLTAGE-CURRENT CHARACTERISTICS OF AN ARC WHEN

UTILIZING EQUATIONS OF MAGNETOHYDRODYNAMICS

Cz. Królikowski, A. Kamińska-Pranke

To cite this version:

Cz. Królikowski, A. Kamińska-Pranke. AN ATTEMPT TO DESCRIBE VOLTAGE- CURRENT CHARACTERISTICS OF AN ARC WHEN UTILIZING EQUATIONS OF MAG- NETOHYDRODYNAMICS. Journal de Physique Colloques, 1979, 40 (C7), pp.C7-353-C7-354.

�10.1051/jphyscol:19797174�. �jpa-00219151�

JOURNAL DE PHYSIQUE CoZZoque C7, suppZe'ment au n07, Tome 40, JuiZZet 1979, page C7- 353

A N ATTEMPT TO DESCRIBE VOLTAGE-CURRENT CHARACTERISTICS ff AN ARC WHEN UTILIZING EQUATIONS OF MAGNETOHYDRODYNAMICS

Cz. ~rbljkowski, A. ~arnidska-~ranke.

I n s t i t u t e of EZectroenergetic, The TechnicaZ University of ~ o z n d , PoZand.

The process of o b t a i n i n g low-temperature plasma by h e a t i n g gas flowing through an e l e c t r i c a r c w a s analysed in paper I l l . I n t h e of t h e e y l i n d r i c d a r e a flow, two re- g i o n s can be assigned, t h e i n t e r i o r r e g i o n and t h e e x t e r i o r region, s e p a r a t e d by a bo-

s u r f a c e w i t h r a d i u s r

ro ( 9 i g . l ) .

I n t h e i n t e r i o r region, i.e , f o r

ro , ^{g a s}

conductance6>0, whereas

t h e e x t e r i o r re- gion f o r rlz) a r 6

I n t h e paper, t h e

0'

Fig. I. F i e l d node1 of flow

i n t e r i o r flow i s analysed, conside- r i n g t h e problem of a r c d i s c h a r g e s u b j e c t e d t o f r e e g a s flow, p a r a l l e l t o t h e a r c a x i s . On t h e b a s i s of e q u a t i o n s of magnetohydrodynamics, t h e v o l t a g e on t h e a r c h a s been determined, according t o t h e a r c c u r r e n t , p h y s i c a l p r o p e r t i e s of t h e f l e wing gas and geometry of t h e channel.1t has

been asswned t h a t i n t h e i n t e r i o r of t h e flow t h e f o l l o w i n g assumptions a r e v a l i d :

1,Gas flow i s laminar, Mach number i s much s m l e r t h a n unity.

2 .The flow i s a x i a l l y symmetric, it

n o t a c i r c u m f e r e n t i a l component of speed,there- f o r e it h a s no flow r o t a t i o n as well.

3.The r a d i a l component of speed i s much sma- l l e r than t h e a x i a l component; t h i s r e s u l t s i n uniform p r e s s u r e i n t h e plane perpendicu- l a r t o t h e a x i s of t h e a r c .

4. The g a s i s i n thermodynamic equilibrium.

5 .Dependence of thermodynamic p r o p e r t i e s /except g a s mass densitv/ and transwort

p e r t i e s on p r e s s u r e i s n e g l i g i b l e .

6.Axid h e a t t r a n s f e r and r a d i s t i o n energy is s m e l l .

Zquations of magnetohydrodynamics, presen- t e d below, d e s c r i b e p r o c e s s e s o c c u r r i n g i n t h e i n t e r i o r r e g i o n of t h e flow:

Equation of flow c o n t i n u i t y

=+ at d i v ( B e ) = ~ / I / Equation of power

- - - - -

Y . L $ ! . ~ ~

Equation of motion

p = P R S

Ohm's law /4/

j = G

E(z) / 5 /

hTmvell's e l e c t r o m a g n e t i c e q u a t i o n s

U = j + - a5

3L

E = -

diii 0

9

diS 8 = 0

When a n a l y s i n g t h e zbove e q u a t i o n s , a f t e r p r e s e n t i n g them i n c y l i n d r i c a l c o o r d i n a t e s , from t h e p o i n t of view Of assumptions 1-6, equation of power ( 3 ) can be w r i t t e n i n t h e

1; e q u a t i o n /lo/, t h e c o e f f i c i e n t of h e a t exchange occurs; it i s unknown f o r h i g h temperatures of t h e arc. On t h e b a s i s of performed i n v e s t i g a t i o n s in f 2 3, it h a s be- e n assumed t h a t t h e amount of t h e a t , car- r i e d away by means

h e a t conduction from t h e i n t e r i o r r e g i o n t o t h e e x t e r i o r r e g i o n of t h e f l o w , i s p r o p o r t i o n a l t o t h e v a l u e of a r c c u r r e n t , t h e r e f o r e

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19797174

wh2re

- p r o p o r t i o n a l i t y c o n s t a n t 1 - a r c l e n g t h .

The f l . 0 ~ ~ of g a s through t'ne c y l i n d r i c a l c h e n n e l trikes p l a c e under t h e i n f l u e n c e betwe- e n p r e s s u r e on t h e i n l e t t o c h a n n e l p1 and p r e s s u r e on t h e o u t l e t of c h a n n e l po.The di- s t r i b u t i o n of p r e s s u r e a l o n g t h e c h a n n e l , a s i n v e s t i g a t i o n s have shol?in f

, can be fiesc- r i b e d by e q u a t i o n

1

k

c h a n n e l l e n g t h .

Phe flo~::ing g a s h e a t s t h e r e g i o n

a r c d i - s c h a r g e azd a f t e r p a s s l n g t h e

i n t h e a r c r e a c h e s t h e t e n p e r ~ t u . r e of a r c T

. ^.The

c o e f f i c i e n t of t h $ i n c r e a s e i n t e m p e r a t u r e :I can be assumed as e q u a l t o ( T ~ - T ~ ) / ~ ~

- ^{where T} i n i t i a l t e m p e r a t u r e of b e i n g he-

0

a t e d gas. On t h e b a s i s of t h e e q u a t i o n of magnetohydrodynwics

f o r m / I /

n e ;t:a.te t h a t t h e mass of f lo?ri.ng: g a s t h r o -

second i s cons- t a n t , ~ l P r ~ = : ~

c o n s t

and depends on -che -cot& ra~ss of g a s f l o - +:ling t h r o u g h t h e channel i n t h e f o l l o w i n g

G*-

t o t a l flow of g a s through t h e cha- n n e l .

On the b a s i s of She above c o n s i d e r a t i o n s , t h e e q u s t i o n of Fovrer d e n s i t y i n t h e a r c cm- be w r i t t e n i n t h e form

2Ges d e n s i t y P

, o c c u r r i n g j.n e q u a t i o n /15/,

can be determined as Q * m c t i o n of temperatu- r e , o n t h e b a s i s of i n v e s t i g a t e d c u r v e s a t 6 i f f e r e n t p r e s s u r e s . b r c t e m p e r a t u r e T Y can be e x p r e s s e d a s v o l t a g e and a r c c u r r e n t f u - n c t i o n on t h e b a s i s of t h e approximate cu- r v e s of conductance G(T) f o r a d e f i n i t e

nd of gas,whereas s p e c i f i c b e a t h a s a con- s t a n t v a l u e f o r monoatomic g a s e s a n d i s t h e h o v m f u n c t i o n of t e m p e r a t u r e f o r 2 o l y a t o -

gases.0n u t i l i z i n g t h e above r e l a t i o n s and e q u a t i o n /15/ o v e r t h e a r c vollume, t h e e q u a t i o n m a s o b t a i n e d which d e s c r i b e s vol- t a g e r e l a t i o n on t h e a r c in t h e f u n c t i o n of a r c c u r r e n t and t a k e s i n t o a c c o u n t p h y s i c a l p r o p e r t i e s of g a s , a s welL as t h e geometry of t h e d i s c h c r g e c h ~ n n e l . ? o r a r c d i s c h a r - ge i n n i t r o g e n , t h e e q u a t i o n d e s c r i b i n g vol-

c u r r e n t c h n r a c c t e r i s t l c s

have t h e

a,

,

- c o n s t a n t s of c u r v e s appro- x i n a t i o n 6/T/ and /T/

stM& S q u a t i o n /

^6/ h a s

50

t h e p o s e r chLannel

w i t h a r a d i u s of

(60.

140 120.

XY).

Pig.2.Voltage-current 4 m

30 mmlong.

c h a r a c t e r i s t i c s

The r e s u l t s of ca- been s o l v e d analy-

-

t i c a l l y by n3king

l c u l a t i o n s a r e p r e s e n t e d i n g r a p h i c f o m

w .

- ,..&& c a l c u l a t i o n s f o r

fig.2.and compared w i t h e x p e r i m e n t a l d a t a . On comp,axing t h e measured m d c a l c u l a t e d va- l u e s o f a r c v o l t a g e w i t h e q u a t i o n /16/, it h a s benn s t a t e d t h a t t h e maximum e r r o r n o t exceed '

^BFERENCES

1

.S.fJ.B.Blurthy.

Trans .on n u c l e a r Sciec- c e , 1964.

2 .Cz .Krllikovrski, Yraca d o k t o r s k a ,

Kra- k6w, 1964.

3.Cz.Kr6likowski, Zeszyty Naukowe P o l i t e c h -

n i k i ? o z n & s k i e j , X l e k t r y k a