Breakdown potential of potassium-seeded combustion products

COMBUSTION AND FLAME 21,231-240 (1973)

231

Breakdown Potential of Potassium-Seeded Combustion Products TOSHISUKE HIRANO Department of Mechanical Engineering, Ibaraki University. Japan

The relation between the breakdown potential of potassium-seeded combustion products and the charged particle concentration has been studied. Tile breakdown potentials between electrodes of various diameters in uniform combustion products which were generated by burning a potassiumseeded propane-air mixture have been measured. It was found that the breakdown potential depends on the phenomena occurring within a layer close to the cathode surface. When the ion concentration is below a palrtieular value, the breakdown potential depends slightly on the ion concentration, but for larger values of ion concentration the breakdown potential decreases rapidly with increase of the ion concentration. The critical potential gradient was estimated, and was found to be about 9 kV/em except for the causeof an electrode diameter of 0.3 ram. Most of the experimentally observed phenomena can be explained by exploring the sheath region. The breakdown of an ionized gas is considered to depend on the phenomena in the vicinity of the ion sheath covering the cathode.

1. Introduction The characteristics o f the breakdown of a gas near the hydrocarbon flame reaction zone or a gas consisting of alkali metal-seeded combustion products seem to be very important for understanding the lh'nit of electrical control of the combustion phenomena [1-4] or the initiation characteristics of the electric discharge for an electrically augmented flame [5]. During the control of the combustion phenomena or the initiation of the electric discharge in an electrically augmented flame, electrodes were frequently exposed to a gas including a large number of charged particles [1-9]. For a long time, the characteristics of the break. down o f non-ionized gases have been explored by a number o f investigators [10-12]. Recently, the breakdown between electrodes placed in a gas of very low concentration at both sides of the considerably ionized, sheet.like reaction zone of a hydrocarbon flame has been studied experimentally and theoretically [2-4]. However, in only a few experimental studies, has the breakdown potential of an ionized gas been briefly d~scussed whan the electrodes were exposed to the ionized gas [1, 5].

It has been shown in these experimental stndies, that the breakdown potential of an alkali metal. seeded combustion gas depends strongly on the ion concentration of the gas [1, 5]. Dimmock and Kineyko [1] observed in their study of low pressure flame plasmas that the breakdown potential between electrodes inserted in a flame was directly related to the cc,nductivity of the flame gas. Fells, Gawen, and Harker [5] studied the breakdown potential of an alkali metal-seeded flame during their studies of flames augmented with d.c. electrical power, and found that the breakdown potential was essentially a function of the concentration of seeded constituents and the electrode gap. In these experiraents, however, the measurements were conducted in rather nonuniform fields o f ion concentrations, temperatures, and flow velocities. The breakdown potential should depend not only on ~l~e ion concentration and the electrode gap but also on the dimension and configuration of the electrode, the flow velocity, etc. [10-16]. Therefore, it can hardly be considered that the relation betw,~en the breakdown potential and the ion concentration really has been elucidated.

Copyright © 1973 by The Combustion Institute Published by American Elsevier Publishing Company, Inc.

TOSHISUKE HIRANO

232 The objective of the present study is to explore the relation between the breakdown potential and the charged particle concentration of uniform combustion products, which were generated by burning a potassium-seeded propane-air mixture. The results obtained in this study will be useful in establishing the limit of the electrical control of the combustion phenomena aud the discharge initiation mechanism of the electrically augmented flame. 2. Experimental A stoichiometric propane-air mixture was supplied to the apparatus, and was burnt at a multiple burner (Fig. I). A uniform gas flow of combustion products was obtained at a nozzle exit which was 40 mm in diameter. The characteristics of the apparatus, the velocity, temperature and charged particle density distributions of the gas flow, and the composition of the combustion products have already been described ia detail elsewhere [17, 18]. An aqueous solution of potassium carbonate was added as a fine mist from an atomizer placed in the air feed line in order to enhance the charged particle concentration in the combustion products. The concentration of potassium carbonate introduced into the combustion products was calculated by measuring the

~~_£cmo~s

~ COOLING W, ~NLET

1 GASEOUS MIXTURE

Fig. I. Experimental Apparatus.

quantity of distilled water consumed over a period of I hour, and was adjusted by varying the concentration of potassium carbonate in the aqueous solution [17]. The composition of the combustion products including charged particles was determined by calculation from the temperature and the composition of unhumt mixture introduced in the combustion system [18-21]. The variation of the charged particle concentration was monitored by an electrostatic probe, the characteristics of which had already been studied in detail and described in [17]. When the distilled water without potassium carbonate was added as a fine mist, the ion current measured by the probe was more than one order smaller than that usuaUy used in this experiment. Therefore, the electric charge introduced into the flame fiom static electrification arising during atomization [22] might become negligible through the gasification and combustion reaction, so that the charged particle concentration in tile combustion products could be considered to be calculated on the assumption of thermal equilibrium [21]. The temperature, Tg, of the combustion products measured by the Na D line reversal method was 2100°K. The electrodes used in the present experiment were platinum 20 percent rhodium rods of 0.3 and 1.0 mm diameter and copper rods of 1.4, 2.0, 3.0, and 4.0 mm diameter. An anode and cathode were inserted in the combustion products with their axis normal to the direction of the gas flow as indicated in Fig. 1. It has been shown in recent studies of weakly ionized, high density gases that the pc~tential or current profile in the vicinity of the electrode is very difficult to predict even if the electrode is a sphere, cylinder, or plate. Only the phenomena around an infinite cylinder with a thick sheath [23, 24], near the stagnation regions of a cylinder and sphere [25-28], or over a flat plate [29-32] have been explored by approximate methods. One-dimensional treatment should not be adopted even if the flat plate electrodes parallel to the gas stream direction were used. In this study, cylindrical electrodes were adopted because, except for their ends, the characteristics were rather well known [17, 23, 24, 33],

BREAKDOWNPOTENTIAL OF COMBUSTIONPRODUCTS

233

IO

~

~

0,6

02

o~

5

I0 15 ELECTRIC CURRENT, ornp

20

~6

Fig. 2. Breakdown Charactefistic;d = 1.0 ram, Le = 10 ram, N÷ = 1.5 x l0 II ions/cm3, Tg = 2100°K. U= 13.3 m/s.

and the configuration of the flat end was decided because of its convenience in treatment, such as cleaning and reproducibility. The sharp periphery was useful in order to confine the location of the breakdown initiation wlfich is described later in this section. The surfaces of the electrodes were always kept clean. The electrode temperature was not varied nor controlled because no well established means to heat the electrode uniformly without disturbance in an electric field or flow field could be found. In the studies of the electrostatic probe [ 17, 18, 28, 33] or electrode [34] used in an alkali. metal seeded gas flow, the electrode temperature has been found to have little influence on the probe or electrode characteristics when the sur. face temperature is not high. In this study, the effect of the electrode temperature is not discussed, though the effect should not be neglected, and the discussion is concentrated on the relation between the breakdown potential and the charged particle concentration. A high-voltage d.c. power supply was used to provide the potential to the electrodes. The po. tential of the power supply was gradually increased until the breakdown was observed on an am. meter (Fig. 2). At the initiation of the discharge following to the breakdown, a small light spot was usually observed at the periphery of the upstream side of the electrodes. Therefore, the breakdown might occur at the upstream periphery.

3. Results and Discussion Typical breakdown potentials, Vt, are plotted against the distance, Le. between the anode and cathode and are shown in Fig. 3. V~ increases with Le until Le becomes longer than a critical distance, which can be estimated to be about 2 mm in this case. A further increase in Le results in little change in Vb. This indicates that Vb depends on the phenomena occurring within a layer close to the electrode surfaces, that is, roughly 2 m m in thickness. This critical distance increased as electrode diameter increased and decreased as the charged particle concentration increased. Vt, was also strongly affected by the electrode diameter, d. Therefore, the effects of the electrode diameter, the cathode diameter, d_, and the anode diameter, d÷. on Vb were examined. In Fig. 4, Vb measurements are shown that were obtained by using electrodes of different d_ and d÷. In this case, Le was kept at 10 ram, which is longer than the critical distance. Vb is only slightly sensitive to d . , but depends strongly on d.. This fact means that the breakdown potential depends on the phenomena adjacent to the cathode, i.e., virtually the phenomena in the ion sheath established around the cathode. Just belbre breakdown occurs, the cathode should be covered with a positive ion sheath. Therefore, the breakdown po'tentJal could be considered to depend on the ion concentration, At+, in the combustion, products. The relation be.

234

TOSHISUICEHIRANO

~C oo o

.o----.

>~ z,c

g

,'o

,'~

DISTANCE BETWEEN THE ANODE AND CA~"IODE, L e,

mm

~'o

Fig. 3. Variation of Breakdown Potential With Electrode Gap; d = 2.0 ram, N+ = 3 X 10 t° ions/era3, Tg = 2100°K, U = 13.3 rn/s.

tween Va a n d N . , is shown in Fig. S, in which Vt, is plotted against N÷ in log-log scale. It is found that Vb depends on N . . When N÷ is below .~ particular ion concentration Vb depends slightly

>3C n

rr

rr

~

d. =4'0 mrn-

....

i

$'0"

2,C

~

2,0~

i l'C

xl'O'

x

,'o

2!o

ANODE DIAMETER,

0'5"

3',o ~o d,,

rnm

Fig. 4. Effect of Electrode Diameter on Breakdown Potential;N+ = 7 × 101° ions/cm a, L e = 10 ram, Tg = 2100°K, U= 13.3 m/s.

on N÷, but for larger values of iV., Vn decreases rapidly with the increase of N÷. The results discussed above indicate that for further understanding of the breakdown of the ionized gas, a discussion on the ion sheath covering the cathode seems to be nece~ary. Recently, a large number of studies have been conducted on the behavior of charged particles near an electrically conducting highly negative body inserted in a flowing weakly ionized highdensity gas, such as a gas near the hydrocarbon flame reaction zone and one that consisted of alkali metal-seeded combustion products [17, 23-33]. Although the objectives of these studies were not to explore the breakdown characteristics of an ionized gas, the results are useful for discusshag the phenomena just before breakdown occurs. The flow profile near the upstream periphery of the cathode (region A in Fig. 6), where file breakdown was considered to occur, is supposed to be complicated. However, if it can be assumed that just before the breakdown occurs, the sheath structure of region A is not much different from that of region B, where the assumption of an infinite cylinder can be adopted, the potential profile through the sheath region can be calculated by an approximate method usually used in the

BREAKDOWN POTENTIAL OF COMBUSTIONPRODUCTS ")"'f

I

J

f i'~,m'~

.........

~

235 i

t

J f''')l

)

i

)i~

5O ~>4c 3.c

40rrrn ,A 3'0 o 20 a

O5

)'4 IO 0'5 J,Jl tO~)

v o ~' i J i

,,,.,)

i0)o

I

i ~J,,I

ION C0NCENTRATtON,

Fig, 5.

N+,

lO)*

i ) ~ i.,,

i0)2

ionsA;m3

Variation of Breakdown P_otentiM ,with Ion Concentration;

Le = 10 mm. Tg = 2100°K, U = 13.3 m/s. studies of highly negative cylindrical probes [23, 24, 35]. Poisson's equation v ~ v = -eOV÷ - N - ) / e o

(1)

becomes, in the sheath regions where negative particle concentrations, N_, have been essentially eliminated and with replacement of N . with the radial component of ion current and potential gradient,

ei,

a=V.(l\far\.a~z

~-T * k7) ~ ~-;)" -ao T = (OoK.a--Wa,)'

(2)

where Vis the potential, e the electron charge, eo the permittivity for free space, r the radial distance from the cylinder axis, 0 the angular dis-

CYLINDRICAL

\

CATHODE

L L 2L Fig. 6. Sheath Around Cathode Just Before Breakdown Occurs.

tance from the stagnation lin,,• of the cylinder,/,, tile radial component of ion current, and K÷ the mobility of positive ions. It can be assumed that the local equi-potential lines in the vicinity of the forward stagnation line are symmetric about the 0 = 0 axis and the third term of the left hand side o f e q . (2) can be dropped. From the same assumption, the angular component,/o, of ion current e~,n be neglected as compared with Jr, so that Jr c~r- ~ can be derived by considering the electric currer, t conservation [23]. Thus, eq. (2) can be solved by adopting the following boundary conditions: V=O, d V / d r = O a t r = r ~ ,

(3)

where rs is the radius of the ion sheath edge. The potential gradient profiles in the sheath region are consequently given by

~:L,~e-~,L\7/-'}]

'

(4)

where I is the electric current per unit length of the electrode. It is evident that the maximum of (dV/dr) appears at the cathode surface, and the potential gradient (dV/dr)o at the cathode surface can be expressed as

(dz) =[

236

TOSHISUKE HIRANO

The relation between I and the potential drop Ve in the sheath region can be derived from eq. (2) as follows:

1 = IrV2eK+%/(r2o~,2),

= -0.623 (rslro)3,2 for 5 ~rs/r o ~ 30. (9b)

(6)

These equations give fairly good approximations for "7 as shown in Fig. 7. Consequently, the following equations can be derived from eqs. (5),

(6), and (s):

where

{(;5-f-

I= lreoK+(r°~ ' (dV~"

(10)

\rsl \'~r ]o

tkrol

t\ro/

. (7)

The supply of ions to the outer edge of the sheath will be generated mostly by convection [23] and will consequently be given by ro

/ v~X2r~o r~ l=neoK.[--I _-~ for 2 < - - < 5 \0.272! rs ro

(lla)

I Vc\2ro r~ =aeoK.l~l _~ for 5 ~ - - ~ 3 0

(lib)

~0.623/ r~

ro

1 = 2N.eUr s.

2

(12)

Equations (10) and (12) give where Uis the velocity of the combustion products. Since in this study considerable high potential was applied just before the breakdown occurred, (rs/ro) 2 > > 1 can be assumed. Furthermore, 7 is assumed to be approximated as follows: 3' = -0.272 (rs/ro)2 for 2 < rJro < 5

,

,

i

,

i

,

1 , 1

(ga)

i

r~--[2--E~+~u\~/oJ

'

03)

From eqs. (1 la) through (13), the following equa. tions are derived:

k,eoKj2o/

\0.272]

for 2 ~ r ~ ~ 5

ro

(14a)

=( Vc ~'a[2N÷eU~ ua

Io

for 5 ~ .rs ~ 30.

E

ro

. o

I.C

r,/r,

Fig. 7. Variation of 7 with rs/r o.

(14b)

Just before breakdown occurs, the potential gradient in region A might attain the critical value (d V]dr)o. a at the cathode surface, which is sufficient to initiate the breakdown by the process similar to that in cold gas [ 10, 11 ]. If the ratio of the applied potential Va at the breakdown to the potential drop Vc. in the ion sheath just before ihe breakdown occurs is assumed to be a, i.e., V~ = ~ Vo.,

05)

BREAKDOWN POTENTIAL OF COMBUSTIONPRODUCTS and if the ratio of(dV/dr)o, A to (dV/dr)o,B at region B, which can be given by using eq. (14a) or (14b), is assumed to be fl, i.e.,

(16)

(aVldr)o,A = t3(aV/dr)o.n (dV/dr)o* a e~al be expressed as _ #

Vb

3/s 2 N . e U

us

for 2 < rs ~< 5

ro

(17a)

: n V"[2:~.o.?'" for 5 ~< rs < 30. (17b) ro

From the experimental results, shown in Fig. 5,

(c~sis/(J)(dV/dr)o. A was calculated by using eq. (17a). In the calculation K+ = 30 cm2/(V 'sec) [3, 4] and U = 13.3 m/s were used. The results are shown in Fig. 8. If both a and/3 can be assumed to be constant, (dV[dr)o. A is almost constant in the range of N÷ higher than 10 j° ions/ cm 3 . Furthermore, (dV/dr)o. A is independent of the electrode diameter, except for the case o f d = 0.3 mm. In the range of N+ higher than 101° ions/cm 3, the mean value of (c~sis ]#)(dV/dr)o.A was about 9kV/cm, except for the ease o f d = 0.3 mm. Since (as:s/~) may be close to unity, (dV/dr)o. A can be

237

estimated to be about 9 kV/cm. Considering the gas temperature and the sheath thickness, this value seems to be reasonable as compared with 'the cold gas breakdown data [ 1O, 11 ]. In the present experiment, the surface temperature of the electrode depends on its diameter and material. The temperatures, which were measured by using an optical pyrometer, were 1900 and 1600°K at the surfaces of the cathodes which were 0.3 and 1.0 m m in diameter, respectively. The temp.;rature of each cathode of copper was lower than 1350°K, and decreased as the diameter increased. All of the surface temperatures were below the temperature, at which the thermal emission of electrons appreciably affected the ion cur. rent to the cathode [17, 34]. In this case, the effect of the cathode temperature on (d V/dr)o,A seems to be negligible, except for the case o f d = 0.3 ram. Furthermore, if there was an appreciable effect of the thermal emission of electrons, the value of(dV[dr)o, A should be reduced rts the surface temperature increases [16]. However, the value of(dV[dr)o. A for the case o f d = 0.3 ram, when the surface temperature of the cathode is higher than those of the others, is the highest. It is a well-known fact that the critical potential gradient of a non-ionized gas increases as. the electrode gap decreases [10, 11]. A relatively higher value of (dV/dr)o. A for the case o f d = 0.3 m m might reasonably be attributed ~o the thin sheath thickness as compared with those around the cathodes .of'larger diameters. Since eq. (17a) is valid when 2 ~ rs/r o <. 5, the discussion should be limited in this range.

3C

.

40fnrn ~ 3'0 o 2.0 0 -I 1.4 J I0 ol

2C

~

~

%1~ )c )

. . . . . .

i

......

,.t

ION CONCENTRATION, N,. ions/cm~

Fig. 8. Variation of Critic~flPotential Gradient with Ion Concontration; according to eq. (17a).

TOSHISUKEHIRANO

238 The approximate value of(dV/dr)o*r~ ---(1/~) (dV/dr)o,A can be estimated for all the cathodes, except for that o f d = 0.3 ram, so that the range of N., in which eq. (17a) is valid, can be estimated by using eq. (13). Since a > 1, (dV/dr)o.a will be smaller than (t~als/~)(dV/dr)o.A ~- 9 kV/cm. Substituting (dV/dr)o. a = 6 kV]em and 2 < rr/ro < 5 into eq. (13), the following condition is obtained: 5.63 X 109
Ifr o = 1 mm (d = 2 ram), eq. (17a) will be valid when 5.63 × 10I° ~N÷ < 1.76 X 10 I~ . This range of N~. is a little higher in ion concentration than that covering the constant (dV/dr)o,A in Fig. 8. However, since the value of(dV/dr)o*A is almost constant in the range of N . higher than 101a ions/cm a , eq. (17a) could be considered to he v',didin this range. Furthermore, eq. (18) shows that the range of N÷, where eq. (17a) is valid, shifts to that of lower values of N÷ with the increase oft o. This fact does not coincide with the experimental results. These differences between theory and experiment are considered to be attributable to the experimental error or the assumptions adopted through the deduction of eq. (17a). The relation between (¢ta/4[[.~)(dV/dr)o,A calculated by using eq. (17b) and N÷ is shown in Fig. 9. In the range of N÷ lower than 101° ions/era a, (t~al4/(J)(dV/dr)o,g is almost constant for each electrode, and increases with the decrease of the 30

....

,

,

,

¢

,

,- .......

, , , , , i

,~' o

electrode diam¢t,~r. Equation (17a) is applicable for 5 < rJro < 30. Although, experimentally, the critical distance seemed to be smaller than 10 ram, the edge of the ion sheath might easily reach th~ anode. Furthermore, the dimension of the sh,~alh will be so large that the aspect ratio of the dimension of the sheath to the test section should not be kept sm~.~ll. Therefore, the phenomena w dch occur in this range cannot be further dis. cLssed. l'hroughout this study, the discussion has been c, ,ncentrated on the phenomena within the ion sheath, and most of the experimental observations could be explained. Therefore, the breakdown of an ionized gas should be considered to d~pend on the phenomena in the vicinity of the ion sheath covering the cathode. The parameters which will influence the structure of the sheath are not only cathode diameter and ion concentration but also gas velocity, cathode configuration, cathode temperature, etc. In order to explore further the breakdown phenomena in an ionized gas, a study on the effects of the gas velocity, cathode configuration, cathode temperature on the breakdown seems to be necessary. Also, it will be necessary to explore the effect of the surface condition and thermal emission of electrons. The results obtained in this study will be useful not only in the studies of electrical control of combustion phenomena or augmented flame, but also in the studies of electrode characteristics in an MHD generator using seeded combustion products as its working medium [36].

.v o o ° o ~

~,o _._.~

. . .,oo . . . . . . . . . . . ,.~ °. . . . . . ION C0~,!CENTRATION, N .,

~..

i

........

•

',';" ions/~rn ~

2'0 1.4

o v

I0

O

0'3

'

i

......

io'~

Fig. 9. Vaziationof Critical Potential Gradientwith Ion Concentration; accordingto eq. (17b).

239

BREAKDOWN POTENTIAL OF COMBUSTIONPRODUCTS 4. Conclusions The breakdown potential of potassium-seeded combustion products depends on the phenomena occurring within a layer close to the cathode surface. The breakdown potential is only slightly sensitive to anode diameter but depends strongly on the cathode diameter. When the ion concentration is below a particular value, the breakdown potential depends slightly on the ion concentration, but for larger values of ion concentration, the breakdown potential decreases rapidly with the increase of ion concentration. The critical potential gradie'tt is estimated by calculation. In the range of the ion concentration higher than 1010 ions/cm 3 , the mean value of the critical potential gradient is about 9 kV/cm, except for the case of an electrode diameter of 0.3 ram. A relatively higher value of the critical potential gradient for the case of an electrode diameter of 0.3 m m might reasonably be attributed to the thin sheath as compared with those around the cathodes of larger diameters. Most phenomena observed experimentally can be explained by exploring the sheath region. The breakdown of an inaized gas is considered to depend on the phenomel~a in the vicinity of the ion sheath covering the cathode. The authc, r would like to express his sincere thanks to Prof. H. Tsufi, Institute o f S.A.S., Tokyo University and Dr. H. J. Nielsen, H T Research Institute for their valuable discussions.

Nomenclature d electrode diameter e electron charge 1 electric current per unit length of cathode A radial component of ion current ]o angular component of ion current K mobility of charged particles Le distance between anode and cathode N charged particle concentration r radial distance from cylinder axis rs radius of the ion sheath edge Te temperature of combustion products U flow velocity of comb,:st[on products V potential

Vb breakdown potential Vc potential drop in ion sheath

(dVIdr)o*A/(dVIdr)o*n permittivity for free space angular distance from stagnation line of cylinder Subscripts A region A indicated in Fig. 6 B region B indicated in Fig. 6 o cathode surface * just before breakdown occurs + positive negative eo 0

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240

TOSHISUKE HIRANO

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31. Stahl, N. and Su, C. H., Plays. Fluids 14, 1366 (1971). 32. Rut,so, A. J. and Toucan, K. J.,AIAA 3. 10, 1675 (1972). 33. Tsuji, H. and Hirano, T.,AIAA J. 11, 100 (1973). 34. Zanc~erez,B. and Tate, E.,AIAA 3". 11,149 (1973). 35. Schultz, G. J. and Brown, S. C., Pllys. Rev. 98, 1642 (1955). 36. Witalis, E. A., in Electricity.from MHD, International Atomic Energy Agency, Vienna Austria (1968). Vol. I1, p. 157.

(Received September l 3, 1972; revised version received April 3, 19 73)