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The low pressure, combustion gas plasma
The Low Pressure, Combustion Gas Plasma* T. H. DIMMOCK and W. R. KINEYKO l‘hiokol Chemical
Corporation,
Reaction
Motors Division,
Denville,
New Jersey
(ReceivedJanuary 19631 high-temperature, low-pressure flames have Studies of the electrical properties of seeded, been made to determine the influence of electric and magnetic fields on plasma properties was carried out at pressures The investigation and to evaluate plasma diagnostic techniques. from 20 to 100 mm of mercury where both magnetic and fluid viscosities influenced the flame electrical conductivity, and where the electric field produced abnormal glow and arc discharges. The deflection of flames at low Pressures was found to reach a limit when slippage of charged particles through the flame fanned out the flame rather than further deflecting it.
Description
Introduction BECAUSE a rocket exhaust is known to contain ionized as well as neutral species it seems conceivable that the thrust vector of the exhaust can be measurably altered by the application of electric, magnetic or Lorentz force fields. When considered solely from energy considerations, however, this method of control is marginal at best. Nevertheless since vernier control may be feasible under ideal conditions, and since a low-pressure seeded combustion plasma is a suitable working fluid for magnetohydrodynamic (MHD) propulsion and power generation applications, a study of the plasma and boundary layer properties of seeded flames has been undertaken. The investigation of atmospheric flames has been previously reportedl. This report describes the distribution and intensity of ionization in low pressure flames (0.01 to 0.1 atm) and the interaction of the flame with electrostatic, magnetostatic and Lorentz force fields. The plasma properties in the free stream were first measured by probe and microwave methods. An electric field was then applied to the flame plasma, and the characteristics of the discharges required for Lorentz fields were investigated. Some of the considerations governing flame deflection by Lorentz fields were determined, including the effect of an external magnetic field on the impedance of the flame. *This work was supported by the AF Office of Scientific of the Office of Aeroseace Research under Contract 49(638)-30.5.
of Apparatus
and Procedure
The plasma source was a caesium-enriched flame burning in a low pressure tank, Figure 1. The propellants were stoichiometric mixtures of methane and oxygen with a mass flow rate A half-molar of 12 standard litres/minute. aqueous solution of caesium nitrate was aspirated into the flame and adjusted to provide a caesium atom injection which was one per cent of the propellant mass injection. The pressure range for the plasma source (flame) was 20 to 100 mm of mercury. To achieve stable combustion over this wide pressure range, and to prevent flashback or blowoff, four burner sizes were necessary. Table I shows the essential characteristics of each For each given burner size used, the burner. mass flow per unit area was constant. With proper choice of burner size and ambient pressure, the range of gas velocities was 3 to 14 m/s for propellant mixtures; and 40 to 200 m/s for burnt gas mixtures. Ionization measurements in the plasma were made with microwaves and with probes. For the microwave diagnostics, both interferometer and attenuation methods were used. The theory of microwave plasma diagnostics has been well developed 2--4 both in bounded and unbounded The application of this theory to low media. density flame plasmas is straightforward. Figure 2 is a block diagram of the two circuits In the interferometer circuit, a employed. portion of the transmitted signal is taken from
Research No. Ap
283
T. H. Dimmock
and
W.
R.
Kineyko
Vol.
7
the directional coupler, rectified and monitored on one channel of a dual beam oscilloscope. With the plasma in the test leg of the interferometer, the phase-shifter and attenuator in the reference leg are then adjusted to null the signal detected and observed on the other beam of the oscilloscope. Using the relation given by R. C. WARDER et al” the ionization is then given by the relation G-/P=-
$+&I
. . ..[I]
where z and ,6 are the attenuation and phase shift changes, w is the microwave angular frequency (v = 31.4 kMc/ s), c is the speed of light, $=ne2/ E,m is the plasma frequency (Ed is the dielectric constant ,of free space) and T is the mean free time for collisions between electrons and neutral gas species. Equation 1 can easily be solved for the plasma frequency and hence the electron density when the electron collision frequency is known. The collision frequency is given by the relation
. . . . [2]
~c=~iZiniQei
where C= (SkT/ 7cm)‘/2 is the thermal speed of the electrons, n, is the number density of the ith species and Qei is the collision cross section for electrons with the ith species. For combustion products, the predominant species are CO, and H,O, so that equation 2 can be written ~~~7.24 x 1O’l ($/Pi’)
set-’
. . . [33
where p and T are in lb/ in2 absolute and “K, respectively. In the attenuation circuit, a calibrated attenuator is used to reproduce and indicate the attenuation of the beam through the plasma. If the flame thickness and temperature are known, the electron density can then be read directly from graphical data developed by W. W. BALWANP. Langmuir probe measurements in the flame were made using conventional probe methodG’. The probe itself was a 2 in. long by 0.040 in. diameter, water cooled device which was inserted half way through the flame. It was not used to determine electron temperature or concentration, since it was limited by the positive-
September
The low pressure, combustion
1963
Figure I.
Attenuator
Attenuator
I
Flame
‘L-r
’
Plasma -
I
Oscilloscope Attenuation I:;:,
circuit
Attenuator <
Attenuatw
Horn & lens
GO(p Wry&al
applied between the burner and the probe which was located just above the tip of the low presThe current and voltage sure reaction zone. in the probe circuit were then read on a precision respectively. voltmeter and microammeter When the probe was made a few volts negative, the electrons (exclusive of the high energy ones) were repelled, and the positive ion current (ji) to the probe was space-charge-limited. This current is related to the positive ion concentration by the equation
‘lasma
LA
(kT,/2%)‘/’
Crystal
,.f[2.310g(-$)]
by Figure
2.
. ..%[5]
where Y and L are the radius and length of the probe, and h is electron mean free path given
Oscilloscope interferometer
. . . . [4]
Since there are collisions in the probe sheath, equation 4 must be corrected for this effect by multiplying by the factor
Wavemeter Power supply
apparatus
jl=ne
A LYI Klystron 0
deflection
265
gas plasma
h=2.94
circuit
Block diagram of microwave
circuits
ion space charge which formed on the burner. A variable potential (positive or negative) was
x lo-*
TO/p
cm
. . . . [6]
where TO and P are in “K and atm respectively. The effect of mass motion of the gas on the charge sheath which surrounds the probe can be assessed by comparing the velocity of burnt
T.
286
H.
Dimmock
gases (Table 1) with the thermal speed of the particles given following equation 2. The burnt gas velocity is approximately lo2 m/s, the thermal speed of the electrons and the flame molecules is 3 x lo5 and 1 x lo3 m/s respectively, which is an order of magnitude greater than the velocity of mass motion. Thus the probe sheath suffers only a slight distortion by the mass motion of the gas stream. In deflection experiments the electric field on the flame was produced by an electronic power supply which had a capacity of 05 A and 3 kV d.c. The magnetic field was coaxial with the flame and was generated by a SOO-turn coil which circumscribed the burner. It was energized with 20 A. All of the burners were made of non-magnetic steel so that the field intensity at the burner lip never exceeded 1 kilogauss and the field was uniform through the flame. Results
(A)
and
W.
R.
Vol.
Kineyko
7
do not have the typical Langmuir profile with the effect becoming more pronounced as the pressure is reduced. Two separate effects conIn the first place, the tribute to this distortion. boundary layer between the flame and burner was large at these pressures and substantially impeded the positive ion flow from the flame to the burner which also served as the counterSecondly, a wall potential formed on electrode. the flameholder setting up potential gradients in the flame and distorting the potential profile between the probe and the burner. As mentioned above, positive ion density at the probe was the only information taken from these curves.
‘“‘5FFFR
and
Discussion Free-stream plasma Pro perties
Figure 3 shows typical Langmuir probe curves made in the seeded, low-pressure, stoichiometric methane-oxygen flame. The 20- and 25-mm of
Pressure
Ionization
(mm Hg) (cm-3x10-12)
0
20
2.1
600
Probe current, p A
500 I 400
Probe potential, V
10'2
1
20
Figure
I
l600 Figure
3.
Langmuir
probe ionization
curves
mercury curves were made on the 6.6 cm burner with a perforated flameholder affixed. The curve at 35 mm of mercury was made on the 2.8 cm burner without flameholder. These three curves
4.
Ionization
,
I
40 60 Pressure, mm Hg versus
pressure
80
in seeded
I flame
Results of similar probe measurements and of microwave measurements in the flame are shown in Figure 4. The caesium atom concentration, N,, is taken from flow measurements. It is assumed that the caesium salt was completely dissociated, and that caesium formed no The ion stable bonds at the flame temperature. density was.computed and corrected using equations 4 and 5.
It is shown in ref. 3 that when v,
plotted in Figure 6 for our flame which had a constant mass flow of the reactants and caesium atoms.
0 Pressure, Figure quency
0
-!-! 6 3 co4
60
40 Pressure, Figure Sure
5. flames
297
The low pressure, combustion gas plasma
September 1963
mm Hg
Microwave attenuation through low firesin the vicinity of the plasma frequency
attenuation is asymptotic at v = v,. The evidence from the attenuation measurements of Figure 5, however, indicates that large radial density gradients produce diffraction of the beam which obscures the results in the vicinity vP. In addition it is seen from Table 1 that the plasma (approximately equal to burner thickness diameter at point of measurement) was merely two wavelengths in the 2.1 cm burner required for the higher pressures; thus there was inevitably a leakage of the microwave beam around the flame. The free stream conductivity of the plasma was computed from the standard relation fl=ne2/mv,
. . . . [7-j
using measured ionization densities. This value, the collision frequency (equation 2), and a reciprocal collision frequency* ti,r/ IOB, are *When our value of magnetic field intensity (Pl Wb/m’) this value is numerically equal to the Hall parameter.
is used,
6. Electrical (v), and Hall
mm Hg
conductivity parameter
(WT)
(u), in
freplasmas
~01lisi0n flame
(B) Discharge characteristics In order to produce a significant Lorentz force on the subsonic, low-pressure plasma the electrode current must be in the arc discharge or abnormal glow region beyond the breakdown Although this programme was not regions. principally concerned with low-pressure breakdown phenomena, some observations in the low pressure flame form an interesting sidelight. In the first place, the value of the breakdown potential was found to be governed largely by the rate at which the potential was raised, and hence the time for electrode heating by conduction or ion bombardment. Although the discharge was usually in the abnormal glow region, it occasionally shifted abruptly to the thermionic or non-thermionic arc depending on pressure and cathode conditions (see Figure 7). In the second place, the breakdown potential between electrodes in the flame was found to be directly related to the conductivity of the flame. Thus one would expect to find a lower impedance and breakdown potential in a seeded flame than in an unseeded one, and this is illustrated in Figure 8. In plasma applications involving an electric field, the boundary layer plays a dominant role Generally in the choice of test conditions. speaking, we endeavoured to suppress the effect of thermionic emission by using heat-sink or aircooled electrodes, and to circumvent the influence of pressure on flame thickness by always placing the electrodes just inside the flame boundary. Using these principles as guide lines, it apparently made little difference what
T.
Arc ’ Non- thermionic cathode I multiple
spots
~~[,TG,oyo~L~ ph6 m ion ic cathode
Hiah
!
!
I
arc
Current,
-
Figuve
7.
mA
Initial cathode emission Large (by external heating) Initial cathode emission very Small
Discharge
in low pressure Cobine)
Vol. 7
Dimmock and \Y. R. Kineyko
H.
gases
(after
the electrode shape or material consisted of or whether or not the electrode was covered with platinum whiskers protruding into the flame. When, on occasion, the electrodes happened to be placed outside the flame, there was evidence of charge leakage by ambipolar diffusion to the Breakdown voltage outside of the flame. measurements similar to those of Figure 8 were then made on a 2in. diameter seeded flame burning at 20 mm of mercury to evaluate this leakage. At unit flame diameter electrode separation the breakdown voltage was 100 V, at 14 diameters it was 165 V and at 2& diameters it was 700 V. (C) Flames in a Lorentz field From considerations given above it is evident that a suitable Lorentz field should be one produced with an arc discharge across a seeded flame and an axial magnetic field parallel to Figwe 9 shows typical the flow direction. methane-oxygen flames deflected by direct current and 60 c/s a.c. Lorentz fields. The camera is mounted with optic axis parallel to the electric field, the magnetic field (0.1 The pressure range for Wb / mZ) is vertical. all deflection experiments is shown in Table 1 and lies between 25 and 35 mm of mercury. As long as the collision coupling between the electrons and the gas atoms is adequate, the electrons will not depart significantly from
thermal equilibrium with the gas atoms and the flame will deflect in proportion to the Lorentz field intensity. The cross section for electronatom energy exchange, however, decreases rapidly with the relative electron-atom velocity, until the electron energy becomes codirectional with the Lorentz field and the phenomenon of run-away electrons occurs. When the electron energy becomes essentially unidirectional, the flame is observed to flop over to its limit deflection; the flames shown in Figure 9 are in limit deflection. Figure 10 shows qualitatively this phenomenon of limit deflection which is characteristic of low pressure flames. If the transverse Lorentz field exceeds the limit deflection value, the only result is to fan out the flame rather than to increase the deflection. This phenomenon of ion slip increases in direct proportion ‘to the electron mean-free-path in the field. In a previous investigation on the deflection of atmospheric flames9~‘o, the deflection angle was found to decrease linearly with flame momentum. Tests for this same effect were conducted with the low pressure flame in which the magnetizing current, the mass flow rate and deflection angle were held constant and the power input to the electric field was measured as the flame momentum was increased. The results found previously were thus established in the low pressure flame as shown in Table 2. (The change in momentum resulted automatically when a change in burner size was made at constant mass flow rate.)
Circuit current, mA
Figure 8. Typical low pressure flame discharge characteristics. Electrodes were located at edge of flame plasma
September
The low pressure, combustion
1963
289
gas plasma
(D) Magnetic Hall effects The role of the magnetic field in reducing plasma conductivity has been shown previously. If an external magnetic field B is applied to the electrons are constrained to spiral plasma, around the field lines so that the conductivity is no longer isotropic but in fact becomes a tensor quantity. If an electric field is then applied in a direction transverse to this magnetic field, the conductivity parallel to the electric field is reduced as follows ~B=~J(1+w:i2)
Loventz flame dejection. (a) Right Figure 9. deflection of a flame by a vertical magnetostatic jeld and an electrostatic field directed away from the camera
. . . . [S]
where o,=eB/m, and W,TEW,/V, is the Hall parameter, and u,, is given by equation 7. Figure 6 indicated that there was a monotonic increase in the Hall parameter as the pressure was reduced. Thus from equation 8 it is easy to see that magnetic viscosity will cause the conductivity to decrease monotonically with decreasing pressure (0, = constant) as illustrated in Figure 11. The maximum gyro frequency (o =eB/m) for our magnetic field (B,_.. =O.l Wb/m*) was 1.76 x lOlo /sec. Figure 12 is a typical oscillogram of the voltage and current between the electrodes immersed in the flame burning at a pressure of 20 mm of mercury. The spontaneous transition from glow to arc discharge can be seen, and is followed by the magnetic viscosity effect. Unfortunately, due to power supply limitations, it cannot be stated unequivocally that the transition attributed to the magnetic field was not due, at least in part, to a transition back to glow discharge conditions. This question will be resolved in the future by using a new, high-capacity power supply. Conclusion
Figure 9. Lorentz pame deflection. (b) Right and left dejection of a jame by a vevtical magnetostatic field and an alternating electric jeld parallel to optic axis of camera
Free-stream plasma properties were measured in a Iminar low pressure flame with constant mass
Table 2 Burner
diameter,
System pressure,
mm mm Hg
Momentum density, Newt sec/m3 Electric jeld current, mA Electric jeld voltage, V Electric jeld power, W Magnetic je;d:
I kilogauss
28 30-40 36.2X 10-t 160 300 48
21
14
40-70
70--100
6.5 X 10-Z 300 300 90 Dejection:
20”
142X 10-Z 550 300 165
T. H.
290
Dimmock
and \V. R.
Vol.
Kineyko
7
p=35 30
Lorentz Figure
10.
Deflection
/
force
versus field intensity
/
0.1
30
10
flow rate and seeding. The average value of ionization at different heights above the reaction zone was measured by probes and microwave methods. The probe method gave results which were 70 to 90 per cent of the theoretical value, the best agreement occurring at the higher pressures. This accuracy is a conservative estimate since depletion by chemical equilibria in the flame was not considered in computing the caesium concentration. One-centimetre micro-
I
50 Pressure
Figure
Il.
70
90
,mm Hg
Conductivity suppression viscosity
by
waves, in attenuation and interferometer circuits, were also employed to measure the average electron density through the flame. These two microwave methods did not agree well and yielded electron densities at best only The probe 30 per cent of the theoretical value.
Sweep:
0.5 set/cm
Voltage trace: 250 V/cm
Current trace: 0.5 A/cm
Glow 8 field Figure
magnetic
_
Arc off
_
B field
on --J
h
12. Influence of magnetic viscos’ity on inter-electrode imp’edance oxygen flame at 20 mm of mercury
in the seeded
methane-
September
1963
The low pressure, combustion gas plasma
method is probably superior for most low pressure seeded flames since they do not represent an infinite homogeneous slab. No effort was made to find the saturation ionization in the low pressure methan+oxygen flame since the seeding was maintained at one Even under these conditions the per cent. whereas in ionization exceeded 1Ol3/ cm3, the heavily seeded atmospheric flames previously investigated ionization never exceeded The d.c. conductivity in the low 1014/cm3. pressure flame was 60 to 90 mho/m; for a similar flame at one atmosphere the conductivity was 130 mho/m. In the low pressure deflection’ studies desscribed above, the flame momentum, conductivity, and Magnetic Interaction Parameter* QBfcovered the same range as for the one atmosphere flame studies”‘. For similar conditions it was found that the power dissipated in the electric field was slightly greater at low pressures than at atmospheric pressure. The deflection of the low pressure flame is complicated by two considerations. (2) Gyro magnetic oscillations of the electrons, which become significant when the Hall parameter exceeds unity, decrease the plasma conductivity. (2) Runaway electrons which appear at large Lorentz field intensities cause the flame to fan out in the direction of the field and result in a unique limiting flame deflection for any given low pressure. For the methane-oxygen flames investigated, where 0.4
*ax
a
characteristic
291
limit deflection could be produced by a Lorentz (J x B) field below 100 newtons/m3 (where J is based upon total current and total electrode surface area). References 1 DIMMOCK, T.
H. ‘The electrical properties of ionized flames’, Proceedings of the Fourth Biennial Gas Dynamic SymPosium ala Magnetohydrodynamics. Northwestern University Press : Evanston, 1962 * WARDER, Jr. R. C., BRODWIN, M. and CAMBEL, ‘Microwave measurements of magnetoA. B. Northwestern University gas dynamic plasmas’. AFOSR 1468, August Gas Dynamics Laboratory 1961 3 JAHN, R. G. ‘Microwave probing of ionized gas flames’. Physics of Fluids, June 1962, 5, 678 4 TALBOT, L., KATZ, J. E. and BRUNDIN, C. L. ‘A comparison between Langmuir probe and microwave electron densities in arc heated, supersonic, low density wind tunnels’. University of California, Res. TR HE-150-186, Institute of Engineering, January 1961 5 BALWANZ, W. W. ‘Interaction between electromagnetic waves and flames, Part VI-Theoretical plots of absorption, phase shift and reflection’. Radar Techniques Branch, Radar Division, Naval Research Laboratorv., Washinnton. D.C. NRL 5388 (1959) Sec. 1.8. 6 COBINE, J. D. Gaseous Conductors, Dover : New York, 1958 7 ELLISON, R. and- DIMMOCK, T. H. ‘Research on the influence of ions on rocket combustiop’. Reaction Motors Division, RMD-204~Q2. Second Quarterly Report AF49(638j-305. August 1958 Third 8 COBINE, J. D. ‘MHD and gas discharges’. Symposium on the Engineering AsPects of Magnetohydrodynamics. University of Rochester, March 1962 9
DIMMOCK, T. H., and KINEYKO, W.
MILLER, G.
F.,
NICOL, J.
J.
R. ‘The electrical properties of ionized gases, Part II-Electrostatic and magnetohydrodynamic deflection’. August 1961. AFOSR990 AD 262 368 10 DIMMOCK, T. H. See ref. 1
Corporation,
Reaction
Motors Division,
Denville,
New Jersey
(ReceivedJanuary 19631 high-temperature, low-pressure flames have Studies of the electrical properties of seeded, been made to determine the influence of electric and magnetic fields on plasma properties was carried out at pressures The investigation and to evaluate plasma diagnostic techniques. from 20 to 100 mm of mercury where both magnetic and fluid viscosities influenced the flame electrical conductivity, and where the electric field produced abnormal glow and arc discharges. The deflection of flames at low Pressures was found to reach a limit when slippage of charged particles through the flame fanned out the flame rather than further deflecting it.
Description
Introduction BECAUSE a rocket exhaust is known to contain ionized as well as neutral species it seems conceivable that the thrust vector of the exhaust can be measurably altered by the application of electric, magnetic or Lorentz force fields. When considered solely from energy considerations, however, this method of control is marginal at best. Nevertheless since vernier control may be feasible under ideal conditions, and since a low-pressure seeded combustion plasma is a suitable working fluid for magnetohydrodynamic (MHD) propulsion and power generation applications, a study of the plasma and boundary layer properties of seeded flames has been undertaken. The investigation of atmospheric flames has been previously reportedl. This report describes the distribution and intensity of ionization in low pressure flames (0.01 to 0.1 atm) and the interaction of the flame with electrostatic, magnetostatic and Lorentz force fields. The plasma properties in the free stream were first measured by probe and microwave methods. An electric field was then applied to the flame plasma, and the characteristics of the discharges required for Lorentz fields were investigated. Some of the considerations governing flame deflection by Lorentz fields were determined, including the effect of an external magnetic field on the impedance of the flame. *This work was supported by the AF Office of Scientific of the Office of Aeroseace Research under Contract 49(638)-30.5.
of Apparatus
and Procedure
The plasma source was a caesium-enriched flame burning in a low pressure tank, Figure 1. The propellants were stoichiometric mixtures of methane and oxygen with a mass flow rate A half-molar of 12 standard litres/minute. aqueous solution of caesium nitrate was aspirated into the flame and adjusted to provide a caesium atom injection which was one per cent of the propellant mass injection. The pressure range for the plasma source (flame) was 20 to 100 mm of mercury. To achieve stable combustion over this wide pressure range, and to prevent flashback or blowoff, four burner sizes were necessary. Table I shows the essential characteristics of each For each given burner size used, the burner. mass flow per unit area was constant. With proper choice of burner size and ambient pressure, the range of gas velocities was 3 to 14 m/s for propellant mixtures; and 40 to 200 m/s for burnt gas mixtures. Ionization measurements in the plasma were made with microwaves and with probes. For the microwave diagnostics, both interferometer and attenuation methods were used. The theory of microwave plasma diagnostics has been well developed 2--4 both in bounded and unbounded The application of this theory to low media. density flame plasmas is straightforward. Figure 2 is a block diagram of the two circuits In the interferometer circuit, a employed. portion of the transmitted signal is taken from
Research No. Ap
283
T. H. Dimmock
and
W.
R.
Kineyko
Vol.
7
the directional coupler, rectified and monitored on one channel of a dual beam oscilloscope. With the plasma in the test leg of the interferometer, the phase-shifter and attenuator in the reference leg are then adjusted to null the signal detected and observed on the other beam of the oscilloscope. Using the relation given by R. C. WARDER et al” the ionization is then given by the relation G-/P=-
$+&I
. . ..[I]
where z and ,6 are the attenuation and phase shift changes, w is the microwave angular frequency (v = 31.4 kMc/ s), c is the speed of light, $=ne2/ E,m is the plasma frequency (Ed is the dielectric constant ,of free space) and T is the mean free time for collisions between electrons and neutral gas species. Equation 1 can easily be solved for the plasma frequency and hence the electron density when the electron collision frequency is known. The collision frequency is given by the relation
. . . . [2]
~c=~iZiniQei
where C= (SkT/ 7cm)‘/2 is the thermal speed of the electrons, n, is the number density of the ith species and Qei is the collision cross section for electrons with the ith species. For combustion products, the predominant species are CO, and H,O, so that equation 2 can be written ~~~7.24 x 1O’l ($/Pi’)
set-’
. . . [33
where p and T are in lb/ in2 absolute and “K, respectively. In the attenuation circuit, a calibrated attenuator is used to reproduce and indicate the attenuation of the beam through the plasma. If the flame thickness and temperature are known, the electron density can then be read directly from graphical data developed by W. W. BALWANP. Langmuir probe measurements in the flame were made using conventional probe methodG’. The probe itself was a 2 in. long by 0.040 in. diameter, water cooled device which was inserted half way through the flame. It was not used to determine electron temperature or concentration, since it was limited by the positive-
September
The low pressure, combustion
1963
Figure I.
Attenuator
Attenuator
I
Flame
‘L-r
’
Plasma -
I
Oscilloscope Attenuation I:;:,
circuit
Attenuator <
Attenuatw
Horn & lens
GO(p Wry&al
applied between the burner and the probe which was located just above the tip of the low presThe current and voltage sure reaction zone. in the probe circuit were then read on a precision respectively. voltmeter and microammeter When the probe was made a few volts negative, the electrons (exclusive of the high energy ones) were repelled, and the positive ion current (ji) to the probe was space-charge-limited. This current is related to the positive ion concentration by the equation
‘lasma
LA
(kT,/2%)‘/’
Crystal
,.f[2.310g(-$)]
by Figure
2.
. ..%[5]
where Y and L are the radius and length of the probe, and h is electron mean free path given
Oscilloscope interferometer
. . . . [4]
Since there are collisions in the probe sheath, equation 4 must be corrected for this effect by multiplying by the factor
Wavemeter Power supply
apparatus
jl=ne
A LYI Klystron 0
deflection
265
gas plasma
h=2.94
circuit
Block diagram of microwave
circuits
ion space charge which formed on the burner. A variable potential (positive or negative) was
x lo-*
TO/p
cm
. . . . [6]
where TO and P are in “K and atm respectively. The effect of mass motion of the gas on the charge sheath which surrounds the probe can be assessed by comparing the velocity of burnt
T.
286
H.
Dimmock
gases (Table 1) with the thermal speed of the particles given following equation 2. The burnt gas velocity is approximately lo2 m/s, the thermal speed of the electrons and the flame molecules is 3 x lo5 and 1 x lo3 m/s respectively, which is an order of magnitude greater than the velocity of mass motion. Thus the probe sheath suffers only a slight distortion by the mass motion of the gas stream. In deflection experiments the electric field on the flame was produced by an electronic power supply which had a capacity of 05 A and 3 kV d.c. The magnetic field was coaxial with the flame and was generated by a SOO-turn coil which circumscribed the burner. It was energized with 20 A. All of the burners were made of non-magnetic steel so that the field intensity at the burner lip never exceeded 1 kilogauss and the field was uniform through the flame. Results
(A)
and
W.
R.
Vol.
Kineyko
7
do not have the typical Langmuir profile with the effect becoming more pronounced as the pressure is reduced. Two separate effects conIn the first place, the tribute to this distortion. boundary layer between the flame and burner was large at these pressures and substantially impeded the positive ion flow from the flame to the burner which also served as the counterSecondly, a wall potential formed on electrode. the flameholder setting up potential gradients in the flame and distorting the potential profile between the probe and the burner. As mentioned above, positive ion density at the probe was the only information taken from these curves.
‘“‘5FFFR
and
Discussion Free-stream plasma Pro perties
Figure 3 shows typical Langmuir probe curves made in the seeded, low-pressure, stoichiometric methane-oxygen flame. The 20- and 25-mm of
Pressure
Ionization
(mm Hg) (cm-3x10-12)
0
20
2.1
600
Probe current, p A
500 I 400
Probe potential, V
10'2
1
20
Figure
I
l600 Figure
3.
Langmuir
probe ionization
curves
mercury curves were made on the 6.6 cm burner with a perforated flameholder affixed. The curve at 35 mm of mercury was made on the 2.8 cm burner without flameholder. These three curves
4.
Ionization
,
I
40 60 Pressure, mm Hg versus
pressure
80
in seeded
I flame
Results of similar probe measurements and of microwave measurements in the flame are shown in Figure 4. The caesium atom concentration, N,, is taken from flow measurements. It is assumed that the caesium salt was completely dissociated, and that caesium formed no The ion stable bonds at the flame temperature. density was.computed and corrected using equations 4 and 5.
It is shown in ref. 3 that when v,
plotted in Figure 6 for our flame which had a constant mass flow of the reactants and caesium atoms.
0 Pressure, Figure quency
0
-!-! 6 3 co4
60
40 Pressure, Figure Sure
5. flames
297
The low pressure, combustion gas plasma
September 1963
mm Hg
Microwave attenuation through low firesin the vicinity of the plasma frequency
attenuation is asymptotic at v = v,. The evidence from the attenuation measurements of Figure 5, however, indicates that large radial density gradients produce diffraction of the beam which obscures the results in the vicinity vP. In addition it is seen from Table 1 that the plasma (approximately equal to burner thickness diameter at point of measurement) was merely two wavelengths in the 2.1 cm burner required for the higher pressures; thus there was inevitably a leakage of the microwave beam around the flame. The free stream conductivity of the plasma was computed from the standard relation fl=ne2/mv,
. . . . [7-j
using measured ionization densities. This value, the collision frequency (equation 2), and a reciprocal collision frequency* ti,r/ IOB, are *When our value of magnetic field intensity (Pl Wb/m’) this value is numerically equal to the Hall parameter.
is used,
6. Electrical (v), and Hall
mm Hg
conductivity parameter
(WT)
(u), in
freplasmas
~01lisi0n flame
(B) Discharge characteristics In order to produce a significant Lorentz force on the subsonic, low-pressure plasma the electrode current must be in the arc discharge or abnormal glow region beyond the breakdown Although this programme was not regions. principally concerned with low-pressure breakdown phenomena, some observations in the low pressure flame form an interesting sidelight. In the first place, the value of the breakdown potential was found to be governed largely by the rate at which the potential was raised, and hence the time for electrode heating by conduction or ion bombardment. Although the discharge was usually in the abnormal glow region, it occasionally shifted abruptly to the thermionic or non-thermionic arc depending on pressure and cathode conditions (see Figure 7). In the second place, the breakdown potential between electrodes in the flame was found to be directly related to the conductivity of the flame. Thus one would expect to find a lower impedance and breakdown potential in a seeded flame than in an unseeded one, and this is illustrated in Figure 8. In plasma applications involving an electric field, the boundary layer plays a dominant role Generally in the choice of test conditions. speaking, we endeavoured to suppress the effect of thermionic emission by using heat-sink or aircooled electrodes, and to circumvent the influence of pressure on flame thickness by always placing the electrodes just inside the flame boundary. Using these principles as guide lines, it apparently made little difference what
T.
Arc ’ Non- thermionic cathode I multiple
spots
~~[,TG,oyo~L~ ph6 m ion ic cathode
Hiah
!
!
I
arc
Current,
-
Figuve
7.
mA
Initial cathode emission Large (by external heating) Initial cathode emission very Small
Discharge
in low pressure Cobine)
Vol. 7
Dimmock and \Y. R. Kineyko
H.
gases
(after
the electrode shape or material consisted of or whether or not the electrode was covered with platinum whiskers protruding into the flame. When, on occasion, the electrodes happened to be placed outside the flame, there was evidence of charge leakage by ambipolar diffusion to the Breakdown voltage outside of the flame. measurements similar to those of Figure 8 were then made on a 2in. diameter seeded flame burning at 20 mm of mercury to evaluate this leakage. At unit flame diameter electrode separation the breakdown voltage was 100 V, at 14 diameters it was 165 V and at 2& diameters it was 700 V. (C) Flames in a Lorentz field From considerations given above it is evident that a suitable Lorentz field should be one produced with an arc discharge across a seeded flame and an axial magnetic field parallel to Figwe 9 shows typical the flow direction. methane-oxygen flames deflected by direct current and 60 c/s a.c. Lorentz fields. The camera is mounted with optic axis parallel to the electric field, the magnetic field (0.1 The pressure range for Wb / mZ) is vertical. all deflection experiments is shown in Table 1 and lies between 25 and 35 mm of mercury. As long as the collision coupling between the electrons and the gas atoms is adequate, the electrons will not depart significantly from
thermal equilibrium with the gas atoms and the flame will deflect in proportion to the Lorentz field intensity. The cross section for electronatom energy exchange, however, decreases rapidly with the relative electron-atom velocity, until the electron energy becomes codirectional with the Lorentz field and the phenomenon of run-away electrons occurs. When the electron energy becomes essentially unidirectional, the flame is observed to flop over to its limit deflection; the flames shown in Figure 9 are in limit deflection. Figure 10 shows qualitatively this phenomenon of limit deflection which is characteristic of low pressure flames. If the transverse Lorentz field exceeds the limit deflection value, the only result is to fan out the flame rather than to increase the deflection. This phenomenon of ion slip increases in direct proportion ‘to the electron mean-free-path in the field. In a previous investigation on the deflection of atmospheric flames9~‘o, the deflection angle was found to decrease linearly with flame momentum. Tests for this same effect were conducted with the low pressure flame in which the magnetizing current, the mass flow rate and deflection angle were held constant and the power input to the electric field was measured as the flame momentum was increased. The results found previously were thus established in the low pressure flame as shown in Table 2. (The change in momentum resulted automatically when a change in burner size was made at constant mass flow rate.)
Circuit current, mA
Figure 8. Typical low pressure flame discharge characteristics. Electrodes were located at edge of flame plasma
September
The low pressure, combustion
1963
289
gas plasma
(D) Magnetic Hall effects The role of the magnetic field in reducing plasma conductivity has been shown previously. If an external magnetic field B is applied to the electrons are constrained to spiral plasma, around the field lines so that the conductivity is no longer isotropic but in fact becomes a tensor quantity. If an electric field is then applied in a direction transverse to this magnetic field, the conductivity parallel to the electric field is reduced as follows ~B=~J(1+w:i2)
Loventz flame dejection. (a) Right Figure 9. deflection of a flame by a vertical magnetostatic jeld and an electrostatic field directed away from the camera
. . . . [S]
where o,=eB/m, and W,TEW,/V, is the Hall parameter, and u,, is given by equation 7. Figure 6 indicated that there was a monotonic increase in the Hall parameter as the pressure was reduced. Thus from equation 8 it is easy to see that magnetic viscosity will cause the conductivity to decrease monotonically with decreasing pressure (0, = constant) as illustrated in Figure 11. The maximum gyro frequency (o =eB/m) for our magnetic field (B,_.. =O.l Wb/m*) was 1.76 x lOlo /sec. Figure 12 is a typical oscillogram of the voltage and current between the electrodes immersed in the flame burning at a pressure of 20 mm of mercury. The spontaneous transition from glow to arc discharge can be seen, and is followed by the magnetic viscosity effect. Unfortunately, due to power supply limitations, it cannot be stated unequivocally that the transition attributed to the magnetic field was not due, at least in part, to a transition back to glow discharge conditions. This question will be resolved in the future by using a new, high-capacity power supply. Conclusion
Figure 9. Lorentz pame deflection. (b) Right and left dejection of a jame by a vevtical magnetostatic field and an alternating electric jeld parallel to optic axis of camera
Free-stream plasma properties were measured in a Iminar low pressure flame with constant mass
Table 2 Burner
diameter,
System pressure,
mm mm Hg
Momentum density, Newt sec/m3 Electric jeld current, mA Electric jeld voltage, V Electric jeld power, W Magnetic je;d:
I kilogauss
28 30-40 36.2X 10-t 160 300 48
21
14
40-70
70--100
6.5 X 10-Z 300 300 90 Dejection:
20”
142X 10-Z 550 300 165
T. H.
290
Dimmock
and \V. R.
Vol.
Kineyko
7
p=35 30
Lorentz Figure
10.
Deflection
/
force
versus field intensity
/
0.1
30
10
flow rate and seeding. The average value of ionization at different heights above the reaction zone was measured by probes and microwave methods. The probe method gave results which were 70 to 90 per cent of the theoretical value, the best agreement occurring at the higher pressures. This accuracy is a conservative estimate since depletion by chemical equilibria in the flame was not considered in computing the caesium concentration. One-centimetre micro-
I
50 Pressure
Figure
Il.
70
90
,mm Hg
Conductivity suppression viscosity
by
waves, in attenuation and interferometer circuits, were also employed to measure the average electron density through the flame. These two microwave methods did not agree well and yielded electron densities at best only The probe 30 per cent of the theoretical value.
Sweep:
0.5 set/cm
Voltage trace: 250 V/cm
Current trace: 0.5 A/cm
Glow 8 field Figure
magnetic
_
Arc off
_
B field
on --J
h
12. Influence of magnetic viscos’ity on inter-electrode imp’edance oxygen flame at 20 mm of mercury
in the seeded
methane-
September
1963
The low pressure, combustion gas plasma
method is probably superior for most low pressure seeded flames since they do not represent an infinite homogeneous slab. No effort was made to find the saturation ionization in the low pressure methan+oxygen flame since the seeding was maintained at one Even under these conditions the per cent. whereas in ionization exceeded 1Ol3/ cm3, the heavily seeded atmospheric flames previously investigated ionization never exceeded The d.c. conductivity in the low 1014/cm3. pressure flame was 60 to 90 mho/m; for a similar flame at one atmosphere the conductivity was 130 mho/m. In the low pressure deflection’ studies desscribed above, the flame momentum, conductivity, and Magnetic Interaction Parameter* QBfcovered the same range as for the one atmosphere flame studies”‘. For similar conditions it was found that the power dissipated in the electric field was slightly greater at low pressures than at atmospheric pressure. The deflection of the low pressure flame is complicated by two considerations. (2) Gyro magnetic oscillations of the electrons, which become significant when the Hall parameter exceeds unity, decrease the plasma conductivity. (2) Runaway electrons which appear at large Lorentz field intensities cause the flame to fan out in the direction of the field and result in a unique limiting flame deflection for any given low pressure. For the methane-oxygen flames investigated, where 0.4
*ax
a
characteristic
291
limit deflection could be produced by a Lorentz (J x B) field below 100 newtons/m3 (where J is based upon total current and total electrode surface area). References 1 DIMMOCK, T.
H. ‘The electrical properties of ionized flames’, Proceedings of the Fourth Biennial Gas Dynamic SymPosium ala Magnetohydrodynamics. Northwestern University Press : Evanston, 1962 * WARDER, Jr. R. C., BRODWIN, M. and CAMBEL, ‘Microwave measurements of magnetoA. B. Northwestern University gas dynamic plasmas’. AFOSR 1468, August Gas Dynamics Laboratory 1961 3 JAHN, R. G. ‘Microwave probing of ionized gas flames’. Physics of Fluids, June 1962, 5, 678 4 TALBOT, L., KATZ, J. E. and BRUNDIN, C. L. ‘A comparison between Langmuir probe and microwave electron densities in arc heated, supersonic, low density wind tunnels’. University of California, Res. TR HE-150-186, Institute of Engineering, January 1961 5 BALWANZ, W. W. ‘Interaction between electromagnetic waves and flames, Part VI-Theoretical plots of absorption, phase shift and reflection’. Radar Techniques Branch, Radar Division, Naval Research Laboratorv., Washinnton. D.C. NRL 5388 (1959) Sec. 1.8. 6 COBINE, J. D. Gaseous Conductors, Dover : New York, 1958 7 ELLISON, R. and- DIMMOCK, T. H. ‘Research on the influence of ions on rocket combustiop’. Reaction Motors Division, RMD-204~Q2. Second Quarterly Report AF49(638j-305. August 1958 Third 8 COBINE, J. D. ‘MHD and gas discharges’. Symposium on the Engineering AsPects of Magnetohydrodynamics. University of Rochester, March 1962 9
DIMMOCK, T. H., and KINEYKO, W.
MILLER, G.
F.,
NICOL, J.
J.
R. ‘The electrical properties of ionized gases, Part II-Electrostatic and magnetohydrodynamic deflection’. August 1961. AFOSR990 AD 262 368 10 DIMMOCK, T. H. See ref. 1