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On the potential distributions and currents present when hydrocarbon flames are subjected to radial electric fields
ON THE POTENTIAL DISTRIBUTIONS AND CURRENTS P R E S E N T W H E N H Y D R O C A R B O N F L A M E S ARE S U B J E C T E D TO R A D I A L E L E C T R I C F I E L D S JAMES E. MITCHELL Corporate Research Laboratories, Esso Research and Enginee~_-,g Company, Linden, New Jersey f
Diffusion flames burning propane, ethylene or batane have been subjected to radial electric fields by placing a large d.c. potential on a wire lying along the centreline of the flame while surrounding the flame with a grounded metal cylinder. The distribution of ele~rical potential between the flame and the metal cylinder and the ionic currents flowing from the flame were measured. Both of these quantities behave in accordance with the theory of space-chargelimited currents. The average mobilities of the positive and negative ions comprising the currents were calculated from the current measurements and are 1-7 and 2-1 cm 2 V-1 sec-1, respectively, regardless of the fuel.
Introduction IN RECENT years, a large amount of effort has been expended in studying the effects of electric fields on hydrocarbon flames ~-8. For small diffusion flames, these effects include the stabilization of the flames by longitudinal fields2, the deflection of flames by transverse fields 3, and the destabilization of flames by radial fields4. In part, the interest in these phenomena is related to the ability of the electric field to affect significantly the burning process without the expenditure of large amounts of energy. In a previous paper, Mitchell and Wright 4 described the changes that can be made to occur by the application of radial electric fields. The present work constitutes a description of some of the electrical parameters of the flame such as the distribution of potential about the flame and the magnitude of the resulting ionic currents. These results provide essential information about the currents which appear to cause the effects reported by Mitchell and Wright. In addition, the) ~provide a test of the applicability of the theory of space-charge-limited currents to the ionic currents drawn from a flame by an external field. Ultimately, the response of flames to electric fields arises from the fact that charged species are produced in the combustion processes and acquire sizable concentrations in the flame gases. In premixed flames, where more investigations
have been carried out, the concentration of charged species 9 is of the order of 109/cm 3. Several positive ions including C3H~, H30+, and CHO ÷ have been identified 1°-13 in flames and of these H 3 0 + appears to be the most abundant. The negative species appear to be clectrons 12, which do not attach to electronegative molecules because of the high temperatures. Outside the flame, however, where the temperature is lower, these electrons rapidly attach to gases such as oxygen. The most attractive explanation for the effects observed by Mitchell and Wright is proposed in terms of physical interactions between the charged populations of ions and the neutral species. A particularly fruitful approach appears to be one which deals with the frictional forces between the neutral gases and ion currents in the region between the flame and the cylindrical electrode. In aerodynamic terms, the currents exert body forces on the gases which must eventuate in additional fluid motion or in a redistribution of the pressure. The magnitude of such a body force can be shown to be directly proportional to the current density at any point 14. In the experiments described here, the magnitude of the currents and the distribution of potential are determined for a set of turbulent diffusion flames. These measurements have been limited to d.c. fields because the theory for this 605
606
j. E. mTCH~LL
case can be more fLrmly established and the potential distributions are accessible to measurement.
Vol. 13
A second cylindrical electrode was placed around the lower portion of the flame and was maintained at ground potential. Three sizes of electrode cylinders were used, 254), 36-8 and 45-0cm in diameter. Each of these electrodes consisted of three sections which could be isolated from one another. The bottom edge of the lowest section was placed one cm below the plane of the fuel orifice. The length of this section was about 10 cm and the lengths of the other sections were 5 cm. All ofthese pieces were fabricated from woven wire with about 50 per cent of the electrode's frontal area covered by the metal. In the presence of the fields, the bases of the propane and butane flames were displaced upward. However, in all cases this movement was confined to the region contained in the lower electrode section. Therefore, this movement could not interfere with the measurements of currents or potentials which took place in the region bounded by the middle electrode section. Currents were determined by measuring the voltage difference across a precision resistor
Experimemai The experiments were conducted in the burner shown in Figure 1. Fuel gas entered through a glass nozzle at the bottom of the burner at sufficient velocity to form an axisymmetric turbulent jet. Ignition of this jet resulted in a slender diffusion flame about 100 cm long. When propane or butane fuels were used, the base of the flames was initially situated about 2 or 3 cm above the (~51 cm i.d. orifice. The base of the ethylene flames, on the other hand, touched the nozzle. The fuels were taken from cylinders of technical grade gases. Only one flowrate was used for each rue!, these being 11-5, 14-3 and 12-0 cm3/sec for the ethylene, propane and butane, respectively. The fields were established by connecting the output of a high voltage d.c. power supply to a small Nichrome wire (~76 mm in diameter situated on the centreline of the gas jet.
Insu[ator
Ni chrome wire e l e c t r o d e
Flame ,~ (':yr.,icat)~
Power suppty
t .u,=-,:
"
]
!
Voltmeter -
or
c.r . 0 .
~o or, ~ "" .......
i
111111
111~1 i
ii11 i
ii support
i
i
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I I
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Metat
_
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Teflon inlet ,...J block 1 !
I I,, I///, r / ~__Propane inlet !
I/////l/'/ff
FIGU~ l. Equipment used in current measurements
i/")//
December 1969
HYDROCARBON FLAMES SUlglECTED TO RADIAL ELECTRIC FIELDS
placed between the middle electrode cylinder and ground. Resistors were chosen to provide voltage differences in the range 0.02 to 0-5 V. An electrometer was used to make the measurement. Because gaps were present between the three cylindrical electrode sections, the length used in calculating the current density arriving at the deetrode was determined by adding one half of the combined lengths of the two gaps to the actual length of the middle section. These lengths are listed in Table 1 along with other pertinent data on the electrodes.
temperature measured in the presence of the flame but in the absence of fields using a shielded thermocouple placed 12 cm from the centreline. Also, air temperature measurements taken just outside of the cylindrical electrode did not indicate any changes when ion currents were flowing from the flame. Potential fields were determined by placing a wire probe in the space between the flame and the electrode cylinder and measuring the potential assumed by the probe with an electrometer. The probe was made from a piece of Nichrome wire 0.76 mm in diameter. The part that was actually used for the probe was gold plated and bent 90 ° to the remainder of the wire. The configuration of the probe and its supporting apparatus can be seen in Figure 2. A piece of glass tubing was used to support the lead for the probe. A small cathetometer held horizontally provided a carciage and also allowed the position to be determined. By proper alignment, the probe could traverse one radius between the electrode cylinder and the central wire. The potential assumed by the probe was measured by an electrometer having an input impedance of 10 az ohms. For the potential measured in this manner to be accurate, the current required by the measuring circuit must be small in comparison to the rate at which
TABLE 1. Dimensions of cylindrical electrodes
Radius cm
Length*
12-5 17,8 22-5
6"02 5.71 6.05
607
Material
cm
Gold plated on s.s. Stainless steel Gold plated on s.s.
* 'Length" is the length of metal cylinder +½ (GI + Gz). • • where GI is the distance between upper and middle sections, and Gz is the distance between the middle and lower sections.
The air temperature in the presence of the ion currents has been estimated to be approximately 30°C. This estimate is based on air ,
OSUt'tO
,, , , ,
d.c. power sup,pry
Etectrometer
Probe Probe boom
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mechanism
Frame and electrodes
F m u g E 2. Equipment used to determine potential fields
1
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608
charges impact upon the probe from the gas space. One way to check this point is to measure the probe voltage over a range of input impedanceg, all other things being equal. We did this and it was found that in changing from 1 × 1012 to 2 × 1012 ol~rn.q the measured voltage did not change and that going from 1 X 1012 tO 5 x 1011 only decreased the voltage by six per cent. It was concluded, therefore, that an electrometer having an impedance of 1012 ohms yielded accurate measurements. Theory In the absence of saturation effects, that is, the complete removal of the flame's charge by the field, the flame is assumed to present an impedance to current flow that is negligible compared to the impedance associated with the air surrounding the flame. An analysis of the potential field is carried out over the region bounded by the edge of the flame fro) and the cylindrical electrode (R). The potential at the flame's edge as well as the field strength at that point (ro) are assumed to be known. The ions which constitute the currents originate in the flame and are drawn into the air gap by the field. The voltages applied to the system are limited to values which do not cause additional ionization. Consequently, the ions drifting through the air gap in a positive field, that is, a field produced by a positive potential on the wire, are positive flame ions. Negatively charged species are not expected to be present in the air gap under these conditions. In a negative field, the ions are assumed to be species formed by the attachment of electrons to 02 molecules in the air. A simple calculation shows that electrons drifting in a 1 kV/cm field at s.t.p, would travel only about 2 mm in air before attaching 15. The mathematical analysis of space charge limited currents in a cylindrical system has been reported previously 1+. The resulting expression for the potential gradient is given by
do ( I d--r = \ 2 n L k t J
~-~(r2-r2o)[ r2
Vol. 13
(coul V- 1 c m - 1), L is the length of the cylindrical electrode (cm), k is the mobility of the ionic species (cm 2 V-1 sec-1), ro is the largest radius at which the potential gradient is essentially zero. In writing equation 1, we have utilized the fact that the potential gradient is zero in the flame and have defined ro to be the largest radius for which this is true. Upon integration and use of the boundary condition ~(R) = ouib(ro), where R is the radius of the cylindrical electrode, one obtains for the potential
(ro)
-
/
I
\+ -- (r 2 -- roe)½ + r o cos- 1 (ro/r) ]
We shall see shortly that the potential does not equal zero at r = R because of surface effects. The boundary condition used here is therefore appropriate. An explicit relationship can be written for the current (19 by evaluating equation 2 at r o I = ( 2 x L k e ) [(1 - a) ~b(ro)]2 x [(R e - r2o)½ - r o cos- 1 fro~R)] - 2
[3]
It should be pointed out that the mobility k possesses a sign which depends on the sign of the charge of the ion. Therefore, the current (19 has the same sign as ~(ro) even though this potential appears as a quadratic term. It is convenient to deal with experimentally determined potential curves in the form of 0(r)/0(ro). For purposes of comparison, the theoretical expression for this ratio may be determined from equation 2,
¢,(ro) " (r 2 - r2) + - r o cos (ro/r) -] 1 -- (R 2 _ r~)½ _ ro cos (ro/R) jJ
[4]
Results and discussion P o t e n t i a l fields
[1]
where ~b is the potential (V), r is the radial coordinate (cm), e is the permittivity of space
A typical potential field is shown in Figure 3; these data were taken from a propane flame but similar results were obtained from the other flames. Before proceeding to deal with the details
December 1 9 6 9
HYDROCARBON FLAMES SUBJECTED T ( F R A D I A L ELECTRIC FIELDS
charges on its surface. We wish to compensate for this essentially trivial phenomenon and so define the potential at R to be the value ~t obtained by extrapolating the data to R. A theoretical curve based on the values • = 0.045 and r o = 2.2 cm is shown in Figure 3 as a solid
10
!xperimental data 'o ! i Edge of
0 7 5 - visible
flame
~Equation/,;ro=2-2 cm, ~ / == 0-0/.5
curve.
\
\ \ \ \ 050 -
\ \
\ Logarithmic profite \ (shown for comparison\ only) \\ 025
-
609
\
\
,\ \
N
\
%
5 10 Radial posttion r.cm FIGURE 3. A typical potential distribution. The data were taken from a propane flame. The potential of the central electrode was - 7500 V. The potential ~b(ro}equalled - 73(X) V
of this curve we should point out the magnitude of the effects that space charges have on the shape of the potential profile. To this end, a logarithmic function, which would obtain in the absence of the space charges, is ai,~o shown in Figure 3 as a dashed line. Comparis3n of this curve with the data shows that, i._deed, space charges are important. Near She flame, the potential in the presence of charges is seen to decrease more slowly than the logarithmic function. Farther from the flame, the measured potential becomes a linear function of the radial position and ia this region possesses a voltage gradient which is somewhat larger than that of the logarithmic curve. Inspection of Figure 3 shows that the measured potential does not go to zero at r = R, the position of the grounded electrode. It seems reasonable to guess that a distortion of the field is occurring near the electrode because of
In calculating the theoretical curve shown in Figure 3, a value of r o has been chosen. The choice of this quantity causes some problem because it must be treated as an empirical parameter that is determiaed for each measured potential curve. For any given potential field, we have found that some value of r o will provide very acceptable agreement between the theory and the data. However, when r o is backcalculated from several sets of data and compared, we find that the values obtained from replicate runs exhibit a significant amount of scatter. The nature of this scatter has been studied rather carefully and we conclude that it is caused by uncontrolled deflections of the flame caused by the fields. In experiments that were repeated before the alignment of the electrodes and the fuel nozzle was disturbed, we found quite acceptable agreement. However, movement of any of these parts of the apparatus, even though careful realignment followed, caused the value of r o to change. The range of the variation of rn for a given set oi" conditions was 0.4 cm with an average in the vicinity of 2-0 cm. In a later section, we report more precise values of rn determined in another manner. In spite of the problems mentioned above, certain conclusions about the position of ro may be drawn from these potential profiles. The most interesting of these is the fact that r 0 is several millimetres larger than the visible flame radius. For examnle, the radius of the visible flame from which the data in Figure 3 were taken was slightly less than 1.5 cm whereas the potential was constant out to a radius of about 2-2 cm. The radius of the visible flame was taken to be the point at which the probe touched the flame. This measurement has been checked by other means and is believed to be good to within a millimetrel We also note that the variation in r0 occasioned by changes in the magnitude of the potential
J.E. MITCHELL
610
differences, the size of the cylindrical electrodes. or the pelarity of the fields was smaller than the scatter of the data mentioned earlier. Therefore, we tentatively conclude that these factors have little effect on to. Finally, it should be noted that the potential at the edge of the flames differed from the central electrode potential by an amount ranging from two to five per cent of the total potential difference.
the voltage difference ( 1 - a) O(ro), with the values of 0cdetermined from the potential fields. lO-S
r'~ 10.5 ,, E
E
t~ Currents The currents measured in these fields and lines representing the theory as expressed by equation 3 are presented in Figures 4 and 5 for positive and negative currents, respectively. The ordinates of these log-log graphs are the magnitudes of the currents divided by the lengths of the cylindrical electrodes. The abscissae are taken directly from equation 3; they incorporate the expected dependence of the current on the voltage difference across the system, the electrode radius, and the plasma radius r o. In computing the abscissa quantities, we have used
I
10-'/
lO-e 1o~
I
l
|
*
lli,I
*
10s
i
i
* ,
lJJi
106
i
,
,
.
,,iz
107
[i,-.,¢,ro~ '
F m v ~ 5. Currents measured in negative fields. The abscissa is suggested by equation 3. The figure contains data from propane (31 pts), ethylene (30 pts) and butane (34 pts) flames. Among the data from each fuel are sets taken from each of three electrode sizes: R = 12.5, 17.8 and 22.5 cm
10-s
10-e :-
10-7 ...
10-el
lo4
VOL 13
I
105
[<,-.,, ¢, <,o,]'
106
II
10./
[v'/c,,.,']
{(++-d~%o ~oc;(,oim} + FIGURE 4. Currents measured in positive fields. The abscissa is suggested by equation 3. The figure contains data from propane (31 pts), ethylene (30 pts) and butane 130 pts) flames. Among the data 5om each fuel are sets taken from each of three electrode sizes: R = 12.5, 17.8 and 22-5 cm
The use of equation 3 requires a value of ro and this has been determined for each fuel by a trial and error procedure using the currents measured from the three different electrode sizes. We calculated values of the abscissa quantity for different assumed values of r o until we found a value that would make the three sets of current measurements agree with one another when plotted as in Figure 4. As this operation could be performed on sets of positive or negative currents, we have taken the value of r o that caused the best fit of both sets of data. These values are listed in Table 2. We observed earlier that the ros obtained from the potential fields displayed considerable fluctuations between replicate runs. The variability of ro values obtained from current measurements is much smaller. Probably the values of r o determined from the currents are less sensitive because small deflections of the flames
December 1 9 6 9
HYDROCARBON FLAMES SUBJECTED TO RADIAL ELECTRIC FIELDS
TABLE 2. Values of the plasma radius ro determined from different flames
Fuel
Ethylene Propane Butane
Flo .rate cm 3/sec
ro Cl~l
11.5 14-3 12.0
2.0 2-1 2-1
would cause offsetting changes in the current density from different sides of the flame which would be averaged out in the total current. It should be noted that the ros obtained from the potential fields are in reasonably good agreement with the values obtained from the current measurements. Inspection of Figures 4 and 5 indicates that the currents not only behave in accord with the theory (equation 3) as is shown by the fact that a straight line of unit slope represents the data, but also that all of the currents of each polarity are represented by the same mobility. Calculation of these mobilities from the data yields the following values" k÷ = 1.7cm2V -1 cm -1
61 1
for the negative and positive species taken from a study by Bradbury 1s. For negative ions, the mobility obtained in the present study is within five to ten per cent of the values obtained by the other techniques. This is interesting since electron attachment should account for these ions in all of the experiments. It is also noted that the mobility of the positive flame ions is about the same as the other posi',ive ion mobilities. One would expect the most numerous flame species to be of the general formula H +(H20)n. The positive species in carefully dried air has been thought 16 to be O~. Therefore, the latter agreement might be coincidental. At this point, it is clear that these currents behave in a manner predicted for space-chargelimited currents. It is also apparent that the mobilities of the current carrying species are reasonably close to those obtained previously for ions drifting through air. In addition, the magnitude of the negative currents indicates that the presence of electrons may be neglected when the charges pass through several centimetres of air as they have done in our study.
k_ = 2.2 cm 2 V- ~ cmIt is interesting that the currents from each of these fuels possesses the same average mobility. As was mentioned earlier, ion identification studies ~°-~3 have reported the same species in the charged populations produced by burning several different hydrocarbon fuels. Our results are consistent with those findings. It is of interest to compare the mobilities reported here with the mobilities in air of ions obtained using other sources of ionization. To do this, we should first remark that our values correspond to reduced mobilities at s.t.p, of K + = 1.5 and K_ = 2.0 cm 2 V- ~ sec- ~. The mobilities of charge carriers in air have been determined for a variety of ionization methods including X-ray, alpha ray, and ultraviolet light irradiation and point discharge techniques. Many of these results have been tabulated by Thompson ~6 who also reports probable mean values of 2-1 and 1.36 for the negative and positive species, respectively. The literature has also been reviewed by Loeb 17 whose book contains the values of 2.21 and 1-59
We thank Drs F. H. Field, F. J. Wright, N. E. Wisdom Jr and G. t;. C "~.,ppell for helpful discussions. In addition, we that!" Mr Jerry E. Hankins who performed r,,ust c ., experiments. (Received December 1968 ; revised May 1969)
References I CALCO'IE, H. F. and PEASE, R. N. lndustr. Engng Chem.
(Industr.), 43, 2726 (1951) z HAgKER, .I.H. and PORTER J. E. J. Inst. Fuel, 41,264 (1968) 3 PAYNE, K. G. and WE]NBERG, F. J. P'oc. Roy. Soc. A, 250, 316 (1959) 4 MITCHELL, J. E. and WRIGHT, F. J. Combustion & Flame, 13, 413 (1969) 5 ABRUKOV. S. A., KURZHUNOV, V. V. and MEZDRmOV. V. N. Fi:. Goreniva i V:rvva. 1966(2). 68 {! 966) o FOWLER~R. G. and CORRIGAN, S. J. B. Physics oj Fluids, 9, 2037 ~966) 7 LAWTON, J., Fuel Soc. J., Univ. Sheffield, 16, 8 (1965) s PLACE, F R. and WEINBr_gG, F. J. Proc. Roy. Soc. ,~,,289. 192 (1966) 9 GREEN, J. A. and SUGDEN, T. M. Ninth Symposium (International) on Combustion, p 607. Academic Press: New York (1963)
612
J.E. MITCHELL
to B ~ H. and SUGDEN,T. M. Proc. Roy. Soc. A, 2/~1, 480 {1950) t t Ksewsrtma, P. F. and SUGDEIq,T. M. Seventh Symposium (Internm.imud) on Combustion, p 247. Butterworths: London (1959) 12 CALCOTEs U. F. and JENSiD~, Do E. Ion-Molecule Reactions in the Gas Phase, p 291. American Chemical Society: Advances in Chemistry Series (1966) ~s VAN TJc~3mJ~ A. Ninth Symposium (International) on Combustion, p 634. Academic Press: New York (1963)
VOI. 13
t4. LAw'ro~ J. and WmNmm¢;, F. J. Proc. Roy. Soc. A, 227, 468 0965)
~s LOEB, L. B. Basic Processes of Gaseous Electronics, 2nd ed., p 425. University of California Press (1966) ~6 THOrn,SON, J. J. and THOrn,SON, G. P. C6.tduction of Elecu~ciO, Through Gases, Voi. I, p 128. Cambridge University Press: London (1928) tv Lores, L. B. see ref. 15, p 116 t8 BRADBUtZY,N. E. Phy. Rev. 40, 508 (1932)
Diffusion flames burning propane, ethylene or batane have been subjected to radial electric fields by placing a large d.c. potential on a wire lying along the centreline of the flame while surrounding the flame with a grounded metal cylinder. The distribution of ele~rical potential between the flame and the metal cylinder and the ionic currents flowing from the flame were measured. Both of these quantities behave in accordance with the theory of space-chargelimited currents. The average mobilities of the positive and negative ions comprising the currents were calculated from the current measurements and are 1-7 and 2-1 cm 2 V-1 sec-1, respectively, regardless of the fuel.
Introduction IN RECENT years, a large amount of effort has been expended in studying the effects of electric fields on hydrocarbon flames ~-8. For small diffusion flames, these effects include the stabilization of the flames by longitudinal fields2, the deflection of flames by transverse fields 3, and the destabilization of flames by radial fields4. In part, the interest in these phenomena is related to the ability of the electric field to affect significantly the burning process without the expenditure of large amounts of energy. In a previous paper, Mitchell and Wright 4 described the changes that can be made to occur by the application of radial electric fields. The present work constitutes a description of some of the electrical parameters of the flame such as the distribution of potential about the flame and the magnitude of the resulting ionic currents. These results provide essential information about the currents which appear to cause the effects reported by Mitchell and Wright. In addition, the) ~provide a test of the applicability of the theory of space-charge-limited currents to the ionic currents drawn from a flame by an external field. Ultimately, the response of flames to electric fields arises from the fact that charged species are produced in the combustion processes and acquire sizable concentrations in the flame gases. In premixed flames, where more investigations
have been carried out, the concentration of charged species 9 is of the order of 109/cm 3. Several positive ions including C3H~, H30+, and CHO ÷ have been identified 1°-13 in flames and of these H 3 0 + appears to be the most abundant. The negative species appear to be clectrons 12, which do not attach to electronegative molecules because of the high temperatures. Outside the flame, however, where the temperature is lower, these electrons rapidly attach to gases such as oxygen. The most attractive explanation for the effects observed by Mitchell and Wright is proposed in terms of physical interactions between the charged populations of ions and the neutral species. A particularly fruitful approach appears to be one which deals with the frictional forces between the neutral gases and ion currents in the region between the flame and the cylindrical electrode. In aerodynamic terms, the currents exert body forces on the gases which must eventuate in additional fluid motion or in a redistribution of the pressure. The magnitude of such a body force can be shown to be directly proportional to the current density at any point 14. In the experiments described here, the magnitude of the currents and the distribution of potential are determined for a set of turbulent diffusion flames. These measurements have been limited to d.c. fields because the theory for this 605
606
j. E. mTCH~LL
case can be more fLrmly established and the potential distributions are accessible to measurement.
Vol. 13
A second cylindrical electrode was placed around the lower portion of the flame and was maintained at ground potential. Three sizes of electrode cylinders were used, 254), 36-8 and 45-0cm in diameter. Each of these electrodes consisted of three sections which could be isolated from one another. The bottom edge of the lowest section was placed one cm below the plane of the fuel orifice. The length of this section was about 10 cm and the lengths of the other sections were 5 cm. All ofthese pieces were fabricated from woven wire with about 50 per cent of the electrode's frontal area covered by the metal. In the presence of the fields, the bases of the propane and butane flames were displaced upward. However, in all cases this movement was confined to the region contained in the lower electrode section. Therefore, this movement could not interfere with the measurements of currents or potentials which took place in the region bounded by the middle electrode section. Currents were determined by measuring the voltage difference across a precision resistor
Experimemai The experiments were conducted in the burner shown in Figure 1. Fuel gas entered through a glass nozzle at the bottom of the burner at sufficient velocity to form an axisymmetric turbulent jet. Ignition of this jet resulted in a slender diffusion flame about 100 cm long. When propane or butane fuels were used, the base of the flames was initially situated about 2 or 3 cm above the (~51 cm i.d. orifice. The base of the ethylene flames, on the other hand, touched the nozzle. The fuels were taken from cylinders of technical grade gases. Only one flowrate was used for each rue!, these being 11-5, 14-3 and 12-0 cm3/sec for the ethylene, propane and butane, respectively. The fields were established by connecting the output of a high voltage d.c. power supply to a small Nichrome wire (~76 mm in diameter situated on the centreline of the gas jet.
Insu[ator
Ni chrome wire e l e c t r o d e
Flame ,~ (':yr.,icat)~
Power suppty
t .u,=-,:
"
]
!
Voltmeter -
or
c.r . 0 .
~o or, ~ "" .......
i
111111
111~1 i
ii11 i
ii support
i
i
I I
I I
Metal
!
Metat
_
H,'////////'l//
Teflon inlet ,...J block 1 !
I I,, I///, r / ~__Propane inlet !
I/////l/'/ff
FIGU~ l. Equipment used in current measurements
i/")//
December 1969
HYDROCARBON FLAMES SUlglECTED TO RADIAL ELECTRIC FIELDS
placed between the middle electrode cylinder and ground. Resistors were chosen to provide voltage differences in the range 0.02 to 0-5 V. An electrometer was used to make the measurement. Because gaps were present between the three cylindrical electrode sections, the length used in calculating the current density arriving at the deetrode was determined by adding one half of the combined lengths of the two gaps to the actual length of the middle section. These lengths are listed in Table 1 along with other pertinent data on the electrodes.
temperature measured in the presence of the flame but in the absence of fields using a shielded thermocouple placed 12 cm from the centreline. Also, air temperature measurements taken just outside of the cylindrical electrode did not indicate any changes when ion currents were flowing from the flame. Potential fields were determined by placing a wire probe in the space between the flame and the electrode cylinder and measuring the potential assumed by the probe with an electrometer. The probe was made from a piece of Nichrome wire 0.76 mm in diameter. The part that was actually used for the probe was gold plated and bent 90 ° to the remainder of the wire. The configuration of the probe and its supporting apparatus can be seen in Figure 2. A piece of glass tubing was used to support the lead for the probe. A small cathetometer held horizontally provided a carciage and also allowed the position to be determined. By proper alignment, the probe could traverse one radius between the electrode cylinder and the central wire. The potential assumed by the probe was measured by an electrometer having an input impedance of 10 az ohms. For the potential measured in this manner to be accurate, the current required by the measuring circuit must be small in comparison to the rate at which
TABLE 1. Dimensions of cylindrical electrodes
Radius cm
Length*
12-5 17,8 22-5
6"02 5.71 6.05
607
Material
cm
Gold plated on s.s. Stainless steel Gold plated on s.s.
* 'Length" is the length of metal cylinder +½ (GI + Gz). • • where GI is the distance between upper and middle sections, and Gz is the distance between the middle and lower sections.
The air temperature in the presence of the ion currents has been estimated to be approximately 30°C. This estimate is based on air ,
OSUt'tO
,, , , ,
d.c. power sup,pry
Etectrometer
Probe Probe boom
[
|1
1 !
L
Probe traversing
mechanism
Frame and electrodes
F m u g E 2. Equipment used to determine potential fields
1
J. E. ~rrce~L
608
charges impact upon the probe from the gas space. One way to check this point is to measure the probe voltage over a range of input impedanceg, all other things being equal. We did this and it was found that in changing from 1 × 1012 to 2 × 1012 ol~rn.q the measured voltage did not change and that going from 1 X 1012 tO 5 x 1011 only decreased the voltage by six per cent. It was concluded, therefore, that an electrometer having an impedance of 1012 ohms yielded accurate measurements. Theory In the absence of saturation effects, that is, the complete removal of the flame's charge by the field, the flame is assumed to present an impedance to current flow that is negligible compared to the impedance associated with the air surrounding the flame. An analysis of the potential field is carried out over the region bounded by the edge of the flame fro) and the cylindrical electrode (R). The potential at the flame's edge as well as the field strength at that point (ro) are assumed to be known. The ions which constitute the currents originate in the flame and are drawn into the air gap by the field. The voltages applied to the system are limited to values which do not cause additional ionization. Consequently, the ions drifting through the air gap in a positive field, that is, a field produced by a positive potential on the wire, are positive flame ions. Negatively charged species are not expected to be present in the air gap under these conditions. In a negative field, the ions are assumed to be species formed by the attachment of electrons to 02 molecules in the air. A simple calculation shows that electrons drifting in a 1 kV/cm field at s.t.p, would travel only about 2 mm in air before attaching 15. The mathematical analysis of space charge limited currents in a cylindrical system has been reported previously 1+. The resulting expression for the potential gradient is given by
do ( I d--r = \ 2 n L k t J
~-~(r2-r2o)[ r2
Vol. 13
(coul V- 1 c m - 1), L is the length of the cylindrical electrode (cm), k is the mobility of the ionic species (cm 2 V-1 sec-1), ro is the largest radius at which the potential gradient is essentially zero. In writing equation 1, we have utilized the fact that the potential gradient is zero in the flame and have defined ro to be the largest radius for which this is true. Upon integration and use of the boundary condition ~(R) = ouib(ro), where R is the radius of the cylindrical electrode, one obtains for the potential
(ro)
-
/
I
\+ -- (r 2 -- roe)½ + r o cos- 1 (ro/r) ]
We shall see shortly that the potential does not equal zero at r = R because of surface effects. The boundary condition used here is therefore appropriate. An explicit relationship can be written for the current (19 by evaluating equation 2 at r o I = ( 2 x L k e ) [(1 - a) ~b(ro)]2 x [(R e - r2o)½ - r o cos- 1 fro~R)] - 2
[3]
It should be pointed out that the mobility k possesses a sign which depends on the sign of the charge of the ion. Therefore, the current (19 has the same sign as ~(ro) even though this potential appears as a quadratic term. It is convenient to deal with experimentally determined potential curves in the form of 0(r)/0(ro). For purposes of comparison, the theoretical expression for this ratio may be determined from equation 2,
¢,(ro) " (r 2 - r2) + - r o cos (ro/r) -] 1 -- (R 2 _ r~)½ _ ro cos (ro/R) jJ
[4]
Results and discussion P o t e n t i a l fields
[1]
where ~b is the potential (V), r is the radial coordinate (cm), e is the permittivity of space
A typical potential field is shown in Figure 3; these data were taken from a propane flame but similar results were obtained from the other flames. Before proceeding to deal with the details
December 1 9 6 9
HYDROCARBON FLAMES SUBJECTED T ( F R A D I A L ELECTRIC FIELDS
charges on its surface. We wish to compensate for this essentially trivial phenomenon and so define the potential at R to be the value ~t obtained by extrapolating the data to R. A theoretical curve based on the values • = 0.045 and r o = 2.2 cm is shown in Figure 3 as a solid
10
!xperimental data 'o ! i Edge of
0 7 5 - visible
flame
~Equation/,;ro=2-2 cm, ~ / == 0-0/.5
curve.
\
\ \ \ \ 050 -
\ \
\ Logarithmic profite \ (shown for comparison\ only) \\ 025
-
609
\
\
,\ \
N
\
%
5 10 Radial posttion r.cm FIGURE 3. A typical potential distribution. The data were taken from a propane flame. The potential of the central electrode was - 7500 V. The potential ~b(ro}equalled - 73(X) V
of this curve we should point out the magnitude of the effects that space charges have on the shape of the potential profile. To this end, a logarithmic function, which would obtain in the absence of the space charges, is ai,~o shown in Figure 3 as a dashed line. Comparis3n of this curve with the data shows that, i._deed, space charges are important. Near She flame, the potential in the presence of charges is seen to decrease more slowly than the logarithmic function. Farther from the flame, the measured potential becomes a linear function of the radial position and ia this region possesses a voltage gradient which is somewhat larger than that of the logarithmic curve. Inspection of Figure 3 shows that the measured potential does not go to zero at r = R, the position of the grounded electrode. It seems reasonable to guess that a distortion of the field is occurring near the electrode because of
In calculating the theoretical curve shown in Figure 3, a value of r o has been chosen. The choice of this quantity causes some problem because it must be treated as an empirical parameter that is determiaed for each measured potential curve. For any given potential field, we have found that some value of r o will provide very acceptable agreement between the theory and the data. However, when r o is backcalculated from several sets of data and compared, we find that the values obtained from replicate runs exhibit a significant amount of scatter. The nature of this scatter has been studied rather carefully and we conclude that it is caused by uncontrolled deflections of the flame caused by the fields. In experiments that were repeated before the alignment of the electrodes and the fuel nozzle was disturbed, we found quite acceptable agreement. However, movement of any of these parts of the apparatus, even though careful realignment followed, caused the value of r o to change. The range of the variation of rn for a given set oi" conditions was 0.4 cm with an average in the vicinity of 2-0 cm. In a later section, we report more precise values of rn determined in another manner. In spite of the problems mentioned above, certain conclusions about the position of ro may be drawn from these potential profiles. The most interesting of these is the fact that r 0 is several millimetres larger than the visible flame radius. For examnle, the radius of the visible flame from which the data in Figure 3 were taken was slightly less than 1.5 cm whereas the potential was constant out to a radius of about 2-2 cm. The radius of the visible flame was taken to be the point at which the probe touched the flame. This measurement has been checked by other means and is believed to be good to within a millimetrel We also note that the variation in r0 occasioned by changes in the magnitude of the potential
J.E. MITCHELL
610
differences, the size of the cylindrical electrodes. or the pelarity of the fields was smaller than the scatter of the data mentioned earlier. Therefore, we tentatively conclude that these factors have little effect on to. Finally, it should be noted that the potential at the edge of the flames differed from the central electrode potential by an amount ranging from two to five per cent of the total potential difference.
the voltage difference ( 1 - a) O(ro), with the values of 0cdetermined from the potential fields. lO-S
r'~ 10.5 ,, E
E
t~ Currents The currents measured in these fields and lines representing the theory as expressed by equation 3 are presented in Figures 4 and 5 for positive and negative currents, respectively. The ordinates of these log-log graphs are the magnitudes of the currents divided by the lengths of the cylindrical electrodes. The abscissae are taken directly from equation 3; they incorporate the expected dependence of the current on the voltage difference across the system, the electrode radius, and the plasma radius r o. In computing the abscissa quantities, we have used
I
10-'/
lO-e 1o~
I
l
|
*
lli,I
*
10s
i
i
* ,
lJJi
106
i
,
,
.
,,iz
107
[i,-.,¢,ro~ '
F m v ~ 5. Currents measured in negative fields. The abscissa is suggested by equation 3. The figure contains data from propane (31 pts), ethylene (30 pts) and butane (34 pts) flames. Among the data from each fuel are sets taken from each of three electrode sizes: R = 12.5, 17.8 and 22.5 cm
10-s
10-e :-
10-7 ...
10-el
lo4
VOL 13
I
105
[<,-.,, ¢, <,o,]'
106
II
10./
[v'/c,,.,']
{(++-d~%o ~oc;(,oim} + FIGURE 4. Currents measured in positive fields. The abscissa is suggested by equation 3. The figure contains data from propane (31 pts), ethylene (30 pts) and butane 130 pts) flames. Among the data 5om each fuel are sets taken from each of three electrode sizes: R = 12.5, 17.8 and 22-5 cm
The use of equation 3 requires a value of ro and this has been determined for each fuel by a trial and error procedure using the currents measured from the three different electrode sizes. We calculated values of the abscissa quantity for different assumed values of r o until we found a value that would make the three sets of current measurements agree with one another when plotted as in Figure 4. As this operation could be performed on sets of positive or negative currents, we have taken the value of r o that caused the best fit of both sets of data. These values are listed in Table 2. We observed earlier that the ros obtained from the potential fields displayed considerable fluctuations between replicate runs. The variability of ro values obtained from current measurements is much smaller. Probably the values of r o determined from the currents are less sensitive because small deflections of the flames
December 1 9 6 9
HYDROCARBON FLAMES SUBJECTED TO RADIAL ELECTRIC FIELDS
TABLE 2. Values of the plasma radius ro determined from different flames
Fuel
Ethylene Propane Butane
Flo .rate cm 3/sec
ro Cl~l
11.5 14-3 12.0
2.0 2-1 2-1
would cause offsetting changes in the current density from different sides of the flame which would be averaged out in the total current. It should be noted that the ros obtained from the potential fields are in reasonably good agreement with the values obtained from the current measurements. Inspection of Figures 4 and 5 indicates that the currents not only behave in accord with the theory (equation 3) as is shown by the fact that a straight line of unit slope represents the data, but also that all of the currents of each polarity are represented by the same mobility. Calculation of these mobilities from the data yields the following values" k÷ = 1.7cm2V -1 cm -1
61 1
for the negative and positive species taken from a study by Bradbury 1s. For negative ions, the mobility obtained in the present study is within five to ten per cent of the values obtained by the other techniques. This is interesting since electron attachment should account for these ions in all of the experiments. It is also noted that the mobility of the positive flame ions is about the same as the other posi',ive ion mobilities. One would expect the most numerous flame species to be of the general formula H +(H20)n. The positive species in carefully dried air has been thought 16 to be O~. Therefore, the latter agreement might be coincidental. At this point, it is clear that these currents behave in a manner predicted for space-chargelimited currents. It is also apparent that the mobilities of the current carrying species are reasonably close to those obtained previously for ions drifting through air. In addition, the magnitude of the negative currents indicates that the presence of electrons may be neglected when the charges pass through several centimetres of air as they have done in our study.
k_ = 2.2 cm 2 V- ~ cmIt is interesting that the currents from each of these fuels possesses the same average mobility. As was mentioned earlier, ion identification studies ~°-~3 have reported the same species in the charged populations produced by burning several different hydrocarbon fuels. Our results are consistent with those findings. It is of interest to compare the mobilities reported here with the mobilities in air of ions obtained using other sources of ionization. To do this, we should first remark that our values correspond to reduced mobilities at s.t.p, of K + = 1.5 and K_ = 2.0 cm 2 V- ~ sec- ~. The mobilities of charge carriers in air have been determined for a variety of ionization methods including X-ray, alpha ray, and ultraviolet light irradiation and point discharge techniques. Many of these results have been tabulated by Thompson ~6 who also reports probable mean values of 2-1 and 1.36 for the negative and positive species, respectively. The literature has also been reviewed by Loeb 17 whose book contains the values of 2.21 and 1-59
We thank Drs F. H. Field, F. J. Wright, N. E. Wisdom Jr and G. t;. C "~.,ppell for helpful discussions. In addition, we that!" Mr Jerry E. Hankins who performed r,,ust c ., experiments. (Received December 1968 ; revised May 1969)
References I CALCO'IE, H. F. and PEASE, R. N. lndustr. Engng Chem.
(Industr.), 43, 2726 (1951) z HAgKER, .I.H. and PORTER J. E. J. Inst. Fuel, 41,264 (1968) 3 PAYNE, K. G. and WE]NBERG, F. J. P'oc. Roy. Soc. A, 250, 316 (1959) 4 MITCHELL, J. E. and WRIGHT, F. J. Combustion & Flame, 13, 413 (1969) 5 ABRUKOV. S. A., KURZHUNOV, V. V. and MEZDRmOV. V. N. Fi:. Goreniva i V:rvva. 1966(2). 68 {! 966) o FOWLER~R. G. and CORRIGAN, S. J. B. Physics oj Fluids, 9, 2037 ~966) 7 LAWTON, J., Fuel Soc. J., Univ. Sheffield, 16, 8 (1965) s PLACE, F R. and WEINBr_gG, F. J. Proc. Roy. Soc. ,~,,289. 192 (1966) 9 GREEN, J. A. and SUGDEN, T. M. Ninth Symposium (International) on Combustion, p 607. Academic Press: New York (1963)
612
J.E. MITCHELL
to B ~ H. and SUGDEN,T. M. Proc. Roy. Soc. A, 2/~1, 480 {1950) t t Ksewsrtma, P. F. and SUGDEIq,T. M. Seventh Symposium (Internm.imud) on Combustion, p 247. Butterworths: London (1959) 12 CALCOTEs U. F. and JENSiD~, Do E. Ion-Molecule Reactions in the Gas Phase, p 291. American Chemical Society: Advances in Chemistry Series (1966) ~s VAN TJc~3mJ~ A. Ninth Symposium (International) on Combustion, p 634. Academic Press: New York (1963)
VOI. 13
t4. LAw'ro~ J. and WmNmm¢;, F. J. Proc. Roy. Soc. A, 227, 468 0965)
~s LOEB, L. B. Basic Processes of Gaseous Electronics, 2nd ed., p 425. University of California Press (1966) ~6 THOrn,SON, J. J. and THOrn,SON, G. P. C6.tduction of Elecu~ciO, Through Gases, Voi. I, p 128. Cambridge University Press: London (1928) tv Lores, L. B. see ref. 15, p 116 t8 BRADBUtZY,N. E. Phy. Rev. 40, 508 (1932)