- Email: [email protected]
The estimation of atomic oxygen in open flames and the measurement of temperature
274
LAMINAR COMBUSTION AND DETONATION WAVES 6. SMITHF.: Am. Chem. Rev,, 21,389 (1930).
comparable flames at atmospheric pressure because of the increased effects of dissociation.
7. ANDERSEN, J. W., AND FE1N, R. S.: Univ. of Wise.
Naval Res. f.ab. CM-517. 8. Mactm, H., AND HEBRA, A.: Wiener Akademie Sitzungberichte Ableitung, IIa, 150 band, 157174 (1941). 9. AN~SEN, J. W., ANn R. FRIEDMAN: Rev. Sci. Inst., 20, 61 (1949). 10. COLES, C. H.: Electronic Industries, 5, 74, Feb. (1946). 11. GAYDON, A.: Spectroscopy and Combustion Theory. London, Chapman and Hall (1948). 12. WRIGHT, F. H.: Progress Report 3-23, Jet Propulsion Lab., California Institute of Technology (1951).
ACKNOWI.~DGMI~NT
We are happy to acknowledge the experimental assistance of Lowell W. Bennett, Arthur P. Mattuck and other members of the experimental combustion group at APL and the computational assistance of Mrs. Shirley St. Martin. We would also like to acknowledge a number of helpful suggestions by Dr. H. Lowell Olsen and Capt. E. L. Gayhart of this Laboratory, and discussions of the implications of the data with Professors Hirschfelder and Curtiss of the University of Wisconsin and with Dr. P. Rosen of this Laboratory.
13. MATTUCK, A. P.: Private communication.
14. H~SCK~'~LDER, J. O.: CM-598, Theory of Flame Propagation, II, University of.Wisconsin, NRL.
REFERENCES
DlsegssloN BY J. H. BURGOYNE*
1. WOLFttARD, H., AND KLAUKENS, [q[.; Proc. Roy.
2. 3.
4.
5.
A feature of the temperature profile curves is the discontinuity that occurs between 1000~ and 2000~ The explanation may be as follows. It has been shown by Baldwin, by Walsh and by Burgoyne and Hirsch that in combustion of various paraffin hydrocarbons the stage CO ~ CO~ is inhibited by the hydrocarbon itself. This results in a discontinuity in the rate of heat release from lean mixtures since the final stage of the combustion cannot proceed readily until the concentration of hydrocarbon has been reduced by reaction to a low value.
Soc. (London), A193, 512 (1948). LEWIS, B., AND VON EeriE, G.: J. Chem. Phys., tl, 75 (1943). BROEZE, J. J.: Third Symposium on Combustion, Flame and Explosion Phenomena, p. 146. Baltimore, The Williams & Wilkins Co. (1949). LEwis, B., AND VON ELBE, G.: Combustion, Flames and Explosions, Chap. VII. New York, Academic Press (1951). JOST, W.: Explosion and Combustion Processes in Gases, Chap. III. New York, McGraw-Hill (1946).
* London.
32
THE ESTIMATION OF ATOMIC OXYGEN IN OPEN FLAMES AND THE MEASUREMENT OF TEMPERATURE By A. SMEETON LEAH AND N. CARPENTER INTRODUCTION
The most familiar methods of measuring flame gas temperatures in small scale laboratory open flames are, perhaps, the spectral line-reversal technique, resistance thermometry and the heated wire method. Whatever the definition of gas temperature adopted, and here the gas temperature will be taken to be that corresponding to the mean translational energy of the gas molecules, it is evident that all the methods when applied to a gas in perfect thermal and chemical equilibrium should yield identical gas temperatures after due
correction for losses. However, an inspection of the literature on the various techniques cannot fail to reveal a distinct lack of agreement between the methods, the differences in observed flame gas temperatures frequently being so large as to render improbable any explanation in terms of the different conditions of experiment adopted by different investigators. A prima facie case therefore exists for believing that thermal and chemical equilibrium may not be attained immediately above the inner cone of an open flame and this has been the subject of much discussion in the past. I t was
ESTIMATION OF ATOMIC OXYGEN AND MEASUREMENT OF TEMPERATURE felt that a re-examination of the position might be of value if tile different methods were applied under identical flame conditions with the object of deciding how closely agreement could be obtained. If agreement were not possible it would remain to decide which of the methods yielded the best estimate of the true translational temperature and finally to endeavour to explain the deviations encountered. Complete flame gas temperature plots using the different techniques have been made in CO-Op, CO-air and certain hydrocarbon-air mixtures burning as an open flame on a simple burner. These show the differences in observed flame temperature which were anticipated from a study of previous literature. Lack of chemical equilibrium would appear to be the explanation of the differences and in the case of the CO-02 flame the anomalous results are ascribed to the presence of relatively large concentrations of atomic oxygen within the flame gases above the inner cone. The determination of the concentration of this atomic oxygen from the observed temperatures is then dealt with in some detail. TEMPERATURE MEASURINGAPPARATUS The methods used are well known and only a few words need be said about the arrangements for each.
Spectral line-reversal method The method has been described by a number of investigators (1). A slit type burner was used in the experiments and the optical system was set up parallel to the longer axis, achromatic lens combinations being used. Only the central section of the flame was coloured with sodium salt in order to eliminate error due to the cooler ends of the flame. A 6-volt tungsten filament lamp was used as the comparison radiator, the filament being calibrated for brightness temperature against current input by the use of an optical pyrometer, the usual corrections being made.
Resistance wire method The method has been described by David and co-workers (2) and some extensions of the technique used in the present work are described by Leah, Rounthwaite and Bradley (3). Two types of resistance elements were used, the first being 0.0005 inch diameter platinum-rhodium (10 per cent) wire and the second, quartz-coated platinumrhodiM~ (10 per cent) wire of 0.0005 inch overall
275
diameter with a metal core 0.0002 inch diameter, both types being about 1 inch in length. The wires were electrically welded to the ends of 0.028 inch diameter supporting leads fixed in an insulated holder. Absolute straightness of the wires in the flame was maintained by providing a compensating expansion on the leads. Resistance changes of the wires were recorded photographically by the use of a sensitive optical galvanometer in conjunction with a simple electrical resistance bridge. Calibration records were taken to obtain the wire resistance from the deflections recorded on the films and these were translated into temperature by using the carefully measured resistance coefficients of the wires.
Heated wire method The resistance wires used in the method just outlined lose heat by radiation when inserted in the flame gases causing them to record temperatures which are too low. The error may be eliminated by the method used by Schmidt (4) and Kohn (5). The wire is electrically heated in the flame and a curve of wire temperature against electrical input obtained. When the wire temperature is the same as that of the flame gases surrounding it no interchange of heat occurs by conduction and convection, the only loss being that due to radiation from the wire. The radiation loss at different temperatures may be determined by heating the wire electrically in vacuo or, more conveniently, by calculation from the known emissivity of the wires. On plotting the curve of wire temperature against radiation loss on the previously found heating curve, the true flame gas temperature is given by the point of intersection of the two curves. In the present work the radiation losses were calculated from the StefanBoltzmann law using emissivities given by Pirani (6) for quartz and Brown and Marco (7) for platinumrhodium. GENERAL APPARATUS
The gases used were all of purity exceeding 99.5 per cent with the exception of ethylene for which the value was 98.0 per cent, the impurity being largely methane. The mixtures were made up in a large pressure vessel from which they passed to the burner through a carefully calibrated metering orifice and a flame trap. The trap was built up of cup-shaped porous sintered bronze pots placed end to end in a suitable container. It offered little resistance to flow and was thoroughly
276
LAMINAR COMBUSTION AND DETONATION WAVES
reliable. After leaving the trap the gas stream divided, the larger volume passing directly to the burner, the smaller portion passing through a salt injector before entering the burner. The burner had to be such as to give a broad flame in order to acconlmodate resistance wires of 1 inch in length. A rectangular section burner tube, 19~ inches x ~ a inch and 12 inches in length, was built up of two accurately machined sections bolted together with metal to metal contact. The
subsidiary gas stream in a finely powdered state by being carried in suspension from a mechanical agitator of the paddle wheel type. The experiments contemplated involved the measurement of the temperature by each method at various points across the flame and a t various heights above the burner, to achieve which, relative movement between the flame and the measuring devices in the horizontal and vertical planes had to be provided. In view of the delicacy and length
I
I
BURNE~
=1
RANSVERSE SLIDES
CLUTCH FOR T~ MOVEk DIAl. ,
~L
r-"
GAUGE
I I
b
BRACKI RECORI AND C
i
,
r V2" -ZL,
9
8 4 . . . .
MAIN
GAS
t
--
.....
INLETS
FIG. main portion of the gas mixture entered the burner at both ends of a cross tube fixed to the base of the burner tube thus promoting symrnetry of flow. In addition, a piece of porous sintered bronze was fixed in the bottom of the burner tube to smooth out the flow and, incidentally, to act as a subsidiary flame trap. The salt laden portion of the gas flow entered the burner tube some 6 inches below the top in a central position. A control valve in the supply line for this gas enabled adjustment of the flow rate to give a distinct central band of coloured flame of about ~ inch in width. The sodium chloride salt was injected into the
of the optical system for the line-reversal measurements it was decided to arrange for the burner to move relative to the fixed optical system and the fixed wire holders. The layout of the burner system is shown in figure 1. The burner tube passed through a gland in the base plate of the housing and vertical movement was obtained through an adjusting screw, the height being observed by means of a dial gauge attached to the burner tube. The base plate carrying the burner was mounted in guides permitting lateral movement, this movement being effected by rotating a handwheel carried on an adjusting screw. The
ESTIMATION OF ATOMIC OXYGEN AND MEASUREMENT OF TEMPERATURE turning of the handwheel was made to rotate a recording camera drum through a suitable train of gears, the camera drum making one revolution whilst the burner made a complete lateral traverse, the distance moved being rather more than the thickness of the flame at its widest section. The galvanometer used in the resistance bridge recorded on the camera drum film a continuous plot of wire temperature against distance across the flame as the handwheel was slowly rotated. A family of such curves was recorded on one film for different burner heights, the drum being moved along between each recording to separate the individual lines.
277
RESULTS
The use of platinum-rhodium resistance thermometers limited the strengths of the inflammable mixtures used to those yielding maximum temperatures below 1850~ the fusing point of the wires. Thus, stoichiometric mixtures were ruled out and either weak or over-rich mixtures had to be used. From a wide range of experiments with different mixture strengths using a variety of inflammable gases, a few representative examples will be presented. 11.5 per cent 02 + 0.5 per cent H~ + 88.0 per cent CO mixture d '"~
"
~
f . _ ~
oN.E;.o ." ..... '1-
~ ~'.
-
TEMPERATURE LINE" REVERSAL F ~ TEMPERATgR~FL
__ J; IIEA ED OUARTZ-COATED
,,.o f
,,,,,.E ,rE,,, "
(1)
7 UNHEATED QUARTZ*COATED
9~,ooo a
b
r
,.,,,,E 'E,,,.~AT.,,'E
r
,
7s,j
CALCULATED CENTRE LINE
.
SO
r
}o,
(: io,
0
O.t
0-2 O,$ 0"4 O-S O,E HEIGHT ABOVE BURNER IN INCHES.
~ 0.7
Q o,
o
oq
o*
o,
o
o,
o*
o2
o,
o
o,
TIME FRO'`` MAX. GAS TEMP. IN MILLISEC$.
o2
Fro. 2a, b, c, d Continuous recording of the line-reversal temperatures was not convenient and a means of observing the horizontal movement of the burner had to be provided. This was effected by an optical system, a beam of light being reflected on to a fixed scale from a mirror mounted on a bellcrank lever, one arm of which moved with the burner. The line-reversal temperature could then be taken at any point across the thickness of the flame and at various heights above the burner tip. The burner tube was water cooled, the passages being drilled through the length of the walls in order to bring the water pipes outside the sealing gland. The housing surrounding the burner had windows at each end and carried the wire holders at one side. I t acted as a flame shield and separator and was 3 inches x 5 inches x 12 inches high, tapering at the top to a chimney 2 inches x ~/~ inch in section.
The constituent gases were fairly well dried before use but because small traces of water vapour very materially affect the flame speed, it was decided to add 0.5 per cent of hydrogen to the mixture to ensure absolute consistency and repeatability. The hydrogen slightly increases the flame temperature but has no noticeable effect on the difference of temperature observed between plain and coated wires as was shown for explosion flames of this mixture by Leah, Rounthwaite and Bradley (3). The results are shown in figure 2, temperature contours being plotted as observed by means of plain resistance wires in (a), by heated quartzcoated wires in (b) and by the line-reversal method in (c). I t will be noted that the contours are of much the same shape in all cases although the temperature readings are appreciably different. This is more clearly shown in figure 2 (d) where the
278
LAMINAR COMBUSTION AND DETONATION WAVES
centre-line temperatures are plotted against height above the burner, a time scale also being shown which was obtained in a manner to be described. The unheated quartz-coated wire temperatures are shown in this figure, although they have not been plotted separately as contours. This has been done for economy of space and because the contours are very nearly theqsame as
that within the unburnt interconal gases, where the quartz-coated wires register a low temperature, the line-reversal temperatures appear to be high, so high in fact that reversal of the D-line was difficult to obtain with the comparison radiator used. The plain wires show temperatures well above the quartz-coated wire temperatures and as the unburnt interconal gases are approached the d 2OO0
LIREi. REVERS]M. TEMPERATURE
I 7SO~ _ ~ Q
c
b
o.7
w-,
ISOO
-*f!
~)|350.
( -
HEATED QUARTZ-COATED
~
~l~t~ TEMPERATURE
/ UNHEATED GUART Z - CQAT ED WIRE TEMPERATURE
io.a
7SO
SGQ 0
o o.~
O'I
O-a O G 0"4 O-S ' HEIGHT AmOVE SURNER IN INCHES
0"6
0"?
FIO. 3a, b, c, d IOO0 .so
/ b
o.
,..i//#//( .311111.<
b.
l''
LINE - REVERSAL TEMPERATURE
f
I ~
"~ ~UNHEATED I ~ "~ PLAIN WIRE
..~
r
I g
-- . HEATED Q U A R T Z ' C O A T E D
~[
',o.llllllf Iltkkktll i..llllli m\\/tll
TI[MPERATURE
IOOO
WIRE
;.;;~HEATEO QUARTZ-COATED ~ ~IRE TEMPERATURE
\
7SO
SOD
o
O'I
0"2 0'3 0-4 0"5 0"6 HEIGHT AEOVE BURNER IN INCHES
0'7
FIG. 4a, b, c, d those obtained with heated quartz-coated wires. The radiation correction was found to be of the order of 20~ to 40~ over the range of temperature shown. Both the unheated and heated quartz-coated wire curves show a maximum temperature at a point corresponding with the tip of the inner cone, as would normally be expected. The linereversal temperature varies in a curious way at this point, probably due to refraction of the light beam passing through a zone of very steep temperature gradient. It is also of interest to note
temperature sweeps upwards until fusion occurs. This is undoubtedly due to the catalytic combustion of CO and O~ on the plain wires, as was demonstrated by Davies (8). The first conclusion to be drawn from figure 2 (d) is that the different methods yield temperatures which are widely at variance in the zone immediately above' the inner cone, the values, however, tending to equalise at greater heights above the burner. 27.5 per cent CO + 1 per cent H~ + 71.5 per cent air mixture
(2)
ESTIMATION OF ATOMIC OXYGEN AND MEASUREMENT OF TEMPERATURE The temperature contours for this mixture are shown in figure 3 (a), (b) and (c) and the centreline temperatures are given in figure 3 (d). A general similarity with the previous results will be apparent. The maximum line-reversal temperature observed above the height giving maximum quartz-coated wire temperature is 1820~ This is somewhat lower than the value of 1920~ given
279
Figure 5, representing the olefines. 2.34 per cent benzene + 97.66 per cent air mixture
(5)
Figure 6, representing the aromatics. In table 1, the results are summarised for each of the mixtures examined. The maximum values of d 2OOO
LIN! itEV|RSAL I
,.ol
b.
a.
o, Ill |
t ~!8
o.[#lii\i:7t !o,lm,', \It/'
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Ii
Ili ll ! \ ktttl lllil ii, \lllll L.lll/ll/~, \kt! 'llllv'A\\ttlll ~o.~IIII/~,\\II II////I\\N o88 {111(/~k/till llttt ~ )]JIIRI ,~,1
t -"t----
J [ k t P[~.A t U ~ [ l
~
~
W
.i*TEO C~U*RVZ-COA' rED I RTFMPEI:LATURE F
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i
illkkk I/l.,\kt /(lk' 1~1 ,\t.~.,sj \',.'Jk~Y.I
i
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WIBE TEMPiRATUR[ U...T*O QU*~TZ-CO,,T~O
I
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IOOQ
7Sl]
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0
O.I
O.l 0-3 HEIGHT ABOVE
0-4 O.S 04 OURNi[R IN ~iNCHES
0.7
FIc,. 5a, b, c, d d lO00
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ill!
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,~ ISO0
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UNHEATED GUARTZ-COATED WiRE TEMPERATURE 75Q
500 o=
0.1
o,I FIG.
6a,
by Ellis and Morgan (9) for the same mixture using a similar technique. To complete the picture, three representative hydrocarbon flames are given, namely; 3.5 per cent propane + 96.5 per cent air mixture
(3)
Figure 4, representing the paraffins. 5.2 per cent ethylene + 94.8 per cent air mixture
(4)
0-2 0.3 04 O.S 06 HEIGHT ABOVE BURNER IN INCHES
J 0.7
b, c, d the heated quartz-coated wire temperatures measured on the centre-line of the flame are stated and the corresponding temperatures at the same point are given for the other methods. Inspection of the curves in figures 2 to 6 reveals that the flame temperatures measured by the different methods are not in agreement, the differences, however, gradually diminishing with height above the burner, i.e. with time. The difference between the unheated and heated wire temperatures is, of course, due to the radiation
280
LAMINAR COMBUSTION AND DETONATION WAVES
loss from the unheated wire, the loss being quite small in view of the exceedingly fine wires used. The differences between the two types of heated wire and the line-reversal temperatures point unmistakably to the conclusion that the flame gases are not in thermal and chemical equilibrium unless, indeed, the differences are ascribed to experimental errors. Regarding the possibility of considerable experimental errors, it may be noted that our line-reversal temperatures are in reasonable agreement with those of other investigators, if anything being slightly lower. The heated wire temperatures are corrected for TABLE I Temperatures *C Resistance Thermometer
Heated wires
Mixture
my
"~
11.5%O e
+
0.5~
~
+
~
e
~ ~
"-
1720 1500 1770 1535 1780
88.0% c o 88.0% c o
27.5~ + 1.0~ H~ + 1680 1535 1730 1578 1750 71.5% Air 3.5% propane + 96.5% Air 5.19~ ethylene + 94.81~ ,7| 5s i 8 516 01900 Air 2.34% benzene + 97.66% 1705i 801775,5 5 s50 radiation losses and errors in resistance coefficients are discounted because direct insertion of these wires into a high temperature electric furnace yield identical calibrations. End cooling losses to the wire leads are inappreciable because the lead tips are themselves within the flame gases. The fact, however, which is of the greatest consequence is that the two different types of wires record almost identical temperatures at a height exceeding 0.4 inch above the burner but differ by as much as 200~ near the inner cone. No possible correction can bring them into line at all heights and on this fact alone it seems justifiable to assume that the flame gases are not in chemical equilibrium. This is borne out by the high values of the line-reversal temperatures and also by the fact that the temperatures observed by all the methods tend to equalise with height above the burner as, with the passage of time, equilibrium becomes established.
Unless some large absolute error has occurred in the wire method, it necessarily follows that the heated quartz-coated wire temperatures must represent the nearest approach to the true translational flame gas temperatures, these being the lowest. Direct support for this conclusion is extremely difficult to obtain; only two methods of determining translational flame gas temperature which would be applicable to a non-equilibriumgas appear to be known and these are only applicable to explosion flames. One is the well-known soap bubble method used by Flock and Roeder (10) and the other the photographic explosion technique used by Flock, Marvin, Caldwell and Roeder (11), Lewis and von Elbe (12), and Leah (13). So far as comparisons are possible, these methods yield temperatures which are in fair agreement with quartz-coated wire temperatures in corresponding closed-vessel explosions (13). In the absence of further evidence, the heated quartz-coated wire temperatures must be assumed to give the best approximation to the true translational gas temperature. It is apparent that surface catalysis must be the explanation of the high temperatures recorded by the plain platinum wires. The amount of the catalytic heating can be determined quite simply. If the plain wire temperature is T r , when the flame gas is at a lower temperature Tg, the wire is losing heat by conduction and convection to the flame gas at some rate H watts per sq. cm. and also by radiation to the cooler surroundings at a rate R watts per sq. cm. and is gaining heat at the rate S watts per sq. cm. due to catalytic heating. Then,
S=H+R Values of H + R may be determined directly by heating the wires electrically in the flame gases, the values being found for different flame temperatures, T,j, and a range of wire temperatures, Tp.
In the case of the CO-O~ flame, the results for which are given in figure 2, the catalytic heating rates obtained in the manner just outlined may be used to extend the analysis if certain basic assumptions are made regarding the reaction occurring on the wire surface. The full procedure has been described by Leah, Rounthwaite and Bradley (4) as applied to explosion experiments and will not be repeated here in detail. Attention will be confined to the conditions along the centre-line of the flame and the first step is to
ESTIMATION OF ATOMIC OXYGEN AND MEASUREMENT OF TEMPERATURE estimate the centre-line gas velocities to convert heights above the burner into time intervals. The limits of flame width at any height were determined from the wire temperature records and the mass of gas flowing per second was known from the input to the burner. Hence, knowing the temperature distribution across the flame at any height, the mass flow, the flame width, and assuming parabolic velocity distribution for the vertical component of velocity, the maximum centre-line velocities were easily estimated. The resulting velocities were found to decrease slightly with increasing height above the burner whereas it is known from the experiments of Lewis and von Elbe (14) that the velocity should increase slightly. The discrepancy is due to the neglect of the infiltrated gases which increase the mass of the upward flowing gases but is so small as to have negligible effect upon the time estimates deduced from the velocities. Thus, the time scale may be added to figure 2 (d) as shown. Following Leah, Rounthwaite and Bradley, it would appear that for this CO-O= mixture, the only active species which can be present in appreciable proportion are O atoms and COs*, these resulting from reactions in the combustion zone such as the following suggested by Semenoff (15) and Hinshelwood (16). O + CO --~ CO2"
CO=* + 0 2
(1)
--~C02 + 2 0
(2)
O +CO +O~ -+COs +20
(3)
Any atoms of oxygen or 02 molecules present in excess of the equilibrium concentration will react catalytically with CO on the platinum wire surface. Of these two species, it is certain that after the gas mixture has passed through the zone of intense reaction above the inner cone, 02 molecules alone are not sufficient to account for the observed catalytic heating rates for, if they were, combustion could not have proceeded enough to produce the high flame temperatures observed. It seems most probable that the main catalytic reaction producing the heating is that due to the combination of O atoms with CO. Above the intense reaction zone at the top of the inner cone when the catalytic heating and hence, the O atom concentration, is diminishing it is probable that the disappearance of the O atoms is governed chiefly by the chain breaking reaction, O + CO + M--~ CO2 + M
(4)
281
If this is so, the rate of decay of the O atoms will be,
dO - do] dt
(5)
where g = k4[CO][M], and is very nearly constant since [CO] and [M] are well-nigh constant. Consider an element of gas passing up the centreline of the flame; its temperature Tg, and the temperature of the plain wire immersed in this element, Tp, will vary with time as shown in figure 2 (d). Neglecting, for the moment, the diminishing gas temperature and also the small temperature gradient in the vicinity of the wire, the diffusion of O atoms to the wire surface will be governed by the equation;
dn_D(O2n ion\ [ar 2 "F r ~r f + gn
(6)
where concentration of O atoms at a distance r from the centre of the platinum wire at time t, D = the diffusion coefficient for O atoms diffusing through the flame gases. [Calculated from expressions given by Chapman and Cowling (17) using molecular data given by Rice (18) and in the Smithsonian Physica.l Tables (1934).] For large values of the parameter x = Dt/a2, the solution of equation (6) leads to the following expression; gt
(On) D
2Dn' f
~rr r = a - -
a
"1 i o g ~ ( 4 ~ -- 23`
(7) -- (log. (4x) -- 23`)2 -t- et where # = concentration of O atoms in the flame gases outside the influence of the wire a = radius of the wire 3' = Euler's constant = 0.57722. The left hand side of equation (7) is the rate at which O atoms are striking the wire per unit surface area. The minimum possible value of this rate will be obtained if the probability of reaction of O and CO on the wire surface is assumed to be unity, as it undoubtedly is for other atomic reactions (19). The value is obtained directly from the observed rates of catalytic heating knowing that O + CO = CO2 + 127 kcals. Substitution of this value in equation (7) gives
282
LAMINAR COMBUSTION AND DETONATION WAVFS
the minimum concentration of O atoms in the flame gases, n'. Equations (6) and (7) are only true if g and D are both constant, and this would apply if the flame gases were at constant pressure, as they are in this case, and if they were at constant temperature. The centre-line flame temperature actually falls with time and hence, a mean value must be chosen in applying equation (7). Over a short time interval this introduces but little error. The results of such calculations are shown by the full line curve of figure 7 in which log~0 n' is plotted against time. The time values have been measured
For example, if the third body M , in reaction (4) were an atom of sodium, the sodium would l:eceive excitation energy easily sufficient to excite the D-line radiation. This excessive excitation would cause the line-reversal temperatures to be overestimates of the true translational gas temperatures. As this excessive line-reversal temperature is exactly what the present work shows, a tentative explanation would be that the sodium atoms receive additional excitation energy from the triple body reaction; O +CO
+Na--*COz
+Na
On this basis an attempt ~:an be made to estimate the concentration of O atoms necessary to produce the observed excess of D-line temperature over the gas temperature as given by the heated quartzcoated wires.
16"6 16.4
TABLE 2
16.2
B
C ' - 16.0
\
0 --
15"6
i
15"~
IS.; 0
1
2
4 TIME
6 IN
8
Temperature
~
Percentage 0 atoms by volume
1.20
1530 1520 1510 1500 1485 1465 1450 1410 1370
1.2 0.9 0.6 0.45 0.3 0.25 0.2 0.2 0.15
1.82 2.46 3.10 3.75 4.40 5.06 6.38 7.71
-~. 15.8
o
Time in Milliseconds
Io
t2
MILLISECONDS
FIG. 7 from the instant when the peak flame gas temperature was attained which is at about the level of the tip of the inner cone. The points will be seen to lie on a fairly well defined straight line, its slope being proportional to g, the actual value being 467 sec-1 at the mean gas temperature of 1725~ and at 1 atmosphere pressure from which the value of k, is found to be 3.4 • 10-3~ cm. 6 sec. -I at this temperature. The calculated percentages by volume of O atoms in the flame gases are given in table 2 for different time intervals. These values will be seen to greatly exceed the equilibrium concentration which is 0.0004 per cent by volume at the maximum temperature. If such high concentrations of O atoms are present, then it is not surprising that the sodium line-reversal temperatures arc too high.
In an equilibrium gas at temperature T~, the number of collisions undergone by one atom of sodium per second with other molecules, the collision partners possessing between them energy greater than E in two square terms, is n, = Z o / N e - ~ / n r g , where Z a is the total number of collisions taking place in 1 mole of gas per second at the temperature To 9 I n the flame gases the sodium line-reversal temperature was T, and the sodium atoms emitted D-line radiation as though they were in an equilibrium gas at this temperature T~. The number of effective collisions undergone by a single atom of sodium per second in an equilibrium gas at this temperature would .be, n, = Z J N e -E/Rr*. The sodium atoms in the flame must, therefore, be receiving excitation energy at this latter rate although the equilibrium rate would be no. The difference n, - ng, will, on the assumption made, represent the rate of triple body collisions involved in the process CO + O + N a - - ~ C O 2 + N a .
ESTIMATION OF ATOMIC OXYGEN AND MEASUREMENT OF TEMPERATURE If the total number of triple body collisions occurring in one mole of gas at the temperature To, is Yo, then one atom of sodium will undergo Y / N triple body collisions per second, the collision partners being any other two molecules. Hence, without much error the proportion of O atoms in the flame gases can be taken to be (n, no)N/Yo. The number of 0 atoms per i c.c. of gas is therefore; -
'~' -- Z ~
[~go e-F'/Rr~ --
(8)
Before this expression can be evaluated the ratio, Zo/Yo, must be determined and only a crude approximation is possible. Formulae based upon simplifying assumptions have been given by 1900
18OO
t,
1
,%
1700
1600
o
u.I g: I S O C I..,< 1400
-r, I-
13OO I
120 O IIOO O
]
2
TIME
mean molecular diameter of all the gases in the products of combustion and this was given the value 3.23 • t0 -8 cm in the wire temperature analysis. The excitation energy, E, for the sodium D-line of wave-length 0.589 • 10-4 cm is 48,425 cals per mole. The mean free path was obtained from Maxwell's expression and together with the above values substituted in equation (9) which was then evaluated for different heights above the burner using the temperatures Tg and T~ given in figure 2 (d). The resulting values are plotted as a broken line in figure 7 and this may be compared directly with the full line showing the values obtained from the wire records. The agreement is good although it must be admitted that in view of the assumptions made no real importance can be given to this. The main thing is that the order is right and this, we think, lends strong support to our opinion that O atoms are present in concentration well above the equilibrium value. Furthermore, the straight line relationship obtained seems to confirm the view that equation (5) does represent the law of decay of the O atoms. The atomic oxygen concentrations obtained from the wire temperature analysis can be used in equation (9) to evaluate the line-reversal temperature, T , , at any instant when the flame gas temperature, as found from the heated quartzcoated wires, isTo. The resulting values are shown as a broken line in figure 8, the actually measured values being given by the full line and the heated quartz-coated wire temperatures by the line marked To. The agreement is again remarkably good. DISCUSSION
6
4
8
I0
12
IN M I L L I S E C O N D S
FIG. 8 Herzfeld (20) and by Richardson (21). Herzfeld derives the relationship Zo/Yo = X/or, where X = the mean free path and r = the molecular diameter. Richardson, by a different approach, derives a somewhat similar relationship giving the same order for the ratio. Substituting Herzfeld's relation in equation (8) and remembering that Z,/Zo = %/'~l'-~/To, it follows that,
n'
283
NPX
In equation (9) ~r must be taken to be the
The important problem of deciding on the most reliable method of measuring flame gas temperatures has been much discussed in the past and the conclusion reached depends largely upon whether flame gases can be regarded as being effectively in thermodynamic equilibrium. Concise statements of the arguments have been given by Jost (22), Lewis and yon Elbe (23) and Gaydon (24) and need not be repeated here. Suffice it to say thal most investigators have inclined to the view that in open flames the gases can be so regarded and that, therefore, the line-reversal technique yields reliable temperature estimates. The chief evidence supporting this conclusion has been found in the work of Kohn (5), Griffiths and Awbery (25), Loomis and Perrott (26) and others, who demonstrated that the line-reversal temperatures agreed
284
LAMINAR COMBUSTION AND DETONATION WAVES
well with those obtained by the heated wire method which is possible, and it would seem, only possible, in which, it is important to note, uncoated by assuming that O atoms are present in the platinum-rhodium wires were used. CO-O~ flame gases. The present work shows precisely the same Unfortunately, the analyses used to determine agreement between the line-reversal and the the O atom concentration have limited application heated plain wire temperatures in the zone of since a large excess of CO in the flame gases is highest temperature as was seen in table 1. When essential to both. The basic method used in the the comparison is made between the heated quartz- comparison of catalytic and non-catalytic wires coated wire temperatures and the line-reversal does appear to hold out possibilities for future values the picture is completely changed and it developments and has previously been applied by becomes virtually certain that the agreement with Kondratieva and Kondratiev (28)for measuring plain wires is fortuitous and results from the the concentration of H atoms in slow reaction catalytic reactions occurring on their surface. The flames of H~-O2 mixtures. The discovery of other flame gases cannot therefore, be in equilibrium substances for coating the wire surfaces to give for some considerable height, at least 0.3 inch, them selective catalytic action towards specific above the tip of the inner cone in our experiments. reactions would result in new applications for the Had it been possible to use stoichiometric mixtures technique. the conclusion for them might have been different for the reactions would probably have gone to REFERENCES completion much more rapidly. 1. LEWIS, B. AND VON ELBE, G.: Combustion Flames The heated quartz-coated wire temperatures and Explosions of Gases, Cambridge (1938). must, of course, give the upper limit for the GAYDON, A. G.: Spectroscopy and Combustion flame temperature for there is no certainty that Theory, 2nd Edition, Chapman and Hall (1948). the quartz surface completely inhibits all surface RIBAUD, G., LAURE, Y., AND GAUDRu H. : J. Inst. reactions. In any event, it is quite certain that the Fuel. 12, S. 18 (1939). line-reversal temperatures are too high in com2. DAVID,W. T., ANDJORDAN,J.: Phil. Mag., 17, 172 parison with the true translational gas tempera(1934). tures, the error being greater the nearer to the DAVID, W. T., LEAH, A. S. AND PUGH, B.: Phil. intense reaction zone the measurements are taken. Mag., 31, 156 (1941). 3. LEAH, A. S., ROUNTHWAITE, C. AND BRADLEY, D.: I n this connection, Gaydon and Wolfhard (27) Phil. Mag., 61, 468; Ibid., 61, 478 (1950). have shown that in low pressure acetylene flames 4. SCHM1DT,H.: Ann. Physik., 29, 1027 (1909). the line-reversal temperature measured in the 5. KOHN,H.: Ann. Physik., 44, 749 (1914). extended reaction zone was ll00~ above the 6. PmaNI, M.: J. Scientific Instruments, 16, 377 ideal flame temperature. (1939). For the case of the CO-O.2mixtures, the observed 7. BROWN, A. I. AND MARCO, S. M.: Introduction to differences between the temperatures recorded by Heat Transfer. McGraw-Hill (1942). the various methods can be satisfactorily accounted 8. DAVIES,W.: Phil. Mag., 17, 233 (1934). for on the assumption that O atoms, in concentra9. ELLIS, O. C. DE C., AND MORGAN, D.: Trans. tion far greater than the equilibrium amount, Faraday Soc., 28, 826 (1932). remain in the flame gases above the inner cone for 10. FLOCK, E. F., AND ROEDER, C. H.: Natl. Adv. Comm. Aeronaut. Tech. Rep. No. 532 (1935). some considerable time, in fact, for as long as 11. FlOCK, E. F., MARVIN, C. F., CALDWELL, F. R., 0.008 second. Introduction of nitric oxide into the AND ROEDER, C. H.: Natl. Adv. Comm. Aeroflames we have used in order to apply the O atom naut., Tech. Rep. No. 682 (1939). test of Gaydon gave very positive evidence of the 12. LEwIs, B. The Chemical Background for Engine presence of O atoms in the air mixtures but was Research, Interscience Publishers Inc. (1943). not sufficiently conclusive with the CO-O2 flame 13. LEAH, A. S.: Phil. Mag., 34, 795, (1943); Ibid., to be put forward in support of the views pro37, 657 (1947). pounded here. It is, however, difficult to envisage 14. LEWIS, B., ANn VON ELBE, G.: J. Chem. Phys., 11, 75 (1943). any other species which could be the cause of the 15. SEMENOFF, N. : Chemical Kinetics and Chain Reobserved catalytic heating of the plain wires, 02 actions, Oxford Univ. Press (1935). molecules and excited 02* (3) being proscribed, 16. HINSHELWOOD,C. N.: The Kinetics of Chemical and the strength of the argument must rest upon Change, Oxford Clarendon Press (1940). the striking correlation of all the observations 17. CHAPMAN,S., AND COWLING,T. G.: The Mathe-
RESISTANCE-THERMOMETER MEASUREMENTS IN LOW-PRESSURE FLAME
18. 19. 20. 21. 22.
matical Theory of Non-Uniform Gases, Cambridge (1939). RICE, O. K.: Electronic Structure and Chemical Binding. McGraw-Hill (1940). SMITH, W. V.: J. Chem. Phys., 11, 110 (1943). HERZFELD, K. F.: Z. Phys., 8, 132 (1922). RICHARDSON,L. F.: Proc. Roy. Soc., A. 186, 422 (1946). JosT, W.: Explosion and Combustion Processes in Gases, McGraw-Hill (1946).
285
23. LEWIS, B. AND VON ELBE, G.: Combustion Flames and Explosions of Gases, Cambridge (1938). 24. GAYDON, A. G.: Spectroscopy and Combustion Theory, 2nd Edition, Chapman and Hall (1948). 25. GRIFFITHS, E. AND AWBERY, J. H.: Proc. Roy. Soc., 129, 401 (1929). 26. Looms, A. G., AND PERROTT, G. ST. J.: Ind. Eng. Chem., 20, 1004 (1928). 27. GAYDON, A. G., AND WOLFHARD, H. G.: Proc. Roy. Soc., 194, 169 (1948).
33
RESISTANCE-THERMOMETER MEASUREMENTS IN'A L O W - P R E S S U R E F L A M E 1 By MITCHELL GILBERT 1. INTRODUCTION" This paper describes some research in a lowpressure flame on measurements of translational tcmperature. A measurement technique using a platinum resistance thermometer was developed and found successful, subject to certain limitations. The pertinent background leading to this research is of interest because of the serious problems encountered in any attempts at definitive study of combustion. Previous work (1) with low-pressure flames in a two-dimensional laminar jet at total pressures less than 10 mm Hg abs indicates that detailed explorations of the reaction zones could be made with great resolution of the flame phenomena. Spatial extension and the extraordinary steadiness of the flame make this precision possible. Lowering the total pressure under the proper conditions preserves the Bunsen-like character and isolation of the flame and acts through effects of molecular mean free paths to increase the physical scale of the flame inversely with the pressure. Flames thus extended preserve also the average number of molecular collisions per reaction zone, and the visual luminous character remains unchanged except for greater diffuseness. 1 This paper presents the results of one phase of research carried out at the Jet Propulsion Laboratory, California Institute of Technology under Contract No. W 33-038-ac-4320 sponsored by the Air Materiel Command and Contract No. DA-04-495-Ord 18 sponsored by the Department cf the Army, Ordnance Corps.
AND
JOHN H. LOBDELL
So long as the gas density is appreciable, the collision rate per unit volume remains large, and statistical considerations are unaltered relative to atmospheric conditions. The local temperatures and temperature structure in the flame zones continue to be of major interest as basic parameters governing the flame process. The problem includes the kind as well as the level of temperature: internal as well as translational temperature. Nontranslational temperatures are not the subject of this paper, but pertinent references are given. Some earlier measurements were made by Klaukens and Wolfhard (2) and Gilbert (1) with thermocouples. Certain evaluations of Klaukens' measurements were doubtful because of an assumption that treated a spherical shape as a cylindrical one in determining heat transfer to the thermocouple. This treatment was investigated and clarified (1), but the interpretation of the measurements was disputable even after removing Klaukens' difficulties. Estimates of the thermal conductivity of the gas film surrounding a wire were necessary and yet subject to unavoidable uncertainty. The uncertainty depends on the nature of thermal transport in a gas containing atomic hydrogen, atomic oxygen, and hydroxyl radical in appreciable quantity. The thermalconductivity coefficients were estimated from very simplified considerations (3), and their contributions to total transport were evaluated according to trends observed in theoretical calculations by
LAMINAR COMBUSTION AND DETONATION WAVES 6. SMITHF.: Am. Chem. Rev,, 21,389 (1930).
comparable flames at atmospheric pressure because of the increased effects of dissociation.
7. ANDERSEN, J. W., AND FE1N, R. S.: Univ. of Wise.
Naval Res. f.ab. CM-517. 8. Mactm, H., AND HEBRA, A.: Wiener Akademie Sitzungberichte Ableitung, IIa, 150 band, 157174 (1941). 9. AN~SEN, J. W., ANn R. FRIEDMAN: Rev. Sci. Inst., 20, 61 (1949). 10. COLES, C. H.: Electronic Industries, 5, 74, Feb. (1946). 11. GAYDON, A.: Spectroscopy and Combustion Theory. London, Chapman and Hall (1948). 12. WRIGHT, F. H.: Progress Report 3-23, Jet Propulsion Lab., California Institute of Technology (1951).
ACKNOWI.~DGMI~NT
We are happy to acknowledge the experimental assistance of Lowell W. Bennett, Arthur P. Mattuck and other members of the experimental combustion group at APL and the computational assistance of Mrs. Shirley St. Martin. We would also like to acknowledge a number of helpful suggestions by Dr. H. Lowell Olsen and Capt. E. L. Gayhart of this Laboratory, and discussions of the implications of the data with Professors Hirschfelder and Curtiss of the University of Wisconsin and with Dr. P. Rosen of this Laboratory.
13. MATTUCK, A. P.: Private communication.
14. H~SCK~'~LDER, J. O.: CM-598, Theory of Flame Propagation, II, University of.Wisconsin, NRL.
REFERENCES
DlsegssloN BY J. H. BURGOYNE*
1. WOLFttARD, H., AND KLAUKENS, [q[.; Proc. Roy.
2. 3.
4.
5.
A feature of the temperature profile curves is the discontinuity that occurs between 1000~ and 2000~ The explanation may be as follows. It has been shown by Baldwin, by Walsh and by Burgoyne and Hirsch that in combustion of various paraffin hydrocarbons the stage CO ~ CO~ is inhibited by the hydrocarbon itself. This results in a discontinuity in the rate of heat release from lean mixtures since the final stage of the combustion cannot proceed readily until the concentration of hydrocarbon has been reduced by reaction to a low value.
Soc. (London), A193, 512 (1948). LEWIS, B., AND VON EeriE, G.: J. Chem. Phys., tl, 75 (1943). BROEZE, J. J.: Third Symposium on Combustion, Flame and Explosion Phenomena, p. 146. Baltimore, The Williams & Wilkins Co. (1949). LEwis, B., AND VON ELBE, G.: Combustion, Flames and Explosions, Chap. VII. New York, Academic Press (1951). JOST, W.: Explosion and Combustion Processes in Gases, Chap. III. New York, McGraw-Hill (1946).
* London.
32
THE ESTIMATION OF ATOMIC OXYGEN IN OPEN FLAMES AND THE MEASUREMENT OF TEMPERATURE By A. SMEETON LEAH AND N. CARPENTER INTRODUCTION
The most familiar methods of measuring flame gas temperatures in small scale laboratory open flames are, perhaps, the spectral line-reversal technique, resistance thermometry and the heated wire method. Whatever the definition of gas temperature adopted, and here the gas temperature will be taken to be that corresponding to the mean translational energy of the gas molecules, it is evident that all the methods when applied to a gas in perfect thermal and chemical equilibrium should yield identical gas temperatures after due
correction for losses. However, an inspection of the literature on the various techniques cannot fail to reveal a distinct lack of agreement between the methods, the differences in observed flame gas temperatures frequently being so large as to render improbable any explanation in terms of the different conditions of experiment adopted by different investigators. A prima facie case therefore exists for believing that thermal and chemical equilibrium may not be attained immediately above the inner cone of an open flame and this has been the subject of much discussion in the past. I t was
ESTIMATION OF ATOMIC OXYGEN AND MEASUREMENT OF TEMPERATURE felt that a re-examination of the position might be of value if tile different methods were applied under identical flame conditions with the object of deciding how closely agreement could be obtained. If agreement were not possible it would remain to decide which of the methods yielded the best estimate of the true translational temperature and finally to endeavour to explain the deviations encountered. Complete flame gas temperature plots using the different techniques have been made in CO-Op, CO-air and certain hydrocarbon-air mixtures burning as an open flame on a simple burner. These show the differences in observed flame temperature which were anticipated from a study of previous literature. Lack of chemical equilibrium would appear to be the explanation of the differences and in the case of the CO-02 flame the anomalous results are ascribed to the presence of relatively large concentrations of atomic oxygen within the flame gases above the inner cone. The determination of the concentration of this atomic oxygen from the observed temperatures is then dealt with in some detail. TEMPERATURE MEASURINGAPPARATUS The methods used are well known and only a few words need be said about the arrangements for each.
Spectral line-reversal method The method has been described by a number of investigators (1). A slit type burner was used in the experiments and the optical system was set up parallel to the longer axis, achromatic lens combinations being used. Only the central section of the flame was coloured with sodium salt in order to eliminate error due to the cooler ends of the flame. A 6-volt tungsten filament lamp was used as the comparison radiator, the filament being calibrated for brightness temperature against current input by the use of an optical pyrometer, the usual corrections being made.
Resistance wire method The method has been described by David and co-workers (2) and some extensions of the technique used in the present work are described by Leah, Rounthwaite and Bradley (3). Two types of resistance elements were used, the first being 0.0005 inch diameter platinum-rhodium (10 per cent) wire and the second, quartz-coated platinumrhodiM~ (10 per cent) wire of 0.0005 inch overall
275
diameter with a metal core 0.0002 inch diameter, both types being about 1 inch in length. The wires were electrically welded to the ends of 0.028 inch diameter supporting leads fixed in an insulated holder. Absolute straightness of the wires in the flame was maintained by providing a compensating expansion on the leads. Resistance changes of the wires were recorded photographically by the use of a sensitive optical galvanometer in conjunction with a simple electrical resistance bridge. Calibration records were taken to obtain the wire resistance from the deflections recorded on the films and these were translated into temperature by using the carefully measured resistance coefficients of the wires.
Heated wire method The resistance wires used in the method just outlined lose heat by radiation when inserted in the flame gases causing them to record temperatures which are too low. The error may be eliminated by the method used by Schmidt (4) and Kohn (5). The wire is electrically heated in the flame and a curve of wire temperature against electrical input obtained. When the wire temperature is the same as that of the flame gases surrounding it no interchange of heat occurs by conduction and convection, the only loss being that due to radiation from the wire. The radiation loss at different temperatures may be determined by heating the wire electrically in vacuo or, more conveniently, by calculation from the known emissivity of the wires. On plotting the curve of wire temperature against radiation loss on the previously found heating curve, the true flame gas temperature is given by the point of intersection of the two curves. In the present work the radiation losses were calculated from the StefanBoltzmann law using emissivities given by Pirani (6) for quartz and Brown and Marco (7) for platinumrhodium. GENERAL APPARATUS
The gases used were all of purity exceeding 99.5 per cent with the exception of ethylene for which the value was 98.0 per cent, the impurity being largely methane. The mixtures were made up in a large pressure vessel from which they passed to the burner through a carefully calibrated metering orifice and a flame trap. The trap was built up of cup-shaped porous sintered bronze pots placed end to end in a suitable container. It offered little resistance to flow and was thoroughly
276
LAMINAR COMBUSTION AND DETONATION WAVES
reliable. After leaving the trap the gas stream divided, the larger volume passing directly to the burner, the smaller portion passing through a salt injector before entering the burner. The burner had to be such as to give a broad flame in order to acconlmodate resistance wires of 1 inch in length. A rectangular section burner tube, 19~ inches x ~ a inch and 12 inches in length, was built up of two accurately machined sections bolted together with metal to metal contact. The
subsidiary gas stream in a finely powdered state by being carried in suspension from a mechanical agitator of the paddle wheel type. The experiments contemplated involved the measurement of the temperature by each method at various points across the flame and a t various heights above the burner, to achieve which, relative movement between the flame and the measuring devices in the horizontal and vertical planes had to be provided. In view of the delicacy and length
I
I
BURNE~
=1
RANSVERSE SLIDES
CLUTCH FOR T~ MOVEk DIAl. ,
~L
r-"
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I I
b
BRACKI RECORI AND C
i
,
r V2" -ZL,
9
8 4 . . . .
MAIN
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t
--
.....
INLETS
FIG. main portion of the gas mixture entered the burner at both ends of a cross tube fixed to the base of the burner tube thus promoting symrnetry of flow. In addition, a piece of porous sintered bronze was fixed in the bottom of the burner tube to smooth out the flow and, incidentally, to act as a subsidiary flame trap. The salt laden portion of the gas flow entered the burner tube some 6 inches below the top in a central position. A control valve in the supply line for this gas enabled adjustment of the flow rate to give a distinct central band of coloured flame of about ~ inch in width. The sodium chloride salt was injected into the
of the optical system for the line-reversal measurements it was decided to arrange for the burner to move relative to the fixed optical system and the fixed wire holders. The layout of the burner system is shown in figure 1. The burner tube passed through a gland in the base plate of the housing and vertical movement was obtained through an adjusting screw, the height being observed by means of a dial gauge attached to the burner tube. The base plate carrying the burner was mounted in guides permitting lateral movement, this movement being effected by rotating a handwheel carried on an adjusting screw. The
ESTIMATION OF ATOMIC OXYGEN AND MEASUREMENT OF TEMPERATURE turning of the handwheel was made to rotate a recording camera drum through a suitable train of gears, the camera drum making one revolution whilst the burner made a complete lateral traverse, the distance moved being rather more than the thickness of the flame at its widest section. The galvanometer used in the resistance bridge recorded on the camera drum film a continuous plot of wire temperature against distance across the flame as the handwheel was slowly rotated. A family of such curves was recorded on one film for different burner heights, the drum being moved along between each recording to separate the individual lines.
277
RESULTS
The use of platinum-rhodium resistance thermometers limited the strengths of the inflammable mixtures used to those yielding maximum temperatures below 1850~ the fusing point of the wires. Thus, stoichiometric mixtures were ruled out and either weak or over-rich mixtures had to be used. From a wide range of experiments with different mixture strengths using a variety of inflammable gases, a few representative examples will be presented. 11.5 per cent 02 + 0.5 per cent H~ + 88.0 per cent CO mixture d '"~
"
~
f . _ ~
oN.E;.o ." ..... '1-
~ ~'.
-
TEMPERATURE LINE" REVERSAL F ~ TEMPERATgR~FL
__ J; IIEA ED OUARTZ-COATED
,,.o f
,,,,,.E ,rE,,, "
(1)
7 UNHEATED QUARTZ*COATED
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CALCULATED CENTRE LINE
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TIME FRO'`` MAX. GAS TEMP. IN MILLISEC$.
o2
Fro. 2a, b, c, d Continuous recording of the line-reversal temperatures was not convenient and a means of observing the horizontal movement of the burner had to be provided. This was effected by an optical system, a beam of light being reflected on to a fixed scale from a mirror mounted on a bellcrank lever, one arm of which moved with the burner. The line-reversal temperature could then be taken at any point across the thickness of the flame and at various heights above the burner tip. The burner tube was water cooled, the passages being drilled through the length of the walls in order to bring the water pipes outside the sealing gland. The housing surrounding the burner had windows at each end and carried the wire holders at one side. I t acted as a flame shield and separator and was 3 inches x 5 inches x 12 inches high, tapering at the top to a chimney 2 inches x ~/~ inch in section.
The constituent gases were fairly well dried before use but because small traces of water vapour very materially affect the flame speed, it was decided to add 0.5 per cent of hydrogen to the mixture to ensure absolute consistency and repeatability. The hydrogen slightly increases the flame temperature but has no noticeable effect on the difference of temperature observed between plain and coated wires as was shown for explosion flames of this mixture by Leah, Rounthwaite and Bradley (3). The results are shown in figure 2, temperature contours being plotted as observed by means of plain resistance wires in (a), by heated quartzcoated wires in (b) and by the line-reversal method in (c). I t will be noted that the contours are of much the same shape in all cases although the temperature readings are appreciably different. This is more clearly shown in figure 2 (d) where the
278
LAMINAR COMBUSTION AND DETONATION WAVES
centre-line temperatures are plotted against height above the burner, a time scale also being shown which was obtained in a manner to be described. The unheated quartz-coated wire temperatures are shown in this figure, although they have not been plotted separately as contours. This has been done for economy of space and because the contours are very nearly theqsame as
that within the unburnt interconal gases, where the quartz-coated wires register a low temperature, the line-reversal temperatures appear to be high, so high in fact that reversal of the D-line was difficult to obtain with the comparison radiator used. The plain wires show temperatures well above the quartz-coated wire temperatures and as the unburnt interconal gases are approached the d 2OO0
LIREi. REVERS]M. TEMPERATURE
I 7SO~ _ ~ Q
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LINE - REVERSAL TEMPERATURE
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0'7
FIG. 4a, b, c, d those obtained with heated quartz-coated wires. The radiation correction was found to be of the order of 20~ to 40~ over the range of temperature shown. Both the unheated and heated quartz-coated wire curves show a maximum temperature at a point corresponding with the tip of the inner cone, as would normally be expected. The linereversal temperature varies in a curious way at this point, probably due to refraction of the light beam passing through a zone of very steep temperature gradient. It is also of interest to note
temperature sweeps upwards until fusion occurs. This is undoubtedly due to the catalytic combustion of CO and O~ on the plain wires, as was demonstrated by Davies (8). The first conclusion to be drawn from figure 2 (d) is that the different methods yield temperatures which are widely at variance in the zone immediately above' the inner cone, the values, however, tending to equalise at greater heights above the burner. 27.5 per cent CO + 1 per cent H~ + 71.5 per cent air mixture
(2)
ESTIMATION OF ATOMIC OXYGEN AND MEASUREMENT OF TEMPERATURE The temperature contours for this mixture are shown in figure 3 (a), (b) and (c) and the centreline temperatures are given in figure 3 (d). A general similarity with the previous results will be apparent. The maximum line-reversal temperature observed above the height giving maximum quartz-coated wire temperature is 1820~ This is somewhat lower than the value of 1920~ given
279
Figure 5, representing the olefines. 2.34 per cent benzene + 97.66 per cent air mixture
(5)
Figure 6, representing the aromatics. In table 1, the results are summarised for each of the mixtures examined. The maximum values of d 2OOO
LIN! itEV|RSAL I
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O.l 0-3 HEIGHT ABOVE
0-4 O.S 04 OURNi[R IN ~iNCHES
0.7
FIc,. 5a, b, c, d d lO00
17SO
a.
ill!
i:
c,
b.
,~ ISO0
! ~i!
I 71ffl\\III flili~, \kl' I llll~\\ll I
lill',,\kk~
tW'o
", o
~o''.~, / J o i
~ UNHE*TE. PL*" W,RE / "~.~,E.*TO*t
HEAT[D OUA~TZ'CO
Ilill~\\~ Illillk.,\\~\//~ IIIIIIfA\\k,kkll 1l((//:,~/7 o.,
' ~
~ liSO
IIIIr Ak/
llll~,,\\l ' t ioI IIIIIr~,\lll I
'
#
%4,,\\ Wa\k/
D
~
UNHEATED GUARTZ-COATED WiRE TEMPERATURE 75Q
500 o=
0.1
o,I FIG.
6a,
by Ellis and Morgan (9) for the same mixture using a similar technique. To complete the picture, three representative hydrocarbon flames are given, namely; 3.5 per cent propane + 96.5 per cent air mixture
(3)
Figure 4, representing the paraffins. 5.2 per cent ethylene + 94.8 per cent air mixture
(4)
0-2 0.3 04 O.S 06 HEIGHT ABOVE BURNER IN INCHES
J 0.7
b, c, d the heated quartz-coated wire temperatures measured on the centre-line of the flame are stated and the corresponding temperatures at the same point are given for the other methods. Inspection of the curves in figures 2 to 6 reveals that the flame temperatures measured by the different methods are not in agreement, the differences, however, gradually diminishing with height above the burner, i.e. with time. The difference between the unheated and heated wire temperatures is, of course, due to the radiation
280
LAMINAR COMBUSTION AND DETONATION WAVES
loss from the unheated wire, the loss being quite small in view of the exceedingly fine wires used. The differences between the two types of heated wire and the line-reversal temperatures point unmistakably to the conclusion that the flame gases are not in thermal and chemical equilibrium unless, indeed, the differences are ascribed to experimental errors. Regarding the possibility of considerable experimental errors, it may be noted that our line-reversal temperatures are in reasonable agreement with those of other investigators, if anything being slightly lower. The heated wire temperatures are corrected for TABLE I Temperatures *C Resistance Thermometer
Heated wires
Mixture
my
"~
11.5%O e
+
0.5~
~
+
~
e
~ ~
"-
1720 1500 1770 1535 1780
88.0% c o 88.0% c o
27.5~ + 1.0~ H~ + 1680 1535 1730 1578 1750 71.5% Air 3.5% propane + 96.5% Air 5.19~ ethylene + 94.81~ ,7| 5s i 8 516 01900 Air 2.34% benzene + 97.66% 1705i 801775,5 5 s50 radiation losses and errors in resistance coefficients are discounted because direct insertion of these wires into a high temperature electric furnace yield identical calibrations. End cooling losses to the wire leads are inappreciable because the lead tips are themselves within the flame gases. The fact, however, which is of the greatest consequence is that the two different types of wires record almost identical temperatures at a height exceeding 0.4 inch above the burner but differ by as much as 200~ near the inner cone. No possible correction can bring them into line at all heights and on this fact alone it seems justifiable to assume that the flame gases are not in chemical equilibrium. This is borne out by the high values of the line-reversal temperatures and also by the fact that the temperatures observed by all the methods tend to equalise with height above the burner as, with the passage of time, equilibrium becomes established.
Unless some large absolute error has occurred in the wire method, it necessarily follows that the heated quartz-coated wire temperatures must represent the nearest approach to the true translational flame gas temperatures, these being the lowest. Direct support for this conclusion is extremely difficult to obtain; only two methods of determining translational flame gas temperature which would be applicable to a non-equilibriumgas appear to be known and these are only applicable to explosion flames. One is the well-known soap bubble method used by Flock and Roeder (10) and the other the photographic explosion technique used by Flock, Marvin, Caldwell and Roeder (11), Lewis and von Elbe (12), and Leah (13). So far as comparisons are possible, these methods yield temperatures which are in fair agreement with quartz-coated wire temperatures in corresponding closed-vessel explosions (13). In the absence of further evidence, the heated quartz-coated wire temperatures must be assumed to give the best approximation to the true translational gas temperature. It is apparent that surface catalysis must be the explanation of the high temperatures recorded by the plain platinum wires. The amount of the catalytic heating can be determined quite simply. If the plain wire temperature is T r , when the flame gas is at a lower temperature Tg, the wire is losing heat by conduction and convection to the flame gas at some rate H watts per sq. cm. and also by radiation to the cooler surroundings at a rate R watts per sq. cm. and is gaining heat at the rate S watts per sq. cm. due to catalytic heating. Then,
S=H+R Values of H + R may be determined directly by heating the wires electrically in the flame gases, the values being found for different flame temperatures, T,j, and a range of wire temperatures, Tp.
In the case of the CO-O~ flame, the results for which are given in figure 2, the catalytic heating rates obtained in the manner just outlined may be used to extend the analysis if certain basic assumptions are made regarding the reaction occurring on the wire surface. The full procedure has been described by Leah, Rounthwaite and Bradley (4) as applied to explosion experiments and will not be repeated here in detail. Attention will be confined to the conditions along the centre-line of the flame and the first step is to
ESTIMATION OF ATOMIC OXYGEN AND MEASUREMENT OF TEMPERATURE estimate the centre-line gas velocities to convert heights above the burner into time intervals. The limits of flame width at any height were determined from the wire temperature records and the mass of gas flowing per second was known from the input to the burner. Hence, knowing the temperature distribution across the flame at any height, the mass flow, the flame width, and assuming parabolic velocity distribution for the vertical component of velocity, the maximum centre-line velocities were easily estimated. The resulting velocities were found to decrease slightly with increasing height above the burner whereas it is known from the experiments of Lewis and von Elbe (14) that the velocity should increase slightly. The discrepancy is due to the neglect of the infiltrated gases which increase the mass of the upward flowing gases but is so small as to have negligible effect upon the time estimates deduced from the velocities. Thus, the time scale may be added to figure 2 (d) as shown. Following Leah, Rounthwaite and Bradley, it would appear that for this CO-O= mixture, the only active species which can be present in appreciable proportion are O atoms and COs*, these resulting from reactions in the combustion zone such as the following suggested by Semenoff (15) and Hinshelwood (16). O + CO --~ CO2"
CO=* + 0 2
(1)
--~C02 + 2 0
(2)
O +CO +O~ -+COs +20
(3)
Any atoms of oxygen or 02 molecules present in excess of the equilibrium concentration will react catalytically with CO on the platinum wire surface. Of these two species, it is certain that after the gas mixture has passed through the zone of intense reaction above the inner cone, 02 molecules alone are not sufficient to account for the observed catalytic heating rates for, if they were, combustion could not have proceeded enough to produce the high flame temperatures observed. It seems most probable that the main catalytic reaction producing the heating is that due to the combination of O atoms with CO. Above the intense reaction zone at the top of the inner cone when the catalytic heating and hence, the O atom concentration, is diminishing it is probable that the disappearance of the O atoms is governed chiefly by the chain breaking reaction, O + CO + M--~ CO2 + M
(4)
281
If this is so, the rate of decay of the O atoms will be,
dO - do] dt
(5)
where g = k4[CO][M], and is very nearly constant since [CO] and [M] are well-nigh constant. Consider an element of gas passing up the centreline of the flame; its temperature Tg, and the temperature of the plain wire immersed in this element, Tp, will vary with time as shown in figure 2 (d). Neglecting, for the moment, the diminishing gas temperature and also the small temperature gradient in the vicinity of the wire, the diffusion of O atoms to the wire surface will be governed by the equation;
dn_D(O2n ion\ [ar 2 "F r ~r f + gn
(6)
where concentration of O atoms at a distance r from the centre of the platinum wire at time t, D = the diffusion coefficient for O atoms diffusing through the flame gases. [Calculated from expressions given by Chapman and Cowling (17) using molecular data given by Rice (18) and in the Smithsonian Physica.l Tables (1934).] For large values of the parameter x = Dt/a2, the solution of equation (6) leads to the following expression; gt
(On) D
2Dn' f
~rr r = a - -
a
"1 i o g ~ ( 4 ~ -- 23`
(7) -- (log. (4x) -- 23`)2 -t- et where # = concentration of O atoms in the flame gases outside the influence of the wire a = radius of the wire 3' = Euler's constant = 0.57722. The left hand side of equation (7) is the rate at which O atoms are striking the wire per unit surface area. The minimum possible value of this rate will be obtained if the probability of reaction of O and CO on the wire surface is assumed to be unity, as it undoubtedly is for other atomic reactions (19). The value is obtained directly from the observed rates of catalytic heating knowing that O + CO = CO2 + 127 kcals. Substitution of this value in equation (7) gives
282
LAMINAR COMBUSTION AND DETONATION WAVFS
the minimum concentration of O atoms in the flame gases, n'. Equations (6) and (7) are only true if g and D are both constant, and this would apply if the flame gases were at constant pressure, as they are in this case, and if they were at constant temperature. The centre-line flame temperature actually falls with time and hence, a mean value must be chosen in applying equation (7). Over a short time interval this introduces but little error. The results of such calculations are shown by the full line curve of figure 7 in which log~0 n' is plotted against time. The time values have been measured
For example, if the third body M , in reaction (4) were an atom of sodium, the sodium would l:eceive excitation energy easily sufficient to excite the D-line radiation. This excessive excitation would cause the line-reversal temperatures to be overestimates of the true translational gas temperatures. As this excessive line-reversal temperature is exactly what the present work shows, a tentative explanation would be that the sodium atoms receive additional excitation energy from the triple body reaction; O +CO
+Na--*COz
+Na
On this basis an attempt ~:an be made to estimate the concentration of O atoms necessary to produce the observed excess of D-line temperature over the gas temperature as given by the heated quartzcoated wires.
16"6 16.4
TABLE 2
16.2
B
C ' - 16.0
\
0 --
15"6
i
15"~
IS.; 0
1
2
4 TIME
6 IN
8
Temperature
~
Percentage 0 atoms by volume
1.20
1530 1520 1510 1500 1485 1465 1450 1410 1370
1.2 0.9 0.6 0.45 0.3 0.25 0.2 0.2 0.15
1.82 2.46 3.10 3.75 4.40 5.06 6.38 7.71
-~. 15.8
o
Time in Milliseconds
Io
t2
MILLISECONDS
FIG. 7 from the instant when the peak flame gas temperature was attained which is at about the level of the tip of the inner cone. The points will be seen to lie on a fairly well defined straight line, its slope being proportional to g, the actual value being 467 sec-1 at the mean gas temperature of 1725~ and at 1 atmosphere pressure from which the value of k, is found to be 3.4 • 10-3~ cm. 6 sec. -I at this temperature. The calculated percentages by volume of O atoms in the flame gases are given in table 2 for different time intervals. These values will be seen to greatly exceed the equilibrium concentration which is 0.0004 per cent by volume at the maximum temperature. If such high concentrations of O atoms are present, then it is not surprising that the sodium line-reversal temperatures arc too high.
In an equilibrium gas at temperature T~, the number of collisions undergone by one atom of sodium per second with other molecules, the collision partners possessing between them energy greater than E in two square terms, is n, = Z o / N e - ~ / n r g , where Z a is the total number of collisions taking place in 1 mole of gas per second at the temperature To 9 I n the flame gases the sodium line-reversal temperature was T, and the sodium atoms emitted D-line radiation as though they were in an equilibrium gas at this temperature T~. The number of effective collisions undergone by a single atom of sodium per second in an equilibrium gas at this temperature would .be, n, = Z J N e -E/Rr*. The sodium atoms in the flame must, therefore, be receiving excitation energy at this latter rate although the equilibrium rate would be no. The difference n, - ng, will, on the assumption made, represent the rate of triple body collisions involved in the process CO + O + N a - - ~ C O 2 + N a .
ESTIMATION OF ATOMIC OXYGEN AND MEASUREMENT OF TEMPERATURE If the total number of triple body collisions occurring in one mole of gas at the temperature To, is Yo, then one atom of sodium will undergo Y / N triple body collisions per second, the collision partners being any other two molecules. Hence, without much error the proportion of O atoms in the flame gases can be taken to be (n, no)N/Yo. The number of 0 atoms per i c.c. of gas is therefore; -
'~' -- Z ~
[~go e-F'/Rr~ --
(8)
Before this expression can be evaluated the ratio, Zo/Yo, must be determined and only a crude approximation is possible. Formulae based upon simplifying assumptions have been given by 1900
18OO
t,
1
,%
1700
1600
o
u.I g: I S O C I..,< 1400
-r, I-
13OO I
120 O IIOO O
]
2
TIME
mean molecular diameter of all the gases in the products of combustion and this was given the value 3.23 • t0 -8 cm in the wire temperature analysis. The excitation energy, E, for the sodium D-line of wave-length 0.589 • 10-4 cm is 48,425 cals per mole. The mean free path was obtained from Maxwell's expression and together with the above values substituted in equation (9) which was then evaluated for different heights above the burner using the temperatures Tg and T~ given in figure 2 (d). The resulting values are plotted as a broken line in figure 7 and this may be compared directly with the full line showing the values obtained from the wire records. The agreement is good although it must be admitted that in view of the assumptions made no real importance can be given to this. The main thing is that the order is right and this, we think, lends strong support to our opinion that O atoms are present in concentration well above the equilibrium value. Furthermore, the straight line relationship obtained seems to confirm the view that equation (5) does represent the law of decay of the O atoms. The atomic oxygen concentrations obtained from the wire temperature analysis can be used in equation (9) to evaluate the line-reversal temperature, T , , at any instant when the flame gas temperature, as found from the heated quartzcoated wires, isTo. The resulting values are shown as a broken line in figure 8, the actually measured values being given by the full line and the heated quartz-coated wire temperatures by the line marked To. The agreement is again remarkably good. DISCUSSION
6
4
8
I0
12
IN M I L L I S E C O N D S
FIG. 8 Herzfeld (20) and by Richardson (21). Herzfeld derives the relationship Zo/Yo = X/or, where X = the mean free path and r = the molecular diameter. Richardson, by a different approach, derives a somewhat similar relationship giving the same order for the ratio. Substituting Herzfeld's relation in equation (8) and remembering that Z,/Zo = %/'~l'-~/To, it follows that,
n'
283
NPX
In equation (9) ~r must be taken to be the
The important problem of deciding on the most reliable method of measuring flame gas temperatures has been much discussed in the past and the conclusion reached depends largely upon whether flame gases can be regarded as being effectively in thermodynamic equilibrium. Concise statements of the arguments have been given by Jost (22), Lewis and yon Elbe (23) and Gaydon (24) and need not be repeated here. Suffice it to say thal most investigators have inclined to the view that in open flames the gases can be so regarded and that, therefore, the line-reversal technique yields reliable temperature estimates. The chief evidence supporting this conclusion has been found in the work of Kohn (5), Griffiths and Awbery (25), Loomis and Perrott (26) and others, who demonstrated that the line-reversal temperatures agreed
284
LAMINAR COMBUSTION AND DETONATION WAVES
well with those obtained by the heated wire method which is possible, and it would seem, only possible, in which, it is important to note, uncoated by assuming that O atoms are present in the platinum-rhodium wires were used. CO-O~ flame gases. The present work shows precisely the same Unfortunately, the analyses used to determine agreement between the line-reversal and the the O atom concentration have limited application heated plain wire temperatures in the zone of since a large excess of CO in the flame gases is highest temperature as was seen in table 1. When essential to both. The basic method used in the the comparison is made between the heated quartz- comparison of catalytic and non-catalytic wires coated wire temperatures and the line-reversal does appear to hold out possibilities for future values the picture is completely changed and it developments and has previously been applied by becomes virtually certain that the agreement with Kondratieva and Kondratiev (28)for measuring plain wires is fortuitous and results from the the concentration of H atoms in slow reaction catalytic reactions occurring on their surface. The flames of H~-O2 mixtures. The discovery of other flame gases cannot therefore, be in equilibrium substances for coating the wire surfaces to give for some considerable height, at least 0.3 inch, them selective catalytic action towards specific above the tip of the inner cone in our experiments. reactions would result in new applications for the Had it been possible to use stoichiometric mixtures technique. the conclusion for them might have been different for the reactions would probably have gone to REFERENCES completion much more rapidly. 1. LEWIS, B. AND VON ELBE, G.: Combustion Flames The heated quartz-coated wire temperatures and Explosions of Gases, Cambridge (1938). must, of course, give the upper limit for the GAYDON, A. G.: Spectroscopy and Combustion flame temperature for there is no certainty that Theory, 2nd Edition, Chapman and Hall (1948). the quartz surface completely inhibits all surface RIBAUD, G., LAURE, Y., AND GAUDRu H. : J. Inst. reactions. In any event, it is quite certain that the Fuel. 12, S. 18 (1939). line-reversal temperatures are too high in com2. DAVID,W. T., ANDJORDAN,J.: Phil. Mag., 17, 172 parison with the true translational gas tempera(1934). tures, the error being greater the nearer to the DAVID, W. T., LEAH, A. S. AND PUGH, B.: Phil. intense reaction zone the measurements are taken. Mag., 31, 156 (1941). 3. LEAH, A. S., ROUNTHWAITE, C. AND BRADLEY, D.: I n this connection, Gaydon and Wolfhard (27) Phil. Mag., 61, 468; Ibid., 61, 478 (1950). have shown that in low pressure acetylene flames 4. SCHM1DT,H.: Ann. Physik., 29, 1027 (1909). the line-reversal temperature measured in the 5. KOHN,H.: Ann. Physik., 44, 749 (1914). extended reaction zone was ll00~ above the 6. PmaNI, M.: J. Scientific Instruments, 16, 377 ideal flame temperature. (1939). For the case of the CO-O.2mixtures, the observed 7. BROWN, A. I. AND MARCO, S. M.: Introduction to differences between the temperatures recorded by Heat Transfer. McGraw-Hill (1942). the various methods can be satisfactorily accounted 8. DAVIES,W.: Phil. Mag., 17, 233 (1934). for on the assumption that O atoms, in concentra9. ELLIS, O. C. DE C., AND MORGAN, D.: Trans. tion far greater than the equilibrium amount, Faraday Soc., 28, 826 (1932). remain in the flame gases above the inner cone for 10. FLOCK, E. F., AND ROEDER, C. H.: Natl. Adv. Comm. Aeronaut. Tech. Rep. No. 532 (1935). some considerable time, in fact, for as long as 11. FlOCK, E. F., MARVIN, C. F., CALDWELL, F. R., 0.008 second. Introduction of nitric oxide into the AND ROEDER, C. H.: Natl. Adv. Comm. Aeroflames we have used in order to apply the O atom naut., Tech. Rep. No. 682 (1939). test of Gaydon gave very positive evidence of the 12. LEwIs, B. The Chemical Background for Engine presence of O atoms in the air mixtures but was Research, Interscience Publishers Inc. (1943). not sufficiently conclusive with the CO-O2 flame 13. LEAH, A. S.: Phil. Mag., 34, 795, (1943); Ibid., to be put forward in support of the views pro37, 657 (1947). pounded here. It is, however, difficult to envisage 14. LEWIS, B., ANn VON ELBE, G.: J. Chem. Phys., 11, 75 (1943). any other species which could be the cause of the 15. SEMENOFF, N. : Chemical Kinetics and Chain Reobserved catalytic heating of the plain wires, 02 actions, Oxford Univ. Press (1935). molecules and excited 02* (3) being proscribed, 16. HINSHELWOOD,C. N.: The Kinetics of Chemical and the strength of the argument must rest upon Change, Oxford Clarendon Press (1940). the striking correlation of all the observations 17. CHAPMAN,S., AND COWLING,T. G.: The Mathe-
RESISTANCE-THERMOMETER MEASUREMENTS IN LOW-PRESSURE FLAME
18. 19. 20. 21. 22.
matical Theory of Non-Uniform Gases, Cambridge (1939). RICE, O. K.: Electronic Structure and Chemical Binding. McGraw-Hill (1940). SMITH, W. V.: J. Chem. Phys., 11, 110 (1943). HERZFELD, K. F.: Z. Phys., 8, 132 (1922). RICHARDSON,L. F.: Proc. Roy. Soc., A. 186, 422 (1946). JosT, W.: Explosion and Combustion Processes in Gases, McGraw-Hill (1946).
285
23. LEWIS, B. AND VON ELBE, G.: Combustion Flames and Explosions of Gases, Cambridge (1938). 24. GAYDON, A. G.: Spectroscopy and Combustion Theory, 2nd Edition, Chapman and Hall (1948). 25. GRIFFITHS, E. AND AWBERY, J. H.: Proc. Roy. Soc., 129, 401 (1929). 26. Looms, A. G., AND PERROTT, G. ST. J.: Ind. Eng. Chem., 20, 1004 (1928). 27. GAYDON, A. G., AND WOLFHARD, H. G.: Proc. Roy. Soc., 194, 169 (1948).
33
RESISTANCE-THERMOMETER MEASUREMENTS IN'A L O W - P R E S S U R E F L A M E 1 By MITCHELL GILBERT 1. INTRODUCTION" This paper describes some research in a lowpressure flame on measurements of translational tcmperature. A measurement technique using a platinum resistance thermometer was developed and found successful, subject to certain limitations. The pertinent background leading to this research is of interest because of the serious problems encountered in any attempts at definitive study of combustion. Previous work (1) with low-pressure flames in a two-dimensional laminar jet at total pressures less than 10 mm Hg abs indicates that detailed explorations of the reaction zones could be made with great resolution of the flame phenomena. Spatial extension and the extraordinary steadiness of the flame make this precision possible. Lowering the total pressure under the proper conditions preserves the Bunsen-like character and isolation of the flame and acts through effects of molecular mean free paths to increase the physical scale of the flame inversely with the pressure. Flames thus extended preserve also the average number of molecular collisions per reaction zone, and the visual luminous character remains unchanged except for greater diffuseness. 1 This paper presents the results of one phase of research carried out at the Jet Propulsion Laboratory, California Institute of Technology under Contract No. W 33-038-ac-4320 sponsored by the Air Materiel Command and Contract No. DA-04-495-Ord 18 sponsored by the Department cf the Army, Ordnance Corps.
AND
JOHN H. LOBDELL
So long as the gas density is appreciable, the collision rate per unit volume remains large, and statistical considerations are unaltered relative to atmospheric conditions. The local temperatures and temperature structure in the flame zones continue to be of major interest as basic parameters governing the flame process. The problem includes the kind as well as the level of temperature: internal as well as translational temperature. Nontranslational temperatures are not the subject of this paper, but pertinent references are given. Some earlier measurements were made by Klaukens and Wolfhard (2) and Gilbert (1) with thermocouples. Certain evaluations of Klaukens' measurements were doubtful because of an assumption that treated a spherical shape as a cylindrical one in determining heat transfer to the thermocouple. This treatment was investigated and clarified (1), but the interpretation of the measurements was disputable even after removing Klaukens' difficulties. Estimates of the thermal conductivity of the gas film surrounding a wire were necessary and yet subject to unavoidable uncertainty. The uncertainty depends on the nature of thermal transport in a gas containing atomic hydrogen, atomic oxygen, and hydroxyl radical in appreciable quantity. The thermalconductivity coefficients were estimated from very simplified considerations (3), and their contributions to total transport were evaluated according to trends observed in theoretical calculations by