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Temperature profiles in propane-air flame fronts
TEMPERATURE PROFILES IN PROPANE-AIR FLAME FRONTS
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267
heating and reaction zones can also be calculated, and was found to be of the order of 10-3 sec, whilst the time of passage through the actual reaction zone was only about one quarter of this. The accuracy of these figures has been discussed by Dixon-Lewis and Wilson (1).
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(b) Hydrogen + air flame The refractive index gradients found for the 66.7 per cent hydrogen + air flame at 298 mm pressure are shown in figure 6 (curve 1). Here again, curve 2 is that for the pure thermal conduction case. The temperature distribution is shown in figure 7. The results, however, are of somewhat doubtful validity due to the experimental difficulties encountered, and to the small deflexions which had to be measured.
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ACKNOWLEDGEMENTS
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The author wishes to thank the Director of The Gas Research Board for permission to publish this work. He would also like to offer his very special thanks to Dr. A. G. Gaydon for the loan of a pump which made possible the measurements at low pressure. REFERENCE
1.5
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DIST. FROM COLD SIDE (MM.) FIG. 7. Temperature distribution in a 66.7 per cent hydrogen + air flame at 298 mm.
1. D~xoN-LEwis, G., AND WILSON, M. J. G.: Trans. Faraday Soc., 47, 1106 (1951).
31
TEMPERATURE
PROFILES
IN P R O P A N E - A I R
FLAME FRONTS ~
By R. M. FRISTROM, R. PRESCOTT, R. K. NEUMANN, AND W. H. AVERY" As part of an extensive investigation of combustion in high velocity streams, a study is being made of the detailed temperature profile within the flame front of various propane-air flames. Results obtained provide basic experimental data for checking the validity of recent theories of flame propagation. Supplemented by information being furnished by concurrent programs, the data may be used to indicate the chemical kinetic relationship among pressure, temperature and composition in the flame zone. The specific problem of this research is the determination of the temperature profile (figs. 1 to LWork supported by NOrd 7386 with Bureau of Ordnance, U. S. Navy.
4) of a propane-air Bunsen flame as a function of the composition and ambient pressure. Since it was desirable to maintain a precision of 2 per cent or better and the temperature rises 2000~ in a distance of less than a millimeter (at atmospheric pressure) a method of great delicacy was required. For this reason the usual methods involving probes (1) or spectroscopic pyrometry (2) were discarded as being too coarse while the method of vaporizable particles (3) would have yielded an insufficient number of points. The method chosen for these studies is known as the particle track method (4, 5). It is based on an experimental method introduced by Smith (6) and extended by Lewis and yon Elbe (2). The first application of
268
LAMINAR COMBUSTION AND DETONATION WAVES
this technique to t e m p e r a t u r e profile m e a s u r e m e n t was made b y Andersen a n d Fein (7). The particle track technique uses the flame gases themselves as a gas t h e r m o m e t e r b y analyzing the streamline flow t h r o u g h the flame front. T h e
Phillips' Petroleum pure grade 99 mole per cent. D r y compressed air was used and as a n additional precaution cylinders were discarded as soon as their pressure fell below 600 l b s / i n ~. T h e moisture content should be below 0.1 per cent. 3000
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FIG. 1. Flame temperature profiles of propane-air flames with various compositions at atmospheric pressure. [Absolute temperature (~ vs. distance normal to luminous zone (mm).] Arrows mark the limits of the luminous zones, X marks the point fitted to the thermodynamically calculated temperature. 9 = Fuel/Air/ Stoichiometric Fuel/Air.
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FIG. 3. Flame temperature profiles of propane-air flames with various compositions at atmospheric pressure. [Temperature rise (~ vs. distance normal to luminous zone (mm).] Arrows mark the limits of the luminous zones, X marks the point fitted to the thermodynamically calculated temperature. ~I, = Fuel/Air/ Stoichiometric Fuel/Air.
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FIo. 2. Flame temperature profiles of propane-air flames at several pressures. [Absolute temperature (~ vs. distance normal to luminous zone (mm).] Arrows mark the limits of the luminous zones, X marks the point fitted to the thermodynamically calculated temperature, cI, = Fuel/Air/Stoichiometric Fuel/Air. measurements have been refined until a precision of 2 per cent has been reached in the d e t e r m i n a t i o n of the t e m p e r a t u r e profiles.
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FiG. 4. Flame temperature profiles of propane-air flames at several pressures. [Temperature rise (~ vs. distance normal to luminous zone (ram).] Arrows mark the limits of the luminous zones, X marks the point fitted to the thermodynamically calculated temperature. r = Fuel/Air/Stoichiometric Fuel/Air.
Apparatus EXPERIMENTAL
Materials The flames chosen for s t u d y were premixed propane-air B u n s e n flames. T h e p r o p a n e used was
The a p p a r a t u s used for these studies (fig. S) consists of a B u n s e n b u r n e r housed in a pressurized chamber with a n associated gas handling system. A particle separator and introducer is connected
TEMPERATURE PROFILES IN PROPANE-AIR FLAME FRONTS to the gas handling system and observations are made with a flash lamp illumination system and camera. The burner is a t/~,, nozzle with a constant velocity profile (8, 9) surrounded by a second nozzle which supplies a protective sheath of nitrogen. The gas handling system consists of a set of critical orifice flowmeters (9) regulated byPrecision Moore Regulators coupled with large volume plenum chambers which damp out high frequency pressure variations. Flows remain constant throughout a run to within 0.03 per cent. For
269
of the whole apparatus. The pumping system consists of two high capacity piston pumps (flow rates are of the order of 1 liter per second at one-half atmosphere). The particle introducer and separator (fig. 5) employs a 5-liter Wolff Bottle with the two outside necks containing copper inlet and outlet tubes. In the central neck 5 cm above the inlets is located a pad of steel wool saturated with fine MgO powder (U.S.P.). In operation the separator is cut off from the system by closing the stopcocks and a shower of particles initiated by rapping the central stopper with a plastic mallet. The particles
A. Photograph of apparatus: 1. Pressurized burner B. Block diagram of apparatus: a. Critical flow chamber; 2. Power supply and repetitive timer for pumping system; b. Gas bottles, plenum chambers and flash lamp; 3. Spark gap for starting burner; 4. Camera; plastic bag reservoirs; c. Pressure and flow metering 5. Oscilloscope camera; 6. Oscilloscope for monitoring systems; d. Burner; e. Optical system; f. Thermolight output; 7. Flash lamp; 8. Critical orifice flow- couple; g. Light monitoring system. meters; 9. Particle settling bottle; 10. Standard frequency calibrator. Fro. 5. Flame temperature profile apparatus work at one-half atmosphere, dry air is introduced from a plastic bag held at atmospheric pressure. The pressurized chamber (fig. 5) consists of sections of 10" diameter pipe. The burner section contains four windows to accommodate the camera, illumination system and access port. The interior is painted fiat black and flocked with black nylon fibers to kilt reflections. Pressure regulation within the chamber is accomplished by using critical flow inlet and outlet orifices which makes the rate of flow independent of the pumping speed, and the chamber pressure a function only of the influx of gas. Pressure can be maintained better than 0.3 per cent. The flame induced a slow drift in pressure which was attributed to heating
are allowed to settle under gravity for 30 seconds. Stopcocks are then opened to the air line and the suspended dust is carried into the system. A few seconds later particles enter the flame as indicated by a faint yellow glow due to sodium impurities. Illumination is provided by a pair of Sylvania 2340 flash tamps whose images are focused on the flame by a pair of 2" focal length-f/1.6 projector lenses. To provide light for streak photographs one lamp was excited by a 200 #fd bank of condensers charged to 2200 v. The condenser discharge is coupled to the lamp by an L-C network (fig. 5) which gives a sharp (0.2 millisec) initial pulse of energy followed after a delay of 0.2 millisecond by a longer pulse of 1 millisecond duration. To
270
LAMINAR COMBUSTION AND DETONATION WAVES
provide time markers for velocity determinations the other lamp is excited by three condenser discharges (0.67 ~fd at I0 kv) which are individually controlled by "trigertron" type spark gaps. Timing is accomplished by use of a circuit similar to that of Coles (10) and controlled by the camera shutter. The resulting illumination curve consists of four sharp fronted light pips separated by times which can be controlled by the timing circuits. (The usual spacing was 0.1 millisecond.) These are followed by a long duration (one millisecond) roughly constant light pulse. The tracks left by a moving particle illuminated by this system (fig. 6) allow a determination of gas velocities and gas streamlines through a flame front. An illuminator is being tested which will ~dlow a large number of measurements on the same streamline. The illumination curve for each flame
FIG. 6. Particle track pictures of propane-air flames. 1 attn. a. Left. q = 1.10 1.5 X 105 MgO particles per second b. R i g h t . . ~ 6 • 10~ MgO particles per second picture was monitored by a photo cell (GE-929 driven by 45 volts) whose output was displayed on an oscilloscope (Techtronix ~512) with a sweep calibrated by standard time pips furnished by a Rutherford calibrator which has been compared with the output of station W W V and found to be within 0.1 per cent of true frequency. Photographs of the light output curves were made for each picture with a Fairchild polaroid oscilloscope camera and times between light pips determined by measuring these photographs on a comparator. Accuracy was better than 1 per cent. For recording the data a 4" x 5" Nu Vue camera fitted with an f/2 125 mm Xenon special lens using a magnification ratio of four was employed. An Ilex 2" shutter is operated at 1[.5o second. Ansco Triple S Ortho film is preheated to 140~ and developed twelve minutes in D19. To improve the readability of the film', copies were made on contrast lantern slides. Care was taken to avoid
irregular film shrinkage 2 and measurements indicate it to have been held well below 1 per cent.
Data Analysis The films are read on a Jones and Lamson optical comparator. This instrument allows angular determination to -+l minute and a positional accuracy of 4-0.00005 inch. Tracks for measurement were chosen solely on a basis of their sharpness of focus ~ and the availability of an adjacent track (also in sharp focus) from which stream tube cross-sectional measurements could be made. This was possible because of the efficiency of the particle separator. DISCUSSION
OF
RELIABILITY O F MEASUREMENTS
The reproducibility of the measurements of flames with identical initial conditions varies from 1 per cent at 500~ to 2 per cent at 2000~ The experimental dispersion gave probable errors in angular measurement varying from 1-2 per cent and positional errors averaging 1 per cent. The absolute accuracy obtained depends upon the reliability of the assumptions made in the analysis. These will be discussed in the order of their importance. The first question which must be answered is whether there exists a temperature to be measured. Because of the rapidity of the reactions involved, vibrations and electronic degree of freedom do not always have sufficient time to come into thermal equilibrium with translation and rotation. Evidence of a similar effect in CO-O2 flames exists* and the problem is discussed by Gaydon (11). Regardless of these effects, however, at every point there will exist an effective translational temperature since this is essentially a measure of the root mean average translational energy. Further, if the distances with which we deal are large compared with the mean free path (10 to 100 times), this effective translational temperature will be very nearly that corresponding to a Boltzmann distribution of velocities, which is by definition the thermodynamic perfect gas temperature. At the pressures with which we are dealing the mean free path is of the order of 10 -5 cm and the smallest distance increment is 10- 3 cm, thereFilm was wiped dry with a chamois and dried in a humidified room. This criterion assured us that we were dealing with a streamline lying in the diametral plane. * S. Silverman, Amer. Phys. Soc. Meeting, Washington, D. C., May 2, 1952. The region of excess temperature in this system appears well beyond the luminous zone.
TEMPERATURE PROFILES IN PROPANE-AIR FLAME FRONTS
271
fore the temperature which is measured should be The problem of particle track visualization of essentially the equilibrium translational tempera- streamlines is treated by Wright (12) and his ture corresponding to the thermodynamic transtreatment was applied to this work by Mattuck lational temperature. No conclusions can be (13). These calculations indicate that a Stoke's drawn about the energy distribution among other law particle (see note) with a diameter smaller degrees of freedom without further evidence since than 5 microns will give a track whose tangent this may vary with each chemical species. will differ from the true streamline by less than 2 The second question concerns the effect of the per cent. As the pressure decreases the accuracy composition correction which is used. The meas- increases since the accelerations fall off with urements yield the relative gas density and, in pressure, but the viscosity remains unchanged. order to interpret the data in terms of temperature, Velocity lag due to gravity is less than 0.1 per the composition must be known. The initial and cent. The particle size was checked photographically final compositions are known but the intervening by comparing particle tracks with wires and changes can at present only be speculated upon. captured particles under comparable exposure To minimize this problem we have chosen for our conditions. It was demonstrated that we were present study some flames for which this correction indeed photographing particles smaller than 5/~ in is small (of the order of 3 per cent for an equiv- diameter. A similar conclusion was drawn from a alence ratio of 1.0). This comes about because of microscopic study of particles captured on a the high percentage of the nitrogen diluent in air greased slide, 7 and the width of the tracks on the flames and the choice of a reaction whose average pictures, s Further evidence is furnished by the molecular weight varies only slightly during its data which are self-consistent. course. Therefore, in order to attain the desired The fourth question concerns the effect of the precision of 2 per cent, only a crude estimation of particles on the flame reactions. Andersen and the composition change need be made. 5 The data Fein (7) noted that if too many particles are presented for rich flames are subject to correction introduced the flame velocity is decreased; they when reliable composition data become available. attribute this to the heat capacity of the particles. Work on this problem is progressing at this By improving the illumination system we were Laboratory. able to reduce the particle size and numbers Next in importance is the problem of how necessary, so that the heat capacity of the particles closely the particles actually follow the streamlines abstracts a maximum of 0.03 per cent of the total through the flame front. This is governed by the heat output of the flame. Upon introducing the relative importance of viscous drag and inertial particles we could detect no change in burning forces, and is described approximately by Stoke's velocity (as measured by the cone angle) or in the law which should give a lower limit for reliability3 appearance or shape of the flame front (fig. 6). Qualitatively, it can be seen that the smaller the. The assumption of hydrodynamic equations of particle the better the tracking will be. The lower incompressible flow is quite adequate for our limit of particle size that can be used is set by discussion since the streamlines are defined by the two considerations: the light reflected by a particle tracks and the velocities involved are well particle decreases quadratically with the radius, below that of sound. and secondly, at very small diameters motion There are a number of possible sources of error becomes erratic due to Brownian movement. In in the experimental techniques. Several aberrations practice, available illumination set the limit or could affect the optical system; if the position of usable particle size to a few microns in diameter. the focal plane varied from the diameter, or if it It was assumed that because of diffusion composi- were too broad, tracks of particles outside the tion changed in a linear manner with respect to position within the flame front. The reasons for expecting this diametral plane would appear in sharp focus. This approximation to be quite close are discussed by would result in a foreshortening of the track, the Hirschfelder in Univ. of Wise. CM-600, The Theory angles would be too low and the maximum angle of Flame Propagation III, p. 48. This region was aswould occur too soon. By studying only those sumed to extend from the point at which a temperature rise was first detected to the outer edge of the luminous 7 Particle sizes ranged from 1/~ to 10 ~. Zone. s The apparent diameter of a track on the film ~This is because Steke's law describes smooth forms an upper limit for the actual particle diameter spherical particles. The actual particles are rough and present considerably larger drag forces, thus following since aberrations broaden images. All tracks studied had apparent diameters below 5 microns. the gas streams more cloyely.
272
LAMINAR COMBUSTION AND DETONATION WAVES
tracks in the sharpest focus we have reduced this error below 1 per cent 9.
ANALYSIS DATA OF
The original data are tables of coordinates and slopes of streamlines through the flame front together with gas composition, velocity, and initial temperature determinations. In order to convert these data into temperature profiles we must determine the pointwise density. This can be done by applying the hydrodynamic equation
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not available at the present writing the information in this report is supplied by fitting the final temperature to the calculated thermodynamic value (figs. 1 to 4). Andersen and Fein (7) found that applying this correction results in a maximum temperature within 40~ of the calculated value. These data together with a small linear (with perpendicular position in the flame front) compo-
(1) '~
this assumes that the product of the density, velocity, and cross-section measured normal to the luminous zone is a constant. Referring to figure 8
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FIG. 7. Flame temperature profile showing reducibility between successive pictures. it can be seen that the cross-section can be measured by using two adjacent particle tracks and utilizing the circular symmetry of the flame. The initial density is known from the composition, and the initial velocity from the flow rate and burner cross-section. The change in velocity is derived from the assumption that the burning takes place normal to the burning surface. This means effectively that the original gas velocity component parallel to the flame front remains almost unchanged. A precise measurement of the small change due to the effect of the tip is in process using stroboscopic illumination. Since the data is u A change of focal length of 0.5 mm noticeably broadened a fine line observed in the diametral plane of the nozzle. If a particle track 0.5 mm from the diametral plane were selected an error in the measurement of the tangent of one-half per cent would result. 10For a list of symbols used, see figure 8.
Fro. 8. Coordinates and symbols used in analyzing particle tracks: r0, rr--distance from center of flame to point 0 or r respectively; 00,0r--angle between tangent at point 0 or r respectively and the luminous zone; 6r----distance between adjacent streamfine measured parallel to the luminous zone; To, Tr--temperature at point 0 or r respectively; M0, M,--average molecular weight of point 0 or r respectively; Vo, V,I, Vo]--velocity of gas of points r or 0. Subscript indicates component perpendicular to the luminous zone; A--parallel velocity correction factor. sition correction are sufficient to allow a determination of the pointwise density through the flame front. Therefore, by applying the perfect gas law we can express the temperature at any point in the following way (4, 7):
Tr/To = po/pr M_.__,
(2)
Po/Pr -- Vr~_A , • Vo• do~_
(3)
Mo
For convenience, we choose to measure velocities and areas using coordinates orthogonal to the flame front. Since the distance between adjacent tracks in this coordinate system is constant and
TEMPERATURE PROFILES IN PROPANE-AIR FLAME FRONTS because of the circular symmetry of the flame, the cross-section of an infinitesimal streamtube is proportional only to its horizontal (in the laboratory coordinate system) distance from the center of flame.
p0/o,
-
vr 2- r , V0 2 -
(4)
s
The velocity component of the gas parallel to the flame front can be assumed to be constant except for a correction A whose maximum value was determined by direct velocity measurements and assumed to vary linearly. vr2- = v0 cos 00 (1 + AT) tan 0r
(5)
Combining equations (2), (4), and (5) ~/'~ = To e t n O0 t a n 0~ r~ (1 + At) M~
(6)
rather than liberated. The question of the rate of heat release is being investigated. In the region of the inner edge of the luminous zone the temperature begins to rise more sharply and continues to rise to a point just at or beyond the luminous zone where in the case of the rich mixture a sharp drop in temperature occurs. In the lean mixtures the drop was smaller n. This region is followed by a slow fall in temperature due to heat losses. The sharp temperature peak which occurs with rich mixtures just at the luminous zone seems to be greater than the theoretical maximum flame temperature, and the initial fall from this maximum is more rapid than can be accounted for by ordinary heat transfer. (Note that its log temperature vs. distance plot has a greater slope than the final value attained at distance further out.) After sufficient time had TABLE
M , is determined from a knowledge of the initial and final composition of the gas and the assumption that the average molecular weight of the gas changes linearly with perpendicular distance through the flame front.
1
Propane-air flame charaderislics I
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P
Max T
EquiL T Preheat - -
RESULTS
Analysis of the data yields a series of graphs of relative temperature with distance through the flame front. Graphs are presented for three compositions (~b = .93 thru ql = 1.1) at atmospheric pressure (figs. 1, 3) and three pressure (1.0 thru 0.6 atm) (figs. 2, 4). The results show a number of interesting similarities. All of the atmospheric pressure curves show nearly identical initial region of exponential temperature rise continuing to around 1100~ In the initial region the slope of the distance vs. temperature curves is a measure of the heat transfer rate. The measured value of the heat transfer for these gases is considerably larger than the calculated conductivity of an homogeneous gas. This indicates that a major mechanism for heat transfer in a flame is the diffusion. This observation is in accord with predictions of the theory of flame propagation developed by Hirschfelder, Curtiss and co-workers at the University of Wisconsin. Quantitative estimates of the heat flux effect are being made at the University of Wisconsin through the courtesy of Professor Hirschfelder. Following this exponential rise a break occurs in the temperature profile (this is best visualized on the semi-log plots of figures 3, 4). Here the temperature rise is slow. Heat may even be absorbed
273
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elapsed for the system to return to equilibrium the g a s temperature should rapidly approach the theoretical flame temperature and then fall slowly as the flame transfers heat to the outside. This point would be marked by an inflection in the temperature curve. This effect was predicted by Hirschfelder (14). The effect would be particularly pronounced in the rich flames where unburned fuel enters into the equilibrium adding pyrolysis products such as acetylene, hydrogen, methane, ethylene, carbon and hydrocarbon radicals. The effect of pressure on these curves is primarily an increase in the scale of distance. This can be seen from table 1, the overall thickness of the flame front and the thickness of the individual zones (preheat, reaction, and luminous zones) increases with inverse pressure. The maximum temperatures are slightly lower than those of n (Note added in proof) Present work in which velocities are measured directly using stroboscopic illumination indicates that the temperature peak following the luminous zone may be an artifact of the assumed linear variation of gas velocity component parallel to the flame front.
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
"~300
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TEMPERATURE
(
267
heating and reaction zones can also be calculated, and was found to be of the order of 10-3 sec, whilst the time of passage through the actual reaction zone was only about one quarter of this. The accuracy of these figures has been discussed by Dixon-Lewis and Wilson (1).
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(b) Hydrogen + air flame The refractive index gradients found for the 66.7 per cent hydrogen + air flame at 298 mm pressure are shown in figure 6 (curve 1). Here again, curve 2 is that for the pure thermal conduction case. The temperature distribution is shown in figure 7. The results, however, are of somewhat doubtful validity due to the experimental difficulties encountered, and to the small deflexions which had to be measured.
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ACKNOWLEDGEMENTS
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The author wishes to thank the Director of The Gas Research Board for permission to publish this work. He would also like to offer his very special thanks to Dr. A. G. Gaydon for the loan of a pump which made possible the measurements at low pressure. REFERENCE
1.5
I
DIST. FROM COLD SIDE (MM.) FIG. 7. Temperature distribution in a 66.7 per cent hydrogen + air flame at 298 mm.
1. D~xoN-LEwis, G., AND WILSON, M. J. G.: Trans. Faraday Soc., 47, 1106 (1951).
31
TEMPERATURE
PROFILES
IN P R O P A N E - A I R
FLAME FRONTS ~
By R. M. FRISTROM, R. PRESCOTT, R. K. NEUMANN, AND W. H. AVERY" As part of an extensive investigation of combustion in high velocity streams, a study is being made of the detailed temperature profile within the flame front of various propane-air flames. Results obtained provide basic experimental data for checking the validity of recent theories of flame propagation. Supplemented by information being furnished by concurrent programs, the data may be used to indicate the chemical kinetic relationship among pressure, temperature and composition in the flame zone. The specific problem of this research is the determination of the temperature profile (figs. 1 to LWork supported by NOrd 7386 with Bureau of Ordnance, U. S. Navy.
4) of a propane-air Bunsen flame as a function of the composition and ambient pressure. Since it was desirable to maintain a precision of 2 per cent or better and the temperature rises 2000~ in a distance of less than a millimeter (at atmospheric pressure) a method of great delicacy was required. For this reason the usual methods involving probes (1) or spectroscopic pyrometry (2) were discarded as being too coarse while the method of vaporizable particles (3) would have yielded an insufficient number of points. The method chosen for these studies is known as the particle track method (4, 5). It is based on an experimental method introduced by Smith (6) and extended by Lewis and yon Elbe (2). The first application of
268
LAMINAR COMBUSTION AND DETONATION WAVES
this technique to t e m p e r a t u r e profile m e a s u r e m e n t was made b y Andersen a n d Fein (7). The particle track technique uses the flame gases themselves as a gas t h e r m o m e t e r b y analyzing the streamline flow t h r o u g h the flame front. T h e
Phillips' Petroleum pure grade 99 mole per cent. D r y compressed air was used and as a n additional precaution cylinders were discarded as soon as their pressure fell below 600 l b s / i n ~. T h e moisture content should be below 0.1 per cent. 3000
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O~'rANC[ N O ~ L TO LUU*NOUSZ O N E ( ~
'%
FIG. 1. Flame temperature profiles of propane-air flames with various compositions at atmospheric pressure. [Absolute temperature (~ vs. distance normal to luminous zone (mm).] Arrows mark the limits of the luminous zones, X marks the point fitted to the thermodynamically calculated temperature. 9 = Fuel/Air/ Stoichiometric Fuel/Air.
o~
o.
o.
o.
o.
o.
o.
,o
,,
UISTANGE NORMALTO LUMINOUS ZONE{ram)
FIG. 3. Flame temperature profiles of propane-air flames with various compositions at atmospheric pressure. [Temperature rise (~ vs. distance normal to luminous zone (mm).] Arrows mark the limits of the luminous zones, X marks the point fitted to the thermodynamically calculated temperature. ~I, = Fuel/Air/ Stoichiometric Fuel/Air.
r
ZC~I
,/ /,/
i/"
I
r
J 2~
O59otm
02
04
OS
CtB
I,O
IZ
1.4
1.6
DISTANCE NORMAL TO LUMINOUS ZONE (ram)
FIo. 2. Flame temperature profiles of propane-air flames at several pressures. [Absolute temperature (~ vs. distance normal to luminous zone (mm).] Arrows mark the limits of the luminous zones, X marks the point fitted to the thermodynamically calculated temperature, cI, = Fuel/Air/Stoichiometric Fuel/Air. measurements have been refined until a precision of 2 per cent has been reached in the d e t e r m i n a t i o n of the t e m p e r a t u r e profiles.
02
04
0.6
08
10
IZ
1.4
~6
DISTANCE NORMAL TO LUMINOUS ZONE (mm)
FiG. 4. Flame temperature profiles of propane-air flames at several pressures. [Temperature rise (~ vs. distance normal to luminous zone (ram).] Arrows mark the limits of the luminous zones, X marks the point fitted to the thermodynamically calculated temperature. r = Fuel/Air/Stoichiometric Fuel/Air.
Apparatus EXPERIMENTAL
Materials The flames chosen for s t u d y were premixed propane-air B u n s e n flames. T h e p r o p a n e used was
The a p p a r a t u s used for these studies (fig. S) consists of a B u n s e n b u r n e r housed in a pressurized chamber with a n associated gas handling system. A particle separator and introducer is connected
TEMPERATURE PROFILES IN PROPANE-AIR FLAME FRONTS to the gas handling system and observations are made with a flash lamp illumination system and camera. The burner is a t/~,, nozzle with a constant velocity profile (8, 9) surrounded by a second nozzle which supplies a protective sheath of nitrogen. The gas handling system consists of a set of critical orifice flowmeters (9) regulated byPrecision Moore Regulators coupled with large volume plenum chambers which damp out high frequency pressure variations. Flows remain constant throughout a run to within 0.03 per cent. For
269
of the whole apparatus. The pumping system consists of two high capacity piston pumps (flow rates are of the order of 1 liter per second at one-half atmosphere). The particle introducer and separator (fig. 5) employs a 5-liter Wolff Bottle with the two outside necks containing copper inlet and outlet tubes. In the central neck 5 cm above the inlets is located a pad of steel wool saturated with fine MgO powder (U.S.P.). In operation the separator is cut off from the system by closing the stopcocks and a shower of particles initiated by rapping the central stopper with a plastic mallet. The particles
A. Photograph of apparatus: 1. Pressurized burner B. Block diagram of apparatus: a. Critical flow chamber; 2. Power supply and repetitive timer for pumping system; b. Gas bottles, plenum chambers and flash lamp; 3. Spark gap for starting burner; 4. Camera; plastic bag reservoirs; c. Pressure and flow metering 5. Oscilloscope camera; 6. Oscilloscope for monitoring systems; d. Burner; e. Optical system; f. Thermolight output; 7. Flash lamp; 8. Critical orifice flow- couple; g. Light monitoring system. meters; 9. Particle settling bottle; 10. Standard frequency calibrator. Fro. 5. Flame temperature profile apparatus work at one-half atmosphere, dry air is introduced from a plastic bag held at atmospheric pressure. The pressurized chamber (fig. 5) consists of sections of 10" diameter pipe. The burner section contains four windows to accommodate the camera, illumination system and access port. The interior is painted fiat black and flocked with black nylon fibers to kilt reflections. Pressure regulation within the chamber is accomplished by using critical flow inlet and outlet orifices which makes the rate of flow independent of the pumping speed, and the chamber pressure a function only of the influx of gas. Pressure can be maintained better than 0.3 per cent. The flame induced a slow drift in pressure which was attributed to heating
are allowed to settle under gravity for 30 seconds. Stopcocks are then opened to the air line and the suspended dust is carried into the system. A few seconds later particles enter the flame as indicated by a faint yellow glow due to sodium impurities. Illumination is provided by a pair of Sylvania 2340 flash tamps whose images are focused on the flame by a pair of 2" focal length-f/1.6 projector lenses. To provide light for streak photographs one lamp was excited by a 200 #fd bank of condensers charged to 2200 v. The condenser discharge is coupled to the lamp by an L-C network (fig. 5) which gives a sharp (0.2 millisec) initial pulse of energy followed after a delay of 0.2 millisecond by a longer pulse of 1 millisecond duration. To
270
LAMINAR COMBUSTION AND DETONATION WAVES
provide time markers for velocity determinations the other lamp is excited by three condenser discharges (0.67 ~fd at I0 kv) which are individually controlled by "trigertron" type spark gaps. Timing is accomplished by use of a circuit similar to that of Coles (10) and controlled by the camera shutter. The resulting illumination curve consists of four sharp fronted light pips separated by times which can be controlled by the timing circuits. (The usual spacing was 0.1 millisecond.) These are followed by a long duration (one millisecond) roughly constant light pulse. The tracks left by a moving particle illuminated by this system (fig. 6) allow a determination of gas velocities and gas streamlines through a flame front. An illuminator is being tested which will ~dlow a large number of measurements on the same streamline. The illumination curve for each flame
FIG. 6. Particle track pictures of propane-air flames. 1 attn. a. Left. q = 1.10 1.5 X 105 MgO particles per second b. R i g h t . . ~ 6 • 10~ MgO particles per second picture was monitored by a photo cell (GE-929 driven by 45 volts) whose output was displayed on an oscilloscope (Techtronix ~512) with a sweep calibrated by standard time pips furnished by a Rutherford calibrator which has been compared with the output of station W W V and found to be within 0.1 per cent of true frequency. Photographs of the light output curves were made for each picture with a Fairchild polaroid oscilloscope camera and times between light pips determined by measuring these photographs on a comparator. Accuracy was better than 1 per cent. For recording the data a 4" x 5" Nu Vue camera fitted with an f/2 125 mm Xenon special lens using a magnification ratio of four was employed. An Ilex 2" shutter is operated at 1[.5o second. Ansco Triple S Ortho film is preheated to 140~ and developed twelve minutes in D19. To improve the readability of the film', copies were made on contrast lantern slides. Care was taken to avoid
irregular film shrinkage 2 and measurements indicate it to have been held well below 1 per cent.
Data Analysis The films are read on a Jones and Lamson optical comparator. This instrument allows angular determination to -+l minute and a positional accuracy of 4-0.00005 inch. Tracks for measurement were chosen solely on a basis of their sharpness of focus ~ and the availability of an adjacent track (also in sharp focus) from which stream tube cross-sectional measurements could be made. This was possible because of the efficiency of the particle separator. DISCUSSION
OF
RELIABILITY O F MEASUREMENTS
The reproducibility of the measurements of flames with identical initial conditions varies from 1 per cent at 500~ to 2 per cent at 2000~ The experimental dispersion gave probable errors in angular measurement varying from 1-2 per cent and positional errors averaging 1 per cent. The absolute accuracy obtained depends upon the reliability of the assumptions made in the analysis. These will be discussed in the order of their importance. The first question which must be answered is whether there exists a temperature to be measured. Because of the rapidity of the reactions involved, vibrations and electronic degree of freedom do not always have sufficient time to come into thermal equilibrium with translation and rotation. Evidence of a similar effect in CO-O2 flames exists* and the problem is discussed by Gaydon (11). Regardless of these effects, however, at every point there will exist an effective translational temperature since this is essentially a measure of the root mean average translational energy. Further, if the distances with which we deal are large compared with the mean free path (10 to 100 times), this effective translational temperature will be very nearly that corresponding to a Boltzmann distribution of velocities, which is by definition the thermodynamic perfect gas temperature. At the pressures with which we are dealing the mean free path is of the order of 10 -5 cm and the smallest distance increment is 10- 3 cm, thereFilm was wiped dry with a chamois and dried in a humidified room. This criterion assured us that we were dealing with a streamline lying in the diametral plane. * S. Silverman, Amer. Phys. Soc. Meeting, Washington, D. C., May 2, 1952. The region of excess temperature in this system appears well beyond the luminous zone.
TEMPERATURE PROFILES IN PROPANE-AIR FLAME FRONTS
271
fore the temperature which is measured should be The problem of particle track visualization of essentially the equilibrium translational tempera- streamlines is treated by Wright (12) and his ture corresponding to the thermodynamic transtreatment was applied to this work by Mattuck lational temperature. No conclusions can be (13). These calculations indicate that a Stoke's drawn about the energy distribution among other law particle (see note) with a diameter smaller degrees of freedom without further evidence since than 5 microns will give a track whose tangent this may vary with each chemical species. will differ from the true streamline by less than 2 The second question concerns the effect of the per cent. As the pressure decreases the accuracy composition correction which is used. The meas- increases since the accelerations fall off with urements yield the relative gas density and, in pressure, but the viscosity remains unchanged. order to interpret the data in terms of temperature, Velocity lag due to gravity is less than 0.1 per the composition must be known. The initial and cent. The particle size was checked photographically final compositions are known but the intervening by comparing particle tracks with wires and changes can at present only be speculated upon. captured particles under comparable exposure To minimize this problem we have chosen for our conditions. It was demonstrated that we were present study some flames for which this correction indeed photographing particles smaller than 5/~ in is small (of the order of 3 per cent for an equiv- diameter. A similar conclusion was drawn from a alence ratio of 1.0). This comes about because of microscopic study of particles captured on a the high percentage of the nitrogen diluent in air greased slide, 7 and the width of the tracks on the flames and the choice of a reaction whose average pictures, s Further evidence is furnished by the molecular weight varies only slightly during its data which are self-consistent. course. Therefore, in order to attain the desired The fourth question concerns the effect of the precision of 2 per cent, only a crude estimation of particles on the flame reactions. Andersen and the composition change need be made. 5 The data Fein (7) noted that if too many particles are presented for rich flames are subject to correction introduced the flame velocity is decreased; they when reliable composition data become available. attribute this to the heat capacity of the particles. Work on this problem is progressing at this By improving the illumination system we were Laboratory. able to reduce the particle size and numbers Next in importance is the problem of how necessary, so that the heat capacity of the particles closely the particles actually follow the streamlines abstracts a maximum of 0.03 per cent of the total through the flame front. This is governed by the heat output of the flame. Upon introducing the relative importance of viscous drag and inertial particles we could detect no change in burning forces, and is described approximately by Stoke's velocity (as measured by the cone angle) or in the law which should give a lower limit for reliability3 appearance or shape of the flame front (fig. 6). Qualitatively, it can be seen that the smaller the. The assumption of hydrodynamic equations of particle the better the tracking will be. The lower incompressible flow is quite adequate for our limit of particle size that can be used is set by discussion since the streamlines are defined by the two considerations: the light reflected by a particle tracks and the velocities involved are well particle decreases quadratically with the radius, below that of sound. and secondly, at very small diameters motion There are a number of possible sources of error becomes erratic due to Brownian movement. In in the experimental techniques. Several aberrations practice, available illumination set the limit or could affect the optical system; if the position of usable particle size to a few microns in diameter. the focal plane varied from the diameter, or if it It was assumed that because of diffusion composi- were too broad, tracks of particles outside the tion changed in a linear manner with respect to position within the flame front. The reasons for expecting this diametral plane would appear in sharp focus. This approximation to be quite close are discussed by would result in a foreshortening of the track, the Hirschfelder in Univ. of Wise. CM-600, The Theory angles would be too low and the maximum angle of Flame Propagation III, p. 48. This region was aswould occur too soon. By studying only those sumed to extend from the point at which a temperature rise was first detected to the outer edge of the luminous 7 Particle sizes ranged from 1/~ to 10 ~. Zone. s The apparent diameter of a track on the film ~This is because Steke's law describes smooth forms an upper limit for the actual particle diameter spherical particles. The actual particles are rough and present considerably larger drag forces, thus following since aberrations broaden images. All tracks studied had apparent diameters below 5 microns. the gas streams more cloyely.
272
LAMINAR COMBUSTION AND DETONATION WAVES
tracks in the sharpest focus we have reduced this error below 1 per cent 9.
ANALYSIS DATA OF
The original data are tables of coordinates and slopes of streamlines through the flame front together with gas composition, velocity, and initial temperature determinations. In order to convert these data into temperature profiles we must determine the pointwise density. This can be done by applying the hydrodynamic equation
p~v~ar
povoao
=
=
const.
not available at the present writing the information in this report is supplied by fitting the final temperature to the calculated thermodynamic value (figs. 1 to 4). Andersen and Fein (7) found that applying this correction results in a maximum temperature within 40~ of the calculated value. These data together with a small linear (with perpendicular position in the flame front) compo-
(1) '~
this assumes that the product of the density, velocity, and cross-section measured normal to the luminous zone is a constant. Referring to figure 8
~*
93 P,l~m
3000
-
I000 ~:'0 t. moo
/
LUMINOUS ZONE
I
/
Yr
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soo
ro
~ soo ~,oo
I
.~. . .,FtLMr .......
i
ZOO
I too oz
I 03
04
05 06 or oe og O~$TANCENORMALTOLUMINOUSZONE(ram)
Do
FIG. 7. Flame temperature profile showing reducibility between successive pictures. it can be seen that the cross-section can be measured by using two adjacent particle tracks and utilizing the circular symmetry of the flame. The initial density is known from the composition, and the initial velocity from the flow rate and burner cross-section. The change in velocity is derived from the assumption that the burning takes place normal to the burning surface. This means effectively that the original gas velocity component parallel to the flame front remains almost unchanged. A precise measurement of the small change due to the effect of the tip is in process using stroboscopic illumination. Since the data is u A change of focal length of 0.5 mm noticeably broadened a fine line observed in the diametral plane of the nozzle. If a particle track 0.5 mm from the diametral plane were selected an error in the measurement of the tangent of one-half per cent would result. 10For a list of symbols used, see figure 8.
Fro. 8. Coordinates and symbols used in analyzing particle tracks: r0, rr--distance from center of flame to point 0 or r respectively; 00,0r--angle between tangent at point 0 or r respectively and the luminous zone; 6r----distance between adjacent streamfine measured parallel to the luminous zone; To, Tr--temperature at point 0 or r respectively; M0, M,--average molecular weight of point 0 or r respectively; Vo, V,I, Vo]--velocity of gas of points r or 0. Subscript indicates component perpendicular to the luminous zone; A--parallel velocity correction factor. sition correction are sufficient to allow a determination of the pointwise density through the flame front. Therefore, by applying the perfect gas law we can express the temperature at any point in the following way (4, 7):
Tr/To = po/pr M_.__,
(2)
Po/Pr -- Vr~_A , • Vo• do~_
(3)
Mo
For convenience, we choose to measure velocities and areas using coordinates orthogonal to the flame front. Since the distance between adjacent tracks in this coordinate system is constant and
TEMPERATURE PROFILES IN PROPANE-AIR FLAME FRONTS because of the circular symmetry of the flame, the cross-section of an infinitesimal streamtube is proportional only to its horizontal (in the laboratory coordinate system) distance from the center of flame.
p0/o,
-
vr 2- r , V0 2 -
(4)
s
The velocity component of the gas parallel to the flame front can be assumed to be constant except for a correction A whose maximum value was determined by direct velocity measurements and assumed to vary linearly. vr2- = v0 cos 00 (1 + AT) tan 0r
(5)
Combining equations (2), (4), and (5) ~/'~ = To e t n O0 t a n 0~ r~ (1 + At) M~
(6)
rather than liberated. The question of the rate of heat release is being investigated. In the region of the inner edge of the luminous zone the temperature begins to rise more sharply and continues to rise to a point just at or beyond the luminous zone where in the case of the rich mixture a sharp drop in temperature occurs. In the lean mixtures the drop was smaller n. This region is followed by a slow fall in temperature due to heat losses. The sharp temperature peak which occurs with rich mixtures just at the luminous zone seems to be greater than the theoretical maximum flame temperature, and the initial fall from this maximum is more rapid than can be accounted for by ordinary heat transfer. (Note that its log temperature vs. distance plot has a greater slope than the final value attained at distance further out.) After sufficient time had TABLE
M , is determined from a knowledge of the initial and final composition of the gas and the assumption that the average molecular weight of the gas changes linearly with perpendicular distance through the flame front.
1
Propane-air flame charaderislics I
4,
ZONE THICKNESSES
! [
P
Max T
EquiL T Preheat - -
RESULTS
Analysis of the data yields a series of graphs of relative temperature with distance through the flame front. Graphs are presented for three compositions (~b = .93 thru ql = 1.1) at atmospheric pressure (figs. 1, 3) and three pressure (1.0 thru 0.6 atm) (figs. 2, 4). The results show a number of interesting similarities. All of the atmospheric pressure curves show nearly identical initial region of exponential temperature rise continuing to around 1100~ In the initial region the slope of the distance vs. temperature curves is a measure of the heat transfer rate. The measured value of the heat transfer for these gases is considerably larger than the calculated conductivity of an homogeneous gas. This indicates that a major mechanism for heat transfer in a flame is the diffusion. This observation is in accord with predictions of the theory of flame propagation developed by Hirschfelder, Curtiss and co-workers at the University of Wisconsin. Quantitative estimates of the heat flux effect are being made at the University of Wisconsin through the courtesy of Professor Hirschfelder. Following this exponential rise a break occurs in the temperature profile (this is best visualized on the semi-log plots of figures 3, 4). Here the temperature rise is slow. Heat may even be absorbed
273
]
.93 1.04 1.10 1.12 1.39 -
aim
1 1 1 .76 .59
R e a c - ~L u m i tion nous
I
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2500 2610 2700 2295 2010
2200 2310 2300 2250 1990
#tin
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.42
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15
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.16 .24 .27
.51 .61
mm
elapsed for the system to return to equilibrium the g a s temperature should rapidly approach the theoretical flame temperature and then fall slowly as the flame transfers heat to the outside. This point would be marked by an inflection in the temperature curve. This effect was predicted by Hirschfelder (14). The effect would be particularly pronounced in the rich flames where unburned fuel enters into the equilibrium adding pyrolysis products such as acetylene, hydrogen, methane, ethylene, carbon and hydrocarbon radicals. The effect of pressure on these curves is primarily an increase in the scale of distance. This can be seen from table 1, the overall thickness of the flame front and the thickness of the individual zones (preheat, reaction, and luminous zones) increases with inverse pressure. The maximum temperatures are slightly lower than those of n (Note added in proof) Present work in which velocities are measured directly using stroboscopic illumination indicates that the temperature peak following the luminous zone may be an artifact of the assumed linear variation of gas velocity component parallel to the flame front.
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