A method of analysis of a plane combustion wave

294

LAMINAR COMBUSTION AND DETONATION WAVES 3. GILBERT, M.: Memorandum No. 4-51. Pasadena: Jet Propulsion Laboratory, July 6, 1949. 4. HIRSCRFELDER, J. 0., BIRD, R. B., AND SPOTZ, E. L.: Chem. Rev., 44, 205-231 (1949). 5. SCH~IDT,H.: Annal. Phys., 29, 971-1028 (1909). 6. GAYDON,A. G., ANDWOLFHAm),H. G. : Proc. Roy. Soc. (London), A194, 169-184 (1948). 7. GAYDON,A. G., ANDWOLrHAm),H. G.: Proc. Roy. Soc. (London), A199, 89-104 (1949). 8. GAYnON,A. G., ANDWoLFnARD,H. G.: Proc. Roy. Soc. (London), A201, 561-569, 570-586 (1950). 9. GAYDON,A. G., AND WOLFHARD, H. G.: Proc. Roy. Soc. (London), A208, 63-75 (1951). t0. PENNER, S. S., GILBERT, M., AND WEBER, D.: J. Chem. Phys., 20, 522 March (1952). 1l. BROIDA, H. P.: J. Chem. Phys., 19, 1383-1391 (1951). 12. MCADAMS, W. H.: Heat Transmission, 2nd ed. New York, McGraw-Hill Book Company (1942). 13. GLASSTO~q~,S., LA1DLER, R. J., AND EYING, H.: The Theory of Rate Processes, 1st ed. New York, McGraw-Hill Book Company (1941). 14. Vim~s, R. F.: The Platinum Metals and Their Alloys. New York, International Nickel Company (194l). 15. American Institute of Physics: Temperature, Its Measurement and Control in Science and Industry. New York, Reinhold Publishing Company (1941). 16. KENIqARD,E. H.: Kinetic Theory of Gases, 1st ed. New York, McGraw-Hill Book Company (1938). 17. WisE, H., AND ALTMAN,D.: The Interaction of Gases with Solid Surfaces, a Theoretical Analysis of the Thermal Accommodation Coefficient, Memorandum No. 9-18. Pasadena: Jet Propulsion Laboratory, June 2, 1950. 18. DEVONSItlRE, A. F.: Proc. Roy.. Soc. (London), A158, 269-279 (1937).

A value was obtained for h from the data for several wires, and an average was derived for the thermal conductivity ks in the flame film around the wire. A value of 0.069 Btu/hr ft ~ + 4 per cent was deduced for kf. This value of kf, representing the thermal-conductivity coefficient to a surface from a dissociated flame mixture, suggest unexpected but not unreasonable behavior possibilities for the components of the flame mixture. A possibility is a small accomodation coefficient for H, O, and OH at the platinum surface, whereas the other species accommodate more or less fully. When carefully used, the method is promising for further study of the gradient region of the reaction zone of the flame if materials suitable in regard to their emissive, catalytic, and temperature-resistance properties are used. ACKNOWLEDGMENT

The authors are happy to acknowledge some provocative discussion with Professor H. S. Tsien, of the California Institute of Technology, in stimulating this research. Valuable discussions with Dr. David Altman, Dr. S. S. Penner, and Mr. Leo Davis, all of the Jet Propulsion Laboratory, contributed to the theoretical and experimental aspects of the research. REFERENCES 1. GILBERT, M.: Report No. 4-54. Pasadena: Jet Propulsion Laboratory, August 30, 1949. 2. KLAUKENS,H., AND WOLI~'fIARD,H. G.: Proc. Roy. Soc. (London), A193, 512-524 (1948).

34

A METHOD OF ANALYSIS OF A PLANE COMBUSTION WAVE By .l.H. BURGOYNE AND F. WEINBERG The question of the mechanism of flame propagation in gases has received a great deal of theoretical consideration, which has resulted in equations, or systems of equations, aiming to represent the processes causing the gases to react under the influence of the adjacent combustion zone. Various factors have been thought of as being

the most important in this process of initiation; thus, while the earlier theories postulated a purely thermal mechanism, subsequent workers thought that the initiation by diffusing active radicals or even by quanta of radiation (1) might be of major importance. Some attempts have also been made at forming general theories including all possible

METHOD OF ANAI.YSIS OF PLANE COMBUSTION WAVE factors, but mathematical difficulties and insufficiency of data have made complete solutions impossible without drastic approximations. Since it appears probable that in reality all the processes mentioned above play some part in the propagation of the flame, an experimental method of analysis of combustion waves seems to be called for, not primarily to verify or disprove any particular theory, but rather to render theories unnecessary by providing a complete solution. It is the purpose of this work to establish such a method of analysis. THEORETICAL CONSIDERATIONS In order to analyse a flame, the changing magnitude of one or several variables must be followed throughout the combustion wave. It will be shown

295

function of y since it varies with both temperature and composition. The second term represents the change due to mass flow, where M is the burning velocity in m a s s / s e e / u n i t area (so that M = pv = constant where p = density and v = linear velocity), c is the mean specific heat at constant pressure between 0 ~ and T and is again a function of y. The third term represents the ehange due to reaction, Q being the heat of reaction (assumed constant) and 9 the fraction of the total reaction completed at y. 21,,@9 represents the summation of Qe if n reactions are taking place. Finally, the fourth term represents the change due to radiation, R being the radiant flux at 3'. In this form the equation can be integrated. If the suffix 0 denotes conditions at a value of y

T L DIRECTION

OF"

~

GAS

FLOW

.,V Fla. 1. General form of temperature distribution curve. that a measurement of the temperature distribution throughout the flame is adequate for the purpose. Consider an infinite plane flame-front such that grad (V), V being any one of the variables, is at all points perpendicular to it. The temperature (T) distribution will be of the general shape shown in figure 1, y being the distance co-ordinate. Assuming only that a steady state has been reached, the following equation results:

before reaction or temperature rise has commenced (in practice, of course, this is at some finite value not very far removed from the flame-front) then, integrating between y0 and any y gives:

0T

M (Tc -

+ MZ.O.,.

0

OR

(x)

The four terms represent the four possible factors that might alter the heat content, The first term represents the change due to conduction; k is the conductivity at y and is a

+ (R - Ro) = 0

(2)

Since /T\[O~_} = 0 \ o y l Yo

+ M ~ Z.Q.~o + - ~ = o

To Co)

a n d all

Euo = O.

To simplify the following discussion on the interpretation, this equation will be used as:

k OT_T _ M ( T c Oy

Toco) + MQ~ = 0

(3)

This simplification is not a mathematical necessity, since if radiation and kinetic data were known,

296

LAMINAR COMBUSTION AND DETONATION WAVES

the subsequent method would need little modification. However, the omission of the last term is in itself a most justifiable step. (R - R0) represents the difference in radiant flux between y and y0. Due to the small absorption and emission coefficients of gases and due to the T 4 emission law (so that the significantly radiating zone is narrowly confined) the factor (R - R0) must be extremely small in the pre-ignition zone. This, of course, does not mean that radiation may not be important in initiating the reaction, but merely that it is a very minor heat transfer factor within the region of particular interest. The substitution of Q~ for ~,,Q,~,~requires some discussion. In this work reaction is defined by the amount of "available" heat released. It is therefore important that, if (a) several reactions take place, (b) their heats of reaction differ, (c) the proportions between them are not exactly known, then considering all the molecules in the gas stream, there should be no spatial distribution between the several steps. Thus, substituting Qe for E.Q,~, is equivalent to assuming that the release of a certain fraction of the heat of the overall reaction is indicative of the completion of the same fraction of that reaction. Since complete reaction data are not generally available, some reaction must be chosen which fulfills this condition, to which end it is perhaps safest to employ a reaction in which no stable intermediates at all are formed. The reaction between carbon monoxide and oxygen has been suggested. Using the equation (3) the temperature distribution may now be interpreted in the following manner. The burning velocity M is measured simultaneously, a value of Q is assumed and so is also the ability to calculate k and c at any temperature and for any composition. Of these, the calculation of k presents some difficulties and some work has been done on this subject which will be outlined later. Mathematically, the problem consists of expressing T as a function of y, k and c as functions of e and T, substituting these functions into equation (3) and solving for E in terms of y. The method of interpretation is one of graphical successive approximations. As a first approximation, k and c are assumed to be constant. To obtain effective mean values for these, the effective mean temperature is calculated from the

T-ygraph(=(fTdy/fdy)=

area under

graph, divided by distance over which this area ex-

tends) and the effective mean is at first assumed to be say 0.5. The corresponding values of k and c are calculated, and using the equation (3) and the temperature distribution graph, e is plotted against y. From this graph a better value of the mean i is obtained and this procedure may be repeated until the ~ curve is obtained as accurately as the assumption of the constancy of k and c will permit. However, this assumption is now clearly no longer required since k and c can be calculated for each value of y from an exact T y and an approximate e , . This procedure can again be repeated until as accurate an ~ curve as desired is obtained. Many repetitions should not be required, however, since the variations of k and c are of such an order as usually to have been neglected altogether in the past. A knowledge of the T and ~ distributions constitutes a complete analysis of the flame. Graphs of concentration changes due to reaction against distance and temperature can be plotted directly and since p is now determined, the velocity can be computed using pv = M, and hence the distance coordinate in any of the graphs can be changed to a time (t) coordinate, enabling graphs of (d~/dt) against temperature, time or concentrations to be drawn. THERMAL CONDUCTIVITIES The problem of the calculation of thermal conductivities may be resolved into two parts: (a) the variation of conductivity with temperature for the pure constituents; and (b) the calculation of conductivities of mixtures of gases, those of the constituents being known. Of these, part (a) is of less urgency, for an appreciable amount of information is available. Concerning part (b), however, there is little information. I t appears that the variation of conductivity with composition for a ternary mixture of gases has never been investigated experimentally, and even for binary mixtures, existing theoretical treatments are either complex or inaccurate. A tentative method of calculation of conductivities of mixtures has however been developed and the procedure for a binary mixture (the conductivity of whose constituents are kl and k2) will be outlined. A more detailed publication elsewhere is contemplated. I t appears that, in the absence of molecular associations, the limit of homogeneity of a mixture would be represented by a system in which the conductivities are additive by volume, whilst the

METHOD OF ANALYSIS OF PLANE COMBUSTION WAVE most heterogeneous limit is that in which the reciprocals of the conductivities are additive by volume. Following this assumption, if n represents the volume percentage of the constituent whose conductivity is k2, the conductivity of the mixture must lie between the curves given by k~ = m n -F c where

m--

kl -- k2 100

and

A kb -- - nq-B

where

A -

and

B =

and

c = k~

100k~ k2 kl -- k~ 100k2 lcl - k_~

It has been found that k = (ka + kb/2) provides a fairly close approximation which coincides with the experimental curve in at least three points for the cases tested. I t has been further shown that the maximum possible error depends only on k~/k~, @i > k2) and must be less than 6 per cent for &/k~ < 2 and less than 14 per cent for l,'~/k2 < 3. In practice, the error has been found to be much less than these limits. Thus, for example, in the case of hydrogen/oxygen, for which kl/k2 ~ 5.6, the error does not exceed 11 per cent at its maximum value; whilst for carbon monoxide/oxygen ]q/k2 does not exceed 1.6. This error is well within the limits imposed by the inaccuracies in the determination of kl and k2 themselves. M E A S U R E M E N T OF T E M P E R A T U R E D I S T R I B U T I O N

The problems involved Jn the measurement of temperature distribution in flames are formidable. There are, first of all, purely theoretical difficulties. It is possible that in combustion processes thermodynamic equilibrium between the various forms of energy has not time to be established. If this were so, the magnitude of the temperature would depend on its definition. The difficulty is least likely to arise with slow flames, as used in the present work. In the fundamental equation the temperature should be defined in terms of the kinetic theory. Purely practical difficulties also exist. Even when a flame which closely approximates the onedimensional model has been produced, the very steep temperature gradient extending over such a

297

small distance renders accurate measurement difficult. Since several readings must be taken within that small distance and since due to the steep gradient, a small error in distance corresponds to a large difference in temperature, it becomes necessary to locate very accurately the position at which a reading is taken. This is not only extremely diffficult mechanically but the flame fluctuation itself may be comparable with the permissible error in location. Some means of producing a map of the instantaneous temperature distribution is called for. A thorough review of possible methods of high temperature measurement in gases has been made. Broadly speaking, the methods may be subdivided into three classes: those employing some material thermometer (including suspended particles) ; those using some emission from the flame; and those based on some property of the gas, such as density, refractive index or velocity of sound. Of these, the last was thought to be the least objectionable theoretically and the most suitable mechanically. The difficulty arising in the use of some property of the gas, however, is that the latter usually depends on composition as well as on temperature, and so varies due to reaction. I t is necessary then that this variation with composition can be calculated exactly. Thus, for instance, thermal conductivity would not be satisfactory. I t is further desirable that the variation with composition should be relatively small so that a simple correction may be applied subsequently from the "e curve". On the basis of such considerations, refractive index was chosen as the most suitable property. I t can be measured to a high degree of accuracy by methods such as interferometry. Moreover, the use of a beam of light as a probe offers the possibility of producing an instantaneous map of refractive index ~ ) distribution by means of a photograph. Finally, the variation due to composition change is generally small in comparison with the temperature variation. The choice of a suitable flame remains. A burner rather than a propagating flame is needed since it ensures steady flow conditions as well as comparative ease of observation. The flat flame burner of Powling (2), as modified by Egerton and T h a b e t (3), has been used up to the present, for the following reasons. The flame is a flat stationary disc--a close approximation to the one-dimensional model - - a n d the measurements, including corrections for variations from that model, are rendered easy

298

LAMINAR COMBUSTION AND DETONATION WAVES

by the accessibility of all its zones due to the absence of curvature. The flame is formed away from any solid boundary and is not in contact with any part of the burner. Due to the simple geometrical shape, the flame is particularly suited to the measurements of burning velocities which are needed for the interpretation: in fact the burner was originally designed for this purpose. Finally, the burner is used with limit mixtures having very low burning velocities. The consequent spreading out of all the zones is a factor which greatly reduces the difficulties, errors and corrections of the method of analysis. M E A S U R E M E N T OF R E F R A C T I V E I N D E X D I S T R I B U T I O N

The practical problem is now reduced to the measurement of a refractive index distribution along the axis of a cylinder of gas. Two types of method have been used: interferometry and methods based on the deflection of a light beam by the refractive index gradient.

Fro. 2. Plan of interferometer The principle of the interferometric method is, briefly, as follows. If the slit of an interferometer is placed at right angles to the plane of the flame, and if a path-difference is established in the flame, then due to the variation of # along the slit, this path-difference varies, resulting in curved fringes. These fringes can be photographed and the curves are some function of the refractive index distribution, subject to certain corrections. The usual kind of interferometer used for similar purposes is a 4-mirror Mach-Zehnder type, but some simpler, quicker and less expensive device was sought, particularly since difficulties were anticipated due to beam deflection. The arrangement shown in figure 2, based on interference at a double slit was used; it employs the principle of the Rayleigh refractometer. The source A was a high pressure mercury arc whose light was concentrated by the condenser lens B on to the pin-hole C at the focus of the collimating lens D. A pin-hole must be used instead of a slit in order to produce a beam parallel in all directions. The focal length of D was 100 cm since a highly parallel beam was required without further reducing the size of the hole. The beam was split

by the double-slit E of adjustable width and separation and passed through the flame F, to be collected by G, the long-focus objective of the eyepiece or photographic plate at I. H was a Wratten No. 22 filter transmitting only the yellow lines of mercury. As shown in the diagram, both beams of light pass through the flame but due to the latter's circularity the paths in the flame differ in length and this path difference varies with # along the slits. The sensitivity can thus be altered by moving the flame laterally with respect to the slits, or by altering the separation of the slits. The deflection of the light at right angles to the plane of the diagram by the refractive index gradient proved very troublesome in the pre-ignition zone. In the zones of no immediate relevance to the present work, for instance above the flame, satisfactory results were obtained, but where the steep refractive index gradient occurred, striation effects in the field of view made interpretation difficult. This is unfortunately inherent in any interferometric method, since in order that each ray can give information regarding the zone traversed, a very parallel beam must be used. In such a beam every ray is deflected in exactly the same way as any other ray under the same conditions, thus giving rise to bands of no light at all and others of excess intensity. Since the deflection of the beam proved to be of such considerable magnitude its use for the determination of the refractive index distribution was a fairly obvious next choice. The deflection arises as a result of the bending round of the incident wavefront due to the variation of the velocity of light in the gases. The equation governing this bending is 1/R = ( g r a d ~ ) / # ) . s i n 0 where R is the radius of curvature of the beam and 0 is the angle between the beam and the direction of grad (~). In the case of gases ~ _~ 1 and for the one-dimensional case this reduces, for small angles, to (dZy/dx 2) = (d#/dy) where (x, y) are the coordinates of the path of a ray such that y is perpendicular to the flame front. By the use of this equation, the variation of the deflection can be translated into a distribution of the quantity (d~/dy) from which tile distribution of ~ can be obtained by graphical integration. The arrangement shown in figure 3, employing this principle, was tried first. Part P again represents a means of producing a beam of accurately parallel light (in all directions) entering the burner Q and being brought to a focus by lens R in the plane of the slit, which is

METHOD OF ANALYSIS OF PLANE COMBUSTION WAVE perpendicular to the plane of the diagram. This dit can be moved in a vertical direction by means of a screw. In the absence of a flame, R would produce an image of the pin-hole but due to the deflection by the flame this image is spread out to a vertical line. On viewing or photographing the flame from T, through the slit, one or two bright lines appear. These are the loci of points in the flame which give rise to the particular angle of deflection determined by the position of S and

P

0

FIG. 3. First deflection method : elevation AI,

FIG. 4. General form of ~ and

(d~/dy) distribution

Curves.

the focal length of R. The refractive index distribution is of the form shown in figure 4a and the deflection at any point in the flame is approximately proportional to the value of d#/dy at that point. Thus if the slit is in the plane of the undeflected beam, the field of view is all bright except for a central dark band extending over all the parts of the flame where some deflection takes place. As the slit is moved lower, some particular value of du/dy is selected by its position and two bright lines appear in the flame corresponding to the two values of y (fig. 4b). The movement downwards

299

of the slit is continued and the separation between the two lines decreases until they coalesce at the position of maximum deflection. The method then consists of taking a number of photographs for various known positions of the slit and locating the positions of the bright lines with respect to some fixed point in the flame. This is really a quantitative Schlieren method and it appears particularly suitable for use in conjunction with the interferometric method, since it is merely necessary to replace the eyepiece of the latter method by the adjustable double slit rotated through 90 degrees to convert it to the former. Furthermore the two methods are somewhat complementary as the deflection method is most sensitive just in those parts of the flame where the interferometer becomes difficult to use. The combination of these two should provide a relatively simple tool for following refractive index changes in all parts of the flame. A difficulty with this method, as applied to the present work, however, arises from flame movements. It was found that even the lining up of the flame with the crosswires of a fixed telescope before each photograph was not a sufficiently sensitive criterion of position. The method, however, still retains its advantage of visual location within the flame of the zone of any particular value of (dtz/dy) (approximately). Thus, for instance by using the position of zero deflection it is possible to photograph directly, with very simple equipment, the zone over which # varies. (The slit can be replaced by a blind.) This measurement is not subject to any error since the light passed has not undergone deflection. For the purpose of the work in hand, however, a method registering the refractive index distribution instantaneously seemed necessary. To this end the following method has been devised. If a beam of accurately parallel light is incident to a slit, it will give rise to an image of it anywhere beyond the slit, with unit magnification, (provided the slit is not too narrow, to avoid troublesome diffraction effects). If such a slit is now placed before the flame and diagonally across it (fig. 5) some of the light will be deflected, according to its position in the flame, and the image will be curved as shown. The deflection at any point is equal to the vertical displacement of the straight slit image at that point divided by the distance of the screen (or plate) beyond the flame. The sensitivity of the method can be varied by altering the inclination of the slit and by changing the separation between the flame and the screen.

300

LAMINAR COMBUSTION AND DETONATION WAVES

Using a photographic plate, an exposure with and without the flame can be made using the same plate. This gives rise to an image as shown in figure 6a on which, of course, the dimensions are the same as in the flame. Finally, if instead of a single sIit, a screen with parallel slits is used, an image as shown in figure 6b results. The refractive index distribution can then be obtained instantaneously and simultaneously in as many regions as there are slits, all the data for the associated corrections being obtained from the same photograph.

of flame) but is f0 L f(#)

dL. This

may be corrected

from the horizontal variation obtained by the use of multiple slits, for if a graph is plotted of the measured # against distance from the axis for a particular value of y the ratio of (true #) to (measured/z) is the ratio of ~ at the axis to the mean # from the graph.

C O L L I M J T t NG

~

SLIT

. , . . . ~ F L A M I[

SCRttN OR PHOTOG~APMtr pI.A'r c

FIG. 7. Single slit image: lower limit ethylene-air flame.

I

FIO. 5. Second deflection method

I

6r

I/I//////d-P////// (a)

(to)

FIG. 6. General form of deflected slit images

The complete theory of the method has been worked out: the corrections to be applied are, briefly, as follows: 1. Correction due to deflection of beam in the flame. Since the beam is deflected already in the flame, it traverses zones of varying values of (d#/dy). The path of the beam in the flame is in fact not linear but approximates to a parabola. In the case of the slow flames used a very simple correction for the difference arising between the effective and observed positions of the beam in the flame has been proved adequate. 2. Radial variations. Under this heading the following factors may be included: deviations of flame from flatness, possible cooling at the edges of the flame and the warming up of surrounding gases. In practice this means that if the deflection per unit length of path in the flame is = f(>), the total deflection is not L.f(#) (where L = width

O2

oa

06

FIG. 8. Refractive index curve: derived from figure 7.

V~ gradient

distribution

3. Due to the fact that the slit is inclined, the flame width varies somewhat along the slit. This can be easily corrected from the geometry of the flame. 4. The finite width of the slits is comparable with the dimensions of the zone measured. It has been proved that if measurements are taken from the centre of the image, no serious error can be introduced provided the slit is reasonably narrow. 5. Finally it has been shown that the error due to the horizontal deflection occasioned by the lenseffect of the circular flame is negligible. The method has been tested for a lower limit

301

METHOD OF ANALYSIS OF PLANE COMBUSTION WAVE ethylene-air flame using a single central slit. The curved image obtained is shown in figure 7. The photographic plate was read by means of a travelling microscope and interpreted, yielding the curves of (dta/dy) and Ix against y shown in figures 8 and 9. As has been mentioned earlier, the wide zone of varying g is due to the low burning veloci-

the curves at which the gradient was equal to the slope of the straight slit. It can be shown that this must be the position of maximum deflection. The corresponding points on the straight lines were joined, and it was found that, as can be seen from figure 11, the deviation from the one-dimensional model is a small fraction of the height over which # varies. This method of measuring the variation in the refractive index throughout the flame has proved most satisfactory and work on its use for flame analysis is at present continuing.

FiG. 11. Tracing: enlargement of figure 10. ACKNOWLEDGMENT 20

o!2

o, I

o~I

o,I

,to.

t!2

FIG. 9. Refractive index distribution curve: derived from figure 8.

The work referred to in this paper is being carried out in the Department of Chemical Engineering and Applied Chemistry, Imperial College, London, S.W. 7, as part of the extramural research programme of the Department of Scientific and Industrial Research and Fire Offices Committee Joint Fire Research Organization, and is published by permission of the Director. The authors are indebted to Professor Sir Alfred Egerton, F.R.S., for facilities and advice with regard to the flat-flame burner technique. REFERENCES l. SCHORPIN,S. N.: Izvest. Akad. Nauk., S. S. S. R., 7, 995 (1950) 2. POWLING, J.: Fuel, 28, 25 (1949). 3. EGERTON, SIR ALFREO, AND THABET, S. K.: Proc. Roy. Soc, A211, 445 (1952).

FIG. 10. Multiple slit image: lower limit ethyleneair flame. ties (of the order of 5 cm/sec). Multiple slits were also used to ensure that the radical effect is a relatively small error which can be effectively dealt with by means of correction (2). The calculation has not been carried out for each slit, but the photograph (fig. 10) was enlarged and the centres of the images were traced. On this tracing (fig. 11) the locus of points at which maximum deflection occurs was plotted by finding points on

DISCUSSION BY EDWARD BURKE*

The experimental methods described in this paper are most ingenious. However, several questions arise in connection with the technique employed: (1) An optical method such as this requires a flame which is extremely flat, (say to within 1/~0 of its thickness) if the points plotted in Fig. 9 are to have any real significance. From work (tone by us, but not yet published, it appears that the flames produced by a Powling-type burner, while remarkably flat, do not * Research Laboratories, Corp., East Pittsburgh, Pa.

Westinghouse

Electric

302

LAMINAR COMBUSTION AND DETONATION WAVES they consider that it represents the relative proportions of reactants and products at any point in the reaction zone. On the other hand, as used in their basic differential equation, e represents the proportions of reactants and products in the gases flowing across an imaginary plane normal to the direction of flow; this plane being located in the reaction zone. But, the proportions of reactants and products flowing across a plane are not the same as the proportions in the gas at the plane, since products are diffusing upstream and reactants are diffusing downstream. These diffusion flows are superimposed on the mass flow and are of the same order of magnitude in the region of the most intense reaction. Unless these diffusion flows are taken into account, the analysis of the above authors will be seriously in error This diffusion flow problem has been discussed by Semenov, Zeldovich, and Frank-Kamenetsky~, by Friedman and Burkew and byHirschfelderand Curtiss**.

satisfy this extreme criterion. In this connection it should be mentioned that temperature traverses with a thermocouple are subject to far less stringent requirements. (2) In the zone of gas surrounding the flame (i.e. beyond the edge of the burner) there will be considerable temperature gradients, (with a good deal of turbulence) and the path of the light rays will inevitably be disturbed. One cannot dismiss this boundary zone on the grounds that it is perhaps only a quarter as thick as the diameter of the flat flame, since the gases in this zone are at a moderately low temperature, and consequently a given temperature gradient will alter the refraction of the light far more than a comparable gradient in the hot gases of the flame itself. (3) Figs. 7 and l0 indicate that the slit width is about ~ 0 of the flame thickness, whereas it would appear necessary for results of acceptable accuracy that the slit width be less than 1/~00 of the flame thickness. DISCUSSION BY RAYMOND FRIEDMANt

:~ Cf. N. N. Semenov, N.A.C.A. Tech. Memo. 1026, Sept. 1942. w R. Friedman and E. Burke, Jour. Chem. Physics 17, 667, 1949. ** J. O. Hirschfelder and C. F. Curtiss, .[our. Chem. Phys. 17, 1076, 1949.

The authors of this paper have allowed the parameter to represent two different things. On the one hand, tWestinghouse Research Laboratories, East Pittsburgh, Pa.

35

FLAME VELOCITIES OF HYDROCARBON-OXYGENNITROGEN MIXTURES By GORDON L. DUGGER A~cDDOROTHY D. GRAAB

INTRODUCTION

D a t a for gaseous h y d r o c a r b o n fuels h a v e already shown the marked effect of the percentage of oxygen in oxygen-nitrogen mixtures on m i n i m u m ignition energy, blow-off a n d flashback limit, quenching distance, and flame velocity (1). D a t a of this type should give clues as to the importance of reaction kinetics in flame propagation a n d should yield further information on what the over-all mechanism of flame p r o p a g a t i o n m i g h t be. Further, such data for normally liquid fuels would be of special interest, because they might assist in the interpretation of the combustion process in aircraft engines; the oxygen-nitrogen ratio is a quantity t h a t can be intentionally varied to produce a considerable effect on combustion properties with-

out greatly affecting such processes as fuel atomization and mixing. A t the N A C A Lewis laboratory a program is under way in which some of the combustion properties of isooctane ( 2 , 2 , 4 - t r i m e t h y l p e n t a n e ) in various oxygen-nitrogen mixtures are being studied. The present p a p e r includes d a t a on the laminar flame velocities of homogeneous isooctane-, propane-, and ethylene-oxygen-nitrogen mixtures. Flame velocity has been determined as a function of equivalence ratio (fraction of stoichiometric fuel-oxygen ratio) with air and with oxygen-nitrogen mixtures containing approximately 0.I7, 0.25, 0.30, 0.35, and 0.50 mole fraction of oxygen a t 311 ~ and 422~ T h e experimental values of m a x i m u m flame velocity are compared with the values pre-