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Application of optical methods to combustion research
APPLICATION OF OPTICAL METHODS TO COMBUSTION RESEARCH
765
range of Wien's law, Planck's expression must be utilized.
to that of simulated stripes. If the temperature is within the range where Wien's law may be applied, the following equation may be used:
Accuracy of Method C1X-~e - C 2 / x T ~
T r e i ~ - 5 e -C2/XTH
Temperature measurements made of a ribbon filament lamp calibrated by the National Bureau of Standards to have a brightness temperature of 2800°K i 8°14 when determined by this instrument have been found to be 2802°K with an average deviation of 10.0°K. Temperatures of greater magnitude would be expected to have larger errors.
where X is the best effective wavelength (630 m~), T is the brightness temperature of the phenomena interpolated from the calibrated stripes as if the neutral filter was not there, Tn is the true brightness temperature of the phenomena, CI and C2 are constants, Tr is the transmission of the "neutral filter" at 630 in#. Therefore TH
C:T TX In Tr + C2
REFERENCE 1. MALE, D. W.: Rev. Sci. Instr., 22, 769-772, (1951).
If the temperature is beyond the accurate
101 APPLICATION OF OPTICAL METHODS TO COMBUSTION RESEARCH By F. J. WEINBERG 1. Introduction
2. Schlieren and Shadowgraphs
The experimental study of combustion processes is rendered difficult by the extreme conditions of high temperatures, short times of residence and large magnitudes of concentration and temperature gradients under which reaction occurs in flame zones. These conditions imply the need for "in situ" studies on actual flames and at the same time are responsible for the sensitivity of combustion zones to external interference which renders such studies difficult. In this sphere of activity optical methods offer some obvious advantages, the most notable perhaps being their noninterference with combustion processes, their absence of inertia and their ability of producing instantaneous records by photographic means of transient phenomena. The purpose of this communication is to summarize recent advances in research carried out at the Department of Chemical Engineering of the Imperial College of Science and Technology, London, into the analytical applications of optical methods to combustion research. The summary is confined to optical methods based on ray deflections applied to premixed flames of simple geometry.
Preliminary analytical work and calculations have shown that the maximum rate of change of refractive index in premixed flames occurs at temperatures well beIow those at which reaction becomes appreciable. The greatest magnitudes of deflection of incident light rays occur, in fact, within a zone where refractive index variations due to any composition changes are rendered negligible by those due to temperature changes. Since the temperature distribution in this region is calculable from heat transfer considerations alone, the distribution of ray deflections there can be deduced theoretically. From the point of view of both schlieren and shadow photography, this zone is the most important region within the flame. Thus in the case of schlieren methods the local image intensity is determined by 0, the angle of ray deflection. The calculation of the complete intensity distribution, however, is rendered somewhat uncertain by the superimposed diffraction pattern due to the knife edge which is determined by the exact position and orientation of the latter. For this reason, our calculations have, in the main, been confined to the location of the posi-
766
EXPERIMENTAL AND ANALYTICAL TECHNIQUES IN COMBUSTION
tions and temperatures, To, within flames of simple geometry giving rise to the "schlieren image," i.e., the maximum deflection. Thus in the case of a flat flame, parallel to the initial ray direction (Fig. la), the deflection is given, to a close approximation, 1 by dn d~ D . . . . D dy dy
0 . . . .
(1)
where y is the distance coordinate perpendicular to the flame, n = refractive index, ~ = n - 1 and D is the length of the light beam within the flame. The variation of refractive index with temperature, T, is given by =
(2)
~oTo/T
so that the condition for maximum deflection is d~ dy e
:
o, i e,
r
dy 2
=
2
\dy /
(3)
I n the zone before the onset of appreciable heat
,,
~
lines of const n
la
ib
Fro. 1. Ray deflections by flame facets. due to reaction, the variation of temperature with distance is governed by
release
dT k ~y = M c ( T -- To)
(4)
neglecting the effects of radiation for transparent gases, where k = thermal conductivity, c = mean specific heat at constant pressure, M = mass burning rate, and the subscript denotes the initial state. The solution of Equation (3) with Equation (4) yields T~, the temperature of maximum deflection. The results depend on the manner of variation of k and c with T. If k/c cc T ~ over the relevant range, it can be shown 2 that a+2 Ts = T o a+l
(5)
(All temperatures in °K.) For air in the range of immediate interes~t, a is close to unity and T~ becomes 3/2 To. This theoretical prediction has been found to be in e x c e l l e n t agreement with experimental results. 2
I n the case of flames inclined to the direction of the beam at an angle ¢ (Figure lb), Equation (1) can be shown 3 to become 0 = - (~o - ~b)cot ¢
(6)
the subscripts a and b referring to the points of entry and exit of the ray into the region of disturbance. The combination of Equations (1) and (6) permits an approach to the problem of curved flames, since (i) the deviation of the beam during its flame traverse is very small, and (ii) the thickness of the flame (in terms of the region of refractive index variation) is, in general, negligible in comparison with the radius of curvature of the flame, so that the flame curve may be regarded as constituted of infinitesimal flat facets. Equation (6) then applies to each facet unless ¢ is so small that Equation (1) must be used. Application of these concepts to axial sections of curved flames in cylindrically symmetric systems 3 has led to the following conclusions for flames whose curvature is concave towards the approaching stream of reactants: The temperature of maximum deflection within the flame is even lower than its corresponding value in flat flames parallel to the direction of the incident beam. For the purely mechanical model of a perfectly conical flame surface, maximum deflection would, in fact, occur at the lowest axial temperature available. However, no real flame can conform to this artificial model, because the large curvature at the tip would result in augmented transfer processes there. The consequent local increase in burning velocity and flow line distortion causes all the flame tips to be rounded in practice. Now even a small horizontal portion of the flame surface exercises a profound effect on ray deflection leading to results closely similar to that of the flat flame. Thus for the model of a conical flame-front whose inclination to the horizontal is ¢ having a flattened apex of diameter p, Ts = To
a+2 2v cot ¢ a-t-l+-ps
(7)
where ~ = thermal diffusivity of reactants, s = normal burning velocity and other symbols correspond to those of Equation (5). Equation (7) implies that for the model chosen (a + 2 ) / (a + 1) >_ T / T o >__ 1 always. Insertion of numerical values, however, shows that for an inclination of 45° and a burning velocity of 50
APPLICATION OF OPTICAL METHODS TO COMBUSTION RESEARCH
era/see, for instance, a flattened apex of only 0.05 cm radius suffices to raise this temperature of maximum deflection to within less than 4 per cent of the flat flame solution2 Shadowgraph interpretation was approached in a similar manner. The mode of interpretation depends greatly on the distance separating the flame from the shadowgraph screen or photographic plate. The general statement that local shadowgraph intensities depend only on the rate of change of deflection with distance negleets the fact that points on the shadowgraph are often illuminated by superimposed light rays deriving from more than one position in the flame and applies therefore only to shadowgraphs close to the flame. The general problem is obviously very complex, but a complete solution has been obtained 4 in the case of a flat flame parallel to the beam of light. The full results are too cumbersome for presentation here but a few numerical consequences may be quoted to illustrate the conclusions. In the case of the shadowgraph close to the flame, for reactants containing largely air at an initial temperature of 18°C, the first intensity maximum (from the upstream side) corresponds to a temperature of only 59°C, while the subsequent minimum originates at a flame temperature of 364°C. For shadowgraphs distant from the flame, a new point of reference on the image has been suggested in the first discontinuous rise in intensity and this has been correlated with the temperature of maximum deflection. The distanee ranges within which each type of interpretation is applicable were defined and expressed in terms of the properties of the flame. An interesting conclusion which emerged is that the more generally accepted type of correlation between shadowgraph intensity distribution and the refractive index field, namely, that referred to here as the "shadowgraph close to the flame" is applicable only to separations between flame and screen which may frequently be too small for practical purposes. Comparison with the conelusions on schlieren interpretation suggest that in the ease of shadowgraphs also, results for curved flames may not differ greatly from those derived for the flat flame ease.
3. Analytical Studies A method has been developed ~, 5 in which the refractive index distribution across a flat flamefront is measured by recording the instantaneous
767
distribution of deflections and is used to calculate the corresponding temperature profile. This temperature distribution together with the measured burning velocity, used in conjunction with the steady-state conservation equations of flame propagation makes possible the calculation of the distributions of the "over-all" variables across the flame-front. I t has yielded the distributions of temperature, fraction of total reaction, rates of heat release and reaction, flow velocities, etc., together with values of "ignition temperature," periods of residence, forces on the flame and other parameters. The principle of the method is illustrated schematically in Figure 2. An accurately parallel beam of light is produced by concentrating light from a high intensity source on a pin-hole placed at the focus of a collimating lens of long focal length. If the beam is confined by a slit inclined
FIG. 2. The "inclined slit" method. with respect to a flat flame stabilized on a modified form of the Egerton-Powling burner, G the distribution of ray deflections can be recorded as a distortion of the slit image on a screen or photographic plate at some distance beyond the flame. In practice, a number of parallel slits are used extending across the entire field of disturbance in order that corrections m a y be made for any heating up of the surrounding atmosphere or deviations from flatness of the flame. The full theory of the interpretation is given by Burgoyne and Weinberg. 1 A few of the results are shown below to illustrate the scope of the method; these refer to a lean ethylene-air flame. Figures 3 and 4 show the distribution of temperature (T°K) and fraction of total reaction (~) in space (distance y cm perpendicular to the flame) and time (t sec) respectively. The magnitude of energy flow rates is shown in Figure 5, while Figure 6 illustrates the distribution of the over-all
768
EXPERIMENTAL A N D
ANALYTICAL
reaction rate from which the distribution of volumetric heat release rates can be deduced. Many other conclusions can be drawn from the results concerning the physics, chemistry and aerodynamics of the flame, but for the purpose of oa.
.........
TECHNIQUES
the experimental refinements associated with the production of an accurately flat flame. I n such cases, the measurement of only some of the important parameters by a method identical in experimental principle to that of the "complete interpretation" outlined above is sufficient. A very simple procedure has been evolved for the partial interpretation of the deflected slit image
0.8
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0,4
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~
J.
x - z . - . t - A
I
0-~
;00
Ii° "r°" / oMo° - -0"4-
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1200
FIG. 5. Distribution of energy transfer, a, chemical energy flow; b, total flow; c, mass flow of thermal energy; d, conduction flow; e, radiation flow.
O,I
:1000
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140
,~"
-. . . . . .
120[" O,.f
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2"
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.'
80
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'
' tO0 0.05
FzG. 4. Distribution of temperature and e in time. the present communication these illustrations must suffice to indicate the potentialities of the method as a tool in the study of flames. This method as used for the fullest interpretation possible will henceforth be referred to as "the complete interpretation." I n some of the research projects in progress, the nature of the investigation does not warrant the mathematical labor of such complete analysis or
O'B
1.0
400
y (cm) FzG. 6. Distribution of de/dl. based on some of the more obvious aspects of its shape and this will henceforth be referred to as "partial interpretation." The extent of the information desired and the method by which it is deduced from experimental results depends somewhat on the nature of the particular investigation, but a few of the parameters obtainable Ere discussed below. If the flame under investigation is flat, the distance perpendicular to it over which deflections of the image occur is obviously a measure of the total "flame thickness." The purpose of
APPLICATION OF OPTICAL METHODS TO COMBUSTION RESEARCH
the quotation marks is to emphasize that, since all the variables across the flame-front tend to their initial and terminal values asymptotically, the term "flame thickness" has quantitative significance only within the framework of its definition. The vertical distance over which ray deflections occur furnishes a definition in terms of the sensitivity of the optical method. This sensitivity, however, is less at the higher than at the lower flame temperatures. For this reason, an alternative definition based on a given fraction of the total temperature rise has been correlated with the deflected image shape. This "flame thickness" is deducible from a simple geometric construction upon an enlargement of the image. Its magnitude is of importance in studying the mechanism of flame propagation and the measurement has been carried out successfully for hydrocarbon flames containing a gaseous inhibitor. The conclusions of this work will be published in the near future. Another aspect of the "partial interpretation" is the location of particular values of temperature in the "pre-ignition zone" of the flame, particularly the temperature of maximum deflection, T~, which is easily calculable (see Section 2). I t can be shown that maximum deflection occurs where the tangent to the curved image becomes parallel to its undeflected extremities and the height within the flame at which this deflection occurs is given by the point of intersection of the vertical through the point of tangeney with the undeflected line of the slit. Here again simple geometric construction upon the image suffices. Perhaps the most important aspect of the "partial interpretation" consists of the measurement ef final flame temperature, T / . Its importance lies not only in its applicability to nonflat flames but also in that other flame properties, extremely difficult to measure in other ways, can be deduced by this method if T/ is known. I t has been shown 7, s that the final temperature is related to the area, A, enclosed between the deflected and undeflected slit images in the following manner Am 1 --
&
(8)
- -
DdSo
where ra is the slope of the inclined slit with respect to the part of the flame traversed, D is the path of the ray within the flame region, d is
769
the separation between burner axis and photographic plate, 8 = n - 1, and the subscripts 0, p, r, denote initial state, products and reactants respectively. Equation (8) applies to flat, curved and corrugated flames and the method is applicable, in principle, to any two dimensional flame geometry. The reason is that although the shape of the deflected image depends on flame geometry, the area A does not, other quantities remaining constant. In practice, however, excessive curvature introduces experimental difficulties and the method, up to the time of writing, has been applied only to flames of very gradual curvature, s In special cases, Equation (8) may be used for the determination of one of its variables other than T s . Thus, if t h e flame surface is interrupted, calculation of D will yield the total size of the discontinuities. An illustration of this use of the method is cited in the next section. I t does, of course, necessitate knowledge of T~, which can be obtained conveniently by burning the same mixture under different conditions of geometry and using the method described. 4.
Applications
Of the research projects currently in progress, the "complete interpretation" forms the basis of one attack on the mechanism of flame propagation. In this investigation, which was initiated in October, 1954, the initial temperature of the reactants is varied by uniform preheating and the effect on burning velocities, limits of inflammability as well as on the complete flame structure is studied. The highest degree of accuracy is aimed at by refinements of the optical technique. This constitutes a direct experimental approach to the theory of flame propagation since the initial variable is simple and directly controllable and its final consequences together with the mechanism of their attainment can be measured accurately. The method of "partial interpretation" is in use on two projects investigating the mode of action and the effects of flame inhibitors, s In one of these, the inhibitor is gaseous ("Freon 12," 0C12F2) and is uniformly premixed with the reactants. The dependence of burning velocity and limits of inflammability on inhibitor concentration is measured. The optical method furnishes flame thicknesses and final flame temperatures. The latter gives a measure not only of the over-all heat release due to the "inhibited reaction" but also of the increase in flame temperature required
770
EXPERIMENTALAND ANALYTICALTECHNIQUESIN COMBUSTION
to maintain a particular flame for various inhibitor concentrations and therefore of the effectiveness of the inhibitor. To eliminate the purely physical components of the inhibition process, control experiments with an inert diluent are carried out. In the second project the effects of solid inhibitors in the form of monodisperse alkali halide (in particular NaC1) crystal clouds are investigated. The mechanism of these effects is likely to be rather different from those governing homogeneous gaseous inhibition if the particles do not have time to evaporate and their vapor to diffuse uniformly through the gas before the major part of the flame thickness has been traversed. Unevaporated particles and undiffused vapor spheres might then be expected to disrupt the flame surface locally, introducing "holes" in the flame. From a kno~vledge of the final flame temperature, Equation (8) can be used to deduce D and comparison with its apparent value yields the mean fraction of flame area occupied by these disruptions. Preliminary measurements based on this principle have yielded reasonable results. Another investigation of the early stages of ignition of premixed reactants by optical means is in hand. Details and results of all these investigations have been or will be published elsewhere. In the present summary they are intended merely to
illustrate the scope of the current applications of the optical tool. In the immediate future it is intended to extend its field of application to turbulent and to diffusion flames. The former in particular promises to become a fruitful field of study whose importance is emphasized by the present state of theory in the field of turbulent flame propagation.
Acknowledgments The author is indebted to Dr. J. H. Burgoyne for many helpful discussions and to his colleagues in this work Messrs. A. Levy, J. Reck, J. Sage and K. Sumi. REFERENCES 1. BURGOYNE, J. H., AND WEINBERG, F. J.: Proc.
Roy. Sot., A224, 286 (1954). 2. WEINBERG, F. J. : Fuel, 34, $84 (1955). 3. WEINBERG, F. J. : Fuel, 35, 161 (1956).
4. WEINBERG, F. J.: Proe. Roy. Soc., A235, 510 (1956). 5. BURGOYNE, J. H., AND WEINBERG, F. J. : Fourth Symposium in (International) Combustion, p. 294. Baltimore, The Williams & Wilkins Co., 1953. 6. POWLING,J-. A.: Fuel, 28, 25 (1949). 7. WEINBERG, F. J. : Fuel, 35, 359 (1956). 8. RECK, J., SUMI, K., AND WEINBERG, F. J.: Fuel,
85, 364 (1956).
102
I O N I Z A T I O N STUDIES OF FLAMES STABILIZED IN RAPID FLOW Measurement of Ionic
Density in The
Flame
By G. MATTON 1. Ionic Density and Reaction Zone
2. Experimental Device
There have been a number of qualitative and quantitative studies of ionic density distribution in burner flames), 2 As the value of this density is much higher in the neighborhood of the flame front than in the hot gases, it offers a means of studying the reaction zone distribution. The present paper reports an investigation of this type, applied to flames stabilized by obstacles in a rapidly flowing air-kerosene mixture.
In these measurements, the positive ions are collected by raising the probe electrode to a constant potential that is very negative with respect to the flame gases. All insulating materials tested for insulation of the electrode were found to be conductors at high temperature. After considerable testing, a probe was adopted, consisting of a 0.6-mm diam chromel electrode in a 4-mm diam water-cooled support (Fig.
765
range of Wien's law, Planck's expression must be utilized.
to that of simulated stripes. If the temperature is within the range where Wien's law may be applied, the following equation may be used:
Accuracy of Method C1X-~e - C 2 / x T ~
T r e i ~ - 5 e -C2/XTH
Temperature measurements made of a ribbon filament lamp calibrated by the National Bureau of Standards to have a brightness temperature of 2800°K i 8°14 when determined by this instrument have been found to be 2802°K with an average deviation of 10.0°K. Temperatures of greater magnitude would be expected to have larger errors.
where X is the best effective wavelength (630 m~), T is the brightness temperature of the phenomena interpolated from the calibrated stripes as if the neutral filter was not there, Tn is the true brightness temperature of the phenomena, CI and C2 are constants, Tr is the transmission of the "neutral filter" at 630 in#. Therefore TH
C:T TX In Tr + C2
REFERENCE 1. MALE, D. W.: Rev. Sci. Instr., 22, 769-772, (1951).
If the temperature is beyond the accurate
101 APPLICATION OF OPTICAL METHODS TO COMBUSTION RESEARCH By F. J. WEINBERG 1. Introduction
2. Schlieren and Shadowgraphs
The experimental study of combustion processes is rendered difficult by the extreme conditions of high temperatures, short times of residence and large magnitudes of concentration and temperature gradients under which reaction occurs in flame zones. These conditions imply the need for "in situ" studies on actual flames and at the same time are responsible for the sensitivity of combustion zones to external interference which renders such studies difficult. In this sphere of activity optical methods offer some obvious advantages, the most notable perhaps being their noninterference with combustion processes, their absence of inertia and their ability of producing instantaneous records by photographic means of transient phenomena. The purpose of this communication is to summarize recent advances in research carried out at the Department of Chemical Engineering of the Imperial College of Science and Technology, London, into the analytical applications of optical methods to combustion research. The summary is confined to optical methods based on ray deflections applied to premixed flames of simple geometry.
Preliminary analytical work and calculations have shown that the maximum rate of change of refractive index in premixed flames occurs at temperatures well beIow those at which reaction becomes appreciable. The greatest magnitudes of deflection of incident light rays occur, in fact, within a zone where refractive index variations due to any composition changes are rendered negligible by those due to temperature changes. Since the temperature distribution in this region is calculable from heat transfer considerations alone, the distribution of ray deflections there can be deduced theoretically. From the point of view of both schlieren and shadow photography, this zone is the most important region within the flame. Thus in the case of schlieren methods the local image intensity is determined by 0, the angle of ray deflection. The calculation of the complete intensity distribution, however, is rendered somewhat uncertain by the superimposed diffraction pattern due to the knife edge which is determined by the exact position and orientation of the latter. For this reason, our calculations have, in the main, been confined to the location of the posi-
766
EXPERIMENTAL AND ANALYTICAL TECHNIQUES IN COMBUSTION
tions and temperatures, To, within flames of simple geometry giving rise to the "schlieren image," i.e., the maximum deflection. Thus in the case of a flat flame, parallel to the initial ray direction (Fig. la), the deflection is given, to a close approximation, 1 by dn d~ D . . . . D dy dy
0 . . . .
(1)
where y is the distance coordinate perpendicular to the flame, n = refractive index, ~ = n - 1 and D is the length of the light beam within the flame. The variation of refractive index with temperature, T, is given by =
(2)
~oTo/T
so that the condition for maximum deflection is d~ dy e
:
o, i e,
r
dy 2
=
2
\dy /
(3)
I n the zone before the onset of appreciable heat
,,
~
lines of const n
la
ib
Fro. 1. Ray deflections by flame facets. due to reaction, the variation of temperature with distance is governed by
release
dT k ~y = M c ( T -- To)
(4)
neglecting the effects of radiation for transparent gases, where k = thermal conductivity, c = mean specific heat at constant pressure, M = mass burning rate, and the subscript denotes the initial state. The solution of Equation (3) with Equation (4) yields T~, the temperature of maximum deflection. The results depend on the manner of variation of k and c with T. If k/c cc T ~ over the relevant range, it can be shown 2 that a+2 Ts = T o a+l
(5)
(All temperatures in °K.) For air in the range of immediate interes~t, a is close to unity and T~ becomes 3/2 To. This theoretical prediction has been found to be in e x c e l l e n t agreement with experimental results. 2
I n the case of flames inclined to the direction of the beam at an angle ¢ (Figure lb), Equation (1) can be shown 3 to become 0 = - (~o - ~b)cot ¢
(6)
the subscripts a and b referring to the points of entry and exit of the ray into the region of disturbance. The combination of Equations (1) and (6) permits an approach to the problem of curved flames, since (i) the deviation of the beam during its flame traverse is very small, and (ii) the thickness of the flame (in terms of the region of refractive index variation) is, in general, negligible in comparison with the radius of curvature of the flame, so that the flame curve may be regarded as constituted of infinitesimal flat facets. Equation (6) then applies to each facet unless ¢ is so small that Equation (1) must be used. Application of these concepts to axial sections of curved flames in cylindrically symmetric systems 3 has led to the following conclusions for flames whose curvature is concave towards the approaching stream of reactants: The temperature of maximum deflection within the flame is even lower than its corresponding value in flat flames parallel to the direction of the incident beam. For the purely mechanical model of a perfectly conical flame surface, maximum deflection would, in fact, occur at the lowest axial temperature available. However, no real flame can conform to this artificial model, because the large curvature at the tip would result in augmented transfer processes there. The consequent local increase in burning velocity and flow line distortion causes all the flame tips to be rounded in practice. Now even a small horizontal portion of the flame surface exercises a profound effect on ray deflection leading to results closely similar to that of the flat flame. Thus for the model of a conical flame-front whose inclination to the horizontal is ¢ having a flattened apex of diameter p, Ts = To
a+2 2v cot ¢ a-t-l+-ps
(7)
where ~ = thermal diffusivity of reactants, s = normal burning velocity and other symbols correspond to those of Equation (5). Equation (7) implies that for the model chosen (a + 2 ) / (a + 1) >_ T / T o >__ 1 always. Insertion of numerical values, however, shows that for an inclination of 45° and a burning velocity of 50
APPLICATION OF OPTICAL METHODS TO COMBUSTION RESEARCH
era/see, for instance, a flattened apex of only 0.05 cm radius suffices to raise this temperature of maximum deflection to within less than 4 per cent of the flat flame solution2 Shadowgraph interpretation was approached in a similar manner. The mode of interpretation depends greatly on the distance separating the flame from the shadowgraph screen or photographic plate. The general statement that local shadowgraph intensities depend only on the rate of change of deflection with distance negleets the fact that points on the shadowgraph are often illuminated by superimposed light rays deriving from more than one position in the flame and applies therefore only to shadowgraphs close to the flame. The general problem is obviously very complex, but a complete solution has been obtained 4 in the case of a flat flame parallel to the beam of light. The full results are too cumbersome for presentation here but a few numerical consequences may be quoted to illustrate the conclusions. In the case of the shadowgraph close to the flame, for reactants containing largely air at an initial temperature of 18°C, the first intensity maximum (from the upstream side) corresponds to a temperature of only 59°C, while the subsequent minimum originates at a flame temperature of 364°C. For shadowgraphs distant from the flame, a new point of reference on the image has been suggested in the first discontinuous rise in intensity and this has been correlated with the temperature of maximum deflection. The distanee ranges within which each type of interpretation is applicable were defined and expressed in terms of the properties of the flame. An interesting conclusion which emerged is that the more generally accepted type of correlation between shadowgraph intensity distribution and the refractive index field, namely, that referred to here as the "shadowgraph close to the flame" is applicable only to separations between flame and screen which may frequently be too small for practical purposes. Comparison with the conelusions on schlieren interpretation suggest that in the ease of shadowgraphs also, results for curved flames may not differ greatly from those derived for the flat flame ease.
3. Analytical Studies A method has been developed ~, 5 in which the refractive index distribution across a flat flamefront is measured by recording the instantaneous
767
distribution of deflections and is used to calculate the corresponding temperature profile. This temperature distribution together with the measured burning velocity, used in conjunction with the steady-state conservation equations of flame propagation makes possible the calculation of the distributions of the "over-all" variables across the flame-front. I t has yielded the distributions of temperature, fraction of total reaction, rates of heat release and reaction, flow velocities, etc., together with values of "ignition temperature," periods of residence, forces on the flame and other parameters. The principle of the method is illustrated schematically in Figure 2. An accurately parallel beam of light is produced by concentrating light from a high intensity source on a pin-hole placed at the focus of a collimating lens of long focal length. If the beam is confined by a slit inclined
FIG. 2. The "inclined slit" method. with respect to a flat flame stabilized on a modified form of the Egerton-Powling burner, G the distribution of ray deflections can be recorded as a distortion of the slit image on a screen or photographic plate at some distance beyond the flame. In practice, a number of parallel slits are used extending across the entire field of disturbance in order that corrections m a y be made for any heating up of the surrounding atmosphere or deviations from flatness of the flame. The full theory of the interpretation is given by Burgoyne and Weinberg. 1 A few of the results are shown below to illustrate the scope of the method; these refer to a lean ethylene-air flame. Figures 3 and 4 show the distribution of temperature (T°K) and fraction of total reaction (~) in space (distance y cm perpendicular to the flame) and time (t sec) respectively. The magnitude of energy flow rates is shown in Figure 5, while Figure 6 illustrates the distribution of the over-all
768
EXPERIMENTAL A N D
ANALYTICAL
reaction rate from which the distribution of volumetric heat release rates can be deduced. Many other conclusions can be drawn from the results concerning the physics, chemistry and aerodynamics of the flame, but for the purpose of oa.
.........
TECHNIQUES
the experimental refinements associated with the production of an accurately flat flame. I n such cases, the measurement of only some of the important parameters by a method identical in experimental principle to that of the "complete interpretation" outlined above is sufficient. A very simple procedure has been evolved for the partial interpretation of the deflected slit image
0.8
| ,~,L_
~0 0.~
4 i
? @3
0"2
. . . . . . .
?
0.4
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IN C O M B U S T I O N
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.
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FzG. 3. Curve of e distribution. I
0,4
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y (on")
I
~
J.
x - z . - . t - A
I
0-~
;00
Ii° "r°" / oMo° - -0"4-
~
1200
FIG. 5. Distribution of energy transfer, a, chemical energy flow; b, total flow; c, mass flow of thermal energy; d, conduction flow; e, radiation flow.
O,I
:1000
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140
,~"
-. . . . . .
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-o,oi
I--
6,O4 0.O6 time (s)
'
' tO0 0.05
FzG. 4. Distribution of temperature and e in time. the present communication these illustrations must suffice to indicate the potentialities of the method as a tool in the study of flames. This method as used for the fullest interpretation possible will henceforth be referred to as "the complete interpretation." I n some of the research projects in progress, the nature of the investigation does not warrant the mathematical labor of such complete analysis or
O'B
1.0
400
y (cm) FzG. 6. Distribution of de/dl. based on some of the more obvious aspects of its shape and this will henceforth be referred to as "partial interpretation." The extent of the information desired and the method by which it is deduced from experimental results depends somewhat on the nature of the particular investigation, but a few of the parameters obtainable Ere discussed below. If the flame under investigation is flat, the distance perpendicular to it over which deflections of the image occur is obviously a measure of the total "flame thickness." The purpose of
APPLICATION OF OPTICAL METHODS TO COMBUSTION RESEARCH
the quotation marks is to emphasize that, since all the variables across the flame-front tend to their initial and terminal values asymptotically, the term "flame thickness" has quantitative significance only within the framework of its definition. The vertical distance over which ray deflections occur furnishes a definition in terms of the sensitivity of the optical method. This sensitivity, however, is less at the higher than at the lower flame temperatures. For this reason, an alternative definition based on a given fraction of the total temperature rise has been correlated with the deflected image shape. This "flame thickness" is deducible from a simple geometric construction upon an enlargement of the image. Its magnitude is of importance in studying the mechanism of flame propagation and the measurement has been carried out successfully for hydrocarbon flames containing a gaseous inhibitor. The conclusions of this work will be published in the near future. Another aspect of the "partial interpretation" is the location of particular values of temperature in the "pre-ignition zone" of the flame, particularly the temperature of maximum deflection, T~, which is easily calculable (see Section 2). I t can be shown that maximum deflection occurs where the tangent to the curved image becomes parallel to its undeflected extremities and the height within the flame at which this deflection occurs is given by the point of intersection of the vertical through the point of tangeney with the undeflected line of the slit. Here again simple geometric construction upon the image suffices. Perhaps the most important aspect of the "partial interpretation" consists of the measurement ef final flame temperature, T / . Its importance lies not only in its applicability to nonflat flames but also in that other flame properties, extremely difficult to measure in other ways, can be deduced by this method if T/ is known. I t has been shown 7, s that the final temperature is related to the area, A, enclosed between the deflected and undeflected slit images in the following manner Am 1 --
&
(8)
- -
DdSo
where ra is the slope of the inclined slit with respect to the part of the flame traversed, D is the path of the ray within the flame region, d is
769
the separation between burner axis and photographic plate, 8 = n - 1, and the subscripts 0, p, r, denote initial state, products and reactants respectively. Equation (8) applies to flat, curved and corrugated flames and the method is applicable, in principle, to any two dimensional flame geometry. The reason is that although the shape of the deflected image depends on flame geometry, the area A does not, other quantities remaining constant. In practice, however, excessive curvature introduces experimental difficulties and the method, up to the time of writing, has been applied only to flames of very gradual curvature, s In special cases, Equation (8) may be used for the determination of one of its variables other than T s . Thus, if t h e flame surface is interrupted, calculation of D will yield the total size of the discontinuities. An illustration of this use of the method is cited in the next section. I t does, of course, necessitate knowledge of T~, which can be obtained conveniently by burning the same mixture under different conditions of geometry and using the method described. 4.
Applications
Of the research projects currently in progress, the "complete interpretation" forms the basis of one attack on the mechanism of flame propagation. In this investigation, which was initiated in October, 1954, the initial temperature of the reactants is varied by uniform preheating and the effect on burning velocities, limits of inflammability as well as on the complete flame structure is studied. The highest degree of accuracy is aimed at by refinements of the optical technique. This constitutes a direct experimental approach to the theory of flame propagation since the initial variable is simple and directly controllable and its final consequences together with the mechanism of their attainment can be measured accurately. The method of "partial interpretation" is in use on two projects investigating the mode of action and the effects of flame inhibitors, s In one of these, the inhibitor is gaseous ("Freon 12," 0C12F2) and is uniformly premixed with the reactants. The dependence of burning velocity and limits of inflammability on inhibitor concentration is measured. The optical method furnishes flame thicknesses and final flame temperatures. The latter gives a measure not only of the over-all heat release due to the "inhibited reaction" but also of the increase in flame temperature required
770
EXPERIMENTALAND ANALYTICALTECHNIQUESIN COMBUSTION
to maintain a particular flame for various inhibitor concentrations and therefore of the effectiveness of the inhibitor. To eliminate the purely physical components of the inhibition process, control experiments with an inert diluent are carried out. In the second project the effects of solid inhibitors in the form of monodisperse alkali halide (in particular NaC1) crystal clouds are investigated. The mechanism of these effects is likely to be rather different from those governing homogeneous gaseous inhibition if the particles do not have time to evaporate and their vapor to diffuse uniformly through the gas before the major part of the flame thickness has been traversed. Unevaporated particles and undiffused vapor spheres might then be expected to disrupt the flame surface locally, introducing "holes" in the flame. From a kno~vledge of the final flame temperature, Equation (8) can be used to deduce D and comparison with its apparent value yields the mean fraction of flame area occupied by these disruptions. Preliminary measurements based on this principle have yielded reasonable results. Another investigation of the early stages of ignition of premixed reactants by optical means is in hand. Details and results of all these investigations have been or will be published elsewhere. In the present summary they are intended merely to
illustrate the scope of the current applications of the optical tool. In the immediate future it is intended to extend its field of application to turbulent and to diffusion flames. The former in particular promises to become a fruitful field of study whose importance is emphasized by the present state of theory in the field of turbulent flame propagation.
Acknowledgments The author is indebted to Dr. J. H. Burgoyne for many helpful discussions and to his colleagues in this work Messrs. A. Levy, J. Reck, J. Sage and K. Sumi. REFERENCES 1. BURGOYNE, J. H., AND WEINBERG, F. J.: Proc.
Roy. Sot., A224, 286 (1954). 2. WEINBERG, F. J. : Fuel, 34, $84 (1955). 3. WEINBERG, F. J. : Fuel, 35, 161 (1956).
4. WEINBERG, F. J.: Proe. Roy. Soc., A235, 510 (1956). 5. BURGOYNE, J. H., AND WEINBERG, F. J. : Fourth Symposium in (International) Combustion, p. 294. Baltimore, The Williams & Wilkins Co., 1953. 6. POWLING,J-. A.: Fuel, 28, 25 (1949). 7. WEINBERG, F. J. : Fuel, 35, 359 (1956). 8. RECK, J., SUMI, K., AND WEINBERG, F. J.: Fuel,
85, 364 (1956).
102
I O N I Z A T I O N STUDIES OF FLAMES STABILIZED IN RAPID FLOW Measurement of Ionic
Density in The
Flame
By G. MATTON 1. Ionic Density and Reaction Zone
2. Experimental Device
There have been a number of qualitative and quantitative studies of ionic density distribution in burner flames), 2 As the value of this density is much higher in the neighborhood of the flame front than in the hot gases, it offers a means of studying the reaction zone distribution. The present paper reports an investigation of this type, applied to flames stabilized by obstacles in a rapidly flowing air-kerosene mixture.
In these measurements, the positive ions are collected by raising the probe electrode to a constant potential that is very negative with respect to the flame gases. All insulating materials tested for insulation of the electrode were found to be conductors at high temperature. After considerable testing, a probe was adopted, consisting of a 0.6-mm diam chromel electrode in a 4-mm diam water-cooled support (Fig.