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WpCA 17\- II10
NATTOILAL ADVTSORY COMMITTEE FOR AERONAUTICS
TfCHNICAL MEMOi4FDUM 1HO. 1110
ON CONMUSTION IN A TUIJBULFNT FLOW
Ey K. I. Lhelkin
The characteristics introdr:ccd by the turbulen.ce in the process~ c.f
the flane propagation are consldei ed. On the ba cis of epocmetrical and
dimensional considerations an expression is Dotained for the velocity
of 'te flame propagation in a flow of lazr;j, a.al- of turbulence.
It has long been a well--norn fact that the motion of a gas very
greatly incr-eases the rate of combustion of the gas mixture. The com-
bustion of fuel mixtures under practical conditions al-i-ays occurs in a
flow existing either before the combustion (furnaces, internal-combustion
engines) or arising in the process of c,..mbustion process as a result of
the propagation of the burning gases (the inflammation of mixtures at
rest in pipes, gas reservoirs, inflammation of methane in mines, etc.).
For this reason, it is very essential to study the laws of increase in
the rate of combustion as a function of the properties of the gas flow.
In connection with this problem, it is necessary to distinguish the
effect of the motion of the gas mass with a certain definite velocity
whereby the combustion surface is expanded and thereby the combustion
rate increased, from the effect of the turbulent fluctuations, the veloc-
ity irregularities of smaller scale.
In a gas at rest or in a laminar flow the velocity of propagation of
the flame in a direction perpendicular to the surface of combustion is
constant. This velocity is denoted as the normal or fundamental flame
p velocity; it depends only on the physicochemical properties of the mix-
ture, and does not depend on the motion of the gas. The total rate of
S combustion, the volume of gas burned per unit of time, is equal to the
product of the flame area by the normal conbust-on velocity. In a turbu-
'lent flow; for example, in a burner or pipe, the combustion surface is
S. not smooth as in a laminar flow, but there appear on it small disturb-
ances of the flame front produced by the turbulent fluctuations.
N. 1Jour. Tech. Phys. (USSR), vol. XIII, nos. 9-10, 1943, pp.520-530.
NACA TM No. 1110
If there is considered a sufficiently large surface, the dimensions of
which are large in comparison with the scale of turbulence, the rate of
combustion per unit surface will no longer be constant as in the case of
the laminar flow, but will increase and will depend on the velocity of
the fluctuations. In this sense it is as though the normal velocity of
combustion increased. In this paper an attempt will be made to arrive
at a quantitative estimate of this increase.
Qualitatively, the effect of turbulence on combustion has been
known for 60 years. Mallard and Le Chatelier (reference 1) wrote in
1883 that turbulence (agitation) increases the heat transfer, increases
the surface of the flame, and forms new centers of inflammation. The
turbulence may increase the velocity of the flame 100 times compared with
its velocity in a medium at rest. The fact that the ignition of slowly
burning mixtures in mines may lead to catastrophic explosions was ex-
plained by Mallard and Le Chatelier as due to the effect of the turbulence.
Unfortunately, since the publication of the work of Mallard and
Le Chatelier 60 years ago, the concepts with regard to this phenomenon
have undergone no essential change. The authors know of only one work
(reference 2) in which an attempt is made at a quantitative approach to
the study of this phenomenon; this work will be discussed in the presen-
tation which follows.
Recall the fundamental characteristics of turbulent flow. The lat-
ter is characterized by the degree, scale, and frequency of the turbu-
lence. The degree of turbulence, or simply the turbulence, is quantita-
tively determined by the Karman number K given by
where v2 is the mean square value of the fluctuating component of the
velocity, denoted in what follows by v', and W is the mean velocity
of the flow. The turbulence depends on the geometric dimensions, the
configuration and degree of roughness of the pipe through which the gas
moves, and does not depend on the velocity of the flow and the Reynolds
number Re when the latter is above the critical and the turbulence is
measured at a sufficiently large distance from the entrance or turbulence-
producing screen. This assertion is based on turbulence measurements in
aerodynamic wind tunnels. It possibly is also valid for chambers of
other shape as the combustion chamber of an engine. Thus the fluctuating
velocity, at least in pipes, increases proportionately with the mean flow
The scale of turbulence may be determined by the expression
NACA TM No. 1110
2 = Rdr.
I= l ll
is the coefficient of correlation and x the distance between two points
in the space in which there are simultaneously measured the fluctuating
components v1 and vi. In the physical cerne the scale of turbulence
is the distance for which there exists a relation between the fluctua-
tions. Roughly speaking, it is the distance penetrated by a turbulent
gas element in which the element mixes with those surrounding it. In a
flow there is always observed an entire spectrum of scales starting with
The frequency of the fluctuations may be thought of as connected
with the scale and the velocity of the fluctuations, and hence is not an
independent magnitude characterizing the turbulence.
In all cases of ccubustion in turoulent flow, the most essential
property of the flow as regards combustion is the forced mixing of the
elementary volumes of the gas. The intensity of the turbulent mixing is
determined by the coefficient of the turbulent exchange Zv' which has
the dimensions of temperature conductivity, coefficient of diffusion or
of kinematic viscosity.
The turbulent exchange affects the process of the mixing of air with
the fuel if the latter were not previously mixed. This process, however,
will not be considered in what follows. The combustion of a homogeneous
fuel mixture leaving aside the stage of mixture formation will be consid-
In considering combustion in a turbulent flow, it is necessary to
compare a magnitude having the dimensions of length and characterizing
the turbulence (i.e., the degree of turbulence) with a magnitude of the
same dimensions characterizing the combustion: namely, the width of the
flame front. On the ratio of the scale of turbulence to the width of
the front of the normal flame depends the nature of the effect of the
turbulence on the speed of propagation of the combustion. Two cases may
be considered: namely, when the scale is respectively small and large as
compared with the width of the flame front.
NACA TM No. 1110
The scale of the turbulence is small with respect to the width of
the zone of normal combustion. This case was considered by Damkbhler
(reference 2) who for the speed of the turbulent propagation obtained
UT= N X
where uN is the speed of normal combustion accordingg to Damkohler,
the speed in the laminar flow), XT the coefficient of turbulent ex-
change, and XM the temperature conductivity.
A similar result was arrived at independently by Y. B. Zeldovich
(private communication to the author). This type of relation is ob-
tained, since it is assumed that the reaction time in the flame front
is determined by the speed of the chemical reaction but the process of
mixing in the flame front takes so little time in comparison with the
reaction time that the mixing time may be neglected. This actually oc-
curs when the scale of fluctuations I is small in comparison with the
width of the front, and the coefficient of turbulent exchange cannot be
neglected in comparison with the temperature conductivity.
Consider the flame front under these conditions. On figure 1 is
shown schematically the temperature distribution in the flame. Accord-
ing to-the theory of normal flame propagation (reference 2) the velocity
of the flame, independent of the mechanism of the reaction, is of the
order of the square root of the temperature conductivity divided by the
The reaction time TX in the normal flame is determined for a tempera-
ture near the combustion temperature and depends on it according to
the law of Arrhenius:
where T. is given with an accuracy up to a factor having the dimen-
sions of time.
Let the temperature T at the section B determine the reaction
time. In the case of the absence of turbulence the temperature will be
the same at all points of the section. It is assumed that the same
NACA TM No. 1110 5
temperature distribution is also established in the presence of turbulent
exchecnge. In that case, at a mean temperature T in section B the
temperature at various points of this section will be different; it will
vary approximately from T 2 to T + z It is recalled that I
is the scale of turbulence. The turbulent fluctuations will bring the
gas into section B from the neighboring layers included between sec-
tions A and C and at a distance from B equal to the scale of turbu-
lence. It is evident that the scale of the elementary areas lying in
section B the temperature of which differs from T will be of the
order of 22. In such a distribution of the temperature over the section
the reaction time over the entire section will no longer be determined
by the mean temperature T. To a rough approximation it will be of the
eR (T 41 Z + eR T Z a
The order of magnitude of the temperature gradient is c where
Tc and To are the combustion temperature and the initial temperature,
respectively, and X is the width of the flame front. In the case where
z 4 < T or -(Tc T ;
T e =TX
This condition is realized if 2 << X.
Suppose that Z increases for a constant turbulence exchange coef-
ficient Zv'. The temperature distribution and the gradient depend on
lv' and hence remain unchanged, and X likewise does not change. The
ratio Z/A, however, increases and in the end I cannot be neglected
in comparison with T. The reaction time in section B for the same
mean temperature T will be determined by the exponential curve
T e C i/X (Tc To)]
For some value of Z it will become so large that an element of the gas
with a temperature T Z/x (Tc To) mixes with the neighboring ele-
ments rather than reacts. The combustion will be determined by the rate
of mixing of the element of gas (with subsequent rapid combustion
NACA TM No. 1110
at a higher temperature and a corresponding concentration of reaction
products). For large values of 2 therefore the determining factor
will be the mixing time of an order of magnitude to I/v. It may be
noted that for constant Iv', I/X increases with 2 but the reaction
time depends on the temperature exponentially, and therefore increases
Thus it may be stated that for scales of turbulence of the order of
the width of the combustion zone the reaction time will be determined not
by the speed of the reaction at a given section but by the speed of mixing
of the elementary volumes of the gas. This is what constitutes the new
factor introduced by the turbulence in the mechanism of the propagation.
Bearing in mind what has been said previously, the following resume
may be made. For turbulence of small scale (Z
turbulent exchange to the temperature conductivity. If it is assumed
that the molecular and turbulent (-diffusive) flows combine (X= YT+X M)
S / T = / 1 + (la)
Tx X 1.1
The above formula has the advantage as compared with (1) that in the
limit for XT = 0 it gives uT = uN.
In a flow of small scale of turbulence the flame propagation is
determined by the coefficient of turbulent exchanci. Hence, within
certain limits (as long as Z
For turbulence of large scale, as will be seen later, the scale of
turbulence does not affect the flame speed; the determining factors are
only the velocity of the fluctuations, the degree of turbulence and the
Karman number. In the intermediate range (Z1-) a transition occurs
when, at least for strong turbulence (v>uN), the mixing being begins to
affect not only the heat transfer (as for small scales) but also the time
of chemical reaction in the flame. Thus are presented the laws of flame
propagation at a small scale of turbulence, and the properties that appear
as the scale increases are showed.
It should be pointed out that the case where the scale of turbulence
is small by comparison with the width of the flame front is rarely met
with in pure form. Under normal conditions for homogeneous gas mixtures
the width of the flame front is of the order of 0.1 millimeter. Under
real conditions (gas furnaces, engine combustion chamber) scales of order
of magnitude less than 0.1 millimeter can only accompany larger scales
and occupy only a certain extreme position in the scale spectrum. However,
NACA TM No. 1110
immediately on passing to slowly burning mixtures (e.g., lean mixtures)
the width of the front may considerably exceed the above-mentioned order
of magnitude, and the probability of existence of the case discussed
Next, consider the case where the scale of turbulence is large in
comparison with the width of normal combustion zone. An analysis of this
case in its general form on the basis of dimensionality considerations
permitted Y. Zeldovich to conclude (unpublished work) that the speed of
turbulent propagation of the flame does not depend on the scale of turbu-
lence and can be repres.-ntad by a formula of the type.
UT = UIi f(uN/v )
where f(uU/v') is a function of the ratio of the velocities to be
determined. In the casv of large-scale turbulence the flame surface is
curved. As the velocity of the fluctuating components increases the
curvature increases, and finally the flam.n front begins to break awxy.
At strong turbulence the elementary volumes of gas, both burning and
fresh, move chaotically with respect to one another. In the flame th.-re
remain "isl:- nde," centers of unburned mixture, broken off by the fluctu-
ations into parts and annihiliatd by the flame. If the effect of the
curvature on the speed of flame propagation is neglected, the normal
flame speed may be consde-rcd as constant. The surface of combustion,
however, increases and hence also the total rate of combustion.
Before determining the speed of turbulent combustion over the flame
surface, consider the limiting case of a strong large-scale turbulence
when the combustion zone is filled with islands of unburned mixture.
In figure 2 the sp'ce between the sections AA and BB may be con-
sidered as the reaction zone of the turbulent combustion. In front of
the plane AA is the fresh mixture, and behind the plane BB are the
products of combustion. From A to B the mean concentration over the
cross-sectional areas of the products of combustion increases, and the
concentration of the fresh gas decreases. The distance between the
sections may be considered as the width of the turbulent flame front.
As vas mentioned previously, the speed of the flame, from dimensional
considerations independent of the mechanism of the reaction is a magni-
tude of the order of
u- 7-7T (3)
In a turbulent flame the part of the temperature conductivity is taken
by the coefficient of exchange lv' and the part of the reaction time
by the mixing time Z/v', and this gives for the velocity:
NACA TM No. 1110
Thus the conclusion is reached: for large turbulence when the velocity
of fluctuation v' is large by comparison with the normal velocity uN
(only in this case will the combustion front have a form like that in
fig. 2), the velocity of turbulent flame propagation is proportional
to the mean fluctuating velocity and does not depend on the chemical
nature of the gas mixture.
The reaction time in a turbulent flame may be ccuputed in a differ-
ent manner. The combustion time of an elementary volume Z- may be
where -Su.j is the volume rate of combustion, the product of the flame
area by the normal velocity. It should be taken into account that an
elementary volume with area of the order 22 on entering the combustion
front is broken up into parts by the fluctuations. The breaking up will
continue' as long as the flame with normal velocity uN passes over a
distance equal to the scale of turbulence Z, this time is equal to i/AN.
During this time the total path traversed with the fluctuating velocity
reaches the value L = 1/vN v'.
The ratio L/Z shows how many times during the combustion of the
volume 23 the latter is traversed by fluctuations. Each such traversal
leads to the formation of a new flame area of the order to 1 The
mean area of combustion of an element I3 will be proportional to the
z2 vt/UN (6)
The averaging of this quantity with respect to the combustion time affects
only the constant factor. The time required for burning the volume 13
id found equal to
T _- (7)
The same result is attained ; namcla-, that the combustion time is propor-
tional to the mixing time.
NACA TM No. 1110 9
The case where v'.,> uN has been considered. The case of small
turbulence may be approached only geometrically. It is in this manner
that the problem is considered by Damk6hler. Rightly seeing the reason
for the increase in velocity of combustion in the increased area of the
flame surface, he schematically represents the flame surface as consist-
ing of conical surfaces with their bases at right angles to the direction
of flame propagation (fig. 3). Taking the areas of the cones proportional
to v' he arrives at the expression
The considerations of Damko::Ler are not accurate and for small v' are
not true. According to Damkohler, the absence of turbulence (v'=J) leads
to zero velocity of the flame. Actually a relation like (4) as shown
above is obtained only for strong turbulence v'>uj, and not for weak
turbulence which is the case considered by Damkohler.
Consider this problem more in detail. The ratio of the speed of
turbulent propagation of the flame to the normal speed will be equal to
the ratio of the lateral area of the figure a (fig. 3) to its base.
The height of the figure, which is acsumed ap a cone, will be of the
order Zv'/uN. For an element of the flame front will be carried away
by the fluctuation from the general flame front only during the time re-
quired for the normal of thh flame to traverse the distance Z. This time
is enual to Z/uN. The height of the ccne will therefore be of the order
of Zv'/uN. The lateral area is
Slat AL 1 + v'/u)
where A and B are nondimensional coefficients of the order of unity.
The ratio of the velocities of propagation is
U_ Slat A/ 1+ B(v'/uN)2 (8)
For strong turbulence v'> uN (equation (8))leads to the known relation
The absence of turbulence v' = 0 should lead to the condition uT = uN.
This gives the value A1 = 1.
For any turbulence, including small turbulence, the criterion should
iACA. TM No. 1110
S =. l .B .') (9)
The value of the fluctuating component of the velocity is thus found to
vary hyperbolically with the velocity of turbulent flame propagation
(fig. 4). If v' is replaced by the product of the Kcrman number by
the mean flow velocity, the formula is obtained
I) 1 + BK (10)
-uN .UzlI _
in which all magnitudes are subject to direct measurement.
It is of importance to note that in the finite expression (9) or
(10)' the scale of turbulence dees not enter. Hence, the obtained riela-
tion will be valid for any scale, prm:vicd the latter does not exceed the
width of the normal combustion front.
60ME PRACTICAL REMARKS
From formula (9) it follows that for la:'e ratios vt/uN (or by
formula (10) KN/uy) unit y may be :u;lected under the root sin. The
combustion velocity is then ind1-:-ndeni of the normal flame velocity and
therefore of the physicochemical properties of the mixture, and is pro-
portional to the fluctuating velocity. For a given value of the latter
(large in comparison with ui) different fuels will burn at the same rate.
If the ratio v'/u (KW/uN) is of the oard r of I or less, the rate of com-
bustion will depend on uN. Within increasing fluctuating velocity the
rate of combustion increases hyperbolically. For very small v' the
effect of the turbulence may be neglected as a Euc. nid-order ma:nituda.
By comparing v'/uN with unity, it should be remembered that the value
of B is equal to 1 only in order of magnitude. Furthermore, it will
evidently depend on the structure of the turbulence. For example, in
pjs-ps with roughness of various sh'pez determining the structure of the
turbulence, different values of B may be expected.
Examination of formula (9) permits drawing the conclusion that if
the velocity of fluctuation is not very large in comparison with uN
the effect of the turbulence on the speed of propagation characterized
by the relative increase in the combustion velocity (uT/uN) will be
greater the slower the combustion of the mixture of the same composition
at rest. The lower the value of uN the greater the given v' (given
turbulence), the numerical value of the root in formula (9).
NACA TM No. 1110
This conclusion is confirmed by the published tests on the effect
of swirling and turbulence on the speed of combustion (reference 3).
Swirling always more greatly increases the speed of combustion of lean
and rich mixtures than stochiometric mixtures. The conditions of the
experiment do not permit a quantitative analysis of these data but
qualitatively they correspond in any case to these results. To evalu-
ate the possible effect of turbulence on the flame propagation, it is
necessary first of all to know the normal speed of combustion ull and,
of course, the speed of the fluctuations or, if the turbulence is known
(the iKrman number), the mean flow velocity. In table 1 are given the
normal flame speeds for certain fuel-air mixtures taken from the book
of Jost (reference 4) (the speeds correspond to the composition of the
mixture of maximum combustion rate). As an example, there are also
given the mean flow speeds for 5-percent turbulence (K = 0.05), the
mean fluctuating speed of which is equal to the corresponding normal
speed of the flame.
Fuel N W
Hydrogen 267 53.4
Acetylene 131 26.2
Ethylene 63 12.6
Propylene 43.5 8.7
Methane 37.0 7.4
n-pentane 35.0 7.0
n-hexane 32.0 6.4
Benzol + 0.5 per-
cent H2 38.5 7.7
Carbon monoxide + 1.2
percent water 41.5 8.3
Table 1 gives an indication of the order of flame speed at 5-
percent turbulence when there is to be expected a hyperbolic depend-
ence of uT on W or when this dependence may be considered as linear.
Thus, for hydrogen-air mixtures of stochiometric composition a linear
NACA TM No. 1110
dependence (and independence of the speed of propagation on the normal
flame speed) may be expected at flow speeds exceeding approximately
seven to eight times the speed giving this dependence in pentane or
benzol air mixtures. For hydrogen these will be speeds of the order
of hundreds of meters per second; for benzol, methane, pentane, hexane,
of the order of tens of meters per second. If the turbulence is in-
creased two times, up to 10 percent, then to attain the same result half
the flow speed would be required, and so forth.
The practical independence of the speed of flame propagation on the
physicochemical properties of the fuel in the engine was also observed
by Marvin (reference 5). On figure 5 are given the curves of the flame
path against the crank angle degrees obtained at constant engine speed.
The slope of the curves gives the flame speed. In the center part of the
combustion chasnber where tha flame front is sufficiently developed the
flame speed changes little over a large distance of the chamber, and for
various fuels is approximately the same while the normal combustion
speeds of these fuels differ considerably from one another (table 1),
Different speeds in the engine are observed only in the initial stage
of the flame propagation.
The results of Marvin can readily be explained. The velocities of
the fluctuations of che gas in the engine are large in comparison with
the normal velocities so that the flame propagatiu.n is described by
expression I(4),that is, the rate of combustion is proportional to the
speed of the fluctuation, and does not depend on the normal flame speed.
It is very probable that under the same conditions for hydrogen or
acetylene the speeds would be different. It is possible that for these
gases the same speed of the fluctuations would not be large by compari-
son with uN. These considerations are in the nature of suppositions
since the true value of the speed of the fluctuations under the test
conditions of Marvin is not known.
The absence of an accelerating effect of the turbulence in the
initial phase of the combustion (well known from the engine literature)
may from the author's point of view be explained by the fact that at
the start of combustion when the dimensions of the flame are small in
comparison with the scale of the turbulence the latter does not affect
the rate of combustion. A center of combustion is displaced as a whole
by the fluctuation, and its surface therefore does not become branched.
The rate of combustion is determined only by the normal flame speed.
In this way it is assumed that the turbulence in the engine is of
relatively large scale.
Certain results for comparison of the theory with experiment are
given also by oth-r investigations conducted on engines. There are,
however, fundamental difficulties, in applying the theory previously
presented, to combustion in the engine. Consider a few of these.
NACA TM No. 1110
In the first place, with regard to the effect of the rotational speed
on the combustion rate, it is not known whether the Karman number re-
mains constant when the speed changes. This can only be assumed on
analogy with pipes and special determinations of K, for engines are
lacking. In the second place, the true effect of the motion of the
entire mass of the gas in the engine chamber on the combustion rate is
not clear. It may be supposed that owing to the small length and the
strong turbulence-producing effect of the intake valve, the degree of
turbulence of the flow during intake and then in the chamber will be
very strong, and the part played by the regular motion of the gas is
small. Finally, photographs give the flame speed with respect to the
walls of the chamber and not with respect to the gas, which is of inter-
est in the latter speed. In the latter case, however, the picture is
not clear. It may, moreover, be supposed that rotational flows are pre-
dominant in the engine. This is indicated, for example, by Marvin's
photographs in which a curving of the flame front is noted, explained by
the circular motion of the gas in the cylinder head. These considerations
are confirmed also by the fact that generally over a considerable distance
of the combustion chamber the photographs of the flame in the engine show
an only slightly varying flame speed. In the case of the presence of a
strong flow along the chamber 'from one end to the other) there should
exist also a return flow. It would then be possible to expect large ir-
regularities in the flame propagation. There is, therefore, some basis
for supposing that the principal cause for the increased rate of combus-
tion in the engine is the turbulence and not a mass movement of the gas
in the engine head. In this respect the opinion of engine specialists
may be suscribed to: for example, Bouchard, F. Taylor, and E. Taylor,
who write, "the rapid increase in the maximum combustion rate with ro-
tational speed is due primarily to an increase in the small-scale in con-
trast to the organized motion of the gas in the engine head but not in
the sense of comparison with the width of the flame front of normal com-
bustion, of higher gas velocities through the intake system." (See
reference 6.) The same authors investigated the dependence of the flame
speed on the rotational speed. The curve of flame speed against rota-
tional speed is given in figure 6. The speed of the mixture on intake,
and therefore the speed of the gas in the chamber, increases in propor-
tion:to the rotational speed. Hence, in figure 6 on the axis of ab-
scissas instead of the rotational speed there may be laid off a magnitude
proportional to the speed of the gas or under the assumptions made to the
speed of the fluctuations. The shape of the curve corresponds strongly
to the theoretical relation obtained (fig. 4). Unfortunately, for small
rotational speeds the experimental curve is extrapolated (dotted).
Bouchard, F. Taylor, and E. Taylor drew this part of the curve on the
basis of measurement of the time of combustion of 95 percent of the
charge. The tests of these authors confirm (though indirectly with
account taken of the assumptions made) the conclusions as to the effect
of the speed of the flame propagation. An accurate check of the theory
requires, of course, special tests with parallel measurement of the
speed of combustion, Karman number and flow speed.
NACA TM Nt. 1110
1i With strong turbulence as the scale of the turbulence in-
creases to a value comparable with the width of front of normal com-
bustion, the rate of the combustion reaction begins to depend on the
2. For turbulence the scale of which exceeds the width of the
front of normal combustion (2 >X), the speed of the flame propagation
increases hyperbolically with the speed of the fluctuations. For
large fluctuation speeds (v' > uN) the dependence may be considered
linear, and for small values (vt
3. The data presented in the literature oh the measurement of
the flame speeds of various fuels in the eniCie and the measurement of
the dependence of the flame speed on the rotational speed confirm the
theoretical conclusions, if it is as~m-red that the increase in the com-
bustion rate in the engine is determined by the turbulence.
Translation by S. Reiss,
National Advisory Committee
NAC.-. TM i'o. 1110
1. Mallard and Le Chatelier: Ann. de Mines, 1883.
2. DamkWhler, : Ze'tschr. f Tr Elektrochemie, vol. 46, no. 11, Nov.
1940, pp. 601-626.
3. Lafitte, P.: La Propaaation des Flammes dans les Melanges Gaseux.
Paris, 1939, p. 72.
Lewie, B., and von Elbe, G.: Combustion, Flames, and Explosions
of Gases. 1938, p. 192.
4. Yost, W.: Explosions and Verbrerueungs Vorgange in Gasen. Julius
Springer (Berlin), 1939.
5. Marvin, Charles F. Jr.: Observations of Flame in an Engine. SAE
Jour., 1934, p. 391.
6. Bouchard, C. L., Taylor, C. F., and Taylor, E. S.: Variables
Affecting Flame Speed in the Otto-Cycle Engine. SAE Jour.,
vol. 41, 1937, p. 515.
1. Zeldovich, Y. B.: Jour. Experimental and Theoretical Physics.(USSR),
vol. 11, 1941, p. 159.
NACA TM No. 1110
I I I
15 30 45 60
Degrees of crank rotation
* Ethane x
o Propane A
F1C 23 1947
S ... i
UNIVERSITY OF FLORIDA
3 1262 08106 269 6
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