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The combustion mechanism and burning velocity in a turbulent flow
567
COMBUSTION MECHANISM AND BURNING VELOCITY
58
THE COMBUSTION MECHANISM AND BURNING VELOCITY IN A TURBULENT FLOW By L. KOZACHENKO Introduction
Theories of flame propagation in a turbulent flow1, 2 are based on the mechanism of flame transfer by pulsations U' and by normal flame velocity U~. According to DamkShler I the turbulent burning velocity Ut is proportional to flow pulsations Ut ~ U' or to the Reynolds number Ut ~ Re. DamkShler represents his experimental results as a function of the Re number
ity, IY. Flame propagation relative to V is determined by the maximum gas-stream velocity Vt :
Un + V . . . . - - V .
(5)
The relation (5) corresponds to the case of flame propagation in tubes, in which the flow direction coincides with that of flame propagation. On the basis of Equation (5), the determining pulsations in flame transfer will be those which have the same direction as the flame (or gas~stream) propagation. Ut = f(Re). (1) Karlovitz 7 makes an important amendment to Ut was estiniated from the fuel-flow rate the surface combustion theory, complementing through the inner generator of the flame-cone the physical pattern of increase in the flame surface in a turbulent flow by introducing a flamesurface. generated pulsation U" By making the same assumption as DamkShler 1 that regular cones are formed on the flame surface U / , _ V2 - - V i 1 U~(1 - cos2a) °'5. (6) under the action of pulsating volumes of a magniv1 v~ tude l, Shchelkin 2 obtained the turbulent burning Karlovitz, 7 as well as Williams and Bollinger8 velocity as the following function represent the flame4ransfer mechanism in a turbulent flow as a displacement of an averaged u~ = v,,~y~ ~ + . (2) flame surface, E l , located along the maximum luminosity line In accord with Equation (2), Ut is directly prov portional to the normal velocity U~ and to the u, (7) relative increase in the flame surface Slat/Sb~. F1 In investigating Sl~t/Sba~, Talantov 3 intro- where V is the flow rate of fresh gas across F I . duced a correction into Equation (2)" I t will be noted that both the fresh mixture Sl~t U~ = U n ~ -
U~ + U'.
(3)
In fact, Ut is equal to the velocity of the mixture flow into the base of the cone Un -4- U ~, and the rate of flame surface increase obeys the Michelson cosinus law Slat
Sbas
-
]
COS (~
-
Un -~- V / - -
V~
(4)
in which a is the angle formed by normals to the base surface and to the lateral cone surface. The mechanism of surface combustion is widely referred to in a number of theoretical and experimental works. 4, 5.6 In the theory of Zeldovich, 5 Ut is determined by the presence of gas streams in the flow, their velocities Um~x exceeding the average gas veloc-
and the combustion products flow across F1, and consequently the values of Ut obtained from Equation (7) under conditions of a straight cone will be considerably underestimated. investigations 9, 10 have shown that the theoretical relation (3) which takes into account the turbulence of flame generated U', is in good agreement with experimental results u,=
un+
u'+
u"
(8)
in which experimental Ut values are calculated from the inner generator of the flame cone. Summerfield ll and Shchetinkov 12 proposed a new model of flame transfer in a turbulent flow. The essence of their theories is that the reaction proceeds not on the distorted flame surface, but in the volume. These works refute the flame-transfer schemes suggested by DamkShler and Shchelkin.
568
TURBULENT FLAMES
The diversity of concepts of flame transfer in a turbulent flow, as well as a great variety of methods for investigating U, considerably hinder the comparison of a great amount of data obtained by different authors. The present work is concerned with more explicit t r e a t m e n t in accord with earlier experimental results2 Comparison of these results with those obtained by others TM 14 is made.
t h a t was used in experiments under the following conditions: (1) The approach-flow velocity varied as follows : V = 22
to
76m/see.
(2) The scale of turbulence varied as follows: e = 1.7
to
15 p e r c e n t .
(3) Air excess: a = 0.55
Experimental Procedure
to
1.2.
(4) Temperature of the combustible mixture: 170°C. The turbulent burning velocity was determined from the mixture flow rate, V, through the inner
All experiments were carried out with benzeneair mixtures with the apparatus described briefly2, lo Figure 1 is a schematic view of the apparatus
.b FIG. 1. Schematic view of the experimental apparatus TABLE 1 0.5
V n , ~"
V~
~r
20°C 40°C 170°C 20 °C 40°C 170°C
0.55
0.6
15
17
19
29
33
37
]__ 0.7
0.8
32 35 59
i4
8
8.7
9.0
9.1
5.1
5.5
5.75
]
5.95
9.3 8.8 6.1
0.9
1.0
1.1
1.2
29
25
21.5
18
54
45
39
34
9.0 8.6 5.9
8.4 7.9 5.5
7.4 7.0 4.8
6.5 6.3 4.2
TABLE 2 ~,U,
"~_.~C
20
SO
7S 75
100
12S 125
150
17S
200
225
0.9 0.8
9.0 9.3
8.3 8.6
7.8 8.0
7.25 7.5
6.8 7.0
6.3 6.5
5.8 6.0
5.4 5.0
5.1 5.2
(10) U~
0.9 0.8
29 32
33 36
37 40
42.5 44
46 49
50 53
55 59.5
59 62
63 67
569
COMBUSTION MECHANISM AND BURNING VELOCITY 7
i
m m
.," g = & 5
m m
s
%,
_
y=t~
.
I %1
m ?gg
,
,2.
\
J
benzene-air mixtures at an initial temperature of 20°C also are shown in Figure 2. Under all turbulence conditions investigated (e = 1.7 to 15 per cent), Ut was subject to the same changes as the normal flame velocity. The maximum value of Ut at a velocity of 22 to 76 m/see, and the maximum U,, correspond to an air excess of a --~ 0.8. The results of a series of runs shown in Figure 2 recalculated by
I
U~ -
3O
!
U=J.~ ~ ; d = / . ~
cent
I
8,5
0.6
0,7
0/~
0,9
t0
~1
z£
t.3
,~
,~5
Fro. 2. Burning velocity in a turbulent flow, Ut, as a function of air excess, a, and flow velocity, V. Temperature of the benzene-air mixture: t = 170°C; U,,--at 20°C; e--5 per cent. Smooth tube without turbulence generating grids. ~--1.7 per cent. Smooth tube with a turbulence generating grid. generator, F, of the combustion zone: V U,
-
(9)
F"
Assuming a simplified scheme of the flame surface development as a regular cone, the additional flame-generated pulsation value U" was determined from E q u a t i o n (6), in which cos a was taken as cos a --
U~ Un +
U"
(10)
The normal flame veloeity Un and the expansion of the combustion products lr = Vo~/V~were measured by the constant-volume bomb method. ~° The results of these experiments are summarized in Tables 1 and 2. Results
Ut was measured as a function of V in the combustion of benzene-air mixtures at the port of a smooth rectangular tube 40 x 40 m m (e = 5 per cent) and downflow of the turbulence-generating grid (e = 1.7 per cent (Fig. 2)). U,~ values for
Un
(11)
are shown in Figure 3. These results are seen to be in good agreement with the theoretical relation (8) (full line). Table 3, current numbers 1 to 13, shows experimental results for Ut as a function of V, at a constant value of a and at extreme values for the scale of turbulence e = 1.7 and e = 15 per cent. At a scale of turbulence of E = 15 per cent and a = 0.8, Ut values were slightly higher than at = 1. This can be accounted for by an error in estimating Ut at high turbulence intensity. Besides at e = 15 per cent and a = 1, values were obtained by the method of direct flame photography at an exposure of 5 mill/see and the diserepancy might be due to use of different methods for recording the combustion zone. The ratio of experimental and theoretical Ut values is shown in column 14 of Table 3. The given experiments also show good agreement with the theoretical relation (8). INVESTmATIO~S CARRIED O~¢ ~Y OTHER AUTHORS (a) Dependences of benzene-air mixtures on the initial temperature, t, and air excess, a, were investigated by Khitrin, Golovina and Sorokina. 13 Experiments were carried out on the port of a burner 16 m m in diameter, with peripheral ignition of the mixture. In treating the results obrained in these experiments in accord with Equation (11), the author made use of maximum Ut values from plots 3 and 413 and of U~, values shown in Tables 1 and 2. The data obtained are shown in Table 3. Investigations were carried out within the range of low-intensity turbulences Ut/U~ = 0.37 to 1.34, in which the term (1 - cos 2 a) °.5 is of great importance in estimating the flame tencrated turbulence from E q u a t i o n (6). When investigations were made in the above range without taking into account the flame ten-
570
TURBULENT FLAMES J$
/$ /2
t2
/0 g $ Y I
s
J
1 0
1
,e
$
l
5
$
7
$
$
~0
.q
Y2 ~.
,¢$
15
o'"
U' + U" Ut Fro. 3. Relative burning velocity, ~ - 1, as a function of the dimensionless-flow pulsation, - Un and of air excess, ~, (in accordance with Fig. 2). crated turbulence, the discrepancy between experimental data and Equation (2) or (3) was maximum. When U" was taken into account, experimental data appeared to be in good agreement with Equation (8). (b) Comparison of experimental results with those obtained by other authors who used different techniques, required additional treatment of these results (Fig. 3). Khitrin and Goldenberg 1~ investigated the visual burning velocity in benzene-air mixtures Utv at a high-combustible mixture velocity by the inverse flame-cone method. Let us use, for comparison, certain data obtained in these investigations 14 carried out only with 40-mm diam tubes, at an approach-flow velocity of V = 51 to 300 m/sec. The values obtained as a function of fuel percentage concentration in the mixture, and of flow velocity are shown in figure 2 of the work cited in reference 14. U~ values shown in the same figure 22 were determined by the relation Utv = 17" X sin 0
(12)
in which 17" is the average combustible mixture
velocity, the flow deviation ahead of the flame front is neglected. 6 is the slope of the flame surface. Because the streamlines of the fresh mixture flow into the flame surface were neglected, the Utv value obtained appears to be considerably overestimated as compared with the real burning velocity relative to the combustion mixture. Investigations on burning velocity14 carried out under conditions of point and peripheral ignition of the mixture have shown that the results of Utv determinations from Equation (12) are two to three times higher than those obtained with peripheral ignition. Comparison was made for flow velocities ranging from 5 to 33 m/see. Khitrin and Goldenberg 14 state that the error in estimating Ut under conditions of peripheral ignition was considerable. A flame cone at a constant ignition source, and the flame-sphere development were recorded in experiments of Khitrin, Goldenberg and Soondoueov 15 by stroboscopic photography at instantaneous ignition of the mixture along the stream axis. According to these measurements, the angle, 0, of the flame-surface slope at a constant ignition
571
COMBUSTION MECHANISM AND BURNING VELOCITY
TABLE 3 ~N n.n,
1
I
2
F
3
a
[
U~
I
U~
I
U'
[
~
I
U"
5
I
6
I
7
I
8
I
9
I
10
re~see
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29
0.01 0.01 0.01 0.01 0.01 0.15 0.15 0.15 0.15 0.15 15 15 15 0.05 0.05 0.05 O. 05 0.05 0.05 O. 05 0.05 O. 05 O. 05 0.05 0.05 0.05 O. 05 0.05 O. 05
0.8 0.8 0.8 0.8 0.8
0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8
2.12 2.65 3.25 3.8 4.2 5.7 7.2 8.2 10.0 11.1 6.4 8.8 9.5 1.8 1.9 2.08 2.23 2.40 2.1 2.28 2.40 2.61 2.95 9.0 12.2 17.5 20.0 23.5 26
source is equal to t h a t of t h e flame-sphere surface g e n e r a t o r a t local ignition. As s h o w n b y these experiments, t h e radius, R2, of t h e flame cone w i t h i n a t i m e interval, t, is equal to t h a t of t h e b u r n t - p r o d u c t s sphere w i t h i n t h e same interval.
§12
]Per Cent
13
14
m/see
0.59 ] 0.41 0.59 0.56 0.59 0.92 0.59 1.12 0.59 1.29 0.45 3.6 0.45 5.1 0.45 6.7 0.45 9.2 0.45 10.4 0.59 3.3 0.59 5.1 0.59 6.3 0.32 0.24 0.36 0.24 0.49 0.24 0.58 0.24 0.65 0.24 0.32 0.43 0.40 0.43 0.49 0.43 0.58 0.43 0.67 0.43 0.35 0.35 0.35 4.50 0.35 8.5 0.35 10.0 0.35 12.7 0.35 15.0
FIG. 4. Schematic view of a torch with central ignition source, a - - a t expansion of combustion products, b - - w i t h o u t expansion of combustion products.
§11
6.1 1.29 6.1 ,' 1.36 6.1 ! 1.53 6.1 1.57 6.1 1.60 5.5 1.17 5.5 1.17 5.5 1.17 1.17 5.5 5.5 1.17 6.1 I 1.74 6.1 1.74 6.1 1.74 9.3 1.23 8.6 1.30 6.9 1.24 5.85 1.16 5.35 1.17 9.3 1.35 8.0 1.42 6.9 1.44 5.9 1.37 5.2 1.3 8.8 1.78 8.8 1.78 8.8 1.78 8.8 1.78 8.8 1.78 8.8 1.78
2.59 3.50 4.5 5.45 6.1 11.7 15 17.2 21.2 23.7 9.8 13.9 15.0 4.65 4.30 3.2 2.83
2.9 3.3 4.2 4.6 4.9 0.6 4 7.5 2.4 5.5 8.55 1.6 3.6 4.65 4.3 2.95 2.3
2.7
2.2
5.6 4.7 3.9 3.5 3.4 12.6 17.5 25.5 29.0 34.5 38.2
5.4 4.64 3.82 3.1 2.6 12.4 17.1 29.3 33.6 41.3 48.0
0.895 1.06 1.07 1.18 1.24 1.1 1 .O7 0.98 0.95 0.93 1.14 1.20 1.1 1.0 1.0 1.09 1.23 1.22 i 1 .O4 1.02 1.02 1.13 1.31 1.02 0.98 0.87 0.86 0.84 0.80
-10.5 +6 +7 +18 +24 +10 +7 -2 --5 --7 +14 +20 +10 ±0 ±0 +9 +23 +22 +4 +2 +2 +13 +31 +2 --2 --13 --14 --16 --20
A s s u m i n g t h a t t h e initial b u r n i n g velocity a n d c o m b u s t i o n - p r o d u c t velocities r e m a i n constant, t h e flame cone, o b t a i n e d e x p e r i m e n t a l l y a t a flow velocity of 5 m / s e c a n d a t a n R2 sphere radius t a k i n g into a c c o u n t t h e s t r e a m expansion coefficient 11- = V # V 1 , will be represented as in Figure 4a, a n d t h a t corresponding to a n R1 radius sphere neglecting t h e p r o d u c t s e x p a n s i o n - - a s in Figure 4b. As t h e r e is no expansion in t h e c o m b u s t i o n p r o d u c t s in Figure 4b, t h e gas flow will n o t deviate from t h e axial direction, a n d t h e t u r b u l e n t velocity w i t h respect to t h e c o m b u s t i b l e m i x t u r e will b e U t = V s i n a.
(13)
T h e effect of expansion o n t h e m i x t u r e streamlines a h e a d of t h e flame f r o n t was neglected in
572
TURBULENT FLAMES
2O
8 15
0
I0
k~olackan~ g= l
÷
20
30
~
U'+U"
50
Lln
R e s u l t s and D i s c u s s i o n
FIG. 5. Comparison of the theoretical relation with experimental results obtained,~3, ~4 and also by the author of the present paper at a high scale of turbulence e = 15 per cent. Figure 4a, and only the visual burning velocity was recorded according to Equation (12). The correlation coefficient for recalculation of Ut~ to Ut will be Utv _ V × sin O Ut
V X sin a
-
R~_ R~
~;.
peripheral ignition according to relation (8) are given in column 14 of Table 3. As can be seen from Figure 5 recalculated values are in good agreement with the theoretical relation (8) within a velocity range of V = 50 to 90 m/see. At high-flow velocities of V = 200 to 300 m/see, recalculated values are lower than those obtained from Equation (8) by ~ 2 0 per cent. The given recalculation of Utv into Ut is not rigid; neither is the estimation of Ut,, 14from Equation (12). The given comparison refers rather to the approximate estimation of the correlation coefficient for Equation (12) made in order to obtain comparable results for peripheral and central ignition of the mixture.
(14)
As stated above, Equation (14) was obtained on the assumption that the initial mixture and combustion products velocities remain constant. Measurements of the initial mixture and combustion-product velocities15 have shown that the velocity in the combustion zone is 50 to 60 per cent higher than that of a cold stream. In the central part of the cone at a distance of about two diameters from the tube top the velocities will exceed those of a cold stream by ~ 3 0 per cent. I n determinations of Equation (14), the ~ 3 0 per cent increase in the hot-stream velocity will again diminish the true value by some 30 per cent. The expansion coefficient used in reealculations was equal to
where ~r = 8.8. Results of treatment of maximum experimental values are shown in Table 3, current numbers 24 to 29, and in Figure 5. Comparison of experimental values~4 recalculated for the case of
The results of Ut investigations carried out over a wide range of variations in the scale of turbulence, e = 1.7 to 15 per cent, and in flow velocities are described unambiguously in Equation (8). Experimental results 13obtained by sinfilar methods (peripheral ignition) also show good agreement with the theoretical relation (8). Direct quantitative measurements of Ut were not madC 4 and this reduces the value of the comparison made. More explicit comparison would require estimation of the initial mixture streamlines and of the actual gas-flow rate per surface unit of the flame cone, as well as measurements of combustion product velocities in the axial part of the cone at high V.
Conclusions The following conclusions may be drawn from the above investigation: Combustion in a turbulent subsonic flow proceeds by a surface mechanism. The flame sites most projected toward the burning mixture are the sources of surface combustion. The burning velocity is determined by maximum flame-site velocities relative to averageflow velocity. The physical pattern of flame transfer by normal velocity U~ and flow pulsations U' and U" is confirmed by Equation (3). Occurrence of flame-generated pulsations contributes to the role of normal flame velocity in turbulent flow combustion. The relation Ut = f(Re) is a specific ease fulfilled under experimental conditions. REFERENCES 1. DAMK~HLER, G.: Z. Elektroehem., 46, 601
(1940).
573
COMBUSTION MECHANISM AND BURNING VELOCITY
2. SHCttELKIN, K. I. : Z. Tech. Phys., 8,520 (1943). 3. TALANTOV, A. V.: Trudy Kazanskogo Aviazionnogo Instituta, 31, 157 (1956). 4. FRANK-KAMENETZKY,D. A. : Trudy NauchnoIssled. Instituta-I, No. 7 (1946). 5. ZELDOVICH,Y. B. : Z. Tech. Phys., 18, 3 (1947). 6. LEASON, D. B.: Fuel, 30, 233 (1951). 7. KARLOVITZ,B., DENNISTON, D., AND WELLS, F.: J. Chem. Phys., 19, 541 (1951). 8. WILLIAMS, D. T., AND BOLLINGER, L. M.:
Third Symposium on Combustion, Flame, and Explosion Phenomena, p. 196, The Williams & Wilkins Company, Baltimore, 1949. 9. KOZACnENXO, L. S.: Izv. Akad S. S. S. R., Otdel. Techn. Nauk, Energetika i Avtomatika No 2, 25 (1959).
10. KOZACHENKO, L. S.: h r . Akad. Nauk S. S. S. R., Otdel. Chim. Nauk, No. 1, 45 (1960). Ii. SUMMERFIELD, M.: Jet Propulsion, No. 7, 24 (1954). 12. SHCHETINKOV, E. S.: Nauchno-Issled. Institut-1, Oborongiz, 1956. 13. KHITRIN, L. N., GOLOVINA, E. S., AND SOROKINA, A. V.: Issledovanye Prozessov Gorenya, h d . AN S. S. S. R., 78 (1958). 14. •HITRIN, L. N., AND GOLDENBERG, S. A.: Gazodynamika i Physika Gorenya, Izd. AN S. S. S. R., Moscow, 1959. 15. I[4~HITRIN, L. N., GOLDENBERG, S. A., A N D SOONDOUCOV, I. N. : Gazodynamika i Physika
Gozenya, 110, Izd. AN S. S. S. R., Moscow, 1959.
59 PRELIMINARY OBSERVATIONS OF A ONE-DIMENSIONAL TURBULENT PROPANE-AIR FLAME By WILLIAM T. SNYDER Introduction The objectives of this investigation were to obtain, analytically, an expression for the onedimensional turbulent-flame propagation velocity, and to develop an experimental apparatus for the measurement of turbulent-flame propagation velocities which would closely approximate a one-dimensional situation. The analytical formulation of the problem was based on a perturbation technique which is normally used in turbulence studies. After replacing each variable in the conservation equations by a time-average value plus a fluctuation, the equations were then time averaged. The timeaveraging process gave rise to turbulent fluxes of mass, momentum, and energy. The fluxes were related to the mean property values by means of semi-empirical exchange coefficients. The equations were integrated for the simple case of a onestep reaction. Turbulent-flame propagation velocities were obtained with an apparatus which was a modified flat-flame burner. It was demonstrated that a flat-flame burner is a feasible experimental tool for obtaining turbulent-flame propagation veloci-
ties at low levels of turbulence. Good qualitative agreement was obtained between the measured propagation velocities and the trend predicted from the analysis.
Analytical Formulation of the Problem FORMULATION OF THE FUNDAMENTAL CONSERVATION EQUATIONS CONSERVATION OF MASS
The conservation of mass equation is written on an individual chemical specie basis. Consequently, the rate of production by chemical reaction must be taken into account. For a control volume fixed in space, the instantaneous conservation of mass for chemical specie i may be written: mi
M~
d
dx
UC~ -
~d z ) "
(1)
The assumption is now introduced that each of the dependent variables appearing in Equation (1), with the exception of Di may be replaced by a time-average value plus an instantaneous fluctuation. Making this substitution and performing
COMBUSTION MECHANISM AND BURNING VELOCITY
58
THE COMBUSTION MECHANISM AND BURNING VELOCITY IN A TURBULENT FLOW By L. KOZACHENKO Introduction
Theories of flame propagation in a turbulent flow1, 2 are based on the mechanism of flame transfer by pulsations U' and by normal flame velocity U~. According to DamkShler I the turbulent burning velocity Ut is proportional to flow pulsations Ut ~ U' or to the Reynolds number Ut ~ Re. DamkShler represents his experimental results as a function of the Re number
ity, IY. Flame propagation relative to V is determined by the maximum gas-stream velocity Vt :
Un + V . . . . - - V .
(5)
The relation (5) corresponds to the case of flame propagation in tubes, in which the flow direction coincides with that of flame propagation. On the basis of Equation (5), the determining pulsations in flame transfer will be those which have the same direction as the flame (or gas~stream) propagation. Ut = f(Re). (1) Karlovitz 7 makes an important amendment to Ut was estiniated from the fuel-flow rate the surface combustion theory, complementing through the inner generator of the flame-cone the physical pattern of increase in the flame surface in a turbulent flow by introducing a flamesurface. generated pulsation U" By making the same assumption as DamkShler 1 that regular cones are formed on the flame surface U / , _ V2 - - V i 1 U~(1 - cos2a) °'5. (6) under the action of pulsating volumes of a magniv1 v~ tude l, Shchelkin 2 obtained the turbulent burning Karlovitz, 7 as well as Williams and Bollinger8 velocity as the following function represent the flame4ransfer mechanism in a turbulent flow as a displacement of an averaged u~ = v,,~y~ ~ + . (2) flame surface, E l , located along the maximum luminosity line In accord with Equation (2), Ut is directly prov portional to the normal velocity U~ and to the u, (7) relative increase in the flame surface Slat/Sb~. F1 In investigating Sl~t/Sba~, Talantov 3 intro- where V is the flow rate of fresh gas across F I . duced a correction into Equation (2)" I t will be noted that both the fresh mixture Sl~t U~ = U n ~ -
U~ + U'.
(3)
In fact, Ut is equal to the velocity of the mixture flow into the base of the cone Un -4- U ~, and the rate of flame surface increase obeys the Michelson cosinus law Slat
Sbas
-
]
COS (~
-
Un -~- V / - -
V~
(4)
in which a is the angle formed by normals to the base surface and to the lateral cone surface. The mechanism of surface combustion is widely referred to in a number of theoretical and experimental works. 4, 5.6 In the theory of Zeldovich, 5 Ut is determined by the presence of gas streams in the flow, their velocities Um~x exceeding the average gas veloc-
and the combustion products flow across F1, and consequently the values of Ut obtained from Equation (7) under conditions of a straight cone will be considerably underestimated. investigations 9, 10 have shown that the theoretical relation (3) which takes into account the turbulence of flame generated U', is in good agreement with experimental results u,=
un+
u'+
u"
(8)
in which experimental Ut values are calculated from the inner generator of the flame cone. Summerfield ll and Shchetinkov 12 proposed a new model of flame transfer in a turbulent flow. The essence of their theories is that the reaction proceeds not on the distorted flame surface, but in the volume. These works refute the flame-transfer schemes suggested by DamkShler and Shchelkin.
568
TURBULENT FLAMES
The diversity of concepts of flame transfer in a turbulent flow, as well as a great variety of methods for investigating U, considerably hinder the comparison of a great amount of data obtained by different authors. The present work is concerned with more explicit t r e a t m e n t in accord with earlier experimental results2 Comparison of these results with those obtained by others TM 14 is made.
t h a t was used in experiments under the following conditions: (1) The approach-flow velocity varied as follows : V = 22
to
76m/see.
(2) The scale of turbulence varied as follows: e = 1.7
to
15 p e r c e n t .
(3) Air excess: a = 0.55
Experimental Procedure
to
1.2.
(4) Temperature of the combustible mixture: 170°C. The turbulent burning velocity was determined from the mixture flow rate, V, through the inner
All experiments were carried out with benzeneair mixtures with the apparatus described briefly2, lo Figure 1 is a schematic view of the apparatus
.b FIG. 1. Schematic view of the experimental apparatus TABLE 1 0.5
V n , ~"
V~
~r
20°C 40°C 170°C 20 °C 40°C 170°C
0.55
0.6
15
17
19
29
33
37
]__ 0.7
0.8
32 35 59
i4
8
8.7
9.0
9.1
5.1
5.5
5.75
]
5.95
9.3 8.8 6.1
0.9
1.0
1.1
1.2
29
25
21.5
18
54
45
39
34
9.0 8.6 5.9
8.4 7.9 5.5
7.4 7.0 4.8
6.5 6.3 4.2
TABLE 2 ~,U,
"~_.~C
20
SO
7S 75
100
12S 125
150
17S
200
225
0.9 0.8
9.0 9.3
8.3 8.6
7.8 8.0
7.25 7.5
6.8 7.0
6.3 6.5
5.8 6.0
5.4 5.0
5.1 5.2
(10) U~
0.9 0.8
29 32
33 36
37 40
42.5 44
46 49
50 53
55 59.5
59 62
63 67
569
COMBUSTION MECHANISM AND BURNING VELOCITY 7
i
m m
.," g = & 5
m m
s
%,
_
y=t~
.
I %1
m ?gg
,
,2.
\
J
benzene-air mixtures at an initial temperature of 20°C also are shown in Figure 2. Under all turbulence conditions investigated (e = 1.7 to 15 per cent), Ut was subject to the same changes as the normal flame velocity. The maximum value of Ut at a velocity of 22 to 76 m/see, and the maximum U,, correspond to an air excess of a --~ 0.8. The results of a series of runs shown in Figure 2 recalculated by
I
U~ -
3O
!
U=J.~ ~ ; d = / . ~
cent
I
8,5
0.6
0,7
0/~
0,9
t0
~1
z£
t.3
,~
,~5
Fro. 2. Burning velocity in a turbulent flow, Ut, as a function of air excess, a, and flow velocity, V. Temperature of the benzene-air mixture: t = 170°C; U,,--at 20°C; e--5 per cent. Smooth tube without turbulence generating grids. ~--1.7 per cent. Smooth tube with a turbulence generating grid. generator, F, of the combustion zone: V U,
-
(9)
F"
Assuming a simplified scheme of the flame surface development as a regular cone, the additional flame-generated pulsation value U" was determined from E q u a t i o n (6), in which cos a was taken as cos a --
U~ Un +
U"
(10)
The normal flame veloeity Un and the expansion of the combustion products lr = Vo~/V~were measured by the constant-volume bomb method. ~° The results of these experiments are summarized in Tables 1 and 2. Results
Ut was measured as a function of V in the combustion of benzene-air mixtures at the port of a smooth rectangular tube 40 x 40 m m (e = 5 per cent) and downflow of the turbulence-generating grid (e = 1.7 per cent (Fig. 2)). U,~ values for
Un
(11)
are shown in Figure 3. These results are seen to be in good agreement with the theoretical relation (8) (full line). Table 3, current numbers 1 to 13, shows experimental results for Ut as a function of V, at a constant value of a and at extreme values for the scale of turbulence e = 1.7 and e = 15 per cent. At a scale of turbulence of E = 15 per cent and a = 0.8, Ut values were slightly higher than at = 1. This can be accounted for by an error in estimating Ut at high turbulence intensity. Besides at e = 15 per cent and a = 1, values were obtained by the method of direct flame photography at an exposure of 5 mill/see and the diserepancy might be due to use of different methods for recording the combustion zone. The ratio of experimental and theoretical Ut values is shown in column 14 of Table 3. The given experiments also show good agreement with the theoretical relation (8). INVESTmATIO~S CARRIED O~¢ ~Y OTHER AUTHORS (a) Dependences of benzene-air mixtures on the initial temperature, t, and air excess, a, were investigated by Khitrin, Golovina and Sorokina. 13 Experiments were carried out on the port of a burner 16 m m in diameter, with peripheral ignition of the mixture. In treating the results obrained in these experiments in accord with Equation (11), the author made use of maximum Ut values from plots 3 and 413 and of U~, values shown in Tables 1 and 2. The data obtained are shown in Table 3. Investigations were carried out within the range of low-intensity turbulences Ut/U~ = 0.37 to 1.34, in which the term (1 - cos 2 a) °.5 is of great importance in estimating the flame tencrated turbulence from E q u a t i o n (6). When investigations were made in the above range without taking into account the flame ten-
570
TURBULENT FLAMES J$
/$ /2
t2
/0 g $ Y I
s
J
1 0
1
,e
$
l
5
$
7
$
$
~0
.q
Y2 ~.
,¢$
15
o'"
U' + U" Ut Fro. 3. Relative burning velocity, ~ - 1, as a function of the dimensionless-flow pulsation, - Un and of air excess, ~, (in accordance with Fig. 2). crated turbulence, the discrepancy between experimental data and Equation (2) or (3) was maximum. When U" was taken into account, experimental data appeared to be in good agreement with Equation (8). (b) Comparison of experimental results with those obtained by other authors who used different techniques, required additional treatment of these results (Fig. 3). Khitrin and Goldenberg 1~ investigated the visual burning velocity in benzene-air mixtures Utv at a high-combustible mixture velocity by the inverse flame-cone method. Let us use, for comparison, certain data obtained in these investigations 14 carried out only with 40-mm diam tubes, at an approach-flow velocity of V = 51 to 300 m/sec. The values obtained as a function of fuel percentage concentration in the mixture, and of flow velocity are shown in figure 2 of the work cited in reference 14. U~ values shown in the same figure 22 were determined by the relation Utv = 17" X sin 0
(12)
in which 17" is the average combustible mixture
velocity, the flow deviation ahead of the flame front is neglected. 6 is the slope of the flame surface. Because the streamlines of the fresh mixture flow into the flame surface were neglected, the Utv value obtained appears to be considerably overestimated as compared with the real burning velocity relative to the combustion mixture. Investigations on burning velocity14 carried out under conditions of point and peripheral ignition of the mixture have shown that the results of Utv determinations from Equation (12) are two to three times higher than those obtained with peripheral ignition. Comparison was made for flow velocities ranging from 5 to 33 m/see. Khitrin and Goldenberg 14 state that the error in estimating Ut under conditions of peripheral ignition was considerable. A flame cone at a constant ignition source, and the flame-sphere development were recorded in experiments of Khitrin, Goldenberg and Soondoueov 15 by stroboscopic photography at instantaneous ignition of the mixture along the stream axis. According to these measurements, the angle, 0, of the flame-surface slope at a constant ignition
571
COMBUSTION MECHANISM AND BURNING VELOCITY
TABLE 3 ~N n.n,
1
I
2
F
3
a
[
U~
I
U~
I
U'
[
~
I
U"
5
I
6
I
7
I
8
I
9
I
10
re~see
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29
0.01 0.01 0.01 0.01 0.01 0.15 0.15 0.15 0.15 0.15 15 15 15 0.05 0.05 0.05 O. 05 0.05 0.05 O. 05 0.05 O. 05 O. 05 0.05 0.05 0.05 O. 05 0.05 O. 05
0.8 0.8 0.8 0.8 0.8
0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8
2.12 2.65 3.25 3.8 4.2 5.7 7.2 8.2 10.0 11.1 6.4 8.8 9.5 1.8 1.9 2.08 2.23 2.40 2.1 2.28 2.40 2.61 2.95 9.0 12.2 17.5 20.0 23.5 26
source is equal to t h a t of t h e flame-sphere surface g e n e r a t o r a t local ignition. As s h o w n b y these experiments, t h e radius, R2, of t h e flame cone w i t h i n a t i m e interval, t, is equal to t h a t of t h e b u r n t - p r o d u c t s sphere w i t h i n t h e same interval.
§12
]Per Cent
13
14
m/see
0.59 ] 0.41 0.59 0.56 0.59 0.92 0.59 1.12 0.59 1.29 0.45 3.6 0.45 5.1 0.45 6.7 0.45 9.2 0.45 10.4 0.59 3.3 0.59 5.1 0.59 6.3 0.32 0.24 0.36 0.24 0.49 0.24 0.58 0.24 0.65 0.24 0.32 0.43 0.40 0.43 0.49 0.43 0.58 0.43 0.67 0.43 0.35 0.35 0.35 4.50 0.35 8.5 0.35 10.0 0.35 12.7 0.35 15.0
FIG. 4. Schematic view of a torch with central ignition source, a - - a t expansion of combustion products, b - - w i t h o u t expansion of combustion products.
§11
6.1 1.29 6.1 ,' 1.36 6.1 ! 1.53 6.1 1.57 6.1 1.60 5.5 1.17 5.5 1.17 5.5 1.17 1.17 5.5 5.5 1.17 6.1 I 1.74 6.1 1.74 6.1 1.74 9.3 1.23 8.6 1.30 6.9 1.24 5.85 1.16 5.35 1.17 9.3 1.35 8.0 1.42 6.9 1.44 5.9 1.37 5.2 1.3 8.8 1.78 8.8 1.78 8.8 1.78 8.8 1.78 8.8 1.78 8.8 1.78
2.59 3.50 4.5 5.45 6.1 11.7 15 17.2 21.2 23.7 9.8 13.9 15.0 4.65 4.30 3.2 2.83
2.9 3.3 4.2 4.6 4.9 0.6 4 7.5 2.4 5.5 8.55 1.6 3.6 4.65 4.3 2.95 2.3
2.7
2.2
5.6 4.7 3.9 3.5 3.4 12.6 17.5 25.5 29.0 34.5 38.2
5.4 4.64 3.82 3.1 2.6 12.4 17.1 29.3 33.6 41.3 48.0
0.895 1.06 1.07 1.18 1.24 1.1 1 .O7 0.98 0.95 0.93 1.14 1.20 1.1 1.0 1.0 1.09 1.23 1.22 i 1 .O4 1.02 1.02 1.13 1.31 1.02 0.98 0.87 0.86 0.84 0.80
-10.5 +6 +7 +18 +24 +10 +7 -2 --5 --7 +14 +20 +10 ±0 ±0 +9 +23 +22 +4 +2 +2 +13 +31 +2 --2 --13 --14 --16 --20
A s s u m i n g t h a t t h e initial b u r n i n g velocity a n d c o m b u s t i o n - p r o d u c t velocities r e m a i n constant, t h e flame cone, o b t a i n e d e x p e r i m e n t a l l y a t a flow velocity of 5 m / s e c a n d a t a n R2 sphere radius t a k i n g into a c c o u n t t h e s t r e a m expansion coefficient 11- = V # V 1 , will be represented as in Figure 4a, a n d t h a t corresponding to a n R1 radius sphere neglecting t h e p r o d u c t s e x p a n s i o n - - a s in Figure 4b. As t h e r e is no expansion in t h e c o m b u s t i o n p r o d u c t s in Figure 4b, t h e gas flow will n o t deviate from t h e axial direction, a n d t h e t u r b u l e n t velocity w i t h respect to t h e c o m b u s t i b l e m i x t u r e will b e U t = V s i n a.
(13)
T h e effect of expansion o n t h e m i x t u r e streamlines a h e a d of t h e flame f r o n t was neglected in
572
TURBULENT FLAMES
2O
8 15
0
I0
k~olackan~ g= l
÷
20
30
~
U'+U"
50
Lln
R e s u l t s and D i s c u s s i o n
FIG. 5. Comparison of the theoretical relation with experimental results obtained,~3, ~4 and also by the author of the present paper at a high scale of turbulence e = 15 per cent. Figure 4a, and only the visual burning velocity was recorded according to Equation (12). The correlation coefficient for recalculation of Ut~ to Ut will be Utv _ V × sin O Ut
V X sin a
-
R~_ R~
~;.
peripheral ignition according to relation (8) are given in column 14 of Table 3. As can be seen from Figure 5 recalculated values are in good agreement with the theoretical relation (8) within a velocity range of V = 50 to 90 m/see. At high-flow velocities of V = 200 to 300 m/see, recalculated values are lower than those obtained from Equation (8) by ~ 2 0 per cent. The given recalculation of Utv into Ut is not rigid; neither is the estimation of Ut,, 14from Equation (12). The given comparison refers rather to the approximate estimation of the correlation coefficient for Equation (12) made in order to obtain comparable results for peripheral and central ignition of the mixture.
(14)
As stated above, Equation (14) was obtained on the assumption that the initial mixture and combustion products velocities remain constant. Measurements of the initial mixture and combustion-product velocities15 have shown that the velocity in the combustion zone is 50 to 60 per cent higher than that of a cold stream. In the central part of the cone at a distance of about two diameters from the tube top the velocities will exceed those of a cold stream by ~ 3 0 per cent. I n determinations of Equation (14), the ~ 3 0 per cent increase in the hot-stream velocity will again diminish the true value by some 30 per cent. The expansion coefficient used in reealculations was equal to
where ~r = 8.8. Results of treatment of maximum experimental values are shown in Table 3, current numbers 24 to 29, and in Figure 5. Comparison of experimental values~4 recalculated for the case of
The results of Ut investigations carried out over a wide range of variations in the scale of turbulence, e = 1.7 to 15 per cent, and in flow velocities are described unambiguously in Equation (8). Experimental results 13obtained by sinfilar methods (peripheral ignition) also show good agreement with the theoretical relation (8). Direct quantitative measurements of Ut were not madC 4 and this reduces the value of the comparison made. More explicit comparison would require estimation of the initial mixture streamlines and of the actual gas-flow rate per surface unit of the flame cone, as well as measurements of combustion product velocities in the axial part of the cone at high V.
Conclusions The following conclusions may be drawn from the above investigation: Combustion in a turbulent subsonic flow proceeds by a surface mechanism. The flame sites most projected toward the burning mixture are the sources of surface combustion. The burning velocity is determined by maximum flame-site velocities relative to averageflow velocity. The physical pattern of flame transfer by normal velocity U~ and flow pulsations U' and U" is confirmed by Equation (3). Occurrence of flame-generated pulsations contributes to the role of normal flame velocity in turbulent flow combustion. The relation Ut = f(Re) is a specific ease fulfilled under experimental conditions. REFERENCES 1. DAMK~HLER, G.: Z. Elektroehem., 46, 601
(1940).
573
COMBUSTION MECHANISM AND BURNING VELOCITY
2. SHCttELKIN, K. I. : Z. Tech. Phys., 8,520 (1943). 3. TALANTOV, A. V.: Trudy Kazanskogo Aviazionnogo Instituta, 31, 157 (1956). 4. FRANK-KAMENETZKY,D. A. : Trudy NauchnoIssled. Instituta-I, No. 7 (1946). 5. ZELDOVICH,Y. B. : Z. Tech. Phys., 18, 3 (1947). 6. LEASON, D. B.: Fuel, 30, 233 (1951). 7. KARLOVITZ,B., DENNISTON, D., AND WELLS, F.: J. Chem. Phys., 19, 541 (1951). 8. WILLIAMS, D. T., AND BOLLINGER, L. M.:
Third Symposium on Combustion, Flame, and Explosion Phenomena, p. 196, The Williams & Wilkins Company, Baltimore, 1949. 9. KOZACnENXO, L. S.: Izv. Akad S. S. S. R., Otdel. Techn. Nauk, Energetika i Avtomatika No 2, 25 (1959).
10. KOZACHENKO, L. S.: h r . Akad. Nauk S. S. S. R., Otdel. Chim. Nauk, No. 1, 45 (1960). Ii. SUMMERFIELD, M.: Jet Propulsion, No. 7, 24 (1954). 12. SHCHETINKOV, E. S.: Nauchno-Issled. Institut-1, Oborongiz, 1956. 13. KHITRIN, L. N., GOLOVINA, E. S., AND SOROKINA, A. V.: Issledovanye Prozessov Gorenya, h d . AN S. S. S. R., 78 (1958). 14. •HITRIN, L. N., AND GOLDENBERG, S. A.: Gazodynamika i Physika Gorenya, Izd. AN S. S. S. R., Moscow, 1959. 15. I[4~HITRIN, L. N., GOLDENBERG, S. A., A N D SOONDOUCOV, I. N. : Gazodynamika i Physika
Gozenya, 110, Izd. AN S. S. S. R., Moscow, 1959.
59 PRELIMINARY OBSERVATIONS OF A ONE-DIMENSIONAL TURBULENT PROPANE-AIR FLAME By WILLIAM T. SNYDER Introduction The objectives of this investigation were to obtain, analytically, an expression for the onedimensional turbulent-flame propagation velocity, and to develop an experimental apparatus for the measurement of turbulent-flame propagation velocities which would closely approximate a one-dimensional situation. The analytical formulation of the problem was based on a perturbation technique which is normally used in turbulence studies. After replacing each variable in the conservation equations by a time-average value plus a fluctuation, the equations were then time averaged. The timeaveraging process gave rise to turbulent fluxes of mass, momentum, and energy. The fluxes were related to the mean property values by means of semi-empirical exchange coefficients. The equations were integrated for the simple case of a onestep reaction. Turbulent-flame propagation velocities were obtained with an apparatus which was a modified flat-flame burner. It was demonstrated that a flat-flame burner is a feasible experimental tool for obtaining turbulent-flame propagation veloci-
ties at low levels of turbulence. Good qualitative agreement was obtained between the measured propagation velocities and the trend predicted from the analysis.
Analytical Formulation of the Problem FORMULATION OF THE FUNDAMENTAL CONSERVATION EQUATIONS CONSERVATION OF MASS
The conservation of mass equation is written on an individual chemical specie basis. Consequently, the rate of production by chemical reaction must be taken into account. For a control volume fixed in space, the instantaneous conservation of mass for chemical specie i may be written: mi
M~
d
dx
UC~ -
~d z ) "
(1)
The assumption is now introduced that each of the dependent variables appearing in Equation (1), with the exception of Di may be replaced by a time-average value plus an instantaneous fluctuation. Making this substitution and performing