Characterization of Turbulent
Combustion by Flame Space and Space Heating Rates PROPANE-OXYGEN-NITROGEN FLAMES DOROTHY M. SIMON AND PAUL WAGNER Lewis Flight Propulsion Laboratory, Cleveland 11, Ohio
A
T THIS stage in the development of the field of turbulent combustion, it is necessary to characterize and to classify the various kinds of combustion systems. This means that adequate characterizing parameters ought to be defined and measured and that generalized combustion systems such as free and stabilized flames propagating in isotropic and nonisotropic turbulence fields should be used. As a step in this direction, two characterizing parameters not generally used for laminar flames have been defined and have been used to characterize some propane-oxygen-nitrogen turbulent flames stabilized above pipes. I n the past, the characterization of turbulent flames has followed the methods used for laminar flames. I n particular, the burning velocity, defined as the velocity of the reaction front relative to the unburned gas, has been used to describe flame propagation. Burning velocity of flames stabilized on burners has been defined by the following equation:
For laminar flames, the determination of burning velocity is fairly direct, because the reaction zone is thin and stream tubes may be identified. But turbulent flames are not 80 easily characterized in this way. Even when a turbulent flame is stabilized, the volume occupied by the fluctuating reaction zone is large compared with the volume of a laminar flame zone. I n the measurement of turbulent burning velocity, two experimental difficulties occur: (1) the instantaneous determination of the position and area of the flame front and (2) the identification of the stream tubes which feed it. To overcome the first difficulty, various definitions of smoothedout time average flame front positions based on different methods of identifying the reaction zone front have been used (3, 8, 9, 12, 14). A few methods not requiring area determinations have also been suggested (4, 11). The second difficulty has not yet been overcome; there is no adequate technique for mapping the flow pattern of the unburned gas in the presence of flame. Obviously, further development of the methods of measuring turbulent burning velocity is necessary. Even if burning velocities of turbulent flames were readily measurable, this property alone is insufficient to characterize turbulent combustion. The space requirements for burning and the heat release rates are needed for practical applications. The product of these two factors is the space heating rate. Avery (6) has pointed out the importance of this factor in the treatment of ram-jet combustors as continuous-flow stirred reactors. Flame space heating rate may be defined by the following equations: AH, = ZAH, (2) where
129
Flame space heating rate, AH,, may be determined from a knowledge of the volumetric flow rate, U,, and determinations of flame zone volume, V f , and the specific heat release on passage through the flame front, A H f . Flame space heating rate is a measure of the energy released per unit volume of flame per unit time. Space rates, 2, for turbulent flames measure the quantity of initial gas mixture which will'burn in a unit flame volume per unit time. An increased space rate indicates that more material will pass through a unit flame volume in the same length of time. Both the space rate, 2, and the space heating rate, AHe, should be good characterizing parameters for fihmes. I n particular, turbulent flames ought to be well characterized in t h k manner because the flame zone depth and the degree of the chemical reaction are included. Also, any changes in character of burning, such as those apparently indicated by schlieren photographs or by changes in burning velocity, should be reflected by these parameters. The generality of application of these parameters should be valuable to engineers studying combustor design principles. Many types of combustion may be characterized: (1) premixed and diffusion flames, either turbulent or laminar; (2) homogeneous high temperature reactions; and (3) performance of ramjet and turbojet combustors. I n this study, methods of measuring flame space rate and space heating rates are given and some propane-oxygen-nitrogen turbulent flames stabilized above pipes are characterized. The effects of linear flow rate, laminar burning velocity, and pipe diameter on flame space rate are shown, and these effects are interpreted in terms of a folded flame model and an extended reaction zone model. The measured space heating rates are compared with those for laminar flames, homogeneous reactions, and values calculated from combustor performance. EXPERIMENTAL
Description of Burner. Turbulent flames were stabilized above the pipe burner lip by a small concentric pilot flame. Details of construction are shown in Figure 1. The lip was cooled by water to the temperature of the inlet fuel-air mixture, 25' C. The combustible mixture used for the pilot was of the same composition as the mixture used for the stabilized turbulent flame. Burners of four different diameters were used-0.639, 1.016, 1.459, and 1.89 em. Flow rates of unburned gas were such that pipe Reynolds numbers varied from 4000 to 20,000. All measurements were made at atmospheric pressure. Initial Gas Mixtures. Two mixtures of propane, oxygen, and nitrogen were used-(1) 4.03% propane, 20.1670 oxygen, 75.81% nitrogen (air), and (2) 5.12% propane, 25.80% oxygen, and 64.08% nitrogen. Both mixtures were of stoichiometric composition on the basis of reaction to give carbon dioxide and water. The composition of the unburned gas mixtures was con-
INDUSTRIAL AND ENGINEERING CHEMISTRY
130
Vol. 48, No. 1
exposure from 0.5 t o 2 seconds and f settings of 5.6, 8, 11, and 16, flame volumes measured from the negatives were constant -within Engineers interested in comthe precision of measurement. The best conditions for photographing depend on the intensity of the flame and the rate o€ bustor design principles flame fluctuation. In general, an exposure time of 0.5 second and immediately understan anf setting of 8 were x e d . The dimensions of the flame zone vere measllred directly from results when turbulent combustion is the negatives of the flame photographs. These measurements expressed in terms of flame space were corrected for magnification (magnification factors from 0.6 and space heating rates to 1.75), and plotted on graph paper. The flame zone was divided into three to four segments, and the volume of each calculated according to Thether it was a hollow cylinder, conic segment, or paraboloid. The sum of these segments represented the volume of the flame zone used in Equation 3 to calculate an trolled by critical flow orifices. Propane and oxygen of C.P. average value of flame space rate. Total volumes measured from grade and service air Trere used. The laminar burning velocities 1.5 to 14.3 cc. were 35.5 em. per second for the first mixture, and 71 em. pel The range of repeated measurements of flame zone volumc for second for the second. The initial temperature was 25' C. in one set of conditions was &lo%. Therefore, only variations in all cases. volume of flame space rate greater than this amomt aie significant. Flame Space Rate. This parameter m s defined according to Comparison of flanie volume measurements by different observers Equation 2 as: shovied that for most flames studied, the measured volumes were n ithin the precision of measnrement. (3) Flame Space Heating Rate. The flame space rate multiplied by the heat released by the reaction mixture on passage through the flame zone, AH,, gives the flame space heating rate. The The volumetric f f o ~rate of the unburned gas, C, was deteiquantity A H f is the difference betmen the heat content of the mined from the critical flow orifice calibrations and the burner initial gas miuture and the burned gas, and may be calculated diameter. The volume of the flame, V I ,was considered to be the total turbulent flame brush. This volume mas measured from a fiom the chemical compositions. The initial gas mixture composition was carefully controlled, but the composition of the time exposure photograph of the stabilized turbulent flame. burned gas depends on the cheinical reaction in the flame zone Figure 2 is a drawing of the burner lip and of the flame voluiiie as shown in such photographs. Photographic conditions which Kohl ( 1 4 ) has found that, under some conditions, unburned fuei passes through a turbulent flame zone. showed the luminous flame envelop as clearly as possible, in order To determine the heat releasc for the propane-ail flame, the to facilitate measurements, n-ere chosen by test. Photographs product gases were chemically aiialj zed and the amount of enc.rg.i for the same flame conditions \\-ere taken for various exposure Limes and mith various aperture adjustments. For times of released \\-hen these products v-ere completelv . . oxidized to carbon dioxide and n-ater was meamred by a calorimetric method. The hot gases were sampled at the top of the tutrbulent flame brush as indicated in Figure 2 . A water-cooled probe r i t h an orifice opening >\-asused. The product gases 71-ere analyzed for oxygen, propane, carbon monoxide, hydrogen. and carbon dioxide. Nitrogen was assumed to be unreactive, and thc rvatci. content was calculated from an atom balance. Three samples from propane-air flames burning in gas streams of different Reynolds numbers were analyzed. The three sets or analysis checked within the experimental error. The results of the analyses have been averaged and are compared in Table I with the calculated products for the equilibrium reaction of propaiie-air at equilibrium flame t e m p e r a t u r e . Only the oxygen analysis dil'ers greatly, probably becacse of the diffusion of air into the hot gas mantle. Some unburned propane was detected, but the amount represents only 0.25% of the total propane in the original mixture. The analytical method for propane dcpended on t,he condensat'ion of propane from the hot gases. As some propane %-as found, the accuracy of the propane determination m-as checked by analyzing the products of a butane-air turbulent flame. Even t.hough butane is more easily condensed than propane, the percentage of butane in the flame products -was no larger. This result was Figure 1. Piloting arrangement, cooling system, and burner exit
...
Sanuary 1956
Figure 2.
INDUSTRIAL AND E N G I N E E R I N G CHEMISTRY
Time-exposure photograph of turbulent flame
considered evidence for the reliability of the analytical method. The calorimetric analysis of the products gave 5.45 B.t.u. per cubic foot for complete oxidation to carbon dioxide and water: the value calculated from the chemical analysis was 5.34 B.t.u. per cubic foot. This value is the difference between the heat of combustion of the reactant and the residual enthalpy of products that are not completely burned to carbon dioxide and water. The heat released in the flame zone for these propane-air flames as calculated from product analysis is within 1% of the heat release calculated from equilibrium products. The value calculated from analysis of the products was used to calculate the space heating values. Although approximate equilibrium products were found for the flames studied here, according to work by Wohl and others ( I 4 ) , as noted above, equilibrium should not be assumed as the general condition.
crease for the total range of linear velocities studied is no larger than the variation in measurement of space rate for one velocity, so this trend has not been considered significant. The data of Table I1 also show that flame space rates decrease with increasing burner diameter and increase with the laminar burning velocity of the mixture. In Figure 3, the flame space rate is plotted against the laminar burning velocity divided by burner diameter. For the range of conditions studied the plot is linear ( 2 = 6.1 S J D ) . Flame space rate is proportional to laminar burning velocity and inversely proportional to burner diameter. If reciprocal space rates are considered as a measure of combustion time, then combustion time is proportional to the diameter of the burner and inversely proportional to the laminar burning velocity. The values of combustion time for the turbulent propane-air flames studied are in the range 2.9 to 7.2 X 10-3 second. These times are an order of magnitude greater than the time reported by Longwell and Weiss ( I O ) , 6 x 10-4 second, which was believed to represent the ultimate rate limited by combustion for stoichiometric propane-air mixtures. Wohl and others (14) have pointed out that combustion times determined from turbulent flame volumes are probably larger than the true values, because of the macromotions of the flame front. Folded Flame Mechanism of Turbulent Combustion. Two general types of turbulent flame models have been proposed: the folded flame, and the extended reaction zone. A relation among flame space rate, laminar burning velocity, and scale of turbulence may be derived from the folded flame theories of turbulent combustion. Wohl (14) has pointed out that the following prediction results from four variations of the folded flame theory which include the theories of Shelkin and Karlovitz :
x
Effect of Flow Rate, Burner Diameter, and Laminar Burning Velocity on Flame Space Rate. Within the precision of measurement, flame space rate is independent of stream flow velocity for the propane-oxygen-nitrogen flames studied. Table I1 shows that flame space rates for constant burner diameter and gas mixture composition are, in general, constant to =!=lo%, which is the precision of measurement. In three cases, there is evidence of a slight increase in space rate with linear velocity. The in-
where the gcale of turbulence,,,Z ian, or as a mixing length.
-I .
5
Products N2
cot co
HzO 0 2
H2 C3Hs
Combustion Products
% by Analysis 72.6 10.0 1.0 15.1 1.1 0.3 0.01
% by Calculation at Equilibrium 72.3 10.0 1.3 15.1 0.6 0.3 0.0
>> 1
may be considered to be Euler-
5001
V u) W
0 PROPANE-AIR 0
400
PROPANE-AIR 0, ENRICHED
N W
300
W 0
2
*
200
W
3 SL/D, Figure 3.
Table I.
U'
Zo: >when1, SL
$
DISCUSSION
131
sec;'
Flame space rate
For pipe-generated turbulence as a first approximation, scale may be considered proportional to burner diameter ( 7 ) . For this case, folded flame theories predict:
x
U'
Za Lwhen->> D iSL
3
As previously discussed, measured flame space rate follows this predicted dependency on laminar burning velocity and burner diameter, but whether the ratio u'/SL fulfills the necessary conditions is difficult to decide.
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
132
Table 11.
Laminar Burning Velocity,
Linear Flow Rate,
Volumetric Flow Rate,
Vol. 48, No. 1
Flame Space Rates
Av. Flame Space Rate,
Cm. /Sec. 1648 2000
Cc./Sec. 528 640
cc. 1.49 1.92
Flame Space Rate, 2, See.? 354 334
1.016
800 1173 1605 2030 2410 2780
647 951 1301 1644 1957 2257
2.74 4.61 6.23 7.62 9.01 9.07
236 206 200 216 217 249
222
1.86 X lo2
7.55
x
107
35.5
1.459
782 984 1194
1301 1644 1982
7.36 8.58 9.76
177 192 203
191
1.61 X lo2
6.50
x
107
35.5
1.890
239 661
670 1894
4.65 14.29
144 133
138
1.16 X l o 2
4.69
x
107
71
1.016
1301 1837 2114
1054 1489 1713
2.12 3.36 3.83
498 443 445
456
...,
71
1.459
630 890 1152
1054 1489 1927
3.42 4.52 5.61
308 329 344
327
.
71
1.890
530 610 765
1489 1713 2150
7.20 6.94 8.50
208 247 253
236
Cm./Sec. 35.5
Burner Diameter, D Cm. 0.639
35.5
SL,
UO,
uv,
Flame Volume,
5,
In the first place, what value to use for u' ie not very clear. Even if u' is chosen as the component of the root mean square fluctuating velocity in the direction of stream flo~v,the problem is not solved. The value of u' is not easily measured in the presence of a flame front; therefore, measurements of u' for cold flow must be used. Measurement of u' in turbulent jets by Corrsin and Uberoi ( 5 )shows that the intensity of turbulence, u ' / U o , goes through a maximum of 12% at about eight burner diameters above the pipe exit, and that u'/Umar goes from 2 to 20% as height to diameter ratio changes from 2 to 17. (This is the range of flame heights observed.) If the value of u' for the cold flow a t the position for the top of the flame is used for the ratio ~ ' / S L , then the condition indicated by folded flame theories is probably fulfilled for most of the experimental conditions studied. On
Zav,
Sec.-l 344
Space Heating Values, A H , Cal./(sec.B.t.u./hr.cc.) cu. it. 2.88 X l o 2 1.17 X 10s
....
..
...
...
*...
the other hand, if cold f l o ~approach measurements of stream intensity are applicable, the condition is not fulfilled. Extended Reaction Zone Mechanism of Turbulent Combustion. ih second model used for turbulent flames ( 1 4 ) is the extended reaction zone. The flame zone may be considered as a reactor in which the degree of completion of the chemical reaction varies continuously from the boundary nearest the burner to the top of the flame zone. For that case, the relation between flame space rate and chemical reaction rate is considered. I t is assumed that: (1) diffusion in the direction of f l o ~ is negligible, and (2) the stream of reactants moves longitudinally through the flame front reacting at some average rate. Then, by conservation:
For the case where
X A = a = constant which seems to be true for the propane-air flames according t o chemical analysis Z ar
but experimentally
Za 1 and approximately
.: r I/D, cm;' Figure 4.
Space heating rates of propane-air flames
0:
1 1,
-
Then, as a first approximation, the rate of disappearance of propane molecules increases with decreasing scale of turbulence.
January 1956
*
INDUSTRIAL AND ENGINEERING CHEMISTRY
Space Heating Rates. For turbulent flames, the flame space rate Z, multiplied by the appropriate factor, A H , , gives the space heating rate. The specific heat release factor, A H f , depends on the composition of the initial mixture and the burned gas. Space heating rates for these turbuleqt flames are proportional t o the specific heat release factor and t o the laminar burning velocity, and intensively proportional t o the tube diameter for the range of conditions studied. The inverse relation between space heating rate and burner diameter for propane-air flames is shown in Figure 4. Doubling the burner diameter reduces the space heating value by 39%. This implies that decreasing the scale of turbulence by a factor of 2 would improve space heating values substantially. Space heating rates for various types of combustion systems are listed in Table 111. Comparison of all the values shows that the space heating kalues for the kind of turbulent burner flames studied are greater than reported values for turbulent diffusion flames, but less than the values for laminar flames or Longwell’s homogeneous reactor. It is important t o note that although the measured burning velocities of these turbulent propane-air flames are higher than laminar flames ( I S ) , the space heating values are an order of magnitude lower, If flames in combustors are comparable to the turbulent flames studied, then a reduction in the scale of turbulence should result in an increase in the space heating value and an increase in combustor performance in cases where space for combustion limits performance.
Table 111. Heating Values for Various Types of Combustion
Space Heating Rate, B.t.u.1 Hr.-Cu. Ft. of Flame or Reactor a t Atmospheric Combustion System Pressure Laminar flame, stoichiometric 4 x 108 propane-air 4 . 8 X 108 Laminar flat flame, lean proDane air, 2012’ F., 0.0594 atm. Laminar flame, propane-air, 6 X 108 0.9 stoichiometric, 3200” F., atm. Homogeneous reactor, stirred, 3 X 108 stoichiometric, propane-air Turbulent premixed propane- 5-11 X ’IO’ air, stoichiometric Turbulent diffusion flame, city 1 . 2 X lo6 gas Combustors Order of loe
133
an immediate indication of the significance to him of laboratory experiments in turbulent combustion. NOMENCLATURE
= concentration of fuel in initial mixture a t initial eonditions (25’ C. and atmospheric pressure), mole per cc. = area of reaction zone across the same stream tube for which AOis the area, sq. em. = area of stream tube in unburned gas, sq. cm. = constant = burner diameter, em. = heat release per volume of initial mixture on passage through flame zone, cal. per cc. = flame space heating rate, cal./sec.-cc. of flame zone or B.t.u./hr.-cu. ft. of flame zone = flame thickness, cm. = scale of turbulence, em. = apparent rate of disappearance of fuel moleculee, moles/sec.-cc. = burning velocity, em. per second = laminar burning velocity, cm. per second = linear stream velocity, em. per second = maximum U a t a section on jet axis, em. per second = volumetric flow rate, cc. per second = fluctuating velocity, om. per second = flame zone volume, CC. = fraction of fuel burned in flame zone = flame space rate, sec.-l ACKNOWLEDGMENT
Reference
The authors wish t o acknowledge the suggestions and the help of Robert Hibbard and Albert Evans in the study of the heat conof the combustion products.
(1
LITERATURE CITED
Friedman and Burke (6) Avery (1) Longwell and Weiss ( I O ) This report Scurlock and Grover (1.9)
Calculated from S L = 35.5 cm./sec. and h = 0.03 cm.
CONCLUSION
Flame space rates and flame space heating rates are desirable methods of characterizing turbulent combustion. I n the first place, two observed differences between laminar flames and turbulent flames-the depth of the flame zone and the degree of completion of the chemical reaction-are included in the characterization. Also, the changes in flame space rate and flame space heating rate with experimentally attainable changes in stream flow parameters and combustion chemistry have been shown t o be large enough t o detect. Therefore, these parameters may be used for phenomonological studies of turbulent combustion. Finally, characterization of turbulent flames by space heating rates gives the engineer interested in combustor design principles
Avery, W. A., “Fifth Symposium (Intl.) on Combustion,” in press. Avery, W. H., and Hart, R. W., IND.ENQ. CHEM.45, 1634 (1953). Bollinger, L. M., and Williams, D. T., “Third Symposium on Combustion Flame and Explosion Phenomena,” pp. 17684, Williams & Wilkins, Baltimore, 1949. Clark, T. P., and Bittker, D. A., Natl. Advisory Comm. Aeronaut., NACA RM E54F29 (1954). Corrsin, Stanley, and Uberoi, M. S., Natl. Advisory Comm. Aeronaut., NACA TR 998 (1950). Friedman, R., and Burke, E., J. Chem. Phys. 22, 824 (1954). Gaydon, A. G., and Wolfhard, H. G., “Flames, Their Structure, Radiation, and Temperature,” p. 115, Chapman and Hall, London, 1953. Karlovitz, Bela, “Selected Combustion Problems,” pp. 248-60, AGARD Butterworths, London, 1954. Karlovitz, B., Denniston, D. W., Jr., and Wells, F. E., S.Chem. Phys. 19, 541 (1951). Longwell, J. P., Jr., and Weiss, M. A., Bumblebee Series Report 221, October 1954. Mickelsen, W. R., and Emstein, N. E., Natl. Advisory Comm. Aeronaut., NACA TN 3456 (1955). Sourlock, A. C., and Grover, J. H., “Selected Combustion Problems,” p. 218, AGARD, Butterworths, London, 1954. Wagner, Paul, Natl. Advisory Comm. Aemnaut., NACA TN 3575 (1955). Wohl, Kurt, Shore, L., Rosenberg, G. von, and We& C. R., “Fourth Symposium (Intl.) on Combustion,” pp. 820-35, Williams & Wilkins, Baltimore, 1953. RECEIVED for review June 17, 1955.
ACCEPTED September 23, 1955.
