Lean Hydrocarbon Flames A Method for Predicting the Burning Velocities of Guses SANFORD A. WEIL, Institute of Gas Technology, Chicago 16,111.
METHODS
of predicting burning velocities can be more easily applied to other combusrion properties ( 2 , 9 ) if they do not require the complex calculations that rigorous theories of combustion involve. hlany attempts have been made to describe laminar burning velocities in terms of approximate theories ( 6 ) . Most applications have pertained to hydrocarbon-oxygen-nitrogen mixtures and fuel-oxygen ratios near the stoichiometric value. Analytical functions based on the work of Semenov have been applied over the greatest range ofvariables ( 2 , 5 ) , but these d o not correctly describe the dependence of burning velocity on equivalence ratios significantly different from unity ( 8 >70, 72).
T h e partial success o f approximare theories indicates that, among hydrocarbons, the burning velocity can be expressed as the product of functions of flame temperature and equivalence ratio. Because the physical properties of oxygen and nitrogen are similar, the relation between flame temperature and primary gas composition can be simplified and variation of transport properties in hydrocarbon-oxygen-nitrogen mixtures neglected. These characteristics are used in an empirical method for predicting the laminar burning velocities of hydrocarbon-oxygen-nitrogen mixtures at atmospheric pressure and room temperature.
Experimental Procedure Burning velocities were determined by the total area method from shadowgraphs of Bunsen flames. For flames a t 1800' K., the burner diameter was 6/s inch; a t 2000' K., inch; at 2250' K., '/a inch; and a t 2500' K., 3/16 inch. Wall thicknesses of the brass burners were less than 0.06 inch and a cooling jacket came within '/s inch of the burner rim. Initial gas temperature was 300' K. T h e gas metering system, based on that of Andersen and Friedman (7), and the Z optical system (7) have been described (74). All flame temperatures were calculated with the usual assumptions of chemical equilibrium and adiabatic combustion. Results The hydrocarbons studied M ere methane, propane. and ethylene. The burning velocities of the fuel-oxygennitrogen mixtures were determined over the complete fuel lean region for particular flame temperature levels. The choice of temperature levels was determined by ability to achieire stable laminar flames. In Figure 1, the abscissa is the reciprocal of the more commonly used equivalence ratio, because of the greater convenience for the range covered. For the several fuels and temperature levels, the burning velocity variations \vith equivalence ratio are qualitatively
similar. The strong dependence on equivalence ratio near the stoichiometric point is in qualitative agreement with the proposed correlations (2, 5). With large excesses of oxygen, however, the burning velocity is only weakly dependent on the amount of oxygen. This behavior, while in disagreement with correlations based on the Semenov theory. can be seen in results of other investigations (8, 70). In the cases of propane and ethylene, the burning velocity approaches a limiting value with increasing oxygenfuel ratio along a given temperature level. (For these systems, a constant temperature level very nearly corresponds to a constant volume fraction of fuel in the primary gas.) I n the case of methane, burning velocity decreases about 10% a t the extreme lean end of the curve. This decrease places a minor limitation on the concept that a limiting burning velocity exists at high oxygen-fuel ratios for a particular flame temperature. Correlation of Burning Velocity Data Restriction of these data to ternary mixtures a t 1 atm. and 300' K. initial temperature implies that any adiabatic process parameter such as flame temperature or burning velocity is a function of only two variables for a given ternary system. There exists a limiting value of
Figure 1. Burning velocity variations of lean hydrocarbonoxygen-nitrogen rnixtures are qualitatively similar
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Figure 2. Correlation of burning velocities of methane, propane, and ethylene with primary gas composition has an average deviation of 2.2y0
the burning velocity a t high oxygen-fuel ratios which is characteristic of the flame temperature. With previous correlations as guides (2, 5 ) , an empirical relation was developed among burning velocity ub, limiting burning velocity Lib-,,,, and equivalence ratio 'p. I n Figure 2, ratio v b / V b - , is plotted against Q/V, where the experimental parameter, Q, is dependent on the fuel and has the values of 1.16 for methane, 1.00 for propane, and 1.10 for ethylene. Each point in Figure 2 corresponds to a distinct hydrocarbon-oxygen-nitrogen mixture. T h e curve represents the function ( U ~ U Lm)2
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(1)
up to a / ' p = 4. For a / p > 4, it is assumed the burning velocity is a t the limiting value for the particular flame temperature. Of the 80 mixtures represented, 73 are within 5% and 78 within 10% of the curve. T h e average deviation of the data is 2.2Yc of the burning velocity. T h e burning velocity of these mixtures can be expressed well within experimental precision in the form ub
=
Ubmf
(alv)
F U E L IN MIXTURE, PERCENT Figure 3. Limiting burning velocities of methane-oxygen-nitrogen mixtures can b e correlated with the fuel fraction
T h e third assumption avoids the need of calculating the flame temperature. I t is reasonably accurate below 2500' K. and adequate a t higher temperatures. T h e most extensive data with respect to the composition range are those on methane of Jahn (70) and Singer and Heimel (77), but these are not consistent. Therefore, the burning velocities of Singer and Heimel were multiplied by 0.742, to bring them in line with those of Jahn. ub/vk,,, was obtained from Figure 2 from the reported composition with a = 1.16. ubPm was then computed from the burning velocities as reported by Jahn and the adjusted values of Singer and Heimel. T h e resulting dependence of the limiting burning velocity on the methane fraction is shown in Included are data for 18 Figure 3. fuel-rich flames, for which a l p is greater than unity although l/cp is less than unity. Of the 81 mixtures, the deviations of U b - m from the least squares line are such that 64 are within 570 and 75 within 10%. All the mixtures that show deviations
greater than 10% are binary mixtures of methane and oxygen or contain a t most 1.5% nitrogen. These deviations correspond to low values of the burning velocity and support the observations concerning a maximum in the burning velocity-composition curves for methane (Figure 1). T h e large deviations of nitrogen-free mixtures occur for flames of lower temperatures. T h e limitation on the over-all correlation due to this effect, therefore, occurs in a very small range. T h e data of Jahn and Singer and Heimel on the burning velocity of methane-oxygen-nitrogen mixtures, correlated in Figure 3 through the use of Figure 2, cover: Fuel, 8-36 mole $& Equivalence ratio, 0.25-1.16 Flame temperature, 2000-3000 O K. Burning velocity, 24-330 cm. per srcond
4 s an example of the coalescence of the reported values, the group of seven points near 15% methane corresponds to a range of equivalence ratio of
(2)
where vb-,,, includes all dependence on flame temperature.
Application of Correlation The observed correlation of the data of this study can be applied to hydrocarbons in general. T h e information required for a particular fuel is the values of a and u b - m in terms of known quantities. To test or use Equation 2 for a particular fuel and initial temperature and pressure, it is assumed: T h e function, f ( a / p ) , is given by Figure 2 or Equation 1. The value of Q for propane may be applied to all paraffinic hydrocarbons other than methane. T h e flame temperature is a single valued function of the fuel mole fraction in lean hydrocarbon flames.
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FUEL IN M I X T U R E , P E R C E N T
Figure 4. Limiting burning velocities of hexane-oxygen-nitrogen mixtures further substantiate the proposed correlation
INDUSTRIAL AND ENGINEERING CHEMISTRY
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Figure 5. If a linear correlation is assumed, fuelair mixtures yield the necessary information
Acknowledgment
0.35 to 0.98 and of burning velocity of 99 to 169 cm. per second. Another set of data of sufficient range to test the proposed correlation is that of Golovina and Fyodorov (8) on the burning velocity of hexane. a was assigned the value of 1.00 (Figure 4). Of the 40 mixtures, 22 are within 5% of the least squares line and 28 within 10%. Of the four points that deviate by more than 15%, three represent nitrogen-free mixtures a t low temperatures. These may be considered as further evidence of anomalous behavior of binary fueloxygen mixtures. Figures 3 and 4 substantiate the proposed correlation of Figure 2 over a range of compositions much more extensive than that used to develop the correlation. If its generality is accepted, the data required for the relation of the limiting burning velocity and the fuel fraction can be obtained from fuel-air or similar binary mixture studies. I n Figure 5 the results of Simon and Wong ( 7 3 ) were used for ethylene and propyne and those of Dugger and Graab (3, 4 ) for iso-octane and propane. If, as in the Simon and Wong data, only fuel-air mixtures were used, the flame temperature range and therefore the fuel fraction range would be small. Although the proposed method of correlation is based on empirical determination of the z+,--,-fuel fraction curve, the occurrence of straight lines in the
extensively covered cases of methane and hexane indicates that linear relationships in general may be valid. If so, the line for fuel-air mixtures would be sufficient for the complete lean region of fuel-oxygen-nitrogen mixtures. The use of linear functions is supported by the limited data of ethylene, propyne, and iso-octane. T h e propane results show linearity over most of the range, but do not conform a t low fuel fractions. As in the data of Jahn and of Singer and Heimel, the proposed method of prediction can be expected to describe the results of any investigation only within a proportionality factor. The proposed empirical method of prediction of burning velocity applies to lean mixtures a t ordinary pressures and temperatures. This limitation may be lifted, according to methane results, to include rich mixtures when a / p > 1. Further extension into the rich region must involve modifications, because the fuel fraction is no longer a single valued function of the flame temperature nor is the curve of V , / V , - , us. a / p available. However, correlations based on the Semenov theory (2, 5) imply the same temperature dependence in both rich and lean mixtures and similar equivalence ratio dependence. I t is possible, therefore: that the correlation can be extended to rich flames, if calculation of flame temperature is included.
The author expresses gratitude for financial support for this study by the Office of Naval Research and the American Gas Association through its Promotion-Advertising-Research plan. H e is indebted to John Hasenberg for carrying out the experimental work and much of the calculations and to other members of the staff of the Institute of Gas Technology for helpful advice. literature Cited (1) Andersen, J. W., Friedman, R., Rev. Sa. Znstr. 20, 61-6 (1949). (2) Brokaw, R. S., Gerstein, M., “Sixth Symposium on Combustion,” pp. 66-74, Reinhold, New York, 1957. (3) Dugger, G. L., Graab, D. D., Natl. Advisory Comm. Aeronaut., NACA RM E52524 (1952). (4) Zbid., NACA T N 2680. (5) Dugger, G. L., Simon, D. M., Ibid., Rept. 1158 (1954). (6) Evans, M. W., Chem. Revs. 51, 363--429 (1952). (7) Gaydon, A. G., Wolfhard, H. G., “Flames,” p. 48, Chapman & Hall, London, 1953. (8) Golovina, E. S., Fyodorov, G. G., “Sixth Symposium on Combustion,’’ pp. 88-96, Reinhold, New York, 1957. (9) Grumer, J., Harris, M. E., Rowe, V. R., Bur. Mines, RI 5225 (1956). (10) Lewis, B., von Elbe, G., “Combustion, Flames, and Explosions,” p. 465, Academic Press, New York, 1951. (11) Ibid., p. 467. (12) Potter, A. E., Berlad, A. L., “Sixth Symposium on Combustion,” pp. 27-36, Reinhold, New York, 1957. (13) Simon, D. M., Wong, E. L., Natl. Advisory Comm. Aeronaut., NACA RM E51H09 (1951). (14) Weil, S. A,, SFaright, E. F., Ellington, R. T., IND.ENG. CHEM.50, 1101-4 (1958). RECEIVED for review June 30, 1958 ACCEPTED December 30, 1958 Division of Gas and Fuel Chemistry, ACS, Symposium on Flame Characteristics, Urbana, Ill., May 16, 1958. VOL. 51, NO. 4
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