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The relationship between flame pressure and burning velocity
322
LL~rn~ To ~n~ EDrrons
Voi. 13
In the "pic d'arff:t" region of the high temperature oxidation of propane, an increase in the formation of ethanol, n-propanol and especially isopropanol 9" ts is observed, as well as an increase in aldehyde, probably acetaldehyde 9' 3 (Figure 1). This short study shows the analogy between the "pic d'arr~t' and "oxygen cut-off'. The authors thank Dr J. A. Barnard for helpful suggestions about translation into English. L. R. SOCnET and M. LucQuIN Facultd des Sciences de Lille, Laboratoire de Chimie de la Combustion, B.P. 36, Lille-Gate, France (Received December 1968)
References t LucQurN, M. J. Chim. phys. 55, 827 (1958) 2 SOCnET, L. R. and LUCQUIN, M. J. Chim. phys. 62, 796 (1965) 3 SOCHET, L. R., EGRET, J. and LUCQUIN, M. J. Chim. phys. 63, 1555 (1966) 4 SocnEx, L. R. and LUCQUIN, M. J. Chim. phys. 65, 977 (1968) s LEFEnVRE,M. and LUCQUIN, M. J. Chim. phys. 62, 775 (1965); 62, 784 (1965) o POSTMKOV,L. M., SHLYAPI~rOKH, V. YA. and S ~ I N A , M. N. Kit~etika i Katalysis, 6, 185 (1965); Kinetics and Catalysis, 6, 161 (1965) 7 D~CnAUX, J. C. and LucOtnN, M. J. Chim. phys. 65, 982 (1968) a SAWERVSYN,J. P., SOCHET, L. R. and LUCQUIN, M. C.R. Acad. Sci., Paris, 268, Set. C, 1564. (1969) 9 SOCrmT, L. R., SAW~RVSVN,J. P. and LUCQUIN, M. Advanc. Chem. Ser. 76, I l l (1968) to DECHAUX,J. C., LANGRAND, F., H~MAm', G. and LUCQtnN, M. Bull. Soc. chim. Fr. 4031 (1968) II LLOYD, R. A. Trans. Faraday Soc. 61, 2173 0965); 61, 2182 0965) t2 VASlrmV, R. F. and VICHU~NSKI, A. A. Nature, Lond. 48, 1276 (1962) ~3 VASlLn~V,R. F. Progr. Reaction Kinetics, 4, 305 (1967) t4 BATEMAN,L. and MORRIS, A. L. Trans. Faraday Soc. 49, 1031 (1953) s Socu~r, L. R., SAWERYSVN,J. P. and LUCQUIN, M. Bull. Soc. chim. Ft. 3596 (1968)
The Relationship between Flame Pressure and Burning Velocity Experimentally measured flame pressures are significantly smaller than those predicted by the commonly used equation A P = p,,S 2 [(P,,/Pb) -
1]
It is suggested that this equation may be in error because stream tube area expansion is neglected in the derivation of the equation. Fristrom has shown that stream tube area expansion must be considered if flame models are required t o predict quantitative results. A theoretical analysis taking stream tube area expansion into account yields the result
AP = p.S~[(AjAb) 2 (Pu/Pb) - I] An experimental investigation designed to test the validity of this equation is now in progress.
IT IS well known that there is a small pressure drop across a flame front due to the heating, expansion and acceleration of the gases in the flame. This pressure drop, often termed the flame pressure, is normally calculated from the equationl-a AP = puSU.[(pdp~)- l]
[1]
where AP is the flame pressure, p. and p~ are the densities of the unburnt and burnt gas respectively, and $. is the burning velocity. Values of Pu/Pb required for substitution in equation 1 are calculated on the assumption that adiabatic combustion proceeds to equilibrium.
J~el9~
LETTERS TO THE EDITORS
323 Recent measurements of burning velocity for methane-air flames4, 5 involved direct experimeatal measurement of flame pressure. A comparison of flame pressures predicted by equation 1 with experimentally determined flame pressures is therefore possible. This comparison (Figure 1)'indicates that the predicted flame pressures are much larger than the corresponding experiment:dly determined flame pressures. It is considered that errors in the measurement of AP and S~ and in the calculation of p,/~ are far too small to account for the discrepancy. The validity of equation 1 is therefore in question. The experimental data of von Elbe and Mentser 6 appear to confirm the validity of the equation, but later workers 7, s have suggested that this is a fortuitous result of experimental error. Moreover, Vasilesco 9 and Bollinger, Strauss and Edse a have also reported measurements of flame pressure much smaller than the values predicted by equation 1.
~v~ 0"0040 Ah d // 0 0¢-
./ // Flame front thickness
o,. ,,q 0"0020
t .
i
l
•
t
I
v~
,,
0"0020 0"OO40 AP (meas.), ijL water
Pu
FIGURE 1. Comparison of theoretically predicted and experimentally determined flame pressures
Au
FIGURE 2. Plane flame model incorporating stream tube area expansion
The derivation of equation 1 involves consideration of an idealized one-dimensional flame in which all expansion of the flame gases is considered to take place normal to the flame front. Fristrom l° has made a detailed experimental study of the applicability of such one-dimensional models to threedimensional laminar flame fronts. His measurements indicate that, if quantitatively correct predictions are required, the model must be modified to include the effects of expansion parallel to the flame front (i.e. stream tube area expansion). The effect of such modification on the predicted flame pressure is considered in the following analysis. Figure 2 represents a stationary plane flame front normal to the flow of unburnt gas, velocity V., in a stream tube of initial cross-sectional area A.. In passage through the flame front the stream tube area is considered to increase to A~ and the gas velocity to increase to Vb. P= and Pb represent the initial and final pressures, respectively. Conservation of momentum requires that puV.2 + P= = pbv
.'. Flame pressure 3P = P. By conservation of mass,
-
=
-
+ Pb
p.v
p.V,A= = pbVbAb or
Vb = puVuAu/pbAb
324
LETTERS TO THE EDITORS
VOI. 13
so that AP = p b ( P . V d l d P b A b ) 2 -- p . V 2 and A P = p = V 2 [ ( A j A b ) 2 (PJPb) - !] But for a stationary flame front normal to the unburnt gas flow, burning velocity S~ = gas velocity V~ .'. A P = p ~ S 2 [ ( A d A b ) 2 (PJPb) -
1]
[2]
Equation 2 differs from equation 1 only by inclusion of the factor (AdAb)2. Fristrom ~o has shown that A,,/A~ will generally be less than unity, so flame pressures predicted by equation 2 will be smaller than those predicted by equation 1 and may well agree with experimentally determined flame pressures. An experimental investigation designr.d to test the validity of equation 2 is now in progress. This involves the use of particle tracking techniques to visualize the flow streamlines on the diametral cross section of flames burning on circular nozzle burners. The axial symmetry of such flames permits the required area ratio. A d A b , to be czlculatcd from these data. In view of the important effects of flame pressure on many flame phenomena, it is considered that this preliminary information may be of value to other workers. H. EDMONDSON and M. P. HEAP* Department of Civil Engineering, University of Salford, Lancs. (Received January 1969: revised February 1969)
References t LEW1~ B. and v o s ELBE, G. Combustion, Flames and Explosions of Gases, p 206. 2nd ed. Academic Press: New York (1961) 2 GAVDON, A. G. and WOLFHARO, H. G. Flames: Their Structure, Radiation and Temperature, p 53. 2nd ed. Chapman and Hall: London (.1960) 3 FRISTROM, R. M. and WESTENBERG, A. A. Flame Structure, p 131. McGraw-Hill: New York (1965) * EDMOm~SON, H. and HEAP, i . P. 'A precise test of the flame stretch theory of blow-off'. Paper presented to the 12th International Symposium on Combustion, Poitiers, France, July 1968. (To be published) 5 EDMONDSON, H. and HEAP, M. P. 'The burning velocity of methane-air flames inhibited by methyl bromide'. Paper accepted for publication in Combustion & Flame (1969) 6 YON ELBE, G. and MEtCrSER, M. 3'. chem. Phys. 13, 89 (1945) 7 DUGGER, G. L., SIMON, D. m. and GERSTEIN, i . N.A.C.,4. Rep. No. 1300. "Basic considerations in the combustion of hydrocarbon fuels with air'. Chapter IV: Laminar flame propagation, p 133 (1957) 8 BOLLINGFR. L. E., STRAUSS,W. A. and EDSE, R. lndustr. Engng Chem. (hldustr). 49. 768 (1957) o VASILES('{~. V. ,'Inn. Phys.. Paris, 18, 190 (1943) to FRISTROM, R. M. J. chem. Phys. 24, 888 (1956) * Gas Council Research Scholar
Effect of Snlphur Dioxide on Eqnilibrinm in Hydrogen Flames of the equilibrium composition of the burnt gases of hydrogen-oxygen-nitrogen flames containing about one per cent sulphur show that a considerable proportion of the sulphur should be present as H2S, $2 and S H m fuel-rich flames, whilst SO2 accounts for nearly all the sulphur in lean and stoichiometric flames. It has been suggested t' 2 that the bimolecular reactions:
CALCULATIONS 1
H2 + SO2 -~ H 2 0 + SO I-I2 + S O ~ H 2 0 H 2 + S~SH
+ S + H
H 2 + SH ~ H2S + H SH+SO~S,+OH
[1] [2] [3] [4] [5]
LL~rn~ To ~n~ EDrrons
Voi. 13
In the "pic d'arff:t" region of the high temperature oxidation of propane, an increase in the formation of ethanol, n-propanol and especially isopropanol 9" ts is observed, as well as an increase in aldehyde, probably acetaldehyde 9' 3 (Figure 1). This short study shows the analogy between the "pic d'arr~t' and "oxygen cut-off'. The authors thank Dr J. A. Barnard for helpful suggestions about translation into English. L. R. SOCnET and M. LucQuIN Facultd des Sciences de Lille, Laboratoire de Chimie de la Combustion, B.P. 36, Lille-Gate, France (Received December 1968)
References t LucQurN, M. J. Chim. phys. 55, 827 (1958) 2 SOCnET, L. R. and LUCQUIN, M. J. Chim. phys. 62, 796 (1965) 3 SOCHET, L. R., EGRET, J. and LUCQUIN, M. J. Chim. phys. 63, 1555 (1966) 4 SocnEx, L. R. and LUCQUIN, M. J. Chim. phys. 65, 977 (1968) s LEFEnVRE,M. and LUCQUIN, M. J. Chim. phys. 62, 775 (1965); 62, 784 (1965) o POSTMKOV,L. M., SHLYAPI~rOKH, V. YA. and S ~ I N A , M. N. Kit~etika i Katalysis, 6, 185 (1965); Kinetics and Catalysis, 6, 161 (1965) 7 D~CnAUX, J. C. and LucOtnN, M. J. Chim. phys. 65, 982 (1968) a SAWERVSYN,J. P., SOCHET, L. R. and LUCQUIN, M. C.R. Acad. Sci., Paris, 268, Set. C, 1564. (1969) 9 SOCrmT, L. R., SAW~RVSVN,J. P. and LUCQUIN, M. Advanc. Chem. Ser. 76, I l l (1968) to DECHAUX,J. C., LANGRAND, F., H~MAm', G. and LUCQtnN, M. Bull. Soc. chim. Fr. 4031 (1968) II LLOYD, R. A. Trans. Faraday Soc. 61, 2173 0965); 61, 2182 0965) t2 VASlrmV, R. F. and VICHU~NSKI, A. A. Nature, Lond. 48, 1276 (1962) ~3 VASlLn~V,R. F. Progr. Reaction Kinetics, 4, 305 (1967) t4 BATEMAN,L. and MORRIS, A. L. Trans. Faraday Soc. 49, 1031 (1953) s Socu~r, L. R., SAWERYSVN,J. P. and LUCQUIN, M. Bull. Soc. chim. Ft. 3596 (1968)
The Relationship between Flame Pressure and Burning Velocity Experimentally measured flame pressures are significantly smaller than those predicted by the commonly used equation A P = p,,S 2 [(P,,/Pb) -
1]
It is suggested that this equation may be in error because stream tube area expansion is neglected in the derivation of the equation. Fristrom has shown that stream tube area expansion must be considered if flame models are required t o predict quantitative results. A theoretical analysis taking stream tube area expansion into account yields the result
AP = p.S~[(AjAb) 2 (Pu/Pb) - I] An experimental investigation designed to test the validity of this equation is now in progress.
IT IS well known that there is a small pressure drop across a flame front due to the heating, expansion and acceleration of the gases in the flame. This pressure drop, often termed the flame pressure, is normally calculated from the equationl-a AP = puSU.[(pdp~)- l]
[1]
where AP is the flame pressure, p. and p~ are the densities of the unburnt and burnt gas respectively, and $. is the burning velocity. Values of Pu/Pb required for substitution in equation 1 are calculated on the assumption that adiabatic combustion proceeds to equilibrium.
J~el9~
LETTERS TO THE EDITORS
323 Recent measurements of burning velocity for methane-air flames4, 5 involved direct experimeatal measurement of flame pressure. A comparison of flame pressures predicted by equation 1 with experimentally determined flame pressures is therefore possible. This comparison (Figure 1)'indicates that the predicted flame pressures are much larger than the corresponding experiment:dly determined flame pressures. It is considered that errors in the measurement of AP and S~ and in the calculation of p,/~ are far too small to account for the discrepancy. The validity of equation 1 is therefore in question. The experimental data of von Elbe and Mentser 6 appear to confirm the validity of the equation, but later workers 7, s have suggested that this is a fortuitous result of experimental error. Moreover, Vasilesco 9 and Bollinger, Strauss and Edse a have also reported measurements of flame pressure much smaller than the values predicted by equation 1.
~v~ 0"0040 Ah d // 0 0¢-
./ // Flame front thickness
o,. ,,q 0"0020
t .
i
l
•
t
I
v~
,,
0"0020 0"OO40 AP (meas.), ijL water
Pu
FIGURE 1. Comparison of theoretically predicted and experimentally determined flame pressures
Au
FIGURE 2. Plane flame model incorporating stream tube area expansion
The derivation of equation 1 involves consideration of an idealized one-dimensional flame in which all expansion of the flame gases is considered to take place normal to the flame front. Fristrom l° has made a detailed experimental study of the applicability of such one-dimensional models to threedimensional laminar flame fronts. His measurements indicate that, if quantitatively correct predictions are required, the model must be modified to include the effects of expansion parallel to the flame front (i.e. stream tube area expansion). The effect of such modification on the predicted flame pressure is considered in the following analysis. Figure 2 represents a stationary plane flame front normal to the flow of unburnt gas, velocity V., in a stream tube of initial cross-sectional area A.. In passage through the flame front the stream tube area is considered to increase to A~ and the gas velocity to increase to Vb. P= and Pb represent the initial and final pressures, respectively. Conservation of momentum requires that puV.2 + P= = pbv
.'. Flame pressure 3P = P. By conservation of mass,
-
=
-
+ Pb
p.v
p.V,A= = pbVbAb or
Vb = puVuAu/pbAb
324
LETTERS TO THE EDITORS
VOI. 13
so that AP = p b ( P . V d l d P b A b ) 2 -- p . V 2 and A P = p = V 2 [ ( A j A b ) 2 (PJPb) - !] But for a stationary flame front normal to the unburnt gas flow, burning velocity S~ = gas velocity V~ .'. A P = p ~ S 2 [ ( A d A b ) 2 (PJPb) -
1]
[2]
Equation 2 differs from equation 1 only by inclusion of the factor (AdAb)2. Fristrom ~o has shown that A,,/A~ will generally be less than unity, so flame pressures predicted by equation 2 will be smaller than those predicted by equation 1 and may well agree with experimentally determined flame pressures. An experimental investigation designr.d to test the validity of equation 2 is now in progress. This involves the use of particle tracking techniques to visualize the flow streamlines on the diametral cross section of flames burning on circular nozzle burners. The axial symmetry of such flames permits the required area ratio. A d A b , to be czlculatcd from these data. In view of the important effects of flame pressure on many flame phenomena, it is considered that this preliminary information may be of value to other workers. H. EDMONDSON and M. P. HEAP* Department of Civil Engineering, University of Salford, Lancs. (Received January 1969: revised February 1969)
References t LEW1~ B. and v o s ELBE, G. Combustion, Flames and Explosions of Gases, p 206. 2nd ed. Academic Press: New York (1961) 2 GAVDON, A. G. and WOLFHARO, H. G. Flames: Their Structure, Radiation and Temperature, p 53. 2nd ed. Chapman and Hall: London (.1960) 3 FRISTROM, R. M. and WESTENBERG, A. A. Flame Structure, p 131. McGraw-Hill: New York (1965) * EDMOm~SON, H. and HEAP, i . P. 'A precise test of the flame stretch theory of blow-off'. Paper presented to the 12th International Symposium on Combustion, Poitiers, France, July 1968. (To be published) 5 EDMONDSON, H. and HEAP, M. P. 'The burning velocity of methane-air flames inhibited by methyl bromide'. Paper accepted for publication in Combustion & Flame (1969) 6 YON ELBE, G. and MEtCrSER, M. 3'. chem. Phys. 13, 89 (1945) 7 DUGGER, G. L., SIMON, D. m. and GERSTEIN, i . N.A.C.,4. Rep. No. 1300. "Basic considerations in the combustion of hydrocarbon fuels with air'. Chapter IV: Laminar flame propagation, p 133 (1957) 8 BOLLINGFR. L. E., STRAUSS,W. A. and EDSE, R. lndustr. Engng Chem. (hldustr). 49. 768 (1957) o VASILES('{~. V. ,'Inn. Phys.. Paris, 18, 190 (1943) to FRISTROM, R. M. J. chem. Phys. 24, 888 (1956) * Gas Council Research Scholar
Effect of Snlphur Dioxide on Eqnilibrinm in Hydrogen Flames of the equilibrium composition of the burnt gases of hydrogen-oxygen-nitrogen flames containing about one per cent sulphur show that a considerable proportion of the sulphur should be present as H2S, $2 and S H m fuel-rich flames, whilst SO2 accounts for nearly all the sulphur in lean and stoichiometric flames. It has been suggested t' 2 that the bimolecular reactions:
CALCULATIONS 1
H2 + SO2 -~ H 2 0 + SO I-I2 + S O ~ H 2 0 H 2 + S~SH
+ S + H
H 2 + SH ~ H2S + H SH+SO~S,+OH
[1] [2] [3] [4] [5]