- Email: [email protected]
Response to comments and errata, “influence of temperature and hydroxyl concentration on incipient soot formation in premixed flames”
C O M B U S T I O N A N D F L A M E 67:269-272 (1987)
269
Response to Comments and Errata, "Influence of Temperature and Hydroxyl Concentration on Incipient Soot Formation in Premixed Flames" MARK M. HARRIS, GALEN B. KING, and NORMAND M. LAURENDEAU Flame Diagnostics Laboratory, School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907
1. RESPONSE Before responding to the criticisms of Takahashi and Glassman [1], we must point out that our paper [2] gave generous credit to both these authors [3] and to the pioneering work of Millikan [4]. Takahashi and Glassman [3] provided the first systematic study of the effect of flame temperature on the critical equivalence ratio, Oc, for premixed flames. As a first study, they pursued the obvious approach of employing the adiabatic flame temperature to isolate the major experimental trends, and then suggested an isothermal correlation between ~¢ and the number of carbon-carbon bonds. In our investigation, we instead measured the temperature and found that while the adiabatic flame temperature is useful for demonstrating the relation In 4 ~ ¢ = A - B / R T ,
(1)
a measured flame temperature is needed to associate ~bc with the global kinetics responsible for soot formation more directly. The importance of a measured flame temperature can be shown by the following three considerations. First, because of radiative and convective heat losses, the actual temperature is typically a lower percentage of the adiabatic flame temperature at higher absolute temperatures. Hence, the value of the parameter B in Eq. (1) will normally decrease if adiabatic rather than actual flame temperatures are employed, as demonstrated by the differences between our B-values and those of Takahashi and Glassman [3] for ethane and propane. At higher gas flowrates, heat losses gener-
ally decrease, thus giving more comparable Bvalues, as for ethylene and acetylene (see Table 3 of Harris et al. [2]). Second, even at the high flowrates used in our uncooled fiat-flame burner, the measured flame temperatures were approximately 100-200K below the associated adiabatic flame temperatures. Third, at 1800K, our measured 0c values for C2H6, C3H8, C2H4, and C2H2 are 1.98, 1.93, 1.88, and 1.70, respectively [2]. The resulting values for the critical effective equivalence ratio, C/c, are 1.41, 1.35, 1.25, and 1.02, respectively. Extrapolation from Fig. 4 of Takahashi and Glassman [3] gives ~kc values at an adiabatic flame temperature of 1800K of approximately 1.22, 1.13, 1.12, and 0.97, respectively. Based on our B-values (which are independent of whether one chooses to work with the or ~bc), the difference in ~b¢ values determined by us and by Takahashi and Glassman [31 show that for their Bunsen-type burner, the actual flame temperature is also 100-200K below the adiabatic flame temperature. This difference in flame temperature leads to a 10-30% variation in Oc and a subsequent factor of 2-8 variation in equilibrium hydroxyl concentration. Thus, if we wish to relate Oc or ~b¢directly to temperature and [OH], we should clearly invest in an accurate measurement of temperature, and not rely solely on a rather doubtful calculation. Our statement that " n o satisfactory relationship was developed between sooting tendency and the relevant kinetics controlling soot formation" refers to the fact that Takahashi and Glassman's proposed correlation between ~b~ and the number of C - C bonds is only indirectly related to the
Copyright © 1987 by M. M. Harris, G. B. King, and N. M. Laurendeau Published by Elsevier Science Publishing Co., Inc. 52 Vanderbilt Avenue, New York, NY 10017
270
MARK M. HARRIS ET AL.
kinetics responsible for fuel pyrolysis and precursor oxidation, as indeed admitted by these authors [3]. In comparison, our proposed correlation between In ~b¢/[OH] and 1 / T can be directly related to a global kinetic scheme which is similar to one originally put forward by Millikan [4]. Moreover, the new correlation successfully relates the difference in previous thc data for ethylene/ oxygen and ethylene/air flames to the influence of hydroxyl concentration on the rate of precursor oxidation. We do not understand how Takahashi and Glassman [1] can accuse us of not appreciating the role of the preexponential factor for fuel pyrolysis. We clearly state that the pyrolysis rate for pure hydrocarbons increases dramatically as carbon number increases. Furthermore, our global model explicitly accounts for the influence of fuel pyrolysis through Af, precursor concentration through [P], and precursor oxidation through Ao (see Eq. (5) of Harris et al. [2]). We do, however, agree with Takahashi and Glassman [1] that the assumption ln[P]Ao/dAf o: ln(C/H)
(2)
is the weakest link in our proposed correlation, partly because no explicit recognition is given to the number of carbon atoms. This is the reason for our conclusion that data are needed for a much larger variety of hydrocarbons to confirm our findings, especially for aromatics. Equation (2) represents an initial effort to account for the influence of fuel type on the overall kinetics controlling pyrolysis and oxidation. In future work, we may indeed confirm that this rather weak effect (compared to those of temperature and [OH], which represent the emphasis of our paper) can be better related to Glassman and Takahashi's number of C - C bonds. Unfortunately, for our five fuels, we found no clear relationship between the critical equivalence ratio at a given temperature and the number of C C bonds, regardless of whether we used Oc or ~b¢. For example, at 1800K, we have indicated that ~bc for ethylene is 1.25 and that for propane is 1.35. According to Takahashi and Glassman [3], these ~b~ values should be the same; that they are not casts doubt on using the number of C-C bonds as
the sole correlating parameter for incipient soot formation. Since we only used five fuels, our data is clearly more limited than that of Takahashi and Glassman [3]. Nevertheless, the proposed relationship among 4~¢, hydroxyl concentration, temperature, and C/H ratio certainly correlates well the data that we did obtain, including that for methane. Takahashi and Glassman [1] also contend that our correlation cannot be used to justify the need for measured temperatures (see Fig. 8 of Harris et al. [2]). We suggest, however, that if the correlation can be extended to other fuels, our arguments are appropriate since (1) the form of the correlation separates the effects of temperature from those of fuel structure, and (2) despite the rather large variation in temperature and nitrogen concentration, the correlation displays a constant slope (see Fig. 7 of Harris et al. [2]) for all five fuels.
2. ERRATA We wish to correct here several errors that were discovered during publication and before reception of the comments by Takahashi and Glassman [1]. In our paper, we reported critical equivalence ratios as a function of flame temperature at atmospheric pressure for five fuels--methane, ethane, propane, ethylene, and acetylene. As discussed in the previous section, these data were then used to develop a correlation which relates the critical equivalence ratio in premixed flames to temperature, hydroxyl concentration, and the C/H ratio of the fuel. Several oversights and a numerical error have since been found which alter some of the measured and calculated data. The resulting changes are relatively small, and thus do not affect the overall discussion and conclusions of the original paper. Nevertheless, for the sake of completeness, a new version of Table 2 is provided here to correct the previous data. The values of the parameters A and B in Eq. (1) remain the same and are given in Table 3 of the original paper, except that the values for ethane and propane were inadvertently interchanged. We also present here a corrected version of Fig. 7; comparison with the original figure demonstrates that the errors are indeed relatively minor.
271
RESPONSE TO COMMENTS ON "SOOT FORMATION IN FLAMES" TABLE 2 (Continued)
TABLE 2 Measured Critical Equivalence Ratio, Maximum Flame Temperature, Volume Percent Nitrogen in the Original Mixture and Calculated Equilibrium OH Concentrations for Methane, Ethane, Propane, Ethylene and Acetylene.
Fuel Methane: CH4
Ethane: C2H6
¢c
T (K)
N2 (%)
1.58 1.58 1.67 1.73 1.73 1.81 1.81 1.81 1.84 1.85 1.89 1.91 1.92 1.93 1.93 1.96 1.96 1.97 1.97 1.98 1.98 1.98 1.98 2.01 2.04 2.04 1.75 1.79 1.82 1.82 1.82 1.87 1.87 1.89 1.89 1.94 1.94 1.94 1.94 1.95 1.95 1.96 1.98 1.99 1.99 2.01 2.03
1665 1680 1680 1710 1740 1735 1750 1760 1745 1740 1775 1795 1790 1805 1810 1800 1800 1800 1810 1805 1805 1815 1835 1815 1815 1845 1650 1650 1680 1690 1705 1705 1710 1725 1735 1755 1770 1775 1780 1750 1790 1780 1800 1810 1810 1810 1805
56 56 53 54 54 57 57 57 53 54 54 54 53 53 51 49 50 48 48 47 46 45 45 44 45 45 70 67 68 68 68 66 64 65 65 65 62 61 61 64 57 60 60 59 59 58 57
[OH]/10 t3 (l/cm 3) 1.22 1.48 1.33 1.73 2.35 2.01 2.41 2.62 2.24 2.06 2.79 3.44 3.23 3.69 4.05 3.57 3.58 3.55 3.96 3.77 3.75 4.05 5.10 4.07 3.89 5.15 0.644 0.658 0.860 0.944 1.17 1.13 1.20 1.38 1.55 1.77 2.21 2.30 2.37 1.70 2.80 2.41 2.97 3.17 3.17 3.23 2.97
Fuel
Propane: C3H8
Ethylene: C2H4
Acetylene: C2H2
O~
T (K)
N2 (%)
[OH]/1013 (l/cm 3)
2.07 2.07 2.09 1.69 1.71 1.83 1.85 1.86 1.87 1.87 1.89 1.92 1.92 1.93 1.96 1.99 2.01 2.01 2.02 2.02 2.03 2.09 2.10 2.10 2.11 1.66 1.67 1.73 1.74 1.74 1.75 1.78 1.78 1.78 1.78 1.80 1.81 1.81 1.84 1.84 1.84 1.85 1.87 1.89 1.89 1.89 1.89 1.90 1.91 1.91 1.91 1.48
1830 1835 1830 1665 1680 1730 1705 1780 1730 1745 1775 1810 1810 1795 1805 1810 1825 1830 1845 1860 1840 1845 1855 1860 1875 1620 1630 1655 1665 1670 1685 1705 1715 1735 1740 1700 1755 1755 1765 1775 1780 1790 1795 1805 1810 1820 1825 1810 1810 1825 1840 1610
57 57 55 66 63 66 67 65 63 63 64 64 64 64 63 61 59 60 58 58 58 57 56 56 57 74 75 75 74 74 75 73 72 73 73 75 71 72 69 71 71 71 70 68 69 69 69 69 68 68 68 78
3.61 3.72 3.57 0.853 1.06 1.64 1.13 2.56 1.55 1.82 2.34 3.31 3.31 2.79 3.01 3.08 3.61 3.71 4.33 4.80 3.92 3.95 4.22 4.46 5.10 0.410 0.447 0.563 0.630 0.669 0.748 0.947 1.09 1.36 1.41 0.831 1.63 1.60 1.83 2.01 2.05 2.28 2.35 2.56 2.65 2,96 3.05 2,69 2,68 3.13 3,52 0,332
MARK M. HARRIS ET AL.
272 2.0
TABLE 2 (Continued)
i
,
,
,
i
i
o CzH2
Fuel
~
T (K)
N2 (%)
IOH]/10 t3 (l/cm 3)
o0
t~ CzH 4
1.5
~
0 CzH e C3H e
7
1.52 1.52 1.52 1.54 1.56 1.56 1.56 1.58 1.60 1.62 1.62 1.63 1.64 1.66 1.66 1.66 1.66 1.67 1.68 1.68 1.70 1.70 1.71 1.72
1600 1610 1640 1660 1655 1675 1680 1655 1695 1720 1730 1700 1740 1720 1765 1765 1770 1735 1775 1785 1790 1810 1815 1810
81 81 81 78 77 77 78 82 78 80 80 80 79 81 79 79 79 80 80 79 79 78 78 79
0.251 0.279 0.415 0.555 0.511 0.667 0.678 0.418 0.735 0.934 1.06 0.743 1.14 0.852 1.43 1.45 1.52 1.01 1.57 1.75 1.74 2.21 2.40 2.10
t
..J
0.5
o.o -0.5
- 1.C
5.3
1
i
5.5
t
t
5.7
i
i
5,9
i
i
i
61
6.3
~O'~/T (K~) Fig. 7. Plot of In(q~c/IOH})-(l/3) In(C/H) versus I / T methane, ethane, propane, ethylene, and acetylene.
for
where zaE = 237 + 47 kJ/mol a n d F = 16.2 ___1.4. This expression does not require assumptions to be made about the ln([P]Ao/dAf) term [see Eq. (2)]. However, the resulting curve fit is not as accurate as that for Eq. (3).
(3)
w h e r e A E = 215 ___ 8 k J / m o l a n d D = 14.5 _+ 0.6, and the errors represent two standard deviations. The hydroxyl concentration is in units of 1013 c m - 3 while the In(C/H) term is multiplied by 1/3 rather than b'y 1/2, as in the original paper. The new values of the parameters z~E and D compare favorably with the original values of 250 kJ/mol and 16.5, respectively. If we neglect the In(C/H) term, these same data may be fitted to the equation (see Fig. 6 of Harris et al. [2]) ln(~bc/[OH]) = A E / R T - F,
CH 4
i
The correlation relating Oc to temperature and [OH] now becomes ln(4)c/[OH]) = A E / R T + ( 1 / 3 ) l n ( C / H ) - D ,
o
o
,6:~~
0
m _J 10
o
(4)
We thank C. Ferguson for pointing out a numerical problem which led to 10-50% errors in the computed hydroxyl concentrations. We also thank M. Inbody for reevaluating the parameters in the proposed correlation. REFERENCES 1.
Takahashi, F., and Glassman, I., Combust. Flame (this
2.
Harris, M. M., King, G. B., and Laurendeau, N. M., Combust. Flame 64:99 (1986). Takahashi, F., and Glassman, I., Combust. Sci. Tech. 37:1 (1984). Millikan, R. C., J. Phys. Chem. 66:794 (1962).
issue).
3. 4.
Received 7 May 1986; revised 29 September 1986
269
Response to Comments and Errata, "Influence of Temperature and Hydroxyl Concentration on Incipient Soot Formation in Premixed Flames" MARK M. HARRIS, GALEN B. KING, and NORMAND M. LAURENDEAU Flame Diagnostics Laboratory, School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907
1. RESPONSE Before responding to the criticisms of Takahashi and Glassman [1], we must point out that our paper [2] gave generous credit to both these authors [3] and to the pioneering work of Millikan [4]. Takahashi and Glassman [3] provided the first systematic study of the effect of flame temperature on the critical equivalence ratio, Oc, for premixed flames. As a first study, they pursued the obvious approach of employing the adiabatic flame temperature to isolate the major experimental trends, and then suggested an isothermal correlation between ~¢ and the number of carbon-carbon bonds. In our investigation, we instead measured the temperature and found that while the adiabatic flame temperature is useful for demonstrating the relation In 4 ~ ¢ = A - B / R T ,
(1)
a measured flame temperature is needed to associate ~bc with the global kinetics responsible for soot formation more directly. The importance of a measured flame temperature can be shown by the following three considerations. First, because of radiative and convective heat losses, the actual temperature is typically a lower percentage of the adiabatic flame temperature at higher absolute temperatures. Hence, the value of the parameter B in Eq. (1) will normally decrease if adiabatic rather than actual flame temperatures are employed, as demonstrated by the differences between our B-values and those of Takahashi and Glassman [3] for ethane and propane. At higher gas flowrates, heat losses gener-
ally decrease, thus giving more comparable Bvalues, as for ethylene and acetylene (see Table 3 of Harris et al. [2]). Second, even at the high flowrates used in our uncooled fiat-flame burner, the measured flame temperatures were approximately 100-200K below the associated adiabatic flame temperatures. Third, at 1800K, our measured 0c values for C2H6, C3H8, C2H4, and C2H2 are 1.98, 1.93, 1.88, and 1.70, respectively [2]. The resulting values for the critical effective equivalence ratio, C/c, are 1.41, 1.35, 1.25, and 1.02, respectively. Extrapolation from Fig. 4 of Takahashi and Glassman [3] gives ~kc values at an adiabatic flame temperature of 1800K of approximately 1.22, 1.13, 1.12, and 0.97, respectively. Based on our B-values (which are independent of whether one chooses to work with the or ~bc), the difference in ~b¢ values determined by us and by Takahashi and Glassman [31 show that for their Bunsen-type burner, the actual flame temperature is also 100-200K below the adiabatic flame temperature. This difference in flame temperature leads to a 10-30% variation in Oc and a subsequent factor of 2-8 variation in equilibrium hydroxyl concentration. Thus, if we wish to relate Oc or ~b¢directly to temperature and [OH], we should clearly invest in an accurate measurement of temperature, and not rely solely on a rather doubtful calculation. Our statement that " n o satisfactory relationship was developed between sooting tendency and the relevant kinetics controlling soot formation" refers to the fact that Takahashi and Glassman's proposed correlation between ~b~ and the number of C - C bonds is only indirectly related to the
Copyright © 1987 by M. M. Harris, G. B. King, and N. M. Laurendeau Published by Elsevier Science Publishing Co., Inc. 52 Vanderbilt Avenue, New York, NY 10017
270
MARK M. HARRIS ET AL.
kinetics responsible for fuel pyrolysis and precursor oxidation, as indeed admitted by these authors [3]. In comparison, our proposed correlation between In ~b¢/[OH] and 1 / T can be directly related to a global kinetic scheme which is similar to one originally put forward by Millikan [4]. Moreover, the new correlation successfully relates the difference in previous thc data for ethylene/ oxygen and ethylene/air flames to the influence of hydroxyl concentration on the rate of precursor oxidation. We do not understand how Takahashi and Glassman [1] can accuse us of not appreciating the role of the preexponential factor for fuel pyrolysis. We clearly state that the pyrolysis rate for pure hydrocarbons increases dramatically as carbon number increases. Furthermore, our global model explicitly accounts for the influence of fuel pyrolysis through Af, precursor concentration through [P], and precursor oxidation through Ao (see Eq. (5) of Harris et al. [2]). We do, however, agree with Takahashi and Glassman [1] that the assumption ln[P]Ao/dAf o: ln(C/H)
(2)
is the weakest link in our proposed correlation, partly because no explicit recognition is given to the number of carbon atoms. This is the reason for our conclusion that data are needed for a much larger variety of hydrocarbons to confirm our findings, especially for aromatics. Equation (2) represents an initial effort to account for the influence of fuel type on the overall kinetics controlling pyrolysis and oxidation. In future work, we may indeed confirm that this rather weak effect (compared to those of temperature and [OH], which represent the emphasis of our paper) can be better related to Glassman and Takahashi's number of C - C bonds. Unfortunately, for our five fuels, we found no clear relationship between the critical equivalence ratio at a given temperature and the number of C C bonds, regardless of whether we used Oc or ~b¢. For example, at 1800K, we have indicated that ~bc for ethylene is 1.25 and that for propane is 1.35. According to Takahashi and Glassman [3], these ~b~ values should be the same; that they are not casts doubt on using the number of C-C bonds as
the sole correlating parameter for incipient soot formation. Since we only used five fuels, our data is clearly more limited than that of Takahashi and Glassman [3]. Nevertheless, the proposed relationship among 4~¢, hydroxyl concentration, temperature, and C/H ratio certainly correlates well the data that we did obtain, including that for methane. Takahashi and Glassman [1] also contend that our correlation cannot be used to justify the need for measured temperatures (see Fig. 8 of Harris et al. [2]). We suggest, however, that if the correlation can be extended to other fuels, our arguments are appropriate since (1) the form of the correlation separates the effects of temperature from those of fuel structure, and (2) despite the rather large variation in temperature and nitrogen concentration, the correlation displays a constant slope (see Fig. 7 of Harris et al. [2]) for all five fuels.
2. ERRATA We wish to correct here several errors that were discovered during publication and before reception of the comments by Takahashi and Glassman [1]. In our paper, we reported critical equivalence ratios as a function of flame temperature at atmospheric pressure for five fuels--methane, ethane, propane, ethylene, and acetylene. As discussed in the previous section, these data were then used to develop a correlation which relates the critical equivalence ratio in premixed flames to temperature, hydroxyl concentration, and the C/H ratio of the fuel. Several oversights and a numerical error have since been found which alter some of the measured and calculated data. The resulting changes are relatively small, and thus do not affect the overall discussion and conclusions of the original paper. Nevertheless, for the sake of completeness, a new version of Table 2 is provided here to correct the previous data. The values of the parameters A and B in Eq. (1) remain the same and are given in Table 3 of the original paper, except that the values for ethane and propane were inadvertently interchanged. We also present here a corrected version of Fig. 7; comparison with the original figure demonstrates that the errors are indeed relatively minor.
271
RESPONSE TO COMMENTS ON "SOOT FORMATION IN FLAMES" TABLE 2 (Continued)
TABLE 2 Measured Critical Equivalence Ratio, Maximum Flame Temperature, Volume Percent Nitrogen in the Original Mixture and Calculated Equilibrium OH Concentrations for Methane, Ethane, Propane, Ethylene and Acetylene.
Fuel Methane: CH4
Ethane: C2H6
¢c
T (K)
N2 (%)
1.58 1.58 1.67 1.73 1.73 1.81 1.81 1.81 1.84 1.85 1.89 1.91 1.92 1.93 1.93 1.96 1.96 1.97 1.97 1.98 1.98 1.98 1.98 2.01 2.04 2.04 1.75 1.79 1.82 1.82 1.82 1.87 1.87 1.89 1.89 1.94 1.94 1.94 1.94 1.95 1.95 1.96 1.98 1.99 1.99 2.01 2.03
1665 1680 1680 1710 1740 1735 1750 1760 1745 1740 1775 1795 1790 1805 1810 1800 1800 1800 1810 1805 1805 1815 1835 1815 1815 1845 1650 1650 1680 1690 1705 1705 1710 1725 1735 1755 1770 1775 1780 1750 1790 1780 1800 1810 1810 1810 1805
56 56 53 54 54 57 57 57 53 54 54 54 53 53 51 49 50 48 48 47 46 45 45 44 45 45 70 67 68 68 68 66 64 65 65 65 62 61 61 64 57 60 60 59 59 58 57
[OH]/10 t3 (l/cm 3) 1.22 1.48 1.33 1.73 2.35 2.01 2.41 2.62 2.24 2.06 2.79 3.44 3.23 3.69 4.05 3.57 3.58 3.55 3.96 3.77 3.75 4.05 5.10 4.07 3.89 5.15 0.644 0.658 0.860 0.944 1.17 1.13 1.20 1.38 1.55 1.77 2.21 2.30 2.37 1.70 2.80 2.41 2.97 3.17 3.17 3.23 2.97
Fuel
Propane: C3H8
Ethylene: C2H4
Acetylene: C2H2
O~
T (K)
N2 (%)
[OH]/1013 (l/cm 3)
2.07 2.07 2.09 1.69 1.71 1.83 1.85 1.86 1.87 1.87 1.89 1.92 1.92 1.93 1.96 1.99 2.01 2.01 2.02 2.02 2.03 2.09 2.10 2.10 2.11 1.66 1.67 1.73 1.74 1.74 1.75 1.78 1.78 1.78 1.78 1.80 1.81 1.81 1.84 1.84 1.84 1.85 1.87 1.89 1.89 1.89 1.89 1.90 1.91 1.91 1.91 1.48
1830 1835 1830 1665 1680 1730 1705 1780 1730 1745 1775 1810 1810 1795 1805 1810 1825 1830 1845 1860 1840 1845 1855 1860 1875 1620 1630 1655 1665 1670 1685 1705 1715 1735 1740 1700 1755 1755 1765 1775 1780 1790 1795 1805 1810 1820 1825 1810 1810 1825 1840 1610
57 57 55 66 63 66 67 65 63 63 64 64 64 64 63 61 59 60 58 58 58 57 56 56 57 74 75 75 74 74 75 73 72 73 73 75 71 72 69 71 71 71 70 68 69 69 69 69 68 68 68 78
3.61 3.72 3.57 0.853 1.06 1.64 1.13 2.56 1.55 1.82 2.34 3.31 3.31 2.79 3.01 3.08 3.61 3.71 4.33 4.80 3.92 3.95 4.22 4.46 5.10 0.410 0.447 0.563 0.630 0.669 0.748 0.947 1.09 1.36 1.41 0.831 1.63 1.60 1.83 2.01 2.05 2.28 2.35 2.56 2.65 2,96 3.05 2,69 2,68 3.13 3,52 0,332
MARK M. HARRIS ET AL.
272 2.0
TABLE 2 (Continued)
i
,
,
,
i
i
o CzH2
Fuel
~
T (K)
N2 (%)
IOH]/10 t3 (l/cm 3)
o0
t~ CzH 4
1.5
~
0 CzH e C3H e
7
1.52 1.52 1.52 1.54 1.56 1.56 1.56 1.58 1.60 1.62 1.62 1.63 1.64 1.66 1.66 1.66 1.66 1.67 1.68 1.68 1.70 1.70 1.71 1.72
1600 1610 1640 1660 1655 1675 1680 1655 1695 1720 1730 1700 1740 1720 1765 1765 1770 1735 1775 1785 1790 1810 1815 1810
81 81 81 78 77 77 78 82 78 80 80 80 79 81 79 79 79 80 80 79 79 78 78 79
0.251 0.279 0.415 0.555 0.511 0.667 0.678 0.418 0.735 0.934 1.06 0.743 1.14 0.852 1.43 1.45 1.52 1.01 1.57 1.75 1.74 2.21 2.40 2.10
t
..J
0.5
o.o -0.5
- 1.C
5.3
1
i
5.5
t
t
5.7
i
i
5,9
i
i
i
61
6.3
~O'~/T (K~) Fig. 7. Plot of In(q~c/IOH})-(l/3) In(C/H) versus I / T methane, ethane, propane, ethylene, and acetylene.
for
where zaE = 237 + 47 kJ/mol a n d F = 16.2 ___1.4. This expression does not require assumptions to be made about the ln([P]Ao/dAf) term [see Eq. (2)]. However, the resulting curve fit is not as accurate as that for Eq. (3).
(3)
w h e r e A E = 215 ___ 8 k J / m o l a n d D = 14.5 _+ 0.6, and the errors represent two standard deviations. The hydroxyl concentration is in units of 1013 c m - 3 while the In(C/H) term is multiplied by 1/3 rather than b'y 1/2, as in the original paper. The new values of the parameters z~E and D compare favorably with the original values of 250 kJ/mol and 16.5, respectively. If we neglect the In(C/H) term, these same data may be fitted to the equation (see Fig. 6 of Harris et al. [2]) ln(~bc/[OH]) = A E / R T - F,
CH 4
i
The correlation relating Oc to temperature and [OH] now becomes ln(4)c/[OH]) = A E / R T + ( 1 / 3 ) l n ( C / H ) - D ,
o
o
,6:~~
0
m _J 10
o
(4)
We thank C. Ferguson for pointing out a numerical problem which led to 10-50% errors in the computed hydroxyl concentrations. We also thank M. Inbody for reevaluating the parameters in the proposed correlation. REFERENCES 1.
Takahashi, F., and Glassman, I., Combust. Flame (this
2.
Harris, M. M., King, G. B., and Laurendeau, N. M., Combust. Flame 64:99 (1986). Takahashi, F., and Glassman, I., Combust. Sci. Tech. 37:1 (1984). Millikan, R. C., J. Phys. Chem. 66:794 (1962).
issue).
3. 4.
Received 7 May 1986; revised 29 September 1986