Untitled - Aerobib - Universidad Politécnica de Madrid

6.15. FLAME PROPAGATION IN HYDROGEN-BROMINE MIXTURES 201
The physico-chemical constants given by von Kármán and Penner were used
in our calculations. The values of these constants, as well as those for the integrals
and parameters needed for evaluation of u 0 , are summarized in Table 6.6.
In order to analyze the influence of convection and of dissociation of bromine
upon the value of u 0 , the flame velocity was computed for two cases, using the correct
relation given in Eq. (6.284) for √ Λ. The results are listed in Table 6.5 and 6.6, which
show that the correction is negligible small due to the cancellation of convection and
dissociation energy effects.
X 3,0 0.55 0.60 0.65 0.70
X 2,0 0.45 0.40 0.35 0.30
X 1,f 0.90 0.80 0.70 0.60
X 3,f 0.10 0.20 0.30 0.40
ε 1f 0.997 0.994 0.990 0.984
T f K 1660 1585 1460 1324
10 5 λ f (cal/cm-s-K) 19.8 25.0 29.4 33.1
c p (cal/g-K) 0.105 0.116 0.132 0.151
M (g/mole) 73.1 65.2 57.3 49.4
θ a 12.2 12.75 13.9 15.28
θ r 6.81 7.13 7.83 8.55
θ 0 0.1945 0.204 0.221 0.244
β 1 1.532 1.745 1.762 1.684
β 2 1.380 1.560 1.560 1.470
β 3 0.152 0.185 0.202 0.214
q 1 0.807 0.800 0.787 0.768
q 4 1.63 1.55 1.475 1.42
10 3 I 0.667 1.601 2.639 3.395
√
Λ 24.54 13.82 12.09 10.47
u 0
√
Λ (cm/s) 551 529 369 228
u 0 (cm/s) 22.9 33.7 30.5 21.8
10 3 J -0.87 -0.94 — —
√
Λ from Eq. (6.284) 24.03 15.49 — —
u 0 (cm/s) from Eq. (6.284) 23.34 34.15 —
Table 6.6: Parameters for the computation of flame velocities.
The results given in Table 6.5 show that dissociation of bromine reduces the
flame velocity considerably. Values for u 0 have been plotted in Fig. 6.17 which also
shows the results calculated by von Kármán and Penner [40] and by Gilbert and Altman
[29] . Also listed are experimental data obtained by Anderson and his collaborators
[43]. It will be seen that the influence of dissociation of bromine on u 0 predicted
by Gilbert and Altman is exaggerated. This conclusion is not surprising if one considers
that these authors estimated the influence of dissociation from the results obtained
through a thermal theory. Then they applied the reduction factor obtained from a ther-