Untitled - Aerobib - Universidad Politécnica de Madrid

6.14. HYDRAZINE DECOMPOSITION FLAME 181
Here, X i are the mole fractions of the different species, k i the specific reaction velocities
given by Eq. (6.112) (subscript of k indicates the corresponding reaction in accordance
with the number assigned to them in the preceding paragraph) and c = ρ/M
is the mole concentration per cm 3 .
The following values, also applied by Gilbert and Altman [38], are adopted for
specific velocities
k 1 = 4 × 10 12 e −60 000/RT s −1 (6.174)
k 2 = 10 13 e −4 600/RT cm 3 mol −1 s −1 (6.175)
k 4 = 10 13 e −7 000/RT cm 3 mol −1 s −1 (6.176)
k 5c = 5 × 10 15 cm 6 mol −2 s −1 (6.177)
k 5d = 10 16 cm 6 mol −2 s −1 (6.178)
Reaction velocity of hydrazine under to steady state assumption for
radicals
The steady state assumption is expressed by making to reaction velocities of the radicals
referred by 5, 6 and 7 in (6.187.a) equal to zero. Thereby
k 2 cX 1 X 5 = k 3 X 6 , (6.179)
cX 1 (k 2 X 5 − k 4 X 7 ) = 2k 1 X 1 − k 5c c 2 X 5 X 7 , (6.180)
cX 1 (k 2 X 5 − k 4 X 7 ) = k 5c c 2 X 5 X 7 + 2k 5d c 2 X7 2 . (6.181)
Since mole fraction X 7 of radical H is small throughout the reaction with
respect to reactant X 1 , it occurs that k 5c cX 7
is negligible when compared to 2k 1
.
k 2 X 1 k 2 cX 5
Hence Eqs. (6.180) and (6.181) may be written
k 2 X 5 − k 4 X 7 = 2k 1
c , (6.182)
k 2 X 5 − k 4 X 7 = 2k 5dcX 2 7
X 1
. (6.183)
Consequently, the concentration of radicals H is supplied by
√
k1 √
X 7 = X1
k 5d c 2 . (6.184)