Untitled - Aerobib - Universidad Politécnica de Madrid

6.14. HYDRAZINE DECOMPOSITION FLAME 177
which is the initial reaction in the complex process that is stoichiometrically represented
by (6.163).
Making use of the thermal theory of Zeldovich and Frank-Kamenetskii [33]
and using the specific reaction rate
k = 4 × 10 12 e −60 000/RT , (6.165)
proposed by Szwarc [34], they obtained a theoretical propagation velocity of the flame
of 110 cm/s compared to the 185 cm/s obtained from experiments.
More precise calculations were performed by Hirschfelder [35] and by Kármán
and Penner [6], making use of Murray and Hall’s kinetic scheme with results that
confirm those obtained by Murray and Hall. Hirschfelder and Kármán and Penner
also studied the influence over the propagation velocity of the flame of the diffusion
of the different species. In this case they obtain values considerably smaller than
the experimental ones since diffusion reduces substantially the value of the flame’s
propagation velocity.
The following table summarizes the results of the works by Murray-Hall and
Kármán-Penner.
Experimental value
Theoretical values
Refs. Murray-Hall Murray-Hall Kármán-Penner
Zero diffusion Zero diffusion Non-zero diffusion 10
u 0 185 cm/s 110 cm/s 95 cm/s 42 cm/s
Table 6.3: Theoretical and experimental propagation velocities of the flame in a mixture of
vapour of hydrazine and water. Mass fraction of hydrazine = 0.972. Pressure =
1 atm. Initial temperature of the mixture = 150 ◦ C.
If the reaction controlling the process is the one given by Eq. (6.164) with the
specific reaction rate (6.165), the following two conditions must be satisfied:
1) Since chemical reaction (6.164) is of the first order, the propagation velocity of
the flame must be inversely proportional to the square root of pressure.
2) Since the activation energy E of reaction (6.164) is 60 000 cal/mol and the flame
propagation velocity is approximately proportional to exp (−E/2RT f ) according
to Eq. (6.72) where T f is the flame temperature, when such velocity is represented
as a function of 1/T f in the logarithmic scale one must evidently obtain
a slope equal to −E/2R.
10 For a Lewis number equal to unity.