Environmental Engineering Reference
In-Depth Information
Why eigenvalue detonation is referred here? According to Chapman and
Jouguet, the founders of the classic detonation theory, the theory is completely
based on the kinetic theory of gases. This is not absolutely right. The detonation
theory does not have close relation with kinetic theory of gases, but also chemical
kinetics. Besides the three conservation equations in the kinetic theory of gases, the
equation of chemical kinetics is also being considered. In the equation, the rate of
chemical reactions is important. In the kinetic theory of gases, mechanical quan-
tities are functions of
flow gradients. But in classic chemical kinetics, reaction rates,
which are different from mechanical quantities, are not the functions of
fl
ow gra-
dients, but functions of local thermal dynamic states. Mechanical quantities are
different from chemical reaction rates.
How to solve the problem of combining the chemical reaction equations and the
three equations of gas kinetic theory? It
fl
cult because of the com-
plexity of chemical reaction inside detonation area. There must be a simpli
'
s extremely dif
ed
approach, which stipulates that chemical compositions react stoichiometrically
according to some way, and the proceeding variable (
ʻ
i
) of stoichiometric reactions
represents the complex changes of chemical compositions. This makes a chemical
problem into a physical one. The simplest stoichiometric reaction is Eq.
2.24
.
A
!
B
ð
2
:
24
Þ
is
the decomposition degree of the explosive (the ratio of decomposed explosive mass
to the original explosive mass). The proceeding variable
In the above equation, A is an explosive, B is the product of detonation, and
ʻ
ʻ
reports the chemical
changes.
The state function of detonation reaction is Eq.
2.24
.
E ¼ Ep
; q; k
ð
Þ
ð
:
Þ
2
25
While the chemical reaction rate of detonation is Eq.
2.26
.
d
dt
¼ rp
; q; k
r ¼
k
¼
ð
Þ
ð
2
:
26
Þ
ˁ
Here, r is the chemical reaction rate; p is the pressure of detonation waves;
is
the media density of detonation waves.
Please notice that the reaction rate is assumed to only have relationships with
local state, not with flow gradients.
Von Neumann [
9
] studied the suspended detonation of aluminum in the oxygen
gas. Al
2
O
3
is not the only product because Al
2
O
3
decomposes under high tem-
perature and high pressure. So the chemical formulae have Molar reduction, and a
lot of heat is given off. In irreversible reaction, Von Neumann set up the reaction in
Eq.
2.27
.
