Environmental Engineering Reference
In-Depth Information
production. But the shock wave fronts transport in ultrasound rate, all points of P
and above P follow Eq.
2.21
.
C
D
u
ð
2
:
21
Þ
So compression of products is impossible.
In summary, under the study conditions, the state W, which represents all points
on the weak branch of balance detonation adiabatic curve is not achievable. So
under-pressure or weak detonation points do not exist. Equation
2.21
is a pre-
requisite for the stable transportation of detonation wave fronts.
On the other hand, ultra compression fronts are not compatible with sparse
waves. Stable self-sustaining states need to meet the second prerequisite
—
Eq.
2.22
.
C
D
u
ð
2
:
22
Þ
Therefore, only when
C ¼ D
u
ð
2
:
23
Þ
These two prerequisites should not con
fl
ict with each other. That is the famous
CJ selection rule.
In the same book, Dremin studied another condition. The reaction from k
0
to k
1
is exothermic, while the reaction from k
1
to the balance composition is endothermic.
Now the smallest detonation rate is the ratio of Rayleigh line ON, which represents
the denotation rate. Rayleigh line is the tangential one of the intermediate k
1
under
detonation and in adiabats. The notation of exothermic energy becomes negative
when it is passing this line. The detonation wave fronts spread faster than normal
detonation. In other words, CJ rule (Eq.
2.23
) is not applicable.
In Fig.
2.8
, when the state point shifts from point N or N
′
along Rayleigh line to
point P or P
, the pressure drops, and a chemical peak shows up again. The state
point cannot shift down from point P
′
because the intermediate/mean detonation
adiabatic curve of composition k
1
is above all other detonation adiabatic line/curve.
So the state point can only shift along Rayleigh line from P
′
.
If the state point starts from point P, the shift along Rayleigh line has two
directions: up to point S with pressure increase, and down to point W (it corre-
sponds with the under-pressure detonation) with pressure drop. Under suitable
environmental conditions, under-pressure detonation is also possible when the
pressure continuously decreases in the detonation wave range.
The detonation of liquid explosives is different from that of general condensed
explosives. In common, for same mass/weight of explosives, liquid explosives do
more work than condensed explosives. The under-pressure detonation of self-sus-
taining spreading is studied below.
More than one time, Dremin [
7
] referred two-stage detonation theory. The
pressure inside detonation waves is determined by two-stage detonation. If the
reactions inside detonation waves start slowly, and accelerate gradually, which is
′
to balance point S
′
