Environmental Engineering Reference
In-Depth Information
Fig. 2.12 Hugoniot reaction
curves of under-pressure
detonation
capacity. When D ¼ D, the mass point passes shock waves, and jumps to Point N,
shifts along Rayleigh line to the right until CJ point. In CJ point,
Σ
= 0 and
ʷ
=0.
˃
ʷ
(Here,
is the constant of thermal conductivity;
is the coef
cient of sound speed;
Þ
E
;
v
=q
c
2
,
P
rc
2
; c is sound speed; u is mass velocity)
[
4
]. Then the mass point can return to strong detonation point S along Rayleigh
line, or move to the right until the point W of under-pressure detonation, and then
the under-pressure detonation occurs. When D
\
D, the mass point starts from
r
¼
@
P
=@k
ð
,
g
¼
1
u
=ðÞ
=0
of Hugoniot curve along Rayleigh line. There is no crosspoint of Rayleigh line and
Σ
ʻ
=0,so
d
p
= 0 line. When Rayleigh line crosses the sound track line,
ʷ
d
t
¼
1
.
There is no time-independent solution.
In the explosion of liquid explosives, the two prerequisites of classic under-
pressure detonation are the
final Hugoniot curve, (not the up boundary covered by
frozen Hugoniot curve), and that Rayleigh line passes point
Σ
=0(
ʷ
= 0), and
reaches point W
finally.
Figure
2.13
gives the simultaneous solution of gas dynamic equation and
reaction rate equation (in plane p-
).
In Fig.
2.13
, the contact point of envelope line is at
ʻ
ʻ
= 1/2. There are special
situations from Fig.
2.6
through Fig.
2.13
(Fig.
2.11
).
(1) There is a special detonation rate D, which is the D value when Rayleigh line
is tangential with the envelope curve. When D
[
D, the subsonic speed of
Hugoniot curves separates with supersonic speed (Fig.
2.13
) because part of
Rayleigh line is above the envelope curve. So the detonation only occurs on
the top part of Hugoniot curve. Following the proceeding of reactions, state
point starts from shock wave point N, moves down along Rayleigh line until it
meets envelope curve, and this point is the minimum p. Then state point of p-V
