Environmental Engineering Reference
In-Depth Information
Fig. 2.13 Pathological
detonation of reactions in the
p-V plane
plane moves up along Rayleigh line, until it meets the Hugoniot curve (
ʻ
= 1).
The shock wave of the whole
fl
flowing area is subsonic. The sparse waves from
flowing.
(2) When D ¼ D, the state point starts from shock wave point N to Rayleigh line.
The state point line is tangential to the envelope curve. The state point reaches
strong compression point S or weak detonation point W of the Hugoniot curve
(
the rear degrade the
fl
= 1). The contact point P of Rayleigh line and the envelope line is between S
and W. Von Neumann named point P as the pathological point.
(3) For an irregular reaction, there is a D in the reaction of the molecular amount
reduction. The value of D is related with the property of explosives (state
function) and reaction rate. The under-pressure detonation occurs when D is
with certain value.
(4) When D
\
D, Rayleigh line cannot cross or contact with Hugoniot curve. So
there is no envelope line, and no time-independent solution.
ʻ
Von Neumann explained the key features of pathological detonation with Molar
reduction using one reaction in Fig.
2.14
. When D
[
D, there are two vertical
segmentations. The segmentation, which starts from point N and ends point S, is at
the top. Subsonic
fluctuation is at the end point S. When D
\
D, there are two
horizontal segmentations. The reaction starts from point N, and only reaches partial
reaction point T. When D ¼ D, there is saddle-backed con
fl
guration at point P.
Figure
2.14
shows that the detonation with propagation velocity D ¼ D starts
from the crosspoint N of the Hugoniot curve and shock adiabatic curve. Only after
passing point P is under pressure detonation point (or weak detonation point) is
reached. Von Neumann named the detonation velocity as eigenvalue detonation
