Environmental Engineering Reference
In-Depth Information
A
1
þ dÞ B
ð
2
:
27
Þ
The reaction is Moore fraction reduction. One molecule A reacts to (1 +
ʴ
)
molecule B (
< 0). According to the mass conservation, if the molecular weight of
A is MA, the molecular weight of B is MB
ʴ
MA
1 þd
¼
. The state equation changes to
Eq. 2.28 .
Þ R T
pV ¼
ð
1
þ kd
ð
2
:
28
Þ
Here, R ¼ R = M A , and R is the gas constant of material A.
The state internal energy function is Eq. 2.29 .
"
#
C p
A h 0A þ
e ¼ m 0
þ kd R
1
pV k q
ð
2
:
29
Þ
1
Here, C p is the heat capacity under constant pressure; h 0A is the enthalpy of
composition Molar fraction; q is the heat fraction vector frozen point.
Hugoniot curve is Eq. 2.30 .
"
#
!
p 0 V 0 ¼
C p
C p
R
ð
p þ p 0
Þ
þ kd R
1
pV
1
ð
V 0 V
Þ k q
ð
2
:
30
Þ
2
1
So, the envelope of Hugoniot curve is Eq. 2.31 .
pV d C p
q ¼
ð
2
:
31
Þ
2
R
ð
1
þ kd
Þ
c
˃
Because the reaction is irreversible,
0 , and
is not always larger than 0.
0, the curves of P ¼ r r ¼
r ¼
Σ
When
0 are in Fig. 2.12 (
include all areas except
Rayleigh line).
From Fig. 2.12 , the curve of Σ = 0 and the frozen Hugoniot curve enclose into
one line/curve. Because the line of
= 0 is the enclosed line of Hugoniot curve, the
crosspoint of the sound track line and the curve of
Σ
Σ
= 0 is the tangential point (CJ)
of Rayleigh line and the curve of
= 0. The corresponding detonation rate of
Rayleigh line is D. When D [ D, the mass point starts from the original state,
passes shock waves, and jumps the point N of Hugoniot curve (
Σ
ʻ
= 0). For point N,
ʷ
> 0, so the mass point only moves along the Rayleigh line from the left to
right, until the point
>0,
Σ
Σ
of Rayleigh line and
Σ
= 0 curve. Because
Σ
= 0, all
parameters have extrema. When
Σ
< 0, the reaction shifts along Rayleigh line from
the right to left, and
final stage S1 of Hugoniot curve. S1 is a
strong detonation point. The pressure of reacting zone/area reduces from N1 to
point
finally reaches the
Σ
, then increases to S1. There is a minimum pressure. The capacity V
increases from N to point
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