Environmental Engineering Reference
In-Depth Information
A
!ð
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