Untitled - Aerobib - Universidad Politécnica de Madrid

4.7. INDETERMINACY OF THE SOLUTION 103
y
125
100
x =1/6 0
(a) Detonation branch
75
50
J
25
0
P A
0.0 0.2 0.4 0.6 0.8 1.0
y
1.0
0.8
P
B
(b) Deflagration branch
x
0.6
0.4
J’
0.2
0.0
0
20
40
60
80
100
x
Figure 4.7: Hugoniot curve (x = τ/τ 1, y = p/p 1) corresponding to p 1 = 1 atm, τ 1 =
1000 cm 3 /gr, T 1 = 300 K, γ 1 = γ 2 = 1.4, Q = 1000 cal gr −1 , c p2 = 0.46
cal gr −1 K −1 , ν = 1.
4.7 Indeterminacy of the solution
The study performed in this chapter allows the establishment of the different types of
combustion waves that are compatible with the principles of the conservation of mass,
momentum and energy. This has been attained by comparison between the initial and
final state of the gases. In order to obtain this result it has not been necessary to take
into account the intermediate states undergone by the gas, within the wave. Thus, the
problem is essentially simplified. However, if the influence of the intermediate states
is neglected the result obtained is incomplete, since the propagation velocity of the
combustion wave remains undetermined, whilst experience shows that it takes a well
defined value for each different case. In order to eliminate the said indeterminacy and
select among the combustion waves obtained herein those that will actually occur, it
is necessary to analyze the internal structure of the wave and see the mechanism that