Untitled - Aerobib - Universidad Politécnica de Madrid

4.2. KINDS OF DETONATIONS AND DEFLAGRATIONS 91
Consequently, if p 2 > p 1 , then τ 1 > τ 2 , and if p 2 < p 1 , then τ 1 < τ 2 .
Therefore, when the pressure increases across the wave the gases contract, and if the
pressure decreases, the gases expand. Both types of waves are physically observed.
The first type is called detonation and the second deflagration. The propagation velocity
of a detonation wave in an explosive mixture is of the order of several thousand
meters per second. The propagation velocity of a deflagration wave is normally of the
order of 1 m/s.
4.2 Kinds of detonations and deflagrations
The study can be simplified by representing the state of unburnt and burnt gases in the
diagram (p, τ), Fig. 4.2, proposed by Grussard [1].
p
III
H
I
p 2
A
p 1
II
P
B
IV
0 τ0 τ1 τ2 τ3
Figure 4.2: Sketch of the Hugoniot curve for the final states.
D
τ
In this diagram, let P (p 1 , τ 1 ) be the representative point of the initial state.
Condition (4.9) excludes regions I and II from this diagram, since in these regions
(p 2 − p 1 ) / (τ 1 − τ 2 ) is smaller than zero. The representative points of the final states
must be, consequently, within regions III and IV. The points in region III correspond to
detonations, since, in this region p 2 > p 1 and τ 2 < τ 1 . Points in region IV correspond
to deflagrations.
The possible final states corresponding to the initial state (p 1 , τ 1 ) and compatible
with conditions (4.1), (4.2) and (4.3), lie on a curve H, called the Hugoniot curve.