Untitled - Aerobib - Universidad Politécnica de Madrid

4.4. PROPAGATION VELOCITY 99
p H’
S 2
B ( τ 2
, p 2
)
p 2
S 2
A
H’
Figure 4.6: Position of the isentropic curves in the Hugoniot curve of the admissible initial
states.
τ 2
τ
point (p 2 , τ 2 ), in which F < 0, and the lower region, in which F > 0. Finally, it
is also verified that along the radius vectors that pass through the point (p 2 , τ 2 ) the
variations of F and s 1 are opposite. Now, by combining these properties as previously
done for v 2 , we can determine the relative position of the isentropic that passes
through each point H ′ with respect to the straight line that joins this point to the point
(p 2 , τ 2 ). It results that this position is the one indicated in Fig. 4.6. Therefore, in the
detonation branch α < α S and in the deflagration branch α > α S . Therefore, one
concludes that the propagation velocity of a detonation is always supersonic, and the
propagation velocity of a deflagration is always subsonic.
As a result of the preceding study, the Table 4.1 can be constructed. This
table contains the results of Jouguet’s studies and defines the characteristics of the
combustion waves.
Detonations
Weak Chapman-Jouguet Strong
Velocity before
Supersonic
Velocity after Supersonic Sonic Subsonic
Deflagrations
Weak Chapman-Jouguet Strong
Velocity before
Subsonic
Velocity after Subsonic Sonic Supersonic
Table 4.1: Characteristics of the combustion waves.