Explosion Features of Liquid Explosive Materials - Liquid Explosives - page 91

“ II ” means the zone with re fl ected shock waves passing through. q 1 and q 2 are fl ow

rates of air in zones separately.

After passing the shock wave fronts, both the velocity/rate and direction of air
change. The tangential component parallel to shock wave fronts remains constant,
and the normal component becomes smaller. So the direction of

“ I ” and “ II ”

fl ow turns toward

the wall/surface. Below equation is obtained from Fig. 2.41 .

u 1 ¼ q 1 cos ð u 1 h Þ

q 0 cos

In the two sides of incident wave fronts, both energy and momentum are
conserved.

q 0 q 0 sin u 1 ¼ q 1 q 1 sin ð u 1 h Þ

P 0 þ q 0 q 0 sin 2 u 0 ¼ q 1 q 1 sin 2

ð u 1 h Þ P 1

Likewise, the incident fl flow in “ I ” zone is q 1 .Itin fl ows “ II ” zone with an angle of

u 2 þ h from the fronts OR of re fl ected waves. Because of the impact of velocity

component q 1 cos ow q 2 directs outward and it is parallel

with the rigid surface. For the two sides of re

ð u 2 þ h Þ , the re fl ected fl

fl ected waves, below equations are

established.

q 2 cos u 2 ¼ q 1 cos ð u 2 þ h Þ

q 2 q 2 sin u 2 ¼ q 1 q 1 sin ð u 1 þ h Þ

q 2 q 2 sin 2 u 2 þ P 2 ¼ q 1 q 1 sin 2 ð u 2 þ h Þ P 1

The impact adiabatic function of incident waves and re fl ected waves are

q 1 ð k þ 1 Þ P 1 þ k ð 1 Þ P 0

q 0 ¼ ð k 1 Þ P 1 þ k þ ð 1 Þ P 0

and

q 2
q 1 ¼

ð k þ 1 Þ P 2 þ k ð 1 Þ P 1

ð k 1 Þ P 2 þ k þ ð 1 Þ P 1

are obtainable from above equations. The calculation
process is very complex. As a matter of convenience, the oblique re

P 2 ; q 2 ; u 2 ; q 1 and ʸ

fl ection is

simpli ed to Eq. 2.100 .

6 D P 1
D P 1 þ

7P 0 cos 2

D P 2 ¼

ð 1 þ cos u Þ D P 1 þ u 1 ð 2 : 100 Þ