Handout 1 - Clemson University

p e+- dV +Jp e+ ii -nidS =- pii -idS
dt V 2 ) s( 2)
Equation 3.2-3
where a volume V with surface S is assumed to be fixed in space, and ,i is the normal
vector on a portion dS of the surface S
The above governing equations that no body assume forces are acting on the fluid
particles and no heat transfer or radiation is taking place. These assumptions are valid
since none of these effects are known to play a crucial role in blast wave propagation
[32].
We will consider a normal shock as the one shown in Figure 3.2-1. The shock is
propagating (left illustration) with a velocity of Us into a uniform stream with fluid
particle velocity ul, while the particle velocity behind it is u2. A more convenient way to
handle this phenomenon is to consider the right image of Figure 3.2-1, where a
reference moving frame with Us velocity is considered. Consequently, the velocities in
front and behind the shock front are now U1=u1+Us and U2=u2+Us respectively.
u10
Us
(A)
Moving Shock
U2
Figure 3.2-1: Moving and stationary shock wave [26]
U 1=u 1 + Us U 2=u 2 + Us
(B)
Stationary Shock