3.11 Reflection of a Plane Shock from a Rigid Plane Surface
Let us now consider a plane shock wave propagating to the right down a tube with
velocity U i and incident on a plane rigid end-wall of the tube as shown schematically
in Fig. 3.6. When the shock front reaches the end-wall the gas or particle motion u p
behind the incident shock is suddenly stopped by the immediate generation of a
reflected shock wave propagating to the left with velocity U r , whose magnitude
ensures that the gas behind the reflected shock is at zero velocity and, accordingly, is
at rest relative to the tube.
The conservation equations for the incident shock wave with respect to regions
1 and 2 are
ρ 1 U i ¼ρ 2 U i À u p
À
Á
p 1 þ ρ 1 U
2
i ¼p 2 þ ρ 2 U i À u p
À
Á 2
h 1 þ
U
2
i
2
¼h 2 þ
U i À u p
À
Á 2
2
and corresponding conservation equations for the reflected shock wave with respect
to regions 2 and 3 are
Fig. 3.6 Schematic diagram showing the moving and stationary shocks for both the incident and
reflected shock waves
110
3 Conditions Across the Shock: The Rankine-Hugoniot Equations