Basics of Fluid Mechanics, 2014a

12.2. OBLIQUE SHOCK 519
From these tables the pressure ratio at zone 3 and 4 can be calculated
P 3
= P 3 P 2 P 0 P 1
1 1
=1.6247 × 1.9791
P 4 P 2 P 0 P 1 P 4 1.6963 1.6038 ∼ 1.18192
To reduce the pressure ratio the deflection angle has to be reduced (remember that at
weak weak shock almost no pressure change). Thus, the pressure at zone 3 has to be
reduced. To reduce the pressure the angle of slip plane has to increase from 1.5◦ to a
larger number.
End Solution
Example 12.15:
The previous example gave rise to another question on the order of the deflection angles.
Consider the same values as previous analysis, will the oblique shock with first angle of
15 ◦ and then 12 ◦ or opposite order make a difference (M =5)? If not what order will
make a bigger entropy production or pressure loss? (No general proof is needed).
Solution
Waiting for the solution
End Solution
12.2.3.1 Retouch of Shock Drag or Wave Drag
Since it was established that the common
explanation is erroneous and the steam
lines are bending/changing direction when
they touching the oblique shock (compare
with figure (11.15)). The correct explanation
is that increase of the momentum into
control volume is either requires increase
of the force and/or results in acceleration
of gas. So, what is the effects of the
oblique shock on the Shock Drag? Figure
(12.19) exhibits schematic of the oblique
shock which show clearly that stream lines
are bended. There two main points that
should be discussed in this context are the
stationary control
volume
U 1 = 0 U 1 ≠ 0
ρ ρ 1 2
A 1 A 2
P 1
P 2
stream lines
moving
object
Fig. -12.19. The diagram that explains the
shock drag effects of a moving shock considering
the oblique shock effects.
additional effects and infinite/final structure. The additional effects are the mass start
to have a vertical component. The vertical component one hand increase the energy
needed and thus increase need to move the body (larger shock drag) (note the there
is a zero momentum net change for symmetrical bodies.). However, the oblique shock
reduces the normal component that undergoes the shock and hence the total shock
drag is reduced. The oblique shock creates a finite amount of drag (momentum and
energy lost) while a normal shock as indirectly implied in the common explanation creates
de facto situation where the shock grows to be infinite which of course impossible.