Page 266 - 48Fundamentals of Compressible Fluid Mechanics

228 CHAPTER 13. OBLIQUE-SHOCK

the maximum possible a detached shock is occurs. However, the configuration that
detached shock occurs in many design configurations and the engineers need to
take it into considerations. Such configurations seem sometimes at the first glance
not related to the detached shock issue. Consider, for example, a symmetrical
suction section in which the deflection angle is just between the maximum deflec-
tion angle and above the half of the maximum deflection angle. In this situation,
at least two oblique shocks occur and after their interaction is shown in Figure
(13.13). No detached shock issues are raised when only the first oblique shock
is considered. However, the second oblique shock complicates the situation and
the second oblique shock can cause detached shock. This situation known in the
scientific literature as the Mach reflection.
It can be observed that the
maximum of the oblique shock for
Ideal gas model depends only on θ 1 δ 1
upstream Mach number i.e. for ev-
ery upstream Mach number there U B C
is only one maximum deflection an- θ 2 Slip Plane
A
gle. δ 2
(13.54)
c

Additionally, it can be observed that

Fig. 13.13: The schematic for symmetrical suction
for non maximum oblique shock that
section with Mach reflection

for a constant deflection angle decrease of Mach number results in increase of
. The Mach number de-

creases after every shock. Therefore, the maximum deflection angle decreases

with decrease of the Mach number. Additionally due to the symmetry a slip plane
c . Thus, this

situation causes the detach shock to appear in the second oblique shock. This
Mach angle (weak shock only)

detached shock manifested itself in form of curved shock (see Figure 13.14).
angle can be guessed to be parallel to original flow, hence c
The analysis of this situation log-
ically is very simple yet the mathe- !#"%$'&)(%*,+&
matics is somewhat complicated. The θ 1 δ 1
maximum deflection angle in this case
is, as before, only function of the up-
U B C
stream Mach number. The calculations
of such case can be carried by several A sub sonic
approaches. It seems to this author that flow
most straight way is by the following pro-
cedure:
(a) Let calculation carried for ;
Fig. 13.14: The “detached” shock in compli-
(b) Calculate the maximum deflection cated configuration some times
angle, utilizing (13.31) equation. referred as Mach reflection

utilizing equation (13.12)

(c) Calculate the deflection angle, c)