Basics of Fluid Mechanics, 2014a

508 CHAPTER 12. COMPRESSIBLE FLOW 2–DIMENSIONAL
12.2.3 Application of Oblique Shock
α 1
α 2
α 3
normal shock
oblique shock
Fig. -12.13.
Two variations of inlet suction for supersonic flow.
One of the practical applications of the oblique shock is the design of an inlet
suction for a supersonic flow. It is suggested that a series of weak shocks should replace
one normal shock to increase the efficiency (see Figure (12.13)) 17 . Clearly, with a proper
design, the flow can be brought to a subsonic flow just below M =1. In such a case,
there is less entropy production (less pressure loss). To illustrate the design significance
of the oblique shock, the following example is provided.
Example 12.5:
The Section described in Figure 12.13 and
12.14 air is flowing into a suction section
at M = 2.0, P = 1.0[bar], and
T =17 ◦ C. Compare the different conditions
in the two different configurations.
Assume that only a weak shock occurs.
α 1
7 ◦
ÓÐÕÙ ×Ó×
1
2 3 4
« ¾ 7 ◦
neglect
the detached
distance
Normal shock
Solution
Fig. -12.14. Schematic for Example (12.5).
The first configuration is of a normal shock for which the results 18 are
M x M y
T y
T x
ρ y
ρ x
P y
P x
P 0y
P 0x
2.0000 0.57735 1.6875 2.6667 4.5000 0.72087
17 In fact, there is general proof that regardless to the equation of state (any kind of gas), the entropy
is to be minimized through a series of oblique shocks rather than through a single normal shock. For
details see Henderson and Menikoff “Triple Shock Entropy Theorem,” Journal of Fluid Mechanics 366,
(1998) pp. 179–210.
18 The results in this example are obtained using the graphical interface of POTTO–GDC thus, no
input explanation is given. In the past the input file was given but the graphical interface it is no longer
needed.