Page 253 - 48Fundamentals of Compressible Fluid Mechanics

13.4. SOLUTION OF MACH ANGLE 215
13
the shock angle will jump to the third root . These two angles of the strong and
weak shock are stable for two-dimensional wedge (See for the appendix of this
14
Chapter for a limit discussion on the stability ).

13.4.2 In What Situations No Oblique Shock Exist or When

13.4.2.1

The first range is when the deflection an-
Large deflection angle for given,
gle reaches above the maximum point. For
given upstream Mach number, , a change
in the inclination angle requires a larger en-
ergy to change the flow direction. Once, the
inclination angle reaches “maximum potential

energy” to change the flow direction and no
change of flow direction is possible. Alter-
native view, the fluid “sees” the disturbance
Fig. 13.4: Flow around spherically
(here, in this case, the wedge) in–front of it.
cone-cylinder
Only the fluid away the object “sees” the ob-
with Mach number 2.0.
ject as object with a different inclination angle.
It can be noticed that a
blunted
This different inclination angle sometimes re- normal shock, strong shock,
ferred to as imaginary angle. and weak shock co-exist.
13.4.2.1.1 The simple procedure For ex-
ample, in Figure 13.4 and 13.5, the imaginary angle is shown. The flow far away
the maxi-
. This can be done by
from the object does not “see’ the object. For example, for E
. c .
mum defection angle is calculated when

for
"

evaluating the terms, ,, , and,
.
, E E

With these values the coefficients,
c
are
and

,
,
.

+

"

c
"

< E E
"
E
13 See for historical discussion on the stability. There are those who view this question not as a
c :
9

stability equation but rather as under what conditions a strong or a weak shock will prevail.

14 This material is extra and not recommended for standard undergraduate students.