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Oblique Shock Waves
Here’s a quick refresher on oblique shock waves. We start with the oblique shock
as shown below:
(1)
(2)
Also, the specific flow quantities above are:
v
: flowspeed
M
: Mach number =
a
v
u
: normal velocity to shock
n
M
: Normal Mach
a
u
=
#
w
: tangential velocity to shock
t
M
: Tangential Mach
a
w
=
#
The next step is to apply the 2D Euler equations to derive jump conditions.
Let’s consider the following (wellchosen) control volume across the shock:
Where:
d
a
&
are parallel to shock
e
c
f
b
,
,
,
are parallel to local flow
Apply conservation of mass:
∫
=
•
s
ds
n
V
0
v
v
ρ
But
0
=
•
n
V
v
v
on
,
&
,
,
e
c
f
b
thus:
∫∫
=
•
+
•
−
=
•
+
•
ad
s
s
ds
n
V
ds
n
V
ds
n
V
ds
n
V
0
0
2
2
1
1
v
v
v
v
v
v
v
v
1
u
2
u
y
x
1
1
,
t
M
w
1
1
,
M
v
1
1
,
n
M
u
β
θ
2
2
,
M
v
2
2
,
n
M
u
2
2
,
t
M
w
( )
1
: upstream flow
condition
( )
2
: downstream flow
condition
: angle of shock wave
.
.
.
t
r
w
upstream flow
: deflection angle of flow
b
c
a
f
e
d
g
a
n
n
v
v
−
=
1
v
2
v
s
d
n
n
v
v
+
=
s
n
v
Control volume
s
s
t
v
Shock wave
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View Full Document Oblique Shock Waves
16.100
2002
2
0
2
2
1
1
=
+
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This note was uploaded on 11/06/2011 for the course AERO 100 taught by Professor Willcox during the Fall '03 term at MIT.
 Fall '03
 willcox
 Dynamics, Aerodynamics

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