1. Dr Kamarul Arifin B. Ahmad PPK Aeroangkasa
Gas Dynamics ESA 341 Bab 4
Dr Kamarul Arifin B. Ahmad
PPK Aeroangkasa

2. Oblique shock wave Introduction Control volume and symbols
Equation of motion
Relation between mach number(M) and deflection and shock wave angles ( and )
Ratio of flow properties
Mach number relations
Relation of  and 

3. Introduction Definition
A compression shock wave occurs that is inclined at an angle of the flow
Still represent a sudden, almost discontinuous change in fluid properties
We will be focused on the 2D straight oblique shock wave.
A concave corner
A symmetrical wedge

4. Control volume and symbols
Vt1
Vn1
Vt2
Vn2 V1  y x 1 
Upstream flow angle V2
Downstream flow angle   2 P2 P1 T2 T1 2 1 y x

5. Equations of motion Continuity equation Momentum Equation
Energy equation

6. Relation between mach number(M) and deflection and shock wave angles ( and )
Vn1
Vt1
 -   V1
Vn2 y

7. Ratio of flow propertiesy x 1 
Upstream flow angle

8. Mach number relations
Replacing M1sin for M1 and M2sin (-) for M2

9. Relation of  and  when: Mach Wave Vn1 Vt1  -   V1 Vn2 y Normal
shock
Mach
wave
Mach Wave

11. Physical phenomena associated with the oblique shock wave
1. For any given upstream Mach number M1, there is a maximum deflection angle, max. If the the physical geometry is such that > max, then the shock will be detached.

12. Physical phenomena associated with the oblique shock wave
2)For any given < max, there will be two straight oblique solutions for a given upstream Mach number. For example, for M1=2.0 and =150, then from the graph,  can be equal either 45.3 or The smaller  is called the weak shock solution, and the larger is called the strong shock solution. 
Strong shock
Weak shock

13. Physical phenomena associated with the oblique shock wave
This may sometimes be more conveniently plotted as:

14. Physical phenomena associated with the oblique shock wave
3) For attached shocks with a fixed deflection angle, as the upstream Mach number M1 increases, the wave angle  decreases, and the shock wave becomes stronger. Or, when M1 decreases, the wave angle increases, and the shock becomes weaker.
=200
=53.30
M1=2.0
Mn1=1.60
P2/P1=2.82
=200
=29.90
M1=5.0
Mn1=2.49
P2/P1=7.07

15. Physical phenomena associated with the oblique shock wave
4)For attached shocks with fixed upstream Mach number, as the deflection angle increases, the wave angle  increases, and the shock becomes stronger. However, when > max, the shock wave will be detached.
=530
M1=2.0
Mn1=1.6
P2/P1=2.8
=100
=39.20
M1=2.0
Mn1=1.26
P2/P1=1.69
=200

16. Oblique-shock reflections

17. Oblique-shock reflections cont.
For a given M1 and d1, find 1.
Find M2 and P2/P1.
Since d2 = d1, use M2 to find 2.
Find M3 and P3/P2.
Finally: 1 2
1-  1

18. Oblique-shock Application

19. Application
Oblique shocks desirable on supersonic intakes to reduce total pressure losses.

20. Group Exercises 5
1) Consider a supersonic flow with a Mach number M = 2, with a static pressure p = 105 Pa, and a static temperature T = 288K. The flow is deflected at a compression corner through 20o. Calculate the Mach number, the static pressure, the temperature, the stagnation pressure and the stagnation temperature behind the resulting oblique shock wave.
2) Consider a supersonic flow with M = 2, p = 1 atm, and T = 288K. The flow is deflected at a compression corner through 20o. Calculate M, p, T, po and To behind the resulting oblique shock wave.