1. Oblique Shocks : Less Irreversible Thermodynamic Devices
“The pessimist complains about the Shocks;
the optimist expects it to change;
the realist adjusts the flyers.”
P M V Subbarao
Professor
Mechanical Engineering Department
Means to Supply Controlled Air to Supersonic Flyers !!!

2. Hypersonic Flyers : Comprehensive Mechanism of Intake Air Control

3. Continuity Equation for Oblique Shock Wavewx ux Vx wy uy Vy x y
• For Steady Flow thru an Oblique Shock

4. Momentum Equation for Oblique Shock Wavewx ux Vx wy uy Vy x y
• For Steady Flow w/o Body Forces

5. Oblique Shock is a Barbed Wire Fence

6. Though Experiment : Tangential Component of Momentum( ) - r x u w A + y
= 0
• But from continuity w x = y r x u = y
Tangential velocity is Constant across an oblique Shock wave

7. Normal Component of Momentum Equation
Normal component is always subjected to normal shock!!!

8. h + u = V = u + w & Energy Equation Steady Adiabatic Flow
Write Velocity in terms of components V x 2 = u + w
& y
Tangential component of velocity is not responsible for energy conversion h x + u 2 = y
• thus …

9. Collected Oblique Shock Equations
• Continuity q
b-q b u x y w r x u = y
• Momentum w x = y p x + r u 2 = y
• Energy c p T x + u 2 = y

10. An oblique sock is a normal Shock to Normal Velocity Component
wx & Mtx
ux & Mnx
Vx & Mx
Vy & My
wy & Mty
uy & Mny
• Then by similarity we can write the solution
• Defining:
Mnx=Mxsin(b
Mtx=Mxcos(b M n y = 1 + g - ( ) 2 x æ è ç ö ø ÷

11. The Normal Component of Tamed Devil
All the scalar quantities change only due to change in normal velocity
• Similarity Solution r y x = g + 1 ( ) M n 2 - p y x = 1 + 2 g ( ) M n - T y x = 1 + 2 g ( ) M n - é ë ê ù û ú
Letting M n x = s i b ( )

12. ( ) ( ) r = g + 1 M s i n b - p T é ë ê ù û ú Then …..y = 1 + g - ( ) 2 x s i b æ è ç ö ø ÷
Then ….. r y x = g + 1 ( ) M s i n b 2 - p T é ë ê ù û ú
• Change in Properties across Oblique Shock wave ~ f(Mx, )

13. Total Mach Number Downstream of Oblique Shock
• Consider the geometry of down stream flow M 3 y Mn Mt
b-q M y = n s i b - q ( )

14. Determination of Oblique Shock Wave Angle
• Properties across Oblique Shock wave ~ f(Mx, )
• q is the geometric angle that “forces” the flow thru OS.
• How do we relateqto b 

15. Oblique Shock Wave Angle Chart
max
curve
Mx=5.0
Mx=3.0
Mx=1.5
Mx=4.0
Mx=2.5
Mx=2.0 Mx

16. Limiting Cases of Oblique Shock Wave
qmax

17. Maximum Turning Angle
qmax

18. Highest Angle Objects

19. Performance of An Adiabatic Oblique Shocky x = 1 + 2 g ( ) M n - T y x = 1 + 2 g ( ) M n - é ë ê ù û ú
But
Pressure Recovery Factor or Total Pressure Ratio for the oblique shock :

20. Performance of An Adiabatic Oblique Shock
Across a Shock
Therefore
Pressure Recovery Factor or Total Pressure Ratio for the oblique shock :

21. Special Designs of Center Bodies
If there are multiple shocks: Mx
My1
My2
My3 q