1. P M V Subbarao Professor Mechanical Engineering Department I I T Delhi
Supersonic Wings
P M V Subbarao
Professor
Mechanical Engineering Department
I I T Delhi
An appropriate combination of Shocks & Expansion Waves…

2. Supersonic Flow Over Flat Plates at Angle of Attack

3. Review: Oblique Shock Wave Angle

4. Prandtl-Meyer Expansion Waves
q< We get an expansion wave (Prandtl-Meyer)

5. • Compare to Flat Plate
CD = 0

6. Wings At Zero Angle of Attack
• Subsonic Wing in Subsonic Flow
• Subsonic Wing in Supersonic Flow
• Supersonic Wing in Subsonic Flow
• Supersonic Wing in Supersonic Flow
• Wings that work well sub-sonically generally Don’t work well supersonically, and vice-versa

7. Supersonic Airfoils
• A leading edge in Supersonic Flow has a finite maximum wedge angle at which the oblique shock wave remains attached
g=1.1
g=1.1
g=1.05
g=1.2
g=1.3
g=1.3
g=1.4
g=1.4
• Beyond that angle shock wave becomes detached from leading edge

8. Supersonic Flow Over an Airfoil
g=1.1
Detached shock wave
g=1.3
Localized normal shock wave
• Normal Shock wave formed off the front of a blunt leading
causes significant drag

9. Supersonic Airfoils • Double wedge or “diamond” Airfoil section
• To eliminate this leading edge drag caused by detached bow wave Supersonic wings are typically quite sharp at the leading edge
• Design feature allows oblique wave to attach to the leading edge eliminating the area of high pressure ahead of the wing.
g=1.1
g=1.3
• Double wedge or “diamond” Airfoil section

10. Supersonic Airfoils : Positive Angle of Attack
Dull Oblique Shock 2 4 1 6 3 5
Intense Oblique Shock

11. Supersonic Airfoils : Positive Angle of Attack
• A supersonic airfoil at positive angle of attack :
A dull shock at the top leading edge.
An intense shock at the bottom.
• The airflow over the top of the wing is now faster.
• Further acceleration through the expansion fans.
• The Expansion fan on the top is more intense than the one on the bottom.
• Combined result is faster flow and lower pressure on the top of the airfoil.
g=1.1
g=1.3
• We already have all of the tools we need to analyze the flow on this wing

12. Supersonic Airfoils : Negative Angle of Attack

13. • Result is the airflow over the top of the wing is now faster.
•When supersonic airfoil is at negative angle of attack at the top leading edge there is a expansion fan and oblique shock at the bottom.
• Result is the airflow over the top of the wing is now faster.
• Airflow will also be accelerated through the expansion fans on both sides.
• Result is much faster flow on top surface and therefore lower pressure on the top of the airfoil.

14. Supersonic Flow on Finite Thickness Wings at zero a
• Symmetrical Diamond-wedge airfoil, zero angle of attack s i n ( e ) = t / 2 l D r a g = 2 b p l s i n ( e ) - 3 [ ] Þ
p2 > p1 D r a g = b p 2 - 3 [ ] t

15. Supersonic Wave Drag
• Finite Wings in Supersonic Flow have drag .. Even
at zero angle of attack and no lift and no viscosity…. “wave drag”
• Wave Drag coefficient is proportional to thickness ratio (t/c)
• Supersonic flow over wings
… induced drag (drag due to lift) + viscous drag + wave drag

16. Symmetric Double-wedge Airfoil … Drag
Thickness ratio

17. • Look at mach number Effect on wave drag • Mach Number tends
Increasing mach
• Look at mach number
Effect on wave drag
• Mach Number tends
to suppress wave drag
Thickness ratio

18. + = • How About The effect of angle of attack on drag Induced drag
Wave drag +
a=0 =

19. Total drag
Mach constant
Increasing t/c

20. The effect of angle of attack on Lift+
Lift Coefficient Climbs Almost Linearly with a =

21. + = • For Inviscid flow Supersonic Lift to drag ratio almost infinite
for very thin
airfoil
t/c = 0.035
• But airfoils do not
fly in inviscid flows + =

22. + = t/c = 0.035 • Friction effects have small effect on Nozzle flow
or flow in “large
“ducts”
• But contribute
significantly
to reduce the
performance of
supersonic wings + =

23. Disadvantages of Sharp Edged Wings
• Problem with sharp leading edges is poor performance in
subsonic flight.
• Lead to very high stall speeds, poor subsonic handling
qualities, and poor take off and landing performance for
conventional aircraft

24. Wing Sweep Reduces Wave Drag
• One way to augment the performance of supersonic
aircraft is with wing sweep …
• Lowers the speed of flow
Normal to the wing …
• Decreasing the strength
Of the oblique shock wave
• Result is a Decrease in wave
Drag and enhanced L/D

25. Geometrical Description of Wing Sweep

26. Equivalent 2-D Flow on Swept Wing
• Freestream Mach number resolved into 3 components
i) vertical to wing …
ii) in plane of wing, but tangent to leading edge
iii) in plane of wing, but normal to leading edge

28. • Equivalent Mach Number normal to leading edge

29. • Equivalent angle of attack normal to leading edge

30. • Equivalent chord and span
• Chord is shortened
• Span is lengthened

31. • Equivalent 2-D Lift Coefficient

32. • Equivalent 2-D
Drag Coefficient

33. • Solve for CL, CD, L/D

34. • Unswept Wing
CL: 0.205
CD:
L/D:
• 30 Swept Wing
CL:
CD:
L/D:
• WOW! … 14% IMPROVEMENT IN PERFORMANCE

35. F-14 Tomcat
The F-14's wing sweep can be varied between 20 and 68° in flight, and is automatically controlled by an air data computer.
This maintains the wing sweep to give the optimum lift/drag ratio as the Mach number varies.
The system can be manually overridden by the pilot if necessary.
When the aircraft is parked, the wings can be swept to 75°, where they overlap the tail to save space on tight carrier decks.