Supersonic Wings. P M V Subbarao Professor Mechanical Engineering Department I I T Delhi. An appropriate combination of Shocks & Expansion Waves…. Supersonic Flow Over Flat Plates at Angle of Attack. Review: Oblique Shock Wave Angle. PrandtlMeyer Expansion Waves.
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P M V Subbarao
Professor
Mechanical Engineering Department
I I T Delhi
An appropriate combination of Shocks & Expansion Waves…
q<0 .. We get an expansion wave (PrandtlMeyer)
CD = 0
• Subsonic Wing in Subsonic Flow
• Subsonic Wing in Supersonic Flow
• Supersonic Wing in Subsonic Flow
• Supersonic Wing in Supersonic Flow
• Wings that work well subsonically generally Don’t work well supersonically, and viceversa
• A leading edge in Supersonic Flow has a finite maximum wedge angle at which the oblique shock wave remains attached
Supersonic Airfoilsg=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
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
• 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
Dull Oblique Shock
2
4
1
6
3
5
Intense Oblique Shock
g=1.1
g=1.3
• We already have all of the tools we need to analyze the flow on this wing
g=1.1
g=1.3
• wedge angle at which the oblique shock wave remains attached 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.
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• Symmetrical Diamondwedge airfoil, zero angle of attack
Þ
p2 > p1
• 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
Thickness ratio
Increasing mach wedge angle at which the oblique shock wave remains attached
• Look at mach number
Effect on wave drag
• Mach Number tends
to suppress wave drag
Thickness ratio
• How About The wedge angle at which the oblique shock wave remains attached
effect of angle of
attack on drag
Induced drag
Wave drag
+
a=0
=
Total drag wedge angle at which the oblique shock wave remains attached
Mach constant
Increasing t/c
+
Lift Coefficient Climbs Almost Linearly with a
=
• For Inviscid flow wedge angle at which the oblique shock wave remains attached
Supersonic
Lift to drag ratio
almost infinite
for very thin
airfoil
t/c = 0.035
• But airfoils do not
fly in inviscid flows
+
=
t/c = 0.035 wedge angle at which the oblique shock wave remains attached
• Friction effects
have small effect
on Nozzle flow
or flow in “large
“ducts”
• But contribute
significantly
to reduce the
performance of
supersonic 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
• 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
• 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
• Equivalent Mach Number normal to leading edge wedge angle at which the oblique shock wave remains attached
• Equivalent angle of attack normal to leading edge wedge angle at which the oblique shock wave remains attached
• Equivalent chord and span wedge angle at which the oblique shock wave remains attached
• Chord is shortened
• Span is lengthened
• Equivalent 2D Lift Coefficient wedge angle at which the oblique shock wave remains attached
• Equivalent 2D wedge angle at which the oblique shock wave remains attached
Drag Coefficient
• Solve for C wedge angle at which the oblique shock wave remains attached L, CD, L/D
• Unswept Wing wedge angle at which the oblique shock wave remains attached
CL: 0.205
CD: 0.3606
L/D: 5.68441
• 30 Swept Wing
CL: 0.2533
CD: 0.03909
L/D: 6.4799
• WOW! … 14% IMPROVEMENT IN PERFORMANCE
The F14'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.