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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. Prandtl-Meyer Expansion Waves.

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Supersonic wings

Supersonic Wings

P M V Subbarao

Professor

Mechanical Engineering Department

I I T Delhi

An appropriate combination of Shocks & Expansion Waves…




Prandtl meyer expansion waves
Prandtl-Meyer Expansion Waves

q<0 .. We get an expansion wave (Prandtl-Meyer)



Wings at zero angle of attack
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


Supersonic airfoils

• A leading edge in Supersonic Flow has a finite maximum wedge angle at which the oblique shock wave remains attached

Supersonic Airfoils

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


Supersonic flow over an airfoil
Supersonic Flow Over an Airfoil wedge angle at which the oblique shock wave remains attached

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


Supersonic airfoils1
Supersonic Airfoils wedge angle at which the oblique shock wave remains attached

• 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


Supersonic airfoils positive angle of attack
Supersonic Airfoils : Positive Angle of Attack wedge angle at which the oblique shock wave remains attached

Dull Oblique Shock

2

4

1

6

3

5

Intense Oblique Shock


Supersonic airfoils positive angle of attack1
Supersonic Airfoils : Positive Angle of Attack wedge angle at which the oblique shock wave remains attached

  • • 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


Supersonic airfoils negative angle of attack
Supersonic Airfoils : Negative Angle of Attack wedge angle at which the oblique shock wave remains attached

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.


Supersonic flow on finite thickness wings at zero a
Supersonic Flow on Finite Thickness Wings at zero wedge angle at which the oblique shock wave remains attached a

]

/

t

2

[

=

e

-

e

e

=

2

s

i

n

(

)

s

i

n

(

)

s

i

n

(

)

D

b

p

l

p

l

2

3

r

a

g

l

[

]

=

-

D

b

p

p

t

2

3

r

a

g

• Symmetrical Diamond-wedge airfoil, zero angle of attack

Þ

p2 > p1


Supersonic wave drag
Supersonic Wave Drag wedge angle at which the oblique shock wave remains attached

• 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


Symmetric double wedge airfoil drag
Symmetric Double-wedge Airfoil … Drag wedge angle at which the oblique shock wave remains attached

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


The effect of angle of attack on lift
The effect of angle of attack on Lift wedge angle at which the oblique shock wave remains attached

+

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

+

=


Disadvantages of sharp edged wings
Disadvantages of Sharp Edged Wings wedge angle at which the oblique shock wave remains attached

• 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


Wing sweep reduces wave drag
Wing Sweep Reduces Wave Drag wedge angle at which the oblique shock wave remains attached

• 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


Geometrical description of wing sweep
Geometrical Description of Wing Sweep wedge angle at which the oblique shock wave remains attached


Equivalent 2 d flow on swept wing
Equivalent 2-D Flow on Swept Wing wedge angle at which the oblique shock wave remains attached

• 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 2-D Lift Coefficient wedge angle at which the oblique shock wave remains attached


• Equivalent 2-D 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


F 14 tomcat
F-14 Tomcat wedge angle at which the oblique shock wave remains attached

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.


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