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…

Supersonic Flow Over Flat Plates at Angle of Attack

Review: Oblique Shock Wave Angle

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

• Compare to Flat Plate CD = 0

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 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 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 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

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

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

Supersonic Airfoils : Negative Angle of Attack

• 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.

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

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

Symmetric Double-wedge Airfoil … Drag Thickness ratio

• 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

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

Total drag Mach constant Increasing t/c

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

+ = • 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 + =

+ = 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 + =

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

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

Geometrical Description of Wing Sweep

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

• Equivalent Mach Number normal to leading edge

• Equivalent angle of attack normal to leading edge

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

• Equivalent 2-D Lift Coefficient

• Equivalent 2-D Drag Coefficient

• Solve for CL, CD, L/D

• Unswept Wing 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 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.