OVERVIEW What is M crit ? Sound Barrier Critical Pressure - - PowerPoint PPT Presentation

AE-705 Introduction to Flight Lecture-09 Capsule-05

OVERVIEW

 What is Mcrit ?  Sound Barrier  Critical Pressure Coefficient Derivation  How to find Mcrit ?  Drag Divergence Mach Number  Wave Drag  Swept Wings  Types of Swept Wings

AE-705 Introduction to Flight Lecture-09 Capsule-05

WHAT IS MCRIT ?

Why are you so critical ?

AE-705 Introduction to Flight Lecture-09 Capsule-05

Source: http://www.boldmethod.com/learn-to-fly/aerodynamics/wing-sweep/

AE-705 Introduction to Flight Lecture-09 Capsule-05

When M=1  Weak shock wave Actual Mcrit varies from wing to wing

Deflects air more

Has lower Mcrit

AE-705 Introduction to Flight Lecture-09 Capsule-05

SOUND BARRIER

Can be broken !!!

AE-705 Introduction to Flight Lecture-09 Capsule-05

Source: https://www.youtube.com/watch?v=ugPJYJ-BKkU

AE-705 Introduction to Flight Lecture-09 Capsule-05

At low V  M < ~ 0.3  Cp = constant For ~ 0.3 < M∞< ~ 0.7

𝐷𝑞 = 𝐷𝑞,0 1 − 𝑁∞

2

Prandtl-Glauert Rule

REVISITING PRESSURE COEFFICIENT

Compressibility effects 𝐷𝑞 = 𝐷𝑞,0

AE-705 Introduction to Flight Lecture-09 Capsule-05 Source: EdX course on Introduction to Aeronautical Engineering

Universal Curve

AE-705 Introduction to Flight Lecture-09 Capsule-05

CRITICAL PRESSURE COEFFICIENT DERIVATION

Let’s get to some Math!!

AE-705 Introduction to Flight Lecture-09 Capsule-05

We know that: 𝐷𝑞 = 𝑞 − 𝑞∞ 𝑟∞ 𝑞∞ 𝑟∞ 𝑞 𝑞∞ − 1 = 𝑟∞ = 1 2 𝜍∞𝑊

∞ 2

And 1 2 𝜍∞𝑁∞

2 𝑏∞ 2

= And 𝑏∞

2 = 𝛿 𝜍∞

𝑟∞

𝑟∞ = 1 2 𝑁∞

2 𝛿𝑞∞

(1) …..(2) 𝑡𝑗𝑜𝑑𝑓 𝑁∞ = 𝑊

∞

𝑏∞

AE-705 Introduction to Flight Lecture-09 Capsule-05

𝐷𝑞 = 2𝑞∞ 𝑁∞

2 𝛿𝑞∞

𝑞 𝑞∞ − 1 Substituting (2) in (1), we get 𝑞0 𝑞 = 1 + 𝛿 − 1 2 𝑁2

𝛿 𝛿−1

From the isentropic flow relations 𝑞0 𝑞∞ = 1 + 𝛿 − 1 2 𝑁∞

2 𝛿 𝛿−1

Thus

𝑞 𝑞∞ = 1 + 1 2 𝛿 − 1 𝑁∞

2

1 + 1 2 𝛿 − 1 𝑁2

𝛿 𝛿−1

…..(3)

AE-705 Introduction to Flight Lecture-09 Capsule-05

Substituting (3) in (1) 𝐷𝑞 = 2 𝛿𝑁∞

2

1 + 1 2 𝛿 − 1 𝑁∞

2

1 + 1 2 𝛿 − 1 𝑁2

𝛿 𝛿−1

− 1 From definition of Cp,crit putting M=1 Thus we get

𝐷𝑞,𝑑𝑠𝑗𝑢 = 2 𝛿𝑁∞

2

2 + 𝛿 − 1 𝑁∞

2

𝛿 + 1

𝛿 𝛿−1

− 1 M∞  Mcrit as M=1

AE-705 Introduction to Flight Lecture-09 Capsule-05

HOW TO FIND MCRIT?

Two methods waiting for you!!

AE-705 Introduction to Flight Lecture-09 Capsule-05

 Obtain a plot of

versus

 Obtain the value of

(usually given)

 Plot

from Prandtl-Glauert rule

GRAPHICAL SOLUTION

Mcrit

AE-705 Introduction to Flight Lecture-09 Capsule-05

 From Prandtl-Glauert rule

ANALYTICAL SOLUTION

𝐷𝑞 = 𝐷𝑞,0 1 − 𝑁∞

2

It is seen that as Cp,0 M∞

Cp min at max V

 Cp at sonic condition(M=1) is Cp,crit  Thus

𝐷𝑞,0 1 − 𝑁∞

2 =

2 𝛿𝑁∞

2

2 + 𝛿 − 1 𝑁∞

2

𝛿 + 1

𝛿 𝛿−1

− 1

M∞  Mcrit as M=1

AE-705 Introduction to Flight Lecture-09 Capsule-05

LOCATION OF MAX V POINT ON AIRFOIL Min pressure (max velocity)  X max x/c

NACA 0012

Max V  complete shape of airfoil

Not corresponding 0.3 0.11

Source: Anderson

AE-705 Introduction to Flight Lecture-09 Capsule-05

DRAG DIVERGENCE MACH NUMBER

What’s the difference??

AE-705 Introduction to Flight Lecture-09 Capsule-05

M  Drag rapidly  at times Cd (*10)

Source: http://slideplayer.com/slide/8760031/

AE-705 Introduction to Flight Lecture-09 Capsule-05

M  Drag rapidly  at times Cd (*10) Due to formation

• f shock wave

Flow separates Adverse dp/dx P & V

a c r

• s

s

Source: http://slideplayer.com/slide/8760031/

AE-705 Introduction to Flight Lecture-09 Capsule-05

WAVE DRAG

Drag = Wave Drag??

AE-705 Introduction to Flight Lecture-09 Capsule-05

 Component of drag @ Vtransonic/supersonic  Independent of μeffects  Seen as

Source: http://tousifahmed54.blogspot.in/2013/08/completed-projects-and-researches.html

WHAT IS IT ?

SW considerable energy  Drag

AE-705 Introduction to Flight Lecture-09 Capsule-05

WEDGE BODY @ Vsupersonic

Shock wave Pressure Distribution

P ,T ,ρ ,V , M

AE-705 Introduction to Flight Lecture-09 Capsule-05

Minimize wave  Thin profile/Sharp LE

FLAT PLATE @ Vsupersonic

Pressure Distribution

Region through which P

AE-705 Introduction to Flight Lecture-09 Capsule-05

 

FOR THIN AIRFOILS

𝐷l = 4𝛽 𝑁2∞ − 1 𝐷d,w = 4𝛽2 𝑁2∞ − 1

Note: 𝐷l and 𝐷d,w with M∞ L and D as q∞

Source: http://www.heartlandofamericaband.af.mil/photos/mediagallery.asp?galleryID=529&page=262

Lockheed 104 Starfighter

AE-705 Introduction to Flight Lecture-09 Capsule-05



• bjects @ M∞>1  weak disturbance



• bjects @ M∞>1  shock wave

 Solution:

• Wing sweep
• Thin wings
• Fuselage shape
• Anti-shock bodies
• Supercritical airfoils

TACKLING WAVE DRAG

Source: http://forum.flitetest.com/showthread.php?8139-KFM- Airfoils-and-Swept-Back-wings Source: http://empiresandallies.wikia.com/wiki/Gripen_Fighter Source: https://aviation.stackexchange.com/questions/21620/whats- the-reason-for-the-local-flap-extensions-at-the-shockbody-locations Source:https://www.flickr.com/photos/multiplyleadership/529963 7305

AE-705 Introduction to Flight Lecture-09 Capsule-05

 Airflow~0.8<M<1.2

• Depends on Tsurrounding



Drag  Fuel consumption

 Solution:

• Swept Wings
• Area Rule  Wasp waist

fuselage

Convair F-102A Delta Dagger

Source: https://www.thisdayinaviation.com/24-

• ctober-1953/

TRANSONIC FLIGHT

AE-705 Introduction to Flight Lecture-09 Capsule-05

SWEPT WINGS

AE-705 Introduction to Flight Lecture-09 Capsule-05

HISTORY

• Dr. Adolf Busemann

1901 - 1986 IDEA!! Swept wings

Vair,wing dominated by Vair,n and not Vair,∞ Shock waves formed at ↑ V!!

AE-705 Introduction to Flight Lecture-09 Capsule-05

WHAT IS IT ?

Sweep Angle Mind it!! Can be forward swept also Lateral Axis

AE-705 Introduction to Flight Lecture-09 Capsule-05

WHY SWEPT WINGS ?

AE-705 Introduction to Flight Lecture-09 Capsule-05

Drag divergence delayed to M

AE-705 Introduction to Flight Lecture-09 Capsule-05

Source: https://www.mentor.com/products/mechanical/engineering- edge/volume2/issue3/floefd-external-aero

In reality….complex 3D flow Although our 2D sweeping simplification 𝑁𝑑𝑠 𝑔𝑝𝑠 𝑏𝑗𝑠𝑔𝑝𝑗𝑚 cos 𝛻 Mcr for airfoil < Actual Mcr for swept wing <

AE-705 Introduction to Flight Lecture-09 Capsule-05

OBLIQUE WING

Weird isn’t it ??

Source: http://www.techeblog.com/index.php/tech-gadget/nasa-ad-1-

• blique-wing-aircraft-might-be-strangest-looking-ever-here-are-5-cool-facts

AD-1 NASA

AE-705 Introduction to Flight Lecture-09 Capsule-05

Introduction to Oblique Wing

AE-705 Introduction to Flight Lecture-09 Capsule-05

 Low structural mass  Centre of mass and lift not shifted  Low wave drag 

 Induced drag

BENEFITS OF OBLIQUE WING

AE-705 Introduction to Flight Lecture-09 Capsule-05

 Asymmetric stall  Hinge  Load of fuel tank!  Poor handling  trim and inertial coupling  Engine mounted on fuselage

PROBLEMS

Source: https://www.youtube.com/watch?v=UQJa_FKkYZA Source: https://www.youtube.com/watch?v=vTQwkKameLg

Source: https://www.privatefly.com/private-jets/medium-jet- hire/Learjet-45-45XR.html

Learjet 45

AE-705 Introduction to Flight Lecture-09 Capsule-05

FORWARD SWEPT WING

You gotta be kidding me!!

AE-705 Introduction to Flight Lecture-09 Capsule-05

 Location of main spar  More space  Air flows inwards 

X Tip stall

 Wingtip vortices  Improves maneuverability

WHY THIS IDEA ?

Aileron control remains!! Slats X

Source: http://blogs.bu.edu/biolocomotion/2011/10/18/ winglets-the-anti-vortex-device/

AE-705 Introduction to Flight Lecture-09 Capsule-05

 Yaw instability  Reverse Dutch Roll  Torsional Divergence  Unstable in stall

WHAT WAS THE PROBLEM ?

Video Courtesy: https://www.youtube.com/watch?v=kOBbAFzXrRg Source: http://ascelibrary.org/doi/full/10.1061/(ASCE)AS.1943- 5525.0000427

AE-705 Introduction to Flight Lecture-09 Capsule-05

VARIABLE SWEPT WINGS

What’s the point? Is it a fashion show ??

AE-705 Introduction to Flight Lecture-09 Capsule-05

General Dynamics F-111 Aardvark

AE-705 Introduction to Flight Lecture-09 Capsule-05

MiG 27M Bahadur

3 Wing Sweep Positions 16o

T/O, Land, Low speed Flight

45o

Combat, Transonic Flight

72o

High Speed Dash

AE-705 Introduction to Flight Lecture-09 Capsule-05

 Also called Swing Wing  Suitable for high speeds  Lowers drag  Improves lateral stability

Sees the airfoil thinner Experiences less V  less drag Delays shockwaves

AE-705 Introduction to Flight Lecture-09 Capsule-05

 Added weight (~ 4% extra)  Maintenance Issues  Higher radar cross-section  Tough balancing

WHY DID THEY DIE OUT ?

AE-705 Introduction to Flight Lecture-09 Capsule-05

NEXT CLASS ON FRIDAY8TH SEP

Types of Drag, and its reduction