MA6621 Aerodynamics -Introductionby

Daniel T.H. NewAssistant ProfessorDivision of Aerospace EngineeringSchool of Mechanical and Aerospace Engineering

Recommended textbooks

Aerodynamics for Engineers4th Edition – John Bertin

5th Edition – John Bertin &Russell Cummings

Pearson Higher Education

Fundamentals of Aerodynamics4th and 5th Editions

John AndersonMcGraw-Hill

Lecture slides versus textbooks• Lecture slides are meant to be brief and straight to the important points

• You need to read through the associated details inside the textbook

• Just bring along the textbook and you have everything at your finger tips (wherever you are!)

• You can buy the textbooks at

– NTU campus bookstore

– Online bookstores (may be cheaper)

• Better yet, you can borrow from the library or your seniors

What is Aerodynamics?• Simple question which means a great deal and different things to practicing

and research engineers

• Aerodynamics is the study of forces and the resulting motion of objects through air

– Flying aircrafts

– Flapping of flags on poles

– Smoke dispersion from chimneys

– Speeding cars, and many more

• In this module, we will focus primarily on aerodynamics for use in the aerospace engineering industry

– Actual design and implementations

– Research and development efforts

Aerodynamics = fluid dynamics?• Pretty much but while fluid dynamics encompass all fluids, aerodynamics

focus more on air flows

• Other more specific differences:

– Aerodynamics focus on the forces acting on bodies (i.e. lift and drag forces)

– Aerodynamics typically applied to external flows (i.e. aircrafts, cars)

– Aerodynamics provide parameters for flight dynamics and control

– Aerodynamics usually deal with fast moving air flows

• However, much of the governing concepts between aerodynamics and fluid dynamics are similar

A brief history of aerodynamics

Brief history of aviation

*Franck Cabrol *U.S. Air Force

*Romanian Air Force *Garfield F. Jones, U.S. Air Force *Russian Air Force

*Master SGT Andy Dunaway, USAF *Rob Shenk *NASA

*USAF Museum

*German Federal Archive

Aerodynamic forces

Thrust from engine Drag from air

friction and separation

Lift from wings

Weight from body, engine & payload

• Thrust – propulsion

• Lift and drag – aerodynamics

• Weight – materials and structures

• Coordinating & balancing all four – flight mechanics & control

Brief revision• Commonly encountered variables and associated units

Phenomena Common Symbol

Unit type* SI Unit Imperial Unit

Density M/L3 kg/m3 lbm/ft3

Pressure p M/LT2 Pa (N/m2) psi (lbf/in2)

Force F ML/T2 N (kg m/s2) lbf

Temperature T K F

Velocity u,v,w L/T m/s ft/s

Viscosity, dynamic M/LT Pa s lbm s/ ft2

Viscosity, kinematic L2/T m2/s ft2/s

Volume V L3 m3 in3

* The symbols M, L, T and denote mass, length, time, and temperature resp.

Aircraft components

• Typically, the fuselage is the main aircraft component, followed by

• Wings (the most important component governing aerodynamics)

• Engine nacelles

• Stabilizers

• Flight control devices – flaps, ailerons, elevators, rudder, canards (not shown here)

*Bertin J. J. “Aerodynamics for Engineers”

Brief revision

Streamlines: Lines tangent to the local flow direction

Streaklines: Line of all particles passing through one point

Pathlines:Line showing the path of a single particle

*Streamlines, streaklines and pathlines are identical for steady state flows

Brief revision• Bernoulli equation states that

• In flow situations where the change in elevation/height is small along a streamline, the third term can be neglected

• For instance, for a streamline along flow past an aerofoil:

constant2

1 2 gzUp

smallgz

constant2

1 2 Up

Brief revision• Aerodynamics involve air flows and hence, we need to understand the

basics of Fluid Mechanics, which govern all fluid flows (i.e. air, water etc)

• Fluid mechanics, in turn, are governed by physical laws

– Conservation of mass

– Conservation of momentum

– Conservation of energy

• Distinctions must also be made between

– Steady and unsteady flows (i.e. flow variables varying w.r.t. time)

– Incompressible and compressible flows (i.e. density variations)

– One, two or three-dimensional flows (i.e. flow changes w.r.t. directions)

– Rotational or irrotational flows (i.e. angular deformation of fluids)

Conservation of mass• Consider a flow through a expansion:

Inlet velocity, u1 Outlet velocity, u2

Inlet area, A1 Outlet area, A2

• Conservation of mass (i.e. continuity equation) essentially states that fluid mass entering the inlet must equal to the fluid mass exiting the outlet

• Mathematically, we can write for an incompressible flow:

222111 AuAu

1

2

12 u

A

Au Since 1 = 2 for incompressible flow:

Inlet density, 1 Outlet density, 2

Mass flux (typically kg/s)

*Anderson J. D. “Fundamental of Aerodynamics”

Conservation of mass• To consider the conservation of mass in more non-simplistic terms:

• Consider a small control element of size x by y through which fluid flows, with flow velocities into and out of the element as shown in the figure above. Assuming a 2D, incompressible flow,

0

y

v

x

u

Volume flow rate into control volume = volume flow rate out of control volume

xyy

vvyx

x

uuxvyu

Conservation of mass• On the other hand, for a compressible flow where density varies:

1 ≠ 2

1

2

1

2

12 u

A

Au

Inlet velocity, u1 Outlet velocity, u2

Inlet area, A1 Outlet area, A2

Inlet density, 1 Outlet density, 2

*Anderson J. D. “Fundamental of Aerodynamics”

Conservation of energy• For fluid flows, one of the simplest equations encapsulating the concept of

energy conservation can be found in the Bernoulli equation

• Consider fluid flow through a contraction:

constant2

1 2 uP

1 2

• Bernoulli equation states that along a streamline:

222

211

2

1

2

1uPuP

• No flow losses

• Inviscid fluids

• Incompressible

• No gravity effects

• Since u2 > u1 from mass conservation consideration:

12 PP

Boundary layers• Boundary layers are formed adjacent to surfaces/solid boundaries due to

fluid viscosity

• Due to “no-slip” condition, fluid velocity is zero at the wall but increases gradually to the free-stream velocity as the distance from the surface increases

• The state and characteristics of the boundary layer determine the subsequent behaviour of the wakes and flow separation

Boundary layers• Laminar boundary layers

– More prone to flow separation

– Lower wall shear stress

• Turbulent boundary layers

– More resilient towards flow separation

– Higher wall shear stress

*Y. Nakayama, Tokai University

Turbulent flows• Fluid flows can be classified into laminar or turbulent flows

• Laminar flows

– Stable

– Well-understood theoretically and analytically

– Can sometimes be treated as 2D flow behaviour

• Turbulent flows

– Chaotic

– Flow variables (i.e. velocity, pressure) fluctuate about some mean values

– 3D flow behaviour

(a) Laminar flow (b) Transitional flow (c) Turbulent flow

Reynolds number• To determine whether the flow is laminar or turbulent, one uses the

Reynolds number

• Reynolds number – ratio of inertial forces to viscous forces

• For pipe flows, laminar flow if Re < 2300

• For flat plates, laminar flow is Re < 2.5 x 106

ULULRe

: Dynamic viscosity

: Kinematic viscosity

L : Characteristic length

Generation of lift

• Large surface area of an aircraft wing is important towards producing sufficient lift for flight

• But the shape of the wing cross-section is the basis upon which lift is produced in the first place

• To understand lift, one must first appreciate how lift is generated by wing cross-sections

*EADS Airbus

Aerofoil terminology

• Chord line – straight line joining the leading and trailing edges

• Mean camber line – locus of points midway between the upper and lower aerofoil surfaces

• Thickness – distance between the upper and lower surfaces

• Note that the maximum thickness and thickness distribution affect the shape of the aerofoil, other than the camber

• The aerofoil shape should aim to produce as low a pressure as possible along the upper surface, relative to that along the lower surface

*Bertin J. J. “Aerodynamics for Engineers”

Angle of attack (AOA)

• Angle of attack is the angle between the aerofoil chord line and the free stream direction

• Lift and drag directions are perpendicular and parallel to the freestreamdirection

• The resultant force acting on the aerofoil will be the vector summation of the force and drag forces

*Bertin J. J. “Aerodynamics for Engineers”

How is lift generated by aerofoils?• Theory A – higher flow velocity and hence lower pressure along upper

surface

20

2

1upp s

Bernoulli equation:

• Consider the path of the fluid flow along the upper surface of the aerofoil:

– Larger distance along the aerofoil upper surface

– Lower pressure

• Along the lower surface of the aerofoil:

– Shorter distance along the aerofoil lower surface

– Higher pressure

• Net upwards-acting pressure lift!

How is lift generated by aerofoils?

*Bertin J. J. “Aerodynamics for Engineers”

• Theory B – Newton Theory, whereby lift is the reaction to the downward flow of the deflected airflow, and acts upwards as a result

• Action equal and opposite reaction

How is lift generated by aerofoils?• Theory C – Bernoulli Theory, where the displacement of the wing quenches

the streamtube on the upper surface and accelerates the flow

• This creates lower pressure along the upper aerofoil surface

*Bertin J. J. “Aerodynamics for Engineers”

Aerofoil stall

(a) AOA=2 (b) AOA=5 (c) AOA=10

(d) AOA= just below 15 (e) AOA= just above 15

• As the AOA increases, both lift and drag increase until some critical AOA

• Beyond the critical AOA, flow separation occurs when the flow cannot follow (i.e. remain attached to) the aerofoil surface

Air flow

Mild flow separation

Significant flow separation

*H. Ito, Meiji University

Pressure, lift and drag coefficients• Pressure, lift and drag coefficients are dimensionless values (i.e. no units)

which are used to characterize flight performances of aerofoils/wings

• These values are only dependent upon the configuration geometry and angle of attack

• This is very useful when testing models in laboratories to predict lift and drag performance of actual large-scale aerofoils, wings or aircrafts

• Before any of these coefficients can be determined, the pressure distribution around the object must first be measured or computed

Pressure coefficient

2

2

1

U

ppCp

• Pressure coefficient can be determined for every point where pressure is known by using

• For aerofoils, the pressure coefficient is plotted w.r.t. to the non-dimensionalized chord length as shown in the figure below:

Lift coefficient

2

2

1

UA

FC L

L

• On the other hand, lift coefficient can be calculated using

• Note that “A” is the wing area

• The lift coefficient can also be determined from the area enclosed by the pressure coefficient distribution graph. For example:

Drag coefficient

2

2

1

UA

FC D

D

• Lastly, drag coefficient is defined as

• Note the similar non-dimensionalizing

terms used in lift and drag coefficients

• Non-dimensionalized terms are used in

fluid mechanics and aerodynamics due

to similarity considerations

• Reynolds number, Mach number etc

Lift-to-drag ratio• To make engineering evaluations of aircraft even simpler, lift-to-drag ratios

are often used

• Lift-to-drag ratio is a measure of the efficiency of an aircraft and defined as:

• Clearly, achieving high L/D ratios are desirable for any aircraft designers

D

L

D

L

F

F

C

CDL /

L/D7

Cessna 150

L/D15

Douglas DC-3 Airbus A318

L/D17

*Adrian Pingstone *Flygande Veteranerna *Adrian Pingstone

Lift-to-drag ratioL/D17

L/D37

L/D60

L/D19

Boeing 747 Virgin Atlantic GlobalFlyer

Sailplane ASH-25

Boeing 767

L/D9

Lockheed F104 Starfighter

*Adrian Pingstone *Adrian Pingstone

*Alexander Schleicher GmbH & Co. *Marshall S.L.A.

*Alexander Schleicher GmbH & Co.

Lift curves

• Lift coefficients are usually determined for various angles of attack and plotted as shown above

• The graph allows intuitive and easy appreciation of the aerofoil/wing performance

• Note that the lift curve does not intersect the origin (i.e. lift coefficient not zero at zero angle of attack)

*Anderson J. D. “Fundamental of Aerodynamics”

Wings with finite span

• Aerofoils cannot be infinitely long

• Lengths of real wings directly affect the lift and drag characteristics

• Longer wings usually produce both higher lift and drag

• Finite wings are characterized by their aspect ratio:

• For rectangular wingsA

bAR

2

l

bAR

2

*Anderson J. D. “Fundamental of Aerodynamics”

Aerodynamics investigations• Experimental

– Testing and measurements in wind or water tunnels

– Hot-wire anemometry (HWA)

– Laser Doppler anemometry (LDA)

– Particle image velocimetry (PIV)

– Pressure probes

– Flow visualization

• Computational

– Numerical simulations of governing equations, subjected to flow and boundary conditions

– Direct numerical simulations (DNS)

– Large eddy simulations (LES)

– Detached eddy simulations (DES)

– Reynolds-averaged Navier-Stokes (RANS)