AerodynamicsME-438

Spring’16ME@DSU

Dr. Bilal A. Siddiqui

Course Outline• Introduction to aerodynamics• aerodynamics of incompressible flow• Compressible• ideal fluid flow• airfoils theory• finite wing aerodynamics• blade element theory and aircraft propellers• Cascade aerodynamics• jet propulsion• intake and nozzle performance• aircraft performance measurement.

Course Objectives• To understand the concepts in incompressible airfoil theory, including

• symmetric and cambered airfoils using • analytical and numerical approaches.

• To understand the incompressible wing theory including • down wash• lifting-line theory• elliptic wings• general twisted wings

• Application of fundamentals to the design of a wing to meet given performance criteria.• Recommended Books

• Fundamentals of Aerodynamics by John D. Anderson• Aerodynamics by L.J. Clancy [Available in library]

So what is Aerodynamics?• Aerodynamics is the study of

motion of air.• It is a sub branch of Fluid

Mechanics and Gas Dynamics• However, there is a significant

overlap between all these fields

• Formal study of aerodynamics began 300 years ago, so it is a relatively young science!

Fluid Mechanics

Hydrodynamics Gas Dynamics

Aerodynamics

External Aerodynamics

Internal Aerodynamics

Difference between Aerodynamics and CFD• Think of mechanics of materials. It is a science which predicts

relationships between forces, stresses and deflections.• FEA is the numerical solution of mechanics of materials. It is a TOOL.• Machine Design is the application of mechanics of materials. It is the

PRODUCT.

• Similarly, aerodynamics is applied fluid mechanics.• CFD is just a tool to find numerical solutions to analytically difficult

fluid mechanical problems.• Aerodynamics is the key driver behind external design of many

vehicles in the air and on land….and surface boats.

What do we do in Aerodynamics?• Aerodynamics is an applied science and practical engineering for:

• Prediction of forces / moments on, and heat transfer to aerodynamic bodies • For example, generation of lift, drag, and moments on airfoils, wings, fuselages, engine

nacelles, and whole vehicle configurations. • Estimation of wind force on buildings, ships, and other surface vehicles.• Hydrodynamic forces on surface ships, submarines, and torpedoes.• Aerodynamic heating of flight vehicles

• Determination of flows moving internally through ducts. • Flow properties inside rocket and jet engines and to calculate the engine thrust. • Flow conditions in the test section of a wind tunnel. • Fluid flow through pipes under various conditions. • Gas dynamic lasers are little different than high speed wind tunnels.

Internal Aerodynamics

External Aerodynamics

What to expect in first four weeksIntroductory Concepts Flow Quantities

Sources of Aerodynamic Forces/Moments

Lift/Drag/Moment Coefficients

Center of Pressure Types of Flow

Boundary layers

Historical Context – Motivating Examples• In 1799, Sir George Cayley became the first person to identify the four

aerodynamic forces of flight • In 1871, Francis Herbert Wenham constructed the first wind tunnel, allowing

precise measurements of aerodynamic forces. • In 1889, Charles Renard became the first person to predict the power needed

for sustained flight.• Otto Lilienthal was the first to propose thin, curved airfoils that would

produce high lift and low drag. • However, interestingly the Wright brothers, mechanics – not engineers- found

most of the initial work flawed and did something else….a hundred years after Cayley.

27th of Ramadhan….a Friday• On Dec 15, 1903 (corresponding to Hijri date

above), Wilbur and Orville Wright made history after failing to achieve it for 3 years.

• Cycle mechanics, enthusiastic about flight, they designed airplanes based on aerodynamic data published by Leinthall and Langley.

• All attempts were splendid failures, so they began to doubt the crude theories of their times.

• They built themselves a windtunnel and started testing airfoils. To their surprise, they obtained reliable results and the rest is history.

The [W]Right [Bi]Plane

Motivating Examples….DC-3• The Douglas DC-3 is one of the most famous

aircraft of all time• It is a low-speed subsonic transport designed

during the 1930s.• Without a knowledge of low-speed aerodynamics,

this aircraft would have never existed.• Notice the dorsals, wing-fuse fairings and nacelles.• The fuse shape has not changed fundamentally

for this class of aircraft in a century

Motivating Examples…Boeing 707• The Boeing 707 opened high-

speed subsonic flight to millions of passengers

• Designed in the late 1950s.• Without a knowledge of high-

speed subsonic aerodynamics, this design would not have taken off.

• Notice how many modern aircraft retain many features after 70 years

• Notice the swept wings

Motivating Examples…Bell X-1• Bell X-1 became the first piloted

airplane to fly faster than sound• Captain Chuck Yeager broke the

speed barrier in October 14, 1947..a couple of months after we broke away from the British ;)

• Without a knowledge of transonic aerodynamics (near the speed of sound), the X-1 would have crashed like all previous attempts at breaking the Sound Barrier.

• Notice the pointed nose, thin wings and high tail.

Motivating Examples…the F-104 Starfighter• Designed in the 1950s, it was the

first supersonic fighter to reach Mach 2 in straight flight!

• For a long time, its speed was unmatched, but it had poor flight performance, as it was aptly called “Rocket with a man in it”.

• Knowledge of Supersonic Aerodynamics was fundamental

• The wings were so sharp mechanics could cut hands touching it!

Motivating Examples…F-22 Raptor• Supersonic fighter with

much improved flight performance.

• Notice blended wing/body• Notice twin tails and all

movable tails• The aerodynamic shape

has also to serve the purpose of stealth from radar

Ancient Egyptian Aerospace!• https://en.wikipedia.org/wiki/Helicopter_hieroglyphs [1290 BC]

Forces and Moments in Flight• Straight level flight means constant velocity and altitude.• There are four main forces which govern straight level flight• For level flight, Lift=Weight and Thrust=Drag• In other words, in level flight• Except weight, all other variables dependon Aerodynamics.• Aerodynamics also causes moments in all three axes

Aerodynamic Moments• Aerodynamics also causes moments in all three axes.• Performance of aircraft depends on aerodynamics!

Source of all Aerodynamic Forces &Moments• No matter how complex the body shape and flow, the aerodynamic

forces and moments on the body are due to only two basic sources:a) Pressure distribution p over the body surfaceb) Shear stress distribution τ over the body surface

• Pressure varies with velocity of air over the surface and acts normal to it. For incompressible, inviscid flow, it follows Bernoulli principle.

• Shear stress is due to friction in the boundary layer and acts tangent to the surface. Typically

Net Effect of Pressure and Shear Distribution• Each body shape and flow condition creates unique p & τ distribution• The net effect of the p and τ distributions integrated over the

complete body surface is a resultant aerodynamic force R and moment M on the body.

• Far ahead of the body, the flow is undisturbed and called free stream.• V∞ = free stream velocity=flow velocity far ahead of the body.

Components of Aerodynamic Force R

• Let distance between leading and trailing edges be “chord”=c

• “Angle of attack” is the angle between and c

• R can be resolved into two sets of components: either wrt or c

• But, {L,D} and {N,A} are related through

Source of {N,A} and {L,D}• Pressure p, shear τ , surface slope θ

are functions of path length s.• For a unit span l=1, the forces are

Source of Aerodynamic Moment• The aerodynamic moment exerted on the body depends on the point

about which moments are taken.• Moments that tend to increase α (pitch up) are positive, and moments

that tend to decrease α (pitch down) are negative.• Moment about the leading edge is simply the forces x moment arms.

• In equations above, x, y and θ are known functions of s for given shape.• A major goal of aerodynamics is to calculate p(s) and τ(s) for a given

body shape and freestream conditions ( and α) aerodynamic forces/moments

Getting rid of the Dimensions…convenience• It will become clear later that it is of benefit to non-dimensionalize

forces and moments. • Let be the free stream air density and S and l be reference area and

reference length respectively.• Dynamic pressure, • Lift coefficient,

• Lift coefficient, • Axial and normal force coefficients are similarly defined.

Coefficients makes the math manageable. An aircraft with a 50m2 wing area and weight of 10,000kg at sea level cruise will have a lift coefficient of 0.3 at a speed of 100m/s, rather than a lift of 9.8x104 N.

Reference Area and Length • In these coefficients, the reference area S and

reference length l are chosen to pertain to the given geometric body shape

• E.g., for an airplane wing, S is the planform area, and l is the mean chord length c.

• for a sphere, S is the cross-sectional area, and l is the diameter

• Particular choice of reference area and length is not critical

• But, when using force and moment coefficient data, we must always know what reference quantities the particular data are based upon.

A note on coefficients• When we talk about 2-D object (like airfoils) rather than 3-D (like

aircraft), it is customary to use small letters as the lift, drag etc are reported on unit span (depth). i.e. cl, cd,cm instead of CL, CD,CM.

• Therefore, for 2-D airfoil, S=c(1)=c.• Additionally, we also have the pressure and friction coefficients.

Rewriting the Force/Moment Integrals

• More convenient to write integrals in terms of coefficients and transforming length variable ds to more familiar dx and dy

So are there any other benefit from changing everything into CP ??• In wind tunnels and flight tests, we often do a pressure survey using

manometers and pressure taps!

Example 1.1• Consider the supersonic flow over a 50 half-angle wedge at zero

angle of attack. The freestream Mach number ahead of the wedge is 2.0, and the freestream pressure and density are 1.01×105 N/m2 and 1.23 kg/m3, respectively (this corresponds to standard sea level conditions).

• The pressures on the upper and lower surfaces of the wedge are constant with distance s and equal to each other, namely, pu = pl = 1.31×105 N/m2.

• The pressure exerted on the base of the wedge is equal to p∞.• Shear stress varies over both the upper and lower surfaces as τw

=431s−0.2. Chord length c of the wedge is 2 m. • Calculate the drag, lift and moment coefficients for the wedge.

Solution

Solution continued

• Since angle of attack is zero, there is no lift or moment!• For symmetric bodies (symmetry about chord), zero α means zero lift

and moment but nonzero drag.

Solution 2• We could also have solved using pressure coefficients in a simpler way

Variation of Forces with Angle of Attack• The behavior of lift with α is like behavior of stress vs strain in metals.• It is linear until a linear limit called “stall” .• For some shapes there is lift CL0 even at zero angle of attack• Like , we have • Drag is quadratic with angle of attack.• Therefore,

Center of Pressure• If the aerodynamic force on a body is specified in terms of a resultant

single force R, or its components such as N and A, where on the body should this resultant be placed?

• The answer is that the resultant force should be located on the body such that it produces the same effect as the distributed loads.

• This location is called the center of pressure CP=[xcp, ycp]• If axial force passes through the chord, then only normal force

produces moment and yCP=0

Center of Pressure … continued• Xcp is the location where the resultant of a distributed load effectively

acts on the body. • If moments were taken about the center of pressure, the integrated

effect of the distributed loads would be zero. • An alternate definition of the center of pressure is that point on the

body about which the aerodynamic moment is zero.• For low angles of attack, .• Thus, for ,

From CP to Aerodynamic Center (AC)• As L or N approach zero, the center of pressure moves to infinity (tail)!• As L approaches a high value, xcp approaches zero (nose)• Also, both MLE and L change with α, which means xCP changes with α• Since moment about xcp is zero, we can translate R to any location

using moment laws.• About the quarter-chord point c/4, we can write

𝑥𝐶𝑃≅𝑀𝐿𝐸

𝐿

Aerodynamic Center• It turns out there is a point where the aerodynamic moment does

not change with • This point is called the Aerodynamic Center (AC)• It is located near the

• Quarter chord c/4 for subsonic flows• Half chord c/2 for supersonic flows

• Since we know the moment of the major lift producing element of the aircraft (wing!) is fixed for all angles at AC, we would like to place the wing’s AC near the aircraft’s CG….why?

Examples 1.3 and 1.4• In low-speed, incompressible flow, the following experimental data

are obtained for an NACA 4412 airfoil section at an angle of attack of 4◦: = 0.85 and = −0.09. Calculate the location of the center of pressure.

• Consider the DC-3. Just outboard of the engine nacelle, the airfoil chord length is 15.4 ft. At cruising velocity (188 mi/h) at sea level, the moments per unit span at this airfoil location are M’c/4=−1071 ft lb/ft and M’LE =−3213.9 ft lb/ft. Calculate the lift per unit span and the location of the center of pressure on the airfoil.

Parameters which influence Aerodynamics• By intuition, the resultant aerodynamic force R should depend on

• Freestream velocity (faster air more force and moment)• Freestream density (denser air more force and moment)• Freestream viscosity (viscosity shear stress)• Size of the body (more reference area and length more force and moment)• Compressibility of air (density changes if flow speed is comparable to speed of sound )• Angle of attack Therefore,

Mfor some nonlinear functions , and .• This is not useful as this means a huge combination of parameters needs to be tested or

simulated to find the relationships necessary for designing aerodynamic vehicles and products.

Dimensional Analysis• Fortunately, we can simplify the problem and considerably reduce our time and effort by first employing

the method of dimensional analysis.• Dimensional analysis is based on the obvious fact that in an equation dealing with the real physical

world, each term must have the same dimensions.• So it is equivalent to find relationships between dimensionless groups of parameters rather than the

parameters themselves.• We can show that force and moment coefficients depend on the Reynold and Mach numbers and flow

angles only, i.e.

i.e. fl, fd and fm.• Notice that all parameters are dimensionless!• Notice that we have reduced the number of parameters from 7 to just 3!• There may be other “similarity parameters” other than these 3, depending on problem.

Flow Similarity• Consider two different flow fields over two different bodies. By definition, different flows

are dynamically similar if:1. Streamline patterns are geometrically similar.

2. Distributions of etc., throughout the flow field are the same when plotted against non-dimensional coordinates.

3. Force coefficients are the same.

• If nondimensional pressure (CP) and shear stress distributions () over different bodies are the same, then the force and moment coefficients will be the same.

• In other words, two flows will be dynamically similar if:1. The bodies and any other solid boundaries are geometrically similar for both flows.2. The similarity parameters are the same for both flows.

• This is a key point in the validity of wind-tunnel testing.

Flow Similarities Application – Wind Tunnel• If a scale model of a flight vehicle is tested in a wind tunnel, the

measured lift, drag, and moment coefficients will be the same as for free flight as long as the and of the wind-tunnel test-section flow are the same as for the free-flight case.

• Wind tunnels are large tubes with air moving inside, used to copy the actions of an object in flight. Some wind tunnels are big enough to hold full-size versions of vehicles, but most can hold only scale models

1/3 scale model of space shuttle in NASA’s 40-foot-by-80-foot WT Mercedes-Benz’s Aeroacoustic Wind Tunnel Educational Wind Tunnel

Example 1.5Consider the flow over two circular cylinders, one having four times the diameter of the other. The flow over the smaller cylinder has a freestream density, velocity and temperature given by ρ1, V1, and T1, respectively. The flow over the larger cylinder has a freestream density, velocity, and temperature given by ρ2, V2, and T2, respectively, where ρ2 = 0.25ρ1, V2 = 2V1, and T2 = 4T1. Assume that both μ and a are proportional to T1/2. Show that the two flows are dynamically similar.

Example 1.6Consider a Boeing 747 airliner cruising at a velocity of 550 mi/h at a standard altitude of 38,000 ft, where the freestream pressure and temperature are 432.6 lb/ft2 and 390◦R. A one-fiftieth scale model of the 747 is tested in a wind tunnel where the temperature is 430◦R. Calculate the required velocity and pressure of the test airstream in the wind tunnel such that the lift and drag coefficients measured for the wind-tunnel model are the same as for free flight.

Qinetiq’s pressurised, 5m (16.4ft)-diameter windtunnel in Farnborough, UK.

A note on Example 1.6• In Example 1.6, the wind-tunnel test stream must be pressurized

far above atmospheric pressure in order to simulate the free-flight Re.

• However, most standard subsonic wind tunnels are not pressurized, because of the large extra financial cost involved.

• This illustrates a common difficulty in wind-tunnel testing: simulating both flight M and flight Re number simultaneously.

• In most cases we do not attempt to simulate all the parameters simultaneously

• Mach number simulation is achieved in one wind tunnel, and Re in another tunnel.

• Results from both tunnels are then analyzed and correlated to obtain reasonable values for CL and CD appropriate for free flight.

The NACA variable density tunnel (VDT). Authorized in March of 1921, VDT was a large, subsonic wind tunnel entirely contained withinan 85-ton pressure shell, capable of 20 atm. It was de-commissioned in 1940s