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Pharos UniversityME 253 Fluid Mechanics II

- Flow over bodiesLift and Drag

External External Flows

- Bodies in motion, experience fluid forces and

moments. - Examples include aircraft, automobiles,

buildings, ships, submarines, turbo machines. - Fuel economy, speed, acceleration, stability, and

control are related to the forces and moments.

Airplane in level steady flight drag thrust

lift weight.

Flow over immersed bodies

- flow classification
- 2D, axisymmetric, 3D
- bodies
- streamlined and blunt

Airplane

- Upper surface
- (upper side of wing)
- low pressure
- Lower surface (underside of wing) high pressure

Lift and Drag

- shear stress and pressure integrated over body

surface - drag force component in the direction of

upstream velocity - lift force normal to upstream velocity

AIRFOIL NOMENCLATURE

- Mean Chamber Line Points halfway between upper
- and

lower surfaces - Leading Edge Forward point of mean chamber line
- Trailing Edge Most reward point of mean chamber

line - Chord Line Straight line connecting the leading

and trailing edges - Chord, c Distance along the chord line from

leading to trailing edge - Chamber Maximum distance between mean chamber

line - and chord line

AERODYNAMIC FORCE

- Relative Wind Direction of V8
- We used subscript 8 to indicate far upstream

conditions - Angle of Attack, a Angle between relative wind

(V8) and chord line - Total aerodynamic force, R, can be resolved into

two force components - Lift, L Component of aerodynamic force

perpendicular to relative wind - Drag, D Component of aerodynamic force parallel

to relative wind

Pressure Forces acting on the Airfoil

Low Pressure High velocity

High Pressure Low velocity

Low Pressure High velocity

High Pressure Low velocity

Bernoullis equation says where pressure is high,

velocity will be low and vice versa.

Relationship between L and p

V?

Relationship between L and p(Continued)

Divide left and right sides by

We get

Pressure Coefficient Cp

From the previous slide,

The left side was previously defined as the

sectional lift coefficient Cl.

The pressure coefficient is defined as

Thus,

- Fluid dynamic forces are due to pressure and

viscous forces. - Drag component parallel to flow direction.
- Lift component normal to flow direction.

Drag and Lift

- Lift and drag forces can be found by integrating

pressure and wall-shear stress.

Drag and Lift

- Lift FL and drag FD forces fn ( ? , A,V )
- Dimensional analysis lift and drag coefficients.
- Area A can be frontal area (drag applications),

plan form area (wing aerodynamics).

Example Automobile Drag bile Drag

CD 1.0, A 2.5 m2, CDA 2.5m2

CD 0.28, A 1 m2, CDA 0.28m2

- Drag force FD1/2?V2(CDA) will be 10 times

larger for Scion XB - Source is large CD and large projected area
- Power consumption P FDV 1/2?V3(CDA) for both

scales with V3!

Drag and Lift

- If CL and CD fn of span location x.
- A local CL,x and CD,x are introduced.
- The total lift and drag is determined by

integration over the span L

Friction and Pressure Drag

- Fluid dynamic forces pressure and friction

effects. - FD FD,friction FD,pressure
- CD CD,friction CD,pressure

Friction drag

Pressure drag

Friction pressure drag

Flow Around Objects

Streamlining

- Streamlining reduces drag by reducing

FD,pressure, - Eliminate flow separation and minimize total drag

FD

Streamlining

CD of Common Geometries

- For many shapes, total drag CD is constant for Re

gt 104

CD of Common Geometries

CD of Common Geometries

Flat Plate Drag

- Drag on flat plate is due to friction created by

laminar, - transitional, and turbulent boundary layers.

Flat Plate Drag

- Local friction coefficient
- Laminar
- Turbulent
- Average friction coefficient
- Laminar
- Turbulent

Cylinder and Sphere Drag

Cylinder and Sphere Drag

- Flow is strong function of Re.
- Wake narrows for turbulent flow since turbulent

boundary layer is more resistant to separation. - ?sep, lam 80º
- ?sep,Tur 140º

Lift

- Lift is the net force (due to pressure and

viscous forces) perpendicular to flow direction. - Lift coefficient
- Abc is the planform area

Characteristics of Cl vs. a

Stall

Cl

Slope 2p if a is in radians.

a a0

Angle of zero lift

Angle of Attack, a in degrees or radians

EXAMPLE AIRFOIL STALL

Lift

Angle of Attack, a

Effect of Angle of Attack

- CL2?? for ? lt ?stall
- Lift increases linearly with ?
- ObjectiveMaximum CL/CD
- CL/CD increases until stall.

Effect of Foil Shape

- Thickness and camber affects pressure

distribution and - location of flow separation.

End Effects of Wing Tips

- Tip vortex created by flow from high-pressure

side to low-pressure side of wing. - Tip vortices from heavy aircraft far downstream

and pose danger to light aircraft.

Lift Generated by Spinning

Superposition of Uniform stream Doublet Vortex

Drag Coefficient CD

Stokes Flow, Relt1

Supercritical flow turbulent B.L.

Relatively constant CD

Drag

- Drag Coefficient

with

or

DRAG FORCE

- Friction has two effects
- Skin friction due to shear stress at wall
- Pressure drag due to flow separation

Total drag due to viscous effects Called Profile

Drag

Drag due to skin friction

Drag due to separation

Less for laminar More for turbulent

More for laminar Less for turbulent

COMPARISON OF DRAG FORCES

d

d

Same total drag as airfoil

AOA 2

AOA 3

AOA 6

AOA 9

AOA 12

AOA 20

AOA 60

AOA 90

Drag Coefficient of Blunt and Streamlined Bodies

- Drag dominated by viscous drag, the body is

__________. - Drag dominated by pressure drag, the body is

_______.

streamlined

Flat plate

bluff

Drag

- Pure Friction Drag Flat Plate Parallel to the

Flow - Pure Pressure Drag Flat Plate Perpendicular to

the Flow - Friction and Pressure Drag Flow over a Sphere

and Cylinder - Streamlining

Drag

- Flow over a Flat Plate Parallel to the Flow

Friction Drag

Boundary Layer can be 100 laminar, partly

laminar and partly turbulent, or essentially 100

turbulent hence several different drag

coefficients are available

Drag

- Flow over a Flat Plate Perpendicular to the Flow

Pressure Drag

Drag coefficients are usually obtained

empirically

Flow past an object

Character of the steady, viscous flow past a

circular cylinder (a) low Reynolds number flow,

(b) moderate Reynolds number flow, (c) large

Reynolds number flow.

Drag

- Flow over a Sphere and Cylinder Friction and

Pressure Drag (Continued)

Streamlining

- Used to Reduce Wake and hence Pressure Drag

Lift

- Mostly applies to Airfoils

Note Based on planform area Ap

Lift

- Induced Drag

Experiments for Airfoil Lift Drag

- Examine the surface pressure distribution and

wake velocity profile on airfoil 2-D - Compute the lift and drag forces acting on the

airfoil - Pressure coefficient
- Lift coefficient

- Test Facility
- Wind tunnel.
- Airfoil
- Temp. sensor
- Pitot tubes
- Pressure sensors
- Data acquisition

Test Design

- Airfoil in a wind tunnel with
- free- stream velocity of 15 m/s.
- This airfoil has
- Forces normal to free stream Lift
- Forces parallel to free stream Drag
- Top of Airfoil
- - The velocity of the flow is greater
- than the free-stream.
- - The pressure is negative
- Underside of Airfoil
- - Velocity of the flow is less than the
- free-stream.
- - The pressure is positive
- This pressure distribution contribute
- to the lift Drag

Pressure taps positions

- The lift force, L on the Airfoil will be find

by integration of the - measured pressure distribution over the

Airfoils surface.

Data reduction

- Calculation of lift force
- The lift force L Integration of the measured

pressure over the airfoils surface. - Pressure coefficient Cp where, pi surface

pressure measured, P pressure in the

free-stream - U8 free-stream velocity,
- ? air density
- pstagnation stagnation pressure
- by pitot tube,
- L Lift force, b airfoil span,
- c airfoil chord

Drag Force

- The drag force, D on the Airfoil

Integration of the momentum loss using the axial

velocity profile in the wake of the Airfoil.

Data reduction

- Calculation of drag force
- The drag force D integration of the momentum

loss - The velocity profile u(y) is measured ui at

predefined locations - U8 free-stream velocity,
- ? air density
- pstagnation Stagnation pressure
- by Pitot tube,
- D Drag force, b airfoil span,
- c airfoil chord

Velocity and Drag Spheres

General relationship for submerged objects

Spheres only have one shape and orientation!

Where Cd is a function of Re

Sphere Terminal Fall Velocity

Sphere Terminal Fall Velocity (continued)

General equation for falling objects

Relationship valid for spheres

Drag Coefficient on a Sphere

1000

100

Stokes Law

Drag Coefficient

10

1

0.1

0.1

1

10

102

103

104

105

106

107

Re500000

Reynolds Number

Turbulent Boundary Layer

Drag Coefficient for a SphereTerminal Velocity

Equations

Valid for laminar and turbulent

Laminar flow R lt 1

Transitional flow 1 lt R lt 104

Fully turbulent flow R gt 104

Example Calculation of Terminal Velocity

Determine the terminal settling velocity of a

cryptosporidium oocyst having a diameter of 4 mm

and a density of 1.04 g/cm3 in water at 15C.

Reynolds