lecture5_drag2.pdf

7/28/2019 lecture5_drag2.pdf

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Pressure and Friction Drag II

Hydromechanics VVR090

Drag and Lift General Observations I

Inconvenient to separate between pressure and frictional drag.

Total drag force is taken to be the sum of :

drag in a two-dimensional flow (profile drag)

drag produced by end effects (induced drag)

Induced drag is related to the lift force.

No lift force no induced drag.

tip

vortices


2/17

Drag and Lift General Observations II

Pressure drag depends on the pressure distribution aroundthe body and the size of the separation zone.

Large zone of separation large drag force

The location of separation po ints decisive for the magnitude of

the pressure drag . Such locations are determined by:

body shape

body roughness

flow conditions

Flow Separation

streamlined body cylindral body

Boundary layer growth starts in the stagnation point.

In the phase of acceleration the boundary layer is stable,

whereas during deceleration an unfavorable pressure gradient

develops that leads to separation.


3/17

Laminar and Turbulent Boundary Layers

Ideal fluid

Laminar conditions

Turbulent conditions

Drag Coefficients for Different Shapes

Drag coefficient depends on Re (sphere, disk, streamlined body).

Transition to

turbulent

boundary

layer

Laminar flowLittle variation

with ReNo separation


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Flow around Sphere

Flow separation behind

sphere

Flow separation

point

Flow separation point with trip w ire

Trip

wire

Cricket ball

Drag Coefficient for Laminar Flow

Stokes derived the drag force for laminar conditi ons

(viscous forces dominate):

3= o

D V d

General formulation:

21

2= =

D D oD F C A V

Equivalence yields:

213

2 =

o D oV d C A V

George

Stokes


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Cross-sectional area:

2

4

= dA

Solve for drag coefficient:

24 24

Re

= =

D

o

CV d

Stokes equation valid for Re < 0.1.

Re 10 weak separationRe 1000 fully developed separation zone

Vortex Shedding

Under certain conditions vortices are generated from

the edges of a body in a flow.

Von Karmans vortex street

Theodore

Von KarmanVortex street

behind a cylinder

Vortices at Aleutian Island


6/17

If 6 < Re < 5000, regular vortex sheeding may occur at a

frequency n determined by Strouhals number:

=

o

ndS

V

(S = 0.21 over a wide range of Re)

Vincent Strouhal

Periodic vortex shedding may lead to t ransversal forces

on structures (e.g., pipes, chimneys, bridges) resulting in

vibration and possib le structural damages.

If is close to the natural frequency of the structure, large

effects are expected.

Strouhals Number as a Function of Re

Fully developed

turbulence, no regularvortex sheddingData for cylinder


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Example I: Vortex Shedding f rom Antenna Stand

30 m

0.3 m

What is the frequency of the vort icesshed?

wind

35 m/s

Standard atmosphere

(101 kPa, 20 deg)

Example II: Vortex Shedding from Telegraph Wires

V = 10 m/s

Wires

diameter = 2 mm

What is the frequency of the

vortices shed?


8/17

Ferrybr idge Cooling Towers

Three towers collapsed because (November 1965):

underestmated wind design conditi ons

interaction between towers not considered

Tacoma Bridge

Built 1940

Span: 2,800 ft (850 m)

Plate-girder deck: 8 ft (2.4 m)

Wind-induce vibrations

caused oscillations of the

deck with eventual collapse.


9/17

Example of Drag Force Calculation

parachute jumping

sedimentation of particle

popcorn popper

Basic equation for drag force:

21

2=

D oD C AV

CD

obtained from empirical studies

A is the projected area on a plane

perpendicular to the flow direction

Empirical Values for the Drag Coefficient CD

I


10/17


II

Dolphin drag


III

Lotus

6.400.5919.401.8020.330'90 EspritTurbo SE

6.400.5919.401.8020.330'89 Esprit

Turbo

6.400.5919.401.8020.330'86 Esprit

Turbo

6.400.5919.401.8020.330'83 EspritTurbo

6.400.5919.401.8020.330'94 EspritS4

6.400.5919.401.8020.330'80 Esprit

6.990.6518.401.7090.380'91 Elan

SE

6.990.6518.401.7090.380'95 ElanS2

7.090.6619.691.8300.360'80 Eclat

Cd

x ft 2Cd

x m2Area (ft 2 )Area (m 2

)C

d

Vehicle

Year and

Model

Mercedes-Benz Bionic Concept: 0.19

Hummer H2: 0.57

Lotus


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Example I: Parachute Jumping

FG

FD Terminal speed of a person jumping

with a parachute?

Assumed data:

M = 100 kg

air = 1.2 kg/m3D = 7 m

Example II: Particle Sedimentation

Sediment particle in water what is

the terminal speed?

Newton-Stokes law of sedimentation

(laminar flow)

FG

FB FD

Example of

settling tanks


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Example III: Popcorn Popper

Design the popcorn popper

Unpopped corn:

0.15 g/kernel

6 mm diameter

Popped corn:

18 mm diameter

Al lowable air speed

produced by the fan?

Fan

Heating

coil

Lift Force on Bodies

Important in design of:

airplane

pipelines (e.g., on the seafloor)

pumps and turbines

Flow and pressure

distribution around and airfoil


13/17

Principles of Flight

Horizontal and vertical fo rce

balance for design

FL

= FG

FD

= FP

21

2L L oF C A V =

Lift force:Gliding angle:

tan =D

L

CC

Lift Coefficient CL

CL for typical airfoil sections versus

angele of attack

Stall speed


14/17

Tip Vortices (Induced Drag) I

Tip Vortices (Induced Drag) II

CD

and CL

for different wing aspect ratios


15/17

Example: Takeoff Speed of Airplane

What is the necessary angleof attack (a) for a takeoffspeed of 140 km/hr?

FG

a

FL

Wingspan: 10 m

Chord length: 1.5 mPlane weight: 10 kN

Two passengers at 800 N each

Magnus Effect

Heinrich

Gustav

Magnus

Net force occurs when a sphere or cylinder in a

moving fluid is rotating

Top of cylinder: velocities of the moving fluid and therotating ball enhance each other low pressure

Bottom of cylinder: velocities of the moving fluid and therotating ball counteract each other high pressure

Pressure difference net force


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Importance of Magnus Effect in Sports I

Golf (hook, slice)

Soccer

(banana

shoot)

Table tennis

and tennis

(topspin, slice)

Lateral deflection

of baseball

Importance of Magnus Effect in Sports II

Spinning baseball

(curveball)


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Ship Propulsion

Alcyone

Buckau

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lecture5_drag2.pdf