Pressure and Friction Drag II

Hydromechanics VVR090

ppt by Magnus Larson; revised by Rolf L Jan 2014

SYNOPSIS

1. Drag– General Observations

2. Flow Separation

3. Drag Coefficients for Different Shapes

4. Drag Coefficient for sphere in Laminar Flow

5. Vortex Shedding

6. Examples/Problems

7. Lift Force on Bodies

8. Magnus Effect

1. Drag– 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

Drag – General Observations II

Pressure drag depends on the pressure distribution around the

body and the size of the separation zone.

Large zone of separation large drag force

The location of separation points decisive for the magnitude of the

pressure drag . Such locations are determined by:

• body shape

• body roughness

• flow conditions

2. 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.

Laminar and Turbulent Boundary Layers

Ideal fluid

Laminar conditions

Turbulent conditions

3. 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

Flow around Golf Ball

Turbulent boundary layer stronger

than laminar.

=> Smaller zone of separation and

resulting drag force

Flow around Sphere

Flow separation behind

sphere

Flow separation

point

Flow separation point with trip wire

Trip

wire

Cricket ball

Empirical Values for the Drag Coefficient CD I

Empirical Values for the Drag Coefficient CD II

Dolphin drag

Empirical Values for the Drag Coefficient CD III

LotusVehicle

Year and

Model

Cd Area (m2

)

Area (ft2 ) Cd x m2 Cd x ft2

'80 Eclat 0.360 1.830 19.69 0.66 7.09

'95 Elan

S2

0.380 1.709 18.40 0.65 6.99

'91 Elan

SE

0.380 1.709 18.40 0.65 6.99

'80 Esprit 0.330 1.802 19.40 0.59 6.40

'94 Esprit

S4

0.330 1.802 19.40 0.59 6.40

'83 Esprit

Turbo

0.330 1.802 19.40 0.59 6.40

'86 Esprit

Turbo

0.330 1.802 19.40 0.59 6.40

'89 Esprit

Turbo

0.330 1.802 19.40 0.59 6.40

'90 Esprit

Turbo SE

0.330 1.802 19.40 0.59 6.40

Mercedes-Benz Bionic Concept: 0.19

Hummer H2: 0.57

Lotus

4. Drag Coefficient for sphere in Laminar Flow

Stokes derived the drag force for laminar conditions (viscous

forces dominate):

3 oD V d

General formulation of Drag force:

21

2 D D oD F C A V

Equivalence [ eq. 1 and 2] yields:

213

2 o D oV d C A V

George

Stokes

(eq. 1)

(eq. 2)

(eq. 3)

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 separation

Re 1000 fully developed separation zone

5. Vortex Shedding

Under certain conditions vortices are generated from the

edges of a body in a flow.

Von Karman’s vortex street

Theodore Von

Karman

Vortex street behind a cylinder

Vortices at Aleutian Island

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

frequency n determined by Strouhal’s number:

o

ndS

V

(S = 0.21 over a wide range of Re)

Vincent Strouhal

Periodic vortex shedding may lead to transversal forces on

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

and possible 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 regular

vortex sheddingData for cylinder

6. Examples / problems

Example I: Vortex Shedding from Antenna Stand

30 m

0.3 m

What is the frequency of the vortices shed?

wind

35 m/s

Standard atmosphere

(101 kPa, 20 deg)

Example II: Vortex Shedding from Telegraph Wires

V = 10 m/sWires

diameter = 2 mm

What is the frequency of the vortices shed?

Examples of Drag Force Calculation

III ) parachute jumping

IV ) sedimentation of particle

V ) popcorn popper

Basic equation for drag force:

21

2 D oD C AV

Where:

CD is obtained from empirical studies

A is the projected area on a plane

perpendicular to the flow direction

Example III: Parachute Jumping

FG

FDTerminal speed of a person jumping with a

parachute?

Assumed data:

M = 100 kg

air = 1.2 kg/m3

D = 7 m

Example IV: Particle Sedimentation

Sediment particle in water – what is the

terminal speed?

Newton-Stokes law of sedimentation

(laminar flow)

FG

FB FD

Examples of

settling tanks

Example V: Popcorn Popper

Design the popcorn popper

Unpopped corn:

0.15 g/kernel

6 mm diameter

Popped corn:

18 mm diameter

Allowable air speed produced by the fan?

Fan

Heating

coil

Ferrybridge Cooling Towers

Three towers collapsed (November 1965) because:

• underestimated wind design conditions

• interaction between towers not considered

Tacoma Bridge

Built 1940

Span: 2,800 ft (850 m)

Plate-girder deck: 8 ft (2.4 m)

Wind-induced vibrations

caused oscillations of the

deck with eventual collapse.

7. 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

Principles of Flight

Horizontal and vertical force

balance for design

FL = FG

FD = FP

21

2L L oF C A V

Lift force:Gliding angle:

tan D

L

C

C

Lift Coefficient CL

CL for typical airfoil sections versus

angle of attack

Stall speed

Tip Vortices (Induced Drag) I

Tip Vortices (Induced Drag) II

CD and CL for different wing aspect ratios

8. 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 the

rotating ball enhance each other low pressure

Bottom of cylinder: velocities of the moving fluid and the

rotating ball counteract each other high pressure

Pressure difference net force

Popular explanation

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)

Asymmetric boundary layer

separation

Ship Propulsion

Alcyone

(Cousteau)

Buckau

Anton Flettner