03Lect9BluffBodyAero

8/3/2019 03Lect9BluffBodyAero

http://slidepdf.com/reader/full/03lect9bluffbodyaero 1/29

Basic bluff-body aerodynamics II

Wind loading and structural response

Lecture 9 Dr. J.D. Holmes



Basic bluff-body aerodynamics

• Pressures on prisms in turbulent boundary layer :

• drag coefficient (based on Uh ) 0.8

-0.20 -0.10 -0.20

-0.23 -0.18 -0.23xx x

-0.20 -0.20

x x

xx x

Sym.aboutCL

-0.2

-0.5

-0.8

-0.8

-0.5

-0.8

-0.6

-0.7

0.7

0.50.0

Wind

windward wall

side wall

roof leeward wall




• Pressures on prisms in turbulent boundary layer :

-0.5

-0.4 to –

0.49

Leeward wall

-0.5

-0.5

x -0.6

x -0.6

x-0.6

-0.5

-0.6

-0.6

-0.7

Wind

Side wall

x 0.4

0.3 x

0.9x

0.5 x

Windward wall

-0.6

-0.56 to –

0.59-0.6x x

Wind

Roof

shows effect

of velocity

profile

nearly

uniform




• Circular cylinders :

Complexity due to interacting effects of surface roughness, Reynolds

Number and turbulence in the approach flow

Flow regimes in smooth flow :

Re < 2 105 Cd = 1.2

Sub-critical

Laminarboundary layer Separation

Subcritical regime : most wind-tunnel tests - separation at about 90o from the

windward generator








Supercritical : flow in boundary layer becomes turbulent -

separation at 140o - minimum drag coefficient

Re 5 105 Cd 0.4

Super-critical

Laminar TurbulentSeparation








Post-critical : flow in boundary layer is turbulent - separation at

about 120o

Re 107 Cd 0.7

Post-critical

TurbulentSeparation





Pressure distributions at sub-critical and super-critical Reynolds Numbers

20 60 100 140

1.0

0.5

0

-0.5

-1.0

-1.5

-2.0

-2.5

U

q degrees

q

C p

Drag coefficient mainly determined by pressure on leeward side (wake)





Effect of surface roughness :

Increasing surface roughness : decreases critical Re - increases minimum Cd

1.2

0.8

0.4

U b

104 2 4 8 105 2 4 8 106 2 4 8 107

k/b = 0.02

k/b = 0.007

k/b = 0.002

Sanded surfaceSmooth surface

Cd

Re

increasing surface roughness





Effect of aspect ratio on mean pressure distribution :

Silos, tanks in

atmosphericboundary layer

-2

-1.5

-1

-0.5

0

0.5

1

0 90 180

Angle (degrees)

h/b = 0.5

h/b = 1.0

h/b = 2.0

Cp b

h

Decreasing h/b : increases minimum Cp (less negative)




• Fluctuating forces and pressures on bluff bodies :

Sources of fluctuating pressures and forces :

• Freestream turbulence (buffeting)

- associated with flow fluctuations in the approach flow

• Vortex-shedding (wake-induced)

- unsteady flow generated by the bluff body itself

• Aeroelastic forces

- forces due to the movement of the body (e.g. aerodynamic damping)




• Buffeting - the Quasi-steady assumption :

Fluctuating pressure on the body is assumed to follow the

variations in wind velocity in the approach flow :

p(t) = Cpo (1/2) a [U(t)]2

Cpo is a quasi-steady pressure coefficient

Expanding :

p(t) = Cpo (1/2) a [ U + u(t) ]2

= Cpo (1/2) a [ U2 + 2 U u(t) + u(t)2 ]

Taking mean values :

p = Cpo (1/2) a [ U2 + u2]




• Buffeting - the Quasi-steady assumption :

Small turbulence intensities :

p Cpo (1/2) a U2 = Cp (1/2) a U2

i.e. Cpo is approximately equal to Cp

Fluctuating component :

p' (t) = Cpo (1/2) a [2 U u'(t) + u'(t)2 ]

(e.g. for Iu = 0.15, u2 = 0.0225 U2 )

Squaring and taking mean values :

Cp2 (1/4) a

2 [4 U2 ]= Cp2 a

2 U2 u2 2

p 2u




• Peak pressures by the Quasi-steady assumption :

Quasi-steady assumption gives predictions of either maximum

or minimum pressure, depending on sign of Cp

Time

p(t)

p̂

p

]Uˆ[(1/2)ρC]Uˆ[(1/2)ρCporp̂ 2

ap

2

apo




• Vortex shedding :

On a long (two-dimensional) bluff body, the rolling up of

separating shear layers generates vortices on each side

alternately

• Occurs in smooth or turbulent approach flow

• may be enhanced by vibration of the body (‘lock -in’)

• cross-wind force produced as each vortex is shed




• Vortex shedding :

Strouhal Number - non dimensional vortex shedding

frequency, ns :

• b = cross-wind dimension of body

• St varies with shape of cross section

U

bnSt

s

• circular cylinder : varies with Reynolds Number




• Vortex shedding - circular cylinder :

• vortex shedding not regular in the super-critical Reynolds

Number range




• Vortex shedding - other cross-sections :

0.08

2b

2.5b

~10b

0.12

0.06

0.14




• fluctuating pressure coefficient :

• fluctuating sectional force coefficient :

2

a

2

p

Uρ2

1

pC

bUρ2

1

f C

2

a

2

f

• fluctuating (total) force coefficient :

AUρ2

1

FC

2

a

2

F




• fluctuating cross-wind sectional force coefficient forcircular cylinder :

dependecy on Reynolds Number

105 106 107

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

Fluctuatingside force

coefficientC

l

Reynolds number, Re




• Quasi-steady fluctuating pressure coefficient :

• Quasi-steady drag coefficient :

up2

a

2

ap

2

a

2

p IC2

Uρ2

1

uUρC

Uρ2

1

pC

u D D I C C 2




• Correlation coefficient for fluctuating forces on a two-

dimensional body :

• Correlation length :

2

f

21

2

21

σ

(t)f (t)f

f

(t)f (t)f ρ

dy y

0

)( l

y is separation distance between sections




• Correlation length for a stationary circular cylinder

(smooth flow) :

cross-wind vibration at same frequency as vortex shedding increases

correlation length

6

4

2

0

104 105 106

Reynolds number,Re

Correlationlength / diameter




• Total fluctuating force on a slender body :

We require the total mean and fluctuating forces on the whole body

L

iii f f f

Nf

1f

jf

δ y 1 δy

i δy j

δyN





mean total force : F = f i yi i

L

0

i dyf

instantaneous total fluctuating force : F(t) = f i (t) yi

= f 1 (t) y1 + f 2 (t) y2 + ……………….f N (t) yN

Squaring both sides : [F(t)]2 = [ f 1 (t) y1 + f 2 (t) y2 + ……………….f N (t) yN]2

= [f 1 (t) y1]2 + [f 2 (t) y2]

2 ..+ [f N (t) yN]2+ f 1 (t) f 2(t) y1y2 + f 1 (t) f 3(t) y1y3 +...

ji j

N

j

i

N

i

δyδy(t)f (t)f





Taking mean values :

As yi, y j tend to zero :

writing the integrand (covariance) as :

ji

N

j

ji

N

i

y yt f t f F )()(2

ji ji

L L

dydyt f t f F )()(00

2

)()()( 2

ji ji y y f t f t f

ji

L

ji

L

dydy y yt f F 00

22 )()(

This relates the total mean square fluctuating force to the sectional force





Introduce a new variable (yi - y j) :

Special case (1) - full correlation, (yi-y j) = 1 :

fluctuating forces treated like static forces

mean square fluctuating force is proportional to the correlation length -

applicable to slender towers

)yd(y)yρ(ydyf F ji

yL

y-

ji

L

0

j

22

j

j

222 L(t)f F

Special case (2) - low correlation, correlation length l is much less than L :

l2)yd(y)yρ(y)yd(y)yρ(y ji

-

ji ji

yL

y-

ji

j

j

lL.2(t)f F22





Symmetric about diagonal since (y j-yi) = (yi-y j ). Along the diagonal,

the height is 1.0

The double integral : is represented by the

volume under the graph :

ji

L

0

ji

L

0

dydy)yρ(y

On lines parallel to the diagonal, height is constant

0

0.5

1

1

S1

yi

y j





Consider the contribution from the slice as shown :

Length of slice = (L-z)2

z/ 2

z / 2

L

yi-y j=0

yi-y j= z

y j

yi

Volume under slice = (z)(L-z)22

δz

Total volume = L

0dzz)ρ(z)(L2

L

0

22 dzz)ρ(z)(L2.f F

(reduced to single integral)



End of Lecture 9

John Holmes225-405-3789 [email protected]

03Lect9BluffBodyAero

Documents

Transcript of 03Lect9BluffBodyAero