Download pptx - The 2 nd Cross-Strait Symposium on Dynamical Systems and Vibration 13-19 December 2012 Spectrum Characteristics of Fluctuating Wind Pressures on Hemispherical

The 2nd Cross-Strait Symposium on Dynamical Systems and Vibration13-19 December 2012

Spectrum Characteristics of Fluctuating Wind Pressures on Hemispherical Domes

Yuan-Lung Loren LoChung-Lin Fu

Chii-Ming Cheng

Dept. Civil Eng., Tamkang University, Taiwan

Background

Since the span of dome roof sometimes stretches to more than 100 or 200 m, wind fluctuations on the roof may dominate rather than earthquake loading.

For a prism structure For a curved structure

Roughness on the surfaceOncoming wind speedFlow viscosity Geometric appearance…

1

2

This research intends to investigate spectrum characteristics of wind pressures on dome structures and intends to provide a general model for practical applications.

Cylinder height

Roof height

Wind Tunnel Test

simplifying

Evaluating pressures

Evaluating response

Objective

1. Experimental setting and simulated turbulent flow

2. Zoning of domed roofs

3. Approximation model for power spectra

4. Approximation model for cross spectra

5. Conclusions

Presentation content

)t('uU)t(u

U

uI

2

u

UG: mean wind speed at boundary layer heightUG=5.9m/sec and 11.1m/sec

Urban terrain is attempted.

Experimental setting and simulated turbulent flow


3

21

3

5

k

U

zLff~

f~

1

f~

ku

f,zSf

z

352u

whereГ(-): gamma function; β: shape parameter;L(z): length constant.

β=2: Karman-type spectrum

Power spectra of oncoming winds

Baratron sensor

Pressure Calibration Unit

Power Unit Pressure Sensor UnitSimultaneous Sampling Unit

Sensor Connector

Data Acquisition Unit

MonitorKeyboradMouse

Atmospheric pressure

Pitot tube - dynamic

Pitot tube - reference

Speaker

Base sensor

13

2

Audio Amplifier

Base Sensor Amplifier

Sine Wave

Generator


Wind pressure measurement devices

Transition characteristics of tubing

Fs=1000HzT=120sec


Acrylic domed models

D = 300mmf/D (roof height to span)

0.0 0.1 0.2 0.3 0.4 0.5

h/D(cylind

er height

to span)

0.0 None B0 C0 D0 E0 F00.1 A1 B1 C1 D1 E1 F10.2 A2 B2 C2 D2 E2 F20.3 A3 B3 C3 D3 E3 F30.4 A4 B4 C4 D4 E4 F40.5 A5 B5 C5 D5 E5 F5

35 domed models for wind pressure measurementsHowever, only f/D=0.5 is discussed in this presentation!

D

fhx

z

x

y


Reynolds number ranges

DU

Re H For UG=11.1m/secUH = 5.1m/sec ~ 7.5m/secRe = 1.06×105 ~ 1.56×105Re: Reynolds number

ρ: air density;UH: mean wind speed model heightD: model span (300mm)μ: viscosity constant

According to Fu [12] and Hongo [50], when Re>105, and turbulence intensity larger than 15~18%, the distribution of wind flow will be stable.

Scaling of domed models

400/1L

70/1T

7.5/170/1

400/1U

According to the time scale, 1/70, 8192 samples in tunnel = 10 minute in field scale14 segments of 8192 samples are taken averaged.

Zoning of domed roofs

Contours of Cp,mean

f/D=0.5

-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5

x/D

0

0.1

0.2

0.3

0.4

0.5

y/D

-2

-1.75

-1.5

-1.25

-1

-0.75

-0.5

-0.25

0

0.25

0.5

0.75

1

-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5

x/D

0

0.1

0.2

0.3

0.4

0.5

y/D

-2

-1.75

-1.5

-1.25

-1

-0.75

-0.5

-0.25

0

0.25

0.5

0.75

1

-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5

x/D

0

0.1

0.2

0.3

0.4

0.5

y/D

-2

-1.75

-1.5

-1.25

-1

-0.75

-0.5

-0.25

0

0.25

0.5

0.75

1

-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5

x/D

0

0.1

0.2

0.3

0.4

0.5

y/D

-2

-1.75

-1.5

-1.25

-1

-0.75

-0.5

-0.25

0

0.25

0.5

0.75

1

h/D=0.0 h/D=0.1

h/D=0.2 h/D=0.5

Top View

Side View


Contours of Cp,RMS

f/D=0.5

-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5

x/D

0

0.1

0.2

0.3

0.4

0.5

y/D

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5

x/D

0

0.1

0.2

0.3

0.4

0.5

y/D

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5

x/D

0

0.1

0.2

0.3

0.4

0.5

y/D

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5

x/D

0

0.1

0.2

0.3

0.4

0.5

y/D

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

h/D=0.0 h/D=0.1

h/D=0.2 h/D=0.5

Top View

Side View


fh

xz

Df/D=0.5

Cp,mean along meridian

f/D=0.5

-0.5 -0.3 -0.1 0.1 0.3 0.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0

h/D=0.0 h/D=0.1 h/D=0.2

h/D=0.3 h/D=0.4 h/D=0.5

x/D

Cp,RMS along meridian

f/D=0.5

-0.5 -0.3 -0.1 0.1 0.3 0.5 0.0 0.1 0.2 0.3 0.4 0.5 0.6

h/D=0.0 h/D=0.1 h/D=0.2

h/D=0.3 h/D=0.4 h/D=0.5

x/D

Side View


Correlation coefficients

f/D=0.5

h/D=0.0 h/D=0.1

h/D=0.2 h/D=0.5

-0.5 -0.3 -0.1 0.1 0.3 0.5 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2

x/D-0.5 -0.3 -0.1 0.1 0.3 0.5

0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2

x/D

-0.5 -0.3 -0.1 0.1 0.3 0.5 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2

x/D-0.5 -0.3 -0.1 0.1 0.3 0.5

0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2

x/D

Side View

Power spectra

05

1015

2025

3010

-4

10-2

100

102

10-4

10-3

10-2

10-1

100

No. of channelReduced frequency

Nor

mal

ized

spe

ctru

m

Ch.1Ch.2Ch.3

Ch.29

f/D=0.5h/D=0.0

fD/UH

Windward

Separation Wake

Approximation model for power spectra

Wind

Side View

15

Power spectra

0

5

1015

20

25

30

10-3

10-2

10-1

100

101

102

10-4

10-3

10-2

10-1

100


Nor

mal

ized

spe

ctru

m

f/D=0.5h/D=0.0

Ch.5

6

52

H

2u

H

uk

2

H

2

k2

2t

t

U

fD

D

L8.701

U

L4fS

U

fD1f

fSfffS

1dffS

02t

t

0

2

2t

k dfffS

1Velocity-pressure admittance

Karman velocity spectrum


16

Power spectra

0

5

1015

20

25

30

10-3

10-2

10-1

100

101

102

10-4

10-3

10-2

10-1

100


Nor

mal

ized

spe

ctru

m

f/D=0.5h/D=0.0

Ch.26

Ch.15

zone wake: w i

zone separation :s i

1

2

2

i

H

i

H

i

i

i

U

fD

U

fDffS


17

Power spectra

0.1www

ffSw

ffSw

ffSw

ffS

wst

2w

ww2

s

ss2

t

tt2

p

p

Weighting for approximation


Wind

Side View

18

Power spectra

-0.5

-0

.3 -0

.1

0.1

0.3

0.5

0.0

0.2

0.4

0.6

0.8

1.0

Windward SeparationWake

x/D

We

igh

tin

g f

act

ors

Ch.25

0.1www

ffSw

ffSw

ffSw

ffS

wst

2w

ww2

s

ss2

t

tt2

p

p

Weighting for approximation

Distribution of weighting factors for typical power spectrum model shows the variation of turbulence energy

For f/D=0.5 h/D=0.0


Cross spectrum characteristics of two fluctuating wind pressures are concerned when integrating wind loads over certain area or the whole surface of the roof.

f,riSfSf,rS Q12

C1212

fSfS

Sf,rC

21

C12

12

fSfS

f,riSf,rSf,rR

21

Q12

C12

12

f,rS

f,rStanf,r

C12

Q121

12

F0 (f/D=0.5, h/D=0.0)

Cross spectra

Approximation model for cross spectra

Co-coherence

Root-coherence

Phase Side ViewWind


Cross spectra

F0 (f/D=0.5, h/D=0.0)

Ch.3 – Ch.4

Ch.3 – Ch.5

Ch.10 – Ch.12

Ch.16 – Ch.17

34

5

1012 16 17

Ch.22 – Ch.23

Ch.25 – Ch.272223

25

27Side ViewWind


Cross spectra

F0 (f/D=0.5, h/D=0.0)

78

1017

Ch.7 – Ch.10

Ch.8 – Ch.17

Ch.9 – Ch.23

Ch.18 – Ch.249

1823

24

Ch.3 – Ch.21

Ch.2 – Ch.26

23 26

21

Side ViewWind


Ch3-Ch4 Ch3-Ch5 Ch18-Ch19

Ch7-Ch10 Ch7-Ch18 Ch7-Ch27

3 4 5 7 10 1819 27

Windward Separation Wake

Cross spectrum features

Generally, there are (1)five different distributions of co-coherences can be indicated among all data. In addition, (2)with the distance between two points increases, decaying tendency also changes.

Top View



To approximate root-coherences and phases, Ogawa and Uematsu have applied the following expression.

Hc

H

H12

U

rf

U

U2cos

U

rfkexpf,rC

st

2

H2

stH

t

221

12

f̂Uk

Df1f

f̂U

rfk2cosf

D

rkexpf,rC

st

2

H2

stH

t

221

ij

f̂Uk

Df1f

f̂U

dsfk2cosf

D

dskexpf,dsC

1

12

2

3

Co-coherence value at zero frequencyDecaying tendencyPeak at lower frequency

Phase shift at zero frequency

Kanda’s modelSakamoto’s model

This research



st

2

H2

stH

t

221

12

f̂Uk

Df1f

f̂U

rfk2cosf

D

rkexpf,rC

Conclusions

1) Based on the categories of models and the divisions of zones, same as wind pressure coefficients, power and cross spectra were also investigated to show their various characteristics.

2) From the examination of cross spectrum characteristics, it was shown that various features occur when the two points of cross spectrum are located in different wind flow patterns.

3) A general co-coherence model was proposed by adding three parameters to the commonly used formula. From the approximation results, a uniform model for any location was shown to be insufficient.

Thank you very much for your listening.

The 2nd Cross-Strait Symposium on Dynamical Systems and Vibration13-19 December 2012