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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
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
Experimental setting and simulated turbulent flow
Wind pressure measurement devices
Transition characteristics of tubing
Fs=1000HzT=120sec
Experimental setting and simulated turbulent flow
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
Experimental setting and simulated turbulent flow
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
Zoning of domed roofs
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
Zoning of domed roofs
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
Zoning of domed roofs
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
No. of channelReduced frequency
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
Approximation model for power spectra
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
No. of channelReduced frequency
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
Approximation model for power spectra
17
Power spectra
0.1www
ffSw
ffSw
ffSw
ffS
wst
2w
ww2
s
ss2
t
tt2
p
p
Weighting for approximation
Approximation model for power spectra
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
Approximation model for power spectra
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
Approximation model for cross spectra
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
Approximation model for cross spectra
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
Approximation model for cross spectra
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
Approximation model for cross spectra
Approximation model for cross spectra
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
Approximation model for cross spectra
Approximation model for cross spectra
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