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The 2nd Cross-Strait Symposium on Dynamical Systems and Vibration13-19 December 2012Spectrum Characteristics of Fluctuating Wind Pressures on Hemispherical DomesYuan-Lung Loren LoChung-Lin FuChii-Ming ChengDept. Civil Eng., Tamkang University, TaiwanBackgroundSince 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 structureFor a curved structureRoughness on the surfaceOncoming wind speedFlow viscosity Geometric appearance

12This research intends to investigate spectrum characteristics of wind pressures on dome structures and intends to provide a general model for practical applications.

Cylinder heightRoof height

Wind Tunnel Test

simplifyingEvaluating pressuresEvaluating responseObjectiveExperimental setting and simulated turbulent flow

Zoning of domed roofs

Approximation model for power spectra

Approximation model for cross spectra

ConclusionsPresentation content

UG: mean wind speed at boundary layer heightUG=5.9m/sec and 11.1m/secUrban terrain is attempted.Experimental setting and simulated turbulent flowExperimental setting and simulated turbulent flow

where(-): gamma function; : shape parameter;L(z): length constant.=2: Karman-type spectrum

Power spectra of oncoming winds

Experimental setting and simulated turbulent flowWind pressure measurement devices

Transition characteristics of tubingFs=1000HzT=120secExperimental setting and simulated turbulent flowAcrylic domed modelsD = 300mmf/D (roof height to span)0.00.10.20.30.40.5h/D(cylinder height to span)0.0NoneB0C0D0E0F00.1A1B1C1D1E1F10.2A2B2C2D2E2F20.3A3B3C3D3E3F30.4A4B4C4D4E4F40.5A5B5C5D5E5F535 domed models for wind pressure measurementsHowever, only f/D=0.5 is discussed in this presentation!

DfhxzxyExperimental setting and simulated turbulent flowReynolds number ranges

For UG=11.1m/secUH = 5.1m/sec ~ 7.5m/secRe = 1.06105 ~ 1.56105Re: Reynolds number : air density;UH: mean wind speed model heightD: model span (300mm): viscosity constantAccording 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

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 roofsContours of Cp,meanf/D=0.5

h/D=0.0h/D=0.1h/D=0.2h/D=0.5Top ViewSide ViewZoning of domed roofsContours of Cp,RMSf/D=0.5

h/D=0.0h/D=0.1h/D=0.2h/D=0.5Top ViewSide ViewZoning of domed roofs

fhxzDf/D=0.5Cp,mean along meridianf/D=0.5Cp,RMS along meridianf/D=0.5Side ViewZoning of domed roofsCorrelation coefficientsf/D=0.5

h/D=0.0h/D=0.1h/D=0.2h/D=0.5Side ViewPower spectra

Ch.1Ch.2Ch.3Ch.29f/D=0.5h/D=0.0fD/UH

WindwardSeparationWakeApproximation model for power spectraWindSide View15Power spectra

f/D=0.5h/D=0.0

Ch.5

Velocity-pressure admittanceKarman velocity spectrumApproximation model for power spectra16Power spectra

f/D=0.5h/D=0.0

Ch.26Ch.15

Approximation model for power spectra

17Power spectra

Weighting for approximationApproximation model for power spectraWindSide View18Power spectra

Ch.25

Weighting for approximationDistribution of weighting factors for typical power spectrum model shows the variation of turbulence energyFor f/D=0.5 h/D=0.0Approximation model for power spectraCross spectrum characteristics of two fluctuating wind pressures are concerned when integrating wind loads over certain area or the whole surface of the roof.

F0 (f/D=0.5, h/D=0.0)Cross spectraApproximation model for cross spectraCo-coherenceRoot-coherencePhaseSide ViewWindApproximation model for cross spectraCross spectra

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

Ch.3 Ch.4Ch.3 Ch.5

Ch.10 Ch.12

Ch.16 Ch.1734510121617

Ch.22 Ch.23Ch.25 Ch.2722232527Side ViewWindApproximation model for cross spectraCross spectra

F0 (f/D=0.5, h/D=0.0)781017

Ch.7 Ch.10Ch.8 Ch.17

Ch.9 Ch.23Ch.18 Ch.249182324

Ch.3 Ch.21Ch.2 Ch.26232621Side ViewWindApproximation model for cross spectra

Ch3-Ch4Ch3-Ch5Ch18-Ch19Ch7-Ch10Ch7-Ch18Ch7-Ch27345710181927WindwardSeparationWakeCross spectrum featuresGenerally, 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 ViewApproximation model for cross spectraApproximation model for cross spectraTo approximate root-coherences and phases, Ogawa and Uematsu have applied the following expression.

11223Co-coherence value at zero frequencyDecaying tendencyPeak at lower frequencyPhase shift at zero frequencyKandas modelSakamotos modelThis researchApproximation model for cross spectraApproximation model for cross spectra

ConclusionsBased 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.

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.

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 2012Baratron sensor

Pressure Calibration Unit

Power Unit

Pressure Sensor Unit

Simultaneous Sampling Unit

Sensor Connector

Data Acquisition Unit

Monitor

Keyborad

Mouse

Speaker

Base sensor

1

Atmospheric pressure

Pitot tube - dynamic

Pitot tube - reference

3

2

Audio Amplifier

Base Sensor Amplifier

Sine Wave Generator