Abstract
As high-rise cooling towers are constantly emerging, wind effects on this kind of wind-sensitive structures have attracted more and more attention, especially in typhoon prone areas. Terrain Type B turbulent flow fields under the normal wind and typhoon are simulated by active wind tunnel technology, and rigid-pressure-measurement model and aero-elastic-vibration-measurement model of a large cooling tower are built. The stagnation point, peak suction point, separation point and leeward point of the throat position shell are selected to analyze pressure coefficient, probability distribution, peak factor, power spectral density and dynamic amplification factor under normal wind and typhoon. It is clarified that there exists a significant non-Gaussian characteristic under typhoon condition, which also exists in structural response level. Resonance response ratio of the total response is higher during typhoon condition. The maximum value of dynamic amplification coefficient under typhoon field is up to 1.18 times over that under normal wind. The findings of this study are expected to be of interest and practical use to professional and researchers involved in the wind-resistant designs of super-large cooling towers in typhoon prone regions.
Keywords
cooling towers; active wind tunnel; non-Gaussian characteristic; wind-induced vibration; dynamic amplification coefficient
The rapid development of economics, advances in construction materials and technologies continue to propel cooling towers to new heights and pose new design challenges for structural engineers. As an important part of the industrial cooling water cycle, cooling tower has been widely used, whose height has surpassed 200 m (in German, 2014) and 220 m (in China, 2019) in past decades. It is foreseeable that wind-resistant design of cooling tower as a large-span, high-rise, spatial, thin-walled structure is not an easy task since those structures are generally wind-sensitive due to the enhanced structural flexibility and stronger wind speed, particularly in typhoon prone regions. It is well known that strong typhoons, a rapidly rotating storm system with a low-pressure center, belong to most destructive natural disasters in the world.
Wind loads on large cooling towers are often considered as the predominant load among all potential loading combinations, such as weight, temperature, seismic action, uneven settlement, etc., during the whole life cycl
It is well known that wind characteristics of typhoon climate reported by ever-increasing amounts of observation data were obviously different from wind characteristic of normal wind, increasing boundary layer heigh
A large cooling tower located on the coast line of China is chosen as a case study and the wind field of a terrain Type B turbulent flow field was chosen as simulation target. Generally, the vertical variation of mean wind speed, which is mainly controlled by the evolution of upstream surface roughness, is considered to follow a power law (Eq.(1)) for strong winds in a neutrally-stable atmospheric boundary layer adapted into wind design guidance by most countrie
| (1) |
where
represents wind speed atz height,
the 10 m-height design wind speed, andαthemean wind profile index, which is 0.097 for typhoon and 0.15 for normal win
The fluctuating characteristics of wind employed in engineering applications are usually quantitatively represented by power spectrum density (PSD), turbulence intensity and turbulence integral scale. The turbulence spectrum was proved to follow the von Kármán model (Eq.(2)) in longitudinal direction by Cao et al
| (2) |
where
is the Von Karman spectrum function,
the frequency,
the wind speed,
the turbulence intensity, and
the turbulence integral scale of the along-wind direction. As compared by Kwon et al
| (3) |
where
and
represent the turbulence intensity in typhoon and normal wind, and
is 1.48 for terrain Type B suggested by Sharma and Richard
Turbulence integral scale is a measure of the size of energy-containing eddies that corresponds to the largest magnitude of the turbulence PSD. Because the PSD of strong typhoon winds is consistent with the commonly-used von K rm n model, it is reasonable to assume that the longitudinal turbulence integral length scale can be described by the code specifications. In this study, turbulence integral scale is chosen from the AIJ Code, Japa
| (4) |
where
is the turbulence integral scale and
the gradient wind height, which is 1 400 m for typhoon and 350 m for normal win
Synchronous pressure measurement tests were undertaken in 3-D multi-fan active control wind tunnel (
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Fig.1 Schematic of the 3-D multiple-fan wind tunnel
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Fig.2 Cobra probe placement during wind field measurement
The simulation results of mean wind speed, turbulence intensity and turbulence integral scale shown in
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Fig.3 Turbulence characteristics for a terrain Type B flow field under normal wind
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Fig.4 Turbulence characteristics for a terrain Type B flow field simulated under typhoon
| (5) |
wherea,b,c,m are fitting coefficients. According to turbulent energy spectrum theory proposed by Kolmogorof
| (6) |
| (7) |
A 1∶600 scaled rigid pressure measurement model and aero-elastic model were produced based on 215 m high cooling tower,which were used to record external wind pressure measurements and attain structural dynamic response. The shape of the cooling tower is shown in
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Fig.5 Geometric dimensions and layout of pressure taps on the cooling tower model
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Fig.6 Reynolds number effects simulation of experimental model
The aero-elastic models of large cooling towers were tested in the wind tunnel by Armit
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Fig.7 Aero-elastic model for simultaneous pressure and vibration measurement
Mode | 1 | 2 | 3 | 4 | |
---|---|---|---|---|---|
Prototype structure | Shape profile |
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Frequency / Hz | 0.84 | 0.88 | 0.99 | 1.01 | |
Aero⁃elastic model | Shape profile |
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Test frequency/ Hz | 20.43 | 21.70 | 24.64 | 25.19 | |
Design frequency & frequency error / % | (20.21, 1.12) | (21.14, 2.67) | (23.95, 2.80) | (24.57, 2.46) | |
Circumference & Meridian harmonic number | 4 & 2 | 5 &2 | 6 & 2 | 3 & 1 |
Model shapes of front four orders were attained from aero-elastic model are consistence with prototype structure’s model acquired by FEM calculation. The design deviation of the first mode is 1.12% and the damping ratio of the first-order mode is 3.1%, which satisfies the empirical damping ratio requirement of the concrete structur
Throat region is the adverse position in structural analysi
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Fig.8 Root variances and peak factors of wind pressure under normal wind and typhoon
Fig.8(b) shows peak factors calculated by Sadek-Simiu metho
It is well-known that aerodynamics assumes wind pressure generated by countless different scale point vortexes whose energy obeys stochastic process that is Gaussian process. When organized vortexes are of larger ratio among the various turbulence components, non-Gaussian phenomenon appears. To further analyze mechanism, it is necessary to research non-Gaussian phenomenon.
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Fig.9 Probability density distribution of four throat-region points under normal wind and typhoon
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Fig.10 Renormalized wind pressure spectrum in normal wind and typhoon
Fig.11 shows the renormalized structural displacement response spectrum of four points on the cooling tower shell at throat position. Stochastic fluctuation wind pressure leads to multi-order resonance modes excited, which is consistence with relevant research work based on field measurement and FEM calculatio
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Fig.11 Displacement spectrum of structural response
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Fig.12 Background and resonance response ratio of total response under typhoon and normal wind
Peak factors are similar in structural response level (Fig.13). Probability density distributions of structural displacement response of three throat-region points (Fig.14) under normal wind and typhoon are also analyzed. Except for the leeward point, wind-induced response generally obeys Gaussian distribution under normal wind. Non-Gaussian characteristic shows the separation point under typhoon condition.
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Fig.13 Peak factors of structural displacement response
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Fig.14 Probability density distributions of structural displacement response of three throat-region points under normal wind and typhoon
Structural response induced by stochastic fluctuation wind pressure is usually expressed by dynamic amplification coefficient
(Eq.(8)). The final design wind pressure can be quantified by Eq.(9) according to GLF metho
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Fig.15 Dynamic amplification coefficients under normal wind and typhoon
| (8) |
| (9) |
where
is the design wind pressure,
the circumferential wind pressure coefficients every height,
the interference coefficient,
the wind pressure profile,
the wind speed of 10 m height,
the dynamic amplification coefficient,
the mean response,
the peak factor, and
the total fluctuation response.From normal wind to typhoon states, the dynamic amplification coefficient value gradually increases. The amplification coefficients of four key points at throat position are shown in
Wind field | Stagnation point | Peak suction point | Separation point | Leeward point |
---|---|---|---|---|
Normal wind | 1.10 | 1.12 | 1.52 | 1.50 |
Typhoon | 1.22 | 1.27 | 1.80 | 1.61 |
Some conclusions from this investigation analyzing the wind pressure coefficients and structural response of a large cooling tower under normal wind and typhoon condition are reached as follows:
(1) Typhoon climate is be of stronger turbulence intensity and larger turbulence integral scale, up to 1.7 and 1.1 times than those under normal wind at the top of the cooling tower for a terrain Type B flow field. Moreover, the turbulence spectrum is lower from 0.01 Hz to 0.1 Hz and higher from 0.1 Hz to 1 Hz under typhoon.
(2) Model tests show that larger skewness and kurtosis for non-Gaussian wind pressure samples appear in the typhoon field, especially in the separation region. In accordance with the observation of non-Gaussian samples, the peak value of vortex component is higher under that of typhoon condition. It is indicated that free-stream turbulence affects the vortex energy component of signature turbulence resulting in more organized vortex formation.
(3) Resonance response component of the cooling tower is the dominant of total response. The ratio of resonance response is bigger under typhoon condition and significant amplification effect on some structural resonance modes appears through analyzing renormalized structural response spectrum. It shows that the amplification effects in structural response level under typhoon climate are notable.
(4) The dynamic amplification coefficient on structural displacement level under typhoon field is up to 1.18 times than that under normal wind. The maximum value of dynamic amplification coefficient is shown at the throat position, which belongs to the adverse zone. It is necessary to adopt reasonable amplification coefficient to conduct wind-resistant designs of super-tall cooling towers under typhoon prone regions.
Contributions Statement
Mr. XING Yuan designed the study, complied the models, conducted the analysis, interpreted the results and wrote the manuscript. Prof. ZHAO Lin, Dr. CHEN Xu, and Prof. GE Yaojun contributed to the discussion and background of the study.
Acknowledgements
The work was supported by the National Key Research and Development Program of China (Nos.2018YFC0809600, 2018YFC0809604) and the National Natural Science Foundation of China (No.51678451).
Conflict of Interest
The authors declare no competing interests.
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