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Case Study of Wind⁃Induced Vibration of a Cooling Tower Under Typhoon Environment  PDF

  • XING Yuan 1
  • ZHAO Lin 1,2
  • CHEN Xu 1
  • GE Yaojun 1,2
1. State Key Lab of Disaster Reduction in Civil Engineering, Tongji University,Shanghai 200092,P.R. China ; 2. Key Laboratory of Transport Industry of Wind Resistant Technology for Bridge Structures, Tongji University,Shanghai 200092,P.R. China

CLC: TU33

Pubdate:2020-03-30

DOI:http://dx.doi.org/10.16356/j.1005-1120.2020.01.010

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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.

0 Introduction

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 cycle[

1]. In 1965, three cooling towers in the leeward region of a rhombic arrange with eight-tower two-column type collapsed under only a moderate wind speed with five-year return period in Ferrybridge Power Plant, UK and significant vibration phenomenon was reported[2]. Since then, in-situ measurements and wind tunnel tests were performed to research wind pressure characteristics over the surface of cooling towers[3,4,5,6,7,8,9]. Investigations focusing on wind-induced stochastic dynamic response for shell structures[10,11,12,13,14,15,16] were also conducted.

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 height[17,18]and enhancing turbulence gust factor value and turbulence intensity[19,20]. Zhao et al.[8] found turbulence intensity had an significant impact on fluctuation wind pressure of cooling towers. Based on in-site measurement for super-tall buildings, Zhang et al.[21] reported significant non-Gaussian characteristic under typhoon environment. Ke et al.[15] found that the non-stationary model can better characterize the measured wind-induced responses of a super-large cooling tower. Based on the early cooling tower elastic model wind tunnel test, the dynamic stress and static stress of the cooling tower under the wind load had the same magnitude, and the resonance effect increased according to the fourth power of the wind speed, which was much higher than the quasi-static stress growth rate[

1]. Winney[10] reported the notable resonance effect through field measurement. Furthermore, Jeary et al.[22]measured the 126.31 m high cooling tower in a typhoon environment with a resonance response at a maximum gust condition of 6 m/s. The influence mechanism of the typhoon climatic on structural response is complicated due to its special characteristics. So, it is necessary to further systematically study the wind pressure characteristic and structural response of cooling towers under typhoon as a structural design reference. Compared with in-sit measurement, wind tunnel test is a feasible way to research typhoon-induced adverse effect with the development of active wind tunnel test technology[23,24,25].

1 Overview of Wind Tunnel Tests

1.1 Wind field simulation

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 countries[26]. In order to attain mean wind profile indexα, a large number of direct observations of typhoon vertical profiles had been conducted and Monte-Carlo numerical simulation was performed. More attention is paid on structural wind loads and response in this paper. So, the simulation results are shown directly.

U ( z ) = U ( 10 ) z 10 α
(1)

where U ( z ) represents wind speed atz height, U ( 10 ) the 10 m-height design wind speed, andαthemean wind profile index, which is 0.097 for typhoon and 0.15 for normal wind[27], respectively.

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.[25], Masters et al.[28] and Balderrama et al.[29].

S u ( f ) = 4 I u T 2 L u x U 1 + 70.8 f L u x U 5 6
(2)

where S u is the Von Karman spectrum function, f the frequency, U the wind speed, I u T the turbulence intensity, and L u x the turbulence integral scale of the along-wind direction. As compared by Kwon et al.[30], in most codes or standards, turbulence intensity profile is also expressed in terms of a power law as

I u T ( z ) = c T I u ( z ) = c T I u 10 z 10 α
(3)

where I u T ( z ) and I u ( z ) represent the turbulence intensity in typhoon and normal wind, and c T is 1.48 for terrain Type B suggested by Sharma and Richards[20]. Correspondingly, I u 10 = 0.14 as recommended by the China national code[27].

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, Japan[31] (Eq.(4)),shown as

L u x = 100                   z 30   m 100 × z 30 0.5      30   m < z < H G
(4)

where L u x is the turbulence integral scale and H G the gradient wind height, which is 1 400 m for typhoon and 350 m for normal wind[27], respectively.

Synchronous pressure measurement tests were undertaken in 3-D multi-fan active control wind tunnel (Fig.1) consisting of 99 independent fans in Miyazaki University, Japan. This wind tunnel is an open-circuit one with 99 fans of 270 mm in diameter at the front. The fans are arranged in a 9 wide by 11 high matrix. The test section is 15.5 m length, 2.6 m width, and 1.8 m height. The spatial distributions of some turbulent parameters, such as mean velocity, turbulent intensity, integral scale, power spectrum and Reynolds stress, etc. have been successfully reproduced in the wind tunnel[23,24,32,33]. In order to attain simulated wind field characteristic of the Type B ABL turbulent flow field, Cobra probes placed on a height-moveable bracket (Fig.2) were chosen to measure wind velocity time history which was sampled every 5 cm-height interval (about 30 m height corresponding to prototype) with 1 000 Hz sampling frequency.

Fig.1 Schematic of the 3-D multiple-fan wind tunnel

Fig.2 Cobra probe placement during wind field measurement

The simulation results of mean wind speed, turbulence intensity and turbulence integral scale shown inFig.3 andFig.4 were closed to targets successfully. ComparingFig.3(a) withFig.4(a), stronger turbulence intensity and larger turbulence integral scale were formed in typhoon field up to 1.7 and 1.1 times than those in normal wind field at 36 cm height (the top of the cooling tower). What’s more, the renormalized fluctuation wind speed spectrums of the downwind direction at 36 cm height during the typhoon approximately follows the von K‌ ‌rm‌ ‌n spectrum consistence with references by Tamura et al.[34] and Cao et al.[25], which were fitted by Eq.(5). It is clear fromFig.3(b) andFig.4(b) that the turbulence spectrum is lower from 0.01 Hz to 0.1 Hz and higher from 0.1 Hz to 1 Hz under typhoon.

Fig.3 Turbulence characteristics for a terrain Type B flow field under normal wind

Fig.4 Turbulence characteristics for a terrain Type B flow field simulated under typhoon

n S u ( n ) / σ 2 = a f z r / ( 1 + b f z 1 / m ) c m
(5)

wherea,b,c,m are fitting coefficients. According to turbulent energy spectrum theory proposed by Kolmogoroff[35],c andr obey Eq.(6), furthermore,ris 1 andc is 5/3 in general;nis the frequency and σ the sampling time variance. And f z is reduced frequency following Eq.(7).

c - r = 2 / 3
(6)
f z = n z / U ( z )
(7)

1.2 Test models

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 inFig.5(a), whose height is 215 m and in whichZ, Randt represent height, radius and thickness, subscripts H, T, S and B represent top, throat, inlet and bottom of the tower shell. The rigid model was designed with 36×8 external pressure measurement taps uniformly distributed along the circumferential and meridian directions, respectively. The distribution of the taps (and number) around the circumferential section is shown inFig.5(b), where Sec represents the measured section, ande,krepresent height and width of roughness elements, respectively. Wind pressure was measured using a DSM3000 electronic pressure scanning valve (Scanivalve Company) with a sampling frequency of 500 Hz. A total of 30 000-point data were produced at one measurement point during each run. The Reynolds number (Re) regime for flow around the prototype large cooling towers was 1.5×108—3.5×108 based on the design wind speed. Due to size limitations of the test model, realistic wind effects for a highRe cannot be easily reproduced by increasing the test wind speed and the model size. However, wind flow around a cylinder does not only depend on theRe number, it is also closely related to the surface roughness of the cylinder. Previous investigations[36,37]have shown that wind effects on a cylinder with a highRe number effect can be reproduced on a scale model by increasing the surface roughness of the model. After comparing several types of surface roughness, attaching 36 uniformly distributed four-layered vertical paper tapes (Fig.5(b)) with a specific test wind speed was identified to be the optimal approach to compensate the effects of a post criticalRe number. The simulation criteria involve the mean and fluctuation wind pressure distributions (Fig.6). InFig.6, RE is the roughness element height.

Fig.5 Geometric dimensions and layout of pressure taps on the cooling tower model

Fig.6 Reynolds number effects simulation of experimental model

The aero-elastic models of large cooling towers were tested in the wind tunnel by Armitt[

1], Isyumov et al.[38] and Zhao et al.[39] in previous studies. Design methods of the aero-elastic model mainly consist of the continuous medium method and the equivalent beam-net method. Our previous research indicated that the former was suitable for destructive tests of cooling towers, and the latter could be used to study on wind-induced responses of cooling towers[12,39]. In this study, we mainly focus on the structural vibration response induced by various wind field, so the aero-elastic model is designed through an equivalent beam-net method. Limited to research subject of this article, the detailed design and produce process of aero-elastic model can be found in Ref.[39]. The aero-elastic model is shown inFig.7 and dynamic characteristics of the aero-elastic model are shown inTable 1.

Fig.7 Aero-elastic model for simultaneous pressure and vibration measurement

Table 1 Mode shapes and dynamic characteristics of the design model and prototype structure
Mode1234
Prototype structure Shape profile
Frequency / Hz 0.84 0.88 0.99 1.01
Aero⁃elastic model Shape profile
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 structure[27]. Reynolds number effects simulation was also performed. The simulation method is introduced in Section 1.1 in detailed.

2 Wind Pressure Characteristics for a Cooling Tower

Throat region is the adverse position in structural analysis[13], so wind pressure coefficients and structural response of throat position shells are paid more attention in the following analysis. It is clear fromFig.8(a) that fluctuation wind pressure coefficients under Typhoon are significantly higher than those of normal wind, because stronger turbulence intensity and larger turbulence integral scale, up to 1.5 and 1.2 times separately. Sadeh et al.[40] thought turbulence vortex of free-stream turbulence attain energy from some particular signature scale turbulence vortex, which was called vortex amplification theory. Based on filed measurement and wind tunnel test, Zhao et al.[8] found that fluctuation wind pressure is positively correlated with turbulence intensity further, thus illustrating this amplification effect.

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 method[41] which is suitable to non-Gaussian wind pressure samples[9,21]. Peak factors are bigger from 0° to 60° zone, while appearing opposite phenomenon from 75° to 135° region. There is no obvious relationship between the magnitude of turbulence intensity and the peak factor, which was also reported by Cheng et al.[9].

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.Fig.9 shows probability and statistical characteristics of wind pressure coefficients of four key points including the stagnation point (0˚), the peak suction point (70˚), the separation point (120˚) and the leeward point (180˚). No matter which kind of wind field is in the test, wind pressure coefficients of the stagnation point and the leeward point are close to Gaussian distribution. However, significant skewness and kurtosis appear in the separation point caused by separation vortex and it is crucial that typhoon obviously emphasize this phenomenon.Fig.10 shows renormalized power spectrum of peak suction point and separation point. there is a peak value around 5 Hz (separation vortex frequency) and the peak value is higher during typhoon, because free-stream turbulence affects the vortex energy component of signature turbulence resulting in more organized vortex formation. Typhoon gives rise to significant amplification effect on wind pressure load.

Fig.9 Probability density distribution of four throat-region points under normal wind and typhoon

Fig.10 Renormalized wind pressure spectrum in normal wind and typhoon

3 Wind⁃Induced Performance

3.1 Structural response analysis

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 calculation[10,12]. The resonance responses of the first, second and fifth modes are more appearance at typhoon condition, while the resonance responses of the third and eighth modes are less. Fig.‌12 is background and resonance response ratio of total response under typhoon and normal wind. The resonance response ratio of total response of the stagnation point is the highest. The resonance response ratios of all points are amplified under typhoon condition. it is can be considered that wind pressure distribution formed by more organized vortex in typhoon field is easier to excite resonance response.

Fig.11 Displacement spectrum of structural response

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.

Fig.13 Peak factors of structural displacement response

Fig.14 Probability density distributions of structural displacement response of three throat-region points under normal wind and typhoon

3.2 Amplification effect

Structural response induced by stochastic fluctuation wind pressure is usually expressed by dynamic amplification coefficient β (Eq.(8)). The final design wind pressure can be quantified by Eq.‌(9) according to GLF method[42]. Fig.‌15 shows the dynamic amplification coefficients under normal and typhoon. Dynamic amplification coefficient is up to the maximum value in the throat position in two kinds of environments, since resonance response ratio could reach the largest around circumferential angles (Fig.‌12(b)).

Fig.15 Dynamic amplification coefficients under normal wind and typhoon

β = R ¯ + g P g σ R ¯
(8)
ω ( z , q ) = β C p ( q ) F I μ ( z ) ω 10
(9)

where ω ( z , q ) is the design wind pressure, C p ( θ ) the circumferential wind pressure coefficients every height, F I the interference coefficient, μ ( z ) the wind pressure profile, ω 10 the wind speed of 10 m height, β the dynamic amplification coefficient, R ¯ the mean response, g P the peak factor, and σ 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 inTable 2. The maximum value is 1.80 under typhoon field and the maximum value is 1.52 under normal climate.

Table 2 Amplification coefficients of key points at throat position
Wind fieldStagnation pointPeak suction pointSeparation pointLeeward point
Normal wind 1.10 1.12 1.52 1.50
Typhoon 1.22 1.27 1.80 1.61

4 Conclusions

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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