Extreme and spectrum characteristics of wind loads on super-large cooling tower under different four-tower combinations

Abstract

The wind loads distribution on the super-large cooling tower under the interference effect of tower group is very complicated. Particularly, energy distribution of fluctuation wind loads and extreme model is difficult to be predicted. However, accurate calculations of these two factors are the most direct ways for analysis of wind resistance dynamics of super-large cooling tower. The wind tunnel tests of the highest super-large cooling tower under five typical tower combinations (serial, rectangular, rhombus, L-shaped, and inclined L-shaped) with 320 working conditions were performed. On this basis, non-Gaussian and non-stationary properties of local wind pressure and overall force coefficient of super-large cooling tower were analyzed. Distribution laws of local wind pressure extremes and overall force coefficient extremes were discussed based on Hermite method and peak factor method. Key attention was paid to the mapping relationships of characteristic angles with local and overall aerodynamic force extremes. The effects of four-tower combination modes on fluctuation wind loads energy of super-large cooling tower were studied based on the power spectral density function, intrinsic mode function, and evolution power spectral density function. Besides, the estimation formulas of local wind pressure spectrum and overall pressure coefficient spectrum of super-large cooling tower under four-tower combination were proposed. It can be found that the extremes of local wind pressure and overall aerodynamic force could be predicted based on the linear relationship between characteristic angles and fluctuation wind loads. In addition, it is suggested to choose serial combination first, followed by inclined L-shaped, L-shaped, rhombus, and rectangular modes successively.

Keywords

cooling tower extreme characteristics four-tower combination spectrum characteristics wind tunnel test

Introduction

Many serious accidents represented by wind-induced collapses of cooling towers in Ferrybridge plant in 1965 and Adelman plant in 1973 have been occurred. Many studies on wind loads interface and dynamic amplification effect of cooling tower group have been reported (Ke et al., 2015; Portela and Godoy, 2005; Rajan et al., 2013; Sun and Gu, 1995). They all pointed out that amplification effect of wind loads and dynamic response of cooling tower caused by tower group interference is one of the main causes of wind-induced collapses. After these accidents were occurred, norms of all countries in the world (BS4485-4, 1996; GB/T 50102-2014, 2014; VGB-R 610Ue, 2005) were made standard and strict regulations on height and quantity of cooling tower in the combination were proposed. At present, four-tower combination is the most common in construction of super-large cooling tower (SLCT). As tower height exceeds code values continuously, the potential safety hazards of wind resistance of the structure are further enhanced (Busch et al., 2002; Kareem et al., 1989). This is the hotspot problem of wind engineering field. Relevant studies have both theoretical significance and practical application values.

With respect to wind effect of cooling tower, Niemann and Kopper (1998) discussed the average and fluctuation wind loads distribution laws of two-tower combination under different spaces based on a series of manometric tests. Based on the wind tunnel test, Orlando (2001) discussed variation laws of the interference factors of local average wind pressure and overall force coefficient in the two-tower combination under different relative positions of towers. Zhang et al. (2016) carried out a wind tunnel test of three-tower combination. Based on the test results, they discussed values of interference factor and the corresponding wind-induced responses of the three-tower combination. Chen (2013) performed a wind tunnel test of two rectangular four-tower combinations and discussed the variation laws of resultant force coefficient of the disturbed tower with wind angle. Ke et al. (2015) performed a wind tunnel test on pressure and air-induced vibration of the rigid body of the inclined L-shaped four-tower combination with considerations to terrain. The interference effect of the tower group and its influences on wind-induced stability of cooling towers were studied based on the resultant force coefficient. These studies are mainly based on simple tower combinations (two-tower or three-tower combinations) or tower combinations for specific engineering. No laws on the wind resistance of cooling towers which can be applied directly to four-tower combination have been formed. Recently, the wind resistance safety of four-tower combination is attracting more and more attentions with its wide applications in the heat-engine/nuclear power plants. Currently, the author has studied the interference effect of the overall wind loads under different four-tower combinations (Ke et al., 2017). The interference factor under different combinations was given based on the resultant coefficient. However, the influencing laws of four-tower combination modes on extreme characteristics and energy of wind loads still remain unknown.

Amplitude domain and frequency domain are effective ways to predict and understand the wind effect on large civil engineering structures (Kwon and Kareem, 2013; Spanos et al., 2017). Some scholars have made systematic studies on fluctuating characteristics of wind loads on single cooling tower surface (Viladkar et al., 2006; Wittek and Grote, 2015). Results demonstrated that the singularity of extreme wind pressure caused by non-Gaussian features of wind pressure may cause significant adverse effect on structural failures. Ke and Ge (2015) studied the distribution law of extreme wind pressure on single tower and the circumferential non-Gaussian regional division standards of the cooling tower. Cheng et al. (2015) studied the fluctuation wind pressure distribution pattern on the single tower based on field measurement and compared differences of wind pressure power spectra at different circumferential heights. As an important reference to calculate the wind-induced buffeting response of structures, the distribution pattern of wind pressure power spectra is closely related with the flow turbulence (Lin et al., 2005). The complicated fluid separation and secondary adhesion caused by different four-tower combinations may cause inevitable effects on wind pressure power spectra of SLCT.

In this study, a wind tunnel test based on the highest SLCT in the world under five typical four-tower combinations (serial, rectangular, rhombus, L-shaped, and inclined L-shaped) and 320 working conditions was carried out. Non-Gaussian and non-stationary features under local wind pressure and overall force coefficients were analyzed. The distribution laws of local wind pressure extreme and overall force coefficient extreme of SLCT under four-tower combinations were discussed. The influencing law of four-tower combinations on fluctuation wind load energy of SLCT was disclosed. On this basis, formulas for estimating the local wind pressure spectrum and overall force coefficient spectrum of SLCT under different four-tower combinations were proposed. Their accuracy and validity were verified.

Engineering background and typical four-tower combination

An SLCT (220 m) in inland China was chosen as the research object, which is the highest cooling tower in the world at present. The throat height and bottom diameter were 165 and 185 m, respectively. The tower shell was connected with the annular plate foundation by 64 pairs of X-shaped pillars. These pillars had rectangular sections and the annular plate used the cast-in-place reinforced concrete structure. This SLCT located in the B-type landform and the basic wind pressure was 0.5 kPa.

Five four-tower combination modes are widely used in large heat-engine/nuclear power plants, namely, serial, rectangular, rhombus, L-shaped, and inclined L-shaped modes (Ke et al., 2017). Therefore, a wind tunnel test of cooling tower based on these five typical combinations was implemented. In the test, common facilities of power plants (e.g. plants and chimney) were installed around SLCT to reflect surrounding interferences to SLCT in power plants. In this study, 2D which is widely used in actual engineering projects at present is used as the interval standard between towers, with D being the bottom diameter. Plane layout and position information under different combinations are shown in Figure 1.

Figure 1.

Layouts of four-tower combinations.

Wind pressure data source

The wind tunnel in the test used the atmospheric boundary layer wind tunnel (ABLWT) with reverse-flow rectangular section. In the test section, width and height were 5.0 and 4.5 m, respectively. The wind field was simulated according to B-type landform in China’s Architectural Structure Load Standards (GB 50009-2012, 2012). Simulation effects are shown in Figure 2. The wind field was simulated well, which could meet experimental results.

Figure 2.

Simulation of wind characteristics in ABLWT.

Considering the actual size of wind tunnel and four-tower combination in SLCT, the scale ratio of the wind tunnel test model was chosen 1:450. The experimental model was made of acrylic material in order to protect adequate rigidity and strength. A total of 12 × 36 wind pressure test points were set uniformly on the external surface of the cooling tower shell.

One generally accepted solution is to perform full-scale measurements in combination with wind tunnel model tests, and it seems that the two techniques usually agree well with each other. Same holds true in the field concerning wind effects on cooling towers. Pirner (1982) has described results of model and in situ tests on a cooling tower. It is shown that when certain conditions are preserved, agreement with the experiments is very good. Sun and Zhou (1983) have also compared the external pressure distributions obtained in full-scale study and in wind tunnel test. It is shown that the pressure distribution at large Reynolds number (Re) may be achieved at a smaller Re in wind tunnel test if the surface roughness of the model is increased appropriately. Besides the studies mentioned above, Niemann and Ruhwedel (1980) and Sollenberger et al. (1980) have also conducted researches based on field measurements of wind pressures on cooling towers earlier. The code curve (GB/T 50102-2014, 2014) was obtained on the basis of summarizing the above measured results (mostly based on the research of Sun and Zhou). A total of 10 roughness conditions were set in single-tower wind tunnel test to correct the Reynolds number effect. With the aid of sticking paper belts along the meridian direction and by adjusting the incoming flow velocity (10 m/s), the actual aerodynamic characteristics of the prototype SLCT were successfully re-simulated in the reduced-scale model with lower Re. The shape coefficient curve of throat is shown in Figure 3 and was compared with the code curve (GB/T 50102-2014, 2014). It can be seen that four layers of sticking paper belts can simulate the Reynolds number effect of SLCT well. The final simulation measures are shown in Figure 4.

Figure 3.

Comparison between wind tunnel tests and target curve.

Figure 4.

Diagram of simulation of Reynolds effect measure.

The fluctuation wind pressure curve and relative measurement curve of single tower in the wind tunnel test are shown in Figure 5 (Cheng et al., 2015; Ruscheweyh, 1975; Sageau, 1980; Sun and Gu, 1995). The circumferential fluctuation wind pressure distribution on cooling tower can be divided into three regions: downwind zone (0°≤ θ ≤ 40°), crosswind zone (40°≤ θ ≤ 120°), and leeward zone (120°≤ θ ≤ 180°). The crosswind zone is the region with the most violent fluctuation. The maximum wind pressure is achieved close to 80° and the wind pressure decreases sharply in the region of 100°–120°. Comparatively, the fluctuation wind pressure distribution law along the circumferential direction is consistent with measured curves in the world. Since fluctuation wind pressure distribution of cooling towers is closely related with local landforms, flow turbulence, surrounding interferences and section height, the fluctuation wind pressure which was gained in the wind tunnel test was valid.

Figure 5.

Comparison between fluctuation wind pressure of single tower and measurement data.

In each four-tower combination, a total of 16 wind direction degrees were set in the 360° range at an interval of 22.5°, and all working conditions of four SLCT were measured, with a total of 320 working conditions. The maximum blocking rate of four-tower combinations was 3.22%, which could meet the existing wind tunnel test standards (JSJ/T 338-2014, 2014).

Local extreme wind pressure and its power spectra

Extreme wind pressure

The wind pressure time-history curve on the throat leeside surface and its probability density curve under rectangular combination are shown in Figure 6. The variation trend of wind pressure time-history curve was extracted based on the multi-scale wavelet analysis technology. And the statistics on the skewness and kurtosis value of this wind pressure time-history curve are shown in Figure 6(b), which valued −1.19 and 5.09, respectively. It can be seen from Figure 6 that this time-history curve shows significant non-Gaussian features and certain non-stationary features. The skewness and kurtosis value of wind pressure signals at different measuring points under serial combination and inclined L-shaped combinations are relatively concentrated. Nearly 50% wind pressure signals under rectangular, rhombus, and L-shaped combinations were recognized as non-Gaussian signals. The proportion of non-stationary signals is far lower than that of non-Gaussian signals.

Figure 6.

Wind pressure time-history and the probability density curve: (a) time-history curve and (b) probability density curve.

Based on the above analysis, follow-up studies on wind pressure extremes are all based on Hermite extreme estimation methods with considerations to non-Gaussian features. Specific deduction process of this method is introduced in Kwon and Kareem (2011). Distributions of the maximum negative pressure extreme on SLCT under five combination (320 working conditions) are shown in Figure 7. Incoming flow angle has a decisive role to the maximum negative pressure extremes. The maximum negative pressure extreme under some specific working condition was only about −1.40. Serial combination and inclined L-shaped combination have the highest probability to occur at such conditions. Among five combinations, the negative pressure extremes under rectangular, rhombus, and L-shaped combinations are smaller than −3.40. The negative pressure extreme under the rectangular combination was the highest. The rhombus combination has the highest probability to develop strong suction pressure.

Figure 7.

Distributions of the maximum negative pressure extreme under different combinations: (a) serial, (b) rectangular, (c) rhombus, (d) L-shaped, and (e) inclined L-shaped.

Five four-tower arrangements are shown in Figure 8(a). The tower 1 and tower 2 were the fixed SLCT, which were viewed as the group A. Tower 3 and tower 4 were the group B. Clearly, relative position of Group A and Group B determines the difference of five kinds of arrangements. The included angle between the connection line from the center of Group A to the center of Group B and the X-axis is the characteristic angle of four-tower arrangements (α, the absolute value). In the L-shaped combination, α = 18°. Based on the maximum negative pressure extremes (EC_p) of SLCT under five arrangements, including 320 working conditions, there is a significant linear correlation between α and EC_p (Figure 8(b)). With the increase in α, the local negative extreme effect of the cooling tower group becomes more and more significant. This regression relationship can be expressed as

abs (\min (E C_{p})) = 3.06623 + 0.00595 α

(1)

Figure 8.

Correlation between the characteristic angle (α) and the maximum negative pressure extreme: (a) schematic diagram of characteristic angle and (b) linear relationship.

Distribution curves of extreme wind pressure coefficient at the throat under different five-tower combinations are given in Figure 9. It can be seen from Figure 9 that the extreme pressure of the five combinations in the windward region is close to each other. The distribution of extreme wind pressure coefficient of SLCT under different combinations is similar in the crosswind and leeward regions and is similar to the curve of average wind pressure coefficient given by the Chinese standard (GB/T 50102-2014, 2014). However, the five-tower combination form has significant impact on the amplitude of extreme wind pressure coefficient.

Figure 9.

Distribution curves of extreme wind pressure coefficient under five combinations.

With reference to the calculation formula of average wind pressure of cooling tower given by the Chinese standard (GB/T 50102-2014, 2014), the new one-dimensional estimation formula of extreme wind pressure coefficient for four-tower combination was proposed with the introduction of interference coefficient β. The formula is as follows

E C_{p} (θ) = β (\sum_{k = 0}^{m} a_{k} \cos k θ)

(2)

where θ is the circumferential angle of the local area (0 ≤ θ ≤ 360, unit °) and a_k is the fitting parameter of average wind pressure coefficient which can be found in the Chinese standard (GB/T 50102-2014, 2014). The interference coefficients β could be taken as 1.95, 2.35, 2.15, 2.10, and 2.00 under serial, rectangular, rhombic, L-shaped, and inclined L-shaped combining forms, respectively.

Wind pressure power spectrum characteristics

Power spectra of local wind pressure were obtained for 432 measure points on each of the 320 working conditions. Power spectra of wind pressure at different circumferential measuring points at throat height under typical combinations are shown in Figure 10(a). And the maximum negative pressure signal power spectra at different heights under the serial combination are shown in Figure 10(b). The wind pressure power spectrum (WPPS) statistically represents the energy distribution of a turbulent wind pressure among a range of scales or frequencies and depends mainly on fluctuations in the flow. Although WPPS at measuring points with different circumferential angles and different heights has different numerical values, it shows nearly consistent distribution trend. The maximum negative pressure signal at throat height can well represent local wind pressure spectrum characteristics under four-tower combinations

Figure 10.

Comparison of wind pressure power spectra at measuring points with different circumferential angles and heights: (a) different circumferential angles at throat and (b) different heights.

Local wind pressure spectra of each SLCT under five combinations are shown in Figure 11. It can be seen that the spectrum is sensitive to the mode of four-tower combination, but the variation with the relative position of the SLCT is not obvious. Values of local wind pressure spectra under serial combination and inclined L-shaped combination drop to a very low level quickly. However, spectral values under rectangular, rhombus, and L-shaped combinations maintain at a certain numerical value, emphasizing the influences of violent valley effect on surface turbulence energy of SLCT. Particularly, distinct narrow-band peak was even occurred in the high frequency due to vortex shedding for rhombic combination (Figure 11(c)). This might be because the vortex structure formed under serial and inclined L-shaped combinations is relatively superior and energy in the vortex is higher than those under rest combinations. Energies for vortex formation come from the flow field. Therefore, more energy in the flow field under serial and inclined L-shaped combinations could be consumed, resulting in a sharp reduction of local wind pressure spectrum in the middle- and high-frequency bands.

Figure 11.

Local wind pressure spectrum under different combinations: (a) serial, (b) rectangular, (c) rhombus, (d) L-shaped, and (e) inclined L-shaped.

To further analyze energy distribution of local wind pressure signals under four-tower combination, the maximum negative pressure extreme signal was decomposed into several orders of intrinsic mode functions (IMF components) from high frequency to low frequency. Each IMF was defined and distinguished according to delay between two adjacent extreme points of the signal and then decomposed through screening (Huang et al., 2003). Based on the empirical mode decomposition (EMD) method, signals C_p(t) could be decomposed into the sum of n IMF components and residues.

Decomposition of the maximum negative pressure signal under five combinations is shown in Figure 12. The vertical coordinate ranges of different IMF components were −0.5 to 0.5, and frequencies of IMF components decrease gradually. Obviously, four-tower combination can influence the fluctuating laws of IMF components. The vibration amplitude of IMF in middle- and high-frequency bands under rectangular, rhombus, and L-shaped combinations is significantly higher than those under serial and inclined L-shaped combinations. This reflects that the wind pressure signal on the SLCT surface has high energy in the middle- and high-frequency bands under this circumstance, which agree with distribution laws of WPPS.

Figure 12.

Maximum negative pressure signals and its IMF components: (a) serial and (b) rectangular.

A time-frequency analysis of the maximum negative pressure signal under different combinations was carried out based on the wavelet method. In this study, Morlet wavelet (Iyama and Kuwamura, 1999) with good locality in time domain and frequency was chosen as the base function of wavelet transformation. To increase calculation efficiency and protect validity of time-frequency analysis, the wavelet scale chose (1.5^0.008)^0.7–(1.5^0.08)²⁵⁰. The corresponding analysis frequency range was 0.0009–2.7709 Hz. The evolution power spectra of maximum negative pressure signal are shown in Figure 13. They depict variations in wind pressure energy on SLCT surface from time domain and frequency domain. Based on information of frequency domain, energies of the local wind pressure signal change violently, but frequency components change slightly. IMF which makes great contributions to wind loads energy has not changed significantly. The local wind pressure signal under four-tower combinations presents evolution characteristics of stationary frequency.

Figure 13.

Evolution power spectra of local wind pressures under different combinations: (a) serial and (b) rectangular.

Regression of WPPS

The nonlinear regression analysis of five typical combinations is conducted. Results demonstrated that the expression form of equation (4) has the best fitting effect and the analytic expressions of most fitted spectrum are shown in Table 1. The value of fitted spectrum measured is generally consistent with the measured spectrum. Besides, it can represent differences of local wind pressure spectra under different four-tower combinations

S (f) = b_{1} + b_{2} (\frac{\exp (b_{3} f) - 1}{b_{3}})

(3)

Table 1.

Fitting parameters of WPPS.

Fitting parameters	Serial	Rectangular	Rhombus	L-shaped	Inclined L-shaped
b₁	5.10952	4.17412	3.25795	2.77356	5.33251
b₂	−1.65563	−1.3134	−0.4682	−0.38524	−3.10556
b₃	−0.30292	−0.47205	−0.1741	−0.12614	−0.59013
Goodness of fit	0.9254	0.7795	0.8235	0.8738	0.9255

Overall force coefficient and its power spectrum

Overall force coefficient of SLCT

The resultant force coefficient can be used as the overall aerodynamic coefficient of SLCT. The time-history curve and probability density curve of resultant force coefficient agree well with standard Gaussian distribution (Figure 14). According to statistics on time-history curves of resultant force coefficient under more working conditions, the resultant force coefficient under combinations shows typical Gaussian distribution features. The resultant force coefficient under four-tower combinations (EC_T) could be calculated based on the peak factor method.

Figure 14.

(a) Time-history curve and (b) probability density curve of the resultant force coefficient.

The correlation between maximum resultant force coefficient extreme and the characteristic angle under five four-tower combinations show high linear correlation, and correlation coefficient is 0.94. The regression relationship is shown in equation (4)

\max (E C_{T}) = 0.93393 + 0.00125 α

(4)

Overall force coefficient power spectrum (OFCPS) characteristics

Power spectrum of overall force coefficient was obtained for 320 working conditions. The power spectra of resultant force coefficient of tower 2 under different wind angles in the rhombus combination are shown in Figure 15, and the wind angle of 247.5° is the working condition of the maximum resultant force coefficient. Wind angle can influence the distribution of power spectra of resultant force coefficient significantly. This is because different wind angles correspond to different fluctuating characteristics of incoming flows. The OFCPS contains energy over a wide frequency band and depends mainly on fluctuations in the approach flow. The OFCPS spectrum value under the maximum resultant force coefficient is higher than those under other working conditions, accompanied with obvious distinct narrow-band peak in the middle- and high-frequency bands.

Figure 15.

Power spectra of resultant force coefficient of the tower 2 under different wind directions.

The power spectra of resultant force coefficient under the working condition of maximum resultant force coefficient are used as OFCPS of four-tower combinations (Figure 16). Different from WPPS, spectra values under rhombus and inclined L-shaped combinations decline sharply in the middle- and high-frequency bands. It only maintains a certain value in wide frequency bands under the rectangular combination.

Figure 16.

OFCPS under different five combinations: (a) serial, (b) rectangular, (c) rhombus, (d) L-shaped, and (e) inclined L-shaped.

Regression of OFCPS

OFCPS estimation formulas under five combinations are gained from regression of equation (4). Fitting parameters are shown in Table 2. The fitting formula has high fidelity to the measured spectrum and verifies feasibility of the proposed estimation formula.

Table 2.

Fitting parameters of OFCPS.

Fitting parameters	Serial	Rectangular	Rhombus	L-shaped	Inclined L-shaped
b₁	0.55436	0.63654	0.64267	0.5592	0.40244
b₂	−0.21527	−0.13166	−0.22699	−0.0843	−0.1427
b₃	−0.38869	−0.26786	−0.39349	−0.13167	−0.35435
Goodness of fit	0.8919	0.7856	0.8039	0.7701	0.9209

Conclusion

The influencing laws of four-tower combinations on wind loads extremes and energy and corresponding prediction methods were discussed systematically in this article. It mainly involves wind tunnel test, non-Gaussian characteristics, extreme estimation, power spectrum analysis, time-frequency analysis, and regression analysis. Main conclusions could be drawn as follows:

Under different four-tower combinations, the characteristic angle (α) has an obvious linear correlation with the maximum negative pressure extreme and the maximum resultant force coefficient extreme. It can be used as an effective index of wind loads interference under four-tower combinations. On this basis, the mathematical calculation model of maximum negative pressure extreme and overall force coefficient extreme under four-tower combinations is proposed.

The evolution characteristics of local wind pressure signal of SLCT under four-tower disturbance are manifested as frequency stationary. The proposed estimation formulas of local wind pressure spectrum and overall force coefficient spectrum under four-tower combinations take the four-tower combinations into account. They have high prediction accuracy of differentiation and could provide scientific references to parameter values in wind loads design of the cooling tower group.

Local wind pressure signal of SLCT under four-tower combinations shows significant non-Gaussian characteristics. Non-Gaussian signals account for nearly 50%. Therefore, non-Gaussian characteristics shall be considered in estimation of local wind pressure extreme. But, the extreme of overall force coefficient of SLCT extreme could be estimated directly based on the peak factor method.

Four-tower combinations can influence the positive pressure extreme of SLCT slightly. The negative pressure zone close to the flow separating point is the main sphere of influence. The maximum negative pressure extremes under rectangular, rhombus, and L-shaped combinations are lower than −3.40. Such strong suction is most likely to occur on SLCT under the rhombus combination.

Value of the wind pressure spectra declines sharply to a very low level, while wind pressure signal under rectangular, rhombus, and L-shaped combinations still maintains high energies in the middle and high-frequency bands. Different from WPPS, although OFCPS has a distinct narrow-band peak in the middle and high-frequency bands, the OFCPS values under rhombus and L-shaped combinations drop sharply in the middle- and high-frequency bands. Only a certain numerical value in this frequency bands is maintained under the rectangular four-tower combination.

Footnotes

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This project is jointly supported by the National Natural Science Foundation (51878351, 51761165022 and U1733129), Jiangsu Province Outstanding Natural Science Foundation (BK20160083), high-level talent support project of “Six Talents Summit” in Jiangsu Province (JZ-026), and “Postgraduate Research & Practice Innovation Program of Jiangsu Province” (KYCX18_0244) and sponsored by QingLan Project, which are gratefully acknowledged.

References

Association of Consulting Engineers (1996) Water cooling towers. Part 4: Code of practice for structural design and construction. BS4485-4:1996, British Standard.

Busch

Harte

Kratzig

et al . (2002) New natural draught cooling tower of 200 m of height. Engineering Structures 24(12): 1509–1521.

Cheng

Zhao

(2013) Multiple loading effects on wind-induced static performance of super-large cooling towers. International Journal of Structural Stability & Dynamics 13(8): 1350039.

Cheng

Zhao

et al . (2015) Wind Pressures on a Large Cooling Tower. Advances in Structural Engineering 18(2): 201–220.

GB 50009-2012 (2012) Load code for the design of building structures (in Chinese).

GB/T 50102-2014 (2014) Code for design of cooling for industrial recirculating water (in Chinese).

Huang

Shen

Long

(2003) A new view of nonlinear water waves: the Hilbert spectrum. Annual Review of Fluid Mechanics 31(1): 417–457.

Iyama

Kuwamura

(1999) Application of wavelets to analysis and simulation of earthquake motions. Earthquake Engineering & Structural Dynamics 28(3): 255–272.

JSJ/T 338-2014 (2014) Standard for wind tunnel test of buildings and structures (in Chinese).

10.

Kareem

Cheng

(1989) Pressure and force fluctuations on isolated circular cylinders of finite height in boundary layer flows. Journal of Fluids & Structures 3(5): 481–508.

11.

(2015) Extreme wind pressures and non-Gaussian characteristics for super-large hyperbolic cooling towers considering aeroelastic effect. Journal of Engineering Mechanics: ASCE 141(7): 922.

12.

Zhao

et al . (2015) Stability and reinforcement analysis of super-large exhaust cooling towers based on a wind tunnel test. Journal of Structural Engineering: ASCE 141(12): 04015066.

13.

Wang

(2017) Interference Effect and the Working Mechanism of Wind Loads in super-large cooling towers under Typical Four-Tower Arrangements. Journal of Wind Engineering &Industrial Aerodynamics 170(1): 197–213.

14.

Kwon

Kareem

(2011) Peak factors for non-Gaussian load effects revisited. Journal of Structure Engineering, ASCE 137(12): 1611–1619.

15.

Kwon

Kareem

(2013) Comparative study of major international wind codes and standards for wind effects on tall buildings. Engineering Structures 51(2): 23–35.

16.

Lin

Letchford

Tamura

(2005) Characteristics of wind forces acting on tall buildings. Journal of Wind Engineering & Industrial Aerodynamics 93(3): 217–242.

17.

Niemann

Kopper

(1998) Influence of adjacent buildings on wind effects on cooling towers. Engineering Structures 20(10): 874–880.

18.

Niemann

Ruhwedel

(1980) Full-scale and model tests on wind-induced, static and dynamic stresses in cooling tower shells. Engineering Structures 2(2): 81–89.

19.

Orlando

(2001) Wind-induced interference effects on two adjacent cooling towers. Engineering Structures 23(8): 979–992.

20.

Pirner

(1982) Wind pressure fluctuations on a cooling tower. Journal of Wind Engineering and Industrial Aerodynamics 10(3): 349–359.

21.

Portela

Godoy

(2005) Shielding effects and buckling of steel tanks in tandem arrays under wind pressures. Wind & Structures an International Journal 8(5): 325–342.

22.

Rajan

Babu

Arunachalam

et al . (2013) Interference Factors for Natural Draught Cooling Towers Based on Wind Tunnel Experiments. Eighth Asia-pacific Conference on Wind Engineering: 490–498.

23.

Ruscheweyh

(1975) Wind loadings on hyperbolic natural draught cooling towers. Journal of Wind Engineering & Industrial Aerodynamics 1(5): 335–340.

24.

Sageau

(1980) Caractérisation des champs de pression moyens et fluctuants à la surface des grands aéroréfrigérants. La Houille Blanche 20(1–2): 61–67.

25.

Sollenberger

Scanlan

Billington

(1980) Wind loading and response of cooling towers. Journal of the Structural Division 106(3): 601–621.

26.

Spanos

Sun

Ning

(2017) Advantages of filter approaches for the determination of wind-induced response of large-span roof structures. Journal of Engineering Mechanics 143(9): 1–12.

27.

Sun

Zhou

(1983) Wind pressure distribution around a ribless hyperbolic cooling tower. Journal of Wind Engineering and Industrial Aerodynamics 14(1): 181–192.

28.

Sun

(1995) Interference between wind loading on group of structures. Journal of Wind Engineering and Industrial Aerodynamics 54(55): 213–225.

29.

VGB-R 610Ue (2005) Structural design of cooling tower- technical guideline for the structural design, computation and execution of cooling towers.

30.

Viladkar

Karisiddappa Bhargava

et al . (2006) Static soil–structure interaction response of hyperbolic cooling towers to symmetrical wind loads. Engineering Structures 28(9): 1236–1251.

31.

Wittek

Grote

(2015) Substitute wind concept for elastic stability of cooling tower shells. In: Proceedings of the materials and member behavior, Orlando, FL, 15–19 March, pp. 500–513.

32.

Zhang

Zhao

(2016) Interference effects on global wind loads and wind induced responses for group hyperboloidal cooling towers. Engineering Mechanics 33(8): 15-23. (in Chinese)