Wind effects on two tandem cooling towers with spacing L * =1.5

Abstract

Two grouped cooling towers are widely constructed in China and around the world. The research on wind effects on two closely-spaced tandem large cooling towers is not only of practical significance in guiding related structural design, but can also helpfully fill up the scientific void of related fluid physics in trans-critical Reynolds number (Re) regime. Based on the engineering background of two 167-m height smooth-walled large cooling towers located at Peng-cheng electric power station in Xu-zhou City, China, the present study focuses on flow physics concerning two tandem cooling towers with spacing L^* = 1.5 (L^* = L/D, in which L is the spacing between the centers of the two cylinders and D is the diameter of the cylinder) at Re ≈ 6.5e7 employing both physical experiments (the full-scale measurement and the wind tunnel test) and numerical simulations. A data fusion approach is utilized to synthesize different schools of physical experimental data, and numerical analyses are undertaken to accurately reproduce the realistic flow pattern by calibrating the simulated wind load distributions to the physical experimental results. It is found that the fluid structure concerning the present case belongs to the bi-stable flow, for which the re-attachment phenomenon and the co-shedding phenomenon appear intermittently. Therefore, the dynamic structural responses to the corresponding periodic loadings should be checked by practicing engineers to prevent the resonance in structural design of two closely-spaced cooling towers.

Keywords

Cooling tower tandem cylinder wind load physical experiment numerical simulation

Introduction

Cooling towers are circular cylindrical shells typically constructed in electrical power plants. Because of their huge sizes and their comparatively weak resistance to external actions, cooling towers are usually prone to wind-induced damages. In history, there are some serious accidents of cooling towers’ collapses due to wind excitations, such as the infamous accident of the collapses of three cooling towers under a 20 m/s strong wind at Ferrybridge electrical power plant in Great Britain in 1965. Investigations of the accident suggest that a free-standing tower is likely to be able to stand the 20 m/s wind; however, the collapsed towers are in a tower group which consists of eight closely-spaced towers, and the interference effects from neighboring towers significantly amplified the wind effects on the collapsed towers. In this regard, interference effects should be responsible for the accident, and they deserve in-depth studies to avoid similar accidents in the future.

The simplest case of the grouped cooling towers with interference effects is the two tower group. With varied oncoming flow direction, two standard scenarios can be identified for the two grouped towers, i.e., the tandem arrangement and the side-by-side arrangement. According to Orlando (2001), comparing to the side-by-side arrangement, the interference effects are more significant for the tandem arrangement. In the tandem towers case, the downstream cylinder is utterly submerged in the wake of the upstream cylinder, and the influences of the downstream cylinder on the upstream one cannot be ignored as well. On the contrary, the side-by-side arrangement is comparatively close to the free-standing tower case with respect to the flow field around the structures if the spacing is not extremely small. Since a lot of work (Cheng et al., 2015, 2017a, 2017b, 2019a; Borri et al., 2011; Niemann and Propper, 1975; Niemann and Ruhwedel, 1980; Pirner, 1982; Ruscheweyh, 1975; Sollenberger and Scanlan, 1974; Sun and Zhou, 1983) has been dedicated to understanding the flow around a free-standing cooling tower, the side-by-side arrangement is not the focus of this study.

As stipulated in Chinese Codes of Practice (DL/T 5339-2006, 2006; GB/T 50102-2003, 2003; NDGJ5-88, 1989), the spacing between neighboring cylinders should be greater than L^* = 1.5 (L^* = L/D, in which L is the spacing between the centers of the two cylinders and D is the diameter of the cylinder) for arranging the two-grouped cooling towers at the design stage. Based on economical concern, the spacing between two-grouped cooling towers constructed in China was usually chosen to be L^* = 1.5. Flow fields of two tandem cylinders have been investigated earlier by some studies for the case of L^* = 1.5 (Alam, 2014, 2016; Alam et al., 2003). However, most of the related experiments are conducted in sub-critical Reynolds number (Re) regime (Re < 1e5), and the results so obtained might not be applicable to a trans-critical Re case for full-scale cooling towers (with Re > 3.5e6). With regard to the scientific void, measuring the wind effects on tandem cooling towers with L^* = 1.5 at high Re and analyzing the related flow field are indispensable.

In view of the above, this article focuses on wind effects on two tandem cooling towers and the related flow pattern at high Re. First, a full-scale measurement campaign is utilized to obtain the wind effects on a 167-m height cooling tower subjected to the inference of another tower located at the upstream/downstream position with spacing L^* = 1.5. Secondly, a corresponding wind tunnel pressure measurement experiment is carried out on rigid models with high Re effects simulation to supplement the data missed in the full-scale measurements. This is realized via effective data fusion of different schools of experimental results. The third, numerical analyses are undertaken to accurately reproduce the realistic flow pattern by calibrating the simulated wind load distributions to the full-scale data via changing the spacing between the two simulated objects in order to reveal the flow physics behind the phenomena observed. As no one has ever explored the flow case of two closely-spaced tandem circular cylinders in trans-critical Re regime, these works are undoubtedly of pioneering theoretical significance on the fluid physics of the flow around grouped circular cylinders at high Re.

Overview of full-scale measurement

A 167-m height smooth-walled cooling tower built at Peng-cheng electric power station in Xu-zhou City, China is chosen for full-scale measurements on which pressure transducers are arranged. To its south, an adjacent cooling tower of the same size was built with the spacing L^* = 1.5, and there was an industrial complex to its west (see Figure 1). To its north and east, there was no large interfering building, but a few mounds.

Figure 1.

Peng-cheng electric power station.

During the measuring tower’s construction in 2009, 36 transducers were evenly installed around the tower’s throat section at 130-m height. Besides, another transducer was arranged inside a cabin, which can provide static reference pressure for measurements. The full-scale measurement campaign started immediately after the cooling tower was constructed. From 2010 to 2015, 2-3 times of intensive tests were performed every year. In the huge amount of data measured, those obtained from Nov. 28, 2011 to Dec. 12, 2011 were found to be most representative. According to the daily prevailing wind direction measured from Nov. 28 to Dec. 12 in 2011, it was found that the oncoming flows were from due south and due north on Nov. 28 and Dec. 8, respectively (as shown in Figure 1(b)). These scenarios both represent valid cases of two tandem cooling towers, which are utilized for the following studies. Since wind directions for the 2 days were opposite, wind effects on both the upstream cylinder and the downstream cylinder were obtained for the case of two tandem cooling towers. However, since some transducers installed on the tower’s north surface are unfortunately found ineffective in use (see Figure 2), the data obtained on both Nov. 28 and Dec. 8 are both incomplete. Therefore, the present full-scale measurement results are additionally supplemented by some wind tunnel test data for the required research to take place (see section 5).

Figure 2.

Plan of pressure measurement points.

Full-scale measurement results

The mean wind pressure coefficients measured on actual Peng-cheng tower for both the upstream and the downstream cylinders in the two tandem tower case are shown in Figure 3. Since many transducers malfunction, pressure coefficients are only measured on around a half of the circle of the tower’s throat section. As most of the effective transducers are arranged on the south side, the information so obtained is complete on the windward side for the downstream cylinder and on the leeward side for the upstream cylinder. For the downstream cylinder, the mean pressure coefficient measured at the stagnation is around −0.2, which accords with the observation by Alam et al. (2003) on a similar case with L^* = 3.5 in subcritical Re regime. Besides, the mean coefficients are within the range [−0.5, 0] on one side in the windward region and within the range [−1, −0.5] on the other side. This indicates that the wind effects produced on the two sides separated by the along-wind axis on the downstream cylinder is noticeably asymmetric, probably due to the biased reattachment flow from the upstream cylinder. For the upstream cylinder, the mean coefficient measured at 90° is −1.5, which agrees with the free-standing tower case (Cheng et al., 2019b; Sun and Zhou, 1983). The values produced by most other transducers in the leeward region are at around −0.2, which accords with the observation made on the Maoming tower (Sun and Zhou, 1983), but different from those observed on the present measuring tower in the approximate free-standing cylinder case (side-by-side case) (Cheng et al., 2019b). As can be seen in Figure 3, some unexpected abnormal values are produced by a few transducers (such as the data measured at 130 and 160° on the upstream tower), which are therefore abandoned in processing the full-scale data in further studies.

Figure 3.

Mean wind pressure coefficients measured on location for two tandem tower case.

Overview of wind tunnel experiment

The full-scale scenarios of two tandem cylinders are reproduced in TJ-3 wind tunnel of Tongji University in Shanghai, China. The wind tunnel is a closed circuit rectangular cross-section wind tunnel, wherein the size of the test section is 15 m in width, 2 m in height and 14 m in length. The test wind speed can be continuously controlled in the 1.0 to 17.6 m/s range. The non-uniformity of the wind speed of the flow field in the test zone is less than 1%; the turbulence intensity is less than 0.5 %; the average flow deviation angle is less than 0.5°. Using spires and ground roughness blocks (see Figure 4(a)), the atmospheric boundary layer (ABL) flow field of countryside open terrain is simulated for the test based on the simulation targets (the empirical formulae reported by Simiu and Scanlan (1996)), as is shown by Figure 5. In Figure 5(a), the power spectral density is measured at 1 m height, and the simulated turbulence integral scale at that height is around 0.3 m. Both the test model and the surroundings are modeled on a geometric scale of 1:200 using synthetic glass (see Figure 4(b)).

Figure 4.

Model test scenario in TJ-3 wind tunnel.

Figure 5.

ABL flow field simulated for countryside open terrain in TJ-3 (H_G and U_G refer to the gradient height and the geostrophic velocity, respectively).

36 × 12 taps are arranged on 12 vertical sections and 36 horizontal circular directions for the pressure measuring tower model. DSM3000 electronic pressure scanners of Scanivalve Corp. are used to obtain the wind pressures on the tower surfaces. The signal data are acquired at a sample rate of 312.5 Hz, and the sample length is 6000 data at one tap in each run. According to Chen et al. (2024) and Liu et al. (2025), the Scanivalve pressure scanner employed has different kind of errors, in which the most significant one is the pressure measurement distortion due to the extremely long pressure tube length. Therefore, the distortion of pressure fluctuations caused by the long tubes is corrected using Fourier transform techniques to ensure a higher frequency response (see Dyrbye and Hansen (1997) for details). Besides, with a 1:200 length scaling for the wind tunnel model and the velocity used in the wind tunnel setting a velocity scaling of around 1:1, a time scaling 1:200 or frequency scaling 200:1 is set. Therefore, the 312.5 Hz sampling frequency for the wind tunnel test corresponds to 1.56 Hz in full scale, which well meets the requirement of being greater than the first a few natural frequencies of the structure. For each run, 6000 frames are collected corresponding to 19.2s time length in the wind tunnel test or 64 min in full scale which can fully cover the time length of most strong wind events.

With the aid of sticking paper belts along the vertical direction (Figure 6) and by adjusting the incoming flow velocity, the actual static characteristics of the prototype cooling tower at high Re are successfully simulated in the reduced-scale model with lower Re, which can be proved from a good fitting of mean wind pressure distributions at the free-standing towers’ throat sections based on the model test and the Code GB/T 50102-2003 (2003), respectively. The optimum simulation condition identified is a model with 36 one-layer (0.1 mm thickness) paper tapes and 10 m/s wind speed. The turntable rotates from 0° to 360° at 22.5° intervals, but only the cases with the same wind directions as that observed in the field on Nov. 28 and Dec. 8, 2011 is considered (see Figure 1(b)), so the wind effects obtained from the model test can fairly compare with the full-scale results.

Figure 6.

Pressure measurement model with vertical paper belts for high Re effects simulation.

Data fusion of results from different experiments

The wind tunnel test data measured around a half of three cross sections close to the throat height on the tower model (8th, 9th and 11th cross sections) are compared with the full-scale measurement data in Figure 7. As shown in Figure 7(a), the mean wind pressure distributions measured around the three cross sections on the tower model are close together when the model is located at the upstream position; however, they are noticeably different from the field measurement results in the side region of maximum suction (90–110°). It can be seen that the full-scale measurement data are around 0.7 smaller than the wind tunnel results in magnitude in the side region. In the leeward region (120–180°), the agreement between results from the two schools of experiments is very good. As shown in Figure 7(b), the full-scale data are a little bit smaller than pressure distributions measured around the 9th and the 11th cross sections on the tower model which is at the downstream position. The pressure coefficients measured around the 9th and the 11th cross sections fluctuate at around 0.35 in the full circumferential range. According to Cheng et al. (2024), beside the inherent technical issues with the ABL wind tunnel simulation technique (including the Re effects, the turbulent flow characteristics effects, and the non-stationarity effects) that could be responsible for the observed full-scale/model test discrepancies, the full-scale measurement performed is inherently less accurate and deterministic than the wind tunnel experiment it is supposed to validate, which could also be a significant cause of the full-scale/model test discrepancies observed.

Figure 7.

Wind effects on two towers in tandem case.

It is widely acknowledged that the wind tunnel data is generally complete in both time and space domains with clear rules of fluid physics shown; however, wind effects measured in the wind tunnel are less accurate than the full-scale measurement data. Good ways concerning the use of different physical experimental results are to synthesize different schools of data and to formulate universal empirical models of high theoretical significance accordingly (Cheng et al., 2024), including the data fusion approach which can be regarded as the practice of complementing the missing data in the full-scale measurement based on the pattern observed in the wind tunnel.

Deng et al. (2022) proposes a data fusion algorithm to synthesize the wind tunnel results and the full-scale measurement data for use, which is based on the gradient information. Using the method proposed by Deng et al. (2022) with its fundamental theories presented in Appendix, the full-scale measurement data and the wind tunnel data are synthesized to generate accurate wind loads on the two tandem towers (Figure 8). As can be seen, the two mean wind pressure distributions calculated by fitting the experimental data obtained via data fusion in accordance with the mathematical form of eight-termed Fourier series tend to be equalizing compared with the distribution measured on the free-standing tower by Sun and Zhou (1983), especially the pattern measured on the downstream cylinder. In Figure 8(a), the differences between the mean wind pressure coefficients measured on the upstream cylinder in the two tandem tower case and that measured on the free-standing tower appear to be significant: First, the value at stagnation is 0.45 smaller for the upstream cylinder than for the free-standing tower; Secondly, the occurrence position of the minimum negative pressure is 15° backward for the upstream cylinder; The third, the pressure coefficients in the wake zone are stabilized at a constant of −0.2 for the free-standing tower, while they fluctuate for the upstream cylinder. In Figure 8(b), the pressure coefficients on the fitted curve for the downstream cylinder in two tandem tower case are basically kept at the constant of around −0.5 throughout the circumferential range. According to Farell et al. (1976), equalized mean wind pressure distributions lead to reduced stresses in the shells in structural analyses. Therefore, it appears that the present structural design practice employing the pressure pattern obtained on a free-standing tower (DL/T 5339-2006, 2006; GB/T 50102-2003, 2003; NDGJ5-88, 1989) is more or less conservative for the structural design of two closely-spaced grouped cylinders against the wind action with respect to the tandem tower case.

Figure 8.

Data fusion results for two tandem towers in comparison to free-standing tower case.

Numerical analyses

Based on detailed physical experiments, Alam (2014) found that the spacing between cylinders and the Re were the two most significant parameters influencing the flow pattern around two tandem cylinders. With respect to the wind events concerning large cooling towers, the Re range for effective numerical analyses is generally two orders of magnitude smaller than that for full-scale scenarios. To accurately reproduce the flow around full-scale Peng-cheng tower on Computational Fluid Dynamics (CFD) platform, the spacing between the two tandem towers should be adjusted. In this portion of study, numerical analysis is undertaken to further explore the fluid physics behind the observations made in section 5 on Fluent 6.2.16 CFD platform. Multiple two-dimensional scenarios of two tandem circular bluff bodies with L^* = 1.5, 2.0, 2.5, 3 and 3.5 in a 15 m/s speed and 5% turbulence intensity velocity field are respectively simulated at sub-critical Re regime in order to identify the optimal spacing. The inlet boundary condition is the velocity-inlet type; the outlet boundary condition is the pressure-outlet type. Non-slip wall boundary condition is used for the bluff body surface. The wind field is assumed to be an incompressible flow field. Two equation k-epsilon viscous model is utilized. The pressure-velocity coupling equations are solved using SIMPLE method. Discretization of the pressure term is performed using the standard scheme. The first-order implicit unsteady formulation is used. The residual is set to 0.001; the time length 10s; the time step 0.1s.

With regard to the information concerning the mesh, the mesh size is 2.1 m for all cases, and mesh number 36,967. A plot for the mesh for the case of L* = 2.5 is shown in Figure 9. Via the grid checking, it is found that the mesh quality is good.

Figure 9.

Mesh for the CFD analysis for the case of L* = 2.5.

Through the numerical analyses, it is found that L^* = 2.5 should be the optimal spacing between the two tandem cylinders for reproducing the original wind event. This is because the simulated mean wind pressure distribution around the downstream cylinder in that case agrees comparatively well with the corresponding pattern from physical tests via data fusion in Figure 10. As can be seen in Figure 10, from the windward side to the leeward region, the mean wind pressure coefficient calculated on the downstream cylinder first slightly decreases, and subsequently mildly increases. It starts from 0 at the stagnation, then reaches the minimum of −0.5 at 80°, and finally stabilizes at around −0.05 in the leeward region.

Figure 10.

Mean wind pressure distributions on downstream cylinder obtained from CFD analysis for L^* = 2.5 and physical experiments for L^* = 1.5.

The time-averaged velocity and turbulence intensity contours calculated are presented in Figures 10 and 11, respectively. As can be seen in Figure 11, the velocity field around the upstream cylinder is similar to that around a free-standing tower (see Cheng et al. (2021)), in which the magnitudes are at low levels at the windward and the leeward regions and but high at side regions. For the downstream cylinder, the velocity magnitudes shown in Figure 11 are comparatively low almost around the circumferential range, which can well explain the observation made in Figure 10. With respect to the turbulence intensities, Figure 12 suggests that the magnitudes are high in wakes of both two cylinders; however, the magnitude of turbulence intensity is also comparatively high in front of the downstream cylinder, obviously due to the effects of the wake flow of the upstream cylinder.

Figure 11.

Velocity contour (unit: m/s; wind direction is from the left to the right).

Figure 12.

Turbulence intensity contour (unit: ‰; wind direction is from the left to the right).

Flow patterns for two tandem towers with spacing L^* = 1.5 at high Re

In history, many endeavors have been dedicated to understanding the flow around two tandem circular cylinders. At a determined Re, three main flow patterns were identified by Alam (2014) with the increase in the spacing between cylinders: the re-attachment flow, the bi-stable flow, and the co-shedding flow. When the spacing was very small, it was observed that the free shear layers separated from the upstream cylinder and re-attached on the downstream one, forming the re-attachment flow (see Figure 13(a)). When the spacing was very large, it was found that the shear layers did not re-attach, but rolled-up between the cylinders as well as in the wake, referred to as the co-shedding flow (see Figure 13(b)). When the spacing was in a medium range, re-attachment and co-shedding flows probably appeared intermittently, known as the bi-stable flow (see Figure 13(c)). Besides, the spacing regimes identified for the three flow patterns were totally different at different Re. For example, according to Alam (2014), the spacing regimes for the re-attachment flow, the bi-stable flow, and the co-shedding flow are L^* < 3.9, 3.9 < L^* < 4.2, and L^* > 4.2, respectively at Re = 6.5e4; while they are L^* < 3.5, 3.5 < L^* < 3.9, and L^* > 3.9, respectively at Re = 9.7e3.

Figure 13.

Flow structures for different spacing between cylinders (SP: separation point; RAP: re-attachment point; FSP: front separation point; BSP: back separation point).

To reveal the flow structure in the present case, the instantaneous vorticity contours calculated throughout the time length are checked one by one. It is found that during the majority of the duration, the contours reflect the co-shedding flow pattern, as the shear layer from the upstream cylinder does not re-attach on the downstream one, but rolls up between the cylinders (see cf. Figure 14(a)); however, in many equally-spaced local times, they suggest the re-attachment pattern, as the free shear layers separates from the upstream cylinder and re-attaches on the downstream one (see cf. Figure 14(b)). Basically, it can be identified that for the present flow event of two tandem circular cylinders with L^* = 1.5 in trans-critical Re regime, the flow structure is bi-stable. It is found that in both the transient states of the co-shedding flow and those of the re-attachment flow, the wind pressure distributions calculated around the two cylinders do not seem to lead to greater static structural responses compared with the pattern measured on a free-standing tower; however, the load patterns on the two towers alter periodically in accordance with the two flow structures. We will further validate these observations using other technical approaches, e.g., the particle image velocimetry experiment. If the bi-stable flow and the associated effects are confirmed experimentally, in future structural design of two tandem cooling towers, the dynamic structural responses to the corresponding periodic loadings with the dominant frequency of around 1 Hz should be checked by practicing engineers to prevent the possible structural resonances.

Figure 14.

Representative vorticity contours (unit: Hz; wind direction is from the left to the right).

Conclusions

The main findings of this study concerning wind effects on two tandem cooling towers with spacing L^* = 1.5 and related flow physics are summarized below:

(1) To effectively utilize both full-scale measurements and wind tunnel tests in wind engineering, data fusion can be attempted to synthesize different schools of physical experimental data. The present study indicates the validity of the data fusion method proposed by Deng et al. (2022) in pressure measurement tests.

(2) In tandem scenario, wind loads on two closely-spaced large cooling towers basically lead to less significant static structural responses compared with the design load according to the Chinese standards which is based on the free-standing tower case.

(3) The present study identifies the flow event of two tandem circular cylinders with L^* = 1.5 in trans-critical Re regime to be the bi-stable flow. Therefore, the dynamic structural responses to the corresponding periodic loadings should be one of the engineers’ concerns in structural design of two closely-spaced cooling towers. Initially, the motivation of the present study is on fluid physics aspect. However, on engineering application level, no one has ever identified the periodic dynamic loadings on the two tandem towers due to the formation of the bi-stable flow as the present works have done, which are also of noticeable significance in leading engineers to more safe structural designs. Therefore, the scientific interests of the present research become twofold.

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: The authors gratefully acknowledge the financial supports from the National Natural Science Foundation of China (Grant No. 51908124), the China Postdoctoral Science Foundation (Grant No. 2016M601793) and the State Grid Corporation of China.

ORCID iD

Xiao-Xiang Cheng

Theories of the data fusion method proposed by Deng et al. (2022)

The present study uses the data fusion method proposed by Deng et al. (2022) based on the gradient information, whose theories are as follows. Supposing samples S from wind tunnel tests are in m×n domain with their values Y and first derivatives $\frac{\partial Y}{\partial S}$ below: (1)

{\begin{cases} S = [\begin{array}{l} x_{1}^{(1)} & \dots & x_{1}^{(n)} \\ ⋮ & ⋮ \\ x_{m}^{(1)} & \dots & x_{m}^{(n)} \end{array}] \in R^{(m \times n)} \\ Y = [\begin{array}{l} y_{1}^{(1)} & \dots & y_{1}^{(n)} \\ ⋮ & ⋮ \\ y_{m}^{(1)} & \dots & y_{m}^{(n)} \end{array}] \in R^{(m \times n)} \end{cases}

(2)

\frac{\partial Y}{\partial S} = [\begin{array}{l} \frac{\partial Y}{\partial x_{1}^{(1)}} & \dots & \frac{\partial Y}{\partial x_{1}^{(n)}} \\ ⋮ & ⋮ \\ \frac{\partial Y}{\partial x_{m}^{(1)}} & \dots & \frac{\partial Y}{\partial x_{m}^{(n)}} \end{array}] \in R^{(m \times n)}

and

f (S_{h 0})

and

f (S_{h})

are the sample obtained via full-scale measurements at position

S_{h 0}

and the value to be predicted at position

S_{h}

, respectively, equations (3) and (4) can basically be used to achieve the data fusion. (3)

f (S_{h}) = f (S_{h 0}) + \frac{\partial Y}{\partial S} (S_{h} - S_{h 0})

(4)

{\frac{\partial Y}{\partial S} |}_{(S = S_{h 0})} = {\frac{f (S + Δ S) - f (S - Δ S)}{2 Δ S} |}_{(S = S_{h 0})}

Due to the fact that various predicted values of

f_{i} (S_{h})

can be obtained via equations (3) and (4) using different

f_{i} (S_{h 0})

, equation (5) can be used to calculate the ultimate predicted value

f_{k} (S_{h})

at position

S_{h}

, in which

d_{i}

is the distance between

S_{h}

and

S_{h 0}

. (5)

{\begin{cases} w_{i} = \frac{1 / d_{i}}{\sum_{i = 1}^{n} 1 / d_{i}} \\ f_{k} (S_{h}) = \sum_{y = 1}^{n} w_{i} f_{i} (S_{h}) \end{cases}

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Wind effects on two tandem cooling towers with spacing L * =1.5

Abstract

Keywords

Introduction

Overview of full-scale measurement

Full-scale measurement results

Overview of wind tunnel experiment

Data fusion of results from different experiments

Numerical analyses

Flow patterns for two tandem towers with spacing L* = 1.5 at high Re

Conclusions

Footnotes

Declaration of conflicting interests

Funding

ORCID iD

Theories of the data fusion method proposed by Deng et al. (2022)

References

Flow patterns for two tandem towers with spacing L^* = 1.5 at high Re