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Comparison of comprehensive stress performances of super-large cooling tower in different four-tower arrangements under 3D asymmetric wind loads
Journal of Wind Engineering & Industrial Aerodynamics 179 (2018) 158–172
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Comparison of comprehensive stress performances of super-large cooling tower in different four-tower arrangements under 3D asymmetric wind loads Shitang Ke a, b, *, Hao Wang a, Tongguang Wang a, Yaojun Ge b a b
College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China State Key Laboratory for Disaster Reduction in Civil Engineering, Tongji University, Shanghai, 200092, China
A R T I C L E I N F O
A B S T R A C T
Keywords: Four-tower arrangement Super-large cooling tower Wind tunnel test Wind-induced response Local stability Buckling stability Ultimate bearing capacity
Different four-tower arrangements have a great impact on wind-induced response and stability performance of super-large cooling tower. However, a single indicator (eg., interference factor of overall wind load) cannot provide a comprehensive and objective evaluation of wind-resistance safety of cooling tower. Here five typical four-tower arrangements in engineering practice were experimented, namely, row, rectangular, rhombic, L-shape, and oblique L-shape arrangement. Wind tunnel tests for rigid body were performed to determine the wind loads distribution pattern on the surface of group tower under different four-tower arrangements. Finite element method was employed to analyze the internal force and deformation distributions under the design wind load of return period. The influence of different four-tower arrangements on wind load-induced response was discussed under different incoming wind angles. Then the local stability and overall buckling stability of the cooling tower were estimated, and the ultimate bearing capacities under different four-tower arrangements were compared considering geometric nonlinearity. Instead of using a uniform structural design standard for cooling towers group, the influence rule of different arrangements on wind-induced response and safety performance of the cooling tower group was summarized.
1. Introduction Group tower-induced interference is one of the major factors influencing wind resistance of cooling tower. More and more complex arrangements of cooling towers are emerging recently, and four-tower combination are the most common arrangement. The wind-induced collapse of cooling tower group at the Ferrybridge power station in England in 1965 attracted unprecedented attention to the issue of wind resistance for cooling tower. Many surveys (Bearman, 1967; Swartz et al., 1985; Pope, 1994; Bamu and Zingoni, 2005) were then conducted into the reasons of this wind-induced damage, and the following reasons were proposed: (1) The design wind speed of the cooling tower was lower than the basic wind speed of return period specified in the design code of England; (2) The effect of group tower-induced interference on the wind load of cooling tower has not been considered; (3) Only one reinforcing mesh was designed for the tower shell, and it could not withstand the moment of the tower shell. These reasons for wind-induced damage,
include stress and stability performance of cooling towers under interference, are still the priority concerns of wind-resistance design of large cooling tower. However, the existing cooling tower design codes (DL/T 5339-2006 2006, GB/T 50102-2014, 2014, VGB-Guideline, 2005) rarely provide recommendations in this field. Many of the studies (Niemann and Kopper. 1998; Orlando, 2001; Ke et al., 2012; Cheng et al., 2013; Rajan et al., 2013; Zhao et al., 2016) concerning wind resistance of cooling tower group focus on interference factor. For large cooling tower built as a symmetric towering concrete shell structure with large span, assessment methods and indicators for wind resistance have not yet established. The inference effect estimated from different structural response indicators varies from one study to another, and some are even in conflict with each other (Niemann and Kopper. 1998, Orlando, 2001, Cheng et al., 2013). Other researches (Zhou et al., 2014; Zhang et al., 2017) presented a few response indicators to estimate interference effect based on wind-induced response. However, it remains uncertain whether a specific response indicator can
* Corresponding author. College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China. E-mail addresses: [email protected], [email protected] (S. Ke), [email protected] (H. Wang), [email protected] (T. Wang), yaojunge@tongji. edu.cn (Y. Ge). https://doi.org/10.1016/j.jweia.2018.05.019 Received 16 April 2018; Received in revised form 26 May 2018; Accepted 26 May 2018 0167-6105/© 2018 Elsevier Ltd. All rights reserved.
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Fig. 1. Diagram of different layouts of grouped towers.
Table 1 Geometrical dimension of the cooling tower and layout of the measuring points. Part
Size(unit: m)
Tower height Throat altitude Inlet altitude Top diameter Bottom diameter Throat diameter Thickness Rect. cross sections of columns
220 165 31 128 185 123 0.39–1.85 1.7 1.0
Schematic of the measuring points (unit: m)
imposed by surrounding structures (Noh. 2006, Viladkar et al., 2006, Xu and Bai, 2013). Other scholars are concerned with the ultimate bearing capacity of large cooling towers considering nonlinear effect (Noorzaei et al., 2006; Li et al., 2014; Ke et al., 2015). However, these studies only included one specific group tower arrangement and did not provide a general principle for guiding the choice and engineering design of four-tower combinations. To this end, we compared the wind-induced response and stability performance of five typical four-tower arrangements (Fig. 1) in a
take the place of interference effect of tower group. There are three other documented cooling tower collapse accidents (power plant in Ardeer, England in 1973, power plant in Bouchain, France in 1979, and Fiddler's Ferry Power Station in England in 1984). The major cause of wind-induced damage of cooling tower at these power plants is all attributed to impairment of stability under group tower-induced interference (Bamu and Zigoni, 2005). Some systemic researches have been conducted in local and overall buckling stability of cooling towers under the group tower interference and interference
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Fig. 2. Simulation of wind characteristics in BLWT.
Fig. 5. Power spectral density function at typical measuring points under the single tower arrangement. Fig. 3. Comparison of shape coefficient between wind tunnel tests and target curve.
2. Wind tunnel test 2.1. An overview of the project and layout of measuring points
quantitative and qualitative manner. The super-large cooling tower studied here is the highest cooling tower ever built, which stands 220m. A total of 320 working conditions under five typical four-tower arrangements were considered in wind tunnel tests. Structural response was estimated using finite element method under different conditions. Displacement response, stress performance, local stability and overall buckling stability were compared under different four-tower arrangements. The ultimate bearing capacity of cooling tower under asymmetric wind load considering geometric nonlinearity of large deformation was discussed too. The research findings provide clues for optimization of four-tower arrangements and assessment of wind resistance.
The tower height is 220m, with throat altitude of 165m and inlet altitude of 30.75m; the top diameter is 128m, the throat diameter 123m, and the bottom diameter 185m. The tower is supported by 64 pairs of Xshaped columns which are connected to the annular plate foundation. The X-shaped columns are of a rectangular cross section measuring 1.7 m 1.0 m. The tower to be built is located in Class B terrain with a basic wind pressure of 0.5 kPa. The scale ratio of the model used for wind tunnel tests is 1:450. The model was made of acrylic to ensure sufficient stiffness and strength. Along the meridian direction 12 circles of external pressure measuring
Fig. 4. Diagram of simulation of Reynolds number effect. 160
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Fig. 6. Distribution of wind pressure coefficient of cooling tower under the single tower arrangement.
points were arranged on the tower surface. For each circle 36 measuring points were uniformly and clockwise distributed in the circumferential direction. Thus there are 432 measuring points in total. The detailed geometric dimension of the cooling tower and layout of the measuring points are shown in Table 1. The pressure taps were connected with the measurement system through PVC tubing. To avoid distortion of dynamic pressure, the signals had been modified using the transfer function of the tubing systems. A digital service module (DSM) 3000 scan valve system was used to measure the wind pressures on the model of the tower. The pressure signals were sampled at 312.5 Hz.
row, rectangular, rhombic, L-shape, and oblique L-shape (Fig. 1). For each arrangement, measurements were performed with an increment of 22.5 within the wind direction ranging from 0 to 360 . A total of 320 conditions were tested. The distance between two adjacent towers was 2D, with D being the bottom diameter of the cooling tower. To realistically simulate interference effect, several interference structures were arranged near the group towers. The maximum blockage rate for the group towers was 3.22%, which satisfied the standard for wind tunnel testing (JSJ/T 338-2014 ASCE 49-12-2012 JSJ/T 338-2014 2014, ASCE 49-12-2012).
2.2. Wind field simulation and Reynolds number simulation
2.3. Result of wind tunnel test
The wind tunnel was a closed jet return flow tunnel with a rectangular cross section. The working section was 5m wide and 4.5m high. The wind field was simulated as the class 2 terrain according to the Load Code for the Design of Building Structures (GB50009-2012, 2012). The main indicators of wind field simulation were mean wind speed profile, turbulence intensity profile and along-wind pulsating wind spectrum. Fig. 2 shows the simulation result. It can be seen that the simulated wind field satisfied the experimental requirements. Ten levels of surface roughness were tested in wind tunnel tests for the correction of Reynolds number effect: 1) Smooth surface; 2) With 16 trip wires having a width of 2 mm uniformly attached to the tower surface; 3) With 32 trip wires having a width of 2 mm uniformly attached to the tower surface; 4) With 64 trip wires having a width of 2 mm uniformly attached to the tower surface; 5) With 1 layer of 36 rough paper tapes having a width of 5 mm uniformly attached to the tower surface; 6) With 2 layers of 36 rough paper tapes having a width of 5 mm and uniformly attached to the tower surface; 7) With 2/3 layers of 36 rough paper tapes having a width of 5 mm and intermittently attached to the tower surface; 8) With 3 layers of 36 rough paper tapes having a width of 5 mm and uniformly attached to the tower surface; 9) With 3/4 layers of 36 rough paper tapes having a width of 5 mm and intermittently attached to the tower surface; 10) With 4 layers of 36 rough paper tapes having a width of 5 mm and uniformly attached to the tower surface. The main parameters compared by simulation of Reynolds number effect were minimal shape coefficient, shape coefficient of the wake region, angle corresponding to zero shape coefficient, angle corresponding to minimal shape coefficient and angle at the point of separation (Farell et al., 1976, Suna and Zhoub, 1983, Ke and Ge, 2015). Fig. 3 shows the distribution curves of normalized shape coefficient at the throat under different surface roughness, and they were compared against the standard curves (DL/T 5339-2006 2006, GB/T 50102-2014 2014). It can be seen from the figure that the Reynolds number effect was best simulated by uniformly attaching 4 layers of rough paper tapes. Fig. 4 shows the simulation measures used for formal tests. Five arrangements of the cooling towers were tested in the wind tunnel, namely,
Fig. 5 shows the power spectral density function during the time history of wind pressure coefficient at the typical measuring points under the single tower arrangement. It can be seen that the values of power spectral density function of wind pressure on the windward side were larger than those on the separation point and the leeward side. Fig. 6 shows the wind pressure distribution pattern on the surface of cooling tower and wind pressure distribution at typical measuring points under the single tower arrangement. The wind pressure distribution of cooling tower varied greatly along height, presenting threedimensional features. Fig. 7 shows the wind pressure distribution curves at throat height of tower 2# under different arrangements. It can be seen that (1) the maximum positive pressure varied little under different four-tower arrangements. The regions of maximum negative pressure and leeward side were most greatly affected by the group tower-induced interference; (2) the mean wind pressure under the row arrangement is most greatly affected by interference. Absolute values of negative pressure at the regions of maximum negative pressure and leeward side increased considerably; (3) Wind pressure distributions under the rectangular, rhombic, L-shape and oblique L-shape arrangements displayed a typical asymmetric pattern. 3. Wind-induced response analysis 3.1. Modeling and modal analysis According to the dimension of the cooling tower, cooling tower is modelling based on commercial software ANSYS considering the soilstructure interaction, where foundations and piles were simulated using equivalent soil springs with 6 dimensions. The FEM model of cooling tower is illustrated in Fig. 8. In this model, element types Shell63 and Beam188 were selected to simulate the tower shell and bottom-supported columns, respectively. Element Combin14 was used to simulate the equivalent soil spring stiffness for the coupling among shell structure, inclined column piles and ring foundation. 161
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Fig. 7. Wind pressure coefficient distributions of 2# tower under different wind directions and different four-tower arrangements.
vibration deformations along meridian and circumferential directions are obviously.
Block Lanczos method was used to estimate the natural frequencies and vibration modes of the super-large cooling tower. Table 2 shows the natural frequencies and vibration modes of the first ten orders. The natural frequency of the tower was small and the fundamental frequency was only 0.542Hz. The first ten order frequencies were all below 0.8Hz, and the natural frequencies of vibration were low and densely distributed. The vibration modes presented 3D distribution feature, and
3.2. Displacement response Fig. 9 shows the maximum radial displacements of the tower body under different wind angles for the five typical four-tower arrangements. 162
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deformations and different kind of internal forces. So we took some typical internal forces to identify the key trends and draw some conclusions. Meridional force FS and circumferential moment MS of the tower body are the control internal forces in structural design of cooling tower. We estimated the maximum meridional force and circumferential moment of the tower body under each working condition, as shown in Fig. 10 and 11, respectively. The upper and lower points on the figure represent maximum responses under 16 wind angles for each four-tower arrangement. The upper edge of the rectangle represents the response values with a probability distribution of 75% quantile, and the lower edge represents the values with a probability distribution of 25% quantile of the response. The dots are the mean value with respect to wind direction for each four-tower arrangement. As analyzed above, (1) the mean meridional force under the rectangular and rhombic arrangements were the smallest of all five arrangements. The mean meridional forces and mean circumferential moments were mildly affected by arrangement pattern; (2) taking the mean meridional force as control indicator, the most unfavorable value was observed at tower 4# under all four-tower arrangements, while the value was the most favorable at tower 2#; (3) taking the mean circumferential moment as the control indicator, tower 2# reached the design control working condition under the rectangular, L-shape and oblique L-shape arrangements; tower 4# reached the maximum response under the row and rhombic arrangements; (4) taking mean meridional force as the control indicator, the four-tower arrangements were arranged as follows: Rhombic > rectangular > L-shape > oblique L-shape > row. Taking mean circumferential moment as the control indicator, the four-tower arrangements were arranged as follows: row > oblique Lshape > rhombic > L-shape > rectangular. Figs. 12 and 13 are the box plots of axial force FC and moment MC of the columns under different four-tower arrangements, respectively. It can be seen from the figure that (1) the degree of variation of axial force and moment of columns was the smallest for tower 1#, followed by tower 2# and 3# equally, and that of tower 4# was the greatest; (2) maximum axial forces and extreme moments of columns occurred under the row and oblique L-shape arrangements; (3) taking the axial force of column as the control indicator, the four-tower arrangements were ranked as follows: rhombic > rectangular > L-shape > oblique L-shape > row; (4) taking the moment of columns as the control indicator, the four-tower arrangements were ranked as follows: rectangular > rhombic > Lshape > row > oblique L-shape. Fig. 14 shows the box plot of torque of column TC under different four-tower arrangements. Maximum torques under different four-tower arrangements all occurred under the L-shape arrangement, and the values were higher by 52%, 31%, 39% and 19% compared with the row, rectangular, rhombic and oblique L-shape arrangements, respectively.
Fig. 8. Finite element modeling of cooling tower.
It can be seen that (1) the maximum radial displacement of tower 1# varied least among different four-tower arrangements. The largest radial displacement was 0.11m, which occurred under the L-shape arrangement; (2) the maximum radial displacement of 2% tower fluctuated greatly with wind angle, and the value was about 0.12m under the rectangular and L-shape arrangements; (3) towers 3# and 4# were most greatly affected under different arrangements, and the maximum values both occurred under the rectangular and rhombic arrangements; (4) tower 2# had the highest radial displacement of tower shell, and 1# had the lowest. Table 3 lists displacement equipotential lines of the cooling tower under the most unfavorable working conditions for the single tower arrangement and five typical four-tower arrangements. The maximum deformation was up to 0.13m under the rectangular arrangement, which was considerably higher than that of other arrangements and single tower. Different four-tower arrangements were ranked as follows in terms of displacement response: row > oblique L-shape > Lshape > rhombic > rectangular. 3.3. Internal force response It is quite difficult to gather so much information about interference effect, ranging from wind-pressure distribution on the shell surface,
Table 2 Natural frequencies and vibration modes of the first ten orders.
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Fig. 9. Maximal radial displacement and other data of tower body under different wind angles for five typical four-tower arrangements.
the influence of relative position among the towers on the comprehensive stress performance, we estimated the response increments of displacement and six internal force indices under the five typical four-tower arrangements. The sum of the increments was calculated as well (Sum value), as shown in Fig. 16. Wind-induced response under the four-tower arrangements was significantly affected by the relative position among the towers. Therefore, it is not reasonable to use a uniform standard for structural design for all towers in a tower group. The Sum value was used to measure the degree of influence of relative position among the towers to compare the stress performance of different towers in a towers group.
The torque of tower 1# was least affected by tower arrangement, and it varied by only 8%. The degree of variation was all above 20% for the remaining three towers. Taking the torque of column as the control indicator, the four-tower arrangements were ranked as follows: row > rhombic > rectangular > oblique L-shape > L-shape. Fig. 15 shows the box plot of moment of ring foundation MF under different four-tower arrangements. Taking the moment of ring foundation as the control indicator, the maximum degree of variation under different four-tower arrangements was only 3%. The four-tower arrangements were ranked as follows in terms of moment of ring foundation: rhombic > rectangular > row > L-shape > oblique L-shape.
4. Stability performance analysis 3.4. Comprehensive comparison
4.1. Local stability
Table 4 presents the degree of influence of six typical internal force indices on the stress performance of the cooling tower under different four-tower arrangements. Values in the brackets are the percentages of internal force increment under the most favorable four-tower arrangement. It can be seen that (1) different index was affected differently by the group tower-induced interference. The circumferential moment of tower body and torque of column were the most greatly affected under the four-tower arrangements; (2) row arrangement was the optimal arrangement whether taking either the circumferential moment of tower body or torque of column as the control indicator. The values increased by over 50% under the most unfavorable arrangement compared with the row arrangement; (3) the remaining four internal force indices were less affected by the four-tower arrangement. These four internal force indices were greatly reduced under the rectangular and rhombic arrangements. We observed no consistent pattern in the variation of different windinduced response indicators under the four-tower arrangements. Tower 2# displayed preferable stress performance in terms of most response indicators, while tower 4# had a worse performance. In order to analyze
According to the GB/T 50102-2014 and VGB-R 610Ue 2005 design codes, local stability of the cooling tower was calculated as below: 0:8KB
σ1 σ2 þ þ 0:2KB2 σ cr1 σ cr2
"
σ1 σ cr1
2 þ
σ2 σ cr2
2 # ¼1
(1)
where σ 1 and σ 2 are the circumferential and meridian compressive stresses, respectively; KB is local stability coefficient; σ cr1 and σ cr2 are the circumferential and meridian critical compressive stresses, respectively: 0:985E
4=3 h K1 3 r0
(2)
4=3 h K2 3 r0
(3)
C σ cr1 ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi 4
1 v2c
0:612E
C σ cr2 ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi 4
164
1 v2c
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Table 3 Radial displacements of tower body under the most unfavorable working conditions for single tower arrangement and typical four-tower arrangements.
Fig. 10. Distribution of maximum meridional force of tower shell under different arrangements. 165
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Fig. 11. Distribution of maximum circumferential moment of tower shell under different arrangements.
1) The minimum KB of tower 1# was the least affected of all four-tower arrangements. Except the wind angles of 157.5 and 45 which produced an unfavorable impact on minimum KB under the L-shape and oblique L-shape arrangements, it varied little or increased somewhat compared with the row arrangement. 2) Tower 2# was more greatly affected by the arrangement pattern than tower 1#. There were several wind angles that produced an unfavorable impact on local stability of tower 2# under different arrangements.
where h is the tower body thickness; r0 is the radius of throat; vc is the Poisson's ratio of concrete; Ec is elastic modulus of concrete; K1 and K2 are geometric parameters of the tower. Fig. 17 shows the distribution of minimum local stability factor KB under different wind angles for different four-tower arrangements. The minimum KB was represented in the form of histogram under the row arrangement. The values of other arrangements were expressed as increments or decrements relative to row arrangement under each wind angle. The result was analyzed as below:
Fig. 12. Distribution of maximum axial force of column under different four-tower arrangements. 166
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Fig. 13. Distribution of maximum moment of column under different four-tower arrangements.
Fig. 14. Distribution of maximum torque of column under different four-tower arrangements. 167
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Fig. 15. Distribution of maximum moment of ring foundation under different four-tower arrangements.
load Pcri for buckling of the cooling tower was calculated as follows (Cole et al., 1975):
Some KB values under the rectangular, L-shape and oblique L-shape arrangements were below 4.0. 3) The distribution pattern of local stability factor of tower 3# was similar to that of tower 2#. The minimum KB value of 3.24 was reached for the tower 3# under the rectangular arrangement at the wind angle of 315 . The other four arrangements were favorable for local stability of tower 3#. 4) Tower 4# was most greatly affected by the arrangement pattern. The degree of dispersion of increment/decrement increased apparently, and the minimum KB was reached under the row and rhombic arrangements (4.59 and 3.20, respectively).
Pcri ¼ λi Q
(4)
where Q is the basic acting load; λi is the characteristic value of buckling or buckling load factor. Here Block Lanczos method was used to calculate the characteristic value of buckling, and the governing equation was written as ð½KL þ λi ½KG Þ fδg ¼ 0
(5)
where [KL] is the overall elastic stiffness matrix of the cooling tower; [KG] is the overall geometric matrix of the cooling tower; {δ} is the characteristic displacement vector. Buckling mode and its eigenvalue are important outputs of buckling analysis. Buckling mode reflects the configuration upon structural instability. The first order buckling mode is directly related to the buckling bearing capacity and therefore it has an important value for engineering practice (Mang et al., 1983). Fig. 19 shows the distributions of the first order buckling coefficients under different wind angles for different four-tower arrangements. Either the mean or minimum buckling coefficient of tower 4# was much lower than those of the other three towers regardless of wind angle. Different four-tower arrangements had similar impact on tower 1#, 2# and 3#. Local stability analysis indicated that the local and overall buckling stability of the cooling tower at the margin of the tower group were poor, probably because of the asymmetric wind load acting on tower surface.
Fig. 18 shows the distributions of minimum KB under the working condition most unfavorable for local stability for the single tower and four-tower arrangements. It can be seen that the minimum KB decreased more significantly under the four-tower arrangements than the single tower. The KB value was larger at the bottom and decreased towards the middle, with the minimum occurring near the height of 120m. Of different four-tower arrangements, the row arrangement had a great increase in local stability, followed by oblique L-shape arrangement. In contrast, the local stability of the tower was lower under the rectangular, rhombic and L-shape arrangements compared with the row arrangement. 4.2. Overall buckling analysis Buckling response is usually analyzed based on linear elastic characteristic value so as to assess the overall structural stability. The critical
Table 4 Degree of influence of internal force indices under different four-tower arrangements. No.
Internal force index
Action location
Preference ranking (Increased percent %)
1 2 3 4 5 6
Meridional force Circumferential moment Axial force Moment Torque Moment
Tower shell
Rhombic > Rectangular(2.52) > L-shape(4.91) > Oblique L-shape(6.99) > Row(7.38) Row > Oblique L-shape(25.74) > Rhombic(25.99) > L-shape(46.15) > Rectangular(64.85) Rhombic > Rectangular(2.11) > L-shape(4.32) > Oblique L-shape(5.90) > Row(6.67) Rectangular > Rhombic(0.74) > L-shape(5.69) > Row(7.22) > Oblique L-shape(7.79) Row > Rhombic(9.89) > Rectangular(16.54) > Oblique L-shape(27.92) > L-shape(52.46) Rhombic > Rectangular(0.04) > Row(1.79) > L-shape(2.61) > Oblique L-shape (3.01)
Bottom-supported column
Ring foundation
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Fig. 16. Increments of displacement and six internal force indices under different four-tower arrangements.
Fig. 17. Distribution of minimum KB under different four-tower arrangements.
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Fig. 20. Distributions of buckling coefficient and displacement under different four-tower arrangements.
4.3. Analysis of ultimate bearing capacity Specifically, the initial wind speed of 10 m/s at the height of 10m was taken as the basic design wind speed. Stepwise loading was imposed with a step length of 2.5m/s-10 m/s. When the wind speed was sufficiently large to cause tensile failure of tower wall (ftk1.71 MPa for C40 concrete), the reinforcing bars would bear the tension in these positions. As the wind speed further increased, the compressive regions of the concrete tower wall approached the ultimate compressive state (fck19.1 MPa for C40 concrete). As a result, the static deformation of the cooling tower increased rapidly, and the tower reached the ultimate bearing capacity. For analysis of ultimate bearing capacity, geometric non-linearity was considered under large deformation of the cooling tower. Critical wind speed of instability was calculated from the slope of maximum displacement varying with wind speed and the ultimate compressive state of concrete. Figs. 21 and 22 show the distribution of critical wind speed under different four-tower arrangements and the variations of displacement and slope with wind speed under the most unfavorable working condition, respectively. Comparison revealed the following:
Fig. 18. Distribution of minimum KB under the working condition most unfavorable for local stability.
Fig. 20 shows the buckling modes and maximum displacements under the working condition most unfavorable for buckling stability for different four-tower arrangements. The first order buckling coefficient under the single tower arrangement was 9.43. Of all four-tower arrangements, rhombic and L-shape arrangements had poor overall buckling safety. The first order buckling coefficient of these two arrangements decreased by nearly 10% compared with the single tower. In contrast, the row, rectangular and oblique L-shape arrangements were more favorable for overall buckling stability.
Fig. 19. Distribution of first order buckling coefficient under different four-tower arrangements. 170
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Fig. 21. Distribution of critical wind speed under four-tower arrangements.
2) Tower 2# under rectangular arrangement encountered the most unfavorable working condition under the wind angle of 270 . Under rhombic, L-shape and oblique L-shape arrangement tower 2% had the minimum ultimate bearing capacity under the wind angle of 247.5 , 67.5 and 292.5 , respectively. Under this situation, the incoming flow produces an asymmetric canyon effect to the cooling tower of our concern. 3) Taking ultimate bearing capacity of the control indicator, the fourtower arrangements were ranked as follows: row > oblique Lshape > rhombic > L-shaped > rectangular.
1) All four towers in the row arrangement had a larger critical wind speed at the wind angle of 90 and 270 . Under these working conditions, the cooling tower was mainly affected by the shield effect. The minimum critical wind speed under the row arrangement occurred at tower 4# under the wind angle of 0 .
5. Conclusion Wind tunnel tests for five typical four-tower arrangements were performed, include a total of 320 working condition, and finite element method was used to simulate the influence of arrangement pattern on wind-induced response and stability performance of cooling towers group. The main research contents included wind tunnel test, finite element analysis, dynamic analysis, wind-induced response analysis, local stability estimation, overall buckling analysis and ultimate bearing capacity. The following conclusions were drawn:
Table 5 Preference ranking of four-tower group under five arrangements in terms of wind-induced response.
Fig. 22. Variations of displacement and slope with wind speed under the most unfavorable working conditions for the single tower arrangement and fourtower arrangements. 171
Arrangements
Preference ranking (advantage > disadvantage)
Row Rectangular Rhombic L-shape Oblique L-shape
2# 1# 2# 3# 3#
CT > 3# CT > 1# CT > 4# CT > 4# CT > 3# CT > 2# CT > 1# CT > 3# CT > 4# CT > 2# CT > 4# CT > 1# CT > 2# CT > 1# CT > 4#
CT CT CT CT CT
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Fig. 23. Relative positions of towers in different arrangements under the most unfavorable wind direction.
● The four-tower arrangement had major impact on displacement response, circumferential moment of tower body and torque of column. Row arrangement was the optimal arrangement in terms of these indicators. The values of the three indicators increased by 27.13%, 64.85% and 52.46% under the other three four-tower arrangements increased by 27.13%, 64.85% and 52.46% compared with the row arrangement, respectively. Thus the preference ranking in terms of comprehensive wind-induced response was as follows: row > rhombic > oblique L-shape > rectangular > L-shape. ● The wind-induced response was greatly affected by relative position among the four towers. Thus it is not reasonable to use a uniform standard for structural design for all towers in a tower group. Moreover, the extreme values of different response indicators of the four towers varied inconsistently due to group tower-induced interference and action of adjacent structures. Table 5 shows the preference rankings of four-tower group in terms of wind-induced response. ● Row and oblique L-shape arrangements had higher local stability, overall buckling stability and ultimate bearing capacity. The critical wind speeds of instability of rectangular, rhombic and L-shape is only 60%, 70% and 65% of the critical wind speed at the row arrangement, and these three types of four-tower arrangements should be carefully adopted in areas with high basic wind speed. ● Working conditions most unfavorable for wind resistance safety were identified for the five four-tower arrangements based on comprehensive wind-induced response and stability indicators (Fig. 23). The comprehensive stress performance of the cooling tower was greatly impaired by the asymmetric canyon effect.
Cheng, X.X., Zhao, L., Ge, Y.J., 2013. Multiple loading effects on wind-induced static performance of super-large cooling towers. Int. J. Struct. Stabil. Dynam. 13 (8), 1350039. Cole, P.P., Billington, D.P., Abel, J.F., 1975. Buckling of cooling-tower shells: bifurcation results. J. Struct. Div. 101 (4), 1205–1222. Farell, C., Guven, O., Maisch, F., 1976. Mean wind loading on rough-walled cooling towers. J. Eng. Mech. Div. 102 (6), 1059–1081. Ministry of Housing and Urban-Rural Development of People’s Republic of China, 2014. “Code for Design of Cooling for Industrial Recirculating water.” GB/T 50102-2014. China Planning Press (in Chinese). Ministry of Housing and Urban-Rural Development of People’s Republic of China, 2012. “Lode Code for the Design of Building structures.” GB50009-2012. China Building Industry Press (in Chinese). Ministry of Housing and Urban-Rural Development of People’s Republic of China, 2014. “Standard for Wind Tunnel Test of Buildings and structures.” JSJ/T 338-2014. China Building Industry Press (in Chinese). Ke, S.T., Ge, Y.J., 2015. Extreme wind pressures and non-Gaussian characteristics for super-large hyperbolic cooling towers considering aero-elastic effec. J. Struct. Eng. ASCE 141 (7), 04015010. Ke, S.T., Ge, Y.J., Zhao, L., 2012. A new methodology for analysis of equivalent static wind loads on super-large cooling towers. J. Wind Eng. Ind. Aerod. 111 (3), 30–39. Ke, S.T., Ge, Y.J., Zhao, L., Tamura, Y., 2015. Stability and reinforcement analysis of super-large exhaust cooling towers based on a wind tunnel test. J. Struct. Eng. ASCE 141 (12), 04015066. Li, Y., Lin, F., Gu, X.L., Lu, X.Q., 2014. Numerical research of a super-large cooling tower subjected to accidental loads. Nucl. Eng. Des. 269 (4), 184–192. Mang, H.A., Floegl, H., Trappel, F., Walter, H., 1983. Wind-loaded reinforced-concrete cooling towers: buckling or ultimate load? Eng. Struct. 5 (3), 163–180. Niemann, H.J., Kopper, H.D., 1998. Influence of adjacent buildings on wind effects on cooling towers. Eng. Struct. 20 (10), 874–880. Noh, H.C., 2006. Nonlinear behavior and ultimate load bearing capacity of reinforced concrete natural draught cooling tower shell. Eng. Struct. 28 (3), 399–410. Noorzaei, J., Naghshineh, A., Kadir, M.R.A., Thanoon, W.A., Jaafar, M.S., 2006. Nonlinear interactive analysis of cooling tower–foundation–soil interaction under unsymmetrical wind load. Thin-Walled Struct. 44 (9), 997–1005. Orlando, M., 2001. Wind-induced interference effects on two adjacent cooling towers. Eng. Struct. 23 (8), 979–992. Pope, R.A., 1994. Structural deficiencies of natural draught cooling towers at UK power stations. part 1: failures at ferrybridge and fiddlers ferry. Struct. Build 104 (1), 1–10. Rajan, S.S., Babu, G.R., Arunachalam, S., et al., 2013. Interference factors for natural draught cooling towers based on wind tunnel experiments. Eighth Asia-Pacific Conference on Wind Engineering 490–498. Sun, T.F., Zhou, L.M., 1983. Wind pressure distribution around a ribless hyperbolic cooling tower. J. Wind Eng. Ind. Aerod. 14 (s 1–3), 181–192. Swartz, S.E., Chien, C.C., Hu, K.K., et al., 1985. Tests on microconcrete model of hyperbolic cooling tower. Exp. Mech. 25 (1), 12–23. VGB-Guideline, 2005. “Structural Design of Cooling tower- Technical Guideline for the Structural Design, Computation and Execution of Cooling towers.” VGB-r 610Ue. BTR Bautechnik bei Kühltürmen, Standard Essen (in German). Viladkar, M.N., Karisiddappa, Bhargava, P., Godbole, P.N., 2006. Static soil–structure interaction response of hyperbolic cooling towers to symmetrical wind loads. Eng. Struct. 28 (9), 1236–1251. Xu, Y., Bai, G., 2013. Random buckling bearing capacity of super-large cooling towers considering stochastic material properties and wind loads. Probabilist. Eng. Mech. 33 (10), 18–25. Zhang, J.F., Ge, Y.J., Zhao, L., et al., 2017. Wind induced dynamic responses on hyperbolic cooling tower shells and the equivalent static wind load. J. Wind Eng. Ind. Aerod. 169, 280–289. Zhao, L., Chen, X., Ge, Y.J., 2016. Investigations of adverse wind loads on a large cooling tower for the six-tower combination. Appl. Therm. Eng. 105 (25), 988–999. Zhou, X., Niu, H.W., Chen, Z.Q., Wang, Z.Y., 2014. Discussion on different methodologies for calculating interference factor of large cooling towers. J. Cent. S. Univ. 45 (10), 3637–3644 (in Chinese).
Acknowledgments This project is jointly supported by National Natural Science Foundation (51761165022 and U1733129), Jiangsu Province Outstanding Natural Science Foundation (BK20160083), and Jiangsu Province QingLan Project, which are gratefully acknowledged. Appendix A. Supplementary data Supplementary data related to this article can be found at https://doi. org/10.1016/j.jweia.2018.05.019. References ASCE Structural Engineering Institute, 2012. Wind Tunnel Testing for Buildings and Other Structures.” ASCE 49-12-2012. The American Society of Civil Engineers. Bamu, P.C., Zingoni, A., 2005. “Damage, deterioration and the long-term structural performance of cooling-tower shells: a survey of developments over the past 50 years. Eng. Struct. 27 (12), 1794–1800. Bearman, P.W., 1967. Wind Forces and the proximity of cooling towers to each other. Nature 216 (5050), 735.
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Journal of Wind Engineering & Industrial Aerodynamics journal homepage: www.elsevier.com/locate/jweia
Comparison of comprehensive stress performances of super-large cooling tower in different four-tower arrangements under 3D asymmetric wind loads Shitang Ke a, b, *, Hao Wang a, Tongguang Wang a, Yaojun Ge b a b
College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China State Key Laboratory for Disaster Reduction in Civil Engineering, Tongji University, Shanghai, 200092, China
A R T I C L E I N F O
A B S T R A C T
Keywords: Four-tower arrangement Super-large cooling tower Wind tunnel test Wind-induced response Local stability Buckling stability Ultimate bearing capacity
Different four-tower arrangements have a great impact on wind-induced response and stability performance of super-large cooling tower. However, a single indicator (eg., interference factor of overall wind load) cannot provide a comprehensive and objective evaluation of wind-resistance safety of cooling tower. Here five typical four-tower arrangements in engineering practice were experimented, namely, row, rectangular, rhombic, L-shape, and oblique L-shape arrangement. Wind tunnel tests for rigid body were performed to determine the wind loads distribution pattern on the surface of group tower under different four-tower arrangements. Finite element method was employed to analyze the internal force and deformation distributions under the design wind load of return period. The influence of different four-tower arrangements on wind load-induced response was discussed under different incoming wind angles. Then the local stability and overall buckling stability of the cooling tower were estimated, and the ultimate bearing capacities under different four-tower arrangements were compared considering geometric nonlinearity. Instead of using a uniform structural design standard for cooling towers group, the influence rule of different arrangements on wind-induced response and safety performance of the cooling tower group was summarized.
1. Introduction Group tower-induced interference is one of the major factors influencing wind resistance of cooling tower. More and more complex arrangements of cooling towers are emerging recently, and four-tower combination are the most common arrangement. The wind-induced collapse of cooling tower group at the Ferrybridge power station in England in 1965 attracted unprecedented attention to the issue of wind resistance for cooling tower. Many surveys (Bearman, 1967; Swartz et al., 1985; Pope, 1994; Bamu and Zingoni, 2005) were then conducted into the reasons of this wind-induced damage, and the following reasons were proposed: (1) The design wind speed of the cooling tower was lower than the basic wind speed of return period specified in the design code of England; (2) The effect of group tower-induced interference on the wind load of cooling tower has not been considered; (3) Only one reinforcing mesh was designed for the tower shell, and it could not withstand the moment of the tower shell. These reasons for wind-induced damage,
include stress and stability performance of cooling towers under interference, are still the priority concerns of wind-resistance design of large cooling tower. However, the existing cooling tower design codes (DL/T 5339-2006 2006, GB/T 50102-2014, 2014, VGB-Guideline, 2005) rarely provide recommendations in this field. Many of the studies (Niemann and Kopper. 1998; Orlando, 2001; Ke et al., 2012; Cheng et al., 2013; Rajan et al., 2013; Zhao et al., 2016) concerning wind resistance of cooling tower group focus on interference factor. For large cooling tower built as a symmetric towering concrete shell structure with large span, assessment methods and indicators for wind resistance have not yet established. The inference effect estimated from different structural response indicators varies from one study to another, and some are even in conflict with each other (Niemann and Kopper. 1998, Orlando, 2001, Cheng et al., 2013). Other researches (Zhou et al., 2014; Zhang et al., 2017) presented a few response indicators to estimate interference effect based on wind-induced response. However, it remains uncertain whether a specific response indicator can
* Corresponding author. College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China. E-mail addresses: [email protected], [email protected] (S. Ke), [email protected] (H. Wang), [email protected] (T. Wang), yaojunge@tongji. edu.cn (Y. Ge). https://doi.org/10.1016/j.jweia.2018.05.019 Received 16 April 2018; Received in revised form 26 May 2018; Accepted 26 May 2018 0167-6105/© 2018 Elsevier Ltd. All rights reserved.
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Fig. 1. Diagram of different layouts of grouped towers.
Table 1 Geometrical dimension of the cooling tower and layout of the measuring points. Part
Size(unit: m)
Tower height Throat altitude Inlet altitude Top diameter Bottom diameter Throat diameter Thickness Rect. cross sections of columns
220 165 31 128 185 123 0.39–1.85 1.7 1.0
Schematic of the measuring points (unit: m)
imposed by surrounding structures (Noh. 2006, Viladkar et al., 2006, Xu and Bai, 2013). Other scholars are concerned with the ultimate bearing capacity of large cooling towers considering nonlinear effect (Noorzaei et al., 2006; Li et al., 2014; Ke et al., 2015). However, these studies only included one specific group tower arrangement and did not provide a general principle for guiding the choice and engineering design of four-tower combinations. To this end, we compared the wind-induced response and stability performance of five typical four-tower arrangements (Fig. 1) in a
take the place of interference effect of tower group. There are three other documented cooling tower collapse accidents (power plant in Ardeer, England in 1973, power plant in Bouchain, France in 1979, and Fiddler's Ferry Power Station in England in 1984). The major cause of wind-induced damage of cooling tower at these power plants is all attributed to impairment of stability under group tower-induced interference (Bamu and Zigoni, 2005). Some systemic researches have been conducted in local and overall buckling stability of cooling towers under the group tower interference and interference
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Fig. 2. Simulation of wind characteristics in BLWT.
Fig. 5. Power spectral density function at typical measuring points under the single tower arrangement. Fig. 3. Comparison of shape coefficient between wind tunnel tests and target curve.
2. Wind tunnel test 2.1. An overview of the project and layout of measuring points
quantitative and qualitative manner. The super-large cooling tower studied here is the highest cooling tower ever built, which stands 220m. A total of 320 working conditions under five typical four-tower arrangements were considered in wind tunnel tests. Structural response was estimated using finite element method under different conditions. Displacement response, stress performance, local stability and overall buckling stability were compared under different four-tower arrangements. The ultimate bearing capacity of cooling tower under asymmetric wind load considering geometric nonlinearity of large deformation was discussed too. The research findings provide clues for optimization of four-tower arrangements and assessment of wind resistance.
The tower height is 220m, with throat altitude of 165m and inlet altitude of 30.75m; the top diameter is 128m, the throat diameter 123m, and the bottom diameter 185m. The tower is supported by 64 pairs of Xshaped columns which are connected to the annular plate foundation. The X-shaped columns are of a rectangular cross section measuring 1.7 m 1.0 m. The tower to be built is located in Class B terrain with a basic wind pressure of 0.5 kPa. The scale ratio of the model used for wind tunnel tests is 1:450. The model was made of acrylic to ensure sufficient stiffness and strength. Along the meridian direction 12 circles of external pressure measuring
Fig. 4. Diagram of simulation of Reynolds number effect. 160
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Fig. 6. Distribution of wind pressure coefficient of cooling tower under the single tower arrangement.
points were arranged on the tower surface. For each circle 36 measuring points were uniformly and clockwise distributed in the circumferential direction. Thus there are 432 measuring points in total. The detailed geometric dimension of the cooling tower and layout of the measuring points are shown in Table 1. The pressure taps were connected with the measurement system through PVC tubing. To avoid distortion of dynamic pressure, the signals had been modified using the transfer function of the tubing systems. A digital service module (DSM) 3000 scan valve system was used to measure the wind pressures on the model of the tower. The pressure signals were sampled at 312.5 Hz.
row, rectangular, rhombic, L-shape, and oblique L-shape (Fig. 1). For each arrangement, measurements were performed with an increment of 22.5 within the wind direction ranging from 0 to 360 . A total of 320 conditions were tested. The distance between two adjacent towers was 2D, with D being the bottom diameter of the cooling tower. To realistically simulate interference effect, several interference structures were arranged near the group towers. The maximum blockage rate for the group towers was 3.22%, which satisfied the standard for wind tunnel testing (JSJ/T 338-2014 ASCE 49-12-2012 JSJ/T 338-2014 2014, ASCE 49-12-2012).
2.2. Wind field simulation and Reynolds number simulation
2.3. Result of wind tunnel test
The wind tunnel was a closed jet return flow tunnel with a rectangular cross section. The working section was 5m wide and 4.5m high. The wind field was simulated as the class 2 terrain according to the Load Code for the Design of Building Structures (GB50009-2012, 2012). The main indicators of wind field simulation were mean wind speed profile, turbulence intensity profile and along-wind pulsating wind spectrum. Fig. 2 shows the simulation result. It can be seen that the simulated wind field satisfied the experimental requirements. Ten levels of surface roughness were tested in wind tunnel tests for the correction of Reynolds number effect: 1) Smooth surface; 2) With 16 trip wires having a width of 2 mm uniformly attached to the tower surface; 3) With 32 trip wires having a width of 2 mm uniformly attached to the tower surface; 4) With 64 trip wires having a width of 2 mm uniformly attached to the tower surface; 5) With 1 layer of 36 rough paper tapes having a width of 5 mm uniformly attached to the tower surface; 6) With 2 layers of 36 rough paper tapes having a width of 5 mm and uniformly attached to the tower surface; 7) With 2/3 layers of 36 rough paper tapes having a width of 5 mm and intermittently attached to the tower surface; 8) With 3 layers of 36 rough paper tapes having a width of 5 mm and uniformly attached to the tower surface; 9) With 3/4 layers of 36 rough paper tapes having a width of 5 mm and intermittently attached to the tower surface; 10) With 4 layers of 36 rough paper tapes having a width of 5 mm and uniformly attached to the tower surface. The main parameters compared by simulation of Reynolds number effect were minimal shape coefficient, shape coefficient of the wake region, angle corresponding to zero shape coefficient, angle corresponding to minimal shape coefficient and angle at the point of separation (Farell et al., 1976, Suna and Zhoub, 1983, Ke and Ge, 2015). Fig. 3 shows the distribution curves of normalized shape coefficient at the throat under different surface roughness, and they were compared against the standard curves (DL/T 5339-2006 2006, GB/T 50102-2014 2014). It can be seen from the figure that the Reynolds number effect was best simulated by uniformly attaching 4 layers of rough paper tapes. Fig. 4 shows the simulation measures used for formal tests. Five arrangements of the cooling towers were tested in the wind tunnel, namely,
Fig. 5 shows the power spectral density function during the time history of wind pressure coefficient at the typical measuring points under the single tower arrangement. It can be seen that the values of power spectral density function of wind pressure on the windward side were larger than those on the separation point and the leeward side. Fig. 6 shows the wind pressure distribution pattern on the surface of cooling tower and wind pressure distribution at typical measuring points under the single tower arrangement. The wind pressure distribution of cooling tower varied greatly along height, presenting threedimensional features. Fig. 7 shows the wind pressure distribution curves at throat height of tower 2# under different arrangements. It can be seen that (1) the maximum positive pressure varied little under different four-tower arrangements. The regions of maximum negative pressure and leeward side were most greatly affected by the group tower-induced interference; (2) the mean wind pressure under the row arrangement is most greatly affected by interference. Absolute values of negative pressure at the regions of maximum negative pressure and leeward side increased considerably; (3) Wind pressure distributions under the rectangular, rhombic, L-shape and oblique L-shape arrangements displayed a typical asymmetric pattern. 3. Wind-induced response analysis 3.1. Modeling and modal analysis According to the dimension of the cooling tower, cooling tower is modelling based on commercial software ANSYS considering the soilstructure interaction, where foundations and piles were simulated using equivalent soil springs with 6 dimensions. The FEM model of cooling tower is illustrated in Fig. 8. In this model, element types Shell63 and Beam188 were selected to simulate the tower shell and bottom-supported columns, respectively. Element Combin14 was used to simulate the equivalent soil spring stiffness for the coupling among shell structure, inclined column piles and ring foundation. 161
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Fig. 7. Wind pressure coefficient distributions of 2# tower under different wind directions and different four-tower arrangements.
vibration deformations along meridian and circumferential directions are obviously.
Block Lanczos method was used to estimate the natural frequencies and vibration modes of the super-large cooling tower. Table 2 shows the natural frequencies and vibration modes of the first ten orders. The natural frequency of the tower was small and the fundamental frequency was only 0.542Hz. The first ten order frequencies were all below 0.8Hz, and the natural frequencies of vibration were low and densely distributed. The vibration modes presented 3D distribution feature, and
3.2. Displacement response Fig. 9 shows the maximum radial displacements of the tower body under different wind angles for the five typical four-tower arrangements. 162
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deformations and different kind of internal forces. So we took some typical internal forces to identify the key trends and draw some conclusions. Meridional force FS and circumferential moment MS of the tower body are the control internal forces in structural design of cooling tower. We estimated the maximum meridional force and circumferential moment of the tower body under each working condition, as shown in Fig. 10 and 11, respectively. The upper and lower points on the figure represent maximum responses under 16 wind angles for each four-tower arrangement. The upper edge of the rectangle represents the response values with a probability distribution of 75% quantile, and the lower edge represents the values with a probability distribution of 25% quantile of the response. The dots are the mean value with respect to wind direction for each four-tower arrangement. As analyzed above, (1) the mean meridional force under the rectangular and rhombic arrangements were the smallest of all five arrangements. The mean meridional forces and mean circumferential moments were mildly affected by arrangement pattern; (2) taking the mean meridional force as control indicator, the most unfavorable value was observed at tower 4# under all four-tower arrangements, while the value was the most favorable at tower 2#; (3) taking the mean circumferential moment as the control indicator, tower 2# reached the design control working condition under the rectangular, L-shape and oblique L-shape arrangements; tower 4# reached the maximum response under the row and rhombic arrangements; (4) taking mean meridional force as the control indicator, the four-tower arrangements were arranged as follows: Rhombic > rectangular > L-shape > oblique L-shape > row. Taking mean circumferential moment as the control indicator, the four-tower arrangements were arranged as follows: row > oblique Lshape > rhombic > L-shape > rectangular. Figs. 12 and 13 are the box plots of axial force FC and moment MC of the columns under different four-tower arrangements, respectively. It can be seen from the figure that (1) the degree of variation of axial force and moment of columns was the smallest for tower 1#, followed by tower 2# and 3# equally, and that of tower 4# was the greatest; (2) maximum axial forces and extreme moments of columns occurred under the row and oblique L-shape arrangements; (3) taking the axial force of column as the control indicator, the four-tower arrangements were ranked as follows: rhombic > rectangular > L-shape > oblique L-shape > row; (4) taking the moment of columns as the control indicator, the four-tower arrangements were ranked as follows: rectangular > rhombic > Lshape > row > oblique L-shape. Fig. 14 shows the box plot of torque of column TC under different four-tower arrangements. Maximum torques under different four-tower arrangements all occurred under the L-shape arrangement, and the values were higher by 52%, 31%, 39% and 19% compared with the row, rectangular, rhombic and oblique L-shape arrangements, respectively.
Fig. 8. Finite element modeling of cooling tower.
It can be seen that (1) the maximum radial displacement of tower 1# varied least among different four-tower arrangements. The largest radial displacement was 0.11m, which occurred under the L-shape arrangement; (2) the maximum radial displacement of 2% tower fluctuated greatly with wind angle, and the value was about 0.12m under the rectangular and L-shape arrangements; (3) towers 3# and 4# were most greatly affected under different arrangements, and the maximum values both occurred under the rectangular and rhombic arrangements; (4) tower 2# had the highest radial displacement of tower shell, and 1# had the lowest. Table 3 lists displacement equipotential lines of the cooling tower under the most unfavorable working conditions for the single tower arrangement and five typical four-tower arrangements. The maximum deformation was up to 0.13m under the rectangular arrangement, which was considerably higher than that of other arrangements and single tower. Different four-tower arrangements were ranked as follows in terms of displacement response: row > oblique L-shape > Lshape > rhombic > rectangular. 3.3. Internal force response It is quite difficult to gather so much information about interference effect, ranging from wind-pressure distribution on the shell surface,
Table 2 Natural frequencies and vibration modes of the first ten orders.
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Fig. 9. Maximal radial displacement and other data of tower body under different wind angles for five typical four-tower arrangements.
the influence of relative position among the towers on the comprehensive stress performance, we estimated the response increments of displacement and six internal force indices under the five typical four-tower arrangements. The sum of the increments was calculated as well (Sum value), as shown in Fig. 16. Wind-induced response under the four-tower arrangements was significantly affected by the relative position among the towers. Therefore, it is not reasonable to use a uniform standard for structural design for all towers in a tower group. The Sum value was used to measure the degree of influence of relative position among the towers to compare the stress performance of different towers in a towers group.
The torque of tower 1# was least affected by tower arrangement, and it varied by only 8%. The degree of variation was all above 20% for the remaining three towers. Taking the torque of column as the control indicator, the four-tower arrangements were ranked as follows: row > rhombic > rectangular > oblique L-shape > L-shape. Fig. 15 shows the box plot of moment of ring foundation MF under different four-tower arrangements. Taking the moment of ring foundation as the control indicator, the maximum degree of variation under different four-tower arrangements was only 3%. The four-tower arrangements were ranked as follows in terms of moment of ring foundation: rhombic > rectangular > row > L-shape > oblique L-shape.
4. Stability performance analysis 3.4. Comprehensive comparison
4.1. Local stability
Table 4 presents the degree of influence of six typical internal force indices on the stress performance of the cooling tower under different four-tower arrangements. Values in the brackets are the percentages of internal force increment under the most favorable four-tower arrangement. It can be seen that (1) different index was affected differently by the group tower-induced interference. The circumferential moment of tower body and torque of column were the most greatly affected under the four-tower arrangements; (2) row arrangement was the optimal arrangement whether taking either the circumferential moment of tower body or torque of column as the control indicator. The values increased by over 50% under the most unfavorable arrangement compared with the row arrangement; (3) the remaining four internal force indices were less affected by the four-tower arrangement. These four internal force indices were greatly reduced under the rectangular and rhombic arrangements. We observed no consistent pattern in the variation of different windinduced response indicators under the four-tower arrangements. Tower 2# displayed preferable stress performance in terms of most response indicators, while tower 4# had a worse performance. In order to analyze
According to the GB/T 50102-2014 and VGB-R 610Ue 2005 design codes, local stability of the cooling tower was calculated as below: 0:8KB
σ1 σ2 þ þ 0:2KB2 σ cr1 σ cr2
"
σ1 σ cr1
2 þ
σ2 σ cr2
2 # ¼1
(1)
where σ 1 and σ 2 are the circumferential and meridian compressive stresses, respectively; KB is local stability coefficient; σ cr1 and σ cr2 are the circumferential and meridian critical compressive stresses, respectively: 0:985E
4=3 h K1 3 r0
(2)
4=3 h K2 3 r0
(3)
C σ cr1 ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi 4
1 v2c
0:612E
C σ cr2 ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi 4
164
1 v2c
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Table 3 Radial displacements of tower body under the most unfavorable working conditions for single tower arrangement and typical four-tower arrangements.
Fig. 10. Distribution of maximum meridional force of tower shell under different arrangements. 165
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Fig. 11. Distribution of maximum circumferential moment of tower shell under different arrangements.
1) The minimum KB of tower 1# was the least affected of all four-tower arrangements. Except the wind angles of 157.5 and 45 which produced an unfavorable impact on minimum KB under the L-shape and oblique L-shape arrangements, it varied little or increased somewhat compared with the row arrangement. 2) Tower 2# was more greatly affected by the arrangement pattern than tower 1#. There were several wind angles that produced an unfavorable impact on local stability of tower 2# under different arrangements.
where h is the tower body thickness; r0 is the radius of throat; vc is the Poisson's ratio of concrete; Ec is elastic modulus of concrete; K1 and K2 are geometric parameters of the tower. Fig. 17 shows the distribution of minimum local stability factor KB under different wind angles for different four-tower arrangements. The minimum KB was represented in the form of histogram under the row arrangement. The values of other arrangements were expressed as increments or decrements relative to row arrangement under each wind angle. The result was analyzed as below:
Fig. 12. Distribution of maximum axial force of column under different four-tower arrangements. 166
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Fig. 13. Distribution of maximum moment of column under different four-tower arrangements.
Fig. 14. Distribution of maximum torque of column under different four-tower arrangements. 167
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Fig. 15. Distribution of maximum moment of ring foundation under different four-tower arrangements.
load Pcri for buckling of the cooling tower was calculated as follows (Cole et al., 1975):
Some KB values under the rectangular, L-shape and oblique L-shape arrangements were below 4.0. 3) The distribution pattern of local stability factor of tower 3# was similar to that of tower 2#. The minimum KB value of 3.24 was reached for the tower 3# under the rectangular arrangement at the wind angle of 315 . The other four arrangements were favorable for local stability of tower 3#. 4) Tower 4# was most greatly affected by the arrangement pattern. The degree of dispersion of increment/decrement increased apparently, and the minimum KB was reached under the row and rhombic arrangements (4.59 and 3.20, respectively).
Pcri ¼ λi Q
(4)
where Q is the basic acting load; λi is the characteristic value of buckling or buckling load factor. Here Block Lanczos method was used to calculate the characteristic value of buckling, and the governing equation was written as ð½KL þ λi ½KG Þ fδg ¼ 0
(5)
where [KL] is the overall elastic stiffness matrix of the cooling tower; [KG] is the overall geometric matrix of the cooling tower; {δ} is the characteristic displacement vector. Buckling mode and its eigenvalue are important outputs of buckling analysis. Buckling mode reflects the configuration upon structural instability. The first order buckling mode is directly related to the buckling bearing capacity and therefore it has an important value for engineering practice (Mang et al., 1983). Fig. 19 shows the distributions of the first order buckling coefficients under different wind angles for different four-tower arrangements. Either the mean or minimum buckling coefficient of tower 4# was much lower than those of the other three towers regardless of wind angle. Different four-tower arrangements had similar impact on tower 1#, 2# and 3#. Local stability analysis indicated that the local and overall buckling stability of the cooling tower at the margin of the tower group were poor, probably because of the asymmetric wind load acting on tower surface.
Fig. 18 shows the distributions of minimum KB under the working condition most unfavorable for local stability for the single tower and four-tower arrangements. It can be seen that the minimum KB decreased more significantly under the four-tower arrangements than the single tower. The KB value was larger at the bottom and decreased towards the middle, with the minimum occurring near the height of 120m. Of different four-tower arrangements, the row arrangement had a great increase in local stability, followed by oblique L-shape arrangement. In contrast, the local stability of the tower was lower under the rectangular, rhombic and L-shape arrangements compared with the row arrangement. 4.2. Overall buckling analysis Buckling response is usually analyzed based on linear elastic characteristic value so as to assess the overall structural stability. The critical
Table 4 Degree of influence of internal force indices under different four-tower arrangements. No.
Internal force index
Action location
Preference ranking (Increased percent %)
1 2 3 4 5 6
Meridional force Circumferential moment Axial force Moment Torque Moment
Tower shell
Rhombic > Rectangular(2.52) > L-shape(4.91) > Oblique L-shape(6.99) > Row(7.38) Row > Oblique L-shape(25.74) > Rhombic(25.99) > L-shape(46.15) > Rectangular(64.85) Rhombic > Rectangular(2.11) > L-shape(4.32) > Oblique L-shape(5.90) > Row(6.67) Rectangular > Rhombic(0.74) > L-shape(5.69) > Row(7.22) > Oblique L-shape(7.79) Row > Rhombic(9.89) > Rectangular(16.54) > Oblique L-shape(27.92) > L-shape(52.46) Rhombic > Rectangular(0.04) > Row(1.79) > L-shape(2.61) > Oblique L-shape (3.01)
Bottom-supported column
Ring foundation
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Fig. 16. Increments of displacement and six internal force indices under different four-tower arrangements.
Fig. 17. Distribution of minimum KB under different four-tower arrangements.
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Fig. 20. Distributions of buckling coefficient and displacement under different four-tower arrangements.
4.3. Analysis of ultimate bearing capacity Specifically, the initial wind speed of 10 m/s at the height of 10m was taken as the basic design wind speed. Stepwise loading was imposed with a step length of 2.5m/s-10 m/s. When the wind speed was sufficiently large to cause tensile failure of tower wall (ftk1.71 MPa for C40 concrete), the reinforcing bars would bear the tension in these positions. As the wind speed further increased, the compressive regions of the concrete tower wall approached the ultimate compressive state (fck19.1 MPa for C40 concrete). As a result, the static deformation of the cooling tower increased rapidly, and the tower reached the ultimate bearing capacity. For analysis of ultimate bearing capacity, geometric non-linearity was considered under large deformation of the cooling tower. Critical wind speed of instability was calculated from the slope of maximum displacement varying with wind speed and the ultimate compressive state of concrete. Figs. 21 and 22 show the distribution of critical wind speed under different four-tower arrangements and the variations of displacement and slope with wind speed under the most unfavorable working condition, respectively. Comparison revealed the following:
Fig. 18. Distribution of minimum KB under the working condition most unfavorable for local stability.
Fig. 20 shows the buckling modes and maximum displacements under the working condition most unfavorable for buckling stability for different four-tower arrangements. The first order buckling coefficient under the single tower arrangement was 9.43. Of all four-tower arrangements, rhombic and L-shape arrangements had poor overall buckling safety. The first order buckling coefficient of these two arrangements decreased by nearly 10% compared with the single tower. In contrast, the row, rectangular and oblique L-shape arrangements were more favorable for overall buckling stability.
Fig. 19. Distribution of first order buckling coefficient under different four-tower arrangements. 170
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Fig. 21. Distribution of critical wind speed under four-tower arrangements.
2) Tower 2# under rectangular arrangement encountered the most unfavorable working condition under the wind angle of 270 . Under rhombic, L-shape and oblique L-shape arrangement tower 2% had the minimum ultimate bearing capacity under the wind angle of 247.5 , 67.5 and 292.5 , respectively. Under this situation, the incoming flow produces an asymmetric canyon effect to the cooling tower of our concern. 3) Taking ultimate bearing capacity of the control indicator, the fourtower arrangements were ranked as follows: row > oblique Lshape > rhombic > L-shaped > rectangular.
1) All four towers in the row arrangement had a larger critical wind speed at the wind angle of 90 and 270 . Under these working conditions, the cooling tower was mainly affected by the shield effect. The minimum critical wind speed under the row arrangement occurred at tower 4# under the wind angle of 0 .
5. Conclusion Wind tunnel tests for five typical four-tower arrangements were performed, include a total of 320 working condition, and finite element method was used to simulate the influence of arrangement pattern on wind-induced response and stability performance of cooling towers group. The main research contents included wind tunnel test, finite element analysis, dynamic analysis, wind-induced response analysis, local stability estimation, overall buckling analysis and ultimate bearing capacity. The following conclusions were drawn:
Table 5 Preference ranking of four-tower group under five arrangements in terms of wind-induced response.
Fig. 22. Variations of displacement and slope with wind speed under the most unfavorable working conditions for the single tower arrangement and fourtower arrangements. 171
Arrangements
Preference ranking (advantage > disadvantage)
Row Rectangular Rhombic L-shape Oblique L-shape
2# 1# 2# 3# 3#
CT > 3# CT > 1# CT > 4# CT > 4# CT > 3# CT > 2# CT > 1# CT > 3# CT > 4# CT > 2# CT > 4# CT > 1# CT > 2# CT > 1# CT > 4#
CT CT CT CT CT
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Fig. 23. Relative positions of towers in different arrangements under the most unfavorable wind direction.
● The four-tower arrangement had major impact on displacement response, circumferential moment of tower body and torque of column. Row arrangement was the optimal arrangement in terms of these indicators. The values of the three indicators increased by 27.13%, 64.85% and 52.46% under the other three four-tower arrangements increased by 27.13%, 64.85% and 52.46% compared with the row arrangement, respectively. Thus the preference ranking in terms of comprehensive wind-induced response was as follows: row > rhombic > oblique L-shape > rectangular > L-shape. ● The wind-induced response was greatly affected by relative position among the four towers. Thus it is not reasonable to use a uniform standard for structural design for all towers in a tower group. Moreover, the extreme values of different response indicators of the four towers varied inconsistently due to group tower-induced interference and action of adjacent structures. Table 5 shows the preference rankings of four-tower group in terms of wind-induced response. ● Row and oblique L-shape arrangements had higher local stability, overall buckling stability and ultimate bearing capacity. The critical wind speeds of instability of rectangular, rhombic and L-shape is only 60%, 70% and 65% of the critical wind speed at the row arrangement, and these three types of four-tower arrangements should be carefully adopted in areas with high basic wind speed. ● Working conditions most unfavorable for wind resistance safety were identified for the five four-tower arrangements based on comprehensive wind-induced response and stability indicators (Fig. 23). The comprehensive stress performance of the cooling tower was greatly impaired by the asymmetric canyon effect.
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Acknowledgments This project is jointly supported by National Natural Science Foundation (51761165022 and U1733129), Jiangsu Province Outstanding Natural Science Foundation (BK20160083), and Jiangsu Province QingLan Project, which are gratefully acknowledged. Appendix A. Supplementary data Supplementary data related to this article can be found at https://doi. org/10.1016/j.jweia.2018.05.019. References ASCE Structural Engineering Institute, 2012. Wind Tunnel Testing for Buildings and Other Structures.” ASCE 49-12-2012. The American Society of Civil Engineers. Bamu, P.C., Zingoni, A., 2005. “Damage, deterioration and the long-term structural performance of cooling-tower shells: a survey of developments over the past 50 years. Eng. Struct. 27 (12), 1794–1800. Bearman, P.W., 1967. Wind Forces and the proximity of cooling towers to each other. Nature 216 (5050), 735.
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