Wind-induced static performance of cooling tower considering
multiple loading effects
X.X. Cheng a, L. Zhao a, Y.J. Ge a
a
State Key Laboratory for Disaster Reduction in Civil Engineering, Tongji University,
Shanghai,China
ABSTRACT: The pressure-measuring tests for certain super large cooling towers are first reported,
so the static wind loads on the cooling towers can be easily illustrated with some parameters, such
as the surface extreme value pressure distribution, the tower group factor; and the wind-vibration
factor. With the help of the finite element method (FEM) numerical simulation, the performance of
cooling towers due to the static wind loads, including stress, displacement and local elastic stability
are presented. Then, considering material and geometrical non-linearities about the reinforced
concrete, the ultimate bearing capacity of the structures under static wind action is also discussed.
The analysis process focuses on considerations of some key effects concerning structural design
works, i.e., the internal pressure effect, the distribution mode of external surface pressure, the
boundary effect, the wind profile index and the group tower interference effect.
KEYWORDS: Cooling tower; Pressure-measuring test; Finite element numerical simulation; Local
elastic stability; Material and geometrical non-linearity; Ultimate load bearing capacity
1 INTRODUCTION
Super large hyperbolic cooling towers are extremely sensitive to wind loads, which are usually the
control load in structural design and construction. As China stages its fast-growing performance in
construction of super large cooling towers and tower groups today, more expectations relating to
these huge structures’ wind resistance designs are given from engineering circles. However, it
seems that the present technical supports can hardly meet current requirements based on the
following facts. First, the current Chinese codes (e.g. NDGJ5-88 and GB/T 50102-2003) stipulate
that the terms for computation of important design parameters, such as the tower-group factor and
the wind-vibration factor, can only be applied to towers under a height of 165-meters. Besides, it is
also stipulated in the Chinese codes that group tower interference effects can be ignored for those
with bottom center distances above 1.5 times tower diameter, which is different from some other
countries’ codes (e.g. BTR VGB’Richtlinie Bautechnik bei Kühltürmen and Règles Professionelles
applicable à la Construction des Réfrigérants Atmosphériques en Béton Armé) and has been proved
to be imperfect by some wind tunnel experimental studies.
Rigid model pressure-measured wind tunnel tests of a 176-meter super large cooling tower and
some group towers of different combinations were described briefly in the beginning of this study.
Loading the extreme value wind pressure distribution patterns obtained from wind tunnel tests,
which are taken as strong wind loads with design wind speed in certain return period, the static
structural performances of the cooling towers with different condition combinations based on FEM
numerical simulation introducing a bilinear material constitutive model and large deformation
geometric nonlinearity considerations are presented. Then, results of the numerical studies
including the structural response (internal force and displacement), the tower shell’s local elastic
stability performance as well as the total structure’s ultimate load-carrying capacity are studied. The
research process focus on studies of some key effects influencing the structural static performance,
i.e. internal pressure effect, considerations for external pressure distribution, boundary effect, wind
profile effect and group tower interference effect. The conclusions drawn are of practical
significance to relating structural design works.
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2 WIND TUNNEL TEST AND DATA PROCESSING
In a practical electric power plant situation in southeast China, a set of designing cooling towers are
part of a dense arrangement of large buildings, which are of comparable size with the cooling
towers. As a result, the influence of adjacent buildings or towers on cooling towers cannot be
ignored, even though the towers’ center distances conform to the basic requirements of the Chinese
Codes (> 1.5 times the single tower diameter).
Table.1 Building dimensions in the electric power plant
Cooling tower height
177.147m
Tower top diameter
82.260m
Throat diameter
78.216m
Tower base diameter
134.694m
Minimum distance of towers
≥1.5 tower base diameter
Height of half sphericity bunker
80.0m
Chimney height
210.0 m
Hill height
56.5～136.0 m
Other building height
35.0～135.0m
The second stage of the project features two 177-meter super large cooling towers. To the west,
there are four 80-meter hemispherical coal bunkers and an 80~140-meter high continuous mountain,
and to the south, there is an industrial complex which includes two 210-meter tall chimneys. During
the third stage of the project, two new towers, two additional new hemispherical coal bunkers and
an industrial complex will also be constructed (see Fig.1 and Table.1 for building dimensions and
site plan respectively).
Site plan
Fig.1 Ⅱ and Ⅲ stage cooling tower groups
Site model
The test was conducted in the TJ-3 atmospheric boundary layer wind tunnel, which belongs to
Tongji University’s State Key Laboratory for Disaster Reduction in Civil Engineering. As a closed
return-flow wind tunnel with rectangular cross section, the dimensions of its test section are: 15m in
the lateral direction, 14m in the longitudinal direction, and it has a height of 2m. Both external and
internal pressure-measuring models of the super large cooling tower are 1:200 scale rigid models
(see Fig.2), the blockage ratios of the cooling tower and surroundings are less than 7%.
The surrounding landscape of the project is type A according to NDGJ5-88 or GB/T
50102-2003. Measurement of atmospheric boundary layer uses a Streamline hot-wire anemometer
of DANTEC Corp. It shows the following: the wind profile exponent a =0.12, the ground surface
turbulence intensity is 15%, and the turbulence intensity at the height of the tower top is 10%.
The locations of the taps are shown in Fig.3. For the external pressure measuring tower model,
36 (around the circumferential direction) ×12 (along the meridian direction) taps are arranged. For
the internal pressure measuring model, 36 (around the circumferential direction) ×6 (along the
meridian direction) taps are arranged. DSM3000 electronic pressure scanners of Scanivalve Corp.
are used for mean and fluctuating pressure measurements on model surface. The signal data are
acquired at a sampling rate of 312.5Hz, and for each measuring point, the total sampling length is
2
1605
6000.
Fig.2 b) Model for internal pressure
Fig.2 a) Model for external pressure
177.146
163.23
outsec12
150.23
outsec11
138.56
outsec10
125.58
outsec9
112.65
outsec8
99.82
intsec6
intsec5
outsec7
intsec4
outsec6
87.08
outsec5
75.70
intsec3
outsec4
63.12
outsec3
50.63
intsec2
outsec2
36.95
outsec1
24.57
intsec1
0.00
a) Height label (unit: m)
b) Taps for external pressure
c) Taps for internal pressure
Fig.3 Measured points of outside or inside wind pressure distribution and measured sections of wind-induced vibration
response
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1.5
Test Result
NDGJ5-88
1.0
Pressure Coefficient
0.5
0.0
-0.5
-1.0
-1.5
-2.0
0
20
40
60
80
100
120
140
160
180
Angle(Degree)
Fig.4 Pressure comparison of test and Codes
The Reynolds number scope ranges from 1.5×108 to 3.5×108 for the actual super large cooling
tower of this project considering design wind speed. However, it is difficult to simulate the actual flow
characteristics around the model tower’s surface with a super-high Reynolds number by increasing the
experimental wind speed and maximizing the models’ geometric dimensions for the limitations of wind
tunnel technique. The general practice in solving this problem is to adjust the surface roughness of
tested cooling tower models to obtain the super-high Reynolds number effects for flow around the
surface (see Fig.2), which is successfully done in this study as is shown from a good fitting between
two pressure coefficient curves in Fig.4 which are acquired based on tests and code NDGJ 5-88
respectively. In Fig.4, the test results are the mean value of several pressure coefficient distribution
patterns around some intermediate pressure-measured cross-sections on the surface of the external
pressure measuring model and the data from code NDGJ 5-88 are based on some actual
measurement works. The external pressure distribution patterns around a single tower’s surface fit a
curve in the form of eight-termed trigonometric series according to NDGJ5-88 or GB/T
50102-2003:
m
mp (q) =
å
ak cos k q
(1)
k= 0
in which, fitting parameters a0=-0.779，a1=0.313，a2=1.016，a3=0.737，a4=0.044，a5=-0.1429，
a6=0.074，a7=0.086.
The definition of a cooling tower’s total aerodynamic drag force coefficient (along-wind
direction) is as follows:
n
CD =
å
CPi Ai cos (qi )
i= 1
(2)
AT
in which, CD is the structural total drag force coefficient, Ai is the coverage area of the pressure
measuring point i, θi is the separation angle between the pressure action direction on point i and the
wind axis, AT is the whole structure’s projection area along the wind axis.
Considering the time-history correlation between the shape coefficient on the taps and the total
structural drag or lift force, the mean results of the pressure extreme value distribution patterns on
several intermediate cross-sections are obtained. Fig.5 compares the distribution patterns between
the general envelope of test extreme values and codes, which demonstrates that although the
pressures in the wake zone and the separation points are the same, there exist certain differences:
the maximum and minimum values in the test pressure coefficient extreme value distribution
pattern are 1.298 and -2.307 respectively, which equal to 78% and 87% of the code extreme values
(1.668 and -2.603, respectively), and the difference of the corresponding angles of maximum
negative pressure reaches 10 degrees.
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2.0
Extreme Value of Shape Coefficient
1.5
Test Extreme Value Envelope
NDGJ5-88
1.0
0.5
0.0
-0.5
-1.0
-1.5
-2.0
-2.5
-3.0
0
20
40
60
80
100
120
140
160
180
Angle/Degree
Fig.5 General envelope of test values and codes
According to time domain dynamic analysis based on multipoint fluctuating pressure time
history data and aeroelastic model wind tunnel tests (prior works), the wind-vibration factors have
been obtained for this project: 1.70 for single tower, 2.22 for two-tower group combination (at the
most adverse incoming flow condition), and 2.50 for four-tower group combination (at the most
adverse incoming flow condition).
If the tower surface pressure distribution pattern provided by NDGJ5-88 is adopted, the mean
value of drag coefficient is 0.437 for uniform flow. For comparison study, the tower group factor is
defined as:
Km =
CD ,max,sin gle 创Pch K M if
CD , mean ,sin gle,code ´ b sin gle,test
(3)
in which, CD,max,single is the extreme value of the drag force coefficient for a single tower in
turbulence flow field (0.541); for type A atmospheric flow, Pch=0.541/0.397=1.36 is the ratio of
drag force coefficient for a single tower in uniform flow to that in turbulent flow; Ｋ is the
maximum ratio of the ultimate value of the drag force coefficient of an interfered tower to that of
the single tower; Mif=1.0+βsingle,test/βsingle,code is the correction term of the tower’s wind-induced
inertia force, βsingle,test and βsingle,code are the wind-vibration coefficient results based on experimental
results (1.70) and code NDGJ5-88 (1.60), respectively; CD,mean,single,code is the mean value of a single
tower’s drag force coefficient in uniform flow of NDGJ5-88 (0.437). Intrinsically, Km can be
interpreted as the ratio of the experimental value of the total static wind loads for all conditions to
total wind load on a single tower based on the codes.
For both the second stage project and the third stage project, the most adverse incoming flow
conditions both feature a direction of a clockwise 15° included angle from the east. According to
formula (3), tower group factors for a two tower group and a four tower group are 1.226 and 1.385,
respectively.
The penetration ratio of the packing layer is modeled using a uniformly pierced organic glass
board placed at the bottom of the tower’s main body. Experimental results in type A turbulent flow
show that the penetration rate has no significant effect on internal pressure distribution patterns, but
it is closely related to the internal pressure value. The internal pressure mean value increases when
decreasing the draught penetration ratio (see Table.2). For some experimental conditions, the
draught penetration ratio is 30%, so the internal pressure distributes uniformly inside the tower shell
with the extreme value of -0.656.
Table.2 Internal pressure coefficients of single cooling tower
Draught penetration ratio
100%
55%
30%
15%
3%
Internal pressure mean value* -0.375×1.6 -0.382×1.6 -0.410×1.6 -0.524×1.6 -0.590×1.6
* Reference wind pressure is wind pressure at the top of tower.
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0%
-0.761×1.6
3 FINITE ELEMENT MODEL
The main body of the FEM model is comprised of discrete spatial shell elements, and the top
stiffening ring and 48 pairs of herringbone columns connected to a ring foundation with fixed
bottom ends are modeled using space beam elements. Two different models using a different
number of shell elements (one applies 504 shell elements, the other applies 19008 shell elements)
are compared. Results show that none of the relative errors among their corresponding 1st~ 8th
modal frequencies is less than 3%, and their corresponding vibration modes are the same. For
simplification, the simple model, which applies 504 (36*14) shell elements, is adopted. The main
structural characteristics are presented in table.3. Natural frequencies and vibration shapes of the
1st~4th modes are presented in table.4.
Componen
t
Height/m
Main body
12.216
24.811
37.405
50.000
62.594
75.189
87.784
100.378
112.973
125.568
138.162
150.757
163.351
175.946
Herringbo
ne column
Mode
Table.3 Main structural characteristics of cooling tower
Shell
Concrete
3D View of cooling tower FE
Radius/m
thickness/m
grade
model
1.400
67.347
C40
0.350
63.334
C40
0.340
59.380
C40
0.330
55.217
C40
0.330
51.656
C40
0.320
48.357
C40
0.320
45.685
C40
0.310
43.123
C40
0.300
41.103
C40
0.271
39.731
C40
0.271
39.132
C40
0.271
39.229
C40
0.271
39.543
C40
0.400
39.860
C40
48 pairs, 1300mm diameter
C45
Table.4 Natural frequency and vibration shape of cooling tower
Mode shape
Mode shape
View of
(number of
(number of
mode
Frequency/Hz
Mode Frequency/Hz
harmonic
harmonic
shape
waves)
waves)
1st
0.939
circumferential
5; meridian 2
3rd
1.075
circumferential
4; meridian 2
2nd
1.044
circumferential
5; meridian 2
4th
1.125
circumferential
3; meridian 1
View of
mode
shape
4 SOME KEY EFFECTS ON COOLING TOWERS’ WIND-INDUCED STATIC
PERFORMANCE USING LINEAR ELASTIC FEM ANALYSES
For this part of the study, the 100 years basic design return period wind speed is 33m/s, the wind
profile index is 0.12, and the dead weight is taken into account in load combination.
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4.1 Internal pressure effect
Table.5 Response of cooling tower for different internal pressure conditions
Internal
Maximum total
Maximum primary
Condition
pressure
deformation /m
tensile stress /MPa
extreme value
100%
-0.637
0.0366
0.733
Draught penetration
30%
-0.658
0.0366
0.729
Ratio
10%
-0.717
0.0366
0.717
0%
-1.082
0.0367
0.644
No internal pressure
0.0
0.0364
0.868
General consideration in practical
-0.8
0.0366
0.701
design (NDGJ5-88)
(-0.5×1.6)
Maximum primary
compressive stress
/MPa
4.23
4.23
4.23
4.22
4.23
4.23
The pressure on the external surface of the cooling tower applied for analyses follows the
single tower’s extreme value distribution pattern obtained in the wind tunnel test mentioned above.
Table.5 compares the cooling tower’s response under static wind of different internal pressure
conditions, demonstrating that with the increase of the draught penetration ratio of the stuffing layer,
the absolute value of the negative internal pressure decreases, and the cooling tower’s maximum
total displacement and the primary compressive stress undergo little change. The maximum primary
tensile stress drops smoothly with the increase of the absolute value of the internal pressure as
shown in Table.5 (a 12.14% decrease from 100% to 0% draught penetration ratio condition). An
analysis based on a representative code (NDGJ5-88) renders results of all structural performances
between those of 0% and 10% draught penetration ratio. It is also proved that disregarding the
internal pressure is a risky practice in view of the maximum total deformation response.
4.2 Effect of the external pressure extreme value distribution patterns
Through correlation analysis of multipoint fluctuating wind loads on the cooling tower’s
external surface, the extreme value distribution patterns of the tower’s external pressure are
obtained (see Fig.5). Compared with the traditional methodology using the mean surface wind
pressure distribution pattern from NDGJ5-88 multiplied by a wind-vibration factor, it is found that
the method of loading the experimental extreme pressure distribution causes favorable overall
structural responses, demonstrating the safe consideration of code NDGJ5-88 (see Table.6). From
Table.6, there exists a little disagreement of the occurrence positions of maximum responses
between the two methodologies, which is also a major concern in structural design.
Table.6 Response of cooling tower for different external pressure modes
Maximum total deformation
Maximum primary tensile stress
Maximum primary compressive stress
External
pressure
distribution
pattern
Experimental
result
Traditional
consideration
(NDGJ5-88)
Occurrence
position
Occurrence
position
Occurrence
position
Response
magnitude/m
relative
to
tower
height
Included
angle
from
incoming
flow
Response
magnitude/MPa
relative
to
tower
height
Included
angle
from
incoming
flow
Response
magnitude/MPa
relative
to
tower
height
Included
angle
from
incoming
flow
0.0388
0.746
0°
0.786
0.848
±85°
4.34
0.286
±70°
0.0475
0.783
0°
1.260
0.885
±75°
4.77
0.286
±70°
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4.3 Group tower interference effect
Applying the two methodologies mentioned above to consider the external surface pressure
distribution, Table.7 shows the cooling towers’ responses with different group tower combinations.
The responses obtained by loading the pressure distribution pattern obtained from the codes
(hereinafter referred to as the traditional methodology) are stronger than the corresponding results
obtained by loading pressure distribution patterns based on wind tunnel tests. The occurrence
positions of both the maximum total deformation and the primary tensile/compressive stress of the
traditional methodology are slightly higher than the computational results using experimental
pressure distributions. Difference around 10 to 15 degrees exists between the circumferential
occurrence points of the maximum primary tensile stress on the curves calculated using different
methodologies considering corresponding group tower combination conditions.
It is notable that by loading the experimental extreme value wind pressure distribution patterns
acquired through correlation analysis, the magnitudes of the structural responses of different group
tower conditions demonstrate a variation trend different from that of the tower group factors (i.e.
the tower group factor for the four tower group condition > that for the two tower group condition >
that for the single tower condition, see Section 2). For both the maximum total deformation and the
maximum primary compressive stress, the trend is: the responses of the four tower group condition
> those of the single tower condition > those of the two tower group condition. The phenomenon
can be interpreted that although tower group factors and wind-vibration factors are both increasing
when adding tower numbers in the tower group, the lateral load distribution and the load action
center of vertical wind loads both change, and the shell thickness at the height of the total load
action position changes accordingly, reflected by the descending trends of the heights of the
maximum response positions, which is favorable in view of wind effects on the structures.
Table.7 Response of cooling tower with group tower interference effects
Maximum total
Maximum primary
Maximum primary
deformation
tensile stress
compressive stress
External
pressure
distribution
pattern
Extreme
value
(from
experiment)
Mean value
(from
NDGJ5-88)
×Km×β
Condition
Single
tower
Two
towers
(second
stage)
Four
towers
(third
stage)
Single
tower×
1.70
Single
tower×
2.22
Single
tower×
2.50
Response
magnitude
/m
Occurrence
position
relative
to
tower
height
Included
angle
from
incoming
flow
0.0388
0.746
0°
0.0335
0.746
0.0453
Response
magnitude
/m
Occurrence
position
relative
to
tower
height
Included
angle
from
incoming
flow
0.786
0.848
±85°
0°
1.020
0.921
0.709
0°
1.390
0.0503
0.782
0°
1.35
0.0653
0.782
0°
1.80
0.0734
0.782
0°
2.11
Response
magnitude
/m
Occurrence
position
relative
to
tower
height
Included
angle
from
incoming
flow
4.34
0.286
±70°
＋90°
4.29
0.247
±70°
0.848
＋90°
4.75
0.247
±70°
0.885
±75°
4.91
0.286
±70°
5.66
0.286
±70°
6.07
0.286
±70°
(0.885, ±75°)
or
(0.321, 0°)
4.4 Effect studies based on local elastic stability check
As a large thin-walled shell structure, local elastic stability check should be included in a cooling
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tower’s structural design. According to NDGJ5-88, the following formulae are applied for analyzing
of the shell’s local elastic stability:
0.8 K B (
s cr1 =
s1
s
s
s
+ 2 ) + 0.2 K B2 [( 1 ) 2 + ( 2 ) 2 ] = 1
s cr1 s cr 2
s cr1
s cr 2
0.985 E
h
( ) 4 / 3 K1 ;
4
(1- n ) r0
s cr 2 =
2 3
(4)
0.612 E
h
( )4 / 3 K 2
4
(1- n ) r0
(5a,b)
2 3
in which, σcr1 is circumferential critical pressure; σcr2 is meridian critical pressure; σ1、σ2 are
circumferential and meridian compressive stresses considering internal suction respectively; E，v are
the elastic modulus and the Poisson ratio of shell concrete, respectively; r0 is the throat radius of the
tower body; h is the shell thickness at the tower throat; K1、K2 are both determined by the tower
body’s geometric parameters (in this study, K1=0.138，K2=1.267); KB is the local stability safety
factor.
Table.8 compares the cooling tower shell’s local stability performances with the effect
combinations of different group tower conditions, two kinds of external pressure distribution
patterns and different considerations for internal pressure. The minimum KB on the tower body (the
occurrence position is about 0.286 relative to tower height where shell thickness is 0.330 meters)
considering different effect combinations are listed in Table.8. For all effect combinations in Table.8,
minimum KB are above 5, meeting the requirements of code NDGJ5-88. Taking into account the
internal pressure effects, the circumferential compressive stresses stage an increase of 35.6%, and
the meridian compressive stresses are insensitive to the change. As a result, local stability decreases.
For consideration of external pressure distribution patterns, the local stability check results based on
the traditional methodology is lower than those based on the methodology applying results of prior
wind tunnel tests. It is obtained by quantifying the local stability of the cooling tower shell that:
single tower’s stability >four tower group’s stability > two tower group’s stability, which is still
different from the variation trend of tower group factors (see Section 4.3). The difference should
mainly be attributed to changes to the vertical center of total wind action.
Condition
Single
tower
Single
tower
Single
tower
Two towers
(second
stage)
Four towers
(third stage)
Table.8 The local elastic stability due to several effect combinations
Effect combination
Circumferential
Meridian
Angle of
External
Internal
compressive
compressive
minimum KB
pressure
pressure
position
stress/MPa
stress/MPa
distribution
consideration
pattern
Minimum KB
NDGJ5-88
No
0.382
0.453
±70°
7.153
NDGJ5-88
Yes
0.518
0.454
±70°
6.458
Experimental
result
Yes
0.567
0.382
±60°
6.892
Experimental
result
Yes
0.738
0.355
±70°
6.268
Experimental
result
Yes
0.658
0.384
±80°
6.408
5 SOME KEY EFFECTS ON COOLING TOWERS’ ULTIMATE LOAD-CARRYING
CAPACITY BASED ON NONLINEAR FEM ANALYSES
Comparison studies of the cooling towers’ ultimate load-carrying capacity under wind loads of
different working conditions are conducted, which focus on comparisons of the failure shapes of
shell and ultimate wind speeds. The static wind stability analysis is based on a general finite
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element platform taking into account the dead weight, material and geometric nonlinear effects in
analyzing process. The basic failure process of the cooling tower is simulated as follows. First, wind
loads of design basic wind speed (set 10m/s on a height of 10 meters as the initial wind speed) are
loaded using a step-by-step method (loading step length is around 2.5～10.0m/s). With the increase
of wind loads, some local areas on the concrete shell are damaged under tensile stress (for C40
concrete, ftk≥2.39MPa). As a result, the reinforcement bars withstand the whole tensile strength in
those failed areas. Then, the shell concrete in the compressive region on the tower body comes to its
ultimate compressive condition (for C40 concrete, fck≥26.8MPa). With the rapid increase of
deformation, the structure soon reaches its ultimate condition which can easily be determined from
the critical points on wind speed-deformation gradient curves.
5.1 Wind profile effect
0.7
0.014
Wind Profile Exponent a = 0.00
Wind Profile Exponent a = 0.12
0.5
Deformation/m
Wind Profile Exponent a = 0.00
Wind Profile Exponent a = 0.12
0.012
Deformation Gradient (m/(m/s))
0.6
0.4
0.3
0.2
0.1
0.010
0.008
Critical Point
0.006
Critical Point
0.004
0.002
0.000
0.0
0
20
40
60
80
100
120
140
160
0
180
20
40
60
80
100
120
140
160
180
Basic Wind Speed (m/s)
Basic Wind Speed (m/s)
Fig.6 Displacements and their derivatives for different wind profiles
Wind
profile
exponent
α=0.00
α=0.12
Occurrence position
of maximum
deformation
Included
Relative
angle
to tower
from
height
incoming
flow
0.782
0°
0.782
0°
Table.9 Critical states for different wind profiles
Instability critical state
Critical state in tensile region
(Critical state in compressive region)
Occurrence position
Occurrence position
Primary
Included Critical
Included Critical
wind
wind
compressive
Relative
Relative
angle
angle
speed
speed
stress
to tower
from
to tower
from
(m/s)
(m/s)
(MPa)
height
incoming
height
incoming
flow
flow
0.286
0°
72.5
0.209
±70°
160.0
24.2
0.286
0°
52.5
0.286
±70°
125.0
25.2
Ignoring the internal pressure effect and applying the external wind pressure distribution curve
of code NDGJ5-88, a comparison study of the cooling tower’s ultimate load-carrying strength based
on two different wind profiles (uniform profile and turbulent flow field profile) is conducted (see
Fig.6 and Table.9). Results show that there exist noticeable wind profile effects. With the turbulent
flow field profile, the vertical action center of the surface aerodynamic loads rises and the center of
the maximum compressive stress region rises by 36% compared with that of the uniform flow
condition. As the shell thickness at the position of the vertical action center decreases for the
turbulent flow condition, the instability critical wind speed drops by 23.4%, causing structural
buckling vulnerability.
5.2 Internal pressure effect
The study of the internal pressure effect on the cooling tower’s ultimate load-carrying capacity
is conducted. Results (Fig.7 and Table.10) show that there is no significant internal pressure effect,
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for no notable changes of maximum total static wind-induced deformation have been observed.
There is no change of the occurrence position of the maximum deformation, nor is there any change
of the occurrence position of tensile stress or compressive stress at critical states according to
Table.10. The instability critical wind speed drops by 4.0% after considering the internal pressure
effect.
0.7
0.014
Internal Pressure CP=0.000
Internal Pressure CP=0.409
0.5
Deformation/m
Internal Pressure CP=0.000
Internal Pressure CP=0.406
0.012
Deformation Gradient (m/(m/s))
0.6
0.4
0.3
0.2
0.1
0.0
0.010
Critical Point
0.008
Critical Point
0.006
0.004
0.002
0.000
0
20
40
60
80
100
120
140
0
20
40
60
80
100
120
140
Basic Wind Speed (m/s)
Basic Wind Speed (m/s)
Fig.7 Displacements and its derivatives for different internal pressures
Internal
pressure
Cp=0.000
Cp=0.409
Table.10 Critical states for different internal pressures
Instability critical state
Occurrence positions
Critical state in tensile region
(Critical state in compressive region)
of maximum
deformation
Occurrence position
Occurrence position
Critical
Primary
Included
Included Critical
Included
wind
wind
compressive
Relative
angle
Relative
angle
Relative
angle
speed
speed
stress
to tower
to tower
to tower
from
from
from
(m/s)
(m/s)
(MPa)
height
incoming
height
incoming
height
incoming
flow
flow
flow
0.782
0°
0.286
0°
52.5
0.286
±70°
125.0
25.2
0.782
0°
0.286
0°
52.5
0.286
±70°
120.0
24.0
5.3 Boundary effect
After the Reynolds number effect modeling, the surface pressure mean value distribution of
several intermediate sections coincide with the code results in this study. However, three
dimensional effects (or boundary effect) in end regions (the top/bottom areas) of the tower surface
can be demonstrated by the notable differences between experimental pressure distribution patterns
and the surface pressure curve for sections of all heights given by the code NDGJ5-88, as shown in
Fig.8.
Fig.9 and Table.11 both compare the boundary effect on the structural ultimate load-carrying
capacity. It is shown that there is no significant boundary effect on the structural ultimate
load-carrying capacity by comparison the static wind load deformation-wind speed curves, as well
as the occurrence positions of maximum deformation and tensile or compressive stresses (see Fig.9
and Table.11). Since the critical wind speed of the total structural instability drops by 4.2% after
considering the boundary effect, the overall boundary effect is mildly adverse.
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1.5
NDGJ5-88
Intermediate Sections
Top Section
Bottom Section
1.0
Pressure Coefficient
0.5
0.0
-0.5
-1.0
-1.5
-2.0
0
20
40
60
80
100
120
140
160
180
200
Angle
Fig. 8 Surface pressure curves of different heights
0.7
0.014
NDGJ5-88
Experimental Result
0.6
Deformation Gradient (m/(m/s))
0.012
0.5
Deformation/m
NDGJ5-88
Experimental Result
0.4
0.3
0.2
0.1
0.010
Critical Point
0.008
0.006
Critical Point
0.004
0.002
0.000
0.0
0
20
40
60
80
100
120
0
140
20
40
60
80
100
120
140
Basic Wind Speed (m/s)
Basic Wind Speed (m/s)
Fig.9 Displacements and its derivatives for different boundary conditions
Surface
pressure
NDGJ5-88
Experimenal
results
Table.11 Critical stations for different boundary conditions
Instability critical state
Occurrence
Critical state in tensile region
(Critical state in compressive region)
positions of
maximum
Occurrence position
Occurrence position
deformation
Critical
Critical
Primary
Included
Included
Included
wind
wind
compressive
Relative
angle
Relative
angle
Relative
angle
speed
speed
stress (MPa)
to tower
from
to tower
from
to tower
from
(m/s)
(m/s)
height
height
height
incoming
incoming
incoming
flow
flow
flow
0.782
0°
0.286
0°
52.5
0.286
±70°
120.0
24.0
0.782
0°
0.286
0°
52.5
0.286
±70°
115.0
23.7
5.4 Group tower interference effect
Fig.10 and Table.12 compare the cooling tower’s ultimate load-carrying capacity with different
group tower interference effects. For different group tower conditions, there is no significant change
of the occurrence position of the maximum deformation or the occurrence positions of the
maximum tensile/compressive stress at the critical states. Comparing the critical wind speed, it is
shown in Fig.10 that: the critical wind speed for single tower > that for four tower group condition
> that for two tower group condition. The results coincide with those of the local elastic stability
study (see Section 4.4), proving the change of position of the vertical action center.
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0.7
0.014
Single Tower
Two Towers Combination
Four Towers Combination
0.012
Deformation Gradient (m/(m/s))
0.6
0.5
Deformation/m
Single Tower
Two Towers Combination
Four Towers Combination
0.4
0.3
0.2
0.1
0.010
0.008
Critical Point
Critical Point
0.006
0.004
Critical Point
0.002
0.000
0.0
0
20
40
60
80
100
120
0
140
20
40
60
80
100
120
140
Basic Wind Speed (m/s)
Basic Wind Speed (m/s)
Fig.10 Displacements and its derivatives for different tower group combinations
Group
combination
Table.12 Critical states for different tower group combinations
Instability critical state
Occurrence position
Critical state in tensile region
(Critical state in compressive region)
of maximum
deformation
Occurrence position
Occurrence position
Primary
Included
Included Critical
Included Critical
wind
wind
compressive
Relative
Relative
Relative
angle
angle
angle
speed
speed
stress
to tower
from
to tower
from
to tower
from
（MPa）
height incoming height incoming （m/s） height incoming （m/s）
flow
flow
flow
Single
tower
Two towers
Four towers
0.782
0°
0.286
0°
52.5
0.286
±70°
115.0
23.7
0.782
0.782
0°
0°
0.247
0.247
0°
0°
50.0
52.5
0.286
0.286
±70°
±70°
102.5
107.5
17.5
18.5
Single tower
Two towers (second stage)
Four towers (third stage)
Top
section
Throat
section
Fig.11 Structural failure shapes for different tower group combinations
Further study of structural failure (or buckling) shapes on both top and throat sections of
different tower group combinations conditions are shown in Fig.11. It is demonstrated that the
failure shapes of the second stage condition and the third stage condition are similar and there exist
some differences in deformation symmetry properties as well as the occurrence position of
maximum deformation between the single tower condition and the group tower conditions.
6 CONCLUSIONS
The conclusions drawn in this study are as follows:
(i) Generally, the extreme value wind load action is not taken as the control loading in
cooling towers’ structural design at present. The internal pressure effect on the tower’s local elastic
stability and overall structural ultimate load carrying capacity is mildly adverse. According to the
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comparison study, the traditional methodology of considering extreme value wind pressure
distribution patterns renders adverse structural performance compared with the methodology based
on the wind tunnel tests for a single tower.
(ii) There exist notable group tower interference effects on the total extreme value wind
loads, the structural responses (deformation and internal force), the local elastic stability, the
ultimate load-carrying capacity and the instability shape of the cooling towers situated in the
specific engineering site (described in Section 2). The variation trends of the tower group factor, the
local elastic stability factor and the critical wind speed with different group tower conditions are
different, demonstrating the complexity in considering the group tower interference effect. The
methodology in considering group tower interference effect using the external pressure distribution
obtained from codes, the tower group interference factor and the wind-vibration factor is
conservative compared with the methodology based on the extreme value wind pressure distribution
patterns obtained from wind tunnel tests.
(iii) The wind profile effect is obvious. Considering the wind profile of turbulent flow field,
the critical wind speed of the instability critical state drops significantly, since the vertical center of
the total surface aerodynamic wind action rises.
(iv) The boundary effect causes mildly adverse influence on the cooling tower’s total
structural stability.
(v) For most conditions referred to in this study, local areas on the concrete shell of cooling
tower reach the allowable tensile stress under the action of the wind force with a wind speed of
around 50m/s. The total structure’s instability critical state generally appears before the crushing
of the concrete in the compressive stress region, showing obvious geometric nonlinearity effects.
The FEM numerical simulation in this study applies a simplified way in considering the
material nonlinearity effect of concrete. Our further works will lay more emphasis on the structural
failure mode analyses applying more precise constitutive model of concrete.
7 REFERENCES
[1] NDGJ5-88. Technical specification for hydraulic design of thermal power plant[S].
[2] GB/T 50102-2003. Code for design of cooling for industrial recirculating water[S].
[3] BTR VGB’Richtlinie Bautechnik bei Kühltürmen[S]. VGB Technische Vereinigung der Groβkraftwerksbetreiber
e.V., Essen, 1990.
[4] Règles Professionelles applicable à la Construction des Réfrigérants Atmosphériques en Béton Armé[S], Texte
Provisoire, SNBATI.
[5] Wolfhard Zahlten, Claudio Borri. Time-domain simulation of the non-linear response of cooling tower shells
subjected to stochastic wind loading[J]. Engineering Strutctures, Vol.20 No. 10. pp.881-889,1998.
[6] Goudarzi, Mohammad-Ali, Sabbagh-Yazdi, Saeed-Reza. Modeling wind ribs effects for numerical simulation
external pressure load on a cooling tower of KAZERUN power plant-IRAN[J]. Wind and Structures, An International
Journal, Vol.11, No. 6, pp. 479-496,2008.
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