Wind-induced static performance of cooling tower ...iawe.org/Proceedings/BBAA7/X.X.Cheng.pdf ·...

1

Wind-induced static performance of cooling tower considering multiple loading effects

X.X. Cheng a, L. Zhao a, Y.J. Ge a

aState 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.

1604

2

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 Site model Fig.1 and stage cooling tower groupⅡ Ⅲ s

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

1605

3

6000.

Fig.2 a) Model for external pressure

Fig.2 b) Model for internal pressure

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

intsec1

intsec2

intsec3

intsec4

intsec5

intsec6

outsec1

outsec2

outsec3

outsec4

outsec5

outsec6

outsec7

outsec8

outsec9

outsec10

outsec11

outsec12

0.00

24.57

36.95

50.63

63.12

75.70

87.08

99.82

112.65

125.58

138.56

150.23

163.23

177.146

1606

4

0 20 40 60 80 100 120 140 160 180-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

Pres

sure

Coe

ffic

ient

Angle(Degree)

Test Result NDGJ5-88

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:

0

( ) cosm

p kk

a km q q=

= å (1)

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:

( )1

cosn

Pi i ii

DT

C AC

A

q==

å (2)

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.

1607

5

0 20 40 60 80 100 120 140 160 180-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

Extre

me

Val

ue o

f Sha

pe C

oeffi

cien

tAngle/Degree

Test Extreme Value Envelope NDGJ5-88

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:

,max,sin

, ,sin , sin ,

D gle ch ifm

D mean gle code gle test

C P K MK

C b创 �

=´ (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% 0% Internal pressure mean value* -0.375×1.6 -0.382×1.6 -0.410×1.6 -0.524×1.6 -0.590×1.6 -0.761×1.6

* Reference wind pressure is wind pressure at the top of tower.

1608

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.

Table.3 Main structural characteristics of cooling tower Componen

t Height/m Shell thickness/m Radius/m Concrete

grade 3D View of cooling tower FE

model 12.216 1.400 67.347 C40 24.811 0.350 63.334 C40 37.405 0.340 59.380 C40 50.000 0.330 55.217 C40 62.594 0.330 51.656 C40 75.189 0.320 48.357 C40 87.784 0.320 45.685 C40

100.378 0.310 43.123 C40 112.973 0.300 41.103 C40 125.568 0.271 39.731 C40 138.162 0.271 39.132 C40 150.757 0.271 39.229 C40 163.351 0.271 39.543 C40

Main body

175.946 0.400 39.860 C40 Herringbone column 48 pairs, 1300mm diameter C45

Table.4 Natural frequency and vibration shape of cooling tower

Mode Frequency/Hz

Mode shape (number of harmonic waves)

View of mode shape

Mode Frequency/Hz

Mode shape (number of harmonic waves)

View of mode shape

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

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.

1609

7

4.1 Internal pressure effect

Table.5 Response of cooling tower for different internal pressure conditions

Condition Internal pressure

extreme value

Maximum total deformation /m

Maximum primary tensile stress /MPa

Maximum primary compressive stress

/MPa 100% -0.637 0.0366 0.733 4.23 30% -0.658 0.0366 0.729 4.23 10% -0.717 0.0366 0.717 4.23

Draught penetration Ratio

0% -1.082 0.0367 0.644 4.22 No internal pressure 0.0 0.0364 0.868 4.23

General consideration in practical design (NDGJ5-88)

-0.8 (-0.5×1.6) 0.0366 0.701 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

Occurrence position

Occurrence position

Occurrence position External

pressure distribution

pattern 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

Experimental result 0.0388 0.746 0° 0.786 0.848 ±85° 4.34 0.286 ±70°

Traditional consideration (NDGJ5-88)

0.0475 0.783 0° 1.260 0.885 ±75° 4.77 0.286 ±70°

1610

8

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 deformation

Maximum primary tensile stress

Maximum primary compressive stress

Occurrence position

Occurrence position

Occurrence position External

pressure distribution

pattern

Condition Response magnitude

/m relative

to tower height

Included angle from

incoming flow

Response magnitude

/m relative

to tower height

Included angle from

incoming flow

Response magnitude

/m relative

to tower height

Included angle from

incoming flow

Single tower 0.0388 0.746 0° 0.786 0.848 ±85° 4.34 0.286 ±70°

Two towers (second stage)

0.0335 0.746 0° 1.020 0.921 ＋90° 4.29 0.247 ±70° Extreme value (from

experiment) Four towers (third stage)

0.0453 0.709 0° 1.390 0.848 ＋90° 4.75 0.247 ±70°

Single tower×

1.70 0.0503 0.782 0° 1.35 0.885 ±75° 4.91 0.286 ±70°

Single tower×

2.22 0.0653 0.782 0° 1.80 5.66 0.286 ±70°

Mean value (from

NDGJ5-88)×Km×β Single

tower×2.50

0.0734 0.782 0° 2.11

(0.885, ±75°) or

(0.321, 0°) 6.07 0.286 ±70°

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

1611

9

tower’s structural design. According to NDGJ5-88, the following formulae are applied for analyzing of the shell’s local elastic stability:

2 2 21 2 1 2

1 2 1 2

0.8 ( ) 0.2 [( ) ( ) ] 1B Bcr cr cr cr

K Ks s s ss s s s

+ + + = (4)

4/31 12 34

0

0.985 ( )(1 )

crE h K

rs

n=

-; 4/3

2 22 340

0.612 ( )(1 )

crE h K

rs

n=

- (5a,b)

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.

Table.8 The local elastic stability due to several effect combinations Effect combination

Condition

External pressure

distribution pattern

Internal pressure

consideration

Circumferential compressive stress/MPa

Meridian compressive stress/MPa

Angle of minimum KB

position Minimum KB

Single tower NDGJ5-88 No 0.382 0.453 ±70° 7.153

Single tower NDGJ5-88 Yes 0.518 0.454 ±70° 6.458

Single tower

Experimental result Yes 0.567 0.382 ±60° 6.892

Two towers (second stage)


Four towers (third stage)


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

1612

10

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 20 40 60 80 100 120 140 160 180

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Def

orm

atio

n/m

Basic Wind Speed (m/s)

Wind Profile Exponent a = 0.00 Wind Profile Exponent a = 0.12

0 20 40 60 80 100 120 140 160 180

0.000

0.002

0.004

0.006

0.008

0.010

0.012

0.014

Def

orm

atio

n G

radi

ent (

m/(m

/s))


Wind Profile Exponent a = 0.00 Wind Profile Exponent a = 0.12

Critical Point

Critical Point

Fig.6 Displacements and their derivatives for different wind profiles

Table.9 Critical states for different wind profiles

Critical state in tensile region Instability critical state (Critical state in compressive region)

Occurrence position of maximum deformation Occurrence position Occurrence position Wind

profile exponent Relative

to tower height

Included angle from

incoming flow

Relative to tower height

Included angle from

incoming flow

Critical wind speed (m/s)


Included angle from

incoming flow


Primary compressive

stress (MPa)

α=0.00 0.782 0° 0.286 0° 72.5 0.209 ±70° 160.0 24.2 α=0.12 0.782 0° 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,

1613

11

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 20 40 60 80 100 120 140

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Def

orm

atio

n/m


Internal Pressure CP=0.000


0 20 40 60 80 100 120 140

0.000

0.002

0.004

0.006

0.008

0.010

0.012

0.014

Def

orm

atio

n G

radi

ent (

m/(m

/s))




Critical Point

Critical Point

Fig.7 Displacements and its derivatives for different internal pressures

Table.10 Critical states for different internal pressures


Occurrence positions of maximum deformation Occurrence position Occurrence position

Internal pressure Relative

to tower height

Included angle from

incoming flow


Included angle from

incoming flow



Included angle from

incoming flow


Primary compressive

stress (MPa)

Cp=0.000 0.782 0° 0.286 0° 52.5 0.286 ±70° 125.0 25.2 Cp=0.409 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.

1614

12

0 20 40 60 80 100 120 140 160 180 200-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

Pres

sure

Coe

ffic

ient

Angle

NDGJ5-88 Intermediate Sections Top Section Bottom Section

Fig. 8 Surface pressure curves of different heights

0 20 40 60 80 100 120 140

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Def

orm

atio

n/m


NDGJ5-88 Experimental Result

0 20 40 60 80 100 120 140

0.000

0.002

0.004

0.006

0.008

0.010

0.012

0.014

Def

orm

atio

n G

radi

ent (

m/(m

/s))


NDGJ5-88 Experimental Result

Critical Point

Critical Point

Fig.9 Displacements and its derivatives for different boundary conditions

Table.11 Critical stations for different boundary conditions


Occurrence positions of maximum

deformation Occurrence position Occurrence position Surface pressure Relative

to tower height

Included angle from

incoming flow


Included angle from

incoming flow



Included angle from

incoming flow


Primary compressive stress (MPa)

NDGJ5-88 0.782 0° 0.286 0° 52.5 0.286 ±70° 120.0 24.0 Experimenal

results 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.

1615

13

0 20 40 60 80 100 120 140

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Def

orm

atio

n/m


Single Tower Two Towers Combination Four Towers Combination

0 20 40 60 80 100 120 140

0.000

0.002

0.004

0.006

0.008

0.010

0.012

0.014

Critical PointCritical Point

Def

orm

atio

n G

radi

ent (

m/(m

/s))


Single Tower Two Towers Combination Four Towers Combination

Critical Point

Fig.10 Displacements and its derivatives for different tower group combinations

Table.12 Critical states for different tower group combinations


Occurrence position of maximum deformation Occurrence position Occurrence position

Group combination Relative

to tower height

Included angle from

incoming flow


Included angle from

incoming flow

Critical wind speed

（m/s）


Included angle from

incoming flow

Critical wind speed

（m/s）

Primary compressive

stress（MPa）

Single tower 0.782 0° 0.286 0° 52.5 0.286 ±70° 115.0 23.7

Two towers 0.782 0° 0.247 0° 50.0 0.286 ±70° 102.5 17.5 Four towers 0.782 0° 0.247 0° 52.5 0.286 ±70° 107.5 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

1616

14

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.

1617

Wind-induced static performance of cooling tower ...iawe.org/Proceedings/BBAA7/X.X.Cheng.pdf ·...

Documents

Transcript of Wind-induced static performance of cooling tower ...iawe.org/Proceedings/BBAA7/X.X.Cheng.pdf ·...