Experimental study of wind pressures acting on a cooling tower exposed to stationary tornado-like vortices

J. Wind Eng. Ind. Aerodyn. 145 (2015) 75–86

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Journal of Wind Engineering and Industrial Aerodynamics journal homepage: www.elsevier.com/locate/jweia

Experimental study of wind pressures acting on a cooling tower exposed to stationary tornado-like vortices Shuyang Cao a,n, Jin Wang b, Jinxin Cao a, Lin Zhao a, Xu Chen b a b

State Key Lab of Disaster Reduction in Civil Engineering, Tongji University, Shanghai 200092, China Department of Bridge Engineering, Tongji University, Shanghai 200092, China

art ic l e i nf o

a b s t r a c t

Article history: Received 12 January 2015 Received in revised form 25 March 2015 Accepted 2 June 2015

Wind pressures acting on a cooling tower exposed to stationary tornado-like vortices are studied physically. This study focuses on the effects of swirl ratio and the distance between a cooling tower and a stationary tornado vortex on the pressure distribution around a cooling tower. Particular attention is devoted to the differences of pressure distribution and cross-correlation coefficients of pressures in a tornado with that in a conventional boundary-layer-type straight-line wind. The results show that a cooling tower exposed to a tornado experiences combined effects of pressure drop accompanying a tornado and aerodynamic flow-structure interaction. The pressure drop accompanying a tornado dominates the pressure coefficient magnitudes when the cooling tower is located at the tornado core center. The cooling tower experiences maximum wind force when it is located at the tornado core radius. Results show that the tornado-induced wind pressure is significantly different than that in conventional straight-line winds, and highlight the need to study tornado-induced wind loads on structures. & 2015 Elsevier Ltd. All rights reserved.

Keywords: Tornado-like vortices Wind pressure Aerodynamics Cooling tower

1. Introduction Wind-resistant design of wind-sensitive structures including large-scale cooling towers is generally carried out with respect to synoptic boundary-layer-type strong winds. A tornado is one of the most violent storms, and may cause severe damage to structures. However, due to the too low probability of a tornado event during a cooling tower's service life, tornado-resistant design is not considered in China. However, with the fast development of the Chinese economy, public consciousness and expectations of a structure's safety are rising, especially where increasing energy demand requires large cooling towers to be built in tornado-prone areas. Although tornadoes in China are not as strong as those in the USA, they do occur in eastern China. Golden and Snow (1991) reported that China experiences 10–100 tornadoes per year. Chen et al. (1999) estimated that the majority of reported tornadoes in China have been ranked F0–F2 in terms of intensity. Currently the height of cooling towers in China is approaching 200 m. Thus, wind resistant design of cooling towers is becoming more important than ever. Although comprehensive wind tunnel tests have been carried out to study wind loads on an isolated cooling tower or interference effects on wind loads of a tower group (Ruscheweyh, 1975; Niemann, 1980; Bartoli et al., 1992; Zhao and n

Corresponding author. Tel.: þ 86 21 65981318; fax: þ 86 21 65984882. E-mail address: [email protected] (S. Cao).

http://dx.doi.org/10.1016/j.jweia.2015.06.004 0167-6105/& 2015 Elsevier Ltd. All rights reserved.

Ge, 2010), those studies considered only conventional boundarylayer strong winds. However, it is well known that tornadoes have significant swirling effects with tangential, radial and vertical velocity components that are quite different than those of conventional straight-line boundary-layer winds. Although a cooling tower has been designed to withstand a F1–F2 tornado with respect to wind speed alone, the characteristics of wind pressures acting on a cooling tower in a swirling tornado wind, as well as their differences from those in straight-line winds should be understood in order to achieve safer wind-resistant design. Physical modeling of tornado-like vortices is required to physically investigate tornado-induced wind forces on a structure. Chang (1971) was one of the first to employ physical simulation of tornado-like vortices. Ward (1972) used guide vanes to provide angular momentum to converge flow. The guide vanes were placed on the ground assuming that the vortex structure near the ground was mainly governed by the mechanical supply of angular momentum. Haan et al. (2008) improved the technique of creating swirling flow by placing the guide vanes at a high position to allow vertical circulation of flow in the process of generating a tornado. Recently, Refan et al. (2014) developed a new type of tornado vortex simulator (WindEEE) that can produce swirl winds of variable directionality by manipulating the outflow and direction of the fans provided in the facility. With the aid of tornado-like vortex simulators, there have been many attempts to physically investigate wind loads on generic structures subjected to simulated tornado-like vortices. Jischke

S. Cao et al. / J. Wind Eng. Ind. Aerodyn. 145 (2015) 75–86

A tornado-vortex simulator constructed at Tongji University was utilized to model tornado-like flow and investigate tornado-

1500 mm

Guide vane

d

(Ward, 1972; Church et al., 1979; Haan et al., 2008), where Γ is the flow circulation, Q is the volume flow rate per unit axial length, hd is the inflow height, and r1 is the radius of the domain. Alternatively, it was defined as S¼ tan θ/2a, where θ and a are guide vane angle and aspect ratio a¼ H/ro, respectively (Mitsuta and Monji, 1984; Matsui and Tamura, 2009). In this study, the latter definition was adopted to calculate the value of swirl ratio and the ground floor was fixed at H ¼400 mm, indicating an aspect ratio a¼ 1.6. In addition, the fan speed was fixed at 1500 rpm. Fig. 2 shows the cooling tower model, whose height is 143.3 mm. The prototype cooling tower is a hyperbolic thin-shell structure 215 m in height. The geometric scale λL is 1:1500. The radius of the throat part of the model is about 33.3 mm, and the largest radius is 52.7 mm. The radius of the model is a little smaller than that of the tornado core. The model is fitted with a total of 72 pressure taps distributed evenly over 2 surfaces (external and internal) at three layers at different heights. On each layer, the angle between two adjacent pressure taps is β ¼30°. In addition, 168 pressure taps are distributed over the simulator floor to capture the wind pressures acting on the floor. In order to understand the tornado-like vortex field itself, the three-dimensional velocities and pressures were measured without the cooling tower model on seven horizontal planes at different heights (25 mm, 50 mm, 75 mm, 100 mm, 143 mm, 150 mm and 200 mm above the ground floor) and five swirl ratios (S ¼0.11, 0.18, 0.26, 0.37 and 0.54). The TFI Cobra probe with a 4-hole head 2.6 mm in diameter and a 30 mm long by 2 mm-diameter shaft, which is capable of frequency response from 0 Hz to 2 kHz, was used for the measurement. The probe is available in various ranges

1009 mm

500 mm 2r o 8

7

9

125 mm

=30o 5

4

10 3

11 12

Floor height Adjustable plane

33.3 mm High layer

6

H =150 mm~550mm

Fig. 1. Schematic diagram of tornado vortex simulator at Tongji University.

1

2

36.7mm Middle layer 45.4mm Low layer 52.7mm

Fig. 2. Cooling tower model and layout of pressure taps on it.

H o = 143.3 mm

2. Experimental setup

induced wind pressures acting on a cooling tower. Fig. 1 shows a sketch of the tornado-vortex simulator. The mechanism to generate a tornado-like flow is similar to those at Iowa State University, USA (Haan et al., 2008). A circular duct 1.5 m in diameter and 1.009 m in height is suspended overhead with a 0.5 m-diameter updraft hole (ro ¼250 mm) holding a controlling fan (maximum flow rate is 4.8 m3/s, and maximum rotational speed is 3500 rpm) to generate a strong updraft. The simulator floor could be adjusted up and down, enabling a range of heights for the inflow layer (H¼ 150 mm–550 mm). Both the fan and guide vanes are placed on the top, which allows more spaces to conduct model tests to determine the tornado effects. In addition, this tornado vortex simulator can translate along the ground plane at a given speed (maximum speed is 0.4 m/s), which can simulate the tornado more realistically. The orientation angle of the guide vanes can be adjusted from 10°–60° to obtain different swirl ratios, which is the most important parameter determining the flow structure generated inside the simulator. Swirl ratio accounts for the momentum exchange caused by swirling effect and there were r1Γ two kinds of definition available for it. It was defined as So = 2Qh

h = 107.5 mm

and Light (1983) studied wind loads on rectangular models in a Ward-type tornado simulator by considering three model locations. Bienkiewicz and Dudhia (1993) studied the effects of swirl ratio and surface roughness on a tornadic flow field and measured pressures on a cubic model located at the center of a simulator. Mishra et al. (2008) compared wind loads on a cubic model in TTU-VSII with those exposed to a boundary-layer flow. Sengupta et al. (2008) studied load on a cubic building in a microburst and a tornado considering both quasi-steady and transient wind. Haan et al. (2010) studied aerodynamic loads generated on a one-story gable-roof model exposed to tornado-like vortices of different sizes and compared the resulting loads to the provisions of building standard ASCE-7-05. Sabareesh et al. (2012, 2013) studied the effects of building location and ground roughness on surface pressures on a cubic building and the characteristics of internal pressures and net local roof wind force for buildings. These past studies were conducted mainly for low-rise buildings. Unfortunately, to the authors' knowledge, there has been no physical modeling study of tornado-induced wind loads on a cooling tower. In the present study, several stationary tornado-like vortices with different swirl ratios and vortex core sizes were modeled in a tornado vortex generator, in which the external and internal surface pressures acting on a cooling tower model were measured at a series of locations relative to the tornado core. Although tornado-induced internal pressures of a cooling tower are generally not a serious point, pressure measurements were performed on both external and internal surfaces of the cooling tower because the shape of a cooling tower is close to a thin-wall circular cylinder, which has many engineering applications and could be worth investigation. In this paper, the flow features of tornado-like vortices are presented first, followed by a detailed description of the characteristics of tornado-induced wind pressures on a cooling tower. The effects of swirl ratio and distance between the cooling tower and the tornado center on the pressure distribution around the cooling tower are discussed. In addition, the tornado-induced wind pressures are compared with those in boundary-layer straight-line winds, in order to enhance understanding of tornadostructure interaction.

h =35.9mm h = 71.7mm

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S. Cao et al. / J. Wind Eng. Ind. Aerodyn. 145 (2015) 75–86

3. Tornado-like flow A tornado features two regions: an inner core and an outer region. In the inner region, the tangential velocity increases with distance from the vortex center. After reaching a peak value at the vortex core radius, the tangential velocity component reduces. Fig. 3(a) presents the radial profile of tangential velocity at model height for five swirl ratios (S ¼0.11, 0.18, 0.26, 0.37 and 0.54). It can be found that both the core radius rc and the maximum tangential velocity Vtmax increase with increase in swirl ratio. Fig. 3 (b) compares the radial distribution of normalized tangential velocity with those of radar observation and other experimental data (Haan et al., 2008), where the tangential velocity Vt and the radial distance r from the center of tornado core are normalized by the maximum tangential velocity Vtmax and core radius rc, respectively. Note that the height from the ground of the data set of the present study in Fig. 3(b) is different from that of Haan et al. (2008). The data set of the present study is for the tower model height, corresponding to Z¼2.04rc, 1.59rc and 1.3rc for S¼0.11, 0.26 and 0.54, respectively, while that of Haan et al. (2008) is for the height of Z ¼0.52rc. It should be noted also that the definition of swirl ratio in the present study is different from that in Haan et al.

(2008), as mentioned earlier. The swirl ratio of So ¼ 0.08, 0.24 and 1.14 of Haan et al. (2008) corresponds to the swirl ratio of S ¼0.27, 0.7 and 1.41, respectively. Although the velocity profiles of the present study and Haan et al. (2008) deviate from each other in Fig. 3 due to the differences of swirl ratio and elevation, it can be concluded that the tornado-like vortices generated in the present study possess the general velocity features of a real tornado. The variations of core radius rc with height for five investigated swirl ratios are presented in Fig. 4, where rc and Z are normalized using the radius of the updraft hole ro. Fig. 4 shows that rc increases with increase of height Z and swirl ratio, which can also be observed in Fig. 3(a). The vertical profile of wind velocity is a very important factor in determining wind loads on a structure. Fig. 5 presents the vertical profile of mean tangential velocity at three radial locations, r/ro ¼0.28, 0.52, and 0.84, where the cooling tower model was to be placed for pressure measurement later. The data at three swirl ratios 0.11, 0.26 and 0.54 are shown as examples. The height Z is normalized by ro. It can be found that the tangential velocity increases with swirl ratio at each given radial distance r/ro. When r/ro ¼0.28, the maximum tangential velocity exists at a lower height for three swirl ratios. However, when r/ro ¼0.52, the maximum tangential velocity at S ¼0.11 appears at a higher elevation than that at S¼0.26 and 0.54. When r/ro ¼0.84, the profile of the tangential velocity for three swirl ratios is similar to that of the boundary-layer wind flow. The atmospheric pressure field around a tornado was also measured. The reference pressure was taken far away from the simulator. Fig. 6(a) shows the pressure distributions at the cooling tower model height and on the ground for three swirl ratios. There exists a high suction regime at the center of the vortex core, which may cause damage to structures. It can be seen that neither the pressure magnitude nor the pressure distribution exhibits significant differences between the two levels. However, the pressure 1.0 0.8 0.6

Z/ro

for use between 2 m/s and 100 m/s within a cone of influence of 745°. The wind pressures at all pressure taps on the model surfaces were simultaneously measured by a multi-channel pressuremeasuring system. The sampled frequency was 300 Hz. The atmospheric pressure far away from the vortex core was selected as the reference pressure for all pressure measurements. The pressure measurements were carried out for five swirl ratios (S ¼0.11, 0.18, 0.26, 0.37 and 0.54) and 17 radial cooling-tower locations with r/ro ¼0, 7 0.04, 70.12, 70.2, 70.28, 70.36, 70.52, 70.68 and 70.84, where r is the distance between the tornado core center and the cooling tower center (as shown in Fig. 7). The Reynolds number of the model test is defined as Re¼Vtmax  D/v, where Vtmax is the maximum tangential velocity at the model height without the cooling tower model, D is the diameter of the throat part of the model and v is the kinematic viscosity. The maximum tangential velocity at the model height varies with swirl ratio, so the Reynolds number increases from 3.45  104 to 4.49  104 when the swirl ratio increases from 0.11 to 0.54. In addition, the wind pressures acting on a cooling tower caused by conventional boundary-layer winds were tested, in order to provide pressure data to compare with those in tornadoes. Although the scale ratio and some model details for the two experiments are different, it is considered acceptable to extract qualitative differences between tornado-induced pressure and that caused by general strong winds.

0.0 0.20

Vt / Vtmax

0.8

Vt (m/s)

8

0

0

0.2

0.6

r/ro

0.8

1

0.35

0.40

Present study: S=0.11, Z=2.04rc S=0.26, Z=1.59rc S=0.54, Z=1.3rc

0.6 Haan et al.,2008: So=0.08 So=0.24 So=1.14, Z=0.52rc Mulhall, Z=0.52rc Spencer, Z=0.52rc

0.4 0.2

0.4

0.30

0.45

Fig. 4. Variations of core radius with height.

1

2

0.25

rc /ro

10

4

S=0.11 S=0.18 S=0.26 S=0.37 S=0.54

0.2

1.2

S=0.11 S=0.18 S=0.26 S=0.37 S=0.54

model height 0.4

12

6

77

0

0

1

2

3

4

r/rc

Fig. 3. Radial profile of tangential velocity. (a) Normalized by ro (ro ¼ 250 mm) and (b) normalized by rc.

5

0.50

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S. Cao et al. / J. Wind Eng. Ind. Aerodyn. 145 (2015) 75–86

the maximum horizontal velocity can be adopted as the reference velocity (Mishra et al., 2008), the maximum tangential velocity at the model height Vtmax, measured without the cooling tower model is defined as the reference velocity in the present study as in many other studies (Haan et al., 2008; Sabareesh et al., 2009). The reference pressure cannot be defined as in the conventional boundary layer experiments because the flow is swirling in a tornado. Both Haan et al. (2008) and Sabareesh et al. (2012) selected the atmospheric pressure far away from the vortex core as the reference pressure. Mishra et al. (2008) selected the mean static pressure on the ground surface in the vicinity of an elemental area as the reference pressure. In the present study, the pressure coefficient is calculated by adopting the two options of reference pressure mentioned above. The pressure coefficient is basically calculated by considering the atmospheric pressure far away from the tornado as the reference. However, when the pressure coefficient is compared with those obtained by conventional boundary layer test results, the static pressure accompanying the tornado at the point where the cooling tower was to be placed is chosen as the reference. The difference between Mishra et al. (2008) and the present study is the height used to define the static pressure and the reference velocity. However, as shown in Fig. 6(a), the difference between the pressures on the ground and at the model height is very small. In addition, the aerodynamic force coefficients are calculated using the following equations:

drop increases with increase in swirl ratio. It is noteworthy that, although the pressure drop accompanying the tornado increases with swirl ratio, the increase at a higher swirl ratio is not as significant as that at smaller swirl ratio because the vortex structure tended to transit from a single-celled vortex to a two-celled vortex at a high swirl ratio, which was also found by Haan et al. (2008). The pressure profile measured at the ground floor is normalized in this study and the comparison is shown in Fig. 6(b). The tendency of the surface pressure profile data from the present tornado vortex simulator fits reasonably well with the data of the Rankine model.

4. Wind pressures on cooling tower In the conventional boundary layer model tests, the external and internal wind pressure coefficients of a cooling tower are usually defined as in Eqs. (1) and (2), respectively

C pe (t ) =

C pi (t ) =

Pe (t ) − P∞ 0.5 × ρ × Vt 2

(1)

Pi (t ) − P∞ 0.5 × ρ × Vt 2

(2)

where Pe(t) and Pi(t) are the local pressures acting on the external and internal cooling tower surfaces, respectively. P1 is the static pressure upstream of the tower, which is the reference pressure used to calculate the pressure coefficient. ρ is the density of air, and Vt is the reference velocity upstream of the tower at the tower height. When calculating the tornado-induced wind pressure coefficients of a cooling tower, there are several options to select the reference velocity Vt and the reference pressure P1. Although 1.0

S=0.11

model height

S=0.26

r/ro=0.52

model height

0.5 0.0 1.0

S=0.54

3

6

9

12

Fig. 5. Vertical profile of tangential velocity.

pressure at the model height pressure at the ground level

0.5 × ρ × Vt 2 × AY

(4)

0.2 0 -0.2

P/P min

pressure (Pa)

FY

This section first presents the pressure distributions around the cooling tower separately according to the relative locations, i.e. the distance between the cooling tower center and the tornado core center, and then discusses the variation of pressure characteristics

15

Vt (m/s)

100 0 -100 -200 S=0.11 -300 100 0 -100 -200 S=0.26 -300 100 0 -100 -200 S=0.54 -300 -3 -2

(3)

4.1. Wind pressures acting on a cooling tower at different radial locations

model height

0.5

FX 0.5 × ρ × Vt 2 × A X

where FX and FY are the total wind forces estimated by integrating the surface pressures acting on the cooling tower model along the X and Y directions (the directions of X and Y are defined in Fig. 7), AX and AY are the projected areas of the cooling tower model in the X and Y directions and the maximum tangential velocity at the model height without the model is utilized as the reference velocity Vt.

r/ro=0.84

0.0 1.0

Z/ro

CFY =

r/ro=0.28

0.5

0.0

CF X =

-0.4 -0.6

S=0.11 S=0.26 S=0.54 Rankine vortex model

-0.8 -1

-1

0

r/rc

1

2

3

-1.2

-3

-2

-1

0

1

2

3

r/rc

Fig. 6. Radial distribution of pressure. (a) At model height and ground level, and (b) comparisons with model and experimental data.

S. Cao et al. / J. Wind Eng. Ind. Aerodyn. 145 (2015) 75–86

Tornado

79

Tornado

Cooling tower

rc

Tornado

Cooling tower

rc r

Y

r Y

Y

X

X

X

r/rc >1

r/rc 1

r/r c =0

rc

1-1

1-1 view pressure tap No.7 pressure tap No.10

Y pressure tap No.4 X Tornado

Cooling tower pressure tap No.1

r

Fig. 7. Illustration of model position relative to tornado vortex.

-1

C pe

-2

-3

-4

High layer -5

Low layer

Middle layer

1 2 3 4 5 6 7 8 9 10 11 12

1 2 3 4 5 6 7 8 9 10 11 12

1 2 3 4 5 6 7 8 9 10 11 12

pressure tap number -1

C pi

-2

-3

-4

High layer -5

Low layer

Middle layer

1 2 3 4 5 6 7 8 9 10 11 12

1 2 3 4 5 6 7 8 9 10 11 12

1 2 3 4 5 6 7 8 9 10 11 12

pressure tap number

(

S =0.11

S =0.18

S =0.26

S =0.37

S =0.54)

Fig. 8. Distribution of pressure coefficients on model at r/ro ¼ 0. (a) external pressure coefficients (b) internal pressure coefficients.

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S. Cao et al. / J. Wind Eng. Ind. Aerodyn. 145 (2015) 75–86

with distance. The pressure measurements are conducted at 17 radial locations, r/ro ¼0 and |r/ro| ¼0.04, 0.12, 0.2, 0.28, 0.36, 0.52, 0.68 and 0.84, which can be classified as the cooling tower located at the tornado center (r/rc ¼0), near the tornado core radius (|r/rc| E 1) and outside the tornado (|r/rc| 41), as shown in Fig. 7. As the coordinate origin is set at the center of the model, the negative or positive value of r indicates respectively that the tornado vortex center is at the left or right side of the model center (Fig. 7). Note that rc varies with swirl ratio and height as shown in Fig. 4. For example, rc/ro equals 0.28, 0.3, 0.32, 0.4 and 0.44 at the model height, respectively, for swirl ratio¼0.11, 0.18, 0.26, 0.37 and 0.54. In addition, the variations of pressure coefficients at pressure taps No.1, 4, 7 and 10 with swirl ratio and distance r are checked particularly, because pressure taps No.1 and 7 are near the base point or stagnation point in the swirling flow depending on the relative location between tornado and cooling tower, and pressure taps No. 4 and 10 are close to the separation points. Fig. 8 shows the distribution of external mean pressure coefficients Cpe and internal mean pressure coefficients Cpi at three layers with different heights and for five swirl ratios at r/ro ¼0, which means the tornado is directly on the top of the cooling tower. Obviously, Fig. 8 shows that both the external and internal pressure coefficients are negative due to the pressure drop accompanying the tornado. It is interesting to find that the pressure coefficient is not constant around the surface, especially on the external surface. It is reasonable to suppose that the pressure coefficient must remain almost constant around the tower if the tornado vortex is really standing stably over the tower. The pressure measurement was repeated by changing the experiment

setup several times, but similar results were obtained. The results imply that the tornado is not standing vertically over the cooling tower. The tail-end of the tornado tilts to one side of the cooling tower, which makes the pressures vary with the locations of the pressure taps and exhibit aerodynamic behavior. With respect to the aerodynamic behavior, Fig. 8 shows that pressure tap No.6 plays the role of stagnation point and exhibits the highest pressure around the tower. However, the pressure distribution is not completely symmetric with respect to pressure tap No.6. The pressure decreases from pressure tap No.6 to pressure tap No.9 or No.10 and then recovers a little until pressure tap No.12 (base point) at all investigated swirl ratios. However, the pressure changes more significantly with pressure tap location when the swirl ratio is smaller, implying that the flow-structure interaction contributes more to the wind pressure at small swirl ratio. A tornado with high swirl ratio tends to be able to maintain its posture during the process of tornado-structure interaction, so the tornado core becomes closer to the model center and reduces the aerodynamic effect. Comparison of the magnitude of the pressure coefficient at pressure tap No.6 and No.9 or No.10 shows that the pressure drop accompanying the tornado dominates the pressure coefficient magnitudes compared to pressure variations due to wind-structure interaction. Meanwhile, the pressure coefficient increases with the swirl ratio; in other words, the pressure coefficient becomes less negative with increase in swirl ratio. Note that both Vt and the absolute pressure drop accompanying the tornado increase with increase in swirl ratio as shown in Figs. 3(a) and 6 (a) and contribute together to decide the magnitude of the pressure coefficient. In addition, the pressure coefficient distributions

0 -1

C pe

-2 -3 -4 -5

High layer

Low layer

Middle layer

1 2 3 4 5 6 7 8 9 10 11 12

1 2 3 4 5 6 7 8 9 10 11 12

1 2 3 4 5 6 7 8 9 10 11 12

pressure tap number 0 -1

Cpi

-2 -3 -4

High layer -5

Middle layer

1 2 3 4 5 6 7 8 9 10 11 12

Low layer

1 2 3 4 5 6 7 8 9 10 11 12

1 2 3 4 5 6 7 8 9 10 11 12

pressure tap number S =0.11

S =0.18

S =0.26

S =0.37

S=0.54

Fig. 9. Distribution of pressure coefficients on model at r/ro ¼0.28. (a) external pressure coefficients (b) internal pressure coefficients.

S. Cao et al. / J. Wind Eng. Ind. Aerodyn. 145 (2015) 75–86

81

1

C pe

0 -1 -2 -3

High layer Low layer

Middle layer -4

1 2 3 4 5 6 7 8 9 10 11 12

1 2 3 4 5 6 7 8 9 10 11 12

1 2 3 4 5 6 7 8 9 10 11 12

pressure tap number 0

C pi

-1

-2

High layer -3

Middle layer

1 2 3 4 5 6 7 8 9 10 11 12

Low layer

1 2 3 4 5 6 7 8 9 10 11 12

1 2 3 4 5 6 7 8 9 10 11 12

pressure tap number (

S =0.11

S =0.18

S=0.26

S=0.37

S =0.54)

Fig. 10. Distribution of pressure coefficients on model at r/ro ¼ 0.52. (a) external pressure coefficients (b) internal pressure coefficients.

at three heights are similar. Compared with the external pressure coefficient, the fluctuation of the internal pressure coefficient is small around the tower, although it recovers with increase in swirl ratio. Figs. 9 and 10 show the distribution of mean pressure coefficients on the external and internal surfaces of the cooling tower at three layers and five swirl ratios at r/ro ¼0.28 and 0.52, respectively. When r/ro ¼0.28, r/rc ¼1.00, 0.93, 0.88, 0.70 and 0.64 for the five swirl ratios, corresponding to the situation where the cooling tower center is located inside the tornado core or near the core radius. When r/ro ¼ 0.52, r/rc ¼1.86, 1.73, 1.63, 1.3 and 1.18 for the five swirl ratios, corresponding to the situation where the cooling tower center is just outside but not very far away from the tornado core. Obviously both the external and internal pressure coefficients are negative due to the pressure drop accompanying the tornado at the two locations. Pressure tap No.7 plays the role of stagnation point and exhibits the highest pressure around the cylinder at both r/ro ¼0.28 and r/ro ¼0.52. The pressure coefficient decreases from pressure tap No.7 to pressure tap No.10 or No.11 and then recovers a little until pressure tap No.1 (base point) at all swirl ratios. Note that the pressure coefficients at the stagnation point (pressure tap No. 7) when r/ro ¼0.28 and 0.52 are not as negative as that at r/ro ¼0, while the pressure differences between the stagnation point (pressure tap No.7) and the rough separation point (pressure tap No.10 or 11) are more significant than that at r/ro ¼ 0. This means that the contribution to the pressure distribution of the aerodynamic effects increases while the contribution of the pressure drop accompanying the tornado decreases when the tornado moves away from the center of the cooling

tower. The external pressure coefficient increases with increase in swirl ratio at r/ro ¼ 0.28 as at r/ro ¼ 0. Conversely, the external pressure coefficient decreases with increase in swirl ratio at r/ro ¼0.52. In addition, it is interesting to find that the internal pressure coefficient increases with increase in swirl ratio at r/ro ¼0.28 as at r/ro ¼0, but decreases at r/ro ¼ 0.52, which is similar to the tendency of the external pressure coefficients with swirl ratio. Fig. 11 shows the distribution of mean pressure coefficients on the external and internal surfaces of the cooling tower at r/ro ¼0.84, which corresponds to r/rc ¼3, 2.8, 2.63, 2.1 and 1.91, respectively, for the five investigated swirl ratios. The tower center is located outside and a little away from the tornado core center. The external pressure coefficient decreases with increase in swirl ratio, which is similar to that at r/ro ¼0.52 shown above. Pressure tap No.7 plays the role of stagnation point and exhibits the highest pressure around the cylinder. The pressure decreases from pressure tap No.7 to pressure tap No.10 and then recovers a little until pressure tap No.1 (base point) at all swirl ratios, similar to that at r/ro ¼0.52. The internal pressure coefficient decreases with increase in swirl ratio, which is similar to that at r/ro ¼ 0.52 (outside of the tornado vortex core), but opposite to those at r/ro ¼0 and 0.28 (inside and near the tornado core radius). Fig. 12(a–d) shows more clearly the variation of mean external pressure coefficients at pressure taps No.1, 4, 7, and 10 on the middle layer of the cooling tower with swirl ratio, respectively at r/ro ¼0, 0.28, 0.52 and 0.84. The maximum and minimum external mean pressure coefficients Cpemax and Cpemin, of the 12 pressure taps around the middle layer of the tower are shown together,

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S. Cao et al. / J. Wind Eng. Ind. Aerodyn. 145 (2015) 75–86

1

C pe

0

-1

High layer -2

Middle layer

1 2 3 4 5 6 7 8 9 10 11 12

Low layer

1 2 3 4 5 6 7 8 9 10 11 12

1 2 3 4 5 6 7 8 9 10 11 12

pressure tap number

Cpi

0

-1

High layer -2

Middle layer

Low layer

1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 pressure tap number (

S =0.11

S =0.18

S =0.26

S =0.37

S =0.54)

Fig. 11. Distribution of pressure coefficients on model at r/ro ¼0.84. (a) external pressure coefficients (b) internal pressure coefficients.

because the values of pressure coefficient at pressure taps No.1, 4, 7 and 10 do not necessarily have the highest or lowest values around the circle due to the complicated flow-structure interaction. Fig. 12 shows that the maximum values always coincide with those at the supposed stagnation points, except at r/ro ¼0 where the location of the stagnation point is somewhat random. Fig. 12 (a) and (b) shows that the maximum and minimum mean pressure coefficients and those at four specified pressure taps increase with swirl ratio when the cooling tower model is located inside and near the vortex core where r/ro ¼0, and 0.28. However, when r/ro ¼0.52 and 0.84 (outside the vortex core), the mean pressure coefficients decrease with swirl ratio, i.e, the pressure coefficients become more negative, as shown in Fig. 12(c) and (d). Note again that the magnitude of the pressure coefficient is decided by the reference velocity in addition to the surface pressure, as mentioned before. Fig. 13 shows the variations of maximum and minimum external pressure coefficients, Cpemax and Cpemin, around the cooling tower at the middle layer at distance r. Three swirl ratios, i.e. the smallest (S¼0.11), the middle (S¼0.26) and the largest (S¼0.54) among the five investigated cases are shown. The pressure drop accompanying the tornado at the model height without the cooling tower model and the values estimated from the Rankine model are shown together for comparison, where the pressure drop is calculated as  2.0 in the Rankine model. With increasing distance from the tornado, the maximum and minimum pressure coefficients recover gradually. However, the maximum pressure coefficient remains negative over a wide range of r/rc. It is also shown that the pressure coefficients on the cooling tower model are different in magnitude than those of the

Rankine vortex model and that without the cooling tower model due to the aerodynamic interaction between the tower model and the tornadic wind, although the similarity of pressure coefficient distribution implies a high probability of making an empirical model to express the pressure coefficient based on the Rankine model. In addition, it is interesting to find that the minimum pressure coefficients are almost constant between  1or/rc o1 when S¼0.11, but exhibit a W shape distribution when S¼ 0.54, with the minimum pressure coefficient existing at about r/rc ¼0.8. The double-core vortex structure is considered to be responsible for this phenomenon. Fig. 14 shows the variation of internal pressure coefficients with distance, which is averaged from 12 Cpi values at the middle layer. It can be found that the tendency of variation of Cpi with distance is quite similar to the Rankine Vortex model. The averaged internal mean pressure coefficient changed slightly between 1 or/rc o1 for three swirl ratios. The mean total force coefficients, CFX and CFY, which are important in the design of a structure, are also compared. The coordinates defining the directions of X and Y are shown in Fig. 7. CFX and CFY correspond to the radial and tangential force components, respectively. Because the pressure distribution is not uniform around the cooling tower at r/rc ¼ 0, especially when the swirl ratio is small as shown in Fig. 8, CFX is not zero at r/rc ¼ 0 when S¼0.11. CFX varied from negative to positive for swirl ratios of 0.18, 0.26, 0.37 and 0.54, illustrating that the radial wind force acts toward the vortex core center. Meanwhile, it is a matter of course that CFY changes from positive to negative, indicating that tangential wind force acts along the tangential wind direction. Fig. 15 also reveals clearly that the two components of aerodynamic force acting on the model increase with

-1

-1

-2

-2 Cpe

Cpe

S. Cao et al. / J. Wind Eng. Ind. Aerodyn. 145 (2015) 75–86

-3

-3 -4

-4 -5 0.1

0.2

0.3 0.4 0.5 swirl ratio(S)

-5 0.1

0.6

0.2

0.3 0.4 0.5 swirl ratio(S)

0.6

0.2

0.3 0.4 0.5 swirl ratio(S)

0.6

1

1 0

0 Cpe

Cpe

83

-1

-1 -2 -3 0.1

0.2

0.3 0.4 swirl ratio(S) Cpemin

(

0.5

Cpemax

-2 0.1

0.6 No.1

No.4

No.7

No.10)

Fig. 12. Variations of external pressure coefficients with swirl ratios. (a) r/ro ¼ 0 (b) r/ro ¼ 0.28 (c) r/ro ¼ 0.52 (d) r/ro ¼ 0.84.

1 0

C pe

-1 -2 -3 -4 -5 -6 -3

S =0.11 -2

-1

0

1

2

S=0.26 3

-3

-2

-1

0

1

2

S=0.54 3

-3

-2

-1

0

1

2

3

r/r c

(

C pemin

C pemax

Rankine vortex model

Tornado-like flow(without the model))

Fig. 13. Variation of external pressure coefficients with model location.

increase in distance from the tornado-like vortex center and reach peak values around r /rc = ± 1. In addition, it can be noticed that the positive and negative peak values of CFX and CFY corresponding to r /rc = ± 1 are not equal. This inequality is mainly caused by the increased uncertainty of structure–tornado interaction within r /rc ≤ 1. When r /rc ≤ 1, the stagnation point is not necessarily at the pressure tap No.7 (when r /rc = 1) or No.1 (when r /rc = − 1), and the shift of stagnation point shows some uncertainty. 4.2. Comparisons with conventional boundary-layer wind The characteristics of wind pressure acting on the cooling tower in tornado-like vortices are compared with those obtained

in straight-line boundary-layer-type winds. The experiment in boundary-layer-type winds was conducted on a pressure model of the same shape as that used for the experiment in tornado-like winds but with a different scale ratio, by assuming the mean velocity profile of oncoming straight-line wind has an exponent index of 0.15. In addition, the distribution of wind pressure coefficients in tornado-like vortices are also compared with those specified for straight-line winds by several major national codes, for example, DL/T 5339-2006 (China), BS 4485 Part 4:1996 (British) and VGR-R 610Ue:2005 (Germany). It should be noted that the pressure coefficients in the codes are defined by utilizing the velocity at the pressure tap height as the reference velocity, and

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S. Cao et al. / J. Wind Eng. Ind. Aerodyn. 145 (2015) 75–86

1 0 -1

C pi

-2 -3 -4 -5 -6 -3

S =0.11 -2

-1

0

1

2

Cpi

(

S =0.54

S =0.26 3

-3

-2

-1

0

1

r/rc

2

3

-3

-2

-1

0

1

2

3

Rankine vortex model)

Tornado-like flow(without the model)

Fig. 14. Variation of internal pressure coefficients with model location.

2

2 S=0.11 S=0.18 S=0.26 S=0.37 S=0.54

1

0

0

-1

-1

-2

S=0.11 S=0.18 S=0.26 S=0.37 S=0.54

peak value

CFY

CFX

1

peak value

-3

-2

-1

0

1

2

-2

3

-3

-2

-1

0

1

2

3

r/rc

r/rc Fig. 15. Variation of CFX and CFY with model location.

1 0

r/ro=0 r/ro=0.28 r/ro=0.52 r/ro=0.84

1

CpeT

-1

Cpe

2

r/ro=0 r/ro=0.28 r/ro=0.52 r/ro=0.84

-2

0 -1

-3

-5

Boundary-layer wind DL/T5339 BS4485-4 VGB-R610Ue

-2

-4 0

60

120

180

240

300

360

o

Angle( )

-3

0

60

120

180

240

300

360

o

Angle( )

Fig. 16. Comparisons of external pressure coefficients of middle layer.

the results of wind tunnel tests are obtained by using the velocity at the model height as the reference velocity. Figs. 16 and 17 compare respectively the external and internal pressure distributions around the cooling tower in tornado-like vortices, straight-line winds and codes, in which the X coordinate indicates the angle from the stagnation point where the pressure coefficient is maximum. Only the results obtained at S¼0.54 are presented for the tornado-like flow as an example. The data of pressure coefficients Cpe and Cpi in Figs. 16(a) and 17(a) are the same as those in Figs. 8–11, but Figs. 16(a) and 17(a) display the data by setting the X coordinate starting from the stagnation point. Fig. 16(a) shows that

although all Cpe values are negative in tornado-like winds, the distribution of Cpe around the tower is analogous to that in straight-line winds. The pressure coefficients are re-calculated by defining the pressure drop accompanying the tornado-like winds at the point where the cooling tower is located as reference pressure, and their values symbolized as CpeT and CpiT are displayed in Figs. 16(b) and 17 (b). It is obvious in Fig. 16(b) that the wind pressure around the cooling tower exhibits typical distributions induced by flow-structure interaction, such that the windward face experiences positive pressures whereas the leeward faces experiences negative pressures. Fig. 16 (b) provides a hint on how to estimate the tornado-induced wind

S. Cao et al. / J. Wind Eng. Ind. Aerodyn. 145 (2015) 75–86

pressures from the individual effects of aerodynamics and pressure

0

r/ro=0 r/ro=0.52

drops, which will be a research focus of our future study. Fig. 17(a) and

1

r/ro=0.28 r/ro=0.84

-3

-4

r/ro=0 r/ro=0.28 r/ro=0.52 r/ro=0.84 Boundary-layer wind

0.5 CpiT

Cpi

-1

-2

85

0

-0.5

0

60

120

180

240

300

-1

360

0

60

120

Angle(o)

180

240

300

360

Angle(o)

Fig. 17. Comparisons of internal pressure coefficients of middle layer.

Cross-correlation coefficients

2 r/ro=0 r/ro=0.28 r/ro=0.52 r/ro=0.84 Boundary-layer wind

1

0

-1

0

60

120

180

240

300

360

2 1.5

r/ro=0 r/ro=0.28 r/ro=0.52 r/ro=0.84 Boundary-layer wind

Cross-correlation coefficients

Cross-correlation coefficients

Angle(o)

No.1

1 0.5 0 20

30

40

50

60

70

80

2 1.5

r/ro=0 r/ro=0.28 r/ro=0.52 r/ro=0.84 Boundary-layer wind

1 0.5 0 20

30

40

r/ro=0 r/ro=0.28 r/ro=0.52 r/ro=0.84 Boundary-layer wind

No.7

1 0.5 0 20

30

40

50

h/Ho(%)

50

60

70

80

h/Ho(%) Cross-correlation coefficients

Cross-correlation coefficients

h/Ho(%)

1.5

No.4

60

70

80

2 1.5

r/ro=0 r/ro=0.28 r/ro=0.52 r/ro=0.84 Boundary-layer wind

No.10

1 0.5 0 20

30

40

50

60

70

80

h/Ho(%)

Fig. 18. Cross-correlation coefficients between external pressures. (a) Cross-correlation coefficients at middle layer. (b) Cross-correlation coefficients for meridian line.

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S. Cao et al. / J. Wind Eng. Ind. Aerodyn. 145 (2015) 75–86

(b) shows that the internal surface pressures are slightly changed with pressure tap number in the tornado-induced wind and the tendency is similar to that in the boundary-layer wind. When r/ro ¼ 0, CpiT is close to zero, indicating that the negative pressure drop accompanying the tornado greatly contributes to the pressures acting on the internal surface of the cooling tower model. The cross-correlation coefficient of the external pressures gives an indication of the relation between pressures at different locations of the structure model. It has been shown by some past studies that the spatial correlation of pressure acting on a structure is higher in transient winds than in conventional boundary layer winds (Butler et al., 2010). Fig. 18(a) compares the horizontal cross-correlation coefficients at the middle layer height of the cooling tower model in the tornadolike flow at four different radial locations, r/ro ¼0, 0.28, 0.52 and 0.84, with those in boundary-layer flow. The stagnation point was chosen as the reference point to determine the horizontal correlation coefficients. Fig. 18(a) shows that the pressure exhibits stronger horizontal correlation when the cooling tower is located inside the tornado than that caused by the boundary-layer wind. On the other hand, Fig. 18 (b) gives the vertical cross-correlation coefficients also at four different radial locations, in which the correlation at pressure taps No.1, 4, 7 and 10 are shown because the locations of these pressure taps generally correspond to the characteristic points related to the vortex shedding behavior, as mentioned before. The pressures at the corresponding locations at the highest layer are selected as the reference points to calculate the vertical correlation. It can be found in Fig. 18(b) that the correlation caused by a tornado is higher than that caused by straightline wind at the base point (pressure tap No.1) and pressure tap No.10 at all radial locations. The correlation at the stagnation point remains higher if the cooling tower is located inside the tornado where r/ro ¼ 0 and 0.28, but decreases with distance and even becomes smaller than that in straight-line winds.

5. Conclusions Wind pressures acting on a cooling tower exposed to stationary tornado-like vortices are studied physically. The effects of swirl ratio and distance between a cooling tower and a stationary tornado on the pressure distribution around a cooling tower are studied. Spatial correlation of pressure acting on the cooling tower is also investigated. Particular attention is devoted to the difference between the pressure distributions in a tornado and those in a conventional boundary-layer type straight-line wind. The presented pressure distribution exhibits characteristics that are quite different than those in atmospheric boundary layer flows and Design Codes. The pressure drop accompanying the tornado dominates the pressure coefficient magnitudes compared to the pressure variations due to wind-structure interaction when the cooling tower is located at the tornado core center. The pressures acting on the cooling tower exposed to the tornado-like wind flow may be regarded as the sum of two individual parts: the negative pressure drop accompanying the tornado and the aerodynamic force acting on the cooling tower model, which will allow empirical engineering models to be established to estimate the tornado-induced pressures. The cooling tower experiences maximum wind force when it is located at the tornado core radius. The tornado-like flows push the cooling tower model tangentially, and pull it toward the vortex core. Both the horizontal and vertical correlation coefficients of pressures caused by a tornado-like flow are higher than those in the boundary-layer flow. The results show that the tornadoinduced wind pressure is significantly different than that in

conventional straight-line winds, and highlight the needs to study tornado-induced wind loads on structures.

Acknowledgment The authors wish to acknowledge the financial support from the National Key Basic Research Program of China (973 Program) Grant no. 2013CB036301, National Natural Science Foundation of China (NSFC) Grant no. 51478358 and Research Foundation of State Key Laboratory of Disaster Reduction in Civil Engineering Grant no. SLDRCE14-A-01.

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