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Wind tunnel tests were carried out to measure the wind pressure of a 200 m high natural-draught cooling tower. An analysis of the distribution characteristics of external pressure was then conducted to determine the pressure coefficients

Natural-draught cooling towers are high-rise and thin-walled flexible shell structures commonly used in thermal and nuclear power plants as cooling devices. The shell of a cooling tower is rather thin, and the ratio of the minimum shell thickness to the throat diameter is of the order of 1/400. In areas of negligible seismic activity, the dominating load of natural-draught cooling towers is induced by the action of turbulent wind due to the exposure of a large area to the wind (Bamu and Zingoni [

As seen in equation (

However, with the rapid development of nuclear power plants on the mainland of China, a 200 m high natural-draught cooling tower has been proposed whose height would far exceed the 165 m height limit specified in the existing design codes for cooling towers in China (GB/T 50102 [

The wind tunnel test is conducted at the HD-2 BLWT at Hunan University, whose laboratory is a closed-circuit atmospheric boundary layer. The tests are carried out in turbulent shear flow in the high-speed test section (3.0 m in width and 2.5 m in height), and an artificial thickening of the boundary layer was achieved with the help of spires at the entrance and irregularities on the floor of the wind tunnel. The flow velocity was measured with a Cobra Probe, and the sampling time and sampling frequency were, respectively, set as 30 s and 2000 Hz. The duration of each sample was chosen to obtain an error of less than 0.5% on the mean value. The wind characteristics measured at the center of the rotary plate are shown in Figure

Simulation of wind characteristics in BLWT (_{z} is the wind speed at height _{u} is the turbulent intensity). (a) Mean wind speed. (b) Turbulence intensity. (c) Longitudinal turbulence power spectrum.

The total height of the prototype cooling tower is 200.00 m, the throat section above ground level is 156.70 m, and the inlet opening above ground level is 12.59 m, with a cooling area of 18,000 m^{2}. The diameters of the top, throat section, and bottom of the shell are 96.60 m, 94.60 m, and 153.00 m, respectively. The shell thickness varies with the height

Test model.

Pressure taps arrangement and the definition of

A DTC net electronic type pressure scanning system (Pressure Systems, Inc., USA) was employed to measure the wind pressure. In this study, sixteen modules were used and a total of 1024 pressure measuring points could be monitored simultaneously. The sampling duration of each measurement was 30 s and the sampling frequency was 330 Hz. The pressure taps were linked to the transducers with 500 mm silicon tubes with an inner diameter of 1.0 mm and an outer diameter of 2.0 mm. The system obtained had a flat amplitude and a linear variation of the phase up to the sampling frequency, which could guarantee the transmission of the fluctuations without distortions.

It is important to note that the flow conditions around rounded shapes are sensitive to the Reynolds number. However, the Reynolds number in a wind tunnel is usually 2∼3 magnitudes less than that in full scale. Fortunately, the transcritical flow regime may be obtained by adding sufficient roughness to the model surface in the wind tunnel tests. It should be noted that the design curve is simulated by pasting a rough paper tape on the surface of the model to increase the surface roughness in the wind tunnel test, as shown in Figure _{H} from 12 to 20 m/s. This was monitored using a Pitot tube at the centerline of the test section, about 3 m upstream of the tested model. The test results obtained at the free stream oncoming velocity _{H} = 18 m/s were taken as representative, corresponding to a Reynolds number of 6.03 × 10^{5} based on _{H} and the mean diameter of the tower model.

Roughness simulation of the cooling tower surface.

To enable the data obtained from the wind tunnel tests to be applied to the prototypes, the pressure coefficients presented in this study are nondimensionalized, referring the pressures at a given height

The mean wind pressure coefficients at typical levels _{H} = 18 m/s are shown in Figure

Mean pressure coefficients at typical height.

Figure

Characteristic value of pressure coefficients varying with height.

From Figure

Pressure represents the local load acting on the surface of the shell; however, global forces such as resistance should also be considered in the design. For structures with circular cross sections, such as a cooling tower, the mean drag coefficient _{D} in the downwind direction and lift coefficient _{L} of a section obtained by the area-weighted integral of the mean pressure distributions are given by_{i} and _{i} represent the pressure coefficient and circumferential angle at point

Figure _{L} is basically constant along the height and is mostly close to zero. In fact, for the circular cross-section structure of the cooling tower, due to the symmetrical distribution of the wind pressure on the surface, the theoretical average value of the lift coefficient is zero. The consistency of the theoretical values verifies the correctness of the test results in the present study. The three-dimensional effect of the drag coefficient _{D} is significant, showing the characteristics of a large end and a small middle. The drag coefficient at the top of the tower (_{D} = 0.72) is 41.2% larger than the middle section, and the drag coefficient at the bottom of the tower (_{D} = 0.90) is 76.5% larger than the middle section. It can be seen that if the design load is taken according to the “representative curve,” the design load at both ends of the cooling tower will be significantly smaller than the actual load at the ends.

Aerodynamic coefficients at each section.

The numerical calculations of the wind-induced static response of the prototype cooling tower were carried out with the help of the finite element software ANSYS. The internal forces were calculated using the membrane theory of shells. The body of the tower was simulated using a SHELL63 element with four nodes and both membrane and flexural stiffnesses, and the columns were idealized as three-dimensional Timoshenko beams with a BEAM188 element. The finite element model and analysis result of the first-order modal are shown in Figure

Finite element model and first-order modal. (a) Finite element model. (b) First-order modal (

The combined effects of the dead load _{(10)}∗(^{2α} = 0.45(^{0.32} is applied, where ^{2} and _{(10)} = 0.45 kPa. As mentioned before, two different pressure coefficients were investigated, that is, the simplified height-constant pressure coefficient

In addition to the external surface, the internal surface of the cooling tower also suffers wind load due to allowing wind to pass through to the circulating cooling water. Since no regulations concerning the internal suction of the cooling towers have been included in the existing Chinese code, the value adopted in the present study is incorporated in the German code (VGB [

The buckling safety of the shell is one of the essential factors considered in the design of cooling towers. The Chinese codes have provided stability checking formulas for the entire cooling tower and the tower body, respectively. They are_{cr} is the critical wind pressure; _{0} is the diameter at the throat; _{B} is the safety factor for elastic buckling; _{1} and _{2} refer to the circumferential and meridian pressures, respectively; _{1} and _{2} are the parameters determined from the geometric parameters of the tower body; _{cr1} and _{cr2} are the critical circumferential and meridian pressures, respectively, which are given by

According to equation (_{cr} is calculated by

The critical circumferential and meridian pressures, _{cr1} and _{cr2}, can be calculated by equations (_{B} can be obtained.

Since the maximum positive value (tension) of the membrane forces caused by wind load and dead load is usually at the windward meridian (0° meridian) and their maximum negative value (compression) is usually at about the 70° meridian, the membrane forces at the 0° and 70° meridian were taken as examples to analyze the influence of the pressure distribution on the static response of the cooling tower in this study. The membrane forces induced by the combined effects mentioned before are plotted in Figure

Comparison of membrane forces. (a) Meridional axial force. (b) Hoop axial force. (c) Meridional bending moment. (d) Hoop bending moment.

Figure

Comparison of displacement.

Comparison of meridional stress at typical height.

Table

Comparison of max response.

Pressure coefficient | Max displacement | Max principal tensile stress | Max principal compressive stress | ||||||
---|---|---|---|---|---|---|---|---|---|

Disp. (m) | Stress (MPa) | Stress (MPa) | |||||||

0 | 0.74 | 0.065 | 0 | 0.21 | 3.13 | ±69 | 0.19 | −2.47 | |

0 | 0.72 | 0.060 | 0 | 0.18 | 2.06 | ±73 | 0.17 | −5.22 |

The buckling safety is tabulated in Table

Comparison of overall buckling.

Method | Equation ( | ANSYS | |
---|---|---|---|

Pressure coefficient | — | ||

_{cr} | 123.78 m/s | 119.56 m/s | 112.68 m/s |

Buckling mode | — |

The current relevant design codes for cooling tower design in China respectively give two average wind pressure coefficient distribution curves for smooth and ribbed hyperbolic cooling towers, and the expression adopts the Fourier series as listed in equation (_{i} is the

Wind pressure coefficient in China and German codes.

The Fourier coefficients of each harmonic of specification curves.

Specification curve | Harmonic coefficient | |||||||
---|---|---|---|---|---|---|---|---|

_{0} | _{1} | _{2} | _{3} | _{4} | _{5} | _{6} | _{7} | |

China-with rib | −0.3919 | 0.2581 | 0.6013 | 0.5042 | 0.1052 | −0.0955 | −0.0194 | 0.0475 |

China-without rib | −0.4425 | 0.2460 | 0.6757 | 0.5356 | 0.0609 | −0.1393 | 0.0010 | 0.0644 |

VGB-K1.0 | −0.3181 | 0.4211 | 0.4841 | 0.3844 | 0.1419 | −0.0506 | −0.0718 | 0.0014 |

VGB-K1.1 | −0.3421 | 0.4018 | 0.5106 | 0.4142 | 0.1394 | −0.0687 | −0.0736 | 0.0137 |

VGB-K1.2 | −0.3715 | 0.3773 | 0.5397 | 0.4459 | 0.1351 | −0.0861 | −0.0714 | 0.0269 |

VGB-K1.3 | −0.4012 | 0.3549 | 0.5723 | 0.4756 | 0.1256 | −0.1029 | −0.0630 | 0.0419 |

VGB-K1.5 | −0.4616 | 0.3096 | 0.6408 | 0.5378 | 0.1021 | −0.1412 | −0.0421 | 0.0730 |

VGB-K1.6 | −0.4994 | 0.2937 | 0.6938 | 0.5559 | 0.0711 | −0.1467 | −0.0200 | 0.0714 |

Taking VGB-K1.0 as an example, the comparison of the wind pressure coefficients of the various harmonic components is depicted in Figure _{0} is the direct current component, which is equivalent to the uniform pressure acting in the radial direction of the cooling tower. Since _{0} is a negative value, its effect is expressed as suction. _{i} is the wind pressure coefficient of the _{7} is small. The sum of those terms is the VGB-K1.0 wind pressure curve.

Pressure curves of each harmonic component (VGB-K1.0).

Table _{i} is not zero, so the total resistance _{1} = _{1}

Specification curve | Drag coefficient of each harmonic component | _{D} | |||||||
---|---|---|---|---|---|---|---|---|---|

_{0} | _{1} | _{2} | _{3} | _{4} | _{5} | _{6} | _{7} | ||

China-with rib | 0.00 | 0.41 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.41 |

China-without rib | 0.00 | 0.39 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.39 |

VGB-K1.0 | 0.00 | 0.66 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.66 |

VGB-K1.1 | 0.00 | 0.64 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.64 |

VGB-K1.2 | 0.00 | 0.60 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.60 |

VGB-K1.3 | 0.00 | 0.56 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.56 |

VGB-K1.5 | 0.00 | 0.49 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.49 |

VGB-K1.6 | 0.00 | 0.46 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.46 |

From the analysis of the contribution of each order of harmonics to the drag coefficient, it can be seen that the DC component _{0}, which is probably equal around the surface, induces the uniform expansion of the circular section without rigid body displacement; that is, the drag coefficient of _{0} is zero. The first-order component _{1}, which may be a superposition of uniform force around the surface and a whole deflection force acting on the structure, causes rigid body displacement of the cooling tower without local deformation of the circular section; that is, the drag coefficient of _{1} is equal to the drag of the entire wind pressure curve zero. The higher-order component _{2}∼_{7}, which is not a uniform force around the surface, induces localized deformation in the circular section, but no rigid body displacement; that is, the drag coefficient of _{2}∼_{7} is zero. A schematic diagram of the radial displacement component generated by each order of harmonics is shown in Figure

Radial displacement of each harmonic component. (a) _{0}. (b) _{1}. (c) _{i} (

Taking the finite element model in Figure

Figure

Radial displacement of each harmonic component for rib curve in China code (throat). (a) Displacement of DC and first-order harmonic component. (b) High-order harmonic component displacement and total displacement.

The displacement of each harmonic component at the meridian of 0° (maximum positive pressure zone) and 70° (minimum negative pressure zone) is shown in Figure _{D} of the standard curve. This is because the effect of the first-order harmonic is resistance. The cooling tower structure undergoes a deformation similar to that of a vertical cantilever beam under the action of this component. The deformation size increases with heights; the greater the resistance, the greater the deflection induced. It can be seen from Figure _{D} of the wind pressure curve increases, the minimum wind pressure coefficient amplitude decreases, and the maximum local load decreases, so the local deformation of the shell also decreases. The distribution law of the overall displacement is basically consistent with the displacement of the DC and high-order harmonic components (Figure

Total displacement and component for each component. (a) Displacement of the first-order harmonic component. (b) Displacement of DC and high-order harmonic components. (c) Total displacement.

Figure

Percentage of first-order harmonic displacement.

Figure

Percentage of each harmonic displacement (middle average).

It can be clearly seen from Figure _{D}, its minimum proportion is still above 93%. The “increase” is much smaller than the “decrease,” so the total displacement decreases as the drag coefficient increases.

Percentage of first-order and high-order harmonic displacement (middle average).

Based on rigid model pressure measurement wind tunnel tests, the three-dimensional wind pressure coefficient distribution curve _{p}(_{p}(_{p}(

The wind pressure coefficient on the outer surface of the cooling tower is basically symmetrically distributed along the circumferential direction, and the average value of the lift coefficient is close to zero. The three-dimensional effect of the wind pressure distribution makes the three-dimensional effect of the drag coefficient significant. Besides, the drag coefficient is characterized by a large value at the end of the cooling tower and a small value at the middle of the cooling tower. The drag coefficients at both ends are greater than that of the middle section.

The wind-induced response of the cooling tower is dominated by the local shell deformation. The rigid deformation caused by resistance does not exceed 10% of the total response, while the local shell deformation caused by other harmonics accounts for more than 90% of the total response. The overall response of the cooling tower has no absolute relationship with the drag coefficient but is closely related to the characteristics of the wind pressure distribution.

The coefficient distribution curve of the three-dimensional average wind pressure _{p}(_{p}(_{p}(_{p}(

The data used to support the findings of this study are available from the corresponding author upon request.

The authors declare that there are no conflicts of interest regarding the publication of this paper.

The work presented in this paper was supported by grants received from the National Natural Science Foundations of China (Projects nos. 52078504, 51925808, and U1934209).