- Email: [email protected]
Wind induced interference factor of multirow cooling towers – A glimpse
Engineering Structures 200 (2019) 109673
Contents lists available at ScienceDirect
Engineering Structures journal homepage: www.elsevier.com/locate/engstruct
Wind induced interference factor of multirow cooling towers – A glimpse a,⁎
a
S. Chitra Ganapathi , P. Harikrishna , Devdas Menon a b
T
b
CSIR-SERC, Chennai, India IITM, Chennai, India
A B S T R A C T
Cooling towers constructed in multi rows with close proximity to each other is becoming common in the recent past, a development that is having profound impact on interference. Most of the studies on multirow towers were focused on the arrangement of cooling towers but the effect of wind direction and spacing of cooling towers were not included and very few studies were addressed either wind directions or specific spacings of grouped towers. Wind direction and spacing of cooling towers have an important influence on interference when compared to the arrangement of cooling towers. Effect of interference on specific arrangements like rectangular pattern, rhombic pattern, L-shaped, oblique L-shaped, etc., are less influenced due to the fact that they are effectively controlled by how the interfering cooling towers are positioned with respect to the principal tower whether it is on windward or leeward or on adjacent sides of the principal tower. Further, the cooling towers embedded in wind flow is usually different from the uniform condition drafted in most wind standards since most structures erected in power plants are embedded in the boundary layer flow. Very few researches have addressed the boundary layer flow conditions. Hence in the present study, systematic wind tunnel testing on several combinations of various spacing/diameter ratios of the representative four tower arrangement of cooling tower models are attempted for various wind directions viz. 0–180° under boundary layer flow condition for the interference function of cooling towers. The interference factor values tend to decrease and vary significantly between the spacing ratios (a/dm) 1.9 and 2.5. It is also observed that the IF value has shown high value for spacing ratio of 1.9 with 30% difference when compared to the values of isolated condition. The IF values corresponding to the 2.2, 2.5, 2.8 and 3.1 spacing ratios are 1.26, 1.197, 1.142 and 1.116 which are higher than the isolated values by about 26%, 20%, 14% and 12% respectively. Further from the analysis, a closed form solution is arrived for the interference of multirow towers.
1. Introduction Slenderness of the column and large dimension of the shell make this structure highly vulnerable to wind disturbances. The failure of cooling towers at Ferribridge, 1965 and that of other cooling tower at Scotland, 1973 have led to extensive research for the wind induced load effects of cooling towers. There are various wind tunnel tests have been performed on the isolated cooling tower models [11,7,9,1,13,4]. The exposure condition of cooling towers subjected to wind load is usually different from the isolated condition drafted in most wind standards since cooling towers in power plants are embedded in group arrangements or to the other buildings of same size, so that wind pressure distribution on a cooling tower will be differed significantly from that of an isolated tower. Interference factors are evaluated to quantify the load increase due to the group effect whereas in the case of large spatial structures, they are further sensitive due to the pressure distribution. Hence interference of cooling towers is more critical and will have a direct influence on stresses that enter in to the design. Apart from that, series of wind tunnel tests have been carried out to study the interference effects of wind load on tower group [14,19,8,20,6,21,10,22,3]. Based on the study, the interference factors and the response characteristics of cooling towers have been discussed, but those studies have ⁎
considered only two cooling towers. In today’s scenario, interference for group of more than two towers is an inevitable reality and with Government’s initiatives towards upgrading and augmenting the power plants, cooling towers constructed in multi rows with close proximity to each other is becoming common in the recent past e.g. Drax, Niederaussem, Boxberg and West burton power stations in Europe and Raichur and Rayalaseema, stations in India, etc., Most of these structures have become highly wind sensitive due to interference effect. While there is considerable research reported for the wind induced interference of two cooling towers, only few research studies included the interference effects between cooling towers in multi row configured. Flow around the two tower itself is quite complex for large spatial structures, whereas in the case of towers in multirow configurations, flow is further complex. Most of the studies on multirow towers were focused on the arrangement of cooling towers but the effect of spacing of cooling towers were not included [12] and very few studies were addressed either specific or limited spacings of grouped towers, Zhao et al. [16,17]. On the other hand, Niemann and Kopper [8] and Zhao and Ge [18] studies have shown that the interference of cooling tower is significantly influenced by the spacing of cooling towers. Hence center distance for cooling towers in most design codes are recommended with 1.5db–2.5db, with db being the base diameter [5,15]. As like spacing, the studies on
Corresponding author. E-mail addresses: [email protected] (S. Chitra Ganapathi), [email protected] (P. Harikrishna), [email protected] (D. Menon).
https://doi.org/10.1016/j.engstruct.2019.109673 Received 9 May 2019; Received in revised form 10 September 2019; Accepted 11 September 2019 0141-0296/ © 2019 Elsevier Ltd. All rights reserved.
Engineering Structures 200 (2019) 109673
S. Chitra Ganapathi, et al.
At each level, twenty-eight numbers of pressure taps have been provided along the circumference at every 13 degree intervals with a total number of 280 pressure taps on the entire pressure model (Fig. 2). However, no instrumentation on raker column has been attempted. The pressure signals have been acquired through pressure transducers through PVC pressure tubes with restrictors. The tubing system under consideration has a total length of 150 mm and 1.2 mm internal diameter with restrictor located at 70 mm from the end closer to the model port and is used to acquire the data. Restrictors which are used had an inner diameter of 0.4 mm and a length of 25 mm. To measure the internal pressure of the cooling tower shell, one channel in each pressure transducer is kept open.
multirow towers have also shown that the effect of wind directions were not included and very few studies were addressed limited wind directions of grouped towers. Wind direction and spacing of cooling towers have an important influence on interference when compared to the arrangement of cooling towers. Effect of interference on specific arrangements like rectangular pattern, rhombic pattern, L-shaped, oblique L-shaped, etc., are less influenced due to the fact that they are effectively controlled by how the interfering cooling towers are positioned with respect to the principal tower whether it is on windward or leeward or on adjacent sides of the principal tower. Therefore, it is of great significance to systematically study the interference effect of multirow cooling towers for various angles of wind incidence and spacing ratios. Within the multirow configurations, typical four tower arrangement is selected to perform the case study since it is a basic multirow arrangement in power plants. Further, the cooling towers embedded in wind flow is usually different from the uniform condition drafted in most wind standards since most structures erected in power plants are embedded in the boundary layer flow. Very few researches have addressed the boundary layer flow conditions. Hence in the present study, systematic wind tunnel testing on several combinations of diameter/spacing ratios of the representative four tower arrangement of cooling tower models are attempted for various wind directions under boundary layer flow condition for the interference function of cooling towers. Further from the analysis, a closed form solution is arrived for the interference of multirow towers.
1.2.2. Experimental arrangement Wind tunnel experiments have been carried out on the grouped cooling towers of four numbers arranged in square configuration for various centre-to-centre spacing ratios viz., 1.5–2.5 times of the base diameter db and for various angles of wind incidences ranging from 0° to 180° under the simulated open terrain condition to determine the circumferential pressures at nine different levels along the height. The test setup consisted of an instrumented principal tower ‘PT’ and three non-instrumented interfering towers ‘IT’. Typical schematic diagram of instrumented principal tower model with surrounding cooling towers is shown in Fig. 3. The measurements are made at a mean wind speed of 16 m/s at the height of the model (H = 400 mm). A standard Pitot static tube has been used to measure the mean velocity at the height of the model, located in free stream region of the test section. This velocity has been subsequently used as a reference velocity in computing the dynamic pressure and pressure coefficients. The pressure signals have been acquired through piezoresistive based pressure transducers of 0.36 psi pressure range. All the pressure data are acquired with a sampling rate of 650 Hz and for duration of 15 s. Three trials of measurement are considered for each case. The meridian facing the wind flow is reckoned as 0° angle of wind incidence, as shown in Fig. 4. The pressure data have been obtained for various azimuth angles circumferentially at 13° interval and the pressures have been acquired to experimentally measure and study the variation of external (C¯pe ) and internal pressure coefficient (C¯pi ) distributions at various levels along the height. The pressure transducer having some active ports is fixed at the corresponding levels with no tubing to determine the internal pressure distribution. Fig. 4 shows the orientation and typical view of the model in wind tunnel for 180° angle of wind incidence.
1.1. Flow field simulation in wind tunnel The experiments are performed in the boundary layer wind tunnel (BLWT) facility available at CSIR-SERC. The maximum wind speed attainable at the upstream side of the test section is 55 m/s. In order to translate the results of the boundary layer wind tunnel tests to corresponding prototype conditions, proper simulation of wind characteristics and wind flow field in the boundary layer wind tunnel are essential. Trip boards and roughening elements were used to simulate the natural atmospheric boundary layer stream. Based on the simulated mean velocity profile, the power law coefficient arrived for the simulated terrain is 0.165 and the measured turbulence intensity at the height of the model is 13%. The simulated mean velocity and turbulence intensity profiles are shown in Fig. 1. The spectrum of the horizontal wind speed is also simulated and compared with Von Karman spectrum. Based on the flow scale conditions, a geometric scale of 1:500 has been selected. 1.2. Wind tunnel test
1.2.3. Analysis of data All the acquired data have been reduced and analyzed using the following expressions. For each test case, three different data sets have been collected and the average values have been considered for the analysis. Using the sensitivity factors, the raw voltage data have been converted to engineering units and the variation of pressure distributions have been studied. The mean, standard deviation and peak pressure of a pressure trace p (t), taken over a period of time, and the mean, standard deviation and peak pressure coefficients of all pressure ports are subsequently deduced with respect to the reference pressure (p¯z) at heights (z) of 0.1Hs, 0.2Hs, 0.3Hs, 0.4Hs, 0.6Hs, 0.69Hs, 0.8Hs 0.9Hs and 0.95Hs for Level 1, Level 2, Level 3, Level 4 Level 5 Level 6 Level 7 and Level 8 and Level 9 respectively.
1.2.1. Geometric background and instrumentation The prototype dimension of the cooling tower model for which the study conducted is 200 m height with diameter at base, throat and top of the cooling tower are 136 m, 85.3 m and 88.5 m respectively. The prototype is modelled to a scale of 1:500 for the pressure measurement study. The scale ratio between the model and the prototype depends on the cross sectional area of the wind tunnel. With a geometric scale of 1:500, the overall height, ‘Hs’ of the cooling tower shell is 375 mm in wind tunnel with outer diameter at base, throat and top of the cooling tower model are 272 mm, 170.4 mm and 176.8 mm. For the present study, 3D printer has been used for fabricating the pressure model inhouse. The cooling tower model has a total height (H) of 400 mm including raker column height of about 25 mm. The raker columns are fabricated separately to the same scale using acrylic sheets and which was suitably glued to the shell of the cooling tower for making full model of NDCT. For the measurement of wind induced pressures on the rigid model, it is instrumented for pressures at ten different levels namely z = 0.95Hs, 0.90Hs, 0.80Hs, 0.690Hs, 0.60Hs, 0.40Hs, 0.30Hs, 0.20Hs and 0.10Hs where 'z' is the height of each level from bottom of the model shell and 'Hs' is the model height of the cooling tower shell.
28
C¯pe (z , θ) =
⎛ p¯e (z , θ) − p∞ ⎞ and C¯pi (z , θ) = 1 ρ (U¯ (z ))2 ⎟ ⎝ 2 ⎠
∑⎜ i=1
28
⎛ p¯i (z , θ) − p∞ ⎞ 1 ρ (U¯ (z ))2 ⎟ ⎝ 2 ⎠
∑⎜ i=1
(1) 28
C¯ p′ (z , θ) =
i=1
2
⎛ σ (z , θ) − p∞ ⎞ 1 ρ (U¯ (z ))2 ⎟ ⎝ 2 ⎠
∑⎜
(2)
Engineering Structures 200 (2019) 109673
S. Chitra Ganapathi, et al.
Fig. 1. Simulation of wind characteristics in wind tunnel.
Cp̂ (z , θ) =
28
⌢
⎛ p (z , θ) − p∞ ⎞ 1 ρ (U¯ (z ))2 ⎟ ⎝ 2 ⎠
∑⎜ i=1
Although experiments have been carried out for 13 different angles of wind incidence and nine different levels namely L1 = 0.10Hs, L2 = 0.20Hs, L3 = 0.30Hs, L4 = 0.40Hs, L5 = 0.60Hs, L6 = 0.69Hs, L7 = 0.80Hs, L8 = 0.9Hs and L9 = 0.95Hs where 'Hs' is the height of the cooling tower shell, the mean pressure coefficient envelop corresponding to the throat level (0.69 Hs) is presented here and the envelops have been developed by grouping the maximum/minimum values of C¯pe depending upon the sign at each angle of wind incidence ranging from 0° to 180° for each port. From the variation of mean pressure coefficient distribution, it is seen that the mean pressure coefficient (C¯pe ) trend for spacings 1.5db–2.5db are comparable in general. It has also been observed from the circumferential mean pressure coefficient distribution (C¯pe ) for five different spacings, the transition of positive to negative pressures takes place at a range between 30° and 45° azimuth angle as similar to isolated case. The mean suction pressure coefficient values for all spacings tend to increase significantly between azimuth angles θ = 50° and θ = 100° and with height. The maximum value of mean suction pressure coefficient is observed to be around −2.20, −2.18, −2.06, −2.02 and −2.03 for
(3)
where p¯ (z , θ) is the mean pressure coordinate, σ (z , θ) is the standard ⌢ deviation pressure coordinate and p (z , θ) is the peak pressure coordinate for pressure tap angle θ at z level, suffix ‘e’ and ‘i’ stands for external and internal pressures and p∞ is the static pressure of the ¯ (z) is the mean velocity at approaching flow, ρ is the density of air and U heights, z = 3.8 cm, 7.5 cm, 11.3 cm, 15 cm, 22.5 cm, 26.3 cm, 30.1 cm, 33.8 cm and 35.7 cm for Levels 1, 2, 3, 4, 5, 6, 7, 8 and 9 respectively.
1.3. Wind pressure coefficients under interference 1.3.1. Mean pressure coefficient Wind tunnel results of mean pressure coefficient distribution of grouped cooling towers arranged in square configuration for various centre-to-centre spacing ratios viz., 1.5–2.5 times of the base diameter db of cooling tower model is shown in Fig. 5 for open terrain condition. 3
Engineering Structures 200 (2019) 109673
S. Chitra Ganapathi, et al.
Fig. 2. Typical 3-D view of the fabricated cooling tower models with pressure tap locations.
Fig. 4. Orientation and typical view of the model in wind tunnel for 180° angle of wind incidence.
Fig. 3. Schematic diagram of cooling tower model with surrounding towers.
1.5db, 1.75db, 2.0db, 2.25db and 2.5db spacings respectively. Further, the maximum value of mean suction pressure coefficient is observed to be on higher side than those of isolated study values by about 5–14% for all spacings. The rear suction pressure coefficient, C¯pb of all spacings is observed to be constant between angles θ = 120° and θ = 180°. It is also seen that the value of rear suction pressure coefficient has shown excessively high value for the 1.5db spacing with 23–35% difference when compared to the values of isolated condition and similarly the values of other spacings have shown variation on higher side than the values of next higher spacing. The rear suction pressure coefficient values of 1.75db, 2.0db, 2.25db and 2.5db spacings are −0.39 to −0.53, −0.37 to −0.52, −0.36 to −0.46 and −0.36 to −0.47 which are higher than the isolated values by about 17–26%, 11–20%, 5–12% and 6–10% for 1.75db, 2.0db, 2.25db and 2.5db spacing respectively. However, the mean stagnation pressure coefficient values for all spacings are within 5–10% difference than the isolated flow condition values on windward face.
Fig. 5. Variation of mean pressure coefficient distribution along the circumference of cooling tower model for various spacing ratios under open terrain condition.
1.3.2. Trend of mean pressure coefficient distribution The wind pressure distribution due to the interference is significantly increased in smaller spacings and in specific angles of wind 4
Engineering Structures 200 (2019) 109673
S. Chitra Ganapathi, et al.
Fig. 6. Polar variation of mean pressure coefficient distribution with angles of wind incidence and spacing ratios for throat level.
interference effects are to be appropriately taken care in load estimation for the safe design of cooling towers.
incidence of the tower. Hence the polar diagram variation of mean pressure coefficient distribution along the circumference of cooling tower model for various angles of wind incidence and spacing ratios corresponding to the throat level is shown in Fig. 6. The interfered pressure coefficient distributions are observed to be asymmetrical and magnified particularly in the suction and base pressure zone. In general, there is a prominent variation in the interfered mean pressure coefficient values with upper bounds at throat and bottom levels as compared to the other intermediate levels. The interfered mean pressure coefficient values are also shown with asymmetrical distribution especially at lower heights for all angles of wind incidence and symmetrical distribution of pressure coefficient values at higher heights for most angles of wind incidence which gives the inference that the interference near the ground level is higher hence shows an asymmetrical distribution. This trend has clearly shown that the distance between towers is shorter and the turbulence intensity levels are also higher at lower heights which makes the interference effect high near the lower heights. However, the mean pressure coefficient for 105–165° angles of wind incidence are shown with asymmetrical distributions even for higher heights which implies that the interference effect at these angles of wind incidence are mainly due to the channelization of flow. Similarly, the interference effect for smaller spacing is higher, hence shows an asymmetrical pattern with high mean pressure coefficient values at lower spacings. Whereas at higher spacings, the interference effect of mean pressure coefficient values is observed to be less significant and for the spacings of > 2.0db, the interference effect of mean pressure is further reduced. It is apparent from the above discussion that the interference of mean pressures is significant in the base and suction pressure region. Also the smaller spacings and critical wind incidences of the tower increased the interference effects further. Hence the
1.3.3. Distribution characteristics of mean pressure coefficient The circumferential distribution of mean pressure coefficient of an isolated cooling tower is usually expressed in the form of Fourier cosine terms with following Fourier coefficients, where a1 = −0.00071, a2 = 0.24611, a3 = 0.62296, a4 = 0.48833, a5 = 0.10756, a6 = 0.09579, a7 = −0.01142, a8 = 0.04551 in some codes viz. BIS11504 [2], Chinese code, etc., Whereas the fitting parameters are applicable for the symmetrical distribution of pressures. However, the mean pressure coefficient of interfering cooling towers is shown with asymmetrical distribution of pressures, hence the above expression cannot fit an asymmetrical curve. Therefore, the Fourier cosine, sine and the constant terms with the corresponding coefficients are used to fit the asymmetrical pressure curves. 7
C¯p (θ) =
7
∑ ak cos(kθ) + ∑ bk sin(kθ) + C k=1
k=1
(4)
The representative curves, from the combination of angles of wind incidence, for each spacing of cooling towers can produce thirteen different pressure curves, in which five are asymmetrically distributed and remaining eight are symmetrically distributed. Table 1 gives the fitting parameters for the envelops of 225 asymmetrical and 360 symmetrical distribution of pressure curves of all 585 cases (585 cases = 1 tower × 9 levels × 5 spacings × 13 angles of wind incidence). 1.3.4. Fluctuating pressure coefficient The surface distribution of fluctuating pressure coefficient corresponding to the throat level as a function of angle of wind incidence for 5
Engineering Structures 200 (2019) 109673
S. Chitra Ganapathi, et al.
Table 1 Fitting parameters for mean pressure coefficient distribution under interference. Fourier Coeff
C
a1
a2
a3
a4
a5
a6
a7
a8
b1
b2
b3
b4
b5
b6
b7
b8
Asymm Symm
−0.72 −0.8
0.57 0.49
1.3 1.37
0.58 0.64
−0.11 −0.09
−0.07 −0.05
−0.08 −0.06
−0.12 −0.1
−0.04 −0.02
0.02 −0.01
0.01 −0.05
0.07 −0.01
0.05 −0.01
0.02 −0.01
0.05 0.07
0.02 0.01
0.01 0.05
Fig. 7. Variation of standard deviation pressure coefficient distribution with azimuth angle for various angles of wind incidence and spacing ratio.
takes place for a range between 25° & 75° and 285° & 335° azimuth angle. The standard deviation pressure coefficient values tend to follow the decreasing trend (0.6–0.2) between azimuth angles θ = 75° & θ = 120° and θ = 240° & θ = 285° and with height. There are two peaks in the distribution of fluctuating pressure coefficient (0.6) is observed at the point of 75–90° region and 270–285° region because of the vortex shedding phenomenon. Further, the peaks of standard deviation pressure coefficient values of all levels are observed to be on higher side than those of isolated study values by about 8–17% for all spacings.
the various spacing ratio of cooling tower is shown in Fig. 7. The fluctuating pressure coefficient distribution at each level namely z/ H = 0.1, 0.2, 0.3, 0.4, 0.6, 0.69 0.8, 0.9 and 0.95 are comparable in trend. The fluctuating pressure coefficient values are shown with asymmetrical distribution in the separation and wake zone at lower heights for all angles of wind incidence. It is also seen from the variation of fluctuating pressure coefficient of higher heights, an axially symmetrical distribution is observed for most angles of wind incidence and an asymmetrical distribution of coefficient is observed for 105–165° angles of wind incidence in the separation and wake zone. Further, the fluctuating pressure coefficient values decrease with height as like the turbulence intensity, whereas above the throat level all the regions have become almost independent of standard deviation effect. The values have shown nearly constant variation between levels and spacing ratios in 0–25° & 335–360° azimuth angle region. The fluctuating pressure coefficient values of 0–25° and 335–360° azimuth angles for all spacings are within 5–10% difference than the isolated flow condition values. Similarly, the fluctuating pressure coefficient values of all levels corresponding to the 120–240° azimuth angle regions are on higher side than the isolated values by about 15–42% for all spacings. The fluctuating pressure coefficient values of 120–240° azimuth angle region (i.e. with values 0.10–0.2) is observed with less value when compared to the values of all other azimuth angle regions. It has also been observed from the fluctuating pressure coefficient distribution ' (C¯ p ) of nine different levels, the values with increasing trend (0.4–0.6)
1.3.5. Power spectra of fluctuating pressures Adverse effects of interference arise from the vortex shedding and wake phenomena of the tower. Hence the variation of power spectral density curves of base pressure port corresponding to typical wind direction is shown in Fig. 8 for the various spacing ratios. It is clear from the variation of PSD of interfering pressures, the power spectral amplitude of the base and suction pressure ports are observed with variations on higher side than the isolated variations for most wind directions. These variation have also confirmed the profound effect of interference in the identified regions of concern. Further, irrespective of spacing ratio, all the curves are shown with same trend and the power spectral amplitude of smaller spacings in the considered frequency ranges are on higher side than the power spectral amplitude of successive spacings and isolated arrangement. The higher power spectral 6
Engineering Structures 200 (2019) 109673
S. Chitra Ganapathi, et al.
different zones of interference viz. ITW, ITL and ITS. Figs. 10–12 show the variation of mean and peak suction pressure coefficient with spacing ratio for three different interference zones ITW, ITL and ITS respectively. Similarly, the variation of mean and peak base pressure coefficient with spacing ratio is shown in Figs. 13–15 for three different interference zones ITW, ITL and ITS respectively. From the variation of mean and peak pressure coefficients, it is seen that the presence of interfering cooling towers on the adjacent side of principal tower (ITs zone) has a considerable interference effect on the mean and peak pressure coefficient values and the presence of interfering cooling tower models on the leeward (ITL zone) and windward (ITW zone) side of principal tower have a less significant interference effect on the mean and peak pressure coefficient values. In general, the mean and peak suction pressure coefficient values tend to vary nominally with increase in spacing and the variations are within 5% difference. However, the variation between levels is maintained with 6–13% difference. The mean suction pressure coefficient values of ITs zone for the smaller spacing ratios (1.5–2.0) are observed to be on higher side than the ITL and ITW zones by about 7–13% for all nine levels. It is also observed that the values of mean suction pressure coefficient of ITs zone for the 2.25–2.5 spacing ratio have shown high values with 3–5% difference for all levels when compared to the values of ITL and ITW zones. As similar to the mean suction pressure coefficient values, peak suction pressure coefficient values of 1.5–2.0 spacing ratios of ITS zone are observed to be increased by about 5–12% than the values of other two zones viz. ITL and ITW for all levels. It is also clear that the values of peak suction pressure coefficient of ITL and ITW zones for the larger spacing ratios (2.25–2.5) are observed to be decreased by about 5% for all levels when compared to the values of ITS zones. Further, the mean and peak base pressure coefficient values of all spacing ratios are observed to be decreased gradually with increase in spacing and the differences are maintained as similar to the variation of mean and peak suction pressure coefficient. In comparison with levels, mean and peak base pressure coefficient values of the lower and top levels are on higher side. Moreover, for the middle levels, the values are on lower side than the values of lower and top levels and the differences are between 13 and 25%. The mean base pressure coefficient values of all levels corresponding to the 1.5, 1.75 and 2.0 spacing ratios of ITs zone are on higher side than the mean base pressure coefficient values of ITL zone by about 20–40%, 20–28% &17–30% and the values of ITs zone are increased nearly by 20–40%, 11–25% & 8–20% with ITW zones for 1.5, 1.75 and 2 spacing ratios respectively. However, the mean base pressure coefficient values of ITL and ITW zones for 2.25 and 2.5 spacing ratios are decreased by 10–20% and 3–8% when compared to the values of ITs zone for most levels. As discussed above, the peak base pressure coefficient value of various levels of ITs zone is the highest of all zones by about 10–35%, 10–25% &10–20% for the spacing ratios 1.5, 1.75 and 2.0 respectively. In the spacing ratios of 2.25 and 2.5, the mean base pressure coefficient values of ITL and ITW zones are decreased by 5–12% and 3–8% difference when compared to the values of ITs zone for all levels.
Fig. 8. Variation of power spectral density distribution for various spacing ratios.
amplitude is related with higher energy level; higher the energy level, then higher the energy consumption, the higher energy consumption is obviously resulted from the vortex and wake energy. The above discussions of fluctuating pressure coefficient and the power spectra of fluctuating pressures have also made it clear that the base and suction pressure of the tower most importantly in the smaller spacings and critical wind incidences are more prone to interference effect. 1.4. Interference factors based on various criteria’s Interferences are evaluated based on the aspects of aerodynamic loading or structural response or reinforcement ratio. It is evident from the literatures [4,12] that the interference due to the aerodynamic loading aspect is larger when compared to the aspects of structural responses or reinforcement ratio. Hence to consider the effect of interference, mean interference Factor (MIF) multiplied to the mean pressure coefficient distribution and peak interference factor (PIF) multiplied to the peak pressure coefficient distribution have been evaluated based on the variation of aerodynamic pressure coefficient aspect. 1.4.1. Analysis of the interference effects The parameters suction and base pressure coefficient of the mean and peak pressure distribution of a cooling tower model are the important inputs for the design of a cooling tower structure, hence the variation of these parameters with relative spacing (a/db) of interfering cooling tower models is considered for the evaluation of interference effects. The study has also shown that the angle of wind incidence has a significant influence in determining these parameters in addition to the spacing of cooling tower models, hence the interference zones are grouped based on the range of angles of wind incidence i.e., 0–30° angles of wind incidence is grouped under ITL category, 30–150° angles of wind incidence is grouped under ITS category and 150–180° angles of wind incidence is grouped under ITW category, i.e., ITW, ITL and ITS are the interfering zones corresponding to interfering cooling tower models on windward, leeward and adjacent sides of principal tower (PT). Fig. 9 shows the various zones of interference based on the spacing of interfering cooling tower models, viz. a1 = 1.5db, a2 = 1.75db, a3 = 2.0db, a4 = 2.25db and a5 = 2.5db and based on the zones of angles of wind incidence, viz. ITW, ITL and ITS - interfering cooling tower models are on windward leeward and adjacent sides of PT. The variation of mean & peak suction and base pressure coefficient values of the interfering cooling tower model with various spacing ratios (a/db) viz. 1.5, 1.75, 2.0, 2.25 and 2.5, where ‘a’ is the c/c spacing of cooling tower models and ‘db’ is the base diameter of cooling tower model is studied for nine different levels viz. L1 to L9 and for three
1.4.2. Mean and peak interference factor of suction and base pressure coefficients The mean interference factor is defined as the ratio between the enhanced mean pressure coefficient in the grouped configuration to the corresponding mean pressure coefficient in isolated configuration. In line with MIF, PIF is also defined as the ratio of enhanced peak pressure coefficient in the grouped configuration to the corresponding peak pressure coefficient in isolated configuration. Fig. 16 shows the variation of MIF and PIF values of suction and base pressure coefficient with levels for the various zones of angle of wind incidence of cooling tower models in a typical spacing ratio. The variation of MIF values of suction pressure coefficient between levels are compared well with each other with less than 5–8% difference under all zones of interference. The variation of MIF values of base pressure coefficient between levels are 7
Engineering Structures 200 (2019) 109673
S. Chitra Ganapathi, et al.
Fig. 9. Various zones of interference based on the spacing and angles of wind incidence of cooling tower models.
Fig. 10. Variation of mean and peak suction pressure coefficient with spacing ratio for interfering cooling tower models on leeward side of principal tower (ITL zone or 0–30° angles of wind incidence).
Fig. 11. Variation of mean and peak suction pressure coefficient with spacing ratio for interfering cooling tower models on adjacent side of principal tower (ITS zone or 30–150° angles of wind incidence).
It is also found from the study, that the variation of MIF of suction pressure coefficient between angles of wind incidence is observed with 10–17% difference for all spacing ratios. Mean interference factor values of base pressure coefficient within each spacing ratio is significantly affected by the angle of wind incidence in a tower group, among various angles of wind incidence, 75–105° angle of wind incidences or interfering towers adjacent to the principal cooling tower condition gives the highest percentage of interference effect by about 20–35% than the interference effect of other angles of wind incidence. Similarly, the PIF variation of suction and base pressure coefficient is also consistent with MIF variation. Further, it is also clear from the variation that the MIF or PIF values from suction pressure coefficient criteria are on lower side than the
also compared well with each other with less than 10% difference under ITS zone of interference but a pronounced variation in the MIF values of base pressure coefficient between the levels is found for the ITW and ITL zones of interference whose relative differences are 10–20% and 15–20% respectively. The variation of MIF and PIF values of suction and base pressure coefficient corresponding to typical zone of angle of wind incidence with levels is shown in Fig. 17 for the various spacing ratio (a/db). In general, the mean interference factor values of suction and base pressure coefficient tend to decrease with increase in spacing. It is also seen that the MIF of suction pressure coefficient is varied nominally with spacing ratio for all levels. The MIF values of base pressure coefficient for all levels are found to be significantly varied with spacing ratios by about 3–30%.
8
Engineering Structures 200 (2019) 109673
S. Chitra Ganapathi, et al.
Fig. 12. Variation of mean and peak suction pressure coefficient with spacing ratio for interfering cooling tower models on windward side of principal tower (ITW or 150–180° angles of wind incidence).
Fig. 13. Variation of mean and peak base pressure coefficient with spacing ratio for interfering cooling tower models on leeward side of principal tower (ITL zone or 0–30° angles of wind incidence).
Fig. 14. Variation of mean and peak base pressure coefficient with spacing ratio for interfering cooling tower models on adjacent side of principal tower (ITS zone or 30–150° angles of wind incidence).
values have been chosen among the IF values of mean suction and base pressure coefficient of various angles of wind incidence and levels. The interference factor values tend to decrease and vary significantly between the spacing ratios (a/dm) 1.9 and 2.5. It is also observed from the variation of IF values that the transition of trend takes place between the spacing ratios 2.5 and 2.8. The interference factor values are observed to be nearly constant for the spacing ratios 2.8 & 3.1. It is also observed that the IF value has shown high value for spacing ratio of 1.9 with 30% difference when compared to the values of isolated condition. The IF values corresponding to the 2.2, 2.5, 2.8 and 3.1 spacing ratios are 1.26, 1.197, 1.142 and 1.116 which are higher than the isolated values by about 26%, 20%, 14% and 12% respectively. The variations in these values indicate that the interference effect in smaller spacing ratios shows higher IF value than the next higher spacing. Similarly, the values of other spacing ratios have shown variation on higher side than
values of base pressure coefficient criteria and the variations are also observed to be negligible with angles of wind incidence and spacing ratio. However, the mean and peak interference factor values from base pressure coefficient criteria are shown significant variation with angle of wind incidence and spacing ratio. The variation between MIF and PIF values based on the variation of mean and peak pressures are comparable in trend and the values are also comparable to each other, hence the MIF and PIF values need not be considered independently and the values have been converted in to a single interference factor (IF) value for interference evaluation. 1.4.3. Interference factor for multirow towers In general, it is seen from the above plots that the interference factor (IF) for all spacing ratios is varied considerably with angle of wind incidence and nominally between the levels, hence the maximum IF 9
Engineering Structures 200 (2019) 109673
S. Chitra Ganapathi, et al.
Fig. 15. Variation of mean and peak base pressure coefficient with spacing ratio for interfering cooling tower models on windward side of principal tower (ITW zone or 150–180° angles of wind incidence).
Fig. 16. Variation of MIF and PIF values of mean & peak suction and base pressure coefficient with levels for 1.5db spacing ratio. 10
Engineering Structures 200 (2019) 109673
S. Chitra Ganapathi, et al.
Fig. 17. Variation of MIF and PIF values of mean & peak suction and base pressure coefficient with levels for ITS zone.
proposed for the interference of multirow towers by considering the above effects.
the values of next higher spacing. As spacing of tower increases, interference effect drops. In other words, if the spacing is high, the interference effect is reduced. It is also found from the present study that the fluctuating pressure values of principal tower corresponding to multi tower group have shown larger values than that of isolated one in all spacing ratios by about 14% due to the effect of multirow towers. The variation in these values also infer that the interference effect due to the angle of wind incidence is further doubled from the 14% increase in smaller spacing ratios viz. 1.9 and 2.2 hence shows a higher IF value with 30% difference at lower spacing ratios. Whereas at 2.5 spacing ratio, the interference effect due to angle of wind incidence is nearly increased by one and half times with respect to the 14% increase, thus it gives IF value with 20% difference. Between the spacing ratios 2.8 and 3.1, the interference is found to be independent of wind incidence effect, hence the IF value remains constant with 14% increase. Further from the above analysis, a closed form solution as a function of spacing ratio is
Fi ≈ 1 + 0.14(4 − (a/ dm))
(5)
where a is the centre to centre distance of cooling tower under consideration and the neighboring cooling tower; (d + d ) dm ≈ u 2 t is average diameter of the shell; du = is the diameter at the lower edge and dt = is the diameter at the throat. Further, the interference factor values have been compared with the values provided in the existing cooling tower design codes [15,5]. Fig. 18 shows the variation of IF of wind tunnel results and codal standard with spacing ratio (a/dm). Though the interference factor given in codal standard is mentioned that, it is valid for groups of more than two towers but the interference factor values of present study corresponding to more than two tower groups have given higher values 11
Engineering Structures 200 (2019) 109673
S. Chitra Ganapathi, et al.
interference factor (IF) within each spacing ratios is varied considerably with angles of wind incidence and nominally between the levels, hence the maximum IF values have been chosen among the IF values of suction and base pressure coefficient of various angle of wind incidence and levels. It is also observed that the IF value has shown high value for spacing ratio (a/dm) of 1.9 with 30% difference when compared to the values of isolated condition. Similarly, the values of other spacing ratios have shown variation on higher side than the values of next higher spacing. The IF values corresponding to the 2.2, 2.5, 2.8 and 3.1 spacing ratios are 1.26, 1.197, 1.142 and 1.116 which are higher than the isolated values by about 26%, 20%, 14% and 12% respectively. Further from the analysis, a closed form solution is arrived for the interference of multirow towers. Though the interference factor given in codal standard is mentioned that, it is valid for groups of more than two towers but the interference factor values of present study corresponding to more than two tower groups have given higher values when compared to the values reported in codal standard by about 5–7%. Hence to consider the above effects, the IF empirical relation given in code is also need to be revised with the proposed equation which accounts the additional 5–7% increase of interference load in the existing IF empirical relation.
Fig. 18. Variation of MIF with spacing ratio (a/dm).
when compared to the values reported in codal standard by about 5–7%. Hence to consider the above effects, the IF empirical relation given in code is also need to be revised with the above expression which accounts the additional 5–7% increase of interference load in the existing IF empirical relation.
Declaration of Competing Interest 2. Summary and conclusion The authors declare that they have no conflict of interest. Cooling towers constructed in multi rows with close proximity to each other is becoming common in the recent past, a development that is having profound impact on interference. Most of the studies on multirow cylinders were focused on arrangement of cooling towers but the effect of wind direction and spacing of cooling towers were not included. Wind direction and spacing of cooling towers have an important influence on interference when compared to the arrangement of cooling towers. The present study analyzed the interference effect of four cooling towers in a boundary layer wind tunnel under open terrain condition for various angles of wind incidence viz. 0–180° and spacing ratios (a/dm) viz. 1.9–3.1. Mean and standard deviation pressure coefficient distributions & power spectra of fluctuating pressures are evaluated and the impact of interference on these coefficients is discussed at each of the measured levels for wind induced loads. The maximum value of mean suction pressure coefficient is observed to be on higher side than those of isolated study values by about 5–14% for all spacings. The value of rear suction pressure coefficient has shown excessively high value for the 1.5db spacing with 23–35% difference when compared to the values of isolated condition. The rear suction pressure coefficient values of 1.75db, 2.0db, 2.25db and 2.5db spacings are −0.39 to −0.53, −0.37 to −0.52, −0.36 to −0.46 and −0.36 to −0.47 which are higher than the isolated values by about 17–26%, 11–20%, 5–12% and 6–10% for 1.75db, 2.0db, 2.25db and 2.5db spacing respectively. Similarly, the fluctuating pressure coefficient values of all levels corresponding to the 120–240° azimuth angle regions are on higher side than the isolated values by about 15–42% for all spacings. There are two peaks in the distribution of fluctuating pressure coefficient is observed at the point of 75–90° region and 270–285° region because of the vortex shedding phenomenon. Further, the peaks of standard deviation pressure coefficient values of all levels are observed to be on higher side than those of isolated study values by about 8–17% for all spacings. It is apparent from the above discussion that the interference of these coefficients is significant in the base and suction pressure region. Also the smaller spacings and critical wind incidences of the tower increased the interference effects further. The parameters suction and base pressure coefficient of a cooling tower are the important inputs for the design of a cooling tower structure, hence the variation of these parameters with various angles of wind incidence and relative spacing of interfering cooling tower models is considered for the evaluation of interference effects. The
Appendix A. Supplementary material Supplementary data to this article can be found online at https:// doi.org/10.1016/j.engstruct.2019.109673. References [1] Armitt J. Wind loading on cooling tower. J Struct Eng ASCE 1980;106(3):623–41. [2] IS: 11504 - 1985. Criteria for structural design of reinforced concrete natural draught cooling towers. India: BIS. [3] Ke ST, Liang J, Zhao L, Ge YJ. Influence of ventilation rate on the aerodynamic interference between two extra-large indirect cooling towers by CFD. Wind Struct 2015;20(3):449–68. [4] Lin Z, Ge Y, Kareem A. Fluctuating wind pressure distribution around full-scale cooling towers. J Wind Eng Ind Aerodyn 2017;165:34–45. [5] Ministry of Housing and Urban-Rural Development of People’s Republic of China. Code for design of cooling for industrial recirculating water GB/T 50102-2014. China: China Planning Press; 2014. [in Chinese]. [6] Maurizio O. Wind-induced interference effects on two adjacent cooling towers. Eng Struct 2001;23:979–92. [7] Niemann HJ. Wind effects on cooling-tower shells. J Struct Div 1980;106:643–61. [8] Niemann HJ, Kopper HD. Influence of adjacent buildings on wind effects on cooling towers. Eng Struct 1998;20(10):874–80. [9] Propper H, Welsch J. Wind pressures on cooling tower shells. Wind Eng 1980;1:465–78. [10] Portela G, Godoy LA. Shielding effects and buckling of steel tanks in tandem arrays under wind pressures. Wind Struct 2005;8(5):325–42. [11] Ruscheweyh H. Wind loading on hyperbolic natural draught cooling towers. J Wind Eng Ind Aerodyn 1975;1:335–40. [12] Shitanng K, Hao W, Yaojun G. Interference effect and the working mechanism of wind loads in super-large cooling towers under typical four-tower arrangements. J Wind Eng Ind Aerodyn 2017;170:197–213. [13] Sun TF, Zhou L. Wind pressure distribution around a ribless hyperbolic cooling tower. J Wind Eng Ind Aerodyn 1983;14(1–3):181–92. [14] Sun TF, Gu ZF. Interference between wind loading on group of structures. J Wind Eng Ind Aerodyn 1995;54(55):213–25. [15] VGB-R 610Ue. German design code for Structural design of cooling towers. Essen: VGB Power Tech e.V.; 2010. [16] Zhao L, Zhan Y, Ge Y. Wind induced equivalent static interference criteria and its effects on cooling towers with complex arrangements. Eng Struct 2018;172(1):141–53. [17] Zhao L, Chen X, Ge Y. Investigations of adverse wind loads on a large cooling tower for the six-tower combination. Appl Therm Eng 2016;105:988–99. [18] Zhao L, Ge YJ. Wind loading characteristics of super large cooling towers. Wind Struct 2010;13(3):257–73. [19] Bartoli G, Borri C, Hoeffer R, Orlando M. Wind induced pressures and interference effects on a group of cooling towers in a power plant arrangement. Proceedings of 2nd European and African conference on wind engineering. Genoa, Italy, Padua: SGE; 1997. p. 969–76.
12
Engineering Structures 200 (2019) 109673
S. Chitra Ganapathi, et al.
Istanbul, Turkey. 2004. p. 105–13. [22] Selvi RS, Babu GR, Arunachalam S, et al. Interference factors for natural draught cooling towers based on wind tunnel experiments. Eighth Asia-Pacific conf wind eng. 2013. p. 490–8.
[20] Borri C, Orlando M, Spinelli P. Wind induced stresses on two neighboring cooling towers. Proceedings of 10th ICWE, Copenhagen, Denmark, Rotterdam, vol. 1. Balkema; 1999. p. 401–8. [21] Niemann HJ, Kopper HD. Provision for interference effects in non-symmetric design of cooling towers. Fifth international symposium on natural draught cooling tower,
13
Contents lists available at ScienceDirect
Engineering Structures journal homepage: www.elsevier.com/locate/engstruct
Wind induced interference factor of multirow cooling towers – A glimpse a,⁎
a
S. Chitra Ganapathi , P. Harikrishna , Devdas Menon a b
T
b
CSIR-SERC, Chennai, India IITM, Chennai, India
A B S T R A C T
Cooling towers constructed in multi rows with close proximity to each other is becoming common in the recent past, a development that is having profound impact on interference. Most of the studies on multirow towers were focused on the arrangement of cooling towers but the effect of wind direction and spacing of cooling towers were not included and very few studies were addressed either wind directions or specific spacings of grouped towers. Wind direction and spacing of cooling towers have an important influence on interference when compared to the arrangement of cooling towers. Effect of interference on specific arrangements like rectangular pattern, rhombic pattern, L-shaped, oblique L-shaped, etc., are less influenced due to the fact that they are effectively controlled by how the interfering cooling towers are positioned with respect to the principal tower whether it is on windward or leeward or on adjacent sides of the principal tower. Further, the cooling towers embedded in wind flow is usually different from the uniform condition drafted in most wind standards since most structures erected in power plants are embedded in the boundary layer flow. Very few researches have addressed the boundary layer flow conditions. Hence in the present study, systematic wind tunnel testing on several combinations of various spacing/diameter ratios of the representative four tower arrangement of cooling tower models are attempted for various wind directions viz. 0–180° under boundary layer flow condition for the interference function of cooling towers. The interference factor values tend to decrease and vary significantly between the spacing ratios (a/dm) 1.9 and 2.5. It is also observed that the IF value has shown high value for spacing ratio of 1.9 with 30% difference when compared to the values of isolated condition. The IF values corresponding to the 2.2, 2.5, 2.8 and 3.1 spacing ratios are 1.26, 1.197, 1.142 and 1.116 which are higher than the isolated values by about 26%, 20%, 14% and 12% respectively. Further from the analysis, a closed form solution is arrived for the interference of multirow towers.
1. Introduction Slenderness of the column and large dimension of the shell make this structure highly vulnerable to wind disturbances. The failure of cooling towers at Ferribridge, 1965 and that of other cooling tower at Scotland, 1973 have led to extensive research for the wind induced load effects of cooling towers. There are various wind tunnel tests have been performed on the isolated cooling tower models [11,7,9,1,13,4]. The exposure condition of cooling towers subjected to wind load is usually different from the isolated condition drafted in most wind standards since cooling towers in power plants are embedded in group arrangements or to the other buildings of same size, so that wind pressure distribution on a cooling tower will be differed significantly from that of an isolated tower. Interference factors are evaluated to quantify the load increase due to the group effect whereas in the case of large spatial structures, they are further sensitive due to the pressure distribution. Hence interference of cooling towers is more critical and will have a direct influence on stresses that enter in to the design. Apart from that, series of wind tunnel tests have been carried out to study the interference effects of wind load on tower group [14,19,8,20,6,21,10,22,3]. Based on the study, the interference factors and the response characteristics of cooling towers have been discussed, but those studies have ⁎
considered only two cooling towers. In today’s scenario, interference for group of more than two towers is an inevitable reality and with Government’s initiatives towards upgrading and augmenting the power plants, cooling towers constructed in multi rows with close proximity to each other is becoming common in the recent past e.g. Drax, Niederaussem, Boxberg and West burton power stations in Europe and Raichur and Rayalaseema, stations in India, etc., Most of these structures have become highly wind sensitive due to interference effect. While there is considerable research reported for the wind induced interference of two cooling towers, only few research studies included the interference effects between cooling towers in multi row configured. Flow around the two tower itself is quite complex for large spatial structures, whereas in the case of towers in multirow configurations, flow is further complex. Most of the studies on multirow towers were focused on the arrangement of cooling towers but the effect of spacing of cooling towers were not included [12] and very few studies were addressed either specific or limited spacings of grouped towers, Zhao et al. [16,17]. On the other hand, Niemann and Kopper [8] and Zhao and Ge [18] studies have shown that the interference of cooling tower is significantly influenced by the spacing of cooling towers. Hence center distance for cooling towers in most design codes are recommended with 1.5db–2.5db, with db being the base diameter [5,15]. As like spacing, the studies on
Corresponding author. E-mail addresses: [email protected] (S. Chitra Ganapathi), [email protected] (P. Harikrishna), [email protected] (D. Menon).
https://doi.org/10.1016/j.engstruct.2019.109673 Received 9 May 2019; Received in revised form 10 September 2019; Accepted 11 September 2019 0141-0296/ © 2019 Elsevier Ltd. All rights reserved.
Engineering Structures 200 (2019) 109673
S. Chitra Ganapathi, et al.
At each level, twenty-eight numbers of pressure taps have been provided along the circumference at every 13 degree intervals with a total number of 280 pressure taps on the entire pressure model (Fig. 2). However, no instrumentation on raker column has been attempted. The pressure signals have been acquired through pressure transducers through PVC pressure tubes with restrictors. The tubing system under consideration has a total length of 150 mm and 1.2 mm internal diameter with restrictor located at 70 mm from the end closer to the model port and is used to acquire the data. Restrictors which are used had an inner diameter of 0.4 mm and a length of 25 mm. To measure the internal pressure of the cooling tower shell, one channel in each pressure transducer is kept open.
multirow towers have also shown that the effect of wind directions were not included and very few studies were addressed limited wind directions of grouped towers. Wind direction and spacing of cooling towers have an important influence on interference when compared to the arrangement of cooling towers. Effect of interference on specific arrangements like rectangular pattern, rhombic pattern, L-shaped, oblique L-shaped, etc., are less influenced due to the fact that they are effectively controlled by how the interfering cooling towers are positioned with respect to the principal tower whether it is on windward or leeward or on adjacent sides of the principal tower. Therefore, it is of great significance to systematically study the interference effect of multirow cooling towers for various angles of wind incidence and spacing ratios. Within the multirow configurations, typical four tower arrangement is selected to perform the case study since it is a basic multirow arrangement in power plants. Further, the cooling towers embedded in wind flow is usually different from the uniform condition drafted in most wind standards since most structures erected in power plants are embedded in the boundary layer flow. Very few researches have addressed the boundary layer flow conditions. Hence in the present study, systematic wind tunnel testing on several combinations of diameter/spacing ratios of the representative four tower arrangement of cooling tower models are attempted for various wind directions under boundary layer flow condition for the interference function of cooling towers. Further from the analysis, a closed form solution is arrived for the interference of multirow towers.
1.2.2. Experimental arrangement Wind tunnel experiments have been carried out on the grouped cooling towers of four numbers arranged in square configuration for various centre-to-centre spacing ratios viz., 1.5–2.5 times of the base diameter db and for various angles of wind incidences ranging from 0° to 180° under the simulated open terrain condition to determine the circumferential pressures at nine different levels along the height. The test setup consisted of an instrumented principal tower ‘PT’ and three non-instrumented interfering towers ‘IT’. Typical schematic diagram of instrumented principal tower model with surrounding cooling towers is shown in Fig. 3. The measurements are made at a mean wind speed of 16 m/s at the height of the model (H = 400 mm). A standard Pitot static tube has been used to measure the mean velocity at the height of the model, located in free stream region of the test section. This velocity has been subsequently used as a reference velocity in computing the dynamic pressure and pressure coefficients. The pressure signals have been acquired through piezoresistive based pressure transducers of 0.36 psi pressure range. All the pressure data are acquired with a sampling rate of 650 Hz and for duration of 15 s. Three trials of measurement are considered for each case. The meridian facing the wind flow is reckoned as 0° angle of wind incidence, as shown in Fig. 4. The pressure data have been obtained for various azimuth angles circumferentially at 13° interval and the pressures have been acquired to experimentally measure and study the variation of external (C¯pe ) and internal pressure coefficient (C¯pi ) distributions at various levels along the height. The pressure transducer having some active ports is fixed at the corresponding levels with no tubing to determine the internal pressure distribution. Fig. 4 shows the orientation and typical view of the model in wind tunnel for 180° angle of wind incidence.
1.1. Flow field simulation in wind tunnel The experiments are performed in the boundary layer wind tunnel (BLWT) facility available at CSIR-SERC. The maximum wind speed attainable at the upstream side of the test section is 55 m/s. In order to translate the results of the boundary layer wind tunnel tests to corresponding prototype conditions, proper simulation of wind characteristics and wind flow field in the boundary layer wind tunnel are essential. Trip boards and roughening elements were used to simulate the natural atmospheric boundary layer stream. Based on the simulated mean velocity profile, the power law coefficient arrived for the simulated terrain is 0.165 and the measured turbulence intensity at the height of the model is 13%. The simulated mean velocity and turbulence intensity profiles are shown in Fig. 1. The spectrum of the horizontal wind speed is also simulated and compared with Von Karman spectrum. Based on the flow scale conditions, a geometric scale of 1:500 has been selected. 1.2. Wind tunnel test
1.2.3. Analysis of data All the acquired data have been reduced and analyzed using the following expressions. For each test case, three different data sets have been collected and the average values have been considered for the analysis. Using the sensitivity factors, the raw voltage data have been converted to engineering units and the variation of pressure distributions have been studied. The mean, standard deviation and peak pressure of a pressure trace p (t), taken over a period of time, and the mean, standard deviation and peak pressure coefficients of all pressure ports are subsequently deduced with respect to the reference pressure (p¯z) at heights (z) of 0.1Hs, 0.2Hs, 0.3Hs, 0.4Hs, 0.6Hs, 0.69Hs, 0.8Hs 0.9Hs and 0.95Hs for Level 1, Level 2, Level 3, Level 4 Level 5 Level 6 Level 7 and Level 8 and Level 9 respectively.
1.2.1. Geometric background and instrumentation The prototype dimension of the cooling tower model for which the study conducted is 200 m height with diameter at base, throat and top of the cooling tower are 136 m, 85.3 m and 88.5 m respectively. The prototype is modelled to a scale of 1:500 for the pressure measurement study. The scale ratio between the model and the prototype depends on the cross sectional area of the wind tunnel. With a geometric scale of 1:500, the overall height, ‘Hs’ of the cooling tower shell is 375 mm in wind tunnel with outer diameter at base, throat and top of the cooling tower model are 272 mm, 170.4 mm and 176.8 mm. For the present study, 3D printer has been used for fabricating the pressure model inhouse. The cooling tower model has a total height (H) of 400 mm including raker column height of about 25 mm. The raker columns are fabricated separately to the same scale using acrylic sheets and which was suitably glued to the shell of the cooling tower for making full model of NDCT. For the measurement of wind induced pressures on the rigid model, it is instrumented for pressures at ten different levels namely z = 0.95Hs, 0.90Hs, 0.80Hs, 0.690Hs, 0.60Hs, 0.40Hs, 0.30Hs, 0.20Hs and 0.10Hs where 'z' is the height of each level from bottom of the model shell and 'Hs' is the model height of the cooling tower shell.
28
C¯pe (z , θ) =
⎛ p¯e (z , θ) − p∞ ⎞ and C¯pi (z , θ) = 1 ρ (U¯ (z ))2 ⎟ ⎝ 2 ⎠
∑⎜ i=1
28
⎛ p¯i (z , θ) − p∞ ⎞ 1 ρ (U¯ (z ))2 ⎟ ⎝ 2 ⎠
∑⎜ i=1
(1) 28
C¯ p′ (z , θ) =
i=1
2
⎛ σ (z , θ) − p∞ ⎞ 1 ρ (U¯ (z ))2 ⎟ ⎝ 2 ⎠
∑⎜
(2)
Engineering Structures 200 (2019) 109673
S. Chitra Ganapathi, et al.
Fig. 1. Simulation of wind characteristics in wind tunnel.
Cp̂ (z , θ) =
28
⌢
⎛ p (z , θ) − p∞ ⎞ 1 ρ (U¯ (z ))2 ⎟ ⎝ 2 ⎠
∑⎜ i=1
Although experiments have been carried out for 13 different angles of wind incidence and nine different levels namely L1 = 0.10Hs, L2 = 0.20Hs, L3 = 0.30Hs, L4 = 0.40Hs, L5 = 0.60Hs, L6 = 0.69Hs, L7 = 0.80Hs, L8 = 0.9Hs and L9 = 0.95Hs where 'Hs' is the height of the cooling tower shell, the mean pressure coefficient envelop corresponding to the throat level (0.69 Hs) is presented here and the envelops have been developed by grouping the maximum/minimum values of C¯pe depending upon the sign at each angle of wind incidence ranging from 0° to 180° for each port. From the variation of mean pressure coefficient distribution, it is seen that the mean pressure coefficient (C¯pe ) trend for spacings 1.5db–2.5db are comparable in general. It has also been observed from the circumferential mean pressure coefficient distribution (C¯pe ) for five different spacings, the transition of positive to negative pressures takes place at a range between 30° and 45° azimuth angle as similar to isolated case. The mean suction pressure coefficient values for all spacings tend to increase significantly between azimuth angles θ = 50° and θ = 100° and with height. The maximum value of mean suction pressure coefficient is observed to be around −2.20, −2.18, −2.06, −2.02 and −2.03 for
(3)
where p¯ (z , θ) is the mean pressure coordinate, σ (z , θ) is the standard ⌢ deviation pressure coordinate and p (z , θ) is the peak pressure coordinate for pressure tap angle θ at z level, suffix ‘e’ and ‘i’ stands for external and internal pressures and p∞ is the static pressure of the ¯ (z) is the mean velocity at approaching flow, ρ is the density of air and U heights, z = 3.8 cm, 7.5 cm, 11.3 cm, 15 cm, 22.5 cm, 26.3 cm, 30.1 cm, 33.8 cm and 35.7 cm for Levels 1, 2, 3, 4, 5, 6, 7, 8 and 9 respectively.
1.3. Wind pressure coefficients under interference 1.3.1. Mean pressure coefficient Wind tunnel results of mean pressure coefficient distribution of grouped cooling towers arranged in square configuration for various centre-to-centre spacing ratios viz., 1.5–2.5 times of the base diameter db of cooling tower model is shown in Fig. 5 for open terrain condition. 3
Engineering Structures 200 (2019) 109673
S. Chitra Ganapathi, et al.
Fig. 2. Typical 3-D view of the fabricated cooling tower models with pressure tap locations.
Fig. 4. Orientation and typical view of the model in wind tunnel for 180° angle of wind incidence.
Fig. 3. Schematic diagram of cooling tower model with surrounding towers.
1.5db, 1.75db, 2.0db, 2.25db and 2.5db spacings respectively. Further, the maximum value of mean suction pressure coefficient is observed to be on higher side than those of isolated study values by about 5–14% for all spacings. The rear suction pressure coefficient, C¯pb of all spacings is observed to be constant between angles θ = 120° and θ = 180°. It is also seen that the value of rear suction pressure coefficient has shown excessively high value for the 1.5db spacing with 23–35% difference when compared to the values of isolated condition and similarly the values of other spacings have shown variation on higher side than the values of next higher spacing. The rear suction pressure coefficient values of 1.75db, 2.0db, 2.25db and 2.5db spacings are −0.39 to −0.53, −0.37 to −0.52, −0.36 to −0.46 and −0.36 to −0.47 which are higher than the isolated values by about 17–26%, 11–20%, 5–12% and 6–10% for 1.75db, 2.0db, 2.25db and 2.5db spacing respectively. However, the mean stagnation pressure coefficient values for all spacings are within 5–10% difference than the isolated flow condition values on windward face.
Fig. 5. Variation of mean pressure coefficient distribution along the circumference of cooling tower model for various spacing ratios under open terrain condition.
1.3.2. Trend of mean pressure coefficient distribution The wind pressure distribution due to the interference is significantly increased in smaller spacings and in specific angles of wind 4
Engineering Structures 200 (2019) 109673
S. Chitra Ganapathi, et al.
Fig. 6. Polar variation of mean pressure coefficient distribution with angles of wind incidence and spacing ratios for throat level.
interference effects are to be appropriately taken care in load estimation for the safe design of cooling towers.
incidence of the tower. Hence the polar diagram variation of mean pressure coefficient distribution along the circumference of cooling tower model for various angles of wind incidence and spacing ratios corresponding to the throat level is shown in Fig. 6. The interfered pressure coefficient distributions are observed to be asymmetrical and magnified particularly in the suction and base pressure zone. In general, there is a prominent variation in the interfered mean pressure coefficient values with upper bounds at throat and bottom levels as compared to the other intermediate levels. The interfered mean pressure coefficient values are also shown with asymmetrical distribution especially at lower heights for all angles of wind incidence and symmetrical distribution of pressure coefficient values at higher heights for most angles of wind incidence which gives the inference that the interference near the ground level is higher hence shows an asymmetrical distribution. This trend has clearly shown that the distance between towers is shorter and the turbulence intensity levels are also higher at lower heights which makes the interference effect high near the lower heights. However, the mean pressure coefficient for 105–165° angles of wind incidence are shown with asymmetrical distributions even for higher heights which implies that the interference effect at these angles of wind incidence are mainly due to the channelization of flow. Similarly, the interference effect for smaller spacing is higher, hence shows an asymmetrical pattern with high mean pressure coefficient values at lower spacings. Whereas at higher spacings, the interference effect of mean pressure coefficient values is observed to be less significant and for the spacings of > 2.0db, the interference effect of mean pressure is further reduced. It is apparent from the above discussion that the interference of mean pressures is significant in the base and suction pressure region. Also the smaller spacings and critical wind incidences of the tower increased the interference effects further. Hence the
1.3.3. Distribution characteristics of mean pressure coefficient The circumferential distribution of mean pressure coefficient of an isolated cooling tower is usually expressed in the form of Fourier cosine terms with following Fourier coefficients, where a1 = −0.00071, a2 = 0.24611, a3 = 0.62296, a4 = 0.48833, a5 = 0.10756, a6 = 0.09579, a7 = −0.01142, a8 = 0.04551 in some codes viz. BIS11504 [2], Chinese code, etc., Whereas the fitting parameters are applicable for the symmetrical distribution of pressures. However, the mean pressure coefficient of interfering cooling towers is shown with asymmetrical distribution of pressures, hence the above expression cannot fit an asymmetrical curve. Therefore, the Fourier cosine, sine and the constant terms with the corresponding coefficients are used to fit the asymmetrical pressure curves. 7
C¯p (θ) =
7
∑ ak cos(kθ) + ∑ bk sin(kθ) + C k=1
k=1
(4)
The representative curves, from the combination of angles of wind incidence, for each spacing of cooling towers can produce thirteen different pressure curves, in which five are asymmetrically distributed and remaining eight are symmetrically distributed. Table 1 gives the fitting parameters for the envelops of 225 asymmetrical and 360 symmetrical distribution of pressure curves of all 585 cases (585 cases = 1 tower × 9 levels × 5 spacings × 13 angles of wind incidence). 1.3.4. Fluctuating pressure coefficient The surface distribution of fluctuating pressure coefficient corresponding to the throat level as a function of angle of wind incidence for 5
Engineering Structures 200 (2019) 109673
S. Chitra Ganapathi, et al.
Table 1 Fitting parameters for mean pressure coefficient distribution under interference. Fourier Coeff
C
a1
a2
a3
a4
a5
a6
a7
a8
b1
b2
b3
b4
b5
b6
b7
b8
Asymm Symm
−0.72 −0.8
0.57 0.49
1.3 1.37
0.58 0.64
−0.11 −0.09
−0.07 −0.05
−0.08 −0.06
−0.12 −0.1
−0.04 −0.02
0.02 −0.01
0.01 −0.05
0.07 −0.01
0.05 −0.01
0.02 −0.01
0.05 0.07
0.02 0.01
0.01 0.05
Fig. 7. Variation of standard deviation pressure coefficient distribution with azimuth angle for various angles of wind incidence and spacing ratio.
takes place for a range between 25° & 75° and 285° & 335° azimuth angle. The standard deviation pressure coefficient values tend to follow the decreasing trend (0.6–0.2) between azimuth angles θ = 75° & θ = 120° and θ = 240° & θ = 285° and with height. There are two peaks in the distribution of fluctuating pressure coefficient (0.6) is observed at the point of 75–90° region and 270–285° region because of the vortex shedding phenomenon. Further, the peaks of standard deviation pressure coefficient values of all levels are observed to be on higher side than those of isolated study values by about 8–17% for all spacings.
the various spacing ratio of cooling tower is shown in Fig. 7. The fluctuating pressure coefficient distribution at each level namely z/ H = 0.1, 0.2, 0.3, 0.4, 0.6, 0.69 0.8, 0.9 and 0.95 are comparable in trend. The fluctuating pressure coefficient values are shown with asymmetrical distribution in the separation and wake zone at lower heights for all angles of wind incidence. It is also seen from the variation of fluctuating pressure coefficient of higher heights, an axially symmetrical distribution is observed for most angles of wind incidence and an asymmetrical distribution of coefficient is observed for 105–165° angles of wind incidence in the separation and wake zone. Further, the fluctuating pressure coefficient values decrease with height as like the turbulence intensity, whereas above the throat level all the regions have become almost independent of standard deviation effect. The values have shown nearly constant variation between levels and spacing ratios in 0–25° & 335–360° azimuth angle region. The fluctuating pressure coefficient values of 0–25° and 335–360° azimuth angles for all spacings are within 5–10% difference than the isolated flow condition values. Similarly, the fluctuating pressure coefficient values of all levels corresponding to the 120–240° azimuth angle regions are on higher side than the isolated values by about 15–42% for all spacings. The fluctuating pressure coefficient values of 120–240° azimuth angle region (i.e. with values 0.10–0.2) is observed with less value when compared to the values of all other azimuth angle regions. It has also been observed from the fluctuating pressure coefficient distribution ' (C¯ p ) of nine different levels, the values with increasing trend (0.4–0.6)
1.3.5. Power spectra of fluctuating pressures Adverse effects of interference arise from the vortex shedding and wake phenomena of the tower. Hence the variation of power spectral density curves of base pressure port corresponding to typical wind direction is shown in Fig. 8 for the various spacing ratios. It is clear from the variation of PSD of interfering pressures, the power spectral amplitude of the base and suction pressure ports are observed with variations on higher side than the isolated variations for most wind directions. These variation have also confirmed the profound effect of interference in the identified regions of concern. Further, irrespective of spacing ratio, all the curves are shown with same trend and the power spectral amplitude of smaller spacings in the considered frequency ranges are on higher side than the power spectral amplitude of successive spacings and isolated arrangement. The higher power spectral 6
Engineering Structures 200 (2019) 109673
S. Chitra Ganapathi, et al.
different zones of interference viz. ITW, ITL and ITS. Figs. 10–12 show the variation of mean and peak suction pressure coefficient with spacing ratio for three different interference zones ITW, ITL and ITS respectively. Similarly, the variation of mean and peak base pressure coefficient with spacing ratio is shown in Figs. 13–15 for three different interference zones ITW, ITL and ITS respectively. From the variation of mean and peak pressure coefficients, it is seen that the presence of interfering cooling towers on the adjacent side of principal tower (ITs zone) has a considerable interference effect on the mean and peak pressure coefficient values and the presence of interfering cooling tower models on the leeward (ITL zone) and windward (ITW zone) side of principal tower have a less significant interference effect on the mean and peak pressure coefficient values. In general, the mean and peak suction pressure coefficient values tend to vary nominally with increase in spacing and the variations are within 5% difference. However, the variation between levels is maintained with 6–13% difference. The mean suction pressure coefficient values of ITs zone for the smaller spacing ratios (1.5–2.0) are observed to be on higher side than the ITL and ITW zones by about 7–13% for all nine levels. It is also observed that the values of mean suction pressure coefficient of ITs zone for the 2.25–2.5 spacing ratio have shown high values with 3–5% difference for all levels when compared to the values of ITL and ITW zones. As similar to the mean suction pressure coefficient values, peak suction pressure coefficient values of 1.5–2.0 spacing ratios of ITS zone are observed to be increased by about 5–12% than the values of other two zones viz. ITL and ITW for all levels. It is also clear that the values of peak suction pressure coefficient of ITL and ITW zones for the larger spacing ratios (2.25–2.5) are observed to be decreased by about 5% for all levels when compared to the values of ITS zones. Further, the mean and peak base pressure coefficient values of all spacing ratios are observed to be decreased gradually with increase in spacing and the differences are maintained as similar to the variation of mean and peak suction pressure coefficient. In comparison with levels, mean and peak base pressure coefficient values of the lower and top levels are on higher side. Moreover, for the middle levels, the values are on lower side than the values of lower and top levels and the differences are between 13 and 25%. The mean base pressure coefficient values of all levels corresponding to the 1.5, 1.75 and 2.0 spacing ratios of ITs zone are on higher side than the mean base pressure coefficient values of ITL zone by about 20–40%, 20–28% &17–30% and the values of ITs zone are increased nearly by 20–40%, 11–25% & 8–20% with ITW zones for 1.5, 1.75 and 2 spacing ratios respectively. However, the mean base pressure coefficient values of ITL and ITW zones for 2.25 and 2.5 spacing ratios are decreased by 10–20% and 3–8% when compared to the values of ITs zone for most levels. As discussed above, the peak base pressure coefficient value of various levels of ITs zone is the highest of all zones by about 10–35%, 10–25% &10–20% for the spacing ratios 1.5, 1.75 and 2.0 respectively. In the spacing ratios of 2.25 and 2.5, the mean base pressure coefficient values of ITL and ITW zones are decreased by 5–12% and 3–8% difference when compared to the values of ITs zone for all levels.
Fig. 8. Variation of power spectral density distribution for various spacing ratios.
amplitude is related with higher energy level; higher the energy level, then higher the energy consumption, the higher energy consumption is obviously resulted from the vortex and wake energy. The above discussions of fluctuating pressure coefficient and the power spectra of fluctuating pressures have also made it clear that the base and suction pressure of the tower most importantly in the smaller spacings and critical wind incidences are more prone to interference effect. 1.4. Interference factors based on various criteria’s Interferences are evaluated based on the aspects of aerodynamic loading or structural response or reinforcement ratio. It is evident from the literatures [4,12] that the interference due to the aerodynamic loading aspect is larger when compared to the aspects of structural responses or reinforcement ratio. Hence to consider the effect of interference, mean interference Factor (MIF) multiplied to the mean pressure coefficient distribution and peak interference factor (PIF) multiplied to the peak pressure coefficient distribution have been evaluated based on the variation of aerodynamic pressure coefficient aspect. 1.4.1. Analysis of the interference effects The parameters suction and base pressure coefficient of the mean and peak pressure distribution of a cooling tower model are the important inputs for the design of a cooling tower structure, hence the variation of these parameters with relative spacing (a/db) of interfering cooling tower models is considered for the evaluation of interference effects. The study has also shown that the angle of wind incidence has a significant influence in determining these parameters in addition to the spacing of cooling tower models, hence the interference zones are grouped based on the range of angles of wind incidence i.e., 0–30° angles of wind incidence is grouped under ITL category, 30–150° angles of wind incidence is grouped under ITS category and 150–180° angles of wind incidence is grouped under ITW category, i.e., ITW, ITL and ITS are the interfering zones corresponding to interfering cooling tower models on windward, leeward and adjacent sides of principal tower (PT). Fig. 9 shows the various zones of interference based on the spacing of interfering cooling tower models, viz. a1 = 1.5db, a2 = 1.75db, a3 = 2.0db, a4 = 2.25db and a5 = 2.5db and based on the zones of angles of wind incidence, viz. ITW, ITL and ITS - interfering cooling tower models are on windward leeward and adjacent sides of PT. The variation of mean & peak suction and base pressure coefficient values of the interfering cooling tower model with various spacing ratios (a/db) viz. 1.5, 1.75, 2.0, 2.25 and 2.5, where ‘a’ is the c/c spacing of cooling tower models and ‘db’ is the base diameter of cooling tower model is studied for nine different levels viz. L1 to L9 and for three
1.4.2. Mean and peak interference factor of suction and base pressure coefficients The mean interference factor is defined as the ratio between the enhanced mean pressure coefficient in the grouped configuration to the corresponding mean pressure coefficient in isolated configuration. In line with MIF, PIF is also defined as the ratio of enhanced peak pressure coefficient in the grouped configuration to the corresponding peak pressure coefficient in isolated configuration. Fig. 16 shows the variation of MIF and PIF values of suction and base pressure coefficient with levels for the various zones of angle of wind incidence of cooling tower models in a typical spacing ratio. The variation of MIF values of suction pressure coefficient between levels are compared well with each other with less than 5–8% difference under all zones of interference. The variation of MIF values of base pressure coefficient between levels are 7
Engineering Structures 200 (2019) 109673
S. Chitra Ganapathi, et al.
Fig. 9. Various zones of interference based on the spacing and angles of wind incidence of cooling tower models.
Fig. 10. Variation of mean and peak suction pressure coefficient with spacing ratio for interfering cooling tower models on leeward side of principal tower (ITL zone or 0–30° angles of wind incidence).
Fig. 11. Variation of mean and peak suction pressure coefficient with spacing ratio for interfering cooling tower models on adjacent side of principal tower (ITS zone or 30–150° angles of wind incidence).
It is also found from the study, that the variation of MIF of suction pressure coefficient between angles of wind incidence is observed with 10–17% difference for all spacing ratios. Mean interference factor values of base pressure coefficient within each spacing ratio is significantly affected by the angle of wind incidence in a tower group, among various angles of wind incidence, 75–105° angle of wind incidences or interfering towers adjacent to the principal cooling tower condition gives the highest percentage of interference effect by about 20–35% than the interference effect of other angles of wind incidence. Similarly, the PIF variation of suction and base pressure coefficient is also consistent with MIF variation. Further, it is also clear from the variation that the MIF or PIF values from suction pressure coefficient criteria are on lower side than the
also compared well with each other with less than 10% difference under ITS zone of interference but a pronounced variation in the MIF values of base pressure coefficient between the levels is found for the ITW and ITL zones of interference whose relative differences are 10–20% and 15–20% respectively. The variation of MIF and PIF values of suction and base pressure coefficient corresponding to typical zone of angle of wind incidence with levels is shown in Fig. 17 for the various spacing ratio (a/db). In general, the mean interference factor values of suction and base pressure coefficient tend to decrease with increase in spacing. It is also seen that the MIF of suction pressure coefficient is varied nominally with spacing ratio for all levels. The MIF values of base pressure coefficient for all levels are found to be significantly varied with spacing ratios by about 3–30%.
8
Engineering Structures 200 (2019) 109673
S. Chitra Ganapathi, et al.
Fig. 12. Variation of mean and peak suction pressure coefficient with spacing ratio for interfering cooling tower models on windward side of principal tower (ITW or 150–180° angles of wind incidence).
Fig. 13. Variation of mean and peak base pressure coefficient with spacing ratio for interfering cooling tower models on leeward side of principal tower (ITL zone or 0–30° angles of wind incidence).
Fig. 14. Variation of mean and peak base pressure coefficient with spacing ratio for interfering cooling tower models on adjacent side of principal tower (ITS zone or 30–150° angles of wind incidence).
values have been chosen among the IF values of mean suction and base pressure coefficient of various angles of wind incidence and levels. The interference factor values tend to decrease and vary significantly between the spacing ratios (a/dm) 1.9 and 2.5. It is also observed from the variation of IF values that the transition of trend takes place between the spacing ratios 2.5 and 2.8. The interference factor values are observed to be nearly constant for the spacing ratios 2.8 & 3.1. It is also observed that the IF value has shown high value for spacing ratio of 1.9 with 30% difference when compared to the values of isolated condition. The IF values corresponding to the 2.2, 2.5, 2.8 and 3.1 spacing ratios are 1.26, 1.197, 1.142 and 1.116 which are higher than the isolated values by about 26%, 20%, 14% and 12% respectively. The variations in these values indicate that the interference effect in smaller spacing ratios shows higher IF value than the next higher spacing. Similarly, the values of other spacing ratios have shown variation on higher side than
values of base pressure coefficient criteria and the variations are also observed to be negligible with angles of wind incidence and spacing ratio. However, the mean and peak interference factor values from base pressure coefficient criteria are shown significant variation with angle of wind incidence and spacing ratio. The variation between MIF and PIF values based on the variation of mean and peak pressures are comparable in trend and the values are also comparable to each other, hence the MIF and PIF values need not be considered independently and the values have been converted in to a single interference factor (IF) value for interference evaluation. 1.4.3. Interference factor for multirow towers In general, it is seen from the above plots that the interference factor (IF) for all spacing ratios is varied considerably with angle of wind incidence and nominally between the levels, hence the maximum IF 9
Engineering Structures 200 (2019) 109673
S. Chitra Ganapathi, et al.
Fig. 15. Variation of mean and peak base pressure coefficient with spacing ratio for interfering cooling tower models on windward side of principal tower (ITW zone or 150–180° angles of wind incidence).
Fig. 16. Variation of MIF and PIF values of mean & peak suction and base pressure coefficient with levels for 1.5db spacing ratio. 10
Engineering Structures 200 (2019) 109673
S. Chitra Ganapathi, et al.
Fig. 17. Variation of MIF and PIF values of mean & peak suction and base pressure coefficient with levels for ITS zone.
proposed for the interference of multirow towers by considering the above effects.
the values of next higher spacing. As spacing of tower increases, interference effect drops. In other words, if the spacing is high, the interference effect is reduced. It is also found from the present study that the fluctuating pressure values of principal tower corresponding to multi tower group have shown larger values than that of isolated one in all spacing ratios by about 14% due to the effect of multirow towers. The variation in these values also infer that the interference effect due to the angle of wind incidence is further doubled from the 14% increase in smaller spacing ratios viz. 1.9 and 2.2 hence shows a higher IF value with 30% difference at lower spacing ratios. Whereas at 2.5 spacing ratio, the interference effect due to angle of wind incidence is nearly increased by one and half times with respect to the 14% increase, thus it gives IF value with 20% difference. Between the spacing ratios 2.8 and 3.1, the interference is found to be independent of wind incidence effect, hence the IF value remains constant with 14% increase. Further from the above analysis, a closed form solution as a function of spacing ratio is
Fi ≈ 1 + 0.14(4 − (a/ dm))
(5)
where a is the centre to centre distance of cooling tower under consideration and the neighboring cooling tower; (d + d ) dm ≈ u 2 t is average diameter of the shell; du = is the diameter at the lower edge and dt = is the diameter at the throat. Further, the interference factor values have been compared with the values provided in the existing cooling tower design codes [15,5]. Fig. 18 shows the variation of IF of wind tunnel results and codal standard with spacing ratio (a/dm). Though the interference factor given in codal standard is mentioned that, it is valid for groups of more than two towers but the interference factor values of present study corresponding to more than two tower groups have given higher values 11
Engineering Structures 200 (2019) 109673
S. Chitra Ganapathi, et al.
interference factor (IF) within each spacing ratios is varied considerably with angles of wind incidence and nominally between the levels, hence the maximum IF values have been chosen among the IF values of suction and base pressure coefficient of various angle of wind incidence and levels. It is also observed that the IF value has shown high value for spacing ratio (a/dm) of 1.9 with 30% difference when compared to the values of isolated condition. Similarly, the values of other spacing ratios have shown variation on higher side than the values of next higher spacing. The IF values corresponding to the 2.2, 2.5, 2.8 and 3.1 spacing ratios are 1.26, 1.197, 1.142 and 1.116 which are higher than the isolated values by about 26%, 20%, 14% and 12% respectively. Further from the analysis, a closed form solution is arrived for the interference of multirow towers. Though the interference factor given in codal standard is mentioned that, it is valid for groups of more than two towers but the interference factor values of present study corresponding to more than two tower groups have given higher values when compared to the values reported in codal standard by about 5–7%. Hence to consider the above effects, the IF empirical relation given in code is also need to be revised with the proposed equation which accounts the additional 5–7% increase of interference load in the existing IF empirical relation.
Fig. 18. Variation of MIF with spacing ratio (a/dm).
when compared to the values reported in codal standard by about 5–7%. Hence to consider the above effects, the IF empirical relation given in code is also need to be revised with the above expression which accounts the additional 5–7% increase of interference load in the existing IF empirical relation.
Declaration of Competing Interest 2. Summary and conclusion The authors declare that they have no conflict of interest. Cooling towers constructed in multi rows with close proximity to each other is becoming common in the recent past, a development that is having profound impact on interference. Most of the studies on multirow cylinders were focused on arrangement of cooling towers but the effect of wind direction and spacing of cooling towers were not included. Wind direction and spacing of cooling towers have an important influence on interference when compared to the arrangement of cooling towers. The present study analyzed the interference effect of four cooling towers in a boundary layer wind tunnel under open terrain condition for various angles of wind incidence viz. 0–180° and spacing ratios (a/dm) viz. 1.9–3.1. Mean and standard deviation pressure coefficient distributions & power spectra of fluctuating pressures are evaluated and the impact of interference on these coefficients is discussed at each of the measured levels for wind induced loads. The maximum value of mean suction pressure coefficient is observed to be on higher side than those of isolated study values by about 5–14% for all spacings. The value of rear suction pressure coefficient has shown excessively high value for the 1.5db spacing with 23–35% difference when compared to the values of isolated condition. The rear suction pressure coefficient values of 1.75db, 2.0db, 2.25db and 2.5db spacings are −0.39 to −0.53, −0.37 to −0.52, −0.36 to −0.46 and −0.36 to −0.47 which are higher than the isolated values by about 17–26%, 11–20%, 5–12% and 6–10% for 1.75db, 2.0db, 2.25db and 2.5db spacing respectively. Similarly, the fluctuating pressure coefficient values of all levels corresponding to the 120–240° azimuth angle regions are on higher side than the isolated values by about 15–42% for all spacings. There are two peaks in the distribution of fluctuating pressure coefficient is observed at the point of 75–90° region and 270–285° region because of the vortex shedding phenomenon. Further, the peaks of standard deviation pressure coefficient values of all levels are observed to be on higher side than those of isolated study values by about 8–17% for all spacings. It is apparent from the above discussion that the interference of these coefficients is significant in the base and suction pressure region. Also the smaller spacings and critical wind incidences of the tower increased the interference effects further. The parameters suction and base pressure coefficient of a cooling tower are the important inputs for the design of a cooling tower structure, hence the variation of these parameters with various angles of wind incidence and relative spacing of interfering cooling tower models is considered for the evaluation of interference effects. The
Appendix A. Supplementary material Supplementary data to this article can be found online at https:// doi.org/10.1016/j.engstruct.2019.109673. References [1] Armitt J. Wind loading on cooling tower. J Struct Eng ASCE 1980;106(3):623–41. [2] IS: 11504 - 1985. Criteria for structural design of reinforced concrete natural draught cooling towers. India: BIS. [3] Ke ST, Liang J, Zhao L, Ge YJ. Influence of ventilation rate on the aerodynamic interference between two extra-large indirect cooling towers by CFD. Wind Struct 2015;20(3):449–68. [4] Lin Z, Ge Y, Kareem A. Fluctuating wind pressure distribution around full-scale cooling towers. J Wind Eng Ind Aerodyn 2017;165:34–45. [5] Ministry of Housing and Urban-Rural Development of People’s Republic of China. Code for design of cooling for industrial recirculating water GB/T 50102-2014. China: China Planning Press; 2014. [in Chinese]. [6] Maurizio O. Wind-induced interference effects on two adjacent cooling towers. Eng Struct 2001;23:979–92. [7] Niemann HJ. Wind effects on cooling-tower shells. J Struct Div 1980;106:643–61. [8] Niemann HJ, Kopper HD. Influence of adjacent buildings on wind effects on cooling towers. Eng Struct 1998;20(10):874–80. [9] Propper H, Welsch J. Wind pressures on cooling tower shells. Wind Eng 1980;1:465–78. [10] Portela G, Godoy LA. Shielding effects and buckling of steel tanks in tandem arrays under wind pressures. Wind Struct 2005;8(5):325–42. [11] Ruscheweyh H. Wind loading on hyperbolic natural draught cooling towers. J Wind Eng Ind Aerodyn 1975;1:335–40. [12] Shitanng K, Hao W, Yaojun G. Interference effect and the working mechanism of wind loads in super-large cooling towers under typical four-tower arrangements. J Wind Eng Ind Aerodyn 2017;170:197–213. [13] Sun TF, Zhou L. Wind pressure distribution around a ribless hyperbolic cooling tower. J Wind Eng Ind Aerodyn 1983;14(1–3):181–92. [14] Sun TF, Gu ZF. Interference between wind loading on group of structures. J Wind Eng Ind Aerodyn 1995;54(55):213–25. [15] VGB-R 610Ue. German design code for Structural design of cooling towers. Essen: VGB Power Tech e.V.; 2010. [16] Zhao L, Zhan Y, Ge Y. Wind induced equivalent static interference criteria and its effects on cooling towers with complex arrangements. Eng Struct 2018;172(1):141–53. [17] Zhao L, Chen X, Ge Y. Investigations of adverse wind loads on a large cooling tower for the six-tower combination. Appl Therm Eng 2016;105:988–99. [18] Zhao L, Ge YJ. Wind loading characteristics of super large cooling towers. Wind Struct 2010;13(3):257–73. [19] Bartoli G, Borri C, Hoeffer R, Orlando M. Wind induced pressures and interference effects on a group of cooling towers in a power plant arrangement. Proceedings of 2nd European and African conference on wind engineering. Genoa, Italy, Padua: SGE; 1997. p. 969–76.
12
Engineering Structures 200 (2019) 109673
S. Chitra Ganapathi, et al.
Istanbul, Turkey. 2004. p. 105–13. [22] Selvi RS, Babu GR, Arunachalam S, et al. Interference factors for natural draught cooling towers based on wind tunnel experiments. Eighth Asia-Pacific conf wind eng. 2013. p. 490–8.
[20] Borri C, Orlando M, Spinelli P. Wind induced stresses on two neighboring cooling towers. Proceedings of 10th ICWE, Copenhagen, Denmark, Rotterdam, vol. 1. Balkema; 1999. p. 401–8. [21] Niemann HJ, Kopper HD. Provision for interference effects in non-symmetric design of cooling towers. Fifth international symposium on natural draught cooling tower,
13