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Field test study on water droplet diameter distribution in the rain zone of a natural draft wet cooling tower
Applied Thermal Engineering 162 (2019) 114252
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Field test study on water droplet diameter distribution in the rain zone of a natural draft wet cooling tower
T
⁎
Xuehong Chen, Fengzhong Sun , Dongqiang Lyu School of Energy and Power Engineering, Shandong University, Jinan 250061, China
H I GH L IG H T S
diameter distribution in a NDWCT is quantitatively studied by field test. • Droplet d in the rain zone of the NDWCT is scattered between 0.312 mm and 15 mm. • The number ratio of water droplets at a d of 0.812 mm and 5.5 mm is relatively large. • The crosswind markedly increases the number ratio of droplets at d < 3.25 mm. • High-speed • Cumulative number fraction of water droplets is obtained by fitting the test data.
A R T I C LE I N FO
A B S T R A C T
Keywords: Field test Wet cooling tower Rain zone Water droplet diameter distribution Crosswind
A field test study was conducted on a natural draft wet cooling tower to quantitatively investigate the water droplet diameter distribution in the rain zone for the first time. A test rig with alterable test positions was designed and constructed. The test time for each set of data is 300 s. The test data are presented in the form of a number ratio (R) with water droplet diameter (d). The results manifest that d is scattered between 0.312 mm and 15 mm, regardless of the crosswind velocity. Under low crosswind speed conditions, R has nearly an identical distribution pattern along the circumferential and radial directions, which are relatively large at d = 0.812 mm and 5.5 mm, respectively. As the droplets move from the position of c1r1h1 to c1r1h3, the R at d > 3.75 mm increases significantly, and the difference in R at d = 0.812 mm and d = 5.5 mm increases from 0.7% to 4.1%, respectively. When the crosswind speed is relatively high, the R is basically consistent at different height positions and shows a difference on the windward side, leading to a noticeable increase in R at d < 3.25 mm. For engineering applications, the cumulative distribution of water droplet diameter is further obtained.
1. Introduction Natural draft wet cooling towers (NDWCTs) are widely used to cool the feed water of condensers in thermal and nuclear power plants, and NDWCT performance deterioration will weaken the heat transfer efficiency of condensers, eventually leading to a decrease in the thermal cycle efficiency of the unit [1,2]. For a NDWCT, the heat transfer and pressure drop characteristics of the rain zone, which mainly depend on the water droplet diameter, have an evident impact on the tower cooling performance. To date, some studies on NDWCTs and the rain zone have been conducted through experimental investigations [3–17] and numerical simulations [18–30]. According to Li [3], the ambient crosswind has a noticeable effect on the wet cooling tower, with sensitivity to the crosswind velocity. Gao [4–7] conducted a series of field test studies to ⁎
evaluate the thermal and ventilation performances of natural draft wet cooling towers, including the high level water collecting wet cooling tower with cross walls (HWCT) and the usual wet cooling tower (UWCT). The main findings of their studies are as follows. The thermal and ventilation performances for a wet cooling tower gradually decrease with increasing crosswind velocity due to the uniformity decline in the circumferential inflow air. For the HWCT, the tower performance is also related to the angle between the cross walls and crosswind direction. With the increase in crosswind velocity, the cooling capacity of the filling zone decreases while the cooling capacity of the rain zone increases. For the UWCT, the structural improvement, which includes both the air ducts and air deflectors, can improve the tower performance under various crosswind velocities. Through a thermal state model experiment, Zhou [8,9] concluded that both the forced draft and nonuniform fillings had positive effects on the thermal performance of
Corresponding author. E-mail address: [email protected] (F. Sun).
https://doi.org/10.1016/j.applthermaleng.2019.114252 Received 13 May 2019; Received in revised form 17 July 2019; Accepted 11 August 2019 Available online 16 August 2019 1359-4311/ © 2019 Elsevier Ltd. All rights reserved.
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Nomenclature
r1–r6 , r1′–r6′ v vc We
c1–c3 , c1′–c3′ position of circumferential measuring points C cumulative number fraction of water droplets (%) C(d) cumulative number fraction of water droplets with a diameter of d (%) d water droplet diameter (mm) di initial water droplet diameter (mm) h height (m) h1–h3 position of height measuring point n coefficient N(d) number of water droplets at the diameter of d Ntotal total number of water droplets during the test Q1, Q3 first quartile and third quartile of a data sequence R number ratio of water droplets (%) R(d), R(i) number ratio of water droplets with a diameter of d or i
(%) position of radial measuring point velocity (m/s) ambient crosswind velocity (m/s) Weber number
Greek letters α, β, θ σ ρ
coefficient surface tension of water droplet (N) air density (kg/m3)
Subscripts lw hw
wet cooling towers. That is, nonuniform fillings can alleviate the adverse effect of the crosswind, and the forced draft can enhance the ventilation rate of the cooling tower. Missimer et al. [10] and Sedina et al. [11] studied the water droplet size in the rain zone through a laboratory model test and proposed an equivalent diameter of water droplets to replace the complex diameter distribution. Based on laboratory experiments and validation calculations, Zhao [12] recommended an equivalent diameter of water droplets of 2.65–3 mm in a NDWCT. However, the equivalent diameter will create a significant error in the NDWCT pressure drop calculation. Previous researchers [13–17] studied the water droplet diameter in the rain zone using imaging technology. In these studies, the water droplet diameter distribution was measured photographically below three different fills and a number of splash grid configurations. However, the geometric dimension of the test zone (1.0 m × 1.5 m) was far less than the actual rain zone, and the SLR camera was fixed in a position; thus, the achieved water droplet diameter distribution was unrepresentative of the NDWCT rain zone. With the development of numerical technology, many scholars have carried out numerical simulations on NDWCT rain zones. Using the k-ε turbulence model and discrete phase model (DPM), Waked [18,19] performed a three-dimensional numerical study of heat and mass transfer in a NDWCT and found that the rain zone could somewhat reduce the adverse effect of ambient crosswind on the tower cooling performance. The discrete phase model was also employed in previous studies [20–24]. In the discrete phase model, the particle size distribution built into the CFD software is unrepresentative of the water droplet diameter distribution inside the NDWCT. Therefore, the DPM model is imprecise and oversimplified in the performance computation of NDWCTs. Another method used to address the water droplet diameter distribution is the equivalent water droplet diameter. Pedraza [25] numerically investigated the suitable equivalent size of water droplets in a cooling tower to reduce water losses, indicating that the equivalent diameter of the water droplets should be higher than 3 mm and the air velocities should be lower than 5 m/s to avoid drifting. Based on the equivalent water droplet diameter, Zhao [26,27] established a threedimensional numerical model for NDWCTs, and the numerical results agreed with the actual running results. Through numerical research, Chen [28,29] investigated two kinds of retrofit methods for improving the thermal performance of NDWCTs, and Dang [30] studied the thermal performance of super large-scale wet cooling towers equipped with an axial fan. In their studies, the water droplet diameter in the rain zone was still replaced with an equivalent water droplet diameter. However, the specific surface area and the number of water droplets per unit volume in the equivalent water droplet diameter method were both greater than the actual conditions. Not only will this cause the
low crosswind speed condition high crosswind speed condition
proportion of heat transfer capacity to increase in the rain zone and decrease in the fill zone but will also lead to more air flow hindrance by water droplets; that is, the pressure rises in the rain zone and declines in the fill zone. Therefore, the performance and fill selection of NDWCTs will be greatly affected when employing the equivalent water droplet diameter. Based on the above-cited literature, the currently used processing methods for water droplet diameter distribution will bring large errors to the performance computation of NDWCTs, while the laboratory findings were imprecise because the interactions among water droplets in the rain zone were difficult to reproduce in the laboratory investigations. To accurately study the water droplet diameter distribution in the rain zone, a field test was conducted on a NDWCT for the first time in this study. By measuring the water droplet diameter with the corresponding test instrument at different positions, the distribution characteristics of the water droplet diameter in the rain zone are obtained and discussed. To easily integrate the test results into engineering applications, the cumulative distribution of water droplet diameter is further acquired by fitting the test data. The cumulative distribution of the water droplet diameter, which has a higher precision in the cooling tower calculation, can substitute for the equivalent water droplet diameter in future studies. The results of work can lay a theoretical foundation for optimizing NDWCT designs.
2. Field test system 2.1. Test object This field test was conducted on a NDWCT for a 660 MW unit during the spring season, and the main geometrical dimensions of the studied NDWCT are listed in Table 1. The fill used in the NDWCT is made of plastic, with a thickness of 1.5 m and a bottom elevation of 11.3 m. During the field test, the circulating water flow rate of the NDWCT remains at 78150 t/h, that is, the water spray density is 2.41 kg/(m2·s).
Table 1 Main geometrical dimensions of the NDWCT.
2
Item
Value
Unit
Diameter of tower base Diameter of tower throat Diameter of tower outlet Height of the tower Height of tower throat Height of tower air inlet Filling area
118.85 66.50 71.42 150.00 112.48 10.33 9000.00
m m m m m m m2
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anemometers. The test instrument for water droplet diameter is the OTT Parsivel2 raindrop spectrometer (hereinafter referred to as OTT Parsivel2), as shown in Fig. 1. The main performance parameters of the OTT Parsivel2 are listed in Table 2. The theory behind the OTT Parsivel2 is a laser sensor capable of producing a horizontal beam. The emitter and receiver of the laser sensor are integrated into a single protective housing and then placed in the sensor head. As shown in Fig. 2, if there are no water droplets in the laser beam, the maximum voltage is outputted at the receiver. Water droplets passing through the laser beam block off the portion of the beam corresponding to their diameter, thus reducing the output voltage and generating a signal, which determines the particle size. A signal begins as soon as a water droplet enters the laser beam and ends when it has completely left the laser beam; thus, the signal duration is measured. When obtaining the water droplet diameter and the duration of the signal, the water droplet speed can be calculated. Some parameters, including the size spectrum, type of precipitation, kinetic energy and intensity of the precipitation, can be derived from the diameter and speed of the water droplet. The splash protection attached to the sensor head prevents the precipitation particles from deflecting off the housing and falling into the laser beam, which falsifies the measurements. In addition, the test time for each set of data is 300 s. A rocker arm with a test range of 0– 17 m in the radial direction and 0–8 m in the height direction is expressly designed and manufactured for this test study. The rocker arm is made of aviation aluminum. As shown in Fig. 3, the OTT Parsivel2 is connected to the clamping device by bolts, and the clamping device is placed on the rocker arm. Due to the specific structure of the rocker arm, the OTT Parsivel2 always remains vertically stable during the testing process. In addition, the water repellent agent is daubed on the goggle laser transmitter to form a water-repellent film.
Fig. 1. Picture of the OTT Parsivel2. Table 2 Main performance parameters of OTT Parsivel2. Item
Value
Accuracy
Measuring area Measuring range Measuring speed Temperature Test time
54 cm2 0.2–25 mm 0.2–20 m/s −40–70 ℃ 10–3600 s
– ± 5% ± 0.01 m/s ± 0.1 ℃ –
2.3. Test point layout The layout of measuring points for the crosswind around the NDWCT is shown in Fig. 4. As seen in Fig. 4(a), there were eight crosswind measuring points along the circumferential direction. These measuring points were approximately 2 m away from the NDWCT, and there was one anemoscope and two cup anemometers at two heights (3 m and 6 m, respectively) for each measuring point, as shown in Fig. 4(b). For the measuring points of water droplet diameter in the rain zone,
Fig. 2. Functional principle of the OTT Parsivel2.
2.2. Test apparatus The direction and velocity of the ambient crosswind are measured with anemoscopes and cup anemometers, respectively. The measurement accuracy is ± 0.05° for the anemoscope and ± 0.1 m/s for the cup
Fig. 3. Placement of OTT Parsivel2. 3
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Cup anemometers
Anemoscope
(a) Measuring points at different circumferential
(b) Measuring apparatus at different height
positions
positions
Fig. 4. Layout of measuring points for ambient crosswind around the tower.
(a) Vertical view
(b) Front view
Fig. 5. Layout of measuring points for water droplet diameter in the rain zone.
Fig. 6. Variation in R with d along the circumferential direction of rain zone under low vc conditions.
Fig. 7. Variation in R with d along the radial direction of rain zone under low vc conditions.
six circumferential positions, three radial positions and three height positions are selected to research the raindrop size distribution. Therefore, there are 6 × 3 × 3 = 54 measuring points altogether in the rain zone. A graphic of the arrangement mode of these measuring
points is shown in Fig. 5.
4
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Table 3 Cumulative number fraction under low speed and high speed crosswind conditions. Water droplet diameter d (mm)
0.312 0.437 0.562 0.687 0.812 0.937 1.062 1.187 1.375 1.625 1.875 2.125 2.375 2.75 3.25 3.75 4.25 4.75 5.5 6.5 7.5 8.5 9.5 11 13 15
Fig. 8. Variation in R with d along the height direction of the rain zone under low vc conditions.
Cumulative number fraction (%) Drop height = h1, low speed crosswind
Drop height = h2, low speed crosswind
Drop height = h3, low speed crosswind
High speed crosswind
0.216 0.745 2.634 10.362 19.241 27.072 32.605 36.290 41.243 45.248 48.586 51.583 54.286 59.814 64.783 69.640 74.378 78.984 86.450 91.225 94.691 96.956 98.760 99.644 100 100
0.296 0.973 2.712 8.627 18.930 27.133 32.455 36.899 42.847 47.877 52.257 56.262 59.643 64.776 69.143 73.701 77.932 81.559 88.086 92.151 95.240 97.455 98.989 99.669 99.999 100
0.158 0.654 1.902 6.102 16.116 23.728 30.119 34.468 41.553 46.979 51.161 55.127 58.629 64.503 69.583 74.663 78.638 82.391 87.663 91.596 94.518 96.657 98.217 99.437 99.999 100
0.176 0.668 2.057 6.294 16.776 25.604 32.319 37.266 44.943 50.851 55.788 59.975 63.522 69.347 74.285 78.214 81.730 84.861 89.531 92.971 95.345 97.006 98.217 99.376 100 100
Fig. 9. Variation in R with d along the height direction of the rain zone at the windward side under high vc conditions.
Fig. 11. Cumulative number fraction under low crosswind speed conditions.
3. Results and discussion Existing studies indicated that the rain zone could weaken the adverse effects of crosswinds on the heat and mass transfer processes in the NDWCT, but little research has been conducted on the impact of ambient crosswind on the water droplet diameter distribution in the rain zone. According to the literature [31], the breakage and collision of water droplets are the main factors affecting their diameter, wherein the breakage is closely related to the horizontal air velocity. Therefore, the crosswind velocity needs to be considered. From the literature [32], it can be inferred that the Weber number We is the determining factor for the breakage of water droplets. When we exceed a We of 8, the
Fig. 10. Variation in R with d along the radial direction of rain zone at the windward side under high vc conditions.
5
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The number ratio can directly reveal the percentage of the water droplets at a specific diameter in the total number of water droplets, as defined in Eq. (3). By analyzing the number ratio, the diameter distribution of water droplets as well as its influencing factor in the rain zone can be discussed in depth.
R (d ) =
N (d ) Ntotal
(3)
where R(d) and N(d) are the number ratio and number of water droplets at the diameter of d, respectively, and Ntotal is the total number of water droplets during the test. In addition, to make the research results convenient for engineering applications, the cumulative number fraction is proposed in this paper, where the cumulative number fraction at a specific water droplet diameter is the sum of the water droplet number ratio of which the droplet diameters are smaller than that specific diameter, as described in Eq. (4). Fig. 12. Cumulative number fraction under high crosswind speed conditions.
C (d ) =
Maximum standard deviation
Relative uncertainty
Water droplet diameter d Number ratio R Cumulative number fraction C
± 0.1 mm ± 0.04 ± 0.04
± 0.05 0.6% 0.6%
ρd i Δv 2 σ
To analyze the water droplet diameter distribution in the rain zone under windless conditions, Figs. 6–8 depict the variation in R with d at six circumferential positions, three radial positions, and three height positions, respectively. The crosswind velocity of each set of data is marked in these figures. As seen in Fig. 6, the water droplet diameter d has a nearly identical distribution pattern along the circumferential direction under low wind speed conditions, which is in the range of 0.312–15 mm. The difference in the number ratio R under various values of d is no more than 1% at the different circumferential positions, with a maximum difference of 0.8% occurring at a d of 0.817 mm. The R of the water droplets within the diameter range from 0.687 mm to 0.937 mm are 23.2%, 22.9%, 23.6%, 23.1%, 23.9%, and 23.0% at the positions of c1r1h1, c2r4h1, c3r7h1, c1′ r1′ h1, c2′ r4′ h1 , and c3′ r7′ h1, respectively, which are significantly greater than other diameter ranges. In addition, the water droplets at a d of 5.5 mm also account for a relatively large number ratio, which is more than 7.4% at all circumferential positions. A visible phenomenon observed in Fig. 6 is that when d exceeds 5.5 mm, R decreases with increasing d, and the magnitude of the decrease continues to decline. In addition, the water droplet diameter distribution is virtually impervious to the crosswind within the speed range of 2.3 m/s, which verifies that the low speed wind has no impact on the water droplet diameter along the circumferential direction. It can be concluded from Fig. 7 that the maximum difference in R is 1.1% at a d of 1.187 mm, which demonstrates the similarity of the water droplet diameter distribution at different radial positions. That is, the difference in R between the three radial positions at each water droplet diameter is negligible. Taking the c3r7h2 position as an example, the relatively large number ratio of water droplets mainly occurs at d values of 0.812 mm, 0.937 mm, 1.375 mm and 5.5 mm, which are 10.0%, 8.9%, 6.9% and 7.0%, respectively. At the water droplet diameter range of 0.312 mm to 5.5 mm, the R follows a saw tooth shape distribution. Similar to that seen in Fig. 6, when the d is greater than 5.5 mm, the R decreases in a nonlinear way along the increase in d. In addition, the crosswinds within the test speed do not affect the water droplet diameter distribution along the radial direction.
(1)
where Δv is the relative horizontal velocity between the air and the water droplet, di is the initial water droplet diameter, i.e., the diameter of a water droplet when it first forms, σ is the surface tension of the water droplet, and ρ is the air density. According to Eq. (1), the minimum relative velocity between the air and the water droplets that breaks up the water droplets within the initial diameter can be calculated using Eq. (2).
Δv =
8σ ρd i
(4)
3.2. Water droplet diameter distribution under low crosswind speed conditions
water droplets will break into smaller water droplets, and then, the water droplet diameter distribution will be altered. We can be calculated using Eq. (1).
We =
i⩽d
where C(d) is the cumulative number fraction of water droplets with a diameter of d, and R(i) is the number ratio for water droplets with diameters equal to or less than d. The cumulative number fraction of water droplets can be applied directly to the performance computation of wet cooling towers to replace the equivalent water droplet diameter with higher accuracy.
Table 4 Uncertainty analysis of the test measurement. Parameter
∑ R (i),
(2)
According to our test results, the initial water droplet diameter is approximately 5.5 mm. Therefore, the water droplets will be broken up when Δv reaches 9.5 m/s. Under windless conditions, the inlet horizontal air velocity reaches 5 m/s at heights of 6 m and 3 m/s at heights of 3 m due to the NDWCT draft; thus, the water droplets with initial diameters will not be broken up. However, the water droplets at a height of 6 m in the windward rain zone will be markedly affected by the breakage phenomenon when the ambient crosswind velocity vc reaches 4.5 m/s. Therefore, the crosswind velocity can be used to judge whether the breakage of water droplets occurs, and the field test on the water droplet diameter can be divided into low wind speed conditions (when vc < 4.5 m/s, the breakage of water droplets rarely occurs) and high wind speed conditions (when vc > 4.5 m/s, breakage of water droplets would occur). 3.1. Data process In this study, the distributions of the water droplet diameter (d) at different positions are presented in the form of a number ratio (R) and a cumulative number fraction of water droplets (C). 6
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water droplet diameter is more pronounced than the drop height. Although the high-speed crosswind has an impact on the water droplet diameter, the impact range of the crosswind is confining, and the crosswind mainly alters only the water droplet diameter distribution at the periphery of the windward rain zone, namely, the c2r4h2 position in Fig. 10. This is because under the NDWCT draft, the air will turn upward after flowing horizontally over a certain distance, which lowers the horizontal air flow velocity. Thus, at the c2r5h2 position and c2r6h2 position, the horizontal air velocity is insufficient to break up the water droplets, and the crosswind is nearly impervious to the water droplet diameter distribution in these regions. At the c2r4h2 position, the R at d < 3.25 mm increases evidently under high crosswind conditions, and the maximum increment of R is 2.0% at d = 1.062 mm in comparison with the c2r5h2 position. The maximum difference in R at the c2r4h2 position between the low-speed and high-speed crosswind conditions occurs at d = 5.5 mm, which are 4.4% and 7.0% at vc = 7.9 m/s and vc = 2.4 m/s, respectively. In addition, the difference in R between d = 0.812 mm and d = 5.5 mm is 6.9% under vc = 7.9 m/ s, which is much higher than that of 2.4% under vc = 2.4 m/s. Therefore, under high crosswind speed conditions, the uniformity of the water droplet diameter distribution deteriorates. In general, the crosswind has a remarkable impact on the water droplet diameter distribution at the windward side of the rain zone, and the number ratio of water droplets with a diameter less than 3.25 mm rises significantly.
In contrast to Figs. 6 and 7, the water droplet diameter distribution is altered with obvious regularity along the height direction of the rain zone, as shown in Fig. 8. Most of the water droplet diameters are distributed in a range between 0.812 mm and 5.5 mm. The maximum number ratio occurs at a d of 0.812 mm, which includes 8.2%, 9.4% and 9.9% at the c1r1h1, c1r1h2 and c1r1h3 positions, respectively. At the c1r1h1 position, the number ratio at d = 5.5 mm is 7.5%, with a difference of 0.7% from that at d = 0.812 mm. When the water droplets move vertically down from the c1r1h1 position to the c1r1h2 position, the R declines in the diameter range between 3.25 mm and 9.5 mm, and the R with a smaller diameter presents a rising tendency. In addition, the R at d = 5.5 mm is 7.0%, and the difference in R between d = 0.812 mm and d = 5.5 mm increases to 2.4%. As water droplets continue to move down to the c1r1h3 position, the R within the diameter range between 5.5 mm and 9.5 mm further decreases, while the R with a diameter from 1.875 mm to 4.75 mm increases. The R becomes 5.8% at the d of 5.5 mm, and the difference in R at the d of 0.812 mm and 5.5 mm is 4.1%. Based on the above analysis, as the drop height increases, the number ratio of water droplets with larger diameters decreases, and the uniformity of the water droplet diameter distribution degrades, which is due to the increase in collision frequency between water droplets. In addition, the initial water droplet diameter is approximately 5.5 mm, the change of which is most affected by drop height. In summary, under low wind speed conditions, the water droplet diameter distribution in the rain zone is irregular, and the diameter range of all water droplets is from 0.312 mm to 15 mm, which is mostly distributed from 0.812 mm to 5.5 mm. The water droplet diameter distribution is not affected by the circumferential or radial directions, and the drop height is the decisive factor for the water droplet diameter distribution inside the cooling tower. Typically, from the h1 position to the h3 position, the R at d = 0.812 mm increases from 8.2% to 9.9%, and the R at d = 5.5 mm decreases from 7.5% to 5.8%.
3.4. Cumulative distribution of water droplet diameter To directly apply the test data in the thermodynamic and aerodynamic calculations, the cumulative number fraction C is proposed in this study. To obtain the distribution of C, the test data are processed using the IQR method as follows to obtain the representative distribution of R(d). Under low speed crosswind conditions, all test data at the same test height are grouped according to different water droplet diameters. For each water droplet diameter, the test data are sorted as a data sequence in ascending order, and the data at the positions of 1/4 and 3/4 in the data sequence are the first quartile Q1 and third quartile Q3 of this data sequence, respectively. Next, we find the average value of each data sequence between the corresponding Q1 and Q3, i.e., the most reliable number ratio of water droplets. Thus, the most representative distribution of water droplet diameter at different height positions in the rain zone is obtained. Under high-speed crosswind conditions, all test data at the periphery of the windward rain zone are also processed with the IQR method. After obtaining the representative distributions of the R(d) under low crosswind speed conditions and high crosswind speed conditions, the cumulative number fraction can be obtained, as listed in Table 3. The formula for calculating the cumulative distribution of water droplets under both low crosswind speed and high crosswind speed conditions can be fitted with a hyperbolic curve. By fitting each data point in Fig. 11, the calculation formula for the cumulative distribution of water droplets under low crosswind speed conditions is obtained using Eqs. (5)–(9):
3.3. Raindrop size distribution under high crosswind speed conditions To reflect the crosswind effects on the water droplet diameter distribution, some high wind speed conditions are presented in this section. Figs. 9 and 10 illustrate the variation in the number ratio with water droplet diameter, where the specific crosswind speed for each set of data is marked. All test positions in Figs. 9 and 10 are on the windward side during the test. As seen in Fig. 9, the water droplet diameter is also scattered between 0.312 mm and 15 mm when the crosswind speed exceeds 7.3 m/ s. However, the water droplet diameter distribution at different height positions is basically the same, which shows a great difference from the windless condition. Taking the c2r4h1 position as an example, compared with that under the vc of 1.4 m/s, the R of the water droplets within the diameter range between 3.25 mm and 9.5 mm is significantly greater under the vc of 8.6 m/s. The R at a d of 5.5 mm is reduced from 7.8% to 4.3% when the crosswind speed increases from 1.4 m/s to 8.6 m/s, which indicates that the water droplets with an initial diameter are significantly affected by the high-speed crosswind. For the water droplets in the diameter range of less than 3.25 mm, their number ratio will increase when the crosswind speed reaches the high crosswind velocity conditions. This outcome occurs because under the action of a high speed crosswind, water droplets no longer execute simple motion, and the breakage of water droplets caused by horizontal air velocity significantly influences the water droplet diameter. Thus, the main factor affecting the water droplet diameter distribution in the rain zone is no longer the drop height but the crosswind. Furthermore, the distribution pattern of the water droplet diameter at the windward side under high speed crosswind conditions is most similar to that at the height of h3 with a low speed crosswind, as shown in Fig. 8, while the former has a larger number ratio of water droplets with smaller diameters. This phenomenon verifies that the effect of the high-speed crosswind on
C (d ) lw = α + βd n/(θ n + d n ) (R2 = 0.99)
(5)
α = - 0.44387 + 0.05922h − 0.00323h2
(6)
0.01323h2
(7)
θ = 2.71036 − 0.38532h + 0.03193h2
(8)
0.01317h2
(9)
β = 2.03381 − 0.20158h +
n = 0.37838 + 0.22158h −
where h is the drop height and d is the water droplet diameter. In addition, the cumulative distribution of the water droplet diameter under high crosswind speed conditions shown in Fig. 12 is fitted using Eq. (10). 7
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Therm. Eng. 133 (2018) 439–445. [6] Dang Zhigang, Gao Ming, Long Guoqing, et al., Crosswind influence on cooling capacity in different zones for high level water collecting wet coolingtowers based on field test, J. Wind Eng. Ind. Aerodyn. 190 (2019) 134–142. [7] Zhang Zhengqing, Gao Ming, Wang Mingyong, et al., Field test study on thermal and ventilation performance for natural draft wet cooling tower after structural improvement, Appl. Therm. Eng. 155 (2019) 305–312. [8] Zhou Yang, Gao Ming, Long Guoqing, et al., Experimental study regarding the effects of forced ventilation on the thermal performance for super-large natural draft wet cooling towers, Appl. Therm. Eng. 155 (2019) 40–48. [9] Zhou Yang, Wang Kun, Gao Ming, et al., Experimental study on the drag characteristic and non-uniform fillings for wet cooling towers under thermal performance of crosswind conditions, Appl. Therm. Eng. 140 (2018) 398–405. [10] O.J.G. Pedraza, J.J.P. Ibarra, C. Rubio-Maya, et al., Numerical study of the drift and evaporation of water droplets cooled down by a forced stream of air, Appl. Therm. Eng. 142 (2018) 292–302. [11] J.R. Missimer, C.A. Brackett, Model tests of the rain zone of a counterflow natural cooling tower, in: 5th International Association for Hydraulics Research Cooling Tower Workshop, Monterey, October, 1986. [12] M. Sedina, Heat and mass transfer and pressure drop in the rain zone of cooling towers, in: 8th International Association for Hydraulic Research Cooling Tower and Spraying Pond Symposium, Karlsruhe, October, 1992. [13] Zhao Zhenguo, Shi Jinling, Chen Xiansong, The equivalent diameter of water droplets in the rain zone of natural draught cooling towers, J. Hydrodyn. 7 (1992) 79–84 (in Chinese). [14] R. Terblanche, Investigation of Performance Enhancing Devices for the Rain Zone of Wet-Cooling Towers, University of Stellenbosch, Stellenbosch, 2008. [15] H.R. Oosthuizen, Enhancement of Cooling Tower Performance by Manipulating of Rain Zone Drop Size, University of Stellenbosch, Stellenbosch, 1995. [16] R. Terblanche, Evaluation of Drop Break-up after Impingement on Horizontal Slat Grids and the Effect of Drop Size of Cooling Tower Rain Zone Performance, University of Stellenbosch, Stellenbosch, 2011. [17] R. Terblanche, Drop size distribution below different wet-cooling tower fills, Appl. Therm. Eng. 29 (2009) 1552–1560. [18] D.J. Pierce, Evaluation and Performance Prediction of Cooling Tower Rain Zones, University of Stellenbosch, Stellenbosch, 2007. [19] Al-Waked Rafat, Behnia Masud, CFD simulation of wet cooling tower, Appl. Therm. Eng. 26 (4) (2006) 382–395. [20] R. Al-Waked, M. Behnia, Enhancing performance of wet cooling towers, Energy Convers. Manage. 48 (10) (2007) 2638–2648. [21] H.R. Goshayshi, J.F. Missenden, R. Tozer, Cooling tower-an energy conservation resource, Appl. Therm. Eng. 19 (11) (1999) 1223–1235. [22] J. Khan, S.M. Zubair, M. Yaqub, Performance characteristics of counter flow wet cooling towers, Energy Convers. Manage. 44 (13) (2003) 2073–2091. [23] S.P. Fisenko, A.A. Brin, Simulation of a cross-flow cooling tower performance, Int. J. Heat Mass Transf. 50 (15–16) (2007) 3216–3223. [24] S.P. Fisenko, A.I. Petruchik, Toward to the control system of mechanical draft cooling tower of film type, Int. J. Heat Mass Transf. 48 (1) (2005) 31–35. [25] S.P. Fisenko, A.I. Petruchik, A.D. Solodukhin, Evaporative cooling of water in a natural draft cooling tower, Int. J. Heat Mass Transf. 45 (23) (2002) 4683–4694. [26] Zhao Yuanbin, Sun Fengzhong, Long Guoqing, Comparative study on the cooling characteristics of high level water collecting natural draft wet cooling tower and the usual cooling tower, Energy Convers. Manage. 116 (10) (2016) 150–164. [27] Lyu Dongqiang, Sun Fengzhong, Zhao Yuanbin, Impact mechanism of different fill layout patterns on the cooling performance of the wet cooling tower with water collecting devices, Appl. Therm. Eng. 75 (2015) 1106–1117. [28] Xuehong Chen, Fengzhong Sun, Youliang Chen, et al., Novel method for improving the cooling performance of natural draft wet cooling towers, Appl. Therm. Eng. 147 (2019) 562–570. [29] Xuehong Chen, Fengzhong Sun, Youliang Chen, et al., New retrofit method to improve the thermal performance of natural draft wet cooling towers based on the reconstruction of the aerodynamic field, Int. J. Heat Mass Transf. 132 (2019) 671–680. [30] Dang Zhigang, Zhang Zhengqing, Gao Ming, et al., Numerical simulation of thermal performance for super large-scale wet cooling tower equipped with an axial fan, Int. J. Heat Mass Transf. 135 (2019) 220–234. [31] Lyu Dongqiang, Research on The Raindrop Size Distribution and its Effect on the Cooling Performance and Pressure Drop of the Rain Zone in the Large Wet Cooling Tower, Shandong University, Jinan, 2018. [32] J.R. Adam, N.R. Lindblad, C.D. Hendricks, The collision, coalescence, and disruption of water droplets, J. Appl. Phys. 39 (11) (2003) 5173–5180. [33] R.J. Mofat, Describing the uncertainties in experimental results, Exp. Therm Fluid Sci. 1 (1988) 3–17.
C (d ) hw = 1.20605d1.44802/(1. 471841.44802 + d1.44802) − 0.16252 (R2 = 0.99) (10) The correlation coefficients in Eqs. (5) and (10) are both 0.99, which shows high precision. Therefore, these formulae can be used in the design calculation of NDWCTs. 4. Uncertainty analysis Based on the accuracy of the test apparatus listed in Table 2, an uncertainty analysis is conducted using theoretical procedures [33]. The analytical results are shown in Table 4. According to the uncertainty analysis results, the error is within the allowable range for the field test. 5. Conclusions In this study, the OTT Parsivel2 raindrop spectrometer is employed to test the water droplet diameter distribution in the rain zone of a NDWCT. To reduce the error, the test data were processed using the IQR method to obtain the representative water droplet diameter distribution. Based on the field test, the principal results are as follows. (1) Due to the deformation, collision and breakup, the water droplet diameter is not evenly distributed but scattered between 0.312 mm and 15 mm and mostly distributed between 0.812 mm and 5.5 mm. (2) Under low crosswind speed conditions, a larger drop height leads to a larger number ratio of water droplets at d < 3.25 mm. From the c1r1h1 position to the c1r1h3 position, the R at d = 0.812 mm increases from 8.2% to 9.9%, and the R at d = 5.5 mm decreases from 7.5% to 5.8%. In addition, there is little variation in the water droplet diameter distribution at different circumferential and radial positions. (3) Under high crosswind speed conditions, the water droplet diameter distribution is basically the same at the windward side, and the number ratio of water droplets at d = 5.5 mm increases obviously. In addition, the crosswind mainly alters the water droplet diameter distribution at the periphery of the windward rain zone. (4) The cumulative number fraction of water droplets derived in this study can be used to replace the particle size distribution in the DPM model or the equivalent water droplet diameter, which is more accurate for calculating the thermal and pressure drop performance of NDWCTs. References [1] D.G. Kröger, Air-cooled Heat Exchangers and Cooling Towers, Penn Well Corporation, Tulsa, USA, 2004. [2] N. Williamson, S. Armfield, M. Behnia, Numerical simulation of flow in a natural draft wet cooling tower: the effect of radial thermofluid fields, Appl. Therm. Eng. 28 (2–3) (2008) 178–189. [3] X.X. Li, H. Gurgenci, Z.Q. Guan, et al., A review of the crosswind effect on the natural draft cooling towers, Appl. Therm. Eng. 150 (2019) 250–270. [4] Gao Ming, Zou Jian, He Suoying, Sun Fengzhong, Thermal performance analysis for high level water collecting wet cooling tower under crosswind conditions, Appl. Therm. Eng. 136 (2018) 568–575. [5] Zou Jian, He Suoying, Long Guoqing, et al., Field test on ventilation performance for high level water collecting wet cooling tower under crosswind conditions, Appl.
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Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Field test study on water droplet diameter distribution in the rain zone of a natural draft wet cooling tower
T
⁎
Xuehong Chen, Fengzhong Sun , Dongqiang Lyu School of Energy and Power Engineering, Shandong University, Jinan 250061, China
H I GH L IG H T S
diameter distribution in a NDWCT is quantitatively studied by field test. • Droplet d in the rain zone of the NDWCT is scattered between 0.312 mm and 15 mm. • The number ratio of water droplets at a d of 0.812 mm and 5.5 mm is relatively large. • The crosswind markedly increases the number ratio of droplets at d < 3.25 mm. • High-speed • Cumulative number fraction of water droplets is obtained by fitting the test data.
A R T I C LE I N FO
A B S T R A C T
Keywords: Field test Wet cooling tower Rain zone Water droplet diameter distribution Crosswind
A field test study was conducted on a natural draft wet cooling tower to quantitatively investigate the water droplet diameter distribution in the rain zone for the first time. A test rig with alterable test positions was designed and constructed. The test time for each set of data is 300 s. The test data are presented in the form of a number ratio (R) with water droplet diameter (d). The results manifest that d is scattered between 0.312 mm and 15 mm, regardless of the crosswind velocity. Under low crosswind speed conditions, R has nearly an identical distribution pattern along the circumferential and radial directions, which are relatively large at d = 0.812 mm and 5.5 mm, respectively. As the droplets move from the position of c1r1h1 to c1r1h3, the R at d > 3.75 mm increases significantly, and the difference in R at d = 0.812 mm and d = 5.5 mm increases from 0.7% to 4.1%, respectively. When the crosswind speed is relatively high, the R is basically consistent at different height positions and shows a difference on the windward side, leading to a noticeable increase in R at d < 3.25 mm. For engineering applications, the cumulative distribution of water droplet diameter is further obtained.
1. Introduction Natural draft wet cooling towers (NDWCTs) are widely used to cool the feed water of condensers in thermal and nuclear power plants, and NDWCT performance deterioration will weaken the heat transfer efficiency of condensers, eventually leading to a decrease in the thermal cycle efficiency of the unit [1,2]. For a NDWCT, the heat transfer and pressure drop characteristics of the rain zone, which mainly depend on the water droplet diameter, have an evident impact on the tower cooling performance. To date, some studies on NDWCTs and the rain zone have been conducted through experimental investigations [3–17] and numerical simulations [18–30]. According to Li [3], the ambient crosswind has a noticeable effect on the wet cooling tower, with sensitivity to the crosswind velocity. Gao [4–7] conducted a series of field test studies to ⁎
evaluate the thermal and ventilation performances of natural draft wet cooling towers, including the high level water collecting wet cooling tower with cross walls (HWCT) and the usual wet cooling tower (UWCT). The main findings of their studies are as follows. The thermal and ventilation performances for a wet cooling tower gradually decrease with increasing crosswind velocity due to the uniformity decline in the circumferential inflow air. For the HWCT, the tower performance is also related to the angle between the cross walls and crosswind direction. With the increase in crosswind velocity, the cooling capacity of the filling zone decreases while the cooling capacity of the rain zone increases. For the UWCT, the structural improvement, which includes both the air ducts and air deflectors, can improve the tower performance under various crosswind velocities. Through a thermal state model experiment, Zhou [8,9] concluded that both the forced draft and nonuniform fillings had positive effects on the thermal performance of
Corresponding author. E-mail address: [email protected] (F. Sun).
https://doi.org/10.1016/j.applthermaleng.2019.114252 Received 13 May 2019; Received in revised form 17 July 2019; Accepted 11 August 2019 Available online 16 August 2019 1359-4311/ © 2019 Elsevier Ltd. All rights reserved.
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Nomenclature
r1–r6 , r1′–r6′ v vc We
c1–c3 , c1′–c3′ position of circumferential measuring points C cumulative number fraction of water droplets (%) C(d) cumulative number fraction of water droplets with a diameter of d (%) d water droplet diameter (mm) di initial water droplet diameter (mm) h height (m) h1–h3 position of height measuring point n coefficient N(d) number of water droplets at the diameter of d Ntotal total number of water droplets during the test Q1, Q3 first quartile and third quartile of a data sequence R number ratio of water droplets (%) R(d), R(i) number ratio of water droplets with a diameter of d or i
(%) position of radial measuring point velocity (m/s) ambient crosswind velocity (m/s) Weber number
Greek letters α, β, θ σ ρ
coefficient surface tension of water droplet (N) air density (kg/m3)
Subscripts lw hw
wet cooling towers. That is, nonuniform fillings can alleviate the adverse effect of the crosswind, and the forced draft can enhance the ventilation rate of the cooling tower. Missimer et al. [10] and Sedina et al. [11] studied the water droplet size in the rain zone through a laboratory model test and proposed an equivalent diameter of water droplets to replace the complex diameter distribution. Based on laboratory experiments and validation calculations, Zhao [12] recommended an equivalent diameter of water droplets of 2.65–3 mm in a NDWCT. However, the equivalent diameter will create a significant error in the NDWCT pressure drop calculation. Previous researchers [13–17] studied the water droplet diameter in the rain zone using imaging technology. In these studies, the water droplet diameter distribution was measured photographically below three different fills and a number of splash grid configurations. However, the geometric dimension of the test zone (1.0 m × 1.5 m) was far less than the actual rain zone, and the SLR camera was fixed in a position; thus, the achieved water droplet diameter distribution was unrepresentative of the NDWCT rain zone. With the development of numerical technology, many scholars have carried out numerical simulations on NDWCT rain zones. Using the k-ε turbulence model and discrete phase model (DPM), Waked [18,19] performed a three-dimensional numerical study of heat and mass transfer in a NDWCT and found that the rain zone could somewhat reduce the adverse effect of ambient crosswind on the tower cooling performance. The discrete phase model was also employed in previous studies [20–24]. In the discrete phase model, the particle size distribution built into the CFD software is unrepresentative of the water droplet diameter distribution inside the NDWCT. Therefore, the DPM model is imprecise and oversimplified in the performance computation of NDWCTs. Another method used to address the water droplet diameter distribution is the equivalent water droplet diameter. Pedraza [25] numerically investigated the suitable equivalent size of water droplets in a cooling tower to reduce water losses, indicating that the equivalent diameter of the water droplets should be higher than 3 mm and the air velocities should be lower than 5 m/s to avoid drifting. Based on the equivalent water droplet diameter, Zhao [26,27] established a threedimensional numerical model for NDWCTs, and the numerical results agreed with the actual running results. Through numerical research, Chen [28,29] investigated two kinds of retrofit methods for improving the thermal performance of NDWCTs, and Dang [30] studied the thermal performance of super large-scale wet cooling towers equipped with an axial fan. In their studies, the water droplet diameter in the rain zone was still replaced with an equivalent water droplet diameter. However, the specific surface area and the number of water droplets per unit volume in the equivalent water droplet diameter method were both greater than the actual conditions. Not only will this cause the
low crosswind speed condition high crosswind speed condition
proportion of heat transfer capacity to increase in the rain zone and decrease in the fill zone but will also lead to more air flow hindrance by water droplets; that is, the pressure rises in the rain zone and declines in the fill zone. Therefore, the performance and fill selection of NDWCTs will be greatly affected when employing the equivalent water droplet diameter. Based on the above-cited literature, the currently used processing methods for water droplet diameter distribution will bring large errors to the performance computation of NDWCTs, while the laboratory findings were imprecise because the interactions among water droplets in the rain zone were difficult to reproduce in the laboratory investigations. To accurately study the water droplet diameter distribution in the rain zone, a field test was conducted on a NDWCT for the first time in this study. By measuring the water droplet diameter with the corresponding test instrument at different positions, the distribution characteristics of the water droplet diameter in the rain zone are obtained and discussed. To easily integrate the test results into engineering applications, the cumulative distribution of water droplet diameter is further acquired by fitting the test data. The cumulative distribution of the water droplet diameter, which has a higher precision in the cooling tower calculation, can substitute for the equivalent water droplet diameter in future studies. The results of work can lay a theoretical foundation for optimizing NDWCT designs.
2. Field test system 2.1. Test object This field test was conducted on a NDWCT for a 660 MW unit during the spring season, and the main geometrical dimensions of the studied NDWCT are listed in Table 1. The fill used in the NDWCT is made of plastic, with a thickness of 1.5 m and a bottom elevation of 11.3 m. During the field test, the circulating water flow rate of the NDWCT remains at 78150 t/h, that is, the water spray density is 2.41 kg/(m2·s).
Table 1 Main geometrical dimensions of the NDWCT.
2
Item
Value
Unit
Diameter of tower base Diameter of tower throat Diameter of tower outlet Height of the tower Height of tower throat Height of tower air inlet Filling area
118.85 66.50 71.42 150.00 112.48 10.33 9000.00
m m m m m m m2
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anemometers. The test instrument for water droplet diameter is the OTT Parsivel2 raindrop spectrometer (hereinafter referred to as OTT Parsivel2), as shown in Fig. 1. The main performance parameters of the OTT Parsivel2 are listed in Table 2. The theory behind the OTT Parsivel2 is a laser sensor capable of producing a horizontal beam. The emitter and receiver of the laser sensor are integrated into a single protective housing and then placed in the sensor head. As shown in Fig. 2, if there are no water droplets in the laser beam, the maximum voltage is outputted at the receiver. Water droplets passing through the laser beam block off the portion of the beam corresponding to their diameter, thus reducing the output voltage and generating a signal, which determines the particle size. A signal begins as soon as a water droplet enters the laser beam and ends when it has completely left the laser beam; thus, the signal duration is measured. When obtaining the water droplet diameter and the duration of the signal, the water droplet speed can be calculated. Some parameters, including the size spectrum, type of precipitation, kinetic energy and intensity of the precipitation, can be derived from the diameter and speed of the water droplet. The splash protection attached to the sensor head prevents the precipitation particles from deflecting off the housing and falling into the laser beam, which falsifies the measurements. In addition, the test time for each set of data is 300 s. A rocker arm with a test range of 0– 17 m in the radial direction and 0–8 m in the height direction is expressly designed and manufactured for this test study. The rocker arm is made of aviation aluminum. As shown in Fig. 3, the OTT Parsivel2 is connected to the clamping device by bolts, and the clamping device is placed on the rocker arm. Due to the specific structure of the rocker arm, the OTT Parsivel2 always remains vertically stable during the testing process. In addition, the water repellent agent is daubed on the goggle laser transmitter to form a water-repellent film.
Fig. 1. Picture of the OTT Parsivel2. Table 2 Main performance parameters of OTT Parsivel2. Item
Value
Accuracy
Measuring area Measuring range Measuring speed Temperature Test time
54 cm2 0.2–25 mm 0.2–20 m/s −40–70 ℃ 10–3600 s
– ± 5% ± 0.01 m/s ± 0.1 ℃ –
2.3. Test point layout The layout of measuring points for the crosswind around the NDWCT is shown in Fig. 4. As seen in Fig. 4(a), there were eight crosswind measuring points along the circumferential direction. These measuring points were approximately 2 m away from the NDWCT, and there was one anemoscope and two cup anemometers at two heights (3 m and 6 m, respectively) for each measuring point, as shown in Fig. 4(b). For the measuring points of water droplet diameter in the rain zone,
Fig. 2. Functional principle of the OTT Parsivel2.
2.2. Test apparatus The direction and velocity of the ambient crosswind are measured with anemoscopes and cup anemometers, respectively. The measurement accuracy is ± 0.05° for the anemoscope and ± 0.1 m/s for the cup
Fig. 3. Placement of OTT Parsivel2. 3
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Cup anemometers
Anemoscope
(a) Measuring points at different circumferential
(b) Measuring apparatus at different height
positions
positions
Fig. 4. Layout of measuring points for ambient crosswind around the tower.
(a) Vertical view
(b) Front view
Fig. 5. Layout of measuring points for water droplet diameter in the rain zone.
Fig. 6. Variation in R with d along the circumferential direction of rain zone under low vc conditions.
Fig. 7. Variation in R with d along the radial direction of rain zone under low vc conditions.
six circumferential positions, three radial positions and three height positions are selected to research the raindrop size distribution. Therefore, there are 6 × 3 × 3 = 54 measuring points altogether in the rain zone. A graphic of the arrangement mode of these measuring
points is shown in Fig. 5.
4
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Table 3 Cumulative number fraction under low speed and high speed crosswind conditions. Water droplet diameter d (mm)
0.312 0.437 0.562 0.687 0.812 0.937 1.062 1.187 1.375 1.625 1.875 2.125 2.375 2.75 3.25 3.75 4.25 4.75 5.5 6.5 7.5 8.5 9.5 11 13 15
Fig. 8. Variation in R with d along the height direction of the rain zone under low vc conditions.
Cumulative number fraction (%) Drop height = h1, low speed crosswind
Drop height = h2, low speed crosswind
Drop height = h3, low speed crosswind
High speed crosswind
0.216 0.745 2.634 10.362 19.241 27.072 32.605 36.290 41.243 45.248 48.586 51.583 54.286 59.814 64.783 69.640 74.378 78.984 86.450 91.225 94.691 96.956 98.760 99.644 100 100
0.296 0.973 2.712 8.627 18.930 27.133 32.455 36.899 42.847 47.877 52.257 56.262 59.643 64.776 69.143 73.701 77.932 81.559 88.086 92.151 95.240 97.455 98.989 99.669 99.999 100
0.158 0.654 1.902 6.102 16.116 23.728 30.119 34.468 41.553 46.979 51.161 55.127 58.629 64.503 69.583 74.663 78.638 82.391 87.663 91.596 94.518 96.657 98.217 99.437 99.999 100
0.176 0.668 2.057 6.294 16.776 25.604 32.319 37.266 44.943 50.851 55.788 59.975 63.522 69.347 74.285 78.214 81.730 84.861 89.531 92.971 95.345 97.006 98.217 99.376 100 100
Fig. 9. Variation in R with d along the height direction of the rain zone at the windward side under high vc conditions.
Fig. 11. Cumulative number fraction under low crosswind speed conditions.
3. Results and discussion Existing studies indicated that the rain zone could weaken the adverse effects of crosswinds on the heat and mass transfer processes in the NDWCT, but little research has been conducted on the impact of ambient crosswind on the water droplet diameter distribution in the rain zone. According to the literature [31], the breakage and collision of water droplets are the main factors affecting their diameter, wherein the breakage is closely related to the horizontal air velocity. Therefore, the crosswind velocity needs to be considered. From the literature [32], it can be inferred that the Weber number We is the determining factor for the breakage of water droplets. When we exceed a We of 8, the
Fig. 10. Variation in R with d along the radial direction of rain zone at the windward side under high vc conditions.
5
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The number ratio can directly reveal the percentage of the water droplets at a specific diameter in the total number of water droplets, as defined in Eq. (3). By analyzing the number ratio, the diameter distribution of water droplets as well as its influencing factor in the rain zone can be discussed in depth.
R (d ) =
N (d ) Ntotal
(3)
where R(d) and N(d) are the number ratio and number of water droplets at the diameter of d, respectively, and Ntotal is the total number of water droplets during the test. In addition, to make the research results convenient for engineering applications, the cumulative number fraction is proposed in this paper, where the cumulative number fraction at a specific water droplet diameter is the sum of the water droplet number ratio of which the droplet diameters are smaller than that specific diameter, as described in Eq. (4). Fig. 12. Cumulative number fraction under high crosswind speed conditions.
C (d ) =
Maximum standard deviation
Relative uncertainty
Water droplet diameter d Number ratio R Cumulative number fraction C
± 0.1 mm ± 0.04 ± 0.04
± 0.05 0.6% 0.6%
ρd i Δv 2 σ
To analyze the water droplet diameter distribution in the rain zone under windless conditions, Figs. 6–8 depict the variation in R with d at six circumferential positions, three radial positions, and three height positions, respectively. The crosswind velocity of each set of data is marked in these figures. As seen in Fig. 6, the water droplet diameter d has a nearly identical distribution pattern along the circumferential direction under low wind speed conditions, which is in the range of 0.312–15 mm. The difference in the number ratio R under various values of d is no more than 1% at the different circumferential positions, with a maximum difference of 0.8% occurring at a d of 0.817 mm. The R of the water droplets within the diameter range from 0.687 mm to 0.937 mm are 23.2%, 22.9%, 23.6%, 23.1%, 23.9%, and 23.0% at the positions of c1r1h1, c2r4h1, c3r7h1, c1′ r1′ h1, c2′ r4′ h1 , and c3′ r7′ h1, respectively, which are significantly greater than other diameter ranges. In addition, the water droplets at a d of 5.5 mm also account for a relatively large number ratio, which is more than 7.4% at all circumferential positions. A visible phenomenon observed in Fig. 6 is that when d exceeds 5.5 mm, R decreases with increasing d, and the magnitude of the decrease continues to decline. In addition, the water droplet diameter distribution is virtually impervious to the crosswind within the speed range of 2.3 m/s, which verifies that the low speed wind has no impact on the water droplet diameter along the circumferential direction. It can be concluded from Fig. 7 that the maximum difference in R is 1.1% at a d of 1.187 mm, which demonstrates the similarity of the water droplet diameter distribution at different radial positions. That is, the difference in R between the three radial positions at each water droplet diameter is negligible. Taking the c3r7h2 position as an example, the relatively large number ratio of water droplets mainly occurs at d values of 0.812 mm, 0.937 mm, 1.375 mm and 5.5 mm, which are 10.0%, 8.9%, 6.9% and 7.0%, respectively. At the water droplet diameter range of 0.312 mm to 5.5 mm, the R follows a saw tooth shape distribution. Similar to that seen in Fig. 6, when the d is greater than 5.5 mm, the R decreases in a nonlinear way along the increase in d. In addition, the crosswinds within the test speed do not affect the water droplet diameter distribution along the radial direction.
(1)
where Δv is the relative horizontal velocity between the air and the water droplet, di is the initial water droplet diameter, i.e., the diameter of a water droplet when it first forms, σ is the surface tension of the water droplet, and ρ is the air density. According to Eq. (1), the minimum relative velocity between the air and the water droplets that breaks up the water droplets within the initial diameter can be calculated using Eq. (2).
Δv =
8σ ρd i
(4)
3.2. Water droplet diameter distribution under low crosswind speed conditions
water droplets will break into smaller water droplets, and then, the water droplet diameter distribution will be altered. We can be calculated using Eq. (1).
We =
i⩽d
where C(d) is the cumulative number fraction of water droplets with a diameter of d, and R(i) is the number ratio for water droplets with diameters equal to or less than d. The cumulative number fraction of water droplets can be applied directly to the performance computation of wet cooling towers to replace the equivalent water droplet diameter with higher accuracy.
Table 4 Uncertainty analysis of the test measurement. Parameter
∑ R (i),
(2)
According to our test results, the initial water droplet diameter is approximately 5.5 mm. Therefore, the water droplets will be broken up when Δv reaches 9.5 m/s. Under windless conditions, the inlet horizontal air velocity reaches 5 m/s at heights of 6 m and 3 m/s at heights of 3 m due to the NDWCT draft; thus, the water droplets with initial diameters will not be broken up. However, the water droplets at a height of 6 m in the windward rain zone will be markedly affected by the breakage phenomenon when the ambient crosswind velocity vc reaches 4.5 m/s. Therefore, the crosswind velocity can be used to judge whether the breakage of water droplets occurs, and the field test on the water droplet diameter can be divided into low wind speed conditions (when vc < 4.5 m/s, the breakage of water droplets rarely occurs) and high wind speed conditions (when vc > 4.5 m/s, breakage of water droplets would occur). 3.1. Data process In this study, the distributions of the water droplet diameter (d) at different positions are presented in the form of a number ratio (R) and a cumulative number fraction of water droplets (C). 6
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water droplet diameter is more pronounced than the drop height. Although the high-speed crosswind has an impact on the water droplet diameter, the impact range of the crosswind is confining, and the crosswind mainly alters only the water droplet diameter distribution at the periphery of the windward rain zone, namely, the c2r4h2 position in Fig. 10. This is because under the NDWCT draft, the air will turn upward after flowing horizontally over a certain distance, which lowers the horizontal air flow velocity. Thus, at the c2r5h2 position and c2r6h2 position, the horizontal air velocity is insufficient to break up the water droplets, and the crosswind is nearly impervious to the water droplet diameter distribution in these regions. At the c2r4h2 position, the R at d < 3.25 mm increases evidently under high crosswind conditions, and the maximum increment of R is 2.0% at d = 1.062 mm in comparison with the c2r5h2 position. The maximum difference in R at the c2r4h2 position between the low-speed and high-speed crosswind conditions occurs at d = 5.5 mm, which are 4.4% and 7.0% at vc = 7.9 m/s and vc = 2.4 m/s, respectively. In addition, the difference in R between d = 0.812 mm and d = 5.5 mm is 6.9% under vc = 7.9 m/ s, which is much higher than that of 2.4% under vc = 2.4 m/s. Therefore, under high crosswind speed conditions, the uniformity of the water droplet diameter distribution deteriorates. In general, the crosswind has a remarkable impact on the water droplet diameter distribution at the windward side of the rain zone, and the number ratio of water droplets with a diameter less than 3.25 mm rises significantly.
In contrast to Figs. 6 and 7, the water droplet diameter distribution is altered with obvious regularity along the height direction of the rain zone, as shown in Fig. 8. Most of the water droplet diameters are distributed in a range between 0.812 mm and 5.5 mm. The maximum number ratio occurs at a d of 0.812 mm, which includes 8.2%, 9.4% and 9.9% at the c1r1h1, c1r1h2 and c1r1h3 positions, respectively. At the c1r1h1 position, the number ratio at d = 5.5 mm is 7.5%, with a difference of 0.7% from that at d = 0.812 mm. When the water droplets move vertically down from the c1r1h1 position to the c1r1h2 position, the R declines in the diameter range between 3.25 mm and 9.5 mm, and the R with a smaller diameter presents a rising tendency. In addition, the R at d = 5.5 mm is 7.0%, and the difference in R between d = 0.812 mm and d = 5.5 mm increases to 2.4%. As water droplets continue to move down to the c1r1h3 position, the R within the diameter range between 5.5 mm and 9.5 mm further decreases, while the R with a diameter from 1.875 mm to 4.75 mm increases. The R becomes 5.8% at the d of 5.5 mm, and the difference in R at the d of 0.812 mm and 5.5 mm is 4.1%. Based on the above analysis, as the drop height increases, the number ratio of water droplets with larger diameters decreases, and the uniformity of the water droplet diameter distribution degrades, which is due to the increase in collision frequency between water droplets. In addition, the initial water droplet diameter is approximately 5.5 mm, the change of which is most affected by drop height. In summary, under low wind speed conditions, the water droplet diameter distribution in the rain zone is irregular, and the diameter range of all water droplets is from 0.312 mm to 15 mm, which is mostly distributed from 0.812 mm to 5.5 mm. The water droplet diameter distribution is not affected by the circumferential or radial directions, and the drop height is the decisive factor for the water droplet diameter distribution inside the cooling tower. Typically, from the h1 position to the h3 position, the R at d = 0.812 mm increases from 8.2% to 9.9%, and the R at d = 5.5 mm decreases from 7.5% to 5.8%.
3.4. Cumulative distribution of water droplet diameter To directly apply the test data in the thermodynamic and aerodynamic calculations, the cumulative number fraction C is proposed in this study. To obtain the distribution of C, the test data are processed using the IQR method as follows to obtain the representative distribution of R(d). Under low speed crosswind conditions, all test data at the same test height are grouped according to different water droplet diameters. For each water droplet diameter, the test data are sorted as a data sequence in ascending order, and the data at the positions of 1/4 and 3/4 in the data sequence are the first quartile Q1 and third quartile Q3 of this data sequence, respectively. Next, we find the average value of each data sequence between the corresponding Q1 and Q3, i.e., the most reliable number ratio of water droplets. Thus, the most representative distribution of water droplet diameter at different height positions in the rain zone is obtained. Under high-speed crosswind conditions, all test data at the periphery of the windward rain zone are also processed with the IQR method. After obtaining the representative distributions of the R(d) under low crosswind speed conditions and high crosswind speed conditions, the cumulative number fraction can be obtained, as listed in Table 3. The formula for calculating the cumulative distribution of water droplets under both low crosswind speed and high crosswind speed conditions can be fitted with a hyperbolic curve. By fitting each data point in Fig. 11, the calculation formula for the cumulative distribution of water droplets under low crosswind speed conditions is obtained using Eqs. (5)–(9):
3.3. Raindrop size distribution under high crosswind speed conditions To reflect the crosswind effects on the water droplet diameter distribution, some high wind speed conditions are presented in this section. Figs. 9 and 10 illustrate the variation in the number ratio with water droplet diameter, where the specific crosswind speed for each set of data is marked. All test positions in Figs. 9 and 10 are on the windward side during the test. As seen in Fig. 9, the water droplet diameter is also scattered between 0.312 mm and 15 mm when the crosswind speed exceeds 7.3 m/ s. However, the water droplet diameter distribution at different height positions is basically the same, which shows a great difference from the windless condition. Taking the c2r4h1 position as an example, compared with that under the vc of 1.4 m/s, the R of the water droplets within the diameter range between 3.25 mm and 9.5 mm is significantly greater under the vc of 8.6 m/s. The R at a d of 5.5 mm is reduced from 7.8% to 4.3% when the crosswind speed increases from 1.4 m/s to 8.6 m/s, which indicates that the water droplets with an initial diameter are significantly affected by the high-speed crosswind. For the water droplets in the diameter range of less than 3.25 mm, their number ratio will increase when the crosswind speed reaches the high crosswind velocity conditions. This outcome occurs because under the action of a high speed crosswind, water droplets no longer execute simple motion, and the breakage of water droplets caused by horizontal air velocity significantly influences the water droplet diameter. Thus, the main factor affecting the water droplet diameter distribution in the rain zone is no longer the drop height but the crosswind. Furthermore, the distribution pattern of the water droplet diameter at the windward side under high speed crosswind conditions is most similar to that at the height of h3 with a low speed crosswind, as shown in Fig. 8, while the former has a larger number ratio of water droplets with smaller diameters. This phenomenon verifies that the effect of the high-speed crosswind on
C (d ) lw = α + βd n/(θ n + d n ) (R2 = 0.99)
(5)
α = - 0.44387 + 0.05922h − 0.00323h2
(6)
0.01323h2
(7)
θ = 2.71036 − 0.38532h + 0.03193h2
(8)
0.01317h2
(9)
β = 2.03381 − 0.20158h +
n = 0.37838 + 0.22158h −
where h is the drop height and d is the water droplet diameter. In addition, the cumulative distribution of the water droplet diameter under high crosswind speed conditions shown in Fig. 12 is fitted using Eq. (10). 7
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Therm. Eng. 133 (2018) 439–445. [6] Dang Zhigang, Gao Ming, Long Guoqing, et al., Crosswind influence on cooling capacity in different zones for high level water collecting wet coolingtowers based on field test, J. Wind Eng. Ind. Aerodyn. 190 (2019) 134–142. [7] Zhang Zhengqing, Gao Ming, Wang Mingyong, et al., Field test study on thermal and ventilation performance for natural draft wet cooling tower after structural improvement, Appl. Therm. Eng. 155 (2019) 305–312. [8] Zhou Yang, Gao Ming, Long Guoqing, et al., Experimental study regarding the effects of forced ventilation on the thermal performance for super-large natural draft wet cooling towers, Appl. Therm. Eng. 155 (2019) 40–48. [9] Zhou Yang, Wang Kun, Gao Ming, et al., Experimental study on the drag characteristic and non-uniform fillings for wet cooling towers under thermal performance of crosswind conditions, Appl. Therm. Eng. 140 (2018) 398–405. [10] O.J.G. Pedraza, J.J.P. Ibarra, C. Rubio-Maya, et al., Numerical study of the drift and evaporation of water droplets cooled down by a forced stream of air, Appl. Therm. Eng. 142 (2018) 292–302. [11] J.R. Missimer, C.A. Brackett, Model tests of the rain zone of a counterflow natural cooling tower, in: 5th International Association for Hydraulics Research Cooling Tower Workshop, Monterey, October, 1986. [12] M. Sedina, Heat and mass transfer and pressure drop in the rain zone of cooling towers, in: 8th International Association for Hydraulic Research Cooling Tower and Spraying Pond Symposium, Karlsruhe, October, 1992. [13] Zhao Zhenguo, Shi Jinling, Chen Xiansong, The equivalent diameter of water droplets in the rain zone of natural draught cooling towers, J. Hydrodyn. 7 (1992) 79–84 (in Chinese). [14] R. Terblanche, Investigation of Performance Enhancing Devices for the Rain Zone of Wet-Cooling Towers, University of Stellenbosch, Stellenbosch, 2008. [15] H.R. Oosthuizen, Enhancement of Cooling Tower Performance by Manipulating of Rain Zone Drop Size, University of Stellenbosch, Stellenbosch, 1995. [16] R. Terblanche, Evaluation of Drop Break-up after Impingement on Horizontal Slat Grids and the Effect of Drop Size of Cooling Tower Rain Zone Performance, University of Stellenbosch, Stellenbosch, 2011. [17] R. Terblanche, Drop size distribution below different wet-cooling tower fills, Appl. Therm. Eng. 29 (2009) 1552–1560. [18] D.J. Pierce, Evaluation and Performance Prediction of Cooling Tower Rain Zones, University of Stellenbosch, Stellenbosch, 2007. [19] Al-Waked Rafat, Behnia Masud, CFD simulation of wet cooling tower, Appl. Therm. Eng. 26 (4) (2006) 382–395. [20] R. Al-Waked, M. Behnia, Enhancing performance of wet cooling towers, Energy Convers. Manage. 48 (10) (2007) 2638–2648. [21] H.R. Goshayshi, J.F. Missenden, R. Tozer, Cooling tower-an energy conservation resource, Appl. Therm. Eng. 19 (11) (1999) 1223–1235. [22] J. Khan, S.M. Zubair, M. Yaqub, Performance characteristics of counter flow wet cooling towers, Energy Convers. Manage. 44 (13) (2003) 2073–2091. [23] S.P. Fisenko, A.A. Brin, Simulation of a cross-flow cooling tower performance, Int. J. Heat Mass Transf. 50 (15–16) (2007) 3216–3223. [24] S.P. Fisenko, A.I. Petruchik, Toward to the control system of mechanical draft cooling tower of film type, Int. J. Heat Mass Transf. 48 (1) (2005) 31–35. [25] S.P. Fisenko, A.I. Petruchik, A.D. Solodukhin, Evaporative cooling of water in a natural draft cooling tower, Int. J. Heat Mass Transf. 45 (23) (2002) 4683–4694. [26] Zhao Yuanbin, Sun Fengzhong, Long Guoqing, Comparative study on the cooling characteristics of high level water collecting natural draft wet cooling tower and the usual cooling tower, Energy Convers. Manage. 116 (10) (2016) 150–164. [27] Lyu Dongqiang, Sun Fengzhong, Zhao Yuanbin, Impact mechanism of different fill layout patterns on the cooling performance of the wet cooling tower with water collecting devices, Appl. Therm. Eng. 75 (2015) 1106–1117. [28] Xuehong Chen, Fengzhong Sun, Youliang Chen, et al., Novel method for improving the cooling performance of natural draft wet cooling towers, Appl. Therm. Eng. 147 (2019) 562–570. [29] Xuehong Chen, Fengzhong Sun, Youliang Chen, et al., New retrofit method to improve the thermal performance of natural draft wet cooling towers based on the reconstruction of the aerodynamic field, Int. J. Heat Mass Transf. 132 (2019) 671–680. [30] Dang Zhigang, Zhang Zhengqing, Gao Ming, et al., Numerical simulation of thermal performance for super large-scale wet cooling tower equipped with an axial fan, Int. J. Heat Mass Transf. 135 (2019) 220–234. [31] Lyu Dongqiang, Research on The Raindrop Size Distribution and its Effect on the Cooling Performance and Pressure Drop of the Rain Zone in the Large Wet Cooling Tower, Shandong University, Jinan, 2018. [32] J.R. Adam, N.R. Lindblad, C.D. Hendricks, The collision, coalescence, and disruption of water droplets, J. Appl. Phys. 39 (11) (2003) 5173–5180. [33] R.J. Mofat, Describing the uncertainties in experimental results, Exp. Therm Fluid Sci. 1 (1988) 3–17.
C (d ) hw = 1.20605d1.44802/(1. 471841.44802 + d1.44802) − 0.16252 (R2 = 0.99) (10) The correlation coefficients in Eqs. (5) and (10) are both 0.99, which shows high precision. Therefore, these formulae can be used in the design calculation of NDWCTs. 4. Uncertainty analysis Based on the accuracy of the test apparatus listed in Table 2, an uncertainty analysis is conducted using theoretical procedures [33]. The analytical results are shown in Table 4. According to the uncertainty analysis results, the error is within the allowable range for the field test. 5. Conclusions In this study, the OTT Parsivel2 raindrop spectrometer is employed to test the water droplet diameter distribution in the rain zone of a NDWCT. To reduce the error, the test data were processed using the IQR method to obtain the representative water droplet diameter distribution. Based on the field test, the principal results are as follows. (1) Due to the deformation, collision and breakup, the water droplet diameter is not evenly distributed but scattered between 0.312 mm and 15 mm and mostly distributed between 0.812 mm and 5.5 mm. (2) Under low crosswind speed conditions, a larger drop height leads to a larger number ratio of water droplets at d < 3.25 mm. From the c1r1h1 position to the c1r1h3 position, the R at d = 0.812 mm increases from 8.2% to 9.9%, and the R at d = 5.5 mm decreases from 7.5% to 5.8%. In addition, there is little variation in the water droplet diameter distribution at different circumferential and radial positions. (3) Under high crosswind speed conditions, the water droplet diameter distribution is basically the same at the windward side, and the number ratio of water droplets at d = 5.5 mm increases obviously. In addition, the crosswind mainly alters the water droplet diameter distribution at the periphery of the windward rain zone. (4) The cumulative number fraction of water droplets derived in this study can be used to replace the particle size distribution in the DPM model or the equivalent water droplet diameter, which is more accurate for calculating the thermal and pressure drop performance of NDWCTs. References [1] D.G. Kröger, Air-cooled Heat Exchangers and Cooling Towers, Penn Well Corporation, Tulsa, USA, 2004. [2] N. Williamson, S. Armfield, M. Behnia, Numerical simulation of flow in a natural draft wet cooling tower: the effect of radial thermofluid fields, Appl. Therm. Eng. 28 (2–3) (2008) 178–189. [3] X.X. Li, H. Gurgenci, Z.Q. Guan, et al., A review of the crosswind effect on the natural draft cooling towers, Appl. Therm. Eng. 150 (2019) 250–270. [4] Gao Ming, Zou Jian, He Suoying, Sun Fengzhong, Thermal performance analysis for high level water collecting wet cooling tower under crosswind conditions, Appl. Therm. Eng. 136 (2018) 568–575. [5] Zou Jian, He Suoying, Long Guoqing, et al., Field test on ventilation performance for high level water collecting wet cooling tower under crosswind conditions, Appl.
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