Introduction

The mechanical draft wet cooling tower, a key cooling device in high-water-consumption industries such as power generation and chemical manufacturing, relies primarily on heat and mass exchange to maintain the proper temperature of process water. Its thermal performance directly influences the operational efficiency and economic performance of industrial systems1. During operation, the circulating cooling water is atomized into fine droplets by the spray device and undergoes intensive heat and mass exchange with the rising airflow inside the tower, thereby achieving cooling. After heat exchange, the humid and hot air moves toward the tower outlet while carrying small liquid droplets that have not fully settled, escaping from the top and forming the “floating water” phenomenon2,3. Floating water poses a significant safety challenge to power plants, and for those using seawater or saltwater as cooling media, its consequences are even more severe. Vegetation surrounding the cooling tower is damaged by salt accumulation caused by floating water. Meanwhile, salt-laden drift droplets deposit on equipment, pipelines, and steel structures, accelerating metal corrosion and, in severe cases, causing power system failures. In cold seasons, drift droplets may condense on surrounding roads and buildings, creating icing risks and safety hazards4. In addition, drift loss is a major component of the total water loss in cooling towers. Floating water not only reduces the circulating water volume and increases the demand for makeup water, but also increases pretreatment and operating costs5. Therefore, in-depth quantitative research on the influencing factors and mechanisms of floating water is of great theoretical and engineering significance for effectively controlling floating water in wet cooling towers and optimizing structural design and operational strategies.

The water loss of wet cooling towers mainly consists of three components: evaporation loss, blowdown loss, and drift loss6. Evaporation accounts for approximately 1.2–1.6% of the total circulating water7, representing an unavoidable loss for cooling towers. Blowdown loss is relatively minor and can be reduced by increasing the cycles of concentration; however, this approach complicates circulating water treatment and exacerbates equipment corrosion8. Water conservation mainly depends on reducing drift loss9. The drift ratio is a key indicator of the water-saving performance of cooling towers, and installing high-efficiency drift eliminators is a common measure for reducing drift loss. However, drift eliminators increase the overall airflow resistance of a tower. Lucas et al.10,11 employed the chemical equilibrium method and a mechanical draft wet cooling tower with a gravity-based water distribution system to study droplet loss and thermal performance under different drift eliminators. They proposed design criteria for drift eliminators to optimize both collection efficiency and cooling performance, and analyzed their interaction with the water distribution system. Yu et al.12 proposed the use of curved bends and drainage hooks as enhanced structural designs for wave-plate demisters, aiming to improve separation efficiency while simultaneously reducing pressure loss. On-site monitoring, as a direct means of obtaining operational drift ratio data, remains a fundamental research approach. However, it typically requires long monitoring periods and high costs, making it difficult to accurately capture droplet dynamics and their spatial distribution. Nevertheless, some researchers have made valuable contributions in this area13,14. For instance, Israel et al.15 developed an automatic drift sampler and compared its results with model-predicted drift deposition rates. The results demonstrated that the sampler is effective for collecting on-site data to test and validate drift dispersion models. Li et al.16 combined on-site meteorological observations with photogrammetry to monitor droplet dispersion and deposition in the thermal plume of large power plant cooling towers, and further analyzed their environmental impacts. Shen17 conducted four on-site investigations of drift droplets and salt deposition in naturally ventilated seawater cooling towers. The results revealed that maximum salt deposition occurred predominantly in the downwind direction of prevailing winds, with the highest levels observed in spring. They recommended reducing the drift ratio of cooling towers to mitigate environmental impacts. Compared with on-site monitoring, numerical simulation offers the advantages of lower cost and shorter cycles, enabling the flexible adjustment of parameters such as wind speed, temperature, and droplet size distribution, while allowing repeated verification of results. Current numerical simulation methods mainly focus on SACTI (seasonal annual cooling tower impact) models18,19,20 and computational fluid dynamics (CFD) techniques21,22,23. Wang et al.24 applied SACTI to predict drift droplets and salt deposition in nuclear power plants and proposed generating simulation data via SACTI during the design process of nuclear plant cooling towers. Michioka et al.25 compared CFD simulations with on-site tracer gas experiments and found good agreement in droplet trajectory predictions, confirming the reliability and effectiveness of CFD for simulating droplet transport in cooling towers. Klimanek26 developed a comprehensive CFD model for natural draft wet cooling towers to predict performance under various operating conditions, analyze heat and mass transfer in the spray zone, and simulate rain and spray regions. Shi et al.27 simulated the flow field near cooling towers and assessed drift droplets and salt deposition effects on the local environment using CFD and SACTI, validating the results with on-site experiments. Although numerical simulations are efficient, their accuracy strongly depends on boundary conditions and computational parameters. Moreover, numerical models often require experimental or field data for validation, yet the validation process is constrained by data acquisition challenges and experimental limitations. For model testing, Ben et al.28 employed wind tunnel experiments to study the pressure distribution in spray packing under varying wind directions and speeds, evaluating the impact of environmental wind on prototype cooling tower packing. A review of the current literature indicates that few physical experiments have addressed drift droplet behavior and drift ratio patterns in cooling towers.

Floating water is the primary cause of wind-induced water loss in cooling towers, and strict control of the drift ratio is a critical measure for both water conservation and environmental protection⁵. In this context, the in-depth investigation of drift droplets, the development of reliable experimental techniques to obtain high-quality benchmark data, and the establishment of accurate and efficient models for predicting drift ratios are of urgent practical importance for improving cooling tower performance, promoting industrial water conservation, and advancing sustainable development. Nevertheless, existing research remains limited in terms of quantitative experimental analysis of drift droplets, largely due to the lack of systematic experimental data and mechanistic understanding. To address this gap, our group designed and constructed a controllable mechanical draft wet cooling tower drift ratio testing system. Employing a reliable and adaptable filter paper moisture absorption method, we systematically examined the effects of three key parameters—the nozzle diameter, water drenching density, and sectional wind velocity—on the drift ratio in a model cooling tower without a drift eliminator. Through comparative analysis under varying operating conditions, this study not only clarifies the mechanisms governing drift droplet generation but also provides critical data and experimental support for understanding influencing factors and developing effective strategies for drift ratio control.

Experimental design

Design of the experimental apparatus

The primary cause of drift droplets in cooling towers is the collision of sprayed droplets with the packing. Driven by upward airflow, these droplets detach from the packing, escape through the tower outlet, and disperse into the surrounding environment. The experiment conducted for this work employed a drift rate test platform developed by our research group to measure the droplet loss of water. The platform adopts a sectional simulation approach, incorporating key components such as nozzles, packing, and water distribution networks at scales consistent with the actual engineering height, to accurately reproduce droplet generation under practical conditions. To clarify the impact of overlapping nozzle flows on drift droplets and balance site space and power load limitations, the platform was designed with four symmetrically arranged nozzles. The platform cross-section is shown in Fig. 1(a), while Fig. 1(b) illustrates its dimensions and nozzle arrangement.

Fig. 1
figure 1

The cross-section of the drift rate test platform. (a) A cross-section of the drift rate test platform., (b) The test platform cross-sectional dimensions and nozzle layout.

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The three-dimensional structural diagram of the drift rate test platform is shown in Fig. 2(a). The platform is based on a blower-type mechanical draft wet cooling tower. Steel observation platforms (5 × 5 m) are installed in the airflow channel at heights of 3 m, 5.5 m, and 8 m. Each observation platform is surrounded by safety fences of appropriate height for maintenance. The structure of the mechanical draft wet test tower is shown in Fig. 2(b). The tower frame consists of four I-beams. The spray section measures 2 m × 2 m, with an adjustable water drenching density ranging from 7 to 13 t/(h·m²) and a sectional wind velocity ranging from 0 to 2.5 m/s, installable nozzle models include reflective type and rotary spray type. For the experiment, the test tower was not equipped with a drift eliminator, and the structure was divided into three sections from top to bottom: (1) Spraying stage: The spraying stage was located at the top of the tower, with nozzles installed 1 m above the upper packing. (2) Packing section: Located above the inlet section, the packing section contained two layers of packing supported by frames: the upper layer (1.5 m) reduced the water velocity and increased the spray area, while the lower layer (0.5 m) acted as a rectifier. (3) Air inlet section: Positioned above the bottom reservoir and below the packing, the air inlet section supplied airflow through a fan installed at the bottom inlet of the channel.

The experimental operation of the drift rate test platform proceeded as follows: (1) Water was pumped from the pond into the distribution pipeline and evenly supplied to four nozzles. The nozzles sprayed hot water onto the packing surface. A collection tank was placed below the packing to capture the downward-flowing spray water. The collected water then returned to the pond for recycling. (2) The blower fan delivered air into the tower, where it exchanged heat and mass with the circulating water. The fan speed, and thus the inlet wind speed, was precisely controlled by adjusting the frequency of the electromagnetic flowmeter. After heat exchange, the humid hot air, driven by the pressure difference inside and outside the tower, flowed toward the outlet and was discharged.

Fig. 2
figure 2

A diagram of the drift rate test platform. (a) The three-dimensional structural diagram of the drift rate test platform., (b) The structural diagram of the test tower, (unit: m).

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The drift rate test platform measurement system consisted of three subsystems: (1) Circulating water measurement system: This system recorded the circulating water flow rate (Q1) and the inlet/outlet temperatures (t), measured using electromagnetic flowmeters and thermometers. (2) Air measurement system: Parameters included the circulating air volume (Q2), ambient dry- and wet-bulb temperatures, inlet dry- and wet-bulb temperatures (\({t_{\text{\varvec{\uptau}}}}\) and \({t_{\text{\varvec{\uptheta}}}}\)), and atmospheric pressure (P). Q2 was measured by eight vortex flowmeters, the dry- and wet-bulb temperatures were measured with an Assmann psychrometer, and P was obtained from a barometer. (3) Filter paper moisture absorption system: A high-precision electronic balance measured the filter paper mass before and after the experiment to calculate the moisture absorption and drift ratio. The instruments and their measurement accuracies are listed in Table 1.

Table 1 Instruments and measurement accuracy used in the drift rate test platform measurement system.
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In this experiment, S-wave spray packing with a 30 mm sheet spacing was used. Water was distributed through a tubular system, with a reflective spray device installed below the distribution pipe. Four nozzle types with diameters of 32, 34, 36, and 38 mm were selected, as shown in Fig. 3. Circulating water was evenly delivered to the four nozzles through the distribution pipe, where it exited as a columnar jet. Upon striking the splash plate, the jet dispersed outward onto the packing surface.

Fig. 3
figure 3

A physical image of nozzles with different diameters.

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Calculating the drift ratio

According to the current Chinese standard, the drift ratio is defined as the ratio of the water discharged from the cooling tower outlet to the water entering the tower per unit time. For cooling towers with a circulating water volume below 1000 m³/h, the drift ratio should not exceed 0.010%29. For those with a volume above 1000 m³/h, the drift ratio should remain below 0.005%30. In this experiment, the drift ratio of the test tower was measured using the filter paper moisture absorption method. Each operating condition was tested three times, and the arithmetic mean of the measured drift loss was taken as the representative value for that condition. To ensure acceptable repeatability of the triplicate experimental data, an F-test (Fisher’s test) was conducted to examine the homogeneity of variances under each operating condition prior to calculating the arithmetic mean. The results showed that all p-values were greater than 0.05, indicating no significant differences among the repeated measurements at the 95% confidence level, thus satisfying the prerequisite for using the arithmetic mean. The representative drift loss \(\Delta Q\) was calculated using Eqs. (1)–(3):

$${\text{\varvec{\Delta}}}Q=\frac{{{\text{\varvec{\Delta}}}qS}}{{{S_{\text{a}}}{\text{\varvec{\Delta}}}t}} \times 60 \times {10^{ - 6}}$$
(1)
$${\text{\varvec{\Delta}}}q=\frac{1}{x}\sum\limits_{{i=1}}^{x} {{\text{\varvec{\Delta}}}{q_x}}$$
(2)
$${\text{\varvec{\Delta}}}{q_x}=\frac{1}{n}\sum\limits_{{j=1}}^{n} {{\text{(\varvec{\Delta}}}{m_{xn}} - {\text{\varvec{\Delta}}}{m_{xt}})}$$
(3)

In the formulas above: \(\Delta Q\) represents the amount of water lost due to drifting droplets (m³/h); S is the cross-sectional area of the test section (m²), which is 4 m² in this experiment; Sa is the area of the filter paper (m²); \(\Delta t\) is the residence time of the filter paper (min), which is fixed at 1 min in this experiment; \(\Delta q\) is the amount of water absorbed by the filter paper (g/min); x is the total number of repeated tests (dimensionless); \(\Delta {q_x}\) is the amount of water absorbed by the filter paper in the xth test (g/min); n is the number of measurement points (dimensionless); \(\Delta {m_{xn}}\) is the measured weight gain of the filter paper at the nth measurement point in the xth test (g); and \(\Delta {m_{xt}}\) is the corrected weight gain of the filter paper (g), obtained after eliminating the effects of background moisture absorption and secondary drifting.

The drift ratio W is determined using the following equation:

$$W=\frac{{{\text{\varvec{\Delta}}}Q}}{Q} \times 100\% =\frac{{\frac{{{\text{\varvec{\Delta}}}qS}}{{{S_{\text{a}}}{\text{\varvec{\Delta}}}t}} \times 60 \times {{10}^{ - 6}}}}{{qS}} \times 100{\text{\% }}=\frac{{{\text{\varvec{\Delta}}}q}}{{q{S_{\text{a}}}{\text{\varvec{\Delta}}}t}} \times 60 \times {10^{ - 4}}{\text{\% }}$$
(4)

where W is the drift ratio, expressed as a percentage, %; Q is the circulating water flow rate, m³/h; and q is the water drenching density, t/(h·m²).

According to the error transfer theory, we can obtain:

$$\frac{{u{\text{(}}W{\text{)}}}}{W}=\sqrt {{{\left( {\frac{{u{\text{(\varvec{\Delta}}}q{\text{)}}}}{{{\text{\varvec{\Delta}}}q}}} \right)}^2}+{{\left( {\frac{{u{\text{(}}q{\text{)}}}}{q}} \right)}^2}+{{\left( {\frac{{u{\text{(}}{S_a}{\text{)}}}}{{{S_a}}}} \right)}^2}+{{\left( {\frac{{u{\text{(}}\Delta t{\text{)}}}}{{\Delta t}}} \right)}^2}}$$
(5)
$$u{\text{(\varvec{\Delta}}}q{\text{)}}=\frac{{u{\text{(\varvec{\Delta}}}{q_x}{\text{)}}}}{{\sqrt x }}$$
(6)

where u(i) denotes the measurement uncertainty or precision, i is\(\Delta q\), q, Sa, \(\Delta t\).

Defining\({d_{\text{j}}}=\Delta m_{{xn}}^{{(j)}} - \Delta m_{{xt}}^{{(j)}}\),we can obtain:

$$\Delta {q_x}=\overline {d}$$
(7)
$$u(\Delta {q_x})=\frac{{{s_d}}}{{\sqrt n }}$$
(8)

where sd represents the sample standard deviation of dj.

$$\frac{{u(\Delta q)}}{{\Delta q}}=\frac{{{s_d}}}{{\sqrt {nx} \cdot \Delta q}}$$
(9)

The relative error is calculated using the following equation:

$$\frac{{u(W)}}{W}=\sqrt {\frac{{s_{d}^{{\text{2}}}}}{{nx{{(\Delta q)}^2}}}+{{\left( {\frac{{u(q)}}{q}} \right)}^2}+{{\left( {\frac{{u({S_a})}}{{{S_a}}}} \right)}^2}+{{\left( {\frac{{u(\Delta t)}}{{\Delta {\text{t}}}}} \right)}^2}}$$
(10)

Measuring the drift ratio

Accurate measurement of the drift ratio forms the foundation of all related research, and different countries employ different testing methods. For instance, after accumulating practical experience in drift loss testing, the United States developed the standard ATC-140 in 1995, which adopts tracer analysis with isokinetic sampling31. In China, the commonly used methods for measuring the drift ratio include the secondary water collection method, the silica gel absorption method, the droplet spectrum method, and the filter paper moisture absorption method. The national standard Testing Regulations for Industrial Cooling Towers (DL/T1027-2006)32 provides a detailed description of the filter paper moisture absorption method for measuring the drift ratio of cooling towers. Measurement points are arranged in equal-area rings according to the fan diameter, and the drift ratio is calculated from the change in the filter paper mass before and after exposure.

In this work, the concentration of airborne droplets carried by the rising airflow was measured after all water purifiers were removed from the test area. This experiment followed the Testing Regulations for Industrial Cooling Towers (DL/T1027-2006) to measure the drift ratio of a mechanical draft wet model tower. Measuring points were arranged at the outlet of the cooling tower duct, where the square area defined by the nozzle was divided into four equal sections. The center of each section was selected as the measurement point, yielding a total of four points. The spatial arrangement of these points is illustrated in Fig. 1(b). The drift ratio test was conducted on the observation platform, located 8 m above the test tower. Each operating condition was repeated three times to ensure consistency. The overall testing process is shown in Fig. 4, and the detailed experimental steps are as follows:

  1. (a)

    Preparation and weighing of the filter paper: Prior to the experiment, dried filter papers were placed into self-sealing plastic bags, which were labeled according to the sequence of designated measurement points. Each bag was weighed using a high-precision electronic balance to record the initial mass. All self-sealing plastic bags corresponding to one set of experimental conditions were then placed into a larger white plastic bag.

  2. (b)

    Installation at the measurement point: The test was conducted at the tower exit. The filter paper was removed from the self-sealing plastic bag and rapidly secured at the center of the support clamp. The clamp was then positioned horizontally at the designated measurement point, ensuring that the filter paper plane was perpendicular to the airflow direction.

  3. (c)

    Testing procedure: Data collection began with a 1-minute exposure at the designated measurement point. After 1 min, the moisture-absorbing filter paper was removed from the support clamp and promptly resealed in the self-sealing plastic bag. The same procedure was repeated for each measurement point. To minimize potential errors caused by moisture absorption, weight gain, or secondary drift water, after completing measurements at all four points, a piece of dry filter paper was clamped on the support and briefly (1 s) exposed to the ambient air around the tower before being returned to its original plastic bag.

  4. (d)

    Post-test weighing: After the test, the self-sealing plastic bag was reweighed using a high-precision electronic balance, and the post-test mass was recorded. The difference between the pre- and post-test weights represents the amount of water deposited by drift droplets within the effective collection area of the filter paper at the designated measurement point.

Fig. 4
figure 4

A flowchart of the drift ratio test.

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Experimental conditions

The purpose of this experiment was to investigate the formation of drift droplets during cooling tower operation. Previous studies have shown that the nozzle diameter, water drenching density, and sectional wind velocity are key parameters affecting the drift ratio33. Accordingly, this study selected these three factors as the independent variables and the drift ratio as the performance indicator, and conducted 96 sets of droplet loss of water experiments. The set of experiments conducted is presented in Table 2.

Table 2 The test sequence for the droplet loss of water experiments.
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Analysis of experimental results

Influence of the nozzle diameter on the drift ratio

Figure 5 illustrates the relationship between the drift ratio and the sectional wind velocity for different nozzle diameters, under fixed water drenching densities of 7, 10, and 13 t/(h·m²). (1) Across all three water drenching densities, the 32 mm nozzle produces the highest drift ratio, followed by the 34 mm nozzle, whereas the 36 mm and 38 mm nozzles show the lowest values. (2) At a water drenching density of 7 t/(h·m²), the variation in drift ratio among nozzles of different diameters is relatively small. However, at 10 and 13 t/(h·m²), the drift ratios of the 32 mm and 34 mm nozzles differ significantly from those of the 36 mm and 38 mm nozzles. (3) Notably, between the 36 mm and 38 mm nozzles, the 38 mm nozzle produces a slightly higher drift ratio. Nevertheless, the difference is minimal, particularly at water drenching densities of 10 and 13 t/(h·m²), where their drift–wind speed curves nearly overlap.

Fig. 5
figure 5

The relationship between the sectional wind velocity and drift ratio under different water drenching densities. (a) Water drenching density 7 t/(h·m2)., (b) Water drenching density 10 t/(h·m2)., (c) Water drenching density 13 t/(h·m2).

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Analysis shows that for nozzles with diameters of 32 mm and 34 mm, the drift ratio decreases as the nozzle diameter increases. This occurs because, under the same water drenching density, a smaller nozzle diameter generates higher internal pressure34. The water column discharged from the nozzle and dispersed around the splash plate produces smaller droplets, which enhances atomization and makes them more easily carried out of the tower by the fan, thereby increasing the drift ratio. In contrast, a larger nozzle diameter produces larger droplets, leading to poorer atomization and reducing the amount of water that can be entrained by the fan. Consequently, nozzles with diameters of 36 mm and 38 mm generate lower drift ratios. Lucas et al.10,11 conducted experimental studies on mechanical draft wet cooling towers and found that the drift ratio strongly depends on the airflow velocity and droplet size distribution. Similarly, Zhang et al.5 and He9 observed that higher sectional wind velocity leads to a rapid increase in drift loss, whereas larger nozzle or droplet sizes help reduce the drift ratio.

Figure 6 presents the on-site spray patterns of nozzles with diameters of 32, 34, 36, and 38 mm under water drenching densities of 7, 10, and 13 t/(h·m²). (1) At a water drenching density of 7 t/(h·m²), the limited water volume results in relatively large droplets after passing through the splash plate. The differences in droplet characteristics among nozzle diameters are minimal, leading to small variations and overall low drift ratios. At water drenching densities of 10 and 13 t/(h·m²), the nozzle flow rate increases, resulting in pronounced differences in spray patterns and atomization among nozzle diameters. In this case, droplet sizes are smaller than those observed at 7 t/(h·m²). (2) At water drenching densities of 10 and 13 t/(h·m²), the 32 mm nozzle produces finer mist and better atomization than the 34 mm nozzle. The spray patterns of the 36 mm and 38 mm nozzles show little difference. In contrast, the 36 mm and 38 mm nozzles generate larger droplets with poorer atomization compared to the 32 mm and 34 mm nozzles. These results indicate that the nozzle diameter strongly influences the drift ratio, with smaller diameters being more sensitive to wind speed variations. (3) Overall, the spray patterns in Fig. 6 are consistent with the trends observed in Fig. 5.

Fig. 6
figure 6

A comparison of the spray states of different nozzle diameters under different water drenching densities. (a) Nozzle diameter 32 mm., (b) Nozzle diameter 34 mm., (c) Nozzle diameter 36 mm., (d) Nozzle diameter 38 mm.

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Effect of the water drenching density on the drift ratio

This section examines the relationship between the drift ratio and sectional wind velocity at water drenching densities of 7, 10, and 13 t/(h·m²) for different nozzle diameters. The corresponding curves are presented in Fig. 7. (1) For all tested nozzle diameters and water drenching densities, the drift ratio increases with the sectional wind velocity. Data fitting reveals an approximately exponential relationship between the drift ratio and sectional wind velocity. (2) Figs. 7(a) and 7(b), corresponding to 32 mm and 34 mm nozzles, show that the highest drift ratio occurs at a water drenching density of 13 t/(h·m²), followed by 10 t/(h·m²), with the lowest at 7 t/(h·m²). (3) In contrast, Figs. 7(c) and 7(d), corresponding to 36 mm and 38 mm nozzles, reveal the opposite trend: the highest drift ratio occurs at 7 t/(h·m²), followed by 10 t/(h·m²), and the lowest at 13 t/(h·m²). (4) Overall, the variation in drift ratio with water drenching density shows opposite trends for the 32/34 mm nozzles and the 36/38 mm nozzles at 7 and 13 t/(h·m²).

Fig. 7
figure 7

The relationship between the sectional wind velocity and drift ratio under different nozzle diameters. (a) Nozzle diameter 32 mm., (b) Nozzle diameter 34 mm., (c) Nozzle diameter 36 mm., (d) Nozzle diameter 38 mm.

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According to Eq. (4), the variation in the drift ratio is determined by both the volume of floating water and the water drenching density. Figure 8 illustrates the relationship between the floating water volume and sectional wind velocity for four nozzle diameters under different water drenching densities. (1) For all nozzle diameters and water drenching densities, the floating water volume increases with the sectional wind velocity, exhibiting an exponential relationship. Shi et al.33 arrived at a similar conclusion based on droplet spectrum analysis. (2) For the 32 mm and 34 mm nozzles, the maximum floating water volume occurs at 13 t/(h·m²), followed by 10 t/(h·m²), with the minimum at 7 t/(h·m²). This indicates that, for a given nozzle diameter and sectional wind velocity, the floating water volume increases with the water drenching density. This is because increasing the water drenching density directly increases the total droplet output and droplet number per unit area, allowing more droplets to be entrained by the fan and thus increasing the floating water volume33. (3) Figs. 8(c) and 8(d) show that, for the 36 mm and 38 mm nozzles, the floating water volume curves under different water drenching densities nearly overlap, with differences of no more than 0.0048. This indicates that, for the 36 mm and 38 mm nozzles, the floating water volume is largely unaffected by the water drenching density.

The trends in the drift ratio observed in Fig. 7 can be explained with reference to Fig. 8: (1) At a fixed water drenching density, the drift ratio increases with the floating water volume, and both the drift ratio and sectional wind velocity exhibit exponential growth. (2) At the same sectional wind velocity, the largest floating water volume and drift ratio occur at 13 t/(h·m²), while the smallest occur at 7 t/(h·m²). This indicates that the effect of the floating water volume on the drift ratio is stronger than that of the water drenching density. In practical applications, increasing the water drenching density thus leads to a higher drift ratio. (3) For sprinkler heads with diameters of 36 mm and 38 mm, increasing the water drenching density leaves the floating water volume nearly unchanged, thereby reducing the drift ratio. (4) It can be inferred that in practical engineering applications, when the sprinkler head diameter exceeds a certain threshold (D ≥ 36 mm), increasing the water drenching density does not affect the floating water volume but significantly decreases the drift ratio; conversely, when the sprinkler head diameter falls below a threshold (D ≤ 34 mm), the growth in the floating water volume outpaces that of water drenching density, so increasing the water drenching density leads to both a higher floating water volume and an elevated drift ratio.

Fig. 8
figure 8

The relationship between the sectional wind velocity and floating water volume under different nozzle diameters. (a) Nozzle diameter 32 mm., (b) Nozzle diameter 34 mm., (c) Nozzle diameter 36 mm., (d) Nozzle diameter 38 mm.

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Comparison of drift ratios

Figure 9 presents the relationship between the drift ratio, nozzle diameter, water drenching density, and sectional wind velocity. The results indicate that the nozzle diameter, water drenching density, and sectional wind velocity jointly influence the drift ratio. For the 32 mm and 34 mm nozzles, the drift ratio increases with both the water drenching density and sectional wind velocity. For the 36 mm and 38 mm nozzles, the drift ratio decreases with the water drenching density but increases slightly with sectional wind velocity, showing only a weak growth trend. For practical nozzle selection and operation, the following guidelines can be proposed. When using small-diameter nozzles (D ≤ 34 mm), both the sectional wind velocity and water drenching density should be strictly controlled to minimize the drift ratio. Values of v < 0.5 m/s are recommended. Large-diameter nozzles (D ≥ 36 mm) are more suitable for conditions with large sectional wind velocity and large floating water volumes.

Fig. 9
figure 9

The relationship between the drift ratio and nozzle diameter, water drenching density, and sectional wind velocity.

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Regression model for the drift ratio

When evaluating cooling tower efficiency, the drift ratio serves as the key indicator of water-saving performance and operational effectiveness. Results from droplet tests and prior studies indicate a strong correlation between the drift ratio (W), water drenching density (q), nozzle diameter (D), and sectional wind velocity (v). To quantify this relationship, 96 sets of experimental data were analyzed, with the water drenching density (q), nozzle diameter (D), and sectional wind velocity (v) as independent variables, and the drift ratio (W) as the dependent variable. Multiple linear regression was employed to derive a functional relationship between the drift ratio and its influencing factors. To improve fitting accuracy, nozzles were grouped by diameter (32, 34, 36, and 38 mm). For each group, an exponential regression model was established, relating the drift ratio (y) to the water drenching density (x1) and sectional wind velocity (x2). The model takes the following form:

$$y=a \cdot {e^{(b{x_1}+c{x_2}+d{x_1}{x_2})}}$$
(5)

In the equation, a, b, c, and d denote the fitted parameters, x1 represents the water drenching density q (t/(h·m²)), and x2 represents the sectional wind velocity v (m/s).

By taking the logarithm of both sides of Eq. (5), the following expression is obtained:

$${\text{lny}}=\ln a+b{x_1}+c{x_2}+d{x_1}{x_2}$$
(6)

Defining Y = ln y and A = ln a, the nonlinear model in Eq. (6) can be transformed into a multiple linear regression form:

$$Y\,=\,A\,+\,b{x_1}\,+\,c{x_2}\,+\,d{x_1}{x_2}$$
(7)

The values of coefficients A, b, c, and d are obtained through linear regression, from which the relation \(a={e^A}\) is derived. By applying the least-squares method to fit the logarithmically transformed linear model, the estimated coefficients and the regression equation describing the relationships among the drift ratio (W), water drenching density (q), and sectional wind velocity (v) are summarized in Table 3.

Table 3 Multiple linear regression coefficients and regression equations.
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(1) Coefficient a represents the drift ratio under baseline conditions. For the 32 mm nozzle, a = e¹·⁸⁹⁶⁸; for the 34 mm nozzle, a = e¹·⁶⁸⁹. For the 36 mm and 38 mm nozzles, the value of a increases slightly with the diameter and remains higher than those for the 32 mm and 34 mm nozzles. (2) Coefficient b: For D = 36 mm and 38 mm, b < 0, indicating that the water drenching density has a negative effect; increasing the water drenching density reduces the drift ratio. For D = 34 mm, b = − 0.001 ≈ 0, suggesting negligible influence. For D = 32 mm, b > 0 but small, implying a weak positive effect in which a higher water drenching density slightly increases the drift ratio. (3) Coefficient c: In all cases, c > 1.35, indicating a strong positive effect. Hence, a higher sectional wind velocity substantially increases the drift ratio. The magnitudes of the different effects can be ranked as follows: D = 36 mm (c = 2.8698) > D = 38 mm (c = 2.7748) > D = 34 mm (c = 1.7581) > D = 32 mm (c = 1.3585). (4) Coefficient d (interaction term q·v): For D = 36 mm and 38 mm, d < 0, indicating that simultaneous increases in the water drenching density and sectional wind velocity reduce the drift ratio. For D = 32 mm and 34 mm, d > 0, implying that simultaneous increases in the water drenching density and sectional wind velocity enhance the drift ratio. (5) Combined effects: For D = 32 mm and 34 mm, simultaneous increases in the water drenching density and sectional wind velocity elevate the drift ratio. For D = 36 mm and 38 mm, a higher water drenching density reduces the drift ratio, whereas a higher sectional wind velocity alone increases it; however, the interaction term offsets this effect by lowering the drift ratio. (6) Model performance: The goodness-of-fit for all regression models is R2 > 0.98, demonstrating excellent predictive accuracy. (7) Model assumptions: The model is constructed under the assumption of an exponential functional form. In practical applications, it requires validation for specific nozzle types and operating conditions.

Conclusion

This study has focused on the problem of drift droplets generated during the operation of cooling towers. An experimental platform for measuring the drift ratio was independently designed and assembled by our research team, on which 96 sets of experiments on drift loss caused by drift droplets were conducted. These experiments investigated the characteristics of drift droplets in cooling towers and the variation patterns of the drift ratio. Furthermore, a fitting formula was derived to describe the relationship between the drift ratio, nozzle diameter, water drenching density, and sectional wind velocity, based on which an accurate prediction model for the drift ratio was established. The main conclusions are summarized as follows:

(1) Experiments on the drift loss due to drift droplets revealed that the drift ratio is jointly influenced by the nozzle diameter, spray density, and sectional wind velocity. For all nozzle types and water drenching densities, the drift ratio increased with the sectional wind velocity, showing an approximately exponential relationship. Based on 96 sets of experimental data, an exponential regression model was established to describe the relationship among the drift ratio (W), water drenching density (q), and sectional wind velocity (v). Grouped by nozzle diameter, the model achieved a goodness of fit exceeding 98%, demonstrating excellent predictive performance.

(2) The experimental results indicate that the nozzle diameter is a key factor influencing the drift ratio: larger diameters significantly reduce the drift ratio, particularly under higher sectional wind velocity. The sectional wind velocity must also be strictly controlled, as increases in the sectional wind velocity consistently raise the drift ratio, with the effect being more pronounced for small-diameter nozzles (D ≤ 34 mm). The influence of the water drenching density is relatively minor: its effect depends on the nozzle diameter, but overall, it is weaker than that of the sectional wind velocity. From an engineering perspective, large-diameter nozzles (D ≥ 36 mm) are preferable under high sectional wind velocity and high water volume conditions. For small-diameter nozzles, the sectional wind velocity (recommended v < 0.5 m/s) and water drenching density must be strictly controlled to minimize the drift ratio.

(3) Future studies on the drift ratio of mechanical draft wet cooling towers should incorporate a drift eliminator to examine combined influencing factors, and extend experimental ranges to include nozzle diameters beyond the present scope (e.g., D < 32 mm or D > 38 mm), in order to further validate the influence of the nozzle size on the drift ratio. It should be noted that, although clear relationships were observed between the drift ratio and influencing factors at the tested scale, further verification is required in practical applications under specific operating conditions and nozzle configurations.

(4)The conclusions and the proposed predictive model are derived from experiments conducted on a mechanical draft wet cooling tower without a drift eliminator, using reflection-type nozzles under controlled conditions. The tested operational ranges were nozzle diameter: 32–38 mm, water drenching density: 7–13 t/(h·m²), and sectional wind velocity: 0–2.5 m/s. Therefore, the results and the model are directly applicable only within these ranges and under similar structural configurations. When applied to other cooling tower types (e.g., natural draft towers or systems equipped with different nozzle types and drift eliminators), the drift behavior and model accuracy may vary, and further validation or recalibration is recommended.