Thermal Performance Analysis of Dry Unit of Hybrid Closed Cooling Tower

Effective cooling technology is essential for ensuring the sustainable development of industrial enterprises. Therefore, this study aimed to propose a hybrid closed cooling tower (CCT) with a fill unit composed of a finned pipe coil and inclined corrugated plates (ICP). A mathematical model of the hot water cooling process in the proposed cooler, operating in dry mode was developed using the number of heat transfer units (NTU). The model was validated with experimental data across different mass flow rates of process water, cooling air, and initial temperature conditions. The results showed that the finned surface of the coil pipes enhanced the heat flow rate by 2.63–3.22 times, depending on the Reynolds number by air, and improved the efficiency of heat transfer by 2.34 times.

Heat transfer; NTU; Pipe finning; Water cooling

Water recycling systems are crucial in optimizing water resource utilization, forming a cornerstone of sustainable development of modern enterprises (Liang et al., 2024; Whulanza et al., 2024; Sati and Periaswamy, 2024; Berawi., 2014). Among the various coolers used in the systems, cooling towers are the most prevalent (Madyshev et al., 2020; Bahadori, 2016). Cooling towers are categorized into wet and dry types based on the heat transfer mechanism (Nemati et al., 2024). wet cooling towers consume substantial quantities of water (Muthukumar et al., 2019), with a significant portion lost to evaporation, leading to resource wastage (Al-Wakedet and Behnia, 2007). Additionally, the operating cost is high due to the need for regular water quality stabilization (Arefimanesh & Heyhat, 2024; Gao et al., 2016). The dry cooling tower is widely used in water-scarce areas due to the lower operational and maintenance costs, as well as the water conservation ability. However, its thermal performance is considerably lower compared to wet towers (Sun et al., 2017; He et al., 2016). 

The most versatile and promising cooling tower for chilling process water is a hybrid-type design (Rahem, 2018). Its operation includes the liquid flowing through the internal heat exchanger and cooling using both air and water supplied from above through a sprayer. Since this is a closed circuit, the loss of liquid is excluded in the primary circuit, ensuring water remains clean, preventing the formation of precipitation, and avoiding corrosion of heat exchange surfaces. At low ambient temperatures, the tower operates only in dry mode, relying on air for cooling. When the ambient temperature rises above 16–18°C, supplementary spraying of the heat exchange surfaces was adopted to maintain effective cooling. 

2.1. Experimental part

The perforated ICP were located perpendicular to each other, forming a zigzag pattern within the profile of the dry unit in the hybrid cooler. Coil pipes, designated for process water, were mounted across the plates. The operation of the hybrid cooler in dry mode includes water circulating inside the coil pipes, which forms a closed cooling system. In this context, hot water, heated in the process equipment, entered through the pipe installed at the bottom of the unit. The flow sequentially passed through other pipes, moving from the bottom to the top of the unit. The process water was cooled by ambient air, which was introduced at the base of the unit, flowing perpendicular to the coil pipes and along the external surfaces of the heated coils. Furthermore, the warm air after absorbing heat, was released into the ambient environment from the unit top. In this system, the primary resistance to heat transfer arises from the air-side heat exchange process, where HTC values had significant variability, differing by several orders of magnitude. 

Figure 2 The experimental installation of the dry unit of the hybrid cooler.

Experimental studies were conducted using a water-air system to evaluate the thermal characteristics of process water chilling in the dry unit of the cooler, which featured a square cross-section of 100 mm, as detailed in Figure 1. The unit consists of 4 ICPs with a total height of 340 mm. Each plate had a thickness of 0.6 mm and a curvature radius of 7.5 mm. Holes of different diameters were drilled into the surfaces of the plates to facilitate the passage of cooling air. The pipe coil comprised a circuit of 30 copper pipes, each with a diameter of 8 mm and a length of 125 mm, connected by silicone hoses. Circular finning was applied to each pipe by fixing 19 steel rings with a thickness of 0.5 mm and spaced 5 mm apart. The fin had a height of 3.5 mm, enhancing the heat transfer surface, as presented in Figure 3.

The experiment includes 4 test series, with 2 conducted on the coil with plain-wall pipes and the remaining on finned-wall. Before conducting experiments, the cooler was turned on for 5 minutes to ensure the steady-state conditions of the system. The accuracy of the different sensors is shown in Table 1, while the locations were labeled with circles, as detailed in Figure 2.

During the tests, a constant mass flow rate of water was established in the pipe coil of the dry unit in the hybrid cooler using a valve. The water temperature was set at the inlet to the coil and observed changes did not exceed 0.2–0.4 °C, reflecting an insignificant variation in the parameter over time. When the constant values of the parameters presented in Table 1 were achieved, the rotation speed of the centrifugal fan was changed using the Mitsubishi FR E-700 inverter. As a result, the fan capacity was adjusted as well as the average air velocity in the dry unit of the hybrid cooler. After each change in the rotation speed of the centrifugal fan during a series of tests, a steady state was reached within an average of 5 to 7 minutes. To obtain the accuracy of the measurements, each experimental procedure was repeated 3–5 times. 

Figure 3 The real image (a) and the model (b) of a finned pipe of the coil of the dry unit

Uncertainty analysis was performed for each experiment according to the standard method (Coleman and Steele, 2009). For every measurement, uncertainty was obtained by calculating the standard deviation using the following formula:

Where is the standard deviation; n is the number of repetitions; xi is the measurement value; is the arithmetic average of the measurements.

The standard uncertainty or standard deviation of the average for every set of measurements, accounting for random errors and time fluctuations in the measured values with a probability of 95% was determined using the following formula:

Whereis the mean standard deviation; St is the Student coefficient.

The combined standard uncertainty for each test was determined by the following equation:

Where is uncertainty due to errors in unmeasured systematic deviations of measured parameters, which can be calculated using the following formula:

Where f represents the uncertainty influence factor, which signifies how changes in a parameter depend on other measured values denotes the tolerance deviations of measuring sensors that characterize the accuracy of measurements.

For example, when determining the uncertainty t in measuring the temperature of the hot process water at the inlet of the pipe coil, the influence of some factors should be taken into account. These factors were the temperature of the hot water tin,1 and chilled water at the outlet of the pipe coil tout,1, and the mass flow rate of water in the pipe coil Lm,1. Others include the velocity of the cooling air in the dry unit of the hybrid cooler  and the air temperature at the inlet to the dry unit tin,2 with the corresponding accuracy of the sensors used, as presented in Table 1.

Table 1 Specification of the sensors used.

The average values with combined standard uncertainty of temperatures of the process water and cooling air at the inlet of the pipe coil and dry unit of the hybrid cooler are presented in Table 2 (for the plain pipes) and Table 3 (for the finned pipes). The mass flow of water in the pipe coil varied from 72.9 kg/h to 115.2 kg/h and the mass flow of the cooling air was between 76 kg/h and 320 kg/h, corresponding to the Reynolds numbers from 1.246·103 to 5.262·103.

Table 2 Average values with a combined standard uncertainty of temperature at the inlet of the plain pipe coil (tin,1) and temperature at the inlet of the dry unit of the hybrid cooler (tin,2) (experimental data)

The combined standard uncertainty calculations were performed for water mass flow rate measurements in the pipe coil of the dry unit. The results showed that the maximum combined standard uncertainty was 3.4044 kg/h, corresponding to an average value of 115.2 kg/h, leading to a maximum deviation of 3.01%. Therefore, the data analysis achieved an uncertainty of less than 5%.

2.2. Theoretical part

A mathematical model was developed to determine the thermal performance of the dry unit in the hybrid CCT. The input parameters of this model were the mass flow rate of process water, the temperature of the process water at the inlet to the pipe coil, the mass flow rate of cooling air, the air temperature at the inlet to the irrigation unit, and the geometrical dimensions of the plain and finned pipes.

In this study, the concept of capacitance rate is defined as the product of mass flow rate and heat capacity of the flow. The capacitance rate for hot process water C1, corresponding to liquid moving inside the pipe coil, can be expressed as

C1=Lm,1cp,1. (1)

The capacitance rate for cooling air flowing around the outer surface of the coil pipes is calculated using the following formula:

C2=Lm,2cp,2. (2)

The efficiency of the heat exchanger was generally determined by the ratio of the capacitance rates Cmin/Cmax, the NTU, and the flow arrangement. When considering heat transfer through the cylindrical wall and a constant value of the HTC, the following equation can be used to determine NTU.

where Cmin is the lower value of C1 and C2, calculated using Equations 1–2.

The linear HTC through the cylindrical wall of the pipe coil, considering the thermal resistance, can be formulated as:

where Rl is the thermal resistance to heat transfer through the cylindrical pipe wall, is the thermal resistance to heat transfer from process water to the coil wall, is the resistance of thermal conductivity of the cylindrical pipe wall, is the thermal resistance to heat transfer from the pipe wall to spray water.

In the case of the plain pipes of the coil, Equation 3 can be transformed into

1 is the convective HTC between the flow of process water within the pipes and the coil wall, 2 is the convective HTC between cooling air and the outer wall of the coil pipe, is the coefficient of thermal conductivity of the pipe material, din and dout are inner and outer diameters of the coil pipe, respectively.

Table 3 Average values with a combined standard uncertainty of temperature at the inlet of the finned pipe coil (tin,1) and temperature at the inlet of the dry unit of the hybrid cooler (tin,2) (experimental data)

In the case of the finned outer surface of the pipe coil, Equation 3 can be rewritten as

where is the normalized HTC from cooling air to the outer wall of the coil pipe, and Fpl and Ffin are the areas of the plain and finned surface, respectively.

Table 4 presents Equation (4) for determining the HTC for the longitudinal flow of straight pipes, based on the water flow regime within the pipe coil (Mikhailov et al. 2007).

Table 4 Calculating equations for

For a corridor arrangement of the pipes in the coil bundle (as in the experimental installation), the average HTC for the cross-flow of cooling air was determined from Equation (5) presented in Table 5. S is the longitudinal pitch of the pipes, which is the distance between the axes of adjacent pipe rows along the airflow.

Table 5 Calculating equations for (Thulukkanam, 2024).

Where is the correction coefficient.

The Reynolds number, referred to as the diameter of the outer pipe, can be calculated using the following Equation 6.

where fmin is the minimal open flow area of the air in the pipe bundle.

The average air temperature in the dry unit of the hybrid CCT has been identified as the determining temperature in Equations 5–6. The normalized HTC from cooling air to the outer wall of the circular finned pipe of the coil was calculated using Equation 7 (Madyshev et al., 2023; Kharkov et al., 2022). 

where is the correction coefficient, considering heat transfer in vertical sections of circular fins and horizontal sections of the pipe without finning, and it can be calculated using the following equation:

E is the fin efficiency coefficient, ? is the correction factor for fin efficiency. The vertical surface area of the fins was calculated using the following equation:

the equation for the horizontal surface area of the fins and the sections between the fins is expressed as:

The fin efficiency coefficient can be determined from

where  is the hyperbolic tangent, b can be calculated using the following formula

The correction factor for fin efficiency, applicable for bhfin = 0.43–0.69 can be calculated using Equation (Yudin and Tokhtarova, 1974), which remains valid for bhfin within the range of 0.1 to 3.7:

Based on Equations 4–6, the overall HTC can be calculated for the plain pipes of the hybrid CCT coil. Additionally, Equations 7–8 should also be included for the finned pipes.

In general, the efficiency of heat transfer in heat exchangers was determined by the ratio of the actual energy exchanged to the maximum possible energy transfer (Liang et al., 2023):

In the case of series connections of pipes in the dry unit, the flow arrangement corresponds to multipass cross flow with counter connection for the passes. The number of pipes in the coil determines the number of passes. Therefore, the efficiency of the counter flow multipass dry unit of the hybrid CCT at different ratios of capacitance rates Cmin/Cmax can be defined using Equation 10, where is the efficiency of a pass (a pipe) of the coil and Cmax is the highest value of C1 and C2.

and the efficiency of a pass is given by

Based on the calculated efficiency of the dry unit, the heat flow rate Q can be determined using Equation 9. The temperature of process water at the outlet of the pipe coil of the dry unit can be expressed as:

The mathematical model should incorporate additional parameters, including overall HTC kl, NTU (for single and multiple passes), and efficiency of a pass (a pipe) of the coil . The output parameters of the model comprised the efficiency of multipass crossflow with counterflow connection of the passes heat flow rate Q, and water temperature at the outlet of the pipe coil tout,1.

To validate the mathematical model developed for the removal of heat from the surface of the plain and finned pipes in the hybrid CCT coil, experimental studies were conducted. The input parameters of the mathematical model correspond to the range of conditions used in the experiments. For the pipe coil examined, the surface area of the plain pipes was 0.0613 m2, while the area of the finned pipes was 0.227 m2. 

The finning coefficient, defined as the ratio of the finned to the plain areas, was 3.01. The thermal conductivity coefficients of copper pipes and steel fin material were assumed to be 394 W/(m·K) and 17.5 W/(m·K), respectively.

Previous studies of the dry unit of the CCT showed that the share of heat transfer due to natural convection (the share of heat loss in the ambient) reached 25%, especially at low air velocities (Madyshev and Khar’kov, 2024). In this regard, when experimentally determining the heat flow rate, the influence of heat loss on the temperature of the water at the outlet of the pipe coil tout,1 should be considered. Therefore, the experimental values of the heat flow rate can be corrected using the following formula:

where Qloss is the heat loss, expressed as

Where lb is the total length of the return bends with outer diameter db, tw,b is the average temperature of the outer wall of the return bends, and t0 is the average ambient temperature.

The heat flow from hot water into the ambient during the fluid flow in the return bends of the dry unit in hybrid CCT can be determined by heat transfer at free convection. Since the return bends possess horizontal and vertical parts, the HTC will be calculated as the average value. Therefore, with Gr·Pr from 103 to 108, the criterion equation describing the average heat transfer from the surface of horizontally curved pipes can be calculated using Equation 12, where is a coefficient considering the curvature of the return bends.

The criterion Equations (13) describing the average heat transfer from the vertically positioned curved return bends depending on the Gr·Pr value are presented in Table 6 (Madyshev et al., 2023).

Table 6 Calculating equations 

The curvature of the return bend with radius r should be considered using the coefficient, given by

In Equations 12–13, the air properties were defined at the average ambient temperature. The coefficient of heat transfer from the outer surface of the return bend to the ambient can be determined using the following formula:

The temperature of the process water at the outlet of the pipe coil, considering the correction of the experimental value of the heat flow rate Q', can be written as:

According to the determined values of HTC from the cooling air in the dry unit of the hybrid CCT, shown in Figure 4, the normalized HTC for the pipes with fins is lower than that of plain pipes in the coil. This occurs because the addition of fins increases the heat transfer area, leading to a reduction in HTC. It was important to acknowledge that the value of the correction coefficient  was less than 1. Across the entire range of Reynolds numbers analyzed, the decrease in did not exceed 12.7%.

Figure 4 HTC curves from cooling air for plain pipes (1) and finned pipes (2).

Figure 5 presents the change in the overall HTC, calculated using Equations 4–8, for the dry unit of the hybrid CCT under different types of coil pipes. Despite the slight decrease in the normalized HTC ??2 from the air side (Figure 4), the circular finning with steel fins enhanced the coefficient kl by a factor ranging from 2.56 to 2.74 times, depending on the Reynolds number. This increase was attributed to the significant expansion of the heat transfer area, which was 3.7 times for finned pipes compared to plain pipes. Additionally, the maximum fin efficiency coefficient depends on the material used, with E = 0.997 for copper and E = 0.942 for carbon steel.

Figure 5 Overall HTC curves of the dry unit for plain pipes (1) and finned pipes (2).

The estimation results of the thermal resistance of the dry unit in the hybrid CCT, presented in Figure 6, show that the primary resistance was observed in the heat transfer from the cooling airflow (Rl,?2/Rl more than 92%). Therefore, changing the mass flow of water in the pipe coil Lm,1 had practically no influence on the value of the overall HTC. Based on observation, the circular finning of the pipe led to a slight decrease (on average by 2.3–4.2%) in the ratio of Rl,?2/Rl. with an increase in the mass flow rate of the air (and, respectively, the Reynolds number).

Figure 6 Ratio Rl,?2/Rl for plain (dashed lines) and finned pipes (solid lines) under changes in the mass flow rate of process water in the pipe coil Lm,1: (1) 72.9 kg/h; (2) 108.4 kg/h; (3) 95.1 kg/h; (4) 115.2 kg/h.

The incorporation of fins into the pipe coil of the dry unit greatly enhanced NTU and the efficiency of heat transfer. In the case of plain pipes, the maximum heat transfer efficiency ? and NTU were 0.198 and 0.2266, respectively, as shown in Figure 7a. At the same time, for the case of finned pipes the ? = 0.462 and NTU = 0.652, representing 2.34 fold improvement in efficiency.

The highest values of NTU were observed at low mass flow rates of cooling air. This can be attributed to the increase in the Reynolds number for airflow, which elevates the maximum possible amount of heat transferred Qmax, leading to lowered efficiency ?. Additionally, increasing the mass flow rate in the pipe coil led to a slight improvement in the heat transfer efficiency. For example, when using plain pipes, an increase in Lm,1 by 48.5% corresponds to an average rise in ? by 1.6%, while an increase in Lm,1 by 21.1% led to an average rise of 1.3% in ? (Figure 7).

Figure 7 Efficiency for plain pipes (dashed lines) and finned pipes (solid lines) of the dry unit against NTU under changes in the mass flow rate of process water in the pipe coil Lm,1: (1) 72.9 kg/h; (2) 108.4 kg/h; (3) 95.1 kg/h; (4) 115.2 kg/h.

Calculations based on the developed mathematical model showed that the fins on the coil pipes in the dry unit of the hybrid CCT significantly enhanced the heat flow rate Q. As presented in Figure 8, the Q values, influenced by the Reynolds number, increased by a factor of 2.63–3.22. This is due to a rise in the overall HTC on average by 2.64 times, as well as an increase in the temperature difference between the water entering the inlet to the pipe coil and the air at the inlet to the unit (by an average of 3.0 °C). As the Re2 value increases, there is a tendency for the heat flow rate to improve. Furthermore, the rise in the mass flow rate of the airflow by 2.7 times in the hybrid CCT, led to an increase in Q by 70% and 50% for plain and finned pipes.

Figure 8 Experimental (points) and calculated values (solid lines) of the heat flow rate of the dry unit for plain pipes (1) and finned pipes (2) under changes in the mass flow rate of process water in the pipe coil Lm,1: (3) 72.9 kg/h, (4) 108.4 kg/h, (5) 95.1 kg/h, (6) 115.2 kg/h.

The validation of calculated and experimental data on the estimation of the thermal performance of the designed CCT dry unit showed satisfactory convergence, as presented in Figure 8. The experimental value of the heat flow rate was determined by Equation 11, considering the additional water chilling in the return bends of the dry unit during natural convection. For plain pipes of the coil, the average deviation was 6.52% at water mass flow rate Lm,1 of 72.9 kg/h and 8.43% at Lm,1 = 108.4 kg/h. The maximum relative error in this case did not exceed 14.1%.

In the case of finned coil pipes, the experimentally obtained heat flow rates were generally lower than the calculated values. At Lm,1 = 95.1 kg/h, the maximum relative error was 12.8%, with an average error of 8.37%. The smallest deviation between the experimental and calculated values of the heat flow rate occured at Lm,1 = 115.2 kg/h, where the average error was 6.14%, and the maximum reached 10.4%.

The outlet water temperature from the pipe coil of the dry unit tout,1, considering the correction of the experimental value of the heat flow rate, was estimated using Equation 14. The value of tout,1 was influenced by the initial temperature of water at the inlet to the pipe coil, the mass flow rate, and the heat flow rate. As shown in Figure 9, tout,1 decreases with an increasing Reynolds number of the air in all examined cases. The highest value was observed in the coil with plain pipes, which is caused by the low efficiency of heat transfer. When using finned pipes, as presented in Figure 9, 2 curves are obtained at different mass flow rates of water in the coil. The variation arises from differing water temperatures at the coil inlet. For instance, the inlet water temperature was 0.6–0.8 °C at Lm,1 = 115.2 kg/h, which was higher at Lm,1 = 95.1 kg/h, as detailed in Table 3). This determined the presence of the temperature difference (no more than 1.1 °C) between 2 mass flow rates of water in the finned pipe coil.

A comparison of the calculated and experimental values of the water temperature at the outlet from the pipe coil of the dry unit of the hybrid CCT proves the adequacy of the developed mathematical model. For example, when using plain pipes, the maximum deviation between the experimental and calculated values of tout,1 is 0.39% with the mass flow rate of water in the coil Lm,1 of 72.9 kg/h, and 0.26% with Lm,1 = 108.4 kg/h. In the case of finned pipes, the maximum deviation of the calculated and experimentally obtained values of the water temperature is 0.82% at Lm,1 = 95.1 kg/h and 0.635% at Lm,1 = 115.2 6 kg/h (Figure 9).

Figure 9 Experimental (points) and calculated values (solid lines) of the water temperature at the outlet of the pipe coil for plain pipes (1) and finned pipes (2) under changes in the mass flow rate of process water in the pipe coil Lm,1: (3) 72.9 kg/h; (4) 108.4 kg/h; (5) 95.1 kg/h; (6) 115.2 kg/h.

The results on the distribution of thermal resistance of heat transfer, HTC, and efficiency of the developed design of the dry unit of the hybrid CCT with the finned pipe coil and the ICP were obtained. The application of the mathematical model makes it possible to evaluate the heat transfer efficiency at different mass flow rates of cooling air and process water. Furthermore, the model can be used to improve the heat flow rate by selecting the appropriate design characteristics of the pipe bundle, including the flow arrangement and fin dimensions. 

Further studies of the hybrid CCT for chilling process water, operating in dry mode, are intended to determine the optimal ratio of gas and liquid phase rates to improve the thermal performance, as well as to evaluate the effect of the fin material of the coil pipes. The impact of the initial water and air temperatures on the thermal characteristics of the dry unit of the hybrid CCT was also planned.

In conclusion, this study developed a mathematical model to estimate the heat transfer efficiency of the dry unit in hybrid CCT. The results showed that the variation in the mass flow of water in the pipe coil from 72.9 kg/h to 115.2 kg/h did not influence the linear HTC in the unit operating in dry mode. This is because the primary thermal resistance of more than 92% occurred in heat transfer from cooling air. The finning of the pipes led to increased NTU and a rise in the heat transfer efficiency by 2.34 times.  Furthermore, a finned coil of the dry unit of the CCT, which operated in dry mode, facilitated the rise in the heat flow rate by 2.63–3.22 times, depending on the Reynolds number for the cooling airflow. The proposed mathematical model of the water chilling in the pipe coil of the dry unit was in line with the results of the experimental determination of the heat flow rate (the maximum deviation is less than 14.1%) and the temperature of the water at the outlet of the coil (the maximum deviation is 0.82%).

The authors are grateful to the Russian Science Foundation, received in 2023, Project No. 23-79-01034), https://rscf.ru/project/23-79-01034/, for supporting the study.

Author Contributions

I. Madyshev: Conceptualization, Funding acquisition, Investigation, Methodology, Project administration, Writing – original draft. V. Kharkov: Data curation, Investigation, Resources, Supervision, Writing – review & editing. M. Vakhitov: Software, Visualization. M. Kuznetsov: Formal analysis, Validation.

Conflict of Interest

The authors declare no conflicts of interest.

List of abbreviations and symbols

C = capacitance rate, W/K

cp = heat capacity, J/(kg·K)

CT = cooling tower

d = diameter of the coil pipe, m

F = surface area, m2

Gm = mass flow rate of gas (air), kg/s

Gr = Grashof number, unitless

h = height, m

HTC = heat transfer coefficient

ICP = inclined-corrugated plates

k = overall HTC, W/(m?K)

l = total length of the coil pipes, m

Lm = mass flow rate of liquid (water), kg/s

NTU = heat transfer units, pcs.

Nu = Nusselt number, unitless

Pr = Prandtl number, unitless

Q = heat flow rate, W

R = thermal resistance, (m?K)/W

Re = Reynolds number, unitless

s = spacing, m

t = temperature, K

z = number of passes, pcs.

Greek Symbols

Subscripts

* = normalized value

1 = process water

2 = cooling air

b = return bend

f = film

fin = fin/finning

in = inlet, inner

l = linear

max = maximum

min = minimum

out = outlet, outer

pl = plain

w = wall

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