Comparative Study on the Cooling Characteristics of Different Fill Layout Patterns on a Single Air Inlet Induced Draft Cooling Tower

Abstract

To enhance the cooling capacity of a single air inlet induced draft cooling tower (SIDCT), the stepped fill layout pattern is proposed in this paper. A three-dimensional numerical model is established and validated by field measurement data. The cooling capacity of towers equipped with uniform fill and stepped fill is compared under various crosswind velocities (0 m/s–12 m/s) and crosswind angles (0°–180°). The results showed that the ventilation rate of the total tower with stepped fill is increased. Under the studied crosswind velocity and angle, the cooling capacity of the stepped fill tower is superior to the uniform fill tower. After using stepped fill, the mean drop of outlet water temperature rises by 0.29 °C, 0.27 °C, 0.17 °C, 0.10 °C, and 0.19 °C, corresponding to crosswind angles from 0° to 180°. The increment of cooling capacity is the maximum under the crosswind angles of 0° and 45° and is the minimum under the crosswind angles of 90° and 135°. The maximum increased value of $N$ is 0.65 under the crosswind velocity of 4 m/s, 0.85 under 8 m/s, and 0.95 under 12 m/s.

1. Introduction

Mechanical draft cooling towers (MDCTs) are mainly cooling equipment, with heat transfer from circulating water (heat water) to the ambient air. With different installation positions of a fan, MDCTs can be classified into forced draft cooling towers (FDCTs) and induced draft cooling towers (IDCTS) [1]. MDCTs are widely used in metallurgy, the pharmaceutical industry, and air conditioner cooling. The cooling capacity and ventilation performance of MDCTs markedly affect the working efficiency of these industrial processes. In recent years, researchers have been interested in the effect mechanism of ambient wind on the performance of the MDCT. Performance optimization methods of MDCTs are becoming research hotspots.

Many investigations have been performed by scholars to analyze the impact of operation parameters on ventilation and thermal performance of the MDCT. Rahmati et al. [2,3] revealed that input parameters influence the cooling tower performance, including hot water temperature, water flow rate, air mass flow rate, and stage numbers of packing, with combination thermal image technology. The results indicated that the air mass flow rate, hot water temperature, and stage numbers of packing directly influence cooling efficiency. Meanwhile, the water temperature difference and cooling efficiency are larger when the water flow rate is lower. To estimate the water uptake rate of an environment’s air, Naik and Muthukumar [4] proposed a calculation model for a cross-flow wet cooling tower, finding that the water evaporation loss increases with the rising temperature of inlet water. Lucas et al. [5,6] clarified the influence of drift eliminators on thermal performance and concluded an optimization scheme between different water distribution systems and drift eliminators for a MDCT. Their results showed that drift eliminators can be seen as an additional fill with the heat and mass transferred, and the pressure water distribution systems have superior cooling capacity. To obtain thermal characteristics of a SIDCT, Chen et al. [1] conducted field measurement for the SIDCT under crosswind conditions, elaborating that the air–water ratio and heat transfer coefficient increase with the rising crosswind velocity under the crosswind directions of the α₁ and α₂, however drop under α₃ (i.e., α₁, α₂ and α₃ standing for the angle between the crosswind direction and the normal of air inlet plane). That is, the crosswind direction has a significant influence on the thermal performance of the SIDCT due to special form of the air inlet. However, this study fails to discuss the impact on the crosswind angles of 90° and 135° under the anti-clockwise direction of normal of air inlet. Singh et al. [7,8,9,10] experimentally investigated trickle, film, splash, and wire mesh fill impact on water evaporation, heat rejection, and Merkel number. They demonstrated that the Merkel number is directly influenced by the air–water ratio, and the wire mesh is the best fill pattern in lab conditions; then, an optimization model was proposed to improve thermal performance of the tower. To degrade energy waste, Muller and Craig [11] conducted a control model using a genetic algorithm, and provided an optimization scheme of the pump and fan combination. Ruiz et al. [12] performed drift deposition for the MDCT in the urban environment and discussed the relationship between environmental parameters and downwind deposition, finding that area and amount of drift deposition are substantially impacted by wind velocity and direction. Viljoen et al. [13] established a dynamic model for a MDCT with parallel heat exchangers, pumps, and cooling water networks; however, the heat transfer process was not mentioned. Based on the MDCT, Guo et al. [14] developed a parallel hybrid model to optimize and evaluate the cooling ability of the tower. In past years, the influence of crosswind on the Merkel number [15], water droplet diameter distribution [16], cooling capacity [17], ventilation efficiency [18], and air intake uniformity coefficient [19] of towers have been researched substantially, with research aimed at natural draft cooling towers and not mechanical draft cooling towers.

Many measures, including the dry–wet hybrid rain zone, air duct, wind deflector, arranging fan inside the tower etc., have been employed by scholars.

To intensify ventilation rate and decrease water temperature of the tower under crosswind conditions, Zhang et al. [19,20] presented a dry–wet hybrid rain zone, which can classify an existing rain zone into the dry parts and wet parts. Their finding was that the dry–wet hybrid rain zone can increase ventilation rate and eliminate the high temperature zone of center of the tower. To sufficiently use the water-dropping potential of the rain zone, Dang et al. [21] and Zhou et al. [22] installed an axial fan on the top of the fill. The fan was driven by the water-dropping potential of the rain zone, and the influence of the fan diameter on pumping force of cooling tower was analyzed. Chen et al. [23,24] firstly arranged the air duct in the rain zone, and a 3D numerical model was performed for this study. The results showed that the ventilation rate of the center of the rain zone was significantly enhanced. The water surface temperature reduced by a maximum of 0.68 °C compared with no air duct. For making full use of the cooling capacity of the fill in a natural draft wet cooling tower, Zhou et al. [25] and Gao et al. [26] presented a non-uniform fill so that the height of the fill is higher in the air inlet, while lower in the center of the tower, and found that non-uniform fill improved thermal performance and decreased outlet water temperature, compared to uniform fill. Lye et al. [27] also researched non-uniform fill in the wet cooling tower with high-level water-collecting devices, where the height of fill is higher in the center of the tower region and the height is lower in the air inlet. The results revealed that the uniformity of the airflow distribution is improved when one adopts a non-uniform fill. The research conclusion indicated that injecting flue gas into the tower can intensify the cooling capacity of the tower [28,29,30].

A non-uniform fill is widely used to improve the cooling performance of the natural draft wet cooling tower. However, the application of non-uniform fill in MDCT has not been found. There are many differences between the natural draft wet cooling tower and the MDCT, such as the form of air intake, aerodynamic field and pumping force distribution inside the tower. Therefore, research on the non-uniform fill in the MDCT is necessary.

In this study, a stepped fill is applied to a SIDCT for the first time. The synergistic mechanism of the stepped fill of the SIDCT is analyzed under the studied crosswind velocity and angle. To conduct this research more accurately, a 3D numerical model of the SIDCT with stepped fill is established and validated by field measurement dates. The parameters, including air dynamic field, Merkel number, water temperature drop, and the cooling percentage in each zone, are investigated for both types of tower. The findings of this study produced a theoretical reference for the energy-saving optimization of a SIDCT.

2. Numerical Model

In this part, the working process of the SIDCT and the structure size of stepped fill are introduced. The mathematical model, boundary conditions, and solution method are proposed. Finally, the verification of both grid independence and mathematical model is conducted.

2.1. Geometric Model

The structural sketch of the SIDCT is described in Figure 1. Figure 1a is a sketch of the measured SIDCT and Figure 1b is working principle of the SIDCT. The SIDCT has a width of 18 m, a depth of 16 m, a height of 17.5 m and an air inlet height of 7.8 m. A fan is installed at the tower outlet with a diameter of 10 m and a design total pressure of 150 Pa. The total water spray area is 288 m² and the fill thickness is 1.5 m. The circulating water is distributed by a water distribution system, which flows into the spray zone, fill zone, and rain zone. The air is drafted into the tower from the air inlet, then it passes into the rain zone, fill zone, spray zone, and flows out from the tower outlet. The specific arrangement of the stepped fill is shown in Figure 2. It begins with an air inlet, and the fill is numbered as part 1, part 2, and part 3 sequentially. Part 1, part 2, and part 3 have the same width, but the height is 1.5 m, 1.25 m, and 1 m and the depth is 5 m, 6 m, and 5 m, respectively. The volume of the stepped fill and uniform fill is equal. According to the site operation conditions of the SIDCT, the circulating water flow rate and temperature are 4522 m³/h and 33 °C. The angles between wind direction and normal of the air inlet are 0°, 45°, 90°, 135°, and 180°, as shown in Figure 3. The ambition wind velocities are defined as 0 m/s, 2 m/s, 4 m/s, 6 m/s, 8 m/s, 10 m/s, and 12 m/s in this paper.

2.2. Governing Equations

The ambient air around SIDCT can be taken as an incompressible gas with slight variation in pressure and temperature. Therefore, the steady-state Reynolds averaged Navier–Stokes equations are employed to describe airflow around the cooling tower, which can be closed by the standard κ-ε turbulence model.

2.2.1. Governing Equations for Air Flow

The mass conservation equation:

$$\nabla \cdot \left({\rho }_{\mathrm{a}}\overrightarrow{v}\right)=S_{\mathrm{m}}$$

(1)

where ${\rho }_{\mathrm{a}}$ is the air density, kg/m³; $\overrightarrow{\nu }$ is the air velocity vector; $S_{\mathrm{m}}$ is mass source term, W/m³.

The momentum conservation equation:

$$\nabla \cdot ({\rho }_{\mathrm{a}}\overrightarrow{v}\overrightarrow{v})=-\nabla p+\nabla \left(\mu +{\mu }_{\mathrm{t}}\right)\left[\left(\nabla \overrightarrow{v}+\nabla {\overrightarrow{v}}^T\right)-\frac{2}{3}\nabla \overrightarrow{v}I\right]+\rho \overrightarrow{g}+\overrightarrow{F}$$

(2)

where $p$ represents the static pressure, Pa; $\mu$ and ${\mu }_{\mathrm{t}}$ are laminar viscosity and turbulent viscosity coefficients of air, Pa·s; $\rho \overrightarrow{g}$ is gravitational body; $\overrightarrow{F}$ is external body forces, N; $I$ stands for unit tensor.

The energy conservation equation:

$$\nabla \left({\rho }_{\mathrm{a}}\overrightarrow{v}{\displaystyle {\int }_{t_{\mathrm{ref}}}^t{c}_{\mathrm{a}}dt}\right)=\nabla \left(\left(k_1+k_2\right)\nabla T-{\displaystyle \sum _{\mathrm{j}}{h}_{\mathrm{j}}{\overrightarrow{J}}_{\mathrm{j}}}\right)+S_{\mathrm{ae}}$$

(3)

where $t_{\mathrm{ref}}$ is the referent temperature, °C; $h_{\mathrm{j}}={\displaystyle {\int }_{t_{\mathrm{ref}}}^t{c}_{\mathrm{a}}}dt$ stands for the sensible enthalpy of the species $j$, J/kg; the $k_1$ and $k_2$ are the laminar and turbulence thermal conductivity coefficient, W/(m²·K). ${\overrightarrow{J}}_{\mathrm{j}}$ represents the diffusion flux of species $j$; $S_{\mathrm{ae}}$ indicates the energy source, W/m³.

The species transport equations:

$$\nabla \cdot \left({\rho }_{\mathrm{a}}\overrightarrow{v}{Y}_{\mathrm{v}}\right)=-\nabla \cdot \left[{\rho }_{\mathrm{a}}\left(D+D_{\mathrm{t}}\right)\nabla Y_{\mathrm{v}}\right]+S_{\mathrm{m}}$$

(4)

where $Y_{\mathrm{v}}$ represents the mass fraction of the vapor; $D$ and $D_{\mathrm{t}}$ stand for laminar and turbulence diffusion coefficient of moist air, m²/s.

The state equation of moist air:

$${\rho }_{\mathrm{a}}=\frac{p_{\mathrm{s}}}{\left(\frac{R}{M_{\mathrm{a}}}t\right)}$$

(5)

where $p_{\mathrm{s}}$ is air static pressure; $R$ is the universal gas constant; $t$ is the local air temperature; $M_{\mathrm{a}}$ is the air molecular weight.

The stand κ-ε turbulence models:

$$\nabla \cdot \left({\rho }_{\mathrm{a}}\overrightarrow{v}k\right)=\nabla \cdot \left[\rho \left(\mu +\frac{{\mu }_{\mathrm{t}}}{{\sigma }_{\mathrm{k}}}\right)\nabla k\right]+G_{\mathrm{k}}+G_{\mathrm{b}}-{\rho }_{\mathrm{a}}\epsilon$$

(6)

$$\nabla \cdot \left({\rho }_{\mathrm{a}}\overrightarrow{\nu }\epsilon \right)=\nabla \cdot \left[{\rho }_{\mathrm{a}}\left(\mu +\frac{{\mu }_{\mathrm{t}}}{{\sigma }_{\epsilon }}\right)\nabla \epsilon \right]+C_{1\epsilon }\frac{\epsilon }{k}\left(G_k+C_{3\epsilon }{G}_{\mathrm{b}}\right)-C_{2\epsilon }{\rho }_{\mathrm{a}}\frac{{\epsilon }^2}{k}$$

(7)

$${\mu }_{\mathrm{t}}={\rho }_{\mathrm{a}}{C}_{\mu }\frac{k^2}{\epsilon }$$

(8)

$$C_{3\epsilon }=\tanh \left|\frac{v_z}{\sqrt{v_{\mathrm{x}}^2+v_{\mathrm{y}}^2}}\right|$$

(9)

Elaborating on $G_{\mathrm{k}}$, $G_b$, $C_{1\epsilon }$, $C_{2\epsilon }$, $C_{3\epsilon }$, $C_{\mu }$, ${\sigma }_{\mathrm{k}}$ and ${\sigma }_{\epsilon }$ can be seen in Launder et al. [31].

2.2.2. Governing Equations for Circulating Water

The inclination movement of circulating water is ignored into the cooling tower. The final control volume is revealed in Figure 4; the governing equations of circulating water are as follows.

$$\frac{\mathrm{d}q}{\mathrm{d}\left(-z\right)}=-S_{\mathrm{m}}$$

(10)

$$\frac{\mathrm{d}}{\mathrm{d}\left(-z\right)}\left(c_w{t}_{w}q\right)=-S_{\mathrm{we}}$$

(11)

where $q$ is circulating water mass flow rate, kg/(m³·s); $S_{\mathrm{m}}$ is the water volume evaporation rate, kg/(m³·s); $S_{\mathrm{we}}$ is the volume energy reduction rate of water.

The momentum conservation equation:

$$\frac{\mathrm{d}{\nu }_{\mathrm{wz}}}{\mathrm{d}\left(-\mathrm{z}\right)}=\frac{\left({\rho }_{\mathrm{w}}-\rho \right)g}{{\rho }_{\mathrm{w}}\cdot v_{\mathrm{wz}}}-\frac{f_{\mathrm{z}}}{m_{\mathrm{w}}\cdot v_{\mathrm{wz}}}$$

(12)

where $v_{\mathrm{wz}}$ is the dropping speed of water droplets, m/s; $f_{\mathrm{z}}$ is the resistance force form the airflow, N.

2.2.3. Heat and Mass Transfer from Water to Air

Based on a previous report [32], the expressions of $S_{\mathrm{m}}$, $S_{\mathrm{ae}}$, $S_{\mathrm{we}}$ are defined as:

$$S_{\mathrm{m}}=K_{\mathrm{a}}\left({\chi }_{\mathrm{w}}^{″}-\chi \right)$$

(13)

$$S_{\mathrm{ae}}=\left(K_{\mathrm{h}}+S_{\mathrm{m}}{c}_{\mathrm{v}}\right)\left(t_{\mathrm{w}}-t_{\mathrm{a}}\right)$$

(14)

$$S_{\mathrm{we}}=K_{\mathrm{h}}\left(t_{\mathrm{w}}-t_{\mathrm{a}}\right)+S_{\mathrm{m}}{r}_{\mathrm{w}}$$

(15)

where $K_{\mathrm{a}}$ is mass transfer coefficient, kg/(m³·K). $K_{\mathrm{h}}$ is thermal conductivity, Kw/(m³·K). ${\chi }_{\mathrm{w}}^{″}$ and $\chi$ represent the humidity ratio of the saturated air membrane at the vapor water interface and the humidity ratio of airflow, kg/kg, respectively. $c_{\mathrm{v}}$ is the specific heat of water vapor, J/(kg °C); $r_{\mathrm{w}}$ is latent heat of vaporization of circulating water, kJ/kg.

In the rain and spray zone, $K_{\mathrm{a}}$ and $K_{\mathrm{h}}$ can be written as follows:

$$K_{\mathrm{a}}={\rho }_{\mathrm{a}}{N}_{\mathrm{wd}}{A}_{\mathrm{wd}}\frac{\gamma }{d_{\mathrm{wd}}}\left(2.0+0.6R{\mathrm{e}}_{\mathrm{wd}}^{1/2}S{c}_{\mathrm{a}}^{1/3}\right)$$

(16)

$$K_{\mathrm{h}}=N_{\mathrm{wd}}{A}_{\mathrm{wd}}\frac{\lambda }{d_{\mathrm{wd}}}\left(2.0+0.6R{\mathrm{e}}_{\mathrm{wd}}^{1/2}{\mathrm{Pr}}_{\mathrm{a}}^{1/3}\right)$$

(17)

where $N_{\mathrm{wd}}$ represents the number of water droplets per unit volume; $A_{\mathrm{wd}}$ stands for the surface area of one droplet, m²; the $S{c}_{\mathrm{a}}$ means the Schmidt number of moist air; ${\mathrm{Pr}}_{\mathrm{a}}$ represents the Prandtl number of moist air.

In the fill zone, according to fill experiment, $K_{\mathrm{a}}$ and $K_{\mathrm{h}}$ can be expressed as Equations (18) and (19).

$$K_{\mathrm{a}}=B{q}^{\mathrm{m}}{g}_{\mathrm{a}}^{\mathrm{n}}$$

(18)

$$K_{\mathrm{h}}=L{e}_{\mathrm{f}}{K}_{\mathrm{a}}$$

(19)

where fill characteristics decide $B$, $m$ and $n$; $g_{\mathrm{a}}$ is air ventilation density of tower outlet surface, kg/m³; $L{e}_{\mathrm{f}}$ is the Lewis factor form Bosnjakovic formula [33].

For rain and spray zone, the water droplets are assumed to be perpendicular (z direction) due to less movement in x and y direction, and the air flow resistance is expressed as follows:

$$F_{\mathrm{i}}=-\frac{6q{C}_{\mathrm{d}}R\mathrm{e}\mu }{8{\rho }_{\mathrm{w}}\left|v_{\mathrm{wz}}\right|d_{\mathrm{p}}^2}\left(v_{\mathrm{z}}+v_{\mathrm{wz}}\right)$$

(20)

where $i$ is the coordinates x, y, z; $v_{\mathrm{wz}}$ represents water droplets speed, m/s; $\mathrm{Re}$ is Reynolds number; $C_{\mathrm{d}}$ is resistance coefficient.

In the fill zone, the air flow resistance can be taken as Equation (21):

$$F_{\mathrm{z}}=\frac{\Delta P}{H_{\mathrm{fill}}}$$

(21)

$$\Delta P={\rho }_{\mathrm{a}}A{v}_{\mathrm{z}}^M$$

(22)

$$A=0.0008q^2+0.0122q+0.741$$

(23)

$$M=-0.0015q^2+0.0152q+2.00$$

(24)

where $\Delta P$ represents the pressure drop of the air passing the fill, Pa. $H_{\mathrm{fill}}$ stands for the height of fill, m.

2.3. Boundary Conditions and Solution Method

To sufficiently show the effect of environmental conditions on the aerodynamic field and temperature field, the simulation domain is much larger than the studied SIDCT. The simulation domain is depicted in Figure 5. The simulation domain is a cuboid with a size of 140 m × 140 m × 100 m. Under windless conditions, for the simulation domain, the pressure inlet is selected as the inlet boundary condition, and the top boundary is set as pressure outlet. The bottom boundary and tower shell are set as no sliding wall with the standard wall functions in near-wall treatment used in Figure 5. Under crosswind condition, the windward boundary is set as velocity inlet and the leeward boundary is set as the pressure outlet.

In this work, the spray zone, fill zone, and rain zone are taken as the heat and mass transfer zone with the reversing flow between air and water. In the water spray zone, the initial velocity of water droplet is 3.5 m/s with a diameter of 3 mm. Below the fill zone, the water droplet has an initial velocity of 0.4 m/s with the diameter of 5 mm [34,35].

The relationship between the crosswind velocity and the simulation domain height is shown in Equation (25) [36].

$$\frac{v_{\mathrm{a}}}{v_{\mathrm{a},\mathrm{ref}}}={\left(\frac{z}{z_{\mathrm{ref}}}\right)}^{0.28}$$

(25)

where $v_{\mathrm{a}}$ stands for wind speed in the height of $z$, m/s; $v_{\mathrm{a},\mathrm{ref}}$ represents reference speed in the reference height of $z_{\mathrm{ref}}=10$, m/s.

Fluent software is used for air–water flowing calculation in this paper. The circulating water flow process is described by User Defined Function (UDF). The circulating water flow rate, water temperature, and water droplet speed of both the spray zone and rain zone are employed by User Defined Scalars (UDS). The coupling relationship between pressure–velocity adopts the SIMPLE method, and all fluxes are discretized by second-order upward scheme, except the pressure term which is discretized by the body force weighted scheme. The numerical calculation can be regarded as convergent when the calculation residual of energy equation is no more than 10⁻⁶ and the other less than 10⁻⁴, and the outlet water temperature varies less than 0.01 °C under 100 solver iterations.

2.4. Mesh Scheme

The hexahedron cell is adopted in this study. The simulation domain can be divided into four zones (i.e., mass and heat transfer zone, tower shell zone, fan zone, and outside the tower zone), which are merged in Fluent by the interface. To enhance calculation accuracy, the mesh of the mass and heat transfer zone is refined.

The outlet water temperature is the important symbol of the tower cooling capacity and is selected as an evaluating indicator of mesh independence. For elaborating uncorrelated values between mesh number and simulation result, the four groups mesh system that mesh numbers of 784,915, 1,196,816, 1,488,224, 1,804,915 are established in

Table 1. Mesh independence validation.

Mesh Number	784,915	1,196,816	1,488,224	1,804,915
Inlet water temperature $t_{1\mathrm{d}}$ (°C)	33.02	33.02	33.02	33.02
Measured outlet water temperature $t_{2\mathrm{d}}$ (°C)	24.26	24.26	24.26	24.26
Numerical outlet water temperature $t_{2\mathrm{c}}$ (°C)	23.63	23.89	24.08	24.10
Error $\left|t_{2\mathrm{d}}-t_{2\mathrm{c}}\right|$	0.63	0.37	0.18	0.16
Relative error $\sigma =\left|\frac{t_{2\mathrm{d}}-t_{2\mathrm{c}}}{t_{1\mathrm{d}}-t_{2\mathrm{d}}}\right|\times 100\%$ (%)	7.20	4.22	2.05	1.71

. The corresponding operating parameters are that the ambient dry-bulb temperature is 15.1 °C, ambient wet-bulb temperature is 10.1 °C, crosswind angle is 0°, crosswind velocity is 2.13 m·s⁻¹, water flow rate is 4520 m³·h⁻¹. Based on Table 1, the relative error is less than 3% when the mesh numbers exceed 1,488,224, and the calculation accuracy meets the requirement. Therefore, the mesh numbers of 1,488,224 are adopted in this work.

2.5. Validation

For proving the accuracy of the numerical model, five groups of outlet water temperature with different operating conditions are obtained (i.e., B1–B5, standing for five groups of measured conditions in the chemical enterprise in Shandong, China). Monitoring parameters and corresponding measuring instruments for the measurements are listed in

Table 2. Monitoring parameters and corresponding measuring instrument for the measurement.

Monitoring Parameters	Measuring Instrument	Accuracy
Circulating water flow rate	FLEXIM ultrasonic flow meter	±0.5%
Inlet and outlet water temperature	Platinum resistance thermometer	±0.1 °C
Ambient air dry–wet bulb temperature	Platinum resistance thermometer	±0.1 °C
Atmospheric pressure	DYM3 aneroid barometer	±0.01 kPa
Environmental crosswind velocity	Cup anemometer	±0.1 m/s
Environmental crosswind direction	Anemoscope	±0.8%

. The ambient wind velocity, wind direction, ambient air dry–wet bulb temperature, and atmospheric pressure were measured at a height of 3 m from the ground and a distance of 40 m from the SIDCT. The measurement process under each working condition takes 15 min, during which the ambient conditions are measured every 20 s. A total of 25 measuring points are set on the water surface. The distribution of water surface temperature measuring points is shown in Figure 6. The water temperature is measured three times under each measured condition, and the arithmetic average of the three measurements is designated as the measured outlet water temperature.

According to operating parameters, five groups of outlet water temperatures are calculated in

Table 3. Model validation according to measuring values.

Actual Work Conditions	B1	B2	B3	B4	B5
Atmospheric pressure (kPa)	101.7	101.6	101.7	101.7	101.6
Ambient dry-bulb temperature (°C)	15.1	15.3	14.9	15.1	14.8
Ambient wet-bulb temperature (°C)	10.1	10.2	10.1	10.1	9.9
Crosswind angle (±5°)	0°	0°	45°	90°	180°
Crosswind velocity (m·s−1)	2.13	3.86	1.71	4.28	4.36
Water flow rate (m3·h−1)	4520	4516	4532	4526	4518
Inlet water temperature $t_{1\mathrm{d}}$ (°C)	33.02	33.11	33.08	33.05	33.09
Measured outlet water temperature $t_{2\mathrm{d}}$ (°C)	24.26	24.04	24.63	24.81	25.03
Numerical outlet water temperature $t_{2\mathrm{c}}$ (°C)	24.08	23.78	24.44	24.65	24.85
Error (°C)	0.18	0.26	0.19	0.16	0.18
Relative error (%)	2.05	2.87	2.25	1.94	2.25

. It can be seen that under different velocities and angles of crosswind, the relative errors of outlet water temperature between measurement values and calculated values are very small. The maximum relative error is less than 3%. Therefore, the numerical model of thermal performance of the SIDCT is accurate and credible in this paper.

3. Results and Discussion

3.1. Ventilation Rate

The SIDCT has only one air inlet and the aerodynamic field in the SIDCT is very uneven. According to Chen et al. [1], the worst heat transfer zone is the inner zone of the SIDCT. The larger ventilation rate occurs near the air inlet, while less occurs inside the tower, leading to weakening intensity of heat and mass transfer in the tower. In order to optimize the aerodynamics field and improve the ventilation rate in the tower, the thickness of the fill around the air inlet is increased and is reduced in the tower, which is called stepped fill. Due to large ventilation rate in the air inlet, the increasing thickness of fill can enhance the intensity of heat and mass transfer. The decreasing thickness of fill in the tower can increase ventilation and enhance the cooling capacity of the tower.

The three monitor surfaces, corresponding to part 1, part 2, and part 3 of the stepped fill, are established above the drift eliminator. The variation of ventilation rate at different monitor surfaces with the crosswind angle is shown in Figure 7. Compared with the uniform fill, regardless of the crosswind velocity of 4 m/s or 8 m/s, the ventilation rate of part 1 of stepped fill is always less than that of uniform fill. However, the ventilation rate of part 2 and 3 of stepped fill is greater than that of uniform fill. The fill thickness of part 1 is increased, leading to rising airflow resistance and decrease ventilation rate. However, the thickness of fill is reduced in part 3, resulting in an increasing ventilation rate. Due to the structure of stepped fill, the ventilation rate of part 2 is slightly increased. At low wind speed (4 m/s), the minimum ventilation rate occurs at the crosswind angle of 135°. However, at high wind speed (8 m/s), the crosswind angle corresponding to the minimum ventilation rate moves slightly forward compared to that of the low wind speed. In general, the stepped fill can increase the ventilation rate of the total tower and make the airflow distribution more uniform.

Figure 8 indicates the air density difference at the eliminator top (${\rho }_{\mathrm{n}}$ for the stepped fill, ${\rho }_{\mathrm{u}}$ for the uniform fill). The pumping force of the SIDCT is mainly from the fan, and the proportion of the pumping force causing the density difference of moist air is very small. For part 1 of stepped fill, the thickness of fill increases, but the airflow resistance enhances. However, for the cooling capacity, the positive contribution by increased thickness of fill is greater than the adverse influence caused by airflow resistance. Although the airflow velocity decreases in part 1, but the total of heat and mass transfer increases, and the cooling capacity of the tower still rises. The capacity with heat and mass transfer of air per unit mass increases and air density reduces in the part 1. As the fill thickness decreases, the air resistance decreases in part 3. The capacity of the heat and mass transfer is enhanced with the ventilation rate increased. However, the capacity of the heat and mass transfer of unit air is weakened. The moist air density of the part 3 increases slightly. For the part 2, the thickness of fill is unchanged, but the ventilation rate is slightly increased. The capacity of the heat and mass transfer of air per unit mass changes very little and the air density is slightly reduced.

Figure 9 and Figure 10 show the streamlines at the plane of xz and z = 4 m with the crosswind velocity of 8 m/s. When the crosswind angle is 0°, the air velocity gradually decreases from the air inlet to the inner zone of the tower. There are two vortexes derived from low-pressure areas in the leeward side of the tower.

Under the crosswind angle of 45°, there are three vortexes around the tower. One of them occurs inside the tower and the others are outside the tower. The volume of the vortex inside the tower is larger, leading to increased airflow resistance and reduced ventilation volume of the tower.

As seen in Figure 9, the part of moist air leaving the tower flows into the tower again under the crosswind angle of 90°. The heat and mass transfer from water to air is weakened because of decreasing temperature differences and moisture content difference. The moist air can not only prevent cold air entering the tower, but also decrease evaporation heat transfer from water to air, and further reduce the cooling capacity of the tower.

Under the crosswind angle of 135°, at the plane xz, a big vortex occurs in front of the air inlet. As depicted at z = 4 m surface, there are three vortexes, one of them is inside the tower and the others are outside the tower. It can be seen that the big vortex prevents airflow entering the tower, and only partial air leaving from the vortex edge enters the cooling tower along a negative direction of crosswind with lower velocity. Meanwhile, another vortex appears in the leeward wall of the tower where air velocity is low.

Under the crosswind angle of 180°, two vortexes are formed inside the tower. The center of the vortex appears at the tower lateral wall. The place between two vortexes has larger air velocity.

3.2. Cooling Capacity of SIDCT

Figure 11 shows the temperature differences of water outlet temperature with different fill patterns ($T_{\mathrm{n}}$ for the stepped fill, $T_{\mathrm{u}}$ for the uniform fill). The water outlet temperature of the stepped fill tower is lower than that of uniform fill, regardless of the crosswind velocity of 4 and 8 m/s. The cooling capacity of fill in all three parts is increased. For part 1, the thickness of fill increases, leading to an increase of heat transfer area between the air and water, which causes the cooling capacity to be enhanced, although the ventilation rate is slightly reduced. For part 2 and 3, the ventilation rate increases, leading to increases in the ratio of air and water, and the cooling capacity is optimized.

The changes of water surface temperature with various crosswind velocities and angles are depicted in Figure 12. The water temperature drop of the stepped fill tower is larger than that of the uniform fill, regardless of both the crosswind velocity and angle studied. The mean drop of outlet water temperature rises by 0.29 °C, 0.27 °C, 0.17 °C, 0.10 °C, and 0.19 °C, corresponding to the crosswind angles from 0° to 180°. When we adopt a stepped fill, the maximum value of water temperature drop appears at the crosswind angle of 0°, and the minimum value is at the crosswind angle of 135°. By analysis, for both types of tower, the circulating water temperature drop increases under the crosswind angles of 0° and 45° with the rising crosswind velocity. However, it always decreases under the crosswind angles of 90° and 180°, and decreases first and then rises slightly in the crosswind angle of 135°. For a common operating situation (wind velocity of 0 m/s–4 m/s), the average drop of water temperature is sequentially 0.31 °C, 0.27 °C, 0.26 °C, 0.18 °C, and 0.22 °C under the crosswind angles of from 0° to 180°. That is, there is much higher cooling performance with stepped fill under low crosswind velocity.

3.3. Merkel Number

For fully expressing the cooling capacity of tower, the Merkel number can be introduced, which has been widely applied in previous studies. The Merkel number is defined by Equation (26).

$$N=\frac{c_{\mathrm{w}}\Delta t}{6k_e}\left(\frac{1}{h_1^{″}-h_2}+\frac{4}{h_{\mathrm{m}}^{″}-h_{\mathrm{m}}}+\frac{1}{h_2^{″}-h_1}\right)$$

(26)

where the $h_1^{″}$, $h_2^{″}$, $h_{\mathrm{m}}^{″}$ are saturated moist air enthalpy in the $t_1$, $t_2$, $t_{\mathrm{m}}=\left(t_1+t_2\right)/2$, respectively. The $h_1$, $h_2$, $h_3$ are moist air enthalpy in the inlet, outlet, and average, respectively. $k_{\mathrm{e}}$ is the evaporation coefficient. $c_{\mathrm{w}}$ is the specific heat of water. $\Delta t$ is temperature difference between circulating water inlet and outlet.

The changes of $N$ under the different crosswind angles are shown in Figure 13. From Figure 13, regardless of crosswind velocity of 4 m/s, 8 m/s, and 12 m/s, the $N$ of the stepped fill tower is larger than that of the uniform fill tower with the increasing crosswind angle. That is, the stepped fill can optimize the cooling capacity of the tower. For both types of tower, the $N$ decreases first, then increases, with the minimum value appearing under the crosswind angle of 135°. The crosswind angle effect on $N$ is significant under the crosswind conditions studied. After using stepped fill, the maximum increase value of $N$ is 0.65 under the crosswind velocity of 4 m/s and is 0.85 under 8 m/s, and is 0.95 under 12 m/s.

4. Conclusions

Under the studied crosswind velocities (0 m/s–12 m/s) and angles (0°–180°), this work mainly studies the optimization of cooling capacity of the single air inlet induced draft cooling tower (SIDCT) with stepped fill. The main conclusions are as follows.

(1)

The 3D numerical model for the tower with stepped fill is established and validated. The relative error between measured values and numerical values is no more than 3%.

(2)

Compared with uniform fill tower, the total ventilation rate of the stepped fill tower is increased. The stepped fill can increase the ventilation rate in the innermost part of the SIDCT and decrease it around air inlet, not changing in the central part.

(3)

After using stepped fill, the mean drop of outlet water temperature rises by 0.29 °C, 0.27 °C, 0.17 °C, 0.10 °C, and 0.19 °C, corresponding to crosswind angles from 0° to 180°. The maximum increased value of $N$ is 0.65 under the crosswind velocity of 4 m/s and is 0.85 under 8 m/s, and is 0.95 under 12 m/s.

(4)

For the stepped fill tower, the increment of cooling capacity is the maximum under the crosswind angles of 0° and 45°, and is the minimum under the crosswind angle of 90° and 135°.

In a follow-up study, the field test and numerical calculation will focus on high ambient temperature, high inlet water temperature, and variable spray density, etc., to further optimize the applicability of the stepped fill.