Numerical simulation of thermal performance for super large-scale wet cooling tower equipped with an axial fan

International Journal of Heat and Mass Transfer 135 (2019) 220–234

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International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt

Numerical simulation of thermal performance for super large-scale wet cooling tower equipped with an axial fan Zhigang Dang, Zhengqing Zhang, Ming Gao ⇑, Suoying He School of Energy and Power Engineering, Shandong University, Jinan 250061, China

a r t i c l e

i n f o

Article history: Received 5 September 2018 Received in revised form 24 December 2018 Accepted 26 January 2019

Keywords: Super large-scale natural draft wet cooling towers Numerical simulation Thermal performance Axial fan Water dropping potential energy

a b s t r a c t For the super large-scale natural draft wet cooling towers (S-NDWCTs), the higher rain zone produces water dropping potential energy which can be used to drive an axial fan, meanwhile, the larger diameter deteriorate the whole ventilation performance. Based on these issues, a three dimensional (3D) numerical model for a S-NDWCT equipped with an axial fan was established to analyze the thermal performance at different fan diameters and fan power. In order to evaluate the influence of fan, one dimensionless number m, represents the ratio between the fan diameter and the cooling tower diameter, was introduced in this paper, as well as air velocity uniformity coefficient wvel and air temperature uniformity coefficient wtem . Simulation results manifested that, compared with natural draft pattern, the thermal performance and ventilation performance of S-NDWCT with an axial fan improve partly according to these two uniformity coefficient and several thermal performance parameters, and they improve continuously with the increasing of fan diameter and fan power. At the given fan rotate speed (20 rpm), the water temperature drop DT, ventilation rate G, Merkel number N and cooling efficiency g enhance persistently as the diameter of the fan increases, while these parameters enhance firstly, and then reduce at the given power (300 kW). Under 15.0 m fan diameter (m = 0.125) and 300 kW fan power conditions, compared with natural draft pattern, DT, G, N, and g all reach to the maximum of 9.31 °C, 31,549 kg/s, 1.65 and 53.5%, and enhance by 0.14 °C, 611 kg/s, 0.04 and 0.8%, respectively. It demonstrates that the cooling tower shows out the outstanding thermal and ventilation performance when the diameter ratio m is 0.125. Ó 2019 Elsevier Ltd. All rights reserved.

1. Introduction Cooling towers are used to extract heat from hot water to the atmosphere [1–4]. The natural draft cooling towers (NDCTs) consist of mainly dry cooling towers (NDDCTs) [5–7] and wet cooling towers (NDWCTs). Nowadays, the geometric volume of NDWCT becomes more and more larger since the large-scale generator unit appears, and it can be called as super large-scale natural draft wet cooling towers (S-NDWCTs) when the bottom diameter exceeds 100 m. In large-scale thermal power plants or inland nuclear power stations, S-NDWCTs are widely used to cool the circulating water from the condenser, and the water temperature can be close to the air wet-bulb temperature which is much lower than the air dry-bulb temperature inside the NDWCT [8]. Improving the thermal performance of NDWCTs can decrease the water temperature entering the condenser, reduce steam turbine back-pressure and finally improve power generation efficiency.

⇑ Corresponding author. E-mail address: [email protected] (M. Gao). https://doi.org/10.1016/j.ijheatmasstransfer.2019.01.111 0017-9310/Ó 2019 Elsevier Ltd. All rights reserved.

In 1904, the first industrial cooling tower appears in the world. After that, experts from various countries performed many theoretical and experimental researches on them. In the aspect of theoretical study, Lewis [9] deduced the Lewis relation to calculate the heat and mass transfer between air and water, which became the theoretical basis of thermodynamic analysis for the cooling towers, afterwards, a number of researchers began to investigate the heat and mass transfer process and thermal performance of cooling towers. Fisenko [10] presented a mathematical model to evaluate the cooling performance, including water drop cooling in the water-spraying zone and film cooling in the fillings zone, and the results explained that the error between calculated and experimental results was less than 3%. Kloppers and Kröger [11,12] made a detailed comparison between the Poppe [13], Merkel [14] and eNTU [15] methods, and found that the Merkel and e-NTU method can give the similar results, but both of them are less accurate than the Poppe method. However, the above three methods which are used for the theoretical calculation of thermal performance are one-dimensional. In fact, the airflow is entirely threedimensional (3D) [16] and accompanied by complex turbulent vortices, and the airflow and heat transfer process inside the tower are

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221

Nomenclature E q

water dropping potential energy in rain zone (kW) circulating water mass flow rate (kg/s) vrd velocity of raindrops in the z direction (m/s) vbot final velocity of raindrops at the bottom of rain zone (m/s) vtop initial velocity of raindrops at the top of rain zone (m/s) Pe fan effective power (kW) Qfan volume flow rate of air though the fan (m3/s) Pfan total pressure of the fan (pa) Sm volumetric mass transfer rate (kg/(m3
s)) constant-pressure specific heat of water (J/(kg
°C)) cw tw water temperature (°C) Swe volumetric energy transfer rate of water (W) ! va air velocity (m/s) I unit tensor of air g gravitational acceleration (m/s2) F volumetric resistance for air (N/m3) air temperature (°C) ta tref reference temperature (°C) kl laminar thermal conductivity coefficient (W/(m
°C)) kt turbulent thermal conductivity coefficient (W/(m
°C)) specific enthalpy of component n (J/kg) hn ! Jn diffusion flux of component n (kg/m2
s) Sae volumetric energy transfer rate of air (W) Yv vapor mass fraction laminar diffusion coefficient of vapor in wet air (m2/s) Dl Dt turbulent diffusion coefficient of vapor in wet air (m2/s) Pamb ambient pressure (kPa) gas constant of dry air (J/(mol
°C)) Rda Rv gas constant of vapor (J/(mol
°C)) Km volumetric mass transfer coefficient (kg/(m3
s)) Kh volumetric heat transfer coefficient (kW/(m3
°C)) constant-pressure specific heat of vapor (kJ/(kg
°C)) cv Kmfill volumetric mass transfer coefficient of the fillings (kg/(m3
s)) qa ventilation density (kg/(m2
s)) water-spraying density (kg/(m2
s)) qw Khfill volumetric heat transfer coefficient of the fillings (kW/(m3
°C)) Lef Lewis factor constant-pressure specific heat of wet air (kJ/(kg
°C)) ca Kmsr volumetric mass transfer coefficient in water-spraying and rain zone (kg/(m3
s)) volumetric heat transfer coefficient in water-spraying Khsr and rain zone (kW/(m3
°C)) Nrd the volumetric number of raindrops Ard surface area of single raindrop (m2) equivalent diameter of single raindrop (m) drd Red Reynolds number at the raindrop equivalent diameter Sc Schmidt number Pr Prandtl number vwz water flow velocity in the z direction (m/s) fwz water droplet falling resistance caused by airflow (N) mrd mass of single raindrop (kg) vax, vay, vaz velocities of wet air in the x, y and z directions (m/s) Fax, Fay, Faz volumetric air resistance in the x, y and z directions (N/m3) Dpfill pressure drop of wet air passed through the fillings thickness of the fillings (m) Hfill Rea Reynolds number of wet air Crd resistance coefficient of raindrops Dfan fan diameter (m) cooling tower diameter that in the fan plane (m) Dct

m n j

vai va

tai ta DT G N t1 t2 Vfill hsa ha

ratio between fan diameter and cooling tower diameter that in the fan plane fan rotate speed (rpm) the number of data nodes air velocity at data node of number i (m/s) average air velocity (m/s) air temperature at data node of number i (°C) average air temperature (°C) water temperature drop (°C) air mass flow rate (kg/s) Merkel number inlet water temperature (°C) outlet water temperature (°C) fillings volume (m3) specific enthalpies of saturated wet air (kJ/kg) specific enthalpies of wet air (kJ/kg)

Greek letters qa wet air density (kg/m3) ll laminar viscosity coefficient (kg/(m
s)) lt turbulent viscosity coefficient (kg/(m
s)) v0sa0 moisture content of saturated moist air (kg/kg) va moisture content of wet air (kg/kg) qda density of dry air (kg/m3) qw water density (kg/m3) l air dynamic viscosity (N
s/m2) wvel air velocity uniformity coefficient wtem air temperature uniformity coefficient g cooling efficiency (%) s1 wet-bulb temperature of inlet air (°C) a, b, c constant u,k coefficient Super/Subscripts rd raindrop bot bottom top top fan fan m mass w water we water energy a wet air ref reference l laminar t turbulent n component ae air energy amb ambient da dry air v vapor sa saturated wet air h heat mfill volumetric mass transfer coefficient of the fillings hfill volumetric heat transfer coefficient of the fillings f factor msr volumetric mass transfer coefficient in water-spraying and rain zone hsr volumetric heat transfer coefficient in water-spraying and rain zone rd raindrop wz water direction ax, ay, az air direction fill fillings

222

vel tem i

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velocity temperature the serial number of data node

coupled and interactional. As a result, with the development of computational fluid dynamics, two-dimensional (2D) and threedimensional (3D) methods became dominant and widely implemented. Recently, Ghazani [17] performed the comprehensive analysis of a model wet cooling tower by using the laws of thermodynamics, and calculated the entropy generation of every part, these conclusions can help to choose high quality fillings. With the development of research in NDWCTs, many scholars studied the thermal performance of wet cooling towers from many aspects, including model experiment [18–23], numerical simulation [24–31] and field test [32–37]. For the experimental research, Lemouari [18] focused on the hydraulic characteristics of the cooling tower, and studied the effect of the air and water flowrates at different inlet water temperature. Pan [19] proposed that the arrangement of water distribution in the pipe and nozzle affected the cooling effect in the design of cooling tower. Similarly, in the structure optimization of cooling tower, Gao [20,21] studied the influence of nonuniform fillings distribution on the cooling efficiency by the thermal-state model experiment, and obtained the optimal fillings pattern. Additionally, Chen [22] performed the model experiment to investigate the effect of cross walls on the thermal performance under crosswind conditions, and the results showed that cross walls can improve the thermal performance of the NDWCTs. Wang [23] also conducted thermal-state model experiment, and studied the effect of inlet airflow guiding channels on the thermal performance under crosswind conditions. This study found that guiding channels with 70° setting angle lead to better ventilation and cooling performance. Additionally, as one of the main research methods, the numerical simulation becomes a popular method for studying the thermal performance of cooling towers. Hawlader [24] and Williamson [25,26] developed a 2D axisymmetric model to investigate the non-uniformity of flow field inside the NDWCTs, and obtained that the two-dimensional model has the ability to resolve radial non-uniformities across the tower which the onedimensional model only computes as a bulk averaged value. Besides, AL-Waked [27,28] developed a 3D CFD model to simulate both the water flow in the fillings and droplets in the waterspraying and rain zones, and analyzed the effect of crosswind on cooling performance. The simulation results can guide the design and optimization research in the future. Kalimanek [29] presented a study on numerical modeling of a natural draft wet-cooling tower with flue gas injection, and derived that the injected flue gas has insignificant influence on the cooled water temperature. For optimized design of cooling tower performance, Xia [30] proposed and numerically investigated a closed wet cooling tower with novel design, and evaluated the cooling tower performance under different operating conditions. Chen [31] proposed a novel method for improving the cooling performance of natural draft wet cooling towers (NDWCTs) by installing air ducts in the rain zone for the first time, and demonstrated that air ducts improve both the aerodynamic field and the cooling performance of the NDWCT and that the improvement is quite dependent on the crosswind velocity. Finally, field test is also an effective method to conduct the academic research since it can overcome the shortcomings of model experiment and numerical simulation. Zou [32] and Gao [33] performed the field test on the high level water collecting wet cooling

1 2

inlet outlet

towers (HWCTs) of a 1000 MW unit to investigate ventilation and thermal performance under crosswind conditions. The test results manifested that crosswind destroys the uniformity of circumferential inflow air, and reduces wind velocity in the lateral and leeward side. Meanwhile, with the rising of crosswind velocity, crosswind appears an increasingly serious adverse effect on the thermal performance and uniformity of air temperature distribution inside tower. Zhang [34,35] conducted field test on the NDWCT of a 135 MW unit, and proposed the concept of air inlet deflection angle and air inlet uniformity coefficient. The test results showed that crosswind increases ventilation resistance, and destroys the uniformity of circumferential air inlet. Širok [36,37] manufactured a robot which can move over the drift eliminators to measure the velocity and temperature field above the drift eliminators. Based on this study, they also came up with the thermovision method which enables quick detection of the local efficiency of cooling towers. In summary, the previous researchers focused mainly on the medium and large-scale NDWCTs to study the heat and mass transfer performance, and rarely involved super large-scale NDWCTs (S-NDWCTs). Moreover, seldom of them discussed the water dropping potential energy of the rain zone, and no one performed the study of strengthening ventilation by using the axial fan which can be driven by the water dropping potential energy of the rain zone. This study focuses on the thermal and ventilation performance improvement by utilizing the water dropping potential energy, and proposes a new method for both the utilization of the water dropping potential energy and the thermal performance improvement of S-NDWCTs, which can guide the further energysaving research and optimization design of the S-NDWCTs. 2. Modeling 2.1. Physical model for axial fan driven by water dropping potential energy This paper mainly studies the influence of forced ventilation on the thermal performance of the S-NDWCT, the driving principle of the axial fan is briefly introduced. The water dropping potential energy is calculated by the theorem of kinetic energy, which is given by,

Table 1 Main geometrical dimensions of the S-NDWCT. Subject

Value

Unit

Fillings area Height of the tower Height of the air inlet Height of fan section inside tower Thickness of the fillings Thickness of fan Diameter of fan

13,000.0 177.2 12.0 30.0

m2 m m m

2.0 1.0 5.0, 10.0, 12.5, 15.0, 17.5, 20.0, 22.5, 25.0, 27.5, 30.0 120.0

m m m m

133.4 79.3

m m

Diameter of fan section inside tower Diameter of the inlet top Diameter of the outlet

Z. Dang et al. / International Journal of Heat and Mass Transfer 135 (2019) 220–234 Table 2 Operating and environmental conditions. Item

Value

Unit

Circulating water mass flow rate Crosswind velocity Atmospheric pressure Dry bulb temperature of inlet air Wet bulb temperature of inlet air Inlet water temperature

104,540 0 100.14 16.30 14.15 31.54

t/h m/s kPa °C °C °C

E¼

 1 1
qDv 2rd ¼ q v 2bot  v 2top 2 2

ð1Þ

where E is the water dropping potential energy in the rain zone, kW, q represents the circulating water mass flow rate, kg/s, vrd is the velocity of raindrops in the z direction, m/s, vbot is the final velocity of raindrops at the bottom of rain zone, m/s, vtop indicates the initial velocity of raindrops at the top of rain zone, m/s. The main geometrical dimensions of the studied S-NDWCT are listed in Table 1. Moreover, the operating and environmental conditions during the numerical simulation process are shown in Table 2. Under these conditions, the average velocity of raindrops in rain zone reaches to around 5 m/s, and the water dropping potential energy calculated by Eq. (1) is about 400 kW. In order to utilize water dropping potential energy, a water dropping potential energy utilization device is designed in this paper, and its physical model is shown in Fig. 1. As is shown, a hydraulic impeller is arranged on the top surface of water collecting basin, and an axial fan is placed above the drift eliminators. In the S-NDWCT, the hydraulic impeller began to rotate due to the impact by countless raindrops in the rain zone. Afterwards, the hydraulic impeller and the axial fan can realize coaxial rotation

223

through the transmission device, which results in forced ventilation in this S-NDWCT. For S-NDWCTs, the weak ventilation performance deteriorates the heat and mass transfer progress. Therefore, the axial fan is arranged at the center of the cooling tower. In order to simplify the computational model, only the axial fan part of the device is studied in the simulation. One three-dimensional (3D) geometric model of axial fan is established by SolidWorks as illustrated in Fig. 2. In addition, the fan effective power Pe, kW, is introduced to reflect the performance of the axial fan, which can be defined as [38],

Pe ¼

Q fan
Pfan 1000

ð2Þ

where Qfan is the volume flow rate of air though the fan, m3/s, Pfan is the total pressure of the fan, Pa.

2.2. Mathematical model A complex cooling tower consists of many different zones, such as drift eliminators, the water-spraying zone, the fillings zone and the rain zone. The structural complexity leads to the generation of airflow resistance, so that the air holds a turbulent state inside tower. Moreover, the air and water flow inside and outside the SNDWCT can be regarded as the steady flow under constant meteorological and operating conditions. So it can be described by the steady-state Reynolds average Navier-Stokes equations, and the Reynolds stress term can be solved by the standard k-e turbulence model.

Fig. 1. The 3D model of water dropping potential energy utilization device.

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Fig. 2. 3D model of axial fan.








r
qa ! v a! v a ¼ rpa þ r
ll þ lt







 

2 3

r! v a þ r! va  r
! v a I þ qa g þ F T

ð6Þ

where ll and lt are the laminar and turbulent viscosity coefficients, respectively, kg/(m
s), I is the unit tensor of air, g is the gravitational acceleration, m/s2, F is the volumetric resistance for air, N/m3. (III) energy conservation equation

r
qa ! va

Fig. 3. Finite control volume for water flow.

2.2.1. Governing equations for water flow In the finite volume shown in Fig. 3, the mass and energy conservation equations of circulating water can be written as Eqs. (3) and (4).

dq ¼ Sm dðzÞ

ð3Þ

d ðcw tw qÞ ¼ Swe dðzÞ

ð4Þ

where Sm is the volumetric mass transfer rate, kg/(m3
s), cw is the constant-pressure specific heat of water, J/(kg
°C), tw represents the water temperature, °C, Swe is the volumetric energy transfer rate of water, W. 2.2.2. Governing equations for airflow The airflow state can be described by the mass, momentum, energy and component conservation equations [39], which are listed as below, (I) mass conservation equation






r
qa ! v a ¼ Sm

ð5Þ

! where qa is the wet air density, kg/m3, v a is the air velocity, m/s. (II) momentum conservation equation

Z

!

ta

ca dt t ref

¼ r
ðkl þ kt Þrt a 

X

! hn J n

! þ Sae

ð7Þ

n

where ta is the air temperature, °C, tref = 0 °C is the reference temperature, °C, kl and kt are the laminar and turbulent thermal conductivity coefficients, respectively, W/(m
°C), hn is the sensible ! enthalpy corresponding to component n, J/kg, J n is the diffusion P ! flux of component n, kg/m2
s, n hn J n is the sensible enthalpy caused by the diffusion of component n, and Sae is the volumetric energy transfer rate of air, W. (IV) vapor component mass conservation equation






r
qa ! v a Y v ¼ r
½qa ðDl þ Dt ÞrY v  þ Sm

ð8Þ

where Yv is the vapor mass fraction, Dl and Dt are the laminar and turbulent diffusion coefficients of vapor in wet air, m2/s. The airflow around the S-NDWCT can be assumed to be incompressible due to the small variation in air pressure. Therefore, the change in the air density affects only temperature and humidity. Based on this, the wet air state equation is given as,

q¼

Pamb ½Rda ð1  Y v Þ þ Rv Y v ð273:15 þ ta Þ

ð9Þ

where Pamb is the ambient pressure, kPa, Rda and Rv are the gas constant of dry air and vapor, respectively, J/(mol
°C), ta is the air temperature, °C. 2.2.3. Heat and mass transfer model between water and air Based on the literature [26], the volumetric mass transfer rate of water Sm between the wet air and the cooling water can be defined as,

Sm ¼ K m ðv00sa  va Þ

ð10Þ

Z. Dang et al. / International Journal of Heat and Mass Transfer 135 (2019) 220–234

where Km indicates the volumetric mass transfer coefficient, 00 kg/(m3
s), vsa is the moisture content of saturated moist air, kg/kg, va represents the moisture content of wet air, kg/kg. The volumetric energy transfer rate of air Sae can be described as,

Sae ¼ ðK h þ Sm cv Þðt w  t a Þ

ð11Þ

where Kh is the volumetric heat transfer coefficient, kW/(m3
°C). cv is the constant-pressure specific heat of vapor, kJ/(kg
°C). tw and ta are the water and air temperature, respectively, °C. Generally, in the fillings zone, Km can be obtained through experiment, and described as,

K m ¼ K mfill ¼ aqba qcw

ð12Þ

where Kmfill is the volumetric mass transfer coefficient of the fillings, kg/(m3
s), qa and qw are represent the ventilation density and water-spraying density of the tower, respectively, kg/(m2
s), a, b and c are constant, determined by the material and structure of the fillings. Moreover, the volumetric heat transfer coefficient Kh of fillings can be calculated from the correlation of the Lewis factor Lef corrected by Bosnjakovic, and defined by,

K h ¼ K hfill ¼ ca K m Lef

ð13Þ

where Khfill is the volumetric heat transfer coefficient of the fillings, kW/(m3
°C) and ca means the constant-pressure specific heat of wet air, kJ/(kg
°C). In the water-spraying and rain zone, Km and Kh can be written as follows,

K m ¼ K msr ¼ qda Nrd Ard

 Dl
1=3 2 þ 0:6Re1=2 d Sc drd

ð14Þ

K h ¼ K hsr ¼ Nrd Ard

 kl
1=3 2 þ 0:6Re1=2 d Pr drd

225

ð15Þ

where Kmsr indicates the volumetric mass transfer coefficient in water-spraying and rain zone, kg/(m3
s) and Khsr represents the volumetric heat transfer coefficient in water-spraying and rain zone, kW/(m3
°C), qda is the density of dry air, kg/m3, Nrd is the volumetric number of raindrops, Ard is the surface area of single raindrop, m2, drd is the equivalent diameter of single raindrop, m, Red is Reynolds number at the droplet equivalent diameter, Sc and Pr are the Schmidt number and Prandtl number, respectively. 2.2.4. Resistance model for water flow In the fillings zone, the cooling water flows in a film way. And, the resistance of the airflow to the water film can be given by the empirical equation [4]. In the water-spraying and rain zone, the downward flow of circulating water can be taken as nearly vertical direction with the following equation,

dv wz ðq  qa Þg f wz  ¼ w dðzÞ qw v wz mrd
v wz

ð16Þ

where vwz is the water flow velocity in the z direction, m/s, qw is the water density, kg/m3, fwz is the water droplet falling resistance caused by airflow, N, mrd is the mass of single raindrop, kg. 2.2.5. Resistance model for airflow The airflow resistance from inlet to outlet mainly includes the water film resistance in fillings zone and the droplets resistance in water-spraying and rain zone. For convenient calculation, the fillings resistance which can be expressed as,

F az ¼

Dpfill qa uv kaz ¼ Hfill Hfill

Fig. 4. Computation domain and its boundaries for air flow.

ð17Þ

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Fig. 5. Grid system of cooling tower.

where Faz is the air resistance in the z direction per unit volume, N/m3, Dpfill is the pressure drop of wet air passed through the fillings, pa, Hfill is the thickness of the fillings, m, vaz is the velocity of wet air in the z direction, m/s, u and k are the coefficient, which are determined by experimental data, respectively. The air resistance in the x, y and z directions of the waterspraying and rain zone can be expressed in the following forms,

F az ¼ 

F ax ¼ 

F ay ¼ 

Fig. 6. Local grids of fan blade.

6qw

qw pjv wz jd3w 6qw

qw pjv

3 wz jdw

6qw

qw pjv wz jd3w

C rd Rea

C rd Rea

C rd Rea

pdw l 8

pdw l 8

pdw l 8

ðv az þ v wz Þ

ð18Þ

v ax

ð19Þ

v ay

ð20Þ

Table 3 Results of mesh independence. Item

Mesh1

Mesh2

Mesh3

Mesh4

Cells of mesh Inlet water temperature (°C) Calculated outlet water temperature (°C) Water temperature drop (°C)

1,070,488 31.64 22.40 9.24

1,416,872 31.64 21.98 9.66

1,714,895 31.64 21.97 9.65

1,936,740 31.64 21.99 9.65

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2.3. Numerical model

Table 4 Comparisons of numerical and measured results. Parameter

Condition (1)

Condition (2)

Condition (3)

Dry bulb temperature of inlet air (°C) Wet bulb temperature of inlet air (°C) Atmospheric pressure (kPa) Cooling water flow rate (t/h) Inlet water temperature (°C) Measured outlet water temperature (°C) Calculated outlet water temperature (°C) Relative error (%)

17.86 15.35 100.90 70,444 31.64 21.25

20.50 15.40 101.30 70,444 31.81 21.43

32.28 25.78 100.33 91,680 39.33 31.27

21.94

21.95

30.61

3.25

2.43

2.11

where Fax and Fay are the air resistance in the x and y directions per unit volume, respectively, N/m3, Rea is the Reynolds number of wet ffi þ 0:4 is the resistance coefficient of raindrops, l þ 1þ6pffiffiffi air, C rd ¼ 24 Re Re

is the air dynamic viscosity, N
s/m2, vax, vay are the velocity of wet air in the x and y direction, respectively, m/s.

2.3.1. Boundary conditions and solution method Under no crosswind condition, the pressure at the inlet and outlet, temperature and humidity are all set as the ambient air values, the computation domain is shown in Fig. 4. Meanwhile, the boundaries such as ground and tower body are defined as adiabatic noslip wall condition with no heat and mass transfer. To eliminate the influence of external environment on the flow field and heat transfer inside the tower, the computation domain is considerably larger than the investigated tower, and the height is 3 times of the tower height and the radius is about 5 times of the tower base radius. Therefore, the air flow at the computation domain inflow boundary is not subject to the tower impact and can be set as the real ambience conditions. The boundary conditions for discrete phase are listed as: inlet, outlet, the surface of water pool and ground are all set to be the escape boundary, which means the water droplets will be deleted from the computation domain once encounter the water basin or the environmental ground. Additionally, the shell of cooling tower is still defined as

Table 5 Values of different m. Item

Value

Dfan (m) Dct (m) m = Dfan/Dct

0 120.0 0

5.0 120.0 0.042

10.0 120.0 0.083

12.5 120.0 0.104

15.0 120.0 0.125

17.5 120.0 0.146

20.0 120.0 0.167

22.5 120.0 0.188

(a) m=0

(b) m=0.083

(c) m=0.125

(d) m=0.25

Fig. 7. Air velocity contours of X = 0 cross section at different m values.

25.0 120.0 0.208

27.5 120.0 0.229

30.0 120.0 0.25

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(a) m=0

(b) m=0.083

(c) m=0.125

(d) m=0.250

Fig. 8. Air temperature contours of X = 0 cross section at different m values.

reflect boundary to simplify the calculation. And the standard wall function is adopted for the near-wall treatments of turbulent flow. In the water-spraying and rain zones, water droplets and wet air are considered as the discrete phase and continuous phase, respectively. The DPM model is utilized to simulate the interaction between discrete phase and continuous phase. The steady simulation is used, and the upper surface of the water-spraying zone is set as the origin of the droplets. The initial velocity of the droplets is set to 3.5 m/s, and the equivalent diameter is set to 3.5 mm in the water-spraying zone. In addition, in the rain zone, the initial velocity of the droplets is set to 0.4 m/s, and the equivalent diameter is set to 5 mm. Moreover, the axial fan is simulated by using MRF model in which to achieve the coupling of the flow area and the fixed area. By using user-defined functions (UDF), the k and e boundary of the pressure outlet is set to the second type of boundary condition. The finite-volume approach is adopted to discrete the governing equations and the convection term is expressed by second-order upwind difference. The typical SIMPLE algorithm is adopted to compute the flow field. 2.3.2. Mesh system SolidWorks and ICEM-CFD software are used for model establishment and mesh generation, respectively, in this part. And the tower body, the fillings zone, the water-spraying zone, the rain zone and the external environment adopt the structural hexahedral mesh, and the axial fan zone is divided by unstructured mesh. The grids of heat transfer zones are refined. Both the axial fan and its surrounding parts are partitioned with the adaptable unstruc-

tured mesh and the blades are mesh-refinement too. Fig. 5 shows the grid system of cooling tower, and the local grids of fan blade are shown in Fig. 6.

2.3.3. Mesh independence and validation To perform the mesh size check, four mesh systems, namely Mesh1, Mesh2, Mesh3 and Mesh4 are generated in this paper. Table 3 shows the simulation results of different mesh systems. To improve the calculation accuracy and reduce the attendant computational costs, Mesh2 is chosen for the following study according to Table 3. The comparison between measured and calculated water temperature under three working conditions is reported in Table 4. The measured water temperature of three working conditions can be seen in our group’s thesis [40]. According to Table 4, it can be found that the relative error between the calculated outlet water temperature and the measured value is small, and the maximum relative error is 3.25%, which verifies the accuracy of the numerical model.

3. Results and discussion In this study, a dimensionless number m represents the ratio between the fan diameter Dfan and the cooling tower diameter Dct in the fan plane, m = Dfan/Dct. For different m, the fan rotate speed n is set to 20 rpm. The values of different m are reported in Table 5.

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229

Fig. 9. The location of monitoring surface 1 and 2 in Y = 0 cross section.

Fig. 10. The schematic diagram of data nodes in monitoring surface 1 and 2.

3.1. Air velocity and temperature distributions inside tower at different m values Taking the fan diameter as the research object to simulate the airflow and temperature fields inside the S-NDWCT, the contours of air velocity and temperature are obtained in this part. Fig. 7 shows the air velocity contours of X = 0 cross section at different m values, where m = 0 represents the natural draft pattern. According to Fig. 7 (a), it can be observed that the air velocity contour inside the tower is axisymmetric under natural draft pattern, and it shows the ‘‘M” type. Due to the effect of the density dif-

ference, the airflow is extracted from the inlet to outlet. Moreover, the cold air keeps exchanging heat and mass with hot water on its way from the inlet to outlet, the air density decreases and the air humidity increases [41]. Along the flow direction, the airflow velocity increases. From Fig. 7 (b), (c) and (d), it can be seen that under forced ventilation pattern, the air velocity contour inside the tower is no longer completely symmetrical. This is because the rotation of the fan drives up the airflow in the center of the tower. Moreover, as the fan diameter increases, this trend becomes more obvious, and the air velocity around the fan reaches to the maximum value.

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center, which leads to the higher air temperature in the central area. Based on the above analysis, due to the forced ventilation, the air velocity increases near the axial fan, thus, compared with the natural draft pattern, the air mass flow rate in the central area increases under the forced ventilation. Additionally, this phenomenon is more obvious as m increases. According to Fig. 8 (b)– (d), under forced ventilation pattern, the air temperature around the center area reduces obviously. The area of low-temperature zone in the tower increases and the area of high-temperature zone decreases, so the temperature field is more uniform. The heat and mass transfer zones inside tower are fully utilized. In this paper, the air velocity uniformity coefficient wvel and the air temperature uniformity coefficient wtem are introduced to act as evaluation criteria to estimate the impact of axial fan on the uniformity of airflow field and temperature field. they can be defined as,

wvel ¼ Fig. 11. Relation curves between wvel and m.

1 þ 1j

wtem ¼

Fig. 12. Relation curves between wtem and m.

At the bottom of the fan, the air velocity also increases. What is more, the outlet air velocity increases with the increasing of m. Fig. 7 (d) shows that the area of the low-velocity zone reduces significantly and the area of the high-velocity zone increases, correspondingly. Obviously, the axial fan with larger diameter can significantly improves airflow velocity in the central area of the tower. Besides, the air temperature contours of X = 0 cross section at different m values are also analyzed, and presented in Fig. 8. Fig. 8 (a) demonstrates that the air temperature inside tower appears the axisymmetric distribution under natural draft pattern, which is similar to the air velocity field. For the S-NDWCTs, the rain zone is large relatively in diameter and height, and the cooled air goes through a long path from external environment to the tower

1þ

Pj

1

v

 v aÞ

1 Pj 



i¼1 ð ai

1 j

i¼1

tai  t a

ð21Þ

ð22Þ

where j is the number of data nodes in monitoring surface 1 and 2, respectively, and j equals to 200 in this paper, vai stands for the air velocity at data node of number i, m/s, and v a represents the average air velocity, m/s, tai stands for the air temperature at data node of number i, °C, and t a represents the average air temperature, °C. Figs. 9 and 10 show the location of monitoring surface 1 and 2, additionally, the height of monitoring surface 1 and 2 are 25 m and 35 m. Generally speaking, when these tow coefficients equal to 1, it means that the air velocity of all data nodes are the same at monitoring surface 1 and 2, and the airflow field is absolutely uniform. In cooling tower operation, the airflow field and temperature field inside the tower are not absolutely uniform due to the suction force, which leads to both wvel and wtem less than 1. Thus, the smaller the w is, the worse the uniformity becomes. Figs. 11 and 12 depict the changing rules of wvel and wtem for different m under Z1 = 25 m and Z2 = 35 m conditions. It can be seen that wvel decreases rapidly with the increase of m, while wtem decreases firstly and then increases. Based on the above analysis, the air velocity in the central area of the tower increases under forced ventilation pattern, and this trend becomes more obvious with the increasing of fan diameter, which causes a non-uniform air velocity field. Besides, these phenomena become more obvious at Z2 = 35 m position, because 35 m position lies in the outlet of fan, and the larger suction force easily results in the aerodynamic field at this position. In brief, although larger diameter fan reduces the velocity uniformity, it increases the temperature uniformity obviously, which contributes to the heat and mass transfer process in the tower. In addition, as the diameter of the fan increases, these phenomena become more apparent, which can enhance the suction force of S-NDWCT to some extent.

Table 6 Relationship between fan power and m. Item

Value

m Dfan/m Pe/kW

0 0 0

0.042 5.0 0.04

0.083 10.0 1.30

0.104 12.5 4.0

0.125 15.0 9.9

0.146 17.5 21.3

0.167 20.0 41.6

0.188 22.5 75.0

0.208 25.0 127.0

0.229 27.5 204.5

0.250 30.0 315.9

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Fig. 13. Relation curves between thermal performance parameters and m under constant fan rotate speed condition.

Table 7 Relationship between n and m. Item

Value

Pe/kW Dfan/m m n/rpm

300 0 0 0

300 5.0 0.042 428

300 10.0 0.083 135

300 12.5 0.104 93

3.2. Thermal performance analysis of the S-NDWCT under constant fan rotate speed condition In this part, the numerical simulation of thermal performance for the S-NDWCT with an axial fan is conducted under the constant fan rotate speed (20 rpm) condition. Table 6 depicts the relationship between the fan effective power Pe and the diameter ratio m. According to Table 6, the maximum diameter of the fan is set to 30 m when the fan rotate speed is 20 rpm, and the corresponding fan power is 316 kW by terms of Eq. (2). Additionally, based on the analysis of Part. 2.1, the total water dropping potential energy of the rain zone for this S-NDWCT is about 400 kW, so it can meet with the requirement of fan power even if considering partly energy loss. In this study, four representative parameters, which are the water temperature drop DT, ventilation rate G, Merkel number N

300 15 0.125 68

300 17.5 0.146 53

300 20 0.167 43

300 22.5 0.188 35

300 25 0.208 29

and cooling efficiency g, are adopted to evaluate the thermal performance of the S-NDWCT. Supposing other operating conditions keep steady, the water temperature drop DT is the most intuitive criteria to evaluate the cooling performance of wet cooling towers, which is given by,

DT ¼ t 1  t 2

ð23Þ

where t1 and t2 are the inlet and outlet water temperature, respectively, °C. The cooling efficiency g is another evaluation indicator, which is written by,

g¼

DT t1  s1

where

s1 is the wet-bulb temperature of inlet air, °C.

ð24Þ

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Fig. 14. Relation curves between thermal performance parameters and m under constant fan power condition.

In addition, the Merkel number N is another very important parameter to reflect the thermal performance of wet cooling towers, it can be defined as,

N¼

K mfill V fill ¼ q

Z

t1

t2

cw dt w ðhsa  ha Þ

ð25Þ

where Kmfill represents the volumetric mass transfer coefficient of the fillings, kg/(m3
s), Vfill is the fillings volume, m3, hsa and ha are the specific enthalpies of saturated wet air and wet air, respectively, kJ/kg. The changing rules of, DT G, N and g with diameter ratio m under constant rotate speed (20 rpm) are shown in Fig. 13. According to Fig. 13, it can be observed that DT, G, N and g are quite dependent on the m, and these four parameters simultaneously increase with the rising of m. When m rises from 0 to 0.205, the performance parameters increase slowly, which indicates that the diameter has little effect on the thermal performance when the diameter of the fan is small. Under this condition, the fan could not significantly increase the air velocity inside the tower because the diameter is small and fan rotation speed is low. The thermal performance of the tower is almost the same as that of the natural draft pattern. However, when m rises from 0.208 to 0.250 (the fan diameter increases from 25 m to 30 m), these four performance parameters

show a rapid upward trend, which indicates that the fan results in positive impact on the thermal performance. When m = 0.250, DT reaches to a maximum of 9.30 °C, increases by 0.13 °C, compared with that of the natural draft pattern. Additionally, G, N and g increase by 490 kg/s, 0.20 and 1.0%, respectively, compared with that of the natural draft pattern. As a result, the thermal performance of the S-NDWCT notably improves after using the large diameter axial fan to realize forced ventilation inside tower. Furthermore, the larger the axial fan diameter is, the more outstanding the thermal performance becomes. However, the fan power gradually also increases with the rising of m, therefore, in order to obtain the optimal m value, it is extremely necessary to study the thermal performance under constant fan power condition.

3.3. Thermal performance analysis of the S-NDWCT under constant fan power condition In order to obtain the optimal m value, the influence of constant fan power on thermal performance is studied in this part. According to the above-mentioned analysis and the similarity criteria [38], the power of the fan is set to 300 kW for different m after considering the energy loss. Based on this, the relationship between fan rotate speed and diameter ratio m is shown in Table 7.

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Fig. 14 describes the changing rules of DT, G, N and g with m under constant power. It can be found in Fig. 14 that DT, G, N and g all increase firstly and then decrease with the increasing of m, and reach to the maximum at 0.125 m (the fan diameter is 15.0 m). Under one certain power condition, the larger the fan diameter is, the lower its rotation speed becomes. Smalldiameter fan or low- rotation-speed fan cannot optimize the air flow field in the tower, therefore, the thermal performance reaches to the optimal status at m = 0.125. When m = 0.125, the maximum values of DT, G, N, and g are 9.31 °C, 31,549 kg/s, 1.65 and 53.5%, respectively, which are 0.14 °C, 611 kg/s, 0.04 and 0.8% higher than that of the natural draft pattern. Afterwards, with the increasing of m, the downward trends of four parameters are very rapid due to the reduction of fan diameter. Briefly, under 300 kW power condition, when m = 0.125, the water temperature drop DT, Merkel number N, ventilation rate G, and cooling efficiency g all reach to the optimum values. Thus, the conclusion can be drawn that the cooling tower shows out the outstanding relatively thermal performance when the diameter ratio m is 0.125 (the arrangement with a fan diameter of 15.0 m and a rotate speed of 68 rpm for the studied S-NDWCT).

4. Conclusions A three dimensional (3D) numerical model for a super largescale natural draft wet cooling tower (S-NDWCT) equipped with an axial fan is established in this paper. Based on this model, the numerical calculation is conducted to analyze the thermal performance at different fan diameters and fan power. By the discussion of airflow contours, flow fields uniformity and several performance parameters, the main conclusions are as follows, (1) After the forced ventilation is realized by the axial fan, the airflow field and temperature field are affected. When the fan diameter exceeds 15.0 m, the air velocity in the central area of the tower significantly increases and the temperature distribution become more uniform compared with that of the natural draft pattern, and these phenomena become more apparent as the diameter of the fan further increases. Besides, the larger fan diameter enhances the temperature uniformity coefficient, especially in the upper part inside tower. (2) Under forced ventilation pattern, the ventilation rate of the S-NDWCT improves significantly. Furthermore, when the fan rotate speed n is set to 20 rpm, the water temperature drop DT, Merkel number N, ventilation rate G, and cooling efficiency g all rise as the fan diameter increases. When diameter ratio m = 0.25, compared with that of the natural draft pattern, DT, G N and g increase about 0.13 °C, 490 kg/s, 0.20 and 1.0% at most. (3) When the fan power is set to 300 kW, with the increasing fan diameter, DT, G, N and g increase firstly and then decrease rapidly. When m = 0.125, these four parameters all reach to the maximum values of 9.31 °C, 31,549 kg/s, 1.65 and 53.5%, and enhance by 0.14 °C, 611 kg/s, 0.04, 0.8%, respectively. The results demonstrate that the S-NDWCT equipped with an axial fan shows out the outstanding relatively thermal performance when the diameter ratio m is 0.125 in this research (the arrangement with a fan diameter of 15.0 m and a rotational speed of 68 rpm for the studied S-NDWCT). In general, studies in this paper manifest that an axial fan can improve the thermal performance of the S-NDWCTs to a certain

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extent. Moreover, the axial fan can be driven by water dropping potential energy produced by the higher rain zone. Certainly, it is an innovative idea and new direction for the deep energy-saving research of S-NDWCTs.

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