Performance improvement of natural draft dry cooling system by water flow distribution under crosswinds

International Journal of Heat and Mass Transfer 108 (2017) 1924–1940

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Performance improvement of natural draft dry cooling system by water flow distribution under crosswinds Xuebo Wang, Lijun Yang ⇑, Xiaoze Du, Yongping Yang Key Laboratory of Condition Monitoring and Control for Power Plant Equipments of Ministry of Education, Beijing 102206, China School of Energy Power and Mechanical Engineering, North China Electric Power University, Beijing 102206, China

a r t i c l e

i n f o

Article history: Received 9 May 2016 Received in revised form 6 January 2017 Accepted 13 January 2017

Keywords: Natural draft dry cooling system Air-cooled heat exchanger Heat exchanger model Crosswind Water flow distribution Turbine back pressure

a b s t r a c t The cooling performance of natural draft dry cooling system may be deteriorated by ambient winds, so effective measures need to be taken against the adverse wind effects. In this work, a threedimensional numerical model of a typical natural draft dry cooling system coupled with the condenser is developed to investigate the thermo-flow performance improvement of natural draft dry cooling system by circulating water flow distribution, in which the finned tube bundles are dealt with the heat exchanger model to take both the air and circulating water into account. The flow and temperature fields, heat rejection of each sector, outlet water temperature of air-cooled heat exchanger and the corresponding turbine back pressures are obtained. The results show that appropriate water flow distribution can significantly improve the thermo-flow performances of natural draft dry cooling system, while the improper one may deteriorate the cooling performance more seriously at low wind speeds. Based on the entransy dissipation theory, the optimized heterogeneous water distributions are provided under five certain wind conditions by using the numerical-theoretical iterative method. Ó 2017 Elsevier Ltd. All rights reserved.

1. Introduction Owing to the urgent water resource issue, the natural draft dry cooling system (NDDCS) with the air-cooled heat exchanger vertically arranged around the circumference of dry-cooling tower or horizontally installed inside cooling tower is widely used in arid regions where the cooling water is not available or is very expensive [1]. Ambient air is driven by the dry-cooling tower generated buoyancy force to cool the circulating water in the air-cooled heat exchanger, so the thermo-flow performances of NDDCS are easily influenced by the ambient conditions. More and more attentions have been paid to the unsatisfactory performance of NDDCS under crosswinds, and various measures against the adverse wind impacts. He et al. [2] developed three mathematical models and the iterative algorithms to investigate the annual performances of a natural draft dry cooling tower (NDDCT), a pre-cooled NDDCT and a natural draft wet cooling tower (NDWCT), finding that the precooling system can increase the heat rejection and save 70% water consumption in hot months. Hooman investigated the convective heat transfer performance of the air-cooled heat exchanger and

⇑ Corresponding author. E-mail address: [email protected] (L. Yang). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2017.01.049 0017-9310/Ó 2017 Elsevier Ltd. All rights reserved.

dry-cooling tower by using CFD methods [3], and predicted the wind effects on the performance of natural draft dry cooling towers by theoretical analysis, which just lead to a maximum error of 15% compared to the numerical and experimental results [4]. Ma et al. [5] studied the effects of ambient temperature and crosswinds on the performance of NDDCS and found that the outlet water temperature of the air-cooled heat exchanger is approximately liner with ambient temperature whereas nonlinear with wind speed. Yang et al. [6,7] investigated the wind impacts on the thermoflow performances of NDDCS, finding that the performances are deteriorated with increasing the wind speed at low wind speeds and then get improved at high wind speeds. Zhao et al. [8–10] developed a three-dimensional numerical model for both the natural draft dry cooling tower and cooling columns, and studied the crosswind impact mechanism by introducing the inflow air deviation angle, obtained the exit water temperature distribution of cooling columns. Based on the wind effects on the thermo-flow performances of NDDCS, Al-Waked and Behnia [11] suggested the windbreaker configuration and found that the windbreakers can significantly weaken the adverse wind effects. Lu et al. [12] numerically analyzed a small dry-cooling tower, pointing out that the windbreakers installed at the bottom of dry-cooling tower can effectively improve the cooling performance of NDDCS. Following this numerical investigation, Lu et al. [13] used a scaled cooling tower model

X. Wang et al. / International Journal of Heat and Mass Transfer 108 (2017) 1924–1940

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Nomenclature a A b cp C Cr D e f fc g H I k KQ K L m n NTU p Q Re S t u v xj z

core friction coefficient heat transfer surface area (m2) core friction exponent specific heat (J kg
1 K
1) heat capacity rate (W K
1) the ratio of air and water heat capacity rate diameter (m) exponent in the power-law equation of wind speed pressure loss coefficient core friction factor gravitational acceleration (m s
2) height (m) turbulence intensity turbulent kinetic energy (m2 s
2) overall heat transfer coefficient (W m
2 K
1) friction loss coefficient length mass flow rate (kg s
1) number number of transfer unit pressure (Pa) heat rejection (W) Reynolds number source term in generic equation temperature (°C) velocity (m s
1) specific volume (m3 kg
1) coordinate in j direction (m) height above the ground (m)

d e f

g eQ l lt q r u

residual anti-freezing coefficient turbulence dissipation rate (m2 s
3) water flow rate propotion performance improvement degree heat exchanger effectiveness dynamic viscosity (kg
1 m
1 s
1) turbulent viscosity (kg m
1 s
1) density (kg m
3) minimum flow to face area ratio scalar variable

Subscripts a air minimum flow area Amin b base d cooling delta e exit he heat exchanger i inlet m mean min minimum max maximum pb turbine back pressure s sector t tower w wind wa water 1 inlet 2 outlet

Greek symbols diffusion coefficient (m2 s
1)

C

with horizontally arranged heat exchanger to investigate the cooling efficiency of natural draft dry cooling tower (NDDCT), finding that the total heat transfer rate was a combination of a natural convective heat transfer term and a forced convective one. Zhai and Fu [14] experimentally and numerically investigated the airflow and thermal performance of NDDCS, pointing out that about 50% of cooling capacity can be recovered by placing the windbreakers at the lateral sides of cooling tower. Goodarzi and Keimanesh [15] numerically studied the impacts of a radiator-type windbreaker, showing that a better performance can be achieved than the solid-type windbreaker. Goodarzi [16,17] also investigated different types of cooling tower, pointing out that the dry-cooling tower with an elliptical cross section or a loxotic exit has a better performance at high wind speeds. Liao et al. [18] investigated the influence of the height to diameter ratio of dry-cooling tower, pointing out that a lower height to diameter ratio can help NDDCS achieve better performances at strong ambient winds. The aforementioned works show that the thermo-flow performance improvement of NDDCS mainly focuses on the windbreaker and cooling tower configurations. Few researches pay attention to the circulating water distribution under crosswind conditions. Goodarzi and Amooie [19,20] combined the Genetic Algorithm with CFD computational model to optimize the distribution of circulating water. However, they utilized a simplified physical model and merely investigated the water distribution at a certain wind speed. By changing or integrating the geometric structure of NDDCS, the measures of windbreakers and unusual tower geometry undoubtedly lead to a satisfactory improvement of the thermoflow performances of NDDCS in a certain wind direction, but they

may not work well when the wind direction or speed changes. The approach of circulating water distribution needn’t change the configuration of NDDCS, so it can be easily used in practical engineering with a low cost [20]. Moreover, the water distribution can be flexibly adjusted with the changing wind direction and speed, which may improve the energy efficiency of the power generating unit under different wind conditions. In this study, a typical natural draft dry cooling system coupled with the condenser will be investigated, which works under a constant heat load. A three-dimensional physical model is developed for both the tower shell and each cooling delta of air-cooled heat exchanger. For the cooling delta, the heat exchanger model is applied, which takes both the flow and heat transfer on the air side and the heat rejection on the water side into consideration. Because the water flow rate of each sector can be artificially controlled, the circulating water flow distribution of each sector under wind conditions will be investigated. Different from the coupled numerical-theoretical procedure with Genetic Algorithm provided by Goodarzi and Amooie, the theory of entransy dissipation [21] will be integrated with the numerical-theoretical iteration procedure to find the optimized water distribution under various wind conditions.

2. Numerical model 2.1. Physical model A typical natural draft dry-cooling tower of a 200 MW power generating unit, which adopts a hyperbolic tower shell and incor-

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porates vertically arranged air-cooled heat exchanger bundles, is schematically shown in Fig. 1(a), and the specific parameters are listed in Table 1. As shown in Fig. 1(b), two adjacent cooling columns form a triquetrous cooling unit with an intersection angle about 49.08°. They are modeled in a three-dimensional form to consider the circulating water heat rejection. Plenty of such cooling deltas linked by supports constitute the entire air-cooled heat exchanger. For easily distributing the circulating water, all the cooling deltas are divided into several sectors in practical engineering. In this work, the entire air-cooled heat exchanger is divided into ten sectors and each sector contains eleven cooling deltas as shown in Fig. 1(c), where the wind direction and six characteristic angles of air-cooled heat exchanger are also indicated owing to the geometric symmetry. Different sizes of computational domain are tested and the final physical model is shown in Fig. 2. The computational domain is designed large enough compared with the dry cooling tower and air-cooled heat exchanger aiming to eliminate the unrealistic impact of the domain boundaries on the flow field. For the computational zones far from the cooling tower, they are divided into several partitions so as to be meshed by using the multi-block hybrid

Table 1 Geometric parameters of dry-cooling tower and air-cooled heat exchanger. Parameter

Symbol

Value

Tower height (m) Base diameter of tower (m) Outlet diameter of tower (m) Throat height of tower (m) Throat diameter of tower (m) Height of deltas (m) Outlet diameter of deltas (m) Number of sectors Number of cooling deltas

Ht Db Do Htt Dtt Hhe Dod ns nd

125 95.24 60 90 56 14 100.4 10 110

approach. In the domain far from the central part, the hexahedral structured grids are used and the grid interval size adopts the successive ratio grading scheme so that fewer meshes are generated. Fig. 3 shows the detailed mesh discretization of and around the cooling deltas. The hexahedral structured grids are chosen for the rectangular cooling columns, while the tetrahedral unstructured ones mixed with hexahedral, wedge-shaped and fastigiated ones

Fig. 1. Schematics of natural draft dry cooling system. (a) Air-cooled heat exchanger and dry-cooling tower, (b) cooling deltas, (c) sector arrangement.

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Fig. 3. Meshes of cooling columns and around cooling deltas. (a) Cooling columns, (b) around cooling deltas.

Fig. 2. Computational domain and boundary conditions. (a) With winds, (b) without winds.

are adopted for other parts. A grid system with 3,704,047 cells is finally adopted. 2.2. Heat exchanger model As the fin pitch of the heat exchanger bundles is within about 3 mm and the tube diameter is 25 mm, but the outside diameter of the air-cooled heat exchanger arrives at even 100.4 m and the computational domain covers up to 800 m, it is impossible to model the individual fin and tube. Moreover, the circulating water temperature is stratified in the flow direction, leading to the variation of heat rejection over the entire heat exchanger core. So the macro heat exchanger model is used to account for the air pressure loss and the water heat rejection of heat exchanger cores. In the heat exchanger model, the fluid zone representing the heat exchanger core is subdivided into macroscopic cells contained within several macros along the water path. For the cooling column, the water path and the number of macros are shown in Fig. 4. The water inlet temperature to each macro is computed and then subsequently used to compute the heat rejection from each macro. By adopting the porous media model, the pressure loss Dp can be computed using a known pressure loss coefficient as a function of geometric parameters, which is defined as:

1 Dp ¼ f qu2Amin 2

ð1Þ

where q is the air density, uAmin is the air velocity at the minimum flow area, f is the pressure loss coefficient and can be computed as follows [22].

Fig. 4. Schematic of macros and water flow direction in a single column.




f ¼ K c þ 1
r2
ð1
r2
K e Þ

ve ve þ2
1 vi vi

 þ fc

A Ac

vm vi

ð2Þ

where r is the ratio of minimum flow to face area, Kc and Ke are the entrance and exit loss coefficients, A and Ac are the air-side surface area and minimum cross-sectional flow area, vi and ve are the specific volumes at the inlet and exit, vm is the mean specific volume, fc is the core friction factor and takes the following form

f c ¼ aRebA min

ð3Þ

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where a and b are the empirical core friction coefficient and exponent, ReAmin is the Reynolds number based on the air velocity at the minimum flow area. The parameters in the pressure loss coefficient can be obtained by the wind tunnel experiments of the plate finned tube bundles by Kong et al. [23]. The contraction loss in the entrance and the expansion loss in the exit are embodied in fc, so Kc and Ke are set to zero. The coefficients in Eqs. (2) and (3) are listed in Table 2. The heat transfer Q is defined as

fluid zones, the additional momentum and energy source terms are set zero. The realizable k-e model and standard wall function are used to characterize the turbulent flows based on the turbulence kinetic energy k and dissipation rate e, which can accurately predict the flows involving the separation, recirculation and boundary layers under strong adverse pressure gradients around the dry-cooling tower. The k at the inlet boundary is calculated as follows

Q ¼ eðcp mÞmin jt 1
t 2 jmax ¼ eðcpa ma Þðtwai
t ai Þ

k ¼ 1:5ðum IÞ2

ð4Þ

ð14Þ

where (cpm)min represents the minimum heat capacity rate and is equal to cpama, |t1
t2|max is the maximum temperature difference between the two fluids, twai and tai are the inlet temperatures of the circulating water and air, e is the effectiveness of the heat exchanger and depends on the heat exchanger geometry and flow pattern, which is calculated by the following equation:

where um represents the mean velocity, I is the turbulence intensity and assumed to be 10%. The value of e at the inlet boundary can be estimated as follows

ð5Þ

where cl is an empirical constant of 0.09 for calculating the parameters of inlet boundary [25], the turbulent viscosity lt/l is taken as 1.1 as a typical case. Under wind conditions, the wind speed uwind varies with the height z, which is calculated by the power-law equation.

  1 e ¼ 1
exp
NTU 0:22 ½1
expð
C r NTU 0:78 Þ Cr

where Cr is the ratio of Cmin to Cmax and NTU is the number of transfer units with the following forms:

C r ¼ C min =C max ¼ ðcpa ma Þ=ðcpwa mwa Þ NTU ¼ KA=ðcp mÞmin

ð6Þ ð7Þ

where K and A are the heat transfer coefficient and air-side surface area of the heat exchanger. Eqs. (4)–(7) can refer to [22,24]. The heat transfer for a given cell is computed from

Q cell ¼ ecpa ma ðt wa;in
t cell Þ

ð8Þ

where twa,in is the water inlet temperature of the macro containing the cell, tcell is the cell temperature. The heat rejection for a macro is the sum of the heat transfer of all the cells contained within the macro, defined as follow:

X

Q macro ¼

ð9Þ

Q cell

all cells

Then the total heat rejection is given by:

X

Q total ¼

ð10Þ

Q macro

all macros

This approach provides a realistic heat rejection distribution over the entire heat exchanger core. 2.3. Governing equations The governing equations of the air-side flow and heat transfer take the following form:


 @ quj u @ @u þ Su þ Su 0 ¼ Cu @xj @xj @xj

ðj ¼ 1; 2; 3Þ

ð11Þ

where uj is the velocity in the xj direction, u, Su and Cu respectively represent the physical variable, its diffusivity and source term, which are listed in Table 3. For the fluid zone of the heat exchanger core, the additional momentum and energy source terms Su0 are added to the governing equations, which take the following forms.

Su0 ¼


Su0 ¼

Dp Lxj

Q cell V cell

ð12Þ

ð13Þ

where Lxj represents the length of the heat exchanger core in the xj direction, Vcell is the volume of the cell within the macro. For other

2

e ¼ qcl



1

lt l l

k

uwind ¼ uw

 z e 10

ð15Þ

ð16Þ

where uw is the wind speed at the height of 10 m, for which five wind speeds of 4 m/s, 8 m/s, 12 m/s, 16 m/s and 20 m/s are assigned, e is the wind profile index and taken as 0.2 as a representative case. The outflow boundary condition is specified for the downstream surface and the symmetry boundaries are setup for other surfaces as shown in Fig. 2(a). The ground is appointed as the adiabatic wall boundary condition. In the absence of winds, the four vertical domain surfaces are set as pressure inlet. The top surface is set as pressure outlet boundary because the pressure is known but the flow rate or velocity is not known, as shown in Fig. 2(b). For the tower wall, the fluid-solid coupled condition is specified for both the wind and no wind cases. The equations for the continuum, momentum, energy, turbulent kinetic energy and dissipation rate are discretized using the first-order upwind differencing scheme. The solution of pressure and velocity is coupled by using the SIMPLE algorithm. The divergence-free criteria of 10
4 for all the scaled residuals of the variables except for the energy equation with the criterion of 10
6 are prescribed. The air mass flow rate is also used to monitor whether the iteration is converged to a reasonable result. For a typical dry cooling system, the flow and heat transfer of cooling air are coupled with the performances of circulating water and exhaust steam. The water temperature rise in the condenser is equal to the water temperature drop in the air-cooled heat exchanger. As a result, the numerical simulation is an iterative procedure and the convergence criterion is the heat balance between the condenser and air-cooled heat exchanger. The iteration steps of the numerical simulation on the thermo-flow performances of natural draft dry cooling system and the turbine back pressure of power generating unit are shown in Fig. 5. In this work, the thermo-flow performances of natural draft dry cooling system and turbine back pressure will be investigated at various water flow distribution schemes, as listed in Table 4. The optimal water flow distribution will be achieved at which the thermo-flow performances of NDDCS are superior to others. 2.4. Numerical-theoretical iteration for optimization Based on the entransy dissipation-based optimization method, Sun et al. [21] investigated the circulating water distribution, and

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satisfy the requirements of the cooling capacity at the air-side. The heat rejection predicted by the optimization method is higher than that with circulating water uniformly distributed under a certain wind condition. This optimization method is adopted and several corrections are carried out to suit the numerical model used in this work.

Table 2 Coefficients in heat exchanger model.

r

Kc

Ke

a

b

0.492

0

0

0.9255


0.34123

proposed a theoretically global optimization method for water distribution. This optimization method claims that when the air flow rate in one sector increases or the inlet air temperature decreases, the circulating water flow rate should increase correspondingly to

(1) The maximum water flow rate may become considerably larger than the minimum one after redistributing the circulating water. Low water flow rate leads to a large thermal

Table 3 Summary of generic governing equations. Equations

u

Cu

Su

Continuity x-Momentum

1 ui

0

0

le

@p
@x þ 13 i

y-Momentum

uj

le

@p
@x þ 13 j

h

@ @xi



h



h



@ @xi

z-Momentum

uk

le

@p
@x þ 13 k

Energy Turbulence kinetic energy Turbulence dissipation rate

cp t k e

le/rT l + lT/rk l + lT/re

0 Gk + Gb
qe

Fig. 5. Computational flow chart for numerical simulations.

@ @xi









i









i









i

@uj @uk @ @ i le @u @xi þ @xj le @xi þ @xk le @xi @uj @uk @ @ i le @u @xj þ @xj le @xj þ @xk le @xj

@u @ui k le @x þ @x@ j le @xkj þ @x@ k le @u @xk k

qC 1 Se
qC 2 kþepffiffiffiffi þ C 1e ke C 3e Gb ue 2

þ qg

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Table 4 Distribution schemes of water flow rate (unit in kg/s).

Uniform Scheme A Scheme B Scheme C Scheme D

Sector 1, 10

Sector 2, 9

Sector 3, 8

Sector 4, 7

Sector 5, 6

Total

725 1087.5 1160 1450 1812.5

725 906.5 978.75 688.75 688.75

725 507.5 432 217.5 217.5

725 435 362.5 398.75 398.75

725 688.75 688.75 870 507.5

7250 7250 7250 7250 7250

resistance at water-side, which can hardly be ignored, comparing with the thermal resistance at air-side. So the ki [21] used in this paper contains three parts, the convective heat transfer of water-side, the heat conduction of tube wall and the convective heat transfer of air-side. The coefficients and exponents will not keep the same for different sectors. (2) The NDDCS is coupled with the condenser, so the turbine back pressure is used as the evaluation index to predict the improvement of cooling efficiency. The iterative procedure associated with the numerical simulation is applied to the water distribution optimization, as shown in Fig. 6. Before the start of this iterative procedure, the air and water parameters with water uniformly distributed under different wind conditions are set as initial inputs. The total water flow rate keeps a constant during the whole procedure. 2.5. Model validation The wind tunnel experiment in Guodian Academy of Science and Technology of China was carried out to test the validity of the modeling and numerical methods. Inside the actual dry-

cooling tower, the locations of the measuring points are shown in Fig. 7(a) and (b). The volumetric flow rate of the flue gas is about 1218 m3/s and the outlet diameter of the stack is 7.5 m. The scaled tower model in the wind tunnel experiment has the height of 0.58 m with the dimension scale of 1:300. The horizontal cross sections with the heights of 84.2 m and 144.2 m are chosen as illustrated cases, and Fig. 7(c) and (d) show the ascending velocities at these two cross sections in the absence of winds and at the wind speed of 4 m/s. What’s more, the simulated results by utilizing the macro heat exchanger model and traditional radiator model from our previous work are also compared at the height of 164.2 m as shown in Fig. 7(e)–(f) for verifying these two numerical models. It can be seen that the ascending velocities at the tower center of the two cross sections are much higher than other locations due to the flue gas discharge from the stack as shown in Fig. 7 (c) and (d), and the numerical results agree well with the measured data. From Fig. 7(e) and (f), the satisfactory agreement can also be clearly observed among the simulating results by using different models and the experimental data, which prove that the macro heat exchanger model is reliable enough to predict the performance of natural draft dry cooling system.

Fig. 6. Flow chart for numerical-theoretical iterative procedure.

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Fig. 7. Experimental setup and results. (a) Vertical view of measuring points, (b) horizontal view of measuring points, (c) ascending velocities without winds, (d) ascending velocities at wind speed of 4 m/s, (e) comparisons of ascending velocities at the height of 164.2 m without winds, (f) comparisons of ascending velocities at the height of 164.2 m at wind speed of 4 m/s.

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3. Results and discussion 3.1. Uniform water distribution The pressure, streamlines and temperature fields at the horizontal cross sections with the water uniformly distributed in the absence of winds and at different wind speeds are shown in Figs. 8– 10. With no winds as shown in Fig. 8, the centrally symmetric distributions of the pressure, streamlines and temperature can be clearly seen, and the cooling air flows uniformly through each cooling column. In practical engineering, the water temperature is continuously changing during the flowing process and the air flow through different parts of a single cooling column is not uniform, so the outlet air temperature of the cooling column is correspondingly inhomogeneous. Fig. 9(a) shows the local temperature field at the vertical cross section around the cooling deltas. It can be seen that the air near the bottom of the air-cooled heat exchanger reaches a higher temperature, which is also presented in Fig. 9 (b). By using the heat exchanger model, the temperature stratification of the circulating water is successfully presented, leading to

Fig. 9. Temperature fields for air-cooled heat exchanger. (a) Vertical cross section, (b) cooling columns.

Fig. 8. Variable fields at the height of 10 m in absence of winds. (a) Pressure, (b) streamlines and temperature.

also the temperature stratification of the airflow through each cooling column, which can be cleared observed in Fig. 9 (a) and (b). This result agrees will with the study by Tanimizu and Hooman [26] that the air temperature gradually decreases with the height. At the low wind speed of 4 m/s, the pressure, streamlines and temperature fields at the height of 10 m are shown in Fig. 10. It can be seen that the flow and temperature fields vary widely with the cooling deltas and present no longer centrally symmetric. The pressures outside the windward and leeward sectors are higher than those outside the lateral sectors due to the air acceleration near the lateral sectors. The smaller pressure difference between the outer and inner sides of the lateral sector result in fewer air flows compared to the windward and leeward sectors. At the high wind speed of 12 m/s, the pressure, streamlines and temperature present greater differences compared with those without winds and at the wind speed of 4 m/s, as shown in Fig. 11. In Fig. 11(a), it can be observed that there exists a high pressure zone outside the frontal sectors because of the strong ambient winds. Big pressure difference will drive more air to flow through the frontal part of the heat exchanger, so the thermo-flow performances of these sectors are improved. However, the high wind speed also results in a high tangential air flow velocity outside the lateral sectors and the smaller pressure differences

X. Wang et al. / International Journal of Heat and Mass Transfer 108 (2017) 1924–1940

Fig. 10. Variable fields at the height of 10 m at wind speed of 4 m/s. (a) Pressure, (b) streamlines and temperature.

existing in these sectors will seriously hinder the air flows into the dry-cooling tower, deteriorating the cooling performance of the lateral sectors. For the leeward sectors, the cooling air is affected by both the ambient wind and the air flowing easily through the windward sectors with a high velocity. However, their thermoflow performances are still better than the lateral ones. What’s more, the vortices are generated near the center of dry-cooling tower and at both sides of sectors, where the low pressure and high temperature appear accordingly as shown in Fig. 11(a) and (b). Due to the small air flow rate, the temperatures at the lateral sectors are the highest as shown in Fig. 11(b). 3.2. Heterogeneous water distribution As illustrative cases, the schemes A and D with non-uniform water flow distributions are used to compare the thermo-flow performances of natural draft dry cooling system. In the scheme A, more circulating water is allocated to the frontal sectors and the water flow rates at the lateral sectors No. 3 and No. 4 are reduced to 507.5 kg/s and 435 kg/s. At the wind speed of 4 m/s, the pressure fields at the horizontal cross section are shown in Fig. 12(a). The water flow rate change will affect the heat trans-

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Fig. 11. Variable fields at the height of 10 m at wind speed of 12 m/s. (a) Pressure, (b) streamlines and temperature.

fer between the water and air. But it plays a negligible role in the flow resistance of air passing through the heat exchanger, so the pressure is almost the same as the uniform water distribution scheme. However, certain differences of temperature fields at the height of 10 m can be observed in Fig. 12(b) compared to Fig. 10 (b). The air temperature at the exit of windward sectors increases by about 1 °C due to the increased water flow rate and heat transfer enhancement. Moreover, reducing the superfluous water flow rates of sectors No. 3 and No. 4 leads to the reduced air temperatures at the exit of these sectors. The temperature around the leeward sectors varies little compared with that of uniform distribution scheme because the water flow rate in this part does not change more for scheme A. At the wind speed of 12 m/s, the pressures at the height of 10 m for scheme A are still similar to those for the uniform distribution scheme as shown in Fig. 13(a). While the temperature fields for these two schemes are different from each other to a certain extent as shown in Fig. 13(b). After redistributing the water in every sector, the air flowing through the windward sectors can gain more heat, so it is heated to a higher temperature. However, the air near the side sectors can no longer gain as more heat as original.

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Fig. 13. Variable fields at the height of 10 m at wind speed of 12 m/s for Scheme A. (a) Pressure, (b) streamlines and temperature. Fig. 12. Variable fields at the height of 10 m at wind speed of 4 m/s for Scheme A. (a) Pressure, (b) streamlines and temperature.

For the scheme D, the water flow rate in the windward sectors increases by 150%, while the lateral sectors No. 3 and No. 4 are respectively reduced by 70% and 45%, the leeward sector is reduced by 30%. At the wind speed of 4 m/s, the pressure, streamlines and temperature fields are shown in Fig. 14. The pressure inside the drycooling tower at the height of 10 m is a little lower than that in Fig. 10(a), so more air can flow into the cooling tower. The temperature field presented in Fig. 14(b) is significantly different from that of scheme A, and the temperature at the exit of windward sectors further increases, showing that more heat is rejected in sector No. 1 and sector No. 2 due to the increased water flow rate. The temperatures at both sides are conspicuously lower than those at the front, which is caused by drastically reduced water flow rate in sector No. 3, showing that the inflow air in this region cannot be adequately heated while the water with a small flow rate is over cooled. So the excessive reduction of water flow rates of lateral sectors at a low wind speed will be counterproductive. The vortexes can no longer be seen clearly in the center of the dry-cooling tower, so the air flow inside the tower is more even than those of scheme A and uniform scheme.

At the wind speed of 12 m/s, the pressure, streamlines and temperature fields are shown in Fig. 15. From Fig. 15(a), it can be seen that the pressure difference of the windward sectors becomes a littler larger, leading more air flow through these sectors. However, the air can hardly flow into the dry-cooling tower from the lateral sectors. As a result, the pressures at the entrance and exit of this part are almost the same, showing that the wind adverse impacts become even more serious in this distribution scheme. As shown in Fig. 15(b), the hot plume from the windward sectors still has a high temperature similar to the temperature field at the wind speed of 4 m/s. The vortexes at both sides of the heat exchanger become strong so that fewer air can inflow these areas. The reduced airflow rate results in a further deterioration of thermoflow performances of the lateral sectors together with the reduced water flow rate of these sectors. This deterioration will offset the beneficial effect of directing water flow to the windward sectors to a certain extent. 3.3. Performance improvement analysis The heat rejection of each sector for all schemes at various wind speeds are shown in Fig. 16, where the heat rejection symmetry can be observed due to the axial symmetrically arranged sectors

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Fig. 14. Variable fields at the height of 10 m at wind speed of 4 m/s for Scheme D. (a) Pressure, (b) streamlines and temperature.

in the wind direction. In the absence of winds, the heat rejections of different sectors are almost the same as shown in Fig. 16(a). As the wind speed increases, the heat rejections vary widely with each sector. At the wind speed of 20 m/s, the windward sectors reject the heat even more than two times without winds. For the middle front sector No. 2 and No. 9, the heat rejections almost remain constant with increasing the wind speed. The heat rejections of sectors No. 3, No. 4, No. 7 and No. 8 are much lower than other sectors due to the reduced air flow rates through these sectors. The heat rejections of sectors No. 5 and No. 6 are in the middle level, and they firstly increase and then decrease to a level lower than that without winds for uniform distribution scheme and schemes A–D. This is because that at high wind speeds of 16 and 20 m/s, the hot plume penetration appears in part of the leeward sectors, leading to the reduced flow rate and deteriorated cooling performance. The heat rejection increases of frontal sector No. 1 and No. 10 can be observed from Fig. 16(b)–(d) as the wind speed increases. On the contrary, the heat rejections of lateral sectors for schemes A, B, C and D are somehow lower than that with the water uniformly distributed, as a result that different amounts of water are allocated to the windward sectors from lateral ones, improving the thermo-flow performances of upstream cooling deltas while reducing the heat transfer capability of lateral ones to some extent.

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Fig. 15. Variable fields at the height of 10 m at wind speed of 12 m/s for Scheme D. (a) Pressure, (b) streamlines and temperature.

Fig. 17 shows the outlet water temperature of each sector for various water distribution schemes. It can be seen that the changing trends presented in Fig. 17(a) are completely opposite to those in Fig. 16(a), because more heat rejection means the water is cooled to a lower outlet temperature. For the schemes A–D, the outlet water temperatures of frontal sectors No. 1 and No. 10 increase by 3–5 °C at various wind speeds compared with uniform distribution scheme, because more water are allocated to the frontal sectors to match the strong oncoming ambient winds, as shown in Fig. 17(b)–(e). The lowest temperature no longer appears at the frontal sectors but at the lateral sectors at the low wind speed of 4 m/s, as a result of the water flow redistributing. For the schemes C and D, much more water are allocated to the windward sectors and only a little is arranged for the lateral ones, so the outlet water temperature changing trends at the wind speeds lower than 8 m/s become opposite to those of uniform distribution scheme, decreasing at first from the windward sectors to lateral ones and then increasing from the lateral sectors to leeward ones, as shown in Fig. 17(d) and (e). The optimized water distributions by using the numericaltheoretical iteration method for each sector at various wind speeds are list in Table 5. The average outlet water temperature of the

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Fig. 16. Heat rejection of each sector. (a) Uniform distribution scheme, (b) scheme A, (c) scheme B, (d) scheme C, (e) scheme D.

air-cooled heat exchanger and turbine back pressure for different schemes and optimized water distribution are shown in Figs. 18 and 19. For the uniform water distribution, the average outlet

water temperature increases from 36.3 °C to 41.7 °C as the wind speed increases from 4 to 12 m/s, and then decreases to 37.9 °C at the wind speed of 20 m/s. The similar changing tendencies can

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Fig. 17. Outlet water temperature of each sector. (a) Uniform distribution scheme, (b) scheme A, (c) scheme B, (d) scheme C, (e) scheme D.

also be observed in other four schemes. For the schemes A and B with ambient winds, the average outlet water temperatures are always lower than the uniform distribution scheme, showing that

these two schemes can improve the cooling performance at all wind speeds. For the scheme C, the unexpected result is presented at the wind speed of 4 m/s, showing that too much water

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Table 5 Optimized water distributions in the absence and presence of winds (unit in kg/s). Sector number

Sector 1, 10

Sector 2, 9

Sector 3, 8

Sector 4, 7

Sector 5, 6

Total

No wind 4 m/s 8 m/s 12 m/s 16 m/s 20 m/s

725 848.16 1149.02 1420.45 1673.15 1811.51

725 730.23 735.76 703.96 654.18 646.22

725 611.91 272.58 103.54 37.7106 105.72

725 654.4 499.34 226.2 518.84 485.86

725 780.3 968.3 1170.85 741.11 575.69

7250 7250 7250 7250 7250 7250

The turbine back pressure shown in Fig. 19 presents almost similar trends to the average outlet water temperature. For the schemes A and B, the turbine back pressure is from 0.3 to 1.5 kPa lower than the uniform distribution scheme, showing that the energy efficiency of the power generating unit can be improved to a certain extent especially at high wind speeds. The schemes C and D can even obtain a 1.7 kPa lower turbine back pressure at very high wind speeds, but lead to the reduced energy efficiency at low wind speeds. For the optimized scheme, the pressure drop can reach 0.6 kPa at the wind speed of 4 m/s and 1.54 kPa at the wind speed of 12 m/s. Figs. 18 and 19 both show that the optimized water distribution can significantly improve the thermoflow performances of NDDCS. In order to clearly express the performance improvement degree of natural draft dry cooling system by water flow distribution, two dimensionless indexes, gt and gpb, are introduced and defined as follows:

gt ¼ Fig. 18. Average outlet water temperature of air-cooled heat exchanger for various schemes.

t wa2;uniform
twa2  100% t wa2;uniform

ð17Þ

pb;uniform
pb  100% pb;uniform

ð18Þ

gpb ¼

where twa2 and twa2,uniform are the outlet water temperatures for the heterogeneous and uniform water distribution schemes, pb and pb, uniform denote the turbine back pressures for the heterogeneous and uniform water distribution schemes. The gt and gpb at various wind speeds are respectively shown in Figs. 20 and 21. At low wind speeds, the negative values of gt and gpb show that the scheme C and D will deteriorate the thermo-flow performances of NDDCS. For the optimized scheme, it can be seen that the maximum outlet water temperature and turbine back

Fig. 19. Turbine back pressure for various schemes.

redistribution from the lateral sectors to the frontal ones will lead to an even higher average outlet water temperature than that with water uniformly distributed. As the wind speed further increases, the scheme C presents a lower outlet water temperature than other schemes. The optimized scheme is different from the others as also illustrated in Fig. 18. It can be seen that the outlet water temperature is lower than those of the other schemes under the certain wind condition, showing that the theoretically global optimization method associated with a numerical iterative procedure can achieve the best water distribution plan for a typical NDDCS.

Fig. 20. Dimensionless outlet water temperature of air-cooled heat exchanger for various schemes.

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Fig. 21. Dimensionless turbine back pressure for various schemes.

Fig. 23. Comparison of optimized water distributions.

pressure drops are achieved, showing that the optimized water distribution is superior to other water distribution schemes. The turbine back pressure for the optimized water distribution is also compared with that for the optimized windbreaker configuration by Chen et al. [27], as shown in Fig. 22. It can be seen that at high wind speeds, windbreaker configuration is superior to the optimized water distribution in reducing turbine back pressure. At the wind speed of 20 m/s for example, the turbine back pressure decreases by 38.8% for the windbreaker configuration, while the back pressure is only reduced by 11.8% by water flow distribution. However, at low wind speeds like 4 m/s, the optimized water distribution performs a little better than the windbreaker configuration. This may because that at low wind speeds, the windbreaker plays a weak role in the air flow improvement and will hinder the air flow to a certain extent. However, by redistributing the circulating water, the thermo-flow performances of NDDCS and the energy efficiency of the power generating unit will be improved. What’s more, the water distribution is easy to operate in practical engineering, and no additional devices are needed.

The optimized water distribution in this work is compared with that provided by Goodrazi and Amooie [20], as shown in Fig. 23. A dimensionless indexf is defined as follow to express the water flow rate propotion of each cooling delta or sector.

f¼

mi  100% mtotal

ð19Þ

where mi is the water flow rate of each part, mtotal denotes the total water flow rate. The cooling deltas need to be divided into twelve parts from five sectors for the convenience of comparison with the work by Goodrazi and Amooie [20]. It can be seen that the two distribution schemes are almost the same, and the specific proportion for the same cooling deltas is also very close. However, the water distribution proportions of the windward and leeward parts in this work are a little higher than those from Goodarzi and Amooie, but the proportion of lateral parts is lower. This difference may come from the different physical models or computational models. 4. Conclusions With the water flow distributions for the schemes A and B, the cooling performance of NDDCS is improved at any wind speed especially at high wind speeds, which adequately utilize the strong cooling capability of air through the windward sectors and properly make use of the air through the lateral sectors by allocating the water to the windward sectors from the lateral ones to a certain extent. Too much water flow redistribution from the lateral and leeward sectors to the windward ones will result in an adverse effect on the cooling performance at low wind speeds, despite that the performance can be improved at high wind speeds. By combining the numerical simulation with the theoretically global optimization method, the optimum water distributions under five certain wind conditions are obtained, which can contribute to the optimized operation of natural draft dry cooling system by water flow distribution. Acknowledgments

Fig. 22. Comparison of dimensionless turbine back pressure between optimized water distribution and windbreaker configrature.

The financial supports for this research, from the National Natural Science Foundation of China (Grant No. 51476055) and the National Basic Research Program of China (Grant No. 2015CB251503), are gratefully acknowledged.

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