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Auxiliary heat exchanger layout for freeze-proofing and performance recovery of natural draft dry cooling system
International Journal of Heat and Mass Transfer 150 (2020) 119381
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Auxiliary heat exchanger layout for freeze-proofing and performance recovery of natural draft dry cooling system Jingbo Yan, Xianwei Huang, Wenhui Huang, Lijun Yang∗, Xiaoze Du Key Laboratory of Power Station Energy Transfer Conversion and System of Ministry of Education, 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 7 July 2019 Revised 26 December 2019 Accepted 13 January 2020
Keywords: Natural draft dry cooling system Air-cooled heat exchanger Auxiliary heat exchanger Anti-freezing Thermo-flow performances Wind speed
a b s t r a c t Air-cooled heat exchanger faces a severe freezing risk in cold winter, especially for the finned tube bundles of windward sectors. Therefore, it is beneficial to the safe and energy-efficient operation of natural draft dry cooling system to take anti-freezing measures. In this work, the natural draft dry cooling system with auxiliary heat exchanger in front of windward sectors is proposed. By applying macro heat exchanger model to finned tube bundles and three-dimensional modeling on the air side, the freezeproofing and performance improvement of natural draft dry cooling system with auxiliary heat exchanger are numerically studied. The air velocity, pressure, and temperature fields, air mass flow rate, outlet water temperature and anti-freezing turbine back pressure are presented under winter conditions. Moreover, the air flow rate, heat rejection and turbine back pressure are obtained in warm days. The results show that the auxiliary heat exchanger can prevent the air-cooled heat exchanger from freezing at various wind speeds in winter. In warm days, the natural draft dry cooling system with auxiliary heat exchanger is superior to the conventional one at high wind speeds. In the absence of winds, its cooling performance gets deteriorated. © 2020 Elsevier Ltd. All rights reserved.
1. Introduction Owing to urgent water resource shortage, natural draft dry cooling system (NDDCS) has been widely applied to the power stations in arid regions [1]. In the vertically arranged cooling deltas of air-cooled heat exchanger, ambient air takes away the heat rejection from circulating water, so the ambient conditions play important roles in the thermo-flow performances of NDDCS. In cold winter, the circulating water is in danger of freezing and the finned tube bundles may suffer great damages. Therefore, it is of benefit to the safe and energy-efficient operation of natural draft dry cooling system to investigate the freezing characteristics and propose freeze-proofing measures of air-cooled heat exchanger. In the past decades, more emphases have been placed upon the unfavorable wind effects on the flow and heat transfer of NDDCS. Du Preez and Kröger stated that the thermo-flow performances of NDDCS get deteriorated under wind conditions [2]. Besides, the adverse effect is mainly caused by the flow resistance at the tower inlet and the turbulence at the entrance of heat exchanger
∗
Corresponding author. E-mail address: [email protected] (L. Yang).
https://doi.org/10.1016/j.ijheatmasstransfer.2020.119381 0017-9310/© 2020 Elsevier Ltd. All rights reserved.
[3]. Su et al. [4] found that the thermal-flow performance of side sectors gets seriously deteriorated, which could be attributed to the small intersection angle between air flows and heat exchanger surface. Li et al. [5] concluded that the cold air could flow into the top of the cooling tower, which weakens the heat transfer capacity of air-cooled heat exchanger and results in the increased outlet water temperature. Yang et al. [6] pointed out that the performances of upwind cooling deltas are superior to those at the rear and side ones, and a critical wind speed exists at which the cooling performance of NDDCS is worst. By wind tunnel test, Wei et al. [7] investigated the deterioration of thermo-flow performances of NDDCS and proposed some measures against the adverse wind effects. Chen et al. [8] proposed the combined interior and exterior windbreaker configurations of air-cooled heat exchanger to effectively improve the thermal-flow performances of NDDCS. Lu et al. [9,10] investigated the influences of tri-blade-like windbreaker and its orientation on the cooling performance of NDDCS, and recommended that one symmetry axis of windbreaker should be in alignment with the wind direction. Goodarzi [11] proposed a tower configuration with variable height to reduce the wind load without considerable cooling performance reduction of NDDCS. Liao et al. [12] studied the effect of triangularly arranged heat exchanger bundles on the thermo-flow performances of NDDCS, concluding that a higher
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Nomenclature A cp Cr D e H k K L m NTU p Q r Re Sᵩ t uj uw uz V xj z
heat transfer surface area (m2 ) specific heat (J kg−1 K−1 ) the ratio of air and water heat capacity rate diameter (m) exponent of the wind speed in the power-law equation height (m) turbulent kinetic energy (m2 s−2 ) overall heat transfer coefficient (W m2 K−1 ) length (m) mass flow rate (kg s−1 ) number of transfer unit pressure (Pa) heat rejection (W) polynomial factor Reynolds number source term temperature (°C) component of velocity (m s−1 ) wind speed (m s−1 ) ascending velocity inside tower (m s−1 ) volume (m3 ) Cartesian coordinate (m) height above the ground (m)
Greek symbols heat rejection (W) λ turbulence dissipation rate (m2 s−3 ) ε effectiveness of heat exchanger Г diffusion coefficient (kg m−1 s−1 ) ϕ scalar variable η iterative parameter ρ density (kg m−3 ) σ comparison index Subscripts a air ac auxiliary heat exchanger and cooling delta b base c condenser he heat exchanger i inlet o outlet t tower tt throat of tower w wind wa water
cooling efficiency can be achieved in a certain wind direction at high wind speeds. By optimizing the circulating water distribution, Goodarzi and Amooie [13,14] found that the cooling efficiency of NDDCS can be improved by 1.67% compared with uniform scheme. The aforementioned works show that the airside flow and thermal performances of NDDCS are thoroughly investigated, but the waterside is rarely involved. In frozen days, the circulating water may freeze when the ambient temperature is below 0 °C, however only few researches focus on the anti-freezing of NDDCS. Chen et al. [15] numerically studied the anti-freezing of NDDCS by controlling the opening degree of louvers in each sector. Wang et al. [16] obtained the anti-freezing water flow rate of NDDCS with the maximum value in the frontal sector. Besides, Wang et al. [17] proposed the simultaneous control of water flow rate and opening de-
Table 1 Geometric parameters of NDDCS and finned tube bundles.
NDDCS Tower height (m) Outlet diameter of tower (m) Throat height of tower (m) Throat diameter of tower (m) Air-cooled heat exchanger height (m) Base diameter of tower (m) Number of heat exchanger sectors Number of cooling deltas Number of auxiliary heat exchanger unit Distance between cooling delta inlet and auxiliary heat exchanger (m) Finned tube bundles Tube outside diameter (mm) Tube row number Transverse tube pitch (mm) Longitudinal tube pitch (mm) Fin thickness (mm) Fin pitch (mm) Upper slotted strip height (mm) Lower slotted strip height (mm) Slotted strip length (mm) Slotted strip width (mm)
Symbol
Value
Ht Do Htt Dtt Hhe Dohe nhes nco nAHE Lac
150 84.53 119.886 85.548 24 138 10 176 70 2.4
D − S1 S2
25 4 30 35 0.3 3.2 1.1 0.5 7 2.75
δf
Pf H1 H2 L1 L2
gree of louvers as the anti-freezing strategies. Kong et al. [18] proposed the water redistribution among various sectors to avoid freezing of air-cooled heat exchanger. As well known, the windward sector faces a more serious freezing risk than others due to the excessive cooling capacity of ambient air under windy conditions. In this work, the auxiliary heat exchanger (AHE) is proposed to set in front of the windward sectors to reduce the air flow rate. In cold winter, the auxiliary heat exchanger without circulating water is taken as the windbreaker to prevent the windward sectors from freezing. In warm days, the auxiliary heat exchanger with circulating water is put into operation to increase the cooling performance. The influences of auxiliary heat exchanger on the thermo-flow performances of NDDCS are investigated, which may contribute to the safe and energy-efficient operation of power generating unit. 2. Modeling 2.1. Physical model The cold end system in a typical 660MW power generating unit is schematically shown in Fig. 1(a), with the surface condenser and natural draft dry cooling system adopted. It consists of two heat transfer processes, first of which is from the exhaust steam to circulating water and the second takes place between the circulating water and cooling air. The overall NDDCS with the hyperbolic tower and vertically arranged air-cooled heat exchanger is schematically shown in Fig. 1(b), with the detailed geometric parameters listed in Table 1. The air-cooled heat exchanger is usually divided into ten sectors for easy distribution of circulating water. Due to the symmetric structure of NDDCS, only half of the air-cooled sectors are studied. The frontal and middle front sectors usually face greater freezing risks than others under windy conditions, so the auxiliary heat exchanger is arranged in front of these two sectors, as shown in Fig. 2. As the fundamental component of air-cooled heat exchanger, each cooling delta comprises two vertical finned tube bundles with an intersection angle of 49.08°, as shown in Fig. 3(a). For the auxiliary heat exchanger, the vertical finned tube bundles are annu-
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Fig. 1. Cold end system. (a) Condenser and NDDCS, (b) dry-cooling tower and air-cooled heat exchanger.
Fig. 2. Sectors, cooling deltas and auxiliary heat exchanger.
larly arranged in front of the cooling deltas, as shown in Fig. 3(b) and (c). Fig. 3(d) shows the finned tube bundles commonly used by air-cooled heat exchanger with the geometric parameters listed in Table 1.
2.2. Mathematical model The macro heat exchanger model is used to characterize the flow and heat transfer of finned tube bundles, with the porous
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Fig. 3. Air-cooled heat exchanger and auxiliary heat exchanger. (a) Cooling deltas, (b) auxiliary heat exchanger, (c) heat exchanger layout, (d) finned tube bundles.
media adopted to deal with the pressure drop p of air as follows [12]:
1 2
p = kL ρa u2f
(1)
where ρ a is the air density, uf is the face velocity, kL is the flow loss coefficient with the following form:
kL =
N
transfers for the given cell, macro and entire heat exchanger can be computed as follows:
Qcell = ε (mcp )a Tin,auxiliary − Tcell Qmacro =
Qcell
(3) (4)
all cells
rn unf −1
(2)
n=1
where N is set to be 6 in this work, the polynomial factor rn is obtained by fitting the experimental data, with the values of r1 = 51.756, r2 = 32.614, r3 = 11.682, r4 = 2.0986, r5 = 0.1808 and r6 = 0.0059. The heat exchanger core is subdivided into macroscopic cells or macros in the water flow direction, as shown in Fig. 4. The heat
Qtotal =
Qmacro
(5)
all macros
where (mcp )a means the heat capacity of air, Tin,auxiliary and Tcell are the inlet water temperature and air temperature of cell. The heat rejection from a macro is computed by summing all cells within the macro, then the total heat transfer of entire heat exchanger can be obtained. ε is the heat exchanger effectiveness, depending on
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The air side conservation equations are expressed as follows [12,18,20].
∂ρ uj ϕ ∂ ∂ϕ = ϕ + Sϕ + Sϕ ∂ xj ∂ xj ∂ xj
(9)
where ϕ equals 1, u, cp t, k and ε for the continuity, momentum, energy and turbulence equations respectively. Гϕ and Sϕ represent the diffusivity and source term, which are listed in Table 2. In this work, the realizable k-ε model is adopted because it can accurately characterize the turbulent flows involving the rotation, boundary layer under strong adverse pressure gradient, separation and recirculation, which is suitable for the simulation of natural draft dry cooling system. When the air flows through the heat exchanger zone, the pressure drop will be generated and the heat will be gained from the tube bundles, so the additional source terms Sϕ should be appended to the momentum and energy conservation equations, with the following forms.
Sϕ = − Sϕ =
p Lx j
Qhe Vhe
(10) (11)
where Lxj represents the heat exchanger length in the xj direction, Qhe is the heat rejection of heat exchanger, Vhe is the volume of heat exchanger zone. In other zones, the additional source terms equal 0. Sϕ 2.3. Computational domain, mesh and boundary conditions Fig. 4. Heat exchanger macros.
the heat exchanger structure and flow pattern as follows [14,16]:
1 ε = 1 − exp − NT U 0.22 1 − exp −Cr NT U 0.78
(6)
Cr = (mcp )a /(mcp )wa
(7)
NT U = KA/(mcp )a
(8)
Cr
where (mcp )wa is the heat capacity of water, K and A are the overall heat transfer coefficient and heat transfer surface area of air-cooled heat exchanger. In this work, the alternant slotted finned tube bundles in a staggered way are adopted as shown in Fig. 3(d), with the related parameters in heat exchanger model achieved by wind tunnel test [19].
For eliminating the impractical impact of the domain boundaries on the air flow field, the computational domain should be set large enough compared with the NDDCS, as shown in Fig. 5. The hexahedral grids are generated for the central part with heat exchanger and cooling tower, while the tetrahedral/hexahedron hybrid unstructured grids are applied to other zones. In this work, three grid schemes with 1 763 382, 3 469 265 and 5 469 332 cells are tested. The air mass flow rate at the wind speed of 4 m/s varies only 0.39% for the latter two density grid solutions, so the grid with the cell number of 3 469 265 is finally used. In the presence of winds, the windward surface of computational domain is set as velocity inlet, with the wind speed uz at the height of z (m) calculated by the following equation [21]:
uz = uw
z e 10
(12)
where uw is the wind speed at the height of 10 m with 4, 8, 12 and 16 m/s set. e is the wind speed profile index, with the typical value
Fig. 5. Computational domain and boundary conditions.
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J. Yan, X. Huang and W. Huang et al. / International Journal of Heat and Mass Transfer 150 (2020) 119381 Table 2 Summary of generic governing equations. Equations
ϕ
ϕ
Continuity
1
0
0
x-Momentum
ui
− ∂∂xp +
y-Momentum
uj
z-Momentum
uk
Energy Turbulence kinetic energy Turbulence dissipation rate
cp t k ɛ
μe μe μe μe / σ T μ + μ T / σk μ + μ T / σe
Sϕ
i
− ∂∂xp + j
− ∂∂xp + k
1 ∂ [ 3 ∂ xi 1 ∂ [ 3 ∂ xi 1 ∂ [ 3 ∂ xi
∂uj ∂ uk ∂ ∂ ∂ x j (μe ∂ xi ) + ∂ xk (μe ∂ xi )] ∂ (μ ∂ u j ) + ∂ (μ ∂ uk )] e ∂x e ∂x ∂xj ∂ xk j j (μe ∂∂ xuki ) + ∂∂x j (μe ∂∂ uxkj ) + ∂∂xk (μe ∂∂ uxkk )] + ρ g
(μe ∂∂ uxii ) +
(μe ∂∂ xuji ) +
0 Gk + Gb − ρε 2 ρC1 Sε − ρC2 k+ε√uε + C1ε εk C3ε Gb
Fig. 6. Experimental validation for numerical results [8,15]. (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.
of 0.2 in this paper. For the leeward surface, the outflow boundary condition is set due to the unchanged variable profiles. In the absence of winds, the side surfaces are set as the pressure inlet boundaries, and the top surface as the pressure outlet boundary with the gauge pressure of 0 Pa. The ambient temperatures at the domain surfaces are set equal to 303.15 K in warm days. In winter, the ambient temperatures of 263.15 K, 258.15 K and 253.15 K are chosen. The equations are discretized by the second-order upwind differencing scheme, and the pressure and velocity coupling is dealt with the SIMPLE algorithm. The divergence-free criteria of 10−4 for all the scaled residuals of variables are prescribed, except the energy equation with the criterion of 10−6 . The air flow rate is also
Table 3 Water flow rate of each sector (unit in kg/s).
Auxiliary frontal sector Auxiliary middle front sector Frontal sector Middle front sector Middle sector Middle rear sector Rear sector Total
Case 1
Case 2
Case 3
Case 4
0 0 450 425 450 425 450 2200
0 0 450 425 450 425 450 2200
0 0 900 850 900 850 900 4400
450 425 450 425 900 850 900 4400
used to monitor whether the iteration is converged to a reliable level.
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Fig. 7. Temperature fields and streamlines at the cross section with height of 10 m without winds. (a) Case 1, (b) case 2.
The energy equations of exhaust steam and circulating water in condenser are expressed as follows:
Fig. 8. Local pressure without winds for case 1.
2.4. Iteration process In cold winter, the auxiliary heat exchanger without circulating water does not participate in the heat transfer process, which is regarded as a windbreaker to prevent the windward sectors from freezing. During the iteration, the heat balances of circulating water and cooling air are considered simultaneously, and the outlet water temperature of each sector should be above 0 °C to meet the anti-freezing requirement. The iterative process for the anti-freezing calculation is presented as follows. (1) Develop the computational model of NDDCS, input the correlating parameters of finned tube bundles to the heat exchanger model. (2) Keep the water mass flow rate mwa constant, assume the inlet water temperature twa1 of the heat exchanger. (3) By CFD simulation, obtain the total heat rejection of aircooled heat exchanger and outlet water temperature twa2 of each cooling delta, find out the minimum outlet water temperature twa2min in various sectors. (4) Define the iterative parameter as η1 = (twa2min − 273.15)/ (twa1 − twa2min ). If 0 < η1 < 0.5%, the iteration is completed. Otherwise, reassume the inlet water temperature and repeat the process. (5) Output the heat rejection and outlet water temperature of various sectors, calculate the turbine pressure.
c = ms (hs − hwa )
(13)
c = c pw mw (tc,wa1 − tc,wa2 )
(14)
where c is the heat rejection of condenser, ms , mwa are the mass flow rates of steam and water, hs and hwa are the steam and condensate enthalpies, cpwa is the specific heat of circulating water, tc,wa1 , tc,wa2 are the inlet and outlet water temperatures of condenser, which are equal to the outlet and inlet water temperatures of air-cooled heat exchanger if the water heat loss between condenser and heat exchanger is neglected. When the iteration is completed, the inlet and outlet water temperatures of condenser can be achieved, the heat rejection c can be calculated by Eq. (14). The mass flow rate and enthalpy of steam are assumed to be constant, the condensate enthalpy can be calculated by Eq. (13), so the condensate temperature and turbine back pressure pbw are obtained. Once the back pressure pbw gets lower, the cold end system will face a freezing risk, so the pbw is defined as the antifreezing turbine back pressure. In warm days, the auxiliary heat exchanger with circulating water is put into operation. The iterative procedure for the thermoflow performances of NDDCS is described as follows. (1) Input steam flow rate, enthalpy, assume turbine back pressure pbs , calculate the heat rejection of condenser c . (2) In terms of water and steam flow rates, calculate the overall heat transfer coefficient Kc , inlet water temperature tc,wa1 and outlet water temperature tc,wa2 of condenser. (3) Develop the computational model of NDDCS, input the correlating parameters to heat exchanger model, and input water mass flow rate mwa and inlet water temperature twa1 . (4) By CFD simulation, obtain the outlet water temperature twa2 , calculating the total heat rejection of heat exchanger t . (5) Define the iterative parameter as η2 = (t − c )/t . If 0 < η2 < 0.5%, the iteration is completed. Otherwise, reassume the turbine back pressure pb and repeat the process. (6) Output outlet water temperature twa2 of air-cooled heat exchanger and turbine back pressure pb . For convenience, the winter conditions without and with auxiliary heat exchanger are named case 1 and case 2. The warm day conditions without and with auxiliary heat exchanger are named case 3 and case 4. The water flow rate of each sector under various conditions is listed in Table 3. In winter, the water distribution for case 1 is same as that for case 2. In warm days, the
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auxiliary heat exchanger is also filled with water. The sum of water flow rates of auxiliary frontal sector and frontal sector for case 4 is equal to the water flow rate of frontal sector for case 3, which is also applicable for the middle front sector. The water flow rates of other sectors for case 4 are same as those for case 3.
2.5. Model validation Following the scale law, a model dry-cooling tower with vertically arranged heat exchanger bundles around its circumference was tested in a wind tunnel in our previous work [8,15]. Fig. 6(a) and (b) show the measuring points inside the prototype tower. The
Fig. 9. Local pressure without winds for case 2. (a) Frontal sector, (b) middle front sector, (c) middle sector, (d) middle rear sector, (e) rear sector.
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Fig. 10. Temperature fields and streamlines at the cross section with height of 10 m at wind speed of 8 m/s. (a) Case 1, (b) case 2.
Fig. 11. Local pressure at wind speed of 8 m/s for case 1. (a) Frontal sector, (b) middle front sector, (c) rear sector.
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ascending velocities at the heights of 64.2 m and 164.2 m inside the real tower in the absence of winds and at the wind speed of 4 m/s were chosen as illustrative cases to compare the numerical results with the experimental data, as shown in Fig. 6(c) in the absence of winds and Fig. 6(d) at the wind speed of 4 m/s. It can be seen that for both cases, the numerical results agree well with the measured data, showing that the computational models and methods are reliable enough for the performance prediction of natural draft dry cooling system. In this work, the numerical approach is completely same as that based on the tested tower, which justifies in another way the modeling and numerical approaches. 3. Results and discussion 3.1. Winter conditions 3.1.1. Variable fields In winter, the AHE without circulating water can obstruct the air flows through windward sectors to avoid possible freezing. By adjusting the inlet water temperature of heat exchanger, the anti-
freezing of NDDCS can be achieved. As illustrative cases, the variable fields at 258.15 K in the absence of wind, at the wind speed of 8 m/s are presented and analyzed. Fig. 7 shows the temperature fields and streamlines without winds. For case 1, they are centrally symmetric as shown in Fig. 7(a). For case 2 however, this symmetry is disturbed. The outlet air temperatures of frontal and middle front sectors are higher than other sectors due to the reduced airflows obstructed by AHE. Besides, a vortex is generated at the central front of cooling tower as shown in Fig. 7(b) due to the uneven resistance of sectors. For case 1, only the local field of frontal sector is presented as shown in Fig. 8. The pressure is almost constant in the circumferential direction, and the pressure drop across the cooling deltas reaches 93 Pa. For case 2, the pressure drop through the cooling deltas varies clearly with each sector as shown in Fig. 9. For the frontal and middle front sectors, the pressure drop across the AHE is about 83 Pa, and about 34 Pa across the cooling deltas, which is much lower than that for case 1, showing a strong resistance effect from AHE on the air flows. For the middle, middle rear and rear sectors, the pressure drop about 105 Pa is
Fig. 12. Local pressure at wind speed of 8 m/s for case 2. (a) Frontal sector, (b) middle front sector, (c) rear sector.
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generated across the cooling deltas, which are higher than that for case 1. As a result, these sectors face more serious freezing risks. This is because that the velocity of air through the frontal and middle front sectors decreases, resulting in the reduced flow resistance of cooling air through middle, middle rear and rear sectors. Fig. 10 shows the temperature fields and streamlines for case 1 and case 2 at the wind speed of 8 m/s. For case 1 as shown in Fig. 10(a), the outlet air temperatures of the frontal and rear
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sectors are lower than other sectors, resulting in the freezing risk unexpectedly. The strong air flows through the frontal and middle front sectors have an inhibition effect on the rear and middle rear sectors, as a result, two vortices are generated near the middle sector. For case 2 as shown in Fig. 10(b), the AHE can significantly reduce the air flow rate of frontal and middle front sectors, so the inhibition effect on the air inflows at the rear and middle rear sectors gets reduced. As a result, the vortices move forward and the rear sector becomes superior to other sectors in the thermo-flow
Fig. 13. Air mass flow rate of each sector at various wind speeds. (a) Case 1 at 263.15 K, (b) case 2 at 263.15 K, (c) case 1 at 258.15 K, (d) case 2 at 258.15 K, (e) case 1 at 253.15 K, (f) case 2 at 253.15 K.
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performances. For both case 1 and case 2, the outlet air temperature of lateral sector is higher than those of other sectors due to the air inflow large deviation angle at the cooling delta inlet. The heat transfer capacities of the middle front and middle rear sectors are in the middle level. The local pressure fields of frontal, middle front and rear sectors for case 1 at the wind speed of 8 m/s are shown in Fig. 11. It can be seen that the pressure drops of these sectors vary from 157 to 182 Pa, 90 to 140 Pa, 90 to 140 Pa respectively. The frontal
sector shows a better flow performance and faces a greater freezing risk than other sectors due to the large momentum of coming wind. For the frontal and middle front sectors of case 2 shown in Fig. 12(a) and (b), the pressure drops across cooling deltas range from 43 to 50 Pa, 27 to 40 Pa, which are much lower than those for case 1. Besides, the pressure drops across the AHE for frontal and middle frontal sectors vary from 121 to 132 Pa and 35 to 105 Pa, showing a strong impeding effect on air inflows. The freezing risk of frontal and middle front sectors gets weak due to
Fig. 14. Outlet water temperature of each sector at various wind speeds. (a) Case 1 at 263.15 K, (b) case 2 at 263.15 K, (c) case 1 at 258.15 K, (d) case 2 at 258.15 K, (e) case 1 at 253.15 K, (f) case 2 at 253.15 K.
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Fig. 15. Anti-freezing turbine back pressure at various wind speeds and ambient temperatures.
the installation of AHE. For the rear sector of case 2 shown in Fig. 12(c), the pressure drop across the cooling deltas varies from 139 to 190 Pa, which is higher than other sectors, showing that it faces a serious freezing risk. Similar to the case without winds, the block effect of the air through the frontal sector on the air through rear sector is reduced, so the freezing risk of rear sector increases.
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3.1.2. Anti-freezing analysis By means of iterative calculation, the air mass flow rate, outlet water temperature of each sector, anti-freezing turbine back pressure are obtained. Fig. 13 shows the mass flow rates of cooling air through each sector for case 1 and 2 at various ambient temperatures and wind speeds. It can be seen that the air mass flow rate increases as the ambient temperature decreases. Taking the frontal sector of case 1 at the wind speed of 4 m/s as illustrative cases, the air mass flow rates through frontal sector at 263.15 K, 258.15 K and 253.15 K are 5298 kg/s, 6244 kg/s and 7658 kg/s. This is because when the ambient temperature drops, the temperature difference between circulating water and air increases, leading to the increased heat rejection and air mass flow rate. Besides, the mass flow rate changes with wind speed in a similar way at different ambient temperatures. In the absence of winds for case 1, the mass flow rates of various sectors are almost the same. However, for case 2, the air mass flow rates of frontal and middle front sectors are lower than other sectors due to the impeding effect of AHE. Under wind conditions for case 1, as the wind speed increases, the air mass flow rates of frontal and middle front sectors increase due to the wind induced enhancement of air flows. Besides, the air flow rate of frontal sector is higher than other sectors at various wind speeds, showing that the frontal sector faces a more serious freezing risk. The air flow rate of rear sector increases at first and then decreases with increasing the wind speed because the blocking effect on air flows across the rear sector gets strong at high
Fig. 16. Flow characteristics of each sector at various wind speeds. (a) Air flow rate for case 3, (b) air flow rate for case 4, (c) mass flow rate ratio.
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wind speeds. For case 2, the air flow rates of frontal and middle front sectors decrease compared with case 1 owing to the flow resistance generated by the AHE. However, the air flow rate of frontal sector at the wind speed of 16 m/s is still higher than other sectors. The changing trend of air flow rate through the rear sector is similar to that of case 1. Furthermore, the rear sector has a higher air flow rate than other sectors at the wind speeds of 4, 8 and 12 m/s. The flow performances of middle and middle rear sectors are poor at most wind speeds for case 1 and 2, showing that these sectors face no freezing risk. In cold winter, the outlet water temperature of each cooling delta must be above 0 °C. By adjusting the turbine back pressure, the anti-freezing of NDDCS can be achieved. Fig. 14 shows the outlet water temperature of each sector at various wind speeds. For case 1, the outlet water temperature of frontal sector is close to 0 °C at various wind speeds, showing that the frontal sector faces the most serious freezing risk. The outlet water temperatures of other sectors become high as the wind speed increases, because the turbine back pressure is lifted with the increased wind speed to prevent the heat exchanger from freezing, resulting in the increased inlet and outlet water temperatures of air-cooled heat exchanger. For case 2, the rear sector is easy of freezing at the wind speeds of 4, 8 and 12 m/s. At the wind speed of 16 m/s, the frontal sector faces the most serious freezing risk. The sector with maximum heat rejection is not fixed as the wind speed increases, which results in the complex changing trends of outlet water temperature.
Fig. 15 shows the anti-freezing turbine back pressures at various wind speeds and ambient temperatures. It can be seen that the anti-freezing back pressure increases clearly as the ambient temperature drops and the wind speed rises for case 1, and unfortunately it even reaches 65 kPa at the ambient temperature of 253.15 K and wind speed of 16 m/s, showing that only by increasing the turbine back pressure cannot the anti-freezing issues be settled. Other effective measures such as the circulating water redistribution, louver adjustment for various sectors should be taken [15–18]. For case 2, the anti-freezing back pressure varies little with the wind speed. In the absence of winds, the anti-freezing back pressure for case 2 is higher than case 1, however it is always lower than case 1 at various wind speeds, especially at the wind speed of 16 m/s with the maximum difference of 55 kPa, showing that the AHE configuration can effectively improve the energy efficiency and reduce the freezing risk of NDDCS.
3.2. Warm days The changing trends of air velocity, pressure and temperature in each sector in warm days are similar to those in winter, so the variable fields are not presented and only the thermo-flow performances are analyzed. In order to compare the mass flow rate and heat rejection of each sector between case 3 and case 4, two non-dimensional parameters, the mass flow rate ratio δ ma and heat rejection ratio δ ,
Fig. 17. Thermal characteristics of each sector at various wind speeds. (a) Heat rejection for case 3, (b) heat rejection for case 4, (c) heat rejection ratio.
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15
much lower back pressure for case 2 is presented with winds, especially at high wind speeds. For case 1, the frontal sector faces a more serious freezing risk than other sectors at various wind speeds. With the AHE, the rear sector faces a higher freezing risk than others at the wind speeds of 4, 8 and 12 m/s. At the wind speed of 16 m/s, the frontal sector is much easier to freeze. The turbine back pressure increases as the ambient temperature decreases, which obeys the similar changing trend with the wind speed. In warm days, the thermo-flow performances of NDDCS with AHE get poor in the absence of winds. At the wind speed of 4 m/s, they are close to those without AHE. At the wind speeds of 8, 12 and 16 m/s, the thermo-flow performances are improved thanks to the AHE. The heat rejections of frontal and middle front sectors with AHE are lower than those without AHE, but the middle rear and rear sectors have higher heat rejections. Declaration of Competing Interest
Fig. 18. Turbine back pressure at various wind speeds.
Authors declare that they have no conflict of interest.
are introduced.
δma = δ =
ma4 ma3
4 3
(15) (16)
where ma3 and ma4 are the air mass flow rates of each sector for case 3 and case 4; 3 and 4 are the heat rejections of each sector for case 3 and case 4. Fig. 16 shows the flow characteristics of each sector at various wind speeds. The air mass flow rates of frontal and middle front sectors for case 4 are lower than case 3 at various wind speeds due to the increased flow resistance generated by the AHE, and the mass flow rate ratios range from 0.47 to 0.61. For the middle rear and rear sectors, the flow performances for case 4 get remarkably improved compared with case 3. Besides, the improvements at the wind speeds of 8, 12 and 16 m/s are much higher than those in the absence of winds and at the wind speed of 4 m/s, with the mass flow rate ratio even reaching 2.32, showing that the flow performance can be substantially improved by the AHE. Fig. 17 gives the heat rejection of each sector at various wind speeds. It can be seen that for case 3, the heat rejection of each sector is almost positively related to the air flow rate. For case 4 however, the positive correlation with them is not always presented. The heat rejection of frontal sector is close to and even higher than rear sector at various wind speeds. For the frontal and middle front sectors, the heat rejection ratios reach about 0.85, which are higher than the mass flow rate ratio. Because the AHE with circulating water is in operation in warm days, the heat transfer area of frontal and middle front sectors for case 4 is larger than that for case 3. The heat rejections of middle rear and rear sectors for case 4 are higher than those for case 3. For the middle sectors of both case 3 and case 4, the heat rejections are always small at various wind speeds. Fig. 18 shows the turbine back pressures at various wind speeds for case 3 and case 4. It can be observed that the turbine back pressure for case 4 is higher than case 3 in the absence of winds, and very close to case 3 at the wind speeds of 4 m/s. At the wind speeds of 8, 12 and 16 m/s, the turbine back pressure for case 4 gets reduced compared with case 3, showing that the energy efficiency of power generating unit is improved thanks to the AHE. 4. Conclusions In winter, the anti-freezing turbine back pressure for case 2 is higher than that for case 1 in the absence of winds. However, the
CRediT authorship contribution statement Jingbo Yan: Data curation, Formal analysis, Investigation, Methodology, Software, Validation, Writing - original draft. Xianwei Huang: Resources, Software, Validation. Wenhui Huang: Data curation, Formal analysis. Lijun Yang: Conceptualization, Funding acquisition, Project administration, Writing - review & editing. Xiaoze Du: Supervision. Acknowledgments The financial supports for this research, from the National Natural Science Foundation of China (Grant nos. 51776067, 51821004) and the National Basic Research Program of China (Grant no. 2015CB251503), are gratefully acknowledged. References [1] D.G. Kroger, Air-cooled heat exchanger and cooling towers: thermal-flow performance evaluation and design, Penn Well Corp., 2004, pp. 1–49. [2] A.F. du Preez, D.G. Kröger, Effect of wind on performance of a dry-cooling tower, Heat Recovery Syst. CHP 13 (1993) 139–146. [3] A.F. du Preez, D.G. Kröger, The effect of the heat exchanger arrangement and wind-break walls on the performance of natural draft dry-cooling towers subjected to cross-winds, J. Wind Eng. Ind. Aerodyn. 58 (3) (1995) 293–303. [4] M.D. Su, G.F. Tang, S Fu, Numerical simulation of fluid flow and thermal performance of a dry-cooling tower under cross wind condition, J. Wind. Eng. Ind. Aerodyn. 79 (1999) 289–306. [5] X.X. Li, H. Gurgenci, Z.Q. Guan, Y.B. Sun, Experimental study of cold inflow effect on a small natural draft dry cooling tower, Appl. Therm. Eng. 128 (2018) 762–771. [6] L.J. Yang, X.P. Wu, X.Z. Du, Y.P. Yang, Dimensional characteristics of wind effects on the performance of indirect dry cooling system with vertically arranged heat exchanger bundles, Int. J. Heat Mass Transf. 67 (2013) 853–866. [7] Q.D. Wei, B.Y. Zhang, K.Q. Liu, A study of the unfavorable effects of wind on the cooling efficiency of dry cooling towers, J. Wind. Eng. Ind. Aerodyn. 54–55 (1995) 633–643. [8] L. Chen, L.J. Yang, X.Z. Du, Y.P. Yang, Performance improvement of natural draft dry cooling system by interior and exterior windbreaker configurations, Int. J. Heat Mass Transf. 96 (2016) 42–63. [9] Y. Lu, Z. Guan, H. Gurgenci, Z. Zou, Windbreak walls reverse the negative effect of crosswind in short natural draft dry cooling towers into a performance enhancement, Int. J. Heat Mass Transf. 63 (2013) 162–170. [10] Y.S. Lu, H. Gurgenci, Z.Q. Guan, S.Y. He, The influence of windbreak wall orientation on the cooling performance of small natural draft dry cooling towers, Int. J. Heat Mass Transf. 79 (2014) 1059–1069. [11] M.A. Goodarzi, Proposing a new technique to enhance thermal performance and reduce structural design wind loads for natural drought cooling towers, Energy 62 (6) (2013) 164–172. [12] H.T. Liao, L.J. Yang, X.Z. Du, Y.P. Yang, Triangularly arranged heat exchanger bundles to restrain wind effects on natural draft dry cooling system, Appl. Therm. Eng. 99 (2016) 313–324.
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[13] M. Goodarzi, H. Amooie, A proposed heterogeneous distribution of water for natural draft dry cooling tower to improve cooling efficiency under crosswind, in: 2012 4th Conference on Thermal Power Plants (CTPP), IEEE, 2012, pp. 1–6. [14] M. Goodarzi, H. Amooie, Heat transfer enhancement in a natural draft dry cooling tower under crosswind operation with heterogeneous water distribution, J. Nucl. Power 61 (2016) 252–259. [15] L. Chen, L.J. Yang, X.Z. Du, Y.P. Yang, Anti-freezing of air-cooled heat exchanger by air flow control of louver in power plants, Appl. Therm. Eng. 106 (2016) 537–550. [16] W.J. Wang, L.J. Yang, X.Z. Du, Y.P. Yang, Anti-freezing water flow rates of various sectors for natural draft dry cooling system under wind conditions, Int. J. Heat Mass Transf. 102 (2016) 186–200. [17] W.J. Wang, X.W. Huang, L.J. Yang, X.Z. Du, Anti-freezing operation strategies of natural draft dry cooling system, Int. J. Heat Mass Transf. 118 (2018) 165–170.
[18] Y.Q. Kong, W.J. Wang, L.J. Yang, X.Z. Du, Y.P. Yang, Water redistribution among various sectors to avoid freezing of air-cooled heat exchanger, Int. J. Heat Mass Transf. 141 (2019) 294–309. [19] Y.Q. Kong, L.J. Yang, X.Z. Du, Y.P. Yang, Effects of continuous and alternant rectangular slots on thermo-flow performances of plain finned tube bundles in in-line and staggered configurations, Int. J. Heat Mass Transf. 93 (2016) 97–1007. [20] F. Chu, Q. Gao, S. Li, G. Yang, Y Luo, Mass transfer characteristic of ammonia escape and energy penalty analysis in the regeneration process, Appl. Energy 258 (2020) 113975. [21] L. Chen, L.J. Yang, X.Z. Du, Y.P. Yang, A novel layout of air-cooled condensers to improve thermo-flow performances, Appl. Energy 165 (2016) 244–259.
Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/hmt
Auxiliary heat exchanger layout for freeze-proofing and performance recovery of natural draft dry cooling system Jingbo Yan, Xianwei Huang, Wenhui Huang, Lijun Yang∗, Xiaoze Du Key Laboratory of Power Station Energy Transfer Conversion and System of Ministry of Education, 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 7 July 2019 Revised 26 December 2019 Accepted 13 January 2020
Keywords: Natural draft dry cooling system Air-cooled heat exchanger Auxiliary heat exchanger Anti-freezing Thermo-flow performances Wind speed
a b s t r a c t Air-cooled heat exchanger faces a severe freezing risk in cold winter, especially for the finned tube bundles of windward sectors. Therefore, it is beneficial to the safe and energy-efficient operation of natural draft dry cooling system to take anti-freezing measures. In this work, the natural draft dry cooling system with auxiliary heat exchanger in front of windward sectors is proposed. By applying macro heat exchanger model to finned tube bundles and three-dimensional modeling on the air side, the freezeproofing and performance improvement of natural draft dry cooling system with auxiliary heat exchanger are numerically studied. The air velocity, pressure, and temperature fields, air mass flow rate, outlet water temperature and anti-freezing turbine back pressure are presented under winter conditions. Moreover, the air flow rate, heat rejection and turbine back pressure are obtained in warm days. The results show that the auxiliary heat exchanger can prevent the air-cooled heat exchanger from freezing at various wind speeds in winter. In warm days, the natural draft dry cooling system with auxiliary heat exchanger is superior to the conventional one at high wind speeds. In the absence of winds, its cooling performance gets deteriorated. © 2020 Elsevier Ltd. All rights reserved.
1. Introduction Owing to urgent water resource shortage, natural draft dry cooling system (NDDCS) has been widely applied to the power stations in arid regions [1]. In the vertically arranged cooling deltas of air-cooled heat exchanger, ambient air takes away the heat rejection from circulating water, so the ambient conditions play important roles in the thermo-flow performances of NDDCS. In cold winter, the circulating water is in danger of freezing and the finned tube bundles may suffer great damages. Therefore, it is of benefit to the safe and energy-efficient operation of natural draft dry cooling system to investigate the freezing characteristics and propose freeze-proofing measures of air-cooled heat exchanger. In the past decades, more emphases have been placed upon the unfavorable wind effects on the flow and heat transfer of NDDCS. Du Preez and Kröger stated that the thermo-flow performances of NDDCS get deteriorated under wind conditions [2]. Besides, the adverse effect is mainly caused by the flow resistance at the tower inlet and the turbulence at the entrance of heat exchanger
∗
Corresponding author. E-mail address: [email protected] (L. Yang).
https://doi.org/10.1016/j.ijheatmasstransfer.2020.119381 0017-9310/© 2020 Elsevier Ltd. All rights reserved.
[3]. Su et al. [4] found that the thermal-flow performance of side sectors gets seriously deteriorated, which could be attributed to the small intersection angle between air flows and heat exchanger surface. Li et al. [5] concluded that the cold air could flow into the top of the cooling tower, which weakens the heat transfer capacity of air-cooled heat exchanger and results in the increased outlet water temperature. Yang et al. [6] pointed out that the performances of upwind cooling deltas are superior to those at the rear and side ones, and a critical wind speed exists at which the cooling performance of NDDCS is worst. By wind tunnel test, Wei et al. [7] investigated the deterioration of thermo-flow performances of NDDCS and proposed some measures against the adverse wind effects. Chen et al. [8] proposed the combined interior and exterior windbreaker configurations of air-cooled heat exchanger to effectively improve the thermal-flow performances of NDDCS. Lu et al. [9,10] investigated the influences of tri-blade-like windbreaker and its orientation on the cooling performance of NDDCS, and recommended that one symmetry axis of windbreaker should be in alignment with the wind direction. Goodarzi [11] proposed a tower configuration with variable height to reduce the wind load without considerable cooling performance reduction of NDDCS. Liao et al. [12] studied the effect of triangularly arranged heat exchanger bundles on the thermo-flow performances of NDDCS, concluding that a higher
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Nomenclature A cp Cr D e H k K L m NTU p Q r Re Sᵩ t uj uw uz V xj z
heat transfer surface area (m2 ) specific heat (J kg−1 K−1 ) the ratio of air and water heat capacity rate diameter (m) exponent of the wind speed in the power-law equation height (m) turbulent kinetic energy (m2 s−2 ) overall heat transfer coefficient (W m2 K−1 ) length (m) mass flow rate (kg s−1 ) number of transfer unit pressure (Pa) heat rejection (W) polynomial factor Reynolds number source term temperature (°C) component of velocity (m s−1 ) wind speed (m s−1 ) ascending velocity inside tower (m s−1 ) volume (m3 ) Cartesian coordinate (m) height above the ground (m)
Greek symbols heat rejection (W) λ turbulence dissipation rate (m2 s−3 ) ε effectiveness of heat exchanger Г diffusion coefficient (kg m−1 s−1 ) ϕ scalar variable η iterative parameter ρ density (kg m−3 ) σ comparison index Subscripts a air ac auxiliary heat exchanger and cooling delta b base c condenser he heat exchanger i inlet o outlet t tower tt throat of tower w wind wa water
cooling efficiency can be achieved in a certain wind direction at high wind speeds. By optimizing the circulating water distribution, Goodarzi and Amooie [13,14] found that the cooling efficiency of NDDCS can be improved by 1.67% compared with uniform scheme. The aforementioned works show that the airside flow and thermal performances of NDDCS are thoroughly investigated, but the waterside is rarely involved. In frozen days, the circulating water may freeze when the ambient temperature is below 0 °C, however only few researches focus on the anti-freezing of NDDCS. Chen et al. [15] numerically studied the anti-freezing of NDDCS by controlling the opening degree of louvers in each sector. Wang et al. [16] obtained the anti-freezing water flow rate of NDDCS with the maximum value in the frontal sector. Besides, Wang et al. [17] proposed the simultaneous control of water flow rate and opening de-
Table 1 Geometric parameters of NDDCS and finned tube bundles.
NDDCS Tower height (m) Outlet diameter of tower (m) Throat height of tower (m) Throat diameter of tower (m) Air-cooled heat exchanger height (m) Base diameter of tower (m) Number of heat exchanger sectors Number of cooling deltas Number of auxiliary heat exchanger unit Distance between cooling delta inlet and auxiliary heat exchanger (m) Finned tube bundles Tube outside diameter (mm) Tube row number Transverse tube pitch (mm) Longitudinal tube pitch (mm) Fin thickness (mm) Fin pitch (mm) Upper slotted strip height (mm) Lower slotted strip height (mm) Slotted strip length (mm) Slotted strip width (mm)
Symbol
Value
Ht Do Htt Dtt Hhe Dohe nhes nco nAHE Lac
150 84.53 119.886 85.548 24 138 10 176 70 2.4
D − S1 S2
25 4 30 35 0.3 3.2 1.1 0.5 7 2.75
δf
Pf H1 H2 L1 L2
gree of louvers as the anti-freezing strategies. Kong et al. [18] proposed the water redistribution among various sectors to avoid freezing of air-cooled heat exchanger. As well known, the windward sector faces a more serious freezing risk than others due to the excessive cooling capacity of ambient air under windy conditions. In this work, the auxiliary heat exchanger (AHE) is proposed to set in front of the windward sectors to reduce the air flow rate. In cold winter, the auxiliary heat exchanger without circulating water is taken as the windbreaker to prevent the windward sectors from freezing. In warm days, the auxiliary heat exchanger with circulating water is put into operation to increase the cooling performance. The influences of auxiliary heat exchanger on the thermo-flow performances of NDDCS are investigated, which may contribute to the safe and energy-efficient operation of power generating unit. 2. Modeling 2.1. Physical model The cold end system in a typical 660MW power generating unit is schematically shown in Fig. 1(a), with the surface condenser and natural draft dry cooling system adopted. It consists of two heat transfer processes, first of which is from the exhaust steam to circulating water and the second takes place between the circulating water and cooling air. The overall NDDCS with the hyperbolic tower and vertically arranged air-cooled heat exchanger is schematically shown in Fig. 1(b), with the detailed geometric parameters listed in Table 1. The air-cooled heat exchanger is usually divided into ten sectors for easy distribution of circulating water. Due to the symmetric structure of NDDCS, only half of the air-cooled sectors are studied. The frontal and middle front sectors usually face greater freezing risks than others under windy conditions, so the auxiliary heat exchanger is arranged in front of these two sectors, as shown in Fig. 2. As the fundamental component of air-cooled heat exchanger, each cooling delta comprises two vertical finned tube bundles with an intersection angle of 49.08°, as shown in Fig. 3(a). For the auxiliary heat exchanger, the vertical finned tube bundles are annu-
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3
Fig. 1. Cold end system. (a) Condenser and NDDCS, (b) dry-cooling tower and air-cooled heat exchanger.
Fig. 2. Sectors, cooling deltas and auxiliary heat exchanger.
larly arranged in front of the cooling deltas, as shown in Fig. 3(b) and (c). Fig. 3(d) shows the finned tube bundles commonly used by air-cooled heat exchanger with the geometric parameters listed in Table 1.
2.2. Mathematical model The macro heat exchanger model is used to characterize the flow and heat transfer of finned tube bundles, with the porous
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Fig. 3. Air-cooled heat exchanger and auxiliary heat exchanger. (a) Cooling deltas, (b) auxiliary heat exchanger, (c) heat exchanger layout, (d) finned tube bundles.
media adopted to deal with the pressure drop p of air as follows [12]:
1 2
p = kL ρa u2f
(1)
where ρ a is the air density, uf is the face velocity, kL is the flow loss coefficient with the following form:
kL =
N
transfers for the given cell, macro and entire heat exchanger can be computed as follows:
Qcell = ε (mcp )a Tin,auxiliary − Tcell Qmacro =
Qcell
(3) (4)
all cells
rn unf −1
(2)
n=1
where N is set to be 6 in this work, the polynomial factor rn is obtained by fitting the experimental data, with the values of r1 = 51.756, r2 = 32.614, r3 = 11.682, r4 = 2.0986, r5 = 0.1808 and r6 = 0.0059. The heat exchanger core is subdivided into macroscopic cells or macros in the water flow direction, as shown in Fig. 4. The heat
Qtotal =
Qmacro
(5)
all macros
where (mcp )a means the heat capacity of air, Tin,auxiliary and Tcell are the inlet water temperature and air temperature of cell. The heat rejection from a macro is computed by summing all cells within the macro, then the total heat transfer of entire heat exchanger can be obtained. ε is the heat exchanger effectiveness, depending on
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The air side conservation equations are expressed as follows [12,18,20].
∂ρ uj ϕ ∂ ∂ϕ = ϕ + Sϕ + Sϕ ∂ xj ∂ xj ∂ xj
(9)
where ϕ equals 1, u, cp t, k and ε for the continuity, momentum, energy and turbulence equations respectively. Гϕ and Sϕ represent the diffusivity and source term, which are listed in Table 2. In this work, the realizable k-ε model is adopted because it can accurately characterize the turbulent flows involving the rotation, boundary layer under strong adverse pressure gradient, separation and recirculation, which is suitable for the simulation of natural draft dry cooling system. When the air flows through the heat exchanger zone, the pressure drop will be generated and the heat will be gained from the tube bundles, so the additional source terms Sϕ should be appended to the momentum and energy conservation equations, with the following forms.
Sϕ = − Sϕ =
p Lx j
Qhe Vhe
(10) (11)
where Lxj represents the heat exchanger length in the xj direction, Qhe is the heat rejection of heat exchanger, Vhe is the volume of heat exchanger zone. In other zones, the additional source terms equal 0. Sϕ 2.3. Computational domain, mesh and boundary conditions Fig. 4. Heat exchanger macros.
the heat exchanger structure and flow pattern as follows [14,16]:
1 ε = 1 − exp − NT U 0.22 1 − exp −Cr NT U 0.78
(6)
Cr = (mcp )a /(mcp )wa
(7)
NT U = KA/(mcp )a
(8)
Cr
where (mcp )wa is the heat capacity of water, K and A are the overall heat transfer coefficient and heat transfer surface area of air-cooled heat exchanger. In this work, the alternant slotted finned tube bundles in a staggered way are adopted as shown in Fig. 3(d), with the related parameters in heat exchanger model achieved by wind tunnel test [19].
For eliminating the impractical impact of the domain boundaries on the air flow field, the computational domain should be set large enough compared with the NDDCS, as shown in Fig. 5. The hexahedral grids are generated for the central part with heat exchanger and cooling tower, while the tetrahedral/hexahedron hybrid unstructured grids are applied to other zones. In this work, three grid schemes with 1 763 382, 3 469 265 and 5 469 332 cells are tested. The air mass flow rate at the wind speed of 4 m/s varies only 0.39% for the latter two density grid solutions, so the grid with the cell number of 3 469 265 is finally used. In the presence of winds, the windward surface of computational domain is set as velocity inlet, with the wind speed uz at the height of z (m) calculated by the following equation [21]:
uz = uw
z e 10
(12)
where uw is the wind speed at the height of 10 m with 4, 8, 12 and 16 m/s set. e is the wind speed profile index, with the typical value
Fig. 5. Computational domain and boundary conditions.
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J. Yan, X. Huang and W. Huang et al. / International Journal of Heat and Mass Transfer 150 (2020) 119381 Table 2 Summary of generic governing equations. Equations
ϕ
ϕ
Continuity
1
0
0
x-Momentum
ui
− ∂∂xp +
y-Momentum
uj
z-Momentum
uk
Energy Turbulence kinetic energy Turbulence dissipation rate
cp t k ɛ
μe μe μe μe / σ T μ + μ T / σk μ + μ T / σe
Sϕ
i
− ∂∂xp + j
− ∂∂xp + k
1 ∂ [ 3 ∂ xi 1 ∂ [ 3 ∂ xi 1 ∂ [ 3 ∂ xi
∂uj ∂ uk ∂ ∂ ∂ x j (μe ∂ xi ) + ∂ xk (μe ∂ xi )] ∂ (μ ∂ u j ) + ∂ (μ ∂ uk )] e ∂x e ∂x ∂xj ∂ xk j j (μe ∂∂ xuki ) + ∂∂x j (μe ∂∂ uxkj ) + ∂∂xk (μe ∂∂ uxkk )] + ρ g
(μe ∂∂ uxii ) +
(μe ∂∂ xuji ) +
0 Gk + Gb − ρε 2 ρC1 Sε − ρC2 k+ε√uε + C1ε εk C3ε Gb
Fig. 6. Experimental validation for numerical results [8,15]. (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.
of 0.2 in this paper. For the leeward surface, the outflow boundary condition is set due to the unchanged variable profiles. In the absence of winds, the side surfaces are set as the pressure inlet boundaries, and the top surface as the pressure outlet boundary with the gauge pressure of 0 Pa. The ambient temperatures at the domain surfaces are set equal to 303.15 K in warm days. In winter, the ambient temperatures of 263.15 K, 258.15 K and 253.15 K are chosen. The equations are discretized by the second-order upwind differencing scheme, and the pressure and velocity coupling is dealt with the SIMPLE algorithm. The divergence-free criteria of 10−4 for all the scaled residuals of variables are prescribed, except the energy equation with the criterion of 10−6 . The air flow rate is also
Table 3 Water flow rate of each sector (unit in kg/s).
Auxiliary frontal sector Auxiliary middle front sector Frontal sector Middle front sector Middle sector Middle rear sector Rear sector Total
Case 1
Case 2
Case 3
Case 4
0 0 450 425 450 425 450 2200
0 0 450 425 450 425 450 2200
0 0 900 850 900 850 900 4400
450 425 450 425 900 850 900 4400
used to monitor whether the iteration is converged to a reliable level.
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Fig. 7. Temperature fields and streamlines at the cross section with height of 10 m without winds. (a) Case 1, (b) case 2.
The energy equations of exhaust steam and circulating water in condenser are expressed as follows:
Fig. 8. Local pressure without winds for case 1.
2.4. Iteration process In cold winter, the auxiliary heat exchanger without circulating water does not participate in the heat transfer process, which is regarded as a windbreaker to prevent the windward sectors from freezing. During the iteration, the heat balances of circulating water and cooling air are considered simultaneously, and the outlet water temperature of each sector should be above 0 °C to meet the anti-freezing requirement. The iterative process for the anti-freezing calculation is presented as follows. (1) Develop the computational model of NDDCS, input the correlating parameters of finned tube bundles to the heat exchanger model. (2) Keep the water mass flow rate mwa constant, assume the inlet water temperature twa1 of the heat exchanger. (3) By CFD simulation, obtain the total heat rejection of aircooled heat exchanger and outlet water temperature twa2 of each cooling delta, find out the minimum outlet water temperature twa2min in various sectors. (4) Define the iterative parameter as η1 = (twa2min − 273.15)/ (twa1 − twa2min ). If 0 < η1 < 0.5%, the iteration is completed. Otherwise, reassume the inlet water temperature and repeat the process. (5) Output the heat rejection and outlet water temperature of various sectors, calculate the turbine pressure.
c = ms (hs − hwa )
(13)
c = c pw mw (tc,wa1 − tc,wa2 )
(14)
where c is the heat rejection of condenser, ms , mwa are the mass flow rates of steam and water, hs and hwa are the steam and condensate enthalpies, cpwa is the specific heat of circulating water, tc,wa1 , tc,wa2 are the inlet and outlet water temperatures of condenser, which are equal to the outlet and inlet water temperatures of air-cooled heat exchanger if the water heat loss between condenser and heat exchanger is neglected. When the iteration is completed, the inlet and outlet water temperatures of condenser can be achieved, the heat rejection c can be calculated by Eq. (14). The mass flow rate and enthalpy of steam are assumed to be constant, the condensate enthalpy can be calculated by Eq. (13), so the condensate temperature and turbine back pressure pbw are obtained. Once the back pressure pbw gets lower, the cold end system will face a freezing risk, so the pbw is defined as the antifreezing turbine back pressure. In warm days, the auxiliary heat exchanger with circulating water is put into operation. The iterative procedure for the thermoflow performances of NDDCS is described as follows. (1) Input steam flow rate, enthalpy, assume turbine back pressure pbs , calculate the heat rejection of condenser c . (2) In terms of water and steam flow rates, calculate the overall heat transfer coefficient Kc , inlet water temperature tc,wa1 and outlet water temperature tc,wa2 of condenser. (3) Develop the computational model of NDDCS, input the correlating parameters to heat exchanger model, and input water mass flow rate mwa and inlet water temperature twa1 . (4) By CFD simulation, obtain the outlet water temperature twa2 , calculating the total heat rejection of heat exchanger t . (5) Define the iterative parameter as η2 = (t − c )/t . If 0 < η2 < 0.5%, the iteration is completed. Otherwise, reassume the turbine back pressure pb and repeat the process. (6) Output outlet water temperature twa2 of air-cooled heat exchanger and turbine back pressure pb . For convenience, the winter conditions without and with auxiliary heat exchanger are named case 1 and case 2. The warm day conditions without and with auxiliary heat exchanger are named case 3 and case 4. The water flow rate of each sector under various conditions is listed in Table 3. In winter, the water distribution for case 1 is same as that for case 2. In warm days, the
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auxiliary heat exchanger is also filled with water. The sum of water flow rates of auxiliary frontal sector and frontal sector for case 4 is equal to the water flow rate of frontal sector for case 3, which is also applicable for the middle front sector. The water flow rates of other sectors for case 4 are same as those for case 3.
2.5. Model validation Following the scale law, a model dry-cooling tower with vertically arranged heat exchanger bundles around its circumference was tested in a wind tunnel in our previous work [8,15]. Fig. 6(a) and (b) show the measuring points inside the prototype tower. The
Fig. 9. Local pressure without winds for case 2. (a) Frontal sector, (b) middle front sector, (c) middle sector, (d) middle rear sector, (e) rear sector.
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Fig. 10. Temperature fields and streamlines at the cross section with height of 10 m at wind speed of 8 m/s. (a) Case 1, (b) case 2.
Fig. 11. Local pressure at wind speed of 8 m/s for case 1. (a) Frontal sector, (b) middle front sector, (c) rear sector.
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ascending velocities at the heights of 64.2 m and 164.2 m inside the real tower in the absence of winds and at the wind speed of 4 m/s were chosen as illustrative cases to compare the numerical results with the experimental data, as shown in Fig. 6(c) in the absence of winds and Fig. 6(d) at the wind speed of 4 m/s. It can be seen that for both cases, the numerical results agree well with the measured data, showing that the computational models and methods are reliable enough for the performance prediction of natural draft dry cooling system. In this work, the numerical approach is completely same as that based on the tested tower, which justifies in another way the modeling and numerical approaches. 3. Results and discussion 3.1. Winter conditions 3.1.1. Variable fields In winter, the AHE without circulating water can obstruct the air flows through windward sectors to avoid possible freezing. By adjusting the inlet water temperature of heat exchanger, the anti-
freezing of NDDCS can be achieved. As illustrative cases, the variable fields at 258.15 K in the absence of wind, at the wind speed of 8 m/s are presented and analyzed. Fig. 7 shows the temperature fields and streamlines without winds. For case 1, they are centrally symmetric as shown in Fig. 7(a). For case 2 however, this symmetry is disturbed. The outlet air temperatures of frontal and middle front sectors are higher than other sectors due to the reduced airflows obstructed by AHE. Besides, a vortex is generated at the central front of cooling tower as shown in Fig. 7(b) due to the uneven resistance of sectors. For case 1, only the local field of frontal sector is presented as shown in Fig. 8. The pressure is almost constant in the circumferential direction, and the pressure drop across the cooling deltas reaches 93 Pa. For case 2, the pressure drop through the cooling deltas varies clearly with each sector as shown in Fig. 9. For the frontal and middle front sectors, the pressure drop across the AHE is about 83 Pa, and about 34 Pa across the cooling deltas, which is much lower than that for case 1, showing a strong resistance effect from AHE on the air flows. For the middle, middle rear and rear sectors, the pressure drop about 105 Pa is
Fig. 12. Local pressure at wind speed of 8 m/s for case 2. (a) Frontal sector, (b) middle front sector, (c) rear sector.
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generated across the cooling deltas, which are higher than that for case 1. As a result, these sectors face more serious freezing risks. This is because that the velocity of air through the frontal and middle front sectors decreases, resulting in the reduced flow resistance of cooling air through middle, middle rear and rear sectors. Fig. 10 shows the temperature fields and streamlines for case 1 and case 2 at the wind speed of 8 m/s. For case 1 as shown in Fig. 10(a), the outlet air temperatures of the frontal and rear
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sectors are lower than other sectors, resulting in the freezing risk unexpectedly. The strong air flows through the frontal and middle front sectors have an inhibition effect on the rear and middle rear sectors, as a result, two vortices are generated near the middle sector. For case 2 as shown in Fig. 10(b), the AHE can significantly reduce the air flow rate of frontal and middle front sectors, so the inhibition effect on the air inflows at the rear and middle rear sectors gets reduced. As a result, the vortices move forward and the rear sector becomes superior to other sectors in the thermo-flow
Fig. 13. Air mass flow rate of each sector at various wind speeds. (a) Case 1 at 263.15 K, (b) case 2 at 263.15 K, (c) case 1 at 258.15 K, (d) case 2 at 258.15 K, (e) case 1 at 253.15 K, (f) case 2 at 253.15 K.
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performances. For both case 1 and case 2, the outlet air temperature of lateral sector is higher than those of other sectors due to the air inflow large deviation angle at the cooling delta inlet. The heat transfer capacities of the middle front and middle rear sectors are in the middle level. The local pressure fields of frontal, middle front and rear sectors for case 1 at the wind speed of 8 m/s are shown in Fig. 11. It can be seen that the pressure drops of these sectors vary from 157 to 182 Pa, 90 to 140 Pa, 90 to 140 Pa respectively. The frontal
sector shows a better flow performance and faces a greater freezing risk than other sectors due to the large momentum of coming wind. For the frontal and middle front sectors of case 2 shown in Fig. 12(a) and (b), the pressure drops across cooling deltas range from 43 to 50 Pa, 27 to 40 Pa, which are much lower than those for case 1. Besides, the pressure drops across the AHE for frontal and middle frontal sectors vary from 121 to 132 Pa and 35 to 105 Pa, showing a strong impeding effect on air inflows. The freezing risk of frontal and middle front sectors gets weak due to
Fig. 14. Outlet water temperature of each sector at various wind speeds. (a) Case 1 at 263.15 K, (b) case 2 at 263.15 K, (c) case 1 at 258.15 K, (d) case 2 at 258.15 K, (e) case 1 at 253.15 K, (f) case 2 at 253.15 K.
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Fig. 15. Anti-freezing turbine back pressure at various wind speeds and ambient temperatures.
the installation of AHE. For the rear sector of case 2 shown in Fig. 12(c), the pressure drop across the cooling deltas varies from 139 to 190 Pa, which is higher than other sectors, showing that it faces a serious freezing risk. Similar to the case without winds, the block effect of the air through the frontal sector on the air through rear sector is reduced, so the freezing risk of rear sector increases.
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3.1.2. Anti-freezing analysis By means of iterative calculation, the air mass flow rate, outlet water temperature of each sector, anti-freezing turbine back pressure are obtained. Fig. 13 shows the mass flow rates of cooling air through each sector for case 1 and 2 at various ambient temperatures and wind speeds. It can be seen that the air mass flow rate increases as the ambient temperature decreases. Taking the frontal sector of case 1 at the wind speed of 4 m/s as illustrative cases, the air mass flow rates through frontal sector at 263.15 K, 258.15 K and 253.15 K are 5298 kg/s, 6244 kg/s and 7658 kg/s. This is because when the ambient temperature drops, the temperature difference between circulating water and air increases, leading to the increased heat rejection and air mass flow rate. Besides, the mass flow rate changes with wind speed in a similar way at different ambient temperatures. In the absence of winds for case 1, the mass flow rates of various sectors are almost the same. However, for case 2, the air mass flow rates of frontal and middle front sectors are lower than other sectors due to the impeding effect of AHE. Under wind conditions for case 1, as the wind speed increases, the air mass flow rates of frontal and middle front sectors increase due to the wind induced enhancement of air flows. Besides, the air flow rate of frontal sector is higher than other sectors at various wind speeds, showing that the frontal sector faces a more serious freezing risk. The air flow rate of rear sector increases at first and then decreases with increasing the wind speed because the blocking effect on air flows across the rear sector gets strong at high
Fig. 16. Flow characteristics of each sector at various wind speeds. (a) Air flow rate for case 3, (b) air flow rate for case 4, (c) mass flow rate ratio.
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wind speeds. For case 2, the air flow rates of frontal and middle front sectors decrease compared with case 1 owing to the flow resistance generated by the AHE. However, the air flow rate of frontal sector at the wind speed of 16 m/s is still higher than other sectors. The changing trend of air flow rate through the rear sector is similar to that of case 1. Furthermore, the rear sector has a higher air flow rate than other sectors at the wind speeds of 4, 8 and 12 m/s. The flow performances of middle and middle rear sectors are poor at most wind speeds for case 1 and 2, showing that these sectors face no freezing risk. In cold winter, the outlet water temperature of each cooling delta must be above 0 °C. By adjusting the turbine back pressure, the anti-freezing of NDDCS can be achieved. Fig. 14 shows the outlet water temperature of each sector at various wind speeds. For case 1, the outlet water temperature of frontal sector is close to 0 °C at various wind speeds, showing that the frontal sector faces the most serious freezing risk. The outlet water temperatures of other sectors become high as the wind speed increases, because the turbine back pressure is lifted with the increased wind speed to prevent the heat exchanger from freezing, resulting in the increased inlet and outlet water temperatures of air-cooled heat exchanger. For case 2, the rear sector is easy of freezing at the wind speeds of 4, 8 and 12 m/s. At the wind speed of 16 m/s, the frontal sector faces the most serious freezing risk. The sector with maximum heat rejection is not fixed as the wind speed increases, which results in the complex changing trends of outlet water temperature.
Fig. 15 shows the anti-freezing turbine back pressures at various wind speeds and ambient temperatures. It can be seen that the anti-freezing back pressure increases clearly as the ambient temperature drops and the wind speed rises for case 1, and unfortunately it even reaches 65 kPa at the ambient temperature of 253.15 K and wind speed of 16 m/s, showing that only by increasing the turbine back pressure cannot the anti-freezing issues be settled. Other effective measures such as the circulating water redistribution, louver adjustment for various sectors should be taken [15–18]. For case 2, the anti-freezing back pressure varies little with the wind speed. In the absence of winds, the anti-freezing back pressure for case 2 is higher than case 1, however it is always lower than case 1 at various wind speeds, especially at the wind speed of 16 m/s with the maximum difference of 55 kPa, showing that the AHE configuration can effectively improve the energy efficiency and reduce the freezing risk of NDDCS.
3.2. Warm days The changing trends of air velocity, pressure and temperature in each sector in warm days are similar to those in winter, so the variable fields are not presented and only the thermo-flow performances are analyzed. In order to compare the mass flow rate and heat rejection of each sector between case 3 and case 4, two non-dimensional parameters, the mass flow rate ratio δ ma and heat rejection ratio δ ,
Fig. 17. Thermal characteristics of each sector at various wind speeds. (a) Heat rejection for case 3, (b) heat rejection for case 4, (c) heat rejection ratio.
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much lower back pressure for case 2 is presented with winds, especially at high wind speeds. For case 1, the frontal sector faces a more serious freezing risk than other sectors at various wind speeds. With the AHE, the rear sector faces a higher freezing risk than others at the wind speeds of 4, 8 and 12 m/s. At the wind speed of 16 m/s, the frontal sector is much easier to freeze. The turbine back pressure increases as the ambient temperature decreases, which obeys the similar changing trend with the wind speed. In warm days, the thermo-flow performances of NDDCS with AHE get poor in the absence of winds. At the wind speed of 4 m/s, they are close to those without AHE. At the wind speeds of 8, 12 and 16 m/s, the thermo-flow performances are improved thanks to the AHE. The heat rejections of frontal and middle front sectors with AHE are lower than those without AHE, but the middle rear and rear sectors have higher heat rejections. Declaration of Competing Interest
Fig. 18. Turbine back pressure at various wind speeds.
Authors declare that they have no conflict of interest.
are introduced.
δma = δ =
ma4 ma3
4 3
(15) (16)
where ma3 and ma4 are the air mass flow rates of each sector for case 3 and case 4; 3 and 4 are the heat rejections of each sector for case 3 and case 4. Fig. 16 shows the flow characteristics of each sector at various wind speeds. The air mass flow rates of frontal and middle front sectors for case 4 are lower than case 3 at various wind speeds due to the increased flow resistance generated by the AHE, and the mass flow rate ratios range from 0.47 to 0.61. For the middle rear and rear sectors, the flow performances for case 4 get remarkably improved compared with case 3. Besides, the improvements at the wind speeds of 8, 12 and 16 m/s are much higher than those in the absence of winds and at the wind speed of 4 m/s, with the mass flow rate ratio even reaching 2.32, showing that the flow performance can be substantially improved by the AHE. Fig. 17 gives the heat rejection of each sector at various wind speeds. It can be seen that for case 3, the heat rejection of each sector is almost positively related to the air flow rate. For case 4 however, the positive correlation with them is not always presented. The heat rejection of frontal sector is close to and even higher than rear sector at various wind speeds. For the frontal and middle front sectors, the heat rejection ratios reach about 0.85, which are higher than the mass flow rate ratio. Because the AHE with circulating water is in operation in warm days, the heat transfer area of frontal and middle front sectors for case 4 is larger than that for case 3. The heat rejections of middle rear and rear sectors for case 4 are higher than those for case 3. For the middle sectors of both case 3 and case 4, the heat rejections are always small at various wind speeds. Fig. 18 shows the turbine back pressures at various wind speeds for case 3 and case 4. It can be observed that the turbine back pressure for case 4 is higher than case 3 in the absence of winds, and very close to case 3 at the wind speeds of 4 m/s. At the wind speeds of 8, 12 and 16 m/s, the turbine back pressure for case 4 gets reduced compared with case 3, showing that the energy efficiency of power generating unit is improved thanks to the AHE. 4. Conclusions In winter, the anti-freezing turbine back pressure for case 2 is higher than that for case 1 in the absence of winds. However, the
CRediT authorship contribution statement Jingbo Yan: Data curation, Formal analysis, Investigation, Methodology, Software, Validation, Writing - original draft. Xianwei Huang: Resources, Software, Validation. Wenhui Huang: Data curation, Formal analysis. Lijun Yang: Conceptualization, Funding acquisition, Project administration, Writing - review & editing. Xiaoze Du: Supervision. Acknowledgments The financial supports for this research, from the National Natural Science Foundation of China (Grant nos. 51776067, 51821004) and the National Basic Research Program of China (Grant no. 2015CB251503), are gratefully acknowledged. References [1] D.G. Kroger, Air-cooled heat exchanger and cooling towers: thermal-flow performance evaluation and design, Penn Well Corp., 2004, pp. 1–49. [2] A.F. du Preez, D.G. Kröger, Effect of wind on performance of a dry-cooling tower, Heat Recovery Syst. CHP 13 (1993) 139–146. [3] A.F. du Preez, D.G. Kröger, The effect of the heat exchanger arrangement and wind-break walls on the performance of natural draft dry-cooling towers subjected to cross-winds, J. Wind Eng. Ind. Aerodyn. 58 (3) (1995) 293–303. [4] M.D. Su, G.F. Tang, S Fu, Numerical simulation of fluid flow and thermal performance of a dry-cooling tower under cross wind condition, J. Wind. Eng. Ind. Aerodyn. 79 (1999) 289–306. [5] X.X. Li, H. Gurgenci, Z.Q. Guan, Y.B. Sun, Experimental study of cold inflow effect on a small natural draft dry cooling tower, Appl. Therm. Eng. 128 (2018) 762–771. [6] L.J. Yang, X.P. Wu, X.Z. Du, Y.P. Yang, Dimensional characteristics of wind effects on the performance of indirect dry cooling system with vertically arranged heat exchanger bundles, Int. J. Heat Mass Transf. 67 (2013) 853–866. [7] Q.D. Wei, B.Y. Zhang, K.Q. Liu, A study of the unfavorable effects of wind on the cooling efficiency of dry cooling towers, J. Wind. Eng. Ind. Aerodyn. 54–55 (1995) 633–643. [8] L. Chen, L.J. Yang, X.Z. Du, Y.P. Yang, Performance improvement of natural draft dry cooling system by interior and exterior windbreaker configurations, Int. J. Heat Mass Transf. 96 (2016) 42–63. [9] Y. Lu, Z. Guan, H. Gurgenci, Z. Zou, Windbreak walls reverse the negative effect of crosswind in short natural draft dry cooling towers into a performance enhancement, Int. J. Heat Mass Transf. 63 (2013) 162–170. [10] Y.S. Lu, H. Gurgenci, Z.Q. Guan, S.Y. He, The influence of windbreak wall orientation on the cooling performance of small natural draft dry cooling towers, Int. J. Heat Mass Transf. 79 (2014) 1059–1069. [11] M.A. Goodarzi, Proposing a new technique to enhance thermal performance and reduce structural design wind loads for natural drought cooling towers, Energy 62 (6) (2013) 164–172. [12] H.T. Liao, L.J. Yang, X.Z. Du, Y.P. Yang, Triangularly arranged heat exchanger bundles to restrain wind effects on natural draft dry cooling system, Appl. Therm. Eng. 99 (2016) 313–324.
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J. Yan, X. Huang and W. Huang et al. / International Journal of Heat and Mass Transfer 150 (2020) 119381
[13] M. Goodarzi, H. Amooie, A proposed heterogeneous distribution of water for natural draft dry cooling tower to improve cooling efficiency under crosswind, in: 2012 4th Conference on Thermal Power Plants (CTPP), IEEE, 2012, pp. 1–6. [14] M. Goodarzi, H. Amooie, Heat transfer enhancement in a natural draft dry cooling tower under crosswind operation with heterogeneous water distribution, J. Nucl. Power 61 (2016) 252–259. [15] L. Chen, L.J. Yang, X.Z. Du, Y.P. Yang, Anti-freezing of air-cooled heat exchanger by air flow control of louver in power plants, Appl. Therm. Eng. 106 (2016) 537–550. [16] W.J. Wang, L.J. Yang, X.Z. Du, Y.P. Yang, Anti-freezing water flow rates of various sectors for natural draft dry cooling system under wind conditions, Int. J. Heat Mass Transf. 102 (2016) 186–200. [17] W.J. Wang, X.W. Huang, L.J. Yang, X.Z. Du, Anti-freezing operation strategies of natural draft dry cooling system, Int. J. Heat Mass Transf. 118 (2018) 165–170.
[18] Y.Q. Kong, W.J. Wang, L.J. Yang, X.Z. Du, Y.P. Yang, Water redistribution among various sectors to avoid freezing of air-cooled heat exchanger, Int. J. Heat Mass Transf. 141 (2019) 294–309. [19] Y.Q. Kong, L.J. Yang, X.Z. Du, Y.P. Yang, Effects of continuous and alternant rectangular slots on thermo-flow performances of plain finned tube bundles in in-line and staggered configurations, Int. J. Heat Mass Transf. 93 (2016) 97–1007. [20] F. Chu, Q. Gao, S. Li, G. Yang, Y Luo, Mass transfer characteristic of ammonia escape and energy penalty analysis in the regeneration process, Appl. Energy 258 (2020) 113975. [21] L. Chen, L.J. Yang, X.Z. Du, Y.P. Yang, A novel layout of air-cooled condensers to improve thermo-flow performances, Appl. Energy 165 (2016) 244–259.