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Performance improvement of natural draft dry cooling system by interior and exterior windbreaker configurations
International Journal of Heat and Mass Transfer 96 (2016) 42–63
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International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Performance improvement of natural draft dry cooling system by interior and exterior windbreaker configurations Lei Chen, Lijun Yang ⇑, Xiaoze Du, Yongping Yang Key Laboratory of Condition Monitoring and Control for Power Plant Equipments 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 27 June 2015 Received in revised form 5 January 2016 Accepted 6 January 2016 Available online 21 January 2016 Keywords: Natural draft dry cooling system Air-cooled heat exchanger Dry-cooling tower Windbreakers Crosswinds Back pressure
a b s t r a c t Ambient winds are basically unfavorable to the thermo-flow performances of natural draft dry cooling system, and may result in a reduced thermal efficiency for the power generating unit in power plants, so it is of benefit to the natural draft dry cooling system to propose the measures against the adverse effects of ambient winds. For a typical natural draft dry cooling system, the computational models of the flow and heat transfer of cooling air coupled with the energy balances of circulating water and exhaust steam are developed, by which the performance improvement due to the interior and exterior windbreaker configurations is investigated. The flow and temperature fields of cooling air, the flow rate and heat rejection of each sector, the outlet water temperature of heat exchanger for the natural draft dry cooling systems with and without windbreaker configurations, and the corresponding turbine back pressures are obtained. The results show that the exterior windbreakers are superior to the interior ones in thermo-flow performances. The turbine back pressure can be reduced by the windbreaker configurations in the presence of ambient winds, especially at high wind speeds. Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction In the past years, natural draft dry cooling system in power plants has been increasingly developed and widely used in arid places thanks to its superiority in water saving [1]. Dry-cooling tower is one of the most important parts of natural draft dry cooling system, with air-cooled heat exchanger bundles vertically arranged around the circumference of cooling tower, or horizontally configured inside cooling tower. Cooling air flows through the heat exchanger bundles under the action of buoyancy force, removing the heat rejection of circulating water. As is well known, the thermo-flow performances of natural draft dry cooling system are sensitive to ambient conditions, especially the crosswinds. More attentions have been paid to the unfavorable wind effects on the performances of air-cooled heat exchangers and drycooling towers. With CFD methods, Al-Waked and Behnia [2] investigated the effects of crosswinds and windbreakers on the thermal performance of natural draft dry cooling system, finding that the windbreakers can weaken the adverse impacts of crosswinds. Goodarzi ⇑ Corresponding author. Tel.: +86 10 61773373; fax: +86 10 61773877. E-mail address: [email protected] (L. Yang). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2016.01.021 0017-9310/Ó 2016 Elsevier Ltd. All rights reserved.
[3] proposed a tower exit configuration to restrain the throat effect of deflective plume, by which the cooling efficiency is improved up to 9 percent. He also [4] introduced a method to utilize a variable tower height, which can reduce the structural wind loads without a considerable thermal performance reduction. Goodarzi and Keimanesh [5] studied the effect of a radiator-type windbreaker on natural draft dry cooling system, pointing out that a higher cooling efficiency can be achieved compared with the solid-type windbreaker. Goodarzi and Ramezanpour [6] proposed an elliptical geometry for natural draft dry cooling tower, which can bring on a higher cooling efficiency under crosswind condition. Zhai and Fu [7] put forward the windbreaker solutions in and around cooling towers, finding that 50% of cooling capacity can be recovered by placing side windbreakers of cooling tower. Lu et al. [8,9] studied the effects of tri-blade-like windbreaker and its orientation on natural draft dry cooling tower performance, suggested that one symmetry axis of the windbreaker should be in alignment with the prevailing wind direction. Zhao et al. [10] investigated the outlet water temperatures for different sectors with air deflectors under crosswind conditions, indicating that the air deflectors can weaken the air inflow distortion and improve the cooling performance of natural draft dry cooling tower.
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Nomenclature A cp d e g Gk Gb h hn hs hwa H I k kL K L m n p P q rn S1 S2 Su t uf
heat transfer surface area (m2) specific heat (J kg1K1) diameter (m) exponent of the wind speed in the power-law equation gravitational acceleration (m s2) turbulence kinetic energy generation due to mean velocity gradients (m2 s2) turbulence kinetic energy generation due to buoyancy (m2 s2) convection heat transfer coefficient (W m2 K1) polynomial coefficient for the convection heat transfer coefficient enthalpy of the exhaust steam (J kg1) enthalpy of the condensate (J kg1) height (m) turbulence intensity turbulent kinetic energy (m2 s2) flow loss coefficient overall heat transfer coefficient (W m2 K1) length of fin perpendicular to air flow direction (mm) mass flow rate (kg s1) number pressure (Pa) fin spacing (mm) heat flux (W m2) polynomial coefficient of non-dimensional loss coefficient tube spacing perpendicular to air flow direction (mm) tube spacing along air flow direction (mm) source term temperature (°C) frontal velocity (m s1)
uj uz uw W xj z
component of velocity (m s1) ascending velocity inside the tower (m s1) wind speed (m s1) width of fin along air flow direction (mm) Cartesian coordinate (m) height above the ground (m)
Greek symbols thickness of tube wall (mm) d1 d2 thickness of fin (mm) e turbulence dissipation rate (m2 s3) l dynamic viscosity (kg m1 s1) lt turbulent viscosity (kg m1 s1) q density (kg m3) r turbulent Prandtl number U diffusion coefficient (kg m1 s1) U heat rejection (W) u scalar variable Subscripts 1 inlet 2 outlet a air avg average B back c condenser s steam t tower w wind wa water
Fig. 1. Schematic of the power generating unit with natural draft dry cooling system. 1-boiler, 2-superheater, 3-turbine, 4-condenser, 5-condensate pump, 6-condensatescavening installation, 7-low pressure heater, 8-deaerator, 9-feed pump, 10-high pressure heater, 11-circulation water pump, 12-air-cooled heat exchanger, 13-dry-cooling tower, 14-generator.
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L. Chen et al. / International Journal of Heat and Mass Transfer 96 (2016) 42–63 Table 1 Geometric parameters of air-cooled heat exchanger and dry-cooling tower.
Tower height Base diameter of tower Outlet diameter of tower Throat height of tower Throat diameter of tower Height of air-cooled heat exchanger Outlet diameter of heat exchanger Number of heat exchanger sectors Number of cooling deltas
Symbol
Value
Ht db do Htt dtt Hhe dohe nhes ncd
170 m 151 m 90 m 145 m 87 m 24 m 159 m 10 180
Table 2 Geometric parameters of finned tube bundles. d d1 (mm mm)
L W d2 (mm mm mm)
P (mm)
S1 (mm)
S2 (mm)
/25 1
660 132 0.3
3.2
25
30
(a)
(b)
The aforementioned researches mainly focus on the flow and heat transfer characteristics of natural draft dry cooling system with different measures against adverse wind effects. It is still not clear the turbine back pressure changing trends thanks to the windbreaker configurations and other measures. Furthermore, the particular iterative procedure of the flow and heat transfer of cooling air coupled with the energy balances of circulating water and exhaust steam, which can clarify the actual running status of natural draft dry cooling system under windy conditions, is not found in related literatures either. In this work, the natural draft dry cooling system coupled with the condenser will be thoroughly investigated in their thermoflow performances, and the iteration procedure for the numerical simulations on the performances of cooling air, circulating water and exhaust steam will be developed, based on which the turbine back pressure can be calculated at various wind speeds. The impacts of interior and exterior windbreaker configurations on the performance of natural draft dry cooling system will be clarified, which can contribute to the optimal design and operation of the air-cooled heat exchanger and dry-cooling tower in power plants. 2. Modeling and methods 2.1. Physical model
(c) Fig. 2. Schematic of natural draft dry cooling system. (a) Air-cooled heat exchanger and dry-cooling tower, (b) cooling deltas of heat exchanger, (c) configuration of finned tube.
A 660 MW power generating unit with a natural draft dry cooling system is taken into account in this paper, whose schematic view of the working medium loop and cooling loop is shown in Fig. 1. A reaction type steam turbine composed of a HP-IP combined cylinder and two LP cylinders is utilized. The main steam at the pressure of 24.2 MPa and temperature of 566 °C flows through one impulse governing stage and nine reaction stages in the HP cylinder and then passes through six reaction stages in the IP cylinder after being reheated to 566 °C at the pressure of 2.14 MPa. Finally, the steam goes through seven reaction stages in each LP cylinder and ejects to the condenser. The surface condenser and air-cooled heat exchanger are adopted, in which the circulating water is in a closed cycle. The surface condenser has a heat transfer surface area of 40,000 m2, and consists of 34,160
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Fig. 3. Schematic of windbreakers and sector numbering. (a) No windbreakers, (b) inside tower, (c) at both sides of heat exchanger, (d) combined exterior and interior windbreakers.
tubes with the diameter of 25 mm. As shown in Fig. 2(a), the natural draft dry cooling system comprises a hyperbolic dry-cooling tower with vertically arranged air-cooled heat exchanger bundles. The geometric parameters of the air-cooled heat exchanger and dry-cooling tower are listed in Table 1. The height of cooling tower is 170 m, the base and outlet diameters of drycooling tower are 151 m and 90 m respectively, and the heat exchanger effective height is 24 m. Hundreds of cooling deltas as shown in Fig. 2(b) compose the air-cooled heat exchanger. Each cooling delta consists of two vertical finned tube bundles arranged in an apex angle of 49.08°. Fig 2(c) shows the four-row aluminum
finned tube bundles with the rectangular plate fins and staggered base tubes, which are widely adopted by the air-cooled heat exchanger. The geometric parameters of the four-row finned tube bundles are listed in Table 2. The outer diameter and thickness of the base tube are 25 mm and 1 mm respectively. The transverse tube spacing perpendicular to the air flow direction is 25 mm, and the longitudinal tube spacing along the air flow direction is 30 mm. For the plate fin, its thickness and spacing are 0.3 mm and 3.2 mm respectively, and the width along the air flow direction is 132 mm. Fig. 3 shows the schematic of windbreakers and sector numbering. All cooling deltas are equally divided into ten sectors
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Fig. 3 (continued)
as shown in Fig. 3(a). With the purpose of restraining the adverse effects of ambient winds, the windbreakers are arranged inside and outside the cooling tower as shown in Fig. 3(b) and (c). For the interior configuration, ten pieces of windbreakers are equally divided inside the cooling tower. For the exterior windbreakers, they are configured at both sides of the heat exchanger, which are perpendicular to the wind direction. All windbreakers are set as 30 m in length and 26 m in height. Fig. 3(d) shows the combined configuration of windbreakers at both the inner and outer of the dry-cooling tower. For convenience, the cooling tower without windbreakers is appointed as case A. The tower with ten windbreakers arranged inside is termed case B, the tower with two windbreakers arranged at the both sides of heat exchanger is designated case C, and the tower with both interior and exterior windbreakers is named case D. The dimensions of the computational domain, as shown in Fig. 4, are 3000 m in length and width and 2000 m in height, which
are large enough to eliminate the unrealistic effect of domain boundaries on the flow fields of ambient winds entering the natural draft dry cooling system. For the generation of high quality mesh, the computational domain is divided into regular cubic blocks in Gambit, a commercial modeling and meshing software. The tetrahedral and hexahedral mixed grids are applied to the central zone with dry-cooling tower, and the hexahedral structured grids are adopted in other blocks. The detailed mesh generated in the central zone with the heat exchanger and cooling tower is shown in Fig. 5, where the grid interval size for the radiator zone is set 0.2 m, however for the zone of dry-cooling tower, the grid interval size is set as 2 m. As a result, 4,248,684 cells are created for the simulation. Meanwhile, when the grid interval sizes of the radiator and cooling tower are set equal to 0.1 m and 1 m respectively, 6,890,006 cells are generated. When the grid interval sizes of the radiator and cooling tower are set equal to 0.5 m and 2 m separately, 2,587,949 cells are generated. The mass flow rate
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Fig. 4. Computational domain and boundary conditions. (a) With winds, (b) without winds.
of cooling air through the dry-cooling tower at the wind speed of 4 m/s varies by only about 0.3% when the former two dense grids are applied to the numerical simulation, so the cell number of 4,248,684 is finally adopted.
2.2. Mathematical model In this study, the lumped parameter radiator model is used to describe the flow and heat transfer characteristics of air-cooled heat exchanger bundles. Both the pressure drop and heat transfer
coefficient are specified as a function of the frontal velocity normal to the radiator surface. For the pressure drop Dp [11]:
1 Dp ¼ kL qu2f 2
ð1Þ
where q is the air density, uf is the frontal velocity normal to the radiator surface. kL is the loss coefficient, can be expressed as a polynomial function,
kL ¼
N X r n un1 f n¼1
ð2Þ
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Fig. 5. Local details of the grids for air-cooled heat exchanger and dry-cooling tower.
Table 3 Summary of the governing equation. Equations
u
Uu
Continuity x-Momentum
1 ui
0
0
le
@p j @ i @x þ @x@ i ðle @u @xi Þ þ @xj ðle @xi Þ i
Su @u
þ @x@ k
y-Momentum
uj
le
z-Momentum
uk
le
ðl @uj @p @ui @ @ @x þ @xi le @xj þ @xj le @xj j k þ @x@ k le @u @xj @u
@p @ui @x þ @x@ i ðle @x Þ þ @x@ j ðle @xkj Þ k k
þ @x@ k Energy Turbulence kinetic energy Turbulence dissipation rate
cpT k
e
le/rT l + lT/rk l + lT/re
@uk e @xi Þ
@uk e @xk Þ
ðl
þ qg
Sh GK þ Gb qe e ffi qC 1 Se qC 2 kþepffiffiffi me þ C 1e k C 3e Gb 2
Fig. 6. Temperature profiles of exhaust steam, circulating water and cooling air.
where N is set to be 3, rn is the polynomial factor and has the following value, r1 = 48.675, r2 = 6.305, r3 = 0.299, which is in accordance with the experimental results of heat exchanger bundles. The heat flux q of the radiator is expressed as
q ¼ hðt wa t a2 Þ
ð3Þ
where ta2 is the outlet air temperature of heat exchanger, t wa is the mean temperature of circulating water, equals the average value of the inlet and outlet water temperatures twa1, twa2 of heat exchanger.
t wa ¼ twa1 þ twa2 2
ð4Þ
In Eq. (3), the conduction resistance of tube wall and the convection resistance of water are both neglected compared with the convection resistance of cooling air, so t wa is treated as the outer wall temperature of tube. h means the empirical convective heat transfer coefficient, which can be expressed as follows:
h¼
N X hn un1 f n¼1
ð5Þ
where N is also set 3. hn is the polynomial factor and h1 = 17683.43, h2 = 9167.38, h3 = 1938.02, which are obtained from the heat transfer experimental results of heat exchanger bundles. The governing equations of the air-side flow and heat transfer take the following form:
@ quj u @ @u þ Su ¼ Cu @xj @xj @xj
ðj ¼ 1; 2; 3Þ
ð6Þ
where uj is the velocity in the xj direction. u, Uu and Su represent the variable, its diffusivity and source term respectively, which are listed in Table 3. In this work, the realizable k–e model is adopted to simulate the turbulent flow based on the turbulence kinetic energy (k) and dissipation rate (e) equations. The realizable k–e model can accurately predict the flows involving rotation, boundary layers under strong adverse pressure gradients, separation and recirculation, so it is applicable for the flow simulation of natural draft dry cooling system. At the windward boundary of the computational domain, the power-law equation is used to compute the wind speed uw at the height z.
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Fig. 7. Flow chart of numerical simulation on thermo-flow performances of natural draft dry cooling system.
uw ¼ u10
z e 10
ð7Þ
where u10 is the wind speed at the height of 10 m, for which five wind speeds of 4, 8, 12, 16 and 20 m/s are assigned. As a contrast, the dry cooling system performance under windless condition is also studied. The exponent e is set 0.2 as a typical case in this work. The air temperature at the surfaces of the computational domain is set equal to 30.5 °C. The k imposed at the inlet boundary is calculated as follows
k ¼ 1:5ðuavg IÞ2
ð8Þ
where uavg is the mean velocity; I is the turbulence intensity, assumed to be 10% in this study. The e at the inlet
boundary can be estimated from the turbulent viscosity ratio as follows 2
e ¼ qcl
1
lt l l
k
ð9Þ
where cl is an empirical constant of 0.09, the turbulent viscosity ratio lt/l is taken as 1.1 as a representative case. In the presence of ambient winds, the downstream surface is appointed as the outflow boundary due to the unchanging velocity and temperature profiles. On the other surfaces, the symmetry boundaries are setup as shown in Fig. 4(a). The ground is given the adiabatic boundary. For the cooling tower wall, the fluid–solid coupled condition is configured. In the absence of ambient winds,
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Fig. 8. Experimental setup and computed and measured 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.
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Fig. 8 (continued)
the four vertical domain surfaces are set as pressure inlet boundary conditions, and the top surface is appointed pressure outlet boundary as shown in Fig. 4(b), because the pressure is known but the flow rate or velocity is not known on these surfaces. The governing equations of continuum, momentum, energy, turbulent kinetic energy and dissipation rate are discretized using the first-order upwind differencing scheme. The SIMPLE algorithm is employed in the pressure–velocity coupling. A divergence-free criterion of 104 based on the scaled residual is prescribed for the case at ambient winds. For the case in the absence of winds, the residual of continuum equation can hardly arrive at 104, the mass flow rate through the dry-cooling tower
is used to monitor whether the iteration is converged to a reasonable result. Because the flow and heat transfer of cooling air are coupled with the performances of circulating water and exhaust steam, the condenser should be taken into account besides the aircooled heat exchanger and dry-cooling tower. Fig. 6 shows the temperature profiles of exhaust steam, circulating water and cooling air for the condenser and air-cooled heat exchanger. The condensation temperature ts is a key issue to the thermal efficiency of the power generating unit, the lower the condensation temperature is, the higher the thermal efficiency of the power generating unit.
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Fig. 9. Variable fields in absence of winds. (a) Pressure at horizontal cross section with the height of 10 m, (b) velocity and temperature at horizontal cross section with the height of 10 m, (c) pressure at middle vertical section, (d) velocity and temperature at middle vertical section.
As everyone knows, once the flow and heat transfer characteristics of cooling air through the heat exchanger bundles and drycooling tower vary with wind speeds, the changes of circulating water temperature and turbine back pressure will correspondingly take place. Conversely, the circulating water temperature change will influence the air-side flow and temperature fields. As a result, the numerical simulation is an iterative procedure. By means of the CFD simulations and heat balance analyses, the changing trends of turbine back pressure with the windbreaker type at various wind speeds can be obtained. The flow chart of the numerical simulation on the thermo-flow performances of natural draft dry cooling system and the turbine back pressure of power generating unit is shown in Fig. 7. In the condenser, the energy balance equations for both the exhaust steam and circulation water as well as the heat transfer equation are as follows
U0 ¼ ms ðhs hwa Þ
ð10Þ
U0 ¼ cpwa mwa ðt wa1 0 t0wa2 Þ
ð11Þ
U0 ¼ K c Ac Dt c ¼ K c Ac
twa1 0 t0wa2 t s t 0
ln ts twa2 0
ð12Þ
wa1
0
where U is the heat rejection of condenser, ms, hs, hwa are the exhaust steam mass flow rate, exhaust steam enthalpy and condensate enthalpy respectively, cpwa is the specific heat of circulating 0 0 water, mwa is the circulating water mass flow rate. twa1, twa2 are the outlet and inlet water temperatures of condenser, which are equal to the inlet and outlet water temperature of heat exchanger if the water heat loss between the air-cooled heat exchanger and condenser is ignored. Kc, Ac, Dtc are the overall heat transfer
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Fig. 10. Variable fields at wind speed of 4 m/s. (a) Pressure at horizontal cross section with the height of 10 m, (b) velocity and temperature at horizontal cross section with the height of 10 m, (c) pressure at middle vertical section, (d) velocity and temperature at middle vertical section.
coefficient, heat transfer surface area, log mean temperature difference of condenser. During the iteration, the exhaust steam mass flow rate and enthalpy, as well as the circulating water mass flow rate remain constant, but the turbine back pressure is unknown in advance. Before the numerical simulation, the back pressure is assumed, so the heat rejection of condenser can be calculated by Eq. (10). The overall heat transfer coefficient of condenser can be calculated in terms of the HEI standard of ASME. By solving 0 0 Eqs. (10)–(12), the inlet and outlet temperature twa2, twa1 can be obtained as follows:
ms ðhs hwa Þekc Ac =cpwa mwa cpwa mwa ð1 ekc Ac =cpwa mwa Þ
ð13Þ
ms ðhs hwa Þ ¼ ts þ cpwa mwa ð1 ekc Ac =cpwa mwa Þ
ð14Þ
t 0wa2 ¼ twa2 ¼ t s þ t 0wa1 ¼ twa1
After the mean circulating water temperature is determined, the outlet air temperature, air flow rate and heat gain by the air for natural draft dry cooling system can be obtained by means of numerical simulations. It should be pointed out that the mean circulating water temperatures assigned to the radiators in different sectors are calculated respectively during each iteration due to different heat rejection of each sector under various wind conditions. If the relative error between the heat gain U by cooling air and the 0 heat rejection U from condenser is within the allowed error, the final turbine back pressure of the power generating unit with different windbreaker configurations at various wind speeds can be achieved. Otherwise, the process should restart. 2.3. Experimental validation The air-cooled heat exchanger and dry-cooling tower in power plants are very complicated in structure and quite big in scale, and
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Fig. 11. Variable fields at wind speed of 12 m/s. (a) Pressure at horizontal cross section with the height of 10 m, (b) velocity and temperature at horizontal cross section with the height of 10 m, (c) pressure at middle vertical section, (d) velocity and temperature at middle vertical section.
moreover, the ambient conditions such as the wind speed and direction at the place of the power plant will basically experience a frequent change within one day, so the thermo-flow performances of natural draft dry cooling system can hardly be achieved by means of spot experiments. As an alternative method, the wind tunnel model test in the laboratory has been widely adopted to investigate the flow and heat transfer characteristics of natural draft dry cooling system. Generally, the approach of model experiments follows the scaling laws, which are developed from the dimensional analysis based on the principle of dimensional homogeneity. After the dimensional analysis is performed, the similarity between the model tested and the prototype to be designed can be achieved, which consists of particular types such as the geometric, kinematic, dynamic and thermal similarities. By the scaling laws of model experiments, the data from a cheap, small model can be
converted to the design information for an expensive, large prototype [12]. In our previous work, a dry-cooling tower with vertically arranged air-cooled heat exchanger bundles around the circumference of tower was investigated by a wind tunnel experiment [13,14]. Inside the actual dry-cooling tower, the flue gas desulfurization and stack were configured as shown in Fig. 8(a). The volumetric flow rate of the flue gas is about 1218 m3/s and the outlet diameter of the stack is 7.5 m. In terms of the scaling laws of model experiments, the models of dry-cooling tower and aircooled heat exchanger were made. The scaled dry-cooling tower has the height of 0.58 m with the dimension scale of 1:300, that is, the dimension ratio of the model tower to the actual tower is 1/300. The model test of the natural draft dry cooling system was carried out in the wind tunnel system of Guodian Academy of
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Fig. 12. Variable fields at wind speed of 4 m/s with inner windbreakers. (a) Pressure at horizontal cross section with the height of 10 m, (b) velocity and temperature at horizontal cross section with the height of 10 m, (c) pressure at middle vertical section, (d) velocity and temperature at middle vertical section.
Science and Technology in China, and the test section of the wind tunnel has the cross-section size of 3 m 3 m. During each test, nine points along one tower axis at a horizontal cross section of the model tower were simultaneously measured when the operation of the scaled natural draft dry cooling system was in a steady state. The ascending velocities at twelve cross sections in total inside the model dry-cooling tower were achieved by using the Hot-wire anemometer IFA-300 with an accuracy of 0.1% in the absence of ambient winds and at the wind speed of 0.23 m/s (corresponding to 4 m/s in the prototype natural draft dry cooling system). Based on the similarity principle, the locations of the measuring points in the model tower were converted to the actual values inside the real dry-cooling tower as shown in Fig. 8(a) and (b), and the converted ascending velocities inside the actual tower were shown in Fig. 8(c) and (d). According to the actual prototype configuration of the tested air-cooled heat exchanger and dry-cooling tower, the computa-
tional models were developed and the ascending velocities at the same locations inside the dry-cooling tower were obtained by means of numerical simulations. As illustrative cases, only two horizontal cross sections of the actual dry-cooling tower with the heights of 64.2 m and 164.2 m were used to compare the numerical and experimental results. Fig. 8(c) and (d) show the numerical results and experimental data in the absence of winds and at the wind speed of 4 m/s respectively, from which different changing tendencies of the ascending velocities at various cross sections can be observed. For both cases in the absence of winds and at the wind speed of 4 m/s, the ascending velocity at the tower center for the cross section with the height of 64.2 m is much higher than that at other location due to the flue gas discharge from the stack. At the height of 164.2 m without winds as shown in Fig. 8(c), the ascending velocity at the tower center decreases because of the flue gas diffusion during the ascending process. At the height of 164.2 m close to the tower exit at the wind speed of 4 m/s as
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Fig. 13. Variable fields at wind speed of 12 m/s with inner windbreakers. (a) Pressure at horizontal cross section with the height of 10 m, (b) velocity and temperature at horizontal cross section with the height of 10 m, (c) pressure at middle vertical section, (d) velocity and temperature at middle vertical section.
shown in Fig. 8(d), the ambient winds block the air flow at the upstream of the tower exit, resulting in a throttling effect at the exit plane, so the highest ascending velocity is at the position deviating to the downstream. Whether in the absence or in the presence of ambient winds, the calculated results are in good agreements 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 dry-cooling tower is a traditional tower with no flue gas desulfurization and stack inside, but the numerical approach is completely same as that based on the tested tower, which verifies in another way that the modeling and methods in this work are also reliable and accurate enough for the natural draft dry cooling system simulation.
3. Results and discussion 3.1. Variable fields The pressure, velocity and temperature fields at the horizontal and vertical cross sections for case A in absence of winds and at different wind speeds are shown in Figs. 9–11. Fig. 9(a) and (b) presents the variable distributions at the horizontal cross section with the height of 10 m, where the pressure, velocity and temperature fields are centrally symmetric due to the geometric symmetry of heat exchanger and dry-cooling tower. It can also be seen that the cooling air flows uniformly through each cooling delta, and the air temperature rises equally. From Fig. 9(c) and (d) it can be observed that the reverse pressure
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Fig. 14. Variable fields at wind speed of 4 m/s with side windbreakers. (a) Pressure at horizontal cross section with the height of 10 m, (b) velocity and temperature at horizontal cross section with the height of 10 m, (c) pressure at middle vertical section, (d) velocity and temperature at middle vertical section.
gradient is formed inside the dry-cooling tower, as a result of the force balance between the buoyancy force and viscous force. Fig. 10 shows the pressure, velocity and temperature fields at the wind speed of 4 m/s, from which can be seen that the variable fields are no longer centrally symmetric about the tower axis, and the bilateral symmetry along the wind direction is presented. From Fig. 10(a) and (b) it can be observed that the flow and temperature fields of sectors vary widely with each other. The low inlet pressure regions exist in the lateral sectors due to the air acceleration, which is similar to the behavior of the flow around a cylinder. Few cooling air can flow through these sectors due to small pressure difference between the outer and inner of the heat exchanger. As a result, the outlet air temperatures for these sectors are higher than those for the upwind and leeward sectors. The streamlines at the horizontal cross section show that cooling air flows almost straightly through the upwind sectors, resulting in an outstanding cooling capability.
On the contrary, the air turns its flow direction severely to flow through the lateral sectors, which will deteriorate the flow performance conspicuously. The pressure, streamlines and temperature at the vertical cross section are shown in Fig. 10(c) and (d). It can be clearly observed that cooling air flows through the frontal sectors and deflects downstream, impeding the cooling air flowing through the leeward sectors. What’s more, ambient winds restrain the hot plume rising inside the dry-cooling tower, and lead to the backward deviation for hot plume, thus weaken the air discharge at the tower exit. Fig. 11 shows the pressure, streamlines and temperature at the wind speed of 12 m/s. As shown in Fig. 11(a) and (b), ambient winds accelerate at both sides of dry-cooling tower, where flow separations take place. Pressures are almost the same at the inlet and outlet of the lateral sectors, so few cooling air can pass through these heat exchanger bundles. For the frontal sectors, cooling air
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Fig. 15. Variable fields at wind speed of 12 m/s with side windbreakers. (a) Pressure at horizontal cross section with the height of 10 m, (b) velocity and temperature at horizontal cross section with the height of 10 m, (c) pressure at middle vertical section, (d) velocity and temperature at middle vertical section.
flows easily through the heat exchanger bundles with a high velocity, resulting in a block of flows across the leeward sectors. As a result, the vortices are generated at the central back of the cooling tower and at both sides of sectors, where the low pressure appears accordingly. It shows that the flow and thermal performances of lateral sectors will be severely deteriorated as well as the leeward ones. In Fig. 11(c), the pressure at the exit of leeward sector increases compared with that at the wind speed of 4 m/s, so the blocking effect from the upwind sectors on the leeward ones becomes more conspicuous. The throttling action at the tower exit due to strong ambient winds can be clearly observed in Fig. 11(d), which restrains the hot plume discharge to a great extent. For case B, the windbreakers are arranged inside the dry-cooling tower. Fig. 12 shows the variable fields at the horizontal and vertical cross sections at the wind speed of 4 m/s. It can be observed that the vortices at the center of cooling tower are broken by the windbreakers, and the passage of hot plume discharge from the
leeward sectors is expanded compared to case A, showing that the hot plume inhibition effect from the upwind sectors on the leeward ones is weakened. At the wind speed of 12 m/s shown in Fig. 13, the low pressure area is enlarged. The windbreakers installed inside the cooling tower play roles of leading the hot plume and breaking the re-circulation flows of cooling air. Consequently, the windbreakers can balance the air flow through each sector by impairing the impacts of upstream air flows. For case C, the windbreakers are arranged at both sides of heat exchanger. At the wind speed of 4 m/s, shown in Fig. 14, ambient wind is greatly affected when it passes by both sides of heat exchanger where the windbreakers are installed. The wind speed is reduced near the lateral sectors, which will reinforce the air flow through the lateral sectors, even though the vortices are generated behind the windbreakers. At the wind speed of 12 m/s, the pressure near the windbreakers increases as shown in Fig. 15(a), which may benefit the lateral sectors. The vortices behind the
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Fig. 16. Variable fields at wind speed of 4 m/s with both inner and side windbreakers. (a) Pressure at horizontal cross section with the height of 10 m, (b) velocity and temperature at horizontal cross section with the height of 10 m, (c) pressure at middle vertical section, (d) velocity and temperature at middle vertical section.
windbreakers are enlarged as shown in Fig. 15(b). On the other hand, the pressures downstream the heat exchanger are much smaller, where a large low pressure region is formed. For leeward sectors, the low pressure will result in a reduced air flow rate through the cooling deltas. Additionally, the vortices inside the cooling tower move backwards, which may be unfavorable to the leeward sectors. The windbreakers are arranged both inside and outside the drycooling tower for case D, which combines case B with case C. At the wind speed of 4 m/s shown in Fig. 16, not only does the pressure increase near the lateral sectors, but the vortices are also broken inside the cooling tower. As a result, the positive effects of windbreakers in case B and C are presented conjointly in case D, which can significantly improve the thermo-flow performances of natural draft dry cooling system. At the wind speed of 12 m/s shown in Fig. 17, the vortices behind the windbreakers are expanded, and
two low pressure regions are formed downstream. Moreover, the vortices inside the cooling tower move rearward close to the leeward sectors. Because the pressure difference between the outlet and inlet of these sectors is reduced, it will consequentially hinder the air flowing through the cooling deltas and deteriorate the thermal performance of the leeward sectors. 3.2. Thermo-flow performances By means of the iterative simulation and computation, the mass flow rate, heat rejection and outlet water temperature of each sector are obtained. The final condensation temperature and turbine back pressure are calculated. Fig. 18(a)–(d) shows the mass flow rate of cooling air through each sector for cases A, B, C and D respectively. It is clearly observed that the mass flow rates of frontal sectors No. 2, No. 3
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Fig. 17. Variable fields at wind speed of 12 m/s with both inner and side windbreakers. (a) Pressure at horizontal cross section with the height of 10 m, (b) velocity and temperature at horizontal cross section with the height of 10 m, (c) pressure at middle vertical section, (d) velocity and temperature at middle vertical section.
and No. 4 are higher than others at various wind speeds. However, the mass flow rates of lateral sectors No. 1, No. 5, No. 6 and No.10 are lower than others. The mass flow rates of leeward sectors No. 7, No. 8 and No. 9 are in the middle level. As the wind speed increases, the mass flow rates of frontal sectors always increase due to the wind induced enhancement of cooling air flow for all cases. However, the mass flow rates of lateral sectors always decrease with increasing the wind speed for cases A and case B, as a result of the reduced pressure difference between the outer and inner of the cooling deltas owing to the strong wind flows around the tower. For the leeward sector No. 8, the mass flow rates increase at first and then decrease with increasing wind speed for cases A and B because at high wind speeds of 16 and 20 m/s, the plume penetration happens in part of the cooling deltas for the leeward sector. For cases C and D however, the changing trends vary widely. From Fig. 18(c) and (d) it can be seen that the mass flow rates of the lateral sectors No. 1 and No. 5 for cases C and D
increase conspicuously as the wind speed increases, showing that the higher the wind speed is, the better the flow performance of the lateral sectors in the front of the windbreakers. With the windbreakers inside the dry-cooling tower for case B, the mass flow rates of sectors vary little with case A at low wind speeds, but at higher wind speeds, the lateral and leeward sectors get improved in mass flow rate compared with case A. With the windbreakers only arranged at both sides of dry-cooling tower for case C, the flow performances of the upwind lateral sectors No. 1 and No. 5 are tremendously improved compared with case A. For case D, the combined windbreakers can restrain the adverse impacts of winds to a great extent, thus improve the flow performance of natural draft dry cooling system. The heat rejections of each sector for all cases at various wind speeds are shown in Fig. 19. As the heat rejection of each sector is positively related to the mass flow rate, the changing tendencies of heat rejection are basically same as mass flow rate. It can be seen
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Fig. 18. Mass flow rates of cooling air in each sector. (a) Without windbreakers, (b) with inner windbreakers, (c) with side windbreakers, (d) with both inner and side windbreakers.
that the heat rejections of frontal sectors are much higher than those of other sectors. For cases A, B, C and D, the heat rejections of frontal sectors No. 2, No. 3 and No. 4 decrease successively. The heat rejections of lateral sectors are basically small at high wind speeds except sectors No. 1 and 5 in case C and D, which are enhanced by the windbreakers. As for the leeward sectors, the heat rejections generally decline compared to case A. It shows that the heat rejections of each sector with the windbreakers are more evenly distributed, which contributes to improving the thermal performance of natural draft dry cooling system. Fig. 20 shows the total mass flow rate of cooling air, total heat rejection of circulating water, average outlet water temperature of heat exchanger and turbine back pressure for different cases at various wind speeds. For case C with exterior windbreakers and case D with both interior and exterior windbreakers, the total mass flow rate of cooling air conspicuously increase at high wind speeds compared with case A. For case B with only interior windbreakers, the flow rate also increases at high wind speeds, despite that this increase is not as large as case C and case D, as shown in Fig. 20
(a). For the total heat rejection shown in Fig. 20(b), it decreases at first, and then goes up as wind speed increases. Furthermore, the heat rejections for different cases vary widely, especially at high wind speeds. For the windbreaker configurations in case C and D, the total heat rejection increase substantially with respect to case A without windbreakers, and a definite improvement can be observed for case B as well. For the mean outlet water temperature shown in Fig. 20(c), it goes up with increasing wind speed at the lower wind speeds than 12 m/s for all cases. When the wind speed increases further, the outlet water temperature continues to increase slowly for all cases. At the wind speed of 20 m/s, the outlet water temperature begins to drop gently except for case C. The outlet water temperature of heat exchanger is a key issue to the performance of natural draft dry cooling system. Generally speaking, the lower the outlet water temperature is, the better the dry cooling system operates. From the changing trends of outlet water temperature, it can be seen that the thermo-flow performances of natural draft dry cooling system will benefit from the application of windbreakers at ambient winds. The variations of
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Fig. 19. Heat rejection of each sector. (a) Without windbreakers, (b) with inner windbreakers, (c) with side windbreakers, (d) with both inner and side windbreakers.
the turbine back pressure with the wind speed for different cases are shown in Fig. 20(d), from which can be observed that the back pressure basically increases with increasing wind speed, due to the adverse impacts of ambient winds on the thermo-flow performances of natural draft dry cooling system. At high wind speeds however, the back pressure doesn’t rise sharply. Instead, it remains to a certain extent. As for the cases with the windbreakers, the back pressures are dramatically reduced compared with that without windbreakers, especially at high wind speeds, showing that the energy efficiency of the power generating unit can be improved by means of the windbreaker configurations. 4. Conclusions The combined model of the thermo-flow performances of natural draft dry cooling system and the heat transfer process of
condenser is developed, by which the impacts of the interior and exterior windbreakers on the natural draft dry cooling system and power generating unit are investigated. With the windbreakers installed at the both sides of heat exchanger, inside the dry-cooling tower, and the above combined configuration, the thermo-flow performances of lateral sectors are all improved. On the contrary, the mass flow rates and heat rejections of frontal sectors decrease a little, which narrows the difference among sectors and improves the thermo-flow performances of dry cooling system. The windbreaker configurations have positive effects on the thermal efficiency of power generating unit at any wind speed, especially at high wind speeds. Generally speaking, the exterior windbreakers are superior to the interior ones in the thermo-flow performances of natural draft dry cooling system, which is recommended in the optimal design and operation of natural draft dry cooling system in power plants.
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Fig. 20. Thermo-flow performances of natural draft dry cooling system for different windbreaker configurations. (a) Total mass flow rate, (b) total heat rejection, (c) average outlet water temperature of heat exchanger, (d) turbine back pressure.
Acknowledgments 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. References [1] D.G. Kroger, Air-cooled Heat Exchangers and Cooling Towers: Thermal-flow Performance Evaluation and Design, vol. 2, PennWell Corp, Tulsa, Oklahoma, USA, 2004. [2] R. Al-Waked, M. Behnia, The performance of natural draft dry cooling towers under crosswind: CFD study, Int. J. Energy Res. 28 (2004) 147–161. [3] M. Goodarzi, A proposed stack configuration for dry cooling tower to improve cooling efficiency under crosswind, J. Wind. Eng. Ind. Aerodyn. 98 (2010) 858– 863. [4] M. Goodarzi, Proposing a new technique to enhance thermal performance and reduce structural design wind loads for natural drought cooling tower, Energy 62 (2013) 164–172. [5] M. Goodarzi, R. Keimanesh, Heat rejection enhancement in natural draft cooling tower using radiator-type windbreakers, Energy Convers. Manage. 71 (2013) 120–125.
[6] M. Goodarzi, R. Ramezanpour, Alternative geometry for cylindrical natural draft cooling tower with higher cooling efficiency under crosswind condition, Energy Convers. Manage. 77 (2014) 243–249. [7] Z. Zhai, S. Fu, Improving cooling efficiency of dry-cooling towers under crosswind conditions by using wind-break methods, Appl. Therm. Eng. 26 (2006) 1008–1017. [8] 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 Transfer 79 (2014) 1059–1069. [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 Transfer 63 (2013) 162–170. [10] Y.B. Zhao, G.Q. Long, F.Z. Sun, Y. Li, C.J. Zhang, J.B. Liu, Effect mechanism of air deflectors on the cooling performance of drycooling tower with vertical delta radiators under crosswind, Energy Convers. Manage. 93 (2015) 321–331. [11] 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 Transfer 67 (2013) 853– 866. [12] F.M. White, Fluid Mechanics, seventh ed., McGraw Hill, 2009. [13] L.J. Yang, L. Chen, X.Z. Du, Y.P. Yang, Effects of ambient winds on the thermoflow performances of indirect dry cooling system in a power plant, Int. J. Therm. Sci. 64 (2013) 178–187. [14] H.T. Liao, L.J. Yang, X.Z. Du, Y.P. Yang, Influences of height to diameter ratios of dry-cooling tower upon thermo-flow characteristics of indirect dry cooling system, Int. J. Therm. Sci. 94 (2015) 178–192.
Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Performance improvement of natural draft dry cooling system by interior and exterior windbreaker configurations Lei Chen, Lijun Yang ⇑, Xiaoze Du, Yongping Yang Key Laboratory of Condition Monitoring and Control for Power Plant Equipments 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 27 June 2015 Received in revised form 5 January 2016 Accepted 6 January 2016 Available online 21 January 2016 Keywords: Natural draft dry cooling system Air-cooled heat exchanger Dry-cooling tower Windbreakers Crosswinds Back pressure
a b s t r a c t Ambient winds are basically unfavorable to the thermo-flow performances of natural draft dry cooling system, and may result in a reduced thermal efficiency for the power generating unit in power plants, so it is of benefit to the natural draft dry cooling system to propose the measures against the adverse effects of ambient winds. For a typical natural draft dry cooling system, the computational models of the flow and heat transfer of cooling air coupled with the energy balances of circulating water and exhaust steam are developed, by which the performance improvement due to the interior and exterior windbreaker configurations is investigated. The flow and temperature fields of cooling air, the flow rate and heat rejection of each sector, the outlet water temperature of heat exchanger for the natural draft dry cooling systems with and without windbreaker configurations, and the corresponding turbine back pressures are obtained. The results show that the exterior windbreakers are superior to the interior ones in thermo-flow performances. The turbine back pressure can be reduced by the windbreaker configurations in the presence of ambient winds, especially at high wind speeds. Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction In the past years, natural draft dry cooling system in power plants has been increasingly developed and widely used in arid places thanks to its superiority in water saving [1]. Dry-cooling tower is one of the most important parts of natural draft dry cooling system, with air-cooled heat exchanger bundles vertically arranged around the circumference of cooling tower, or horizontally configured inside cooling tower. Cooling air flows through the heat exchanger bundles under the action of buoyancy force, removing the heat rejection of circulating water. As is well known, the thermo-flow performances of natural draft dry cooling system are sensitive to ambient conditions, especially the crosswinds. More attentions have been paid to the unfavorable wind effects on the performances of air-cooled heat exchangers and drycooling towers. With CFD methods, Al-Waked and Behnia [2] investigated the effects of crosswinds and windbreakers on the thermal performance of natural draft dry cooling system, finding that the windbreakers can weaken the adverse impacts of crosswinds. Goodarzi ⇑ Corresponding author. Tel.: +86 10 61773373; fax: +86 10 61773877. E-mail address: [email protected] (L. Yang). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2016.01.021 0017-9310/Ó 2016 Elsevier Ltd. All rights reserved.
[3] proposed a tower exit configuration to restrain the throat effect of deflective plume, by which the cooling efficiency is improved up to 9 percent. He also [4] introduced a method to utilize a variable tower height, which can reduce the structural wind loads without a considerable thermal performance reduction. Goodarzi and Keimanesh [5] studied the effect of a radiator-type windbreaker on natural draft dry cooling system, pointing out that a higher cooling efficiency can be achieved compared with the solid-type windbreaker. Goodarzi and Ramezanpour [6] proposed an elliptical geometry for natural draft dry cooling tower, which can bring on a higher cooling efficiency under crosswind condition. Zhai and Fu [7] put forward the windbreaker solutions in and around cooling towers, finding that 50% of cooling capacity can be recovered by placing side windbreakers of cooling tower. Lu et al. [8,9] studied the effects of tri-blade-like windbreaker and its orientation on natural draft dry cooling tower performance, suggested that one symmetry axis of the windbreaker should be in alignment with the prevailing wind direction. Zhao et al. [10] investigated the outlet water temperatures for different sectors with air deflectors under crosswind conditions, indicating that the air deflectors can weaken the air inflow distortion and improve the cooling performance of natural draft dry cooling tower.
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Nomenclature A cp d e g Gk Gb h hn hs hwa H I k kL K L m n p P q rn S1 S2 Su t uf
heat transfer surface area (m2) specific heat (J kg1K1) diameter (m) exponent of the wind speed in the power-law equation gravitational acceleration (m s2) turbulence kinetic energy generation due to mean velocity gradients (m2 s2) turbulence kinetic energy generation due to buoyancy (m2 s2) convection heat transfer coefficient (W m2 K1) polynomial coefficient for the convection heat transfer coefficient enthalpy of the exhaust steam (J kg1) enthalpy of the condensate (J kg1) height (m) turbulence intensity turbulent kinetic energy (m2 s2) flow loss coefficient overall heat transfer coefficient (W m2 K1) length of fin perpendicular to air flow direction (mm) mass flow rate (kg s1) number pressure (Pa) fin spacing (mm) heat flux (W m2) polynomial coefficient of non-dimensional loss coefficient tube spacing perpendicular to air flow direction (mm) tube spacing along air flow direction (mm) source term temperature (°C) frontal velocity (m s1)
uj uz uw W xj z
component of velocity (m s1) ascending velocity inside the tower (m s1) wind speed (m s1) width of fin along air flow direction (mm) Cartesian coordinate (m) height above the ground (m)
Greek symbols thickness of tube wall (mm) d1 d2 thickness of fin (mm) e turbulence dissipation rate (m2 s3) l dynamic viscosity (kg m1 s1) lt turbulent viscosity (kg m1 s1) q density (kg m3) r turbulent Prandtl number U diffusion coefficient (kg m1 s1) U heat rejection (W) u scalar variable Subscripts 1 inlet 2 outlet a air avg average B back c condenser s steam t tower w wind wa water
Fig. 1. Schematic of the power generating unit with natural draft dry cooling system. 1-boiler, 2-superheater, 3-turbine, 4-condenser, 5-condensate pump, 6-condensatescavening installation, 7-low pressure heater, 8-deaerator, 9-feed pump, 10-high pressure heater, 11-circulation water pump, 12-air-cooled heat exchanger, 13-dry-cooling tower, 14-generator.
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L. Chen et al. / International Journal of Heat and Mass Transfer 96 (2016) 42–63 Table 1 Geometric parameters of air-cooled heat exchanger and dry-cooling tower.
Tower height Base diameter of tower Outlet diameter of tower Throat height of tower Throat diameter of tower Height of air-cooled heat exchanger Outlet diameter of heat exchanger Number of heat exchanger sectors Number of cooling deltas
Symbol
Value
Ht db do Htt dtt Hhe dohe nhes ncd
170 m 151 m 90 m 145 m 87 m 24 m 159 m 10 180
Table 2 Geometric parameters of finned tube bundles. d d1 (mm mm)
L W d2 (mm mm mm)
P (mm)
S1 (mm)
S2 (mm)
/25 1
660 132 0.3
3.2
25
30
(a)
(b)
The aforementioned researches mainly focus on the flow and heat transfer characteristics of natural draft dry cooling system with different measures against adverse wind effects. It is still not clear the turbine back pressure changing trends thanks to the windbreaker configurations and other measures. Furthermore, the particular iterative procedure of the flow and heat transfer of cooling air coupled with the energy balances of circulating water and exhaust steam, which can clarify the actual running status of natural draft dry cooling system under windy conditions, is not found in related literatures either. In this work, the natural draft dry cooling system coupled with the condenser will be thoroughly investigated in their thermoflow performances, and the iteration procedure for the numerical simulations on the performances of cooling air, circulating water and exhaust steam will be developed, based on which the turbine back pressure can be calculated at various wind speeds. The impacts of interior and exterior windbreaker configurations on the performance of natural draft dry cooling system will be clarified, which can contribute to the optimal design and operation of the air-cooled heat exchanger and dry-cooling tower in power plants. 2. Modeling and methods 2.1. Physical model
(c) Fig. 2. Schematic of natural draft dry cooling system. (a) Air-cooled heat exchanger and dry-cooling tower, (b) cooling deltas of heat exchanger, (c) configuration of finned tube.
A 660 MW power generating unit with a natural draft dry cooling system is taken into account in this paper, whose schematic view of the working medium loop and cooling loop is shown in Fig. 1. A reaction type steam turbine composed of a HP-IP combined cylinder and two LP cylinders is utilized. The main steam at the pressure of 24.2 MPa and temperature of 566 °C flows through one impulse governing stage and nine reaction stages in the HP cylinder and then passes through six reaction stages in the IP cylinder after being reheated to 566 °C at the pressure of 2.14 MPa. Finally, the steam goes through seven reaction stages in each LP cylinder and ejects to the condenser. The surface condenser and air-cooled heat exchanger are adopted, in which the circulating water is in a closed cycle. The surface condenser has a heat transfer surface area of 40,000 m2, and consists of 34,160
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Fig. 3. Schematic of windbreakers and sector numbering. (a) No windbreakers, (b) inside tower, (c) at both sides of heat exchanger, (d) combined exterior and interior windbreakers.
tubes with the diameter of 25 mm. As shown in Fig. 2(a), the natural draft dry cooling system comprises a hyperbolic dry-cooling tower with vertically arranged air-cooled heat exchanger bundles. The geometric parameters of the air-cooled heat exchanger and dry-cooling tower are listed in Table 1. The height of cooling tower is 170 m, the base and outlet diameters of drycooling tower are 151 m and 90 m respectively, and the heat exchanger effective height is 24 m. Hundreds of cooling deltas as shown in Fig. 2(b) compose the air-cooled heat exchanger. Each cooling delta consists of two vertical finned tube bundles arranged in an apex angle of 49.08°. Fig 2(c) shows the four-row aluminum
finned tube bundles with the rectangular plate fins and staggered base tubes, which are widely adopted by the air-cooled heat exchanger. The geometric parameters of the four-row finned tube bundles are listed in Table 2. The outer diameter and thickness of the base tube are 25 mm and 1 mm respectively. The transverse tube spacing perpendicular to the air flow direction is 25 mm, and the longitudinal tube spacing along the air flow direction is 30 mm. For the plate fin, its thickness and spacing are 0.3 mm and 3.2 mm respectively, and the width along the air flow direction is 132 mm. Fig. 3 shows the schematic of windbreakers and sector numbering. All cooling deltas are equally divided into ten sectors
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Fig. 3 (continued)
as shown in Fig. 3(a). With the purpose of restraining the adverse effects of ambient winds, the windbreakers are arranged inside and outside the cooling tower as shown in Fig. 3(b) and (c). For the interior configuration, ten pieces of windbreakers are equally divided inside the cooling tower. For the exterior windbreakers, they are configured at both sides of the heat exchanger, which are perpendicular to the wind direction. All windbreakers are set as 30 m in length and 26 m in height. Fig. 3(d) shows the combined configuration of windbreakers at both the inner and outer of the dry-cooling tower. For convenience, the cooling tower without windbreakers is appointed as case A. The tower with ten windbreakers arranged inside is termed case B, the tower with two windbreakers arranged at the both sides of heat exchanger is designated case C, and the tower with both interior and exterior windbreakers is named case D. The dimensions of the computational domain, as shown in Fig. 4, are 3000 m in length and width and 2000 m in height, which
are large enough to eliminate the unrealistic effect of domain boundaries on the flow fields of ambient winds entering the natural draft dry cooling system. For the generation of high quality mesh, the computational domain is divided into regular cubic blocks in Gambit, a commercial modeling and meshing software. The tetrahedral and hexahedral mixed grids are applied to the central zone with dry-cooling tower, and the hexahedral structured grids are adopted in other blocks. The detailed mesh generated in the central zone with the heat exchanger and cooling tower is shown in Fig. 5, where the grid interval size for the radiator zone is set 0.2 m, however for the zone of dry-cooling tower, the grid interval size is set as 2 m. As a result, 4,248,684 cells are created for the simulation. Meanwhile, when the grid interval sizes of the radiator and cooling tower are set equal to 0.1 m and 1 m respectively, 6,890,006 cells are generated. When the grid interval sizes of the radiator and cooling tower are set equal to 0.5 m and 2 m separately, 2,587,949 cells are generated. The mass flow rate
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Fig. 4. Computational domain and boundary conditions. (a) With winds, (b) without winds.
of cooling air through the dry-cooling tower at the wind speed of 4 m/s varies by only about 0.3% when the former two dense grids are applied to the numerical simulation, so the cell number of 4,248,684 is finally adopted.
2.2. Mathematical model In this study, the lumped parameter radiator model is used to describe the flow and heat transfer characteristics of air-cooled heat exchanger bundles. Both the pressure drop and heat transfer
coefficient are specified as a function of the frontal velocity normal to the radiator surface. For the pressure drop Dp [11]:
1 Dp ¼ kL qu2f 2
ð1Þ
where q is the air density, uf is the frontal velocity normal to the radiator surface. kL is the loss coefficient, can be expressed as a polynomial function,
kL ¼
N X r n un1 f n¼1
ð2Þ
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Fig. 5. Local details of the grids for air-cooled heat exchanger and dry-cooling tower.
Table 3 Summary of the governing equation. Equations
u
Uu
Continuity x-Momentum
1 ui
0
0
le
@p j @ i @x þ @x@ i ðle @u @xi Þ þ @xj ðle @xi Þ i
Su @u
þ @x@ k
y-Momentum
uj
le
z-Momentum
uk
le
ðl @uj @p @ui @ @ @x þ @xi le @xj þ @xj le @xj j k þ @x@ k le @u @xj @u
@p @ui @x þ @x@ i ðle @x Þ þ @x@ j ðle @xkj Þ k k
þ @x@ k Energy Turbulence kinetic energy Turbulence dissipation rate
cpT k
e
le/rT l + lT/rk l + lT/re
@uk e @xi Þ
@uk e @xk Þ
ðl
þ qg
Sh GK þ Gb qe e ffi qC 1 Se qC 2 kþepffiffiffi me þ C 1e k C 3e Gb 2
Fig. 6. Temperature profiles of exhaust steam, circulating water and cooling air.
where N is set to be 3, rn is the polynomial factor and has the following value, r1 = 48.675, r2 = 6.305, r3 = 0.299, which is in accordance with the experimental results of heat exchanger bundles. The heat flux q of the radiator is expressed as
q ¼ hðt wa t a2 Þ
ð3Þ
where ta2 is the outlet air temperature of heat exchanger, t wa is the mean temperature of circulating water, equals the average value of the inlet and outlet water temperatures twa1, twa2 of heat exchanger.
t wa ¼ twa1 þ twa2 2
ð4Þ
In Eq. (3), the conduction resistance of tube wall and the convection resistance of water are both neglected compared with the convection resistance of cooling air, so t wa is treated as the outer wall temperature of tube. h means the empirical convective heat transfer coefficient, which can be expressed as follows:
h¼
N X hn un1 f n¼1
ð5Þ
where N is also set 3. hn is the polynomial factor and h1 = 17683.43, h2 = 9167.38, h3 = 1938.02, which are obtained from the heat transfer experimental results of heat exchanger bundles. The governing equations of the air-side flow and heat transfer take the following form:
@ quj u @ @u þ Su ¼ Cu @xj @xj @xj
ðj ¼ 1; 2; 3Þ
ð6Þ
where uj is the velocity in the xj direction. u, Uu and Su represent the variable, its diffusivity and source term respectively, which are listed in Table 3. In this work, the realizable k–e model is adopted to simulate the turbulent flow based on the turbulence kinetic energy (k) and dissipation rate (e) equations. The realizable k–e model can accurately predict the flows involving rotation, boundary layers under strong adverse pressure gradients, separation and recirculation, so it is applicable for the flow simulation of natural draft dry cooling system. At the windward boundary of the computational domain, the power-law equation is used to compute the wind speed uw at the height z.
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Fig. 7. Flow chart of numerical simulation on thermo-flow performances of natural draft dry cooling system.
uw ¼ u10
z e 10
ð7Þ
where u10 is the wind speed at the height of 10 m, for which five wind speeds of 4, 8, 12, 16 and 20 m/s are assigned. As a contrast, the dry cooling system performance under windless condition is also studied. The exponent e is set 0.2 as a typical case in this work. The air temperature at the surfaces of the computational domain is set equal to 30.5 °C. The k imposed at the inlet boundary is calculated as follows
k ¼ 1:5ðuavg IÞ2
ð8Þ
where uavg is the mean velocity; I is the turbulence intensity, assumed to be 10% in this study. The e at the inlet
boundary can be estimated from the turbulent viscosity ratio as follows 2
e ¼ qcl
1
lt l l
k
ð9Þ
where cl is an empirical constant of 0.09, the turbulent viscosity ratio lt/l is taken as 1.1 as a representative case. In the presence of ambient winds, the downstream surface is appointed as the outflow boundary due to the unchanging velocity and temperature profiles. On the other surfaces, the symmetry boundaries are setup as shown in Fig. 4(a). The ground is given the adiabatic boundary. For the cooling tower wall, the fluid–solid coupled condition is configured. In the absence of ambient winds,
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Fig. 8. Experimental setup and computed and measured 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.
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Fig. 8 (continued)
the four vertical domain surfaces are set as pressure inlet boundary conditions, and the top surface is appointed pressure outlet boundary as shown in Fig. 4(b), because the pressure is known but the flow rate or velocity is not known on these surfaces. The governing equations of continuum, momentum, energy, turbulent kinetic energy and dissipation rate are discretized using the first-order upwind differencing scheme. The SIMPLE algorithm is employed in the pressure–velocity coupling. A divergence-free criterion of 104 based on the scaled residual is prescribed for the case at ambient winds. For the case in the absence of winds, the residual of continuum equation can hardly arrive at 104, the mass flow rate through the dry-cooling tower
is used to monitor whether the iteration is converged to a reasonable result. Because the flow and heat transfer of cooling air are coupled with the performances of circulating water and exhaust steam, the condenser should be taken into account besides the aircooled heat exchanger and dry-cooling tower. Fig. 6 shows the temperature profiles of exhaust steam, circulating water and cooling air for the condenser and air-cooled heat exchanger. The condensation temperature ts is a key issue to the thermal efficiency of the power generating unit, the lower the condensation temperature is, the higher the thermal efficiency of the power generating unit.
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Fig. 9. Variable fields in absence of winds. (a) Pressure at horizontal cross section with the height of 10 m, (b) velocity and temperature at horizontal cross section with the height of 10 m, (c) pressure at middle vertical section, (d) velocity and temperature at middle vertical section.
As everyone knows, once the flow and heat transfer characteristics of cooling air through the heat exchanger bundles and drycooling tower vary with wind speeds, the changes of circulating water temperature and turbine back pressure will correspondingly take place. Conversely, the circulating water temperature change will influence the air-side flow and temperature fields. As a result, the numerical simulation is an iterative procedure. By means of the CFD simulations and heat balance analyses, the changing trends of turbine back pressure with the windbreaker type at various wind speeds can be obtained. The flow chart of the numerical simulation on the thermo-flow performances of natural draft dry cooling system and the turbine back pressure of power generating unit is shown in Fig. 7. In the condenser, the energy balance equations for both the exhaust steam and circulation water as well as the heat transfer equation are as follows
U0 ¼ ms ðhs hwa Þ
ð10Þ
U0 ¼ cpwa mwa ðt wa1 0 t0wa2 Þ
ð11Þ
U0 ¼ K c Ac Dt c ¼ K c Ac
twa1 0 t0wa2 t s t 0
ln ts twa2 0
ð12Þ
wa1
0
where U is the heat rejection of condenser, ms, hs, hwa are the exhaust steam mass flow rate, exhaust steam enthalpy and condensate enthalpy respectively, cpwa is the specific heat of circulating 0 0 water, mwa is the circulating water mass flow rate. twa1, twa2 are the outlet and inlet water temperatures of condenser, which are equal to the inlet and outlet water temperature of heat exchanger if the water heat loss between the air-cooled heat exchanger and condenser is ignored. Kc, Ac, Dtc are the overall heat transfer
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Fig. 10. Variable fields at wind speed of 4 m/s. (a) Pressure at horizontal cross section with the height of 10 m, (b) velocity and temperature at horizontal cross section with the height of 10 m, (c) pressure at middle vertical section, (d) velocity and temperature at middle vertical section.
coefficient, heat transfer surface area, log mean temperature difference of condenser. During the iteration, the exhaust steam mass flow rate and enthalpy, as well as the circulating water mass flow rate remain constant, but the turbine back pressure is unknown in advance. Before the numerical simulation, the back pressure is assumed, so the heat rejection of condenser can be calculated by Eq. (10). The overall heat transfer coefficient of condenser can be calculated in terms of the HEI standard of ASME. By solving 0 0 Eqs. (10)–(12), the inlet and outlet temperature twa2, twa1 can be obtained as follows:
ms ðhs hwa Þekc Ac =cpwa mwa cpwa mwa ð1 ekc Ac =cpwa mwa Þ
ð13Þ
ms ðhs hwa Þ ¼ ts þ cpwa mwa ð1 ekc Ac =cpwa mwa Þ
ð14Þ
t 0wa2 ¼ twa2 ¼ t s þ t 0wa1 ¼ twa1
After the mean circulating water temperature is determined, the outlet air temperature, air flow rate and heat gain by the air for natural draft dry cooling system can be obtained by means of numerical simulations. It should be pointed out that the mean circulating water temperatures assigned to the radiators in different sectors are calculated respectively during each iteration due to different heat rejection of each sector under various wind conditions. If the relative error between the heat gain U by cooling air and the 0 heat rejection U from condenser is within the allowed error, the final turbine back pressure of the power generating unit with different windbreaker configurations at various wind speeds can be achieved. Otherwise, the process should restart. 2.3. Experimental validation The air-cooled heat exchanger and dry-cooling tower in power plants are very complicated in structure and quite big in scale, and
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Fig. 11. Variable fields at wind speed of 12 m/s. (a) Pressure at horizontal cross section with the height of 10 m, (b) velocity and temperature at horizontal cross section with the height of 10 m, (c) pressure at middle vertical section, (d) velocity and temperature at middle vertical section.
moreover, the ambient conditions such as the wind speed and direction at the place of the power plant will basically experience a frequent change within one day, so the thermo-flow performances of natural draft dry cooling system can hardly be achieved by means of spot experiments. As an alternative method, the wind tunnel model test in the laboratory has been widely adopted to investigate the flow and heat transfer characteristics of natural draft dry cooling system. Generally, the approach of model experiments follows the scaling laws, which are developed from the dimensional analysis based on the principle of dimensional homogeneity. After the dimensional analysis is performed, the similarity between the model tested and the prototype to be designed can be achieved, which consists of particular types such as the geometric, kinematic, dynamic and thermal similarities. By the scaling laws of model experiments, the data from a cheap, small model can be
converted to the design information for an expensive, large prototype [12]. In our previous work, a dry-cooling tower with vertically arranged air-cooled heat exchanger bundles around the circumference of tower was investigated by a wind tunnel experiment [13,14]. Inside the actual dry-cooling tower, the flue gas desulfurization and stack were configured as shown in Fig. 8(a). The volumetric flow rate of the flue gas is about 1218 m3/s and the outlet diameter of the stack is 7.5 m. In terms of the scaling laws of model experiments, the models of dry-cooling tower and aircooled heat exchanger were made. The scaled dry-cooling tower has the height of 0.58 m with the dimension scale of 1:300, that is, the dimension ratio of the model tower to the actual tower is 1/300. The model test of the natural draft dry cooling system was carried out in the wind tunnel system of Guodian Academy of
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Fig. 12. Variable fields at wind speed of 4 m/s with inner windbreakers. (a) Pressure at horizontal cross section with the height of 10 m, (b) velocity and temperature at horizontal cross section with the height of 10 m, (c) pressure at middle vertical section, (d) velocity and temperature at middle vertical section.
Science and Technology in China, and the test section of the wind tunnel has the cross-section size of 3 m 3 m. During each test, nine points along one tower axis at a horizontal cross section of the model tower were simultaneously measured when the operation of the scaled natural draft dry cooling system was in a steady state. The ascending velocities at twelve cross sections in total inside the model dry-cooling tower were achieved by using the Hot-wire anemometer IFA-300 with an accuracy of 0.1% in the absence of ambient winds and at the wind speed of 0.23 m/s (corresponding to 4 m/s in the prototype natural draft dry cooling system). Based on the similarity principle, the locations of the measuring points in the model tower were converted to the actual values inside the real dry-cooling tower as shown in Fig. 8(a) and (b), and the converted ascending velocities inside the actual tower were shown in Fig. 8(c) and (d). According to the actual prototype configuration of the tested air-cooled heat exchanger and dry-cooling tower, the computa-
tional models were developed and the ascending velocities at the same locations inside the dry-cooling tower were obtained by means of numerical simulations. As illustrative cases, only two horizontal cross sections of the actual dry-cooling tower with the heights of 64.2 m and 164.2 m were used to compare the numerical and experimental results. Fig. 8(c) and (d) show the numerical results and experimental data in the absence of winds and at the wind speed of 4 m/s respectively, from which different changing tendencies of the ascending velocities at various cross sections can be observed. For both cases in the absence of winds and at the wind speed of 4 m/s, the ascending velocity at the tower center for the cross section with the height of 64.2 m is much higher than that at other location due to the flue gas discharge from the stack. At the height of 164.2 m without winds as shown in Fig. 8(c), the ascending velocity at the tower center decreases because of the flue gas diffusion during the ascending process. At the height of 164.2 m close to the tower exit at the wind speed of 4 m/s as
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Fig. 13. Variable fields at wind speed of 12 m/s with inner windbreakers. (a) Pressure at horizontal cross section with the height of 10 m, (b) velocity and temperature at horizontal cross section with the height of 10 m, (c) pressure at middle vertical section, (d) velocity and temperature at middle vertical section.
shown in Fig. 8(d), the ambient winds block the air flow at the upstream of the tower exit, resulting in a throttling effect at the exit plane, so the highest ascending velocity is at the position deviating to the downstream. Whether in the absence or in the presence of ambient winds, the calculated results are in good agreements 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 dry-cooling tower is a traditional tower with no flue gas desulfurization and stack inside, but the numerical approach is completely same as that based on the tested tower, which verifies in another way that the modeling and methods in this work are also reliable and accurate enough for the natural draft dry cooling system simulation.
3. Results and discussion 3.1. Variable fields The pressure, velocity and temperature fields at the horizontal and vertical cross sections for case A in absence of winds and at different wind speeds are shown in Figs. 9–11. Fig. 9(a) and (b) presents the variable distributions at the horizontal cross section with the height of 10 m, where the pressure, velocity and temperature fields are centrally symmetric due to the geometric symmetry of heat exchanger and dry-cooling tower. It can also be seen that the cooling air flows uniformly through each cooling delta, and the air temperature rises equally. From Fig. 9(c) and (d) it can be observed that the reverse pressure
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Fig. 14. Variable fields at wind speed of 4 m/s with side windbreakers. (a) Pressure at horizontal cross section with the height of 10 m, (b) velocity and temperature at horizontal cross section with the height of 10 m, (c) pressure at middle vertical section, (d) velocity and temperature at middle vertical section.
gradient is formed inside the dry-cooling tower, as a result of the force balance between the buoyancy force and viscous force. Fig. 10 shows the pressure, velocity and temperature fields at the wind speed of 4 m/s, from which can be seen that the variable fields are no longer centrally symmetric about the tower axis, and the bilateral symmetry along the wind direction is presented. From Fig. 10(a) and (b) it can be observed that the flow and temperature fields of sectors vary widely with each other. The low inlet pressure regions exist in the lateral sectors due to the air acceleration, which is similar to the behavior of the flow around a cylinder. Few cooling air can flow through these sectors due to small pressure difference between the outer and inner of the heat exchanger. As a result, the outlet air temperatures for these sectors are higher than those for the upwind and leeward sectors. The streamlines at the horizontal cross section show that cooling air flows almost straightly through the upwind sectors, resulting in an outstanding cooling capability.
On the contrary, the air turns its flow direction severely to flow through the lateral sectors, which will deteriorate the flow performance conspicuously. The pressure, streamlines and temperature at the vertical cross section are shown in Fig. 10(c) and (d). It can be clearly observed that cooling air flows through the frontal sectors and deflects downstream, impeding the cooling air flowing through the leeward sectors. What’s more, ambient winds restrain the hot plume rising inside the dry-cooling tower, and lead to the backward deviation for hot plume, thus weaken the air discharge at the tower exit. Fig. 11 shows the pressure, streamlines and temperature at the wind speed of 12 m/s. As shown in Fig. 11(a) and (b), ambient winds accelerate at both sides of dry-cooling tower, where flow separations take place. Pressures are almost the same at the inlet and outlet of the lateral sectors, so few cooling air can pass through these heat exchanger bundles. For the frontal sectors, cooling air
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Fig. 15. Variable fields at wind speed of 12 m/s with side windbreakers. (a) Pressure at horizontal cross section with the height of 10 m, (b) velocity and temperature at horizontal cross section with the height of 10 m, (c) pressure at middle vertical section, (d) velocity and temperature at middle vertical section.
flows easily through the heat exchanger bundles with a high velocity, resulting in a block of flows across the leeward sectors. As a result, the vortices are generated at the central back of the cooling tower and at both sides of sectors, where the low pressure appears accordingly. It shows that the flow and thermal performances of lateral sectors will be severely deteriorated as well as the leeward ones. In Fig. 11(c), the pressure at the exit of leeward sector increases compared with that at the wind speed of 4 m/s, so the blocking effect from the upwind sectors on the leeward ones becomes more conspicuous. The throttling action at the tower exit due to strong ambient winds can be clearly observed in Fig. 11(d), which restrains the hot plume discharge to a great extent. For case B, the windbreakers are arranged inside the dry-cooling tower. Fig. 12 shows the variable fields at the horizontal and vertical cross sections at the wind speed of 4 m/s. It can be observed that the vortices at the center of cooling tower are broken by the windbreakers, and the passage of hot plume discharge from the
leeward sectors is expanded compared to case A, showing that the hot plume inhibition effect from the upwind sectors on the leeward ones is weakened. At the wind speed of 12 m/s shown in Fig. 13, the low pressure area is enlarged. The windbreakers installed inside the cooling tower play roles of leading the hot plume and breaking the re-circulation flows of cooling air. Consequently, the windbreakers can balance the air flow through each sector by impairing the impacts of upstream air flows. For case C, the windbreakers are arranged at both sides of heat exchanger. At the wind speed of 4 m/s, shown in Fig. 14, ambient wind is greatly affected when it passes by both sides of heat exchanger where the windbreakers are installed. The wind speed is reduced near the lateral sectors, which will reinforce the air flow through the lateral sectors, even though the vortices are generated behind the windbreakers. At the wind speed of 12 m/s, the pressure near the windbreakers increases as shown in Fig. 15(a), which may benefit the lateral sectors. The vortices behind the
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Fig. 16. Variable fields at wind speed of 4 m/s with both inner and side windbreakers. (a) Pressure at horizontal cross section with the height of 10 m, (b) velocity and temperature at horizontal cross section with the height of 10 m, (c) pressure at middle vertical section, (d) velocity and temperature at middle vertical section.
windbreakers are enlarged as shown in Fig. 15(b). On the other hand, the pressures downstream the heat exchanger are much smaller, where a large low pressure region is formed. For leeward sectors, the low pressure will result in a reduced air flow rate through the cooling deltas. Additionally, the vortices inside the cooling tower move backwards, which may be unfavorable to the leeward sectors. The windbreakers are arranged both inside and outside the drycooling tower for case D, which combines case B with case C. At the wind speed of 4 m/s shown in Fig. 16, not only does the pressure increase near the lateral sectors, but the vortices are also broken inside the cooling tower. As a result, the positive effects of windbreakers in case B and C are presented conjointly in case D, which can significantly improve the thermo-flow performances of natural draft dry cooling system. At the wind speed of 12 m/s shown in Fig. 17, the vortices behind the windbreakers are expanded, and
two low pressure regions are formed downstream. Moreover, the vortices inside the cooling tower move rearward close to the leeward sectors. Because the pressure difference between the outlet and inlet of these sectors is reduced, it will consequentially hinder the air flowing through the cooling deltas and deteriorate the thermal performance of the leeward sectors. 3.2. Thermo-flow performances By means of the iterative simulation and computation, the mass flow rate, heat rejection and outlet water temperature of each sector are obtained. The final condensation temperature and turbine back pressure are calculated. Fig. 18(a)–(d) shows the mass flow rate of cooling air through each sector for cases A, B, C and D respectively. It is clearly observed that the mass flow rates of frontal sectors No. 2, No. 3
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Fig. 17. Variable fields at wind speed of 12 m/s with both inner and side windbreakers. (a) Pressure at horizontal cross section with the height of 10 m, (b) velocity and temperature at horizontal cross section with the height of 10 m, (c) pressure at middle vertical section, (d) velocity and temperature at middle vertical section.
and No. 4 are higher than others at various wind speeds. However, the mass flow rates of lateral sectors No. 1, No. 5, No. 6 and No.10 are lower than others. The mass flow rates of leeward sectors No. 7, No. 8 and No. 9 are in the middle level. As the wind speed increases, the mass flow rates of frontal sectors always increase due to the wind induced enhancement of cooling air flow for all cases. However, the mass flow rates of lateral sectors always decrease with increasing the wind speed for cases A and case B, as a result of the reduced pressure difference between the outer and inner of the cooling deltas owing to the strong wind flows around the tower. For the leeward sector No. 8, the mass flow rates increase at first and then decrease with increasing wind speed for cases A and B because at high wind speeds of 16 and 20 m/s, the plume penetration happens in part of the cooling deltas for the leeward sector. For cases C and D however, the changing trends vary widely. From Fig. 18(c) and (d) it can be seen that the mass flow rates of the lateral sectors No. 1 and No. 5 for cases C and D
increase conspicuously as the wind speed increases, showing that the higher the wind speed is, the better the flow performance of the lateral sectors in the front of the windbreakers. With the windbreakers inside the dry-cooling tower for case B, the mass flow rates of sectors vary little with case A at low wind speeds, but at higher wind speeds, the lateral and leeward sectors get improved in mass flow rate compared with case A. With the windbreakers only arranged at both sides of dry-cooling tower for case C, the flow performances of the upwind lateral sectors No. 1 and No. 5 are tremendously improved compared with case A. For case D, the combined windbreakers can restrain the adverse impacts of winds to a great extent, thus improve the flow performance of natural draft dry cooling system. The heat rejections of each sector for all cases at various wind speeds are shown in Fig. 19. As the heat rejection of each sector is positively related to the mass flow rate, the changing tendencies of heat rejection are basically same as mass flow rate. It can be seen
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Fig. 18. Mass flow rates of cooling air in each sector. (a) Without windbreakers, (b) with inner windbreakers, (c) with side windbreakers, (d) with both inner and side windbreakers.
that the heat rejections of frontal sectors are much higher than those of other sectors. For cases A, B, C and D, the heat rejections of frontal sectors No. 2, No. 3 and No. 4 decrease successively. The heat rejections of lateral sectors are basically small at high wind speeds except sectors No. 1 and 5 in case C and D, which are enhanced by the windbreakers. As for the leeward sectors, the heat rejections generally decline compared to case A. It shows that the heat rejections of each sector with the windbreakers are more evenly distributed, which contributes to improving the thermal performance of natural draft dry cooling system. Fig. 20 shows the total mass flow rate of cooling air, total heat rejection of circulating water, average outlet water temperature of heat exchanger and turbine back pressure for different cases at various wind speeds. For case C with exterior windbreakers and case D with both interior and exterior windbreakers, the total mass flow rate of cooling air conspicuously increase at high wind speeds compared with case A. For case B with only interior windbreakers, the flow rate also increases at high wind speeds, despite that this increase is not as large as case C and case D, as shown in Fig. 20
(a). For the total heat rejection shown in Fig. 20(b), it decreases at first, and then goes up as wind speed increases. Furthermore, the heat rejections for different cases vary widely, especially at high wind speeds. For the windbreaker configurations in case C and D, the total heat rejection increase substantially with respect to case A without windbreakers, and a definite improvement can be observed for case B as well. For the mean outlet water temperature shown in Fig. 20(c), it goes up with increasing wind speed at the lower wind speeds than 12 m/s for all cases. When the wind speed increases further, the outlet water temperature continues to increase slowly for all cases. At the wind speed of 20 m/s, the outlet water temperature begins to drop gently except for case C. The outlet water temperature of heat exchanger is a key issue to the performance of natural draft dry cooling system. Generally speaking, the lower the outlet water temperature is, the better the dry cooling system operates. From the changing trends of outlet water temperature, it can be seen that the thermo-flow performances of natural draft dry cooling system will benefit from the application of windbreakers at ambient winds. The variations of
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Fig. 19. Heat rejection of each sector. (a) Without windbreakers, (b) with inner windbreakers, (c) with side windbreakers, (d) with both inner and side windbreakers.
the turbine back pressure with the wind speed for different cases are shown in Fig. 20(d), from which can be observed that the back pressure basically increases with increasing wind speed, due to the adverse impacts of ambient winds on the thermo-flow performances of natural draft dry cooling system. At high wind speeds however, the back pressure doesn’t rise sharply. Instead, it remains to a certain extent. As for the cases with the windbreakers, the back pressures are dramatically reduced compared with that without windbreakers, especially at high wind speeds, showing that the energy efficiency of the power generating unit can be improved by means of the windbreaker configurations. 4. Conclusions The combined model of the thermo-flow performances of natural draft dry cooling system and the heat transfer process of
condenser is developed, by which the impacts of the interior and exterior windbreakers on the natural draft dry cooling system and power generating unit are investigated. With the windbreakers installed at the both sides of heat exchanger, inside the dry-cooling tower, and the above combined configuration, the thermo-flow performances of lateral sectors are all improved. On the contrary, the mass flow rates and heat rejections of frontal sectors decrease a little, which narrows the difference among sectors and improves the thermo-flow performances of dry cooling system. The windbreaker configurations have positive effects on the thermal efficiency of power generating unit at any wind speed, especially at high wind speeds. Generally speaking, the exterior windbreakers are superior to the interior ones in the thermo-flow performances of natural draft dry cooling system, which is recommended in the optimal design and operation of natural draft dry cooling system in power plants.
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Fig. 20. Thermo-flow performances of natural draft dry cooling system for different windbreaker configurations. (a) Total mass flow rate, (b) total heat rejection, (c) average outlet water temperature of heat exchanger, (d) turbine back pressure.
Acknowledgments 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. References [1] D.G. Kroger, Air-cooled Heat Exchangers and Cooling Towers: Thermal-flow Performance Evaluation and Design, vol. 2, PennWell Corp, Tulsa, Oklahoma, USA, 2004. [2] R. Al-Waked, M. Behnia, The performance of natural draft dry cooling towers under crosswind: CFD study, Int. J. Energy Res. 28 (2004) 147–161. [3] M. Goodarzi, A proposed stack configuration for dry cooling tower to improve cooling efficiency under crosswind, J. Wind. Eng. Ind. Aerodyn. 98 (2010) 858– 863. [4] M. Goodarzi, Proposing a new technique to enhance thermal performance and reduce structural design wind loads for natural drought cooling tower, Energy 62 (2013) 164–172. [5] M. Goodarzi, R. Keimanesh, Heat rejection enhancement in natural draft cooling tower using radiator-type windbreakers, Energy Convers. Manage. 71 (2013) 120–125.
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