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Thermo-flow performances of air-cooled condenser cell with oblique finned tube bundles
International Journal of Thermal Sciences 135 (2019) 478–492
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Thermo-flow performances of air-cooled condenser cell with oblique finned tube bundles
T
Ruonan Jin, Xiaoru Yang, Lijun Yang∗, Xiaoze Du, Yongping Yang Key Laboratory of Condition Monitoring and Control for Power Plant Equipment of Ministry of Education, School of Energy Power and Mechanical Engineering, North China Electric Power University, Beijing, 102206, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Air-cooled condenser cell Axial flow fan Oblique finned tube bundles Inclined angle Thermo-flow performances
The A-frame configuration of finned tube bundles and complex aerodynamics of axial flow fan result in the increased pressure loss of cooling air and unfavorable thermo-flow performances of air-cooled condenser cell. In this work, an air-cooled condenser cell with oblique finned tube bundles is proposed to weaken the adverse effects due to the geometric flaws of conventional condenser cell. By means of CFD simulation and experimental validation, the pressure drop and heat transfer for the oblique finned tube bundles with the inclined angles of 0°, 15°, 30°, 45° and 60° are obtained. Using a lumped parameter radiator approach, the air-cooled condenser cell model is developed, by which the velocity and temperature fields as well as the total mass flow rate and heat transfer rate are computed and compared. The results show that the thermo-flow performances of the proposed condenser cell are greatly improved at the lower regions, especially for the inclined angle of 45° with the mass flow and heat transfer growth rates reaching up to 12.81% and 8.96% respectively, so the angle of 45° is preferred in the practical application of oblique finned tube bundles to air-cooled condenser.
1. Introduction Direct dry cooling system has been increasingly applied to power or chemical plants in arid regions thanks to its significant water-saving capability [1], for which ambient air is used as a cooling medium to directly take away the heat released from the exhaust steam in aircooled condenser (ACC). Air-cooled condenser consists of many condenser cells, and each condenser cell comprises two intersecting finned tube bundles in the form of A-frame with an axial flow fan below. Owing to the different direction from the fan shaft of rectangular fin channels, the air leaving the fan must change its direction to pass through the finned tube bundles, which inevitably results in the increased pressure loss and reduced flow rate of cooling air. Wavy finned flat tube bundles are commonly used in air-cooled condenser for the excellent cooling, anti-freezing and maintenance performances. Wen and Ho [2] studied the finned tube bundles with plate, wave and compounded fins, recommended the compounded fin by comparing the Colburn and friction factors. Duan et al. [3] investigated the effects of geometric parameters and intermittent tube on the wavy finned flat tube performance, pointing out that the longitudinal vortices enhance, while the transversal ones weaken the heat transfer. Tian et al. [4] numerically studied the heat transfer enhancement by the delta winglets in staggered and in-line arrangements. ∗
Mahmud et al. [5] investigated the effect of surface waviness, finding that the heat transfer and pressure drop increase with increasing waviness. Xiao el al [6]. experimentally studied the heat transfer enhancement of wavy finned flat tubes by water spray cooling, and obtained the flow and heat transfer correlations at various inlet air velocities. Kong et al. [7] analyzed the impacts of geometric structures on the thermo-flow performances of plate fin-tube bundles. Yang et al. [8] proposed a new type of wave-finned flat tube bundles to prevent the dust from gathering on the fins and analyzed the thermo-flow performances. The aforementioned studies show that many attentions were paid to the fin surface to enhance the heat transfer of wavy finned flat tube bundles. Besides, other geometric parameters and wind effects were also investigated for air-cooled condenser. Meyer and Kroger [9] numerically investigated the effect of axial flow fan on the plenum chamber aerodynamic behavior, finding that the setting angle and flow rate of fan both take effect. Hotchkiss et al. [10] investigated the effect of offaxis inflow on the axial flow fan performance by using the actuator disk fan model. Duvenhage and Kroger [11] studied the wind influences on the fan performance and recirculation in a direct dry cooling system, finding that the cross winds significantly reduce the air flow rate in the upwind fans and cause increased hot plume circulation of side condenser cells along the longitudinal axis. Yang et al. [12] reported that
Corresponding author. E-mail address: [email protected] (L. Yang).
https://doi.org/10.1016/j.ijthermalsci.2018.09.036 Received 2 March 2018; Received in revised form 29 September 2018; Accepted 29 September 2018 1290-0729/ © 2018 Elsevier Masson SAS. All rights reserved.
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Nomenclature a A b h h’ hn H I k kL l L Lj m M
M˙ N p P q q˙ qf Q
r rn S Sφ′ t v vj xj
base tube short axis (mm) heat transfer area (m2) base tube long axis (mm) convection heat transfer coefficient (W m−2 K−1) empirical convective heat transfer coefficient (W m−2 K−1) polynomial factor for convection heat transfer coefficient fin height (mm) turbulence intensity turbulent kinetic energy (m2 s−2) pressure loss coefficient hydraulic diameter fin length (mm) thickness of finned tube bundles in three dimensions mass flow rate (kg s−1) mass flow rate per unit fan power consumption (kg s−1 W−1) mass flow growth rate (%) number pressure (Pa) fin pitch (mm) heat transfer per unit fan power consumption heat transfer growth rate (%) heat flux (W m−2) heat transfer rate (W)
rotational speed of axial flow fan (r min−1) polynomial factor for pressure loss coefficient source term additional source term temperature (K) face velocity (m s−1) component of velocity (m s−1) Cartesian coordinate (m)
Greek symbols α δ ε μ μt ρ Г φ
inclined angle of fin surface (°) fin thickness (mm) turbulence dissipation rate (m2 s−3) dynamic viscosity (kg m−1 s−1) turbulent viscosity (kg m−1 s−1) density (kg m−3) diffusion coefficient (kg m−1 s−1) scalar variable
Subscripts a avg b o
air average wavy finned flat tube bundles outlet
wavy finned flat tube bundles, which leads to a turning air flow and increased pressure loss. In this work, a novel configuration of wavy finned flat tube bundles with the direction of fin channel changing, that is oblique finned tube bundles, is studied. Based on the thermo-flow performances of finned tube bundles and complicated aerodynamics of axial flow fan, the air-cooled condenser cell with oblique finned tube bundles is investigated, which can contribute to the optimal design of ACC in practical engineering.
the reverse flow in the upwind condenser cells and hot plume recirculation result in the deteriorated performance of air-cooled condenser. So far, various measures against unfavorable effects on direct dry cooling system have been proposed. Meyer [13] suggested to install a walkway at the fan platform edge or remove the periphery fan inlet section to enhance the cooling performance of ACC at ambient winds. Wang et al. [14] proposed a side board below or above the platform to avoid the plume recirculation. Yang et al. [15,16] and Huang et al. [17] proposed wind flow guiding, periphery fans regulation and wind-break wall to weaken the unfavorable wind effects. Owen and Kroger [18] studied the cross-type porous wind screens below the fan platform, concluding that the overall performance is improved even though the fans downstream are badly affected. Yang et al. [19] suggested a trapezoidal array of air-cooled condenser to restrain the adverse wind impacts, finding that the reverse flows in the upwind condenser cells are avoided and the hot plume recirculation gets weak. Zhang et al. [20] proposed a V-frame air-cooled condenser cell with the axial flow fan installed below the intersection of two finned tube bundles rather than the centroid of cell chamber. Chen et al. [21] studied a novel layout of air-cooled condenser with V-frame cells and induced axial flow fans, so as to restrain the flow distortions through the induced fans and reduce the inlet air temperature. Chen et al. [22] also proposed a vertical arrangement of air-cooled condenser to weaken the adverse wind effects and utilize the wind power, thus improve the cooling capacity. Kong et al. [23] put forward a novel circularly arranged aircooled condenser to restrain adverse wind effects. From the aforementioned works, it can be found that the related studies with finned tube bundles are mainly concentrating on the geometric structures, but not connected with the air-cooled condenser performance. While for the improvement of thermo-flow performances of air-cooled condenser, the emphases are basically placed on additional structures such as the walkway, air flow guiding and windbreak wall, the effects of finned tube bundles are seldom considered. As is well known, the fan shaft and the fin channels are not aligning due to the A-frame configuration of condenser cell and special structure of
2. Modeling and methods 2.1. Physical model and grid generation The conventional air-cooled condenser cell is schematically shown in Fig. 1(a) and (b), with the wavy finned flat tube bundles basically applied and an intersection angle of 59.4° formed between the two finned tube bundles. The tube is made of steel while the fin is aluminum. What's more, the fin surface is arranged parallel to the long axis of the flat tube. The complex aerodynamics of axial flow fan and the Aframe configuration of wavy finned flat tube bundles lead to the air flow turning about 60° before entering the heat exchanger regions. To get better flow and heat transfer performances of condenser cell, a novel oblique wavy finned flat tube is proposed as shown in Fig. 1(c) so that the cooling air can flow easily across the finned tube bundles. For the oblique wavy finned flat tube bundles, the size and structure are totally same as the conventional one as shown in Figs. 1(b) and Fig. 2(a) except the fin surface with the inclined angle of α, which is defined as the angle between the fin surface and long axis of the base tube as shown in Fig. 2(b). When the inclined angle is zero, the oblique wavy finned flat tube bundles become the conventional ones. In this work, the inclined angles of 15°, 30°, 45° and 60° are investigated, relative to the fan shaft of about 45°, 30°, 15° and 0° respectively. The geometric parameters of finned tube bundles are listed in Table 1. In Fig. 2, the computational domains for the conventional and proposed oblique finned tube bundles are shown respectively. For the oblique finned tube bundles, as the inclined angle increases, the total 479
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fin length also increases while the vertical distance between two adjacent fins and the tube length remain the same. Because the tube length is about 10 m and far longer than the fin length, the end effect of fin can be neglected, and the total heat transfer surface areas are nearly same for these two types of finned tube bundles. Considering the symmetric and periodic structure, only half of the finned tube bundles between adjacent fins is investigated, with the entire computational domain dotted by lines as shown in Fig. 2(a) and (b). For a better demonstration, Fig. 2(c) presents the computational domain for the traditional finned tube bundles in the three-dimensional form as a typical example. The extended 1500 mm zones are both configured at the inlet and outlet of the computational domain to eliminate the effects of unrealistic domain boundaries on the air flow fields. The geometric model of finned tube bundles is meshed using the software Gambit. Due to the high velocity and temperature gradients near the tube wall and fin surface, the boundary layer mesh is adopted to realize the reliable and accurate simulations, with the first row set 0.04 mm and growth factor set 1.2. The row of boundary layer mesh is set 8 and the total depth is about 0.66 mm. The grid independence [24] is tested by evaluating the heat flux of finned tube bundles at the air velocity of 0.5 m/s, 2 m/s and 4 m/s. For the conventional ones, three different grid numbers of 2816521, 963321 and 408470 are selected with mesh A, B and C named respectively. The grid interval sizes of the finned tube area are 0.1 mm, 0.2 mm and 0.5 mm and the hexahedral structured meshes are used in these three types of mesh systems. From the results listed in Table 2, it can be observed that the relative error of computed heat flux between mesh A and B is small enough, so the grid number of 963321 is finally accepted. With the same way, the grid systems with the numbers of 975139, 1014812, 1107974 and 1295712 are finally adopted for the proposed oblique finned tube bundles at the inclined angles of 15°, 30°, 45°, and 60°. The cooling performance of each condenser cell in the system is almost the same and only one condenser cell is studied. For the condenser cell modeling, the A-frame chamber size is far bigger than the fin pitch, so the fin channels cannot be considered. In this work, the zones of finned tube bundles in the condenser cell are simplified as cuboids as shown in Fig. 1 and dealt with the radiator model. The blades of axial flow fan are developed according to the real geometric parameters provided by the manufacture, as listed in Table 3. To guarantee the condenser cell simulation more reliable, some auxiliary parts such as the motor are also taken into account. The studied condenser cell is located inside the direct dry cooling system, and mainly affected by the adjacent condenser cells rather than the unrealistic domain boundaries, so a cuboid-shaped computational domain is developed as presented in Fig. 3. The domain is divided into the condenser cell core block and other blocks to easily generate the high-quality meshes. For the core block, the hexahedral structured grids are applied to the finned tube bundles area and tetrahedral unstructured grids are produced in the A-frame plume chamber. The effects of the unrealistic domain boundaries on the air flow fields at the outlet of condenser cell cannot be neglected, so the extended 100 m along the y axis is set at the outlet block of the computational domain, with the hexahedral structured grids adopted. Using the same method as the aforementioned grid independence test, a mesh system with 3848862 grids is finally taken for the condenser cell simulation. 2.2. Mathematical models and approaches The multi-scale characteristics of air-cooled condenser cell result in the simulation difficulties for its thermo-flow performances. In this work, the flow and heat transfer performances of finned tube bundles with various fin inclined angles are obtained at first by means of numerical simulation. For the condenser cell, the finned tube bundles are simplified as porous media with the shape of cuboids. At the downward surface of the cuboid porous media, the radiator model is employed, so that the pressure drop and heat transfer rate of finned tube bundles can
Fig. 1. Geometric schematics of air-cooled condenser cell with two types of finned tube bundles. (a) Conventional air-cooled condenser cell, (b) air-cooled condenser cell with conventional finned tube bundles, (c) air-cooled condenser cell with proposed finned tube bundles.
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Fig. 2. Detailed geometric parameters, computational domain and boundary conditions of finned tube bundles. (a) Conventional, (b) proposed, (c) conventional in 3D form.
be provided.
∂ρvj φ ∂x j
=
∂ ⎛ ∂φ ⎞ ⎜Γφ ⎟ + Sφ (j = 1,2,3) ∂x j ⎝ ∂x j ⎠
(1)
where ρ is the density, vj is the velocity in the xj direction, φ, Γφ and Sφ represent the physical variable, diffusivity and source term respectively, as listed in Table 4. The low Reynolds number k-ε model [25] is adopted considering the low turbulence intensity effect on the air flow across the finned tube bundles. The corresponding parameters in the
2.2.1. Finned tube bundles For the finned tube bundles, the conservation equations of air-side flow and heat transfer take the following form
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conditions because of great amount of fins in the direction of tube length. The other two boundaries are set symmetric. The turbulent kinetic energy k at the inlet takes the following form
Table 1 Geometric parameters of wavy finned flat tube bundles. Characteristic parameter
Value
Base tube major axis (b/mm) Base tube short axis (a/mm) Fin thickness (δ/mm) Fin height (H/mm) Fin length (L/mm) Fin pitch (P/mm)
219 19 0.25 19 200 2.3
k=
3 (vavg I )2 2
where vavg is the average flow velocity. The turbulence intensity I is set to be 6% in this study. The ε at the inlet can be estimated as follows 3
ε = cμ4
Table 2 Heat flux relative errors between different mesh systems at various air velocities for grid independence test. Velocity
Mesh A and B
Mesh B and C
0.5 m/s 2 m/s 4 m/s
2.74% 3.23% 4.05%
0.12% 0.20% 0.31%
Value
Diameter of fan (mm) Number of fan blade Rotational speed of fan (r/min) Installation angle of fan blade (°)
9144 6 80 18.5
3
k2 0.07l
(3)
where the hydraulic diameter l is set 7.51 mm. The governing equations with boundary conditions are solved by the commercial software Fluent. The equations for the continuity, momentum, energy, turbulence kinetic energy and its dissipation rate are discretized using the second-order upwind scheme, and the SIMPLE algorithm is used to the velocity and pressure coupling. A divergencefree criterion of 10−6 based on the scaled residual is defined for the continuity, momentum, k and ε equations, while 10−8 for the energy equation. By means of numerical simulation, the pressure drop and heat transfer of finned tube bundles with various inclined angles can be obtained, which are used as the data sources of radiator model. The air flow directions differ from each other for the finned tube bundles with various inclined angles, so a cuboid-shaped porous zone is defined coupled with the radiator model to precisely control different air flow directions. In the radiator model, both the pressure loss and heat transfer coefficient are simplified as the function of face velocity. For the pressure drop Δpb,
Table 3 Detailed geometric parameters of axial flow fan. Characteristic parameter
(2)
1 Δpb = kL ρv 2 2
(4)
where v is the face velocity of finned tube bundles. kL is the non-dimensional pressure loss coefficient, and specified as a polynomial function, N
kL =
∑ rn v n−1 n=1
(5)
where the term number N is set to be 7 in this study for the excellent accuracy compared with other forms. rn is the polynomial factor of pressure loss coefficient. The heat transfer rate Qb of finned tube bundles is basically expressed as
Qb = hA (twall − ta)
(6)
where twall is the tube outer wall temperature, ta is the air mean temperature. A is the area of heat transfer surface, h is the convective heat transfer coefficient. In the radiator model, the heat transfer rate is specifically dealt with the following form
Fig. 3. Computational domain and boundary conditions of air-cooled condenser cell.
transport equations of turbulence kinetic energy k and dissipation rate ε are shown in Table 4, with σk = 1.0 and σε = 1.3 as the turbulence Prandtl numbers for k and ε, and the constants Cμ = 0.09, C1ε = 1.44 and C2ε = 1.92, respectively. Fig. 2 shows the boundary conditions for the simulation of finned tube bundles. Because of the strong condensation heat transfer at the steam side and the high heat conduction of tube wall, the temperature of the tube outer wall is assumed to keep the constant of 323.8 K. The computational domain inlet is defined as the velocity inlet boundary with the values from 0.5 m/s to 7 m/s, and the temperature of the inlet air keeps a constant of 289.15 K. The domain outlet is set the outflow boundary due to the unchanged flow and temperature fields. The domain boundaries between fins are appointed as the periodic boundary
Qb = h′A (twall − ta, o) = h′A (ts − ta, o)
(7)
where ta,o is the air temperature at the outlet of radiator. The condensation thermal resistance and wall conduction thermal resistance are so small that twall can be regarded as the steam condensate temperature ts. h’ is the empirical convective heat transfer coefficient as follows. N
h′ =
∑ hn v n − 1 n=1
(8)
where hn is the polynomial factor of empirical convective heat transfer coefficient, N is also set to be 7 for its great accuracy. 482
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Table 4 Summary of governing equations. Equations
φ
Гφ
Continuity x-momentum
1 vi
0 μe
y-momentum
μe
vj
Sφ 0
− −
∂p ∂xi
+
∂p ∂xj
+
∂p ∂xk
+
1⎡ ∂ 3 ⎢ ∂xi
⎣
⎣
vk
μe
Energy Turbulence kinetic energy in low Re k-ε model Turbulence dissipation rate in low Re k-ε model
cpt k ε
μe/σT μe + μT/σk μe + μT/σε
0 GK − ρε
Turbulence kinetic energy in realized k-ε model Turbulence dissipation rate in realized k-ε model
k ε
μe + μT/σk μe + μT/σε
GK + Gb − ρε
∂x j
=
∂ ⎛ ∂φ ⎞ ′ (j = 1,2,3) ⎜Γφ ⎟ + Sφ + Sφ ∂x j ⎝ ∂x j ⎠
(9)
In the non-finned tube bundles zones, the additional source term Sφ′ is set zero. In the finned tube bundles zone however, the additional momentum sink term Sm’ and energy source term Se’ should be imposed on the corresponding equations.
Sm′ = −
Se′ =
(10)
(11)
where Lj is the thickness of finned tube bundles in three dimensions, Δpj and qfj are the pressure drop and heat flux in three directions respectively. φ, Γφ and Sφ are listed in Table 4. The realizable k-ε turbulence model is adopted to deal with the air turbulent flows through air-cooled condenser cell, thanks to its better prediction for the flows involving the vortices, rotation, separation, and boundary layer under strong adverse pressure gradient. Multiple reference frame (MRF) model is used to describe the aerodynamic characteristics of axial flow fan. The MRF model is a method for multiple zones, in which the individual cell zone can be assigned different rotational or translational speeds, the flow in each moving cell zone is solved using the moving reference frame equations. According to the actual operating parameters, the rated rotational speed of axial flow fan is set to be 80 r/min. As shown in Fig. 3, the air temperature at the inlet surfaces of computational domain is taken to be 289.15 K. Because of the fact that the velocity at the inlet surfaces is not known, the pressure inlet boundary is appointed. At the top exit surface, the pressure outlet boundary condition is set. The ground is regarded as the no-slip adiabatic wall. The condenser cell is a representative unit of direct dry cooling system, so the symmetry boundary conditions are set at the edge surfaces of condenser cell. The turbulent kinetic energy k at the inlet takes the same form as Eq. (2), with the turbulence intensity I set to be 10%. The ε at the inlet can be estimated as follows
1⎡ ∂ ⎛μ ∂vi ⎞ 3 ⎢ ∂xi ⎝ e ∂xk ⎠ ⎣
ε k
C1ε Gk − C2ε ρ
ρC1 Sε − ρC2
+
(μ ) ⎤⎥⎦
∂ ⎛ ∂vj ⎞ μe ∂xj ∂xj
+
∂ ∂xk
⎛μ ∂vk ⎞ ⎤−ρg e ⎝ ∂xj ⎠ ⎥ ⎦
⎜
⎟
⎝
⎠
∂v ∂ ⎛μ j ⎞ ∂xj ⎝ e ∂xk ⎠
+
∂vk e ∂x i
⎜
∂ ∂xk
⎟
∂v ⎛μe k ⎞ ⎤ ⎝ ∂xk ⎠ ⎥ ⎦
ε2 k
ε2 k + νε
ε k
+ C1ε C3ε Gb
3. Results and discussion 3.1. Finned tube bundles Fig. 5 and Fig. 6 show the variations of the pressure drop and heat flow rate of the studied finned tube regions with the inlet air velocity at various inclined angles. In Fig. 5, the total pressure drop through the finned tube bundles increases as the inclined angle goes up owing to the increased flow channel length. It can be found from Fig. 6 that when the inclined angle increases, the total heat flow rate also increases thanks to the increased heat transfer surface area. At any inclined angle, these
−1
k2 μ ε = ρcμ ⎛⎜ t ⎞⎟ μ ⎝μ⎠
+
∂ ∂xk
The wind tunnel test has been carried out to verify the modeling and numerical methods for the simulation of finned tube bundles in our previous work [7]. With the alternant staggered slotted finned tube bundles as a sample, the experimental system consists of the air loop and water loop. The water inlet temperature and flow rate are controlled to be constant. The inlet air velocity varies from 0.5 to 3.5 m/s, and the air pressures and temperatures at the inlet and outlet are respectively measured. The numerical and experimental results arrive at a good agreement with the highest deviations of the Nusselt number and friction factor as low as 5.3% and 8.3% respectively. The modeling and numerical approaches for the wavy finned flat tube bundles in this work are completely same as the aforementioned, which verifies in another way that they are reliable and accurate enough for the thermo-flow predictions of oblique finned tube bundles. Based on a 600 MW power generating unit, a performance experiment for a scaled model of ACC cell was made to validate the radiator model for conventional finned tube bundles and MRF model for fan [23]. Fig. 4 shows the experimental scheme for scaled condenser cell, with the air flow, steam condensation and vacuum system. Table 5 lists the experimental and numerical mass flow rates, inlet and outlet air temperatures and heat rejections. The average relative error of heat rejections for cases (1–10) is 7.19%, and the maximum is 10.57% for case 4, which can be accepted in practical engineering. The modeling and numerical methods for the condenser cell in this work are exactly same as those for the aforementioned numerical simulation, showing that the computational approaches are reliable for the performance predictions of the conventional and proposed condenser cells.
qfj Lj
⎟
⎠
+
2.3. Experimental validation
Δpj Lj
⎜
⎝
∂v ∂ ⎛μ j ⎞ ∂xj ⎝ e ∂xi ⎠
first-order upwind differencing scheme. The pressure and velocity fields are coupled by using SIMPLE algorithm. The divergence-free criteria of 10−4 are set for all the scaled residuals except that the criterion of the energy equation is prescribed as 10−6. The air mass flow rate across the air-cooled condenser cell is also monitored to judge whether the iteration is converged to a reasonable level.
2.2.2. Condenser cell For the condenser cell, the air-side conservation equations have the following form
∂ρvj φ
∂vi e ∂x i
1 ⎡ ∂ ⎛ ∂vi ⎞ μe ∂xj 3 ⎢ ∂xi
z-momentum
−
(μ ) +
(12)
where the empirical constant Cμ is set 0.09, μ is the air viscosity, and the turbulent viscosity ratio μt/μ is assumed to be 1.1 as a typical case. The governing equations for condenser cell are all discretized using 483
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Fig. 4. Experimental system of air-cooled condenser cell [23]. (a) Axial flow fan, finned tube bundles and condenser cell, (b) experimental scheme and measuring points. 484
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Table 5 Experimental and numerical results for the scaled model of condenser cell. case
1 2 3 4 5 6 7 8 9 10
experimental
numerical
ma (kg/s)
ta1(°C)
ta2 (°C)
Q (kW)
ma (kg/s)
ta1 (°C)
ta2 (°C)
Q (kW)
8.19 9.72 11.21 12.73 14.62 17.39 19.91 22.05 24.82 27.72
7.81 7.82 7.31 7.07 6.96 7.91 6.96 6.25 6.37 5.74
85.81 83.43 77.15 72.14 67.53 62.72 57.14 55.93 53.95 51.51
641.93 736.79 785.13 831.97 889.52 957.56 1002.77 1101.36 1187.33 1274.81
8.22 9.54 11.08 12.95 14.96 17.98 21.54 22.09 23.58 27.77
7.81 7.82 7.31 7.07 6.96 7.91 6.96 6.25 6.37 5.74
92.81 90.43 84.22 77.75 72.12 65.85 57.83 58.13 57.51 51.14
702.27 792.08 856.53 919.96 979.71 1047.05 1099.35 1152.91 1213.39 1267.19
Table 6 Polynomial factors of pressure loss coefficient at various inclined angles. inclined angle
r1
r2
r3
r4
r5
r6
r7
0° 15° 30° 45° 60°
23.384 23.945 25.807 25.426 28.037
−24.89 −22.19 −22.77 −14.55 −3.116
13.639 10.79 10.226 1.4998 −13.23
−4.136 −2.927 −2.453 1.427 8.5977
0.6935 0.4474 0.3108 −0.547 −2.232
−0.060 −0.036 −0.019 0.0742 0.2651
0.0021 0.0012 0.0004 −0.004 −0.012
Table 7 Polynomial factors of empirical convective heat transfer coefficient at various inclined angles.
Fig. 5. Pressure drop for studied finned tube regions with different inclined angles at various inlet velocities.
inclined angle
h1
h2
h3
h4
h5
h6
h7
0° 15° 30° 45° 60°
22.348 22.580 23.511 26.059 14.539
13.579 12.498 8.6448 −0.227 20.995
−5.102 −4.231 −1.114 6.064 −12.40
1.5639 1.2333 0.0352 −2.774 4.9272
−0.337 −0.273 −0.038 0.5348 −1.118
0.0412 0.0351 0.0121 −0.047 0.1291
−0.002 −0.002 −0.001 0.0015 −0.006
coefficient in Eq. (5) and polynomial factor of empirical convective heat transfer coefficient in Eq. (8) can be obtained, which are listed in Table 6 and Table 7 respectively. 3.2. Condenser cell The velocity and temperature fields at the outlet of condenser cell, the streamlines and temperature fields inside the A-frame chamber are obtained. The variations of total mass flow rate and heat rejection are also presented and analyzed at various rotational speeds of fan. Finally, two non-dimensional parameters, mass flow growth rate and heat transfer growth rate, are defined to evaluate the thermo-flow performances of condenser cell. 3.2.1. Variable fields Fig. 7 shows the velocity contours at the surfaces with 10 mm apart from the outlet surfaces of finned tube bundles, and at the fan rotational speed of 80 r/min. For the conventional layout shown in Fig. 7(a), four velocity dead zones appear at the lower parts of finned tube bundles with the velocity close to 0 m/s, which is unfavorable to the cooling performance. Due to the flow direction turning of about 60°, the local flow loss of cooling air increases. Moreover, the cooling air tends to flow upward due to the driving force from fan. As a result, less air can flow across the lower regions to participate in the heat transfer process. When the inclined angle increases to 15° and 30°, the areas of dead zones only decrease a little, but the velocity at the middle region grows. When the angle rises to 45° and 60°, the areas of dead zones get reduced
Fig. 6. Heat transfer rate for studied finned tube regions with different inclined angles at various inlet velocities.
two variables both increase as the inlet air velocity increases. Based on the pressure drop and heat transfer simulation results of the finned tube bundles, the polynomial factor of pressure loss
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Fig. 7. Velocity fields at the outlet of condenser cell with various inclined angles at rotational speed of 80 r/min. (a) 0°, (b) 15°, (c) 30°, (d) 45°, (e) 60°.
accordingly. The air temperatures at the same surfaces as Fig. 7 with five inclined angles at the rotational speed of 80 r/min are shown in Fig. 8. From the temperature distribution for the conventional condenser cell shown in
a lot and the velocity increases to a certain extent at other parts especially the central part. Though the velocity distribution is a little uneven, the total mass flow rate participating in the heat transfer increases, so the overall thermo-flow performances get improved 486
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Fig. 8. Temperature fields at the outlet of condenser cell with various inclined angles at rotational speed of 80 r/min. (a) 0°, (b) 15°, (c) 30°, (d) 45°, (e) 60°.
45° and 60°. What's more, a low temperature zone is formed at the middle area, showing a better heat transfer performance. However, a high temperature zone is presented at the central upper part with the inclined angle of 60° as shown in Fig. 8(e), and the temperature is nearly up to 316 K. Fig. 9 presents the velocity fields in the A-frame chamber at various
Fig. 8(a), it can be clearly seen that four high temperature regions are presented at the four corners of finned tube bundles with the temperature even reaching 320 K, which greatly deteriorates the air cooling capacity. As shown in Fig. 8(b)-(e) at the fin inclined angles of 15°, 30°, 45° and 60°, with the inclined angle increases, the areas of the four high temperature regions are conspicuously reduced and even disappear at 487
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Fig. 9. Velocity fields in A-frame chamber with various inclined angles at rotational speed of 80 r/min. (a) 0°, (b) 15°, (c) 30°, (d) 45°, (e) 60°.
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grows to 15° and 30° shown in Fig. 9(b) and (c), the airflow just turns smaller angles of 45° and 30°. However, the reverse flow is generated at the top of the A-frame chamber for these two cases, and the low velocity zone downsteam the fan tends to expand to the upper area. As the inclined angle increases to 45° and 60°, the air at the lower region flows
inclined angles with the rotational speed of 80 r/min. For the conventional condenser cell shown in Fig. 9(a), the cooling air flows across the finned tube bundles with a direction turning of about 60°. Two vortices are formed downsteam the fan due to the aerodynamic characteristics of axis flow fan and the A-frame finned tube bundles. When the angle
Fig. 10. Temperature fields in A-frame chamber with various inclined angles at rotational speed of 80 r/min. (a) 0°, (b) 15°, (c) 30°, (d) 45°, (e) 60°. 489
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through the finned tube bundles easily. However, the location of the two vortices becomes higher and moves to both sides from 0° to 60°, especially as the inclined angle reaches to 60°, the reverse flow gets serious and more upper zones are influenced, so the cooling performance at this part is weakened, that is why the higher temperature region is formed at the condenser cell top shown in Fig. 8(e). It can be estimated that there exists an optimal inclined angle with best thermoflow performances. Fig. 10 shows the temperature details in the A-frame chamber at 80 r/min. For the conventional condenser cell shown in Fig. 10(a), the temperature at the lower part of finned tube bundles is high which coincides with the results in Fig. 8(a). From the local enlarged details, it can be observed that the lower part of finned tube bundles along the air flow direction is in a high temperature and does not get fully cooled. The temperature at the top of condenser cell is high, because it is adjacent to the steam duct and cannot acquire sufficient airflows to be cooled. As the inclined angle increases from 15° to 60°, a reduced temperature at the lower part of finned tube bundles can be clearly observed, and the depth of the regions with high temperatures decreases especially for the angles of 45° and 60° that only a few areas at the exit of finned tube bundles have high temperatures. What's more, the highest temperature at this region decreases as well which is about 320 K at the inclined angles of 0° and 15°, but 318 K at 45° and 60°. Nevertheless, becauses of more cooling air at the lower and middle parts of finned tube bundles as well as the reverse flow at the top of Aframe chamber, the thermo-flow performances at the top region are not as good as the case of 0°, especially at the inclined angle of 60°.
where Ma,proposed is the mass flow rate per unit fan power of the proposed condenser cell with oblique finned tube bundles. Ma,conventional stands for the mass flow rate per unit fan power of the conventional layout. Similar to the mass flow growth rate, the heat transfer growth rate is the ratio of the heat transfer rate per unit fan power difference to the heat transfer rate per unit fan power for the conventional condenser cell as follows.
q˙ a =
(14)
4. Conclusions In the conventional air-cooled condenser cell, four dead velocity zones with high temperatures are formed at the lower corners of finned tube bundles, resulting in poor thermo-flow performances. For the proposed condenser cell with oblique finned tube bundles, the high
Ma, proposed − Ma, conventional Ma, conventional
qa, conventional
where qa,proposed is the heat transfer rate per unit fan power of the condenser cell with oblique finned tube bundles. qa,conventional stands for the heat transfer rate per unit fan power of the conventional layout. Fig. 13 shows the mass flow growth rate at various fan rotational speeds. It can be clearly found that the mass flow growth rate with the inclined angle of 45° is much higher than other angles, and even arrives at 12.81% at 56 r/min, showing that the 45° is the optimal angle for the oblique finned tube bundles. As the rotational speed increases, the mass flow growth rate increases at first and then decreases for the inclined angle of 45°. This non-dimensional parameter at 30° is much higher than 60° at low rotational speeds, because the reverse flow appears at the top of finned tube bundles, which weakens the thermo-flow performances more than the performance improvement at the lower part of condenser cell. The mass flow growth rate decreases as the rotational speed increases for 15°, showing the flow performance is deteriorated with increasing the rotational speed. The heat transfer growth rate is shown in Fig. 14, from which can be observed that it is the highest at the inclined angle of 45° for all the rotational speeds, and reaches up to 8.96% at 56 r/min. It takes the second place at the inclined angle of 30° and becomes higher than 60° for all the rotational speeds while the differences between them decrease as the rotational speed increases. At the inclined angle of 15°, the heat transfer growth rate increases as the rotational speed falls, which is similar to the changing trend of mass flow growth rate. It is even higher than 60° when the rotational speed reaches to 40 and 48 r/min.
3.2.2. Thermo-flow performances Fig. 11 gives the total mass flow rate of condenser cell at various fin inclined angles, with the fan operating at the rotational speeds of 80 r/ min, 72 r/min, 64 r/min, 56 r/min, 48 r/min and 40 r/min, respectively. It can be seen that the mass flow rate drops as the rotational speed decreases due to the reduced driving force. The mass flow rate arrives at the highest value at the inclined angle of 45°, showing that the thermo-flow performances of condenser cell are greatly improved, because the flow at the lower part of condenser cell is enhanced a lot while it is weakened slightly at the upper region. The 60° takes the second place and gets closer to the 30° when the rotational speed is reduced. When the rotational speed is shifting to about 48 r/min, the mass flow rate is nearly equal for these two cases and then it gets smaller than 30°. The mass flow rate of the proposed condenser cell with oblique finned tube bundles is always higher than conventional condenser cell. Fig. 12 presents the total heat transfer rate of condenser cell versus the rotational speed at various inclined angles. It can be seen that the total heat transfer rate decreases as the fan rotational speed drops, which is in keeping with the changing trend of mass flow rate. The heat transfer rate reaches the maximum at the inclined angle of 45°, and then the 30°, 60°, 15°, 0° respectively when the rotational speed increases from 48 r/min to 72 r/min. The heat transfer rate at 60° surpasses the case of 30° and takes the second place at 80 r/min. At the rotational speed of 40 r/min, the heat transfer rate at 15° transcends the 60° and ranks the third place. Similar to the mass flow rate, the inclined angle of 45° is the optimal one with the most enhanced heat transfer. To clarify the improvement of thermo-flow performances of the proposed condenser cell at different rotational speeds, two non-dimensional parameters of mass flow growth rate and heat transfer growth rate are introduced. Mass flow growth rate is the ratio of the mass flow rate per unit fan power difference between the proposed and conventional condenser cell to the mass flow rate per unit fan power for the conventional layout, with the following form
M˙ a =
qa, proposed − qa, conventional
Fig. 11. Mass flow rate of condenser cell with different inclined angles at various fan rotational speeds.
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Fig. 14. Heat transfer growth rate of condenser cell with different inclined angles at various fan rotational speeds.
Fig. 12. Heat transfer rate of condenser cell with different inclined angles at various fan rotational speeds.
gratefully acknowledged. References [1] 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. [2] M.Y. Wen, C.Y. Ho, Heat-transfer enhancement in fin-and-tube heat exchanger with improved fin design, Appl. Therm. Eng. 29 (2009) 1050–1057. [3] F. Duan, K.W. Song, H.R. Li, L.M. Chang, Y.H. Zhang, L.B. Wang, Numerical study of laminar flow and heat transfer characteristics in the fin side of the intermittent wavy finned flat tube heat exchanger, Appl. Therm. Eng. 103 (2016) 112–127. [4] L. Tian, Y. He, Y. Tao, W. Tao, A comparative study on the air-side performance of wavy fin-and-tube heat exchanger with punched delta winglets in staggered and inline arrangements, Int. J. Therm. Sci. 48 (2009) 1765–1776. [5] S. Mahmud, A.S. Islam, C. Feroz, Flow and heat transfer characteristics inside a wavy tube, Heat Mass Tran. 39 (2003) 387–393. [6] L. Xiao, T. Wu, S. Feng, X. Du, L. Yang, Experimental study on heat transfer enhancement of wavy finned flat tubes by water spray cooling, Int. J. Heat Mass Tran. 110 (2017). [7] Y.Q. Kong, L.J. Yang, X.Z. Du, Y.P. Yang, Impacts of geometric structures on thermo-flow performances of plate fin-tube bundles, Int. J. Therm. Sci. 107 (2016) 161–178. [8] L. Yang, H. Tan, X. Du, Y. Yang, Thermal-flow characteristics of the new wavefinned flat tube bundles in air-cooled condensers, Int. J. Therm. Sci. 53 (2012) 166–174. [9] C.J. Meyer, D.G. Kröger, Numerical investigation of the effect of fan performance on forced draught air-cooled heat exchanger plenum chamber aerodynamic behaviour, Appl. Therm. Eng. 24 (2004) 359–371. [10] P.J. Hotchkiss, C.J. Meyer, T.W.V. Backström, Numerical investigation into the effect of cross-flow on the performance of axial flow fans in forced draught aircooled heat exchangers, Appl. Therm. Eng. 26 (2006) 200–208. [11] K. Duvenhage, D.G. Kröger, The influence of wind on the performance of forced draught air-cooled heat exchangers, J. Wind Eng. Ind. Aerod. 62 (1996) 259–277. [12] L.J. Yang, X.Z. Du, Y.P. Yang, Wind effect on the thermo-flow performances and its decay characteristics for air-cooled condensers in a power plant, Int. J. Therm. Sci. 53 (2012) 175–187. [13] C.J. Meyer, Numerical investigation of the effect of inlet flow distortions on forced draught air-cooled heat exchanger performance, Appl. Therm. Eng. 25 (2005) 1634–1649. [14] Q.W. Wang, D.J. Zhang, M. Zeng, M. Lin, L.H. Tang, CFD simulation on a thermal power plant with air‐cooled heat exchanger system in north China, Eng. Comput. 25 (2008) 342–365. [15] L.J. Yang, X.Z. Du, Y.P. Yang, Measures against the adverse impact of natural wind on air-cooled condensers in power plant, Sci. China Technol. Sci. 53 (2010) 1320–1327. [16] L.J. Yang, X.Z. Du, Y.P. Yang, Influences of wind-break wall configurations upon flow and heat transfer characteristics of air-cooled condensers in a power plant, Int. J. Therm. Sci. 50 (2011) 2050–2061. [17] X. Huang, L. Chen, Y. Kong, L. Yang, X. Du, Effects of geometric structures of air deflectors on thermo-flow performances of air-cooled condenser, Int. J. Heat Mass Tran. 118 (2018) 1022–1039. [18] M.T.F. Owen, D.G. Kröger, The effect of screens on air-cooled steam condenser performance under windy conditions, Appl. Therm. Eng. 30 (2010) 2610–2615. [19] L.J. Yang, M.H. Wang, X.Z. Du, Y.P. Yang, Trapezoidal array of air-cooled
Fig. 13. Mass flow growth rate of condenser cell with different inclined angles at various fan rotational speeds.
temperature and velocity dead zones decrease as the inclined angle increases, and even vanish at the inclined angles of 45° and 60°. However, two vortices at both sides of A-frame chamber result in the reverse flow at the upper area, which becomes serious as the inclined angle increases. The performance gets improved for the proposed condenser cell as the rotational speed increases. The mass flow growth rate and heat transfer growth rate for the inclined angle of 45° reach to12.81% and 8.96% at the rotational speed of 56 r/min. The thermo-flow performances of condenser cell with the inclined angle of 45° are much better than other angles, so the inclined angle of 45° is preferred for the oblique finned tube bundles of air-cooled condenser. Acknowledgments The financial supports for this research, from the National Natural Science Foundation of China (Grant No. 51776067) and the National Basic Research Program of China (Grant No. 2015CB251503), are 491
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[23] Y. Kong, W. Wang, X. Huang, L. Yang, X. Du, Y. Yang, Circularly arranged aircooled condensers to restrain adverse wind effects, Appl. Therm. Eng. 124 (2017) 202–223. [24] E. Jak, P.C. Hayes, Procedure of estimation and reporting of uncertainty due to discretization in CFD applications, J. Fluid Eng. 130 (2008) 78001. [25] X. Du, L. Feng, Y. Yang, L. Yang, Experimental study on heat transfer enhancement of wavy finned flat tube with longitudinal vortex generators, Appl. Therm. Eng. 50 (2013) 55–62.
condensers to restrain the adverse impacts of ambient winds in a power plant, Appl. Energy 99 (2012) 402–413. [20] Z. Zhang, J. Yang, Y. Wang, A favorable face velocity distribution and a V-frame cell for power plant air-cooled condensers, Appl. Therm. Eng. 87 (2015) 1–9. [21] L. Chen, L. Yang, X. Du, Y. Yang, Novel air-cooled condenser with V-frame cells and induced axial flow fans, Int. J. Heat Mass Tran. 117 (2018) 167–182. [22] L. Chen, L. Yang, X. Du, Y. Yang, A novel layout of air-cooled condensers to improve thermo-flow performances, Appl. Energy 165 (2016) 244–259.
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International Journal of Thermal Sciences journal homepage: www.elsevier.com/locate/ijts
Thermo-flow performances of air-cooled condenser cell with oblique finned tube bundles
T
Ruonan Jin, Xiaoru Yang, Lijun Yang∗, Xiaoze Du, Yongping Yang Key Laboratory of Condition Monitoring and Control for Power Plant Equipment of Ministry of Education, School of Energy Power and Mechanical Engineering, North China Electric Power University, Beijing, 102206, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Air-cooled condenser cell Axial flow fan Oblique finned tube bundles Inclined angle Thermo-flow performances
The A-frame configuration of finned tube bundles and complex aerodynamics of axial flow fan result in the increased pressure loss of cooling air and unfavorable thermo-flow performances of air-cooled condenser cell. In this work, an air-cooled condenser cell with oblique finned tube bundles is proposed to weaken the adverse effects due to the geometric flaws of conventional condenser cell. By means of CFD simulation and experimental validation, the pressure drop and heat transfer for the oblique finned tube bundles with the inclined angles of 0°, 15°, 30°, 45° and 60° are obtained. Using a lumped parameter radiator approach, the air-cooled condenser cell model is developed, by which the velocity and temperature fields as well as the total mass flow rate and heat transfer rate are computed and compared. The results show that the thermo-flow performances of the proposed condenser cell are greatly improved at the lower regions, especially for the inclined angle of 45° with the mass flow and heat transfer growth rates reaching up to 12.81% and 8.96% respectively, so the angle of 45° is preferred in the practical application of oblique finned tube bundles to air-cooled condenser.
1. Introduction Direct dry cooling system has been increasingly applied to power or chemical plants in arid regions thanks to its significant water-saving capability [1], for which ambient air is used as a cooling medium to directly take away the heat released from the exhaust steam in aircooled condenser (ACC). Air-cooled condenser consists of many condenser cells, and each condenser cell comprises two intersecting finned tube bundles in the form of A-frame with an axial flow fan below. Owing to the different direction from the fan shaft of rectangular fin channels, the air leaving the fan must change its direction to pass through the finned tube bundles, which inevitably results in the increased pressure loss and reduced flow rate of cooling air. Wavy finned flat tube bundles are commonly used in air-cooled condenser for the excellent cooling, anti-freezing and maintenance performances. Wen and Ho [2] studied the finned tube bundles with plate, wave and compounded fins, recommended the compounded fin by comparing the Colburn and friction factors. Duan et al. [3] investigated the effects of geometric parameters and intermittent tube on the wavy finned flat tube performance, pointing out that the longitudinal vortices enhance, while the transversal ones weaken the heat transfer. Tian et al. [4] numerically studied the heat transfer enhancement by the delta winglets in staggered and in-line arrangements. ∗
Mahmud et al. [5] investigated the effect of surface waviness, finding that the heat transfer and pressure drop increase with increasing waviness. Xiao el al [6]. experimentally studied the heat transfer enhancement of wavy finned flat tubes by water spray cooling, and obtained the flow and heat transfer correlations at various inlet air velocities. Kong et al. [7] analyzed the impacts of geometric structures on the thermo-flow performances of plate fin-tube bundles. Yang et al. [8] proposed a new type of wave-finned flat tube bundles to prevent the dust from gathering on the fins and analyzed the thermo-flow performances. The aforementioned studies show that many attentions were paid to the fin surface to enhance the heat transfer of wavy finned flat tube bundles. Besides, other geometric parameters and wind effects were also investigated for air-cooled condenser. Meyer and Kroger [9] numerically investigated the effect of axial flow fan on the plenum chamber aerodynamic behavior, finding that the setting angle and flow rate of fan both take effect. Hotchkiss et al. [10] investigated the effect of offaxis inflow on the axial flow fan performance by using the actuator disk fan model. Duvenhage and Kroger [11] studied the wind influences on the fan performance and recirculation in a direct dry cooling system, finding that the cross winds significantly reduce the air flow rate in the upwind fans and cause increased hot plume circulation of side condenser cells along the longitudinal axis. Yang et al. [12] reported that
Corresponding author. E-mail address: [email protected] (L. Yang).
https://doi.org/10.1016/j.ijthermalsci.2018.09.036 Received 2 March 2018; Received in revised form 29 September 2018; Accepted 29 September 2018 1290-0729/ © 2018 Elsevier Masson SAS. All rights reserved.
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Nomenclature a A b h h’ hn H I k kL l L Lj m M
M˙ N p P q q˙ qf Q
r rn S Sφ′ t v vj xj
base tube short axis (mm) heat transfer area (m2) base tube long axis (mm) convection heat transfer coefficient (W m−2 K−1) empirical convective heat transfer coefficient (W m−2 K−1) polynomial factor for convection heat transfer coefficient fin height (mm) turbulence intensity turbulent kinetic energy (m2 s−2) pressure loss coefficient hydraulic diameter fin length (mm) thickness of finned tube bundles in three dimensions mass flow rate (kg s−1) mass flow rate per unit fan power consumption (kg s−1 W−1) mass flow growth rate (%) number pressure (Pa) fin pitch (mm) heat transfer per unit fan power consumption heat transfer growth rate (%) heat flux (W m−2) heat transfer rate (W)
rotational speed of axial flow fan (r min−1) polynomial factor for pressure loss coefficient source term additional source term temperature (K) face velocity (m s−1) component of velocity (m s−1) Cartesian coordinate (m)
Greek symbols α δ ε μ μt ρ Г φ
inclined angle of fin surface (°) fin thickness (mm) turbulence dissipation rate (m2 s−3) dynamic viscosity (kg m−1 s−1) turbulent viscosity (kg m−1 s−1) density (kg m−3) diffusion coefficient (kg m−1 s−1) scalar variable
Subscripts a avg b o
air average wavy finned flat tube bundles outlet
wavy finned flat tube bundles, which leads to a turning air flow and increased pressure loss. In this work, a novel configuration of wavy finned flat tube bundles with the direction of fin channel changing, that is oblique finned tube bundles, is studied. Based on the thermo-flow performances of finned tube bundles and complicated aerodynamics of axial flow fan, the air-cooled condenser cell with oblique finned tube bundles is investigated, which can contribute to the optimal design of ACC in practical engineering.
the reverse flow in the upwind condenser cells and hot plume recirculation result in the deteriorated performance of air-cooled condenser. So far, various measures against unfavorable effects on direct dry cooling system have been proposed. Meyer [13] suggested to install a walkway at the fan platform edge or remove the periphery fan inlet section to enhance the cooling performance of ACC at ambient winds. Wang et al. [14] proposed a side board below or above the platform to avoid the plume recirculation. Yang et al. [15,16] and Huang et al. [17] proposed wind flow guiding, periphery fans regulation and wind-break wall to weaken the unfavorable wind effects. Owen and Kroger [18] studied the cross-type porous wind screens below the fan platform, concluding that the overall performance is improved even though the fans downstream are badly affected. Yang et al. [19] suggested a trapezoidal array of air-cooled condenser to restrain the adverse wind impacts, finding that the reverse flows in the upwind condenser cells are avoided and the hot plume recirculation gets weak. Zhang et al. [20] proposed a V-frame air-cooled condenser cell with the axial flow fan installed below the intersection of two finned tube bundles rather than the centroid of cell chamber. Chen et al. [21] studied a novel layout of air-cooled condenser with V-frame cells and induced axial flow fans, so as to restrain the flow distortions through the induced fans and reduce the inlet air temperature. Chen et al. [22] also proposed a vertical arrangement of air-cooled condenser to weaken the adverse wind effects and utilize the wind power, thus improve the cooling capacity. Kong et al. [23] put forward a novel circularly arranged aircooled condenser to restrain adverse wind effects. From the aforementioned works, it can be found that the related studies with finned tube bundles are mainly concentrating on the geometric structures, but not connected with the air-cooled condenser performance. While for the improvement of thermo-flow performances of air-cooled condenser, the emphases are basically placed on additional structures such as the walkway, air flow guiding and windbreak wall, the effects of finned tube bundles are seldom considered. As is well known, the fan shaft and the fin channels are not aligning due to the A-frame configuration of condenser cell and special structure of
2. Modeling and methods 2.1. Physical model and grid generation The conventional air-cooled condenser cell is schematically shown in Fig. 1(a) and (b), with the wavy finned flat tube bundles basically applied and an intersection angle of 59.4° formed between the two finned tube bundles. The tube is made of steel while the fin is aluminum. What's more, the fin surface is arranged parallel to the long axis of the flat tube. The complex aerodynamics of axial flow fan and the Aframe configuration of wavy finned flat tube bundles lead to the air flow turning about 60° before entering the heat exchanger regions. To get better flow and heat transfer performances of condenser cell, a novel oblique wavy finned flat tube is proposed as shown in Fig. 1(c) so that the cooling air can flow easily across the finned tube bundles. For the oblique wavy finned flat tube bundles, the size and structure are totally same as the conventional one as shown in Figs. 1(b) and Fig. 2(a) except the fin surface with the inclined angle of α, which is defined as the angle between the fin surface and long axis of the base tube as shown in Fig. 2(b). When the inclined angle is zero, the oblique wavy finned flat tube bundles become the conventional ones. In this work, the inclined angles of 15°, 30°, 45° and 60° are investigated, relative to the fan shaft of about 45°, 30°, 15° and 0° respectively. The geometric parameters of finned tube bundles are listed in Table 1. In Fig. 2, the computational domains for the conventional and proposed oblique finned tube bundles are shown respectively. For the oblique finned tube bundles, as the inclined angle increases, the total 479
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fin length also increases while the vertical distance between two adjacent fins and the tube length remain the same. Because the tube length is about 10 m and far longer than the fin length, the end effect of fin can be neglected, and the total heat transfer surface areas are nearly same for these two types of finned tube bundles. Considering the symmetric and periodic structure, only half of the finned tube bundles between adjacent fins is investigated, with the entire computational domain dotted by lines as shown in Fig. 2(a) and (b). For a better demonstration, Fig. 2(c) presents the computational domain for the traditional finned tube bundles in the three-dimensional form as a typical example. The extended 1500 mm zones are both configured at the inlet and outlet of the computational domain to eliminate the effects of unrealistic domain boundaries on the air flow fields. The geometric model of finned tube bundles is meshed using the software Gambit. Due to the high velocity and temperature gradients near the tube wall and fin surface, the boundary layer mesh is adopted to realize the reliable and accurate simulations, with the first row set 0.04 mm and growth factor set 1.2. The row of boundary layer mesh is set 8 and the total depth is about 0.66 mm. The grid independence [24] is tested by evaluating the heat flux of finned tube bundles at the air velocity of 0.5 m/s, 2 m/s and 4 m/s. For the conventional ones, three different grid numbers of 2816521, 963321 and 408470 are selected with mesh A, B and C named respectively. The grid interval sizes of the finned tube area are 0.1 mm, 0.2 mm and 0.5 mm and the hexahedral structured meshes are used in these three types of mesh systems. From the results listed in Table 2, it can be observed that the relative error of computed heat flux between mesh A and B is small enough, so the grid number of 963321 is finally accepted. With the same way, the grid systems with the numbers of 975139, 1014812, 1107974 and 1295712 are finally adopted for the proposed oblique finned tube bundles at the inclined angles of 15°, 30°, 45°, and 60°. The cooling performance of each condenser cell in the system is almost the same and only one condenser cell is studied. For the condenser cell modeling, the A-frame chamber size is far bigger than the fin pitch, so the fin channels cannot be considered. In this work, the zones of finned tube bundles in the condenser cell are simplified as cuboids as shown in Fig. 1 and dealt with the radiator model. The blades of axial flow fan are developed according to the real geometric parameters provided by the manufacture, as listed in Table 3. To guarantee the condenser cell simulation more reliable, some auxiliary parts such as the motor are also taken into account. The studied condenser cell is located inside the direct dry cooling system, and mainly affected by the adjacent condenser cells rather than the unrealistic domain boundaries, so a cuboid-shaped computational domain is developed as presented in Fig. 3. The domain is divided into the condenser cell core block and other blocks to easily generate the high-quality meshes. For the core block, the hexahedral structured grids are applied to the finned tube bundles area and tetrahedral unstructured grids are produced in the A-frame plume chamber. The effects of the unrealistic domain boundaries on the air flow fields at the outlet of condenser cell cannot be neglected, so the extended 100 m along the y axis is set at the outlet block of the computational domain, with the hexahedral structured grids adopted. Using the same method as the aforementioned grid independence test, a mesh system with 3848862 grids is finally taken for the condenser cell simulation. 2.2. Mathematical models and approaches The multi-scale characteristics of air-cooled condenser cell result in the simulation difficulties for its thermo-flow performances. In this work, the flow and heat transfer performances of finned tube bundles with various fin inclined angles are obtained at first by means of numerical simulation. For the condenser cell, the finned tube bundles are simplified as porous media with the shape of cuboids. At the downward surface of the cuboid porous media, the radiator model is employed, so that the pressure drop and heat transfer rate of finned tube bundles can
Fig. 1. Geometric schematics of air-cooled condenser cell with two types of finned tube bundles. (a) Conventional air-cooled condenser cell, (b) air-cooled condenser cell with conventional finned tube bundles, (c) air-cooled condenser cell with proposed finned tube bundles.
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Fig. 2. Detailed geometric parameters, computational domain and boundary conditions of finned tube bundles. (a) Conventional, (b) proposed, (c) conventional in 3D form.
be provided.
∂ρvj φ ∂x j
=
∂ ⎛ ∂φ ⎞ ⎜Γφ ⎟ + Sφ (j = 1,2,3) ∂x j ⎝ ∂x j ⎠
(1)
where ρ is the density, vj is the velocity in the xj direction, φ, Γφ and Sφ represent the physical variable, diffusivity and source term respectively, as listed in Table 4. The low Reynolds number k-ε model [25] is adopted considering the low turbulence intensity effect on the air flow across the finned tube bundles. The corresponding parameters in the
2.2.1. Finned tube bundles For the finned tube bundles, the conservation equations of air-side flow and heat transfer take the following form
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conditions because of great amount of fins in the direction of tube length. The other two boundaries are set symmetric. The turbulent kinetic energy k at the inlet takes the following form
Table 1 Geometric parameters of wavy finned flat tube bundles. Characteristic parameter
Value
Base tube major axis (b/mm) Base tube short axis (a/mm) Fin thickness (δ/mm) Fin height (H/mm) Fin length (L/mm) Fin pitch (P/mm)
219 19 0.25 19 200 2.3
k=
3 (vavg I )2 2
where vavg is the average flow velocity. The turbulence intensity I is set to be 6% in this study. The ε at the inlet can be estimated as follows 3
ε = cμ4
Table 2 Heat flux relative errors between different mesh systems at various air velocities for grid independence test. Velocity
Mesh A and B
Mesh B and C
0.5 m/s 2 m/s 4 m/s
2.74% 3.23% 4.05%
0.12% 0.20% 0.31%
Value
Diameter of fan (mm) Number of fan blade Rotational speed of fan (r/min) Installation angle of fan blade (°)
9144 6 80 18.5
3
k2 0.07l
(3)
where the hydraulic diameter l is set 7.51 mm. The governing equations with boundary conditions are solved by the commercial software Fluent. The equations for the continuity, momentum, energy, turbulence kinetic energy and its dissipation rate are discretized using the second-order upwind scheme, and the SIMPLE algorithm is used to the velocity and pressure coupling. A divergencefree criterion of 10−6 based on the scaled residual is defined for the continuity, momentum, k and ε equations, while 10−8 for the energy equation. By means of numerical simulation, the pressure drop and heat transfer of finned tube bundles with various inclined angles can be obtained, which are used as the data sources of radiator model. The air flow directions differ from each other for the finned tube bundles with various inclined angles, so a cuboid-shaped porous zone is defined coupled with the radiator model to precisely control different air flow directions. In the radiator model, both the pressure loss and heat transfer coefficient are simplified as the function of face velocity. For the pressure drop Δpb,
Table 3 Detailed geometric parameters of axial flow fan. Characteristic parameter
(2)
1 Δpb = kL ρv 2 2
(4)
where v is the face velocity of finned tube bundles. kL is the non-dimensional pressure loss coefficient, and specified as a polynomial function, N
kL =
∑ rn v n−1 n=1
(5)
where the term number N is set to be 7 in this study for the excellent accuracy compared with other forms. rn is the polynomial factor of pressure loss coefficient. The heat transfer rate Qb of finned tube bundles is basically expressed as
Qb = hA (twall − ta)
(6)
where twall is the tube outer wall temperature, ta is the air mean temperature. A is the area of heat transfer surface, h is the convective heat transfer coefficient. In the radiator model, the heat transfer rate is specifically dealt with the following form
Fig. 3. Computational domain and boundary conditions of air-cooled condenser cell.
transport equations of turbulence kinetic energy k and dissipation rate ε are shown in Table 4, with σk = 1.0 and σε = 1.3 as the turbulence Prandtl numbers for k and ε, and the constants Cμ = 0.09, C1ε = 1.44 and C2ε = 1.92, respectively. Fig. 2 shows the boundary conditions for the simulation of finned tube bundles. Because of the strong condensation heat transfer at the steam side and the high heat conduction of tube wall, the temperature of the tube outer wall is assumed to keep the constant of 323.8 K. The computational domain inlet is defined as the velocity inlet boundary with the values from 0.5 m/s to 7 m/s, and the temperature of the inlet air keeps a constant of 289.15 K. The domain outlet is set the outflow boundary due to the unchanged flow and temperature fields. The domain boundaries between fins are appointed as the periodic boundary
Qb = h′A (twall − ta, o) = h′A (ts − ta, o)
(7)
where ta,o is the air temperature at the outlet of radiator. The condensation thermal resistance and wall conduction thermal resistance are so small that twall can be regarded as the steam condensate temperature ts. h’ is the empirical convective heat transfer coefficient as follows. N
h′ =
∑ hn v n − 1 n=1
(8)
where hn is the polynomial factor of empirical convective heat transfer coefficient, N is also set to be 7 for its great accuracy. 482
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Table 4 Summary of governing equations. Equations
φ
Гφ
Continuity x-momentum
1 vi
0 μe
y-momentum
μe
vj
Sφ 0
− −
∂p ∂xi
+
∂p ∂xj
+
∂p ∂xk
+
1⎡ ∂ 3 ⎢ ∂xi
⎣
⎣
vk
μe
Energy Turbulence kinetic energy in low Re k-ε model Turbulence dissipation rate in low Re k-ε model
cpt k ε
μe/σT μe + μT/σk μe + μT/σε
0 GK − ρε
Turbulence kinetic energy in realized k-ε model Turbulence dissipation rate in realized k-ε model
k ε
μe + μT/σk μe + μT/σε
GK + Gb − ρε
∂x j
=
∂ ⎛ ∂φ ⎞ ′ (j = 1,2,3) ⎜Γφ ⎟ + Sφ + Sφ ∂x j ⎝ ∂x j ⎠
(9)
In the non-finned tube bundles zones, the additional source term Sφ′ is set zero. In the finned tube bundles zone however, the additional momentum sink term Sm’ and energy source term Se’ should be imposed on the corresponding equations.
Sm′ = −
Se′ =
(10)
(11)
where Lj is the thickness of finned tube bundles in three dimensions, Δpj and qfj are the pressure drop and heat flux in three directions respectively. φ, Γφ and Sφ are listed in Table 4. The realizable k-ε turbulence model is adopted to deal with the air turbulent flows through air-cooled condenser cell, thanks to its better prediction for the flows involving the vortices, rotation, separation, and boundary layer under strong adverse pressure gradient. Multiple reference frame (MRF) model is used to describe the aerodynamic characteristics of axial flow fan. The MRF model is a method for multiple zones, in which the individual cell zone can be assigned different rotational or translational speeds, the flow in each moving cell zone is solved using the moving reference frame equations. According to the actual operating parameters, the rated rotational speed of axial flow fan is set to be 80 r/min. As shown in Fig. 3, the air temperature at the inlet surfaces of computational domain is taken to be 289.15 K. Because of the fact that the velocity at the inlet surfaces is not known, the pressure inlet boundary is appointed. At the top exit surface, the pressure outlet boundary condition is set. The ground is regarded as the no-slip adiabatic wall. The condenser cell is a representative unit of direct dry cooling system, so the symmetry boundary conditions are set at the edge surfaces of condenser cell. The turbulent kinetic energy k at the inlet takes the same form as Eq. (2), with the turbulence intensity I set to be 10%. The ε at the inlet can be estimated as follows
1⎡ ∂ ⎛μ ∂vi ⎞ 3 ⎢ ∂xi ⎝ e ∂xk ⎠ ⎣
ε k
C1ε Gk − C2ε ρ
ρC1 Sε − ρC2
+
(μ ) ⎤⎥⎦
∂ ⎛ ∂vj ⎞ μe ∂xj ∂xj
+
∂ ∂xk
⎛μ ∂vk ⎞ ⎤−ρg e ⎝ ∂xj ⎠ ⎥ ⎦
⎜
⎟
⎝
⎠
∂v ∂ ⎛μ j ⎞ ∂xj ⎝ e ∂xk ⎠
+
∂vk e ∂x i
⎜
∂ ∂xk
⎟
∂v ⎛μe k ⎞ ⎤ ⎝ ∂xk ⎠ ⎥ ⎦
ε2 k
ε2 k + νε
ε k
+ C1ε C3ε Gb
3. Results and discussion 3.1. Finned tube bundles Fig. 5 and Fig. 6 show the variations of the pressure drop and heat flow rate of the studied finned tube regions with the inlet air velocity at various inclined angles. In Fig. 5, the total pressure drop through the finned tube bundles increases as the inclined angle goes up owing to the increased flow channel length. It can be found from Fig. 6 that when the inclined angle increases, the total heat flow rate also increases thanks to the increased heat transfer surface area. At any inclined angle, these
−1
k2 μ ε = ρcμ ⎛⎜ t ⎞⎟ μ ⎝μ⎠
+
∂ ∂xk
The wind tunnel test has been carried out to verify the modeling and numerical methods for the simulation of finned tube bundles in our previous work [7]. With the alternant staggered slotted finned tube bundles as a sample, the experimental system consists of the air loop and water loop. The water inlet temperature and flow rate are controlled to be constant. The inlet air velocity varies from 0.5 to 3.5 m/s, and the air pressures and temperatures at the inlet and outlet are respectively measured. The numerical and experimental results arrive at a good agreement with the highest deviations of the Nusselt number and friction factor as low as 5.3% and 8.3% respectively. The modeling and numerical approaches for the wavy finned flat tube bundles in this work are completely same as the aforementioned, which verifies in another way that they are reliable and accurate enough for the thermo-flow predictions of oblique finned tube bundles. Based on a 600 MW power generating unit, a performance experiment for a scaled model of ACC cell was made to validate the radiator model for conventional finned tube bundles and MRF model for fan [23]. Fig. 4 shows the experimental scheme for scaled condenser cell, with the air flow, steam condensation and vacuum system. Table 5 lists the experimental and numerical mass flow rates, inlet and outlet air temperatures and heat rejections. The average relative error of heat rejections for cases (1–10) is 7.19%, and the maximum is 10.57% for case 4, which can be accepted in practical engineering. The modeling and numerical methods for the condenser cell in this work are exactly same as those for the aforementioned numerical simulation, showing that the computational approaches are reliable for the performance predictions of the conventional and proposed condenser cells.
qfj Lj
⎟
⎠
+
2.3. Experimental validation
Δpj Lj
⎜
⎝
∂v ∂ ⎛μ j ⎞ ∂xj ⎝ e ∂xi ⎠
first-order upwind differencing scheme. The pressure and velocity fields are coupled by using SIMPLE algorithm. The divergence-free criteria of 10−4 are set for all the scaled residuals except that the criterion of the energy equation is prescribed as 10−6. The air mass flow rate across the air-cooled condenser cell is also monitored to judge whether the iteration is converged to a reasonable level.
2.2.2. Condenser cell For the condenser cell, the air-side conservation equations have the following form
∂ρvj φ
∂vi e ∂x i
1 ⎡ ∂ ⎛ ∂vi ⎞ μe ∂xj 3 ⎢ ∂xi
z-momentum
−
(μ ) +
(12)
where the empirical constant Cμ is set 0.09, μ is the air viscosity, and the turbulent viscosity ratio μt/μ is assumed to be 1.1 as a typical case. The governing equations for condenser cell are all discretized using 483
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Fig. 4. Experimental system of air-cooled condenser cell [23]. (a) Axial flow fan, finned tube bundles and condenser cell, (b) experimental scheme and measuring points. 484
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Table 5 Experimental and numerical results for the scaled model of condenser cell. case
1 2 3 4 5 6 7 8 9 10
experimental
numerical
ma (kg/s)
ta1(°C)
ta2 (°C)
Q (kW)
ma (kg/s)
ta1 (°C)
ta2 (°C)
Q (kW)
8.19 9.72 11.21 12.73 14.62 17.39 19.91 22.05 24.82 27.72
7.81 7.82 7.31 7.07 6.96 7.91 6.96 6.25 6.37 5.74
85.81 83.43 77.15 72.14 67.53 62.72 57.14 55.93 53.95 51.51
641.93 736.79 785.13 831.97 889.52 957.56 1002.77 1101.36 1187.33 1274.81
8.22 9.54 11.08 12.95 14.96 17.98 21.54 22.09 23.58 27.77
7.81 7.82 7.31 7.07 6.96 7.91 6.96 6.25 6.37 5.74
92.81 90.43 84.22 77.75 72.12 65.85 57.83 58.13 57.51 51.14
702.27 792.08 856.53 919.96 979.71 1047.05 1099.35 1152.91 1213.39 1267.19
Table 6 Polynomial factors of pressure loss coefficient at various inclined angles. inclined angle
r1
r2
r3
r4
r5
r6
r7
0° 15° 30° 45° 60°
23.384 23.945 25.807 25.426 28.037
−24.89 −22.19 −22.77 −14.55 −3.116
13.639 10.79 10.226 1.4998 −13.23
−4.136 −2.927 −2.453 1.427 8.5977
0.6935 0.4474 0.3108 −0.547 −2.232
−0.060 −0.036 −0.019 0.0742 0.2651
0.0021 0.0012 0.0004 −0.004 −0.012
Table 7 Polynomial factors of empirical convective heat transfer coefficient at various inclined angles.
Fig. 5. Pressure drop for studied finned tube regions with different inclined angles at various inlet velocities.
inclined angle
h1
h2
h3
h4
h5
h6
h7
0° 15° 30° 45° 60°
22.348 22.580 23.511 26.059 14.539
13.579 12.498 8.6448 −0.227 20.995
−5.102 −4.231 −1.114 6.064 −12.40
1.5639 1.2333 0.0352 −2.774 4.9272
−0.337 −0.273 −0.038 0.5348 −1.118
0.0412 0.0351 0.0121 −0.047 0.1291
−0.002 −0.002 −0.001 0.0015 −0.006
coefficient in Eq. (5) and polynomial factor of empirical convective heat transfer coefficient in Eq. (8) can be obtained, which are listed in Table 6 and Table 7 respectively. 3.2. Condenser cell The velocity and temperature fields at the outlet of condenser cell, the streamlines and temperature fields inside the A-frame chamber are obtained. The variations of total mass flow rate and heat rejection are also presented and analyzed at various rotational speeds of fan. Finally, two non-dimensional parameters, mass flow growth rate and heat transfer growth rate, are defined to evaluate the thermo-flow performances of condenser cell. 3.2.1. Variable fields Fig. 7 shows the velocity contours at the surfaces with 10 mm apart from the outlet surfaces of finned tube bundles, and at the fan rotational speed of 80 r/min. For the conventional layout shown in Fig. 7(a), four velocity dead zones appear at the lower parts of finned tube bundles with the velocity close to 0 m/s, which is unfavorable to the cooling performance. Due to the flow direction turning of about 60°, the local flow loss of cooling air increases. Moreover, the cooling air tends to flow upward due to the driving force from fan. As a result, less air can flow across the lower regions to participate in the heat transfer process. When the inclined angle increases to 15° and 30°, the areas of dead zones only decrease a little, but the velocity at the middle region grows. When the angle rises to 45° and 60°, the areas of dead zones get reduced
Fig. 6. Heat transfer rate for studied finned tube regions with different inclined angles at various inlet velocities.
two variables both increase as the inlet air velocity increases. Based on the pressure drop and heat transfer simulation results of the finned tube bundles, the polynomial factor of pressure loss
485
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Fig. 7. Velocity fields at the outlet of condenser cell with various inclined angles at rotational speed of 80 r/min. (a) 0°, (b) 15°, (c) 30°, (d) 45°, (e) 60°.
accordingly. The air temperatures at the same surfaces as Fig. 7 with five inclined angles at the rotational speed of 80 r/min are shown in Fig. 8. From the temperature distribution for the conventional condenser cell shown in
a lot and the velocity increases to a certain extent at other parts especially the central part. Though the velocity distribution is a little uneven, the total mass flow rate participating in the heat transfer increases, so the overall thermo-flow performances get improved 486
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Fig. 8. Temperature fields at the outlet of condenser cell with various inclined angles at rotational speed of 80 r/min. (a) 0°, (b) 15°, (c) 30°, (d) 45°, (e) 60°.
45° and 60°. What's more, a low temperature zone is formed at the middle area, showing a better heat transfer performance. However, a high temperature zone is presented at the central upper part with the inclined angle of 60° as shown in Fig. 8(e), and the temperature is nearly up to 316 K. Fig. 9 presents the velocity fields in the A-frame chamber at various
Fig. 8(a), it can be clearly seen that four high temperature regions are presented at the four corners of finned tube bundles with the temperature even reaching 320 K, which greatly deteriorates the air cooling capacity. As shown in Fig. 8(b)-(e) at the fin inclined angles of 15°, 30°, 45° and 60°, with the inclined angle increases, the areas of the four high temperature regions are conspicuously reduced and even disappear at 487
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Fig. 9. Velocity fields in A-frame chamber with various inclined angles at rotational speed of 80 r/min. (a) 0°, (b) 15°, (c) 30°, (d) 45°, (e) 60°.
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grows to 15° and 30° shown in Fig. 9(b) and (c), the airflow just turns smaller angles of 45° and 30°. However, the reverse flow is generated at the top of the A-frame chamber for these two cases, and the low velocity zone downsteam the fan tends to expand to the upper area. As the inclined angle increases to 45° and 60°, the air at the lower region flows
inclined angles with the rotational speed of 80 r/min. For the conventional condenser cell shown in Fig. 9(a), the cooling air flows across the finned tube bundles with a direction turning of about 60°. Two vortices are formed downsteam the fan due to the aerodynamic characteristics of axis flow fan and the A-frame finned tube bundles. When the angle
Fig. 10. Temperature fields in A-frame chamber with various inclined angles at rotational speed of 80 r/min. (a) 0°, (b) 15°, (c) 30°, (d) 45°, (e) 60°. 489
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through the finned tube bundles easily. However, the location of the two vortices becomes higher and moves to both sides from 0° to 60°, especially as the inclined angle reaches to 60°, the reverse flow gets serious and more upper zones are influenced, so the cooling performance at this part is weakened, that is why the higher temperature region is formed at the condenser cell top shown in Fig. 8(e). It can be estimated that there exists an optimal inclined angle with best thermoflow performances. Fig. 10 shows the temperature details in the A-frame chamber at 80 r/min. For the conventional condenser cell shown in Fig. 10(a), the temperature at the lower part of finned tube bundles is high which coincides with the results in Fig. 8(a). From the local enlarged details, it can be observed that the lower part of finned tube bundles along the air flow direction is in a high temperature and does not get fully cooled. The temperature at the top of condenser cell is high, because it is adjacent to the steam duct and cannot acquire sufficient airflows to be cooled. As the inclined angle increases from 15° to 60°, a reduced temperature at the lower part of finned tube bundles can be clearly observed, and the depth of the regions with high temperatures decreases especially for the angles of 45° and 60° that only a few areas at the exit of finned tube bundles have high temperatures. What's more, the highest temperature at this region decreases as well which is about 320 K at the inclined angles of 0° and 15°, but 318 K at 45° and 60°. Nevertheless, becauses of more cooling air at the lower and middle parts of finned tube bundles as well as the reverse flow at the top of Aframe chamber, the thermo-flow performances at the top region are not as good as the case of 0°, especially at the inclined angle of 60°.
where Ma,proposed is the mass flow rate per unit fan power of the proposed condenser cell with oblique finned tube bundles. Ma,conventional stands for the mass flow rate per unit fan power of the conventional layout. Similar to the mass flow growth rate, the heat transfer growth rate is the ratio of the heat transfer rate per unit fan power difference to the heat transfer rate per unit fan power for the conventional condenser cell as follows.
q˙ a =
(14)
4. Conclusions In the conventional air-cooled condenser cell, four dead velocity zones with high temperatures are formed at the lower corners of finned tube bundles, resulting in poor thermo-flow performances. For the proposed condenser cell with oblique finned tube bundles, the high
Ma, proposed − Ma, conventional Ma, conventional
qa, conventional
where qa,proposed is the heat transfer rate per unit fan power of the condenser cell with oblique finned tube bundles. qa,conventional stands for the heat transfer rate per unit fan power of the conventional layout. Fig. 13 shows the mass flow growth rate at various fan rotational speeds. It can be clearly found that the mass flow growth rate with the inclined angle of 45° is much higher than other angles, and even arrives at 12.81% at 56 r/min, showing that the 45° is the optimal angle for the oblique finned tube bundles. As the rotational speed increases, the mass flow growth rate increases at first and then decreases for the inclined angle of 45°. This non-dimensional parameter at 30° is much higher than 60° at low rotational speeds, because the reverse flow appears at the top of finned tube bundles, which weakens the thermo-flow performances more than the performance improvement at the lower part of condenser cell. The mass flow growth rate decreases as the rotational speed increases for 15°, showing the flow performance is deteriorated with increasing the rotational speed. The heat transfer growth rate is shown in Fig. 14, from which can be observed that it is the highest at the inclined angle of 45° for all the rotational speeds, and reaches up to 8.96% at 56 r/min. It takes the second place at the inclined angle of 30° and becomes higher than 60° for all the rotational speeds while the differences between them decrease as the rotational speed increases. At the inclined angle of 15°, the heat transfer growth rate increases as the rotational speed falls, which is similar to the changing trend of mass flow growth rate. It is even higher than 60° when the rotational speed reaches to 40 and 48 r/min.
3.2.2. Thermo-flow performances Fig. 11 gives the total mass flow rate of condenser cell at various fin inclined angles, with the fan operating at the rotational speeds of 80 r/ min, 72 r/min, 64 r/min, 56 r/min, 48 r/min and 40 r/min, respectively. It can be seen that the mass flow rate drops as the rotational speed decreases due to the reduced driving force. The mass flow rate arrives at the highest value at the inclined angle of 45°, showing that the thermo-flow performances of condenser cell are greatly improved, because the flow at the lower part of condenser cell is enhanced a lot while it is weakened slightly at the upper region. The 60° takes the second place and gets closer to the 30° when the rotational speed is reduced. When the rotational speed is shifting to about 48 r/min, the mass flow rate is nearly equal for these two cases and then it gets smaller than 30°. The mass flow rate of the proposed condenser cell with oblique finned tube bundles is always higher than conventional condenser cell. Fig. 12 presents the total heat transfer rate of condenser cell versus the rotational speed at various inclined angles. It can be seen that the total heat transfer rate decreases as the fan rotational speed drops, which is in keeping with the changing trend of mass flow rate. The heat transfer rate reaches the maximum at the inclined angle of 45°, and then the 30°, 60°, 15°, 0° respectively when the rotational speed increases from 48 r/min to 72 r/min. The heat transfer rate at 60° surpasses the case of 30° and takes the second place at 80 r/min. At the rotational speed of 40 r/min, the heat transfer rate at 15° transcends the 60° and ranks the third place. Similar to the mass flow rate, the inclined angle of 45° is the optimal one with the most enhanced heat transfer. To clarify the improvement of thermo-flow performances of the proposed condenser cell at different rotational speeds, two non-dimensional parameters of mass flow growth rate and heat transfer growth rate are introduced. Mass flow growth rate is the ratio of the mass flow rate per unit fan power difference between the proposed and conventional condenser cell to the mass flow rate per unit fan power for the conventional layout, with the following form
M˙ a =
qa, proposed − qa, conventional
Fig. 11. Mass flow rate of condenser cell with different inclined angles at various fan rotational speeds.
(13) 490
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Fig. 14. Heat transfer growth rate of condenser cell with different inclined angles at various fan rotational speeds.
Fig. 12. Heat transfer rate of condenser cell with different inclined angles at various fan rotational speeds.
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Fig. 13. Mass flow growth rate of condenser cell with different inclined angles at various fan rotational speeds.
temperature and velocity dead zones decrease as the inclined angle increases, and even vanish at the inclined angles of 45° and 60°. However, two vortices at both sides of A-frame chamber result in the reverse flow at the upper area, which becomes serious as the inclined angle increases. The performance gets improved for the proposed condenser cell as the rotational speed increases. The mass flow growth rate and heat transfer growth rate for the inclined angle of 45° reach to12.81% and 8.96% at the rotational speed of 56 r/min. The thermo-flow performances of condenser cell with the inclined angle of 45° are much better than other angles, so the inclined angle of 45° is preferred for the oblique finned tube bundles of air-cooled condenser. Acknowledgments The financial supports for this research, from the National Natural Science Foundation of China (Grant No. 51776067) and the National Basic Research Program of China (Grant No. 2015CB251503), are 491
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