1. Introduction
In thermal and nuclear power plants, the natural draft-dry cooling system (NDDCS) has been adopted throughout the world, which shows significant water conservation, compared with the wet-cooling system, with a closed circulating water circulation [
1,
2]. For the NDDCS, the fundamental function is to take away the heat rejection of circulating water by cooling air flowing through the heat exchanger finned tube bundles, but the crosswinds could intensively cripple the thermo-flow performances of NDDCS. Thus, in the past, an investigation of the wind effects and the relevant approaches for improving the thermo-flow performances, has been carried out with the computational fluid dynamics (CFD) method.
As for ambient wind effects, Yang et al. [
3] numerically investigated the air flows, concluding that the fluid flows through NDDCS are dominated by the wind-induced and buoyancy-driven air flows, as a result of the balance between the inertial force and the viscous, buoyancy forces. Besides, Yang et al. [
4] studied the flow and heat transfer performances of the condenser/NDDCS with the CFD method, obtaining a critical wind speed with the lowest air flow rate and the maximum outlet water temperature, which indicates the most deteriorated performances of the entire system. With the vertically arranged heat exchanger bundles of the dry-cooling system, Zhao et al. [
5,
6] numerically presented detailed aerodynamic fields around the cooling deltas in the absence of winds, and at wind speeds of 4 m/s and 12 m/s. Ma et al. [
7] proposed a new theoretical model for the CFD process, to predict dry-cooling system performance, by using the power function of the initial temperature difference for the evaluation of ambient temperature effects and the outlet air velocity for the calculation of heat rejection.
In order to weaken the adverse wind effects on NDDCS, many researchers have proposed various innovative measures with the numerical computation. Liao et al. [
8] numerically studied the influence of the tower height-to-diameter ratio on the thermo-flow characteristics of the dry-cooling system, and proposed a lower value for the better thermo-flow performances at high wind speeds. As for the geometrical layouts of the multi-towers, Liao et al. [
9] developed the numerical models, and concluded the tower spacing effects depended on the wind speed and tower arrangement. With Munters as the pre-cooling media, He et al. [
10] numerically investigated the trade-off between the air pressure drop and the evaporative pre-cooling of the inlet air, and obtained the critical ambient temperature of the pre-cooling application to the natural draft dry cooling system. As with the traditional windbreaker first recommended by Preez and Kröger [
11], Chen et al. [
12] subsequently presented the interior and exterior windbreaker configurations with a numerical simulation, showing that the exterior windbreakers were superior to the interior ones, especially at high wind speeds. Furthermore, Zavaragh et al. [
13] numerically proposed the internal flat and the combination of internal flat-external rounded windbreakers, which can move axially around the cooling tower, leading to the air mass flow rate increase from the wind momentum effect. Moreover, Gu et al. [
14] investigated the optimization of different wind-break structures, as the cross walls, wind-break walls, cross line-screen, and the louvers, concluding the most optimal structure is the wind-break wall, and the optimal louver opening as the second option, owing to its flexible adjustment. Considering the circumferential non-uniform ventilation and the vortices inside the cooling tower, Wang et al. [
15] proposed an enclosure with an opening at the windward side with the CFD method, which can enhance the cooling performance at all investigated wind speeds. Combined with the solar energy, Yuan et al. [
16] numerically studied the strengthened cooling efficiency of the dry-cooling system by revealing the effects from the collector diameter, the ambient temperature, and also the heat exchanger layout. Additionally, Zou and Gong [
17] investigated the optimal structural arrangement of the solar enhanced natural draft dry cooling system by a numerical simulation, finding out the design with the partial blockage at the collector entrance, horizontal sunroof, and parabolic tower would be the optimal selection, considering the thermal performance and structural robustness.
Conclusively, although the wind effects on the thermo-flow characteristics of natural draft dry cooling system and corresponding approaches have been thoroughly investigated, the aforementioned studies only focused on the overall analysis of the large scale air-cooled heat exchanger, and they have not yet determined the detailed velocity or temperature fields of the cooling deltas for various air-cooled sectors been fully disclosed at various wind speeds. So, in this research, the macro heat exchanger model for the finned tube bundles are adopted, so as to specifically investigate the thermo-flow characteristics of the air-cooled sectors and cooling deltas with the numerical method, which differs from the CFD method with the previous radiator model.
It is worth noting that the natural draft dry cooling system (NDDCS) possesses a complicated large-scale structure, like the closed wet cooling tower (CWCT), and for the large-scale CWCT, Zhu et al. [
18] proposed a CFD model and compared the numerical and experimental results, which shows good agreement. For the large-scale air-cooled heat exchanger model of the NDDCS in this research, the simulation results with the two numerical models were also compared with the experimental results, which showed a better prediction of the thermo-flow performances of NDDCS using the proposed macro heat exchanger model, since the thermo-hydraulic characteristics of the heat exchanger bundle for airside was coupled with waterside. Additionally, by adopting the macro heat exchanger model, the numerical results can provide not only the 3D overall outlet air temperature fields of the large scale air-cooled heat exchanger, but also very detailed variable fields for each cooling delta of the NDDCS. In summary, this research provides quite a comprehensive investigation of the large-scale air-cooled heat exchanger, which may contribute to more targeted approaches towards the performance improvement of the natural draft dry cooling system.
2. Models
2.1. Natural Draft Dry Cooling System
In power plants, the NDDCS incorporates a concrete hyperbolic dry-cooling tower and a large-scale air-cooled heat exchanger around the circumference of the tower base, as shown in
Figure 1a. As for the large-scale air-cooled heat exchanger model in this research, it consists of 110 vertically arranged delta-type cooling units, which are divided into 10 air-cooled sectors, so as to distribute the circulating water feasibly, so that each sector comprises 11 cooling deltas as shown in
Figure 1b. In practical engineering, the slotted finned tube bundles, which constitute the cooling deltas, are commonly adopted, due to the enhanced convective heat transfer, compared with the plain ones [
19]. Furthermore,
Table 1 lists the geometric parameters of the dry-cooling tower and slotted finned tube bundles.
As must be pointed out, due to the symmetric layout of the large scale air-cooled heat exchanger, only the first five air-cooled sectors ranging at 0°–180° are investigated for their thermo-flow performances. Besides, sectors No.1–No.5 were respectively named as the frontal, middle-front, middle, middle-rear, and leeward sectors, as shown in
Figure 2.
2.2. Governing Equations
The air density can be calculated based on ideal gas behaviors, because the variation of the airflow static pressure within the flow field is reported to be just 1–2% of the atmospheric pressure. Furthermore, the effect of the buoyancy force is also considered in the vertical momentum equation, based on the Boussinesq approximation. The realizable k-ε turbulence model is adopted for closing the conservation equations, due to its good prediction of the turbulence flow of viscous fluids.
In the present research, the continuity, momentum, energy, and turbulence modeling equations for a steady incompressible buoyant flow field are introduced in a united form [
5,
6].
where
ρ is the air density,
ui is the velocity in the
xi direction,
Γφ is the diffusion coefficient for
φ,
Sφ is the internal source of the air conservation equation,
Sφ′ represents the energy or momentum source term for the zone of the heat exchanger, describing the flow and heat-mass transfer conditions of crossflow air when it flows through the heat exchanger [
20,
21].
According to the actual configurations of the large-scale air-cooled heat exchanger of the NDDCS, it is impractical to model the individual fins and tubes of the heat exchanger bundles. In this research, the macro heat exchanger model was used to characterize the finned tube bundles, by introducing a pressure drop to the cooling air, and the heat transfer from the circulating water to the cooling air.
The pressure drop Δ
p of the airside is expressed as follows:
where
ρ is the mean air density, and
uw is the air velocity normal to the finned tube bundles.
f is the pressure-loss coefficient, which can be specified from the experimental data described below.
In the practical condition of the heat exchanger bundles, the water temperature distribution is not constant along the entire finned tube, and the macro heat exchanger model can simulate the water temperature variation along the flow direction.
The heat rejection from the control volume of the heat exchanger model is as shown in
Figure 3. The heat transfer rate
Qmacro is computed with the following form:
where
macpa is the heat capacity rate of the cooling air.
twa represents the heat transfer unit temperature for the circulating water, and
ta is the cooling air temperature inside heat exchanger unit.
εmacro is the heat exchanger effectiveness, defined as:
where
Cr is the ratio of the heat capacity rate of air to that of water,
NTU is the number of transfer units with the following form:
where
K and
A are the heat transfer coefficient and areas, respectively.
The heat rejection from a cell unit is calculated by summing the heat transfer of all the macros:
The total heat dissipated from heat exchanger is computed as the sum of the heat rejection from all cooling cell units:
The air-cooled heat exchanger bundles are constructed by a cuboid shape, applying a porous media model to make the air flows perpendicular to the inlet surface of the heat exchanger bundles. More detailed descriptions of the CFD model can be referred to our previous study [
22].
2.3. Computational Domain and Boundaries
The cooling heat exchanger and the tower shell were modeled and computed in this work, as shown in
Figure 4a.
Table 2 shows the boundary settings used in this model. For the far-field boundaries, including the windward, top and leeward surfaces, the turbulence level of airflow field was quite low, and the turbulence intensity and viscosity ratios could be roughly set as 0.1% and 0.1, respectively [
23,
24]. During windy conditions, the crosswind velocity profile at the windward surface obeys the power law below, and imports a computational model by the UDF (user-defined function) [
3,
4,
5,
6,
8,
9]:
where
Hh denotes the vertical height above the ground, and
uwd represents the crosswind speed at a reference height
Href of 10 m. The exponent
e is related to the ground roughness and the atmosphere stability, set as 0.2 in this paper.
In order to eliminate the boundary domain impacts on the air flow, independent verification has was conducted for various computational domain dimensions, and a size of 1500 m × 1500 m × 900 m was finally adopted. Both the central block and the extended regions were employed with hexahedral grids, due to the cylindrical configuration of NDDCS. For an accurate simulation of the flow and heat transfer details, the boundary layer mesh near the tower wall region, and the very small sizes meshed in the air-cooled condenser section were employed, while the mesh size increased proportionately for the other regions to meet both the computational accuracy and the cost demands. The detailed meshes for the dry-cooling tower and the heat exchanger are shown in
Figure 4b. For the cooling system, the grid interval size for the heat exchanger was set to 0.4 m; however, for the cooling tower zone, the grid interval size was set to 4 m with a 1.03 growth ratio along the tower height. For the farmost field from the dry-cooling tower, an initial interval size of 10 m and a successive ratio of 1.1 was adopted. As a result, 2,805,587 grid cells were created. Moreover, when the grid interval sizes of the heat exchanger cell and cooling tower were set to be equal to 0.3 m and 3 m, 0.2 m and 2.5 m, and 0.1 m and 2 m, 3,775,980, 4,951,524, and 6,141,276 grid cells were successively generated. To check the mesh independence of the computed results, the exit air mass flow rate of cooling tower, and the heat transfer rate between the airflow and heat exchanger bundles were selected to test the grid number, since it represents the cooling performance of the NDDCS. The mass flow rate of the cooling air through the tower outlet, and the heat rejection of the heat exchanger bundles at a wind speed of 4 m/s varied by merely ~0.26% and ~0.32% for the latter two dense grids, so that the cell number of 4,951,524 for the cooling system was finally adopted, with acceptable computation results.
The CFD package ANSYS fluent 14.0, based on the finite volume method, was used to govern the equations with prescribed boundary conditions. The second-order upwind differencing scheme was adopted to discretize the momentum, energy, and turbulent kinetic energy equations. The SIMPLE algorithm was applied for pairing the velocity and pressure fields. The numerical iterations continued until all of the residuals of the dependent variables reached reasonable levels. Additionally, the air mass flow rate through the cooling tower was also monitored, and the relative errors between the two iterates should be continuously less than 10−4, to guarantee that the computational results are converged to a rational level.
2.4. Heat Exchanger Experiments
To obtain
f and
εmacro, an experimental analysis of flow and heat transfer performance for a four-row staggered slotted finned tube heat exchanger was carried out, using the thermal state experimental tunnel system presented here. A schematic diagram of the experimental system and the photos of the experimental facilities are shown in
Figure 5. The wind tunnel has a test section that is covered by an asbestos layer, to minimize heat losses, which closely matched the experimental sample, to eliminate contraction and expansion losses. The staggered configuration is characterized by transverse and longitudinal pitches of 35 mm, a diameter of 35 mm, a fin spacing of 3.2 mm, and a fin thickness of 0.3 mm, with the tubes and fins of the heat exchanger are made from aluminum. The test section size is 400 mm in width, 700 mm in height, and 1000 mm long. In the air loop, the flow rate was controlled by a digital blower speed controller that was able to provide a windward air velocity of between 0.5 and 5 m/s, which was adjusted based on a hotwire anemometer with a precision of ±0.05 m/s. Two strings of L-type Pitot tubes were implanted upstream and downstream of the exchanger, to measure the pressure drop along the test section, using an inclined single tube microdifferential pressure gauge with a precision of ±0.15 Pa. Two fine metal grids were placed in the inlet (12 T-type thermocouples) and outlet (16 T-type thermocouples) of the test section.
The water loop was supplied by a water temperature control system that was able to provide a constant hot water inlet temperature of 60 °C. The output of the water flow rate was equipped with a turbine flowmeter with a precision of ±0.5%, and kept at approximately 0.694 kg/s during the experiments. Both the inlet and outlet tube wall temperatures were measured by setting six T-type thermocouples at the inlet and outlet parts of the tubes, respectively. In order to achieve accurate measurements, the thermocouples were pre-calibrated by using the ice point calibration method, with an error range of ±0.1 °C. The energy imbalance between the air and water sides was within 7.57%.
As the temperature maintains stabilized, all of the experimental data signals were collected and converted by the data acquisition system and the host computer. The experimental results of the core friction coefficient, and the heat exchanger effectiveness with the windward air velocity have been plotted in
Figure 5c.
2.5. Numerical Model Validation
To evaluate the modeling and numerical methods, flow performance experiment of the scale model for an NDDCS was carried out, and the measurement point schematic design is shown in
Figure 6a. Wind speeds are measured by a hot-wire anemometer, IFA-300, with an accuracy of ±0.1%, and 108 measuring points were placed inside the cooling tower far from the main structures, with 12 layers in the
z direction and nine columns in the
y direction. Moreover, the vertical and horizontal intervals between measuring points were 10 m and 9 m for the model tower, respectively. Both the results were processed and output by the data acquisition unit and computer, and the experimental uncertainties of the measured rising velocity were about 0.6% [
25].
Two horizontal cross-sections with heights of 84.2 m and 144.2 m were used to compare the numerical and experimental results, which are shown in
Figure 6b. It can be concluded that the calculated results by using the heat exchanger model agreed well with the measured data. This verifies that the heat exchanger model is reliable enough for the performance prediction of the NDDCS.
4. Conclusions
With the macro heat exchanger model, the 3D overall outlet temperature fields are presented for a large-scale air-cooled heat exchanger, and the quantitative thermo-flow performances are also compared at various wind speeds. The results show that the air mass flow rate and heat rejection for the frontal sector increase as the wind speed increases, but they show little variation for the middle-front sector. For the middle and middle-rear sectors, the thermo-flow performances vary dramatically with the wind speed, and they are the most deteriorated at a wind speed of 12 m/s; however, the rear sector receives the best performance at 12 m/s.
Most importantly, the local thermo-flow characteristics for the cooling deltas in various air-cooled sectors are specifically analyzed. For the frontal and middle-front cooling deltas, the thermo-flow performances become worse along the circumferential angle. The middle deltas show extremely deteriorated performances at high wind speeds, due to the hot-flow recirculation and the air-flow vortices, as well as the extremely chaotic outlet air temperature distribution. Most of the middle-rear deltas present the worst thermo-flow performances at 12 m/s, but the best performances are achieved for the sixth to 11th deltas, at 16 m/s. The rear deltas show the best flow and heat transfer performances at 12 m/s. Additionally, even most of the rear deltas have minimal air mass flow rates at 16 m/s, the heat rejection is higher than that at 4 m/s due to the expanded lower temperature regions along the upper parts of the cooling deltas.