A decoupled method to identify affecting mechanism of crosswind on performance of a natural draft dry cooling tower

Abstract

The natural draft dry cooling tower (NDDCT) has been increasingly used for cooling in power generation in arid area. As crosswind affects the performance of a NDDCT in a complicated way, and the basic affecting mechanism is unclear, attempts have been made to improve the performance of a NDDCT based on limited experiences. This paper introduces a decoupled method to study the complicated crosswind effects on the inlet and outlet of a NDDCT separately by computational fluid dynamics (CFD) modeling and hot state experiments. Accordingly, the basic affecting mechanism of crosswind on the NDDCT performance is identified. Crosswind changes the inlet flow field of a NDDCT and induces mainstream vortices inside the tower, so as to degrade the ventilation. Besides, low crosswind deflects the upward plume at the outlet to further degrade the ventilation, while high crosswind induces the low pressure area at the outlet to reduce the ventilation degradation.

Keywords

affecting mechanism / crosswind / decoupled method / mainstream vortices / natural draft dry cooling tower (NDDCT) / degradation

Introduction

The indirect dry cooling technology is favored in arid countries and regions, since it specifies water saving, low operation and maintenance cost, and long service time [¹]. As the main facility of indirect dry cooling system, a natural draft dry cooling tower (NDDCT) is found to be sensitive to ambient crosswind [²]. Previous studies indicated that the crosswind at 20 m/s might decrease the ventilation rate of a NDDCT by 36%; the inner wall vortices, the mainstream vortices, and the circumferential uneven air intake were the main factors degrading the cooling performance [³]; the tangential velocity outside the side sections increased linearly as crosswind increased, leading to a gradually decreased local static pressure, as a result, the air intake decreased gradually [⁴]; and the crosswind could cause an air temperature increment of 7.5°C inside the tower [⁵], resulting in more than 25% decrement of the heat transfer efficiency [⁶].

As the affecting mechanism of crosswind on a NDDCT is critical for the endeavor to improve the cooling performance under crosswind, it has been discussed generally and qualitatively in a few studies. Wei et al. [⁵] reported that the crosswind might affect the cooling efficiency of a NDDCT by forming an unfavorable pressure distribution at the tower inlet, disturbing the hot plume flow field, and causing cold air back flow at the leading edge of the tower outlet. Tang et al. [⁷] reported that the crosswind caused a horizontal air flow or even a cross ventilation inside the tower. Zhai et al. [⁸,⁹] reported that the inlet air flow from the leading and rear radiators converged to produce complex vortices. Both Zhang et al. [¹⁰] and Goodarzi [¹¹] reported that the crosswind squeezed the plume flow. The previous studies found that the influence of the flow field deformation of different sections on the performance of a NDDCT changed as the crosswind increased [⁴].

It is obviously observed that the performance of a NDDCT is affected by crosswind through a very complicated way. Moreover, the effects on the inlet and the outlet mingle together. As a result, the basic affecting mechanism still remains uncovered. Attempts have been made to improve the performance of NDDCT only by proposing some simple methods based on experiences, like the windbreaks [⁴,¹²] and enclosure [³], which may neither be good enough to avoid the negative effects, nor competent to fully utilize the energy of crosswind.

To identify the effect of crosswind on the inlet and outlet of a NDDCT separately, and quantitatively study the basic affecting mechanism of crosswind on the performance of a NDDCT, a decoupled method is introduced by using a division plate to separate the outside flow field of the NDDCT into two parts from the throat plane. As the experimental study is limited in obtaining qualified and comprehensive flow field information [¹³–¹⁷], computational fluid dynamics (CFD) is adopted to study the comprehensive flow around the NDDCT under crosswind condition [¹⁸–²⁰]. Besides, based on the previous studies [³,²¹], a flow loss factor (FLF) is adopted to quantify the effect of local flow field change on the overall ventilation rate [²¹].

Based on the numerical and experimental studies [²²], the affecting mechanism found in this study is expected to be critical for scheming out new methods to improve the performance of NDDCT under the crosswind condition.

Numerical and experimental methods

Problem description

The NDDCT of interest is of the Heller type and installed in a large scale coal-fired dry cooling power plant in China. It has a total height of 170 m, an extension platform height of 27.5 m, a radiator height of 24 m, a radiator support height of 2 m, an outlet diameter of 84.466 m, a throat diameter of 82 m, and a base radiator diameter of 146.17 m respectively [³]. The structural parameters of the NDDCT are listed in Table 1.

Given a certain power load, as the back pressure increases in a certain range, the steam rate per unit power generation increases slightly, and the latent heat of the saturated vapor decreases correspondingly [²³–²⁵]. As a result, the variation of the heat rejection in the condensing process could be negligible. It is found that a 5 kPa increment of back pressure results in only approximately a 2% increment of the exhaust heat. In this study, the heat released in a condenser is approximated as constant under different crosswind conditions, i.e., the heat release of the radiator bundle is simplified as a constant heat source in CFD modeling, and mimicked by the evenly assembled heating rods in the experiment.

CFD modeling

Based on the symmetry characteristic of the flow field around a NDDCT under crosswind condition, a half-cylinder computational field is chosen to numerically study the NDDCT performance as shown in Fig. 1(a). The computational field has a dimension of 1200 m (in diameter) × 1700 m (in height), which is ten times as large as the NDDCT in each direction to eliminate the unrealistic effect of the domain boundaries. The structure of the cooling deltas, tower shell, support base, and joint faces between adjacent radiators are all constructed in accordance with the real conditions as shown in Fig. 1(b), which is identified as the baseline model.

To investigate the effect of crosswind on the flow field of the tower through tower outlet and tower inlet separately, a division plate is set on the throat horizontal plane outside the tower. The crosswind velocity above or below the division plane could be set as zero, which is taken as an outlet boundary in the numerical model. To study the effect of crosswind on the NDDCT through tower inlet, an inlet-model is designed as shown in Fig. 1(c), where the boundary condition of surfaces above the division plate and the leeward cylinder surface under the division plate are all set as ‘outflow’, and the windward cylinder surface under the division plate is set as ‘velocity inlet’. To study the effect of crosswind on the NDDCT through tower outlet, an outlet-model is designed as shown in Fig. 1(d), where the boundary condition of the cylinder surface under the division plate is sate as ‘pressure inlet’, that of the windward cylinder surface above the division plate is set as ‘velocity inlet’, and other surfaces above the division plate are set as ‘outflow’.

As the crosswind could develop a reasonable velocity profile within a certain distance as in the large computational domain, the crosswind at the inlet boundary condition is set as a constant. Other surfaces of wall type are all set as adiabatic wall with no slip condition. Regarding to the steady-state problem with incompressible fluid, the pressure-based solver in FLUENT with the pressure-velocity coupling SIMPLEC method is adopted. The governing equations of the momentum, energy, turbulent kinetic energy and dissipation rate are discretized using the second-order upwind differencing scheme.

The Boussinesq approximation is used in the vertical momentum equation to consider the buoyancy force [²⁶]. For a steady-state, the buoyant, turbulent flow and heat transfer problem, governing equations include continuity, momentum, energy, and turbulence modeling equations. A standard model is used to describe the turbulent flow. Based on a grid checking in Table 2, the model of hexahedral meshing with a grid number of approximately 13700000 is adopted. Detailed descriptions about the CFD model can be referred to in Ref. [³]. The crosswind speed range of 0 – 20 m/s is investigated in the numerical model.

Experiment system

To validate the numerical results, a corresponding experiment is designed, where the division plate with a windshield having a dimension of 4 m (length) × 2 m (width) × 0.84 m (height) is arranged on the horizontal plane of throat (0.84 m in height), as demonstrated in Fig. 2(a). The windshield is placed on the ground at the windward side in the wind tunnel to eliminate the crosswind effect on the inlet of the NDDCT, so as to study the effect of the crosswind on the outlet of the NDDCT separately, as equivalent to the numerical separated outlet crosswind case.

The NDDCT model and experimental system are placed in a wind tunnel, as demonstrated in Fig. 2(b). The NDDCT model, mainly consisting of a chimney, resistance bundle, heating rods, is established according to the geometric scaling law. The resistance bundle is composed of a series of parallel arranged zigzag iron pieces to mimic the resistance characteristic of the NDDCT radiators according to the Euler scaling law. The tuneable electrical heating rods are circumferentially mounted onto the inside of the resistance pieces to mimic the heat rejection from the radiators according to the Froude scaling law. The wind tunnel can supply precisely controlled crosswind to mimic the environmental crosswind according to the momentum scaling law. Based on the Froude number similarity, the investigated crosswind velocity in a range of 0–2.4 m/s is studied in the experiment [²²].

Results and discussion

Quantitative description of flow characteristic

As introduced in Ref. [²¹], a FLF is adopted to quantify the effects of local flow field change on the NDDCT performance as expressed in Eq. (1). The subscripts –r and –t denote the reference and the total conditions respectively. A brief derivation process is as follows. Based on the Bernoulli equation as shown in Eq. (2) [²⁷], by merging the static pressure, the dynamic pressure, and the gravity differential pressure into a total one, , the resistance coefficient in Eq. (2) is described as Eq. (3). Then, a mass flow rate based the relation could be deduced as expressed in Eq. (4), where S is the sectional area. Finally, by defining a flow resistance factor {{\displaystyle \Omega }}_f and a potential flow factor {{\displaystyle U}}_f as expressed in Eqs. (5)–(6), a relation in Eq. (7) could be obtained. Accordingly, Eq. (1) can be obtained by a simple differential process.

(1)\mathrm{F}\mathrm{L}\mathrm{F}={\displaystyle \frac{\Delta {{\displaystyle \Omega }}_{\mathrm{f}}}{{{\displaystyle \Omega }}_{\mathrm{f}-\mathrm{r}-\mathrm{t}}}}={\mathrm{F}\mathrm{L}\mathrm{F}}_{\mathrm{0}}+{\displaystyle \frac{{{\displaystyle q}}_{\mathrm{m}-\mathrm{r}-\mathrm{t}}}{{{\displaystyle q}}_{\mathrm{m}}}}\sqrt{{\displaystyle \frac{\mathrm{\Delta }{P}^{*}}{\mathrm{\Delta }{{\displaystyle P}}_{r-t}^{*}}}}\left[{\displaystyle \frac{\mathrm{d}(\mathrm{\Delta }{P}^{*})}{\mathrm{2}\mathrm{\Delta }{P}^{*}}}-{\displaystyle \frac{\mathrm{d}({{\displaystyle q}}_{\mathrm{m}})}{{{\displaystyle q}}_{\mathrm{m}}}}\right],

(2){{\displaystyle P}}_{\mathrm{1}}+{{\displaystyle \rho }}_{\mathrm{1}}\mathrm{g}{{\displaystyle Z}}_{\mathrm{1}}+{\displaystyle \frac{\mathrm{1}}{\mathrm{2}}}{{\displaystyle \rho }}_{\mathrm{1}}{{\displaystyle v}}_{\mathrm{1}}^{\mathrm{2}}={{\displaystyle P}}_{\mathrm{2}}+{{\displaystyle \rho }}_{\mathrm{2}}\mathrm{g}{{\displaystyle Z}}_{\mathrm{2}}+{\displaystyle \frac{\mathrm{1}}{\mathrm{2}}}(\mathrm{1}+\xi ){{\displaystyle \rho }}_{\mathrm{2}}{{\displaystyle v}}_{\mathrm{2}}^{\mathrm{2}},

(3)\xi ={\displaystyle \frac{\mathrm{2}\Delta P^{*}}{\rho v^{\mathrm{2}}}},

(4){\displaystyle \frac{\sqrt{\xi }}{S}}=\sqrt{{\displaystyle \frac{\mathrm{2}\rho \mathrm{\Delta }{P}^{*}}{{\rho }^{\mathrm{2}}{V}^{\mathrm{2}}{S}^{\mathrm{2}}}}}={\displaystyle \frac{\sqrt{\mathrm{2}\rho \mathrm{\Delta }{P}^{*}}}{{{\displaystyle q}}_{\mathrm{m}}}},

(5) {{\displaystyle \Omega }}_{\mathrm{f}}={\displaystyle \frac{\sqrt{\xi }}{S}},

(6){{\displaystyle U}}_{\mathrm{f}}=\sqrt{\mathrm{2}\rho \mathrm{\Lambda }{p}^{*}},

(7){{\displaystyle U}}_{\mathrm{f}}={{\displaystyle q}}_{\mathrm{m}}{{\displaystyle \Omega }}_{\mathrm{f}}.

According to the flow characteristics along the streamline, five areas are defined as pressure surfaces, which are the far field inlet surface, the radiator inlet surface, the radiator outlet surface, the chimney inlet surface, and the tower outlet surface, respectively as exhibited in Fig. 3. Then, the FLF between each two pressure surfaces could be calculated according to Eq. (1), so as to study the effects of crosswind on different flow sections.

Crosswind effect on inlet of a NDDCT

The performance of the NDDCT on the baseline case, the inlet-model case, and the outlet-model case are calculated under different crosswind conditions respectively. According to the data of each pressure surfaces demonstrated in Fig. 3, the FLFs of each interested region are calculated and depicted in Figs. 4 and 5. As Fig. 4 shows, all of the FLFs increases slightly as the crosswind velocity increases to below 10 m/s while as the crosswind velocity further increases to above 10 m/s, the FLF-outlet declines greatly, and the FLF-inlet quickly exceeds other ones. However, these abrupt changes of FLF-inlet and FLF-outlet do not occur in inlet-model as depicted in Fig. 5, where all of the FLFs increase gradually as the crosswind increases within the velocity range in the research. Compared to the baseline case, the FLFs on inlet-model case are greatly reduced under low crosswind conditions while at a crosswind of above 10 m/s, the FLF-outlet begins to increase substantially, other than barrelling down as shown in the baseline case, resulting in a corresponding increment in the FLF-total.

In the inlet-model case, without being directly influenced by the crosswind, the outlet flow field region can only be affected by the crosswind indirectly through inlet, radiator, bottom and chimney step by step. Likewise, the crosswind influence on the flow regions of radiator, bottom, chimney and outlet are all transmitted from the inlet region. Consequently, the increasing rates of each FLF maintain a stable relationship as crosswind increases, where the FLF-radiator is close to the FLF-chimney, the FLF-inlet is close to the FLF-bottom, and the FLF-out leads the race in most range, exhibiting a good monotonic transferring effect. As an accumulative result, the FLF-total naturally changes as the FLF-outlet changes, also exhibiting a fixed ratio of increasing rate compared to the other FLFs.

The streamline of the NDDCT under three typical crosswind conditions are displayed in Fig. 6, where different colors represent different streams of fluid. Under the crosswind condition, affected by the uneven air intake from the inlet, two mainstream vortices (The other one is in the other symmetric half NDDCT.) are induced at the bottom of the NDDCT, and extend progressively from the tower chimney to the outlet. Without being influenced by the crosswind from the outlet, the plume keeps an upward direction. Besides, the vortices induced by the inlet crosswind remain in the upward plume flow. As the crosswind increases to above 6 m/s, the vortices inside the tower grow swiftly bigger and stronger, and even fills the whole NDDCT chamber up as shown in Fig. 6(c). The variation of streamline is in consistent with the variation of FLFs.

Under the baseline condition, when the crosswind increases to above approximately 10 m/s, the high speed horizontal crosswind at the outlet produces a low pressure area, as shown in Fig. 7(a), which is beneficial for the outlet flow. As a result, the FLF-outlet swiftly decreases to be minus, and the other FLFs are all reflected in some extent to reduce the increasing rate as the crosswind increases as shown in Fig. 4. In the inlet-model case, in absence of outlet low pressure area, the FLFs can only increase steadily as the crosswind increases.

A comparison of the ventilation rate of NDDCT between the baseline case and the inlet-model case is demonstrated in Fig. 8. In the inlet-model case, it is found that the ventilation rate does not decrease as much as does the baseline case, which is coherent to the great reduction of FLFs under the low crosswind condition. As the crosswind increases to above 10 m/s, the ventilation rate decreases correspondingly with the increases of the FLF-outlet and other FLFs. The variation of the ventilation rate is inversely proportional to that of the FLF-total, and hence confirms the validation in Section 3.1.

Crosswind effect on outlet of a NDDCT

The performance of the NDDCT with its outlet area exposed to crosswind is calculated under different crosswind conditions, named outlet-model, whose CFD model is shown in Fig. 1(b). The FLFs of each interested region are also calculated and shown in Fig. 9. Compared to the baseline case shown in Fig. 4, all of the FLFs in the outlet-model case are changed to be minus values and decrease as the crosswind increases under low crosswind conditions. At a crosswind of above 10 m/s, the FLF-chimney, the FLF-bottom, and the FLF-inlet begin to increase as the crosswind increases, and the decreasing rates of other FLFs are also reduced.

The variation of different FLFs in the outlet-model suggest that, the crosswind at the outlet of a NDDCT generally has a promotion effect on the overall ventilation, although this effect is gradually cut down at a crosswind of above 10 m/s. However, a conjoint analysis of Figs. 5 and 9 indicates that, in the presence of inlet crosswind, the crosswind at the outlet reverses to be a deterioration factor to the NDDCT ventilation under the low crosswind condition, while at a crosswind of above 10 m/s, the positive effect of the outlet crosswind begins to emerge. The ventilation rate comparison between the baseline NDDCT and the inlet-model case shown in Fig. 10 indicates that the ventilation is enhanced over all investigated crosswind range, and the enhancement increases as the crosswind increases. These results further confirm the positive function of the crosswind effect at the outlet exclusively.

To find out the deterioration mechanism of the outlet crosswind at the presence of the inlet crosswind, the streamline of the NDDCT at 10 m/s in the baseline case and the outlet-model case are exhibited in Fig. 11. It is seen that the outlet plume in the outlet-model is very stiff, while the plume in the baseline case is easy to be deflected by the same crosswind. The deflection of the plume squeezes the effective outlet cross section, results in a stagnation phenomenon, and reflects to the upstream flow field. Consequently, the FLFs of the whole flow field are intensified, as shown in Fig. 4.

It can be found from Fig. 11(a) that the induced mainstream vortex is clockwise (seen from the top), and the symmetric one (not shown) must be anticlockwise. As a result, the upward mainstream is first separated into two parts inside the tower chimney, with the tangential velocity at the interface of the two vortices the same as the crosswind at the outlet. Then, the upward plume is transferred into two small swirling plumes with a relatively low stiffness, which is easy to be deflected by the upcoming outlet crosswind.

Experimental validation of ventilation rate

The ventilation rates of the outlet-model and the baseline case are measured in bench scale under different tunnel crosswind conditions, whose dimensionless results in comparison with numerical results are shown in Fig. 12. It can be seen that as the tunnel crosswind increases, the ventilation rate of the baseline NDDCT model decreases gradually, which is consistent with the simulation result shown in Fig. 10. Besides, although the experimental ventilation rates of the outlet-model are generally less than the corresponding numerical results, with an average error of about 9%, they do not decline as the increase of the crosswind either. This means that the ventilation rate of a NDDCT could not be degraded by the crosswind through the tower outlet. This result at least validates the conclusion that the crosswind degrades the performance of a NDDCT mainly by influencing the inlet flow field.

Conclusions

As the crosswind affects a NDDCT in a very complicated way, while the basic affecting mechanism is not clear investigated previously, attempts have been made to improve the cooling performance of a NDDCT at the presence of crosswind based on limited experiences. Based on CFD simulation, an inlet-model (crosswind affecting the inlet area separately) and an outlet-model (crosswind affecting the outlet area separately) are proposed to study the affecting mechanism of crosswind on a NDDCT in a decoupled way. By adopting a FLF, the affecting process of crosswind on a NDDCT is analyzed quantitatively. Consequently, the basic affecting mechanism of crosswind on a NDDCT is identified as follows.

The crosswind changes the flow field at the inlet area, inducing two symmetric mainstream vortices at the bottom of the tower. As the vortices move along the streamline, the FLFs are increased. When the vortices rise to the outlet of the tower, the plume is split up into two symmetric ones, and further deflected by the upcoming crosswind. At a crosswind below approximately 10 m/s, the deflected plume contracts the flow area, which reflects to the upstream flow field, resulting in an overall increment of FLFs, and an obvious reduction of the NDDCT ventilation rate, while as the crosswind increases to above approximately 10 m/s, a significant low pressure area is produced, which greatly decreases the FLF at the outlet area, and reduces the increment of other FLFs, hence, the decrement of the NDDCT ventilation rate is weakened to some extent.

The above basic affecting mechanism is validated by a wind tunnel experiment. Based on these results, more effective performance enhancement approaches of a NDDCT in crosswind are supposed to be designed in the future.

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