Effect of guide wall on the potential of a solar chimney power plant

Renewable Energy 96 (2016) 209e219

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Renewable Energy journal homepage: www.elsevier.com/locate/renene

Effect of guide wall on the potential of a solar chimney power plant Siyang Hu a, Dennis Y.C. Leung a, *, Michael Z.Q. Chen a, John C.Y. Chan b a b

Department of Mechanical Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong, China Locision Technology Limited, Thrive United IFC, Shilong South Road, Foshan, Guangdong 528200, China

a r t i c l e i n f o

a b s t r a c t

Article history: Received 27 October 2015 Received in revised form 16 March 2016 Accepted 19 April 2016

A solar chimney power plant (SCPP) converts solar thermal energy into electricity by generating a buoyant flow in a chimney. To assist the air flow in shifting its direction from horizontal to vertical, a guide wall (GW) is usually set in the collector-to-chimney transition region. The primary objective of this study is to examine the impact of the GW geometry on the power output of a SCPP. A reduction in mass flow rate after adding a GW in the system was observed in a small-scale experimental prototype. Numerical simulations on a large-scale SCPP further found that the mass flow rate was linearly and inversely proportional to the increase of GW height. The driving force, however, nonlinearly increased with increasing the GW height. Subsequently, the potential maximum power output, which was mainly governed by the driving force, increased with increasing the GW height. Furthermore, a divergentchimney system which can improve the performance of SCPPs had different reactions with the geometry of GWs compared with a cylindrical-chimney system. Under the optimal GW configuration, the power output of the SCPP increased by ~40% in a cylindrical-chimney system and by ~9.0% in a divergentchimney system with respect to the system without a guide wall. © 2016 Elsevier Ltd. All rights reserved.

Keywords: Solar chimney power plant Guide wall Power output CFD Small-scale prototype

1. Introduction A solar chimney power plant (SCPP) is a system that converts solar energy into electricity with a chimney, a greenhouse-like solar insolation collector and a wind turbine. The system utilizes the greenhouse effect in the collector to generate a buoyant updraft in the chimney which can drive wind turbines for electricity generation. SCPP has advantages in its low cost of construction and operation, and providing renewable energy to communities without aggravating environmental pollution and intensifying climate change. SCPP is believed to have a high application potential in developing countries with large available lands and abundant solar insolation [1]. Studying the impact of different components in a solar chimney is a primary task for designing a solar chimney power plant. Haaf et al. [2,3] indicated that the critical roles of chimney height and air temperature in determining the system power output. Pasumarthi et al. [4,5] established a mathematical model for estimating the heat transferring process and the air flow in a SCPP. They reported

* Corresponding author. Department of Mechanical Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong, China. E-mail address: [email protected] (D.Y.C. Leung). http://dx.doi.org/10.1016/j.renene.2016.04.040 0960-1481/© 2016 Elsevier Ltd. All rights reserved.

that system efficiency of the SCPP was determined by the chimney height as well as the solar insolation. Dos S. Bernardes et al. [6] presented an analysis of a solar chimney under natural laminar convection condition and emphasized the effects of geometric characteristics on the performance of the SCPP. Dai et al. [7] reported that the increasing trend of system performance along the modification in dimensions should be faster in small-scale systems than that in large-scale systems. Pretorices [8] revealed that the collector diameter can also determine the power output of a SCPP and optimized the structure of collector with a multiple-layer roof. Shahreza et al. [9] reported an innovative SCPP in which an air tank coupled with two intensifiers replaced the collector and successfully enlarged the heat flux to the working air. Nia et al. [10] introduced the passive flow control approach by locating a set of obstacles at the ground surface for adjusting the heat transfer process in the thermal collector. A theoretical model established by Ming et al. [11] comprehensively considered the impact of different parameters (i.e. collector diameter, chimney height, solar radiation and other ambient conditions) on the system's power output. Koonsrisuk et al. [12,13] extended a mathematical model for a new SCPP with slope-collector and investigated the impact of flow area changes in both the collector and the chimney on the system's potential. The later study found a remarkable enhancement in the potential of SCPP with divergent chimneys (as shown in Fig. 1). Von

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Fig. 1. A schematic of solar chimney (assembled with a cylindrical or a divergent chimney) with a guide wall subset (in shadow) located at the chimney entrance and holding the blades of a turbine.

Backstrom [14] implied that a diffusor-like flow channel for the updraft would lower the kinetic energy loss and thus improve the system power output. OKada et al. [15] reported a similar improvement in a small-scale divergent chimney prototype. Patel [16] examined multiple opening angles of divergent chimney and found that the power output cannot be enlarged infinitely with increasing wall angles. On the other hand, Ming et al. [17] presented a negative attitude towards the divergent chimneys, arguing that although there would be slight improvement, the additional difficulties and cost in construction of the divergent chimneys do not justify its contribution as compared with conventional cylindrical chimneys. The guide wall (GW) is another prominent subset located at the collector-to-chimney transition region as it can be used to shift the horizontal air flow to the updraft and be the holder of a turbine for power generation (as shown in Fig. 1). Several previous studies have reported this subset would have influence on the SCPP's performance. Dos S. Bernarders [6] emphasized the care for designing the collector-to-chimney region after examining the flow with and without a guide wall or a curved junction. Inlet guide vanes (IGVs) and guide wall were all built but less attention was paid to the later component in the experiments conducted by Van Backstorm et al. [18]. Ming et al. [11] compared the flow in the collector-to-chimney domain before and after adding a guide wall subset and found that the subset was capable of modifying the velocity of the flow with ~18% which might significantly improve the potential of the SCPP. However, there was only one configuration of the GW examined in their study. Hence, the knowledge on the impact of the GW geometry on system performance is still limited. Considering that the presence of GWs may have significant impact on SCPP's performance but evaluation of this issue is superficial and ambiguous, this study aimed to investigate on the role of GW in a SCPP more comprehensively through examining the flow under the influence of GWs with variant heights and radii. This can help us better understand the characteristics of the local flow in the collector-to-chimney transition domain with GWs. For these purposes, this study was mainly conducted by numerical simulation approach, while a small-scale experimental prototype was used to verify the mass flow rate degradation observed in simulations. Furthermore, a remarkable improvement in the flow velocity in divergent chimneys was reported in several articles. Thus, both

the groups of a cylindrical chimney and a divergent chimney coupled with different GWs will be studied as different reactions from the divergent-chimney SCPP compared with the cylindrical one with varying GW configurations would be expected. 2. Methodology 2.1. Experiments in a small-scale prototype A small-scale prototype of the SCPP was built in the laboratory for investigating the chimney shape impact on the performance of the SCPP (as shown in Fig. 2). A moveable guide wall was added into the prototype initially aimed for reducing the loss caused by the flow direction shifting. As more than suppressing the loss, the guide wall may have further contribution in improving the system potential as reported by Ming et al. [11], the moveable wall provided chances to examine preliminarily the variation in the buoyant flow caused by the GW subset: one additional group of experiments without the GW was conducted for the small-scale prototype and compared with the earlier experiments with the GW. The following sections presented a brief introduction on the configurations of the experiments. More details can be found elsewhere. 2.1.1. Geometry of prototype The small-scale prototype consisted of two fundamental components of a SCPP, that is, the collector and the chimney. A transparent chamber of 3 m (L) x 3 m (W) x 0.1 m (H) composed of steel frames and organic glass, was used as the thermal collector. Two types of chimney, made in PVC material, were used. The two chimneys were all 2 m high and 0.1 m in their entrance diameter while the exit diameter of the divergent chimney was set to 0.2 m. As to the heat source, we utilized an electrical infra-radiation film heater instead of direct solar radiation in the prototype in order to keep the input heat consistent for different cases. The film heater, with a fixed total power of 1520 W, overlaid the bottom of the collector and covered by several thin aluminum sheets for producing a more uniform heating surface. The moveable GW, placed below the chimney entrance, was 0.15 m high and 0.4 m in its base width. 2.1.2. Data measurement Two parameters, that is, the air temperature and the flow

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Fig. 2. The small-scale prototype (left) and the collector-to-chimney transition section with a white solid guide wall subset (right).

velocity inside the chimneys, were monitored during the smallscale experiments. The temperature was measured by a group of LM35 precision centigrade temperature sensors distributed along the chimney from the entrance to the exit. The resolution of LM35 sensors was further improved to 0.1 K by modifying the reference voltage in the connected Arduino microcontroller. The chimney entrance was 25 cm above the ground, where the velocity was usually at the maximum in the prototype. The maximum velocity is one critical index for evaluating the performance of a SCPP [2,11,19]. However, in the pre-tests, a sampling point was set at the chimney entrance that experienced large fluctuations in the hot-film anemometer measurement which lowered the reliability of the data. Thus, the velocity measured in the chimney was the transient updraft velocity at the section center which was 15 cm above the chimney entrance instead of the chimney entrance to avoid unstable velocity records by the sensors. The hot-film anemometer can provide a resolution of velocity in 0.1 m/s within 1.5% error in the measurement. All of the analog signals from the temperature and velocity sensors were recorded by an Arduino microcontroller with a sampling interval of 5 s. As the turbulent flow in the chimneys was fully developed, the measured velocity should represent the typical flow speed at the sections. With the recorded temperature of air mass, the observed velocity was further converted into the mass flow rate in the system and the calculated mass flow rate was used in the later discussion. 2.2. Numerical simulation of a full-scale SCPP Numerical simulation is capable of providing convenience for examining multiple structures of the SCPP which was the primary approach to evaluating the geometric impact of GW on system performance. 2.2.1. Physical model As Manzanares Power Plant is the only existing large-scale SCPP in the world, the simulated solar chimney was based on its dimensions. Detailed geometry of the physical model can be found in Table 1. Similar to the chimneys in the small-scale experiments, the divergent chimney in the numerical model had the same entrance radius to the cylindrical one whereas the radius at the exit end was 2 times of that at the entrance. Previous studies [13,16] indicated that the divergent chimney with an area ratio (the area of exit vs. the area of entrance) of 4 could be capable of generating an updraft with 2 times faster compared with that in the cylindrical chimney, which should be sufficient for demonstrating the different reactions between the divergent and the cylindrical systems. Unfortunately, there were few articles describing detailed configurations of the centerpiece part, that is, the GW, at the collectorto-chimney transition section in which we are interested. The

Table 1 Critical geometry of the physical model. Parameter

Value

Collector radius Collector roof height Soil layer depth Chimney height Chimney entrance radius Chimney entrance height Cylindrical chimney outlet radius Divergent chimney outlet radius Guide wall height Guide wall (base) radius Guide wall top radius

122 m 1.8 m 5.0 m 195 m 5.0 m 10.0 m 5.0 m 10.0 m 4.0, 6.0, 8.0, 10.0, 12.0 m 2.8, 5.4, 8.0, 10.6, 13.2 m 1.6 m

simulation research conducted by Pastohr et al. [20] included a GW subset that was 10 m high and 13.2 m in the base radius. GWs were used in other studies as well but there was little description of its dimensions [21e23]. Basic dimensions of the GWs examined in this study were mainly referred to the physical model reported by Pastohr et al. [20] and determined by the height and the base radius (as shown in Fig. 3 and Table 1). For investigating the impact of GW height, the height varied from 2 m to 12 m in an interval of 2 m with a fixed radius of 13.2 m; and for studying the impact of radius, the radius increased from 2.8 m to 13.2 m in an interval of 2.6 m while the height remained at 10 m. The 3.2 m-wide circular platform at the top of the GW was preserved and remained constant considering its role for holding the blades and the dome of a huge vertical-axial wind turbine. It is noted that the profile of the GW surface was equivalent to one quarter of an ellipse determined by the height and the radius of the GWs. The configurations without GWs were also simulated and used as the benchmark cases for highlighting the relative variation in the system potential. For identifying different configurations, each configuration was labeled as GW-HxRy in the following sections: ‘GW’ stands for ‘Guide Wall’, ‘Hx’ stands for the guide wall height in ‘x’ meters and ‘Ry’ for the guide wall base radius in ‘y’ meters. 2.2.2. Mathematical model Governing equations of a fluid flow are fundamentally obeying the principles of momentum conservation, energy conservation and mass continuity. However, these equations need further adjustment according to the characteristics of a particular flow state in order to be more computable and achieve the numerical results from the computational fluid dynamics (CFD) programme. It is widely agreed that the buoyant flow in SCPP is highly turbulent [20,24e26]. Thus, the equations of the conservation of momentum, energy and mass were adjusted into Reynolds Averaged Navier-

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Fig. 3. Configurations of GW utilized in the numerical simulation of Section 3.2. Inset diagram at the top-left is the configuration without GW.

Stokes (RANS) form and coupled with the standard k-ε model for dealing with the turbulence in its flow domain. Simultaneously, an axisymmetric and steady-state flow in a SCPP was assumed in our simulation for saving computational resource and time. Subsequently, the governing equations in our mathematical model are as follows: Continuity equation

vðruÞ vðrvÞ þ ¼0 vx vy

(1)

Navier-Stokes equation

vðruuÞ vðruvÞ v2 u v2 u þ ¼ rgbðT  T∞ Þ þ m þ vx vy vx2 vy2 vðrvuÞ vðrvvÞ vp v2 v v2 v þ ¼ þm þ vx vy vy vx2 vy2

! (2)

! (3)

Energy conservation equation

!     v ruCp T v rvCp T v2 T v2 T þ ¼l þ vx vy vx2 vy2

(4)

k-ε model

vðrkui Þ v ¼ vxi vxj vðrεui Þ v ¼ vxi vxj







!

m vk mþ t þ Gk þ Gb  εr þ Sk sk vxj

mþ



(5)

pffiffiffiffiffiffiffiffiffiffiffi m_ Pout ¼ x$ 1  x$ht $Dp$

r0

!

mt vε ε2 þ C1ε ðGk þ C3ε Gb Þ  C2ε r þ Sε sε vxj k (6)

The variation of air density due to the heating process was calculated by using the Boussinesq Approximation that only considered the buoyant impact in the body force term in the Navier-Stokes equation [20]:

r ¼ r0  r0 bðT  T0 Þ

2.2.3. Boundary conditions Rationality of boundary conditions is important to ensure the validity of the numerical simulations. Referring to the previous studies [20,24e26], the boundary conditions adapted in our model were as follows: (1) at the surface of the collector roof, thermal convection and radiation emission between the roof and the ambient were taken into consideration by using a ‘mixing’ condition; (2) solar insolation input was converted into a heat source within a 0.1 mm-thin layer below the ground surface with a heat generation rate of 720 W/m2 assuming the total solar insolation, the transmissivity of the roof and the absorption of the ground were 1000 W/m2, 0.9 and 0.8, respectively [20,21,26]; (3) the bottom of the solid ground was set to a constant-temperature surface according to the experimental results in Manzanares [3] while the lateral sides of the ground layer were assumed to be adiabatic; (4) the adiabatic condition was also implemented for other solid boundaries in the model; (5) the entrance of collector and the exit of chimney were set to pressure-inlet and pressure-outlet conditions and were at zero pressure. The turbine is shielded by the chimney shell in a SCPP which makes it different from conventional wind turbines. The velocity of air flow remains constant but the static pressure declines after passing through the blades. Therefore, the static pressure, instead of the kinetic energy, is converted into the shaft work. The pressure drop was calculated by an anti-fan model with discrete values in previous studies [17,26,27]. However, it is difficult to use this method in our study due to the multiple cases with different configurations of the GW. Instead, we utilized a mathematical model to calculate the potential power output of the system as follows [19]:

(7)

The mathematical model mentioned above was solved by the commercial CFD software, ANSYS FLUENT 14.0.

(8)

The maximum extractable power output of the system can be obtained by making x equal to 2/3 [19]. Meanwhile, the electricity conversion coefficient of turbine, ht , was set to 80% in this study. The driving force of the whole system, Dp, was quantitatively equal to the absolute value of the area-weighted averaged gauge pressure at the chimney entrance acquired from the numerical outcomes. 2.2.4. Solution methods and validity The flow domain and the soil layer in the simulated solar chimney were divided into a structured grid that was further refined in the near wall regions for dealing with the rapid changes in the parameters appearing in these regions. The second-order

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scheme was implemented for the discretization of the pressure term and other terms, that is, momentum, energy, turbulent dissipation and kinetic energy terms, were discretized by the second-order upwind scheme for suppressing the numerical diffusion error. The SIMPLE algorithm was applied to solve the pressure-velocity couple in the governing equations with the relevant boundary conditions mentioned above. The calculation residuals were kept below 106 in all the monitored terms but 109 in the energy term. Grid independence study was conducted for confirming that the numerical results were reliable and independent of the grid size. Given the solar radiation in 1000 W/m2, the ambient temperature in 302 K and other boundary conditions shown in Table 2, the case of GW-H10R13.2 ought to be fairly close to the scenario of the SCPP in Manzanares. Thus, the result from the GW-H10R13.2 case was first used to evaluate the validity of our numerical model. The calculated velocity was 16.4 m/s, which is 7.4% higher than the measurement (~15 m/s) due to the overestimation of the air temperature rise, △T (21.8 K V.S. 20 K). Pastohr et al. [22] revealed that the solid ground with heat generation rate in the steady simulation could overestimate the surface temperature of the ground. That should further provide contribution to the error in calculating the air temperature as well as in the updraft velocity. Besides, the uncertainties in the soil properties and the adiabatic assumption at the solid boundaries may contribute to the overestimation as well. Thus, the accuracy of our model was still acceptable for the subsequent study. On the other hand, the normalization analysis was also implemented during the comparison to minimize the inherent errors. 3. Results and discussion 3.1. Results from the small-scale experiments Based on the temperature and velocity measurement, the temperature difference between the chimney entrance and the ambient, △T, and the mass flow rate were calculated and further averaged over the last 3600 s in each case during which the flow was stable. The statistics of the time serials of △T and mass flow rate were shown in Fig. 4. Changes in the mass flow rate were observed after adding the GW in the prototype. Within 18.0 K ± 1.0 K, the mass flow rate in the divergent-chimney system without the GW (~0.024 kg/s) was ~9.0% higher than that with the GW (~0.022 kg/s). The fitting results demonstrated the difference in mass flow rate between the zero-GW and GW group as well. However, the difference was relatively weaker in the cylindricalchimney group as shown by the curves. It is noted that the GW subset is proposed to suppress the loss caused by the shift of air flow direction at the collector-to-chimney transition section. By this, we initially supposed that the mass flow rate in the system were meant to increase with the existence of GWs. However, the experimental outcomes were opposite to our expectation. Furthermore, the drop in mass flow rate was also observed in numerical simulations which would be discussed in the

213

Fig. 4. Averaged △T and mass flow rate in the small-scale (a) cylindrical-chimney and (b) divergent-chimney system with and without the GW. Dashed curves are the fitting results. The bars indicate the relevant deviation.

following sections. Nevertheless, it is premature to state that GWs might lower the potential of a SCPP as the potential power output is determined by the mass flow rate as well as the driving force of SCPP as shown in Eqn. (8). However, we did not measure the pressure in the small-scale prototype as the pressure variation was too small to detect by the sensors we used. This is one of the reasons why subsequent numerical study was conducted for acquiring more detailed information in the flow domain. On the other hand, more configurations of the GW geometry were examined in the numerical study which could further distinguish the difference in impacts between the GW height and radius. 3.2. Results from the numerical simulation 3.2.1. Effect of the GW height The effect of GW height was discussed with a set of GWs with heights from 4 m to 12 m and an invariant GW radius (as shown in Fig. 3). Table 3 showed the effect of GW heights on different parameters (mass flow rate, temperature and power output). The air temperature at the chimney entrance section showed little changes when the guide wall height increased from 0 to 12 m. The temperature reached the peak when the height was 8 m in both the cylindrical-chimney and divergent-chimney group but the variations were fairly small, þ0.5 K in the cylindrical group and þ1.1 K in the divergent group as compared with the zero GW case. The relatively higher temperature underneath the solar collector of the

Table 2 Boundary conditions of numerical simulation. Surface

Type

Value

Collector roof Soil layer bottom Soil lateral boundaries Chimney shell Guide wall surface Ground Inlet of collector Outlet of chimney

Wall Wall Wall Wall Wall Wall Pressure-inlet Pressure-outlet

Mixed; Text ¼ 302 K, hs ¼ 10 W/m2K, εext ¼ 0.89 T ¼ 302 K Adiabatic Adiabatic free-slip Adiabatic free-slip Coupled; Q ¼ 7200 kW/m3; Dthickness ¼ 0.0001 m Text ¼ 302 K, pgauge ¼ 0 Pa Text ¼ 300 K, pgauge ¼ 0 Pa

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Table 3 Variations in the potential of the system along GW height. Chimney shape

Parameter

GW-H0

GW-H4

GW-H6

GW-H8

GW-H10

GW-H12

Cylindrical chimney

Ta (K) Mass flow rate (kg/s) Driving forcea (Pa) Power output (kW)

323.7 1403.7 131.9 50.5

323.7 1403.8 131.8 50.5

323.8 1402.7 132.6 50.8

324.2 1399.5 146.4 56.0

323.8 1394.8 163.4 62.2

323.9 1389.3 172.6 65.5

Divergent chimney

Ta (K) Mass flow rate (kg/s) Driving forcea (Pa) Power output (kW)

313.1 2881.1 577.2 440.2

313.2 2880.1 576.8 439.8

313.3 2857.5 572.3 433.1

314.2 2806.3 611.9 456.0

313.7 2732.4 646.0 468.0

314.1 2650.5 646.8 455.0

a

The area-weighted average values at the chimney entrance section.

SCPP fundamentally lowers the air density and hence causes the negative pressure near the chimney bottom, which is regarded as the driving force of the air flow in a SCPP [2,5,11]. The slight difference in air temperature should induce consistency in the driving force. However, there were significant changes in the driving force

with the modification of GW height as shown in Table 3. For instance, GWs higher than 8 m enlarged the driving force by 10e30% with respect to the case of zero GW in the cylindrical group. In the divergent-chimney group, GW-H4 and -H6 slightly diminished the driving force whereas the driving force increased by

Fig. 5. Contours of the pressure and the velocity in four cylindrical-chimney system cases: (a) zero GW; (b) GW-H4R13.2; (c) GW-H8R13.2; (d) GW-H12R13.2. Results under other configurations (including the divergent-chimney system cases) were similar to those above and thus not shown here.

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34.7 Pa (6.0%), 68.8 Pa (11.9%), 69.6 Pa (12.1%) with the 8 m-, 10 mand 12 m-high walls. The contours of pressure (as shown in Fig. 5) also indicated the increasing tendency of the driving force through the extending negative gauge pressure region and denser contours induced by the increasing GW height. Fig. 5 also illustrated the contours of the velocity in the collector-to-chimney transition region. The variation in the velocity caused by the modification in GW height was in line with the changes in the driving force. Besides, the contours of the velocity and the pressure both showed that for the case of zero GW there was a confluence region below the chimney entrance inducing a negative velocity gradient against the main flow direction. After adding the GWs, the confluence was effectively suppressed but still existed in the case of GW-H4. Keep heightening the GW finally eliminated the negative gradient. In contrast, a reduction in the mass flow rate was found with increasing the GW height as shown in Table 3. In the cylindrical group, the mass flow rate in the system with the highest GW was

215

just ~1% less than that in the zero GW case while the drop was more distinct in the divergent group, which reached 24e231 kg/s, corresponded to 1%e8% less than the zero GW configuration. This result was verified by the small-scale experiments, in which a more evident decline in mass flow rate was found in the divergentchimney group. The maximum extractable power output of a SCPP is the product of the driving force and the mass flow rate as indicated by Eqn. (8). The mass flow rate varied a little in the cylindrical group with different GW heights, thus the potential of the system was mainly improved by the increased driving force. The cases GW-H8, -H10 and -H12 improved the power output by 6 kW (10.8%), 12 kW (23.1%) and 15 kW (29.8%), respectively. As to the divergent group, the power output of GW-H4 and -H6 was lower than the GW-H0 case due to the decline in both of the mass flow rate and the driving force. Even the driving force was enlarged under the cases GW-H8 to -H12 configuration, the lower mass flow rate restricted the improvement in the power output. Consequently, the peak

Fig. 6. Contours of the pressure and the velocity in four divergent-chimney system cases: (a) zero GW; (b) GW-H4R13.2; (c) GW-H8R13.2; (d) GW-H12R13.2. Results under other configurations (including the cylindrical-chimney system cases) were similar to those above and thus not shown here.

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Table 4 Variations in the potential of the system along GW radius. Chimney shape

Parameter

GW-H0

GW-H4

GW-H6

GW-H8

GW-H10

GW-H12

Cylindrical chimney

Ta (K) Mass flow rate (kg/s) Driving forcea (Pa) Power output (kW)

323.7 1403.7 131.9 50.5

323.7 1403.8 162.2 50.5

323.8 1402.7 162.4 50.8

324.2 1399.5 162.6 56.0

323.8 1394.8 162.9 62.2

323.9 1389.3 163.4 65.5

Divergent chimney

Ta (K) Mass flow rate (kg/s) Driving forcea (Pa) Power output (kW)

313.1 2881.1 577.2 440.2

313.2 2880.1 642.7 439.8

313.3 2857.5 645.6 433.1

314.2 2806.3 649.7 456.0

313.7 2732.4 652.3 468.0

314.1 2650.5 646.0 455.0

a

The area-weighted average values at the chimney entrance section.

power output acquired in the divergent-chimney group was only 6.7% higher than the case GW-H0. 3.2.2. Effect of the GW radius The effect of GW radius was analyzed with a set of GWs with the radii of 2.6 me13.2 m and an invariant GW height (as shown in Fig. 3). Fig. 6 illustrated that the decay of the negative velocity gradient can be obviously identified when the radius varied from 2.8 m to 13.2 m. Nevertheless, the pressure and the velocity distribution near the chimney entrance were barely changed with different radii in both the cylindrical- (not shown here) and the

divergent-chimney system. Table 4 further indicated the effect of varying radii on different parameters. The temperature was nearly invariant with radius in both group. Meanwhile, the mass flow rate, the driving force and the power output showed obvious differences before and after adding the GWs. Values of the parameters in the cases of GW-R2.8 to -R10.6 were all very close to those in GW-(H10) R13.2 which has been discussed in Section 3.2.1. Thus, it can be inferred that the variation should be caused by the height of GWs not by the radius. In other words, the impact from GWs radius on the potential of SCPP was much weaker than the height effect. In addition to that, the tendency in the driving force and the

Fig. 7. Variations in the normalized potentials of the cylindrical-chimney SCPP with different height-and-radius couples and the fitting results: (a) mass flow rate; (b) driving force; (c) power output.

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power output with varying GW radius in the divergent-chimney system differed from that in the cylindrical-chimney system. Instead of the continuously increasing regularity in the cylindrical chimney, the performance of the divergent-chimney system started to drop when the radius exceeded 10.6 m.

3.2.3. Discussion on the variations in system potential According to the conservation of mass, the reduction in crosssection area of the flow channels can lead to an acceleration of the air. Thus, the enhancement in the driving force and the velocity could be attributed to the fact that the presence of GWs narrows the flow channel at the collector-to-chimney transition section. Nonetheless, the blockage of the GWs conversely decreased the effective volume of the system for the air flow. Therefore, the mass flow rate in the SCPP with GWs decreased in both the small-scale experiments and full-scale numerical simulation. On the other hand, the turbulence caused by the blockage of GWs and the backward-facing step flow after the top of GWs might induce an additional energy loss and then lower the mass flow rate. By this, it is easy to explain why the reduction in the mass flow rate was more distinguished in the divergent group: as the divergent chimneys dramatically increased the velocity in the system, the turbulence in the system should be correspondingly stronger than

217

that in the cylindrical chimney. Figs. 5 and 6 also illustrated that the contours of pressure and velocity were almost uniform before the end of the collector and away from the chimney entrance even the GW was varied. In other words, the GWs were only capable of adjusting the local flow field, especially the flow in the collector-to-chimney transition region, which was consistent to the study of Ming et al. [11].

3.3. Optimization of the height-and-radius couple An interesting phenomenon arose in the previous discussions: there were opposite tendencies in the mass flow rate and the driving force when the GW configuration was varied. Meanwhile, the quantitative variation of the two parameters were different as well. These results motivated us to conduct a subsequent numerical study for optimizing the height-and-radius couple of the GWs. The optimization was based on the configurations utilized in the last sections. The 5 alternations in the wall height were separately coupled with the 5 alternations in the radius which produced 25 pairs of configuration of the GW in consequence. Meanwhile, the optimal GW configuration was separately discussed in the cylindrical- and the divergent-chimney system as the previous discussions indicated the buoyant flow under the two chimney

Fig. 8. Variations in the normalized potentials of the divergent-chimney SCPP with different height-and-radius couples and the fitting results: (a) mass flow rate; (b) driving force; (c) power output.

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Table 5 Curve fitting in the cylindrical-chimney group and the prediction of optimal geometry. Curve equation

A B C D R2 Optimal height Optimal normalized output

y ¼ A þ Bx þ Cx2 þ Dx3 R2.8

R5.4

R8.0

R10.6

R13.2

1.7454 0.3636 0.0537 0.0023 0.9931 11.5 m 1.267

1.2536 0.1260 0.0175 0.0005 0.9776 12.0 m 1.382

1.6479 0.3194 0.0470 0.0019 0.9987 11.5 m 1.265

1.6230 0.3051 0.0444 0.0018 0.9996 11.8 m 1.281

1.5943 0.2886 0.0415 0.0016 1.0000 12.0 m 1.289

configurations showed different reactions to the geometry of GWs. The cylindrical- and the divergent-chimney cases without the GW were still used as the benchmark scenario for normalization analysis. The numerical outcomes with multiple height-and-radius couples of GW firstly revealed a more universal regularity in the impact of GW geometry based on the previous discussions. Although there was strong effect imposed by the GW heights coupling with the radius of 13.2 m as discussed in Section 3.2.1, the result would be valid under other scenarios as the variations in simulated results are insensitive to the GW radius as shown in Figs. 7 and 8. The mass flow rate generally had a linear relationship with increasing GW height as indicated by the lines in Figs. 7(a) and 8(a) except the dramatic reduction when the radius was 5.4 m. As the absolute changes in the driving force was larger than those in the mass flow rate, the potential power output tended to be governed by the regularity in the driving force (as shown in Figs. 7(b,c) and 8(b,c)). Furthermore, the impact of the GW height on both the driving force and the power output can be generally described by 3rd-order curve functions. The radius impact should be generally much slighter than the height as the neighboring points in the same column indicated the impact from radii should be negligible (<1%) under all of the height values. However, there were still some features that needed attention. The radius impact could be a little stronger in the divergent-chimney system considering the wider distance between the fitted curves with respect to the cylindrical-chimney system. In addition to that, the cluster of the curves tended to be divergent indicating the difference caused by the GW radius became more distinct when the wall height was approaching 12 m in both the cylindrical and the divergent group. Notably, an exception against the general regularity of the 3rdorder curve functions could be found in the cylindrical-chimney system. The cylindrical cases with R5.4 had a factor of the 3rd-order term in the function that was approximated to zero (shown in Table 5). Thus, the curves with R5.4 was unique compared with the others and approximately parabolic indicating an unbounded increase in the power output. Even so, it needs additional caution in practical design considering the infeasibility of infinitely heightening the GWs. Fig. 9 illustrated the variations of the system performance along the slenderness, that is, height/radius ratio, of the 25 GW cases. Given a certain H/R ratio, say 0.75, changes of the power output, in relative to the zero GW cases, distributed in a wide range: 0.5e23% in the cylindrical-chimney group; and 1.8e6.5% in the divergentchimney group. Meanwhile, the system performance did not show any significant tendency along the range of H/R ratio. Hence, it should be difficult to discuss the optimal geometry of GW with the non-dimensional parameter, namely its slenderness. Notably, with the GW in the slenderness of 0.75, the decrease of the mass flow rate in the small-scale experiment was comparable to the numerical simulation in the divergent-chimney group (as shown in the red solid point in Fig. 9(b)), which verified the numerical result of

the drop of the mass flow rate in the system. However, the temperature difference among the cylindrical-chimney cases was too large for comparison. The discrete points in Figs. 7(c) and 8(c) preliminarily indicated the geometry of that GW that induced a better performance: for the cylindrical-chimney system, the case GW-H12R5.4 might provide the higher power output and the case GW-H10R10.6 was the outstanding configuration for the divergent-chimney system. However, the limitation in the discrete values of the height and the radius made it possible to miss the optimal geometry. Thus, the fitted curve functions were further utilized for the optimization of the GW geometry in the Manzanares Power Plant. Considering the impact from the GW radius was much weaker than the height, the fitted equations considered the GW height as the only independent variable while the values of radius were still discrete. The optimal height was acquired from each fitted equation with the 5 radii values first. After that, we picked up the peak power output in the 5 equations and the corresponding height and radius constituted the optimal height-and-radius couple of GW. As shown in Tables 5 and 6, for the divergent-chimney system, the optimal GW geometry should be H10.5R10.6, which would provide the optimal potential power output of ~480 kW, which was ~9% higher than the case of zero GW. In response to the unbounded and continuous increasing tendency in the cylindrical cases with R5.4, the optimal solution of the geometry should still be the case GWH12R5.4 being able to provide ~70 kW power output, which was ~40% higher than the benchmark case.

Fig. 9. Normalized potentials with different slenderness of GWs: (a) cylindrical chimneys and (b) divergent chimneys.

S. Hu et al. / Renewable Energy 96 (2016) 209e219

219

Table 6 Curve fitting in the divergent-chimney group and the prediction of optimal geometry. Curve equation

A B C D R2 Optimal height Optimal normalized output

y ¼ A þ Bx þ Cx2 þ Dx3 R2.8

R5.4

R8.0

R10.6

R13.2

1.4648 0.2291 0.0335 0.0015 0.7832 10.2 m 1.073

1.5966 0.2942 0.0436 0.0012 0.9599 9.7 m 1.064

1.4420 0.2151 0.0313 0.0013 0.9117 10.5 m 1.084

1.4516 0.2171 0.0315 0.0013 0.9338 10.5 m 1.089

1.4302 0.2073 0.0230 0.0013 0.9485 10.3 m 1.066

4. Conclusions

References

In this study, we have examined the effect of the geometry of GWs on the performance of a SCPP through experiments on a small-scale prototype and numerical simulations with 25 configurations of the GW in full-scale dimension. A reduction in mass flow rate was found in the small-scale experiments as well as the numerical outcomes after adding GWs into the system, which approximately had a linear relationship with the GW height but was almost independent of the GW radius. On the other hand, the driving force and the velocity at the chimney entrance were significantly improved by the presence of a GW in both the cylindrical-chimney and the divergent-chimney system but the improvement was mainly affected by the GW height. Simultaneously, a nonlinear relationship between the driving force and the GW height was obtained in the numerical simulation. As to the GW radius, its impact on the system performance was small but became a little higher when the wall height was close to 12 m. As the potential power output was mainly governed by the driving force, the improvement in the power output was fairly similar to the tendency in the driving force enhancement. These results suggested that the height should be an important criterion in the selection of GW geometry, which would be helpful in a practical plant design. As expected, the divergent-chimney system showed different reactions to the geometry of GWs compared with the cylindrical-chimney system. The different reactions also implied that the impact of the GWs on the divergent-chimney system may be sensitive to the configuration (e.g. area ratio) of the divergent chimneys, which requires subsequent studies. An extended investigation was conducted for the purpose of optimizing the geometry of the GW under the scenario of the SCPP in Manzanares after we found that the mass flow rate and the driving force should have qualitative and quantitative differences in their variations induced by the GWs. With the fitted equations of the height-power curves, the optimal height-and-radius couple of the GW was GW-H12R5.4 for the cylindrical-chimney system that could obtain ~40% more in power output; and was GW-H10.5R10.6 for the divergent-chimney system that could acquire ~9% more in power output than the cases with zero GW. Furthermore, the fitted equations, to some extents, can provide quantitative adjustment in the prediction from the conventional mathematical models of the SCPP that barely consider the impact from the local subsets on the system performance.

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Acknowledgement This project is funded by the CRCG Grant of the University of Hong Kong, the GRF Grant (HKU_17205414) of HKRGC and the “LanHai” Innovation Talent Project Grant of the Nanhai District Government, Foshan, China.