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Annual performance analysis of the solar chimney power plant in Sinkiang, China
Energy Conversion and Management 87 (2014) 392–399
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Annual performance analysis of the solar chimney power plant in Sinkiang, China Peng-hua Guo, Jing-yin Li ⇑, Yuan Wang School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an 710049, PR China
a r t i c l e
i n f o
Article history: Received 1 May 2014 Accepted 14 July 2014
Keywords: Solar chimney Power generation Sinkiang Solar radiation model
a b s t r a c t To obtain more accurate prediction of the annual performance of solar chimney power plants (SCPPs), a comprehensive theoretical model is developed by taking into account the hourly variation of solar radiation. The effects of the collector and chimney radii on the power output of the SCPP are analyzed, and the results reveal that a limitation on the maximum collector radius exists for the maximum attainable power output of the SCPP. Then four designs of 100 MW SCPPs with different combinations of collector and chimney radii are proposed and the most cost effective one is chosen from among the four SCPPs. The annual power output of the chosen SCPP in the Hami region is estimated at an interval of 1 h for a whole year. The results indicate that the power generation of SCPP presents obvious seasonal variation. Furthermore, the use of 14% of the unused land in the Hami region for the installation of SCPPs would satisfy the annual power requirement for the whole of the Sinkiang region. Ó 2014 Elsevier Ltd. All rights reserved.
1. Introduction China has become the largest emitter of greenhouse gases following the rapid increase in the usage of coal to fuel the industrial and economic boom in China. To mitigate the escalating environmental concerns, the government has prompted for 40–45% reduction in carbon emission by 2020 (compared to 2005 level). Accordingly, the new energy industry was firstly listed in the encouraged category in the Catalog of Guidance of Industrial Structural Adjustment (2011 version) issued by the National Development and Reform Commission (NDRC) of China. The initiation of an investment project in the encouraged category will enjoy several benefits, including reduction in taxation, and low interest rate for bank loans. The solar chimney power plant (SCPP), which is a relatively new technology that is in accordance with the energy policy of China, has become a hot topic of research in the field of solar engineering. The SCPP was originally conceived and designed in 1931 by the German researcher Hanns Gunther. Later on, in 1978, Professor Schlaich revisited this technology [1]. Fig. 1 shows the schematic of the SCCP. As is seen, the SCPP consists of three main components, namely, the solar collector, chimney, and turbine. In the typical operation of the SCPP, the solar collector heats up the ambient air entering the system using the solar radiation, based on the phenomenon of greenhouse effect. Following that, the heated airflow ⇑ Corresponding author. Tel.: +86 29 13152181528; fax: +86 29 82668723. E-mail address: [email protected] (J.-y. Li). http://dx.doi.org/10.1016/j.enconman.2014.07.046 0196-8904/Ó 2014 Elsevier Ltd. All rights reserved.
exits the collector and flows into the chimney. The difference in air density between inside and outside of the chimney causes pressure difference between the system and the ambient air (chimney effect). The pressure difference reaches maximum at the base of the chimney, which drives the wind turbine to generate electricity (turbine effect). In less than 4 years after the conceptualization of SCPP by Schlaich, the German government and a Spanish utility built a pilot plant in Manzanares, Spain, featuring a peak output of 50 kW. Subsequently, Haaf and his colleague conducted preliminary theoretical research and demonstrated their experimental results about this pilot plant [2,3]. Since then, various studies on the SCPP system have been published around the world [4–10]. A detailed review on this topic has been reported by Zhou et al. [11], which provides a comprehensive picture of the research and development of the SCPP technology in the past few decades. As an eco-friendly energy technology, the SCPP offers the following advantages: (1) Compared with the conventional concentrated solar thermal systems, such as parabolic trough, dish stirlings, concentrating linear Fresnel reflector, and solar power tower, which are based on the beam radiation, the SCPP can utilize both beam and diffuse solar radiation. (2) Unlike conventional thermal power plant, the SCPP does not require water for cooling the system. This is especially beneficial for use in regions that suffer from water shortage.
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Nomenclature cp f G g h M _ m n P Qv q t v Z z
specific heat capacity (J kg1 K1) friction factor solar radiation (W m2) gravitational acceleration (m s2) heat transfer coefficient (W m2 K1) air mass mass flow rate (kg s1) number power generation volume flow rate (m3 s1) heat flux (W m2) temperature (K) air velocity (m s1) altitude above sea level (m) altitude above the chimney base (m)
Greek symbols a absorptance c1 lapse rate of atmospheric air temperature (K m1) Dp pressure drop (Pa) d solar declination (°) e emissivity f loss coefficient g efficiency (%) h solar altitude angle (°) k thermal conductivity (W m1 K1) l dynamic viscosity of air (N s m2) q density of air (kg m3) s transmittance
(3) SCPP is typically constructed using concrete and glass that are readily available in sufficient quantities in most regions. In addition, the structure of SCPP is not complicated, which results in a low maintenance cost. However, the efficiency of the SCPP system is low, especially when the scale of system is small. This can be improved by increasing the size or dimensions of the system [12,13]. Hence, SCPP often demands a large area of land for constructing the collector that should be available at a low cost. Ideally, areas that are not suitable for agricultural or commercial usage are needed. The most favorable locations for SCPPs are in the arid or semi-arid desert regions, where there are abundant solar and land resources. Given these
u w x
latitude (°) longitude (°) hour angle (°)
Subscripts a ambient b beam bw bracing wheel c collector c, a collector to ambient c, s collector to sky ch chimney ch, a chimney to ambient d diffuse f airflow f, a airflow to ambient f, c airflow to collector f, ch airflow to chimney out chimney out sky sky sc solar constant t turbine/total tran transition section w ground surface w, c ground surface to collector w, f ground surface to airflow w, s ground surface to soil storage
considerations, Sinkiang is an excellent place for constructing SCPP systems in China. Thus far, some studies have reported valuable feasibility analysis for the SCPP all over the world [14–21]. However, these studies have considered the monthly or annual mean solar radiation data, rather than the hourly data, in predicting the system performance. In such case, the prediction of the annual power generation may be inaccurate, as the collector efficiency can be influenced obviously by the solar radiation. Hence to obtain more accurate performance estimation, it is necessary to consider the hourly variation of the solar radiation in the theoretical model of SCPP. The objective of this paper is to analyze the potential for the generation of electrical energy by the SCPPs at the Hami region in Sinkiang. To this end, we have established and validated theoretical models for both the solar radiation and the SCPP. Besides, we analyzed the effects of chimney and collector radii on the performance of SCPP. Finally, we designed a 100 MW SCPP and evaluated its annual performance in the Hami region by performing calculations at an interval of one hour for a whole year. 2. Geographical features of the Hami region
Fig. 1. Schematic of the solar chimney power plant.
As a typical geographical location in Sinkiang, Hami (longitude between E91°060 and E96°230 , latitude between N40°520 and N45°050 ) was chosen for this analysis. According to the twelfth ‘‘Five-Year Plan’’ of China, 50 billion yuan of RMB will be invested in the construction of a railway facility at Hami, to make it an important railway hub in the Northwest of China. Consequently, the electric power demand in this region is expected to increase rapidly. However, Hami is located in the arid and semi-arid areas, and its local ecosystem is fragile due to the extreme deficit of water. According to the statistic data presented in 2003 [22], the
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per capita water resource in this region is less than 1/6th of the world average level. The fragile local ecological environment limits the construction of conventional thermal power stations, which depend heavily on water resource. Accordingly, it is a judicious choice to effectively utilize the local renewable energy resources to generate electric power. Hami has an abundant resource of solar energy, ranking high in the list of annual global solar radiation and sunshine duration in Sinkiang. The comparison of annual solar radiation and sunshine duration between Hami and other cities of same latitude in China is presented in Table 1 [23]. It is obvious that the annual solar radiation and sunshine duration in Hami are greater than that in other cities. Hami is also rich in land resource and features a very low population density. Additionally, about 95% of the population occupies only 5% of its land area, leaving behind extensive unused land that account for more than 70% of the total area in the Hami region. The water shortage severely restricts the utilization of land resources. However, the large-scale installation of SCPP can provide an effective approach for exploiting the arid lands and deserts. Therefore, the construction budget for such a SCPP at Hami would be relatively low. Based on the local ecological environment and the features of the SCPP, the unique advantages of constructing an SCPP in the Hami region can be summarized as follows: (1) This region is rich in solar energy, which is an important factor affecting the power output of SCPP. Besides, this region has surplus land resources suitable for constructing SCPP. (2) Hami region belongs to a typical temperate continental climate region and features large diurnal temperature ranges, which is particularly beneficial for the continuous operation of SCPP even after sunset. (3) In such an underdeveloped region, it is possible to build large-scale SCPP with lower expenditure by using local resources and work force.
Fig. 2. Theoretical model for thermal balance analysis in the collector.
Ground : qw;c þ hw;s ðt w ts Þ þ hw;f ðtw t f Þ ¼ Gt ðsaÞ
ð1Þ
Collector : qw;c þ hf ;c ðtf t c Þ ¼ hc;a ðtc ta Þ þ qc;s
ð2Þ
Airflow : hw;f ðtw t f Þ hf ;c ðt f t c Þ ¼
_ p dt f mc 2pr dr
ð3Þ
where hw,s, hw,f, hf,c, and hc,a are the heat transfer coefficients from the ground surface to soil storage, ground surface to airflow, collector to the airflow, and collector to the ambient, respectively; ta, tc, tf, tw, and ts represent the temperatures of the ambient, collector, airflow, ground surface, and soil storage, respectively; qw,c and qc,s represent the radiation heat fluxes from the ground surface to collector, and the collector to the sky; Gt is the total solar radiation on a horizontal surface; and (sa) is the product of collector transmittance and ground absorptance. Substituting Eqs. (1) and (2) in Eq. (3) yields ðGt ðsaÞ qw;c Þ þ hw;s ðt s t f Þ hc;a ðt f t a Þ ðqw;c qc;s Þ dt f 2pr hf ;c ¼ h _ p w;f dr mc hw;f þ hw;s hc;a þ hf ;c
ð4Þ
3. Theoretical model for predicting the SCPP performance To evaluate the performance of the SCPP, we developed a comprehensive theoretical model by taking into account the detailed thermal equilibrium equations of the collector, the system driving force, and flow losses, based on the existing experimental data or formulae. The model is briefly introduced in the following sections. 3.1. Thermal equilibrium equations in the collector
3.2. System driving force in the chimney The chimney, in itself, can be considered the thermal engine of the power plant. The pressure difference between the chimney base and the ambient, Dp, is defined as the system driving force to impel the air to flow inside the system. It can be calculated as
Dp ¼ g
Z 0
H
ðq1 ðzÞ qin ðzÞÞdz
ð5Þ
In principle, the collector essentially functions as a solar air heater that can be treated as two parallel plates. On the basis of the thermal model shown in Fig. 2, the increase in air temperature at the collector exit can be obtained from the thermal analysis of the collector as follows:
where q1(z) and qin(z) are the density of air at any altitude z outside and inside the chimney, respectively. Using an approximation formula between the air density and the temperature, the system driving force can be modified as
Table 1 Annual solar radiation and sunshine duration in some cities in China.
Dp ¼ 0:00353g
Z
H
ðt in ðzÞ t 1 ðzÞÞdz
ð6Þ
0
Region Shenyang Urumqi Yining Hami Yinchuan Datong Beijing Changchun Tianjin Kashgar
Latitude 0
N41°46 N43°470 N43°570 N42°490 N38°290 N40°060 N39°560 N43°540 N39°060 N39°280
Annual solar radiation (MJ/ m2)
Sunshine duration (h)
4781.456 5078.441 5530.671 6296.969 6030.888 5554.111 5178.754 4990.875 5152.363 5673.439
2555.0 2662.1 2955.1 3300.1 3011.4 2772.5 2755.5 2709.2 2612.7 2825.7
Taking into consideration the effect of gradual lapse of atmospheric air temperature, the term t1(z) can be written as
t1 ðzÞ ¼ ta c1 z
ð7Þ
where c1 is the lapse rate of atmospheric air temperature. According to the standards of the International Civil Aviation Organization (ICAO), the international standard atmosphere (ISA) is defined with a temperature lapse rate of 0.00649 K/m [24]. Hence, in the following analysis, this standard value is used as the rate at which the atmospheric temperature decreases with height.
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In the chimney, by taking into account the heat loss between the chimney and the ambient, the term tin(z) can be written as follows:
_ in ðzÞ ¼ hf ;a ½tin ðzÞ t 1 ðzÞpDdz þ mgdz _ cp mdt
ð8Þ
where hf,a is the total heat transfer coefficient from chimney airflow to atmospheric air. The value of tin(z) can be obtained by solving the differential Eq. (8) by using Runge–Kutta method. Subsequently, the system driving force, Dp, can be computed by substituting the value of tin(z) in the numeral integral of Eq. (6). 3.3. Flow losses in the system Because of the flow losses along the flow paths, the turbine uses only a part of the system driving force for power generation. The main flow losses in the system are analyzed as follow: I. Pressure loss in the transition section
Dptran ¼ ftran
q 2
v2
ð9Þ
The transition section is located between the exit of the collector and the base of the chimney. Kirstein and von Backström performed experimental and numerical studies on the pressure loss coefficient in the transition section by considering the Reynolds number scale effect [25]. According to their study, the value of 0.0558 was adopted in the calculation of pressure loss occurred in this section. II. Friction loss in the chimney
Dpf ¼ f
l q 2 v D2
ð10Þ
To determine the friction loss in the chimney by using Eq. (10), we first calculated the wall friction factor f using the Colebrook formula:
! 1 D=D 2:51 pffiffiffi ¼ 2:0 log þ pffiffiffi 3:7 Re f f
ð11Þ
III. Bracing wheels loss in the chimney
Dpbw ¼ fbw
q 2
v 2 nbw
ð12Þ
where fbw is the loss coefficient and nbw is the number of bracing wheels. In reality, the chimney of the SCPP is usually very tall, and therefore is a flexible structure. Consequently, the chimney has to be reinforced using bracing wheels at certain intervals. Von Backström et al. [26] studied the pressure drop through a representative solar chimney with internal bracing wheels, and determined the coefficient of the bracing wheels loss. The recommended value of fbw = 0.0897 for each bracing wheel was used in the following analysis. In our study, it is assumed that the bracing wheels are installed at an interval of every 100 m.
395
3.4. Power output of the turbine The turbine is the main power generation element in the SCPP. Hence, several studies have performed detailed investigations on the turbine [27–30]. The wind turbine in the solar chimney is a shrouded turbine, similar to a gas turbine with a casing, rather than a standard wind turbine used in wind farms, which belongs to the category of open turbo-machine. The air velocities are almost the same, although there is a significant change in pressure before and after the turbine. In principle, such a pressure-stage wind turbine does not follow the Betz limit. The power output of the turbine is proportional to the product of the volume flow rate and the pressure drop, Dpt. In general, the flow losses increase with the flow rate through the SCPP, which results in a drop in Dpt; and vice versa. Therefore, there should exist an optimal value of the Dpt/Dp ratio for realizing maximum power generation. According to previous studies reported in the literature, the optimal Dpt/Dp ratio is recommended in the range of 0.8–0.9 [31–34]. Accordingly, we used the Dpt/Dp value of 0.85 in this paper. The power generated by the turbine can be expressed as
P ¼ gt Dpt Q v
ð15Þ
where gt and Qv represent the turbine efficiency and volume flow rate, respectively. In this study, we considered the value of turbine efficiency as 0.8, to be consistent with the previous studies on the power output of an SCPP [35–38]. 4. Theoretical model for the prediction of solar radiation As mentioned earlier in the introduction, previous studies mainly used monthly or annual mean solar radiation data, neglecting the diurnal variation of solar radiation. This often leads to inaccurate prediction. Fig. 3 shows the predictions of collector efficiency for the Spanish prototype, as determined by using the theoretical model explained in Section 3. As is seen, the collector efficiency is as low as 15.6% at a solar radiation level of 200 W/m2, while the collector efficiency reaches 28.9% when the solar radiation is 1000 W/m2. In addition, the collector efficiency does not increase linearly with solar radiation intensity. Hence, to obtain more accurate prediction of the system performance, it is necessary to acquire the hourly solar radiation data on a specified earth surface. Given the fact that the distribution of the solar observation stations is sparse, the theoretical model has to be adopted in predicting the local solar intensity. The radiation that is being incident on the horizontal surface includes both the beam and diffuse solar radiations. To predict the incident solar radiation on any specified area, it is first necessary to calculate the solar declination and solar altitude angle by using the following two equations:
IV. Kinetic energy loss at the chimney exit
Dpout ¼ fout
q 2
v2
ð13Þ
The airflow that exits the chimney is not uniform, and hence we adopted a kinetic energy correction factor, fout. The common value of fout = 1.058 was used according to the 1/7th power law turbulent velocity profile. Accordingly, the pressure drop that is used to drive the turbine can be finally calculated as follows:
Dpt ¼ Dp Dptran Dpf Dpbw Dpout
ð14Þ
Fig. 3. Influence of solar radiation on the collector efficiency of the Spanish prototype.
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284 þ n d ¼ 23:45 sin 360 365
ð16Þ
sin h ¼ sin u sin d þ cos u cos d cos x
ð17Þ
where d, h, and x correspond to the solar declination, solar altitude angle, and hour angle, respectively; w and u represent the longitude and latitude; n is the day of the year, and thus it is an integer with values ranging between 1 and 365. At a specific day, the extraterrestrial radiation incident on a horizontal surface outside the atmosphere can be expressed as
360 n G0 ¼ Gsc 1 þ 0:034 cos 365
ð18Þ
where G0 is the extraterrestrial radiation and Gsc is the solar constant taking a value of 1367 W/m2 in this study. The solar radiation is attenuated due to the absorption and scattering of the atmosphere when traveling through it. The more is the atmosphere through which the solar radiation passes, the greater is the attenuation. Consequently, a dimensionless path length of the sunlight through the atmosphere, namely, the air mass M, is used to indicate the path length relative to that at the zenith at sea level. For solar altitude angle larger than 30°, the approximation equation is given as
M ¼ 1= sin h
ð19Þ
For smaller altitudes, the effect of the earth’s curvature becomes significant. Accordingly, M is given by [39]: 2 1=2
M ¼ ½1229 þ ð614 sin hÞ
614 sin h
ð20Þ
The above two equations are used to calculate the air mass at the sea level. Introducing a correction coefficient for the air mass at altitude Z above sea level:
M z ¼ M ½ð288 0:0065 ZÞ=2885:256
ð21Þ
Accordingly, the air mass can be used to estimate the atmospheric transmittance sb for a beam radiation, as follows:
sb ¼ 0:56 ðe0:56Mz þ e0:096Mz Þ
ð22Þ
Besides, it is also necessary to estimate the diffuse radiation transmittance sd. An empirical relationship between the transmission coefficients for beam and diffuse radiations is used here [40]:
sd ¼ 0:271 0:2939 sb
ð23Þ
The beam and diffuse radiations on a specified earth surface at a specific time can be calculated as
Gb ¼ G0 sb sin h
ð24Þ
Gd ¼ G0 sd sin h
ð25Þ
Fig. 4 presents the comparison between the calculated solar radiation and the typical annual meteorological data of the Hami region [41]. As is seen, the calculated values are in close agreement with the meteorological data. Fig. 5(a) shows the comparison of air temperature between the calculated and experimental data for the Spanish prototype during the day on September 2, 1982 [3]. The calculated results seem to overestimate the temperature in the morning, and underestimate the temperature in the afternoon. This could be attributed to the fact that the theoretical model is valid for steady flows, while the actual flow is unsteady. As a matter of fact, the soil storage has thermal inertia. Therefore, more heat than that predicted is absorbed by the soil storage due to its low initial temperature in the morning. On the other hand, in the afternoon, the ground surface releases more heat than expected. Fig. 5(b) compares the calculated power output with that of the experimental data [13]. Apparently, the calculated results agree quite well with the experimental results. Based on these results, it can be concluded that the theoretical model proposed in this study can be regarded as a reasonable model for evaluating the performance of the SCPP system. 5.2. Designing of a 100 MW SCPP at Hami The SCPPs were designed at a rated power of 100 MW, as recommended to be a typical value in previous studies. Similarly, the chimney height was set as 1000 m, on the basis of the values reported in the cited references. Solar radiation intensity and atmospheric temperature were assumed to be 1000 W/m2 and 300 K, respectively. Under such conditions, the important parameters influencing the power output of the SCPP are the collector radius and chimney radius. To gain deeper insights on the effect of these radii on the performance of SCPP, the collector radius was varied from 2000 to 4000 m, and the chimney radius was varied in the range of 45–60 m. Fig. 6 shows the power output plotted as a function of collector radius for different chimney radii. As can be evidenced from the plot, the power output of the SCPP is almost linearly proportional to the collector radius when the radius is small. Then the slope of the power output vs. collector radius curves becomes lower with increase in collector radius. There are two probable reasons that account for this phenomenon. The airflow temperature rise with the increase of the collector radius, and this results in an increase in heat losses. The lost heat may be transmitted from the collector to the sky via radiation, from the collector to the ambient via convection, and from the ground to the soil storage via conduction. On the other hand, a higher airflow temperature
The total solar radiation is defined as the sum of the beam and diffuse radiations, which can be calculated from the abovementioned equations, as follows:
Gt ¼ Gb þ Gd
ð26Þ
5. Results and discussion 5.1. Validation of the theoretical models The solutions for the abovementioned theoretical models were obtained using a self-developed MATLAB program. To validate the theoretical models, the calculated results were compared with the measured data.
Fig. 4. Comparison of calculated and measured solar radiation in Hami region.
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Fig. 5a. Comparison of air temperature between the calculated and experimental data of the Spanish prototype during the day on September 2, 1982. Fig. 7. Plot of volume flow rate and air speed in the chimney as a function of chimney radius.
Fig. 5b. Comparison of the power output between the calculated and experimental data of the Spanish prototype.
Fig. 6. Influence of collector radius and chimney radius on the power generation of SCPP.
will bring an increase in volume flow rate of the system, which leads to a rise of the flow losses. Hence the power output will reap fewer benefits from the increase of the collector radius. According to the variation trend shown in Fig. 6, there exists a maximum collector radius for a given chimney, above which there is no further increase in the power output. For the given environmental conditions, when the working air flows to the abovementioned maximum collector radius, it achieves thermal equilibrium with the other collector components due to the thermal balance between the heat losses and the incident solar radiation. Hence a
larger collector will not increase the airflow temperature further. Given that the system driving force and mass flow rate are determined by the air temperature at the collector outlet for a given chimney, the power output ceases to rise for larger collector radius. Besides, Fig. 6 also indicates that the power generation would increase with the chimney radius for an SCPP with the given collector radius. The mechanism underlying this variation tendency can be explained from the viewpoint of energy conservation. Fig. 7 shows the computed results for a constant collector radius of 2000 m and varied chimney radii. It is evident that the volume flow rate through the chimney increases with the chimney radius, while the airflow speed in the chimney decreases with increase in chimney radius. At the given conditions of incident solar radiation, collector radius, and chimney height, an increase in volume flow rate of the SCPP system will lead to a decrease in the temperature rise of the airflow. Thus, the heat transfer (heat loss) from the heated airflow to the atmosphere and soil storage is reduced accordingly. In addition, the airflow speed decreases with increase in chimney radius, which will directly lead to the reduction in flow losses. Accordingly, the observed increase in power output of the SCPP with increase in chimney radius can be attributed to the two mechanisms of reduction in both heat loss and flow loss. As is seen, for a SCPP with a tall chimney of height 1000 m, a smaller collector would need a chimney with a larger radius to meet the given power output demand. Accordingly, a 100 MW SCPP system can be designed with four different combinations of collector and chimney radii, as shown in Fig. 8. Among the four designs, only one optimal design can be determined from the economic perspective. The cost analysis for the construction of SCPP was performed, according to the method presented by Fluri et al. [42]. The total cost involved for all the four designs (mainly the collector and chimney cost) was computed and presented in Fig. 9 for comparison. As is seen, an increase in the chimney radius would slightly increase the cost related to the chimney. Nevertheless, the associated decrease in collector radius with increase in the chimney radius leads to a rapid drop in the cost of the collector. According to Fig. 9, the most economical design is that with the largest chimney radius. The main dimensions and design conditions for this optimal design are shown in Table 2. 5.3. Performance of SCPP in Hami region For the first time, in this study, we integrated the solar radiation model involving the hourly variation of the solar radiation with the theoretical model, to predict the SCPP performance. The hourly solar radiation was calculated and used as the incident radiation
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Fig. 8. Four designs of the 100 MW power plant with different dimensions.
Fig. 9. Cost comparison of the 4 designs with different collectors and chimneys.
to obtain a more accurate performance estimation of the SCPP. Fig. 10 shows the total solar radiation energy and power generation of the 100 MW SCPP for each month in Hami. As expected, the power generation profile has the same tendency with the solar radiation profile and has an obvious seasonal variation. The high values are reached between May and August, while the profiles drop to the nadir in December and January. The peak power generation reaches 72.16 TJ in June, contributing to the annual total power generation of about 522.0 TJ. According to the statistical data presented for the year 2009 [43], the annual total energy consumption in Sinkiang is 0.197 million TJ. Fig. 11 presents the histogram projecting the increase in annual power generation of the SCPPs corresponding to the percentage of unused land for the SCPPs construction ranging from 2% to 14%. If 14% of the unused
Table 2 Design parameters for the most cost effective 100 MW SCPP. Parameter
Value
Unit
Chimney height Chimney radius Collector radius Atmospheric temperature Solar radiation intensity Turbine efficiency Power output
1000 60 2750 300 1000 0.8 100
m m m K W/m2 – MW
Fig. 10. Total solar radiation energy and power generation of the SCPP in each month of the year.
Fig. 11. Histogram of the annual power generation with increase in the percentage of unused land for SCPP installation, together with the total energy consumption of Sinkiang in 2009.
land in the Hami region is used for SCPPs installation, the estimated annual power generation will be enough to meet the energy need of the whole of Sinkiang. Based on these analyses, it can be concluded that the construction of SCPPs in Sinkiang is profitable from the viewpoints of both economic development and environmental protection. 6. Conclusions In this paper, a comprehensive theoretical model taking account of the hourly variation of solar radiation is introduced to the performance simulation of the SCPP as an early attempt to obtain more accurate prediction. The effects of the collector and chimney radii on the power output of the SCPP are analyzed. A 100 MW SCPP is designed for the Hami region from the viewpoint of minimizing the construction cost and its annual power output is estimated at an interval of 1 h for a whole year. The following conclusions can be drawn from the analyses: (1) The Hami region is rich in solar energy and unused land, but lacks water resources. Therefore, this region is considered suitable for the construction of SCPP, utilizing the favorable natural resources. (2) The power output increases apparently with the collector radius when the radius is small, and then the trend becomes slower with the increase in collector radius. There is a
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limitation on the maximum collector radius, beyond which there is no further increase in the power output. On the other hand, the power output increases with the chimney radius. (3) The power generation has an obvious seasonal variation, with the performance of the SCPP being obviously better during summer. According to the estimated data, the utilization of 14% of the unused land in Hami region for the installation of SCPP will satisfy the electrical power needs for the whole of the Sinkiang region.
Acknowledgement This work was supported by National Natural Science Foundation of China (Nos.: 51276137, 11272252). References [1] Schlaich J. The solar chimney – electricity from the sun. Stuttgart: Axel Menges; 1995. [2] Haaf W, Friedrich K, Mayr G, Schlaich J. Solar chimneys Part I: principle and construction of the pilot plant in Manzanares. Int J Sustain Energy 1983;2(1):3–20. [3] Haaf W. Solar chimneys Part II: preliminary test results from the Manzanares pilot plant. Int J Sol Energy 1984;2(2):141–61. [4] Zhou XP, Xiao B, Liu WC, et al. Comparison of classical solar chimney power system and combined solar chimney system for power generation and seawater desalination. Desalination 2010;250:249–56. [5] Patel SK, Prasad D, Ahmed MR. Computational studies on the effect of geometric parameters on the performance of a solar chimney power plant. Energy Convers Manage 2014;77:424–31. [6] Xu GL, Ming TZ, Pan Y. Numerical analysis on the performance of solar chimney power plant system. Energy Convers Manage 2011;52:876–83. [7] Kasaeian AB, Heidari E, Vatan SN. Experimental investigation of climatic effects on the efficiency of a solar chimney pilot power plant. Renew Sustain Energy Rev 2011;15(9):5202–6. [8] Li WB, Wei P, Zhou XP. A cost-benefit analysis of power generation from commercial reinforced concrete solar chimney power plant. Energy Convers Manage 2014;79:104–13. [9] Guo PH, Li JY, Wang Y. Numerical simulations of solar chimney power plant with radiation model. Renewable Energy 2014;62:24–30. [10] Kasaeian A, Ghalamchi M, Ghalamchi M. Simulation and optimization of geometric parameters of a solar chimney in Tehran. Energy Convers Manage 2014;83:28–34. [11] Zhou XP, Wang F, Ochieng RM. A review of solar chimney power technology. Renew Sustain Energy Rev 2010;14(8):2315–38. [12] Ming TZ, Liu W, Xu GL. Analytical and numerical investigation of the solar chimney power plant systems. Int J Energy Res 2006;30(11):861–73. [13] Schlaich J, Bergermann R, Schiel W, Weinrebe G. Design of commercial solar updraft tower systems – utilization of solar induced convective flows for power generation. J Sol Energy Eng – Trans ASME 2005;127(1):117–24. [14] Nizetic S, Ninic N, Klarin B. Analysis and feasibility of implementing solar chimney power plants in the Mediterranean region. Energy 2008;33(11):1680–90. [15] Fasel HF, Meng FL, Shams E, Gross A. CFD analysis for solar chimney power plants. Sol Energy 2013;98:12–22. [16] Zhou XP, Wang F, Fan JA, et al. Performance of solar chimney power plant in Qinghai-Tibet Plateau. Renew Sustain Energy Rev 2010;14(8):2249–55.
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Contents lists available at ScienceDirect
Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman
Annual performance analysis of the solar chimney power plant in Sinkiang, China Peng-hua Guo, Jing-yin Li ⇑, Yuan Wang School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an 710049, PR China
a r t i c l e
i n f o
Article history: Received 1 May 2014 Accepted 14 July 2014
Keywords: Solar chimney Power generation Sinkiang Solar radiation model
a b s t r a c t To obtain more accurate prediction of the annual performance of solar chimney power plants (SCPPs), a comprehensive theoretical model is developed by taking into account the hourly variation of solar radiation. The effects of the collector and chimney radii on the power output of the SCPP are analyzed, and the results reveal that a limitation on the maximum collector radius exists for the maximum attainable power output of the SCPP. Then four designs of 100 MW SCPPs with different combinations of collector and chimney radii are proposed and the most cost effective one is chosen from among the four SCPPs. The annual power output of the chosen SCPP in the Hami region is estimated at an interval of 1 h for a whole year. The results indicate that the power generation of SCPP presents obvious seasonal variation. Furthermore, the use of 14% of the unused land in the Hami region for the installation of SCPPs would satisfy the annual power requirement for the whole of the Sinkiang region. Ó 2014 Elsevier Ltd. All rights reserved.
1. Introduction China has become the largest emitter of greenhouse gases following the rapid increase in the usage of coal to fuel the industrial and economic boom in China. To mitigate the escalating environmental concerns, the government has prompted for 40–45% reduction in carbon emission by 2020 (compared to 2005 level). Accordingly, the new energy industry was firstly listed in the encouraged category in the Catalog of Guidance of Industrial Structural Adjustment (2011 version) issued by the National Development and Reform Commission (NDRC) of China. The initiation of an investment project in the encouraged category will enjoy several benefits, including reduction in taxation, and low interest rate for bank loans. The solar chimney power plant (SCPP), which is a relatively new technology that is in accordance with the energy policy of China, has become a hot topic of research in the field of solar engineering. The SCPP was originally conceived and designed in 1931 by the German researcher Hanns Gunther. Later on, in 1978, Professor Schlaich revisited this technology [1]. Fig. 1 shows the schematic of the SCCP. As is seen, the SCPP consists of three main components, namely, the solar collector, chimney, and turbine. In the typical operation of the SCPP, the solar collector heats up the ambient air entering the system using the solar radiation, based on the phenomenon of greenhouse effect. Following that, the heated airflow ⇑ Corresponding author. Tel.: +86 29 13152181528; fax: +86 29 82668723. E-mail address: [email protected] (J.-y. Li). http://dx.doi.org/10.1016/j.enconman.2014.07.046 0196-8904/Ó 2014 Elsevier Ltd. All rights reserved.
exits the collector and flows into the chimney. The difference in air density between inside and outside of the chimney causes pressure difference between the system and the ambient air (chimney effect). The pressure difference reaches maximum at the base of the chimney, which drives the wind turbine to generate electricity (turbine effect). In less than 4 years after the conceptualization of SCPP by Schlaich, the German government and a Spanish utility built a pilot plant in Manzanares, Spain, featuring a peak output of 50 kW. Subsequently, Haaf and his colleague conducted preliminary theoretical research and demonstrated their experimental results about this pilot plant [2,3]. Since then, various studies on the SCPP system have been published around the world [4–10]. A detailed review on this topic has been reported by Zhou et al. [11], which provides a comprehensive picture of the research and development of the SCPP technology in the past few decades. As an eco-friendly energy technology, the SCPP offers the following advantages: (1) Compared with the conventional concentrated solar thermal systems, such as parabolic trough, dish stirlings, concentrating linear Fresnel reflector, and solar power tower, which are based on the beam radiation, the SCPP can utilize both beam and diffuse solar radiation. (2) Unlike conventional thermal power plant, the SCPP does not require water for cooling the system. This is especially beneficial for use in regions that suffer from water shortage.
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Nomenclature cp f G g h M _ m n P Qv q t v Z z
specific heat capacity (J kg1 K1) friction factor solar radiation (W m2) gravitational acceleration (m s2) heat transfer coefficient (W m2 K1) air mass mass flow rate (kg s1) number power generation volume flow rate (m3 s1) heat flux (W m2) temperature (K) air velocity (m s1) altitude above sea level (m) altitude above the chimney base (m)
Greek symbols a absorptance c1 lapse rate of atmospheric air temperature (K m1) Dp pressure drop (Pa) d solar declination (°) e emissivity f loss coefficient g efficiency (%) h solar altitude angle (°) k thermal conductivity (W m1 K1) l dynamic viscosity of air (N s m2) q density of air (kg m3) s transmittance
(3) SCPP is typically constructed using concrete and glass that are readily available in sufficient quantities in most regions. In addition, the structure of SCPP is not complicated, which results in a low maintenance cost. However, the efficiency of the SCPP system is low, especially when the scale of system is small. This can be improved by increasing the size or dimensions of the system [12,13]. Hence, SCPP often demands a large area of land for constructing the collector that should be available at a low cost. Ideally, areas that are not suitable for agricultural or commercial usage are needed. The most favorable locations for SCPPs are in the arid or semi-arid desert regions, where there are abundant solar and land resources. Given these
u w x
latitude (°) longitude (°) hour angle (°)
Subscripts a ambient b beam bw bracing wheel c collector c, a collector to ambient c, s collector to sky ch chimney ch, a chimney to ambient d diffuse f airflow f, a airflow to ambient f, c airflow to collector f, ch airflow to chimney out chimney out sky sky sc solar constant t turbine/total tran transition section w ground surface w, c ground surface to collector w, f ground surface to airflow w, s ground surface to soil storage
considerations, Sinkiang is an excellent place for constructing SCPP systems in China. Thus far, some studies have reported valuable feasibility analysis for the SCPP all over the world [14–21]. However, these studies have considered the monthly or annual mean solar radiation data, rather than the hourly data, in predicting the system performance. In such case, the prediction of the annual power generation may be inaccurate, as the collector efficiency can be influenced obviously by the solar radiation. Hence to obtain more accurate performance estimation, it is necessary to consider the hourly variation of the solar radiation in the theoretical model of SCPP. The objective of this paper is to analyze the potential for the generation of electrical energy by the SCPPs at the Hami region in Sinkiang. To this end, we have established and validated theoretical models for both the solar radiation and the SCPP. Besides, we analyzed the effects of chimney and collector radii on the performance of SCPP. Finally, we designed a 100 MW SCPP and evaluated its annual performance in the Hami region by performing calculations at an interval of one hour for a whole year. 2. Geographical features of the Hami region
Fig. 1. Schematic of the solar chimney power plant.
As a typical geographical location in Sinkiang, Hami (longitude between E91°060 and E96°230 , latitude between N40°520 and N45°050 ) was chosen for this analysis. According to the twelfth ‘‘Five-Year Plan’’ of China, 50 billion yuan of RMB will be invested in the construction of a railway facility at Hami, to make it an important railway hub in the Northwest of China. Consequently, the electric power demand in this region is expected to increase rapidly. However, Hami is located in the arid and semi-arid areas, and its local ecosystem is fragile due to the extreme deficit of water. According to the statistic data presented in 2003 [22], the
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per capita water resource in this region is less than 1/6th of the world average level. The fragile local ecological environment limits the construction of conventional thermal power stations, which depend heavily on water resource. Accordingly, it is a judicious choice to effectively utilize the local renewable energy resources to generate electric power. Hami has an abundant resource of solar energy, ranking high in the list of annual global solar radiation and sunshine duration in Sinkiang. The comparison of annual solar radiation and sunshine duration between Hami and other cities of same latitude in China is presented in Table 1 [23]. It is obvious that the annual solar radiation and sunshine duration in Hami are greater than that in other cities. Hami is also rich in land resource and features a very low population density. Additionally, about 95% of the population occupies only 5% of its land area, leaving behind extensive unused land that account for more than 70% of the total area in the Hami region. The water shortage severely restricts the utilization of land resources. However, the large-scale installation of SCPP can provide an effective approach for exploiting the arid lands and deserts. Therefore, the construction budget for such a SCPP at Hami would be relatively low. Based on the local ecological environment and the features of the SCPP, the unique advantages of constructing an SCPP in the Hami region can be summarized as follows: (1) This region is rich in solar energy, which is an important factor affecting the power output of SCPP. Besides, this region has surplus land resources suitable for constructing SCPP. (2) Hami region belongs to a typical temperate continental climate region and features large diurnal temperature ranges, which is particularly beneficial for the continuous operation of SCPP even after sunset. (3) In such an underdeveloped region, it is possible to build large-scale SCPP with lower expenditure by using local resources and work force.
Fig. 2. Theoretical model for thermal balance analysis in the collector.
Ground : qw;c þ hw;s ðt w ts Þ þ hw;f ðtw t f Þ ¼ Gt ðsaÞ
ð1Þ
Collector : qw;c þ hf ;c ðtf t c Þ ¼ hc;a ðtc ta Þ þ qc;s
ð2Þ
Airflow : hw;f ðtw t f Þ hf ;c ðt f t c Þ ¼
_ p dt f mc 2pr dr
ð3Þ
where hw,s, hw,f, hf,c, and hc,a are the heat transfer coefficients from the ground surface to soil storage, ground surface to airflow, collector to the airflow, and collector to the ambient, respectively; ta, tc, tf, tw, and ts represent the temperatures of the ambient, collector, airflow, ground surface, and soil storage, respectively; qw,c and qc,s represent the radiation heat fluxes from the ground surface to collector, and the collector to the sky; Gt is the total solar radiation on a horizontal surface; and (sa) is the product of collector transmittance and ground absorptance. Substituting Eqs. (1) and (2) in Eq. (3) yields ðGt ðsaÞ qw;c Þ þ hw;s ðt s t f Þ hc;a ðt f t a Þ ðqw;c qc;s Þ dt f 2pr hf ;c ¼ h _ p w;f dr mc hw;f þ hw;s hc;a þ hf ;c
ð4Þ
3. Theoretical model for predicting the SCPP performance To evaluate the performance of the SCPP, we developed a comprehensive theoretical model by taking into account the detailed thermal equilibrium equations of the collector, the system driving force, and flow losses, based on the existing experimental data or formulae. The model is briefly introduced in the following sections. 3.1. Thermal equilibrium equations in the collector
3.2. System driving force in the chimney The chimney, in itself, can be considered the thermal engine of the power plant. The pressure difference between the chimney base and the ambient, Dp, is defined as the system driving force to impel the air to flow inside the system. It can be calculated as
Dp ¼ g
Z 0
H
ðq1 ðzÞ qin ðzÞÞdz
ð5Þ
In principle, the collector essentially functions as a solar air heater that can be treated as two parallel plates. On the basis of the thermal model shown in Fig. 2, the increase in air temperature at the collector exit can be obtained from the thermal analysis of the collector as follows:
where q1(z) and qin(z) are the density of air at any altitude z outside and inside the chimney, respectively. Using an approximation formula between the air density and the temperature, the system driving force can be modified as
Table 1 Annual solar radiation and sunshine duration in some cities in China.
Dp ¼ 0:00353g
Z
H
ðt in ðzÞ t 1 ðzÞÞdz
ð6Þ
0
Region Shenyang Urumqi Yining Hami Yinchuan Datong Beijing Changchun Tianjin Kashgar
Latitude 0
N41°46 N43°470 N43°570 N42°490 N38°290 N40°060 N39°560 N43°540 N39°060 N39°280
Annual solar radiation (MJ/ m2)
Sunshine duration (h)
4781.456 5078.441 5530.671 6296.969 6030.888 5554.111 5178.754 4990.875 5152.363 5673.439
2555.0 2662.1 2955.1 3300.1 3011.4 2772.5 2755.5 2709.2 2612.7 2825.7
Taking into consideration the effect of gradual lapse of atmospheric air temperature, the term t1(z) can be written as
t1 ðzÞ ¼ ta c1 z
ð7Þ
where c1 is the lapse rate of atmospheric air temperature. According to the standards of the International Civil Aviation Organization (ICAO), the international standard atmosphere (ISA) is defined with a temperature lapse rate of 0.00649 K/m [24]. Hence, in the following analysis, this standard value is used as the rate at which the atmospheric temperature decreases with height.
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In the chimney, by taking into account the heat loss between the chimney and the ambient, the term tin(z) can be written as follows:
_ in ðzÞ ¼ hf ;a ½tin ðzÞ t 1 ðzÞpDdz þ mgdz _ cp mdt
ð8Þ
where hf,a is the total heat transfer coefficient from chimney airflow to atmospheric air. The value of tin(z) can be obtained by solving the differential Eq. (8) by using Runge–Kutta method. Subsequently, the system driving force, Dp, can be computed by substituting the value of tin(z) in the numeral integral of Eq. (6). 3.3. Flow losses in the system Because of the flow losses along the flow paths, the turbine uses only a part of the system driving force for power generation. The main flow losses in the system are analyzed as follow: I. Pressure loss in the transition section
Dptran ¼ ftran
q 2
v2
ð9Þ
The transition section is located between the exit of the collector and the base of the chimney. Kirstein and von Backström performed experimental and numerical studies on the pressure loss coefficient in the transition section by considering the Reynolds number scale effect [25]. According to their study, the value of 0.0558 was adopted in the calculation of pressure loss occurred in this section. II. Friction loss in the chimney
Dpf ¼ f
l q 2 v D2
ð10Þ
To determine the friction loss in the chimney by using Eq. (10), we first calculated the wall friction factor f using the Colebrook formula:
! 1 D=D 2:51 pffiffiffi ¼ 2:0 log þ pffiffiffi 3:7 Re f f
ð11Þ
III. Bracing wheels loss in the chimney
Dpbw ¼ fbw
q 2
v 2 nbw
ð12Þ
where fbw is the loss coefficient and nbw is the number of bracing wheels. In reality, the chimney of the SCPP is usually very tall, and therefore is a flexible structure. Consequently, the chimney has to be reinforced using bracing wheels at certain intervals. Von Backström et al. [26] studied the pressure drop through a representative solar chimney with internal bracing wheels, and determined the coefficient of the bracing wheels loss. The recommended value of fbw = 0.0897 for each bracing wheel was used in the following analysis. In our study, it is assumed that the bracing wheels are installed at an interval of every 100 m.
395
3.4. Power output of the turbine The turbine is the main power generation element in the SCPP. Hence, several studies have performed detailed investigations on the turbine [27–30]. The wind turbine in the solar chimney is a shrouded turbine, similar to a gas turbine with a casing, rather than a standard wind turbine used in wind farms, which belongs to the category of open turbo-machine. The air velocities are almost the same, although there is a significant change in pressure before and after the turbine. In principle, such a pressure-stage wind turbine does not follow the Betz limit. The power output of the turbine is proportional to the product of the volume flow rate and the pressure drop, Dpt. In general, the flow losses increase with the flow rate through the SCPP, which results in a drop in Dpt; and vice versa. Therefore, there should exist an optimal value of the Dpt/Dp ratio for realizing maximum power generation. According to previous studies reported in the literature, the optimal Dpt/Dp ratio is recommended in the range of 0.8–0.9 [31–34]. Accordingly, we used the Dpt/Dp value of 0.85 in this paper. The power generated by the turbine can be expressed as
P ¼ gt Dpt Q v
ð15Þ
where gt and Qv represent the turbine efficiency and volume flow rate, respectively. In this study, we considered the value of turbine efficiency as 0.8, to be consistent with the previous studies on the power output of an SCPP [35–38]. 4. Theoretical model for the prediction of solar radiation As mentioned earlier in the introduction, previous studies mainly used monthly or annual mean solar radiation data, neglecting the diurnal variation of solar radiation. This often leads to inaccurate prediction. Fig. 3 shows the predictions of collector efficiency for the Spanish prototype, as determined by using the theoretical model explained in Section 3. As is seen, the collector efficiency is as low as 15.6% at a solar radiation level of 200 W/m2, while the collector efficiency reaches 28.9% when the solar radiation is 1000 W/m2. In addition, the collector efficiency does not increase linearly with solar radiation intensity. Hence, to obtain more accurate prediction of the system performance, it is necessary to acquire the hourly solar radiation data on a specified earth surface. Given the fact that the distribution of the solar observation stations is sparse, the theoretical model has to be adopted in predicting the local solar intensity. The radiation that is being incident on the horizontal surface includes both the beam and diffuse solar radiations. To predict the incident solar radiation on any specified area, it is first necessary to calculate the solar declination and solar altitude angle by using the following two equations:
IV. Kinetic energy loss at the chimney exit
Dpout ¼ fout
q 2
v2
ð13Þ
The airflow that exits the chimney is not uniform, and hence we adopted a kinetic energy correction factor, fout. The common value of fout = 1.058 was used according to the 1/7th power law turbulent velocity profile. Accordingly, the pressure drop that is used to drive the turbine can be finally calculated as follows:
Dpt ¼ Dp Dptran Dpf Dpbw Dpout
ð14Þ
Fig. 3. Influence of solar radiation on the collector efficiency of the Spanish prototype.
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284 þ n d ¼ 23:45 sin 360 365
ð16Þ
sin h ¼ sin u sin d þ cos u cos d cos x
ð17Þ
where d, h, and x correspond to the solar declination, solar altitude angle, and hour angle, respectively; w and u represent the longitude and latitude; n is the day of the year, and thus it is an integer with values ranging between 1 and 365. At a specific day, the extraterrestrial radiation incident on a horizontal surface outside the atmosphere can be expressed as
360 n G0 ¼ Gsc 1 þ 0:034 cos 365
ð18Þ
where G0 is the extraterrestrial radiation and Gsc is the solar constant taking a value of 1367 W/m2 in this study. The solar radiation is attenuated due to the absorption and scattering of the atmosphere when traveling through it. The more is the atmosphere through which the solar radiation passes, the greater is the attenuation. Consequently, a dimensionless path length of the sunlight through the atmosphere, namely, the air mass M, is used to indicate the path length relative to that at the zenith at sea level. For solar altitude angle larger than 30°, the approximation equation is given as
M ¼ 1= sin h
ð19Þ
For smaller altitudes, the effect of the earth’s curvature becomes significant. Accordingly, M is given by [39]: 2 1=2
M ¼ ½1229 þ ð614 sin hÞ
614 sin h
ð20Þ
The above two equations are used to calculate the air mass at the sea level. Introducing a correction coefficient for the air mass at altitude Z above sea level:
M z ¼ M ½ð288 0:0065 ZÞ=2885:256
ð21Þ
Accordingly, the air mass can be used to estimate the atmospheric transmittance sb for a beam radiation, as follows:
sb ¼ 0:56 ðe0:56Mz þ e0:096Mz Þ
ð22Þ
Besides, it is also necessary to estimate the diffuse radiation transmittance sd. An empirical relationship between the transmission coefficients for beam and diffuse radiations is used here [40]:
sd ¼ 0:271 0:2939 sb
ð23Þ
The beam and diffuse radiations on a specified earth surface at a specific time can be calculated as
Gb ¼ G0 sb sin h
ð24Þ
Gd ¼ G0 sd sin h
ð25Þ
Fig. 4 presents the comparison between the calculated solar radiation and the typical annual meteorological data of the Hami region [41]. As is seen, the calculated values are in close agreement with the meteorological data. Fig. 5(a) shows the comparison of air temperature between the calculated and experimental data for the Spanish prototype during the day on September 2, 1982 [3]. The calculated results seem to overestimate the temperature in the morning, and underestimate the temperature in the afternoon. This could be attributed to the fact that the theoretical model is valid for steady flows, while the actual flow is unsteady. As a matter of fact, the soil storage has thermal inertia. Therefore, more heat than that predicted is absorbed by the soil storage due to its low initial temperature in the morning. On the other hand, in the afternoon, the ground surface releases more heat than expected. Fig. 5(b) compares the calculated power output with that of the experimental data [13]. Apparently, the calculated results agree quite well with the experimental results. Based on these results, it can be concluded that the theoretical model proposed in this study can be regarded as a reasonable model for evaluating the performance of the SCPP system. 5.2. Designing of a 100 MW SCPP at Hami The SCPPs were designed at a rated power of 100 MW, as recommended to be a typical value in previous studies. Similarly, the chimney height was set as 1000 m, on the basis of the values reported in the cited references. Solar radiation intensity and atmospheric temperature were assumed to be 1000 W/m2 and 300 K, respectively. Under such conditions, the important parameters influencing the power output of the SCPP are the collector radius and chimney radius. To gain deeper insights on the effect of these radii on the performance of SCPP, the collector radius was varied from 2000 to 4000 m, and the chimney radius was varied in the range of 45–60 m. Fig. 6 shows the power output plotted as a function of collector radius for different chimney radii. As can be evidenced from the plot, the power output of the SCPP is almost linearly proportional to the collector radius when the radius is small. Then the slope of the power output vs. collector radius curves becomes lower with increase in collector radius. There are two probable reasons that account for this phenomenon. The airflow temperature rise with the increase of the collector radius, and this results in an increase in heat losses. The lost heat may be transmitted from the collector to the sky via radiation, from the collector to the ambient via convection, and from the ground to the soil storage via conduction. On the other hand, a higher airflow temperature
The total solar radiation is defined as the sum of the beam and diffuse radiations, which can be calculated from the abovementioned equations, as follows:
Gt ¼ Gb þ Gd
ð26Þ
5. Results and discussion 5.1. Validation of the theoretical models The solutions for the abovementioned theoretical models were obtained using a self-developed MATLAB program. To validate the theoretical models, the calculated results were compared with the measured data.
Fig. 4. Comparison of calculated and measured solar radiation in Hami region.
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Fig. 5a. Comparison of air temperature between the calculated and experimental data of the Spanish prototype during the day on September 2, 1982. Fig. 7. Plot of volume flow rate and air speed in the chimney as a function of chimney radius.
Fig. 5b. Comparison of the power output between the calculated and experimental data of the Spanish prototype.
Fig. 6. Influence of collector radius and chimney radius on the power generation of SCPP.
will bring an increase in volume flow rate of the system, which leads to a rise of the flow losses. Hence the power output will reap fewer benefits from the increase of the collector radius. According to the variation trend shown in Fig. 6, there exists a maximum collector radius for a given chimney, above which there is no further increase in the power output. For the given environmental conditions, when the working air flows to the abovementioned maximum collector radius, it achieves thermal equilibrium with the other collector components due to the thermal balance between the heat losses and the incident solar radiation. Hence a
larger collector will not increase the airflow temperature further. Given that the system driving force and mass flow rate are determined by the air temperature at the collector outlet for a given chimney, the power output ceases to rise for larger collector radius. Besides, Fig. 6 also indicates that the power generation would increase with the chimney radius for an SCPP with the given collector radius. The mechanism underlying this variation tendency can be explained from the viewpoint of energy conservation. Fig. 7 shows the computed results for a constant collector radius of 2000 m and varied chimney radii. It is evident that the volume flow rate through the chimney increases with the chimney radius, while the airflow speed in the chimney decreases with increase in chimney radius. At the given conditions of incident solar radiation, collector radius, and chimney height, an increase in volume flow rate of the SCPP system will lead to a decrease in the temperature rise of the airflow. Thus, the heat transfer (heat loss) from the heated airflow to the atmosphere and soil storage is reduced accordingly. In addition, the airflow speed decreases with increase in chimney radius, which will directly lead to the reduction in flow losses. Accordingly, the observed increase in power output of the SCPP with increase in chimney radius can be attributed to the two mechanisms of reduction in both heat loss and flow loss. As is seen, for a SCPP with a tall chimney of height 1000 m, a smaller collector would need a chimney with a larger radius to meet the given power output demand. Accordingly, a 100 MW SCPP system can be designed with four different combinations of collector and chimney radii, as shown in Fig. 8. Among the four designs, only one optimal design can be determined from the economic perspective. The cost analysis for the construction of SCPP was performed, according to the method presented by Fluri et al. [42]. The total cost involved for all the four designs (mainly the collector and chimney cost) was computed and presented in Fig. 9 for comparison. As is seen, an increase in the chimney radius would slightly increase the cost related to the chimney. Nevertheless, the associated decrease in collector radius with increase in the chimney radius leads to a rapid drop in the cost of the collector. According to Fig. 9, the most economical design is that with the largest chimney radius. The main dimensions and design conditions for this optimal design are shown in Table 2. 5.3. Performance of SCPP in Hami region For the first time, in this study, we integrated the solar radiation model involving the hourly variation of the solar radiation with the theoretical model, to predict the SCPP performance. The hourly solar radiation was calculated and used as the incident radiation
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Fig. 8. Four designs of the 100 MW power plant with different dimensions.
Fig. 9. Cost comparison of the 4 designs with different collectors and chimneys.
to obtain a more accurate performance estimation of the SCPP. Fig. 10 shows the total solar radiation energy and power generation of the 100 MW SCPP for each month in Hami. As expected, the power generation profile has the same tendency with the solar radiation profile and has an obvious seasonal variation. The high values are reached between May and August, while the profiles drop to the nadir in December and January. The peak power generation reaches 72.16 TJ in June, contributing to the annual total power generation of about 522.0 TJ. According to the statistical data presented for the year 2009 [43], the annual total energy consumption in Sinkiang is 0.197 million TJ. Fig. 11 presents the histogram projecting the increase in annual power generation of the SCPPs corresponding to the percentage of unused land for the SCPPs construction ranging from 2% to 14%. If 14% of the unused
Table 2 Design parameters for the most cost effective 100 MW SCPP. Parameter
Value
Unit
Chimney height Chimney radius Collector radius Atmospheric temperature Solar radiation intensity Turbine efficiency Power output
1000 60 2750 300 1000 0.8 100
m m m K W/m2 – MW
Fig. 10. Total solar radiation energy and power generation of the SCPP in each month of the year.
Fig. 11. Histogram of the annual power generation with increase in the percentage of unused land for SCPP installation, together with the total energy consumption of Sinkiang in 2009.
land in the Hami region is used for SCPPs installation, the estimated annual power generation will be enough to meet the energy need of the whole of Sinkiang. Based on these analyses, it can be concluded that the construction of SCPPs in Sinkiang is profitable from the viewpoints of both economic development and environmental protection. 6. Conclusions In this paper, a comprehensive theoretical model taking account of the hourly variation of solar radiation is introduced to the performance simulation of the SCPP as an early attempt to obtain more accurate prediction. The effects of the collector and chimney radii on the power output of the SCPP are analyzed. A 100 MW SCPP is designed for the Hami region from the viewpoint of minimizing the construction cost and its annual power output is estimated at an interval of 1 h for a whole year. The following conclusions can be drawn from the analyses: (1) The Hami region is rich in solar energy and unused land, but lacks water resources. Therefore, this region is considered suitable for the construction of SCPP, utilizing the favorable natural resources. (2) The power output increases apparently with the collector radius when the radius is small, and then the trend becomes slower with the increase in collector radius. There is a
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limitation on the maximum collector radius, beyond which there is no further increase in the power output. On the other hand, the power output increases with the chimney radius. (3) The power generation has an obvious seasonal variation, with the performance of the SCPP being obviously better during summer. According to the estimated data, the utilization of 14% of the unused land in Hami region for the installation of SCPP will satisfy the electrical power needs for the whole of the Sinkiang region.
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