Modeling and numerical simulation of solar chimney ...

Available online at www.sciencedirect.com

Solar Energy xxx (2011) xxx–xxx www.elsevier.com/locate/solener

Modeling and numerical simulation of solar chimney power plants Roozbeh Sangi ⇑, Majid Amidpour, Behzad Hosseinizadeh Department of Mechanical Engineering, K.N. Toosi University of Technology (KNTU), Tehran, Iran Received 20 March 2010; received in revised form 1 January 2011; accepted 26 January 2011

Communicated by: Associate Editor S.A. Sherif

Abstract The solar chimney power plant is a simple solar thermal power plant that is capable of converting solar energy into thermal energy in the solar collector. In the second stage, the generated thermal energy is converted into kinetic energy in the chimney and ultimately into electric energy using a combination of a wind turbine and a generator. The purpose of this study is to conduct a more detailed numerical analysis of a solar chimney power plant. A mathematical model based on the Navier–Stokes, continuity and energy equations was developed to describe the solar chimney power plant mechanism in detail. Two different numerical simulations were performed for the geometry of the prototype in Manzanares, Spain. First, the governing equations were solved numerically using an iterative technique. Then, the numerical simulation was performed using the CFD software FLUENT that can simulate a two-dimensional axisymmetric model of a solar chimney power plant with the standard k-epsilon turbulence model. Both the predictions were compared with the available experimental data to assess the validity of the model. The temperature, velocity and pressure distributions in the solar collector are illustrated for three different solar radiations. Reasonably good quantitative agreement was obtained between the experimental data of the Manzanares prototype and both the numerical results. Ó 2011 Elsevier Ltd. All rights reserved. Keywords: Solar chimney power plant; Collector; Chimney; Mathematical modeling; Numerical simulation

1. Introduction The scarcity of available energy resources has been further aggravated by the ever-increasing of the world energy demand. In addition, current energy production from coal and oil is damaging to the environment and nonrenewable. Therefore, it is urgent to develop the technologies utilizing renewable and clean energy sources to solve these problems. A solar chimney power plant offers interesting opportunities to use pollution free resources of energy. Solar chimney power technology, designed to produce electric power on a large-scale, utilizes solar energy to produce ventilation that drives wind turbines to produce electric power. The solar chimney concept was originally proposed by Professor Schlaich of Stuttgart in the late 1970s. Less than ⇑ Corresponding author.

E-mail address: [email protected] (R. Sangi).

4 years after he presented his ideas at a conference, construction on a pilot plant began in Manzanares, Spain, as a result of a joint venture between the German government and a Spanish utility. A 36-kW pilot plant was built, which produced electricity for 7 years, thus proving the efficiency and reliability of this novel technology. The chimney tower was 194.6 m high, and the collector had a radius of 122 m. Fundamental investigations for the Spanish system were reported by Haaf et al. (1983) in which a brief discussion of the energy balance, design criteria, and cost analysis was presented. Krisst (1983) demonstrated a ‘back yard type’ device with a power output of 10 W in West Hartford, Connecticut, USA. In a later study, Haaf (1984) reported preliminary test results of the plant built in Spain. Kulunk (1985) produced a micro scale electric power plant of 0.14 W in Izmit, Turkey. Sampayo (1986) suggested the use of a multi-cone diffuser on the top of the chimney to allow the operation as a high-speed chimney and to act

0038-092X/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.solener.2011.01.011

Please cite this article in press as: Sangi, R. et al. Modeling and numerical simulation of solar chimney power plants. Sol. Energy (2011), doi:10.1016/ j.solener.2011.01.011

2

R. Sangi et al. / Solar Energy xxx (2011) xxx–xxx

Nomenclature A cF cp d g H h m_ Nu p q r T u v x z b

area (m2) friction coefficient specific heat capacity (J kg1 K1) diameter (m) gravitational acceleration (ms2) height (m) heat-transfer coefficient (W m2) mass flow rate (kg s1) Nusselt number pressure (Pa) solar radiation (W m2) radial coordinate (m) temperature (K) velocity in the radial direction (ms1) velocity in the axial direction ðm s1 Þ length (m) axial coordinate (m) volume coefficient of expansion (k1)

as a draft tube for any natural wind blowing. Mullet (1987) presented an analysis to derive the overall efficiency of the solar chimney. The governing differential equations were developed by Padki and Sherif (1988) to describe the chimney performance. In later studies, Padki and Sherif (1989a,b) conducted an investigation of the viability of solar chimneys for medium-to-large scale power production and power generation in rural areas. Schlaich et al. (1990) studied the transferability from the experimental data of the prototype in Manzanares to large power plants (5, 30 and 100 MW). Yan et al. (1991) reported on a more comprehensive analytical model in which practical correlations were used to derive equations for the air flow rate, air velocity, power output and thermofluid efficiency. Padki and Sherif (1992) briefly discussed the effects of the geometrical and operating parameters on the chimney performance. Kreetz (1997) presented a numerical model for the use of water storage in the collector. His calculations showed the possibility of a continuous day and night operation of the solar chimney. Pasumarthi and Sherif (1998a,b) conducted experimental and theoretical analyses on a solar chimney model built on a university campus. Padki and Sherif (1999) developed a simple model to analyze the performance of the solar chimney. Bernardes et al. (1999) presented a theoretical analysis of a solar chimney operating on natural laminar convection in the steady state. Lodhi (1999) presented a comprehensive analysis of the chimney effect, power production and efficiency and estimated the cost of the solar chimney power plant set up in developing nations. Gannon and Backstrom (2000a,b) developed an analysis of the solar chimney including chimney friction, exit kinetic losses and a simple model of the solar collector. More thorough analyses of

k e q r s

thermal conductivity (W m1 k1) emissivity density (kg m3) Stefan–Boltzmann constant (W m2 k4) transmissivity

Subscripts a ambient c collector ch chimney e earth f fluid F friction i inner o outer T turbine

solar chimney power plant performance were conducted by Kro¨ger and Buys (2001) and Gannon and Von Backstro¨m (2002), and Gannon and Von Backstro¨m (2003) studied the performance of turbines employed in solar chimney power plants. Bernardes et al. (2003) developed an analytical and numerical model for a solar chimney power plant, comparing simulation predictions to experimental results from the prototype plant at Manzanares. Pastohr et al. (2004) conducted a basic CFD analysis on the solar chimney power plant and compared their results to another simple model. A relatively detailed numerical model was developed by Pretorius et al. (2004), simulating the performance of a large-scale reference solar chimney power plant. Schlaich et al. (2005) presented the theory, practical experience, and economy of solar chimney power plants to give a guide for the design of 200-MW commercial solar chimney power plant systems. A mathematical model was developed by Bilgen and Rheault (2005) for evaluating the performance of solar chimney power plants at high latitudes. A refined numerical model for simulating large solar chimney plants was presented by Pretorius and Kro¨ger (2006). Later, Ming et al. (2006) developed a comprehensive model to evaluate the performance of a solar chimney power plant system in which the effects of various parameters on the relative static pressure, driving force, power output and efficiency were further investigated. Ming et al. (2008) presented a numerical analysis of the flow and heat transfer characteristics in a solar chimney power plant with an energy storage layer. Zhou et al. (2007), Ketlogetswe et al. (2008) and Ferreira et al. (2008) conducted experimental analyses on solar chimney systems. Koonsrisuk and Chitsomboon (2007) and later Zhou et al. (2009) performed numerical simula-



tions of solar chimneys using a commercial CFD software. Bernardes et al., (2010) evaluated the operational control strategies applicable to solar chimney power plants. Koonsrisuk et al. (2010) described the constructal-theory search for the geometry of a solar chimney. Because the pressure equation is used to obtain the mass flow rate of air and the mass flow rate is one the most important factors that influences the power output considerably, many attempts have been made to develop a correct equation for the pressure. Nonetheless, the issue of pressure distribution was a controversial one in analyzing solar chimney power plant performance. Some researchers ignored the role of the pressure difference on the performance of solar chimney systems. Pastohr et al. (2004) performed a basic comprehensive CFD analysis on the solar chimney power plant. In contrast to the numerical results shown by them in which the static pressure inside the collector is positive and increases along the flow direction, Ming et al. (2006) illustrated that the relative static pressure is negative and decreases along the flow direction inside the collector. To obtain the pressure difference, the Bernoulli equation was applied, which is not suitable for a flow that receives solar radiation. The correct pressure equation should be derived from the Navier–Stokes equations. Because the other solar chimney performance parameters directly depend on the pressure equation, there is a need to derive the right pressure equation to modify the other main parameters, which were negatively affected. In this investigation, the correct pressure equation is developed. To obtain the accurate pressure drop, the friction is taken into consideration. Furthermore, in this study, models for the collector cover and the surface of earth are presented, which increase the accuracy of the general model. 2. System description A solar chimney is a combination of three established technologies, namely, the greenhouse, the chimney, and the wind turbine. The chimney, which is a long tubular structure, is placed in the center of the circular greenhouse, while the wind turbine is mounted inside the chimney. This unique combination accomplishes the task of converting solar energy into electrical energy. This solar-to-electric conversion involves two intermediate stages. In the first stage, conversion of solar energy into thermal energy is accomplished in the greenhouse (also known as the collector) by means of the greenhouse effect. In the second stage, the chimney converts the generated thermal energy into kinetic energy and ultimately into electric energy by using a combination of a wind turbine and a generator. Fig. 1 provides an overall view of a solar chimney power plant. In its simplest form, the collector is a glass or plastic film cover stretched horizontally and raised above the ground. This covering serves as a trap for re-radiation from the ground. It transmits the shorter wavelength solar radiation but blocks the longer wavelength radiation emitted by the ground. As a result, the ground under the cover heats up,

3

Fig. 1. Schematic illustration of a solar chimney power plant.

which, in turn, heats the air flowing radially above it. A flat collector of this kind can convert a significant amount of the irradiated solar energy into heat. The soil surface under the collector cover is a convenient energy storage medium. During the day, a part of the incoming solar radiation is absorbed by the ground and is later released during the night. This mechanism is capable of providing a continuous supply of power all year round. The chimney itself is the actual thermal engine. It is similar to a pressure tube with low frictional losses. The up thrust of the air heated in the collector is proportional to the increase in air temperature in the collector and the volume of the air flow. The latter depends on the height of the chimney. Mechanical output in the form of rotational energy can be extracted from the vertical air current flowing in the chimney by using suitable turbine(s). The principle of operation of these turbines is similar to the turbo-generators used in hydroelectric power stations, where the static pressure is converted into mechanical work. The power output achieved is proportional to the product of the volume flow rate and the pressure drop across the turbine. The air flow through the turbine can be regulated by varying the turbine blades’ pitch angle. This mechanical energy can be converted into electric energy by coupling the turbine(s) to the generator(s). Solar chimneys do not necessarily need direct sunlight. They can exploit a component of the diffused radiation when the sky is cloudy. The lack of system dependence on the natural occurrence of wind, which is intermittent, makes it a very attractive development. 3. Modeling 3.1. Basic equations The Navier–Stokes equations, the continuity equation, the equation for the energy and ke equations describe the movement of the flow generally.


4


3.1.1. Navier–Stokes equations du @p @ @u 2l þ l0 r ~ q ¼ þ v dt @r @r @r @ @u @v 2l @u v l þ þ þ ð1Þ @z @z @r r @r r dv @p @ @v @ @u @v 2l þ l0 r ~ lr þ q ¼ þ qgz þ v þ dt @z @z @z r@r @z @r ð2Þ 3.1.2. Continuity equation @p 1 @ @ þ ðrquÞ þ ðqvÞ ¼ 0 @t r @z @z 3.1.3. Energy equation @T 1 @ @ qcp þ ðrTuÞ þ ðTvÞ qt r @r @z 1 @ @T @ @T @p 1 @ ¼ rk k þ ðrpuÞ þ þ r @r @r @z @z @t r @r @ þ ðpvÞ þ U @z 3.1.4. k–e equations 1 @ @ @ lt @k q ðrkuÞ þ ðkvÞ ¼ lþ r @r @z @z rk @z 1 @ l @k l @T r lþ t qe þ þ Gk þ bgz t r @r rk @r Prt @z 1 @ @ @ l @e q ðreuÞ þ ðevÞ ¼ lþ t r @r @z @z re @z 1 @ l @e e e2 þ r lþ t þ C 1e Gk C 2eq r @r k re @r k

ð3Þ

ð4Þ

ð5Þ

qa cp uf H c

The variable r, which stands for the radial coordinate, corresponds to the radial direction in the collector, and the variable z, which represents the axial coordinate, corresponds to the chimney axial direction.

ð9Þ

In this form of the energy equation, convective heat transfer is considered for every contact surface. Surface temperatures are required for the integration of Eq. (9). At first, initial values for surface temperatures and heat transfer coefficients are assumed. Using this simplification, considering the air density constant, substituting uf from Eq. (8) into Eq. (9) and finally integrating equation (9), a simplified equation for temperature is obtained: 2ph ðr2 r2 Þ 1 o T c þ T e þ ð2T a T c T e Þecp m_ T f ðrÞ ¼ ð10Þ 2 The temperature profile of the fluid flowing through the collector at a given flow rate is shown in Fig. 2. To demonstrate the effect of surface temperatures on the temperature profile of fluid more clearly, three different values were selected for the earth and roof temperatures. Assuming m = 1000 kg/s and h = 5 W/m2 K (Pastohr, 2004), Eq. (10) is solved for constant surface temperatures. Fig. 2 illustrates the increase of the air temperature through the collector. The temperature difference between the collector inlet and outlet describes the performance of the system generally. The results indicate that at the higher the surface temperatures, the greater the temperature difference is. Unfortunately, the temperature distribution in the surfaces is not known. The following investigations were conducted on the heat balance in the glass roof and earth. Considering surface temperatures as functions of the collector radius, the energy equation of the air in the collector can be extended as qa cp H c uf

ð6Þ

@T f ¼ hc ðT f T c Þ þ he ðT f T e Þ @r

@T f ¼ hc ðT f T c ðrÞÞ þ he ðT f T e ðrÞÞ @r

ð11Þ

3.2.1. Heat balance of the glass roof For the glass roof, heat balance equation (12) is used. Heat conduction in the very thin cover is neglected compared with heat convection. The term (1 s)q shows the

3.2. Mathematical model of the collector By assuming one-dimensional and steady flow, the following equation for mass flow rate is obtained: m_ ¼ qf Auf

ð7Þ

Substituting the flow area into Eq. (7) results in the following expression for the velocity of the fluid: Uf ¼

m_ 2prH c qf

ð8Þ

The energy equation for the warm air in the collector can be expressed as

Fig. 2. Temperature profile of the fluid flowing through the collector for m = 1000 kg/s.



absorption of radiation, and s = 0.85 is assumed (Grigull et al., 1991). The term ea rðT 4c T 4a Þ considers the radiation of the glass roof, and the term ec rT4c ee rT4e shows a simplistic calculation of radiation in the collector. The heat transfer equation of the glass roof is ð1 sÞq ¼ hc ðT f T c Þ ha ðT a T c Þ þ ec rT 4c ee rT 4e þ ea rðT 4f T 4a Þ

3.2.2. Heat balance of the earth The steady-state heat conduction equation is valid in the ground: ð13Þ

Two boundary conditions are required to solve equation (13). The boundary condition on the earth’s surface z = 0 is he ðT f T e Þ þ sq þ ec rT 4c ee rT 4e ¼ ke

@T e @z

ð15Þ

3.2.3. Heat transfer coefficients It is necessary to adjust the model by taking into account the temperature and velocity dependence of the heat transfer coefficient at the ground and the glass roof. The heat transfer coefficient between the glass roof and atmosphere is ha ¼

Nux k x

@pc ¼ qa ba gðT f T a Þ @z

ð16Þ

The heat transfer coefficient is not steady, and it is generally a function of the Reynolds number (compulsive convection) and the Grashof number (natural convection). According to Kreetz (1997), the heat transfer coefficient between the glass roof and the fluid flowing through the collector is 4 4 !14 kf kf hc ¼ Nuf þ Nuc ð17Þ 2H c Hc The heat transfer coefficient between the surface of the earth and the fluid flowing through the collector is 4 4 !14 kf kf he ¼ Nuf þ Nue ð18Þ 2H c Hc 3.2.4. Pressure equation of the collector The pressure equation of the system is used to find the unknown mass flow rate, which is a key requirement to solve the whole model. The pressure equation can be

ð20Þ

Integrating equation (20) and considering Pc(r = ro) = 0 give pc ðrÞ ¼ H c qa ba gðT f ðr ¼ ri Þ T a Þ

ð21Þ

The Navier–Stokes equation in the radial direction is qa uf

@uf @p ¼ c @r @r

ð22Þ

Integrating equation (22) and substituting Eq. (8) into Eq. (22) yields

ð14Þ

Eq. (14) involves the terms for heat convection, absorption of solar energy, simplistic radiation and heat conduction. The boundary condition in the earth’s depth (z = ze) can be defined as Te ¼ Ta

derived by simplifying the Navier–Stokes equation. The density model can be expressed by Boussinesq approximation (Jaluria, 1980): 1 ð19Þ qf ¼ qa ð1 ba ðT f T a ÞÞ; ba ¼ Ta The Navier–Stokes equation in the axial direction is

ð12Þ

@2T e ¼0 @z2

5

pc ðrÞ ¼

2 m_ 2 qa ðr2 o r Þ 8H 2c p2 q2f

ð23Þ

Friction should also be considered in the collector to obtain an accurate pressure drop. Thus, analogous to the pipe flow, the frictional pressure drop in the collector is obtained (Jischa, 1982): qf m2 4cF @pF @pF ¼ @r @r þ 0 r 2 A2c q2f 2H c

ð24Þ

3.3. Turbine model With the Beetz power limit (Haaf et al., 1983), the pressure jump at the turbine is given by dpT ¼

8qT u2T 27

ð25Þ

The terms qT and uT , respectively, are the average air density and the average air velocity at the turbine section. 3.4. Mathematical model in the chimney Neglecting the temperature decrease in the chimney, the energy equation simplifies to @T ch qch cp uch ¼0 ð26Þ @z The temperature in the chimney is assumed to be constant. Thus, the integration yields T ch ¼ T f ðr ¼ ri Þ

ð27Þ

3.4.1. Pressure equation in the chimney The general Navier–Stokes equation in the axial direction is reduced to @pch ¼ qa ba gðT ch T a Þ @z

ð28Þ


6


The integration of the pressure equation in the chimney results in pch ðzÞ ¼ pc ðr ¼ ri Þ H ch qf ba gðT f ðr ¼ ri Þ T 0 Þ

ð29Þ

For the friction model of the chimney, the Colebrook results of the developed pipe current are used (Jischa, 1982). Considering friction losses in the chimney yields @pF dpF q m_ 2 4cF ¼ ch 2 2 @z H ch 2 Ach qch d ch

ð30Þ

3.5. Pressure equation of the whole model For the whole model, the single terms of the pressure equation are added. To sum up, the following pressure equation is achieved by superposition:

Fig. 3. Temperature profile of the fluid flowing through the collector.

p ¼ H ch qa ba gðT f ðr ¼ ri Þ T 0 Þ þ 2

m_ 2 A2ch qch

2 m_ 2 qa ðr2 m_ 2 cF o ri Þ 2 ðro ri Þ 2 2 2 8H c p qf Ac qch H ch

H ch cF 8 m_ 2 27 A2T qch d ch

ð31Þ

Eq. (31) indicates that, with a given solar radiation, the pressure equation is a function of the geometry, material and mass flow rate. At the chimney exit, the static pressure must be equal to the ambient atmospheric static pressure at the same altitude: Dpout ¼ 0

ð32Þ

Fig. 4. Velocity profile of the fluid flowing through the collector.

This equation is in agreement with Mahr (1991) and Unger (1988). It is assumed that no fluid from the exterior reaches the chimney. The pressure equation (31) is a helpful equation indicating the mass flow rate. In the general case of the flow with friction, the calculation of the mass flow rate from the pressure equation can be conducted only iteratively. 4. Results and discussion 4.1. Model results The numerical solution of the model was obtained for the geometry of the prototype in Manzanares, Spain (Schlaich, 1995), which from now on is called the model results. Because the whole model can be solved only iteratively, an algorithm based on iteration is proposed, and the initial values were assumed for mass flow rate and heat transfer coefficients. Figs. 3–5 illustrate the temperature, velocity and pressure distributions in the solar collector of the solar chimney power plant for three different solar radiations. The flow direction is from right to left in all the following figures. Fig. 3 shows the influence of solar radiation and collector radius on the temperature profile of fluid flowing through the collector. When the solar radiation is constant,

Fig. 5. Static pressure profile of the fluid flowing through the collector.

the temperature of fluid increases by decreasing the radius. Fig. 3 implies that, when the solar radiation increases, the air temperature increases for the same collector radius. Fig. 4 shows the air velocity profile through the collector. The velocity increases through the collector by decreasing the radius, but it increases more sharply by reaching the chimney base. When the collector radius is constant, an increase of solar radiation causes an increase of the air velocity, but the effect is not very significant.



Fig. 6. Temperature profiles of the roof, earth and fluid through the collector.

Fig. 5 shows the static pressure profile, which decreases through the collector and drops dramatically near the chimney base. It also demonstrates that increasing solar radiation results in a decrease in the static pressure when the collector radius is constant. Fig. 6 illustrates the roof, earth and fluid temperature profiles through the collector. As shown in Fig. 6, by decreasing the collector radius, all the temperatures increase, but the air temperature increases more steeply. As expected, the earth temperature is much higher than the others. 4.2. FLUENT results In this part of the study, the numerical simulation of the solar chimney power plant is presented. A physical model

7

for a solar chimney power plant was built based on the geometrical dimensions of the prototype Manzanares. The basic equations including the models discussed up to now were numerically solved with the help of the commercial simulation program FLUENT (version 6.3). The basic equations were simplified to axisymmetric and steady state. Because a turbulence model is necessary for the description of the turbulent flow conditions, the standard k–e model and standard wall mode were selected to describe the fluid flow inside the collector and the chimney (Fluent Inc., 2005). The plant was divided into the areas of the collector, collector inlet, chimney, turbine, earth, chimney outlet and environment and the connecting point between the collector and chimney. The main boundary conditions are illustrated in Table 1. The domain was discretized with 95,780 two-dimensional unstructured mesh elements, with cell sizes ranging between 0.1 m and 1.0 m and mesh growth rates of 5%. Because large gradients appeared near the walls, the grid was refined adaptively. The accuracy of all approximations

Table 1 The main boundary conditions. Place

Type

Description

Glass roof Ground surface Chimney wall Chimney axis Collector inlet Chimney outlet

Wall Wall Wall Axis Pressure_inlet Pressure_outlet

T = g(r) K T = f(r) K q = 0 W m2 Symmetry Dp = 0 Pa, T0 = 293 K Dp = 0 Pa

Fig. 7. Temperature, velocity and pressure distributions of the solar chimney power plant for q = 600 W m2.


8


was second order. All numerical calculations had to be performed with the solver with double precision. The iteration error was at least 106 for all calculations, and was at least 109 for the energy equation. Under these conditions, the solution converged in less than 3000 iterations. Fig. 7 shows the temperature, pressure and velocity distributions in the collector for a given solar radiation. Fig. 7a shows the temperature distribution of the solar chimney power plant. This figure shows that the temperature of fluid inside the chimney reaches about 314.5 K. Fig. 7b shows the velocity distribution of the power plant. From the figure, it is evident that the air velocity increases through the collector and the maximum velocity is at the chimney base. When the solar radiation is 600 W m2, the maximum velocity inside the power plant is about 11.8 ms1. The static pressure distribution of the solar chimney power plant has shown in Fig. 7c. The static pressure decreases through the collector up to 123.8 Pa and starts increasing through the chimney up to zero. It is obvious that the minimum value of static pressure lies at the bottom of the chimney.

Fig. 8. Temperature profile of the fluid flowing through the collector for q = 600 W m2.

4.3. Validation of the numerical results with the experimental data To validate the numerical results, the temperature increase in the collector and the upwind velocity at the chimney base are compared with the experimental data of the Spanish prototype (Haaf et al., 1983). The experimental results indicate that, when the solar radiation is 1000 W m2, the upwind velocity at the chimney base is 15 ms1, and the temperature increase through the collector with no-load condition reaches 20 K. As is shown in Table 2, good quantitative agreement was obtained between the experimental data of the Manzanares prototype and both of the numerical results.

Fig. 9. Velocity profile of the fluid flowing through the collector for q = 600 W m2.

4.4. Comparison between the model and FLUENT results After validating the numerical results, the main parameters, such as temperature, pressure and velocity distribution were compared between the calculations of the model and the FLUENT results. The temperature, pressure and velocity profiles in the collector for both numerical results are shown in Figs. 8– 10 for a given solar radiation (q = 600 W m2). As Fig. 8 shows, the temperature of fluid increases by decreasing the radius. By comparing the profiles in Fig. 8, a good correspondence is proven, except for the entrance area. Table 2 Comparison between the numerical results and the experimental data. Results

Temperature increase

Upwind velocity

Experimental data Model FLUENT

DT = 20 K DT = 20.25 K DT = 20.96 K

V = 15 ms1 V = 15.05 ms1 V = 14.81 ms1

Fig. 10. Pressure profile of the fluid flowing through the collector for q = 600 W m2.

Fig. 9 shows the air velocity profile through the collector for both the model and FLUENT results. The velocity increases through the collector by decreasing the radius and reaching the chimney base, where it increases more sharply. Fig. 9 also shows good agreement between model and FLUENT results.



Fig. 10 shows the pressure profile, which decreases through the collector, and, when it approaches the chimney base, it drops dramatically. By comparing the profiles in Fig. 10, a complete correspondence is proven, except for the middle area. 4.5. Comparison of the model and the results of Pastohr et al. Figs. 11–13 display a comparison between this model and Pastohr et al.‘s results. The temperature, pressure

Fig. 11. Temperature profile of the fluid flowing through the collector for q = 500 W m2.

9

and velocity distributions for a given solar radiation (q = 500 W m2) are compared. In contrast to the numerical results shown by Pastohr et al. in which the static pressure inside the collector is positive and increases along the flow direction, Fig. 13 illustrates that the relative static pressure is negative, and it decreases along the flow direction inside the collector. 5. Conclusions A more in-depth numerical analysis of solar chimney power plants was presented in this paper. A mathematical model was developed to accurately describe the solar chimney power plant mechanism. Two different numerical simulations were performed to analyze the characteristics of the flow for the geometry of the prototype in Manzanares, Spain, and both results are consistent with the experimental data of the Manzanares prototype. Numerical profiles for the temperature, velocity and pressure in the collector of the solar chimney power plant were shown for three different solar radiations. The results demonstrate the reliability and accuracy of the mathematical model and also suggest that the simple two-dimensional axisymmetric simulation can be used for engineering calculations. Acknowledgements The authors express their acknowledgments to the reviewers for their valuable suggestions. We also extend our gratitude to Professor Mehrzad Shams for the helpful comments and discussions. References

Fig. 12. Velocity profile of the fluid flowing through the collector for q = 500 W m2.

Fig. 13. Pressure profile of the fluid flowing through the collector for q = 500 W m2.

Bernardes, M.A., dos, S., Valle, R.M., Cortez, M.F., 1999. Numerical analysis of natural laminar convection in a radial solar heater. International Journal of Thermal Science 38, 42–50. Bernardes, M.A., dos, S., Voss, A., Weinrebe, G., 2003. Thermal and technical analyzes of solar chimneys. Solar Energy 75, 511–524. Bernardes, M.A., dos, S., von Backstro¨m, T.W., 2010. Evaluation of operational control strategies applicable to solar chimney power plants. Solar Energy 84, 277–288. Bilgen, E., Rheault, J., 2005. Solar chimney power plants for high latitudes. Solar Energy 79, 449–458. Ferreira, A.G., Maia, C.B., Cortez, M.F.B., Valle, R.M., 2008. Technical feasibility assessment of a solar chimney for food drying. Solar Energy 82, 198–205. Fluent Inc., 2005. Fluent 6.3 User Guide. Gannon, A.J., Backstrom, T.W., 2000a. Compressible flow through solar power plant chimneys. Transaction of the ASME Journal of Solar Energy Engineering 122, 138–145. Gannon, A.J., Backstrom, T.W., 2000b. Solar chimney cycle analysis with system loss and solar collector performance. Transaction of the ASME Journal of Solar Energy Engineering 122, 133–137. Gannon, A.J., Von Backstro¨m, T.W., 2002. Controlling and maximizing solar chimney power output. In: 1st International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, Kruger Park, South Africa. Gannon, A.J., Von Backstro¨m, T.W., 2003. Solar chimney turbine performance. Journal of Solar Energy Engineering 125, 101–106.


10


Grigull, U., Siegel, S., Howell, J.R., Lohrengel, J., 1991. Wa¨rmeu¨bertragung durch Strahlung Teil 2 Strahlungsaustausch zwischen Oberfla¨chen und in Umhu¨llungen. Springer Verlag. Haaf, W., 1984. Solar chimneys: part ii: preliminary test results from the Manzanares pilot plant. International Journal of Solar Energy 2, 141– 161. Haaf, W., Friedrich, K., Mayr, G., Schlaich, J., 1983. Solar chimneys: part I: principle and construction of the pilot plant in Manzanares. International Journal of Solar Energy 2, 3–20. Jaluria, J., 1980. Natural convection heat and mass transfer. Pergamon Press, Oxford. Jischa, M., 1982. Konvektiver impuls-wa¨rme-und stoffaustausch. Vieweg Verlag, Wiesbaden. Ketlogetswe, C., Fiszdon, J.K., Seabe, O.O., 2008. Solar chimney power generation project – The case for Botswana. Renewable and Sustainable Energy Reviews 12, 2005–2012. Koonsrisuk, A., Chitsomboon, T., 2007. Dynamic similarity in solar chimney modeling. Solar Energy 81, 1439–1446. Koonsrisuk, A., Lorente, S., Bejan, A., 2010. Constructal solar chimney configuration. International Journal of Heat and Mass Transfer 53, 327–333. Kreetz, H., 1997. Theoretische Untersuchungen und Auslegung eines tempor. Diplomarbeit, TU Berlin, Berlin. Krisst, R.J.K., 1983. Energy transfer system. Alternative Source Energy 63, 8–11. Kro¨ger, D.G., Buys, J.D., 2001. Performance Evaluation of a Solar Chimney Power Plant. ISES 2001 Solar World Congress. Adelaide, Australia. Kulunk, H., 1985. A prototype solar convection chimney operated under Izmit conditions. In: Proceedings of the 7th Miami International Conference on Alternative Energy Sources, Veiroglu, TN, vol. 162. Lodhi, M.A.K., 1999. Application of helio-aero-gravity concept in producing energy and suppressing pollution. Energy Conversion and Management 40, 407–421. Mahr, M., 1991. Numerische und experimentelle Untersuchungen des thermodynamischen Verhaltens von solaren Aufwindanlagen. Dissertation Mu¨nchen. Ming, T.Z., Liu, W., Xu, G.L., 2006. Analytical and numerical simulation of the solar chimney power plant systems. International Journal of Energy Research 30, 861–873. Ming, T.Z., Liu, W., Pan, Y., Xu, G.L., 2008. Numerical analysis of flow and heat transfer characteristics in solar chimney power plants with energy storage layer. Energy Conversion and Management 49, 2872– 2879. Mullet, L.B., 1987. The solar chimney overall efficiency, design and performance. International Journal of Ambient Energy 8 (1), 35–40. Padki, M.M., Sherif, S.A., 1988. Fluid dynamics of solar chimneys. In: Morrow, T.B., Marshall, L.R., Simpson, R.L. (Eds.), . In: Forum on Industrial Applications of Fluid Mechanics, FED-vol. 70. ASME, New York, pp. 43–46. Padki, M.M., Sherif, S.A., 1989a. Solar chimney for medium-to-large scale power generation. In: Proceedings of the Manila International

Symposium on the Development and Management of Energy Resources, Manila, Philippines, vol. 1, pp. 432–437. Padki, M.M., Sherif, S.A., 1989b. Solar chimney for power generation in rural areas. In: Seminar on Energy Conservation and Generation through Renewable Resources. Ranchi, India, pp. 91–96. Padki, M.M., Sherif, S.A., 1992. A mathematical model for solar chimneys. In: Proceedings of 1992 International Renewable Energy Conference, Amman, Jordan, vol. 1, pp. 289–294. Padki, M.M., Sherif, S.A., 1999. On a simple analytical model for solar chimneys. International Journal of Energy Research 23, 345–349. Pastohr, H., 2004. Thermodynamische Modellierung eines Aufwindkraftwerkes. Dissertation Weimar. Pastohr, H., Kornadt, O., Gurlebeck, K., 2004. Numerical and analytical calculations of the temperature and flow field in the upwind power plant. International Journal of Energy Research 28, 495–510. Pasumarthi, N., Sherif, S.A., 1998a. Experimental and theoretical performance of a demonstration solar chimney model – part I: mathematical model development. International Journal of Energy Research 22, 277–288. Pasumarthi, N., Sherif, S.A., 1998b. Experimental and theoretical performance of a demonstration solar chimney model – part II: experimental and theoretical results and economic analysis. International Journal of Energy Research 22, 443–461. Pretorius, J.P., Kro¨ger, D.G., 2006. Solar chimney power plant performance. Journal of Solar Energy 128 (3), 302–311. Pretorius, J.P., Kro¨ger, D.G., Buys, J.D., Von Backstro¨m, T.W., 2004. Solar tower power plant performance characteristics. In: Proceedings of the ISES EuroSun2004 International Sonnenforum, Freiburg, Germany, vol. 1, pp. 870–879. Sampayo, E.A., 1986. Solar–wind power system. Spirit of Enterprise: The 1986 Rolex Awards pp. 3–5. Schlaich, J., 1995. The Solar Chimney Edition Axel Menges. Stuttgart, Germany. Schlaich, J., Schiel, W., Friedrich, K., Schwarz, G., Wehowsky, P., Meinecke, W., Kiera, M., 1990. Abschlußbericht Aufwindkraftwerk, ¨ bertragbarkeit der, Ergebnisse von Manzanares auf gro¨ßere AnlaU gen. BMFT- Fo¨rderkennzeichen, Stuttgart, 0324249D. Schlaich, J., Bergermann, R., Schiel, W., Weinrebe, G., 2005. Design of commercial solar updraft tower systems – utilization of solar induced convective flows for power generation. Journal of Solar Energy Engineering 127, 117–124. Unger, U., 1988. Konvektionsstro¨mungen. Teubner Verlag, Stuttgart. Yan, M.Q., Kridli, G.T., Sherif, S.A., Lee, S.S., Padki, M.M., 1991. Thermo-fluid analysis of solar chimneys. In: Industrial Applications of Fluid Dynamics. ASME, New York, FED-vol. 132, pp. 125–130. Zhou, X.P., Yang, J.K., Xiao, B., Hou, G.X., 2007. Experimental study of the temperature field in a solar chimney power setup. Applied Thermal Engineering 27, 2044–2050. Zhou, X.P., Yang, J.K., Wang, J.B., Xiao, B., Hou, G.X., Wu, Y.Y., 2009. Numerical investigation of a compressible flow through solar chimney. Heat Transfer Engineering 30, 670–676.
