Evaluation of the influence of soil thermal inertia on the performance of a solar chimney power plant

Energy 47 (2012) 213e224

Contents lists available at SciVerse ScienceDirect

Energy journal homepage: www.elsevier.com/locate/energy

Evaluation of the influence of soil thermal inertia on the performance of a solar chimney power plant F.J. Hurtado, A.S. Kaiser, B. Zamora* Dpto. Ingeniería Térmica y de Fluidos, Universidad Politécnica de Cartagena, Doctor Fleming s/n, 30202 Cartagena, Spain

a r t i c l e i n f o

a b s t r a c t

Article history: Received 20 January 2012 Received in revised form 20 August 2012 Accepted 19 September 2012 Available online 17 October 2012

Solar chimney power plants are a technology capable to generate electric energy through a wind turbine using the solar radiation as energy source; nevertheless, one of the objectives pursued since its invention is to achieve energy generation during day and night. Soil under the power plant plays an important role on the energy balance and heat transfer, due to its natural behavior as a heat storage system. The characteristics of the soil influence the ability of the solar chimney power plant to generate power continuously. Present work analyzes the thermodynamic behavior and the power output of a solar chimney power plant over a daily operation cycle taking into account the soil as a heat storage system, through a numerical modeling under non-steady conditions. The influence of the soil thermal inertia and the effects of soil compaction degree on the output power generation are studied. A sizeable increase of 10% in the output power is obtained when the soil compaction increases. Ó 2012 Elsevier Ltd. All rights reserved.

Keywords: Updraft solar chimney Thermal inertia Turbulent convective flow Numerical simulation

1. Introduction Solar chimney power plants (also called solar updraft towers or briefly solar towers) are a technology able to generate electric energy from solar radiation as primary energy source. It can be regarded as a combination of technologies: solar greenhouse, convective chimney (or tower), and wind turbine; in fact, its operation is based on the exploitation by a wind turbine of the airflow generated inside the system by heat convection and chimney effect. The first prototype on record was built by Isidoro Cabanyes [1] (Colonel in Artillery) in Cartagena (Spain) in 1903. He called this pioneering prototype as solar engine. In more recent times, Prof. Jörg Schlaich presented this technology in a congress at the end of the seventies (Pasumarthi and Sherif [2], Schlaich [3]). Schlaich and colleagues (company Schlaich, Bergermann und Partner) designed and constructed the first modern prototype (able to generate electric power) in Manzanares, located in the region called La Mancha (Spain), in 1981. The structural characteristics and experimental data resulted of the operation of this prototype between 1981 and 1983 were published by Haaf et al. [4] and Haaf [5]. Following the key studies conducted in Manzanares, it can be found different experimental prototypes (Gannon and Backström [6], Zhou et al. [7], Maia et al. [8]) and a large number of studies, carried out over the last decade, which proved that this technology

* Corresponding author. Tel.: þ34 968 325 982; fax: þ34 968 325 999. E-mail address: [email protected] (B. Zamora). 0360-5442/$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.energy.2012.09.040

is able to generate clean and profitable energy (Sangi [9]). A variety of proposals for the construction of solar chimney power plants by several governments, companies or institutions can be found. Zhou et al. [10] have conducted a detailed review work. 1.1. Current trends Studies about solar chimneys power plants developed since 1980 cover many fields. Several thermodynamic studies analyzed the design parameters of solar chimney power plants and obtained mathematical models to establish correlations between the fluid dynamics variables of airflow and the structural characteristics of the plant (Yan et al. [11], Bernardes et al. [12], Backström and Gannon [13], Zhou et al. [14], for instance). The influence of several soil types on the energy production of the plant was studied by Bernardes et al. [15], and Pretorius and Kröger [16]. Exergy analysis of airflow inside the system to determine available energy and humidity influence was developed by Ninic [17] and Petela [18], who in addition discussed the possibility of including a heat concentration system at ground level. The optimization of the system was analyzed in several studies to determine the influence of different parameters such as chimney height by Zhou et al. [19], or to maximize the power production by Backström and Fluri [20]. Fluri and Backström [21], and Nizetic and Klarin [22] studied the optimum pressure drop in the wind turbine. Cost production analysis and environmental impact studies were developed and compared with other energy technologies by Trieb et al. [23], Nizetic et al. [24], Fluri et al. [25], Zhou et al. ([26] [27],) or

214

F.J. Hurtado et al. / Energy 47 (2012) 213e224

Nomenclature a,.,e cp f g Gr H I It k N m P p Pr R Rg Ra T t Uj us yþ

adjustment coefficients in polynomial correlations specific heat at constant pressure (J kg1 K1) exploitation factor, dimensionless gravitational acceleration (m s2) Grashof number, dimensionless height (m) solar radiation (W m2) turbulence intensity, dimensionless turbulent kinetic energy (m2 s2) output power (W) mass flow rate (kg s1) average pressure relative to the ambient (N m2) pressure (N m2) Prandtl number, mcp/k, dimensionless radius (m) air constant (J kg1 K1) Rayleigh number, (Gr) (Pr), dimensionless temperature (K) time (s) average components of velocity (m s1) friction velocity, us¼(sw/r)1/2 (m s1) y1us/n, dimensionless

distance between the wall and the first grid point (m)

y1

Greek symbols thermal diffusivity (m s2) thermal expansion coefficient, 1/TN (K1) pressure drop (N m2) temperature difference, T  TN (K) ( C) ε dissipation rate of k (m2 s3) k thermal conductivity (W m1 K1) h efficiency, dimensionless m viscosity (kg m1 s1) n kinematic viscosity, m/r (m2 s1) r density (kg m3) ra apparent density (kg m3) sw wall shear stress (N m2)

a b DP DT

Subscripts B base of the chimney (wind turbine inlet) C collector T tower (chimney) S soil t turbulent W wind turbine N ambient or reference conditions

Hamdan [28]. Structural analysis of wind effects over the behavior of a solar tower were developed by Schlaich [29] and Harte et al. [30], who proposed different solutions to provide stiffness and dynamic stability. Load factor, degree of reaction and efficiency of the wind turbine were analized by Backström and Gannon [31]. Different models for the performance of wind turbines and their locations within the plant were proposed by Denantes et al. [32], and Fluri and Backström [33]. The use of the conceptual device solar cyclone in a solar chimney power plant has been studied by Kashiwa and Kashiwa [34]. A current trend is to use ground under the power plant as energy storage system, in order to achieve energy generation during times without solar radiation. Some studies developed numerical models that included soil as a heat storage system through a porous medium, such as those conducted by Ming et al. [35] and later by Xu et al. [36], who besides analyzed the pressure drop influence over the wind turbine for different airflow conditions. Ming et al. [35], Xu et al. [36] and Sangi et al. [37] (who analyzed the effects of collector dimensions) studied solar chimneys power plant with energy storage system only under steady conditions. 1.2. Briefly system description. The role of soil The system is composed on one side by a collector of translucent material located at certain height above the soil surface, and on the other side by a large chimney (tower) installed at the center of the collector (see 1Figs. 1 and 2). The collector acts like a greenhouse, allowing solar radiation to reach soil surface and heating the air by convection from soil surface through the space comprised between the collector outside and the chimney base. The updraft established as a result of the pressure drop caused by the buoyancy effects is exploited through a wind turbine coupled to an electric generator, located within the chimney or around its base.

1

Graphic design: S. Diaz-Madroñero M.

Fig. 1. Scheme of a solar chimney power plant a) overview. b) Basic operation.

F.J. Hurtado et al. / Energy 47 (2012) 213e224

215

radius of the collector HC ¼ 1.85 m and RC ¼ 122 m, respectively (Fig. 2). The base of the chimney (subscript B) is regarded as the union section between the chimney and the canopy (collector); therefore, this section is also regarded as the inlet of the wind turbine (subscript W). The placement height of the inlet of wind turbine is HW ¼ 9 m above ground. The airflow established within the collector and the chimney is simulated by the numerical solution of the governing equations of motion. In order to study the influence of soil behavior in the operation of the solar tower, it is mandatory to carry out transient computations for the regarded problem. 2.1. Proposed thermal balance

Fig. 2. Computational domain and boundary conditions for a typical solar chimney power plant.

The natural behavior of the ground is like a heat storage system; due to its material constitution and stratification, the soil stores some of the radiation received during the day. At no-radiation time, when the ambient temperature is lower than the soil temperature, then soil releases the energy accumulated during the day, producing the same buoyancy effects explained above (but in this case without solar radiation). The effects of the soil properties on the updraft generated within the plant, and on the daily cycle of absorbed and transferred energy in the soil surface, must be taken into account to determine on one hand the power output of the solar chimney power plant and on the other hand, to analyze the ability to generate daily continuous power.

To carry out a study under non-steady conditions and reproduce the daily solar radiation cycle, it is necessary to identify the energy balance of the system. From some experimental data obtained by Haaf [5], and completing the study through the analysis of the radiative properties of the materials present in the Manzanares pilot plant, it is possible to raise a balance for the distribution of the received solar radiation in the Manzanares prototype. The regarded values of absorptivity, transmisivity and reflectivity were respectively equal to 5%, 79% and 16%, for the collector cover, and equal to 80%, 0% and 20%, for the surface layer of the ground. It should be noted that although Haaf [5] pointed out that the absortivity of soil reached 91% due to the bitumen coating (explained later), in this work it is assumed to be equal to 80%, because of the mixing of bitumen with the original soil material. Summarily, the solar radiation received by the collector cover is divided into three parts. The first part is the radiation absorbed by the collector itself (5%, from which 2/3 is transferred by convection effects to outside air, and 1/3 to the working air). The second part is the radiation that reaches the ground (79%); it is assumed that 20% of this radiation is reflected. The third part is the reflected radiation to the outside air (16%). According Haaf [5], 1/3 of the longwave radiation emitted by the surface layer of soil can be regarded as lost. Finally, 42.3% of the incident solar radiation is distributed from the soil surface to working air by convection and to the underground by conduction.

1.3. The aim of this work 2.2. Starting data Since a lack of systematic studies on the soil thermal inertia influence on the performance of solar chimney power plants has been detected, present work analyzes the thermodynamic behavior and the power production of a solar chimney power plant over a daily operation cycle under non-steady conditions, taking into account the soil as a heat storage system. In fact, a detailed study on the limestone soils stratification is presented, in order to describe adequately a given soil type. Firstly, some boundary conditions and medium properties, such as ambient properties of air and soil properties and its depth dependence, as well as the performance of the wind turbine, are reproduced through analytical correlations, from the analysis of experimental data on Manzanares power plant, throughout the day 2 September, 1982 (Haaf et al. [4], Haaf [5]). Secondly, transient numerical results for the fluid motion established in the Manzanares prototype are presented, including the required validation with appropriate experimental results. Finally, the effects of the soil thermal inertia and the soil compaction on the behavior and the output power of the system are analyzed and determined. 2. Physical model The geometry of the Manzanares prototype is reproduced in this work (Fig. 1). The main dimensions are: height and radius of the chimney HT ¼ 194.6 m and RT ¼ 5.08 m, respectively; height and

The ambient conditions of air (TN, PN) and solar radiation (I), updraft temperature and updraft velocity of air at the base of chimney (TB and UB, respectively), pressure drop (DP)W at the wind turbine, and soil properties and its depth dependence, as a function of the time of day, were determined by Haaf [5] in the Manzanares prototype (on the day 2 September, 1982). In order to obtain accurate numerical solutions, the parameters measured experimentally by Haaf [5] are fitted on one hand to time-dependent analytical correlations for the solar radiation and ambient conditions of air, and on the other hand, to correlations dependent on the depth for soil properties and dependent on the updraft conditions (at base of chimney) for the wind turbine performance. In Fig. 3, it can be observed the solar radiation I and the ambient temperature TN, as a function of the time of day t. Both variables have been fitted to polynomial functions, TN ¼ at3þbt2þct þ d, I ¼ at4þbt3þct2þdt þ e, with t in seconds and the adjustment coefficients a,b,c,d,e according to different periods of the day (see Table 1). Note that the averaged value of the correlation coefficient R2 is about 0.99. The performance curve of the suitable wind turbine (that is, the relationship between the pressure drop and the updraft velocity) shown in Fig. 4, has been obtained through the relationship between the pressure drop and the updraft velocity at the base of the chimney, experimentally measured by Haaf [5]. The

216

F.J. Hurtado et al. / Energy 47 (2012) 213e224

Fig. 3. Solar radiation and ambient temperature versus the time of day, for the Manzanares prototype.

experimental values of the updraft velocity as a function of time of day are correlated following a procedure similar to that described above for TN and I, with a correlation factor R2 ¼ 0.96. Note that the turbine starts for values of the inlet air velocity higher than 4.5 m/s. These correlations are implemented as boundary or initial conditions in the numerical modeling. Summarily, it can be concluded that this procedure allows the validation of the numerical model that reproduces the Manzanares plant with soil heat storage system and permit us to carry out realistic transient simulations. 2.3. Physical modeling of the soil It is well-known that the power generation in a solar chimney power plant is mainly determined by the difference of temperature between the inlet and the outlet sections of the chimney, which in turn depends on the heat transfer processes between the working air inside the collector, the soil surface layer and the lower soil strata. The soil thermal inertia is concerned with the heat transfer rate caused by a given temperature gradient. Thus, it seems clear that the thermal diffusivity of the soil aS¼(k/rcp)S plays a key role in the regarded problem. Therefore, the variations of the thermal conductivity kS, density rS and specific heat cp,S with the depth must be determined. Manzanares power plant was built over a limestone soil. Due to stratification and the effect of pressure from upper layers, different characteristic parameters of the soil, such as the grain size and the interstitial space can vary significantly with depth. In this way, superficial strata of the soil can be considered as a porous material with a certain apparent (or bulk) density, ra,S, lower than the own density (or mass density) of the material forming the soil, rS. It is expected that for high enough depths, ra,S tends to be equal to rS. The variation of these properties with depth depends largely on the soil composition, the exposure to environmental agents and the effects of human activity. At least, three layers can be distinguished in the surface stratification of limestone soils: a) the superficial thin

layer (high compacted, due to exposure to environment), which acts like an insulation of the following layer; b) the intermediate layer, with high porosity, and c) the lower strata. The nominal properties of a limestone soil as Manzanares plant are: density and apparent density, rS ¼ 1900 kg/m3 and ra,S ¼ 950 kg/m3, respectively; specific heat cp,S ¼ 840 J/Kg K, and thermal conductivity kS ¼ 1.26e1.33 W/m K. A surface coating of bitumen with 1 mm thickness is considered for modeling purposes, with absorptivity and reflectivity equal to 80% and 20%, respectively. In order to be used in the numerical computations, soil thermal conductivity (Fig. 5a) and soil apparent density (Fig. 5b) as a function of depth are determined by an analysis of the limestone soil stratification, along with experimental data of the thermal conductivity (Haaf [5], Fig. 5a) and the experimental values of the soil temperature for the Manzanares prototype. The specific heat is assumed constant, cp,S ¼ 840 J/Kg K. In the Manzanares plant, the experimentally measured soil temperature at 1 m depth was 31.3  C. It can be observed in the experimental data of Haaf [5] that the maximum values of temperature are reached for each depth at different times of the day, due to thermal inertia of soil; in this way, the reference time for initial conditions of the transient study is taken at noon. Summarily, it should be remarked that the soil is simulated as a solid body with the appropriate physical properties, taken from the experimental Manzanares data, to act as a heat storage element (Pastohr et al. [38]). It is assumed that the process of heat transfer occurs only by transient conduction, without convective effects. Other approaches are possible for this energy storage layer, such as assuming the soil as a porous media, for which the conservation equations for the fluid flow and heat transfer are solved (Ming et al. [35], for instance). 3. Mathematical modeling 3.1. Background The conservation equations for the airflow established within the collector and the chimney are described below. Given the geometry of the model, it is assumed that the flow is axisymmetric. The energy equation is also applied to the soil in order to simulate the transient conduction heat transfer. The characteristic values of the Rayleigh number, this given by Ra¼(Gr) (Pr), being Gr ¼ gb(DT) H3/n2 and Pr ¼ rcp/k the Grashof and Prandtl numbers respectively, are always above the threshold 1010. Therefore, the fluid motion must be simulated as turbulent. As explained above, the ambient temperature are given by Fig. 3, whereas the ambient pressure is taken equal to 101,325 N/m2, regarded as constant; in addition, thermal conductivity and apparent density of the soil is set according to depth dependence shown on Fig. 5a and b, respectively. The airflow can be simulated using a cylindrical coordinate system, assuming axisymmetric hypothesis (see Fig. 2). The governing equations expressed in a cylindrical reference system can be found in Maia et al. [8], for instance. The turbulence closure problem is solved through the two transport equations k  ε (see

Table 1a Polynomial coefficients (and R2 factor) to correlate experimental values of: a) the ambient temperature TN (K). Time interval of day 00: 05: 10: 20:

00 20 00 40

< < < <

t t t t

   

05: 10: 20: 24:

20 00 40 00

a 2.13 1.66 2.22 1.66

b    

13

10 1012 1014 1012

4.42 4.08 2.17 4.08

c    

09

10 1007 1009 1007

1.25 2.36 4.85 3.36

R2

d    

04

10 1002 1004 1002

2.95 1.23 2.85 1.23

   

02

10 1003 1002 1003

0.988 0.997 0.949 0.994

F.J. Hurtado et al. / Energy 47 (2012) 213e224

217

Table 1b Polynomial coefficients (and R2 factor) to correlate experimental values of: b) the solar radiation I (W/m2). Time interval of day 00: 05: 08: 10: 20:

00 40 20 00 40

< < < < <

t t t t t

    

05: 08: 10: 20: 24:

40 20 00 40 00

a

b

c

d

e

R2

0 2.71  1014 0 0 0

0 2.89  1009 3.22  1012 3.61  1010 0

0

0 2.03  1000 1.58  1001 3.95  1000 0

0

1 0.999 0.999 0.999 1

1.16  1004 1.59  1006 6.58  1005 0

Wilcox [39], for instance). Given the big scale of the airflow within the chimney, it can be considered that the turbulent regime is fully established, so that wall functions are used to describe the flow behavior near the walls. With respect to the thermophysical properties of air, the specific heat at constant pressure is considered constant cp ¼ cp,N, and the perfect gas assumption leads to the state equation r ¼ p/RgT, with Rg the air constant, equal to 287 J/Kg K, whereas the following temperature dependence laws of the viscosity and the thermal conductivity are introduced




m T ¼ mN TN

3=2


3=2 TN þ110:6 k T TN þ202:2 ¼ ; : T þ110:6 kN TN T þ202:2

(1)

3.2. Boundary conditions In order to describe the boundary conditions required for the present problem, it is necessary to consider the locations depicted on Fig. 2; for example (1) means the inlet section to the collector; (2) means the cover collector, and so on. e Entry/exit sections. The continuity condition is imposed in section (1) and (10) of Fig. 2, and the streamwise variations of velocity components, temperature and turbulent magnitudes k and ε are neglected. In addition, the following boundary conditions for pressure are used:  Entry section (1). A reduced total-pressure P P þ rð 3j¼1 Uj2 Þ=2 ¼ 0 is assumed, which is equivalent to using the Bernoulli equation at the entrance region out the collector. The air temperature is fixed equal to the ambient temperature TN. Initial values of k and ε at the entry had to be applied to start the computations. The initial value for turbulent kinetic energy k is applied by the turbulence intensity concept It, defined as:

It ¼

1.29  1004 2.73  1003 7.74  1004 0

½ð2=3Þk1=2 ; U

(2)

 where U is the main average velocity at the entry section. In 2 this way, it is imposed k ¼ ð3=2ÞIt2 U and ε ¼ k2/nt at the entrance, with nt z 40 n as reference value. In order to obtain systematic results the turbulence intensity It is limited to 5%.  Exit section (10). A reduced pressure P ¼ 0 (pressure equal to the ambient pressure) is applied.

0

00

e Walls. At walls (23 3 568) the no-slip boundary condition is imposed on the average and turbulent velocity components, along with turbulent wall functions. At the tower wall (8), the heat flux is assumed negligible in comparison with the heat generation at the ground and equivalent to shadow projected over collector and ground; therefore the chimney wall is assumed as an adiabatic wall (k[vT/vn] ¼ 0, with n a coordinate perpendicular to the wall). With regard to the limestone soil (4), the lower limit (40 ) is assumed as isothermal (with TS ¼ 31.3  C, experimentally measured in Manzanares plant on 2 September, 1982), whereas the side limits (400 ) are assumed as adiabatic walls. e Collector cover and soil surface layer. From the experimental solar radiation I given in Fig. 3, and by using the energy balance depicted in Fig. 3, it can be deduced that the energy transferred by convection from collector cover (2) to working air is fixed at 1.67% of I. In addition, the useful energy over the soil surface layer (30 ) (which can be transferred by convection to working air or conduction to lower soil strata) is fixed at 42.13% of I, as above explained (at noon). For modeling purposes, the collector cover (2) and the surface soil layer (30 ) are regarded as energy generating elements, on which the above heat flux values are imposed, taking into account the influence of solar incidence angle over transmittance of the collector. The soil surface below the junction cover between the collector and the 00 chimney (3 ) is considered shaded, so that without energy generation caused by solar radiation but able to transmit heat energy from underground. e Inlet of the wind turbine. The behavior of the wind turbine is given by its inlet conditions (7), through the curve shown in Fig. 4, considering a minimum air velocity at the inlet of 4.5 m/s.

3.3. Initial conditions

Fig. 4. Performance curve of the wind turbine, obtained through pressure drop and updraft velocity experimentally measured by Haaf [5] in the Manzanares prototype, at the base of the chimney.

To carry out an appropriate transient simulation along the time of one day, including the effects of the soil heat storage, the numerical calculation should be based in the status of the last day. To simulate the natural thermal inertia of soil (which is derived from its continuous and repetitive exposure to the daily solar cycle throughout the year), it is necessary to start the transient study from conditions whose conform accurately to the experimental data obtained in a time of the day 1 September, 1982. Hence, the

218

F.J. Hurtado et al. / Energy 47 (2012) 213e224

Fig. 5. Properties of the soil in the Manzanares prototype at the center of the collector, at different depths. a) Thermal conductivity. b) Apparent density.

study should be conducted from this moment until the end of day 2 September, 1982. The initial conditions for the transient simulation are adjusted to those taken at 12:00 h on 1 September, 1982; since experimental data are only available on 2 September, 1982, it is assumed that the ambient conditions on 1 September, 1982, are identical to the conditions on 2 September. 4. Numerical approach The governing equations are discretized and solved numerically assuming axisymmetric flow in the domain showed on Fig. 2 by using the general-purpose ANSYS-Fluent code, based on a finite volume procedure. The equations are discretized using the PRESTO scheme, which is similar to the well-known staggered-grid scheme. To avoid the appearance of false diffusion, the results are achieved employing the linear third-order ‘quick’ scheme (Leonard [41]). The SIMPLE algorithm is used to solve the coupling between continuity and momentum equations through pressure. With regard  convergence, for each time step, the  to numerical   criterion was ðfiþ1  fi Þ=fi   105 , where f can stand for any of the dependent variables and i denotes the iteration number; besides the normalized residuals for mass, momentum, energy and turbulent variables for the full flow field had to be below 105. The number of time step was chosen by one side to satisfy the Courant limit and on the other to get sufficiently accurate solutions. Structured, non-uniform meshes are employed to obtain the numerical results. Different power-law distributions are applied mainly to get fine meshing near the walls, entry and exit sections. The accuracy of the numerical results was tested by a grid dependence study. The presented results are obtained by using a structured tetrahedral mesh integrated by 182,574 elements. Since standard wall functions are employed near the walls, the values of the non-dimensional distance to wall yþ (yþ ¼ y1us/n, being us¼(sw/ r)1/2 the friction velocity, and y1 the distance between the wall and the first grid point) are comprised in the range 30e100. In the soil, the concentration of elements is adapted by a power-law distribution according to soil properties variation with depth. The modeling of ambient conditions, limestone soil properties, cover collector and soil surface layer as energy generating elements, and the wind turbine behavior, which have been previously explained, are implemented in Fluent through six appropriate subroutines, written in the own programming language of the code (UDF, Fluent’s User-Defined Function).

5. Results and discussion As a preliminary matter, it should be noted that the analysis of experimental data obtained in the Manzanares prototype shows that the chimney behavior is strongly influenced by the environmental conditions outside. The variability in the experimentally measured air velocity at the inlet to the turbine is a result of these factors, which have not been taken into account in developing the numerical model because it aims to be generic. Focusing on the numerical results, from the proposed thermal balance, it can be observed in Fig. 6 the obtained thermal network for the Manzanares prototype, at noon. Firstly, the validation of the developed model is presented below, through the comparison with the experimental data obtained by Haaf [5] in the Manzanares plant, respectively for stationary and transient conditions. Secondly, a relevant note on the overall behavior of the plant is discussed. Thirdly, the influences of the thermal inertia of soil, as well as the effects of its degree of compaction, are studied. 5.1. Validation of the model The numerical model described in this work has been previously applied by the authors to accurately simulate the flows induced by buoyancy effects in thermal passive systems (Trombe walls, solar chimneys), as it can be found for instance in Zamora and Kaiser [40]. The temperature and the velocity of air at the chimney base, as well as the soil temperature for different depths at 12:00 h on 2nd September, 1982, was obtained by numerical computation and was used as the initial conditions for the transient calculation. It can be observed in the Table 2 the ratio of accuracy with the experimental data reported by Haaf [5]. With regard to the transient simulation, it can be observed in Fig. 7 that the numerical results obtained for the temperature of air in the inlet section of the wind turbine, depending on time of day, follow a same trends that the experimental results of Haaf [5], with an average deviation of 12%. The results obtained for the air velocity in the same section are shown in Fig. 8. In this figure, if the values for intervals around 8:00 and 20:00 are discarded (the respective rapid increase and decrease reached in the stack effect can be due to external atmospheric agents), the average deviation is equal to 11%. The numerical results have been also compared with those theoretically obtained by Zhou et al. [19], obtaining a good agreement.

F.J. Hurtado et al. / Energy 47 (2012) 213e224

219

Fig. 6. Thermal network for the Manzanares prototype, at noon.

It can be observed in Fig. 9 the comparison between the expected results for the power obtainable from wind turbine, given by

  2 NW ¼ hW ðDPÞT UB pR2T ; 3

(3)

and those obtained by Haaf [5], obtaining the same trend and an average relative deviation equal to 18%. It is assumed that it is possible to exploit 2/3 of the total-pressure drop through the chimney (DP)T, and hW ¼ 0.83, with UB the updraft velocity at the chimney base (Haaf [5]). Finally, it can be observed in Fig. 10 the evolution with the time of the soil temperature at several depths, along a vertical coordinate at the center of the collector. The results shown in Fig. 10 should be compared with those experimentally obtained by Haaf [5]. Note that the agreement is very satisfactory, being the trends similar, with average deviations with respect to the experimental results 4.57, 5.34, 5.53 and 1.73%, at 0, 5, 10 and 50 cm depth, respectively. Summarily, the numerical model can be considered valid because of the successful comparison with experimental data obtained in the Manzanares pilot plant. The transient model reproduces the variation throughout the day of the updraft properties and the pressure drop caused by the turbine, with a low deviation. In addition, the numerical model reproduces with accuracy the behavior of the soil as a heat storage system, the soil temperature variation with depth and the soil energy contribution in the hours with no solar radiation.

5.2. Note on the overall performance of the plant In order to show an overall idea on the solar chimney plant performance, Fig. 11 shows the clear relationship established between the updraft velocity (at the turbine inlet) and the difference of temperature (between the chimney base and the ambient). Note that the numerical results shown in this figure are obtained for any time of day. The trend of the results is essentially linear; the following correlation fits the numerical results with a coefficient of determination of 0.978,

UB ¼ 3:13 þ 0:212ðDTÞB :

(4)

The mass flow rate m established through the chimney (m ¼ rBUB(pRT2)) is presented in Fig. 12, for the diurnal cycle. The obtained numerical results are compared with those obtained for

Table 2 Comparison with some experimental data of Haaf [5], for the Manzanares prototype. Variable (air)

Location

Value

Temperature Velocity Temperature Temperature Temperature Temperature

Chimney base Chimney base Center of collector, Center of collector, Center of collector, Center of collector,

46.48 9.244 64.60 39.46 37.12 33.73

surface 5 cm depth 10 cm depth 50 cm depth

Deviation (%) 

C m/s  C  C  C  C

6.0 4.0 0.01 2.3 5.8 0.1

Fig. 7. Comparison between the numerical results and the experimental values of updraft temperature (at the wind turbine inlet) as a function of the time of day.

220

F.J. Hurtado et al. / Energy 47 (2012) 213e224

Fig. 8. Comparison between the numerical results and the experimental values of updraft velocity (at the wind turbine inlet) as a function of the time of day.

Fig. 10. Comparison between the numerical results and the experimental soil temperature versus the time of day, at different depths, measured by Haaf [5].

a hypothetical free chimney case (that is, without wind turbine), in which can be assumed that

m follow roughly the trend corresponding to f ¼ 4/5, instead that corresponding to 2/3. This fact indicates that the wind turbine could exploit about 80% of the available pressure drop.

ðDPÞT ¼ gHT ðrN  rB Þ;

5.3. Influence of the soil thermal inertia

(5)

being rB the density at the chimney base, and then the updraft velocity (at the chimney base) can be estimated as

 UB ¼

2

ðDPÞT

1=2

rB

:

(6)

As expected, the obtained mass flow rate is higher for the free chimney scenario. Since the pressure drop exploited by wind turbine causes that the established air velocity decreases, it can be written that

 UB ¼

2

ð1  f ÞðDPÞT

rB

1=2 ;

(7)

being f an exploitation factor of the pressure drop, whose value was established by Haaf [5] at around 2/3 (as exposed above). However, it can be observed in Fig. 12 how the numerical results obtained for

Fig. 9. Comparison between the numerical results and the experimental values of power obtainable from the wind turbine as a function of the time of day.

At the ground, the heat received from solar radiation is stored in the lower strata of the soil; in this way, at not too large depth, the temperature becomes constant throughout a daily cycle. It was probed experimentally that the changes in the working air temperature affect only a surface layer of soil (about 10 cm thick); this effect has been reproduced successfully in this work through numerical simulation. The obtained distribution of the solar radiation reaching the ground along a daily cycle is shown in Fig. 13. It can be observed how the ground surface reaches an energy level higher than the air inside the collector (in a short period of time); this can be explained by the difficulty to transmit heat to lower strata, caused by the intermediate layer of high porosity of the soil. The amount of energy collected by the air within the collector depends on the reached solar radiation and the energy stored in the soil that is transferred to the working air. During the period of rising solar radiation (from dawn to the zenith), the energy is stored in the

Fig. 11. Overall performance. Updraft velocity (at the wind turbine inlet) as a function of the corresponding updraft temperature difference. Numerical results obtained for different times of day.

F.J. Hurtado et al. / Energy 47 (2012) 213e224

Fig. 12. Overall performance. Mass flow rate established in the chimney as a function of the updraft temperature difference (at the wind turbine inlet), diurnal cycle. Numerical results obtained for different times of day.

221

Fig. 15. Soil thermal inertia. Updraft velocity (at the wind turbine inlet) versus solar radiation, obtained numerically.

soil, which acts as a cold focus, while the air in the collector is heated mainly by solar radiation. For a given point in the period of falling solar radiation (from the zenith to sunset), the soil acts like a hot focus, giving up its accumulated energy to the air within the collector (this fact occurs approximately after 16:00 in Manzanares plant). Thus, for the same solar radiation (excluding zenith situation), it can be found two different values for the heat flow

Fig. 13. Soil thermal inertia. Distribution of the solar radiation reaching the ground surface, obtained numerically.

Fig. 14. Soil thermal inertia. Updraft temperature difference (at the wind turbine inlet) versus solar radiation, obtained numerically.

Fig. 16. Numerical investigation on the soil compaction influence. a) Energy transferred to underground, versus time of day. b) Soil temperature, as a function of time of day.

222

F.J. Hurtado et al. / Energy 47 (2012) 213e224

Fig. 18. Numerical investigation on the soil compaction influence. Obtainable wind turbine power as a function of time of day.

Fig. 17. Numerical investigation on the soil compaction influence. a) Updraft temperature (at the wind turbine inlet) versus time of day. b) Updraft velocity (at the wind turbine inlet) as a function of time of day.

established between the air within the collector and the soil, depending on the solar period (upward or downward solar trajectory). It can be observed in Figs. 14 and 15 that the values of the temperature and the velocity of air at the wind turbine inlet obtained during the downward solar trajectory are substantially higher than those obtained during the upward solar trajectory. The evolution of updraft temperature and velocity follow a sizeable hysteresis loop. Note that the highest differences occur for values of I around the range 300e400 W/m2. It can be concluded that in situations with low solar radiation (cloudy weather), or during the night, the energy released by the soil leads to maintain the airflow within the collector, and therefore the wind turbine can continue working. At night, the numerical simulation resulted in released energy values of 10e17 W/m2 in the soil, with values of velocity 3e 4.5 m/s at the inlet of the wind turbine.

due to the material stratification. In order to study the effects of increased soil compaction on the behavior of the solar tower, a soil with a constant density of 1900 kg/cm2 has been considered (that is, the apparent density ra,S becomes to be equal to the nominal density rS). The heat transfer from the soil surface to the lower strata is higher when a more compacted soil is considered because of the elimination of the intermediate zone porosity (between the soil surface layer and the lower strata). This causes a relevant decrease of the values of the daytime temperature at the soil surface, due to a higher thermal conductivity inward, with the advantage that the stored energy is also easier to release and keeps the soil surface at a higher temperature at night. The accumulation of energy in the soil is higher during the day when a more compacted soil is regarded (see Fig. 16a); this fact corresponds to an increased release of energy from the soil during the night. The soil temperature at different depths is shown in Fig. 16b. By comparing Fig. 10 and Fig. 16b, it can be stated that the temperature evolution during the day tends to be uniform when the degree of soil compaction increases. The maximum values of temperature and velocity at the inlet of the wind turbine reached during the day are lower than those obtained with the soil compaction degree (see Fig. 17a and b); this

5.4. Influence of the soil compaction An essential requirement in the operation of a solar tower may consist of a continuous operation mode of the wind turbine, including the night. Thus, it is necessary to improve the behavior of the soil as an energy storage system. If the compaction degree of soil is increased, its apparent density tends to increase reaching a constant value due to the reduction of the interstitial space, while its thermal conductivity tends to keep its dependence with depth,

Fig. 19. Numerical investigation on the soil compaction influence. Accumulated power output.

F.J. Hurtado et al. / Energy 47 (2012) 213e224

effect can be explained because of the increased energy storage at the soil. During the day, the expected power output of the wind turbine decreases slightly (see Fig. 18), but note that this effect is offset by a significant recovery during the night (or during hours with low solar radiation). This recovery effect could be increased in the case of installing turbines that require less operating velocity in the airflow through it. Finally, Fig. 19 shows the accumulated power output over 24 h a day; the compaction of soil causes an increase on total energy generation of 10% (274 kWh/day compared to 249 kWh/day). This fact can be explained on one side by an increased time in the turbine operation and on the other side by higher stability of its operation near the point of maximum efficiency.

6. Conclusions Transient numerical simulations for a solar chimney power plant with heat storage system have been carried out, based on the Manzanares pilot plant. The numerical results have been validated with the experimental data of Haaf [5], with a successful agreement. The effects of the soil thermal inertia and the soil compaction degree have been analyzed. The following conclusions remarks can be made: 1. It is found a clear relationship (essentially linear) between the updraft temperature difference and the updraft velocity, for any time of day. 2. The behavior of the soil as cold focus (storing energy) during the rising solar radiation period, but as hot focus during the falling solar period (releasing energy), causes a sizeable hysteresis loop in the evolution of updraft temperature and velocity as a function of solar radiation. 3. The analysis of the composition and stratification of soil prior to the installation of a solar chimney power plant is a relevant factor. In fact, a higher compaction of soil causes a relevant increase on total energy generation; when the apparent density of soil tends to be equal to the mass density, the energy output increases 10%. Finally, depending on the energy strategy and the role of solar tower in the electric power system, the following recommendations can be stated.  In a scenario where the solar power plant operates exclusively during periods with relevant solar radiation, a soil type with high thermal diffusivity, low thermal inertia and high porosity, accumulates a relatively small amount of energy and therefore most of the solar radiation is absorbed by the working air; consequently, the system gives higher energy output during peak hours of irradiation. If the soil has not these characteristics, the described effect could be developed by installing a layer with a high absorptivity separated from the soil surface by an insulating layer, which avoid the heat transfer to the soil strata.  In a scenario where the plant operates producing energy continuously (during the day and the night), a soil type with low thermal diffusivity, high thermal inertia and high compaction is appropriate, because of the increase in the energy released by it during the night. In this case, it is recommended to perform a soil compaction prior to installation of the plant, in order to increase the thermal inertia of ground, eliminating the high porosity layer that reduces the energy flow between the ambient and the soil lower strata.

223

References [1] Cabanyes I. Proyecto de motor solar. Magazine ‘La Energía Eléctrica’ (in Spanish). Cited due to http://en.wikipedia.org/wiki/solar_updraft_tower [accessed 15.01.12]. [2] Pasumarthi N, Sherif SA. Experimental and theoretical performance of a demonstration solar chimney modelepart I: mathematical model development. Int J Energy Res 1998;22:277e88. [3] Schlaich J. The solar chimney: electricity from the sun. Stuttgart: Axel Menges; 1995. [4] Haaf W, Friedrich K, Mayr G, Schlaich J. Solar chimneysepart I: principle and construction of the pilot plant in Manzanares. Int J Sol Energy 1983;2:3e20. [5] Haaf W. Solar chimneysepart II: preliminary test result from Manzanares pilot plant. Int J Sol Energy 1984;2:141e61. [6] Gannon AJ, Backström TW. Solar chimney cycle analysis with system loss and solar collector performance. ASME J Sol Energy Eng 2000;122:133e7. [7] Zhou X, Yang J, Xiao B, Hou G. Experimental study of temperature field in a solar chimney power setup. Appl Thermal Eng 2007;27:2044e50. [8] Maia CB, Ferreira AG, Valle RM, Cortez MFB. Theoretical evaluation of the influence of geometric parameters and materials on the behavior of the airflow in a solar chimney. Comput Fluids 2009;38:625e36. [9] Sangi R. Performance evaluation of solar chimney power plants in Iran. Renew Sust Energy Rev 2012;16:704e10. [10] Zhou X, Wang F, Ochieng RM. A review of solar chimney power technology. Renew Sust Energy Rev 2010;14:2315e38. [11] Yan MQ, Sherif SA, Kridli GT, Lee SS, Padki MM. Thermo-fluid analysis of solar chimneys. In: Morrow TB, Marshall LR, Sherif SA, editors. Industrial applications of fluid mechanics, vol. 132. New York: ASME FED; 1991. p. 125e30. [12] Bernardes MAS, Backström TW, Kröger DG. Analysis of some available heat transfer coefficients applicable to solar chimney power plant collectors. Sol Energy 2009;83:264e75. [13] Backström TW, Gannon AJ. Compressible flow through solar power plant chimneys. ASME J Sol Energy Eng 2000;122:138e45. [14] Zhou X, Bernardes MAS, Ochieng RM. Influence of atmospheric cross flow on solar updraft tower inflow. Energy 2012;42:393e400. [15] Bernardes MAS, Vob A, Weinrebe G. Thermal and technical analyses of solar chimneys. Sol Energy 2003;75:511e24. [16] Pretorius JP, Kröger DG. Critical evaluation of solar chimney power plant performance. Sol Energy 2006;80:535e44. [17] Ninic N. Available energy of the air in solar chimneys and the possibility of its ground-level concentration. Sol Energy 2006;80:804e11. [18] Petela R. Thermodynamic study of a simplified model of the solar chimney power plant. Sol Energy 2009;83:94e107. [19] Zhou X, Yang J, Xiao B, Hou G, Xing F. Analysis of chimney height for solar chimney power plant. Appl Thermal Eng 2009;29:178e85. [20] Backström TW, Fluri TP. Maximum fluid power condition in solar chimney power plantseAn analytical approach. Sol Energy 2006;80:1417e23. [21] Fluri TP, Backström TW. Performance analysis of the power conversion unit of a solar chimney power plant. Sol Energy 2008;82:999e1008. [22] Nizetic S, Klarin B. A simplified analytical approach for evaluation of the optimal ratio of pressure drop across the turbine in solar chimney power plants. Appl Energy 2010;87:587e91. [23] Trieb F, Langnib O, Klaib H. Solar electricity generationea comparative view of technologies, costs and environmental impact. Sol Energy 1997;59:89e99. [24] Nizetic S, Ninic N, Klarin B. Analysis and feasibility of implementing solar chimney power plants in the Mediterranean region. Energy 2008;33:1680e90. [25] Fluri TP, Pretorius JP, Dyk C, Backström TW, Kröger DG, Zijl GPAG. Cost analysis of solar chimney power plants. Sol Energy 2009;83:246e56. [26] Zhou X, Yang J, Wang F, Xiao B. Economic analysis of power generation from floating solar chimney power plant. Renew Sust Energy Rev 2009;13:736e49. [27] Zhou X, Wang F, Fan J, Ochieng RM. Performance of solar chimney power plant in Qinghai-Tibet Plateau. Renew Sust Energy Rev 2010;14:2249e55. [28] Hamdan MO. Analysis of a solar chimney power plant in the Arabian Gulf region. Renew Energy 2010;36:2593e8. [29] Schlaich J. Tension structures for solar electricity generation. Eng Struct 1999; 21:658e68. [30] Harte R, Gideon PAG, Zijl V. Structural stability of concrete wind turbines and solar chimney towers exposed to dynamic wind action. J Wind Eng Ind Aerod 2007;95:1079e96. [31] Backström TM, Gannon AJ. Solar chimney turbine characteristics. Sol Energy 2004;76:235e41. [32] Denantes F, Bilgen E. Counter-rotating turbines for solar chimney power plants. Renew Energy 2006;31:1873e91. [33] Fluri TP, Backström TW. Comparison of modelling approaches and layouts for solar chimney turbines. Sol Energy 2008;82:239e46. [34] Kashiwa BA, Kashiwa CB. The solar cyclone: a solar chimney for harvesting atmospheric water. Energy 2008;33:331e9. [35] Ming T, Lin W, Pan Y, Xu G. Numerical analysis of flow and heat transfer characteristics in solar chimney power plants with energy storage layer. Energy Convers Manage 2008;49:2872e9. [36] Xu G, Ming T, Pan Y, Meng F, Zhou C. Numerical analysis on the performance of solar chimney power plant system. Energy Convers Manage 2011;52:876e83. [37] Sangi R, Amidpour M, Hosseinizadeh B. Modeling and numerical simulation of solar chimney power plants. Sol Energy 2011;85:829e38.

224

F.J. Hurtado et al. / Energy 47 (2012) 213e224

[38] Pastohr H, Kornadt O, Gürlebeck K. Numerical and analytical calculations of the temperature and flow field in the upwind power plant. Int J Energy Res 2004;28:495e510. [39] Wilcox DC. Turbulence modeling for CFD. 2nd ed. La Cañada (USA): DCW Industries; 2006.

[40] Zamora B, Kaiser AS. Numerical study on mixed buoyancy-wind driving induced flow, in a solar chimney for building ventilation. Renew Energy 2012; 35:2080e8. [41] Leonard BP. A stable and accurate convective modelling procedure based on quadratic upstream interpolation. Comp Meth Appl Mech Eng 1979;19:59e98.