Numerical simulations of solar chimney power plant ...

Renewable Energy 62 (2014) 24e30

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Numerical simulations of solar chimney power plant with radiation model 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

a b s t r a c t

Article history: Received 29 March 2013 Accepted 24 June 2013 Available online 16 July 2013

A three-dimensional numerical approach incorporating the radiation, solar load, and turbine models proposed in this paper was first verified by the experimental data of the Spanish prototype. It then was used to investigate the effects of solar radiation, turbine pressure drop, and ambient temperature on system performance in detail. Simulation results reveal that the radiation model is essential in preventing the overestimation of energy absorbed by the solar chimney power plant (SCPP). The predictions of the maximum turbine pressure drop with the radiation model are more consistent with the experimental data than those neglecting the radiation heat transfer inside the collector. In addition, the variation of ambient temperature has little impact on air temperature rise despite its evident effect on air velocity. The power output of the SCPP within the common diurnal temperature range was also found to be insensitive to ambient temperature. Ó 2013 Elsevier Ltd. All rights reserved.

Keywords: Solar chimney power plant Numerical simulation Radiation model Solar load model

1. Introduction A rapid increase in renewable energy utilization has been observed worldwide because of environmental and energy crisis issues. The solar chimney power plant (SCPP) system presents an interesting option for the large-scale use of solar energy. The prototype at Manzanares, Spain, which ran automatically from mid1986 to early 1989, has proven that the SCPP is a reliable approach in generating electricity [1,2]. As shown in Fig. 1, a typical SCPP is mainly composed of a solar collector, chimney, and turbine. The collector is used to heat the incoming air through the greenhouse effect. The heated air flows into the chimney and finally escapes to the atmosphere. The chimney effect results in a large pressure difference between the chimney base and collector entrance. The pressure difference, often defined as the system driving force, makes the chimney the actual thermal engine of the system, and drives the turbine installed at the chimney base to generate electric power. The SCPP has no adverse effect on the environment, requires no cooling water, and has low maintenance costs. These distinct advantages make the SCPP a promising technique for generating electricity in vast desert regions that lack water resources but are abundant in solar energy.

* Corresponding author. Tel.: þ86 29 13152181528; fax: þ86 29 82668723. E-mail address: [email protected] (J.-y. Li). 0960-1481/$ e see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.renene.2013.06.039

Many papers on SCPP have been published since Haaf et al. [1,2] reported their fundamental studies on the Spanish prototype. Two methods are generally employed to compute SCPP characteristics: the analytical and numerical methods. The typical analytical method is mainly based on a one-dimensional thermal equilibrium analysis inside the collector. For example, Pasumarthi and Sherif [3,4] published an approximate model to investigate the effects of various parameters on air temperature and velocity distribution. Zhou et al. [5] developed a mathematical model to determine the power output for varying solar radiation, collector area, and chimney height, and validated their findings against experimental results from a small-scale pilot plant. Bernardes et al. [6] established an analytical model to predict the characteristics of a largescale commercial SCPP. They also discussed the optimal proportion of driving force used to drive the turbine. Li et al. [7] recently proposed a comprehensive theoretical model for SCCP performance evaluation that considers the effects of flow and heat losses on SCPP performance. The number of studies on numerical methods adopting the computational fluid dynamic (CFD) programs to predict SCPP performance has been increasing rapidly. As a pioneer, Pastohr et al. [8] performed a 2-D numerical simulation on SCPP to study the temperature and flow fields in the collector. A similar numerical method was used by Xu et al. [9], the only difference being the settings of the energy storage layer and turbine model. Ming et al. [10] conducted numerical simulations for the Spanish prototype with a three-blade turbine and presented the simulation results of a

P.-h. Guo et al. / Renewable Energy 62 (2014) 24e30

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2. Numerical models 2.1. Physical model No experimental results on a large-scale SCPP system have ever been reported, except for the prototype in Spain. Thus, the Spanish prototype was selected as the physical model to verify the numerical method. The computational domain, as shown in Fig. 2, is divided into the following zones: the collector (z1), energy storage layer (soil, z2), chimney (z3), and airflow (z4). The main dimensions of the Spanish prototype are listed in Table 1. The collector and the chimney are smoothly connected to facilitate the computation. As indicated in the measured data of the Spanish prototype [2], soil temperature at 0.5 m depth underneath the ground remained unchanged with time. A similar phenomenon was found in the study of Pretorius and Kröger [13]. Therefore, a ground thickness of 2 m is believed to be sufficiently deep to facilitate the isothermal condition of the bottom boundary of the soil layer.

Fig. 1. Schematic diagram of solar chimney power plant.

MW-graded SCPP with a five-blade turbine. Koonsrisuk and Chitsomboon [11,12] used numerical simulations to test their dimensional analysis on SCPP and the validity of their proposed dimensionless variables. Compared with the analytical method, fewer assumptions are used in numerical simulations but more detailed descriptions of temperature and flow field could be obtained. Although many numerical studies have been published, they mainly focused on the 2-D simulations. In addition, the radiation heat transfer inside the system has rarely been considered in previous numerical simulations. Radiation heat transfer, however, is an important factor in the greenhouse effect and is therefore worthy of investigation. As an early attempt in considering radiation heat transfer in the collector, this paper first verified the 3-D numerical simulation method incorporating the radiation, solar load, and turbine models, by comparing with the experimental data obtained from the Spanish prototype. Based on the proposed numerical approach, the effects of solar radiation, turbine pressure drop, and ambient temperature on the SCPP system performance were investigated in detail.

2.2. Models for heat transfer and airflow in SCPP All simulations were conducted for steady flow using the finite volume-based solver FLUENT. Heat transfer in the SCPP system involves all three modes: conduction, convection, and radiation. In simulating the flow in SCPP, computations using models that only focus on conduction or convection are the simplest, whereas those involving buoyancy-driven flow and radiation models are more complex. Radiation heat transfer mainly occurs in the collector, which is covered by different types of semi-transparent materials such as glass or plastic. The cover materials are nearly transparent for incident solar radiation but partly opaque for infrared radiation from the ground. In the present simulations, the discrete ordinate (DO) radiation model was adopted to solve the radiative transfer equation for the following reasons: (1) only the DO model can be used to model semi-transparent walls of various types, (2) only the DO model can be used to compute non-gray radiation using a gray band model, and (3) the DO model can work well across a full range of optical thicknesses. In previous studies, incident solar radiation on the ground through the semi-transparent collector was commonly treated as an internal heat source or heat flux. For example, Pastohr et al. [8] and Xu et al. [9] considered solar radiation as an internal heat source in the ground’s thin layer. In Koonsrisuk and Chitsomboon’s study [12], solar heat absorption per unit volume of air is modeled as a uniform heat source within the airflow in the collector. Li et al. [14] treated the absorption of solar radiation as heat flux from the ground to the airflow. In the present study, a solar ray-tracing model provided by FLUENT was used to calculate the radiation effects of the sun’s rays entering the computational domain. The ray-tracing model is an efficient and practical approach to applying solar loads as heat sources in energy equations. Solar radiation is modeled using the sun’s position vector and illumination parameters, which can be specified by users or by a solar calculator utility provided by FLUENT. Solar load is available for 3-D simulation only and can be used to model steady and unsteady flows. Table 1 Main dimensions of the Spanish prototype.

Fig. 2. Main zones and boundary conditions.

Parameter

Value

Mean collector radius Mean collector height Chimney height Chimney radius Ground thickness

122.0 m 1.85 m 194.6 m 5.08 m 2m

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Flow in SCPP is a kind of buoyancy-driven flow, the strength of which is usually measured by the Rayleigh number. Rayleigh number less than 108 indicates a laminar flow, with a transition to turbulence occurring over the range of 108 < Ra < 1010. The Rayleigh number in a large SCPP such as the Spanish prototype is evidently higher than 1010, and its inner airflow should be a turbulent flow. Therefore, the RNG keε turbulence model was selected to describe the airflow inside the system. The Boussinesq model was adopted in this simulation. This model treats density as a constant value in all solved equations, except for the buoyancy term in the momentum equation

ðr ra Þgz ra bðT Ta Þg

(1)

where ra is the density of ambient air, Ta is the ambient temperature, and b is the thermal expansion coefficient. For the buoyancydriven flow, faster convergence can be achieved by using the Boussinesq model than by setting air density as a function of temperature. 2.3. Boundary conditions and solution method The main boundary conditions are indicated in Fig. 2. The upper boundary of the collector was set as a combined convection and external radiation boundary condition, considering heat transfer by convection and long-wave radiation from the external surface of collector. Such boundary condition (b1 boundary condition in Fig. 2) is called the “mixed” boundary in FLUENT. For such a thermal boundary condition, the free stream temperature outside the collector was set as the ambient temperature, whereas external radiation temperature was set as the equivalent temperature of the sky according to Ref. [15]

Tsky ¼ 0:0552Ta1:5

hcoll ¼

_ DT cp m prc2 Ira

(4)

where ht, Dpt, and Qv represent turbine efficiency, turbine pressure _ DT, rc, and Ira drop, and volume flow rate, respectively; and m, denote mass flow rate, air temperature rise, collector radius, and incident solar radiation, respectively. Turbine efficiency usually ranges from 0.8 to over 0.9 for different turbine layouts, as indicated in investigations conducted both analytically and experimentally [19e22]. The turbine efficiency was set at 0.8 to be consistent with other studies in predicting SCPP performance [3,13,23,24]. Although the value 0.8 might be somewhat low for the best efficiency point of the turbine, such an assumed value can be a compromise, considering the large variation of operating points and different turbine layouts in practical applications. The SIMPLEC algorithm was applied to the couple of pressuree velocity, and the body force weighted algorithm was selected as the discretization method for the pressure term. Structured grid was adopted with the grid near the walls being refined adaptively. The second-order upwind scheme was chosen for the convective terms. Simulation results using different grid distributions and different strategies for grid refinement indicated that the grids are sufficiently fine to obtain grid-independent solutions. 3. Validation of numerical models Numerical investigations were validated through comparison with the experimental data of the Spanish prototype [25]. von Backström and Gannon [20] suggested that the ideal characteristic curve of a solar chimney turbine is a straight line. The experimental

(2)

The temperature at the bottom of the soil layer was at 300 K and then kept constant (b2 boundary condition). The temperatures at the inner surface of the collector and upper surface of the ground were determined based on the convection of the airflow in the collector, and the “coupled” condition (b3) in FLUENT was used for such boundaries. The collector inlet and chimney outlet were set as pressure-inlet and pressure-outlet boundaries (b4 and b5), respectively. For a buoyancy-driven flow problem with pressure boundary conditions, no pressure difference should exist between the inlet and outlet. Following previous researchers [8,9,16e18], pressures at the collector inlet and the chimney outlet were both set at 0 Pa. The Spanish SCPP has a shrouded turbine, which is different from a wind turbine. Before and after going through the shrouded turbine, airflow has almost the same axial velocity component, whereas pressure changes significantly. The pressure drop across the turbine was determined by using the pressure drop model (b6). This model treats the turbine as an infinitely thin disk, such that a detailed configuration of the turbine is unnecessary, but the effect of pressure drop across the turbine can be conveniently considered. The pressure drop across the turbine can be determined in two ways: (1) specified using a constant value and (2) determined as a function of velocity across the turbine. The second approach, i.e., a linear polynomial of velocity, was applied to determine the pressure drop across the turbine in the validation section. However, when investigating the effect of turbine pressure drop on SCPP performance, the first approach with the given pressure drop condition was adopted. The power output of the turbine and the collector efficiency can be expressed as

P ¼ ht Dpt Qv

(3)

Fig. 3. a. Experimental data and fitting curve of load coefficient vs. flow coefficient, b. Experimental data and fitting curve of turbine pressure drop vs. updraft velocity.


data on the turbine characteristics of the Spanish prototype are shown in Fig. 3a after reorganization and processing. Evidently, a linear polynomial is the best fit for the experimental data of the Spanish turbine [25], which conforms to the ideal characteristic curve of such a turbine. As mentioned in Section 2.3, the relationship between pressure drop and velocity across the turbine is necessary for the use of the turbine model in FLUENT. The characteristics of the fixed geometry turbine running at a fixed speed in the Spanish prototype can also be plotted as the relationship between the turbine pressure drop and updraft velocity, as shown in Fig. 3b. The relationship of turbine pressure drop against updraft velocity is fitted as follows:

Dpt ¼ 18:87 v 57:59

(5)

The root-mean-square error (RMSE) and the coefficient of multiple determinations, R2, are 1.698 (a value closer to 0 indicates a better fit) and 0.9537 (a value closer to 1 indicates a better fit), respectively, indicating that the above fitting is rational. Fig. 4a and b shows a comparison between the simulation results and experimental data. The simulation results are consistent with the experimental data, which indicates that the proposed numerical method is a suitable approach for investigating SCPP performance. The following two reasons are deemed responsible for the slight overestimation of updraft velocity and power output: (1) support in the collector was not included in the physical model,

Fig. 4. a. Comparison of updraft velocity between simulation results and experimental data, b. Comparison of power output between simulation results and experimental data.

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such that its drag forces could not be included; and (2) the simulation is for steady flows, whereas the soil layer has thermal inertia in reality. 4. Results and discussion 4.1. Effect of the radiation model on the simulation of SCPP performance The effects of the radiation model on the simulation of SCPP performance could be determined by comparing the results with and without incorporating the model in the computations. Fig. 5a shows an increase in airflow temperature rises at the exit of the collector with solar radiation. Differences between the two computational curves of airflow temperature rises are remarkable, such that, a significantly higher air temperature rise would be achieved in the case without the radiation model. This condition means that heat losses through the collector roof by convection and long-wave radiation are extremely underestimated. Collector efficiency is shown in Fig. 5b. The predicted collector efficiencies of the Spanish prototype with radiation model are evidently closer to the experimental data that are approximately 30% in Ref. [2]. By contrast, the numerical simulation neglecting radiation heat transfer resulted in significantly higher collector efficiencies.

Fig. 5. a. Comparison of temperature rises with and without radiation model, b. Comparison of collector efficiencies with and without radiation model.

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The greenhouse effect of the collector is responsible for the aforementioned difference. The actual heat transfer process in the collector is that the collector roof absorbs some radiative energy from the ground, but only part of the absorbed energy will be reemitted back to the ground. Neglecting the radiation heat transfer, however, would cause the ground to absorb almost all the incident radiation energy, given that no radiation effect on the ground is considered. We can thus conclude that the radiation effect inside the collector must be considered in simulating the flows in SCPP. 4.2. Effects of turbine pressure drop and solar radiation on SCPP performance A group of constants at an interval of 20 Pa was assigned to the turbine pressure drop in the following simulations to investigate the effects of turbine pressure drop on SCPP performance under a certain solar radiation condition. The effects of turbine pressure drop and solar radiation on airflow temperature rise and updraft velocity at the entrance of the chimney are shown in Fig. 6a and b, respectively. Under constant solar radiation, air temperature rise increases with increasing turbine pressure drop, which can be attributed to the turbine blockage effect that decreases air velocity or flow rate in the chimney. Meanwhile, when turbine pressure

Fig. 6. a. Effects of solar radiation and turbine pressure drop on temperature rise, b. Effects of solar radiation and turbine pressure drop on updraft velocity.

drop is constant, both updraft velocity and temperature rise increase significantly with solar radiation. The computed power output of the SCPP is shown in Fig. 7. A maximum value exists for turbine pressure drop for a specific solar radiation. For example, when the solar radiation is 800 W/ m2, the maximum value of the turbine pressure drop allowed in the simulation is approximately 140 Pa. By contrast, Xu et al. [9] also assigned a set of constants to turbine pressure drop to investigate its effect on the performance of the Spanish prototype. Given that the radiation model was not incorporated into their computations, their assigned turbine pressure drop ranged from 0 Pa to 480 Pa, which is apparently higher than the maximum value in our study. The experimental data measured by Haaf [2] indicate that the turbine pressure drop of the Spanish prototype is less than 100 Pa even when solar radiation is slightly higher than 800 W/m2. Thus, the present simulation results are more consistent with the experimental data, which indicates that the numerical approach proposed in this paper could provide a more reasonable prediction of the maximum turbine pressure drop at a certain solar radiation. An accurate prediction of the maximum turbine pressure drop is known to be beneficial in the determination of the design point and regulation strategy of the turbine; otherwise, a mismatch between the turbine and the solar chimney system will occur. The driving force is composed of the static pressure drop across the turbine, the exit kinetic energy from the turbine (also the discharged kinetic energy from the chimney), and the flow losses. If the total pressure of the turbine is defined as the sum of exit kinetic energy from the turbine and static pressure drop across the turbine, then differences between the system driving force and the total pressure of turbine are the flow losses occurring in the flow passage of the whole system. As Fig. 8 shows, with the turbine pressure drop increasing, the turbine total pressure becomes closer to the driving force, which indicates that flow losses gradually approach zero. In the present simulations, setting a large value for the turbine pressure drop may cause this value to be larger than the driving force, which could not occur in actual situations. Therefore, the computations will diverge with such an assigned value. To investigate the flow losses in the system, the variation of flow losses with the updraft velocity in the chimney under different conditions is plotted in Fig. 9 and then fitted using a quadratic polynomial. The drag coefficient of the whole system can be obtained from the following fitting expression:

Fig. 7. Effects of solar radiation and turbine pressure drop on power output.


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Fig. 10. Effects of ambient temperature on temperature rise and updraft velocity. Fig. 8. Variations of the driving force and total pressure of the turbine with turbine pressure drop and solar radiation.

1 2

Dplosses ¼ 0:2471 r v2

(6)

The RMSE and R2 of the above fitting are 0.2121 and 0.9981, respectively, which indicates that the computed flow losses are closely proportional to the square of velocity. This condition also verifies the rationality of the simulations. 4.3. Effects of ambient temperature on the SCPP performance In the unsteady numerical simulations of SCPP, investigators usually assign a constant value to ambient temperature because changing the ambient temperature in computations is difficult [16]. In addition, ambient temperature varies even if solar radiation changes only slightly. Thus, the effects of ambient temperature variation on SCPP performance must be investigated. For this purpose, the following simulations were conducted for the Spanish prototype with ambient temperatures ranging from 287 K to 307 K at intervals of 5 K, while maintaining constant values for solar radiation at 800 W/m2 and turbine pressure drop at 80 Pa. Fig. 10 shows the effects of ambient temperature on air temperature rise and updraft velocity in the chimney. The variation of ambient temperature has a negligible effect on air temperature rise, but has an evident effect on updraft velocity. Updraft velocity

Fig. 9. Fitting curve of computed flow losses in the SCPP system.

decreases with increasing ambient temperature mainly because of the variation of the density and thermal expansion coefficient of ambient air. According to Eq. (1), the buoyancy term is directly proportional to ambient air density, thermal expansion coefficient, and temperature rise. When ambient temperature increases, both air density and thermal expansion coefficient decrease, which facilitates a decrease in buoyancy force. This effect overshadows that of the slight increase in air temperature rise and results in a decrease in updraft velocity. Fig. 11 shows the effects of ambient temperature on power output. Power output decreases almost linearly with increasing ambient temperature. The relative deviation of the power output at different ambient temperatures is small (see the lower figure), where the power output under an ambient temperature of 297 K is taken as reference. The diurnal temperature range typically varies with the latitude, and its value is approximately 12 K for the lowlatitude region, 8.0e9.0 K for the middle-latitude region, and 3.0e4.0 K for the high-latitude region. If ambient temperature ranges from 292 K to 302 K, which corresponds to a diurnal temperature range of 10 K, the relative deviation would be approximately 3%. The relative deviation reaches nearly 6% when the ambient temperature ranges from 287 K to 307 K, which represents

Fig. 11. Effects of ambient temperature on power output and relative deviation.

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a diurnal temperature range of 20 K. The SCPP power output is evidently insensitive to ambient temperature. Consequently, the assumption of a constant ambient temperature in an unsteady numerical simulation might be acceptable in predicting the SCPP power output for a common diurnal temperature range. 5. Conclusion In simulating the performance of the SCPP system, the radiation, solar load, and turbine models were incorporated into a 3-D numerical computation for the first time. The adopted numerical approach was first validated by the experimental data of the Spanish prototype and then was used to investigate the effects of solar radiation, turbine pressure drop, and ambient temperature on system performance. The following are some conclusions that can be drawn: (1) Radiation heat transfer is an important factor in the heat transfer process inside the SCPP and should be considered in the numerical simulation. Otherwise, heat losses would be dramatically underestimated. (2) The effects of solar radiation and turbine pressure drop on SCPP performance are considerable. Furthermore, the proposed numerical approach could provide a reasonable prediction of the maximum turbine pressure drop at a certain solar radiation, which is a important factor in the determination of turbine design point and operation range. (3) The variation of ambient temperature has a negligible effect on air temperature rise, but has an evident effect on air velocity. The SCPP power output within the common diurnal temperature range is found to be insensitive to ambient temperature. Acknowledgment This work was supported by “the Fundamental Research Funds for the Central Universities” and the National Natural Science Foundation of China under Contract No. 51276137. Nomenclature cp g Ira _ m P Qv Ra rc Ta Tsky

n

specific heat capacity (J kg1 K1) gravitational acceleration (m s2) incident solar radiation (W m2) mass flow rate (kg s1) power generation (kW) volume flow rate (m3 s1) Rayleigh number collector radius (m) ambient temperature (K) equivalent temperature of the sky (K) updraft velocity (m s1)

Greek symbols thermal expansion coefficient (K1) turbine pressure drop (Pa)

b Dpt

Dplosses DT hcoll ht r F J

flow losses (Pa) temperature rise (K) collector efficiency (%) turbine efficiency (%) density of air (kg m3) flow coefficient load coefficient

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