Numerical study of the influence of geometric form of chimney on the performance of a solar updraft tower power plant

Abstract

Today, solar radiation is known as an important renewable energy which can be exploited in several ways such as solar updraft tower power plants, photovoltaic power plants, etc. In a solar updraft tower power plant, sunshine heats the air beneath a wide collector surrounding a tall tower and causes a hot air updraft in the tower by the chimney effect. This airflow drives wind turbines, placed almost in the chimney base, to produce electricity. In this study, the effect of the geometric form of the chimney on the performance of one solar updraft tower power plant is numerically investigated. Regarding the importance of the kinetic power of the hot air on power generation, it is intended to increase the air velocity by varying the forms of the chimney without changing the main dimensions of solar updraft tower power plant such as tower height and collector geometries. This approach may decrease the financial costs of the solar updraft tower power plant. For the numerical simulations, a finite volume computational fluid dynamics code solves the governing equations on an axisymmetric pi-shape domain (15° of whole geometry). To validate the results, the Manzanares solar updraft tower power plant experimental data are utilized. In this study, 15 forms of chimney based on a logical three-step procedure (from a basic cylindrical to a parabolic form) are examined. So, an appropriate/final form with a parabolic curve of chimney wall with divergence angle is obtained. Results indicate that the final form has the highest updraft air velocity. In fact, the average updraft air velocity increases from 15.66 m/s for the basic form to the value of 23.36 m/s (around 49.17% increments) for the final form.

Keywords

Solar updraft tower power plant numerical study solar chimney form of chimney airflow velocity

Introduction

A solar updraft tower power plant (SUTPP) is a renewable power technology which is able to convert heat energy of solar radiations to mechanical powers. This kind of solar power plants consists of three main parts including the collector, the turbogenerator(s) as a power conversion unit (PCU), and the solar tower.¹ The hot airflow is allowed to pass through the tall chimney and it is then applied to drive the turbogenerator(s) which will generate the electrical power. Actually, the tower is the thermal driving engine of these power plants which works based on natural convection and air density difference between the base and top of the tower. Since SUTPPs are using solar radiation as fuel, they are entirely free of carbon emissions, when they are operating. As a result, SUTPP is the most sustainable power plant that generates power by using natural resources.¹

Research efforts on SUTPP are categorized by a number of numerical and theoretical studies, but with inadequate experimental work. The idea of using a solar chimney to produce electricity was first proposed in 1903 by the Spanish engineer, Cabanyes² and until the late 20th century, some researchers studied on SUTPP and proposed some ideas for executing such power plants. Finally, the experiments accomplished on the first prototype in Manzanares of Spain, by Schlaich (1982) (a chimney diameter 10 m, a height 195 m, and a collector diameter of 240 m), for a 50 kW wind turbine, showed that the concept of SUTPP is technically feasible.^3,4,5

After designing and construction of the Manzanares power plant, researches on SUTPP were developed on many ﬁelds. Several thermodynamic and numerical studies analyzed the design parameters of SUTPP and obtained mathematical models to establish performance, efficiency, and economy of the plant. For example, Bernardes et al.⁶ developed a comprehensive analytical and numerical model for simulating the performance of the SUTPP. Their results illustrated that the height of the chimney, the pressure drop at the turbine, and the diameter of the collector are important parameters on the design of solar chimneys. Dai et al.⁷ analyzed a solar chimney power plant for remote villages in Northwestern China. They investigated the effect of some important parameters such as chimney height, diameter of the solar collector, ambient temperature, solar irradiance, and the efﬁciency of wind turbine on the performance of power generation. Pastohr et al.⁸ carried out a numerical analysis to improve the description of the operation mode and efficiency of the upwind power plant by FLUENT. In that study, the ground, collector, chimney, and turbine were modeled together numerically. In addition to the calculations using FLUENT, a simple model was developed for comparison purposes and parameter studies. Their works illustrated that the numerical results with FLUENT matched well with the results given by the simple model. Bilgen and Rheault⁹ investigated a novel solar chimney system (the sloped collector ﬁeld, which also acted as a chimney with a short vertical chimney to install the vertical axis air turbine) for power production at high latitudes. In that stdy, a mathematical model and a code on MATLAB platform were developed based on monthly average meteorological data and thermodynamic cycle. Their results showed that solar chimney power plants at higher latitudes may have satisfactory thermal performance and produce as much as 85% power of the same plants in southern locations with horizontal collector ﬁeld. Ninic¹⁰ analyzed the available work potential of the atmospheric air that acquired while passing through the collector of a SUTPP. Also, he established and analyzed various collector types using dry and humid air with various chimney heights. He determined that the work potential on the air ﬂowing into the air collector depends on the heat gained inside the collector, air humidity, and atmospheric pressure. His study showed that the vortex motion ﬂowing downstream of the turbine could be maintained under pressure and could probably take over the role of the solid structure chimney. Thus, a part of the available energy potential acquired in the collector would be used to maintain the vortex ﬂow in the air column above the ground-level turbine. Burek and Habeb¹¹ did an experimental investigation into heat transfer and mass ﬂow in thermosyphoning air heaters, such as solar chimneys and the Trombe walls. The test rig comprised a vertical open-ended channel with closed sides, resembling a solar collector or solar chimney approximately 1.0 m². The results indicated that the mass ﬂow rate through the channel is a function of both the heat input and the channel depth. Also, the thermal efﬁciency of the system (as a solar collector) is a function of the heat input and not dependent on the channel depth. Fluri and Backström¹² compared three conﬁgurations with the performance of the PCU of a large SUTPP and its interaction with the plant from efficiency and energy yield points of view. Their results illustrated that, as certain loss mechanisms are not present, the single vertical axis turbine has a slight advantage with regards to the efficiency and energy yield. But its output torque is tremendous, making its feasibility questionable. Additionally, they depicted that by designing the ﬂow passage in an appropriate manner, the aerodynamic losses can be kept low and the PCU efficiency deteriorates signiﬁcantly with increasing diffuser area ratios but improves slightly with reducing the diffuser area ratio below unity. Zhou et al.¹³ investigated an alternative method of heat and moisture extraction from seawater under the collector of a solar chimney system for power generation and seawater desalination. Their results illustrated that due to the release of vapor latent heat as the air rises up the chimney, the temperature and velocity of the airﬂow inside the chimney in the combined plant is less than the temperature and velocity of the airﬂow inside the chimney in the classic plant. Additionally, the power output from air turbine generators and water generators in the combined plant is less than the power output of the classic plant. Hurtado et al.¹⁴ analyzed the thermodynamic behavior and the power output of a SUTPP over a daily operation cycle, through a numerical modeling under nonsteady conditions. In their analysis, the soil was taken into account as a heat storage system. So, the inﬂuence of the soil thermal inertia and the effects of soil compaction degree on the output power generation were studied. Their results demonstrated that when the soil compaction rises, a sizeable increase of 10% in the output power is obtained. Hamdan¹⁵ developed a mathematical thermal model for steady-state airﬂow inside a SUTPP using modiﬁed Bernoulli equation with buoyancy effect and the ideal gas equation. His finding showed that using a constant density assumption through the solar chimney can simplify the analytical model; however, it overpredicts the power generation. Furthermore, the results illustrated that the chimney height, the collector radius, the solar irradiance, and the turbine head are essential parameters for the design of solar chimneys and the maximum power generation depends on the turbine head. Koonsrisuk and Chitsomboon¹⁶ developed a theoretical model of a solar collector, chimney, and turbine of one SUTPP. Their results indicated that the plant size, the factor of pressure drop at the turbine, and the solar heat ﬂux are important parameters for performance enhancement of large-scale commercial solar chimneys. Furthermore, it was shown that the optimum ratio between the turbine extraction pressure and the available driving pressure for the proposed plant is approximately 0.84. Guo et al.¹⁷ developed a comprehensive theoretical model by taking into account the hourly variation of solar radiation to obtain a more accurate prediction of the annual performance of SUTPPs. Moreover, the effects of the collector and chimney radius on the power output of the SUTPP were analyzed. The results revealed that a limitation on the maximum collector radius exists for the maximum attainable power output of the SUTPP. Then, four designs of 100 MW SUTPPs with different combinations of collector and chimney radius were proposed and the most cost-effective one was chosen among the four SUTPPs. The annual power output of the chosen SUTPP in the Hami region was estimated at an interval of 1.0 h for a whole year. Their findings explained that the power generation of SUTPP presents an obvious seasonal variation. To a greater extent, the use of 14% of the unused land in the Hami region for the installation of SUTPPs would satisfy the annual power requirement for the whole of the Sinkiang region. Guo et al.¹⁸ carried out a 3D numerical study on the performance of a SUTPP. In their study, they considered the radiation model, solar load model, and a real turbine. The results depicted that, for analyzing the performance and cost of the SUTPP, considering the hourly variation of the zenith angle of the sun and conducting shading calculation, are necessary. “by” The results depicted that, considering the hourly variation of the zenith angle of the sun and conducting shading calculation are necessary for estimating the performance of the SUTPP in the finantial and design analysis. Mehrpooya et al.¹⁹ developed a model of energy and exergy analysis for a SUTPP using Tehran climate data. The findings illustrated that, by variation of the solar radiation from the winter nights to the summer noon, the output of power generation of SUTPP changes from $180$ to $64.0 kW$ , respectively. In addition, the energy and exergy efficiencies change from $3.5$ to $93.3 %$ and $2.0$ to $29.0 %$ , respectively. Zhou et al.²⁰ presented a theoretical model for analyzing the wind turbine pressure drop and the effect of flow area to the fluid power of SUTPPs. They considered both constant and nonconstant densities for airflows. The results indicated that, by increasing the chimney flow area, the turbine pressure drop factors and the fluid power increase accordingly. Zhou and Xu²¹ developed a theoretical model for investigating the effect of roof heights of the collector, internal stiffening appurtenance of the chimney, and main dimensions of the chimney on all the pressure losses in a SUTPP. Their results showed that the exit kinetic energy loss accounts for the majority of the total pressure loss, while other losses such as the collector inlet loss constitute only small portions of the total pressure loss. Ayadi et al.²² analyzed the effect of the wind turbine diameter on the generated power of a SUTPP and the local characteristics of the airflow inside its chimney. Their obtained results revealed that by increasing the turbine diameter, the generated power increases.

Besides the above-mentioned literatures, the issue of optimization in components of a SUTPP system is observed in several previous studies. For example, dos Santos Bernardes et al.²³ developed a numerical analysis of natural laminar convection in a radial solar heater to predict the thermo-hydrodynamic behavior of the SUTPP. In that study, the mathematical model was analyzed by the finite volumes method in generalized coordinates and the solution was obtained in a fixed computational domain independent of the geometrical shape of the physical system. Koonsrisuk and Chitsomboon²⁴ studied the effect of the tower cross-section area on the potential of the flow kinetic energy, using the computational fluid dynamics (CFD) technology. They found that the divergent tower top leads to augmentations in kinetic energy at the tower base significantly. Zhou et al.²⁵ analyzed the maximum chimney height for convection avoiding negative buoyancy at the latter chimney and the optimal chimney height for maximum power output. Also, sensitivity analyses were performed to examine the inﬂuence of various lapse rates of atmospheric temperatures and collector radius on the maximum height of the chimney. Their results indicated that the maximum power output of 102.2 kW is obtained for the optimal chimney height of 615 m, which is lower than the maximum chimney height with a power output of 92.3 kW. Koonsrisuk and Chitsomboon²⁶ developed ﬁve simple theoretical models to compare the predictions of performances of SUTPPs. The parameters used in their study were various plant geometrical parameters and the solar radiation properties. Additionally, they also conducted a CFD simulation and then the results were compared with the theoretical predictions. Eventually, the power output and the efficiency of the SUTPPs as functions of the studied parameters were used to compare the relative merits of the ﬁve theoretical models. Larbi et al.²⁷ studied the performance analysis of a SUTPP expected to provide the remote villages located in the Algerian southwestern region with electrical power. Their findings showed that according to an estimate made on the monthly average of sunning, the desired SUTPP could produce from 140 to 200 kW of electricity during the year. Ghalamchi et al.²⁸ investigated a performance evaluation of SUTPP by FLUENT software by changing three parameters including collector slope, chimney diameter, and entrance gap of the collector. The increasing output power of the system was observed by simulation and numerical optimization of many cases with dimensional variations in different cases. Filkoski et al.²⁹ analyzed the technical features of SUTPP by using the CFD approach, as a way for effective optimization of the object’s geometry and thermo-fluid aspects. Their obtained initial results demonstrated that the CFD, as a powerful research and engineering tool capable to analyze the complex aerodynamic and thermal systems. Koonsrisuk and Chitsomboon³⁰ analyzed the effects of ﬂow area changes on the potential of solar chimney power plants. It was found that the sloping collector roof affects the plant performance. The divergent-top chimney leads to augmentations in kinetic energy at the chimney base signiﬁcantly. The proper combination between the sloping collector roof and the divergent-top chimney can produce the power as much as hundreds times that of the conventional solar chimney power plant. Patel et al.³¹ optimized the geometry of the major components of the SUTPP by using ANSYS-CFX software to study and improve the ﬂow characteristics inside the SUTPP. In their research, the overall chimney height and the collector diameter of the SUTPP were kept constant at $10$ and $8 m$ , respectively. The collector inlet opening was varied from $0.05$ to $0.2 m$ . The collector outlet diameter was also varied from $0.6$ to $1.0 m$ . These modiﬁed collectors were tested with chimneys of different divergence angles $(0 ° - 3 °)$ and also different chimney inlet openings of $0.6 - 1 m$ . The diameter of the chimney was also varied from $0.25$ to $0.3 m$ . The results showed that the best conﬁguration was achieved by using the chimney with a divergence angle of 2° and chimney diameter of $0.25 m$ together with the collector opening of $0.05 m$ and collector outlet diameter of $1.0 m$ . Also, the temperature inside the collector was higher for the lower opening resulting in a higher ﬂow rate and power. Chuen-Yu et al.³² presented a new renewable energy technology concept for electricity generation based on an upward momentum created by a balanced forced air movement, which is initiated by an air blower, inside a telescopic divergent chimney constructed with adiabatic materials and equipped with a gas turbine. In that study, a theoretical model based on the principles of mass and energy conservation, and continuity was developed to investigate the forced air ﬂow inside the system using a criterion deﬁned as the difference between ambient pressure and static pressure at the outlet aloft of the chimney. The model results indicated that, as the air ﬂow increasing to reach a threshold, there exists a steady state when the pressure difference equals to zero. In addition, the extractable energy was found to have an exponential relationship with the chimney heights. Vieira et al.³³ analyzed the influence of some geometric parameters on the available power in the SUTPP and its physical principle by a numerical study. The main objectives were to test the applicability of the studied numerical model in future studies of SUTPP geometric optimization and to test the action of the collector inlet height and the chimney outlet diameter on the available power of the device. Siyang et al.³⁴ developed a numerical model to evaluate the effect of divergent chimneys on the performance of a solar chimney power plant. The findings indicated that the area ratio and the divergent angle have different impacts on this enhancement effect. The area ratio may dominate the strength of the enhancement effect while the divergent angle may dominate the change rate of the enhancement effect along the varying shape-controlling parameters. Siyang et al.³⁵ investigated a numerical modeling and comparison of the performance of diffuser-type solar chimneys for power generation. The simulating outcomes indicated that the diffuser-type solar chimneys generally have a better power generation performance than the cylindrical solar chimney.

The current study investigates numerically the effect of chimney geometry form on the performance of a 1.0 MW SUTPP with predetermined tower height, collector diameter, collector inlet opening, collector outlet height, and chimney (tower) inlet opening. Regarding the importance of the kinetic power of the hot air (inside the chimney) on power generation of SUTPP, this article aims to propose an approach to increase the air velocity by considering the various forms of the chimney without changing the main dimensions of SUTPP, such as tower height and collector geometries. The desired geometrical parameters are vertical section convergence and divergence of the tower (tower convergence and divergence angles) with convex and concave forms of the tower wall (e.g. arc and parabolic forms). The variation of these parameters on improving the airﬂow velocity inside the SUTPP chimney is investigated. For the numerical simulations, a commercial CFD code solver of the finite volume method is implemented. To simulate the problem in a 3D setting, a pi-shape domain is created by cutting a 15° wedge out of the whole power plant geometry. In order to validate the obtained results, the Manzanares Power Plant experimental data are utilized. This study proves to be original since 15 forms of chimney wall based on a logical three-step procedure (from a cylindrical form to a parabolic form) are investigated. These forms are based on cylindrical, convergent/divergent, circular concave/convex, and parabolic curves. It should be noted that the main novelty of this study is to propose an approach to increase the performance of the SUTPP (i.e. increase the updraft air velocity) based on a logical three-step procedure by finding a suitable form of the chimney without changing the main dimensions of the SUTPP (i.e. tower height, collector diameter, collector height, etc.). Thus, the desired geometrical parameters in this investigation are tower convergence and divergence angles with convex and concave forms of the tower wall (e.g. arc and parabolic forms). The obtained results include the maximum and average updraft air velocities inside the tower. After performing this procedure, an appropriate parabolic form for the chimney wall is obtained. The results demonstrate that the final form (i.e. form 14 with the parabolic curve of chimney wall) has the highest updraft air velocity, which is an important factor on wind turbine power generation. It is worthwhile to mention that the average updraft air velocity increases from 15.66 m/s for the basic form to the value of 23.36 m/s for the final form 14 (i.e. around 49.17% increment).

Definition of the problem

In this study, a 1.0 MW SUTPP with the main geometrical parameters given in Table 1 is selected. Regarding the importance of the kinetic power of the hot air flowing inside the chimney on power generation of SUTPP, it is intended to increase the air velocity by considering the various forms of the chimney without changing the main dimensions of SUTPP. In order to obtain a suitable form for the chimney, three steps of the simulation are performed. The detail of these steps and their properties are given in Table 2 and Figure 1.

Table 1.

Main dimensions of the basic form of a 1.0 MW SUTPP, proposed for improving its performance.

Geometric parameters	Values (m)
Height of the tower (chimney) ( $H_{T}$ )	280
Radius of the tower inlet ( $R_{T I}$ )	20
Height of the collector inlet ( $H_{C I}$ )	2.0
Height of the collector outlet ( $H_{C O}$ )	6.0
Radius of the collector ( $R_{C}$ )	500
Turbine diameter ( $D_{T u}$ )	40
Bend junction radius ( $R_{B J}$ )	5.0
The soil depth (thermal storage) ( $D_{S}$ )	1.0

Figure 1.

Diagram of the SUTPP with the various tower geometries.

Table 2.

Different conﬁgurations of the tower (chimney) forms analyzed in the present work.

Step no.	Samples	Convergence or divergence angle (°)	Chimney outlet diameter $2 R_{T o}$ (m)	Second point location related to straight chimney wall (m)	Geometry of tower wall
Step1	Form 1	−0.50°	36.00	–	Convergence straight line
	Basic form	0.0°	40.00	–	Cylindrical form
	Form 2	1.00°	49.39	–	Divergence straight line
	Form 3	1.50°	54.09	–	Divergence straight line
	Form 4	2.00°	58.79	–	Divergence straight line
	Form 5	2.50°	63.49	–	Divergence straight line
	Form 6	3.00°	68.19	–	Divergence straight line
	Form 7	3.01°	68.30	–	Divergence straight line
	Form 8	3.02°	68.40	–	Divergence straight line
	Form 9	3.50°	73.16	–	Divergence straight line
Step2	Form 10	–	68.30	−1.50	Arc ( $R$ = 6055.88)
	Form 11	–	68.30	−2.00	Arc ( $R$ = 4542.34)
	Form 12	–	68.30	−2.50	Arc ( $R$ = 3634.32)
	Form 13	–	68.30	+1.50	Arc ( $R$ = 6055.88)
Step3	Form 14	–	68.30	−2.00	parabolic curve

In the first step, a straight chimney wall with the convergence angle of $- 0.5 °$ through divergence angles of $3.5 °$ is set to change the geometry of the chimney. During the simulation of these forms, the best value of the chimney outlet radius ( $R_{T o}$ ) for the case of having maximum air velocity is obtained. In the second step, by considering the obtained chimney outlet radius ( $R_{T o}$ ) and other geometries mentioned in Table 1, a concave/convex form of the tower wall is taken into account. For this purpose, an arc of a circle passing through three points is supposed. The first and third points of this arc are fixed and matched to the lower and upper endpoints of the tower wall. So, to draw convex or concave form, the second point of the arc (which is considered at the middle of the tower) is varied and set $+ 1.5$ to $- 2.5 m$ (in increments of $0.5 m$ ) far from the straight chimney wall as shown in Figure 1. During the simulation of these concave/convex forms, the best value of the second point of the arc for the case of having maximum air velocity is found. And finally, in the third step, a parabolic curve, which passes through the lower and upper endpoints of the tower wall and the second point obtained in step 2, is considered as the final form of the chimney wall. The equation of the parabolic curve is applied as follows

R_{T} = (1.12 \times 10^{- 4}) y_{T}^{2} + (1.99 \times 10^{- 2}) y_{T} + 19.81

(1)

where

R_{T}

and

y_{T}

are the radial and vertical locations of the chimney wall, respectively. To simulate the problem in a 3D condition, a pi-shape domain is created by cutting a 15° wedge out of the whole power plant geometry, as illustrated in Figure 2.

Figure 2.

Three-dimensional computational domain of SUTPP.

Methodology

For the numerical simulations, the ANSYS CFX 2016 solves the conservation equations for mass, momentum, and energy using the ﬁnite volume method. These equations are presented below and the details can be found in the literature^26,31,36

Mass conservation : \frac{\partial}{\partial x_{i}} (ρ u_{i}) = 0

(2)

Momentum conservation : \frac{\partial}{\partial x_{i}} (ρ u_{i} u_{j}) = - \frac{\partial p}{\partial x_{i}} + S_{M}

(3)

Energy conservation : \frac{\partial}{\partial x_{i}} (ρ u_{i} h_{total}) = \frac{\partial}{\partial x_{i}} (λ \frac{\partial T}{\partial x_{i}}) + u_{i} S_{M} + S_{E}

(4)

where the details of source terms, i.e.

S_{E} = q ″ / h_{r}

(source term in energy equation) and

S_{M} = (ρ - ρ_{\infty}) g

(source term in momentum equations) are presented in the literature.^26,31,36

Numerical method and boundary conditions

In this study, the governing equations are discretized and solved numerically assuming symmetry flow inside a 3D computational domain by using ANSYS-CFX code, based on finite volume procedure. For the simulation, the steady-state analysis is considered. The computational domain is divided into two parts which consisted of the air domain (containing the fluid inside the solar chimney and the solar collector) and the solid domain. The working ﬂuid is air which is modeled as an ideal gas. The reference pressure is set as $1.0 atm$ . The model of the chimney is built from the origin and developed in the positive y-direction. The buoyancy model is then applied by specifying the gravity of −g in the y-direction. The heat transfer model of the air domain and soil domain is total energy and thermal energy, respectively. Also, the shear stress transport is considered to set the turbulence model of this simulation (see Table 3 for the procedure and characteristic of the numerical simulation).

Table 3.

The procedure and characteristic of the numerical simulation.

Subject	Numerical method
Computational domain	Air domain/solid domain
Type of modeling/software	3D/ANSYS-CFX
Method of analysis	Steady-state analysis
Fluid characteristic	Air ideal gas
Fluid model (heat transfer)	Total energy
Energy source term	Radiation source
Fluid turbulence model	Shear stress transport (SST)
Reference pressure	1.0 atm
Buoyancy model	Buoyant model
Solid model (heat transfer)	Thermal energy

The boundary conditions of this study are shown in Figure 3. The boundary type at the inlet of collector and chimney outlet are two openings with zero relative pressure and a static temperature of $298.6 K$ . The thermal and velocity boundary conditions for chimney and bend junction walls are adiabatic and no-slip conditions, respectively. The boundary type at the collector is set as no-slip wall with a radiation source of $832 W / m^{2}$ and convection heat transfer coefficient of $8.5 W / m^{2} K$ . The tower axis is set as symmetry. The bottom surface of the soil domain is assumed as isothermal $T_{S} = 31.3 ° C$ . The edge surface of the soil domain is assumed as an adiabatic wall. The soil axis is also set as symmetry. Eventually, the appropriate interface region is created between the collector (air domain) and the soil (solid domain). In this study, the physical characteristics of soil and air are assigned similar to those of the Manzanares prototype^4,5,14 and they are presented in Table 4. Also, the depth of the soil is assigned $1.0 m$ and the density and thermal conductivity of the soil are varied with depth based on the graph mentioned in the litearature.^4,5,14 The automatic mesh connection method is selected for the interface. The simulation is run for 2000 iterations; for convergence, residual type of RMS and the residual target value of 1 × 10⁻⁵ are set as the criteria.

Figure 3.

Boundary conditions of this study.

Table 4.

Soil and air physical properties of the Manzanares prototype.^4,5,14

Property	Soil	Air
Density (kg/m³)	UDF (variable with depth)	$1.18$
Thermal conductivity (w/m K)	UDF (variable with depth)	$0.0271$
Expansion coefficient (K⁻¹)	–	$0.0033$
Viscosity (kg/m s)	–	$1.83 \times 10^{- 5}$
Specific heat (J/kg K)	$840$	$1004$
Pressure (Pa)	–	$1$

UDF: User-defined function.

Mesh and grid characteristic

ICEM CFD software is used for grid generation. The ICEM CFD Hex-Mesher method is used to discretize the computational domain. Meshing for all domains is shown in Figure 4. To perform the grid independency analysis, four different grid sizes of 92,852,152,893, 273,018, and 443,204 meshes are considered. The judging criterion is the average air velocity at the wind turbine inlet (by considering the turbine pressure difference). The average air velocities obtained for four mentioned grid sizes are 7.99, 8.13, 8.54, and 8.60 m/s, respectively. The obtained air velocities show that the results for third and fourth mesh grid sizes are approximately the same. So a grid size of 273,018 meshes is chosen for all the simulations.

Figure 4.

Meshing for the all domains of SUTPP.

Validation

Due to the fact that the Manzanares power plant was the first successful experimental prototype in the world, it is also replicated in this work to validate the results. To this aim, some boundary conditions and environmental characteristics, such as air properties and soil features (e.g. thermal conductivity and apparent density), as well as the efficiency of the wind turbine, are reproduced through analytical correlations, from the analysis of the experimental data on Manzanares prototype, throughout the day 2 September 1982.^4,5 The geometry of the Manzanares prototype is shown in Figure 5. The system geometry consists of a chimney with 200 m height and 5 m radius surrounded by a collector with 120 m radius and 1.85 m height (see Table 5).^4,5,37 The physical characteristics of soil and air are given in Table 2. Since the pressure drop exploited by wind turbine causes the established air velocity decreases, it can be concluded that $U_{B} = {[2 (1 - f) Δ P_{s c} / (ρ_{B})]}^{\frac{1}{2}}$ where $ρ_{B}$ is the air density at the chimney base, $Δ P_{s c}$ is the total pressure difference from the chimney entrance to the top of the tower, $U_{B}$ is the updraft air velocity at the chimney base, and $f$ is an exploitation factor of the pressure drop. The value of $f$ was experimentally established by Haaf⁵ at around $2 / 3 (66 %)$ and was numerically obtained by Hurtado et al.¹⁴ at around $4 / 5 (80 %)$ . This fact indicates that the wind turbine could exploit about $f$ -percent of the available pressure drop. In the current study, the value of $f = 2 / 3 = 0.66$ which is more practical and realistic is considered. The current simulation and its numerical results (average air temperature and velocity at the wind turbine inlet) are presented and compared with the experimental data of Haaf,⁵ theoretical results of Zhou et al.,²⁵ and numerical results of Hurtado et al.,¹⁴ at three different times in a day, i.e. 8 am, 12 noon, and 16 pm, 14 September (see Figures 6 and 7). The results show a good agreement with those data reported in the literature.^5,14,25 In addition, the percentage errors between the present simulation and the experimental data of Haaf,⁵ and the numerical results of Hurtado et al.,¹⁴ are calculated and tabulated in Table 6. The results given in Figures 7 and 8 and Table 6 show a good agreement with those data reported by the mentioned references.

Figure 5.

Areas, boundaries, and the coordinate system of the Manzanares prototype.

Figure 6.

Updraft temperature of the air at the wind turbine inlet in Manzanares prototype.

Table 5.

Dimensions of the Manzanares prototype.^4,5,37

Geometric parameters	Values (m)
Height of the tower (chimney) (H_T)	$194.60$
Radius of the tower (R_T)	$5.08$
Height of the collector (H_C)	$1.85$
Radius of the collector (R_C)	$122$

Table 6.

The percentage deviation between numerical results of this work and experimental results of Manzanares prototype.

Item	Time of day	Present work, numeric	Haaf,⁵ experiment	Hurtado et al.,¹⁴ numeric	Percentage deviation to Hurtado et al.¹⁴	Percentage deviation to Haaf⁵
Updraft temp. (°C)	8 am	36.20	29	33.14	9.23	24.80
	12 noon	44.40	44	48.51	8.47	0.90
	16 pm	40.23	40	45.79	12.14	0.57
Updraft velocity (m/s)	8 am	5.27	6.31	4.82	9.33	16.48
	12 noon	8.65	8.84	8.12	6.5	2.14
	16 pm	6.63	6.67	6.40	3.59	0.59

Figure 7.

Updraft velocity of the air at the wind turbine inlet in Manzanares prototype.

Figure 8.

Velocity contours for (a) basic form (cylindrical case), (b) form 1 (convergence angle), and (c) form 7 (divergence angle).

Results and discussions

After performing the validation for Manzanares prototype, the three steps of simulation for obtaining the suitable form for the chimney of the mentioned $1.0 MW$ SUTPP with the main geometry given in Table 1 can be started. The simulation results of these steps are presented in this section. It should be noted that in the simulation performed for these three steps the effect of turbine pressure drop is not considered (because in this study, the use of a particular wind turbine has not been emphasized). Figure 8 shows the air velocity contours for the different chimney’s geometries considered in step 1, i.e. the basic form (cylindrical case), form 1 ( $- 0.50 °$ convergence angle—the worst case), and form 7 ( $+ 3.01 °$ divergence angle—the best case). It can be concluded from the figure that the maximum and average updraft air velocities at the base of the tower are low when the angle of the vertical wall of the tower is convergent. For example, these values for the form 1 (the convergence angle of $- 0.5 °$ ) are around $23.33 m / s$ (max) and $13.51 m / s$ (average). However, in the cylindrical form (basic form), the maximum and average updraft air velocities at the base of the tower are around $26.70$ and $15.66 m / s$ , respectively. In addition, the results reveal that by changing the cylindrical form to the truncated cone with the divergence wall, the maximum and average updraft air velocities at the base of the tower increase regularly. However, this increment stops when the divergent angle becomes larger than $+ 3.01 °$ in form 7. The maximum and average updraft air velocities at the base of the tower (in form 7) are around $38.46$ and $22.52 m / s$ , respectively. So, the chimney geometry based on form 7 could be the suitable case in step 1 of the simulation. Figure 9 shows the updraft air velocity distribution for the different tower forms (basic form and forms 1, 2, 7, and 9) at $y = 11$ (the elevation of the wind turbine). It can be seen from the figure that the minimum and maximum velocity occurs at the tower’s centerline and near the tower wall, respectively. It is evident from this figure that the lowest flow rate value occurs in form 1 (tower with $- 0.50 °$ convergent angle) and the highest flow rate value occurs in form 7 (tower with $+ 3.01 °$ divergent angle).

Figure 9.

The updraft air velocity distribution for the different tower forms (basic form and forms 1, 2, 7, and 9) at $y = 11$ (the elevation of the wind turbine).

After finishing the simulation of the mentioned chimney forms in step 1 and obtaining the best value of the chimney outlet radius (i.e. $R_{T o} = 34.15$ m in form 7), the results of the second step of the simulation are presented below. As mentioned in “Definition of the problem” section, in the second step, by considering the applied chimney outlet radius (i.e. $R_{T o} = 34.15$ m) and other geometries referred in Table 1, a concave/convex form of the tower wall is taken into account. The details of this procedure have been discussed in “Definition of the problem” section. Figure 10 illustrates the air velocity contours for the different chimneys of the concave and convex forms of the tower wall at second steps of this study (i.e. forms 10–13). The figure depicts that the maximum and average updraft air velocities at the base of the tower are high, when the tower’s wall has a concave curve. These values for the form 11 (the best concave form) are around $39.50 m / s$ (max) and $22.97 m / s$ (average), while for the form 13 (the convex form) they are around $37.52 m / s$ (max) and $20.58 m / s$ (average). As discussed earlier in “Definition of the problem” section, during the simulation of these concave/convex forms, the best value of the second point location related to straight chimney wall is obtained as $- 2.0 m$ (for form 11).

Figure 10.

Velocity contours for different forms of a tower with concave and convex walls. (a) Form 10, (b) form 11, (c) form 12, and (d) form 13.

And finally, in the third step, a parabolic curve, which passes through the lower and upper endpoints of the tower wall (obtained in step 1) and the second point (obtained in step 2), is considered as the final form of the chimney wall (form 14). As mentioned in “Definition of the problem” section, the equation of the parabolic curve is based on equation (1). Figure 11 illustrates the air velocity contours for the parabolic curve of the chimney wall. It can be seen from the results that the maximum and average updraft air velocities at the base of the tower are $41.57$ and $23.36 m / s,$ respectively. The results show that the final form (i.e. form 14 with the parabolic curve of chimney wall) has the highest updraft air velocity, which is an important parameter on wind turbine power generation. For better comparison, the updraft air velocity distribution for the basic form (cylindrical tower), form 7 (the best form obtained in step 1), form 11 (the best form obtained in step 2), and form 14 (final form obtained in step 3) at $y = 11$ (the elevation of the wind turbine) are plotted in Figure 12. This figure displays how the design procedure defined by step 1–3 can improve the chimney wall form to have a maximum updraft air velocity inside the tower at the elevation of the wind turbine. It is worth to mention that, by implementing this design procedure to the defined $1.0 MW$ SUTPP in Table 1, the average updraft air velocity increases from $15.66 m / s$ for the basic form to the value of $23.36 m / s$ for the final form (form 14) (i.e. around $49.17 %$ increment).

Figure 11.

Velocity contours for the tower with the parabolic wall.

Figure 12.

The updraft air velocity distribution for the different tower forms (basic form, forms 7, 11, and 14) at $y = 11$ (the elevation of the wind turbine).

Conclusions

The present work investigates numerically the effect of chimney geometry form on the performance of a typical $1.0 MW$ SUTPP with predetermined tower height, collector diameter, collector inlet opening, collector outlet height, and chimney (tower) inlet opening. Due to the importance of kinetic power of the hot air (updraft air velocity inside the chimney) on power generation of SUTPP, this study aims to propose an approach to increase the air velocity by considering the various forms of the chimney without changing the main dimensions of SUTPP, such as tower height and collector geometries. The desired geometrical parameters in this investigation are tower convergence and divergence angles with convex and concave forms of the tower wall (e.g. arc and parabolic forms). The variation of these parameters on increasing the updraft airﬂow velocity inside the SUTPP chimney is highlighted. For the numerical simulations, a commercial CFD code solver based on the finite volume method is implemented. In this study, 15 forms of chimney wall based on a logical three-step instruction (from a cylindrical form to a parabolic form) are simulated. These forms are based on cylindrical, convergent/divergent, circular concave/convex, and parabolic curves for the chimney wall. The discussed results are included as the maximum and average updraft air velocities inside the tower. After implementing the three-step procedure, a parabolic form for the chimney wall is acquired. The results illustrate that the geometric variations in the components of one SUTPP (such as collector and tower) can have a significant effect on the airflow velocity and, hence, increase the amount of energy production. For example, the findings showed that by changing the cylindrical form to the truncated cone with the divergence wall, the maximum and average updraft air velocities at the base of the tower increase regularly. Also, the maximum and average updraft air velocities at the base of the tower are higher, when the tower’s wall forms a concave curve geometry (relative to the straight line of chimney wall). Moreover, the results reveal that the final form (i.e. form 14 with the parabolic curve of chimney wall) has the highest updraft air velocity, which is an important factor on wind turbine power generation. It is worth to note that the average updraft air velocity increases from $15.66 m / s$ for the basic form to the value of $23.36 m / s$ for the final form (form 14) (i.e. around $49.17 %$ increment).

Footnotes

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The authors would like to acknowledge the Imam Khomeini International University and the Shahrood University of Technology, which supported this study.

A Jameei is a PhD student in Department of Architectural Engineering, Imam Khomeini International University, Qazvin, Iran. He obtained his BSC in Architectural Engineering from Shahroud University of Technology, Iran, and MSC in Technology of Architecture from University of Tehran, Iran. He is a membership of the Iranian Institute of Spatial Structures. His main research interests are renewable and sustainable energy systems and spatial structures.

P Akbarzadeh is an associate professor of Mechanical Engineering in Faculty of Mechanical and Mechatronics Engineering, Shahrood University of Technology, Shahrood, Iran. He obtained his BSC in Mechanical Engineering from Tehran Polytechnique University (or Amirkabir University of Technology), Tehran, Iran, and MSC and PhD in Mechanical Engineering from University of Tehran, Tehran, Iran. His main research interest is CFD (Fluid and Cavitation simulation, nanofluids simulation, biofluids simulation, Heat transfer and energy simulation, and also journal bearings simulation).

H Zolfagharzadeh is an associate professor in Department of Architectural Engineering, Imam Khomeini International University, Qazvin, Iran. He obtained his BSC and MSC in Architecture from Polytechnic University of Torino, Italy, and PhD in Architecture from Shahid-Beheshti University, Tehran, Iran. His main research interest is Islamic Iranian Architecture.

SR Eghbali is an associate professor in Department of Architectural Engineering, Imam Khomeini International University, Qazvin, Iran. He obtained his BSC, MSC, and PhD in Architectural Engineering from University of Tehran, Iran. His main research interests are architectural design, renewable energy, and sustainable architecture.

Appendix

References

Backstrom

Hart

Hoffer

et al . State and recent advances in research and design of solar chimney power plant technology. VGB PowerTech 2008; 7: 64–71.

Cabanyes

Proyecto de motor solar. La Energia Eléctrica – Revista General de Electricidad Ysus Aplicaciones 1903; 8: 61–65.

Ngo

Natowitz

Our energy future: Resources, alternatives and the environment. 2nd ed. Hoboken, NJ: John Wiley & Sons, 2016, p.184.

Haaf

Friedrich

Mayr

et al . Solar chimneys. Part I: principle and construction of the pilot plant in Manzanares. Int J Solar Energy 1983; 2: 3–22.

Haaf

Solar chimneys. Part II: preliminary test results from the Manzanares plant. Int J Solar Energy 1984; 2: 141–161.

Bernardes

MAS

Voß

Weinrebe

Thermal and technical analyses of solar chimneys. Solar Energy 2003; 75: 511–524.

Dai

Huang

Wang

RZ.

Case study of solar chimney power plants in Northwestern regions of China. Renew Energy 2003; 28: 1295–1304.

Pastohr

Kornadt

Gürlebeck

Numerical and analytical calculations of the temperature and ﬂow ﬁeld in the upwind power plant. Int J Energy Res 2004; 28: 495–510.

Bilgen

Rheault

Solar chimney power plants for high latitudes. Solar Energy 2005; 79: 449–458.

10.

Ninic

Available energy of the air in solar chimneys and the possibility of its ground-level concentration. Solar Energy 2006; 80: 804–811.

11.

Burek

SAM

Habeb

Air ﬂow and thermal efﬁciency characteristics in solar chimneys and Trombe walls. Energy Build 2007; 39: 128–135.

12.

Fluri

Backström

TW.

Performance analysis of the power conversion unit of a solar chimney power plant. Solar Energy 2008; 82: 999–1008.

13.

Zhou

Xiao

Liu

et al . Comparison of classical solar chimney power system and combined solar chimney system for power generation and seawater desalination. Desalination 2010; 250: 249–256.

14.

Hurtado

Kaiser

Zamora

Evaluation of the influence of soil thermal inertia on the performance of a solar chimney power plant. Energy 2012; 47: 213–224.

15.

Hamdan

MO.

Analysis of solar chimney power plant utilizing chimney discrete model. Renew Energy 2012; 56: 50–54.

16.

Koonsrisuk

Chitsomboon

Mathematical modeling of solar chimney power plants. Energy 2013; 51: 314–322.

17.

Guo

Wang

Annual performance analysis of the solar chimney power plant in Sinkiang, China. Energy Convers Manage 2014; 87: 392–399.

18.

Guo

Wang

et al . Numerical study on the performance of a solar chimney power plant. Energy Convers Manage 2015; 105: 197–205.

19.

Mehrpooya

Shahsavan

Moftakhari Sharifzadeh

MM.

Modeling, energy and exergy analysis of solar chimney power plant-Tehran climate data case study. Energy 2016; 115: 257–273.

20.

Zhou

Hou

Effect of flow area to fluid power and turbine pressure drop factor of solar chimney power plants. J Solar Energy Eng 2017; 139: 041012.

21.

Zhou

YY.

Pressure losses in solar chimney power plant. J Solar Energy Eng 2018; 140: 024502.

22.

Ayadi

Driss

Bouabidi

et al . Effect of the turbine diameter on the generated power of a solar chimney power plant. Energy Environ2018; 29(5): 822–8365.

23.

dos Santos Bernardes

Molina Valle

Cortez

MFB.

Numerical analysis of natural laminar convection in a radial solar heater. Int J Therm Sci 1999; 38: 42–50.

24.

Koonsrisuk

Chitsomboon

Effect of tower area change on the potential of solar tower. In: The 2nd joint international conference on Sustainable Energy and Environment (SEE 2006), Bangkok, Thailand, 21–23 November 2006.

25.

Zhou

Yang

Xiao

et al . Analysis of chimney height for solar chimney power plant. Appl Therm Eng 2009; 29: 178–185.

26.

Koonsrisuk

Chitsomboon

Partial geometric similarity for solar chimney power plant modeling. Solar Energy 2009; 83: 1611–1618.

27.

Larbi

Bouhdjar

Chergui

Performance analysis of a solar chimney power plant in the southwestern region of Algeria. Renew Sustain Energy Rev 2010; 14: 470–477.

28.

Ghalamchi

Ahanj

Numerical simulation for achieving optimum dimensions of a solar chimney power plant. Sustain Energy 2013; 1: 26–31.

29.

Filkoski

Stojkovski

A CFD study of a solar chimney power plant operation. In: The 6th international conference on Sustainable Energy and Environmental Protection (SEEP 2013), Maribor, Slovenia, 20–23 August 2013.

30.

Koonsrisuk

Chitsomboon

Effects of ﬂow area changes on the potential of solar chimney power plants.

Energy 2013; 51: 400–406.

31.

Patel

Prasad

Ahmed

MR.

Computational studies on the effect of geometric parameters on the performance of a solar chimney power plant. Energy Convers Manage 2014; 77: 424–431.

32.

Chuen-Yu

Si-Yang

Marc

et al . A telescopic divergent chimney for power generation based on forced air movement: principle and theoretical formulation. Appl Energy 2014; 136: 873–880.

33.

Vieira

Garcia

Junior

ICA

et al . Numerical study of the influence of geometric parameters on the available power in a solar chimney. Engenharia Térmica (Therm Eng)2015; 14(1): 103–109.

34.

Siyang

Dennis

YCL

Michael

ZQC.

Effect of divergent chimneys on the performance of a solar chimney power plant. Energy Procedia 2017; 105: 7–13.

35.

Siyang

Dennis

YCL

John

CYC.

Numerical modelling and comparison of the performance of diffuser-type solar chimneys for power generation. Appl Energy 2017; 204: 948–957.

36.

Koonsrisuk

Chitsomboon

Accuracy of theoretical models in the prediction of solar chimney performance. Solar Energy 2009; 83: 1764–1771.

37.

Schlaich

The solar chimney: electricity from the sun. 1st ed. Stuttgart: Edition Axel Menges, 1995.