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Effects of geometric parameters on the performance of solar chimney power plants
Accepted Manuscript Effects of geometric parameters on the performance of solar chimney power plants Davood Toghraie, Amir Karami, Masoud Afrand, Arash Karimipour PII:
S0360-5442(18)31622-0
DOI:
10.1016/j.energy.2018.08.086
Reference:
EGY 13562
To appear in:
Energy
Received Date: 10 November 2017 Revised Date:
17 July 2018
Accepted Date: 11 August 2018
Please cite this article as: Toghraie D, Karami A, Afrand M, Karimipour A, Effects of geometric parameters on the performance of solar chimney power plants, Energy (2018), doi: 10.1016/ j.energy.2018.08.086. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Effects of geometric parameters on the performance of solar chimney power plants Davood Toghraie1, Amir Karami1, Masoud Afrand2,*, Arash Karimipour2
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Department of Mechanical Engineering, Khomeinishahr Branch, Islamic Azad University, Khomeinishahr, Iran
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Department of Mechanical Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran
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* Corresponding Author
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Email: [email protected]
Abstract
In this study, the influences of geometrical properties on a solar chimney were investigated numerically by applying the κ − ε turbulence model, continuity, momentum, and energy equations in the 3D finite volume approach inside a solar chimney power plant. The
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following variables should be involved: collector radius (Rcl), collector height (Hcl), chimney height (Hch), chimney radius (Rch), and heat flux ( q ′′ ). The effects of changes in these variables on temperature, velocity, pressure distributions, efficiency, and output power were
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investigated. The results indicated that output power and solar chimney efficiency have positive relationships with chimney height and collector radius but a negative one with collector height. In addition, it was found that the parameter of chimney radius has an
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optimum range which has the maximum values for efficiency and output power.
Keywords: Solar chimney; Efficiency; Output power; Numerical simulation; Renewable energy;
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1. Introduction Two major problems, poverty and dependence on fossil fuels, are prevalent worldwide. Fossil fuels are non-renewable sources of pollution, and poverty negatively affects the livelihood of millions around the world. The livelihoods of impoverished people can be dramatically
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improved with cheap energy. Energy can improve the sanitation of food and water, make many educational tools possible, allow students to study during the night, bolster the local economy by setting up and encouraging the location of businesses, and much more. The most
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potent, dependable, and sustainable source of energy in our solar system is the sun. There is great interest in harnessing its power, both efficiently and economically. Solar energy is one
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affordable type of renewable energy. Other energy sources have several problems such as discontinuous availability [1]. One innovative system that is receiving more and more attention is the solar updraft tower, or solar chimney. The absence of contamination by solar power plants is an interesting symbol of solar chimney operation to produce a large amount
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of solar powered electricity. The working properties of the solar chimney rely on the buoyant nature of air to turn a turbine that generates electricity. The system has 3 primary parts: the chimney, a collector, and a turbine. The chimney is a large pressure tower typically made
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from adiabatic materials. The collector is made of a transparent material, such as glass, and
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functions similarly to a greenhouse. The turbine operates as a low wind pressure generator to convert pressure into energy using cased turbines. During the day, solar radiation penetrates the transparent collector to warm the thermal storage layer. Some thermal energy is maintained in the thermal reservoir layer, and some is moved on to the air of the thermal reservoir surface. The warm airflow accelerates along the solar collector to the bottom of the chimney, drives the turbine and then the generator to produce electricity, and finally leaves the system through the top of the chimney. Outside air flows over the system of the solar collector and is called a continuous air current. Thermal
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ACCEPTED MANUSCRIPT energy is released from the thermal storage layer at night or on cloudy days, and the system continuously produces electricity. The basic fundamentals and descriptions of a solar chimney power plant were reported by Cabanyes [2] and Gunther [3]. Similar research was carried out by Schlaich in 1970 and in
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1981 to construct a pilot solar chimney of 50 kW power [4]. After this plant was established, many researchers proposed their solar chimney designs and buildings [5, 6]. The prototype solar chimney with a 50 kW power output was designed by Bergermann approximately 150
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km south of Madrid, Spain in 1981 [1]. The plant had a solar chimney measuring 194.6 m in height, 5.08 m in diameter, and a 0.00125-m thick metallic wall; it also had a collector with a
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radius of 122 m. Krisst et al. [7] built four pilot solar chimney power plants measuring 10 m in height and 6 m in diameter, which had a power capacity of 10 W. A demonstration power plant using a solar chimney was built in 1997 [8], in which an intermediate absorber and an extending collector were applied to achieve greater efficiency
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[9]. In 2002, a pilot solar chimney with a power capacity of 5 W was set up by Zhou et al. on the roof of a building in China [10, 11]. The pilot plant, which had a height of 8 m and a collector measuring 10 m in diameter, was rebuilt several times for different purposes. In
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2011, another pilot solar chimney was built by Kasaeian et al. [12] on the campus of the
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University of Zanjan, Iran. This solar chimney was constructed with a covered collector measuring 10 m in diameter and a chimney with a 12 m polyethylene pipe. Based on the temperature and air velocity at various collector positions, the maximum air velocity and chimney temperature were obtained. Measurements showed that on hot and cold days, the air at the lower section of the chimney appeared after sunrise. Khanal and Lei performed an experimental study on an inclined passive wall solar chimney [13]. The active wall of this model had uniform heat flux. The researchers observed that the air velocity in the air gap width depended significantly on the inclination angle.
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ACCEPTED MANUSCRIPT Patel et al. [14] optimized the shape of important sections of the solar chimney to numerically improve its performance. Their collector inlet and outlet, angle divergence, and chimney inlet opening were changed as the diameter of the collector was adjusted. Hurtado et al. [15] developed a numerical model under transient conditions based on the pilot one produced by
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Manzanares [6] to analyze the efficiency and thermodynamic properties of an SCPP over a daily operation cycle while considering soil as the heat storage material. Their results showed a significant increase in power as the soil compression was increased.
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Sangi et al. [16] investigated the simulation of a Manzanares prototype configuration. They compared their results with the experimental achievements of Schlaich [4] and Pastohr et al.
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[17]. Their results showed that a 2-D axis symmetric model could be utilized. Pastohr et al. [17] solved the complicated Navier-Stokes correlation at an upwind power plant. Koonsrisuk and Chitsomboon [18] established a dynamic correspondence among the prototype and the models by combining eight primary variables into one dimensionless variable. Moreover,
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three geometrical figures of a plant were numerically tested in their work. A numerical investigation of a solar chimney measuring 1 km in height and 2 km in radius and intended to create multi-climate conditions inside the collector was reported from China [19]. Buonomo
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et al. [20] presented a numerical study of a solar chimney in a south-facing building. They
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analyzed the effects of the height and spacing of a solar chimney on increasing system energy efficiency.
Gholamalizadeh and Kim [21] studied the greenhouse effect on the natural convection heat transfer characteristics in a solar chimney. They used an unsteady CFD model to analyze SCPP. They also used the discrete ordinates method to solve the equations of radiation heat transfer by Dehghani and Mohammadi [22], and they carried out the multi-objective optimization of solar chimney dimensions. The researchers considered the capital cost and
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ACCEPTED MANUSCRIPT power output of the system to be minimized and maximized, respectively. They found this optimization method to be effective and useful. Hanna et al. [23] studied the distribution of temperature effects in Egypt. Their results revealed that the temperature of the exit air of a solar collector depended on weather
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conditions and was also related to differences in air temperature in the solar collector.
Gholamalizadeh and Kim [24] reported the optimization of a solar chimney power plant utilizing genetic algorithms. They applied an inclined roof as the collector and showed that its
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shape played a significant role in the setup optimization approach.
Attig Bahar et al. [25] developed a new numerical research for a solar chimney according to
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the well-known three-dimensional CFD models; they also validated the accuracy of the achieved results versus the experimental ones of Manzanares.
Nilesh et al. [26] reviewed the numerical simulation of a solar chimney by changing its radius and height. It was seen that the various tower domains changed the power plant flow rates
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and efficiency.
Sudprasert et al. [27] investigated the influence of using moist air through the solar chimney in a vertical position. They recommended a suitable aspect ratio to achieve more ventilation
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and less backward fluid in the inlet.
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Karami and Toghraie [28] performed a computational fluid dynamics analysis and geometric optimization of a solar chimney power plant using genetic algorithms. They concluded that the output power of the plant could be increased considerably by increasing the height of the solar chimney, but increasing the radius of the collector could slightly reduce output power. In this study, by keeping the characteristics of the grids fixed, the influence of physical and geometric variables such as the collector radius (Rcl), collector height (Hcl), chimney height (Hch), chimney radius (Rch), and heat flux ( q ′′ ) on the solar chimney output power was investigated numerically using a three-dimensional compressible CFD method [see Fig. 1].
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ACCEPTED MANUSCRIPT The effects of changes in temperature, velocity, pressure distributions, efficiency, and output power were investigated. To the best of the authors' knowledge, there has been no comprehensive and thorough investigation of the influence of physical and geometric
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variables on the performance of solar chimney power plants to date.
2. Mathematical Modeling
The fundamental governing equations were summarized and important assumptions were
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explained. The viscous effect was not included as a variable. The cited study had concluded
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and proven that flow in a solar tower, with a low ratio of tower height to radius, could be approximated as an inviscid flow without sacrificing much in accuracy. Therefore, the current study investigated only inviscid flow. Turbine work was also not included because it was beyond the scope of this study, in which determining the amount of no-load air kinetic energy was the main aim. The numerical approach to solar chimney treatment was provided by
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applying the well-known classic transport Navier–Stokes equations for the thermo-physical properties of air. Moreover, the equations for energy and κ − ε for investigating the flow
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movements should be involved. The governing equations are as follows: The conservation of mass is:
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∂ (ρ ui ) = 0 ∂x i
(1)
The conservation of momentum is:
∂ ∂P ∂ ρ ui u j = − + ∂x j ∂x i ∂x j
(
)
∂u ∂u j µ i + ∂x j ∂x i
The conservation of energy equation is: 6
(
∂ −ρ u /i u / j + ∂x j
)
(2)
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∂ ∂ ∂T u E ρ + P = k ( ) ( ) (i ) ∂x ∂x ∂x i j j
(3)
u2 E =h− + ρ 2 P
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(4)
The standard κ − ε turbulence model was used throughout this study, and it was assumed that the flow is turbulent so that the influence of viscosity can be neglected. In the κ − ε
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turbulence approach, the kinetic energy of turbulence ( κ ) beside its dissipation rate are
µ ∂κ (µ + t ) σ κ ∂x j
µ ∂ε (µ + t ) σ ε ∂x j ∂u j
∂ ∂ (ρ ε ui ) = ∂x i ∂x j
(
) ∂x
ε ε2 ρ + C 1 ε G κ − C 2ε κ κ
(5)
(6)
i
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G κ = − ρ u /i u / j
+ Gκ − ρ ε
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∂ ∂ ( ρ κ ui ) = ∂x i ∂x j
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calculated from the governing equations:
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where σ k and σ ε indicate turbulent Prandtl numbers for the variables of k and ε; C 1ε , C 2ε are also the constant ones.
Now, the kinetic energy of turbulence ( G k ) is expressed in this way: G k = µt S 2
(7)
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ACCEPTED MANUSCRIPT where S and µt show the average rate-of-strain tensor modulus and turbulent viscosity, respectively:
S = 2S ij S ij
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(8)
κ2 µt = C µ ρ ε
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(9)
where, C µ is based on the mean rate of strain. The parameters in Equations (5) and (6) are
chimney is defined by [28]:
∆p =
1 ρV 2
2 t ,max
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defined as C 1ε = 1.44, C 2ε = 1.92, σ k =1.0, and σ ε = 1.3. The pressure drop in a solar
(10)
& Ptot = mgH
∆T T0
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is given by [28]:
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w here Vch ,max is the maximum air velocity in a chimney without a turbine. The output power
(11)
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where m& represents the air flow rate, g is the gravity acceleration, H is the height of the chimney, ∆T is the temperature difference, and T0 illustrates the inlet temperature. The efficiency of the solar chimney was calculated from:
η=
& mgH
∆T T0
(12)
Q in
where Q in is the input thermal power [28],
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ACCEPTED MANUSCRIPT & p (T 2 −T 1 ) = mc & p ∆T Q in = mc
(13)
and
m& = ρaπ DColl H Collv Coll = ρa π4 D12V Coll
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(14)
3. Numerical solution
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Basic equations were simplified to axisymmetric and steady state equations. The governing
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equations were solved using a pressure-based solver with a finite volume method. With the pressure-based solver for the incompressible flow, pressure became a primitive variable. The SIMPLE algorithm was chosen to couple the pressure and velocity equations. It uses a momentum equation to estimate the pressure and then corrects both the pressure and velocity until the conservation of mass equation is satisfied with the second order upwind scheme.
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The operation principle of solar chimney is presented in Fig. 1. Air enters the space at a low circular transparent that is open at the periphery and receives heat from solar radiation. The
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solar air collector consists of a roof and the ground under it. The height of the collector roof varies from the inlet to the junction with the chimney in accordance with the law of meridian
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flow theory. Table 1 illustrates the dimensions of the modeled power plant. The selected variables, including the main geometric parameters of the SCPP, were collector radius (Rcl), collector height (Hcl), chimney height (Hch), chimney radius (Rch), and heat flux ( q ′′ ). Each variable was generally required to be within a reasonable range as follows:
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ACCEPTED MANUSCRIPT 25 m ≤ H ch ≤ 500 m 1 m ≤ Rch ≤ 10 m 25 m ≤ Rcl ≤ 500 m
(15)
1 m ≤ H cl ≤ 10 m
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600 W / m 2 ≤ q ′′ ≤ 800 W / m 2
The present work used the unstructured tetrahedral grids at different mesh sizes which led to
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98,730 grid points in the grid independent study, as shown in Table 2.
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Those plants in which the tower centerline is the axis were considered to be axisymmetric. A five-degree part of the plant was cut out from the periphery to investigate the 3-D setting (see Fig. 2).
Governing equations were solved numerically with the following boundary conditions at each
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one of all 4 models. In each model, one of the geometric parameters of the chimney was variable and the rest were fixed. •
Model 1: Variable chimney height, constant chimney radius, constant collector radius,
•
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and constant collector height.
Model 2. Variable chimney radius, constant chimney height, constant collector radius,
•
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and constant collector height. Model 3: Variable collector height, constant chimney radius, constant chimney height, and constant collector height.
•
Model 4. Variable collector radius, constant chimney height, constant chimney radius, and constant collector height.
The temperature and pressure at the inlet of the roof were known, while zero pressure was considered at the outlet of the chimney with a symmetry condition along 2 walls of the sector. 10
ACCEPTED MANUSCRIPT Moreover, the insulated no-slip condition walls were supposed and illustrate the frictionless flow on the boundaries. The suitably accurate residual coefficients for mass and other
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equations were chosen to achieve the convergence situation (See Table 3).
4. Results and discussion
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4.1. Validation
A CFD model was used to simulate a solar chimney for the generation of power; the results
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were compared with those of [18] in Fig. 3. The average relative error rates between the obtained results and the data obtained by Koonsrisuk and Chitsomboon [18] are less than 5.0% and 4.7% for power and efficiency, respectively. It is clear that the model predicts the output power and efficiency of a Manzanares power plant with good agreement [18]. The
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results of the solar chimney power plant from the present work can be provided for different elements such as chimney and collector heights, chimney and collector radiuses, and heat
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flux.
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4.2. Investigation of heat flux
The air velocity and temperature distributions were analyzed for different heat fluxes, and the results are presented in Figs. 4 and 5. The velocity magnitude increased with a rise in the heat flux, and its maximum value was located near the walls of the chimney. The velocity contours showed an appreciable increase in the flow. This means that the transfer was done primarily by convection and predominated the conduction.
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ACCEPTED MANUSCRIPT 4.3. Investigation of collector height Changes in the temperature and pressure of the air at the end of the collector were analyzed for different collector inlet heights. The output data at collector heights of 1 m to 10 m were
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simulated, and the results are shown in Fig. 6. The inlet temperature in all numerical simulations was 308 K. According to Fig. 6a, the maximum difference in air temperature was 12.1 K at a collector height of 1 m, and the minimum temperature difference was 4.7 K at a
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collector height of 10 m for q ′′ =800 W/m2. Moreover, it became clear that when the heat flux decreased, the temperature difference at all heights had less magnitude. At the first state
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shown in Fig. 6b, the collector flow rate was in its smallest value; hence, the greatest number of air temperature variations was seen. With increases in the radius of the collector, the air pressure in the solar chimney decreased. For a thermal flux of 800 W/m2, the amount of pressure in the radius of 25m was -157 Pa. In a radius of 500 m, the air pressure was -1607
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Pa, which is 90% less than that of the 25-m radius, and for the thermal flux of 600 W/m2at radii of 25 and 500 m, the pressure was -133.64Pa and -1365.9Pa. As can be seen, the pressure in the thermal flux 800 W/m2was less than the thermal flux of 600 W/m2, which has
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a greater effect on the output power, but the variation process is similar for both thermal quantities; this reduction in pressure had a positive effect on tensile strength. Figure 6b shows
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that the maximum output power was obtained at a radius of 500 meters. By comparing the output power chart with a measurable pressure variation of 500 meters radius, the pressure is found to be at the minimum limit. In other words, the output power was increased by decreasing pressure.
Fig. 7 shows the influence of changes in collector height Hcl from 1 m to 10 m on the power and efficiency of the solar chimney power plant. Numerical results revealed that the output power decreased from 82.5 kW to 52.5 kW when the collector height was increased from 1 m
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ACCEPTED MANUSCRIPT to 10 m at a heat flux of 800 W/m2. This trend was also seen for a heat flux of 600 W/m2. Increasing the collector height caused pressure to increase and, due to the ideal gas law, the temperature and output power both decreased. Efficiency curves for different heat fluxes had similar behaviors and were decreased with increments in collector height. In Figs. 8a and 8b,
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the variations in air pressure and temperature versus different collector heights are shown. The fluid temperature difference rose and the fluid pressure declined in the solar chimney
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when collector height was increased. 4.4. Investigation of collector radius
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In Fig. 9, changes to output power and solar chimney efficiency are indicated where the value of Rcl varies from 25 m to 200 m, which means that flow power would be greater at more Rcl while the inverse process is confirmed for efficiency.
As seen in Fig. 9, for q ′′ =800W/m2, the output power and efficiency were 14.25kW and
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0.003 at the collector radius of 25 m, respectively. At a collector radius of 500 m, output power and efficiency both had different behavior. The output power increased to 1415 kW, and efficiency decreased to 0.00195. The main reason for the augmentation in output power
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can be the reduction in pressure caused by the increase in collector radius (as shown in Fig. 8b), which caused the air mass flow rate and temperature to increase. However, by increasing
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the collector radius, the area of heat transfer increased, and with respect to the constant heat flux, efficiency decreased.
4.5. Investigation of chimney height Variations in air pressure and mass flow rate were simulated at different chimney heights. Results for the heights of 25 m to 500 m are shown in Figs. 10a and 10b, respectively. Then 13
ACCEPTED MANUSCRIPT the influence of the chimney height, Hch, was investigated. The Hch was changed from 25 m to 500 m. The higher Hch corresponded with a higher level of efficiency and power (see Fig. 11). Fig. 11 (a) shows the power of the solar chimney variation against chimney height for different heat fluxes. It can be seen that for q ′′ =800 W/m2 the output power increased from
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24 kW for a chimney height of 25 m to 313.5 kW for a chimney height of 500 m. Also, for q ′′ =600 W/m2, the output power was 16 kW and 209 kW for chimney heights of 25 m and
500 m, respectively. However, a higher chimney height led to lower air pressure and larger
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velocity and mass flow rate. Augmentation in the flow rate caused increased output power. In Fig. 11 (b), the efficiency of the solar chimney for heat fluxes of 600 W/m2 and 800 W/m2 are
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shown. Similar to the variation in output power, efficiency increased from 0.00063 at a chimney height of 25 m to 0.0083 at a chimney height of 500 m. 4.6. Investigation of chimney radius
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The numerical investigation of the chimney radius was performed for 1 m to 10 m values. Figs. 12a and 12b indicate the mass flow rate and pressure magnitude distribution of air for different chimney radii. As seen in Fig. 12, the maximum mass flow rate of working fluid for
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a chimney radius of 5 m at q ′′ =800 W/m2 was 45.29 kg/s, which is 70% and 30.8% higher
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than the mass flow rate for chimney radii of 1 m and 10 m, respectively. It is worthy to note that the main n for this behavior can be that this radius had the minimum pressure value, according to Fig. 12b.
Effects of chimney radius, Rch, variations are displayed in Fig. 13, where Rch was varied from 1 m to 10 m. Fig. 13 (a) shows that output power increased when chimney radius was increased from 1 m to 5 m, and its maximum value equaled 85.5 kW for q ′′ =800W/m2. One possible explanation for this could be the greater mass flow inlet due to less chimney pressure. Then, by increasing the chimney radius from 5 m to 10 m, the output power 14
ACCEPTED MANUSCRIPT decreased 28%. This trend was also seen in the output power curve for q ′′ =600W/m2. It can be seen in Fig. 13 (b) that for the chimney radius of 5 m, the maximum efficiency was
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0.00334; however, at 10 m, the efficiency decreased 28% for q ′′ =800 W/m2.
5. Conclusion
The present study demonstrated the capabilities of the CFD technique as a powerful research
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and engineering tool for the analysis of complex aerodynamic and thermal systems like solar chimney power plants. The CFD approach might enable the conversion of an experimental
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work on this subject to a simpler and more economical one. Thus, this approach can be further developed and upgraded for a more detailed analysis. In this study, three-dimensional numerical simulations were performed to investigate the influences of geometrical parameters on the performance of the solar chimney. A three-dimensional region supposed with κ − ε
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turbulence model was simulated. Firstly, the numerical results for the base case were validated with [18]. Furthermore, the effects of geometric characterizations of the solar chimney power plant on flow and performance were investigated. The profiles of
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temperature, pressure, and mass flow rate are presented in various geometrical parameters. It
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is seen that output power can be increased considerably by increasing solar chimney height, while increasing the collector radius can increase output power slightly. Through the analysis, it was found that the chimney radius parameter had an optimum range with maximum values for efficiency and output power. The extension of this paper for CFD simulation according to our previous works [28-56] affords engineers a good option for CFD simulation.
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[26] Nilesh N. Ubhale, Santosh R. Mallah, Dr. Lavendra S. Bothra, A Review: Numerical Simulation for Solar Chimney by Changing its Radius and Height, International Journal on Recent Technologies in Mechanical and Electrical Engineering (IJRMEE) Volume: 3 Issue: 6, June 2016, pp. 5-8 [27] S. Sudprasert, C. Chinsorranant, P. Rattanadecho, Numerical study of vertical solar chimneys with moist air in a hot and humid climate, International Journal of Heat and Mass Transfer 102 (2016) 645–656 [28] A Karami, D Toghraie, Computational Fluid Dynamics Analysis and Geometric Optimization of Solar Chimney Power Plants by Using of Genetic Algorithm, Journal of Simulation & Analysis of Novel Technologies in Mechanical Engineering, Volume 10, 2017, 49-60 [30] Karimipour A. Alipour H. Akbari OA. Semiromi DT. Esfe MH., Studying the Effect of Indentation on Flow Parameters and Slow Heat Transfer of Water-Silver Nano-Fluid with
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ACCEPTED MANUSCRIPT Varying Volume Fraction in a Rectangular Two-Dimensional Micro Channel, Indian Journal of Science and Technology, 2016, 8, 2015 [31] Akbari OA. Karimipour A. Toghraie D. Karimipour A, Impact of ribs on flow parameters and laminar heat transfer of Water/Alumina nanofluid with different nanoparticle volume fractions in a three-dimensional rectangular microchannel, Adv Mech Eng, 2016; 7: 1–11
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[32] Akbari OA. Karimipour A. Toghraie D. Safaei MR. Alipour M. Goodarzi H. and Dahari M. Investigation of Rib's Height Effect on Heat Transfer and Flow Parameters of Laminar WaterAl2O3 Nanofluid in a Two Dimensional Rib-Microchannel. Appl Math Comp, 2016, 290, 135– 153
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[33] Akbari OA. Toghraie D. Karimipour A. Numerical simulation of heat transfer and turbulent flow of Water nanofluids CuO in rectangular microchannel with semi attached rib. Adv Mech Eng. 2016; 8: 1–25
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[34] Alipour H. Karimipour A. Safaei MR. Semiromi DT. Akbari OA., Influence of T-semi attached rib on turbulent flow and heat transfer parameters of a silver-Water nanofluid with different volume fractions in a three-dimensional trapezoidal microchannel. Physica E, 2016; 88: 60-76 [35] Nazari S. Toghraie D. Numerical simulation of heat transfer and fluid flow of Water-CuO Nanofluid in a sinusoidal channel with a porous medium. Physica E, 123; 87: 134-140 [36] Sajadifar SA. Karimipour A. Toghraie D. Fluid flow and heat transfer of non-Newtonian nanofluid in a microtube considering slip velocity and temperature jump boundary conditions,
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European Journal of Mechanics-B/Fluids, 2017; 61: 25-32
[37] Aghanajafi A, Toghraie D. Mehmandoust B., Numerical simulation of laminar forced convection of Water-CuO nanofluid inside a triangular duct, Physica E, 2017: 85: 103-108
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[38] Afrand M. Toghraie D. Karimipour A. Wongwises SA. Numerical Study of Natural Convection in a Vertical Annulus Filled with Gallium in the Presence of Magnetic Field, Journal of Magnetism and Magnetic Materials, 2017, 430: 22–28
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[39] Faridzadeh MR. Semiromi DT. Niroomand A. Analysis of laminar mixed convection in an inclined square lid-driven cavity with a nanofluid by using an artificial neural network. Heat Transfer Research. 2014; 45 [40] D Toghraie, Numerical thermal analysis of Water's boiling heat transfer based on a turbulent jet impingement on heated surface, Physica E, 84, 454-465, 2016 [41] Qumars Gravndyan, Omid Ali Akbari, Davood Toghraie, Ali Marzban, Ramin Mashayekhi, Reza Karimi, Farzad Pourfattah, The effect of aspect ratios of rib on the heat transfer and laminar water/TiO2 nanofluid flow in a two-dimensional rectangular microchannel, Journal of Molecular Liquids 236, 254-265, 2017 [42] OA Akbari, HH Afrouzi, A Marzban, D Toghraie, H Malekzade, A Arabpour, Investigation of volume fraction of nanoparticles effect and aspect ratio of the twisted tape in the tube, Journal of Thermal Analysis and Calorimetry 129 (3), 1911-1922, 2017 18
ACCEPTED MANUSCRIPT [43] MR Shamsi, OA Akbari, A Marzban, D Toghraie, R Mashayekhi, Increasing heat transfer of nonNewtonian nanofluid in rectangular microchannel with triangular ribs, Physica E: Lowdimensional Systems and Nanostructures 93, 167-178, 2017 [44] O Rezaei, OA Akbari, A Marzban, D Toghraie, F Pourfattah, R Mashayekhi, The numerical investigation of heat transfer and pressure drop of turbulent flow in a triangular microchannel, Physica E: Low-dimensional Systems and Nanostructures 93, 179-189, 2017
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[45] M Heydari, D Toghraie, OA Akbari, The effect of semi-attached and offset mid-truncated ribs and Water/TiO2 nanofluid on flow and heat transfer properties in a triangular microchannel, Thermal Science and Engineering Progress 2, 140-150, 2017
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[46] GR Ahmadi, D Toghraie, Energy and exergy analysis of Montazeri steam power plant in Iran, Renewable and Sustainable Energy Reviews 56, 454-463, 2016
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[47] M. Afrand, S. Farahat, A.H. Nezhad, G.A. Sheikhzadeh, F. Sarhaddi, 3-D numerical investigation of natural convection in a tilted cylindrical annulus containing molten potassium and controlling it using various magnetic fields, International Journal of Applied Electromagnetics and Mechanics, 46 (2014) 809-821. [48] M. Afrand, Using a magnetic field to reduce natural convection in a vertical cylindrical annulus, International Journal of Thermal Sciences, 118 (2017) 12-23.
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[49] M. Afrand, S. Farahat, A.H. Nezhad, G.A. Sheikhzadeh, F. Sarhaddi, S. Wongwises, Multiobjective optimization of natural convection in a cylindrical annulus mold under magnetic field using particle swarm algorithm, International Communications in Heat and Mass Transfer, 60 (2015) 13-20. [50] G Ahmadi, D Toghraie, OA Akbari, Efficiency improvement of a steam power plant through solar repowering, International Journal of Exergy 22 (2), 158-182, 2017
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[51] M. Afrand, S. Rostami, M. Akbari, S. Wongwises, M.H. Esfe, A. Karimipour, Effect of induced electric field on magneto-natural convection in a vertical cylindrical annulus filled with liquid potassium, International Journal of Heat and Mass Transfer, 90 (2015) 418-426.
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[52] M. Afrand, S. Farahat, A.H. Nezhad, G.A. Sheikhzadeh, F. Sarhaddi, Numerical simulation of electrically conducting fluid flow and free convective heat transfer in an annulus on applying a magnetic field, Heat Transfer Research, 45 (2014) 749-766. [53] G Ahmadi, D Toghraie, A Azimian, OA Akbari, Evaluation of synchronous execution of full repowering and solar assisting in a 200 MW steam power plant, a case study, Applied Thermal Engineering 112, 111-123, 2017 [54] A Moraveji, D Toghraie, Computational fluid dynamics simulation of heat transfer and fluid flow characteristics in a vortex tube by considering the various parameters, International Journal of Heat and Mass Transfer 113, 432-443, 2017 [55] G Ahmadi, D Toghraie, OA Akbari, Solar parallel feed water heating repowering of a steam power plant: a case study in Iran, Renewable and Sustainable Energy Reviews 77, 474-485, 2017
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[56] E Keshavarz, D Toghraie, M Haratian, Modeling industrial scale reaction furnace using computational fluid dynamics: a case study in Ilam gas treating plant, Applied Thermal Engineering 123, 277-289, 2017
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Figure Legends: Fig. 1. The solar chimney configuration
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Fig. 2. The numerical grids of object Fig 3. Compared obtained results for (a) Power, (b) Efficiency with [18]
Fig. 4. Contours of temperature magnitude in the base case for a) 600 W/m2, b) 800 W/m2
Fig. 6. Effect of collector height on a) temperature, b) pressure
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Fig. 5. Velocity contours for base case at a) 600 W/m2, b) 800 W/m2
Fig. 7. Influence of collector height on the solar chimney performance
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Fig. 8. Influence of collector radius on a) temperature, b)pressure
Fig. 9. Influence of collector radius on solar chimney plant performance Fig. 10. Influence of chimney height on a) mass flow rate, b) pressure Fig. 11. Influence of chimney height on plant
Fig. 12. Influence of chimney radius on a) mass flow rate, b) pressure
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Fig. 13. Effect of chimney radius on solar chimney plant performance
Parameter
Chimney Height 100 m
Chimney Radius
Collector Radius
Collector Height
4m
100 m
2m
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Value
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Table 1 Dimensions of modeled power plant.
Table 2. Relative errors of power and efficiency at different mesh sizes against to [18]. Grid 1
Grid 2
Grid 3
Grid 4
Grid 5
(26192
(54960
(78842
(98730
(126314
elements)
elements)
elements)
elements)
elements)
Power
65%
28%
12%
4.8%
4.6%
Efficiency
71%
30%
14%
4.4%
4.3%
Parameter
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Pressure = 0 Pa T = 308 K W q ′′ =0 2 m W q ′′ =600 2 m W q ′′ =800 2 m -
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Highlights Investigating the influences of geometrical properties on a solar chimney performance
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Using the κ − ε turbulence model and the 3D finite volume approach
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Presenting variables effects on temperature, velocity, pressure, efficiency, and output power
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Power and efficiency have positive relationships with chimney height and collector radius.
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Chimney radius has an optimum range for obtaining maximum efficiency and output power.
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S0360-5442(18)31622-0
DOI:
10.1016/j.energy.2018.08.086
Reference:
EGY 13562
To appear in:
Energy
Received Date: 10 November 2017 Revised Date:
17 July 2018
Accepted Date: 11 August 2018
Please cite this article as: Toghraie D, Karami A, Afrand M, Karimipour A, Effects of geometric parameters on the performance of solar chimney power plants, Energy (2018), doi: 10.1016/ j.energy.2018.08.086. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Effects of geometric parameters on the performance of solar chimney power plants Davood Toghraie1, Amir Karami1, Masoud Afrand2,*, Arash Karimipour2
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Department of Mechanical Engineering, Khomeinishahr Branch, Islamic Azad University, Khomeinishahr, Iran
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Department of Mechanical Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran
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* Corresponding Author
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Email: [email protected]
Abstract
In this study, the influences of geometrical properties on a solar chimney were investigated numerically by applying the κ − ε turbulence model, continuity, momentum, and energy equations in the 3D finite volume approach inside a solar chimney power plant. The
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following variables should be involved: collector radius (Rcl), collector height (Hcl), chimney height (Hch), chimney radius (Rch), and heat flux ( q ′′ ). The effects of changes in these variables on temperature, velocity, pressure distributions, efficiency, and output power were
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investigated. The results indicated that output power and solar chimney efficiency have positive relationships with chimney height and collector radius but a negative one with collector height. In addition, it was found that the parameter of chimney radius has an
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optimum range which has the maximum values for efficiency and output power.
Keywords: Solar chimney; Efficiency; Output power; Numerical simulation; Renewable energy;
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1. Introduction Two major problems, poverty and dependence on fossil fuels, are prevalent worldwide. Fossil fuels are non-renewable sources of pollution, and poverty negatively affects the livelihood of millions around the world. The livelihoods of impoverished people can be dramatically
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improved with cheap energy. Energy can improve the sanitation of food and water, make many educational tools possible, allow students to study during the night, bolster the local economy by setting up and encouraging the location of businesses, and much more. The most
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potent, dependable, and sustainable source of energy in our solar system is the sun. There is great interest in harnessing its power, both efficiently and economically. Solar energy is one
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affordable type of renewable energy. Other energy sources have several problems such as discontinuous availability [1]. One innovative system that is receiving more and more attention is the solar updraft tower, or solar chimney. The absence of contamination by solar power plants is an interesting symbol of solar chimney operation to produce a large amount
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of solar powered electricity. The working properties of the solar chimney rely on the buoyant nature of air to turn a turbine that generates electricity. The system has 3 primary parts: the chimney, a collector, and a turbine. The chimney is a large pressure tower typically made
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from adiabatic materials. The collector is made of a transparent material, such as glass, and
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functions similarly to a greenhouse. The turbine operates as a low wind pressure generator to convert pressure into energy using cased turbines. During the day, solar radiation penetrates the transparent collector to warm the thermal storage layer. Some thermal energy is maintained in the thermal reservoir layer, and some is moved on to the air of the thermal reservoir surface. The warm airflow accelerates along the solar collector to the bottom of the chimney, drives the turbine and then the generator to produce electricity, and finally leaves the system through the top of the chimney. Outside air flows over the system of the solar collector and is called a continuous air current. Thermal
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ACCEPTED MANUSCRIPT energy is released from the thermal storage layer at night or on cloudy days, and the system continuously produces electricity. The basic fundamentals and descriptions of a solar chimney power plant were reported by Cabanyes [2] and Gunther [3]. Similar research was carried out by Schlaich in 1970 and in
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1981 to construct a pilot solar chimney of 50 kW power [4]. After this plant was established, many researchers proposed their solar chimney designs and buildings [5, 6]. The prototype solar chimney with a 50 kW power output was designed by Bergermann approximately 150
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km south of Madrid, Spain in 1981 [1]. The plant had a solar chimney measuring 194.6 m in height, 5.08 m in diameter, and a 0.00125-m thick metallic wall; it also had a collector with a
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radius of 122 m. Krisst et al. [7] built four pilot solar chimney power plants measuring 10 m in height and 6 m in diameter, which had a power capacity of 10 W. A demonstration power plant using a solar chimney was built in 1997 [8], in which an intermediate absorber and an extending collector were applied to achieve greater efficiency
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[9]. In 2002, a pilot solar chimney with a power capacity of 5 W was set up by Zhou et al. on the roof of a building in China [10, 11]. The pilot plant, which had a height of 8 m and a collector measuring 10 m in diameter, was rebuilt several times for different purposes. In
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2011, another pilot solar chimney was built by Kasaeian et al. [12] on the campus of the
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University of Zanjan, Iran. This solar chimney was constructed with a covered collector measuring 10 m in diameter and a chimney with a 12 m polyethylene pipe. Based on the temperature and air velocity at various collector positions, the maximum air velocity and chimney temperature were obtained. Measurements showed that on hot and cold days, the air at the lower section of the chimney appeared after sunrise. Khanal and Lei performed an experimental study on an inclined passive wall solar chimney [13]. The active wall of this model had uniform heat flux. The researchers observed that the air velocity in the air gap width depended significantly on the inclination angle.
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Manzanares [6] to analyze the efficiency and thermodynamic properties of an SCPP over a daily operation cycle while considering soil as the heat storage material. Their results showed a significant increase in power as the soil compression was increased.
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Sangi et al. [16] investigated the simulation of a Manzanares prototype configuration. They compared their results with the experimental achievements of Schlaich [4] and Pastohr et al.
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[17]. Their results showed that a 2-D axis symmetric model could be utilized. Pastohr et al. [17] solved the complicated Navier-Stokes correlation at an upwind power plant. Koonsrisuk and Chitsomboon [18] established a dynamic correspondence among the prototype and the models by combining eight primary variables into one dimensionless variable. Moreover,
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three geometrical figures of a plant were numerically tested in their work. A numerical investigation of a solar chimney measuring 1 km in height and 2 km in radius and intended to create multi-climate conditions inside the collector was reported from China [19]. Buonomo
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et al. [20] presented a numerical study of a solar chimney in a south-facing building. They
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analyzed the effects of the height and spacing of a solar chimney on increasing system energy efficiency.
Gholamalizadeh and Kim [21] studied the greenhouse effect on the natural convection heat transfer characteristics in a solar chimney. They used an unsteady CFD model to analyze SCPP. They also used the discrete ordinates method to solve the equations of radiation heat transfer by Dehghani and Mohammadi [22], and they carried out the multi-objective optimization of solar chimney dimensions. The researchers considered the capital cost and
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ACCEPTED MANUSCRIPT power output of the system to be minimized and maximized, respectively. They found this optimization method to be effective and useful. Hanna et al. [23] studied the distribution of temperature effects in Egypt. Their results revealed that the temperature of the exit air of a solar collector depended on weather
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conditions and was also related to differences in air temperature in the solar collector.
Gholamalizadeh and Kim [24] reported the optimization of a solar chimney power plant utilizing genetic algorithms. They applied an inclined roof as the collector and showed that its
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shape played a significant role in the setup optimization approach.
Attig Bahar et al. [25] developed a new numerical research for a solar chimney according to
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the well-known three-dimensional CFD models; they also validated the accuracy of the achieved results versus the experimental ones of Manzanares.
Nilesh et al. [26] reviewed the numerical simulation of a solar chimney by changing its radius and height. It was seen that the various tower domains changed the power plant flow rates
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and efficiency.
Sudprasert et al. [27] investigated the influence of using moist air through the solar chimney in a vertical position. They recommended a suitable aspect ratio to achieve more ventilation
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and less backward fluid in the inlet.
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Karami and Toghraie [28] performed a computational fluid dynamics analysis and geometric optimization of a solar chimney power plant using genetic algorithms. They concluded that the output power of the plant could be increased considerably by increasing the height of the solar chimney, but increasing the radius of the collector could slightly reduce output power. In this study, by keeping the characteristics of the grids fixed, the influence of physical and geometric variables such as the collector radius (Rcl), collector height (Hcl), chimney height (Hch), chimney radius (Rch), and heat flux ( q ′′ ) on the solar chimney output power was investigated numerically using a three-dimensional compressible CFD method [see Fig. 1].
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variables on the performance of solar chimney power plants to date.
2. Mathematical Modeling
The fundamental governing equations were summarized and important assumptions were
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explained. The viscous effect was not included as a variable. The cited study had concluded
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and proven that flow in a solar tower, with a low ratio of tower height to radius, could be approximated as an inviscid flow without sacrificing much in accuracy. Therefore, the current study investigated only inviscid flow. Turbine work was also not included because it was beyond the scope of this study, in which determining the amount of no-load air kinetic energy was the main aim. The numerical approach to solar chimney treatment was provided by
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applying the well-known classic transport Navier–Stokes equations for the thermo-physical properties of air. Moreover, the equations for energy and κ − ε for investigating the flow
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movements should be involved. The governing equations are as follows: The conservation of mass is:
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∂ (ρ ui ) = 0 ∂x i
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∂ ∂P ∂ ρ ui u j = − + ∂x j ∂x i ∂x j
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∂ −ρ u /i u / j + ∂x j
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u2 E =h− + ρ 2 P
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µ ∂ε (µ + t ) σ ε ∂x j ∂u j
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(
) ∂x
ε ε2 ρ + C 1 ε G κ − C 2ε κ κ
(5)
(6)
i
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G κ = − ρ u /i u / j
+ Gκ − ρ ε
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∂ ∂ ( ρ κ ui ) = ∂x i ∂x j
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calculated from the governing equations:
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where σ k and σ ε indicate turbulent Prandtl numbers for the variables of k and ε; C 1ε , C 2ε are also the constant ones.
Now, the kinetic energy of turbulence ( G k ) is expressed in this way: G k = µt S 2
(7)
7
ACCEPTED MANUSCRIPT where S and µt show the average rate-of-strain tensor modulus and turbulent viscosity, respectively:
S = 2S ij S ij
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(8)
κ2 µt = C µ ρ ε
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(9)
where, C µ is based on the mean rate of strain. The parameters in Equations (5) and (6) are
chimney is defined by [28]:
∆p =
1 ρV 2
2 t ,max
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defined as C 1ε = 1.44, C 2ε = 1.92, σ k =1.0, and σ ε = 1.3. The pressure drop in a solar
(10)
& Ptot = mgH
∆T T0
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is given by [28]:
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w here Vch ,max is the maximum air velocity in a chimney without a turbine. The output power
(11)
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where m& represents the air flow rate, g is the gravity acceleration, H is the height of the chimney, ∆T is the temperature difference, and T0 illustrates the inlet temperature. The efficiency of the solar chimney was calculated from:
η=
& mgH
∆T T0
(12)
Q in
where Q in is the input thermal power [28],
8
ACCEPTED MANUSCRIPT & p (T 2 −T 1 ) = mc & p ∆T Q in = mc
(13)
and
m& = ρaπ DColl H Collv Coll = ρa π4 D12V Coll
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(14)
3. Numerical solution
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Basic equations were simplified to axisymmetric and steady state equations. The governing
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equations were solved using a pressure-based solver with a finite volume method. With the pressure-based solver for the incompressible flow, pressure became a primitive variable. The SIMPLE algorithm was chosen to couple the pressure and velocity equations. It uses a momentum equation to estimate the pressure and then corrects both the pressure and velocity until the conservation of mass equation is satisfied with the second order upwind scheme.
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The operation principle of solar chimney is presented in Fig. 1. Air enters the space at a low circular transparent that is open at the periphery and receives heat from solar radiation. The
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solar air collector consists of a roof and the ground under it. The height of the collector roof varies from the inlet to the junction with the chimney in accordance with the law of meridian
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flow theory. Table 1 illustrates the dimensions of the modeled power plant. The selected variables, including the main geometric parameters of the SCPP, were collector radius (Rcl), collector height (Hcl), chimney height (Hch), chimney radius (Rch), and heat flux ( q ′′ ). Each variable was generally required to be within a reasonable range as follows:
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ACCEPTED MANUSCRIPT 25 m ≤ H ch ≤ 500 m 1 m ≤ Rch ≤ 10 m 25 m ≤ Rcl ≤ 500 m
(15)
1 m ≤ H cl ≤ 10 m
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600 W / m 2 ≤ q ′′ ≤ 800 W / m 2
The present work used the unstructured tetrahedral grids at different mesh sizes which led to
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98,730 grid points in the grid independent study, as shown in Table 2.
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Those plants in which the tower centerline is the axis were considered to be axisymmetric. A five-degree part of the plant was cut out from the periphery to investigate the 3-D setting (see Fig. 2).
Governing equations were solved numerically with the following boundary conditions at each
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one of all 4 models. In each model, one of the geometric parameters of the chimney was variable and the rest were fixed. •
Model 1: Variable chimney height, constant chimney radius, constant collector radius,
•
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and constant collector height.
Model 2. Variable chimney radius, constant chimney height, constant collector radius,
•
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and constant collector height. Model 3: Variable collector height, constant chimney radius, constant chimney height, and constant collector height.
•
Model 4. Variable collector radius, constant chimney height, constant chimney radius, and constant collector height.
The temperature and pressure at the inlet of the roof were known, while zero pressure was considered at the outlet of the chimney with a symmetry condition along 2 walls of the sector. 10
ACCEPTED MANUSCRIPT Moreover, the insulated no-slip condition walls were supposed and illustrate the frictionless flow on the boundaries. The suitably accurate residual coefficients for mass and other
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equations were chosen to achieve the convergence situation (See Table 3).
4. Results and discussion
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4.1. Validation
A CFD model was used to simulate a solar chimney for the generation of power; the results
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were compared with those of [18] in Fig. 3. The average relative error rates between the obtained results and the data obtained by Koonsrisuk and Chitsomboon [18] are less than 5.0% and 4.7% for power and efficiency, respectively. It is clear that the model predicts the output power and efficiency of a Manzanares power plant with good agreement [18]. The
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results of the solar chimney power plant from the present work can be provided for different elements such as chimney and collector heights, chimney and collector radiuses, and heat
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flux.
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4.2. Investigation of heat flux
The air velocity and temperature distributions were analyzed for different heat fluxes, and the results are presented in Figs. 4 and 5. The velocity magnitude increased with a rise in the heat flux, and its maximum value was located near the walls of the chimney. The velocity contours showed an appreciable increase in the flow. This means that the transfer was done primarily by convection and predominated the conduction.
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ACCEPTED MANUSCRIPT 4.3. Investigation of collector height Changes in the temperature and pressure of the air at the end of the collector were analyzed for different collector inlet heights. The output data at collector heights of 1 m to 10 m were
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simulated, and the results are shown in Fig. 6. The inlet temperature in all numerical simulations was 308 K. According to Fig. 6a, the maximum difference in air temperature was 12.1 K at a collector height of 1 m, and the minimum temperature difference was 4.7 K at a
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collector height of 10 m for q ′′ =800 W/m2. Moreover, it became clear that when the heat flux decreased, the temperature difference at all heights had less magnitude. At the first state
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shown in Fig. 6b, the collector flow rate was in its smallest value; hence, the greatest number of air temperature variations was seen. With increases in the radius of the collector, the air pressure in the solar chimney decreased. For a thermal flux of 800 W/m2, the amount of pressure in the radius of 25m was -157 Pa. In a radius of 500 m, the air pressure was -1607
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Pa, which is 90% less than that of the 25-m radius, and for the thermal flux of 600 W/m2at radii of 25 and 500 m, the pressure was -133.64Pa and -1365.9Pa. As can be seen, the pressure in the thermal flux 800 W/m2was less than the thermal flux of 600 W/m2, which has
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a greater effect on the output power, but the variation process is similar for both thermal quantities; this reduction in pressure had a positive effect on tensile strength. Figure 6b shows
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that the maximum output power was obtained at a radius of 500 meters. By comparing the output power chart with a measurable pressure variation of 500 meters radius, the pressure is found to be at the minimum limit. In other words, the output power was increased by decreasing pressure.
Fig. 7 shows the influence of changes in collector height Hcl from 1 m to 10 m on the power and efficiency of the solar chimney power plant. Numerical results revealed that the output power decreased from 82.5 kW to 52.5 kW when the collector height was increased from 1 m
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ACCEPTED MANUSCRIPT to 10 m at a heat flux of 800 W/m2. This trend was also seen for a heat flux of 600 W/m2. Increasing the collector height caused pressure to increase and, due to the ideal gas law, the temperature and output power both decreased. Efficiency curves for different heat fluxes had similar behaviors and were decreased with increments in collector height. In Figs. 8a and 8b,
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the variations in air pressure and temperature versus different collector heights are shown. The fluid temperature difference rose and the fluid pressure declined in the solar chimney
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when collector height was increased. 4.4. Investigation of collector radius
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In Fig. 9, changes to output power and solar chimney efficiency are indicated where the value of Rcl varies from 25 m to 200 m, which means that flow power would be greater at more Rcl while the inverse process is confirmed for efficiency.
As seen in Fig. 9, for q ′′ =800W/m2, the output power and efficiency were 14.25kW and
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0.003 at the collector radius of 25 m, respectively. At a collector radius of 500 m, output power and efficiency both had different behavior. The output power increased to 1415 kW, and efficiency decreased to 0.00195. The main reason for the augmentation in output power
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can be the reduction in pressure caused by the increase in collector radius (as shown in Fig. 8b), which caused the air mass flow rate and temperature to increase. However, by increasing
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the collector radius, the area of heat transfer increased, and with respect to the constant heat flux, efficiency decreased.
4.5. Investigation of chimney height Variations in air pressure and mass flow rate were simulated at different chimney heights. Results for the heights of 25 m to 500 m are shown in Figs. 10a and 10b, respectively. Then 13
ACCEPTED MANUSCRIPT the influence of the chimney height, Hch, was investigated. The Hch was changed from 25 m to 500 m. The higher Hch corresponded with a higher level of efficiency and power (see Fig. 11). Fig. 11 (a) shows the power of the solar chimney variation against chimney height for different heat fluxes. It can be seen that for q ′′ =800 W/m2 the output power increased from
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24 kW for a chimney height of 25 m to 313.5 kW for a chimney height of 500 m. Also, for q ′′ =600 W/m2, the output power was 16 kW and 209 kW for chimney heights of 25 m and
500 m, respectively. However, a higher chimney height led to lower air pressure and larger
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velocity and mass flow rate. Augmentation in the flow rate caused increased output power. In Fig. 11 (b), the efficiency of the solar chimney for heat fluxes of 600 W/m2 and 800 W/m2 are
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shown. Similar to the variation in output power, efficiency increased from 0.00063 at a chimney height of 25 m to 0.0083 at a chimney height of 500 m. 4.6. Investigation of chimney radius
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The numerical investigation of the chimney radius was performed for 1 m to 10 m values. Figs. 12a and 12b indicate the mass flow rate and pressure magnitude distribution of air for different chimney radii. As seen in Fig. 12, the maximum mass flow rate of working fluid for
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a chimney radius of 5 m at q ′′ =800 W/m2 was 45.29 kg/s, which is 70% and 30.8% higher
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than the mass flow rate for chimney radii of 1 m and 10 m, respectively. It is worthy to note that the main n for this behavior can be that this radius had the minimum pressure value, according to Fig. 12b.
Effects of chimney radius, Rch, variations are displayed in Fig. 13, where Rch was varied from 1 m to 10 m. Fig. 13 (a) shows that output power increased when chimney radius was increased from 1 m to 5 m, and its maximum value equaled 85.5 kW for q ′′ =800W/m2. One possible explanation for this could be the greater mass flow inlet due to less chimney pressure. Then, by increasing the chimney radius from 5 m to 10 m, the output power 14
ACCEPTED MANUSCRIPT decreased 28%. This trend was also seen in the output power curve for q ′′ =600W/m2. It can be seen in Fig. 13 (b) that for the chimney radius of 5 m, the maximum efficiency was
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0.00334; however, at 10 m, the efficiency decreased 28% for q ′′ =800 W/m2.
5. Conclusion
The present study demonstrated the capabilities of the CFD technique as a powerful research
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and engineering tool for the analysis of complex aerodynamic and thermal systems like solar chimney power plants. The CFD approach might enable the conversion of an experimental
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work on this subject to a simpler and more economical one. Thus, this approach can be further developed and upgraded for a more detailed analysis. In this study, three-dimensional numerical simulations were performed to investigate the influences of geometrical parameters on the performance of the solar chimney. A three-dimensional region supposed with κ − ε
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turbulence model was simulated. Firstly, the numerical results for the base case were validated with [18]. Furthermore, the effects of geometric characterizations of the solar chimney power plant on flow and performance were investigated. The profiles of
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temperature, pressure, and mass flow rate are presented in various geometrical parameters. It
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is seen that output power can be increased considerably by increasing solar chimney height, while increasing the collector radius can increase output power slightly. Through the analysis, it was found that the chimney radius parameter had an optimum range with maximum values for efficiency and output power. The extension of this paper for CFD simulation according to our previous works [28-56] affords engineers a good option for CFD simulation.
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[24] E. Gholamalizadeh and M. Kim, Multi-Objective Optimization of a Solar Chimney Power Plant with Inclined Collector Roof Using Genetic Algorithm, Energies 2016, 9, 971; doi:10.3390/en9110971
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[25] A. Bahar F, Guellouz M S, Sahraoui M and Kaddeche. S, A NUMERICAL study of solar chimney power plants in Tunisia, Journal of Physics: Conference Series 596 (2015) 012006 Doi:10.1088/1742-6596/596/1/012006
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[26] Nilesh N. Ubhale, Santosh R. Mallah, Dr. Lavendra S. Bothra, A Review: Numerical Simulation for Solar Chimney by Changing its Radius and Height, International Journal on Recent Technologies in Mechanical and Electrical Engineering (IJRMEE) Volume: 3 Issue: 6, June 2016, pp. 5-8 [27] S. Sudprasert, C. Chinsorranant, P. Rattanadecho, Numerical study of vertical solar chimneys with moist air in a hot and humid climate, International Journal of Heat and Mass Transfer 102 (2016) 645–656 [28] A Karami, D Toghraie, Computational Fluid Dynamics Analysis and Geometric Optimization of Solar Chimney Power Plants by Using of Genetic Algorithm, Journal of Simulation & Analysis of Novel Technologies in Mechanical Engineering, Volume 10, 2017, 49-60 [30] Karimipour A. Alipour H. Akbari OA. Semiromi DT. Esfe MH., Studying the Effect of Indentation on Flow Parameters and Slow Heat Transfer of Water-Silver Nano-Fluid with
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ACCEPTED MANUSCRIPT Varying Volume Fraction in a Rectangular Two-Dimensional Micro Channel, Indian Journal of Science and Technology, 2016, 8, 2015 [31] Akbari OA. Karimipour A. Toghraie D. Karimipour A, Impact of ribs on flow parameters and laminar heat transfer of Water/Alumina nanofluid with different nanoparticle volume fractions in a three-dimensional rectangular microchannel, Adv Mech Eng, 2016; 7: 1–11
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[32] Akbari OA. Karimipour A. Toghraie D. Safaei MR. Alipour M. Goodarzi H. and Dahari M. Investigation of Rib's Height Effect on Heat Transfer and Flow Parameters of Laminar WaterAl2O3 Nanofluid in a Two Dimensional Rib-Microchannel. Appl Math Comp, 2016, 290, 135– 153
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[33] Akbari OA. Toghraie D. Karimipour A. Numerical simulation of heat transfer and turbulent flow of Water nanofluids CuO in rectangular microchannel with semi attached rib. Adv Mech Eng. 2016; 8: 1–25
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[34] Alipour H. Karimipour A. Safaei MR. Semiromi DT. Akbari OA., Influence of T-semi attached rib on turbulent flow and heat transfer parameters of a silver-Water nanofluid with different volume fractions in a three-dimensional trapezoidal microchannel. Physica E, 2016; 88: 60-76 [35] Nazari S. Toghraie D. Numerical simulation of heat transfer and fluid flow of Water-CuO Nanofluid in a sinusoidal channel with a porous medium. Physica E, 123; 87: 134-140 [36] Sajadifar SA. Karimipour A. Toghraie D. Fluid flow and heat transfer of non-Newtonian nanofluid in a microtube considering slip velocity and temperature jump boundary conditions,
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European Journal of Mechanics-B/Fluids, 2017; 61: 25-32
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[38] Afrand M. Toghraie D. Karimipour A. Wongwises SA. Numerical Study of Natural Convection in a Vertical Annulus Filled with Gallium in the Presence of Magnetic Field, Journal of Magnetism and Magnetic Materials, 2017, 430: 22–28
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[46] GR Ahmadi, D Toghraie, Energy and exergy analysis of Montazeri steam power plant in Iran, Renewable and Sustainable Energy Reviews 56, 454-463, 2016
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[56] E Keshavarz, D Toghraie, M Haratian, Modeling industrial scale reaction furnace using computational fluid dynamics: a case study in Ilam gas treating plant, Applied Thermal Engineering 123, 277-289, 2017
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Figure Legends: Fig. 1. The solar chimney configuration
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Fig. 2. The numerical grids of object Fig 3. Compared obtained results for (a) Power, (b) Efficiency with [18]
Fig. 4. Contours of temperature magnitude in the base case for a) 600 W/m2, b) 800 W/m2
Fig. 6. Effect of collector height on a) temperature, b) pressure
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Fig. 5. Velocity contours for base case at a) 600 W/m2, b) 800 W/m2
Fig. 7. Influence of collector height on the solar chimney performance
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Fig. 8. Influence of collector radius on a) temperature, b)pressure
Fig. 9. Influence of collector radius on solar chimney plant performance Fig. 10. Influence of chimney height on a) mass flow rate, b) pressure Fig. 11. Influence of chimney height on plant
Fig. 12. Influence of chimney radius on a) mass flow rate, b) pressure
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Fig. 13. Effect of chimney radius on solar chimney plant performance
Parameter
Chimney Height 100 m
Chimney Radius
Collector Radius
Collector Height
4m
100 m
2m
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Value
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Table 1 Dimensions of modeled power plant.
Table 2. Relative errors of power and efficiency at different mesh sizes against to [18]. Grid 1
Grid 2
Grid 3
Grid 4
Grid 5
(26192
(54960
(78842
(98730
(126314
elements)
elements)
elements)
elements)
elements)
Power
65%
28%
12%
4.8%
4.6%
Efficiency
71%
30%
14%
4.4%
4.3%
Parameter
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Pressure = 0 Pa T = 308 K W q ′′ =0 2 m W q ′′ =600 2 m W q ′′ =800 2 m -
Locatiob
Pressure inlet
A B
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Wall
Boundary Inlet
Surface of Earth
Wall
C
Collector ceiling
Wall
D
Symmetry
E
Chimney surface Collector's surroundings
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-
Pressure outlet
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Pressure = 0 Pa T = 308 K
Boundary condition
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Specifications
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Table 3. Explaintion about the 4 models
22
F
Chimney outlet
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Figures
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Fig. 1. The solar chimney configuration
23
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Fig. 2. The numerical grids of object
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a
Ref. [18] 210
Present study
150
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Power (kW)
180
120 90
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60
0
0
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30
50
100
150
200
250
200
250
Chimney height (m) b
Ref. [18]
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Present study
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0.6
0.4
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Efficiency (%)
0.8
0.2
0
0
50
100
150
Chimney height (m) Fig 3. Compared obtained results for (a) Power, (b) Efficiency with [18]
25
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a
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Fig. 4. Contours of temperature magnitude in the base case for a) 600 W/m2, b) 800 W/m2
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a
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Fig. 5. Velocity contours for base case at a) 600 W/m2, b) 800 W/m2
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15 2 2
q=800 W/m 12
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Temperature variation (K)
q=600 W/m
4
6
8
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Collector height (m) b
TE D
200
EP
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AC C
Pressure (Pa)
0
q=600 W/m2 q=800 W/m2
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Collector height (m) Fig. 6. Effect of collector height on a) temperature, b) pressure
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Power (kW)
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M AN U
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Collector height (m)
b
q=600 W/m2
TE D
EP
0.2
AC C
Efficiency (%)
0.3
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q=800 W/m
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Collector height (m) Fig. 7. Influence of collector height on the solar chimney a) power and b) efficiency
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Temperature variation (K)
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Collector radius (m)
0
b
TE D
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q=800 W/m2
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Pressure (Pa)
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q=600 W/m2
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Fig. 8. Influence of collector radius on a) temperature, b) pressure
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Collector radius (m) 2
q=600 W/m
2
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EP
Efficiency (%)
0.4
TE D
0.5
b
AC C
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Collector radius (m) Fig. 9. Influence of collector radius on solar chimney a) power and b) efficiency
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b
q=600 W/m2
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TE D EP
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q=800 W/m2
AC C
Pressure (Pa)
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Chimney height (m) Fig. 10. Influence of chimney height on a) mass flow rate, b) pressure
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Efficiency (%)
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Chimney height (m) Fig. 11. Influence of chimney height on solar chimney a) power and b) efficiency
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Chimney radius (m)
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TE D
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Pressure (Pa)
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Chimney radius (m) Fig. 12. Influence of chimney radius on a)mass flow rate, b)pressure
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Efficiency (%)
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Chimney radius (m) Fig. 13. Effect of chimney radius on solar chimney a) power and b) efficiency
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ACCEPTED MANUSCRIPT
Highlights Investigating the influences of geometrical properties on a solar chimney performance
•
Using the κ − ε turbulence model and the 3D finite volume approach
•
Presenting variables effects on temperature, velocity, pressure, efficiency, and output power
•
Power and efficiency have positive relationships with chimney height and collector radius.
•
Chimney radius has an optimum range for obtaining maximum efficiency and output power.
AC C
EP
TE D
M AN U
SC
RI PT
•