IMPORTANCE OF THE NUMERICAL SIMULATION IN A SOLAR CHIMNEY ANALYSIS

In this work, computational fluid dynamics was used to investigate the airflow in a solar chimney through a mathematical model that is presented. Solar chimneys appear as an interesting alternative to obtain cleaner energy resources, since they are able to generate electricity from solar radiation. A typical solar chimney combines three known elements: solar air collector, tower and wind turbine. This device uses the solar radiation to generate a hot airflow and this is usually used to drive wind turbines coupled to an electric generator. Pilot plants showed large solar chimneys are necessary for be economically competitive with conventional power plants, however small solar chimneys can be used for other applications, as drying agricultural products. This paper analyzes the turbulent flow in a small solar chimney, where the Finite Volume Method was adopted to solve the system of equations, which describe the two-dimensional steady state airflow. The numerical analysis of the airflow uses the RSM turbulence model. The simulations are compared with experimental data available in the literature. This work aims to show the importance of the numerical simulation to evaluate the thermal and dynamic conditions of the flow, and consequently to verify the technical and economic viability of the plant.


INTRODUCTION
With the growing global population, together with industrial activities, the energy demand increased in large scale in the world and consequently the use of fossil fuels.Evidently, environmental impacts caused by them have grown and nowadays concern the society because not only these sources affect the environment but also they are harmful to human health.Another issue is that the fossil fuels are non-renewable resources and are being depleted at high rates.Therefore, energy has become an essential issue for sustainable development in the new global economy, and the search for alternative energy sources that are cleaner and cheaper than conventional energies has become extremely important (KASAEIAN et. al, 2017).
Inside this context, solar chimney appears as an interesting alternative since solar energy is a renewable and non-pollutant source of energy.This device are capable of generating electric power through solar radiation.According to Cao et al. (2017), the conventional solar chimney plant is composed of a high vertical tubular central tower, a horizontal circular solar collector, with a coverage made of a translucent material, and a group of turbine power generators, as can be seen in the Figure 1.
The operation principle of solar chimney is explained by the three components above mentioned.The solar radiation is transmitted by the coverage and reaches the ground, which increases its temperature, causing a convection heat transfer between the ground and the air under the cover.Therefore, the air mass inside the dispositive is heated and flows to the tower due to the buoyancy forces in function of the temperature gradients.The accumulated buoyancy causes a large pressure difference between the system and the ambient air.During the night, when there is no more solar radiation, a portion of the thermal energy stored in the deeper layers of the soil is transferred to the air, which allows the continuous operation of the system (MING et al., 2017).The airflow generated by natural convection and chimney effect drives a wind turbine coupled to an electric generator, where happens the converting the kinetic energy into electricity (YETIMGETA; MU-LUGETA, 2014).According to Ming et al. (2017), in 1970s Jörg Schlaich introduced the approach of solar chimney to generate electricity.Between 1981 and 1982, he built the first solar chimney plant in Manzanares, Spain.This prototype had a tower with 195 m high and 10 m of diameter, with a coverage with 240 m of diameter and a height variable of 2 m in the entrance and 6 m in the center of the cover, generating 50kW of electrical power (SCHLAICH;SCHIEL, 2000).This pilot plant showed large plants are necessary to generate energy with viable costs to be competitive with conventional power plants.Then, Ferreira et al. (2006), Maia et al. (2005a) and Maia et al. (2005b) investigated a new application for smaller plants, where the hot airflow generated in the solar chimney can be used to dry agricultural products.
In order to evaluate the solar chimney as a radial solar dryer, a prototype was built in the Federal University of Minas Gerais.The tubular tower was constructed in wood and covered in fiberglass, with the height of 12.3 m and the diameter of 1 m.A thermo--diffuser plastic film was used as translucent material for the circular coverage.The cover has a diameter of 25 m.The ground was built in concrete and painted in black color to increase the radiation absorption (FER-REIRA et al., 2006).This paper evaluates the turbulent airflow in the prototype above mentioned through the RSM turbulence model.
Engineering problems can be analyzed by analytical methods, numerical experimentation or laboratory experimentation.The analytical approach usually presents hypotheses that distance the model from the real physical problem, while laboratory experiments, despite reproducing the actual configuration of the problem, are expensive and may be impossible in some situations, especially for safety reason.The numerical experimentations are able to handle complex geometries and boundary conditions, and reduce The RSM model (Reynolds Stress Model) is an alternative to these models, based on the determination of direct equations for Reynolds transport.The RSM model is usually referred to as the direct closure model or the second order model.The transport equations for the Reynolds stress can be determined by the Navier-Stokes equations and are given by the Eq. 6.
The left side of Eq. 6 concerns the convective transport of the Reynolds tensor over the average flow.The first term on the right side is called diffusive transport term and represents the diffusion rate caused by the molecular viscosity of the fluid, the pressure fluctuations and the turbulence.The diffusive transport term is given by Eq. 7.
The second term is the term of stress production and represents the rate of production of the turbulent stress at the same time that it is transported over the flow, under the influence of the mean velocity gradients.This term is presented in the Eq. 8.
The pressure term , given by Eq. 9, involves correlations between strain rates and pressure fluctuations and acts on the redistribution of energy between the normal components of the Reynolds stress when and the shear stress reduction when .This term tends to make turbulence more isotropic and its modeling has been the objective of several studies, being one of the main themes in the development of second order closure models.
The term refers to the dissipation rate of the Reynolds tensor caused by the viscosity given by Eq. 10.

NUMERICAL METHODOLOGY
The numerical analysis of the turbulent airflow in a small solar chimney used in this paper was based project time and cost.Inside this context, the Computational Fluid Dynamics (CFD) plays an important role to assist engineers in the design of new equipment, as in current engineering problems.CFD is widely used to simulate the airflow in solar chimneys and to investigate modeling techniques (HU et al., 2017;KASAEIAN et al., 2017;CAO et al., 2017).

MATHEMATICAL MODEL
The governing equations are given for average quantities in cylindrical coordinates (r,x), where the conservation of mass, momentum (r,x) and energy are described respectively by: The adopted models consider the two-dimensional turbulent flow in a steady state and the hypotheses for the solution are based on incompressible airflow, constant properties and Newtonian fluid.Where cp, ρ, β and Pr are respectively, the air specific heat, density, volumetric expansion coefficient and Prandlt number.The subscript "t" indicates the turbulent amount.The effective viscosity μe is given by, where μ is the viscosity of the air and μt is the viscosity of the flow or eddy viscosity.The Reynolds Stress Model (RSM) is used to analyze the turbulent airflow in the solar chimney.
The Reynolds Averages Navier-Stokes equations (RANS) models are based on the Boussinesq Hypothesis, where these models present a good solution to the problem of turbulence closure, but they present some faults, generally related to the limitations imposed by the concept of turbulent viscosity.

RESULTS
As mentioned, the energy stored by the deeper layers of the ground plays an important role for the continuous operation of the solar chimney.The explanation for this fact is because during the day, the solar energy is transferred to the ground and at night when there is no more incidence of solar radiation, the heat flux is reversed, where the heat stored in the soil is transferred to the ground surface.Consequently, the airflow in the solar chimney continues unceasingly along the day (MAIA et al., 2005b).
The following results are referents the simulation cited previously and were obtained using the RSM turbulence model.They are compared with experimental data found in the literature.
The air entering in the solar chimney follows in the radial direction of the collector and on the junction between the collector and the tower there is a change in the airflow to the axial direction of the tower.Due to the reduction of area in this position, the velocity increases in the tower and only small variations in the velocity profile are observed, however the average velocity remains constant, since the diameter does not change in the tower, as seen in the Figure 4.The Figure 5 shows the velocity profile in the tower, evaluated at a position corresponding to half the tower height.From the graphic, it is possible to observe the variation of the velocity with the radius of the solar chimney.As expected, the velocity profile obtained by the RSM turbulence model are typical of turbulent flow.It is perceived the velocity is maximum in the center of the chimney (r=0) and tends to zero in the wall, due to the non-slip condition (wall condition).According to Maia et al. (2005b), in the period of highest temperature during the day, the ex-in the work of Marinho Junior et al. (2015) and Silva et al. (2015).The tower of solar chimney has 12.3 m high and 1 m in diameter, the collector has 25 m of diameter and variable height relative to the ground.Using the concept of axisymmetric, the dimensions of the chimney can be seen in the Figure 2.
The software ANSYS-FLUENT 15.0 solves the governing equations, which the discretization is based on the Finite Volume Method, the Multigrid iterative method solves the system of algebraic equations and the pressure and velocity is coupled by SIMPLE algorithm scheme (PATANKAR;SPALDING, 1972).The boundary conditions adopted are showed in the Figure 3.The prescribed temperature of 333.95K is used for the ground, the tower is assumed adiabatic and the coefficient of heat exchange by convection for the coverage is evaluated to 18.88 W/m²K.The conditions for the air at inlet is ambient temperature with a mass flow of 2.15 kg/s (MARINHO JUNIOR et al., 2015;SILVA et al., 2015).The tower walls, the ground, the coverage and the junction between the cover and the tower are all wall regions and the non-slip conditions is adopted.The depth of the ground surface is equal to 0.5 m, since as seen in the work of Maia et al. (2005b), the differences of temperature along the time are insignificant for depths superior to 0.4 m.The Figure 7 shows the temperature profile in the coverage, in an axial position corresponding to half the coverage radius.From the graph, it is possible to observe the variation of the temperature with the collector height.It is noted by numerical simulation that the temperature is highest in the regions close to the ground surface (y=0) and tend to free stream temperature in the cover surface (y=0.5 m).According to Maia et al. (2005a), in the period of highest temperature along the day, the experimental temperature in y=0,25m was around 310 K. Therefore, the numerical simulation by RSM turbulence model presented satisfactory results for the temperature in the coverage.
Figure 8 shows the temperature profile in the tower, evaluated at a position corresponding to half the tower height.From the graph, it is observed the variation of the temperature with the radius of the solar chimney.The numerical simulation shows that the temperature in the center is larger and decreases toward the tower wall.The boundary condition used in the numerical simulation for the chimney is thermal insulation, then it expected temperature gradients not very large in the cross section of the tower.Evidently, the air that is nearest to the ground has a higher temperature, since the ground surface has a prescribed temperature of 333.95K (boundary condition), and as the collector height increases this temperature decreases, as discussed in Figure 7.At the junction between the solar collector and the tower, there is a change in the flow direction, then the air that was in the collector upper layers with a lower temperature tends to go to the nearest part of the tower wall.Furthermore, the air that is closer to the ground, with a higher temperature tends to go to the central region, therefore higher temperatures are observed in this position.Evidently, the air flow is turbulent and the tower is considered adiabatic, so at a certain chimney height the fluid temperature redistributes inside perimental air velocity in the tower center was about 2.5 m/s.Therefore, the numerical simulation presented great results.The Figure 6 shows the temperature fields along the solar chimney obtained by RSM model.It is clean the importance of the numerical simulation to the thermal and dynamics analysis in the chimney solar, since the temperature and velocity in any position along the solar chimney can be evaluated.analysis in the solar chimney.Evidently, this study is valid for the prototype with geometric dimensions and boundary conditions established here, if some of these parameters change, differences may be observed.
the tower and the isothermal flow behavior is reached, since the heat can not escape through the boundaries.
Figure 9 depicts a comparison between the experimental data presented by Silva et al. (2015) and the numerical simulation with RSM.The results are compared in the outlet of the chimney, evaluated at tower center, in the middle of the coverage, evaluated at a position corresponding to half of the cover height and in the ground surface, respectively.From the Figure 9 notes that the temperature obtained by the numerical simulation with RSM presents great agreement with experimental data, as the relative errors are less than 0.01.

CONCLUSION
From the presented results can clearly see the importance of computational fluid dynamics to evaluate the thermal and dynamics conditions of the airflow in the solar chimney, as well in other devices.Therefore, the numerical simulations can assist the engineers in the development of news projects, as also in the solution of current engineering problems.Growing energy consumption and concerns about climate change have encouraged the search for cleaner and more reliable energies.Inside this context, solar chimney appears as an interesting alternative since this device are capable of generating electric power through solar radiation.Besides this, solar chimney can be used for other applications, as drying agricultural products.Airflow numerical simulations in this device is a great alternative to evaluate the thermal and dynamic conditions of the flow, and consequently to evaluate the technical and economic viability of the plant.The results obtained by the RSM turbulence model were satisfactory to represent the thermal and dynamic

Figure 1 -
Figure 1 -Schematic of a solar chimney.

Figure 4 -
Figure 4 -Streamlines of the airflow along the solar chimney in the numerical simulation using the RSM model.

Figure 2 -
Figure 2 -The geometric dimensions of the solar chimney.

Figure 3 -
Figure 3 -Boundary conditions for numerical analysis.

Figure 8 -
Figure 8 -Temperature profile in the tower by RSM turbulence model.

Figure 5 -
Figure 5 -Velocity profile in the tower by the RSM turbulence model.

Figure 6 -
Figure 6 -Temperature profile in the solar chimney in the numerical simulation using the RSM model.

Figure 7 -
Figure 7 -Temperature profile in the coverage by RSM turbulence model.

Figure 9 -
Figure 9 -Temperature in different positions of the solar chimney.