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Solar collector is a thermal device that uses the heated air in the power generation and many engineering applications. The purpose of the present work is to study the performance and temperature distribution for the solar collector which uses heated air in solar chimney power generation that it consist of three parts, a turbine-generator unit which is used in the generation of electric energy, and cylindrical chimney is fixed vertically and finally a solar collector under the climatic conditions of Egypt-Aswan is studied. This site is specified as the hottest site because the nearest of this location from the Tropic of cancer. Experiments are performed in ten summer days of May and June 2015 with different solar radiations and clarity of the sky. Hourly values of global solar radiation and some meteorological data (temperature, pressure, velocity, etc.) for measuring days are obtained by measuring devices. Inlet and outlet temperatures of air from a solar collector and velocity at junction region. In this work, attempt has been made to present the effect of environmental factors such as ambient temperature, the clarity of the sky and solar radiation on the performance of solar collector. The temperature of the base and the cover of the solar collector, the variation of solar radiation, solar collector efficiency, heat transfer coefficient, the velocity at the junction region between the chimney base, the outlet of the solar collector and temperature distribution along the air heater are discussed. A prediction for the results of the solar collector were performed by using developed theoretical model was made by this study which is based on the previous works. The numerical study has used a commercial code CFX, ANSYS 16.1 to simulate the flow through the collector. The study show that the outlet air temperatures from the solar collector and the velocity at the junction are depending on the climate condition such as ambient temperature and solar radiation, the differences in air temperature at the solar collector ranging between 8 ° - 24 °. It is concluded that the theoretical model is basically valid for the system under study, and theCFD simulation can be used conveniently to predict the performance of the system, the comparison between them and experimental result shows a good agreement.

Solar chimney is a simple and modern energy source also classified as efficient solar power technology. The Solar Chimney Power Plant system represents a possibility for the use of solar energy as a clean energy. As shown in

kW power plant in Manzanares, Spain in the early 1980s [

The SCPP which is a kind of renewable energy technologies was first proposed by professor Jörg Schlaich [

Most existing publications, mainly studied certain aspects of an SCPP with turbine. Backström and Gannon [

Kirstein and von Backström [

There are many other studies carried out with small-sized physical models constructed on-site. Krisst (1983) [^{2} collector and 2 m high tower of 3.5 cm radius with power output of 0.14 W in Izmit, Turkey. Pasumarthi and Sherif (1998) [

In this paper, a detailed investigation of the performance for a solar collector as apart from the solar chimney power plant using experimentally, developed mathematical and numerical models are carried out to analyze the temperature field inside the collector, heat transfer coefficient, heat added and the velocity at the junction region between the outlet section of the solar collector and the chimney base in the meteorological site Aswan, Egypt.

In order to evaluate the performance of solar collector as apart of solar chimney power plant, the experimental test rig was constructed in Faculty of Energy Engineering, Aswan University, and Aswan, Egypt as shown in

The height of the solar collector cover is slowly increasing with inclination along the radius from the outer rim (0.25 m) to the inner rim of the solar collector (0.5 m) to minimize the friction losses and make the air slowly to accept more hat inside the solar collector under green house effect. A cross-sectional view of the solar collector is shown in

Variable measurements Point’s distributions for the in the solar collector were shown in

The temperatures of the air in the solar collector are measured using thermocouples data accusation card (Daq-2005) works with several types of thermocouples which has

uncertainty of ±0.2˚C. The temperature of the solar collector cover and the ground.

The air speed was measured using PASCO PS-2100A USB Link that it has an interface that uses the Universal Serial Bus protocol to enable communication between PASCO sensors and a USB-compatible computer that is running PASCO’s data acquisition software which has uncertainty of ±0.1 m/s. The solar radiation is measured using Protective Glass Dome and Solar Shield (pyranometer) with uncertainty of ±0.1 W/m^{2}.

To predict the performance of the device under study, this study was developed mathematical model based on previous work [_{2}, this section is nearly at the chimney entrance.

The thermal analysis of a solar chimney depends on parameters such as the ambient conditions and structural dimensions of the system. The former includes quantities such as the solar radiation intensity and ambient temperature.

The following analytical expressions are obtained for the mathematical model that it will be predict the solar collector cover, ground temperatures and the amount of heat gained by the land from the solar radiation.

The energy balance equations for the solar radiation incident on the solar collector can be written as follows [

Which ^{2}),

The following expressions for the first mathematical model are obtained for the temperatures of the solar collector cover through the following steps to calculate the solar collector cover temperature and overall heat transfer coefficient:

Initially the equation of overall heat transfer coefficient can be expressed as follow;

where,

Radiation heat transfer coefficients that were mentioned in Equation (2) can be expressed as follows;

Which

That

After calculations the radiant heat transfer coefficients, the remaining part of the Equation (2) can be expressed as follows;

Which

The convective heat transfer coefficient was the last term in the Equation (2), the following Expression can represent it;

Which

For^{ }

Which θ is the tilt angle of the solar collector that is represents the inclination of the solar collector cover; It has a value of 4.76˚ in the current work. Rayleight number; is dimensionless number defined as;

where h is heat transfer coefficient, L is the space between the collector cover and the ground, k is represent the thermal conductivity of the air for heat acceptance from the ground, g is gravitational constant,

The notations [^{+} in the Equation (8) are used to denote that if the quantity in the bracket is negative it should be equal to zero.

Convective heat transfer coefficient

By compensation equations from (3) to (6) within the Equation (2), overall heat transfer coefficient now can be obtained by solving Equation (2).

After substituting the values of

These results are then used to calculate (T_{c}) from the Equation (9). If

After the heat added to the air inside the solar collector and heat transfer coefficient are calculated, the outlet air temperatures from the solar collector and mass flow rate are calculated using the following set of analytical expression

Under conservation of mass;

where;

Which

The following expression that it will be representing the mass flow rate inside the chimney, it is shown as a function in the temperature of air inlet to the chimney

By substituting with Equation (12) into Equation (11) then;

For simplicity, frictional effect has been ignored since the velocity in this region is quite low. Because the flow is in the very low Mach number regime, the kinetic energy contribution can be safely neglected, therefore:

where,

The Mach number (

Which;

From Equation (14), the following analytical expression can be obtained for the outlet temperature of the air from the solar collector:

If the work extraction process at the turbine is assumed to be an isentropic process, then;

Furthermore, by rearranging the momentum and continuity equations for the flow through a constant area vertical tower of height, h_{c}, and the following analytical expression can be obtained;

If we consider the air is atmospheric air outside the solar chimney system, the hydrostatic equilibrium requires that;

According to Ref. Calvert et al [

Assuming that the air obeys the ideal gas equation of state, Equation (20) can be substituted into Eq. (19) to give the value of the air flow pressure p_{4} at the outlet section for the chimney outside air as;

In accordance with Equation (20) and consider that a dry adiabatic lapse rate can be applied to the flow in a chimney, the following expression can be obtained for the air temperature at the outlet section a of the chimney.

For an ideal gas, according to [

_{2} then The steps of calculating the outlet temperatures from the solar collector are proceeding.

The efficiency of the flat plate solar collector is the ratio of the useful energy from radiation incident from the sun represented by

where T_{1} is the inlet air temperature of the solar collector, T_{2} is the outlet air temperature of the solar collector, C_{p} is the specific heat of air at constant pressure and _{r} is the area of the solar collector.

The iteration for the above loop begin by Guess p_{3}, and then calculate T_{3}, ρ_{3}, T_{4}, ρ_{4} using Equations ((17), (23), (22)) and Equation (23), respectively. Calculate p_{3} using Equation (18), and then compare the new p_{3} to the former p_{3}. Perform the iteration and Calculation using Equation (13).

In this part of the study, the numerical simulation of the solar collector is presented. A physical model for a solar collector was built based on the geometrical dimensions of the experimental test rig. The numerical study has used a commercial code CFX, ANSYS 16.1 to simulate the flow through the solar collector, computations using a radiation model that it was solved the heat transfer through the solar collector, radiation heat transfer mainly occurs in the collector, which is covered by a semi-transparent material (plastic cover). The cover material is nearly transparent for incident solar radiation, but partly opaque to infrared radiation from the ground. In the present simulations, the discrete radiation model model was adopted to solve the radiated transfer equation, Numerical results are used for comparison with the theoretical predictions. . Heat transfer in the solar collector involves three modes: conduction, convection, and radiation. In simulating the flow in the solar collector, computations using models that only focus on conduction and convection are the simplest, whereas those involving driven force of the flow and radiation model are more complex.

Discrete radiation model was used to solve the radiative transfer equation for the following reasons:

Only this model can be used to solve the solar collector using semi-transparent walls of various types, it can be used to compute non-gray radiation using a gray band model and it can work well across a full range of optical thicknesses.

The Boussinesq model was inserted in this simulation. This model treats density as a constant value in all solved equations for the solar collector.

where _{a} is the ambient temperature, and

The model simulation was depends on the boundary condition that it was collected from the theoretical model, the boundary conditions and the geometries of the model are tabulated in

All numerical calculations had to be carried out with the solver with double precision. The iteration error was at least 10^{−6} on all calculations, for the energy equation at least 10^{−9}. Under these conditions, the solution converged in less than 6000 iterations but this simulation was completely converged in 8000 iterations. The thermal properties of the solar collector components [

The main boundary conditions are shown in

Description | Values |
---|---|

Collector radius ( | 3 m |

chimney high ( | 6 m |

chimney radius ( | 0.075 m |

Plastictransmissivity, visible light range. ( | 0.86 |

Plastic conductivity ( | 0.2 W/m∙K |

Plastic thickness ( | 0.0015 m |

Ground emissivity ( | 0.9 |

Ground conductivity ( | 0.6 W/m∙K |

Ground heat transfer coefficient ( | 2.4 kJ/kg∙K |

Collector inlet temperature at (2:00 pm) | 38˚C |

Collector inlet pressure | 98.3 kPa |

Thermal storage depth | 0.04 m |

Wind speed at collector inlet | 1.2 m/s |

dius by taking into account the axisymmetric air flow in the collector shown in the second assumption above, and the functions will vary with different solar radiations.

An investigation of grid independence was carried out to find the proper mesh. The test was performed on the velocity along the chimney. Four different grids were checked (705,521 elements, 1,253,241 elements, 1,596,164 elements, and 1,850,644 elements). There are relatively small (typically less than 5 percent) differences between the respective grid no. 3 (1,596,164 elements) and grid no. 4 (1,850,644 elements) results for the most stringent quantities of the velocity along the chimney. This indicates that both of the two grids are approaching grid independence as shown in

The aim of this section is to present the experimental results obtained in the present research for the performance of the solar collector. A series of test runs are carried out in ten days of May and June 2015 with different ambient conditions to test the performance of the solar collector in terms of the outlet air temperatures from the solar collector, the velocity of the air at the chimney entrance and heat added to the solar collector, Moreover, comparisons between experimental work, theoretical and Numerical results are carried out.

Figures 8-10 are shown that air temperature T_{a} inside the solar collector increases from the beginning of the solar collector to the outlet section of the solar collector, where T_{a} is investigated for all run days at various values of solar radiation. It is noticed that air temperature; T_{a} increases significantly from the outer rim of the collector until

it reaches at collector radius at 0.75 m, still increasing but by the small difference until at collector radius 0.05 m. The temperature at this location of the solar collector represents the outlet air temperature of the solar collector the values of T_{a}, the observations shows that the maximum temperatures are obtained in the interval from 12:00 PM to 3:00 PM. Peak values will be around 3:00 PM. Practically at the beginning of the sunrise, the air temperature inside the solar collector is nearly close to the ambient temperature. After sunrise, the ground absorbs and stores the radiant energy and of course its temperature is low at the beginning. So, because of low temperature and heat transfer via the solar collector, when the sunrise increases the temperature under the collector warms up, due to the air displacement. The solar warmth is first absorbed by the ground and then the air moving on the surface, absorbs the heat and carries to the upper layers in the direction of the collector cover. Therefore, the temperature decreases from the ground and to the collector cover. The air temperature has the maximum reading near the center of the solar collector and the lowest temperature is related to ambient temperatures at the inlet of the solar collector. The maximum temperature difference between inlet and outlet of the solar collector was recorded at (2:00 PM. On 6^{th} of June, 2015), it was reached 24.5˚C.

On the other hand; it is noticed that the main reason that the air temperatures T_{a} are increasing inside the collector is the heat accepted from the ground, _{g} for all run days. It is observed that the ground temperatures would be depending strongly on the solar radiation, the maximum temperature of the ground was recorded at 3:00 PM in all run days.

The collector cover temperature is affected by the solar radiation from the sun as shown by

Further, it may be observed from the Figures 13-16 that the average outlet air temperature is strongly affected by heat added to the solar collector through the ground that would be added by solar radiation. It may be observed from

a day the outlet average temperature of the flowing air through the solar collector increases with increasing solar radiation through a day. The reason for this observations that the increasing in solar radiation at sunrise would be caused increases in heat added to the ground that The ground surface warms and reject the heat to the air layers over the ground that is heated by natural convection due to heat transfer from the ground that will cause rising in air temperature layers from the ground to the collector cover, this observation are shown from

It may be concluded from the above figures that for solar chimney power plant in the present study, the maximum efficiency range of the solar collector has the dimension stated is recommended to be in range 22% to 28% at 60.03˚C outlet temperature and heat added 270 W/m^{2}.

chimney base increase significantly with the increase in the average outlet temperature of the solar collector, The reason is when all the other parameters such as the environment parameters and the solar radiation are constant, large amount of heat added to the flow in the solar collector increase the energy of the flow, that it was dissipated a part of this energy on the shape of kinetic energy at the chimney entrance. The maximum velocity recorded at 60.3˚C with a value of 4.2 m/s.

Comparison between Experimental Results, Numerical Results and Theoretical Prediction^{th} June from 6:00 AM to 6:00 PM.

The observations show a little higher value in the simulation result than the outlet temperatures from the solar collector than the experimental result by 5.8%, the mathematical model result is higher than the experimental result by 3.03%, on the other hand; for the solar collector efficiency,

On the basis of the experimental, numerical and theoretical results obtained for ten run days for the solar collector manufactured and tested in Aswan, Egypt, the following conclusions can be drawn:

1) The existence of Aswan near the pass of Tropic of Cancer is a major reason for the high solar radiation values that it has been recorded a high value about 1200 W/m^{2}.

2) Air, ground and the collector cover temperatures in general increase along the solar collector.

3) Solar radiation, climate condition and clarity of the sky are predominant factors which affect the performance of the solar collector. Increasing the solar radiations with clarity of the sky was caused a consequent increase of air, ground and the collector cover temperatures.

4) Despite of the smaller scale of the solar chimney power plant but the difference between the outlet air temperatures from the solar collector above the ambient air temperature was reached 24.5˚C; this is specified as the highest performance because the climate of the location that the system is built.

5) The maximum outlet temperature of the solar collector is 60.3˚C that it is produce maximum velocity at the chimney inlet with 5.5 m/s.

6) In sunshine period, heat added to the solar collector would increase until maximum values reached afternoon at 2:00 PM and decrease until the 6:00 PM period.

7) The heat transfer coefficient in the solar collector that represent by heat added to the air in the solar collector was affected by solar intensity and clarity of the sky.

8) This study produced a modified a mathematical model that it was based on previous research

9) It is concluded that the mathematical model is basically valid for the solar collector system, and the simulation with the model can be used conveniently to predict the performance of the system, the comparison between them and experimental result shows a good agreement.

10) Aswan is the good site to solar chimney power plant generation technology according to the clarity of the sky and the warming of the climate.

Hanna, M.B., Mek- hail, T.A.-M., Dahab, O.M., Esmail, M.F.C. and Abdel-Rahman, A.R. (2016) Performance Investigation of the Solar Chimney Power Plants Heater Case Study in Aswan, Egypt. Journal of Power and Energy Engineering, 4, 39-60. http://dx.doi.org/10.4236/jpee.2016.410003

A Flow area, m^{2} q_{added} Heat added, W/m^{2}

A_{r} Collector cover, m^{2} R Ideal gas constant, J/kg K

C_{p} Specific heat capacity at constant pressure, J/(kg K) T Absolute temperature, C

g gravitational acceleration, m/s^{2} U Collector loss coefficient, W/m^{2} C

l_{ch} Chimney height, m h_{r} Radiant heat transfer coefficient, W/m^{2} C

l_{r} Solar collector height, m h_{c} Convective heat transfer coefficient, W/m^{2} C

I Solar irradiation, W/m^{2} V Flow velocity, m/s

x Pressure ratio h_{w} Wind heat transfer coefficient, W/m^{2} C

Nu local average Nusselt number Pr local average Prandtl number

α Solar collector absorption coefficient β coefficient of volumetric thermal expansion, 1/K

γ Specific heat ratio ρ Density, kg/m^{3}

∆T temperature rise between ambient and collector outlet, K ε Emission

η_{coll} The solarcollector efficiency

1, 2, 3, 4 position along the solar chimney (as depicted in

SCPP Solar chimney power plant c-a Collector to air

ch Chimney g-c Ground to collector

coll Solar collector