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A NUMERICAL ANALYSIS OF THE ENERGY BEHAVIOR OF A PARABOLIC TROUGH CONCENTRATOR

The solar power is a clean and a durable energy; there are several techniques for using them. When necessary to elevated temperatures of heat transfer fluid, this energy must concentration. This paper presents the efficiencies study of a linear solar concentrator of a parabolic trough type. This study was conducted on the device in Guemar area, this region is located in the state of El-Oued, which it is found in the south-east of Algeria. Six typical days were selected to conduct the study in them. The solar collector has been studied optically and thermally. The optical study was using SolTrace. Matlab was used as device of programmation to solve the non-linear system of mathematical equations. The method of finite differences in the implicit case was used as way of solution. The thermal efficiencies of the concentrator are very acceptable, it have exceeded 82 %.


INTRODUCTION
Algeria is the first country in Africa by area, over four-fifths of their territory is desert.
Algeria has a very important energy source from its location. Figure (1  This paper is concerned with examining the effectiveness of a linear solar concentrator of a parabolic trough type. The main objective of this work is determining the water vapor temperature which can be reached through this collector in Guemar region, Algeria. This technology is mature and highly efficient; it is available today in Algeria (the hybrid power plant of Hassi R'Mel and the solar village of Adrar). An energy balance was chosen which is based on heat exchange between the four absorber tubes, the heat transfer fluid and glass tubes. A program Matlab was developed using the finite difference method in case implicit to simulate the performance of the concentrator. This study was done using real data from the parabolic trough collector of R'Mel Hassi hybrid power plant, Province of Laghouat, Algeria.

THE PARABOLIC TROUGH CONCENTRATOR
The parabolic trough solar concentrator has a circular absorber tubes of copper metal with a suitable selective layer located in the focal line of the parabola; the selective surface that has a high absorption coefficient and a good absorber of solar radiation, it has a high infrared emittance waves [4,5]. The receiver is surrounded by a glass envelope (glass). A direct incident solar radiation is focused by the mirrors on the receiver. A heat transfer fluid (HTF) circulates inside the receiver, in this case the fluid is water. The heated water where the temperature can exceed 160 ° C [6][7][8].
The parabolic trough concentrators are the most widely used linear concentrator for thermodynamic conversion of solar energy, especially in industrial and domestic areas where requiring an operating temperature between 80 ° C and 160 ° C [9]. For example, electricity production requires high temperatures of 400 ° C to 1200 ° C. We can produce superheated steam in power plants with parabolic trough concentrators, where the temperature up to 1500 ° C [7,8,10].
The parabolic trough concentrator is the most promising technologies to take the place of non-renewable energies (fossil fuels and nuclear energy), especially in the industrial sector (power plants, hybrid systems, desalination, air-conditioning, refrigeration, irrigation, etc.) [8,11,12].  Table (1) shows the geometrical characteristics of   the absorber tubes for a segment. Table1. The geometrical characteristics of the absorber tubes.

Geometric characteristic Value [mm]
External diameter of the absorber (D A,ext ) 70 Internal diameter of the absorber (D A,int ) 65 External diameter of the glass (D V,ext ) 115 Internal diameter of the glass (D V,int ) 109 Mirror length (L) 12270 mirror width (W) 11900 Six days of the year were chose for such modeling. These days are the typical days of February, April, June, August, October and December for 2014. These measures were taken from the meteorological measurements archive of Guemar station; this station is locating in Guemar Airport [13].

OPTICAL STUDY
The optical modeling was performed using the SolTrace software; it is developed by the National Renewable Energy Laboratory (NREL), it is American laboratory [14]. The optical system of the concentrator is composed of two parts, the reflecting surface of the concentrator and four absorber tubes. The reflecting surface of the concentrator is modeled as a single mirror of parabolic section. The four absorber pipes are located in the focal line center of the concentrator to absorb the greatest possible amount of solar energy. The emissivity of the absorber tube (ε A ) 0.12 The emissivity of the glass (ε V ) 0.935 The optical simulation is used to estimate the flow and thermal concentration incident on the surface of the absorber tubes. During the optical study took into account all of:  The solar radiation value in every moment;  The incidence angle of solar radiation on the reflecting mirror;  The properties of each mirror (geometrically and optically);  The properties of the absorber tubes (geometrically and optically). It is assumed that the optical properties (coefficient of reflection, absorbency, etc.) are uniform over the entire reflecting surface. It is considered that the solar tracking is very precise; the opening of the hub is constantly perpendicular to the rays from the solar disk.

THERMAL STUDY
During the thermal modelisation of the solar thermal concentrator, numerical solution was used to simplify the energy balance equations. this model was used to estimate the variation of the output temperature of the liquid carrier of heat (water) based on the direct sunlight (DNI) in the site Guemar (61 meter altitude, latitude and longitude 33.51 ° N 6.78 ° E), Province of El Oued, Algeria.
Heat exchange occurs between three components: the heat transfer fluid, the absorber tubes and the glass tubes. The temperature modelisation is based on energy balances characteristic by differential equations of the three temperatures: T F (fluid), T V (glass) and T A (absorber tubes). These equations vary during the illumination time (t) for a length (X) of the absorber.
The discretization of method finite difference was chose for solving the nonlinear equations of heat balance at the absorber tubes. A computer program was developed in Matlab after discretization equations. For the calculation of energy balance was asks these assumptions:  The heat transfer fluid is incompressible;  The parabolic shape is symmetrical;  The ambient temperature around the concentrator is uniform;  The effect of the shadow of the mirror on the absorber tube is negligible;  Solar flux at the absorber is uniformly distributed;  The glass is considered opaque to infrared radiation;  The exchanges by conduction in the absorber and the glass are negligible. The optical efficiency of the concentrator was expressed as [15]: ρ m is reflectance factor of the mirror; K cam is the angle of incidence correction factor modified; α is the absorbion coefficient of the absorber tubes and  is the intercept factor.
The heat flow transmitted to the fluid (the power gained to the collector "q u (W)") is given by the following relationship [16,17]: Where, A A,int is the internal surface of absorber tube (m²); T A is the absorber tube temperature (°C); T F is the fluid's temperature (°C).
h F is the coefficient of heat exchange by convection; it is often given by the relation follows [17]: K F is the thermal conductivity of the fluid; Nu is the Number of Nusselt. Gnielinski provides a linear interpolation in the transition region between the laminar and turbulent flow, in this case the useful transfer coefficient depends on two dimensionless Reynolds numbers and Prandtl [18,19]   With (Re F ) presents Reynolds number which is expressed by the following relation [17,20]: With F μ is the dynamic viscosity of the fluid (Kg/m.s); ρ F is the fluid density (Kg/m 3 ) A c is the collector aperture area (m 2 ) and Q v is volume flow rate (m 3 /s).

Energy balance for the fluid
The energy balance for the heat transfer fluid circulating in the absorber tube is expressed by the following relationship [6,7]: Where, C F is the specific heat of fluid (J. kg -1 .k -1 ).
Initial conditions and boundary conditions of equation (8) are [6,7]: All thermophysical characteristics of the water are a function of its temperature.

Energy balance for the absorbers
The energy balance for the absorber is given by the following equation [6,7]: With, ρ F is the fluid density (Kg.m -3 ); C A is the specific heat of absorber tube (J. kg -1 .k -1 ) and A A is the difference between the inner surface and the outer surface of absorber tube (m²).
q absorbed is the heat quantity absorbed by the absorber tube (W).
Where, A C is the collector aperture area (m²) and DNI is direct radiation (W.m -2 ). q exit is the heat quantity of the fluid when it came out of the absorber tubes (W); The initial conditions for the equation (10) are:

Energy balance of the glass tubes
Similarly the energy balance for the glass is given by [6,7]: Where, ρ V is the glass density (Kg/m 3 ); C V is the specific heat of glass tube (J/ kg.k) and A V is the difference between the inner surface and the outer surface of glass tube (m²). q int is the internal power (by convection and radiation) between absorber tube and glass tube (W); q ext is the external power (by convection and radiation) between glass tube and the atmosphere (W).
The initial condition of equation (14) is:

Thermal efficiency
The thermal efficiency of the concentrator was expressed as [15,17]: With, A A,ext is the external surface of the absorber tube, T amb is the ambient temperature (K) and U L is the heat loss coefficient (W/m 2 .K).

Heat loss
The use of the solar concentrators to to focus the sun's rays can greatly reduce the size of the absorber tube, thereby reducing heat loss and allow increasing the efficiency of the system at high temperatures. In addition, the concentrators are significantly less expensive per unit area compared to flat plate collectors. The factor (U L ) is the heat loss coefficient, it is expressed by: Where, ε A is the emissivity of the absorber tube; ε V is the emissivity of the transparent glass envelope; σ is Stefan-Boltzmann constant (σ = 5.670 .10 -8 W/m 2 .K 4 ).
With the factor (f) takes into account the loss ratio of the wind, and which can be obtained by the following equation: The term h v is the convection coefficient of the wind; it is given by the following equation (according McAdams (1954)) [17,18] According Watmuff and al. (1977), h v can be obtained by the following equation [18]: Where; V is the wind speed (m.s -1 ).
This work was to model the concentrator by using the finite deference method in implicit model. The nonlinear algebraic equation is solved using the iterative method of Gaussian-Seidel. Algebraic equations were written in Matlab programming language.

RESULTS AND INTERPRETATIONS
The solar contributions are given for the town of Guemar. The concentration of solar radiation by using the parabolic trough collector produces the water vapor with a very high temperature.  The optical efficiency is written according to the modified incidence angle. Figure (6) represents the variation of the optical efficiency as a function of true solar time.   The optical performance of collector is higher of 83.61 %. The maximum value of thermal efficiency can reach up 82.80 %, because the inlet temperature of water is almost identical to the ambient temperature, which thus corresponds to a very good thermal insulation and the lower heat loss to the atmosphere. This reduction in the thermal efficiency after the maximum value, is due to thermal losses believe that with increasing water temperatures respectively at the inlet and outlet of the absorber. The water turns into steam at temperature up to 488 [K] or more. The fluid temperature at outlet of the absorber tubes is inversely proportional to the direct sunlight, and it mainly depends with the heat quantity absorbed by absorbed tubes (q absorbed (t)), which is based on optical and geometric parameters of concentrator.
So, the quantity of heat absorbed by the absorber tubes has a direct relationship with the direct radiation (DNI), this quantity is based on optical and geometrical parameters of the concentrator, and it is not entirely transmitted the heat transfer fluid, wherein a part is dissipated as heat loss between the absorber and the glass, and another portion between the glass and the ambient environment. Figure (10) shows the variation of thermal losses coefficient as a function of the difference in temperature between the absorber tube and the atmosphere. The dependence of the heat loss coefficient with the absorber tube temperature is very clear. It is observed that the losses increase with the increase of the temperature of the absorber, so the absorber is the seat of heat loss. The creating vacuum between the absorber is the transparent glass envelope, could significantly reduce losses by convection.
The glass is transparent to visible solar radiation but opaque to infra-red rayans (IR). Thus, the absorber tube is covered by a glass envelope, thus the radiative losses infra-red emission is greatly reduced.
It can be said that this study made it possible to calculate the thermal efficiency and fluid temperature at outlet of absorber tubes; this means it possible to evaluate the thermal performance of the collector. We can say that the incident solar radiation directly affects the performance of the concentrator. Weather conditions (wind speed, the ambient temperature, etc.) which vary from season to season influes on the performance of the solar concentrator.
The simulation results are very encouraging for the exploitation of solar energy in the field of water vapor exploitation in the site of Guemar, El Oued Province, Algeria.

CONCLUSION
Along the year, Guemar and its suburbs have strong sunlight. The solar energy is natural, clean, non-polluting and inexhaustible energy. The application of solar renewable energy systems such as solar concentration systems in many industrial and domestic areas can solve many problems. These systems can also completely replace fossil fuels.