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Cameroon lives in the era of great infrastructures in order to reach the economic emergence by 2035. These infrastructures require a solid framework of energy provisions from many natural energy sources and resources that the country possesses. Speaking of natural energy resources, the country is particularly gifted by solar energy potential in the far north. This region of the land is densely populated but much of the populations do not have access to electricity since they live in remote areas far from national electricity grid. Solar thermal energy appears then as real potential to fulfill the growing demand of energy and reduce fossil fuel use dependence. Moreover, it would also be a grandiose opportunity for hospitals in these regions to provide hot water for Sterilization. As the design of a solar thermal plant strongly relies on the potential of direct solar irradiance and the performance of a solar parabolic trough collector (PTC) estimated under the local climate conditions, in this paper, we annually compute direct solar radiation based on monthly average Linke turbidity factor and various tracking modes in two chosen sites in the far north region of Cameroon. Also, a detailed two dimensional numerical heat transfer analysis of a PTC has been performed. The receiver has been divided into many control volumes along his length and each of them is a column consisting of glass, vacuum, absorber and fluid along which mass and energy balance have been applied. Direct solar irradiation, ambient temperature optical and thermal analyses of the collector receiver takes into consideration all modes of heat transfer and the nonlinear algebraic equations were solved simultaneously at each instant during a day of computation using Engineering Equation Solver (EES). To validate the numerical results, the model was compared with experimental data obtained from Sandia National Laboratory (SNL). It has shown a great concordance with a maximum relative error value of 0.35% and thermal efficiency range of systems about 66.67% - 73.2%. It has also been found that the one axis polar East-West and horizontal East-West tracking with 96% and 94% of full tracking mode respectively, were most suitable for a parabolic trough collector throughout the whole year in the two towns considered.

The solar collector’s technology offers a promising method for the large scale use of solar energy. The interest of this has been continuously growing since theirs utilizations do not have dire effects on environment and the availability of the solar resource is endless. In a study carried by Greenpeace [_{2} by 2020. Just one 50 MWel parabolic trough power plant can cut the annual heavy oil consumption by 30 million liters and thus eliminate 90,000 tons of carbon dioxide (CO_{2}) emissions [

Various studies have been carried out in order to predict, evaluate and estimate performance of parabolic trough collector under many weather conditions and configurations. A detailed heat transfer solar receiver model has been performed by Forristall [

A model for the solar field was developed by Patnode [

Kalogirou Soteris [

In order to evaluate the performance of a tracking solar parabolic trough collector, a heat transfer model has been developed by Ouagued et al. [

Cheng et al. [

Wang et al. [

Lobón et al. [

Marif et al. [

Basbous et al. [_{2}O_{3}-Syltherm 800 as a working fluid. The mathematical model used in this work was based on energy balances of the collector and has been validated with experimental data of SNL. The results have shown that the nanoparticles significantly improve the convection coefficient between the receiver and the heat transfer fluid and could decrease the heat losses in about 10%.

Our ongoing model performs using values of the monthly Linke coefficient according to the four main tracking modes present in the literature direct solar irradiation annually. This is one operating in two chosen sites in Cameroon in order to predict which one is the most efficient in the considered regions. The second part of this paper is dedicated to a numerical simulation of the parabolic trough solar collector in Makari situated in the far north region of Cameroon using Therminol VP1 synthetic oil as heat Transfer Fluid (HTF). Based on a two-dimensional energy Balance equations written on Engineering Equation solver Program (EES), the model takes into consideration all modes of heat transfer: convection into the receiver pipe, in the annulus between the receiver and the glass cover, and from the glass cover to ambient air; conduction through the metal receiver pipe and glass cover walls; and radiation from the metal receiver pipe to the glass cover and from the glass cover to the sky. Besides evaluating efficiency, optical and thermal losses and pressure drop along the flowing pipe, the great feature of this model is that it performs and evaluates all of the aforementioned parameters during a test day.

Based on a cross-section of the collector represented in

The average monthly values of linke turbidity factor

Region | Makari | Maroua |
---|---|---|

Latitude | 12˚33'45"N | 10˚26'01"N |

Longitude | 14˚26'51"E | 14°26'00"E |

Altitude | 291 m | 401 m |

Period of Measurement | 2001-2012 | 2001-2012 |

January | 3.4 | 3.4 |

February | 3.6 | 3.6 |

March | 4.0 | 4.0 |

April | 4.1 | 4.2 |

May | 4.1 | 4.3 |

June | 4.3 | 4.6 |

July | 4.7 | 4.9 |

August | 4.6 | 5.0 |

September | 4.6 | 4.7 |

October | 3.9 | 4.2 |

November | 3.6 | 3.8 |

December | 3.6 | 3.7 |

The modes of tracking for PTCs can be generally separated into a single axis tracking or two axes tracking. Two axes tracking follows not only the sun’s changing altitude, but also the sun’s changing azimuth, so as to concentrate the parallel rays incident on the reflectors right onto the receiver tube, whereas for single axis tracking, the collectors can be orientated in one of the three ways: North-South direction, which tracks the sun from east to west (horizontal E-W tracking), or an East-West direction, tracking the sun from north to south (horizontal N-S tracking), or tilted at an angle equal to the latitude of the installation site facing directly to the sun to track the sun’s east-west movement (polar E-W tracking).

The incidence angle between the sun beam and the main normal direction of PTCs, affects the amount of incident irradiation obtained on the reflectors (cosine loss), which relies on the mode of tracking, as shown in

The equation for the solar absorption in the glass envelope in the cross-section considered depends on the tracking mode given by:

And

where the incident angle modifier K is expressed as in [

Tracking modes | Incidence Angle |
---|---|

Full Tracking | 0˚ |

Polar E-W | |

Horizontal E-W | |

Horizontal N-S |

The solar energy absorbed by the absorber occurs very close to the surface; therefore, it is treated as a heat flux. Consequently, the equation for the solar absorption in the absorber section can be expressed as following:

with

and

Even though no glazing PTC’s receiver are used for low-temperature applications, only the glazed receiver is taken into account in this paper. The receiver collector is divided into “n” sections along the longitudinal cutting as shown in

In the sections below, several heat transfer analyses have been depicted taking

into account of every heat interactions between collector receiver components firstly, as well as between collector receiver and its surrounding environment. From the top side of the glass envelope to heat fluid transfer, heat transfer interactions follow the five points stated in

Replacing each term with its value and ordering we obtain:

where

With

The bracket heat loss

The average convection coefficient of bracket

wind cases with the average temperature of

low us the determine

The pressure drop along the pipe is expressed in [

The Darcy friction factor

The roughness coefficient of the pipe is equal to

Convection and radiation are both transfer modes by which glass envelope heat is transferred from the glass envelope to the atmosphere. The convection can either be forced or free relying on the presence or absence of wind, respectively. Radiation heat loss supervenes owing to the temperature difference between the glass envelope and the sky.

To predict the performance of solar collectors, it is necessary to evaluate the radiation exchange between the glass envelope and the sky. The sky can be considered as a blackbody at some equivalent sky temperature

where

And

From Newton’s law of cooling, the convection heat transfer from the glass envelope to the atmosphere is given by:

With

The Nusselt number depends on whether the convection heat transfer is natural (no wind) or forced (with wind). Thus, we will distinguish two cases as following:

The correlation developed by Churchill and Chu [

This correlation assumes a long isothermal horizontal cylinder. Also, all the fluid properties are determined at the film temperature,

In the presence of wind, the convection becomes forced and the Zhukauskas’s correlation [

According to [

All fluid properties are evaluated at the atmospheric temperature,

Between the absorber and the glass envelope, two heat transfer modes take place namely: Convection and radiation. The convection mechanism depends on the annulus pressure. Depending on whether this pressure is low or high the heat interaction occurring is either molecular or free convection respectively. Radiation results from temperature differences between the outer absorber surface and the inner glass envelope surface.

When the annulus is under vacuum (pressure < 0.013 Pa), the convection heat transfer between the receiver pipe and glass envelope occurs by free-molecular convection and is given by [

For:

As the gas annulus in this is air, the mean-free-path between collisions of a molecule,

In reverse when the annular space is under pressure (pressure > 0.013 Pa), the free convection phenomenon takes place there, obeying the Raithby and Holland’s correlation between concentric horizontal cylinders given in [

All physical properties are evaluated at the average temperature

Estimated by the following equation [

b | λ [cm] | γ | δ [cm] | ^{2}-K] | |
---|---|---|---|---|---|

0.02551 | 1.571 | 88.67 | 1.39 | 3.53E−8 | 0.0001115 |

absorber and glass envelope is given as:

From Newton’s law of cooling, the convection heat transfer from the inside surface of the absorber pipe to the HTF is:

As the Nusselt Number relies on flow type, we distinguish three main cases of flows:

In the case of laminar flow (Re < 2300), assuming the problem of heat transfer in laminar flow of an incompressible, constant property fluid in the fully developed region of a circular, constant heat flux, as in the case of a PTC, the Nusselt number is equal to 4.36 [

In the case of turbulent flow (Re > 4000), the Nusselt number is given by the Gnielinski correlation in [

With

In the transition region

where

Conduction heat transfer through the absorber pipe wall is determined by the Fourier’s law of conduction through a hollow cylinder as following:

The absorber pipe thermal conductivity

There are two programs solution which have been developed based on the characteristics of the solar PTC used in

The first one has been written in Matlab in order to evaluate the annual solar energy received on the absorber pipe according to various tracking modes operating in the considered locality. In the Matlab code, solar irradiation has been computed each five minutes from the sunrise to the sunset each day during a year. Results revealed that Makari locality has more than 3500 h/year sunshine duration. Also, the yearly energy received based on different tracking modes is illustrated in

Heat Collector Element (HCE) length, | 4.06 m |
---|---|

Aperture Area, | 39 m^{2} |

HCE Number | 2 |

Glass envelope inner and outer diameter; | 0.115 m, 0.105 m |

Absorber pipe inner and outer diameter, | 0.07 m, 0.066 m |

Absorber pipe thermal absorptance, | 0.92 |

Glass envelope thermal absorptance, | 0.02 |

Glass envelope transmittance, | 0.935 |

Glass envelope thermal conductivity, | 1.04 W/m-K |

Glass envelope emissivity, | 0.86 |

HCE Shadowing (bellows, shielding, supports), | 0.974 |

Tracking Error, | 0.994 |

Geometry Error (mirror alignment), | 0.98 |

Unaccounted, | 0.96 |

Reflectivity | 0.93 |

Clean Mirror Reflectance, | 0.935 |

Effective bracket perimeter for convection heat transfer, | 0.2032 m |

Effective bracket diameter, | 0.0508 m |

Minimum bracket cross-sectional area for conduction heat transfer, | 0.00016129 m^{2} |

Conduction coefficient for carbon steel at 600 K, | 48 W/m-K |

The dirt on mirror, |

Tracking Modes | Absorbed Irradiance per length (MW/m) | Percent to full tracking (%) | |||||||
---|---|---|---|---|---|---|---|---|---|

SE | AE | SS | SW | SE | AE | SS | SW | ||

Makari | Full Tracking | 3.30 | 3.68 | 3.87 | 3.31 | 100 | 100 | 100 | 100 |

E-W Polar | 3.17 | 3.51 | 3.87 | 3.18 | 96.06 | 95.38 | 100 | 96.16 | |

E-W Horizontal | 2.98 | 3.62 | 3.81 | 2.98 | 90.30 | 98.36 | 98.44 | 90.18 | |

N-S Horizontal | 2.58 | 2.78 | 2.86 | 2.59 | 78.21 | 75.54 | 73.70 | 78.30 | |

Maroua | Full Tracking | 3.29 | 3.58 | 3.82 | 3.30 | 100 | 100 | 100 | 100 |

E-W Polar | 3.17 | 3.43 | 3.82 | 3.17 | 96.14 | 95.68 | 100 | 96.05 | |

E-W Horizontal | 3.00 | 3.52 | 3.78 | 3.01 | 91.35 | 98.16 | 98.86 | 91.20 | |

N-S Horizontal | 2.57 | 2.72 | 2.82 | 2.58 | 78.10 | 75.92 | 73.85 | 78.19 |

In this figure it can be seen that compared to other tracking modes, the irradiation of full tracking mode is highest at each period of the year due to the physical movement of the PTC along two axes. But for E-W polar and horizontal tracking modes, irradiation is larger in the summer period and smaller in the winter period. Additionally, as far as N-S horizontal tracking mode is concerned, the amount of irradiation in the winter is more than that in the summer due to the seasonal position of the earth in relation to the sun; for both these periods, the collected irradiation remains less than those of E-W tracking modes in Makari.

From the

The second one program code is developed on EES to evaluate the performance of HCE since EES automatically identifies all unknowns and groups of equations for most efficient solutions. In addition, it provides built-in mathematical and thermal-physical property functions and numerous HTFs in its library. Nonetheless, one inconvenience of this software is that it does not allow a large amount of variables. This is the reason we have implemented annually solar absorbed energy in Matlab and divided our receiver length in 8 cross-sections. Furthermore, the step-time of irradiation’s variable is the quarter of an hour. However, the present EES code can performs daily analyses on HCE. Hence, (Equation (1)) to (Equation (39)) are solved simultaneously at each instant for a day long.

The model results have been compared to experimental data provided by Sandia National Laboratory (SNL) with Great satisfaction as illustrated in

Inasmuch as the efficiency of the collector is strongly related to the mass flow rate of the fluid in the absorber pipe, we computed the program with many values of mass flow rates and deduced how much flow rate influences the efficiency in ^{2} as direct normal solar irradiation, 30˚C as ambient temperature and Therminol-VP1 as HTF, wind speed equal to 3 m/s and 25˚C as inlet fluid temperature, it has been noted from simulation findings that the more flow mass flow rate increases the higher the efficiency (

^{2}) | Error (%) | ||||||
---|---|---|---|---|---|---|---|

933.7 | 2.6 | 21.6 | 102 | 0.6856 | 124 | 123.7 | 0.24 |

968.2 | 3.7 | 22.4 | 151 | 0.6522 | 173 | 173.6 | 0.34 |

982.3 | 2.5 | 24.3 | 197 | 0.6351 | 219 | 219.3 | 0.13 |

909.5 | 3.3 | 26.2 | 250 | 0.6601 | 269 | 268.1 | 0.33 |

937.9 | 1.0 | 28.8 | 297 | 0.6234 | 316 | 316.2 | 0.063 |

880.6 | 2.9 | 27.5 | 299 | 0.6225 | 317 | 317 | 0 |

903.2 | 4.2 | 31 | 355 | 0.5685 | 374 | 373.6 | 0.10 |

fact efficiency decreases. At 0.1 kg/s the temperature recorded is the highest, but the efficiency is the lowest among various values of mass flow rate tested, namely 66.67%. Also, the temperature of fluid has been monitored during his route inside the absorber pipe and shown in

Also, the collector efficiency depends on useful energy as the absorbed energy does not vary in this case. The useful energy, in its turn, mainly depends on mass flow rate and temperature variation. From a certain mass flow rate value, the temperature difference tends to slightly change, but as we lower the mass flow rate, the efficiency is negatively affected. Hence the rapid drop of efficiency observed between 0.2 and 0.1 kg/s.

As mentioned above, the irradiation obtained from the full tracking mode and ambient temperature vary based on each quarter of an hour as shown in

At each single value of time-step, the five points’ temperatures are then computed

The energy rate on the HCE has been also studied in this paper as illustrated by

this energy to a range of values from approximately 70 W/m, just after sunrise, to 700 W/m, just before sunset. However the remaining lowest of the three considered graphs also follows a similar growth shape linked to that of the temperature of the glass outer cover such as highlighted in

values are established between 110 W/m and 1020 W/m.

The pressure drop in the pipe has been analyzed as exemplified in

In this paper, we have first evaluated local solar potential for the four tracking modes and unearthed that the one axis polar East-West and horizontal East- West tracking annually with 96% and 94% of full tracking mode respectively, were most suitable for a parabolic trough collector throughout the whole year in the two towns considered. Also, we have numerically investigated thermal and optical analyses on a PTC’s receiver in Makari based on a two dimensional model of a receiver written on EES taking into account all of heat transfer interactions. Although many assumptions have been taken for the elaboration of this model, simulation findings have revealed that their impacts on the study are almost negligible due to the fact that the maximum relative error value between outlet numerical and experimental fluid temperature does not exceed 0.35%.

Keou, C.-J.N., Njomo, D., Sambou, V., Finiavana, A.R.A. and Tidiane, A.D. (2017) Two-Dimension Numerical Simulation of Parabolic Trough Solar Collector: Far North Region of Cameroon. Energy and Power Engineering, 9, 147-169. https://doi.org/10.4236/epe.2017.93012

Symbols

^{2})

^{2})

^{2}-K),

Enthalpy [J/kg]

^{2})

^{2})

L Receiver Length (m)

P Pressure (mmHg), perimeter (m)

Solar irradiation absorption rate per unit receiver

Length (W/m)

^{2})

Greek

^{−1})^{ }

^{3})

Subscripts

walls of absorber

wall and inner glass

Loss Lost

glass envelope

and ambient air

and sky

Opt Optical

E-W East west

N-S North south

AE Autumnal Equinoxes

SE Spring Equinoxes

SS Summer Solstice

WS Winter Solstice