feUPM

Received 27 December 2013Accepted 10 June 2014

Keywords:Optical efciency of PTCParabolic trough collectorSolar energyThermal efciency of PTCThermo-economic analysis

is a need to present to the open literature a detailed modeling procedure and cost analyses to help

the economics of using parabolic troughs under Saudi weatherconditions where solar energy is abundant. Thus, parabolic troughCSP technology has been selected for the present thermo-economicstudy. Performance and cost analyses are the two main criteria inselecting a power plant technology type and therefore there is a

aboratories (SNL)nd analyzat inuency et al. [4]

oped an analytical model of SEGS LS-2 parabolic trough coThe thermal loss model for the heat collection elementwas one-dimensional and steady-state heat transfer modeon thermal resistance analysis. This model was validated withexperimental data collected by SNL[2] for two types of receiverselective coatings combined with three different receiver congu-rations; glass envelope with either vacuum or air in the receiverannulus, and glass envelope removed from the receiver. The resultsshowed a reasonable agreement between the theoretical andexperimental heat losses. Thomas and Thomas [5] developed a

Corresponding author. Address: Mechanical Engineering Department, KingFahd University of Petroleum & Minerals (KFUPM), P.O. Box: 279, Dhahran 31261,Saudi Arabia.

E-mail address: esmailm@kfupm.edu.sa (E.M.A. Mokheimer).

Energy Conversion and Management 86 (2014) 622633

Contents lists availab

Energy Conversion

seamong them. The rst commercial power plant using PTC technol-ogy was built in 1984 in California. Currently, several power plantsunder operation and many others under construction. However,there is no study reported the optical and thermal efciencies or

measured data obtained from Sandia National Lcollector test facility [2]. Clark [3] identied aeffects of design and manufacturing factors ththermal and economic performance of PTC. Dudlehttp://dx.doi.org/10.1016/j.enconman.2014.06.0230196-8904/ 2014 Elsevier Ltd. All rights reserved.ed theed thedevel-llector.(HCE)

l basedThe main four concentrating solar thermal power technologiesare parabolic trough collectors, Fresnel reector, solar tower, anddishes. Parabolic trough collector (PTC) currently represents themost mature technology for solar thermal power production

a plant. Given the importance of the heat transfer analysis in PTCsystem, since the 1970s a number of models has been proposed.

Edenburn [1] predicted the efciency of a parabolic trough col-lector by using an analytical heat transfer model for evacuated andnon-evacuated cases. The results showed good agreement with1. Introductionresearchers, engineers, and decision makers. The main objectives of this work are to develop a codeand to evaluate the optical and thermal efciencies of parabolic trough collectors (PTCs) solar eld con-sidering average hourly, daily, monthly, or annually averaged weather data; in addition to detailed costanalysis of the solar eld. In this regard, a computer simulation code was developed using EngineeringEquations Solver (EES). This simulation code was validated against Thermoex code and data previouslypublished in the public literature, and excellent agreements ware observed. The types of the PTC consid-ered in the simulation are EuroTrough solar collector (ET-100) and for LUZ solar collector LS-3. The pres-ent study revealed that the maximum optical efciency that can be reached in Dhahran is 73.5%, whereasthe minimum optical efciency is 61%. This study showed also that the specic cost for a PTC eld perunit aperture area and the specic cost of different mechanical works can be cut by about 46% and48% at 10 hectare and by about 72% and 75% at 160 hectare, respectively, compared to that at 2.8 hectare.On the other hand, the specic civil costs remain constant independent of the plant size. It was found thatthe ratio of the cost of the PTC to the solar eld area decreases signicantly as the solar eld sizeincreases. This decrement is very signicant until the solar eld size reaches 60 hectare and then theslope of the decrement is becoming insignicant. Therefore, it is recommended to have a solar eld sizeof 60 hectare or larger.

2014 Elsevier Ltd. All rights reserved.

need to have clear method that shows how to model and analyzeArticle history: The main criteria to assess a new solar thermal power plant are its performance and cost. Therefore, thereTechno-economic performance analysis oin Dhahran, Saudi Arabia

Esmail M.A. Mokheimer , Yousef N. Dabwan, MohamMechanical Engineering Department, King Fahd University of Petroleum & Minerals (KF

a r t i c l e i n f o a b s t r a c t

journal homepage: www.elparabolic trough collector

d A. Habib, Syed A.M. Said, Fahad A. Al-Sulaiman), Dhahran 31261, Saudi Arabia

le at ScienceDirect

and Management

vier .com/locate /enconman

rsionNomenclature

ANI aperture normal irradianceAa aperture areaAr receiver areaAir inside cross sectional area of the absorber tubeCP specic heatDci inner diameter of glass envelopeDco outer diameter of glass envelopeDi inner diameter of absorber tubeDNI direct normal irradianceDo outer diameter of absorber tubeE equation timefend loss performance factor that accounts for losses from ends of

heat collector elementfclean cleanliness factorfrow shadow performance factor that accounts for mutual shading

of parallel collector rows during early morning and lateevening

F0 collector efciency factorF00 collector ow factorf2 friction factor for the inner surface of the absorber pipefn focal length of the collectorsFR collector heat removal factorh heat transfer coefcient inside tube

E.M.A. Mokheimer et al. / Energy Conveset of curve-tting equations based on a numerical heat transfermodel for the heat losses in the HCE of a PTC for different proper-ties of the HCE and weather conditions. A detailed heat transfermodel for the HCE of PTC was developed by Forristall [6]. Bothone- and two-dimensional analyses were used in the code. Thismodel was used to determine the thermal performance of para-bolic trough collectors under different operating conditions.

It is known that the collector outlet temperature is mainlyaffected by changes in the sun intensity, by the collector inlettemperature, and by the volume ow rate of the HTF. Stuetzle [7]proposed an unsteady state analysis of HCE of PTC to calculatethe collector eld outlet temperature. Their results showed goodagreement with measured outlet temperatures. Valladares andVelsquez [8] developed a detailed numerical model for a single-pass and double-pass solar parabolic trough collector. The single-pass solar device numerical model has been validated withexperimental data obtained by SNL. Their results showed that theproposed double-pass could enhance the thermal efciency com-pared with the single-pass. Recently, three dimensional heat trans-fer analysis of PTC system was performed by combining the MonteCarlo Ray Trace Method (MCRT) and CFD analysis [9,10]. Theresults indicated that the ange (support bracket) and bellowunder non-vacuum conditions bring a high conductive heat loss.

Lobn et al. [11] performed CFD simulation of parabolic troughsolar collector considering steam as a heat transfer uid usingSTAR-CCM+ code. However, such a code does not consider severalparameters that are function of solar time variation. In a different

hw wind heat transfer coefcientIAM incidence angle modierkc thermal conductivity of the glass envelopeL collector lengthLloc the longitude of the location of the collector siteLst standard meridian for the local time zoneLspace distance between two parallel collectorsLSCA length of a single solar collectorn the day number of the yearPr Prandtl numberQabs solar radiation absorbed by the receiver tubesQu net energy transferred to the uid in receiver tubesr local mirror radiusTa ambient temperatureTi absorber inner surface temperatureTco outer glass envelope temperatureTci inner temperature of glass envelopeT uid temperature at inlet of receiverTfm main uid temperatureToi uid temperature at outlet of receiver.Tsky sky temperatureUL receiver loss coefcient based on the receiver outside

surface areaUo receiver overall heat transfer coefcient based on the

receiver outside tube diameterVf velocity of HTF inside the tubeWa parabolas aperture width

Greek lettersac absorptance of the absorber surface coating(sac)n the effective product of s and acc intercept factorr StefanBoltzman constant. latitude location of the solar eld.

and Management 86 (2014) 622633 623study, Ceylan and Ergun [12] conducted thermodynamic analysisof temperature controlled parabolic trough collector. Nevertheless,their analysis did not consider the optical performance and solartime variation. Ouagued et al. [13] presented a thermal model ofparabolic trough solar collector considering Algeria weather condi-tions. However, they have ignored some of the optical performanceparameters and their study did not consider any cost analysis.

It can be noticed from the literature review that there is nodetailed thermal model that presents the detailed performance ofthe PTC considering complete set of variables that affect the perfor-mance. The model developed in this study considers several keyPTC performance parameters, such as:

angle of incidence and angle of incidence modier, heat end losses of the heat collector element, cleanliness factor, row shadowing, day number of the year, zenith angle, focal length of the collectors, aperture normal irradiance, collector ow factor, velocity of the Heat Transfer Fluid (HTF) inside the tube, and friction factor of the absorber inner surface.

Therefore, the developed model considers a complete modelingof PTC and it will be a key for researchers and engineers in the area.The present model was developed in EES and validated with

l absolute viscosity for heat transfer uid.gnominal nominal optical efciencygopt optical efciencygth,collector thermal collector efciencyh angle of incidencehz zenith angleqcl clean mirror reectivityqf density for heat transfer uids transmittance of the glass envelopeeci emittance of glass envelope inner surfaceeco emittance of glass envelope outer surfaceer emittance of the receiver

Thermoex. It is worth mentioning here that Thermoex + PEACEsoftware has a model library containing all components necessaryfor the simulation of conventional power plants. This library hasbeen recently extended to include all relevant solar componentsmodels of the three CSP technologies. These three CSP technologiesare solar tower, parabolic trough collectors, and linear Fresnelreectors. The Thermoex parabolic trough model has been usedto validate the parabolic trough simulation model developed dur-ing the present work.

Furthermore, in this study detailed cost analysis versus solareld size has been carried out and validated with literature as dis-cussed later. The cost analysis considers installation cost, installed

B is the parabolas depth. Wa is the parabolas aperture width.This collector shape focuses incoming solar radiation that is paral-lel to the axis and normal to the aperture to the focal point.

To maximize energy capture, the solar collector trough isrotated by a drive system so it faces the sun as much as possible.The tracking system operates to keep the axis coplanar with thesuns central ray. Collector troughs are often aligned along merid-ians and rotate so they can track the sun from sunrise to sunset.However, other orientations are used, including perpendicular tomeridians to more evenly balance the amount of captured energythroughout the year.

The heat collection element (HCE) is carefully aligned with theparabolic troughs focal line, which shown as a point in the Fig. 1. A

624 E.M.A. Mokheimer et al. / Energy Conversion and Management 86 (2014) 622633cost of mechanical works, installed cost of civil work, structure,drivers and position system cost per aperture area, receiver costper unit length, reector cost per unit aperture area, headers andpiping per receiver length, mechanical labor cost per aperture area,among others. The selected city for simulation is Dhahran, SaudiArabia, which is located in MENA region where more than35 GW of solar thermal power is planned in the upcoming25 years; and therefore, this add further value to this study, espe-cially for engineers and decision makers. The analysis considersannual, monthly, and hourly weather conditions of Dhahran. ThePTC type considered in the simulation are Euro Trough solar collec-tor (ET-100) and for LUZ solar collector LS-3, which are relativelytwo new designs that have implemented in new PTC solar thermalpower plants.

2. System description

A PTC system consists of curved mirrors, a receiver, steel struc-ture, and a tracking system. The curved mirrors are reecting andconcentrating the solar radiation into an absorber tube (receiver)which is located in the focal line of the collector. The receiver con-sists of a special tube through which a heat transfer uid (HTF) isowing heated up to about 400 C. When the geometry and ther-mal properties of PTC are known, the thermal performance andenergy gained by the HTF can be calculated under different cong-urations and weather conditions. The heat transfer analysis of PTCis essential for the calculation of thermal losses and sizing of thesolar eld during initial design.

To understand how the model of parabolic trough collector(PTC) works, a brief description of the collector is provided in thissection. A schematic cross section of the PTC is shown in Fig. 1. Thearc shape of PTC as shown in Fig. 1 is selected because of its focus-ing properties. The axis is the line that passes through the vertexand the focal point. The rim angle is measured from the axis tothe line connecting the focus to the rim (edge) of the parabola.The aperture area is the distance from rim to rim multiplied bythe reective length of the reector. Three characteristic dimen-sions are labeled in this diagram. fn is the parabolas focal length.Fig. 1. A schematic cross section ofcross section of the HCE is shown in Fig. 2. It consists of the receivertube that carrying the uid being heated. The receiver tube iscoated with an optically selective coating so it absorbs much ofthe incident solar radiation while emitting only a small amountof thermal radiation.

The receiver tube is surrounded by a glass envelope to reduceheat losses from the receiver tube. The envelope should be hightransparent to incoming solar radiation and high opaque to outgo-ing thermal radiation emitted from wall of the tube. The annulusbetween receiver tube and the envelope is evacuated to virtuallyeliminate convective heat transfer between the tube and envelope.

Solar radiation consists of direct and indirect radiations. Con-centrating collectors only focus direct normal irradiance (DNI),which is the radiation streaming directly from the sun withouthaving been scattered by atmosphere. Indirect (diffuse) irradiancecannot be focused by these collectors. Furthermore, PTC can onlyfocus the component of DNI normal to the aperture, which is calledaperture normal irradiance (ANI). One can compute ANI from theDNI based on the collectors orientation on the earth; it is tiltedaway from horizontal, and the sun position in the sky. Assume thatthe collector is tracking the sun in one direction to makes thegeometry straightforward that is because the sun central ray andthe parabolas axis are coplanar.

The performance parameters of the PTC are listed as follows:

i. Concentration ratio: ratio of the aperture area to the receiverarea. It gives indication of the maximum temperature pro-duced by the collector.

ii. Optical efciency; which gives information of the fraction oftotal solar energy incident on collector area absorbed by theabsorber.

iii. Thermal efciency; which gives information of the fractionof total energy incident on the collector area that we get inthe form of heat from the collector.

The thermal efciency of the parabolic trough solar collectorsystem depends on the optical efciency of the system. Havingthe parabolic trough collector.

larger optical efciency of the reector results in improvement ofthe thermal efciency and hence the overall performance of thesystem is improved.

3. Mathematical modelling

The incident solar radiation uctuates hourly and seasonally. Asa result, the aperture normal irradiance (ANI) changes also withtime. On the other hand, not all ANI is absorbed by the receivertube due to the optical losses. The surfaces of the reector, theglass envelope, and the tube itself are not optically perfect. The

the absorbed energy is lost to the surroundings by radiation, con-vection, and conduction.

The absorbed radiation, Qabs, is dened as the incidence solarenergy on the collector that is actually absorbed by the heat trans-fer uid through the HCE. The absorbed radiation is a fraction ofthe direct normal irradiance that is adjusted due to the effects ofincidence angle, row shading, solar eld availability, collectorcleanliness, the collector eld, and HCE surface properties. Thegross energy absorbed by the receiver tube is as follows:

Qabs gopt ANI 1

where Qabs is the solar radiation absorbed by the receiver tubes [W/m2], gopt is optical efciency, and ANI is aperture normal irradiance(W/m2) that can be calculated by:

ANI DNI cosh 2DNI is the direct normal irradiance (W/m2), h is angle of incidence(deg.).

The optical efciency could be calculated by the followingequation:

gopt gnominal IAM fend loss fclean fraw shadow 3

where gnominal is the nominal optical efciency, IAM is incidenceangle modier, fend loss is performance factor that accounts for losses

Fig. 2. A cross section of the heat collection element (HCE).

E.M.A. Mokheimer et al. / Energy Conversion and Management 86 (2014) 622633 625optical efciency of the collector accounts for losses at these sur-faces. The optical efciency is a characteristic of the reector/absorber system and depends on the materials, coating, and align-ment. Fig. 3 shows the different parameters that affect the opticalefciency of the parabolic solar collector.

The nominal design point of the collector optical efciencycharacterizes the collectors ability to focus incoming direct (beam)radiation on the receiver tube. This value applies when the sunscentral rays are perpendicular to the collector aperture. Correctionsto this efciency are applied when the central rays strikes the aper-ture at other angles. The corrected optical efciency dictates thepercentage of ANI that is absorbed by the receiver tube. Some ofFig. 3. Parameters affectifrom the ends of the heat collector element; it is also called inter-cept factor (fraction of the reected radiation that is not interceptedby the receiver). It happens at the end portion of HCE, where there isno focused radiation on that portion as shown in Fig. 4 and Eq. (14),fclean is cleanliness factor, and frowshadow is performance factor thatconsiders the mutual shading of parallel collector rows during earlymorning and late evening.

The nominal efciency (gnominal) can be expressed as

gnominal qcl saCn c 4where qcl is the clean mirror reectivity, s is transmittance of theglass envelope, ac is absorptance of the absorber surface coating,ng optical efciency.

he

sionand (saC)n is the effective product of s and ac. A modied value of(sac)n is recommended by Stuetzle [7] as 1.01(sac).

The nominal optical efciency depends on selected solar collec-tor type. There are currently several collector types for concen-trated solar power plants applications that have beensuccessfully tested under real operating conditions. For example,the Luz International Ltd. (Luz) developed and designed three par-abolic trough collectors, called LS-1, LS-2 and LS-3 [14]. These col-lectors were installed in solar electric generating plants. The othercollector is EuroTrough collector, which is an improved model ofthe analysis of several different collector structures and its charac-teristics are given in [15].

Only the direct normal irradiance can be focused by linear con-centrated solar collectors. The angle between the direct normalirradiance (DNI) on a surface and the plane normal to that surfaceis called the angle of incidence (h). The angle of incidence variesover the whole day as well as throughout the year. As a result,the performance of the solar collector is heavily inuenced by thisvariation. The angle of incidence (h) for a parabolic solar collectorrotating about a horizontal northsouth axis with continuousadjustment to minimize the angle of incidence, so that more DNIis focused on the HCE, can be calculated by the following equation[16]:

cosh cos2 hz cos2 d sin2x1=2 5

On the right hand side of this equation, there are three angles,which are namely, the declination angle (d), the angular hour(x), and the zenith angle (hz). Expressions for calculating theseangles can be found in [16].

As mentioned earlier, the energy absorbed in the solar receiveris affected by the optical properties and imperfections of the solar

Fig. 4. End losses from

626 E.M.A. Mokheimer et al. / Energy Convercollector ensemble. The optical efciency of a PTC eld (gopt) can bedened as the fraction of the direct solar irradiance incident on theaperture of the collector which is absorbed at the surface of theHCE. Substituting Eq. (4) into Eq. (3), one can get:

gopt qcl sacn c IAM frow shadow fend loss fclean 6According to Eq. (6), the solar collector/receiver system optical

efciency considers mirror reectivity, the transmittance of thereceiver glass envelope, the absorptance of the absorber surfacecoating, the intercept factor, the incident angle effects, the cleanli-ness of the mirrors, the row to row shadowing, and the receiverend losses.

In this study, the effect of correction parameters for the para-bolic solar collector assembly, mirrors and heat collection element,are accounted the intercept factor, c, which is a fraction of thereected radiation that is incident on the absorbing surface ofthe receiver. The factors that affect the intercept factor are [6,1720]: Losses from shading of ends of heat collection element due tobellows, shielding, and supports, c1.

Twisting and tracking error associated with the collector type,c2.

Geometry accuracy of the collector mirrors, c3. Losses due to shading of HCE by dust on the envelope, c4. Miscellaneous factors to adjust for other HCE losses, c5.

Thus, the intercept factor is dened as:

c Yi5i1ci 7

where the values for ci (i = 1, 2, 3, 4, 5) are given in [6,1720] as0.974, 0971, 0.994, 0.98, 0.98, 0.96, respectively.

For a PTC system, the nominal optical efciency occurs whenthe direct beam radiation is normal to the collector aperture area.In addition to the losses due to the deviation of the angle of inci-dence from zero, there are other losses from the collector thatcan be correlated to the angle of incidence if it is greater than 0[16]. Hence, a factor called Incident Angle Modier (IAM) is usedwhen the beam radiation is not normal. The IAM is considered inall optical and geometric losses when the incident angle is greaterthan 0. The incident angle modier depends on the geometry andthe optical characteristics of the solar collector. The incident anglemodier is dened as [4,21]

IAM ghgnominal

8

The incident angle modier function is dened by:

IAM max0; IAMh 9

at collector element.

and Management 86 (2014) 622633Incidence angle modier is given as an empirical formula interm of incidence angle (h). Each specic solar collector has its for-mula. Table 1 [4,18,2225] lists the incident angle modier func-tion for different solar collector types. These functions wereplotted as shown in Fig. 5.

The positioning and geometry of the collector troughs and HCEscan introduce further losses. These losses are due to shading of par-allel rows in the sunrise and sunset in addition to the end lossesfrom the HCE. The collectors are arranged in parallel rows, and theytrack the sun during the daytime. Due to the sunrise and sunset,row shading occurs. For example, due to the low solar altitudeangle of the sun in the morning, the eastern-most row of collectorscan receive full sun, but this row will shade all subsequent rows tothe west. As the sun rises and the collectors track the sun, thismutual row shading effect decreases, until a critical zenith angleis reached at which no row shading occurs. Collector rows remainun-shaded through the middle of the day. Due to tracking of thesolar collectors to the sun at different sun positions in the morning,

rsionTable 1Incident angle modier functions for different solar collectors.

IAM for LS-2

1 8:84 104 hcosh 5:369 105 h2

cosh [4]

IAM for IST

1 3:178 104 hcosh 3:985 105 h2

cosh [22]

IAM for LS-3

1 2:2307 104h 1:1 104h2 3:18596 106h3 4:85509 108h4[18,23]

IAM for ET-100

1 5:25097 104 hcosh 2:859621 105 h2

cosh [24,25]

h: incident angle in degrees.

Fig. 5. Incident angle modiers for different parabolic trough solar collectors.

E.M.A. Mokheimer et al. / Energy Convethe row shading varies as the sun position changes. The shadingfactor is dened as [7,17]:

frow shadow LspaceWa coshzcosh 10

where Lspace is the distance between two parallel collectors [m], Wais aperture width [m], and hz is zenith angle.

The shading factor equation is bounded with a minimum valueof 0 (rows are fully shaded) and a maximum value of 1 (rows arenot shaded). For optimization purpose, the following equationcan be imposed:

frow shadow min max 0:0; LspaceWa coshzcosh ;1:0

11

In a solar collector eld, the two terminals of the absorber tubeof each collector are not illuminated by the reected solar radiationfrom the mirrors. In other words, end losses take place at the endsof the heat collection elements, where there is no focused radiationon those portions as shown in Fig. 4. End losses depend on the solarcollector average focal length, the solar incidence angle, and thelength of solar collector. As shown in Fig. 4, the part of the receiverthat is not illuminated (z) is as follows:

Z r tanh 12The distance r shown in Fig. 6 can be dened as [16,26]:

r fn x2

4f13

The fraction of the receiver that is illuminated is:

fend loss 1 rLSCA tanh 14

where r is the local mirror radius [m], LSCA is length of a single solarcollector [m], and fn is focal length of the collectors [m].Lippke [27] proposed that r = fn which found acceptance in theliterature [16,17]. This proposed equation leads to minimum endlosses for certain geometric conguration. A previous work devel-oped by Gaul and Rabl [21] suggested the use of an average valueof r. This value was used in this study and it is dened as:

r fn 1 W2a

48f 2n

!15

Replacing the value of r, then, the collector geometrical endlosses [18,21] can be formulated as:

fend loss max 0;1 fnLSCA 1W2a48 f 2n

!tanh

" #16

As discussed before, collector thermal efciency includes theeffect of the collectors optical efciency, end losses (resulting fromcollector geometry), and the thermal loss (from the hot receivertube to the surroundings). It does not include heat losses at theinlet and exit header. If the receiver tube has zero heat loss andthere were no end losses, the solar efciency would equal the opti-cal efciency. It should be noticed that collector thermal efciencyis a measure of the collector-only performance, independent of

Fig. 6. Parabola geometry for a rim angle of hr [16,26].

and Management 86 (2014) 622633 627installation details. Thermal performance of solar collector is char-acterized by the thermal efciency:

gth;collector Qu

ANIAa 17

Some of the absorbed energy heats the receiver tube and theuid owing inside it. The balance is lost to the surroundings viaradiation, convection, and conduction. The wall tube radiates tothe glass envelope and the surroundings. In this model, the smallconvective heat transfer from the tube to the ultra-low pressuregases in the annulus is ignored (evacuated glass envelope). Theglass envelope loses heat to the environment by convection andradiation. According to Ref. [16], net heat transfer to the uid inreceiver tube (Qu) is:

Qu FR Aa Qabs ArAa

ULTi Ta

18

F 00 FRF 0

_m CpAr UL F 0

1 exp Ar UL F0

_m Cp

19

F 0 UOUL

20

Uo 1UL Do

hfi Di Do ln DoDi

2 k

0@

1A

1

21

Aa Wa Do L 22

Ar A p Do L 23The heat loss (Qloss) is estimated for each step using a one

dimensional heat transfer model. For each station along the tube,one can compute a one-dimensional heat balance using energy bal-ance with a gray body radiative exchange from the receiver tube tothe glass envelope, and a combined radiative and convective heatlosses from the glass envelope to the environment. The heatabsorbed by the uid conducts through the tube wall and heatsthe uid by convection heat transfer from the inner wall of theabsorber tube to the bulk uid.

Fig. 7 depicts the cross section at a location along the tube. Theambient temperature is the same as other site temperature. Theexternal heat transfer coefcient is assumed constant along the

the average temperature between the cover and ambient temper-atures, which is dened as:

Re qVDcol

25

The wind heat transfer coefcient is then found from:

hw Nuout kDco 26

For ow of air across a single tube in an outdoor environment,the equations recommended by Ref. [16] have been used.

Nuout 0:40 0:54Re0:52 For0:1 < Re < 1000 27

Nuout 0:30Re0:6 For1000 < Re < 50;000 28To solve the above set of equations, ones usually use an iterative

procedure. At the beginning, one needs to assume the cover tem-perature (Tco), which will be much closer to the ambient tempera-ture than the receiver temperature. The inner cover temperaturecan be found by calculating the conduction heat transfer between

628 E.M.A. Mokheimer et al. / Energy Conversion and Management 86 (2014) 622633tube length; also the radiative properties of the surfaces areassumed constants. The mathematical code computes the thermalconductivity of the tube based on its material and its local temper-ature. The mathematical code computes internal heat transfercoefcient based on the uid properties at the local uid condi-tions. Considering Fig. 7 the heat losses between the receiver andthe ambient are discussed next.

First of all, one needs to calculate heat losses between glassenvelope and environment. As stated above, the heat will transferfrom the glass envelope to the atmosphere by convection and radi-ation. The convection will be either forced or natural, depending onwhether there is wind or not. Radiation heat loss occurs due to thetemperature difference between the glass envelope and sky. Thetotal heat losses between glass envelope and environment can befound using the following equation [16]:

Qloss pDcoLhwTco Ta pDcoLcorT4co T4sky 24where sky temperature equal ambient temperature 5 C, and Ste-fanBoltzmann constant (r) equal 5.67 108 [16].

Where hw is the convective heat transfer coefcient betweenthe receiver outer cover tube and the ambient air. To estimatethe wind heat transfer coefcient, it is necessary to nd Reynoldsnumber of the wind in which the physical properties depends onFig. 7. Temperature and heat owthe outer and the inner surface of the glass envelope, where the(Qloss) will be calculated using Eq. (29).

Qloss 2pkcLTci Tco

ln DcoDci

29The heat loss by radiation from the receiver and inner surface of

the glass envelope is

Qloss pDrLrT4r T4ci

1r 1cir DrDci

30The heat losses in Eqs. 24, 29, and 30 are equal. If they do not

equal, it is necessary to make another guess of the outside covertemperature (Tco) till the solution converge. Then one can calculateUL from the following equation:

Qloss UL ArTr Ta 31Reynolds number for heat transfer element is given by the fol-

lowing equation:

ReHTF qf VDirlf

4 _mfp Air 32from heat collection element.

rsionAir p4 D2ir 33

In order to calculate Reynolds number for the ow inside thetube, properties of HTF such as absolute viscosity, and densityshould be known. Hence, these properties are given at the meanuid temperature (Tfm). By assuming the value of the temperatureat the outlet of receiver (Tfo), the mean uid temperature can becalculated by the following equation:

Tfm Tfo Tfi2 34

In order to calculate Nusselt number inside the tube, propertiesof HTF are taken at the mean uid temperature (Tfm). Value of Nus-selt number depends on status of uid ow, laminar or turbulent.When Reynolds number (Re) is lower than 2300, the laminaroption is selected and the Nusselt number will be constant. Forow inside the tube, the value will be 4.36 [16]. When Reynoldsnumber (Re) is greater than 2300, the Nusselt number is given bythe following equation [28]:

Nuinside tube f28 Re 10000 Pr1

1 12:7 f28 2

Pr321 1 Pr1Pr2

0:1135

f2 is the Friction factor for the inner surface of the absorber pipe, Pr1is Prandtl number evaluated at the HTF inlet temperature, (T), Pr2 isPrandtl number evaluated at the absorber inner surface tempera-ture (Ti), where (Ti) can be assumed as a rst guess as: Ti = Tfm + 2and Tfm is mean uid temperature.

After determining the value of the Nusselt number, heat trans-fer coefcient (hinside tube) can be calculated by the followingequation:

hinside tube Nuinside tube kfDir 36

where (kf) is thermal conductivity of heat transfer uid, also itshould be found at the mean uid temperature (Tfm).

4. Results and discussion

Performance and cost analysis are the two major criteria inassessing a solar thermal system. The validation and results ofoptical and thermal efciencies of the parabolic trough solar col-lector and its detailed cost analysis are discussed hereunder. Theanalysis considers the variation of the solar radiation on hourly,daily and monthly average basis. Furthermore, detailed cost analy-ses versus solar eld size are presented and discussed.

4.1. Validation and performance results

An EES code has been developed to solve the set of equationslisted in Section 3 above in order to estimate the optical and ther-mal efciency of parabolic troughs under any weather and operat-ing conditions. In the present work, the optical and thermalefciency of the parabolic trough has been calculated under Dhah-ran, Saudi Arabia weather conditions. The results obtained by thepresently developed EES code have been rstly validated againstresults from the literature and against those obtained by Thermo-ex software. In this regard, the performance of LS-3 parabolictrough has been simulated under Mojave desert, California (Lati-tudes of 35.4 and longitude of 115.58) and under Dhahran, SaudiArabia (Latitude 26.267/Longitude 50.15) weather conditions.The results of this simulation are presented in Fig. 8(a) for a clean-

E.M.A. Mokheimer et al. / Energy Conveliness factor of 1 (clean surface). The results shows that the maxi-mum optical efciency predicted under Mojave desert weathercondition is 77.39% which is very close the corresponding experi-mentally measured value of 77% as reported by [14]. The deviationis about 0.5%, which reects the validity of the program. It is worthreporting here that the deviation between the optical efciency ofLS3 parabolic trough under Mojave desert and Dhahran weatherconditions is mainly attributed to the change of the clearanceindex which is site dependent as shown in Fig. 8(b). The large devi-ation between the clearance index at Mojave desert, California,from that at Dhahran, Saudi Arabia in winter months lead to a pro-portional larger deviation between the optical efciency of the par-abolic trough LS-3 collector at the two locations compared to thedeviation during summer months. On the other hand, the parabolictrough models developed in Thermoex models are based on man-ufacturer data [29]. Thus, the hourly, daily and monthly perfor-mance of the parabolic trough estimated by the presentlydeveloped EES code is validated against those predicted usingThermoex software under Dhahran, Saudi Arabia weather condi-tions. For fair validation, we carried out a comparative analysis ofthe variation of the optical and thermal efciency of ET-100 para-bolic trough estimated using the presently developed EES code andthose estimated using Thermoex software. The comparison ofhourly variation of the optical efciency is shown in Fig. 8 whilethe hourly variation of the thermal efciency is depicted in Fig. 9for two typical months of the year, (a) represents summer and(b) represents winter. These two gures clearly show excellentagreement between the results of our presently developed EEScode and that of Thermoex software which is originally validatedwith manufacturer data [29].

These results presented in Figs. 9 and 10, reveal that the hourlyvariations of optical and thermal efciencies in the winter monthsare more pronounced than the variations in the summer months.Moreover, the optical and thermal efciencies of the summermonths start from lower values at early hours in the morningand increases to reach the maximum values that will slightlydecrease at noon time. On the other hand, the optical and thermalefciencies of the winter months start from maximum values inearly morning and decrease to reach the lowest values at noontime.

Results of the monthly-averaged peak optical and thermal ef-ciencies for Euro Trough solar collector (ET-100) under weatherdata of Dhahran, Saudi Arabia as obtained by the presently devel-oped EES code and those obtained by Thermoex software are notpresented here due to space limitation. In general, the monthly-averaged peak optical and thermal efciencies obtained by EEScode showed excellent agreements (almost matching) with thoseobtained by THERMOFLEX during all months of the year. The ther-mal efciency of the parabolic trough solar collector systemdepends mainly on the optical efciency of the system. The higherthe optical efciency of the reector is, the better is the thermalefciency and hence the overall performance of the system. Theseresults revealed that the optical efciency varies between 65% toabout 73.5% while the thermal efciency varied between a mini-mum of 60% to about 71%. The high efciencies are in summermonths (April to August) under Dhahran, Saudi Arabia weatherconditions and cleanliness factor of 0.95.

Having validated our EES code, we have used it to carry out per-formance analysis of different parabolic troughs under Dhahran,Saudi Arabia weather conditions. Fig. 11 depicts the variation ofthe daily-averaged optical efciency of the EuroTrough solar col-lector ET-100 and LS-3 parabolic troughs over a year. As shown,the optical efciency for ET-100 is better than that for LS-3, espe-cially during a winter session. The difference between the two ef-ciencies comes from incidence angle modier, where the incidenceangle modier for ET-100 is better than that for LS-3. The EES code

and Management 86 (2014) 622633 629has been used for further thermo-economic analysis and assess-ment of parabolic trough systems under Dhahran, Saudi Arabiaweather conditions as outlined hereunder.

sion630 E.M.A. Mokheimer et al. / Energy Conver4.2. Cost analysis and cost reduction for parabolic trough systems

The costs of electric power generated by a line-focus solarpower system are dependent on the capital equipment cost andthe performance, as well as, the operating and maintenance costs.Innovative plant designs can also impact delivered energy costs.The size of the plant plays also an important role in reducing theoverall installation and operation cost. The proposed parabolictrough system under investigation in this study was proposed tobe integrated to a gas turbine cogeneration power plant that pro-duces 150 MWe and steam with constant ow rate of (81.44 kg/s) at 45.88 bar output pressure. A comprehensive thermo-eco-nomic investigation of different alternatives of integrating a para-bolic trough solar eld to this plant has been carried out. Thedetails of this comprehensive thermo-economic investigation of

(a)Fig. 8. (a) Monthly averaged optical efciency of LS-3 Parabolic Trough and (b) monthly afor a clean collector).

Fig. 9. Comparison of hourly variation of optical efciency of ET-100 parabolicTrough obtained by presently developed EES code and THERMOFLEX code, Thermoex, - -- --- --- - EES code.

Fig. 10. Comparison of hourly variation of thermal efciency of ET-100 parabolicTrough obtained by presently developed EES code and THERMOFLEX code, Thermoex, - -- --- --- - EES code.(b)veraged clearance index at Dhahran and Mojave Desert (at noon solar time using EES

and Management 86 (2014) 622633the gas turbine cogeneration plant is beyond the scope of this arti-cle and can be found in [30]. The present study focuses on theeffect of solar eld size on its cost.

The capital equipment for a concentrated solar power (CSP) sys-tem involves the important solar components (solar collector eld,heat transfer piping, and storage subsystem) and more-or-less con-ventional thermodynamic power cycle components. We will focuson the solar components and address the suitable opportunities forboth cost reduction and performance improvement.

Increasing plant size is one of the easiest ways to reduce thecost of the solar electricity from parabolic trough power plants.Previous studies have shown that doubling the size of the plantreduces the capital cost by approximately 1214% [3133]. Forexample, Pilkington solar international report [31] has shown thatthe specic cost for a parabolic trough power plant with 40 MWcan be cut by 14.5% at 80 MW and by 28% at 160 MW. A similaranalysis identied that the specic cost for a parabolic troughpower plant can be cut by 12.1% if the plant size is increased from50 MW to 100 MW and by 20.3% if it is increased from 50 MW to200 MW [32,33]. According to Ref. [34] (Renewable Energy Tech-nology Characterizations), the specic cost for a parabolic troughpower plant with 10 MW can be cut by 19% at 20 MW, by 37% at40 MW, by 48% at 80 MW, and by 61% at 160 MW.

Like any other industry, PTC business actors are not willing todisclose internal information on the cost structures in an unlimitedway. Still, some commercial cost information has been made avail-able, which is analyzed and referenced hereunder.

To study the cost reduction of a PTC as solar eld size increases,a simple solar thermal plant has been used. This plant has a para-bolic solar eld, one pump, one water supply, and process output.

Fig. 11. Daily-averaged optical efciency of PTC throughout a year under Dhahran,Saudi Arabia weather conditions, (using EES).

Steam output from this plant was considered to have a constantow rate of (81.44 kg/s) at 45.88 bar output pressure, but the out-put temperature was changing during increasing solar eld size.The solar eld area of the thermal plant (under study) varies from2.8 hectare to 160 hectare.

One can increase the solar eld size by increasingnumberof solarcollectors rows. The variations of total installed cost of parabolicsolar eld with solar eld size are presented in Fig. 12. The totalinstalled cost of parabolic solar eld involves the cost of mechanicaland civilworks. As shown in Fig. 12, the cost ofmechanicalworks is amajor contributor to the total installation cost.

The mechanical cost includes the cost of the receiver, reector,structure and drives system, piping with headers system, andmechanical labor. The civil cost includes the cost of foundationmaterial and equipment, excavation/backll material and equip-ment, and civil labor. The cost variations of mechanical works withincreasing solar eld size are shown in Fig. 13. On the other hand,

is worth noting that the change in the cost per unit area of the solarled becomes negligible beyond the solar eld size of 60 hectare.

The key components to reduce the solar eld material cost arethe support structures including tracking system, and receivers.Fig. 17 shows the percentage of the material cost of PTC. This gureillustrates the structure and drives systems represent about 36% ofthe collector eld material cost, the receiver tubes and ttings rep-resent about 28% of the collector eld material cost, the reectorsystem represents about 23% of the collector eld material cost.The remaining percentage (13%) is for headers, piping, and miscel-laneous materials and equipment cost.

As illustrated in Fig. 17, the structure and drives system repre-sent 36% of the collector eld materials cost. This factor is exam-ined further with the solar eld size. It was found that thespecic structure and tracking system cost per unit aperture areawith 2.8 hectares can be cut by almost 140 USD at 10 hectaresand by almost 218 USD at 160 hectares which is a signicantreduction in the cost.

Fig. 13. Variation of installation costs of mechanical works with solar eld size (forPTC).

Fig. 14. Variation of installation costs of civil works with solar eld size (for PTC).

E.M.A. Mokheimer et al. / Energy Conversionthe cost variations of civil works with increasing solar eld size arepresented in Fig. 14.

For parabolic trough collectors, there are three important differ-ent areas: one of them is called reective area, the other one iscalled aperture area, and the third one is called solar eld area(size). The reective area is the area that is covered by shiny mate-rial on the parabolic reector surface. It is the area you would get ifyou attened out the trough. Aperture area is the distance betweenrim to rim multiplied by the reective length of the reector. Thesolar eld area is a required area for solar collector eld (land area).Fig. 15 shows the variation of solar collector aperture and thereected area with the solar eld required land area (solar eldsize).

The cost per unit area is an important scale for solar collectorworks. Fig. 16 demonstrates how the total installation cost per unitarea varies with solar eld size. As shown in the gure, the totalinstallation cost is calculated for three different unit areas, whichare reective, aperture, and land unit area. However, the most pop-ular one is the total installed cost per unit aperture area. The totalinstallation cost is reduced by increasing the solar eld size; thecost reduction is almost halved down by increasing solar eld sizefrom 2.8 hectare to 10 hectare. It can be observed that the costdeclines rapidly when the solar eld size increases from 10 hectareto 60 hectare, after that the cost declination is almost gradual withincreasing the solar eld size. Therefore, it may not be recom-mended to consider the use of parabolic troughs for concentratedsolar power applications of small scale while it is recommendedfor large scale applications where the cost per unit area of the solareld decrease to its minimal possible values available presently. ItFig. 12. Variation of installation costs of PTC with solar eld size.and Management 86 (2014) 622633 631The receivers (heat collection elements) are a major contributorto trough solar eld performance. The heat collection elementsconstitute a major portion of the direct capital cost; the vacuum

632 E.M.A. Mokheimer et al. / Energy ConversionFig. 15. Variation of total collector area with solar eld size (for PTC).receiver cost about (200300) per m receiver length [32]. Thus,the solar eld size increases the total receiver length increasesas. Unpresented results demonstrated how the receiver cost perunit length varies with solar eld size. The unit length receiver costdecreases as the solar eld size increases. The receiver unit cost isalmost halved when the solar eld size increases from 2.8 hectareto 10 hectare (from about 1400 USD to 760 USD), then it sharplydeclined by increasing the solar eld size from 10 hectare to60 hectare, after that the declination is just incremental such that

Fig. 16. Variation of installation cost per unit area with solar eld size (for PTC).

Fig. 17. Cost breakdown for parabolic trough collector components.it decreases from 408 USD/m to 352 USD/m when the solar eldsize increases from 60 hectare to 160 hectare.

The other important factor is the reector cost per unit aperturearea. According to the results of the present study, the specicreceiver cost with 2.8 hectare can be cut by about 98 USD (48%)at 10 hectare and by about 152 USD (75%) at 160 hectare comparedto the cost at 2.8 hectare.

The variation of the headers, piping, and miscellaneous materialcost per unit receiver length with the solar eld size shows that thespecic receiver cost with 2.8 hectare can be cut by around 450USD at 60 hectare (70%), and by around 480 USD (75%) at 160 hect-are compared to the cost at 2.8 hectare. The variation of mechani-cal labor cost per unit aperture area also increase with the solareld size. It was found that the mechanical labor cost almosthalved by increasing solar eld size from 2.8 hectare to 10 hectare(from about 450 USD to 230 USD). The unit cost continue to declinesignicantly by increase solar eld size from 10 hectare to 60 hect-are. After that the declination is almost gradual from 130.6 USD/mto 112 USD/m by increasing the solar eld size from 60 hectare to160 hectare.

Fig. 18. Comparison between the present study and literatures in terms of PTCinstallation cost per unit reective area.

and Management 86 (2014) 622633Unpresented results of the costs of civil works per unit aperturearea have been shown to be invariant with increasing solar eldsize. The civil works include foundation work (material and equip-ment which was found to be constant at the rate of about $ 17.5/m2 of the aperture area); excavation/backll work (material andequipment) that was xed at about $ 12/m2; and civil labor wasconstant at about $ 18/m2. As shown, the costs of different civilworks per unit aperture area are constants when the solar eld sizeis increasing.

Fig. 18 shows the comparison between the results in currentstudy and the results reported in [31,32,35] in terms of PTC instal-lation cost per unit reective area. As shown, the cost per unit areaof the solar eld collector in the current study matches very wellthe results from the others studies.

5. Conclusions

The optical and thermal efciencies of PTC have been evaluatedthroughout a year under Dhahrans weather conditions. A com-puter simulation code was developed using EES software. Thissimulation code was validated using available experimental dataand against the results obtained by THERMOFLEX code; the datafor EuroTrough solar collector (ET-100) and for LUZ solar collectorLS-3 have been considered in the simulation. Furthermore. This

cost in which the specic cost per unit aperture area can be

E.M.A. Mokheimer et al. / Energy Conversion and Management 86 (2014) 622633 633cut by about 75%. The specic cost of different mechanical works drops by about48% at 10 hectare and by about 75% at 160 hectare capacity.On the other hand, the specic civil costs remain constant,where these cost items almost remain constant in absolutenumbers, independent of the plant size.

Since the costs of the solar eld depend on the plant size, onlysmall changes can be observed regarding the labor, and the col-lector material, as material cost is the dominant cost fraction inthese areas.

The PTC cost per unit area in the current study demonstrated anexcellent agreement with those results from the others studies.is recommended.

The study demonstrates that the cost declines rapidly when thesolar eld size increases from 10 hectare to 60 hectare, afterthat the cost declination becomes gradual with increasing thesolar eld size. Therefore, it is recommended to consider theuse of parabolic troughs collectors for concentrated solar powerapplications of large scale where the cost per unit area of thesolar eld reaches its minimal values.

Acknowledgment

The support of King Fahd University of Petroleum and Mineralsthrough DSR under grant # FT100022 to carry out this investiga-tion is highly acknowledged. This work has been supported in partby the KFUPM-MIT Research Collaboration Center through grant #R12-CE-10.

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Techno-economic performance analysis of parabolic trough collector in Dhahran, Saudi Arabia1 Introduction2 System description3 Mathematical modelling4 Results and discussion4.1 Validation and performance results4.2 Cost analysis and cost reduction for parabolic trough systems

5 ConclusionsAcknowledgmentReferences