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Renewable Energy 74 (2015) 727e736

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Renewable Energy

journal homepage: www.elsevier .com/locate/renene

Design, manufacture, and test of a prototype for a parabolic troughcollector for industrial process heat

Gianluca Coccia a, *, Giovanni Di Nicola a, Marco Sotte b

a Marche Polytechnic University, Department of Industrial Engineering and Mathematical Sciences, Via Brecce Bianche, 60131 Ancona, Italyb Studio Associato Master Tech, Viale del Lido 15, 63900 Fermo, Italy

a r t i c l e i n f o

Article history:Received 27 March 2014Accepted 29 August 2014Available online 20 September 2014

Keywords:Solar energyFiberglassExtruded polystyreneLow-costThermal efficiencyPTC

* Corresponding author. Tel.: þ39 0712204277; faxE-mail addresses: g.coccia@univpm.it, coccia_gianl

dinicola@univpm.it (G. Di Nicola), marcosotte@gmail.

http://dx.doi.org/10.1016/j.renene.2014.08.0770960-1481/© 2014 Elsevier Ltd. All rights reserved.

a b s t r a c t

The manufacture of low-cost parabolic trough collectors (PTCs) for industrial process heat applicationsranging from 70 to 250 �C is crucial for the widespread availability of this solar technology. Thus, wepresent a prototype of a PTC with a 90� rim angle and a small concentration ratio of 9.25 built infiberglass and extruded polystyrene, called UNIVPM.01. Fiberglass is used as the external shell andextruded polystyrene as the inside fill component. The receiver is an aluminum pipe of circular cross-section, contained within a low-iron glass envelope. The tracking system is based on a solar-positioncomputer program. The main features of this prototype are its cost-effectiveness, low weight, highmechanical resistance, and ease of manufacture. First, we show the design and manufacturing process indetail. Then, we describe the test bench used to evaluate the collector thermal efficiency. Tests wereperformed following the directives of ASHRAE Standard 93-2010 and using demineralized water fortemperatures up to 85 �C. Results show that the equation for thermal efficiency is comparable to that ofother similar collectors available in the literature: the intercept is 0.658 and the slope is �0.683.

© 2014 Elsevier Ltd. All rights reserved.

1. Introduction

In OECD (Organization for Economic Co-operation and Devel-opment) countries, industry accounts for 30% of overall energyconsumption. In EU (European Union) countries, two-thirds of thisconsists of heat rather than electrical energy. Studies confirm thatabout 50% of this industrial heat demand is located at temperaturesof up to 250 �C: in 2000, this energy demand in the EU-15 wasestimated at about 300 TWh [1]. Among solar technologies suitablefor satisfying this heat demand, concentrating solar collectors suchas PTCs (parabolic trough collectors) are one of the most promising.

The development of low-cost PTCs plays a decisive role in thespread of this technology. This objective can be reached only bystudying and testing profoundly innovative prototype designs. Forthis reason, a research program called PTC.project has been startedat the Marche Polytechnic University regarding the development ofPTCs for industrial heat production in the range of 70e250 �C.

The systematic study of PTC design began several decades ago.In his paper of 1976, Treadwell [2] considered how optical andthermal effects influence the efficiency of a PTC. He found that rim

: þ39 0712204770.uca@hotmail.it (G. Coccia), g.com (M. Sotte).

angles of 90� minimize the maximum distance between the para-bolic reflector and the focus. Since the receiver diameter is pro-portional to this distance, thermal losses, which are proportional tothe diameter itself, are reduced.

In a detailed work published in 1992, Thomas and Guven [3]outlined the main structural design requirements for a PTC. A PTCshould: a) provide and maintain the correct optical shape of thereflective surfaces; b) maintain its shape within the specified tol-erances during operations; c) protect the reflective surfaces underextreme weather conditions; d) withstand long-term environ-mental exposure. In other words, the stresses and deflectionsexperienced by the receiver and the reflector must remain belowspecified levels under gravitational, wind, and thermal loads. Onthe other hand, the choice of materials depends on environmentalstability, durability, mechanical and physical properties, suitabilityof the construction method, fitness for high production rates, lowtotal weight, and cost. The authors also state that a sandwichstructure is a good design, but high precision moulds are requiredin order to successfully fabricate high quality PTCs.

In 1994, Kalogirou et al. [4] presented a PTC design with highstiffness-to-weight ratio and a low-labor manufacturing process.The structure is made of polyester resin and woven fiberglass cloth,with plastic conduits that provide reinforcement. In a paper pub-lished the same year [5], the authors outlined an optimization ofthe design based on three parameters: a) collector aperture; b) rim

Table 1Characteristics of the UNIVPM.01 concentrator.

Characteristic Symbol Value

Focal length (m) 0.250Length (m) 2.100Aperture (m) 1.000Mirror length (m) Lc 2.000Mirror aperture (m) 0.925Aperture area (m2) Aa 1.85Total sandwich thickness (m) 0.050Rim angle (�) fr 90

G. Coccia et al. / Renewable Energy 74 (2015) 727e736728

angle; c) receiver diameter. They also proposed a tracking mecha-nism with a control system consisting of three light-dependentresistors.

The EUROTROUGH project [6] carried out in 2001 proposed atorque box designwith lowerweight and less collector deformationthan other designs. This technology presents different advantages:a) the possibility of connecting more collector elements on onedrive, so that their number, in addition to costs and thermal losses,is reduced; b) reducing the torsion and bending increases the op-tical performance and wind resistance. A torque box structure wasalso used by Brooks et al. [7] with a mix of advanced and less so-phisticated technologies to manufacture a reflector made of stain-less steel sheets covered with aluminized acrylic film. This solutiongrants accessibility, accuracy, ease of fabrication, and costreduction.

In 2007, Valan Arasu and Sornakumar [8] presented a simple,low-cost hand lay-up method for manufacturing PTCs based on theprevious work of Kalogirou et al. [4]. The design proposed consistsof a smooth 90� rim angle, reinforced parabolic trough made oflayers of polyester resin and chopped strand fiberglass.

In 2011, Rosado Hau and Escalante Soberanis [9] illustrated theproduction of a water-heating system based on PTC technologylimited to a maximum temperature of 55 �C. The collector pre-sented uses a sheet of polished stainless steel. The receiver is acopper tube coated with a thin black paint, and shielded by a pol-ycarbonate glass; it is not evacuated.

In their work of 2012, Venegas-Reyes et al. [10] described a lightbut robust structure of aluminummade only using hand tools. ThisPTC has a rim angle of 45� and, since it is designed for low-enthalpysteam generation and hot water, it presents an unshielded receiverwithout a glass cover in order to reduce costs. In another workpublished in 2013 [11], the authors presented five PTCs for the samepurpose; three of them have a rim angle of 90� and the other twohave a rim angle of 45�.

The main feature of the PTC prototype presented in this work isthe parabolic support structure: it is a composite of fiberglass (usedas an external shell) and extruded polystyrene (XEPS, as inside fillcomponent). These two materials have been chosen for differentreasons: a) cost; b) weight; c) resistance to atmospheric agents; d)ease of manufacturing. This solution is preferred to the simplefiberglass structure because it offers extremely high structuralperformances and low weight. The prototype has also been testedand has shown a performance similar to different PTCs reported onby other authors.

The present work is organized as follows. Section 2 presents thegeometrical and structural characteristics of the PTC prototype. Wealso describe the manufacturing technique adopted to constructthe collector, the tracking system used and an estimate of the initialcost. In Section 3, we illustrate the methodology and test benchused to carry out experimental investigations. The thermal effi-ciency and other relevant aspects useful in defining the perfor-mance of a PTC are outlined in Section 4. In Section 5.1 we providethe experimental results and a detailed comparison with othercollectors available in the literature. Finally, we discuss the resultsobtained in Section 6.

2. Design and manufacture

Two important factors to be considered in the construction of aPTC are the accuracy of the parabolic shape and the torsionalresistance of the collector [3]. Since PTCs are generally arranged inlines parallel to each other and each line is rotated in the middle,the weight of the collectors and external forces, mainly wind loads,can generate large moments on the section next to the rotatingsystem.

These two key issues are usually solved via different solutions:

� a metallic frame running through each line provides thenecessary torsional rigidity to hold each module at the rightangle;

� an accurate parabolic shape, which is obtained by anchoringsmall (typically 1.5 m2) pre-shaped glass or metal mirrors to theframe.

In the case of a parabolic chord between 4 and 6 m (common inPTC plants for electric power production), this method has severaladvantages: e.g., the movement of small parts rather than bigsections and the possibility of adjusting the position of eachreflective surface with respect to the frame, which is necessary toobtain the desired accuracy on a large parabolic arch. But thisapproach is time consuming and expensive. For smaller chordvalues (0.5e2.5 m), it is useful to adopt a structure that considersboth the parabolic shape and the frame, thus ensuring a very ac-curate parabolic profile and a highly resistant mechanical structure.

For this reason, the present project has led to a PTC prototypecalled UNIVPM.01 realized with a sandwich of fiberglass andextruded polystyrene. The advantage in using a sandwich lies in itsmechanical properties, and fiberglass is a very common componentof such composite materials.

2.1. Design of the PTC prototype

The PTC designed is quite small. It presents a focal length of0.25 m and a rim angle fr of 90�. This particular rim-angle valuewas chosen to minimize slope and tracking errors [2,12].

Other characteristics of the concentrator are reported in Table 1.Since the prototype is to be used for testing, the supports for thereceiver were designed to allow the position of the receiver itself tobe adjusted (both in terms of height and angle with respect to theorigin of the parabola). This was done in order to be able to testdifferent receivers on the same parabolic reflector. The presentstudy makes use of one particular receiver with the geometricalcharacteristics reported in Table 2. The receiver is an aluminumpipe of circular cross-section: the outer surface is painted with ablack high-temperature-resistant paint. It is contained in a low-ironglass envelope (the same glass used for evacuated tube collectors).We used a receiver made of aluminum for the following reasons: itis light, ductile, and easy to be coated with paint. Bending wasavoided because the PTC prototype was tested for temperatures upto 85 �C.

Three teflon rings hold the glass in place on the aluminumreceiver. Small holes were drilled in the rings to allow air circula-tion inside the annulus and prevent condensation on the glass. Aschematic of the receiver is shown in Fig. 1, while the thermal/optical properties of the materials used are provided in Table 3.

With such a receiver, the concentration ratio C, i.e., the ratiobetween the aperture area of the collector Aa and the absorberouter surface Ar, is [14]:

Table 2Characteristics of the UNIVPM.01 receiver.

Characteristic Symbol Value

Inner absorber diameter (m) Dai 0.025Outer absorber diameter (m) Dao 0.030Inner cover diameter (m) 0.046Outer cover diameter (m) 0.048Length (m) 2.100Absorber outer surface area (m2) Ar 0.20

Fig. 1. Schematic of the receiver. Note the RTD (resistance temperature detector)inserted at the far end of the receiver.

Fig. 2. Mould realized with nine pieces of light plastic.

G. Coccia et al. / Renewable Energy 74 (2015) 727e736 729

C ¼ Aa

Ar¼ 1:85

0:20¼ 9:25: (1)

2.2. Manufacture of the fiberglass/XEPS parabola

The parabolic support structure was made with a composite ofextruded polystyrene (XEPS) within a fiberglass shell. The me-chanical and chemical characteristics of fiberglass are well known:this material was used for the first time for the construction of PTCsby Kalogirou et al. [4]. XEPS, however, is not as common in com-posite materials, but it has several advantages: a) it is veryeconomical; b) it is light (its surface density is x200 kg m�2); c) itpresents good mechanical properties. It has a high resistance tocompression from evenly distributed forces, so it is very suitable foruse in a sandwich structure. It is widely used in buildings forthermal insulation and is therefore sold in sheets of variousdimension and thickness. Different varieties of polystyrene areused in construction, but the extruded one presents the best me-chanical properties at a low price (about 2.5 EUR m�2 for 40 mmthick sheets).

The mould for the structure, inspired by the one used fromKalogirou et al. [4], was constructed by joining nine pieces of lightplastic sheets (13 mm thick) that were water-cut on a computer-controlled machine to obtain a very accurate profile, as shown inFig. 2. A stainless steel sheet (0.8 mm thick) was laid on the plastic

Table 3Thermal/optical properties of the elements of UNIVPM.01. Optical properties wereevaluated at normal incidence conditions. Note that, with the exception of specularreflectance rn, other properties were derived from the literature.

Property Symbol Value

Cover transmittance tn 0.93Absorber absorptance an 0.95Foil specular reflectance rn 0.94Absorber conductivity (W m�1 �C�1) la 237

pieces and held in place by two transverse wooden beams screwedto the plastic parts to create a parabolic profile.

For the design of the parabolic support, a 40-mm thick XEPSsheet was cut into small strips. This allows for adoption of a para-bolic shape when all strips are positioned one next to the other onthe mould; the empty spaces were filled with epoxy resin. In twosymmetrical places, two XEPS strips were replaced with aluminumtubes with rectangular cross-section. These tubes are necessary tolink the concentrator to the support and tracking structure andwere firmly attached to the XEPS with four smaller tubes posi-tioned perpendicularly (see Fig. 3).

After the application of a wax polish on all necessary surfaces,the first and second fiberglass and resin layers were applied to thestainless steel parabolic surface. Normal mesh fiberglass tissue wasused: this kind of mesh presents mechanical properties that arebetter defined than those of chopped strand fiberglass, so it isgenerally preferred for thin layers, although it is more expensive.While the compound was still liquid, all the XEPS strips andaluminum frame pieces were arranged in place. All remainingsurfaces were then covered with two layers of resin and fiberglass;it was carefully ensured that the resin penetrated well between theXEPS pieces.

When the application of the resin was finished, the upper sur-face was covered with a plastic sheet and three straps wereattached to it. Both the sheet and straps were screwed down to thesupports to ensure perfect adhesion of the new structure to themould. Once dry, the structure was removed from the mould and ahighly reflective aluminum foil (MIRO-SUN Weatherproof Reflec-tive 90 [15]) was glued to the concave surface to create a parabolicreflective surface. The reflective foil consists of anodized aluminumwith a specially coated surface on one side studied for outdoor solar

Fig. 3. Parabolic profile equipped with two aluminum, rectangular-cross-section tubes.

Fig. 5. A picture of the motor, worm drives, and drive belt used in the tracking system.

G. Coccia et al. / Renewable Energy 74 (2015) 727e736730

applications that require high reflectance and resistance to atmo-spheric agents. The use of a replaceable foil allows for certainflexibility in the use of the collector.

The weight of the concentrator is approximately 12 kg. A three-dimensional representation of the prototype UNIVPM.01 providedwith the support structure is shown in Fig. 4.

2.3. Tracking system

The tracking system is composed of five elements:

1. an asynchronous three-phase motor (0.18 kW power, 1320 RPMspeed) with 4/8 poles;

2. an inverter that allows the motor speed to be regulated;3. three worm drives with gear ratios of 1/60, 1/60, and 1/35;4. a belt drive with a transmission ratio of approximately 1/5 that

couples the last worm gear to the PTC axis;5. a 5000 position-per-revolution encoder, coupled to the rotation

axis of the collector.

A picture representing themotor, theworm drives, and the drivebelt is shown in Fig. 5. The motor was attached to the supportstructure via four bolts and two plates. This allowed to regulate theheight of the motor with respect to the ground and to set thecorrect tension of the belt drive. The presence of the worm driveswas necessary in order to reduce the maximum rotational speed ofthe collector: in fact, the motor was too fast and the transmissionratio of the belt drive too small to guarantee a correct tracking ofthe sun. The belt drive also acts as a clutch to prevent torques thatare too high from being transmitted from the PTC to the trackingsystem.

The use of a common industrial asynchronous motor and a gearreduction system is a solution that can easily be scaled up. The ideais to rotate an entire line with just one motor, for this reason, it isnecessary to adopt a solution that can be adapted to produce a largetorque on the final axis. Other solutions, such as stepper motors areeasier to adapt to smaller systems, but become very expensivewhen a relevant torque has to be produced. Additionally, the non-reversibility of motion in worm drives is an advantage because itallows the system to be kept in position without powering themotor.

The encoder and the inverter communicate with a PC throughappropriate electronics. A diagram of the electronic signals isshown in Fig. 6. A solar-position routine based on Michalsky's al-gorithm [16] was implemented in LabVIEW to calculate the correct

Fig. 4. The PTC prototype UNIVPM.01.

rotational speed to be given the PTC at any instant. The date andtime inputs are imported into LabVIEW from the PC operativesystem. The routine elaborates the desired position for the collector,b, with a time-step of 1 s. Even though experimental tests werecarried out with the axis of the collector oriented in the EW(EasteWest) direction (see Section 5.1), the tracking system is able

Fig. 6. Data flow schematic of the electronic signals.

Fig. 7. Flow chart of the tracking mechanism.

Table 4Initial cost of the prototype comparedwith similar PTCs presented in literature. Notethat the costs of the elements of other PTCs were aggregated differently with respectof the original references.

Item UNIVPM.01 [11](PTC90)

[11](PTC45)

[10] [8]

EUR USD USD USD INR

Mould 104.00 233.00 206.00 379.00Wax polish 3.00XEPS 15.00Fiberglass 37.00 2200Epoxy resin 31.00Reflective foil 45.00 52.00 52.00 110.00 3000Support structure 47.00 105.00 170.00 302.00 4000Glass cover 28.00Absorber 24.00 17.00 17.00 35.00 800Tracking system 128.00 164.00 7000Miscellaneous 15.00 40.00 40.00 50.00 5000

Total 477.00 447.00 485.00 1040.00 22 000Cost per m2 258.00 172.32 167.47 179.53 22 000Cost per m2 (þlabor) 383.00 182.10Cost per m2 (þmarkup) 441.00

G. Coccia et al. / Renewable Energy 74 (2015) 727e736 731

to follow the sun with the PTC oriented in two different directions;e.g., when the PTC axis has an EW orientation, the desired positionis given by [14]:

tan b ¼ tan qzjcos gsj: (2)

Instead, when the PTC axis has a NS (NortheSouth) orientation,the desired position can be obtained by [14]:

tan b ¼ tan qzjcosðgPTC � gsÞj: (3)

In Eqs. (2) and (3), qz is the zenith angle, gs is the solar azimuthangle, and gPTC is the PTC axis azimuth angle.

At the instant t, the correct value for the angular speed to trackthe sun, u, is:

u ¼ btþDt � bt

Dt; (4)

where Dt ¼ 1 s. It is worth noting that the angular speed u has aminimum equal to 4.7 � 10�5 rad s�1 and a maximum equal to1.7 � 10�4 rad s�1 throughout a year: in the present case, for a PTCaxis with NS orientation and situated in Ancona, Italy (latitude43.5867 N, longitude 13.5150 E), the minimum and the maximumspeed occur, respectively, during the sunrise (or sunset) of summersolstice and during the solar noon of winter solstice. The rotationalspeed of the collector can be adjusted at the minimum andmaximum speed via both on the double speed control of the motorand on the inverter: in particular, when 8 poles of the motor arepowered and the inverter frequency is set tox23 Hz, the minimumspeed is obtained. Alternatively, when 4 poles are powered and afrequency of x40 Hz is set, the PTC axis rotates at the maximumspeed. All these settings were automatized in the solar-positionroutine.

The proposed tracking mechanism would be correct only for anideal collector that was always in focus. In reality, the collector canbe misaligned during normal working conditions, or at the start.Thus, for each time step the calculated value of b is used as an inputfor the motor control system: this compares the desired position, b,with the current position read on the encoder, bexp. If we introducea tolerance position error equal to the resolution of the encoder:

Db ¼ 3605000

¼ 0:072+; (5)

three cases are possible (see the flow chart of Fig. 7):

� if b < bexp � Db, the motor is slowed down to the minimumspeed in order to regain focus;

� if b<��bexp � Db

��, the collector is in focus and the trackingmechanism previously described is adopted;

� if b > bexp þ Db, then the motor is accelerated to the maximumspeed to regain focus.

In addition, the LabVIEW environment allows to manually: a)turn on and off the motor; b) set the appropriate degree of rotation;c) give a user-defined rotational speed (see Fig. 6). A soft start wasalso included in the inverter to avoid damage to the motor or gears.

Computing the solar position has some advantages with respectto systems that move the PTC based on a feedback signal: there isno disturbance due to clouds or sky shading and a high precisioncan be reached. But there are also some disadvantages: a posi-tioning error in the PTC axis (not pointing due north or east) orsmall misalignments or imperfections in the geometry can producetracking errors.

2.4. Costs

A summary of the initial cost, compared with that of similarPTCs presented in literature, is provided in Table 4. The mould isone of the most expensive item because high precision is requiredfor this element in order to obtain an accurate parabolic profile.From an industrial point of view, however, this cost can beamortized by considering that several collectors can be manu-factured with a single mould. On the other hand, XEPS is veryeconomical. Taking into account the price of the mould, the totalcost necessary to realize the PTC prototype is 477 EUR. Consideringan aperture area Aa of 1.85 m2, the cost per m2 of reflecting surfaceis 258 EUR.

Labor costs for constructing the prototype were added in Table 4to the final price and are equal to 125 EURm�2. Note that this cost isreasonable for a minimum of 100 m2 aperture-area production. Inthis way, the total cost is 383 EUR m�2. The profit for the manu-facturer should be also taken into account to have a more realisticpicture of the total cost of the PTC: therefore, we considered areasonable percentage markup of 0.15% which gives a final cost of441 EUR m�2.

G. Coccia et al. / Renewable Energy 74 (2015) 727e736732

3. Testing loop and methodology

Outdoor tests were performed in Ancona, Italy (latitude43.5867 N, longitude 13.5150 E) and the ASHRAE (American Societyof Heating, Refrigerating and Air-Conditioning Engineers) Standard93-2010 [17] was adopted as a reference. In order to define thethermal efficiency of the PTC, the following quantities need to bemeasured: mass flow rate _m, inlet (Tfi) and outlet (Tfo) fluid tem-perature, and direct normal irradiance DNI. The specific heat atconstant pressure of the working fluid cp and aperture area Aa mustalso be calculated.

The test bench is composed of two parts: the hydraulic circuitand the signal acquisition and calculation system.

3.1. Hydraulic circuit

The hydraulic system used for the tests is composed of just afew elements. The heat transfer fluid is demineralized water atatmospheric pressure, which is forced into the PTC by a pump. Apin valve regulates the desired flow into the collector system. Tomore finely adjust the mass flow and to reduce the nominal flowrate of the pump, which was larger than necessary, a by-passprovided with a gate valve was installed, as outlined in Fig. 8.In this way, the flow rate through the pump could be maintainedwhile adjusting the rate through the PTC. Additionally, since theflow rate on the by-pass was very large, a certain recirculation ofthe fluid in the storage tank was obtained to prevent stratificationof the liquid.

The mass flow rate _mwas chosen to be 0.045 kg s�1, thus a littlelarger than the value suggested by the ASHRAE Standard for liquidheat transfer fluids (0.037 kg s�1 for the adopted collector aperturearea). However, this choice does not represent a problem and isonly due to the fact that a turbulent flow in the chosen absorber isdesired.

No cooling system is present in the circuit. To overcome thisabsence, a very large storage tank (x300 L) was adopted. In thisway, the increase in system temperature during each acquisition isso small that it can be neglected. In the most sunny conditions itwas measured to be less than 0.02 �C min�1. Since the length ofeach acquisition was about 5 min, the maximum variation in inlet

Fig. 8. Hydraulic circuit.

temperature during a single acquisition was about 0.1 �C. Themaximum operating temperature for the system is about 85 �C,mainly due to restrictions on the materials' maximumtemperature.

3.2. Instruments and computational procedure

The remaining part of the test loop consists of the signalacquisition and calculation system. Fig. 6 shows a schematic of thedata flow through the instrumentation. Four temperatures, windvelocity, and two values of direct normal irradiance DNI aremeasured. Themass flow rate _m is acquired only at the beginning ofeach measurement and is manually inserted into the calculationsystem.

The temperatures measured are: the ambient temperatureTamb, the temperature in the tank close to the inlet of the pumpTtank, and the temperature of the heat transfer fluid at the inlet (Tfi)and the outlet (Tfo) of the receiver. The first two temperatures aremeasured with T-type thermocouples, while the temperatures ofthe fluid entering and exiting the receiver are measured using AAClass RTDs (resistance temperature detectors). In this way, anaccuracy of about 0.8 �C is obtained for the range of measuredtemperatures.

An Agilent 34970A data-acquisition unit [18] was used for alldata acquisition and for thermocouple compensation. The twoRTDs for measuring inlet and outlet temperature were inserted inthe double end of the receiver, as shown in Fig. 1.

DNI was measured using two first-class [19] normal-incidencepyrheliometers (NIPs) mounted on solar trackers [20]. The calcu-lation system uses the average of the signals produced by the twoinstruments.

4. Thermal and optical analysis

The thermal efficiency of a PTC, h, is defined as the ratio of usefulenergy delivered to the heat transfer fluid to the energy collectedfrom the aperture area of the collector. It is a function of the opticalperformance of the PTC and the amount of thermal losses.

When the angle of incidence, q, defined as the angle betweenthe Sun's rays and the normal to the aperture area of the collector, isx0 (i.e., when solar rays are nearly parallel to the normal), theanalytic expression relating the parameters mentioned above is (asderived from Kalogirou [12]):

h ¼_mcp

�Tfo � Tfi

�DNIAa

¼ FR

�ho;n � UL

C

�Tfi � Tamb

DNI

��: (6)

While the first ratio in Eq. (6) derives directly from the definitionof thermal efficiency and includes experimentally measurablequantities, the second expression can be obtained by carrying outan energy balance calculation for the receiver. In the secondexpression, ho,n is the optical efficiency of the collector at normalincidence, defined as the ratio of solar radiation reaching theabsorber to the energy collected from the aperture area. It can beexpressed as (adapted from the ASHRAE Standard 93-2010 [17])

ho;n ¼ ½ðtaÞrg�n�1� Af ;n

�; (7)

where:

� (ta) is the transmittanceeabsorptance product;� r is the specular reflectance of the parabolic mirror;� g is the intercept factor, the fraction of reflected energy that isdirected towards the receiver [21];

Fig. 9. Experimental results and fit of the thermal efficiency of UNIVPM.01. R2 is thecoefficient of determination.

G. Coccia et al. / Renewable Energy 74 (2015) 727e736 733

� Af is the ratio of ineffective area due to geometrical effects [13](e.g., shading due to blockages and the receiver, and solar raysreflected from the mirror past the end of the receiver) to thewhole aperture area of the collector.

The heat removal factor FR and the overall loss coefficient ULdepend on heat losses and are independent of the angle ofincidence. In particular, heat loss from the collector is relatedto [22]:

� the collector geometry and materials;� working conditions (inlet fluid temperature Tfi, mass flow rate

_m, thermophysical properties of the heat transfer fluid);� environmental conditions (ambient temperature Tamb, windvelocity, relative humidity, direct normal irradiance DNI).

Experimental investigations show that, if thermal efficiency h isplotted against the operative term (Tfi � Tamb)/DNI, the data arerelated linearly. Thus, the expression on the right-hand side of Eq.(6) can be considered as a straight line, with intercept a and slope bdefined as follows:

� a ¼ FRho,n;� b ¼ �(FRUL)/C.

Actually, the thermal efficiency of a PTC is generally given in theform of a linear equation. If we define the operative termT* ¼ (Tfi � Tamb)/DNI, we can write

h ¼ aþ bT*: (8)

We will now show a method derived in a previous paper by theauthors [22] in which experimental data is used to estimate theoptical efficiency ho,n and the intercept factor gn at normal inci-dence conditions, i.e., when q x 0. Let us consider the system ofthree equations of variables FR, UL, and F' (see Duffie and Beckman[14] for further details, and note that we have indicated with la thethermal conductivity of the absorber pipe):

8>>>>>>><>>>>>>>:

b ¼ �ðFRULÞ=C

FR ¼ _mcpArUL

�1� exp

�� ArULF

0

_mcp

��

F 0 ¼ 1=UL

1=UL þ Dao

.�hf Dai

�þ DaolnðDao=DaiÞ=ð2laÞ

:

(9)

In order to solve this system of equations to obtain a more usefulexpression for FR, the experimental value b, geometrical (C, Ar, Dai,Dao), process ( _m, cp), and material (la) parameters have to bedetermined. The convective heat transfer coefficient between theabsorber and the fluid hf must be calculated. In this way, bysubstituting the expressions for b and F0 in the expression of FR, wefind that

FR ¼ bC

26664 Ar

_mcpln�1þ ArbC

_mcp

�þ Dao

hfDaiþ Dao

2laln�Dao

Dai

�37775: (10)

Once FR has been determined, the optical efficiency at normalincidence ho,n may be obtained from the expression of the interceptvalue a. If we then consider that for qx 0 the contribution of Af,n isonly due to the shading of the receiver on the collector, the inter-cept factor at normal incidence gn may be calculated from Eq. (7)when the tn, an, and rn are known.

5. Results

5.1. Thermal efficiency

Fig. 9 shows experimental thermal-efficiency data fromUNIVPM.01 for various combinations of inlet fluid temperature,ambient temperature, and direct normal irradiance. Tests wereconducted during clear sky and near-normal incident conditions,with the PTC axis oriented in the EW direction. By fitting theexperimental data, the following equation for the straight linerepresenting the thermal efficiency was determined:

h ¼ 0:658� 0:683 T*: (11)

Eq. (11) is shown in Fig. 9 along with the experimental data.Comparisonwith efficiency expressions, derived from the literaturefor collectors equipped with shielded receivers reveals a slope thatis higher than average (see Table 5). This can be justified by thedifferent concentration ratios employed for the collectors tested. Infact, if we consider the�bC product reported in Table 5, we find outthat the value assumed by UNIVPM.01 is low. In general, theparameter �bC represents a good way to estimate the thermallosses of a PTC when FR, and therefore UL, are not available.

From the intercept a and the slope b we may gain insightregarding the optical efficiency ho,n and the intercept factor gn atnormal incidence, as seen in Section 4. In the turbulent regime, theconvective heat transfer coefficient between the absorber and thefluid can be evaluated by considering the Gnielinski [26] correlationfor the Nusselt number:

hf ¼lfDai

Nu ¼ lfDai

"ðf =8ÞðRe� 1000ÞPr

1þ 12:7ðf =8Þ1=2Pr2=3 � 1#; (12)

valid for 0.5 � Pr� 2 � 103 and 3 � 103 < Re < 5 �106. In Eq. (12), lfis the thermal conductivity of the heat transfer fluid, Re is theReynolds number, Pr is the Prandtl number, and f is the coefficientof friction, which can be calculated from the Colebrook equation[27]. Considering liquid water as the heat transfer fluid, we haveused amodel based on the IAPWS (International Association for theProperties of Water and Steam) industrial formulation [28] tocalculate hf ¼ 637 W m�2 �C�1. Thus, Eq. (10) yields FR ¼ 0.985 andfrom the definition of the intercept a, we get:

ho;n ¼ aFR

¼ 0:668: (13)

Table 5Comparison of different PTC parameters. The symbol (�) indicates that the receiver considered is unshielded.

Reference Year a �b (W m�2 �C�1) C �bC fr (�) ho,n gn tn an rn FR UL (W m�2 �C�1)

UNIVPM.01 2014 0.658 0.683 9.25 6.32 90 0.668 0.829 0.93 0.95 0.94 0.985 6.42[11] (PTC90) 2013 0.613 2.302 13.3 30.62 90 0.70 0.84 e 0.90 0.92 0.88 34.98[11] (PTC45) 2013 0.351 2.117 14.9 31.54 45 0.48 0.58 e 0.90 0.92 0.73 43.09[10] 2012 0.561 2.047 14.87 30.44 45 0.60 0.665 e 0.95 0.95 0.94 32.56[9] 2011 0.054 0.189 38.84 7.32 65.56 n.a. n.a. 0.95 0.95 0.59 n.a. n.a.[8] 2007 0.69 0.39 19.89 7.76 90 0.694 0.879 0.9 0.9 0.97 0.99 7.79[7] (shielded) 2005 0.538 1.059 16.7 17.69 82.2 0.553 0.823 0.92 0.88 0.83 0.97 18.23[7] (unshielded) 2005 0.552 2.009 16.7 33.55 82.2 0.601 0.823 e 0.88 0.83 0.92 36.47[23] 1996 0.638 0.387 21.2 8.20 90 0.647 0.94 0.90 0.90 0.85 0.99 8.29[5] 1994 0.642 0.441 21.2 9.36 90 0.648 0.98 n.a. n.a. n.a. 0.99 9.44[24] 1984 0.65 0.382 n.a. n.a. n.a. n.a. n.a. n.a. n.a. n.a. n.a. n.a.[25] 1982 0.66 0.233 16.42 3.83 90 n.a. n.a. 0.9 0.94 0.78 n.a. n.a.

G. Coccia et al. / Renewable Energy 74 (2015) 727e736734

Finally, if we consider shading on the collector aperture area dueto the presence of the receiver, Af,n ¼ (DaoLc)/Aa¼ 0.03, and from Eq.(6) and the optical properties of the materials provided in Table 3,we obtain:

gn ¼ ho;n

½ðtaÞr�n�1� Af ;n

� ¼ 0:829: (14)

5.2. Incident angle modifier

The optical efficiency in Eq. (7) is independent of the angle ofincidence but, in reality, it strongly depends on this quantity. Sinceho is difficult to be described analytically and measured for off-normal incidence angles, a factor called incident angle modifier,Kta, is usually provided to take into account the effect of the angle ofincidence. The incidence angle modifier is given by [17]:

Kta ¼ðtaÞrg

�1� Af

�½ðtaÞrg�n

�1� Af ;n

� ¼ hoho;n

: (15)

For the PTC prototype presented in this work, the incident anglemodifier was obtained according to the ASHRAE Standard 93-2010.Fig. 10 shows the incident angle modifier data points plottedagainst the angle of incidence; the regression curve is also pro-vided. It is possible to note that Kta decreases rather rapidly with q:this can be explained by considering that the receiver is not longerthan the concentrator (see Section 2.1). Therefore, end effects [13]are relevant for higher angles of incidence, and the optical effi-ciency is consequently reduced.

Fig. 10. Incident angle modifier curve of UNIVPM.01.

The regression curve depicted in Fig. 10 is a third order poly-nomial equal to (q is expressed in degrees):

Kta ¼ 1:00082� 4:52462� 10�3 qþ 9:99349� 10�5 q2

� 2:17541� 10�6 q3: (16)

5.3. Wind load

Outdoor tests carried out over more than a year have shown thatthe prototype is able to operate in average wind speeds of 15 m s�1,a condition that satisfies the design requirements of the SandiaLaboratory (as reported in Thomas and Guven [3]). In addition, theprototype was tested adding weights that correspond to the loadapplied by a wind speed of 15 m s�1, 30 m s�1, and 45 m s�1. Asimilar method was used by Kalogirou et al. [4]. Table 6 reports thecorresponding deflections measured at the center of the concen-trator with a dial gage. For a load equivalent to a wind speed of45 m s�1, the maximum deflection is 2.3 mm, which can beconsidered acceptable.

5.4. Error analysis

The estimation of the error in the measure of the thermal effi-ciency requires an analysis of the propagation of uncertainty. If weconsider the experimental expression of the thermal efficiency (thefirst ratio in Eq. (6)), the corresponding expanded uncertainty, uh, isin first approximation given by [29]:

uhh

¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi�u _m

_m

�2þ�ucpcp

�2þ�uDTDT

�2þ�uDNIDNI

�2þ�uAa

Aa

�2;

s(17)

where the ui are the expanded uncertainties of each measuredquantity (note thatDT¼ Tfo� Tfi).When the central limit theorem isapplicable, the distribution of probability obtained with Eq. (17) isGaussian even if not all the input quantities have the same distri-bution [29].

The expressions and the values used to calculate the ui are re-ported in Table 7. Note that, with the exception of the aperture area,all the expanded uncertainties are provided as Gaussian distribu-tions with confidence intervals of 95%; with this assumption, one

Table 6Deflections measured at the center of the concentrator with weightscorresponding to different wind speeds.

Wind speed (m s�1) Deflection (mm)

15 0.330 1.045 2.3

Table 7Expanded uncertainties of the quantities that influence the thermal efficiency.

Uncertainty Expression Distribution

u _m (kg s�1) ±0.00063 Gaussianucp (J kg�1 �C�1) See Section 5.4 GaussianuDT (�C) ±(0.20 þ 0.0017(Tfi þ Tfo)) GaussianuDNI (W m�2) ±0.030DNI GaussianuAa

(m2) ±0.00084 Uniform

uh,max ±0.059 Gaussianuh,m ±0.051 Gaussian

G. Coccia et al. / Renewable Energy 74 (2015) 727e736 735

can demonstrate that uh also represents a confidence level of 95%[29]. In Table 7, uh,max is the maximum expanded uncertaintycalculated for h, while uh,m is the mean expanded uncertainty.

It is worth noting that cp was calculated with IAPWS industrialformulation [28] as a function of the mean temperatureTm ¼ (Tfi þ Tfo)/2. Therefore, ucp was obtained by [29]:

ucp ¼vcpvTm

uTm ; (18)

where uTm ¼ uDT .Finally, error bars for h were plotted in Fig. 9. It is possible to

observe that the error is greater when T* increases: this is due to thetemperature error that, as reported in Table 7, is a linear function ofthe temperature itself.

6. Conclusions

Although a concentration ratio of 9.25 is quite small, tests showthat the thermal efficiency is comparable with that of other similarcollectors available in the literature. The slope of the linearthermal-efficiency equation, which can be associated with thermallosses and is equal to �0.683, is low when released from the con-centration ratio term: this means that the receiver has been welldesigned and built. On the other hand, the intercept value (equal to0.658 and representative of the optical performance) is one of thebest available in the literature. One of the main features ofUNIVPM.01 is its low weight. But this aspect must not be inter-preted as a possible source of structural issues: in fact, the proto-type has shown good resistance properties throughout the one-year period of experimental tests. The prototype has confirmedthat the manufacturing process is reliable and the design is func-tional for industrial process heat applications; therefore, we believethat themethod presented in this work could be used to design andmanufacture small, low-cost, and high-performance parabolictrough collectors. However, wewill work on a prototypewith largerconcentration ratio in order to validate the proposedmanufacturing process and design.

Acknowledgments

We wish to thank Dr. Tommaso Recanatini and Dr. MichelePanni for their contributions to the present work.

Nomenclature

Latin symbolsAa aperture area (m2)Af ratio of ineffective area to the total aperture areaAr absorber outer surface area (m2)a intercept of the linear fit of thermal efficiencyb slope of the linear fit of thermal efficiency (W m�2 �C�1)

C concentration ratiocp specific heat at constant pressure (J kg�1 �C�1)Dai inner absorber diameter (m)Dao outer absorber diameter (m)DNI direct normal irradiance (W m�2)F0 collector efficiency factorFR heat removal factorf coefficient of frictionhf convective heat transfer coefficient of the fluid

(W m�2 �C�1)Lc mirror length (m)Kta incident angle modifier_m mass flow rate (kg s�1)Nu Nusselt numberPr Prandtl numberRe Reynolds numberR2 coefficient of determinationTamb ambient temperature (�C)Tfi inlet fluid temperature (�C)Tfo outlet fluid temperature (�C)Tm mean fluid temperature (�C)Ttank temperature in the storage tank (�C)T* independent variable of the linear fit of thermal efficiency

(�C W�1 m2)DT temperature difference between inlet and outlet (�C)t time (s)UL overall loss coefficient (W m�2 �C�1)u expanded uncertainty

Greek symbolsa absorptance of the absorberb desired slope angle of the collector (�)bexp current slope angle of the collector (�)Db tolerance angular position error (�)g intercept factorgPTC collector axis azimuth angle (�)gs solar azimuth angle (�)h thermal efficiencyho optical efficiencyq angle of incidence (�)qz Zenith angle (�)la thermal conductivity of the absorber (W m�1 �C�1)lf thermal conductivity of the fluid (W m�1 �C�1)r specular reflectance of the mirrort transmittance of the cover(ta) transmittanceeabsorptance productfr rim angle (�)u tracking angular speed (rad s�1)

AcronymsASHRAE American Society of Heating, Refrigerating and Air-

Conditioning EngineersEU European UnionEW EasteWestEUR EuroXEPS extruded polystyreneIAPWS International Association for the Properties of Water and

SteamINR Indian RupeeNIP normal incidence pyrheliometerNS NortheSouthOECD Organization for Economic Co-operation and

DevelopmentPTC parabolic trough collectorRTD resistance temperature detector

G. Coccia et al. / Renewable Energy 74 (2015) 727e736736

UNIVPM Marche Polytechnic UniversityUSD United States Dollar

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