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Solar Energy 86 (2012) 1053–1062

Conical receiver for a paraboloidal concentrator with large rim angle

Nestor Hernandez a, David Riveros-Rosas b, Eduardo Venegas a, Ruben J. Dorantes c,Armando Rojas-Morın d, O.A. Jaramillo a, Camilo A. Arancibia-Bulnes a,⇑,1,

Claudio A. Estrada a

a Centro de Investigacion en Energıa, Universidad Nacional Autonoma de Mexico, Privada de Xochicalco S/N, A.P. 34, Temixco, 62580 Morelos, Mexicob Instituto de Geofısica, Universidad Nacional Autonoma de Mexico, Ciudad Universitaria, Col. Copilco, Coyoacan, 04510 D.F., Mexico

c Departamento de Energıa, Universidad Autonoma Metropolitana – Azcapotzalco, Av. San Pablo No. 180, Col. Reynosa Tamaulipas, 02200 D.F., Mexicod Facultad de Ingenierıa, Universidad Nacional Autonoma de Mexico, Ciudad Universitaria, Col. Copilco, Coyoacan, 04510 D.F., Mexico

Available online 7 October 2011

Communicated by: Associate Editor C. Estrada-Gasca

Abstract

The design and optimization of novel type of receiver for a paraboloidal concentrator with 90� rim angle is carried out by means ofdetailed ray tracing simulations. Cylindrical, conical, and spherical geometries are compared and their dimensions optimized. The chosendesign is based on a conical cavity, which differs from similar receivers developed for concentrators with smaller rim angles. In particular,the receiver is able to catch concentrated solar energy both on its outer side and on the inner walls. Water flows inside the receiver alongthe conical geometry, in a double layer configuration. The receiver was built and implemented in a 90� rim angle paraboloidal concen-trator. Thermal efficiency of the system is evaluated for different flow rates and inlet temperatures, both in stationary and in transientregimes, and results for fluid temperatures are compared with the results predicted by a thermal model. The time constant is evaluated.� 2011 Elsevier Ltd. All rights reserved.

Keywords: Solar concentrator; Paraboloidal concentrator; Conical receiver; Cavity receiver

1. Introduction

The starting point for the present work was the reusing ofan old microwave telecommunication antenna as a solarconcentrator (Jimenez Magana et al., 1997). The antennahas a paraboloidal shape made in aluminum and this pre-sents a continuous reflective surface, two characteristics thatare interesting from the point of view of solar concentration.Therefore, the possibility of adapting this kind of antennasto produce industrial process heat was investigated.

The antenna was mechanically polished to obtain ahighly reflective surface, and an optical characterizationwas carried out, obtaining an average reflectance of 0.8

0038-092X/$ - see front matter � 2011 Elsevier Ltd. All rights reserved.

doi:10.1016/j.solener.2011.09.008

⇑ Corresponding author. Tel./fax: +52 55 56229791.E-mail address: caab@cie.unam.mx (C.A. Arancibia-Bulnes).

1 On sabatical leave at Departamento de Ingenierıa Quımica y Meta-lurgia, Universidad de Sonora.

in the visible range, and of 0.9 in the infrared up to a3000 nm wavelength.

The antenna, with aperture diameter of 3.32 m and focallength of 0.83 m, has rim angle /r equal to 90�; i.e., the cir-cular rim of the paraboloidal dish and the focal point arelocated in the same plane (see Fig. 1). This concentratorwas called COSPAA-90 (for the Spanish acronym of “90�Rim Angle Paraboloidal Solar Concentrator”). The aboveconfiguration is rather uncommon in dish concentrators,where usually the rim angles are closer to 45�.

In fact, rim angle of 45� is the theoretical optimum thatgives the maximum concentration ratio for ideal parabo-loids with flat receivers, although the actual value varieswith the specific concentrator characteristics, like numberof facets and facet error (Riveros-Rosas et al., 2011). Forreceivers with other geometries the optimal rim angle isnot necessarily close to 45�. However, such small rimangles allow using cavity receivers, which considerably

Nomenclature

Aa aperture area of the concentrator (m2)Ar surface area of the receiver (m2)C geometrical concentration factorCp specific heat of the fluid (J kg�1 K�1)FR receiver heat removal factorF0 collector efficiency factorGb irradiance of beam solar radiation (W m�2)ge length of the generatrix of the cone (m)hwi convection coefficient of the wall (W m�2 K�1)k thermal conductivity of receiver material

(W m�1 K�1)_m water mass flow rate (kg s�1)Qu useful heat (kW)qr radial heat flux (W/m2)Ri internal radius of the receiver cone (m)Re external radius of receiver cone (m)Rter thermal resistance of the receiver (W�1 m2 K)Ta ambient temperature (K)Ti fluid inlet temperature (K)To fluid outlet temperature (K)

T average surface temperature of the receiver (K)UL receiver global heat loss coefficient (W m�1 K�1)(UA)s thermo-tank heat loss coefficient (W K�1)

Acronyms

COSPAA-90 90� Rim Angle Paraboloidal SolarConcentrator (in Spanish)

Greek Symbols

a absorptance of the receiver surfacec intercept factor of the receiver/r concentrator rim angle (�)gi global thermal efficiency of the concentrator-

receiver systemq reflectance of the concentratorr Stefan–Boltzman constantre standard deviation of the angular optical error

(mrad)

1054 N. Hernandez et al. / Solar Energy 86 (2012) 1053–1062

reduce optical and thermal losses to the surroundings(Harris and Lenz, 1985; Perez-Rabago et al., 2006). Inthe present situation, for a 90� rim angle, a cavity receiverwould miss a lot of the radiation concentrated by the out-ermost part of the paraboloid. Actually, this part of theparaboloidal surface, located between 45� and 90� fromthe focal axis, is the segment with the largest collection area(five times more than the segment between 0� and 45�), andtherefore, with the largest contribution in terms of energy.Therefore, it becomes evident that a different type of recei-ver should be designed for this paraboloid.

A paraboloidal concentrator with 90� rim angle was alsostudied by Schmidt et al. (1983), in the context of the develop-ment of a 10 kW point focus solar plant in Kuwait. Theycompared different plant configurations based on heating tol-uene or water to produce power in a turbine system. Theauthors argued that values of rim angle between 90� and110� maximized the amount of collected energy per unit areaof reflective surface, and they designed a spherical receiver tocollect radiation on its outer surface. Actually, for a sphericalreceiver the concentration ratio is maximal for 90� rim angles.

Kaushika and Reddy (2000) studied a 65� rim angle dishfor heat production, and found that a conventional cavity

Focus Rim

Focal axis

Apex

φ

Fig. 1. Scheme of the paraboloidal concentrator showing the rim angle.

design was not adequate. They studied theoretically geom-etries like spherical cavity, modified cavity, and semi cavity,and concluded that the modified cavity was best suited fortheir purposes (Kaushika, 1993). All the studied receiverswere based on spherical geometries.

In spite of the disadvantages of the cavity design for awide rim angle concentrator, it is still attractive due tothe associated reduction in thermal losses. Therefore, inthe present study the receiver design still involves a cavity.However, the idea is to have a cavity with the ability to col-lect radiation both on its inner and outer surfaces.

Several receiver geometries were tested by means of raytracing (Estrada et al., 2000). These included truncatedspheres, cylinders, cones, and different combinations of sec-tions of all these types of geometries. These types of geom-etries were previously studied using ray tracing by Harrisand Lenz (1985), for dishes with smaller rim angles. Dueto those small angles, the possibility of radiation impingingon the external walls of the cavity was not considered,assuming that they were well insulated instead. Morerecently, Shuai et al. (2008) have also analyzed paraboloi-dal concentrators coupled to cavity receiver of differentgeometries by means of reverse Monte Carlo ray tracing,but also, for small rim angles.

2. Design of the receiver

2.1. Determination of focal region size

For the design of the receiver it was first necessary todetermine the dimensions of the focal region of the concen-trator. Due to the fact that off axis rays are not focused in

N. Hernandez et al. / Solar Energy 86 (2012) 1053–1062 1055

the same spot as normally incident rays, this focal region isa volumetric one of ellipsoidal shape.

The size of the focal region was determined by measur-ing the lengths of the three principal axes of this ellipsoid.Two steel wires were attached to the rim of the paraboloidand stretched along two mutually perpendicular diametersof the circular aperture. A steel rod was made to pass fromthe vertex to the focus of the paraboloid, i.e., along theoptical axis of the system. It was therefore perpendicularto the two wires, forming with them a system of threeorthogonal axes along which the dimensions of the ellip-soid were measured. Because of the 90� rim angle, the inter-ception of the three axes in the aperture plane coincideswith the nominal focus.

The following results were obtained for the lengths ofthe three principal axes of the ellipsoid: 8.9 and 8.4 cmalong the two wires, and 10 cm along the optical axis(rod). In this latter case the illuminated area is not symmet-rical with respect to the nominal focus; it measures 5.5 cmtowards the vertex and 4.5 cm in the opposite direction.The uncertainty in the determination of all of these quan-tities was 0.2 cm.

Next, the optical error associated with the concentratorwas determined. To this end, the experimental results werereproduced by means of ray tracing simulations, by usingthe surface error as a free fitting parameter. The simula-tions were carried out with the ray trace code CIRCE2(Romero, 1994), which is a software based on the well-established convolution method (Biggs and Vittitoe,1979). In this technique, both the solar angular distribution(sun shape) and the reflection error distribution of the opti-cal system are taken into account. A numerical 2D convo-lution of the sun shape with the error distribution is carriedout. It is conventionally assumed that the error has aGaussian distribution, where the global optical error is

Fig. 2. Receive

the standard deviation. From this convolution, thedegraded sun distribution, also called effective source, isobtained (Biggs and Vittitoe, 1979; Rabl, 1985; Vant-Hull,1991). This distribution is used as an effective solar cone inthe ray tracing. Moreover, instead of tracing cones of raysfrom the sun to the target, only the central ray of each coneis traced. Then, the degraded solar cone is projected ontothe target, around the ray impact point. In order to calcu-late the final irradiance distribution, the contributions ofmany cones, coming from different points in the concentra-tor surface, are added.

In the simulations, the optical error standard deviationre was varied from 0 to 10 mrad, obtaining the best fitfor a value of 7 mrad (Estrada et al., 2000). In the presentwork this value of re is used in the simulations for thedesign of the receiver. In all calculations the effect of thereceiver shadow was taken into account.

2.2. Receiver geometry

In proposing possible geometries for the receiver, thelarge rim angle of the concentrator (90�) had to be consid-ered. This means that unlike most paraboloidal concentra-tors, in this system radiation arrives to the receiversideways as well as frontally. Therefore, the main concernwas to achieve a receiver able to collect energy both frombelow and from the sides. A spherical receiver could beused for these purposes as has been done by Schmidtet al. (1983). However, in the present case, a cavity seemedappropriate to reduce losses. This has to be a cavity able toabsorb radiation both on its inner and outer walls (seeFig. 2). A fluid circulates over both of these surfaces toremove the heat.

Several cavity geometries were simulated in order tocompare their performance as receivers for the paraboloid

r concept.

Fig. 3. Tested receiver geometries. Dots indicate the location of theparaboloid focus with respect to each receiver.

Table 1Comparison of results for different receivers, with 10 cm height and 9 cmaperture diameter.

Geometry Inner peak flux(suns)

Outer peak flux(suns)

Average flux(suns)

Spherical 200 270 105Conical 240 180 200Cylindrical 150a 170 120

a Simple average of the values for the cylindrical wall and the flat top. Fig. 4. Inner peak flux for different cone diameters and heights.

Fig. 5. External peak flux for different cone diameters and heights.

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(Fig. 3): cylindrical, conical, and spherical. The dimensionswere initially taken similar to the size of the focal region;i.e., 10 cm height and 9 cm aperture diameter.

To evaluate radiative flux distributions in the differentgeometries ray trace simulations were carried out. Thiswas done also by means of the CIRCE2 ray trace code(Romero, 1994), described above. The radiative flux distri-butions were determined for both the inner and outer sur-faces of each cavity. They were compared in terms of theaverage and the peak concentration ratios. Results aresummarized in Table 1.

As can be observed, the spherical receiver is the one thatgives the highest peak of concentrated radiative flux. How-ever, when average flux is considered instead, the conicalreceiver surpasses the other two geometries. The cylinderhast the lowest values in all categories. It may seem strangeat first that the average fluxes of the sphere and the coneare so different from each other, because the peak fluxesare not so. However, simulations show that there are moreregions with low irradiance in the spherical receivers thanin the conical one.

In view of the above results, the conical receiver waschosen for subsequent optimization, because it has higheraverage concentration than the cylinder, and a more bal-anced flux distribution than the sphere. This is convenientfrom the operation point of view, to avoid temperaturepeaks.

2.3. Optimization of the receiver

For the optimization of the receiver a parametric studywas conducted where both cone height and base diameterwhere varied in the ray trace simulations. In Figs. 4 and 5the inner and outer peak flux are presented, respectively,as functions these two parameters. All irradiances areexpressed in units of suns (one sun nominally being1000 W/m2). It can be observed that peak concentrationin the outer part of the cone decreases as the diameterincreases, which is to be expected since the wall area grows

and moves away from the focal zone. On the contrary, thepeak concentration on the inner side increases with diame-ter. The reason is that the cone becomes less acute as thediameter gets larger, and the incidence angle for radiationimpinging inside the cone reduces on the average. For thesame reasons, if receiver height is increased, peak concen-tration diminishes on the inner wall and increases on theouter wall. Actually, if the limiting case of zero receiverheight is considered, one gets a flat receiver, which meansmaximal concentration on the inner surface (the bottom),and zero on the outer surface (the top).

In Fig. 6 the average irradiance over the inner and outerreceiver surfaces is presented as a function of cone diameterand height. This quantity was calculated as the ratio of thetotal intercepted power to the total wall area of the recei-ver. As can be observed, if any of these dimensions isreduced, the average concentrated flux increases, becausethe receiver area is smaller and coincides with the zonesof maximum concentration. However, receiver dimensionscannot be reduced indefinitely in order to increase concen-tration, because the intercept factor (the fraction ofconcentrated energy collected by the receiver) diminishes.

Fig. 6. Average irradiance over the whole (inner and outer) receiver area.

Fig. 7. Fraction of power intercepted by the conical receiver (interceptfactor), as a function of cone diameter and height.

Fig. 8. (a) Distribution of flux concentration in a cone with the idealdimensions, as a function of vertical position, for both the inner (dashedline) and outer surfaces (full line). The focal point of the parabola islocated at Z = 0. (b) The same for the final dimensions of the receiver builtfor the experiments (Section 3).

N. Hernandez et al. / Solar Energy 86 (2012) 1053–1062 1057

The intercept factor of the conical receiver is analyzed inFig. 7, for different receiver sizes.

If an intercept factor above 97% is sought, an aperturediameter above 20 cm and a height above 10 cm arerequired. Further increasing diameter does not providefor much better energy collection. In fact, setting this valueat 20 cm, and considering heights between 14 and 17 cm,98% collection efficiency is obtained. The larger value ofheight (17 cm) is preferred to increase concentration onthe outer surface. As pointed out above, larger dimensionsof the receiver in general only decrease average concentra-tion, without increasing so much the intercept factor. Thereason for the saturation at values less than 100% seemsto be that the conical receiver cannot intercept all raysdue to its narrow tip. This is an intrinsic limitation of thecone geometry.

With all the above considerations, the final dimensionsof the receiver are chosen as 20 cm diameter and 17 cmheight.

In Fig. 8a, results are presented for the flux concentra-tion distribution over the inner and outer faces of the cho-sen receiver (20 cm diameter, 17 cm height cone). As can be

observed, the concentration peaks in both faces are similar.Finally in Fig. 8b, results are presented for the receiver thatwas built for the experiments. Note that the receiver mustaccommodate for the water passages (Fig. 2), so the innerand outer cones are of different sizes (see next section),both differing from the ideal result. The result is an increasein diameter, which affects to higher degree the outer thanthe inner concentration (Figs. 4 and 5). As a result, theinner face of the receiver has a higher concentration thanthe outer one. This, as will be described below, suggeststhe direction of flow of the water to be heated on thereceiver.

3. Experimental methods

A receiver based on the optimized design was built forthe COSPAA-90 solar concentrator. It consists of threeconcentric cylinders of the same aspect ratio with increas-ing base diameter; all of them truncated at the vertex, atthe same height (see Fig. 9). All components were fabri-cated from stainless steel 304. The outer and inner cylindersjoin at the base by a flat piece, forming a conical doublewalled cavity, while the middle one acts as a flow distribu-tor, which creates two concentric passages for the waterbetween the walls. The final dimensions were: external cone

Fig. 9. Geometry and instrumentation of the receiver. At the left side ofthe cone thermocouples measuring surface temperature are depictedtogether with their aluminum shading strip (thick line).

Fig. 10. Photograph of the COSPPA-90 concentrator, with the conicalreceiver in place.

1058 N. Hernandez et al. / Solar Energy 86 (2012) 1053–1062

diameter 27 cm; inner cone diameter 24.5 cm, and height18 cm. These differ somewhat from the ideal dimensions,but were determined by practical construction constraints.

As discussed above, in the design section, the concen-trated radiative flux density is smaller in the outer than inthe inner wall. Therefore, higher temperatures are expectedon the latter. Because of this, water is preheated by circu-lating it first through the external passage from the vertexto the base of the receiver. Then it changes direction atthe edge of the distributor cone, and flows upwards troughthe inner passage to further increase its temperature.

For the instrumentation of the receiver, three thermo-couples were attached to the inner wall of the receiver,and three to the outer wall, as depicted in Fig. 9. Theyare located 5 cm away from each other. Thermocoupleswere shielded from direct concentrated solar radiation byan aluminum strip, and were covered with a gypsum ban-dage. Pressure transducers and thermocouples where alsolocated at the water inlet and outlet. Beam solar radiationwas measured during the experiments, by using an Eppleypyrheliometer. In Fig. 10 a photograph of the concentratorwith the conical receiver is presented.

A system was built to provide preheated water for thecharacterization of the receiver, and at the same time toact as heat storage (Venegas, 2008). It is composed of athermo tank, an electrical water heating system (with auto-matic temperature control), and the hydraulic circuit. Itcan provide hot water with temperatures in the range fromambient up to 70 ± 1.0 �C.

Water in the thermo tank is heated by electrical resistorsof 3 and 6 kW. Temperature is regulated by the tempera-ture control system, whose feedback is a thermocouplelocated in the thermo tank (see Fig. 11). The preheatedwater is fed to the receiver by a ½ hp centrifugal pump.Flow can be controlled by a needle valve and is monitored

by Headland series HB2800 flowmeter. Temperature andpressure are also monitored at the thermo tank exit. Watercan be recirculated to the thermo tank in order to increaseheating speed and to get more uniform temperature (byopening valve V7 and closing V9 and V10). Once thedesired temperature is reached in the thermo tank, V9and V10 are opened (the latter to allow fresh water to enterto the tank) and V7 is closed.

Three different types of experiments were proposed forthe characterization of the receiver: time constant determi-nation, closed loop operation, and open loop operation. Inthe first type, water near ambient temperature is circulatedthrough the receiver, the concentrator is then focused, andafter reaching steady state conditions it is defocused. Thecooling curve for the receiver is used to obtain its time con-stant. In the closed loop experiments, water is recirculatedrepeatedly between the receiver and the thermo tank, so thewater going out from the tank enters the receiver at everincreasing temperatures. This constitutes a dynamic char-acterization method for the receiver. In the open loopexperiments, water at a specified temperature is stored inthe tank and fed to the receiver to be discarded at the exit.In this case, temperature in the thermo tank is kept steadyby means of the electrical heating and temperature controlsystem.

4. Theoretical model

To describe heat transfer to the water circulating in thereceiver a thermodynamic model is established. The Hotel-Willier equation for solar collectors is used (Kalogirou,2004; Tyagi et al., 2006).

Fig. 11. Diagram of the complete experimental system.

Fig. 12. Energy balance for the conical receiver.

N. Hernandez et al. / Solar Energy 86 (2012) 1053–1062 1059

Qu ¼ Ar½CðqacÞGb � ULðT � T aÞ � erðT 4 � T 4aÞ� ð1Þ

where Qu is the useful heat transferred to the water, Ar isthe absorber area, UL is the receiver global loss coefficient,r is the Stefan–Boltzman constant, q; a; e are respectively,the reflectance, absorptance, and emittance the absorbersurface, c is the intercept factor of the receiver, Gb is beamsolar irradiance, T is the average receiver temperature, andTa the ambient temperature.

The useful heat Qu equals the sensible heat removed bythe fluid circulating through the receiver

Qu ¼ _mcpðT o � T iÞ ð2Þ

where To and Ti are the water inlet and outlet tempera-tures, respectively, _m is the mass flow rate and cp is the spe-cific heat of water.

The instantaneous efficiency of the concentrator-receiversystem is defined as

gi ¼Qu

AaGbð3Þ

If radiative losses are neglected in Eq. (1), and substitutingit into Eq. (3), it is obtained that

gi ¼ F Rqca� F RUL

CT i � T að Þ

Gb

� �ð4Þ

where FR is the heat removal factor of the collector, givenby

F R ¼_mCp

ArUL1� exp �ArU LF ’

_mCp

� �� �ð5Þ

With Eqs. (3) and (5), the outlet temperature can be evalu-ated as

T o ¼ T i þF RAr½CðqacÞGb � ULðT i � T aÞ�

_mcpð6Þ

The values of the physical parameters used in Eq. (6) are:a = 0.95, q = 0.64 (Jimenez Magana et al., 1997), andc = 0.98 (as described in the design section; Fig. 7). Withthose parameters and the value of the beam solar irradi-ance Gb, the absorbed heat can be evaluated.

In order to calculate the efficiency factor F0 an energybalance is carried out, by taking into account the conicalgeometry of the receiver (see Fig. 12). Assuming that themain heat transfer occurs in the direction of the radialcoordinate it is possible to write

qr ¼ �kArdTdr

ð7Þ

By considering the internal and external walls of the recei-ver, Eq. (7) becomes

qr

Z Re

Ri

drð�kpge � kpr2Þ ¼

Z Te

TidT ð8Þ

where Re and Ri are the radii of the outer and inner walls ofthe receiver. By solving Eq. (8) it is obtained that

qr ¼ kpgeT e � T ið Þ

ln ReRi

� �þ ln geþRi

geþRe

� � ð9Þ

1060 N. Hernandez et al. / Solar Energy 86 (2012) 1053–1062

Based on the above, the thermal resistance that describesthe behavior of the cone receiver is expressed by the follow-ing relationship:

Rter ¼1

kpgeln

Re

Ri

� �þ ln

ge þ Ri

ge þ Re

� �� �ð10Þ

and therefore one can express the collector efficiency factorF0 as

F 0 ¼ UL

1ULþ 1

hwþ Re

kgeln Re

Ri

� �þ ln geþRi

geþRe

� �� � ð11Þ

where hw is the convective heat transfer coefficient to thesurroundings.

5. Experimental results

Previous to the experiments with the receiver, thethermo tank was characterized ( Venegas, 2008). To thisend, water was heated to 69 �C and left to cool inside thetank for 3 days. The (UA)s was obtained as 3.3 W/K. Asdescribed above, three kinds of experiments were per-formed to evaluate the receiver: time constant, closed loop,and open loop.

5.1. Time constant evaluation

As discussed above. The concentrator was focused andthen defocused to observe the receiver cooling curve.Two flow rates (3 and 4 liters per minute) were used, andtwo tests were carried out for each of these values(Fig. 13). The obtained time constant values were 110 s,and 140 s, for the 4 and 3 lpm flow rates, respectively.

5.2. Closed loop experiments

This experiment intends to measure the energy stored inthe thermo tank, as well as to characterize the thermalbehavior of the system as a whole. The mass flow ratewas kept constant at 2.7 liters per minute. It was observedthat temperature in the tank increased at a rate of 0.96 �Cper minute, as shown in Fig. 14. Also shown in this figureare the results from the theoretical model, which have verygood agreement with the experimental results. It is impor-tant to point out that beam solar irradiance Gb was mea-

Fig. 13. Transient response of the receiver at 4 and 3 lpm.

sured during the experiment, and the obtained data wasused into Eq. (6).

The values obtained for the efficiency of the receiverfrom the above experimental results are presented inFig. 15, together with the linear fit to them. As can beobserved, the efficiency is rather low, but decreases slowlywith temperature; i.e., the heat loss coefficient is not veryhigh. Nevertheless, the optical efficiency of the system(related to the intercept with the y axis) is low, as will bediscussed in the next section.

5.3. Open loop experiments

The objective is to evaluate efficiency at fixed tempera-ture for different flow rates, to determine the global heatloss of the receiver. The inlet temperatures were fixed at30, 40, 50, 60 and 70 �C and the flow rates at 1, 2, and3 lpm. The efficiencies for the different flow rates and tem-peratures are presented in Fig. 16. It can be observed thatefficiency increases with the flow rate, and diminishes withtemperature, as is to be expected. As should be expected,values obtained for 3 lpm are similar to those obtained inthe closed loop experiments with 2.7 lpm.

In Fig. 17 the measured water outlet temperatures arepresented and compared with the predictions of Eq. (6).The relative error between both values is 2.30 ± 0.05%.

As can be seen form the above results, the obtained effi-ciencies for the system were low. However, it is necessary topoint out that the present implementation of the conicalreceiver was only intended as a proof of concept. To a highdegree, these values for the efficiency are a consequence ofthe limitations of the particular concentrator. First of all,due to weathering of the aluminum surface, the reflectanceof the paraboloid was low (0.64), diminishing the globalsystem efficiency; in addition to that, the surface errorwas quite high (7 mrad), due to an evident waviness ofthe surface in the sub-millimeter scale, and due to the pres-ence of many scratches. The latter clearly reduces the sys-tem concentration and increases receiver size, producinghigher losses. In this sense, it is necessary to decouple theperformance of the receiver from that of the concentrator.If we evaluate the qc product, which somehow takes intoaccount the above optical effects, we get a value of 0.59.Therefore, the efficiency reaches above 50% if the curvesare divided by this number. Moreover, improvement dueto reduced losses could be gained, if a smaller surface errorallowed for a smaller receiver. But this is more difficult toestimate.

6. Conclusions

In the present work the design of a receiver for a 90� rimangle paraboloidal concentrator has been undertaken. Anovel solution has been proposed, based on a cavity con-cept. This design differs from standard cavity receiversbecause it is intended to receive radiation both on its innerand outer surfaces. Spherical, conical and cylindrical geom-

Fig. 14. Inlet and outlet water temperatures in the receiver (left) and flow rate (right).

Fig. 15. System efficiency as a function of the inlet temperature for theclosed loop experiments.

Fig. 16. Collector efficiency for different inlet temperatures and flow rates.

Fig. 17. Receiver water outlet temperature for 2 lpm flow. Measurementvs. model.

N. Hernandez et al. / Solar Energy 86 (2012) 1053–1062 1061

etries were compared by means of ray tracing simulations.The analysis of different geometries shows that a conical

cavity receiver gives a good compromise between concen-tration rate and uniformity of the radiation flux.

A stainless steel receiver based on the proposed designwas built and tested in a paraboloidal concentrator builtfrom an old telecommunication antenna. Experiments werecarried out to evaluate the receiver by using water as cool-ing fluid. The time constant, the heat removal factor, aswell as the global heat loss coefficient, were obtained.

Although efficiencies for the system were low, this is to alarge degree attributable to the limitations of the particularconcentrator employed (large surface error and low reflec-tance), rather than to the receiver. The utilization of ahigher quality concentrator should improve considerablythe results, and the conical receiver presented here seemsin principle an attractive idea.

Acknowledgements

J.J. Quinones Aguilar and C.A. Perez Rabago, areacknowledged for technical support in the assembly of

1062 N. Hernandez et al. / Solar Energy 86 (2012) 1053–1062

the hydraulic circuit, and with tracking and instrumenta-tion. This work was partially supported by DGAPA-UNAM through Grant PAPIIT-IN106207-3.

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