Estimating intercept factor of a parabolic solar trough collector with new supporting structure using off-the-shelf photogrammetric equipment Silverio García-Cortés a , Antonio Bello-García b , Celestino Ordóñez a,c,⇑ a Dept. of Mining Exploitation, University of Oviedo, 33600 Mieres, Spain b Dept. of Industrial Manufacturing, University of Oviedo, 33203 Gijón, Spain c Dept. of Natural Resources, University of Vigo, 36211 Vigo, Spain article info Article history: Received 24 March 2011 Received in revised form 29 July 2011 Accepted 19 August 2011 Available online 21 September 2011 Keywords: Close-range photogrammetry Quality control Parabolic trough collector Solar concentrator abstract When a new design for a solar collector is developed it is necessary to guarantee that its intercept factor is good enough to produce the expected thermal jump. This factor is directly related with the fidelity of the trough geometry with respect to its theoretical design shape. This paper shows the work carried out to determine the real shape and the intercept factor of a new prototype of parabolic solar collector. Conver- gent photogrammetry with off-the-shelf equipment was used to obtain a 3D point cloud that is simulta- neously oriented in space and adjusted to a parabolic cylinder in order to calculate the deviations from the ideal shape. The normal vectors at each point in the adjusted surface are calculated and used to deter- mine the intercept factor. Deviations between adjusted shape and the theoretical one suggest mounting errors for some mirror facets, resulting in a global intercept factor slightly below the commonly accepted limit for this type of solar collector. Ó 2011 Elsevier Ltd. All rights reserved. 1. Introduction Power generation through solar fields is starting to increase strongly in Europe (especially in Spain) and the USA [1]. There is also a big interest in sustainable energy supply all over the world with special focus on USA, China and North Africa. Nine large com- mercial scale plants were built in the Mojave Desert (California, USA) during 1980s. Since then, interest in this technology seemed to decline. Andasol 1, a 50 MW parabolic trough solar plant located in Granada (southern Spain), began its construction in 2006. Today there are 10 parabolic trough plants working in this country, ten more are under construction and 26 more are planned [2]. In addi- tion further projects with a capacity over 2000 MW are planned all over the world mainly in the USA, China and North Africa [1]. A concentrating solar plant (CSP) using parabolic trough collector technology (PTC) is composed of a large field of PTC, a heat exchanger block and a conventional turbine–generator system. So- lar fields comprise rows of PTC aligned north–south which can track sun direct radiation during the day (Fig. 1). Loops of parabolic trough solar collectors with lengths about 600 m are used. These loops are in turn composed of smaller modules (150 m) whose basic components are the 12 m long parabolic trough segments. Parabolic trough collectors (PCC, parabolic cylindrical collector) consist of a number of elementary large mirrors (28 mirrors, being 155 cm 170 cm each) forming a parabolic trough surface as per- fect as possible. They transform the sun’s radiant energy into heat energy, which is absorbed by a pipe of oil located on the focal line of the parabolic cylinder. The oil temperature at the end of the so- lar field must be about 400 °C. This thermal energy is transferred to water vapor in a heat exchanger that feeds a turbine for electricity production. Global thermal efficiency of parabolic trough collectors (PTC) depend on several factors but geometric agreement to parabolic profile design is the most important one and is the one considered here. The objective of this article is to determine, for a PTC segment with a new supporting structure design, the deviation of its shape with respect to the theoretical one and estimate its intercept factor (the fraction of the reflected radiation that is incident on the absorbing surface of the receiver). The paper is structured as follows. Section 2 provides a sum- mary of the factors that influence the thermal efficiency of a solar collector. In Section 3, the procedure to obtain the geometry of a PTC segment and its deviation from the theoretical shape is pre- sented. Section 4 explains the methodology employed to estimate the intercept coefficient of the PTC. In Section 5, results obtained for the particular case analyzed are shown. Finally, we present our conclusions. 2. Thermal efficiency of parabolic solar collectors The instantaneous efficiency of a parabolic solar collector can be expressed as a function of three parameters [3]: 0306-2619/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.apenergy.2011.08.032 ⇑ Corresponding author. Address: E.P. Mieres, Calle Gonzalo Gutiérrez Quirós s/n, 33600 Mieres, Asturias, Spain. Tel.: +34 985458020; fax: +34 985458000. E-mail addresses: [email protected], [email protected](C. Ordóñez). Applied Energy 92 (2012) 815–821 Contents lists available at SciVerse ScienceDirect Applied Energy journal homepage: www.elsevier.com/locate/apenergy
Transcript
Applied Energy 92 (2012) 815–821
Contents lists available at SciVerse ScienceDirect
Estimating intercept factor of a parabolic solar trough collector with newsupporting structure using off-the-shelf photogrammetric equipment
Silverio García-Cortés a, Antonio Bello-García b, Celestino Ordóñez a,c,⇑a Dept. of Mining Exploitation, University of Oviedo, 33600 Mieres, Spainb Dept. of Industrial Manufacturing, University of Oviedo, 33203 Gijón, Spainc Dept. of Natural Resources, University of Vigo, 36211 Vigo, Spain
a r t i c l e i n f o
Article history:Received 24 March 2011Received in revised form 29 July 2011Accepted 19 August 2011Available online 21 September 2011
When a new design for a solar collector is developed it is necessary to guarantee that its intercept factor isgood enough to produce the expected thermal jump. This factor is directly related with the fidelity of thetrough geometry with respect to its theoretical design shape. This paper shows the work carried out todetermine the real shape and the intercept factor of a new prototype of parabolic solar collector. Conver-gent photogrammetry with off-the-shelf equipment was used to obtain a 3D point cloud that is simulta-neously oriented in space and adjusted to a parabolic cylinder in order to calculate the deviations fromthe ideal shape. The normal vectors at each point in the adjusted surface are calculated and used to deter-mine the intercept factor. Deviations between adjusted shape and the theoretical one suggest mountingerrors for some mirror facets, resulting in a global intercept factor slightly below the commonly acceptedlimit for this type of solar collector.
� 2011 Elsevier Ltd. All rights reserved.
1. Introduction 155 cm � 170 cm each) forming a parabolic trough surface as per-
Power generation through solar fields is starting to increasestrongly in Europe (especially in Spain) and the USA [1]. There isalso a big interest in sustainable energy supply all over the worldwith special focus on USA, China and North Africa. Nine large com-mercial scale plants were built in the Mojave Desert (California,USA) during 1980s. Since then, interest in this technology seemedto decline. Andasol 1, a 50 MW parabolic trough solar plant locatedin Granada (southern Spain), began its construction in 2006. Todaythere are 10 parabolic trough plants working in this country, tenmore are under construction and 26 more are planned [2]. In addi-tion further projects with a capacity over 2000 MW are planned allover the world mainly in the USA, China and North Africa [1].
A concentrating solar plant (CSP) using parabolic troughcollector technology (PTC) is composed of a large field of PTC, a heatexchanger block and a conventional turbine–generator system. So-lar fields comprise rows of PTC aligned north–south which can tracksun direct radiation during the day (Fig. 1). Loops of parabolictrough solar collectors with lengths about 600 m are used. Theseloops are in turn composed of smaller modules (150 m) whose basiccomponents are the 12 m long parabolic trough segments.
Parabolic trough collectors (PCC, parabolic cylindrical collector)consist of a number of elementary large mirrors (28 mirrors, being
fect as possible. They transform the sun’s radiant energy into heatenergy, which is absorbed by a pipe of oil located on the focal lineof the parabolic cylinder. The oil temperature at the end of the so-lar field must be about 400 �C. This thermal energy is transferred towater vapor in a heat exchanger that feeds a turbine for electricityproduction.
Global thermal efficiency of parabolic trough collectors (PTC)depend on several factors but geometric agreement to parabolicprofile design is the most important one and is the one consideredhere. The objective of this article is to determine, for a PTC segmentwith a new supporting structure design, the deviation of its shapewith respect to the theoretical one and estimate its intercept factor(the fraction of the reflected radiation that is incident on theabsorbing surface of the receiver).
The paper is structured as follows. Section 2 provides a sum-mary of the factors that influence the thermal efficiency of a solarcollector. In Section 3, the procedure to obtain the geometry of aPTC segment and its deviation from the theoretical shape is pre-sented. Section 4 explains the methodology employed to estimatethe intercept coefficient of the PTC. In Section 5, results obtainedfor the particular case analyzed are shown. Finally, we presentour conclusions.
2. Thermal efficiency of parabolic solar collectors
The instantaneous efficiency of a parabolic solar collector can beexpressed as a function of three parameters [3]:
Fig. 1. A view of solar collector field in Extresol 1 solar plant (Spain).
816 S. García-Cortés et al. / Applied Energy 92 (2012) 815–821
gC ¼ f ðFR;UC ;g0Þ
The FR parameter measures the efficiency of the heat transmissionto the absorber fluid. UC quantify the thermal losses per unit ofthe receiver surface area. This factor depends primarily on thetemperature difference between the collector and the environment.Finally g0 is the optical efficiency which depends on solar beamincidence angle (angle between the sun rays and the normal tothe aperture plane), the properties of the collector materials (mirrorreflectance, receiver cover transmittance, absorber tube absorp-tance) and the optical errors.
Optical efficiency g0 of the collector can be studied indepen-dently from the thermal parameters if we assume that the collectormaterial properties are invariant from temperature. In that caseoptical efficiency varies with the incidence angle h, also witheffective transmittance–absorptance factor (sa)n and with inter-cept factor at normal angle of incidence c (fraction of rays incidentupon the aperture that reach the receiver when the incidence angleis zero [3]).
g0 ¼ KðhÞðsaÞnc
In turn, the intercept factor is controlled by the geometric design ofthe collector through the rim angle / (angle between the two endsof the aperture geometry measured from the focal point in a trans-versal section of the collector), random and non-random errors.Random errors are due to the change in the apparent sun width,rsun (the distribution of energy directed to the receiver, also calledsun shape), small and occasional sun tracking errors, rtrack, errors inmirror specularity, rslope (defects in the reflective material) andsmall scale slope errors, rslope (waviness of the mirrors). Theserandom errors can be modeled by a normal probability energy dis-tribution where the total reflected energy standard deviation is [4].
qNon-random errors can be categorized in three classes: themisalignment of the receiver tube with respect the focus line ofthe parabolic cylinder, misalignment of the trough with the sunand the difference in the average shape of the collector with respectto the parabolic section (profile errors). These non-random errorscan be caused by defective manufacturing or assembling, imperfecttracking of sun and poor operation conditions (sand, dust or distor-tion of the collector geometry caused by winds).
All these effects can be grouped in four parameters to model theintercept factor at normal incidence angle [3]:
c ¼ f ðu;r�;b�;d�Þ
The rim angle, /, takes into account the characteristics of the collec-tor design, r� models the effect of random errors (universal randomerror parameter), b� is the universal non-random angular errorsparameter and is modeled by the misalignment angle (angle be-tween the central ray from the sun the normal to the apertureplane), Finally d� is the universal non-random error parameterand takes into account for the profile errors and the misalignmentof the receiver with respect the focal line.
In our case, we measure a collector module fitted with a newsupporting design structure. This module has been assembledalone for measurement purposes only and there is no receiver tubeinstalled. At this point of the process, manufacturer is only inter-ested in testing the rigidity of the structure compared with themechanical design specifications. Thus we have measured themodule in vertical and horizontal positions to assess that thenew designed structure can maintain the parabolic shape for thecollector. Due to this special configuration of the collector, receivertube misalignment, angular non-random errors (misalignment ofcollector with respect the sun) and random errors can be excludedas influence factors. Incidence angle is also not affecting the inter-cept factor at normal incidence. Consequently, only the profile er-rors in the collectors are considered in this study.
Profile errors depend on the degree of adjustment for this set of28 mirrors to the parabolic cylindrical geometry. Movements anddeflections of the supporting structure under its own weight andunder external forces like wind affect the geometry of the collec-tors. Different support designs exist on the market [5]. Each newdesign of the structure supporting the mirrors must be tested tofind if this design and the associated assembly process are ableto maintain the geometry within reasonable limits of solar ray con-centration. Errors in mirror assembly and alignment influence theefficiency of electricity production very much [6].
There are several situations where a collector must be geomet-rically controlled. First, during mirror mounting in the assemblyfacility [7], generally near the solar field location, where only thesupporting structure and mirrors are present. Second, when placedon the solar field for the first time, to control surface deviationscaused during transportation and after receiver tube installation[8]. Third, during normal operation to control evolution and stabil-ity against winds and sun track movement [9,10].
In addition every new collector design must be controlled andmeasured to ensure the supporting structure effectiveness and aminimum intercept factor capability. Plataforma Solar Almeria(PSA) [11] is one of the companies that carry out this assessmentby providing the appropriate certification to the company owningthe design.
3. PTC segment shape estimation with off the shelfphotogrammetric equipment
3.1. Collector targeting
Photogrammetric processes are based on the registration of ob-ject points in several images taken from different positions [12,8].3D coordinates of these points are then reconstructed from theircoordinates on images. For this reason, image coordinates of pointsmust be measured with high precision. Mirror surfaces are prob-lematic because of their reflective behavior. The absence of naturalpoints must be solved using targets arranged on a collector surface.These targets will be detected automatically during the photo-grammetric work. The usual procedure is to attach a sheet of adhe-sive vinyl on the surface, with a printed array of targets withappropriate size and shape.
Target spacing and size depend on mean photographic capturedistance and target detection method implemented on the photo-
S. García-Cortés et al. / Applied Energy 92 (2012) 815–821 817
grammetric software. In general, circular targets, printed or retro-reflective ones, are recommended since automatic detection of cir-cle centroid (which becomes an ellipse because of the perspectiveprojection of the photograph) is a process that can be carried outaccurately by the LSM (‘‘least squares matching’’) technique [12].In this case, signal array has been designed and provided by Plata-forma Solar Almería (PSA) staff [11]. The target array has been de-signed to facilitate the triangulation process and spacing betweenneighboring circular targets is 10 cm. Target diameter is 4 cm andthey must appear as about ten pixel size when used with adequateshooting distance and camera (sensor) resolution (Fig. 2).
In order to achieve a faster process, 14 coded targets wereevenly distributed over the collector surface (Fig. 2). These targetsare automatically recognized by the photogrammetric softwareand automatically matched between images [13]. There wereabout 7150 circular targets covering the collector surface. This highnumber of signals is necessary to improve the reconstruction of thetrough surface by interpolation during the meshing procedure andis not necessary in other studies which are not addressed to inter-cept factor determination [8,14].
3.2. Photographic shooting and 3D processing
Classical photogrammetric technique requires a convergentgeometry of camera axis with respect to the subject [15]. More-over, each point of the object must appear in at least two images.Concentrator modeling has to be done in two different positions:vertical and horizontal, to be aware of the geometry variation dur-ing sun tracking. Being a large object (12 m long and 5.30 m open-ing) the average distance from which the images have to be shot isinfluenced by lens field angle, target size (on image) and accessibil-ity. An off-the-shelf SLR camera with a standard 18–55 mmlens was used. The camera and lens specifications can be seen inTable 1.
In order to determine accurate camera model parameters (focallength, principal point position and lens distortion parameters),the camera must be calibrated. Camera calibration can be carried
Fig. 2. Parabolic cylinder concentrator in vertical position with adhesive vinyl forphotogrammetric targeting. Zoomed view of the circular targets and a coded target.
Table 1Technical specifications of the camera and lens used.
out by two different methods. The first method consists in takingseveral photos convergent to a target grid specially designed forthat purpose. Different distances and camera format positions areused to avoid coupling between internal parameters. This is awell-known procedure [12,15] and was done by creating a specialcamera calibration project inside Photomodeler 6 [16]. Second pos-sibility for calibration is to solve a field calibration. In this caseinternal geometry of camera-lens system is recovered using thesame set of photos used for object reconstruction. This methodtakes into account possible instabilities which can appear duringshooting procedure in the field (principal distance and principalpoint variations and others, due to switch on–off process of thecamera, thermal variations, camera shaking, etc.).
In our case we use the calibration parameters obtained in thefirst method as a base values for the bundle adjustment of the fullblock of photographs during the second procedure. This improvesthe absorption of typical instabilities affecting this commercial(off-the-shelf) camera. The basic calibration parameters are al-lowed to change during bundle adjustment procedure implement-ing the field calibration process mentioned above. Some otherprecautions were adopted to try to get a fixed internal geometry:deactivation of lens stabilization, optic zoom fixing and all photostaken in wide angle zoom position (calibrated position).
Average shooting distance to the collector in a vertical positionwas found to be about 8 m for the nine images, and a little less (6 mapprox.) for horizontal position. This is caused by the height limitthat could be achieved with the existing hydraulic lifting platform.Fig. 3 shows the relative positions of the camera and collector forvertical position.
3D processing was done using Photomodeler 6 software. A gen-eral description of the software workflow can be found on [17]. 3Dprocessing basically relies on bundle adjustment. This phtogram-metric method [18,19] calculate simultaneously external orienta-tion for all images and 3D coordinates for all object points usinga specific formulation with iterative least squares. If there is noexternal control point available for this process, the solution iscalled free network adjustment and is based on pseudoinverse cal-culation for the design matrix of the global equation system [18].This procedure allows for the study of inner (relative) accuracyalone without any external error influence. In addition, as has beenalready mentioned, internal camera parameter can also be allowedto change during this adjustment in a process called fieldcalibration.
Two different projects have been solved for vertical and hori-zontal position, respectively. Quality of these adjustments can bederived from the estimators shown in Table 2. Overall root meansquare is the root mean square for all the measured image coordi-nates in the project and is about 1/10 of pixel size. Therefore it iswithin the recommended range for this estimator [8] in order toguarantee a gross error free project.
Image residuals (RMS) are well below one pixel size, which alsoindicates good quality adjustment. Point accuracy values are alsofound to be below 1 mm (1 sigma). Coordinates obtained for theabove points are referred to the same axis coordinate system inboth cases and were exported to text files for further processing.
3.3. Point cloud adjustment to a parabolic cylinder
Once the cloud point representing the collector has been deter-mined, it is necessary to quantify the degree of discrepancy be-tween measured points and corresponding ones on a perfectparabolic trough surface. This problem has the difficulty that theexact location and orientation of the axis system for parabolic cyl-inder is unknown (it has been placed only approximately for thepoint set) and therefore it is impossible to calculate the theoretical
Fig. 3. Photographic shooting geometry with respect to the solar concentrator, when collector is in horizontal position (left). Hydraulic platform for image shooting (right).
Number of points 7136 6900Total error 0.663 0.531Max. Residual 1.07 pixels 1.023 pixelsOverall RMS 0.078 pixels 0.061 pixelsMax vector length 0.641 mm 0.543 mmMax. X sigma 0.434 mm 0.218 mmMax. Y sigma 0.275 mm 0.389 mmMax. Z sigma 0.544 mm 0.361 mm
Fig. 4. Visual explanation for mathematical model in Eq. (2).
818 S. García-Cortés et al. / Applied Energy 92 (2012) 815–821
coordinates corresponding to each point following the basicequation:
z ¼ y2
2pð1Þ
being y and z coordinates of the points over the parabolic cylindersurface and p, a constant, describing the parabolic shape of trans-versal sections.
To take this problem into account, a coordinate transformationin space (rigid body) is included in the model. Its parameters willaccount for the misalignment and the translation between realand theoretical reference systems. This will allow the ideal para-bolic cylinder to rotate, and change position during adjustment,(a change of scale is not allowed) to fit, under the least square cri-teria, the measured point cloud. The mathematical formulation ofthe model is based on the geometric definition of a parabola. Dis-tance from any point in the parabolic cylinder surface to the focusline must be equal the distance from the same point to the direc-trix plane.
F � q1 � q2 ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiy2 þ z� p
2
� �2q
� zþ p2
� �¼ 0
X
Y
Z
264
375 ¼ Rðx;u;jÞ
x
y
z
264375þ
0TY
TZ
264
375
9>>>>>=>>>>>;
ð2Þ
q1, distance from collector point to parabola focus; q2, distancefrom collector point to directrix line; R, space rotation matrix (Eulerform); TY, TZ, translation components
A graph showing the variables and parameter p in Eq. (2) isdepicted in Fig. 4.
Movement over X axis must be considered a degree of freedom.To avoid ill-conditioning in the problem resolution an additionalzero constraint is imposed to fix the X position using the elimina-tion technique. The linearized model can be seen on Eq. (3).
F � F0 þ J � dx ¼ 0
J ¼ @F@x
� �0
@F@u
� �0
@F@j
� �0
@F@Ty
� �0
@F@Ty
� �0
@F@p
� �0
h i) ð3Þ
To solve this equation system, the Gauss–Newton method is used[20]. Each point generates a new equation while the number of un-knowns are reduced to seven (x, u, j, Ty, Tz, p). In our algorithm theparabola parameter p may be regarded as unknown or consideredfixed in the adjustment. This strategy can detect wrongly-placedmirrors over the structure or defective mirrors.
Results for the adjustment of the point clouds for collector atboth positions are summarized in the Table 3:
Residuals are not linked with any point coordinates but ratherrepresent variations in distance differences q1 and q2 betweenthe measured and the ideal shape. We would need instead, differ-ences in the Z coordinate, which can be corrected using themechanical connection between mirrors and structure. New valuesfor the point coordinates are then calculated using the 3D transla-tion and rotation obtained in adjustment. These coordinates arecompared with those provided by Eq. (1).
4. Collector intercept factor estimation
In order to calculate the intercept factor, normal vector in eachpoint of the model surface is required. This will allow the study of
Table 3Parameters for the geometric adjustment of point cloud to theoretical surface.
Fig. 6. A collector section, 1 m width, with strong deformations and deviated rayintersection with vertical longitudinal plane.
Table 4Design specifications of the parabolic collector.
Collector module design parameters
Length 12 mAperture 5.77 mMirror number 28Mirror dimensions
Inner element 1501 � 1701 mmOuter element 1644 � 1701 mm
Focal distance (z = y2/4f) 1.71 m
S. García-Cortés et al. / Applied Energy 92 (2012) 815–821 819
reflected rays. A mesh was constructed using meshing functions onMATLAB�, which in turn uses the CGAL [21] free library. Themeshing algorithm used was Delaunay in 2D, over the xy planeprojection.
Normal vectors to the centroid of each triangle are calculatedand used to determine the reflected rays over the collector at anypoint. Solar rays coming from a direction parallel to the longitudi-nal symmetry plane of the collector will be reflected symmetricallywith respect to normal. For perfect geometry, all rays should be re-flected on the focal line of parabolic trough. Deviation from thisbehavior reduces the optical efficiency of solar collector [9]. Underthe hypothesis of a perfect collector alignment with solar ray direc-tion, reflected ray direction must be computed. To avoid confusionsand to speed up the process we pose this problem under a vectorformulation (Fig. 5).
Distance between oil pipe center (over focal parabolic line) andthe reflected sun ray on P will define if the ray hits the pipe(dFQ < Rpipe) or not. We can calculate the position vector for the footof the minimum distance segment (Q) between reflected ray andoil pipe with:
OQ ¼ OPþ rkrk tr
tr ¼t � rkrk
ð4Þ
where r is the reflected ray direction vector and tr stands for theprojection of t vector over r (being t the vector connecting the sur-face point P with the focal point F) (Fig. 5, left). Vector t can be eas-ily obtained for each surface point.
Vector r can be found as follows (Fig. 5, right):
r ¼ zþ 2w ¼ zþ 2ðz� vÞv ¼ Nz �NNz ¼ N � z ¼ cos a
ð5Þ
From Eqs. (4) and (5) can be noted the main importance of precisedetermination for the Z axis. The point cloud space orientation
Fig. 5. Graphical representation of the method used to determine reflected ray directionvector r represents the reflected ray, t is the vector between the generic point P and th
implicitly defines this axis. Thus also determine the accuracy of re-flected ray directions.
The intercept factor measures the percentage of rays that inter-sect the absorber tube against the total of all the reflected rays. Forsuch calculation the diameter of the absorber must be considered.A typical value can be 11 cm. It should be noted that distance be-tween collector and absorber pipe is variable depending on thearea of the concentrator that is being considered. Closer zone isthe area in the parabola vertex. Fig. 6 shows the simulated behav-ior of the reflected rays in a 1 m width section with strong defor-mation. This deformation can be appreciated on the edge of thecollector section.
Sunlight can be seen simply as straight lines (as we have donein this study) or they can be considered as functions of energy dis-tribution over a volume of a given solid angle. These features areusually set for some latitude terrestrial value and they define whatis called a ‘‘Sun-shape.’’ In practice, these complex calculations arenot required. It should be noted that the overall efficiency of thecollector is also affected by the accuracy of the orientation, solartracking driving system and other mechanical factors.
s on each point of the collector surface. N represents the normal to the parable in P;e focal point of the parable.
820 S. García-Cortés et al. / Applied Energy 92 (2012) 815–821
5. Results and discussion
The methodology explained in Sections 2 and 3 was applied tothe geometrical study of a PTC designed and constructed for aSpanish company. This collector module has been equipped witha redesign supporting structure. It is based on EuroTrough design(ET150 model) [22,23].
The technical specifications of the PTC used in this study aresummarized in Table 4.
Fig. 7. Z coordinate differences in mm between theoretical cylinder and collector adjusteZ residuals toward negative values for the horizontal collector that is attributed to grav
02000−3000
−2000
−1000
0
1000
2000
3000−10
0
10
Diferences in Z residuals be (Vertical m
Width (mm)
Z re
sidu
al d
ifs.
Fig. 8. Differences in Z residuals (in mm) between vertical and horizontal collector po
Differences between real geometry of the collector studied withrespect to a parabolic cylinder surface are depicted in Fig. 7 for ver-tical and horizontal positions. The transversal and longitudinalseparation between the mirrors can be clearly appreciated (verticaland horizontal lines). Each mirror is connected to the base struc-ture using four ceramic supports. Distances to the bars of the struc-ture are controlled by adjustable screws. Deviations in Z for thosesupport positions can be now calculated and the movement foreach screw will compensate for these differences.
d surface in vertical and horizontal positions. Histograms on the right show a shift ofity.
40006000
800010000
12000
Length (mm)
tween Vertical and Horizontal collector positionsinus Horizontal)
sitions. This differences are caused by the gravitational effect over the structure.
Table 5Intercept coefficient for 11 cm diameter absorber pipe.
Collector position Vertical Horizontal
Intercept factor 90.70% 92.02%
S. García-Cortés et al. / Applied Energy 92 (2012) 815–821 821
The areas of collector surface which differ from the theoreticaldesigned surface can be appreciated in Fig. 7 (gray tone images).Although structural design of support structure is optimized forthe horizontal position taking into account own weight and windeffects, histograms on the right show a deviation of the mean Zresiduals towards a negative value for the collector in the horizon-tal position. This can be justified by the gravity effect, whichpushes down the collector, with the greatest displacements locatedat the edges of the collector in its horizontal position. Fig. 8 showsthe differences, in Z residuals, between the vertical and horizontalpositions of the collector. For each collector point, the positionwith respect the zero level represents the displacement sufferedby this point when the collector is moved from vertical to horizon-tal position. If the deformational and stress study for the supportstructure were available, the gravitational deformations of thisstructure could be discounted from the total displacement provid-ing an indication of defects in mirror fastening. There are, however,important similarities in Z deviations between the two positions. Inthe lower edge (at x = 5000 mm) the collector measured surface isclearly over the theoretical surface. And this behavior is repeatedin the two positions. These suggest a mounting error for this mirrorfacet. The same problem can be seen for other facets in the twoimages.
The calculated values for the intercept factor of 11 cm indiameter are shown in Table 5. These values are slightly belowthe expected value for this type of collector (95% is recommendedin [6]).
The values for this coefficient in both positions are very similar.This can be interpreted as an indication of a solid support structuredesign. Meanwhile, the assembling process of mirror facets overthe structure must be improved.
6. Conclusions
The geometrical characterization of a new prototype of para-bolic solar trough has been performed using close range photo-grammetry for data collection and a mathematical model thatdetermines simultaneously the shape and orientation of the 3Dpoint cloud. Deviations of the collector mirrors from its theoreticalposition were detected. Greatest deviations correspond to theborders of the collector and they are higher for the collector in ahorizontal position rather than in a vertical position. These resultsagree with the expected situation, since the main factor causingthe deformation is the weight of the collector. However, otherdeviations seem to be caused by errors in the assembly of mirrorsrather than in gravity.
By calculating the normal vectors to the adjusted surface theinterception coefficient of the collector was calculated. The results
obtained show that nearly 10% of the incidents rays does not reachthe absorber. This percentage is slightly below the recommendedvalue for the type of collector analyzed. Commonly a 95% valueis expected as optimal [6].
According to our analysis, the mounting of some facets shouldbe revised in order to reduce energy efficiency degradation.
Acknowledgements
To Prof. Ricardo Vijande and Prof. José Manuel Sierra from theMechanics Engineering Dept., University of Oviedo for their invita-tion to get in touch with new methods in mechanic design analysis.
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