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energies Article

Investigation of the Effect of Physical and Optical Factors on the Optical Performance of a Parabolic Trough Collector Majedul Islam 1,3 , Sarah Miller 2 , Prasad Yarlagadda 1 1 2 3

*

ID

and Azharul Karim 1, *

Science and Engineering Faculty, Queensland University of Technology, Brisbane CBD, QLD 4001, Australia; [email protected] (M.I.); [email protected] (P.Y.) Commonwealth Scientific and Industrial Research (CSIRO), 10 Murray Dwyer Circuit, Mayfield West, NSW 2304, Australia; [email protected] Department of Mechanical Engineering, Chittagong University of Engineering & Technology, Chittagong 4349, Bangladesh Correspondence: [email protected]; Tel.: +61-7-31386879; Fax: +61-7-31381529

Received: 30 September 2017; Accepted: 2 November 2017; Published: 20 November 2017

Abstract: The overall thermal performance of a Parabolic Trough Collector (PTC) depends on its optical performance, particularly the uniformity of the irradiance distribution and the resultant optical efficiency of the collector. Local Concentration Ratio (LCR), optical efficiency and average light concentration are three fundamental parameters of the optical performance of a PTC. These parameters are affected by various optical and physical factors. The effects of these individual factors on the performance parameters were investigated in this study using a verified Monte Carlo ray tracing optical simulation model. The investigation revealed that all three performance parameters are directly related to the optical properties of the collector components. The values decreased gradually with the increase of focal length of the mirror. Uniformity of the LCR profile was observed to decrease with increasing rim angle and geometric concentration. Defocus dislocation of the receiver was found to improve the uniformity of the LCR distribution by decreasing its peak concentrations, Cmax . Off-focus dislocation of the receiver, and inward angular deviation of the mirror profile were observed to increase the Cmax and decrease the uniformity of the LCR distribition. Out-focus dislocation of the receiver and solar tracking error distort the bi-symmetry of a normal LCR profile. Keywords: parabolic trough collector; concentrating solar power; optical efficiency; collector performance; uniformity of irradiance distribution

1. Introduction Parabolic trough collectors (PCTs) usually comprise a parabolic reflector and a receiver through which a heat transfer fluid is circulated. The solar radiation reaching the PTC is reflected and focused onto the outer surface of a receiver absorber tube where the radiant energy is converted into thermal energy. This thermal energy is then conducted to the inner surface of the absorber tube and transferred to the heat transfer fluid by forced convection. This is considered a coupled heat transfer problem with complex geometrical conditions [1]. The PTC shown in Figure 1, consists of a single axis North-South tracking parabolic trough mirror that focuses solar radiation onto the receiver comprising an absorber tube surrounding by an evacuated glass envelope. Ideally, the receiver axis is coincident with the focal line of the mirror. The overall energy performance of the collector depends on its optical performance. The optical performance involves various parameters, including irradiance distribution around its receiver tube, optical efficiency (ηopt ) and average light concentration (Cavg ). These three performance parameters are affected by various Energies 2017, 10, 1907; doi:10.3390/en10111907

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The PTC shown in Figure 1, consists of a single axis North-South tracking parabolic trough mirror that focuses solar radiation onto the receiver comprising an absorber tube surrounding by an evacuated glass envelope. Ideally, the receiver axis is coincident with the focal line of the mirror. Energies 2017, 10, 1907 2 of 19 The overall energy performance of the collector depends on its optical performance. The optical performance involves various parameters, including irradiance distribution around its receiver tube, optical efficiency (ηopt) and average light concentration (Cavg). These three performance parameters optical and physical factors including optical properties of the collector components, Direct Normal are affected by various optical and physical factors including optical properties of the collector Irradiance (DNI), collector design parameters, and optical errors. Basic design parameters of the components, Direct Normal Irradiance (DNI), collector design parameters, and optical errors. Basic collector include its Geometric Concentration (GC), rim angle and the focal length of the mirror. The GC design parameters of the collector include its Geometric Concentration (GC), rim angle and the focal is the ratioofofthe the mirror aperture surfacearea area. Forreceiver a givensurface collector length mirror. The GC is thearea ratiotoofthe the receiver mirror aperture to the area.geometry, For a the irradiance distribution and the η are significantly affected by its optical errors, including opt given collector geometry, the irradiance distribution and the ηopt are significantly affected by its the receiver dislocation from the of the mirror, deviation of the profile, and tracking error [2]. optical errors, including thefocus receiver dislocation from the focus of mirror the mirror, deviation of the mirror Optical optimization of the collector systemoptimization from its design to operation requires explicit information profile, and tracking error [2]. Optical of the collector system from its design to operation requires explicit information to understand partial effects, factors of all these to understand the contribution, or partial effects, of the all contribution, these opticalorand physical on the optical and physical of factors on the However, performance the collector. However, isthe performance parameters the collector. the parameters informationofleading to understanding either information leading understanding is either not readily available or scarce in the open literature. not readily available orto scarce in the open literature.

Figure 1. Cross-section of LS2 collector linear dimensions meter) and thecoordinate coordinatesystem systemused Figure 1. Cross-section of LS2 collector (all(all linear dimensions areare inin meter) and the used the ray (a) tracing: (a) the Cartesian coordinate system, , the , forcomplete the complete collector, in the rayintracing: the Cartesian coordinate system, collector, andand (b) the (X, Y, Z),, for the Polarsystem, coordinate , r, β , for the tubular , , −r cosβ) Polar(b) coordinate components suchcomponents that ( X, Y, Zsuch X, r sinβ, ( X, r, βsystem, ), for the tubular ) = (that r β, d,r f, W β and (in ψ theare figure, d, f, W and ψ arehalf depth, focal length, half width rim respectively, angle of (in the, figure, depth, focal length, width and rim angle of the and mirror, the mirror, respectively, and the acronyms PT, GT and RT mean Parabolic Trough, Glass Tube and and the acronyms PT, GT and RT mean Parabolic Trough, Glass Tube and Receiver Tube, respectively). Receiver Tube, respectively).

TheThe literature contains experimental investigations and and theoretical studies performed to measure literature contains experimental investigations theoretical studies performed to or predict along thealong perimeter of the tubular receiver of theofcollector measurethe or irradiance predict the distribution irradiance distribution the perimeter of the tubular receiver the preferably ideal condition, in someand occasions, tracking error. The error. experimental collectoratpreferably at idealand condition, in someconsidering occasions, considering tracking The experimental investigations apply photogrammetry [3–5] and[6,7], fluxand mapping [6,7], studies and theoretical investigations apply photogrammetry [3–5] and flux mapping theoretical apply cone studies apply optics [8–10] and Monte CarloVery ray tracing Very few ofextensively these publications optics [8–10] and cone Monte Carlo ray tracing [11–19]. few of [11–19]. these publications addressed extensively addressed the effects collector design and optical error parameters on the the effects of collector design and of optical error parameters extensively on the extensively optical performance optical performance parameters. Kalogirou et al. [20], and Thomas and Guven [2] investigated parameters. Kalogirou et al. [20], and Thomas and Guven [2] investigated the effect of opticalthe errors effect of optical errors on both light interceptance and irradiance distribution of a PTC considering on both light interceptance and irradiance distribution of a PTC considering the total effect of all the total effect of all the errors as “effective sunshape”, and the energy distribution was obtained the errors as “effective sunshape”, and the energy distribution was obtained applying a convolution applying a convolution technique. However, partial effects of different factors on the performance technique. However, partial effects of different factors on the performance parameters are not evident parameters are not evident from these studies. from these studies. This paper is part of a larger study, to design a hybrid photovoltaic-thermal collector that would provide uniform light distribution on the photovoltaic solar cells and improve the overall energy performance of the collector. A non-uniform flux on the PV solar cells could lead to considerable power loss from hot spots due to the Joule effect, resulting in an overall loss of PV efficiency [21,22]. The solar tracking error further increases the non-uniformity of the irradiance distribution. The voltage output of a concentrating PV solar cell increases logarithmically with irradiance intensity. The “shading effect”, which is caused by non-uniformity of the irradiance on the PV aperture, reduces the overall electrical performance of the PV as the least irradiated cell limits the series current output. Therefore, it is critical to achieve uniform flux distribution in the aperture area of an integrated PV-thermal PTC. Therefore, in this study, an extensive investigation was undertaken to explore the partial effects of various physical and optical factors on the optical performance of a standard PTC, and the information is made readily available to facilitate optical optimization of the collector in various phases

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including design, fabrication, installation and operation. For this purpose, an MCRT simulation model was developed and validated. The MCRT model was implemented in a Zemax optical simulation packages [23]. To be able to verify the MCRT model directly, the Luz Solar 2 (LS2) [24] PTC used in the Solar Energy Generating Systems (SEGS) III-VII plants was modelled. 2. Method of MCRT Simulation A cross sectional view of the 8 m long LS2 collector in a Cartesian coordinate system, and its evacuated glass enveloped receiver tube in a polar coordinate system are shown in Figure 1. A Cartesian coordinate system was used to calculate the instant spatial location and direction of movement of a ray. A cylindrical coordinate system was used to calculate the light incident location and intensity on the tubular components including the glass envelop and the receiver tube. An ideal Parabolic Trough (PT) mirror was developed by adapting a bi-conic surface. The width, length and focal length of the mirror were 5 m, 7.8 m and 1.84 m respectively. On the other hand, the tubular components of the collector including the Receiver Tube (RT) and the Glass Tube (GT) were developed adapting two concentric annular volume objects. The inner diameters of the RT and the GT were 66 mm and 109 mm respectively, whereas the thicknesses of both tubes were 2 mm and 3 mm respectively. The receiver was larger than the mirror by 100 mm at both ends. An ideal coating system was enabled to get desired specular reflectance on the mirror, glass transmittance with anti-reflection coating and receiver absorptance with selective coatings. Algorithm of the MCRT Currently there is few systematic framework or modelling algorithm for MCRT available in the relevant literature. To overcome this gap, this study proposes a comprehensive framework to conduct MCRT simulation of parabolic trough concentrators. The algorithm developed is presented in Figure 2. The steps are easy to follow and are self-explanatory. The rhombuses represent arguments, while the rectangles are decisions of those arguments. All of these arguments and decisions are carried over by applying the fundamental theories and Monte Carlo (MC) concepts as discussed below. Detailed equations of the model can be found in the authors’ previous publication [23]. The rays from the source to the receiver tube were traced according to the flow chart as illustrated in Figure 2. The statements inside the rhombuses are the MC statistical arguments, wile the answers of which depend on the sunshape, optical properties (mirror reflectance, glass transmittance and receiver absorptance), the geometry of the collector components, and the laws of reflection and refraction. The rays were assumed to be emitted from a sunshape, I (ϕ), as given by Equation (1) [25]. The azimuth angle and the deflection angle of the sunshape were 2π and 0.266◦ , respectively. The number of source rays per square meter of aperture area, Nray , was chosen by considering errors in the mirror reflectance and the glass transmittance. The higher the number of rays, the lower the absolute error in the MCRT calculated value, as illustrated in Figure 3. Considering the computational time and efforts, 5 × 107 to 10 × 107 rays per square meter of aperture area of the sunshape were chosen for this MCRT model. Fresnel’s law of reflection, Equation (2), describes the light reflected onto the mirror, and Snell’s law of refraction, Equation (3), describes the light transmitted through the receiver glass tube. Cos(0.05868ϕ/π ) I (ϕ) = (1) Cos(0.05544ϕ/π ) where, ϕ is the deflection angle. DPT = Dn − 2( NPT · Dn ) NPT DGT = DPT − ( NGT · DPT ) NGT +

q

(nGT )2 − (n air )2 + ( NGT · DPT )2 NGT

(2) (3)

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where, Dn , DPT and DGT are the directional vectors of the normal incident ray on the mirror aperture from the sun, reflected ray from the mirror and refracted ray through the glass tube respectively. Similarly, NPT and NGT are the normal vectors at the incident point of the rays on the mirror and the glass envelop respectively, while, nGT and nair are the refractive indices of the glass and air respectively. The normal vectors NPT and NGT , are given by Equations (4) and (5) respectively. NPT = q

NGT = q

− Py_PT Py_PT 2 + 4 f 2 Py_GT

Py_GT 2 + Pz_GT 2

j+ q

j+ q

2f Py_PT 2 + 4 f 2

k

Pz_GT Py_GT 2 + Pz_GT 2

(4)

k

(5)

where, P is the Cartesian coordinates of the incident points of the rays on the PT and the GT, and f is focal length of the mirror. Energies 2017, 10, 1907 4 of 19

Figure Figure 2. 2. Framework Framework for for the the Monte Monte Carlo Carlo ray ray tracing tracing model of Parabolic Trough Collector (PTC).

The rays were assumed to be emitted from a sunshape, I    , as given by Equation (1) [25]. The azimuth angle and the deflection angle of the sunshape were 2π and 0.266°, respectively. The number of source rays per square meter of aperture area, Nray, was chosen by considering errors in the mirror reflectance and the glass transmittance. The higher the number of rays, the lower the absolute error in the MCRT calculated value, as illustrated in Figure 3. Considering the computational time and efforts, 7

7

_ _

_ _

_

(5)

_

where, P is the Cartesian coordinates of the incident points of the rays on the PT and the GT, and f is 5 of 19 focal length of the mirror.

Energies 2017, 10, 1907

Figure 3. Optimum number of source rays per square meter aperture area, Nray . Error = {(True value Figure 3. Optimum number of source rays per square meter aperture area, Nray. Error = {(True value − MCRT calculated value) × 100%}/(True value). True value for mirror reflectance was 0.93 and for − MCRT calculated value) × 100%}/(True value). True value for mirror reflectance was 0.93 and for glass transmittance was 0.95. glass transmittance was 0.95.

3. Verification of the MCRT Model 3. Verification of the MCRT Model Dudley et al. [24] measured the near optical efficiency, (ηopt )Expt , of the LS2 collector for Dudley et al. [24] measured the near optical efficiency, (ηopt)Expt, of the LS2 collector for two two different selective coatings of the absorber tube, being cermet and black chrome, and three different different selective coatings of the absorber tube, being cermet and black chrome, and three different conditions of glass envelop, being evacuated or vacuum, air filled and removed. The mirror was conditions of glass envelop, being evacuated or vacuum, air filled and removed. The mirror was assumed to be perfect and have specular reflective, and the light incidence was assumed normal assumed to be perfect and have specular reflective, and the light incidence was assumed normal to to the mirror aperture for simplification. Mirror reflectance ($PT ), glass transmittance (τGT ), and the the mirror aperture for simplification. Mirror reflectance (ρPT), glass transmittance (τGT), and the absorptance of the cermet and the black chrome selective coatings were 0.9337, 0.935, 0.92 and 0.94 absorptance of the cermet and the black chrome selective coatings were 0.9337, 0.935, 0.92 and 0.94 respectively [26]. Using the same test conditions as Dudley et al. [24], the optical efficiencies, (ηopt )MCRT , respectively [26]. Using the same test conditions as Dudley et al. [24], the optical efficiencies, (ηopt)MCRT, estimated using our MCRT model were compared with the experimental optical efficiencies, (ηopt )Expt , estimated using our MCRT model were compared with the experimental optical efficiencies, (ηopt)Expt, (see Table 1). The model slightly over estimated the efficiency; with the absolute deviations between (see Table 1). The model slightly over estimated the efficiency; with the absolute deviations between 3.72% and 7.24% with an average of 6.19% which is reasonable given the simplifying assumptions. 3.72% and 7.24% with an average of 6.19% which is reasonable given the simplifying assumptions. Table 1. Selected test conditions of LS-2 collector from Dudley et al [24]. TC 1 2 3 4

DNI (W/m2 ) 807.9 925.1 954.5 850.2

Selective Coatings

Glass Tube Condition

(ηopt )Expt (%)

(%)

Cermet Cermet Cermet Black Chrome

Vacuum Air filled Removed Vacuum

72.63 73.68 77.5 73.1

1.91 1.96 2.36

(Eest )Expt

(ηopt )MCRT

(dabs )MCRT

(dabs )avg

(%)

(%)

(%)

77.89 76.42 82.59 78.38

7.24 3.72 6.57 7.22

6.19

In the table, TC, DNI, η, E and d stand for Test Condition, Daily Normal Irradiance, Efficiency, Error and deviation. The suffixes opt, Expt, est, abs and avg mean optical, experimental, estimated, absolute and average.

Since, Dudley et al. [24] did not measure the irradiance distribution around the LS2 receiver, the irradiance profile calculated in this study was verified with Jeter’s [8,9] analytical model. The GC, rim angle and the optical properties of the components of Jeter’s collector were 20×, 90◦ and unity respectively. The DNI was 1 kW/m2 , which was incident normally on the collector aperture from a sunshape of 7.5 mrad angular radius. Jeter calculated the Local Concentration Ratio (LCR) around the receiver of an ideal collector such that LCR = I(β)/DNI. In this study, the LCR profiles of the collector with a 3.5 mm thick evacuated glass envelop around the absorber and without glass envelop were calculated, and compared against Jeter’s analytical profile as shown in Figure 4. Both calculated profiles were found to be quite consistent with Jeter’s analytical one. Jeter’s analyses did not consider glass tube; which causes additional shading on the reflector (see the LCR at the 0◦ angular location of the receiver in the figure). The incoming rays striking the glass tube may be refracted towards

the receiver of an ideal collector such that LCR = I(β)/DNI. In this study, the LCR profiles of the collector with a 3.5 mm thick evacuated glass envelop around the absorber and without glass envelop were calculated, and compared against Jeter’s analytical profile as shown in Figure 4. Both calculated profiles were found to be quite consistent with Jeter’s analytical one. Jeter’s analyses did not consider Energiestube; 2017, which 10, 1907 causes additional shading on the reflector (see the LCR at the 0° angular location 6 of of 19 glass the receiver in the figure). The incoming rays striking the glass tube may be refracted towards either the receiver tube ortube the mirror, altoughaltough with little chance be reflected back to the receiver. very either the receiver or the mirror, with littletochance to be reflected back to theThe receiver. good matching between current profiles and Jeter’s profile confirms the reliability of the current The very good matching between current profiles and Jeter’s profile confirms the reliability of the MCRT currentmodel. MCRT model.

Local Concentration Ratio (×)

50

±180° -90°

40

RT 90°

0° Mirror

30

20 Jeter's profile MCRT result (without glass tube)

10

MCRT result

0 -180

-120

(with glass tube)

-60 0 60 120 Angular location on the receiver surface, β°

180

Figure Figure 4. 4. Comparison Comparison of of calculated calculated LCR LCR profiles profiles around around the the receiver receiver tube tube (RT) (RT) of of aa typical typical PTC PTC with with Jeter’s LCR profile. Jeter’s LCR profile.

4. Results of Parametric Analysis 4. Results of Parametric Analysis The model was The current current MCRT MCRT model was employed employed to to investigate investigate partial partial effects effects of: of: (1) (1) optical optical parameters, parameters, (2) design parameters, and (3) optical error parameters on the LCR distribution around (2) design parameters, and (3) optical error parameters on the LCR distribution around the the receiver receiver tube, η opt, and Cavg of the collector. The ηopt and Cavg were normalised by dividing a certain value by tube, ηopt , and Cavg of the collector. The ηopt and Cavg were normalised by dividing a certain value their respective maxumum value forfor a certain analysis. Where deemed reasonable, thethe uniformity of by their respective maxumum value a certain analysis. Where deemed reasonable, uniformity the LCR distribution was analyzed quantitatively by quantifying as minimum light concentration of the LCR distribution was analyzed quantitatively by quantifying as minimum light concentration (Cmin), maximum light concentration (Cmax), average light concentration (Cavg), and Mean Absolute (Cmin ), maximum light concentration (Cmax ), average light concentration (Cavg ), and Mean Absolute Deviation (MAD). The Cmin , Cmax and Cavg were estimated along the periphery of the cross-section of the absorber tube. The MAD was calculated as average of the absolute deviations of LCRs from their respective Cavg . The rim angle and the focal length of the mirror were about 70◦ and 1.84 m respectively, and the GC of the collector was around 22.74×. The DNI was assumed as 1 kW/m2 . Local specular reflectance of the mirror and the absorptance of the bare receiver were assumed 0.9335 and unity respectively. The characteristics of the LCR profiles were analysed against a normal LCR profile under ideal conditions as calculated using the current MCRT model and shown in Figure 5. The normal profile was found to be bi-symmetric about 0◦ –180◦ axis of the receiver, and almost uniform along the length of the receiver. A normal LCR profile of a PTC under ideal conditions was found to contain four distinct zones, termed as: A: Receiver Shadowing (RS) zone, B: Concentration Increasing (CI) zone, C: Concentration Falling (CF) zone, and D: Direct Sun (DS) zone. RS is the shadowing effect of the receiver on the mirror, which impact the area upto about 15◦ in the LS2 receiver. Inclusion of the glass envelope was observed to increase the shadowing effect (see Figure 4). Once the shadowing effect is diminished, the rest of the light concentrates on the receiver within around 45◦ angular location and raise the Cmax exponentially that forms the CI zone. As soon as the CI zone has peaked to Cmax , the concentration falls rapidly within 90◦ angular location of the receiver, which is called CF zone; and no more concentrated light is available. However, the upper half of the receiver receives the light from direct sun, which is called DS zone. Investigation revealed that this normal LCR profile is affected

receiver on the mirror, which impact the area upto about 15° in the LS2 receiver. Inclusion of the glass envelope was observed to increase the shadowing effect (see Figure 4). Once the shadowing effect is diminished, the rest of the light concentrates on the receiver within around 45° angular location and raise the Cmax exponentially that forms the CI zone. As soon as the CI zone has peaked to Cmax, the concentration falls rapidly within 90° angular location of the receiver, which is called CF zone;7 and Energies 2017, 10, 1907 of 19 no more concentrated light is available. However, the upper half of the receiver receives the light from direct sun, which is called DS zone. Investigation revealed that this normal LCR profile is significantly by collector design variations and optical errors. It was alsoIt observed ηopt , and affected significantly by collector design variations and optical errors. was also that observed that Cηavg opt, were affected also by the optical properties of the collector components as explained below. and Cavg were affected also by the optical properties of the collector components as explained below.

Figure 5. LCR LCR profile profile around the receiver tube (RT) of the LS2 collector at ideal condition. The profile is bi-symmetric about 0°–180° 0◦ –180◦ axis axis of of the the receiver, receiver, and theoretically theoretically uniform uniform along along the length of the receiver. The as,as, A:A: Receiver Shadowing (RS) zone; B: TheLCR LCRprofile profilecontains containsfour fourdistinct distinctzones, zones,such such Receiver Shadowing (RS) zone; B: Concentration Increasing (CI) zone; ConcentrationFalling Falling(CF) (CF)zone, zone,and andD: D:Direct Direct Sun Sun (DS) (DS) zone. Concentration Increasing (CI) zone; C:C: Concentration

4.1. Effect of Optical Properties of the Collector, DNI and Glass Glass Envelop Envelop Thickness Thickness

70

70

60

60

50

Local Concentration Ratio


The optical properties of the collector includes the mirror reflectance, glass transmittance and receiver absorptance. The effect of these properties; properties; the DNI, DNI, and and the the thickness thickness of of the the glass glass envelope; envelope; on the optical performance of a PTC were investigated as presented presented in in Figure Figure 6. 6. As the figure shows, shows, the the LCR, LCR, C Cavg avg and η opt were ηopt were observed observed to to be be directly directly proportional proportional to the mirror reflectance, glass transmittance. The DNI was also observed to have a directly proportional mirror reflectance, glass transmittance. The DNI was also observed to have a directly proportional impact on LCR LCR and and C Cavg avg,, and, indirect effect effect on on ηηopt opt.. The impact on and, however, however, very very little little indirect The glass glass envelop envelop thickness thickness was found found to to have have very very little little and and indirect indirect impact impact on on the the optical optical performance performance parameters. parameters. None of was None of these factors was found to modify the normal shape but vary the local value of the LCR profile. these factors was Energies 2017, 10, 1907found to modify the normal shape but vary the local value of the LCR profile. 8 of 19



40



30

 

20 10

τ = 0.9 τ = 0.9335 τ = 0.95 τ=1 No envelop

50 40 30 20 10 0

0 0

0

30 60 90 120 150 180 Angular location on the receiver outer surface, β°

30 60 90 120 150 180 Angular location on the receiver outer surface, β°

(a)

(b) 70

Figure 6. Cont.

60 50 40 30 20 10 0

DNI = 1 kW

60    



70

DNI = 0.9 kW

50

DNI = 0.75 kW DNI = 0.6 kW

40

DNI = 0.45 kW

30

DNI = 0.35 kW DNI = 0.2 kW

20 10 0 0

30

60

90

120

150

180

Local Co

Local Co



20 10

20 10 0

0 0 10, 1907 30 60 90 120 150 180 Energies 2017, Angular location on the receiver outer surface, β°

0

30 60 90 120 150 180 8 of 19 Angular location on the receiver outer surface, β°

(a)

(b) 70

60 50 

40



30

 

20 10

DNI = 0.9 kW

50

DNI = 0.75 kW DNI = 0.6 kW

40

DNI = 0.45 kW

30

DNI = 0.35 kW DNI = 0.2 kW

20 10 0

0 0

30

60

90

120

150

0

180

30

60

(c)

70

90

120

150

180

Angular location on the receiver outer surface, β°


(d) 1

Normalised optical efficiency and average light concentration

DNI (Opt. effi.)

60


DNI = 1 kW

60



70

t = 0 mm t = 1 mm

50

t = 2 mm

40

t = 3 mm t = 5 mm

30

t = 7 mm

20 10 0 0

30

60

90

120

150

180


DNI (Avg. concentration)

0.8

Mirror reflactance Glass transmittance

0.6

Glass thickness Receiver absorptance

0.4 0.2 0 0

0.2 0.4 0.6 0.8 1 DNI (kW/m2), mirror reflectance, glass thickness

(e)

(f)

Figure6.6. Effect Effectof of (a) (a) mirror mirror reflectance; reflectance;(b) (b)glass glasstransmittance; transmittance;(c) (c)receiver receiverabsorptance; absorptance;(d) (d)DNI DNIand and Figure (e)glass glassthickness thicknesson onthe theLCR LCRdistribution distributionaround aroundthe thereceiver receivertube, tube,and and(f) (f)effect effectof ofthese theseparameters parameters (e) andnormalised normalisedaverage averagelight lightconcentration, concentration,CCavg avg,, of of the the on the thenormalised normalisedoptical opticalefficiency, efficiency,ηopt ηopt, ,and on collector. (These values were normalised dividing by their respective maxumum value). collector. (These values were normalised dividing by their respective maxumum value).

4.2. Effect Effect of of Design DesignParameters Parametersofofthe theCollector Collector 4.2. Focallength, length,rim rimangle angleand andGC GCare arethree threefundamental fundamentaldesign designparameters parametersof ofaaPTC. PTC.Focal Focallength length Focal the characteristic characteristic parameter parameter of of aa parabolic parabolic mirror. mirror. The The depth depth and and width width of of the the mirror mirror depend depend isis the directly on the rim angle. On the other hand, GC is the ratio of the mirror aperture area to the receiver directly on the rim angle. On the other hand, GC is the ratio of the mirror aperture area to the receiver surfacearea. area. The The GC GC of of aa PTC PTC can canbe be varied varied either eitherby byvarying varying the thereceiver receiverdiameter diameteror ormirror mirrorwidth width surface independently or or both both together. together. However, However, variation variation of of the themirror mirrorwidth widthcauses causesvariation variation of ofthe therim rim independently angle. The effects of rim angle and GC on the optical performance of a PTC were investigated with angle. The effects of rim angle and GC on the optical performance of a PTC were investigated witha amirror mirrorofoffixed fixedfocal focallength, length,and andwith withmirrors mirrorsof ofdifferent differentfocal focallengths lengthsas asdescribed describedbelow. below. 4.2.1. Effect of Rim Angle and GC with a Mirror of Fixed Focal Length The GC was increased by decreasing the receiver diameter for a fixed rim angle. In addition, the rim angle was increased by increasing the trough width for a fixed receiver diameter, which is also increased the GC. The effects of these parameters on the optical performance parameters were analysed as presented in Figures 7 and 8 and Table 2.


80

ψ = 7.77° ψ = 15.48° ψ = 23.04° ψ = 30.41° ψ = 44.35° ψ = 57.05° ψ = 68.38° ψ = 78.38° ψ = 87.13° ψ = 91.08° ψ = 94.77°

Without glass tube

70

Local Concentration Ratio (LCR) Local Concentration Ratio (kW/m2)

As shown in Figure 8a,b, the ηopt was decreasing gradually and the Cavg was increasing exponentially with increasing of rim angle. The ηopt of the receiver without the glass envelop was predicted to drop by around 4% in total until a 90° rim angle. On the other hand, the ηopt was estimated to be increased by about 2% in total until a 70° rim angle and then decreased by about 0.5% Energies 2017,rim 10, 1907 9 of 19 until a 90° angle. However, the graphs of the Cavg for both the conditions: with and without glass envelop, were found almost superimposed to one another (see Figure 8b).

60 50 40 30 20 10

80

With glass tube

70

ψ = 15.47° ψ = 23.04° ψ = 30.40° ψ = 44.35° ψ = 57.05° ψ = 68.38° ψ = 78.38° ψ = 87.13° ψ = 94.77°

60 50 40 30 20 10 0

0 0

30

60

90

120

150

0

180

30

60

90

120

150

180

Angular location on the receiver outer surface, β° 10 of 19


Energies 2017, 10, 1907

(a)

(b) Local ConcentrationRatio Ratio Local Concentration

140 140 120 120

GC==53.03 53.03 GC GC==39.77 39.77 GC GC==31.82 31.82 GC GC==22.73 22.73 GC GC==17.68 17.68 GC GC==14.46 14.46 GC GC==13.26 13.26 GC

100 100 80 80 60 60 40 40 20 20

00

60 90 120 00 30 60 90 120 150 150 180 180 Angular location on the receiver outer surface, β° Angular location on the receiver outer surface, β°

(c) (c) Figure 7. 7. Effect Effect of of rim rim angle angle for, for, (a) (a) the the receiver receiver without without glass glass envelop envelop and and (b) (b) the the receiver receiver with with glass glass Figure Figure 7. Effect of rim angle for, (a) the receiver without glass envelop and (b) the receiver with glass envelop, and (c) the effect of Geometric Concentration (GC) on LCR profile of a PTC with a mirror of envelop, and (c) the effect of Geometric Concentration (GC) on LCR profile of a PTC with a mirror of envelop, and (c) the effect of Geometric Concentration (GC) on LCR profile of a PTC with a mirror of fixed focal length. fixed focal length. fixed focal length.

0.995 0.99 0.985 0.98 0.975 0.97

(i)

(ii)

(iii)

0.965

Normalised value of average light concentration, Cavg

Normalised optical efficiency, ηopt

1

0 0.2 0.4 0.6 0.8 1 1.2 Normalised value of rim angle (= ψ ÷ 90°) and normalised geomatric concentration (= GC ÷ 100)

1 0.75 0.5

(iv) (v)

0.25

(vi)

0 0

0.25

0.5

0.75

1

1.25

Normalised value of rim angle (= ψ ÷ 90°) and normalised geomatric concentration (= GC ÷ 100)

(a)

(b)

Figure Figure 8. 8. (a) (a)Effect Effectof, of,(i) (i)rim rimangle anglefor forthe thereceiver receiverwithout without glass glass envelop; envelop; (ii) (ii) rim rim angle angle for for the the receiver receiver opt of a PTC; and (b) effect of, (iv) rim angle for the with glass envelop and (iii) GC on normalised η with glass envelop and (iii) GC on normalised ηopt of a PTC; and (b) effect of, (iv) rim angle for receiver without glass envelop; (v) (v) rimrim angle forfor thethe receiver the receiver without glass envelop; angle receiverwith withglass glassenvelop envelopand and(vi) (vi) GC GC on on avg of a PTC. normalised C normalised C of a PTC. avg

Table 2. Effect of design parameters on the uniformity of the LCR distribution around the receiver of a PTC. Variation of Mirror with Different Focal Length Ideal LS2 collector, GC = 22.74, ψ ≈ 70°, f = 1.84 m GC = 53.03 do = V ψ = C Mirror focal GC = 13.26 length is ψ = 44.35°

Cmin (sun) 0 0.5 0 0

Cmax (sun) 63.5 136.8 38.7 55.3

Cavg (sun) 21.8 50.9 12.8 13.2

MAD 23.7 48.7 14.2 17.6

Energies 2017, 10, 1907

10 of 19

Table 2. Effect of design parameters on the uniformity of the LCR distribution around the receiver of a PTC. Variation of Mirror with Different Focal Length Ideal LS2 collector, GC = 22.74, ψ ≈ Mirror focal length is fixed

Mirror focal length is variable

70◦ ,

f = 1.84 m

Cmin (sun)

Cmax (sun)

Cavg (sun)

MAD

0

63.5

21.8

23.7

do = V ψ = C

GC = 53.03 GC = 13.26

0.5 0

136.8 38.7

50.9 12.8

48.7 14.2

do = C W = V

ψ = 44.35◦ ψ = 87.13◦

0 0.4

55.3 74.3

13.2 30.4

17.6 26.3

GC = C ψ = V

f = 1.4 m f=3m

0.2 0

57.4 85.0

22.0 21.4

20.5 27.2

GC = V ψ = C

f = 1.4 m f=3m

0 0.2

50.4 96.0

16.8 34.6

18.5 35.5

GC = C ψ = C

f = 1.4 m f=3m

0 0

64.4 61.2

22.1 20.9

23.9 22.8

In the table: LS2 = Luz Solar 2 collector, sun = unit of light concentration = 1 kW/m2 ; Cmin , Cmax and Cavg , and MAD stand for minimum, maximum and average light concentration, and Mean Absolute Deviation; GC = Geometric Concentration, ψ = rim angle, f = focal length, do = outer diameter of the receiver, W = half width of the mirror, V = variable and C = constant or fixed.

Figure 7a,b show that increasing the rim angle extends the Concentration Increasing zone by increasing the Cmax . Therefore, the light coverage at the bottom of the receiver was found to be increasing, and the Direct Sun region was decreasing with rim angle. Moreover, as the Cmax was estimated to be increasing, the Concentration Falling zone was also extending with rim angle. However, the slope of the CI zone was found to be independent of the rim angle and they were found to be almost parallel with each other at all rim angles. The presence of the glass envelop was observed to increase shadowing on the mirror, as a result, the Receiver Shadowing zone became deeper. As shown in Figure 8a,b, the ηopt was decreasing gradually and the Cavg was increasing exponentially with increasing of rim angle. The ηopt of the receiver without the glass envelop was predicted to drop by around 4% in total until a 90◦ rim angle. On the other hand, the ηopt was estimated to be increased by about 2% in total until a 70◦ rim angle and then decreased by about 0.5% until a 90◦ rim angle. However, the graphs of the Cavg for both the conditions: with and without glass envelop, were found almost superimposed to one another (see Figure 8b). When the GC was increased by decreasing the receiver diameter, the same amount of light was concentrating on a smaller surface area of the receiver. Therefore, although Cmax was increasing, the Concentration Increasing zone was not extending; rather this zone was merging with Receiver Shadowing zone (see Figure 7c). The slope of the Concentration Falling zone was observed to be decreasing gradually with increasing GC. Since, the mirror width was not increasing, the increase of GC had an indirect, but, insignificant effect on the ηopt , as can be seen from Figure 8a. However, as the receiver surface area was decreasing with the increase of GC, the Cavg was observed to be increasing linearly (see Figure 8b). As presented in Table 2, the increase of both rim angle and GC for fixed focal length were observed to increase non-uniformity of the LCR dsitribution. The non-uniformity was observed more sensitive to the GC than the rim angle. For instance, the MAD was estimated to be increased rapidly from 14 to 49 for the GCs between 13 and 53, whereas, that was estimated to be increased from 18 to 26 for the rim angles between 44◦ and 87◦ . 4.2.2. Effect of Mirrors of Different Focal Lengths Focal length is a characteristic parameter of a parabolic mirror. A variation of focal length refers to a variation of the mirror with a certain focal length. The effects of varying the focal length on the

Energies 2017, 10, 1907

11 of 19

90 90 80 80 70 70 60 60 50 50 40 40 30 30 20 20 10 10 00

120 120

ff==1.25 1.25m m ff==1.4 1.4m m ff==1.6 1.6m m ff==1.84 1.84m m ff==22m m ff==2.2 2.2m m ff==2.4 2.4m m ff==2.6 2.6m m ff==2.8 2.8m m ff==33m m

GC GC was was fixed fixed

Local Concentration Concentration Ratio Ratio Local


optical performance parameters were investigated for various rim angles and GCs. The effects are shown in Table 2, Figures 9 and 10. Energies 10, 12 Energies 2017, 2017, 10,1907 1907 12 of of 19 19 Rim Rim angle angle was was fixed fixed

100 100 80 80 60 60 40 40 20 20 00

00 30 60 90 120 150 180 30 60 90 120 150 180 Angular Angular location location on on the the receiver receiver outer outer surface, surface, β° β°

00


60 60

90 90

120 120

150 150

180 180

(b) ↑,, GC ↑and (b) ifif ff↑ GC↑ and vice vice versa versa

70 70

ff==0.5 0.5m m ff==0.8 0.8m m

60 60

ff==1.1 1.1m m ff==1.4 1.4m m

50 50 40 40

ff==1.84 1.84m m ff==22m m

30 30

ff==2.5 2.5m m ff==33m m

Both Both GC GC and and Rim Rim angle angle were were fixed fixed

ff==3.5 3.5m m

10 10 00

30 30

Angular Angular location location on on the the receiver receiver outer outer surface, surface, β° β°

(a) ↑,, ψψ↓ ↓and (a) ifif ff↑ and vice vice versa versa

20 20

ff==0.5 0.5m m ff==0.8 0.8m m ff==1.1 1.1m m ff==1.4 1.4m m ff==1.84 1.84m m ff==22m m ff==2.5 2.5m m ff==33m m ff==3.5 3.5m m

00

30 60 90 120 150 180 30 60 90 120 150 180 Angular Angular location location on on the the receiver receiver outer outer surface, surface, β° β°

(c) (c)

Normalised optical optical efficiency, efficiency, ηηopt Normalised opt

11 0.98 0.98 0.96 0.96 0.94 0.94 0.92 0.92 GC GCwas wasfixed fixed

0.9 0.9

Rim Rimangle anglewas wasfixed fixed

0.88 0.88 0.86 0.86

Both BothGC GCand andRim Rimangle anglewere werefixed fixed

00

11 22 33 Focal Focal length, length, f,f, of of the themirror mirror(m) (m)

(a) (a)

44

Normalised average average light light concentration, concentration, Normalised Cavg C avg

Figure 9. variations in terms of their focal length, Figure9. 9. Effect Effect of of mirror mirror variations variations in in terms terms of of their their focal focal length, length, f, on local local oncentration oncentration ratio ratio profile profile Figure Effect of mirror f,f, on on local oncentration ratio profile of a PTC for: (a) Fixed Geometric Concentration (GC). The receiver outer diameter and the mirror of aa PTC PTC for: for: (a) (a) Fixed Fixed Geometric Geometric Concentration Concentration (GC). (GC). The The receiver receiver outer outer diameter diameter and and the the mirror mirror of aperture width are fixed. aa mirror aa larger has rim angle vice; aperturewidth widthare are fixed. So mirror of larger focal length length has aa smaller smaller rim angle and vice; aperture fixed. SoSo a mirror of a of larger focal focal length has a smaller rim angle and vice; and (b) Fixed (b) Fixed rim angle, ψ. As the receiver outer diameter and rim angle are fixed, a mirror of a larger (b) Fixed rim angle, ψ. As the receiver outer diameter and rim angle are fixed, a mirror of a larger rim angle, ψ. As the receiver outer diameter and rim angle are fixed, a mirror of a larger focal length focal an aperture width, and so aa larger GC, (c) GC focal length has an larger larger aperture width, and so and larger GC, and andand (c) fixed fixed GC and and rim rim angle. angle. has anlength largerhas aperture width, and so a larger GC, (c) fixed GC rim angle. 11 0.8 0.8 0.6 0.6 0.4 0.4 GC GCwas wasfixed fixed

0.2 0.2 00

Rim Rimangle anglewas wasfixed fixed Both BothGC GCand andrim rimangle anglewere werefixed fixed

00

11 22 33 Focal Focal length, length, f,f, of of the themirror mirror (m) (m)

44

(b) (b)

Figure Figure 10. 10. Effect Effect of of mirror focal length on (a) normalised opt and and (b) (b) normalised normalised C Cavg avg for for different different rim rim Figure 10. Effect ofmirror mirrorfocal focallength lengthon on(a) (a)normalised normalisedηηopt η opt and (b) normalised Cavg for different angle and GC. angle andand GC.GC. rim angle

4.3. 4.3. Effect Effect of of Optical Optical Errors Errors Optical Optical errors errors including including dislocation dislocation of of the the receiver receiver from from the the focus focus of of the the mirror, mirror, deviation deviation of of the the mirror mirror profile profile from from its its ideal ideal parabolic parabolic shape, shape, and and tracking tracking error error can can affect affect the the optical optical performance performance of of the the collector collector adversely. adversely. The The partial partial effect effect of of all all these these individual individual errors errors on on the the optical optical performance performance parameters parameters of of the the collector collector were were investigated investigated as as described described below. below.

Energies 2017, 10, 1907

12 of 19

For a PTC with fixed GC for a fixed receiver, the mirror of a larger focal length has smaller rim angle. So, the light is concentrated onto a smaller surface area of the receiver, and the Cmax was increasing gradually with the increase of focal length as shown in Figure 9a. As a result, the Receiver Shadowing zone and the Concentration Increasing zone were observed to be gradually merging with each other with increasing focal length. Thus, Cmax was estimated to increase from around 55 suns to 85 suns with an increase in mirror focal length from 1.25 m to 3 m. The Concentration Falling zones of all LCR profiles were found almost parallel to each for all focal lengths as shown in the same figure. The increase of focal length was observed to have adverse effect on the ηopt and Cavg . Both the performance parameters were estimated to be dropped almost linearly by around 3% for the focal length variation between 1.25 m and 3 m as is shown in Figure 10. On the other hand, for a PTC with fixed rim angle and fixed receiver diameter, the larger the focal length of the mirror, the larger the GC of the collector and vice versa. Therefore, Cmax was observed to be increasing, the Receiver Shadowing and Concentration Increasing zones merging together, the slope of the Concentration Falling zone was decreasing, and the Direct Sun zone was shortening gradually with the increase of focal length as shown in Figure 9b. However, while Cavg was observed to be increasing, ηopt was decreasing linearly with increasing focal length as illustrated in Figure 10. The calculated ηopt was dropped by about 6% as the focal length increased from 0.5 m to 3.5 m. Finally, the sole effect of mirror focal length on the optical performance of a PTC was investigated for a fixed rim angle and fixed GC. The magnitudes of the LCR were estimated to be gradually decreasing with increasing focal length, although the LCR profiles were almost parallel to each other (see Figure 9c). Both ηopt and Cavg , were found to drop by about 12% as the focal length increased from 0.5 m to 3.5 m. In addition, the drop also gradually increased with increasing focal length. As presented in Table 2, when the GC was varied, GC =V in the table, the uniformity of the LCR profile was found to decrease more quickly than that when the rim angle was varied with an increase in focal length. The MAD estimated was almost doubled for the variable GC case, while MAD increased by only one third for the variable rim angle case with an increase of focal length from 1.4 m to 3 m. However, MAD was found to decrease slightly from 24 to 23 when the range of focal lengths was varied under fixed rim angle and GC conditions. 4.3. Effect of Optical Errors Optical errors including dislocation of the receiver from the focus of the mirror, deviation of the mirror profile from its ideal parabolic shape, and tracking error can affect the optical performance of the collector adversely. The partial effect of all these individual errors on the optical performance parameters of the collector were investigated as described below. 4.3.1. Effect of Dislocation of the Receiver A faulty assembly or structural deformation may cause dislocation of the receiver from the focus of the mirror. The dislocation can modify the LCR, and may have an adverse impact on the optical performance of a collector. Referring to Figure 11, the dislocation was assumed along three different directions: off-focus (↑ in the figure), defocus (↓ in the figure) and out-focus (→ in the figure). The dislocation, d, was expressed as dimensionless value dividing by the radius, r, of the receiver. The findings are described in Figure 11 and Table 3. The light was observed to be gradually concentrating on smaller surface area at the bottom (at β = 0◦ ) of the receiver with an increase in off-focus dislocation as illustrated in Figure 11a. The LCR profile was becoming Gaussian in shape diminishing the Receiver Shadowing and Concentration Increasing zones completely into the Concentration Falling zone. As a result, Cmax reached 240 suns at a unit off-focus dislocation (d↑ = r). The CF zone was moving towards the RS zone, and the Direct Sun zone was extending with the gradual increase of dislocation. The off-focus dislocation was found increase the non-uniformity of the LCR profile gradually. From Table 3, it can be seen that the MAD was increased from 23.7 to 33 when the receiver was dislocated by 77% of its radius.

profile was becoming Gaussian in shape diminishing the Receiver Shadowing and Concentration Increasing zones completely into the Concentration Falling zone. As a result, Cmax reached 240 suns at a unit off-focus dislocation (d↑ = r). The CF zone was moving towards the RS zone, and the Direct Sun zone was extending with the gradual increase of dislocation. The off-focus dislocation was found increase the10,non-uniformity of the LCR profile gradually. From Table 3, it can be seen that the13 MAD Energies 2017, 1907 of 19 was increased from 23.7 to 33 when the receiver was dislocated by 77% of its radius. "Off-Focus" receiver

210

d↑ = 0.14r

180

d↑ = 0.29r

150

d↑ = 0.43r d↑ = 0.57r

120

70

d↑= 0

d↑ = 0.71r

90

d↑ = r

60

d↑ = 1.29r



240

"Defocus" receiver

60 50 40 30 20 10

30

0

0

0

0 30 60 90 120 150 180 Angular location on the receiver outer surface, β°

30

60

60 40

d→ = 0.14r d→ = 0.29r

120

150

180

(b) Normalised optical efficiency and average light concentration


80

d→ = 0

90


(a) 100

d↓ = 0 d↓ = 0.14r d↓ = 0.29r d↓ = 0.43r d↓ = 0.57r d↓ = 0.71r d↓ = 0.77r d↓ = r d↓ = 1.29r

"Out-Focus" receiver

d→ = 0.43r d→ = 0.57r d→ = 0.71r d→ = 0.77r

20 0 -180-150-120-90 -60 -30 0 30 60 90 120 150 180 Angular location on the receiver outer surface, β°

1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

Off-Focus Defocus Out-Focus

0

0.25 0.5 0.75 1 1.25 Ratio of dislocation of the receiver, d, and the radius, r, of the receiver.

(c)

(d)

Figure 11. 11. Effect Effect of ofreceiver receiverdislocation dislocationononthe the LCR profile of the receiver: (a) off-focus; (b) defocus Figure LCR profile of the receiver: (a) off-focus; (b) defocus and and (c) out-focus, and (d) on the η opt and Cavg of the collector. (Here, ‘r’ is the radius of the receiver, ‘d’ (c) out-focus, and (d) on the ηopt and Cavg of the collector. (Here, ‘r’ is the radius of the receiver, ‘d’ is is the amount dislocation, and arrows show direction of dislocation). the amount of of dislocation, and thethe arrows show thethe direction of dislocation). Table 3. Effect of collector operating conditions on the uniformity of the LCR distribution around the receiver of a PTC. Error of the Collector Elements Ideal LS2 collector, GC = 22.74, ψ ≈

Receiver dislocation

f = 1.84 m

Cmin (sun)

Cmax (sun)

Cavg (sun)

MAD

0

63.5

21.8

23.7

Off-focus

d↑ = 0.14r d↑ = 0.77r

0.0 0

69.6 216.4

21.8 21.7

25.5 33.2

Defocus

d↓ = 0.14r d↓ = 0.77r

0.116 1.0

58.9 41.6

21.9 21.8

21.9 12.4

Out-focus

d↔ = 0.14r d↔ = 0.77r

0.0 0

102.6 13.4

21.8 2.8

23.4 3.2

0.2◦ 1◦

0 0.0

69.7 35.9

21.7 9.0

23.4 10.8

Inward deviation

Û = 0.05◦ Û = 0.375◦

0 0

71.0 109.8

21.8 21.8

24.8 30.0

Outward deviation

ˇ = 0.05◦ U ˇ = 0.35◦ U

0.062 0

64.0 67.0

21.9 21.9

22.5 21.9

Tracking error

Mirror profile deviation

70◦ ,

In the table: LS2 = Luz Solar 2, sun = unit of light concentration = 1 kW/m2 ; Cmin , Cmax and Cavg , and MAD stand for minimum, maximum and average light concentration, and Mean Absolute Deviation; GC = Geometric Concentration, ψ = rim angle, f = focus, d = amount of dislocation, r = radius of the receiver and the arrows show the directions of dislocation of the receiver from the focus of the mirror.

Energies 2017, 10, 1907

14 of 19

On the other hand, the effect of defocus dislocation of the receiver on the LCR distribution and its uniformity observed was almost the reverse to that of the off-focus dislocation. As shown in Figure 11b, the concentrated light was observed to be gradually occupying more surface area at the bottom (at β = 0◦ ) of the receiver, which was flattening the Concentration Increasing zone, and shrinking the Direct Sun zone gradually. As a result, Cmax was dropped to 30 suns at unit defocus dislocation (d↓ = r). This dislocation was observed to increase the uniformity of the LCR profile. The MAD was dropped to 12 from 33 for 0.77r defocus dislocation (see Table 3). Both these dislocations were found to have equal and very little effect on the ηopt and the Cavg till 0.75r (dl = 0.75) dislocation as shown in Figure 11d. Dislocation of more than 0.75r was found to affect ηopt and Cavg adversely as the light was missing the receiver. On the other hand, out-focus dislocation of the receiver was observed to diminish the normal bi-symmetry of the LCR profile as shown in Figure 11c. The ηopt and Cavg were observed to be decreased rapidly after just 0.14r out-focus dislocation (d↔ = 0.14r) as shown in Figure 11d. Table 3 shows that, the Cmax and the Cavg were dropped from 103 suns to 13 suns at 0.14r dislocation and 22 suns to 3 suns at 0.77r dislocation, respectively. 4.3.2. Effect of Deviation of Parabolic Profile of the Mirror Perfection of the parabolic profile of a PTC mirror is one of the most important prerequisites for its standard optical performance. Since, any external load such as wind load or dead load during operation may distort a mirror from its ideal profile; one way to simulate this is through rotation of the mirror halves around its vertex. The actual aperture width will decrease for inward (Û◦ ) rotation ˘ ◦ ) rotation from the ideal as shown in Figure 12. The effects of these and will increase for outward (U Energies 2017, 10, 1907 deviations on the optical performance of the PTC were investigated as illustrated in Figure 13.15 of 19

Figure 12. Actual profile versus ideal profile of a parabolic mirror. In the figure, V is the vertex of the Figure 12. Actual profile versus ideal profile of a parabolic mirror. In the figure, V is the vertex of the parabola, and Û° and ˘Ŭ° are the inward and outward angular rotation of two halves of the mirror ◦ are parabola, and Û◦ and U the inward and outward angular rotation of two halves of the mirror with with respect to the vertex from its ideal profile respectively. respect to the vertex from its ideal profile respectively. 120

70



Ǔ = 0.0°surface From Figure 13a, the concentrated Û = 0.0° light was observed to occupy a gradually smaller Ǔ = 0.025° 60 100 = 0.05°an increase of inward angular deviation of the mirror Ǔ = 0.05°profile. area at the bottom of the receiverÛwith Ǔ = 0.075° Û = 0.075° 50 80 Ǔ = Increasing 0.15° This deviation was found to reverse slopes of the Receiver Shadowing and Concentration Û =the 0.15° Ǔ = 0.25° Û =Eventually, 0.25° zones60gradually one after another. these RS40and CI zones aligned with the Concentration Ǔ = 0.35° Û = 0.375° Ǔ = 0.5° 30 the increase of the deviation.ǓThe Falling zone, and formed a Gaussian Û = 0.5° LCR profile with = 0.6°highest Û =around 0.65° value40 of Cmax was estimated to be 110 suns at200.375◦ inward deviation. On the other hand, Û = 0.75° ˘ ◦ ) of the mirror was observed to increase the shadowing effect at from Figure 13b, outward deviation (U 20 10 the bottom of the receiver; and eventually a complete shadow was observed at 0.15◦ deviation. 0 0 ◦ The shadow was found to further increase of120the receiver 30 60location 90 150 180 with 0 30 60 90 120 150 180 towards ±090 angular increasing deviation. Angular location on the receiver outer surface, β° Angular location on the receiver outer surface, β°

(b) fficiency and centration

(a) 1 0.9 0.8 0.7 0.6

Energies 2017, 10, 1907

15 of 19

As shown in Figure 13c, the effect of the deviation (both inward and outward) on ηopt and Cavg were found to be almost equal and similar. The ηopt and Cavg were estimated to be decreased slightly till 0.375◦ angular deviation and then decreased rapidly. As Table 3 shows, the inward deviation was observed to increase the non-uniformity of the LCR distribution, whereas, the outward deviation was observed to 12. have littleprofile effectversus on the uniformity the LCRmirror. profile. Thefigure, MADV was to be Figure Actual ideal profile of aofparabolic In the is theestimated vertex of the ◦ increased by 6 points ideal angular profile,rotation whereasofthe was decreased parabola, and Û° for and0.375 Ŭ° aredeviation the inwardfrom and the outward twosame halves of the mirror by ◦ outward deviation. almostwith 2 points 0.35 respect to the vertex from its ideal profile respectively. 70

Û = 0.0° Û = 0.05° Û = 0.075° Û = 0.15° Û = 0.25° Û = 0.375° Û = 0.5° Û = 0.65° Û = 0.75°

100 80 60 40 20



120

Ǔ = 0.0° Ǔ = 0.025° Ǔ = 0.05° Ǔ = 0.075° Ǔ = 0.15° Ǔ = 0.25° Ǔ = 0.35° Ǔ = 0.5° Ǔ = 0.6°

60 50 40 30 20 10 0

0 0

30

60

90

120

150

0

180

30

60

90

120

150

180



(b) Normalised optical efficiency and average light concentration

(a) 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

Û° Ǔ°

0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Mirror inward profile bending, Û° error, and outward profile bending error Ǔ°

(c) Figure13. 13.Effect Effectofof(a) (a)inward inwarddeviation deviationand and(b) (b)outward outwarddeviation deviationofofthe themirror mirrorprofile profileon onthe theLCR LCR Figure profileofofthe thereceiver, receiver,and and the ηoptand andCCavg of of the the collector. collector. profile (c)(c) onon the ηopt avg

From Figure 13a, the concentrated light was observed to occupy a gradually smaller surface area 4.3.3. Effect of Tracking Error at the bottom of the receiver with an increase of inward angular deviation of the mirror profile. This A (single solar system is used the PTC system to track the sun and maintain it deviation wasaxis) found to tracking reverse the slopes of thefor Receiver Shadowing and Concentration Increasing (the sun) at the sagittal plane of the Eventually, collector. Any angular deviation the incident light and zones gradually one after another. these RS and CI zonesbetween aligned with the Concentration the planezone, of symmetry of the mirror called sunwith tracking error could affect the optical Falling and formed a Gaussian LCR the profile the increase of the deviation. The performance highest value ofofthe collector significantly. effect110 of the error, E andfrom the Cmax was estimated to beThe around sunssun at tracking 0.375° inward deviation. Oninvestigated, the other hand, Tracking , was result is 13b, presented in Figure 14 and Table 3. mirror was observed to increase the shadowing effect at Figure outward deviation (Ŭ°) of the As shown in Figure 14a, similar to the casea of out-focusshadow dislocation the receiver, tracking error the bottom of the receiver; and eventually complete was ofobserved at 0.15° deviation. was observed to distort the bi-symmetry of normal LCR profile. As a result, a single peak concentration in the receiver LCR profile was seen at the side of tracking error; and the magnitude of the peak was calculated to be gradually increasing with the tracking error until around ETracking = 0.6◦ . The Receiver Shadowing and the Concentration Increasing zones of the LCR profile at the opposite side of the tracking error were found to be diminishing in the Concentration Falling zone gradually with the increase of the error. The ηopt and Cavg were estimated to be decreasing very slowly till around 0.6◦ tracking error, and then decreasing fairly quickly afterwards (see Figure 14b). In Table 3, the MAD was

was observed to distort the bi-symmetry of normal LCR profile. As a result, a single peak concentration in the receiver LCR profile was seen at the side of tracking error; and the magnitude of the peak was calculated to be gradually increasing with the tracking error until around ETracking = 0.6°. The Receiver Shadowing and the Concentration Increasing zones of the LCR profile at the opposite side of the tracking error were found to be diminishing in the Concentration Falling zone gradually Energies 2017, 10, 1907 16 of 19 with the increase of the error. The ηopt and Cavg were estimated to be decreasing very slowly till around 0.6° tracking error, and then decreasing fairly quickly afterwards (see Figure 14b). In Table 3, the calculated drop from tofrom 10.8 for 1.0E◦Tracking . However, MAD was to calculated to23.7 drop 23.7ETracking to 10.8 =for = 1.0°.CHowever, Cmaxwere andalso Cavgcalculated were also max and Cavg to drop proportionately from 63.5 to 36 and from 22 to 9 respectively at that tracking error. calculated to drop proportionately from 63.5 to 36 and from 22 to 9 respectively at that tracking error.

70 60 50 40 30

1 0° 0.2° 0.4° 0.5° 0.6° 0.7° 0.8° 0.9° 1° 1.3°

20 10 0 -180 -150 -120 -90 -60 -30 0 30 60 90 120 150 180 Angular location on the receiver outer surface, β°

Normalised optical efficiency and average light concentration


80

0.75

0.5

0.25

0 0

0.25 0.5 0.75 1 Sun tracking error of the collector (°)

(a)

1.25

(b)

◦ ) on Figure 14. 14. Effect Effect of of tracking trackingerror error((°) on(a) (a)LCR LCRprofile profileofofthe thereceiver receiverand and(b) (b)ononthe theηopt ηoptand andCCavg avg of Figure of the collector. the collector.

5. Conclusions Conclusions 5. The effect effect of and optical errors on on thethe LCR distribution, ηopt The of optical opticalparameters, parameters,design designparameters, parameters, and optical errors LCR distribution, and C avg is comprehensively investigated. The optical properties of the collector components were found ηopt and Cavg is comprehensively investigated. The optical properties of the collector components to be directly proportional the LCR, ηoptto and Cavg . TheηDNIand alsoCshowed a directly proportional effect on were found to be directlyto proportional the LCR, opt avg . The DNI also showed a directly the LCR and C avg. However, DNI had no significant effect on the ηopt of the collector. proportional effect on the LCR and Cavg . However, DNI had no significant effect on the ηopt of An increase in GC and rim angle was observed to increase the non-uniformity of the LCR the collector. distribution around a PTC.was However, the to uniformity to be affected An increase in the GCreceiver and rimofangle observed increase was the observed non-uniformity of the more LCR by GC than the rim angle. Larger rim angles were found to concentrate more light. Therefore, distribution around the receiver of a PTC. However, the uniformity was observed to be affected optimally a smaller larger rim rim angle are recommended achieve relatively more uniform more by GC than theGC rimand angle. Larger angles were found totoconcentrate more light. Therefore, light distribution around the receiver, and more energy output. optimally a smaller GC and larger rim angle are recommended to achieve relatively more uniform light distribution around the receiver, and more energy output. A glass envelop around the receiver was observed to improve the optical efficiency of a PTC collector. The ηopt , which was predicted to be dropped by about 4% in 90◦ rim angle for a bare receiver, was increased by about 2% in 70◦ rim angle before dropping by about 0.5% in 90◦ rim angle for a glass enveloped receiver. The magnitudes of LCR, ηopt and Cavg were estimated to drop almost linearly with an increase in mirror focal length. A defocus dislocation of the receiver improves the uniformity of the LCR distribution on the bottom half of the receiver. Off-focus dislocation of the receiver, and inward deviation of the mirror profile from its ideal shape increase the Cmax and non-uniformity of the LCR distribition. On the other hand, out-focus dislocation of the receiver and solar tracking error break the bi-symmetry of the normal LCR profile. Off-focus and defocus dislocation of the receiver more than about 0.75r (r is radius of the receiver), out-focus dislocation more than about 0.15r, deviation of the mirror profile more than 0.375◦ , and tracking error more than 0.6◦ were observed to cause rapid decrease of the optical efficiency and the average light concentration of the collector. Acknowledgments: This article is a part of a PhD project that is supported by a QUT post graduate research award and by a CSIRO Flagship collaboration fund PhD top-up scholarship through the Energy Transformed Flagship. Author Contributions: This article is produced from the PhD work of Majedul Islam. Majedul Islam conceived, designed and accomplished the research, and drafted the article under the principle supervision of Azharul Karim, who is the leader of the research team. Prasad Yarlagadda and Sarah Miller were the associate supervisors for the PhD program. Azharul Karim extremely motivated Majedul Islam to prepare the article. Azharul Karim also reviewed and edited the article. Sarah Miller accomplished a proofread for the article. Conflicts of Interest: No known conflicts of interest could be disclosed.

Energies 2017, 10, 1907

Nomenclature C CF CI DS d D DNI E f GC GT I(ϕ) LCR LS2 MAD MC MCRT N n P PT PTC r RT RS sun t TC W V X, Y, Z X, r, β Symbols ηopt β ψ ϕ ˘ Û, U τGT $PT ↑, ↓ →↔← Suffixes abs avg Expt max min o

Concentration or Constant Concentration Falling zone of a normal LCR profile under ideal condition Concentration Increasing zone of a normal LCR profile under ideal condition Direct Sun zone of a normal LCR profile under ideal condition Depth, diameter, deviation, dislocation Direction vector Direct Normal Irradiance Error Focal length Geometric Concentration (×) (Ratio of mirror aperture area to receiver surface area) Glass Tube Sunshape or light intensity as a function of deflection angle Local Concentration Ratio (sun) Luz Solar 2 collector Mean Absolute Deviation Monte Carlo Monte Carlo Ray Tracing Normal vectors, Number of rays per unit aperture area of the sunshape Refractive indices of glass and air Point of light incidence Parabolic Trough Parabolic Trough Concentrator Radius of the receiver Receiver Tube Receiver Shadowing zone of a normal LCR profile under ideal condition Unit of light concentration (1 kW/m2 ) Thickness Test Conditions Half width of the mirror Variable or varied Cartesian coordinate system Polar coordinate system Optical efficiency Angular location on the receiver Rim angle (◦ ) of the mirror Deflection angle of sun Inward and outward angular deviation of the mirror profile (◦ ) Transmittance of glass tube Reflectance of mirror Increase or upward, decrease or downward lateral direction Absolute Average Experimental or measured value Maximum Minimum Outer or outside

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