Effect of the Orientation Schemes of the Energy Collection Element on the Optical Performance of a Parabolic Trough Concentrating Collector
Abstract
:1. Introduction
2. MCRT Simulation
2.1. Physical Model
2.2. Ray Tracing Technique
- (a)
- The irradiance distribution varies across the axis and uniform along the axis of the ECE. Therefore, the length of the modelled collector was 50 cm.
- (b)
- The trough was locally specularly reflective, and the light incident was perpendicular on the trough aperture.
- (c)
- No shading from the frame and brackets.
- (d)
- No structural deformities in the trough and the receiver.
- (e)
- Diffuse light is negligible.
2.3. Validation of the Model
3. Geometry of the Studied ECE Orientation Schemes
4. Calculated LCR Profile around the ECEs and Respective Optical Efficiency
4.1. Circular
4.2. Semi-Circular
4.3. Flat
4.4. Triangular
4.5. Inverted Triangular
4.6. Rectangular (Square)
4.7. Rectangle on Semi-Circle (RSc) ECE
5. Discussion
6. Conclusions
- (i)
- The ECE orientation schemes (circular, semicircular and RSc) with curved TSS showed much higher ηopt (>79%) than those (flat, triangular, inverted triangular and rectangular) with linear TSS (ηopt ranging between 25% and 38%) in ideal conditions (i.e., no defocus and tracking error) with a trough of 68° rim angle
- (ii)
- Among the linear TSS group, the optical efficiency was calculated to be highest for the inverted triangular ECE (around 37%), lowest for the flat and triangular ECEs (≈26%), and somewhere in middle for the rectangular ECE (in between 30.5% and 33.5%).
- (iii)
- The MAD of the TSS of the rectangular ECE was estimated to be the lowest, ranging from 0.94 at defocus condition to 5.44 at ideal condition. In the event of tracking error and with a trough of higher rim angle, the MAD was found increased insignificantly, only increased to 1.05 from 0.94. That is the uniformity of the irradiance distribution (i.e., the LCR profile) on the TSS of a rectangular ECE was found to be the best among the studied ECE orientation schemes.
- (iv)
- In the event of defocus and tracking error, a significant portion of the concentrated light was observed to be intercepted by the TPSs. Therefore, based on this study, ECEs among the curved TSS group, it is clear that the RSc would be more efficient than the circular and semicircular ones. Similarly, among the linear TSS group the rectangular one would be more efficient than the remaining ECEs of the group.
- (v)
- Sun tracking error and the ECE defocus have negative effect on the optical efficiency of the collector in general. However, ECE defocus helps to reduce the MAD that is the non-uniformity of the LCR profile of the TSS.
- (vi)
- Study of the effect of 90° trough rim angle over a 68° one for the rectangular and RSc ECEs implied that there is an optimum rim angle for each collector design; trough rim angle larger than that would increase the total concentrated light on the ECE and, for few instances, the uniformity of the LCR profile of the TSS, but will decrease the optical efficiency of the collector.
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Nomenclature
C | Light concentration |
d | Depth, diameter, deviation, dislocation |
D | Direction vector |
DNI | Direct normal irradiance |
E | Error |
f | Focal length |
ECE | Energy collection element |
GC | Geometric concentration (Ratio of mirror aperture area to outer surface area of the absorber tube) |
GT | Glass tube |
I(φ) | Sunshape or light intensity as a function of deflection angle |
LCR | Local concentration ratio |
LS2 | Luz Solar 2 collector |
MAD | Mean absolute deviation |
MC | Monte Carlo |
MCRT | Monte Carlo ray tracing |
N | Normal vectors, Number of rays per unit aperture area of the sunshape |
n | Refractive indices of glass and air |
P | Point of light incidence |
PT | Parabolic trough |
PTCC | Parabolic trough concentrating collector |
r | Radius of the receiver |
RSc | Rectangle-on-Semicircle |
RT | Receiver tube |
TC | Test Conditions |
TCPV | Trough concentrating photovoltaic collector |
TCPVT | Trough concentrating hybrid photovoltaic/thermal collector |
X, Y, Z | Cartesian coordinate system |
X, r, β | Polar coordinate system |
Symbols | |
α | Absorptance of ECE material |
ηopt | Optical efficiency |
ψ | Rim angle (°) of the mirror |
φ | Deflection angle of sun |
θ | Angle of light incidence on the ECE |
ρPT | Reflectance of mirror |
τGT | Transmittance of glass |
× | Times |
Suffixes | |
base | Base |
est | Estimated |
l | Local |
mean | Mean |
o | Outer or outside |
peak | Peak |
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Parameters | Value |
---|---|
Concentrator width, W = | 5 m |
Concentrator length, LPT = | 7.8 m |
Receiver length, LRT = | 8 m |
Rim angle, ψ = | ≈68° |
Focal length, f = | 1.84 m |
Close-end plug outer diameter, dP = | 50.8 mm |
Glass tube outside diameter, dGT = | 115 mm |
Glass tube thickness, tGT = | 3 mm |
Receiver tube inside diameter, dRT = | 66 mm |
Receiver tube thickness, tRT = | 2 mm |
Concentrator reflectance, ρPT = | 0.9337 |
Glass tube transmittance, τGT, for evacuated condition = and for bare receiver = | 0.935 1.0 |
Receiver absorptance, αRT, for (mostly used) cermet selective coating = black chrome selective coating (used for the current MCRT model) = | 0.92 0.94 |
Tracking error factor, Eσ = | 0.994 |
Geometry error factor, Egeom = | 0.98 |
General error factor, Egen = | 0.96 |
Optical loss factor for FDirt_on_RT = | 0.981 |
Optical loss factor for FDirt_on_PT = | 0.963 |
Sl No. | DNI (W/m2) | Selective Coatings | Glass Tube Condition | ηopt (%) | Eest (%) |
---|---|---|---|---|---|
1 | 807.9 | Cermet | Vacuum | 72.63 | 1.91 |
2 | 925.1 | Cermet | Air filled | 73.68 | 1.96 |
3 | 954.5 | Cermet | Removed | 77.5 | - |
4 | 850.2 | Black Chrome | Vacuum | 73.1 | 2.36 |
ECE Orientation Schemes | Location of Focus ( ) | Cbase (×) | Cpeak (×) | Cmean (×) | MAD of the TSS | ηTSS (%) | ηTNS (%) | ηopt = Ση (%) |
---|---|---|---|---|---|---|---|---|
Circular | 0 | 63.44 | 21.85 | 23.7 | 79.56 | - | 79.56 | |
Semicircular | 1.26 | 63.44 | 43.01 | 15.46 | 78.3 | 1.02 | 79.32 | |
Flat | 0.03 | 88 | 22.61 | 27.36 | 26.19 | - | 26.19 |
ECE Orientation Schemes | Location of Focus ( ) | Cbase (×) | Cpeak (×) | Cmean (×) | MAD of the TSS | ηTSS (%) | ηTNS (%) | ηopt = Ση (%) |
---|---|---|---|---|---|---|---|---|
Triangular | 0.03 | 88 | 22.61 | 27.36 | 26.19 | 0.31 | 26.51 | |
3.24 | 52.6 | 21.75 | 14.57 | 25.20 | 0.77 | 25.97 | ||
Inverted triangular | 0 | 63.12 | 22.42 | 21.97 | 36.37 | 1.02 | 36.99 | |
0.25 | 45 | 23.08 | 12 | 37.44 | 1.02 | 38.06 | ||
5.89 | 32.2 | 20.41 | 7.35 | 33.11 | 1.02 | 33.73 |
Location of Focus ( ) | ECE Surfaces | Cbase (×) | Cpeak (×) | Cmean (×) | MAD | η (%) | ηopt = Ση (%) |
---|---|---|---|---|---|---|---|
TSS | 8.33 | 25.72 | 18.14 | 5.44 | 21.02 | 33.60 | |
TPSs | 0 | 15.48 | 4.99 | 5.54 | 11.56 | ||
TSS | 9.56 | 17.55 | 14.51 | 2.03 | 16.81 | 32.54 | |
TPSs | 0 | 15.39 | 6.35 | 4.7 | 14.71 | ||
TSS | 9.17 | 13.43 | 11.7 | 0.94 | 13.55 | 30.49 | |
TPSs | 0.17 | 15.71 | 6.87 | 4.26 | 15.92 | ||
TNS (for all cases) | ≈0.88 | - | ≈1.02 | - |
(°) | σ (°) | ECE Surfaces | Cbase (×) | Cpeak (×) | Cmean (×) | MAD | η (%) | ηopt = Ση (%) |
---|---|---|---|---|---|---|---|---|
68 | 0 | TSS | 9.17 | 13.43 | 11.7 | 0.94 | 13.55 | 30.49 |
TPSs | 0.17 | 15.71 | 6.87 | 4.26 | 15.92 | |||
0.3 | TSS | 8.2 | 13.95 | 11.68 | 1.05 | 13.53 | 28.63 | |
TPSσ+ | 0.49 | 16.21 | 5.81 | 4.76 | 6.73 | |||
TPSσ− | 0 | 15.47 | 6.34 | 4.56 | 7.35 | |||
TNS (for both σ) | ≈0.88 | - | ≈1.02 | |||||
90 | 0.3 | TSS | 8.13 | 13.98 | 11.68 | 1.05 | 9.19 | 26.98 |
TPSσ+ | 0.47 | 26.65 | 6.82 | 6.00 | 5.37 | |||
TPSσ− | 0 | 34.5 | 14.9 | 9.98 | 11.73 | |||
TNS | ≈0.88 | - | ≈0.69 |
Location of Focus ( ) | ψ (°) | σ (°) | ECE Surfaces | Cbase (×) | Cpeak (×) | Cmean (×) | MAD | η (%) | ηopt = Ση (%) |
---|---|---|---|---|---|---|---|---|---|
68 | 0 | TSS | 1.26 | 63.44 | 43.01 | 15.46 | 78.3 | 79.32 | |
TPSs | 0 | 0 | 0 | - | - | ||||
0.3 | TSS | 0 | 73.37 | 40.16 | 19.42 | 74.93 | 77.47 | ||
TPSσ+ | 0 | 11.89 | 2.63 | 3.28 | 1.52 | ||||
TPSσ− | 0 | 0 | 0 | - | - | ||||
TNS (for both σ) | ≈0.88 | - | ≈1.02 | ||||||
90 | 0 | TSS | 44.74 | 81.55 | 59.96 | 8.83 | 74.16 | 78.31 | |
TPSs | 0 | 20.09 | 4.39 | 5.18 | 3.46 | ||||
0.3 | TSS | 0.03 | 95.61 | 56.23 | 15.57 | 69.54 | 77.23 | ||
TPSσ+ | 0 | 30.01 | 17.80 | 8.54 | 7.00 | ||||
TPSσ− | 0 | 0 | 0 | - | 0.00 | ||||
TNS (for both σ) | ≈0.88 | - | ≈0.69 | ||||||
68 | 0 | TSS | 23.07 | 33.88 | 29.91 | 1.99 | 54.45 | 67.11 | |
TPSs | 0 | 15.58 | 10.05 | 3.95 | 11.64 | ||||
0.3 | TSS | 22.08 | 49.19 | 30.36 | 6.38 | 55.27 | 64.84 | ||
TPSσ+ | 0 | 16.01 | 10.23 | 3.99 | 5.93 | ||||
TPSσ− | 0 | 13.71 | 4.05 | 4.41 | 2.35 | ||||
TNS (for both σ) | ≈0.88 | - | ≈1.02 | ||||||
90 | 0 | TSS | 23.07 | 33.92 | 29.91 | 1.99 | 36.99 | 55.6 | |
TPSs | 0.00 | 32.77 | 22.77 | 6.51 | 17.92 | ||||
0.3 | TSS | 22.09 | 73.26 | 31.71 | 8.11 | 39.22 | 52.37 | ||
TPSσ+ | 1.5 | 29.77 | 12.23 | 5.61 | 4.81 | ||||
TPSσ− | 0 | 34.37 | 19.43 | 11.17 | 7.65 | ||||
TNS (for both σ) | ≈0.88 | - | ≈0.69 |
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Islam, M.; Yarlagadda, P.; Karim, A. Effect of the Orientation Schemes of the Energy Collection Element on the Optical Performance of a Parabolic Trough Concentrating Collector. Energies 2019, 12, 128. https://doi.org/10.3390/en12010128
Islam M, Yarlagadda P, Karim A. Effect of the Orientation Schemes of the Energy Collection Element on the Optical Performance of a Parabolic Trough Concentrating Collector. Energies. 2019; 12(1):128. https://doi.org/10.3390/en12010128
Chicago/Turabian StyleIslam, Majedul, Prasad Yarlagadda, and Azharul Karim. 2019. "Effect of the Orientation Schemes of the Energy Collection Element on the Optical Performance of a Parabolic Trough Concentrating Collector" Energies 12, no. 1: 128. https://doi.org/10.3390/en12010128