An Analytical Approach Treating Three- Dimensional Geometrical Effects of Parabolic Trough Collectors

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1 An Analytical Approach Treating Three- Dimensional Geometrical Effects of Parabolic Trough Collectors Marco Binotti Guangdong Zhu*, Ph.D., Allison Gray National Renewable Energy Laboratory Giampaolo Manzolini, Ph.D. Politecnico di Milano Denver, CO May 212 NREL is a national laboratory of the U.S. Department of Energy, Office of Energy Efficiency and Renewable Energy, operated by the Alliance for Sustainable Energy, LLC.

Applies first-principle treatment to optical error sources.

2 2 Objective FirstOPTIC (First-principle OPTical Intercept Calculation) Newly developed by Zhu & Lewandowski at NREL. Calculates intercept factor of parabolic trough collectors. Applies first-principle treatment to optical error sources. Suitable for optical analysis involving a large volume of data. Scope of work Expand FirstOPTIC to account for three-dimensional effects.

errors in the longitudinal direction Receiver displacements Spacing between Solar Collector

3 3 Three-Dimensional Effects Cosine effect Widened image of the sun Reduced acceptance angle due to the elongated optical path of reflected rays End losses Longitudinal slope errors Specularity errors in the longitudinal direction Receiver displacements Spacing between Solar Collector Element (SCE) and the active absorber area Materials performance changes with varying incidence angles

4 FirstOPTIC The existing FirstOPTIC can calculate the intercept factor for parabolic trough collectors at normal incidence. Receiver alignment errors and slope errors are treated with a first-principle approach: this means that they are considered as geometric impacts to the optical calculation. Geometry Receiver diameter Focal length Aperture width Collector length + Receiver position error + Transversal slope error Optics Sun shape Mirror specularity Tracking error - Receiver position error - Transversal slope error Receiver diameter Beam spread Sun Shape Focal length Aperture width 4

5 Probability Density Acceptance Angle Window (mrad) Calculation of Intercept Factor Geometry Receiver diameter 25 Acceptance angle variaion for trough (LS2) Receiver diameter Focal length Aperture width Focal length Collector length Aperture width x -- along mirror aperture (m) Optics Beam spread Sun Shape Mirror Specularity Sun Shape 25 Probability Distribution, Total Error Gaussian, Gaussian, w ith mean and sigma.16 Tracking Error variable 5

6 Acceptance Angle (mrad) Acceptance Angle (mrad) 6 Treatment of Slope Error and Receiver Position Error Transversal slope error a: Geometric effect of slope error to beam spread. Beam spread g(β) β β + Sun shape Z Local slope with error b: Acceptance angle window change due to slope error (3 mrad) With slope error Without slope error Receiver position error (x, z) X x -- Along Mirror Aperture (m) a: Geometric effect of receiver position error to beam spread. Sun shape Beam spread g(β) Z b: Acceptance angle window due to receiver position error ( dx = dz = d/2) With receiver misalignment Without receiver position error Displaced receiver β β + δ shift -2 χ (x, z) X x -- Along Mirror Aperture (m)

7 7 Calculation of Acceptance Angle at non-zero Incidence Angles Local coordinate system used. y y z z ω x ω x r β + Reflected sun ray plane R z Incoming sun ray plane I T 1 ε y ε x i Calculated acceptance angels Transversal slope error Longitudinal slope error Receiver position error End loss β n ε n x y P

8 Acceptance Window (mrad) Acceptance Angle (mrad) 8 Variation of Acceptance Angle Under 3-D Effect of incidence angle on acceptance angle x (m) Effects of transversal and longitudinal slopes on acceptance angle. Effects of 1 mrad longitudinal or transversal slope error ( = 6º) T 1 r β β + Reflected sun ray plane R z Incoming sun ray plane I ε y ε x i n ε n x x (m) y P

9 9 Validation of FirstOPTIC on 3-D effects Test cases. Scenario I Optics Sun Shape Mirror Specularity Slope Error Gaussian: σ = 2.5 mrad Gaussian: σ = 6 mrad Receiver Position Error Incidence Angle End Losses None None 3º Yes II Point source None None 6º No III Point source None None IV V Gaussian: σ = 2.5 mrad CSR1 Gaussian: σ = 6 mrad Gaussian: σ = 6 mrad Data set: σ( ) = σ( ) = 5.5 mrad dx = 4 mm; dz = 5 mm. dx = 2 mm; dz = 3 mm. dx = 2 mm; dz = 3 mm. 6º No 3º No 6º No Comparison results of intercept factor. Method FirstOPTIC SolTrace Numerical Scenario I II III IV V

10 Conclusions FirstOPTIC has been successfully extended to account for the 3-D effects of parabolic trough collectors The new approach has been carefully benchmarked and validated against ray-tracing results and numerical solutions. FirstOPTIC provides a fast and reliable tool for new collector designs and associated optical analysis. 1

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