Elsevier

Solar Energy

Volume 111, January 2015, Pages 396-406
Solar Energy

Conversion of parabolic trough mirror shape results measured in different laboratory setups

https://doi.org/10.1016/j.solener.2014.09.021Get rights and content

Highlights

  • A method to convert shape results measured in different setups is demonstrated.

  • Characteristic deformation is determined by optical measurements and FE analyses.

  • The developed finite element models of mirror and support frame are validated.

  • Converted and measured values differ by less than 0.2 mrad (rms slope deviation).

Abstract

Shape accuracy of mirror panels for parabolic trough solar collectors has a significant impact on the optical performance of the collectors in a solar power plant and is therefore carefully assessed by test laboratories and manufacturers. Relevant deformation is induced by gravity or mounting forces, so that shape accuracy data measured in different setups cannot be compared.

This paper presents a method for conversion of shape measured in a vertical laboratory setup into data for a horizontal laboratory setup. Characteristic deformation matrices for parabolic trough mirror panels of RP3 geometry are determined by deflectometric shape measurements on various mirror panels and by validated finite element analyses (FEA).

The resulting root mean square (rms) of measured slope deviation difference (i.e. the gravity induced deformation) between vertical and horizontal setup is on average 2.4 mrad for inner mirrors and 1.25 mrad for outer mirrors loosely positioned on a frame.

Measured data from vertical setup, transformed by such characteristic deformation matrices into horizontal shape results, differ by less than 0.2 mrad in rms slope deviation value from data measured in horizontal setup. Whereas the presented approach to convert shape accuracy measurement results is suitable for the calculation of rms values, some of the analyzed mirror samples show differences in local slope deviation values larger than the deflectometric measurement uncertainty. The amount of deviation depends on details of the accuracy of the positioning of the mirrors on the measurement frame and is affected by the fixation and associated mounting forces at the pads.

Introduction

Shape accuracy of the mirror panels for parabolic trough collectors is a key parameter for optical performance that directly impacts the efficiency of a solar power plant. The high quality of state of the art mirror panels is ensured by measurements performed by independent test laboratories as well as by quality control in series production (Ulmer et al., 2012). Examples of common measurement techniques include the Video Scanning Hartmann Optical Test (VSHOT) developed by Sandia and NREL (Jones et al., 1997), visual inspection systems by ENEA (Montecchi and Maccari, 2007, Montecchi et al., 2011), and fringe reflection or deflectometry techniques by ISE (Burke et al., 2013), Sandia (Andraka et al., 2013) and DLR (März et al., 2011, Ulmer et al., 2011).

Measurement boundary conditions are not yet standardized and the shape measurements are performed in different setups that, for example, differ in measurement position. Previous work (Meiser, 2014, Meiser et al., 2014) quantifies the differences in shape accuracy results between the most common measurement setups for parabolic trough mirror panels and identifies measurement position, mounting mode and support frame employed for the measurement as relevant boundary conditions. If these boundary conditions deviate from one setup to the other, shape accuracy results cannot be compared. Moreover, shape quality specifications cannot be guaranteed to be met in different measurement conditions.

This paper presents a method to convert results obtained in different laboratory setups that allows the comparison of shape accuracy results. The examined setups are a vertical (mounting points vertically and curved direction horizontally aligned) and a horizontal measurement position (mirrors facing upward with mounting points horizontally aligned). Two cases are evaluated in both setups: the mirror tightened with screws to a support frame (fix case) and the mirror not tightened (loose case). The analyses are carried out for mirrors of RP3 geometry (focal length 1.71 m, trough aperture width 5.78 m, panel length 1.7 m) which is the most commonly employed mirror type in current parabolic trough power plant projects. Characteristic gravity-induced deformation and resulting slope deviation difference matrices are determined from measurement results obtained at the deflectometry test bench at DLR’s Test and Qualification Center (QUARZ® Center) in Cologne and finite element analyses. They are added to vertically measured data to calculate horizontal results. The calculated results are compared to measured results in order to evaluate the accuracy of the suggested method. The finite element models prepared for this study are additionally validated.

Section snippets

General definitions and description of reflector panels of RP3 geometry

In collectors that employ reflector mirrors of RP3 geometry the parabolic shape is formed by two inner and two outer mirror panels having dimensions of 1641 × 1700 mm (RP3 inner mirror) and 1501 × 1700 mm (RP3 outer mirror). They are made of 4 mm thick bent float glass sheets. Four ceramic mounting pads are glued to the mirror rear side for mounting it onto the collector support structure.

By definition, the point of origin of the according coordinate system is located in the parabola vertex (compare

Measured mirror shape accuracy in different laboratory positions and mounting modes

Fig. 3 illustrates how measurement position and mounting mode may affect the measured shape accuracy result. Spatially resolved measured slope deviation values of one exemplary RP3 inner mirror panel in all four measurement setups as well as the according slope deviation difference between horizontal and vertical measurement position is depicted.

The mirror panel sags inward between the mounting points from vertical to horizontal position for both fixed and loose mounting modes, while the extent

Discussion

The presented approach to convert shape accuracy measurement results achieved in vertical measurement position into results applying for the horizontal position by adding the characteristic slope deviation difference matrices is suitable for the calculation of root mean square values. For the studied mirror panels the mean difference between measured and calculated rms slope deviation is smaller than the standard uncertainty of 0.2 mrad for the rms value of measured slope deviation. As indicated

Conclusion

The preliminary study of shape accuracy in different setups demonstrates significant gravity-induced mirror deformation and resulting differences in shape accuracy results for different measurement positions and mounting modes. Consequently, when performing measurements of this kind, these measurement parameters should be stated in addition to the measurement result.

A method to convert mirror shape accuracy results of parabolic trough mirror panels obtained in different measurement positions

Acknowledgements

The financial support for part of this work by FLABEG FE GmbH in the framework of a cooperation project is gratefully acknowledged.

References (12)

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