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Research Papers

Validation of a Monte Carlo Integral Formulation Applied to Solar Facility Simulations and Use of Sensitivities

[+] Author and Article Information
Cyril Caliot

Processes,
Materials and Solar Energy Laboratory,
PROMES,
CNRS,
7 rue du Four Solaire,
Font-Romeu-Odeillo 66120, France
e-mail: cyril.caliot@promes.cnrs.fr

Hadrien Benoit, Emmanuel Guillot, Jean-Louis Sans, Alain Ferriere

Processes,
Materials and Solar Energy Laboratory,
PROMES,
CNRS,
7 rue du Four Solaire,
Font-Romeu-Odeillo 66120, France

Gilles Flamant

Processes,
Materials and Solar Energy Laboratory,
PROMES,
CNRS,
7 rue du
Four Solaire, Font-Romeu-Odeillo 66120, France

Christophe Coustet, Benjamin Piaud

HPC-SA Raytracing Solutions,
3 chemin du pigeonnier de la Cépière,
Toulouse 31100, France

1Corresponding author.

Contributed by the Solar Energy Division of ASME for publication in the JOURNAL OF SOLAR ENERGY ENGINEERING: INCLUDING WIND ENERGY AND BUILDING ENERGY CONSERVATION. Manuscript received October 2, 2014; final manuscript received January 5, 2015; published online February 18, 2015. Assoc. Editor: Prof. Nathan Siegel.

J. Sol. Energy Eng 137(2), 021019 (Apr 01, 2015) (8 pages) Paper No: SOL-14-1282; doi: 10.1115/1.4029692 History: Received October 02, 2014; Revised January 05, 2015; Online February 18, 2015

The design of solar concentrating systems and receivers requires the spatial distribution of the solar flux on the receiver. This article presents an integral formulation of the optical model for the multiple reflections involved in solar concentrating facilities, which is solved by a Monte Carlo ray-tracing (MCRT) algorithm that handles complex geometries. An experimental validation of this model is obtained with published results for a dish configuration. The convergence of the proposed algorithm is studied and found faster than collision-based algorithms. In addition, an example of the use of the sensitivity of the power on a target to the mirror rms-slope is given by treating an inverse-problem consisting in finding the equivalent rms-slope of mirrors that best match the flux map measurements.

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References

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Figures

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Fig. 1

Target and mirror elementary surfaces with their normals, positions, the ray solid angles, and directions

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Fig. 2

Mirror elementary surface having a microfacetted subsurface

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Fig. 3

CAD view of the EuroDish in solfast and some green ray paths toward the target

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Fig. 4

Measured normalized flux distribution at the focal plane (z = 4.553 m) for the EuroDish, normalized to 1000 W/m2 and 94% reflectivity (data from Ref. [15])

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Fig. 5

Measured normalized flux distribution at z = 4.673 m for the EuroDish, normalized to 1000 W/m2 and 94% reflectivity (data from Ref. [15])

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Fig. 6

Slope errors (mrad) in the radial direction (positive = tilted to the center; data from Ref. [15])

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Fig. 7

Slope errors (mrad) in the tangential direction (positive = tilted clockwise; data from Ref. [15])

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Fig. 8

Simulated normalized flux distribution at the focal plane (z = 4.553 m) for the EuroDish

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Fig. 9

Simulated normalized flux distribution at z = 4.673 m for the EuroDish

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Fig. 10

Flux on Themis target in function of the number of MC realizations. Two sets of curves are plotted: flux + standard deviation and flux − standard deviation.

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Fig. 11

3D rendering of samples of ray paths used for the optimization study at the 1 MW-CNRS Solar Furnace in Odeillo

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Fig. 12

Comparison of the measured and the optimized flux distributions; isolines of non-dimensional flux on the target

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