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Solar flux density distribution using a separation of variables/superposition technique

Author

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  • Elsayed, M.M.
  • Fathalah, K.A.

Abstract

A separation of variables/superposition technique is used to determine the flux density distribution Γ on the receiver plane of a central receiver system. This distribution is determined in terms of the flux density distribution F on the image plane. The distribution F is found in terms of the algebraic sum of several flux distribution functions. Each of these functions Fi is determined in terms of a basic dimensionless flux density function φ, transferred to have its origin of coordinates at one corner of the principal image of the heliostat. Using a special coordinate system, φ is found to depend only on the angle θ∗ between the sides of the principal image of the heliostat, for a given Sun shape and error function. Calculations of θ∗ and the lengths of the sides of the principal image are performed for a wide range of parameters, which include solar zenith and azimuth angles, radial distance of heliostat and its position azimuth angle, tower height, concentration and dimensions of the heliostat. For a given effective Sun shape, the basic dimensionless flux density distribution φ is calculated for several values of θ∗. This distribution is stored in a computer and used in an illustrative example to determine the flux density distribution on a receiver plane.

Suggested Citation

  • Elsayed, M.M. & Fathalah, K.A., 1994. "Solar flux density distribution using a separation of variables/superposition technique," Renewable Energy, Elsevier, vol. 4(1), pages 77-87.
    • Handle: RePEc:eee:renene:v:4:y:1994:i:1:p:77-87
    DOI: 10.1016/0960-1481(94)90067-1
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    Cited by:

    1. He, Caitou & Duan, Xiaoyue & Zhao, Yuhong & Feng, Jieqing, 2019. "An analytical flux density distribution model with a closed-form expression for a flat heliostat," Applied Energy, Elsevier, vol. 251(C), pages 1-1.
    2. David Jafrancesco & Daniela Fontani & Franco Francini & Paola Sansoni, 2018. "Evaluation of the Spot Shape on the Target for Flat Heliostats," Energies, MDPI, vol. 11(7), pages 1-18, June.
    3. Harnpon Phungrassami & Phairat Usubharatana, 2024. "Development and Analysis of the Heliostat Curve Tracing Parametric Model (HCTPM) for Sustainable Solar Energy in Sun-Tracking Concentrated Solar Power Systems," Sustainability, MDPI, vol. 16(21), pages 1-21, October.
    4. He, Caitou & Zhao, Hanli & He, Qi & Zhao, Yuhong & Feng, Jieqing, 2021. "Analytical radiative flux model via convolution integral and image plane mapping," Energy, Elsevier, vol. 222(C).
    5. Lin, Xiaoxia & He, Caitou & Huang, Wenjun & Zhao, Yuhong & Feng, Jieqing, 2022. "GPU-based Monte Carlo ray tracing simulation considering refraction for central receiver system," Renewable Energy, Elsevier, vol. 193(C), pages 367-382.

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