A Method for Heliostat Field Modeling and Effective Energy Flux Density Calculation
This study addresses the computational bottleneck in heliostat field optical efficiency assessment by proposing a reverse projection method for calculating effective energy flux density on heliostat surfaces. The method replaces conventional cosine efficiency and truncation efficiency calculations with an irradiance function, determines shadowing and blocking occurrences, computes single heliostat power, and accumulates total field power. By reordering the summation in the total power integral, the method derives the energy flux density distribution on the receiver surface and, through an alternative reordering, the effective energy flux density distribution on each heliostat. This distribution enables determination of the heliostat shape that maximizes power under given area or other constraints, and rapid evaluation of optical efficiency across different shapes and layouts. Numerical simulations demonstrate that heliostats shaped according to the proposed algorithm require smaller mirror areas to achieve equivalent power output compared to conventional rectangular and polygonal geometries, while maintaining superior stability. The study employs a no-blocking dense layout combining Campo and EB arrangements. Results show that a single irregular heliostat achieves an optical efficiency of 0.8022, significantly exceeding square (0.7372), pentagonal (0.7453), hexagonal (0.7485), heptagonal (0.7491), octagonal (0.7502), and circular (0.7513) configurations. The method also reveals that heliostats closer to the receiver exhibit higher energy flux density, with the field energy density in the northern hemisphere displaying a north-high/south-low and center-high/edge-low pattern, consistent with other modeling approaches.