In this paper a computer simulation code called CIRCE is discussed and examples of its application to several point-focus concentrating collector geometeries are presented. These capabilities have been used for performance predictions, safety studies, design trade-offs, data analysis problems, the specification and analysis of concentrator quality, and for the general understanding of solar-concentrator technology. Some of the HELIOS routines are described, a few of its capabilities are discussed and illustrated, and comparisons of data with calculations are presented. This model forms a basis for the simulation code HELIOS as well as for other codes under development. The analytical methods used for the statistics, the off-axis reflecting optics, the atmospheric effects, and the various coordinate systems are described and illustrated. The angular distribution of sunrays for the radiation incident on a concentrator is modified by convolution, using the fast Fourier transform, to incorporate the effects of other nondeterministic factors such more ยป as sun-tracking errors, surface slope errors, and reflectance properties. An important output is the flux-density pattern (W/cm/sup 2/) at a grid of points on a surface such as the absorbing surface of a receiver and its integral (power in watts) over the surface. The model follows the incident solar radiation through the system (including the atmosphere) and includes all the factors that influence the optical performance of a collector. The Helios model simulates the optical behavior of reflecting concentrators. Some of the modeling in HELIOS and samples of results are = , Several output choices are available, including graphical display of flux density distributions, of shadowing and blocking and of sunshape. Nondeterministic factors such as sun-tracking errors and facet-surface errors are described statistically and combined with the sunshape by numerical convolution. Measured angular-distributions of incoming photons (sunshapes) and effects of aureole scattering are incorporated. Atmospheric attenuation effects are included. HELIOS calculates the ''sun position'' and uses it to establish alignment geometries. Comparisons of HELIOS results with measurements have given good agreement. HELIOS has been used extensively to analyze questions on safety, performance, design trade-offs, and tower protection engineering. The problem has individual subroutines for each task in order to incorporate options for a variety of facet shapes, heliostat designs, field layouts, and tower-receiver apertures, and to facilitate additions and code improvements. The HELIOS computer code calculates the power concentrated by a field of individually guided heliostats and the resulting flux density (watts/cm/sup 2/) falling upon an arbitrary target grid.
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