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

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 F i 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.