An algorithm for the flux distribution over the flat absorber of a parabolic trough concentrator

Based on the symmetries of the parabolic trough concentrating system and the solar radiation, a descending dimension algorithm has been developed with a computational complexity of O(N2), whereas that of the Monte Carlo ray tracing (MCRT) method and the finite element method are of O(N4) The formula of the energy function ψ(θ) for solar disk slice was constructed to solve the integration of the flux distribution. The numerical results indicated that the results obtained by the presented algorithm have a good agreement with results produced by MCRT, meanwhile CPU time requirement of the algorithm is about a few seconds, much shorter than that of MCRT. The formulas for calculating the number of reflections of ray tracing within a homogenizer and the exact coordinates of the landing location on the absorber of each ray are established from geometrical aspect. The effect of the homogenizer for flux density uniform is clearly characterized.