Derivation of Universal Error Parameters for Comprehensive Optical Analysis of Parabolic Troughs

Abstract

A study is presented where potential optical errors in parabolic troughs are divided into two groups: random and nonrandom. It is shown that the intercept factor is a function of both random and nonrandom errors as well as geometric parameters such as concentration ratio and rim angle. Three error parameters, universal to all collector geometries, that is, “universal” error parameters which combine random and nonrandom errors with collector geometric parameters, are derived analytically. The mathematical derivation of these universal error parameters is presented. A numerical technique, a detailed ray-trace computer routine which maps rays from elemental reflector surfaces to the absorber surface, is used to validate the existence of the universal error parameters. The universal error parameters are made up of one universal random error parameter, σ* ( =σC ), and two universal nonrandom error parameters, β* ( = βC ) and d * (=(d r )y /D ). The use of universal error parameters for comprehensive optical analysis of troughs is also presented.