The Role of Mirror Errors in Solar Energy Conversion

Abstract

Sunlight is an abundant and renewable source of energy, and the expanding solar industry uses many different methods to convert this energy to work. Some of these methods (engines) use mirrors to reflect radiation. However, the mirrors are not perfect and have slope, shape, tracking, and non-specularity errors. This thesis investigates the role that these errors play in decreasing the overall efficiency with which radiation is converted to work in a system that relies on reflection. Three theoretical approaches are taken. Taking a “black box” approach to an open cycle engine which converts radiation to work, basic relations are derived which express the work output as a function of entropy carried by the radiation. When radiation is reflected off a mirror with non-specularity error, entropy is generated. This entropy increase, and the associated decrease in work, are calculated for pillbox and Buie sunshape models. The change in engine efficiency in all cases tested is less than 0.25%. Slope, shape, and tracking errors may possibly be treated in the same way, however no rigorous proof of this is found. Attaining the maximum efficiency of the “black box” model requires several conditions to hold simultaneously, and there is no guarantee that this is possible. However, one conceptual engine commonly referred to in the literature attains this maximum efficiency when operating on radiation enclosed in a perfectly reflective container. The radiation enclosed in this conceptual engine is converted to work by exerting (radiation) pressure on a piston in the same fashion as a classical gas engine. This thesis considers a modified version of this enclosed radiation engine in the hope of better understanding the link (or lack thereof) between conceptual radiation engines that operate on enclosed radiation, and engines that operate with a steady flow of input radiation. The efficiencies computed for the modified engine are far lower than the maximum efficiencies of open cycle engines, meaning that no general conclusions can be made. The effect of slope, shape, and tracking errors on this modified engine are determined, but these results cannot be translated into other engine designs because the efficiency of this engine is lower than the maximum efficiency of an open cycle engine. The most common use for mirrors in solar applications is to concentrate sunlight, before converting it to heat, and then to work. The final part of this thesis considers the implications of converting radiation first to heat, then to work, and the effect that mirror errors have on overall system efficiency. It is demonstrated that maximal concentration of incident radiation is beneficial in such a system, and that slope, shape, and tracking errors decrease the maximum concentration that can be achieved. This decrease is quantified using a pillbox sunshape, and the corresponding decrease in system efficiency is calculated. For errors of a typical magnitude, this loss of efficiency is up to 8.5%. Show more