Design principle and calculations of a Scheffler fixed focus concentrator for medium temperature applications

Abstract

Scheffler fixed focus concentrators are successfully used for medium temperature applications in different parts of the world. These concentrators are taken as lateral sections of paraboloids and provide fixed focus away from the path of incident beam radiations throughout the year. The paper presents a complete description about the design principle and construction details of an 8 m 2 surface area Scheffler concentrator. The first part of the paper presents the mathematical calculations to design the reflector parabola curve and reflector elliptical frame with respect to equinox (solar declination = 0) by selecting a specific lateral part of a paraboloid. Crossbar equations and their ellipses, arc lengths and their radii are also calculated to form the required lateral section of the paraboloid. Thereafter, the seasonal parabola equations are calculated for two extreme positions of summer and winter in the northern hemisphere (standing reflectors). The slopes of the parabola equations for equinox (solar declination = 0), summer (solar declination = +23.5) and winter (solar declination = −23.5) for the Scheffler reflector (8 m 2 surface area) are calculated to be 0.17, 0.28, and 0.13 respectively. The y-intercepts of the parabola equations for equinox, summer and winter are calculated as 0, 0.54, and −0.53 respectively. By comparing with the equinox parabola curve, the summer parabola is found to be smaller in size and uses the top part of the parabola curve while the winter parabola is bigger in size and uses the lower part of the parabola curve to give the fixed focus. For this purpose, the reflector assembly is composed of flexible crossbars and a frame to induce the required change of the parabola curves with the changing solar declination. The paper also presents the calculation procedure of seasonal parabola equations for standing reflectors in the southern hemisphere as well as for laying reflectors in the northern and southern hemispheres. Highly reflective aluminium sheets are used on the crossbar profiles to complete the concentrator. The reflector is installed at the required site by setting its axis of rotation at an angle equal to the latitude of the site. For daily tracking, these concentrators rotate along an axis parallel to the polar axis of the earth at an angular velocity of one revolution per day with the help of simpler and cheaper self-tracking devices. For seasonal tracking, the reflector rotates at half the solar declination angle with the help of a telescopic clamp mechanism. The design procedure is simple, flexible and does not need any special computational setup, thus offering the prospect of potential application in domestic as well as industrial configurations.