Solar Energy Vol. 65, No. 2, pp. 83–89, 1999 1999 Elsevier Science Ltd  Pergamon PII: S0038–092X(98)00123–6 All rights reserved. Printed in Great Britain 0038-092X / 99 / $ - see front matter HIGH-FLUX SOLAR CONCENTRATION WITH IMAGING DESIGNS , , ² DANIEL FEUERMANN*, J. M. GORDON* ** and HARALD RIES*** *Center for Energy and Environmental Physics, Jacob Blaustein Institute for Desert Research, Ben-Gurion University of the Negev, Sede Boqer Campus 84990, Israel **Pearlstone Center for Aeronautical Engineering Studies, Department of Mechanical Engineering, Ben-Gurion University of the Negev, Beersheva 84105, Israel ***Ries & Partners, Bluetenstr. 8, D-80799 Munich, Germany Received 18 November 1997; revised version accepted 23 September 1998 Communicated by LORIN VANT-HULL Abstract—Most large solar concentrators designed for high flux concentration at high collection efficiency are based on imaging primary mirrors and nonimaging secondary concentrators. In this paper, we offer an alternative purely imaging two-stage solar concentrator that can attain high flux concentration at high collection efficiency. Possible practical virtues include: (1) an inherent large gap between absorber and secondary mirror; (2) a restricted angular range on the absorber; and (3) an upward-facing receiver where collected energy can be extracted via the (shaded) apex of the parabola. We use efficiency–concentration plots to characterize the solar concentrators considered, and to evaluate the potential improvements with secondary concentrators.  1999 Elsevier Science Ltd. All rights reserved. 1. INTRODUCTION that were parabolic, spherical, or a combination of the two, with imaging secondary mirrors the Consider the design of a large solar energy magnification of which could augment concen- concentrator where the aim is to maintain high tration (Baum and Strong, 1958). These strategies collection efficiency while generating high aver- were limited to modest improvements in flux age flux levels. The best solutions to date consist concentration relative to the (single-stage) of a large imaging primary mirror and a nonimag- paraboloidal dish, for a given collection ef- ing secondary reflector in the vicinity of the ficiency. absorber, as shown schematically in Fig. 1 for a paraboloidal dish of rim half-angle f, diameter D and effective solar (acceptance) angle 2 u. The theoretical maximum for flux concentration, often referred to as the thermodynamic limit (Rabl, 22 1976; Welford and Winston, 1989), is sin ( u ). The maximum local flux concentration in a 22 22 paraboloidal dish is sin ( f ) sin ( u ). A high-f dish ( f approaching 908 ) produces a high-flux core region in its focal plane, but most of the collectible radiation falls outside that core region. A low-f dish places most of the collect- ible radiation in the core region, but the peak local concentration in that core region is far below the thermodynamic limit. The large-f paraboloidal dish has the practical drawback that, at fixed aperture area, its mirror depth and surface area are considerably greater than those of a low-f dish. Fig. 1. Schematic of a two-stage concentrator with a The earliest designs for high-flux two-stage paraboloidal-dish primary mirror and a second-stage nonimag- ing (in this instance CPC) concentrator. The paraboloidal dish solar concentrators comprised primary reflectors has entrance aperture diameter D, rim half-angle f, and effective solar (acceptance) half-angle u. The size of the second stage and absorber are grossly exaggerated in order to ² Author to whom correspondence should be addressed. illustrate them clearly. 83