Asymmetric design for Compound Elliptical Concentrators (CEC) and its geometric flux implications - eScholarship

Asymmetric design for compound elliptical concentrators (CEC) and its geometric flux implications Lun Jiang a and Roland Winston a* a UC Solar, University of California Merced, 5200 N Lake Rd, Merced,CA, 95343 ABSTRACT The asymmetric compound elliptical concentrator (CEC) has been a less discussed subject in the nonimaging optics society. The conventional way of understanding an ideal concentrator is based on maximizing the concentration ratio based on a uniformed acceptance angle. Although such an angle does not exist in the case of CEC, the thermodynamic laws still hold and we can produce concentrators with the maximum concentration ratio allowed by them. Here we restate the problem and use the string method to solve this general problem. Built on the solution, we can discover groups of such ideal concentrators using geometric flux field, or flowline method. Keywords: CEC, flowline method, asymmetric, string method, geometric flux 1. INTRODUCTION The asymmetric ideal concentrators have been first accomplished by[1] using two parabolas. Other people built on it with a non-flat absorber and produced similar ideal concentrators with infinitely far away source. [2]. Such designs are generally referred to as the asymmetric compound parabolic concentrators (CPC), however, the parabola is not necessarily the accurate name to describe the shape when the absorber is non-flat. For concentrators with finite source, compound elliptical concentrator (CEC) was proposed, and extended to non-flat absorbers[3]. Parallel to this effort, the alternative method for building the CPC or CEC from a geometric flux field (i.e. flowline) perspective, have been showcased in several papers [4][5][6]. More recently, a discussion of using pharosage[7], or effectively the flowline method have been proposed for 3D ideal concentrators[8][9]. A generalized string method has been proposed for double stage symmetric concentrators[10]. Built on it, the asymmetric case was also developed for double stage concentrators[11]. Both the asymmetric and symmetric setups allow the second stage concentrators to degenerate into a small concentrator. This can be accomplished by keeping the absorber below the crossing over edge rays (A’B and AB’). It is also revealed in these discussions that the shape of the absorber can be any convex shape. Such a prior art, with both symmetric and asymmetric setups, will inevitably produce a CEC-type concentrators as the second stage, which is the main topic of discussion for this paper. Within this paper, instead of discussing about double stage concentrators, we give the same solution from the perspective of directly generating the general ideal concentrator. We discuss about the CEC with asymmetric finite sources and propose the method for building the ideal concentrator using the string method. This eliminate the complex setup of both first and second concentrators and directly arrive at the degenerated case. Built on it, we will also include a short derivation of generating a group of flowline concentrators with the asymmetric setup. The concept can be quickly extended to non-flat absorbers due to the flexibility of the string method. At the end of the paper we will predict several other designs that can be extended from the current concentrators. In the end, we will also discuss the potential of this method for angular transformers. Ideal concentrators Ideal concentrators obeying both the first and second law of thermodynamics can be defined using the understanding of the radiative heat transfer between a source and sink at equilibrium temperature ?, assuming both bodies are ideal black bodies[12] [13]. Here we give a more robust argument to reframe the arguments made in [13]. *rwinston@ucmerced.edu; phone 1 209 201-2863; fax 1 209 228-2914; ucsolar.org Nonimaging Optics: Efficient Design for Illumination and Solar Concentration XII, edited by Roland Winston, Jeffrey M. Gordon, Proc. of SPIE Vol. 9572, 957203 © 2015 SPIE · CCC code: 0277-786X/15/$18 · doi: 10.1117/12.2191948 Proc. of SPIE Vol. 9572 957203-1 Downloaded From: http://spiedigitallibrary.org/ on 11/18/2015 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx