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基于椭圆型Monge-Ampére方程的太阳能聚光器设计方法

Design Method of Solar Concentrator Based on Elliptic Type Monge-Ampére Equations

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摘要

基于微分几何原理, 结合折射、反射定律以及能量守恒定律, 将太阳能聚光问题转换成一个带有非线性边界条件的椭圆型Monge-Ampére方程, 并建立了相应的数学模型。根据该数学模型, 设计了自由曲面聚光器, 利用光线追迹软件对所设计的自由曲面聚光系统进行了模拟研究。结果表明: 在考虑菲涅耳损失和光学材料的吸收情况下, 当实际太阳光线以0.27°的发散半角入射时, 1000 mm长度的自由曲面聚光器的几何聚光比达到500, 聚光效率为77.5%。通过该方法设计的自由曲面具有很高的设计自由度, 为设计不同程度聚光需求的太阳能聚光器提供了可能。

Abstract

A novel mathematical model which converts the solar collection problem into a nonlinear boundary problem for the elliptic type Monge-Ampére equations based on differential geometry, refraction law, reflection law and the conservation of energy is proposed. A freeform solar concentrator is designed based on this mathematical model. The freeform concentrator system is simulated by ray-tracing software. The results indicate that considering the Fresnel loss and the absorption of optical materials, when the sunlight possesses 0.27° divergence half-angle, the geometric concentration ratio and the focusing efficiency of the 1000 mm freeform solar concentrator reach 500 and 77.5%, respectively. The freeform designed by this method has higher degree of freedom, which makes it possible to design solar concentrators with different degrees of concentrating requirements.

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中图分类号:TK519

DOI:10.3788/aos201737.0922002

所属栏目:光学设计与制造

基金项目:国家自然科学基金青年基金(61605016)

收稿日期:2017-04-12

修改稿日期:2017-05-12

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作者单位    点击查看

尹 鹏:长春理工大学光电工程学院, 吉林 长春 130022
徐熙平:长春理工大学光电工程学院, 吉林 长春 130022
姜肇国:长春理工大学光电工程学院, 吉林 长春 130022
张璐璐:长春理工大学光电工程学院, 吉林 长春 130022

联系人作者:尹鹏(2013100182@mails.cust.edu.cn)

备注:尹 鹏(1988-), 男, 博士研究生, 主要从事太阳能聚光热发电、光伏发电和发光二极管照明自由曲面设计等方面的研究。

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引用该论文

Yin Peng,Xu Xiping,Jiang Zhaoguo,Zhang Lulu. Design Method of Solar Concentrator Based on Elliptic Type Monge-Ampére Equations[J]. Acta Optica Sinica, 2017, 37(9): 0922002

尹 鹏,徐熙平,姜肇国,张璐璐. 基于椭圆型Monge-Ampére方程的太阳能聚光器设计方法[J]. 光学学报, 2017, 37(9): 0922002

被引情况

【1】陈飞,高崇,杨春曦,李才对,别玉. 新型圆形吸收体太阳能复合抛物聚光器面形构建及光学分析. 光学学报, 2019, 39(6): 608001--1

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