光学学报, 2017, 37 (9): 0922002, 网络出版: 2018-09-07
基于椭圆型Monge-Ampére方程的太阳能聚光器设计方法 下载: 942次
Design Method of Solar Concentrator Based on Elliptic Type Monge-Ampére Equations
光学设计 聚光光伏系统 Monge-Ampére方程; 非成像光学 光波导板 optical design concentration photovoltaics system Monge-Ampére equations; non-imaging optics lightguide
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.
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. Peng Yin, Xiping Xu, Zhaoguo Jiang, Lulu Zhang. Design Method of Solar Concentrator Based on Elliptic Type Monge-Ampére Equations[J]. Acta Optica Sinica, 2017, 37(9): 0922002.