### 基于自由曲面的聚焦型太阳模拟器设计

Design of focusing solar simulator based on free-form surface
1 长春理工大学 空间光电技术研究所, 吉林 长春 130022
2 中广核太阳能开发有限公司, 北京 100000
3 厦门理工学院 光电与通信工程学院, 厦门 361024

Abstract
The concentrating solar simulator can obtain solar radiation spots with high-power convergence, which has important applications in the fields of solar thermal power generation and thermochemical research. To obtain uniform solar radiation spots, a free-form surface condenser design method based on non-imaging optics is proposed, and its design principle and specific method are described. The designed free-form condenser is compared with a non-coaxial ellipsoidal condenser with the same containment angle, and the correctness of its design method is verified by simulation analysis. The simulation results show that when a xenon lamp with a rated power of 6 kW is used as the light source, the single-lamp solar simulator composed of a free-form condenser can produce a spot with an average irradiance of 274.4 kW/m2 in the target region with a diameter of 60 mm. The spot’s unevenness decreases from 18.28% to 5.69% compared with that of a non-coaxial ellipsoidal solar simulator. The seven-lamp solar simulator can produce a spot with an average irradiance of 1.65 MW/m2, with a spot unevenness that decreases from 13.19% to 5.49%.

## 2.1 均匀分配光源能量与目标面面积

#### Fig. 4. Relative intensity distribution

$S = \sum\limits_{i = 1}^{n - 1} {{S_i}}\quad .$ (1)

${p_i} = \frac{{{S_i}}}{S},\sum\limits_{i = 1}^{n - 1} {{p_i}} = 1,\left( {i = 1,2, \cdots ,n - 1} \right)\quad.$ (2)

$\Delta {\alpha _i} = \frac{{{A_{i + 1}} - {A_i}}}{{{p_i} \times \left( {M - 1} \right)}}\quad.$ (3)

${S_0}{\text{ = }}{\text{π}} r_{i + 1}^2 - {\text{π}} r_i^2 = \frac{{{\text{π}} {H^2}}}{{M - 1}}\quad.$ (4)

i个圆半径为ri ( $i=1,2,\cdots,M$)，其中r1=0，其面积为：

${\text{π}} r_i^2 = \left( {i - 1} \right){S_0}\quad.$ (5)

${r_i} = H\sqrt {\frac{{i - 1}}{{M - 1}}}\quad .$ (6)

## 2.2 计算自由曲面聚光镜母线离散点

#### Fig. 5. Schematic diagram of the condenser

${\boldsymbol{N}} = \frac{{{\boldsymbol{I}}_{{\rm{out}}} - {\boldsymbol{I}}_{{\rm{in}}} }}{{\sqrt {2 - 2\left( {{\boldsymbol{I}}_{{\rm{out}}} \cdot {\boldsymbol{I}}_{{\rm{in}}} } \right)} }}\quad.$ (7)

#### Fig. 6. Calculation of adjacent iteration points of the freeform condenser busbars

$\frac{{x{}_t}}{{{y_t}}} = \tan \beta = \tan \alpha = - \frac{{{y_{{{{\boldsymbol{N}}_i}} }}}}{{{x_{{{{\boldsymbol{N}}_i}} }}}}\quad.$ (8)

$\frac{{{y_{{P_i}}} + {y_t}}}{{{x_{{P_i}}} + {x_t}}} = \tan {\theta _{i + 1}}\quad.$ (9)

## 3 设计实例与仿真结果分析

${P}_{{\rm{reflect}}}\text={P}_{{\rm{xenon}}}\times {\eta }_{1}\times {\eta }_{2}\times {\eta }_{3} \quad,$ (11)

#### Fig. 7. Simulation results of free-form condenser with point source

$\sigma {\text{ = }} \pm \frac{{{E_{\max }} - {E_{\min }}}}{{{E_{\max }} + {E_{\min }}}} \times 100{\text{% }} \approx {0.94} {\text{% }}\quad.$ (12)

## 4 结　论

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