Optimization Design Method of Freeform Reflector for Direct Solar Radiation Measurement

Xiaotong Yang; Guoyu Zhang; Jian Zhang; Wei Chong; Zongtao Duan; Zhengjie Niu

doi:10.3788/AOS202242.0922001

Acta Optica Sinica, Volume. 42, Issue 9, 0922001(2022)

Optimization Design Method of Freeform Reflector for Direct Solar Radiation Measurement

Xiaotong Yang¹, Guoyu Zhang^1,2,3、*, Jian Zhang^1,2,3, Wei Chong^1,4, Zongtao Duan¹, and Zhengjie Niu¹

Author Affiliations

¹School of Opto-Electronic Engineering, Changchun University of Science and Technology, Changchun 130022, Jilin, China

²Jilin Engineering Research Center of Photoelectric Measurement & Control Instruments, Changchun 130022, Jilin, China;

³Key Laboratory of Opto-Electronic Measurement and Optical Information Transmission Technology, Ministry of Education, Changchun 130022, Jilin, China

⁴Meteorological Observation Center, China Meteorological Administration, Beijing 100081, China

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Figures & Tables(17)

Fig. 1. Two-dimensional model of global solar direct radiation angle variation

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Fig. 2. Variation of global noon height angle at equinoxes and solstices

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Fig. 3. Range of incidence angle of full latitude solar direct radiation

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Fig. 4. Mapping relationship between solar direct light and reflector surface

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Fig. 5. Initial structure model of freeform surface mirror. (a) Working light path; (b) finite element division model of mirror

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Fig. 6. Optical path model of reflector in actual operation

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Fig. 7. Surface optimization process of free-form reflector

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Fig. 8. Simulation of initial surface shape of freeform mirror. (a) Simulation optical path; (b) normalized result of irradiance of convergent surface

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Fig. 9. Normalized results of irradiance of convergent surface. (a) ε=3°, S_RFU=82.79%; (b) ε=1°, S_RFU=82.36%; (c) ε=0.5°, S_RFU=89.52%; (d) ε=0.25°, S_RFU=92.36%

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Fig. 10. Verification test site for center position of reflected light spot

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Fig. 11. Center position of reflection spot at each incident light angle

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Fig. 12. Test platform of solar direct radiation optical system

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Fig. 13. Normalized results of irradiance of incident light at various angles

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Table 1. Initial structure data of mirror
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Table 1. Initial structure data of mirror
Parameter Value
L /mm 119.5
L₁ /mm 10
L₂ /mm 109.5
γ_S /(°) 33.25
γ_W /(°) 56.75
ρ_S /(°) 30.75
ρ_W /(°) 59.25

Table 2. Accuracy of quadratic to quintic polynomial fitting
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Table 2. Accuracy of quadratic to quintic polynomial fitting
Polynomial fitting Quadratic fitting Cubic fitting Quartic fitting Quintic fitting
Residual sum of squares 0.13733 0.00256 0.00005 0.00009
R-squared value 0.99983 1.00000 1.00000 1.00000

Table 3. Polynomial coefficients of initial surface shape of mirror
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Table 3. Polynomial coefficients of initial surface shape of mirror
Polynomial coefficient a₀ a₁ a₂ a₃ a₄ a₅
Value 10.00001 -0.57888 0.00680 -0.00571 0.00050 -0.00002

Table 4. Polynomial coefficients of freeform surface mirror when ε=0.25°
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Table 4. Polynomial coefficients of freeform surface mirror when ε=0.25°
Polynomial coefficient a₀ a₁ a₂ a₃ a₄ a₅
Value 10.00300 -0.60341 -0.00246 -0.00393 0.00034 -0.00002

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Xiaotong Yang, Guoyu Zhang, Jian Zhang, Wei Chong, Zongtao Duan, Zhengjie Niu. Optimization Design Method of Freeform Reflector for Direct Solar Radiation Measurement[J]. Acta Optica Sinica, 2022, 42(9): 0922001

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