大口径轻量化主镜的温度场等效模型理论计算

针对大口径望远镜主镜在环境温度变化和太阳辐照变化引起的温度场变化进行了理论分析,根据圆柱坐标下设立的非稳态热传导方程和边界条件,利用分离变量法和格林函数法求解了主镜的温度场分布。为了验证求解的有效性,利用求得的温度场解析式和有限元软件分别分析了2.8 m口径望远镜实心主镜,反射面径向温度分布具有良好的一致性。表明该理论解析式能够较好地反映主镜反射面的温度场分布。将轻量化主镜进行无筋板的薄型镜热模型等效,并分别对两种镜子的温度场进行仿真计算,以此验证等效模型的正确性。轻量化主镜温度场的等效理论计算结果在主镜的早期设计研究阶段具有良好的参考价值。

Equivalent analytical calculation of the temperature field of the lightweighted primary mirror for large-aperture telescope

The thermal loads of ambient temperature and solar radiation around the telescope directly influence the temperature distribution within the primary mirror for a large-aperture telescope. Based on the unsteady heat conduction and boundary condition in the cylindrical coordinate system, the analytical temperature field for the primary mirror is calculated by separation of variables and Greens function method. To verify the theoretical model, the temperature distribution of a 2.8 m aperture solid mirror is calculated by the analytical solution. The calculated radial temperature distribution at the optical surface is in good agreement with those of FEA method, which reveal that the analytical solution can well reflect temperature distribution at the optical surface. A lightweighted mirror is equivalent to a thin mirror without ribs in the thermal analysis. The FEA analysis is conducted with both the mirror models, which verifies the validity of the equivalent model. The equivalent analytical calculation results of the temperature field for the lightweighted primary mirror have a significant reference value in the early design of the primary mirror for a large-aperture telescope.