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为了研究光端机附近的流场情况,文中选取了带有共形和平面两种常用光学窗口的整流罩,对比两者在不同参数下的气动光学效应。整流罩的几何模型如图3所示,其中R=0.13 m,H=0.1104 m,L=0.102 m,光学窗口半径r=0.1105 m。
图 3 光学窗口几何模型示意图及视角定义
Figure 3. Geometric model schematic of the optical window and definition of viewing angles
合理的仿真区域和边界条件设置是流场仿真分析的关键,图4为了平面光学窗口方位转角90°的流场计算域和边界条件设置,整体流体域采用27.5R×12R×6R,其中光端机中心距离流场入口的距离为7.5R,采用速度入口边界条件,距离出口的距离为20R,采用静压出口边界条件,上表面及两侧面采用绝热自由滑移边界条件,而下表面和转塔表面则采用绝热无滑移边界条件。
图5为两种窗口表面结构化面网格分布,为了提高模拟精度,对光学窗口周围的网格进行网格加密,共形光学窗口的网格量为1007777;平面光学窗口的网格量为1005263。
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气动光学效应主要有稳态与非稳态两类,在飞行速度较低时,带有整流罩的窗口的气动光学效应通常以稳态像差为主,占比达70%,并且稳态像差会弱化气动光学效应的非稳态特性[15]。由于非稳态气动光学效应十分复杂,难以进行光学补偿,并且占比不高,在很多情况下作为系统误差不予考虑。因此文中主要针对稳态气动光学效应进行分析。
目前,气动光学计算主要采用两种主流方法,即大涡模拟法(LES)和Reynolds平均法(RANS)。LES在提高计算精度方面取得了显著进展,但对于网格数量和计算机性能的要求较高。相比之下,RANS通过求解时均控制方程来模拟流场,具有模型建立简单、使用方便的优势,特别是在工程领域,RANS在保证一定准确性的情况下具有更高的计算效率。文中选择了RANS中的$ {k}-{\varepsilon } $两方程模型。该模型在满足雷诺应力的约束条件下,能够与真实湍流现象保持一致,能够更精确地模拟平面和原形射流的扩散速度,使计算结果更贴近真实情况。
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当湍流介质密度发生变化时,湍流介质的折射率也会随之发生变化,通过GladStone-Dale关系式可知,折射率和空气中的密度直接相关,其表达式如下[16−17]:
$$ n(r) - 1 = {K_{GD}}\rho (r) $$ (1) 式中:$r = xi + yj + zk$,表示光线流场中的位置;$n(r)$和$\rho (r)$分别为该位置处的折射率和密度;${K_{GD}}$为与传播光线波长有关的G-D常数。${K_{GD}}$可以表示为:
$$ {K_{_{GD}}}(\lambda ) = 2.23 \times {10^{ - 4}}\left(1 + \frac{{7.52 \times {{10}^{ - 3}}}}{{{\lambda ^2}}}\right) $$ (2) 式中:$ \mathrm{\lambda } $为工作波长,单位为μm;${K_{GD}}$的单位为m3/kg。通过上式的计算,可以完成由气动流场的密度场分布到折射率场分布的转换过程。在几何光学中,光线沿路径对折射率的积分定义为光程(OPL),其表达式如下:
$$ OPL(x',y') =\displaystyle\int \nolimits_0^L n(x',y',z'){\mathrm{d}}z' $$ (3) 式中:$(x',y')$为光学窗口平面中的光学坐标;$z'$的发射方向。而光线在不均匀流场中的传播导致了各条光线光程的不同,被定义为光程差(OPD),其表达式如下:
$$ OPD(x',y') = OPL(x',y') - < OPL(x',y') > $$ (4) 式中:$ < OPL(x',y') > $表示平均光程差。根据波动方程的射线近似,可以得到光线在不均匀介质中的传播规律如下:
$$ \frac{{\text{d}}}{{{\text{d}}s}}\left[ {n(r)\frac{{{\text{d}}r}}{{{\text{d}}s}}} \right] = \nabla n(r) $$ (5) 式中:$ s $为光线传播路径上的弧长;$ r $为光线矢径;$ n $为折射率;$ \nabla n $为折射率梯度。公式(5)为典型的二阶常微分方程,文中使用四阶龙格—库塔法进行求解。
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理想光束经过湍流大气后,远场光波波面相位将发生畸变。光波的波面相位畸变与光程差有关,用波长$ \mathrm{\lambda } $作参考量,光波的相位畸变为[9]:
$$ \Delta \phi =2\pi \frac{OPD(x{'},y{'},z{'})}{\lambda } $$ (6) 式中:$ \Delta \phi $为波面上的相位分布,即畸变之后的相位差。流场引起的光波相位畸变会严重影响光波的复振幅分布,设定光线的光波复振幅为$ E $,则远场的光波复振幅分布为:
$$ E(x{'},y{'},{z{'}}_{{\rm{far}}})=E(x{'},y{'},{z}_{0}{'}){\mathrm{exp}}[-i\Delta \phi ] $$ (7) 式中:$ E(x{'},y{'},{z}_{0}{'}) $为光瞳平面上的复振幅分布;$E(x{'},y{'},{z{'}}_{{\rm{far}}})$为远场平面的光波复振幅分布。根据波动光学可得,在远场平面的光强分布为:
$$ I(x{'},y{'},{z{'}}_{{\rm{far}}})={\left|E(x{'},y{'},{z{'}}_{{\rm{far}}})\right|}^{2} $$ (8)
Analysis of aerodynamic optical effects in airborne laser communication optical windows
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摘要: 机载激光通信中通信光束散角小、系统跟踪精度高,光学窗口的气动光学效应会引起远场光斑形状和位置发生变化,降低通信性能。为此,通过Fluent对共形和平面两种光学窗口整流罩在不同飞行高度、速度、方位角下的外流场进行稳态仿真分析,利用相位屏分析远场自由衍射光斑变化。结果表明,共形窗口在俯仰、高度和速度变化中的流场更加稳定,呈现更为一致的变化趋势,且在远场衍射中表现更好。平面窗口在方位转角变化大与低速的飞行工况下,RMS值低于共形窗口。远场光斑发生偏移和弥散的程度与波面畸变成正相关,但在波面畸变较大的情况下,RMS值不能完全定义其对光学系统的影响。同时,当俯仰角靠近机体表面、降低飞行高度、增加飞行速度均会增强波面畸变。Abstract:
Objective Wireless laser communication technology has advantages such as high communication speed, good security, and portability, making it widely applicable in both military and civilian communication fields. Aircraft, as one of the crucial platforms for wireless laser communication research, can effectively enhance the reliability and applicability of laser communication, playing a significant role in the future integrated aerospace network. However, the practical application of airborne laser communication faces various challenges. Apart from common atmospheric laser communication issues like atmospheric absorption, scattering, platform vibrations, and cloud cover, aerodynamic optical effects pose a significant constraint on the application of airborne laser communication. Methods This paper addresses the issue of selecting the shape of the optical window for the airborne laser communication optical terminal. It designs streamlined fairings with conformal and planar optical window shapes (Fig.3). Fluent is used to simulate and analyze the flow field around the fairings under different flight altitudes, speeds, and azimuth angles. The refractive index distribution at the front end of the optical window is obtained based on the density and refractive index relationship (Fig.7). Then, using the ray tracing method, the wavefront distortion of the two windows under different conditions is obtained (Fig.6), verifying the independence of the optical grid and tracing length in ray tracing (Fig.8-9). Finally, the far-field free diffraction spot changes are analyzed using phase screen analysis (Fig.13). Results and Discussions The results show that, at different azimuth angles, RMS increases first and then decreases, reaching a minimum at 90°, and rapidly increasing after exceeding 90°, reaching the maximum at 180° (Fig.10). Overall, the RMS caused by the spherical window is slightly larger than that caused by the planar window. When changing the pitch angle, the spherical window exhibits good flow field consistency, while the planar window has some influence on the flow field near the window (Fig.11). Flight altitude and speed are also crucial factors affecting window aerodynamic optical effects. Increasing flight altitude and decreasing flight speed can weaken aerodynamic optical effects, and the RMS change caused by the planar window is smaller than that caused by the conformal window (Fig.12). To gain a deeper understanding of the performance of the optical system under actual working conditions and observe the impact of wavefront distortion on the optical system, we conducted far-field diffraction analysis of the calculated wavefront distortion. With increasing azimuth angle, the changes in intensity and offset become more drastic, resembling the trend of RMS changes. However, for the planar window, after azimuth angle exceeds 150°, its wavefront distortion becomes more severe compared to the conformal window (Fig.14). Increasing flight altitude can weaken the window's impact on aerodynamic optics, and increasing flight speed results in noticeable differences between the two, with speed having a more significant impact on aerodynamic optical effects than altitude (Fig.15). Conclusions When the azimuth angle is less than 90°, there is little difference in the optical transmission performance between the two window shapes. However, beyond 90°, the RMS value of the conformal window consistently exceeds that of the planar window. Nevertheless, after wavefront aberration and far-field diffraction, the distortion of the spot from the conformal window is noticeably smaller than that from the planar window, especially at azimuth angles of 180°, where the planar window's far-field spot shows significant peak intensity reduction and spreading. Changes in pitch angle demonstrate better stability for the conformal window compared to the planar window. Variations in flight altitude and speed significantly affect the peak intensity of the far-field diffraction spot, while having a smaller impact on the spot's displacement. Increasing flight altitude weakens the influence of the window shape on aerodynamic optical effects, while increasing flight speed exacerbates the differences between the two window shapes, with flight speed having a stronger impact on aerodynamic optical effects compared to flight altitude. The wavefront aberrations caused by aerodynamic optical effects are highly complex, and relying solely on wavefront aberration RMS values cannot fully define their impact on the optical system. For instance, although the RMS value of the planar window is smaller than that of the conformal window at azimuth 180°, the spreading degree of the spot during far-field diffraction is stronger than that of the conformal window. Overall, the conformal window exhibits more stable flow fields during variations in pitch, altitude, and speed, showing a more consistent trend and performing better in far-field diffraction. Conversely, the planar window's RMS value is lower than that of the conformal window under conditions of large azimuth angles and low-speed flight. -
Key words:
- airborne laser communication /
- aero-optics /
- far-field diffraction /
- optical window
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[1] Jiang Huilin, Fu Qiang, Zhao Yiwu, et al. Development status and trend of space information network and laser communication [J]. Journal of the Internet of Things, 2019, 3(2): 1-8. (in Chinese) [2] Xing Zhan, Chen Xiaoyi, Peng Zhiyong, et al. Research progress and thinking of infrared aero-optical effect (Invited) [J]. Infrared and Laser Engineering, 2022, 51(4): 20220228. (in Chinese) [3] Sun Xiwang, Liu Wei. Research progress of aero-optical effect [J]. Advances in Mechanics, 2020, 50(0): 249-309. (in Chinese) [4] Weber D C, Trolinger J D, Rose W C. Computer simulation of aero-optic phenomena based on empirical data [J]. Optical Diagnostics for Fluids, Solids, and Combustion, 2001, 4448: 187-196. doi: 10.1117/12.449376 [5] Duffin D A, Jumper E J. Feedforward adaptive-optic correction of aero-optical aberrations caused by a two-dimensional heated jet [J]. AIAA Journal, 2011, 49(6): 1283-1291. doi: 10.2514/1.J050904 [6] Porter C, Gordeyev S, Zenk M, et al. Flight measurements of aero-optical distortions from a flat-windowed turret on the airborne aero-optics laboratory (AAOL)[C]//42nd AIAA Plasmadynamics and Lasers Conference in Conjunction with the 18th International Conference on MHD Energy Conversion (ICMHD), 2011: 3280. [7] White M, Visbal M. Computational investigation of wall cooling and suction on the aberrating structures in a transonic boundary layer[C]//51st AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, 2013: 720. [8] Yin Xingliang. Principles of Aero-optics[M]. Beijing: China Astronautic Publishing House, 2003. (in Chinese) [9] Li Guichun. Aerodynamic Optics [M]. Beijing: National Defense Industry Press, 2003. (in Chinese) [10] Meng Lixin, Zhao Dingxuan, Zhang Lizhong, et al. Boundary layer effect and compensation in airborne laser communication [J]. Optics and Precision Engineering, 2014, 22(12): 3231-3238. (in Chinese) doi: 10.3788/OPE.20142212.3231 [11] Ding Haolin, Yi Shihe, Fu Jia, et al. Experimental investigation of aero-optical effect due to supersonic turbulent boundary layer [J]. Infrared and Laser Engineering, 2016, 45(10): 192-198. (in Chinese) [12] Zhao Xinhai, Yi Shihe, Ding Haolin, et al. Experiment on optical path difference of supersonic semi-free jet [J]. Acta Optica Sinica, 2020, 40(7): 0701001. (in Chinese) [13] Tan Xiaotong, Xu Heyong, Tian Renzhi. Numerical simulation of aero-optical effect of flow around typical optical windows [J]. Acta Aerodynamica Sinica, 2023, 41(6): 71-80. (in Chinese) [14] Dong Hang, Xu Ming. Space-time characteristics of the aero-optical effect around turrets [J]. Acta Optica Sinica, 2018, 38(10): 1001002. (in Chinese) [15] Chen Yong, Xie Weiming, Lu Daju, et al. Study on unsteady aero-optical effect of turret wake [J]. Acta Optica Sinica, 2020, 40(16): 1601001. (in Chinese) [16] Zhang Qingpeng. Study on suppression method of aero-optical effect of beamexpanding system[D]. Chengdu: The Institute of Optics and Electronics, the Chinese Academy of Sciences, 2020. (in Chinese) [17] Thuerey N, Weißenow K, Prantl L, et al. Deep learning methods for Reynolds-averaged Navier–Stokes simulations of airfoil flows [J]. AIAA Journal, 2020, 58(1): 25-36. doi: 10.2514/1.J058291 [18] Xu Liang, Wang Luyang, Wan Ziming, et al. Influence of different altitudes on deviation of aero-opticsimaging of 0°-15° angle of attack [J]. Infrared and Laser Engineering, 2023, 52(5): 20230411. (in Chinese)