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气动光学的研究中, 关联方程(linking equation)是关联湍流力学量与光学量的一个重要的方程. 但是, 基于模型简化的关联方程在亚声速低速流场的应用中通常忽略权重函数对波前方差估计精度的影响. 本文在纳米粒子示踪平面激光散射技术获得超声速混合层流场密度数据的基础上, 应用关联方程计算超声速混合层的流向波前方差, 并进行误差分析. 结果表明: 基于关联方程估计的流向波前方差与直接对密度场的积分计算结果具有较好的一致性; 在适当地定义相干长度、密度脉动协方差高斯模型近似的基础上, 分析了权重函数对关联方程计算精度的影响, 指出了权重函数对关联方程在超声速流场密度高度相关区域中应用的必要性. 研究的开展对于拓展关联方程在高速流场中的应用具有一定指导意义.In aero optics, the linking equation proposed by Sutton is an important equation which can link the fluid-mechanic statistical parameters to the statistical optical degradation parameters. However, in the application of simplified linking equation (SLE) to subsonic flowfields, the weighting function is often ignored. The supersonic mixing layer flowfield is generated in the supersonic wind tunnel. The nanoparticle-based planar laser scattering technology is used to obtain the density field of flowfield. The optics errors between supersonic mixing layer wave-front variances calculated from the SLE and the generalized linking equation are analyzed. The results indicate the validity of using the SLE to estimate the wave-front variance of supersonic mixing layer flowfield. Moreover, the SLE with weighting function has better fitting accuracy than the SLE without weighting function. The weighting function for the application of SLE to the high correlated regions in the supersonic mixing layer is necessary.
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Keywords:
- aerooptics /
- linking equation /
- weighting function /
- wave front variance
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图 1 混合层流场图像 (a)原始图像; (b)噪声和背景光预处理后图像
Fig. 1. Image of mixing layer: (a) Original image; (b) image after pre-processing.
图 2 广义关联方程、指数型和高斯型关联方程计算的波前方差
Fig. 2. Wave-front variance calculated by generalized linking equation, exponential linking equation and Gaussian linking equation.
图 3 高斯型关联方程和广义关联方程计算波前方差的误差
Fig. 3. Errors of using gaussian linking equation and generalized linking equation to calculate wave-front variance.
图 4 密度脉动相关函数分布 (a)中心点(200, 148); (b)中心点(480, 140); (c)中心点(800, 112); (d)中心点(1000, 100)
Fig. 4. Correlations of density fluctuations: (a) Central point (200, 148); (b) central point (480, 140); (c) central point (800, 112); (d) central point (1000, 100).
图 5 部分流向点处的权重函数分布
Fig. 5. Distribution of weighting functions at some stream-wise locations.
图 6 高斯型关联方程加入权重函数前后的积分核分布 (a)未加入权重函数; (b)加入权重函数; (c)积分核分布差
Fig. 6. Integral kernel distribution calculated by Gaussian linking equation before and after adding weighting function: (a) Before adding the weighting function; (b) after adding the weighting function; (c) the integral kernel distribution differences.
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[1] Gilbert K G, Otten L J 1982 AIAA Prog. Astronaut. Aeronaut. 80 1
Google Scholar
[2] Jumper E J, Fitzgerald E J 2001 Prog. Aero. Sp. 37 299
Google Scholar
[3] Havener G 1992 30th Aerospace Sciences Meeting and Exhibit Reno, United States, January 6−9, 1992 AIAA-92-0654
[4] Sutton 1985 AIAA J. 23 1525
Google Scholar
[5] Hugo R J, Jumper E J 2000 Appl. Opt. 39 4392
Google Scholar
[6] Tromeur E, Garnier E, Sagaut P 2006 J. Turbul. 7 1
Google Scholar
[7] Fitzgerald E J, Jumper E J 2004 J. Fluid Mech. 512 153
Google Scholar
[8] Yin K X, Jiang H L, Tong S F 2007 Infrared Laser Eng. 36 689
Google Scholar
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[10] Tromeur E, Garnier E, Sagaut P, Basdevant C 2002 Engin. Turbul. Model. Exp. 4 327
Google Scholar
[11] Wang K, Wang M 2012 J. Fluid Mech. 696 122
Google Scholar
[12] 于涛, 夏辉, 樊志华, 谢文科, 张盼, 刘俊圣, 陈欣 2018 物理学报 67 134203
Google Scholar
Yu T, Xia H, Fan Z H, Xie W K, Zhang P, Liu J S, Chen X 2018 Acta Phys. Sin. 67 134203
Google Scholar
[13] Zhu K C, Li S X, Tang Y, Yu Y, Tang H Q 2012 J. Opt. Soc. Am. A 29 251
Google Scholar
[14] Yu T, Xia H, Fan Z H, Xie W K, Zhang P, Liu J S, Chen X, Chu X X 2019 Opt. Commun. 436 14
Google Scholar
[15] Yi S H, Chen Z, He L, Wu Y, Tian L F 2014 J. Exper. Fluid Mech. 28 1
[16] Gao Q, Yi S H, Jiang Z F, He L, Zhao Y X 2012 Opt. Express 20 16494
Google Scholar
[17] Qiao N S, Zou B J 2013 Optik 124 1889
Google Scholar
[18] 潘宏禄, 史可天, 马汉东 2009 计算力学学报 26 745
Pan H L, Shi K T, Ma H D 2009 Chin. J. Comput. Mech. 26 745
[19] Braunschweiler L, Ernst R R 1983 J. Magn. Reson. 53 521
Google Scholar
[20] [21] Berrzzi F, Dalle Mese E, Pinelli G 1999 Radar Sonar Nav. 146 55
Google Scholar
[22] Takahashi H, Oso H, Kouchi T, Masuya G, Hirota M 2009 47th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition Orlando, United States, January 5−8, 2009 AIAA 2009-23
[23] Ganapathisubramani B, Clemens N T, Dolling D S 2006 J. Fluid Mech. 556 271
Google Scholar
[24] Azmi A M, Zhou T M, Zhou Y, Wang H F, Cheng L 2018 Phys. Rev. Fluids 3 074702
Google Scholar
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