权重函数对关联方程估计超声速混合层波前方差精度的影响

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.

Influence of weighting function on accuracy of supersonic mixing layer wave-front variance estimation with linking equation

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.