复杂流场光偏折层析的理论与实验研究
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摘要
复杂流场的全场显示与测量是气动力学领域仍未完全解决的热点问题，光偏折层析技术因其动态范围大、抗干扰能力强、可以实现非接触、三维、定量测试等优点而成为测量复杂流场的上佳方案。针对光偏折层析在关键技术上的不完善、缺乏完整的技术体系这一发展现状，本文系统地研究了光偏折层析的理论和实现方法，着重对光偏折层析的多方向投影获取、投影信息提取、以及重建算法三方面技术进行了深入研究。首先进行的流场中光偏折特性分析与实验验证，为偏折系统的设计与新重建算法的研究奠定了理论基础。在对莫尔条纹的成像机理和分布特点进行分析的基础上，研制了两种旋转莫尔偏折系统，实现了全场范围内莫尔条纹图的获取。偏折信息提取方面，分别对条纹位移法和相位展开法进行了原理与实验研究，并针对莫尔偏折图的条纹特性，使用小波去噪技术对经典的条纹位移分析法作了改进。对于光偏折层析重建算法这一最薄弱的技术环节，提出了两种解决思路与方法。其一是从光偏折公式中偏导数项的离散数值表达出发，建立了直接使用偏折角进行迭代修正的重建算法族，对多种场分布和重建条件下的大量模拟实验及误差分析验证了这些算法的重建效能。其二，从解决不适定的数学物理反问题的角度出发，建立光偏折层析的Tikhonov正则化重建技术，研究了偏折投影正则方程组的构建、正则参数与正则化矩阵的确定、正则投影方程组的求解等三部分内容。此外，对强偏折场的偏折层析重建技术作了探索性的研究，发展了一种结合光线追迹技术的正则化修正曲线路径反演算法。基于上述建立的光偏折层析技术体系，对大量的实际流场进行了测量或重建，包括小型喷焰温度场、非对称双峰温度场、三烛火焰温度场、火箭燃气流密度场、高超音速风洞中含激波密度场、超音速风洞中非对称密度场等，并使用各种实验或分析技术对重建结果进行了验证，从而证明了光偏折层析技术在复杂流场测量领域的重要实用价值。
The visualization and measurement of complex flow are of major importance inaerodynamics. Compared with other methods applied to flow visualization andmeasurement, deflectometric tomography, a noncoherent method for studying phaseobjects, has many merits such as simple optical configuration, large dynamic range,having no special requirement to light source, and adaptation to tough environment. In thisthesis, a basically complete theoretical system for deflectometric tomography isconstructed, which is supposed to give its guidance in investigating beam deflectionperformances, designing testing configurations, projection extraction methods, andoptimum reconstruction algorithms. Two kinds of rotatable deflectometric systems aredesigned, which is able to capture projection data over an angular range of 180°. Based onthe research of fringe analysis techniques and wave-front retrieval techniques forprojection extraction, a further data processing method is supposed, in which thedeflectometric data are denoised by wavelet-based procedure after projection datareduction. Two kinds of new algorithms are developed to improve the reconstructionaccuracy and applicability of deflectometric tomography. First, a new iterative algorithm,deflection angle revision reconstruction technique, is derived from the basic deflectionformula and distinguished by a high degree of flexibility in reconstructing a distributionfrom limited view-angles projections. A smoothing scheme is supplied for the ill-posedreconstruction. The precision and convergence of the algorithm are analyzed through anumerical simulation. Second, Tikhonov regularization method is developed fordeflectometric tomography to reconstruct two-dimensional distribution. A modifiedregularization technique is applied to the linear projection equations and the conjugategradient method is used to compute the regularized solution for the least-square equations.In numerical simulation, the approach produces reliable reconstructions by computingunderdetermined equations and overdetermined equations respectively for asymmetricaldistribution. Besides, a curved ray algebraic inversion technique, associated geometricalray tracing algorithm, is suggested for the reconstruction of strongly refracting fields.Furthermore, the deflectometric tomography technique is employed to measure orreconstruct the temperature field of butane flame, asymmetric temperature distribution with double-peak-like structure, three-candle flame temperature field, density field inrocket exhausted jet, symmetric and asymmetric density fields in supersonic flow. Someother methods, such as direct thermocouple measurement and computing fluid dynamicalanalysis, verify the validity of the reconstruction results of deflectometric tomography, andprove the important value of the technology in measuring complex flow field.
The visualization and measurement of complex flow are of major importance inaerodynamics. Compared with other methods applied to flow visualization andmeasurement, deflectometric tomography, a noncoherent method for studying phaseobjects, has many merits such as simple optical configuration, large dynamic range,having no special requirement to light source, and adaptation to tough environment. In thisthesis, a basically complete theoretical system for deflectometric tomography isconstructed, which is supposed to give its guidance in investigating beam deflectionperformances, designing testing configurations, projection extraction methods, andoptimum reconstruction algorithms. Two kinds of rotatable deflectometric systems aredesigned, which is able to capture projection data over an angular range of 180°. Based onthe research of fringe analysis techniques and wave-front retrieval techniques forprojection extraction, a further data processing method is supposed, in which thedeflectometric data are denoised by wavelet-based procedure after projection datareduction. Two kinds of new algorithms are developed to improve the reconstructionaccuracy and applicability of deflectometric tomography. First, a new iterative algorithm,deflection angle revision reconstruction technique, is derived from the basic deflectionformula and distinguished by a high degree of flexibility in reconstructing a distributionfrom limited view-angles projections. A smoothing scheme is supplied for the ill-posedreconstruction. The precision and convergence of the algorithm are analyzed through anumerical simulation. Second, Tikhonov regularization method is developed fordeflectometric tomography to reconstruct two-dimensional distribution. A modifiedregularization technique is applied to the linear projection equations and the conjugategradient method is used to compute the regularized solution for the least-square equations.In numerical simulation, the approach produces reliable reconstructions by computingunderdetermined equations and overdetermined equations respectively for asymmetricaldistribution. Besides, a curved ray algebraic inversion technique, associated geometricalray tracing algorithm, is suggested for the reconstruction of strongly refracting fields.Furthermore, the deflectometric tomography technique is employed to measure orreconstruct the temperature field of butane flame, asymmetric temperature distribution with double-peak-like structure, three-candle flame temperature field, density field inrocket exhausted jet, symmetric and asymmetric density fields in supersonic flow. Someother methods, such as direct thermocouple measurement and computing fluid dynamicalanalysis, verify the validity of the reconstruction results of deflectometric tomography, andprove the important value of the technology in measuring complex flow field.
引文
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