横向大剪切量干涉技术及其在物理量检测中的应用
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摘要
激光干涉原理下的各种检测技术在本质上都是直接反映被测场折射率的分布特征,借助于Lorentz-Lorenz关系式及其针对气相介质的简化形式(即Gladstone-Dale关系式),可以实现从折射率到密度、浓度、温度等诸多物理量的无损检测。现有的具备多方向投影能力的实时干涉检测系统都基于双路干涉技术组建。以横向剪切为代表的共光路干涉技术具有前者所没有的布局紧凑、抗振性强、光学元件数量少且没有苛刻的定位要求等适于工业现场应用的优点,只是其输出条纹的分布特征要比前者的复杂得多。
传统的横向剪切干涉应用中缺乏对横向剪切量的重视和讨论,而本文作者发现当横向剪切量超过了被测对象畸变波面半宽时,剪切干涉条纹的两侧将显露出半幅类似于双曝光全息干涉原理的简单条纹；当横向剪切量超过了被测对象畸变波面宽度时,剪切干涉条纹将在水平方向上分裂为两个完整的类似于双曝光全息干涉原理的简单条纹。这意味着横向大剪切量干涉技术在实验流程和数据处理流程两个方面都表现优异,较之现有各类多方向干涉检测系统来说无疑是一种更经济的选择。考虑到实用的光学系统总存在像差,横向剪切干涉系统的背景条纹由此产生。由于它的分布特征可以用简单的球差公式来精确描述,因而不会为剪切干涉条纹的后处理过程带来实质性的影响。当横向剪切量足够大时,用被测对象存在时的条纹相位差直接减去背景条纹相位差即可得到仅由被测对象引发的那部分畸变波面的相位差,而传统的小剪切量干涉条件下的数据处理过程中必不可少的剪切还原算法在这里不再需要了。
我们先将横向大剪切干涉技术应用在肥皂泡液膜厚度(这是一个典型的一维分布)的检测中,对单个肥皂泡从形成初期到临近破裂等几个典型瞬间的全场膜厚分布进行了实验研究。从中可知,被测肥皂泡沿着竖直方向的液膜厚度分布的最大误差为3/8倍波长。破裂之前的各个瞬间的数据显示,它的液膜厚度沿着重力方向的分布均能很好吻合三参数指数膜厚模型,其偏差值不超过0.4倍波长。随着肥皂泡自身排流作用的不断进行,其椭球型轮廓的顶部开始出现一个水层液膜消失而乳化剂层液膜仍保持完整的特殊区域。该区域的边界不断向下扩展,该过程中肥皂泡随时可能破裂。如果将上述三参数指数膜厚模型简化为双参数指数膜厚模型,那么可以推导出等效膜厚值与纵向条纹级数梯度之间的比值随着纵向坐标的分布曲线。在图像分辨率已知的条件下,通过该比值的分布曲线可以评估横向大剪切量干涉技术在任意高度上的液膜厚度检测的极限值。
考虑到同轴燃烧器生成的火焰总存在一定程度的轴向偏移,因而我们将横向大剪切量干涉系统从单方向投影体系扩展为三方向投影体系,然后对给定工况下的准二维轴对称乙烯扩散火焰分别以二维算法以及三维算法进行了温度场检测。在二维假设中,用于求解Radon逆变换的滤波投影重建算法使用180度范围内的虚拟投影方向,同时使用来自燃烧数值模拟的组分浓度分布来获得特别修正系数场。干涉重建结果与热电偶检测数据对比可知,两者在火焰温度峰值坐标的外侧区域或者内侧较远处显示出了很好的一致性,各个高度上的平均偏差在20 K到40 K之间。但热电偶检测数据在火焰温度峰值坐标的内侧紧邻区域明显偏低,两者的最大偏差可达200 K。这是因为火焰温度峰值坐标的内侧紧邻区域为不充分燃烧,其烟黑容积份额较高。即使热电偶节点以很快速度插入被测火焰的待测目标区域,在节点表面仍会出现烟黑沉积并出现尺度渐长的碳球,其辐射热损失使得热电偶节点表面的烟黑的温度明显低于火焰中气相组分的温度。排除掉这个因素之后,二维假设能够为标准的二维轴对称被测火焰对象提供定量的分析结果。
在三维假设中,用于求解Radon逆变换的滤波投影重建算法使用三个真实投影方向,同时将特别修正系数在全场大部分区间的统计均值(即1.05)作为通用修正系数,此时的温度场重建结果会表现出不同程度的非轴对称特征。我们发现3厘米高度上的温度重建结果在全场都表现出明显的扰动,这是因为该高度上的烟黑辐射较强导致干涉条纹图像的对比度变差并最终影响了条纹相位差的识别精度。与二维假设下的轴心反演值对比可知,三维假设下在1厘米高度的轴心反演值存在10%以上的偏差,这是因为该高度附近区域的主要组分为乙烯,它相对于空气组分假设所需的浓度场修正系数远超过1.05的通用修正值。然而在距双筒燃烧器的内筒喷嘴较远的其它高度上,三维假设下的轴心反演值仅存在不超过3.3%的偏差。总体来说,三维假设能够为非轴对称的被测火焰对象提供定性的分析结果,并有望用于工业环境下的非稳态火焰的在线监测。
Laser interferometry has an inherent virtue in measuring the index of refraction in a non-destructive way. Moreover, the index of refraction can be related to many other parameters such as density, concentration and temperature by use of the Lorentz-Lorenz equation and its simplified format (namely the Gladstone-Dale equation) for gas. Modern interferometer systems which afford multi-directional projections and real-time measurements are all constructed from the double paths style interferometry. Although the common paths style interferometry has many virtues such as compact layout, insensitivity to vibration, less hardware demand, easy adjustment and adaptation to real-time measurement, the characters of its fringe pattern which is more complex than the double paths style interferometry's has limited its application.
Although the lateral shearing displacements in the traditional studies about the lateral shearing interferometry are totally small and seem to be unimportant, the author found that when the lateral shearing displacement exceeds half width of the test distorted wave-front, the two sides of the fringe pattern seem similar to the simple one obtained in the double exposure holographic interferometry. Once the lateral shearing displacement exceeds full width of the test distorted wave-front, this fringe pattern would be torn apart and form two separate parts while each part equals the double exposure holographic interferometric fringe pattern. Considering that the primary drawback which limits its applications in comparison with other interferometry could be overcome in the above way, the large lateral shearing displacement interferometry would be a more economic choice to build up a practicable multi-directional interferometric system and has an enormous potential to replace traditional interferometry either in laboratorial conditions or in industrial conditions.
In fact, there exist many kinds of aberration (such as the spherical aberration) in the optics components so the interferometric system still export a kind of special background fringe pattern even though no test object exists. Fortunately, the character of this special background fringe pattern is regular and can be described accurately using simple expressions. When the lateral shearing displacement is large enough, the phase difference between two states of fringe patterns, for example, one state goes with the test object while the other state doesn't, would directly lead to the test distorted wave-front without the use of a complex reductive algorithm which is essential in a condition with small lateral shearing displacement.
Firstly, this large lateral shearing displacement interferometry has been used to measure the full field film thickness of the soap bubble, which is a typical 1-D test object, during the process from its formation to burst. We found that the film thickness distribution along the vertical ordinate of the test soap bubble could be calculated with a maximum error less than 3/8λ. Moreover, this film thickness distribution shows a very good agreement with a kind of exponential model at all times and the maximum discrepancy is less than 0.4λin most of the field. When the compensating effect from the plastic cannulation (used to blow the soap bubble and keep its suspense) is weaker than the drained effect from the top of the soap bubble to its bottom, a special zone where the water layer has drained away but the surfactant solution layer remains would appear at the top of the soap bubble and expand towards the bottom, until its burst. Considering the above exponential model with three parameters could also be simplified into an acceptable exponential model with two parameters, the quotient between the equivalent film thickness and the vertical gradient of the fringe order can be deduced along the vertical ordinate. In condition that the resolution of the fringe pattern is known, the measurement limitation of the film thickness along the vertical ordinate can be evaluated by this quotient.
Considering that the flame of the co-axial burner usually departs slightly from its axis, here we update the above single-directional system and propose a tri-directional large lateral shearing interferometric system. Then this system has been used in the experimental research about the temperature reconstruction of a quasi-axisymmetric diffused ethylene flame under 2-D and 3-D methods.
The 2-D method is based on axisymmetric character in an inverse Radon transform step and the primary result has been corrected by a particular coefficient field from the numerical simulation work. In comparison with the thermocouple results, the final reconstructed result shows a good agreement either outside the peak temperature location or in the further part inside the peak temperature location, with an average discrepancy between 20 and 40 K. However, the discrepancy is obviously higher in the closer part inside the peak temperature location with a maximum discrepancy up to 200 K. Considering that a high soot volume fraction due to the insufficient combustion only exists in the closer part inside the peak temperature location, the thermocouple results in fact correspond to the continuously growing soot ball around the node rather than to the gas flame. When the deposition effect of soot has been excluded, the 2-D reconstructed result would be a credible and quantitative measurement result for the axisymmetric test flame.
The 3-D method doesn't utilize the axisymmetric character and has only been corrected by a universal coefficient value as 1.05, which is the average statistical value of the particular coefficient field. This result is qualitatively similar to the 2-D result but also exhibits some asymmetrical character. However, this reconstructed temperature field at 3 cm height exhibits obvious disturbance because the relative intensity ratio between the laser beam and the flame radiation is the weakest at 3 cm height. The relative discrepancies between the two kinds of reconstructed temperature values along the axis are generally less than 3.3% except at 1 cm height, where it has a high concentration of ethylene and is not suitable to use the universal correct coefficient. Therefore the 3-D method might still afford qualitative analysis for an asymmetrical flame, such as online combustion monitoring for turbulent flow flame in industry.
传统的横向剪切干涉应用中缺乏对横向剪切量的重视和讨论,而本文作者发现当横向剪切量超过了被测对象畸变波面半宽时,剪切干涉条纹的两侧将显露出半幅类似于双曝光全息干涉原理的简单条纹；当横向剪切量超过了被测对象畸变波面宽度时,剪切干涉条纹将在水平方向上分裂为两个完整的类似于双曝光全息干涉原理的简单条纹。这意味着横向大剪切量干涉技术在实验流程和数据处理流程两个方面都表现优异,较之现有各类多方向干涉检测系统来说无疑是一种更经济的选择。考虑到实用的光学系统总存在像差,横向剪切干涉系统的背景条纹由此产生。由于它的分布特征可以用简单的球差公式来精确描述,因而不会为剪切干涉条纹的后处理过程带来实质性的影响。当横向剪切量足够大时,用被测对象存在时的条纹相位差直接减去背景条纹相位差即可得到仅由被测对象引发的那部分畸变波面的相位差,而传统的小剪切量干涉条件下的数据处理过程中必不可少的剪切还原算法在这里不再需要了。
我们先将横向大剪切干涉技术应用在肥皂泡液膜厚度(这是一个典型的一维分布)的检测中,对单个肥皂泡从形成初期到临近破裂等几个典型瞬间的全场膜厚分布进行了实验研究。从中可知,被测肥皂泡沿着竖直方向的液膜厚度分布的最大误差为3/8倍波长。破裂之前的各个瞬间的数据显示,它的液膜厚度沿着重力方向的分布均能很好吻合三参数指数膜厚模型,其偏差值不超过0.4倍波长。随着肥皂泡自身排流作用的不断进行,其椭球型轮廓的顶部开始出现一个水层液膜消失而乳化剂层液膜仍保持完整的特殊区域。该区域的边界不断向下扩展,该过程中肥皂泡随时可能破裂。如果将上述三参数指数膜厚模型简化为双参数指数膜厚模型,那么可以推导出等效膜厚值与纵向条纹级数梯度之间的比值随着纵向坐标的分布曲线。在图像分辨率已知的条件下,通过该比值的分布曲线可以评估横向大剪切量干涉技术在任意高度上的液膜厚度检测的极限值。
考虑到同轴燃烧器生成的火焰总存在一定程度的轴向偏移,因而我们将横向大剪切量干涉系统从单方向投影体系扩展为三方向投影体系,然后对给定工况下的准二维轴对称乙烯扩散火焰分别以二维算法以及三维算法进行了温度场检测。在二维假设中,用于求解Radon逆变换的滤波投影重建算法使用180度范围内的虚拟投影方向,同时使用来自燃烧数值模拟的组分浓度分布来获得特别修正系数场。干涉重建结果与热电偶检测数据对比可知,两者在火焰温度峰值坐标的外侧区域或者内侧较远处显示出了很好的一致性,各个高度上的平均偏差在20 K到40 K之间。但热电偶检测数据在火焰温度峰值坐标的内侧紧邻区域明显偏低,两者的最大偏差可达200 K。这是因为火焰温度峰值坐标的内侧紧邻区域为不充分燃烧,其烟黑容积份额较高。即使热电偶节点以很快速度插入被测火焰的待测目标区域,在节点表面仍会出现烟黑沉积并出现尺度渐长的碳球,其辐射热损失使得热电偶节点表面的烟黑的温度明显低于火焰中气相组分的温度。排除掉这个因素之后,二维假设能够为标准的二维轴对称被测火焰对象提供定量的分析结果。
在三维假设中,用于求解Radon逆变换的滤波投影重建算法使用三个真实投影方向,同时将特别修正系数在全场大部分区间的统计均值(即1.05)作为通用修正系数,此时的温度场重建结果会表现出不同程度的非轴对称特征。我们发现3厘米高度上的温度重建结果在全场都表现出明显的扰动,这是因为该高度上的烟黑辐射较强导致干涉条纹图像的对比度变差并最终影响了条纹相位差的识别精度。与二维假设下的轴心反演值对比可知,三维假设下在1厘米高度的轴心反演值存在10%以上的偏差,这是因为该高度附近区域的主要组分为乙烯,它相对于空气组分假设所需的浓度场修正系数远超过1.05的通用修正值。然而在距双筒燃烧器的内筒喷嘴较远的其它高度上,三维假设下的轴心反演值仅存在不超过3.3%的偏差。总体来说,三维假设能够为非轴对称的被测火焰对象提供定性的分析结果,并有望用于工业环境下的非稳态火焰的在线监测。
Laser interferometry has an inherent virtue in measuring the index of refraction in a non-destructive way. Moreover, the index of refraction can be related to many other parameters such as density, concentration and temperature by use of the Lorentz-Lorenz equation and its simplified format (namely the Gladstone-Dale equation) for gas. Modern interferometer systems which afford multi-directional projections and real-time measurements are all constructed from the double paths style interferometry. Although the common paths style interferometry has many virtues such as compact layout, insensitivity to vibration, less hardware demand, easy adjustment and adaptation to real-time measurement, the characters of its fringe pattern which is more complex than the double paths style interferometry's has limited its application.
Although the lateral shearing displacements in the traditional studies about the lateral shearing interferometry are totally small and seem to be unimportant, the author found that when the lateral shearing displacement exceeds half width of the test distorted wave-front, the two sides of the fringe pattern seem similar to the simple one obtained in the double exposure holographic interferometry. Once the lateral shearing displacement exceeds full width of the test distorted wave-front, this fringe pattern would be torn apart and form two separate parts while each part equals the double exposure holographic interferometric fringe pattern. Considering that the primary drawback which limits its applications in comparison with other interferometry could be overcome in the above way, the large lateral shearing displacement interferometry would be a more economic choice to build up a practicable multi-directional interferometric system and has an enormous potential to replace traditional interferometry either in laboratorial conditions or in industrial conditions.
In fact, there exist many kinds of aberration (such as the spherical aberration) in the optics components so the interferometric system still export a kind of special background fringe pattern even though no test object exists. Fortunately, the character of this special background fringe pattern is regular and can be described accurately using simple expressions. When the lateral shearing displacement is large enough, the phase difference between two states of fringe patterns, for example, one state goes with the test object while the other state doesn't, would directly lead to the test distorted wave-front without the use of a complex reductive algorithm which is essential in a condition with small lateral shearing displacement.
Firstly, this large lateral shearing displacement interferometry has been used to measure the full field film thickness of the soap bubble, which is a typical 1-D test object, during the process from its formation to burst. We found that the film thickness distribution along the vertical ordinate of the test soap bubble could be calculated with a maximum error less than 3/8λ. Moreover, this film thickness distribution shows a very good agreement with a kind of exponential model at all times and the maximum discrepancy is less than 0.4λin most of the field. When the compensating effect from the plastic cannulation (used to blow the soap bubble and keep its suspense) is weaker than the drained effect from the top of the soap bubble to its bottom, a special zone where the water layer has drained away but the surfactant solution layer remains would appear at the top of the soap bubble and expand towards the bottom, until its burst. Considering the above exponential model with three parameters could also be simplified into an acceptable exponential model with two parameters, the quotient between the equivalent film thickness and the vertical gradient of the fringe order can be deduced along the vertical ordinate. In condition that the resolution of the fringe pattern is known, the measurement limitation of the film thickness along the vertical ordinate can be evaluated by this quotient.
Considering that the flame of the co-axial burner usually departs slightly from its axis, here we update the above single-directional system and propose a tri-directional large lateral shearing interferometric system. Then this system has been used in the experimental research about the temperature reconstruction of a quasi-axisymmetric diffused ethylene flame under 2-D and 3-D methods.
The 2-D method is based on axisymmetric character in an inverse Radon transform step and the primary result has been corrected by a particular coefficient field from the numerical simulation work. In comparison with the thermocouple results, the final reconstructed result shows a good agreement either outside the peak temperature location or in the further part inside the peak temperature location, with an average discrepancy between 20 and 40 K. However, the discrepancy is obviously higher in the closer part inside the peak temperature location with a maximum discrepancy up to 200 K. Considering that a high soot volume fraction due to the insufficient combustion only exists in the closer part inside the peak temperature location, the thermocouple results in fact correspond to the continuously growing soot ball around the node rather than to the gas flame. When the deposition effect of soot has been excluded, the 2-D reconstructed result would be a credible and quantitative measurement result for the axisymmetric test flame.
The 3-D method doesn't utilize the axisymmetric character and has only been corrected by a universal coefficient value as 1.05, which is the average statistical value of the particular coefficient field. This result is qualitatively similar to the 2-D result but also exhibits some asymmetrical character. However, this reconstructed temperature field at 3 cm height exhibits obvious disturbance because the relative intensity ratio between the laser beam and the flame radiation is the weakest at 3 cm height. The relative discrepancies between the two kinds of reconstructed temperature values along the axis are generally less than 3.3% except at 1 cm height, where it has a high concentration of ethylene and is not suitable to use the universal correct coefficient. Therefore the 3-D method might still afford qualitative analysis for an asymmetrical flame, such as online combustion monitoring for turbulent flow flame in industry.
引文
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