The effect of astigmatism due to beam refractions on the formation of the measurement volume in LDA measurements

The accuracy of LDA measurements depends on the optical alignment of the laser beams. Improperly designed optical systems lead to fringe distortion in the measurement volume and in earlier investigations this effect has always been taken as the main cause of optical inaccuracy in LDA measurements. In the present work a different cause of fringe distortion is considered: astigmatism due to beam refractions. A quantitative theory for the astigmatism of laser beams is derived for both single and multiple refractions. Parameter calculations with regard to the size of the astigmatism effect have been carried out. It is shown that astigmatism is a relevant parameter which influences the fringe uniformity and fringe distortion in an LDA measurement volume and affects the measurement accuracy of measurements in internal flow. The equations derived enable the change in cross sections of the refracted laser beams to be determined. The spatial deviations of the diverse focusing points of refracted laser beams relative to the position of the LDA measurement volume are found to depend strongly on the incident angle of the beams and therefore on the off-axis alignment angle of the LDA probe (off-axis from the normal to the flow-wall-interface).     

On the overestimation of the flow turbulence due to fringe distortion in LDA measurement volumes

 Fringe distortion with linear longitudinal variation in fringe spacing over the length of LDA measurement volume has been considered to influence the accuracy of flow measurement. The overestimation of the mean velocity and especially of the flow turbulence due to fringe distortion has been derived to be a function both of the fringe distortion number (which is a purely geometrical parameter of the measurement volume) and the flow turbulence to be measured. Against the usual expectation, it has been shown that the overestimation of the flow turbulence due to fringe distortion in the measurement volume could be neglected. Only for very low turbulence intensity dose the error become significant. As a reference this result could be used to estimate measurement errors which occur in the presence of other types of fringe distortion. Received: 2 December 1997/Accepted: 2 May 1998     

An extended algebraic reconstruction technique (ART) for density-gradient projections: laser speckle photographic tomography

An extended algebraic reconstruction technique (ART) is presented for tomographic image reconstruction from the density-gradient projections, such as laser speckle photography. The essence of the extended ART is that the density-gradient projection data of speckle photography (Eq. (1)) are first numerically integrated to the algebraic representation of interferometric fringe number data (Eq. (12)), which ART can readily reconstruct into the cross-sectional field. The extended ART is numerically examined by using two computer synthesized phantom fields, and experimentally by using asymmetric single and double helium jets in air. The experimentally reconstructed images were also compared with the direct measurements of helium concentration using an oxygen analyzing probe. The extended ART method shows an improved accuracy and is proposed to use to tomographically reconstruct the density-gradient projections over the previous Fourier convolution (FC) method (Liu et al. 1989). Received: 26 June 1998/Accepted: 18 March 1999     

Experimental study and large eddy simulation for the turbulent flow around four cylinders in an in-line square configuration

The turbulent flows around four cylinders in an in-line square configuration with different spacing ratios of 1.5, 2.5, 3.5 and 5.0 have been investigated experimentally at subcritical Reynolds numbers from 11,000 to 20,000. The mean and fluctuating velocity distributions were obtained using the laser Doppler anemometry (LDA) measurement. The digital particle image velocimetry (DPIV) was employed to characterize the full field vorticity and velocity distributions as well as other turbulent quantities. The experimental study indicated that several distinct flow patterns exist depending on the spacing ratio and subcritical Reynolds number for turbulent flow. The three-dimensional numerical simulations were also carried out using the large eddy simulation (LES) at Reynolds number of 15,000 with the spacing ratio of 1.5 and 3.5. The results show that the LES numerical predictions are in good agreement with the experimental measurements. Therefore, the three-dimensional vortex structures and the full field instantaneous and mean quantities of the flow field such as velocity field, vorticity field, etc., which are very difficult to obtain experimentally, can be extracted from the simulation results for the deepening of our understanding on the complex flow phenomena around four cylinders in in-line configuration.     

Off-axis alignment of an LDA-probe and the effect of astigmatism on measurements

A theoretical analysis of the positional accuracy of an LDA measurement volume using an off-axis alignment of a probe relative to an internal flow has been carried out. General performance parameters of measurements with a 1D-probe with an off-axis alignment are derived. In particular, the change in the fringe spacing, the relationship between the shift of the measurement volume and the probe movement, and the general 2-dimensional traversing properties of the measurement volume are considered. The displacement between the two LDA measurement volumes of a 2D-probe caused by astigmatism has been determined from exact calculations of the laser beam transmission. The benefits of a water-filled prism to ensure the coincidence of the measurement volumes and to reduce the effect of astigmatism on the data rate and the distortion of the measurement volume has been shown. A calculation procedure for the use of such a prism is given.The authors would like to thank Sulzer Innotec for support of this work and for permission to publish this paper. The work was also sponsored by Sulzer Pumps, Sulzer Turbo and Sulzer Hydro in a research project entitled Unsteady flow in turbomachinery. The support of Dr. Mick Casey is especially acknowledged, particularly for his help with the English text.     

Global Doppler frequency shift detection with near-resonant interferometry

The recent development in measuring 2D Doppler shift distributions for flow velocimetry using the dispersive properties of atomic line filters is presented. On the basis of velocity field measurements on a subsonic jet flow and a tip vortex flow in a medium-sized wind tunnel, the technique was assessed. Atomic line filters near a resonant transition combine imaging capabilities with a sharp frequency cutoff and an associated region of strong anomalous dispersion. While conventional Doppler global velocimetry relies on the absorption of the filter to convert frequency shifts to intensity variations, near-resonant interferometry uses its dispersion to detect frequency shifts as phase changes in an interference pattern. In the present setup, an iodine vapor cell in an imaging Michelson interferometer is used. With the illuminating laser frequency tuned near a resonant transition, the cell’s dispersion converts the frequency content of the field of view into a distortion of the carrier-fringe pattern recorded at the image plane of the interferometer. The phase distribution in the fringe images is reconstructed by filtering the individual images with a 2D Gabor filter pair tuned to the spatial frequencies of the basic carrier-fringe pattern. The post-processing is concluded with subsequent phase-unwrapping and subtraction of the carrier reference fringe phase. The method and the setup were demonstrated and calibrated experimentally on a rotating disc. The capability of the technique to operate in a real experimental environment was validated in a free subsonic jet and a tip vortex flow behind a wing section in a medium-sized wind tunnel facility. The measurements were found to be in generally good agreement with the theoretically predicted system characteristics and the reference measurements. As with other Doppler global techniques, the stability of the pulsed laser system and the secondary scattering in the test volume were identified as the main error sources.     

Diffraction theory of optical interference moiré and a device for production of variable virtual reference gratings: A moiré microscope

Optical interference moiré methods are analyzed using Fraunhoffer diffraction theory to relate general large surface deformations to the fringes observed. This analysis determines the Almansl strain in the current configuration from the gradients of the fringe number function. The analysis shows the advantages of an experimental scheme that allows the virtual reference grating to be varied. The ability to vary the virtual reference grating results in a larger dynamic range and the ability to maintain a fringe spacing for maximum accuracy. A moiré microscope has been constructed which has this ability. Digital image processing coupled with optical filtering and phase control is used to enhance the accuracy of the fringe measurements. The variable virtual-reference-grating capability is demonstrated by using it to highlight several aspects of the deformation field near a crack tip in a single crystal of iron-silicon.     

Investigation of two plane paralleltiinven ilated jets

Measurements of mean velocity components, mean flow direction, turbulent intensities and Reynolds shear stress were made with a split film probe of hot wire anemometer to investigate the flow field generated by two identical jets of air issuing from plane parallel nozzles in a common end wall and mixing with the ambient room air. Due to the sensitivity of the split film probe to the flow direction, the reverse flow in the converging region was detected by the split film probe and observed by flow visualization. The mean velocity approaches self-preservation in both the converging and the combined regions, while the turbulent intensities and Reynolds shear stress approach self-preservation in the combined region only. The trajectory of the maximum velocity is almost unchanged by variance of nozzle spacing in the converging region. The distance of the merging point from the nozzle exit increases linearly with nozzle spacing. The spread of the converging jet increases more rapidly than that of the combined jet.     

Strain determination on curved surfaces by objective white light speckles

A close-range objective white light speckle method has been used for strain determination on simply curved surfaces. The speckle field is not the artificially printed random dots but only the radiance distribution of object surface which was slightly treated before the test to produce fine structure of optical details. The holographic film, instead of holographic plate, is attatched to the curved surface when illuminated by a flash light. Whole field fringe patterns are obtained with high sensitivities and large adjustable range. There is no longer a requirement to derive the speckle movement on the image plane from the object surface. Defocusing problem has been avoided. It can be practically applied to engineering problems with considerable convenience because of the very simple recording system and little demand for environmental stability.     

用白光散斑的直接记录法测量曲面变形

本文提出以物体表面精细光学结构在白光照射下辐射率随机分布函数作为散斑场,以全息软片为记录介质,采取无镜头成象技术,得到宽频域的散斑底片,并用有一定带宽的准单色光进行全场分析,测量可展曲面变形,其结果不仅具有较高的灵敏度,较大的灵敏度调节范围,而且其中的准备过程、记录过程和分析过程比现有的各种测量曲面变形的散斑法都要简单,该方法将可展曲面变形问题简单地转化为平面问题处理,保留了白光散斑直接记录法在测量平面变形时的全部优点,并能脱离暗室在工程现场中应用。     

Tricolor photoviscoelastic technique and its application to moving contact

A new technique for simultaneous determination of both fringe order and principal direction of birefringence in practical photoviscoelastic analysis using white incident light with a set of the primary colors, called tricolor photoviscoelasticity, is described. This method can determine both the fringe order and principal direction of birefringence from a single-color photoviscoelastic image under plane polarization. Then, the authors evaluate time dependent stresses and strains around a contact region in a viscoelastic strip plate under nonproportional loading condition. The variations of the principal stresses and strains are easily obtained over a wide time range by use of the optical constitutive equations of photoviscoelasticity and the characteristic material property functions.     

Millimeter wave rheometry: theory and experiment

A novel millimeter wave (MMW) rheometry is developed to determine the viscosity of fluids based on an unsteady film flow on an inclined plane. The method measures fringes due to MMW interference between the front and back surfaces of a fluid flowing across the field of view of a ceramic wave guide coupled to a MMW receiver operating at 137 GHz. With knowledge of the dielectric constant, the interference fringe spacing is used to calculate the thickness of the fluid layer. This thickness is then transformed into the viscosity by means of a simple hydrodynamic theory. Our results show that the MMW rheometry can practically distinguish between the 30, 100, and 200 Pa·s silicone oils. The geometry of the method allows for potential industrial applications such as measuring viscosity of the flowing slag down the walls of coal gasifiers. The MMW rheometry with simple modifications can be easily extended to measure important non-Newtonian fluid characteristics such as yield stress.     

The influence of particle shape,volume fraction and distribution on post-necking deformation and fracture in uniaxial tension of AA5754 sheet materials

Finite element analysis was performed over a small particle field, edge constraint plane strain post-necking model. The aim is to understand the roles of particle shape, volume fraction and distribution over the post-necking deformation and fracture of AA5754-O sheet materials. For models containing one single particle, the post-necking deformation decreases when the particle varies from circular to elliptical. The inter-particle spacing, the major parameter of distribution to determine whether a pair of particles belongs to a stringer or not, was varied for models with two particles of circular or elliptical shape. The general trend is that the post-necking deformation and fracture strains decrease with decreasing spacing between particles. There is considerable difference in terms of both fracture topographies and strains for models containing 16 particles when distributions varied from random/uniform to stringer distributions. The post-necking deformation and fracture strains monotonically decrease with particle volume fractions for models with 4–64 particles of random or stringer distribution. This indicates that the post-necking behavior for AA5754-O alloys where the matrix material is rather ductile is not solely controlled by a single or pair of particles although they may become initiation places of damage. Multiple damaging sources such as stringers or large particles can act cooperatively and speed up the damaging propagation of the material, and therefore produce small post-necking deformation and early fracture. The center clustering of particles can be beneficial for post-necking behavior and bendability of sheet materials.     

General relations of strain-gradient stress analysis

Some particular fields of stress gradients in plates are investigated analytically and experimentally. Carriers of empirical information are light beam deflections caused by stress or strain gradients in homogeneous beams subjected to a particular case of flexure with shear. This study is based on theories and techniques of the strain-gradient method that was recently introduced by the authors. This is a generalization of prior analytical-experimental examination of strain-gradient light deflections produced in stressed plates, which had concentrated on the simplest case where information of interest is collected along a line of symmetry of the stress field and where both the information carrying light beams are deflected in the plane of symmetry only. The developed relations were tested experimentally, by using an S-beam as representative example of general plane stress field. The main purpose of the present investigation is to document the efficacy of the strain-gradient method in analysis of the general case of stress state and to test the ranges of applicability of the accepted mathematical models and of the subsequently derived relations. In this respect, the most interesting stress state is that in a beam subjected to the Saint-Venant bending, where the transversal and longitudinal axes of the beam are in pure shear. The obtained results are compared, at each step, with the predictions of the developed analytical models and with the predictions of Filon's stress function. The results of comparison are satisfactory. The procedures of evaluating the photoelastic and material coefficients using strain-gradient techniques were tested positively. The developed method can yield valuable information on the actual features of stress states in fracture mechanics. Part of the problems and first results of this investigation will be presented in the authors' paper “Strain-gradient stress analysis in Saint-Venant bending”.     

Interferometric-fiber-optic strain sensor

An interferometric-fiber-optic sensor and an efficient fringe-detection scheme are described. The fiberoptic interferometer consists of two fibers; they are labeled the reference fiber and the sensing fiber. The reference fiber is arranged in a circular pattern, whereas the sensing fiber is arranged in an ‘S’ pattern. These fibers are exposed to the same strain field and each experiences a strain-induced phase shift. A difference in the phase shift between the two fibers indicates a change in strain. The strain-induced phase difference causes the interferometrically produced fringes to shift spatially. Analysis shows that the number of fringes passing an arbitrary point on a screen (the detection point) is linearly related to the strain in the fiber. In this analysis, the strain sensor is assumed to be perfectly bonded so that the fibers experience the same strain field as the specimen. It is further assumed that the sensor covers a sufficiently small area so that the strain can be considered constant over the entire strain sensor. Also, the phase change produced by transverse strain components (with respect to the fiber) induced by the specimen is assumed negligible compared to the phase changes attributable to the axial strain components. A cantilever beam was used as a specimen. Experimentally determined strains correlated well with the strains predicted by beam theory. The fringe-detection scheme described is a high-speed fringe counter. The speed of this counter is necessary to detect vibrational phase noise which is invisible to the human eye. Two photodiodes detect the fringes, and a logic circuit counts the fringe shifts, both strain and noise induced. Since noise is random in nature, it can be averaged out. This fringe detector exhibits good sensitivity and is the key to moving the sensor from the laboratory to the field.     

Residual-stress determination by single-axis holographic interferometry and hole drilling—Part I: Theory

A method is described for the rapid, accurate determination of residual stresses from a holographic interference fringe pattern. The pattern is generated by the displacement field caused by localized relief of residual stresses via the introduction of a small, shallow hole into the surface of a component or test specimen. The theoretical development of the holographic method is summarized. An example is given showing how the method can be applied to a typical experimentally observed fringe pattern to determine principal residual stresses and directions.     

3D stress local nondestructive analysis in the middle plane of a plate

The Isodyne technique based on the scattered light scanning from a thin laser beam can be used to obtain the information inside the loaded object in the room temperature nondestructively, so it is a very powerful technique in 3D stress analysis. The problems are how to interpret the information and how to get sufficient information from the few interference fringe. Birefringence phase shift technique can distinguish the fringe orders automatically and enrich the information in 256 gray levels between maxim and minim light intensity. In the paper the Isodyne birefringence phase shift method with an oblique incidence and equilibrium equation is presented, by which the 3D stresses in the middle plane of a plate with U shape notch are separated successfully. The project supported by the National Natural Science Foundation of China under the Grant No. 1380345     

Development and assessment of a single-image fringe projection method for dynamic applications

A single-image fringe projection profiling method suitable for dynamic applications was developed by combining an accurate camera calibration procedure and improved phase extraction procedures. The improved phase extraction process used a modified Hilbert transform with Laplacian pyramid algorithms to improve measurement accuracy. The camera calibration method used an accurate pinhole camera model and pixel-by-pixel calibration of the phase-height relationship. Numerical simulations and controlled baseline experiments were performed to quantify key error sources in the measurement process and verify the accuracy of the approach. Results from numerical simulations indicate that the resulting phase error can be reduced to less than 0.02 radians provided that parameters such as fringe spacing, random measured intensity noise, fringe contrast and frequency of spatial intensity noise are carefully controlled. Experimental results show that the effects of random temporal and spatial noise in typical CCD cameras for single fringe images limits the accuracy of the method to 0.04 radians in most applications. Quantitative results from application of the fringe projection method are in very good agreement with numerical predictions, demonstrating that it is possible to design both a fringe projection system and a measurement process to achieve a prespecified accuracy and resolution in the point-to-point measurement of the spatial (X, Y, Z) positions.     

从流场干涉图定量计算冲击波传播速度和压力

研究了含冲击波流场干涉图的图像处理方法。首先利用快速条纹细化算法细化干涉条纹,并利用条纹追踪算法提取冲击波波阵面,然后根据配准算法把序列冲击波波阵面配准在同一幅画面上。根据上述算法,在PC-VISION100图像处理机上开发了应用软件。实验结果表明,该方法不但可用于从流场干涉图中提取冲击波波阵面,更重要的是可用于从含冲击波流场干涉图中定量计算冲击波的传播速度和压力分布。