Analysis and treatment of errors due to high velocity gradients in particle image velocimetry

This paper deals with errors occurring in two-dimensional cross-correlation particle image velocimetry (PIV) algorithms (with window shifting), when high velocity gradients are present. A first bias error is due to the difference between the Lagrangian displacement of a particle and the real velocity. This error is calculated theoretically as a function of the velocity gradients, and is shown to reach values up to 1 pixel if only one window is translated. However, it becomes negligible when both windows are shifted in a symmetric way. A second error source is linked to the image pattern deformation, which decreases the height of the correlation peaks. In order to reduce this effect, the windows are deformed according to the velocity gradients in an iterative process. The problem of finding a sufficiently reliable starting point for the iteration is solved by applying a Gaussian filter to the images for the first correlation. Tests of a PIV algorithm based on these techniques are performed, showing their efficiency, and allowing the determination of an optimum time separation between images for a given velocity field. An application of the new algorithm to experimental particle images containing concentrated vortices is shown.     

Estimation of complex air–water interfaces from particle image velocimetry images

This paper describes a method for the estimation of the instantaneous air–water interface directly from particle image velocimetry (PIV) images of a laboratory generated air entraining turbulent hydraulic jump. Image processing methods such as texture segmentation based on gray level co-occurrence matrices are used to obtain a first approximation for the discrete location of the free surface. Active contours based on energy minimization principles are then implemented to get a more accurate estimate of the calculated interface and draw it closer to the real surface. Results are presented for two sets of images with varying degrees of image information and surface deformation. Comparisons with visually-interpreted surfaces show good agreement. In the absence of in-situ measurements, several verification tests based on physical reasoning show that the free surface is calculated to acceptable levels of accuracy. Aside from a single image used to tune the set of parameters, the algorithm is completely automated to process an ensemble of images representative of typical PIV applications. The method is computationally efficient and can be used to track fluid-interfaces undergoing non-rigid deformations.     

A comparative study of the MQD method and several correlation-based PIV evaluation algorithms

 The Minimum Quadratic Difference (MQD) method is compared with methods conventionally used for the evaluation of PIV recordings, i.e. correlation-based evaluation with fixed interrogation windows (auto- or cross-correlation) and correlation-based tracking. The comparison is performed by studying the evaluation accuracy achieved when applying these methods to pairs of synthetic PIV recordings for which the true displacements are known. The influence of the magnitude of the particle image displacement, evaluation window size, density of particle image distribution, and particle image size on the accuracy are investigated. In all these cases the best results in terms of a statistical error are obtained with the MQD method. The superiority of the MQD method can be explained with its potential of accounting for non-uniformities in the particle image distribution and a non-uniform illumination. It is also shown that the conventional correlation-based methods may produce principal errors that are non-existent for the MQD method. The evaluation speed achievable for the MQD method by making use of the FFT is comparable to that common for the generally used auto- or cross-correlation algorithm. Finally, a quantitative explanation is given for the often observed phenomenon that PIV velocity results tend to be smaller than the true values. Received: 15 May 1998/Accepted: 24 April 1999     

A novel architecture for a super-resolution PIV algorithm developed for the improvement of the resolution of large velocity gradient measurements

Three different particle image processing algorithms have been developed for the improvement of PIV velocity measurements characterized by large velocity gradients. The objectives of this study are to point out the limitations of the standard processing methods and to propose a complete algorithm to enhance the measurement accuracy. The heart of the PIV image processing is a direct cross-correlation calculation in order to obtain complete flexibility in the choice of the size and the shape of the interrogation window (IW). An iterative procedure is then applied for the reduction of the size of IW at each measurement location. This procedure allows taking into account the local particle concentration in the image. The results of this first iterative processing, applied to synthetic images, show both a significant improvement of measurement accuracy and an increase of the spatial resolution. Finally, a super-resolution algorithm is developed to further increase the spatial resolution of the measurement by determining the displacement of each particle. The computer time for a complete image processing is optimized by the introduction of original data storage in Binary Space Partitions trees. It is shown that measurement errors for large velocity gradient flows are similar to those obtained in simpler cases with uniform translation displacements. This last result validates the ability of the developed super-resolution algorithm for the aerodynamic characterization of large velocity gradient flows.     

The effect of a discrete window offset on the accuracy of cross-correlation analysis of digital PIV recordings

 This paper describes how the accuracy for estimating the location of the displacement-correlation peak in (digital) particle image velocimetry (PIV) can be optimized by the use of a window offset equal to the integer-pixel displacement. The method works for both cross-correlation analysis of single-exposure image pairs and multiple-exposure images. The effect is predicted by an analytical model for the statistical properties of estimators for the displacement, and it is observed in the analysis of synthetic PIV images of isotropic turbulence, and in actual measurements of grid-generated turbulence and of fully-developed turbulent pipe flow. Received: 29 April 1996/Accepted: 29 October 1996     

Dynamic masking of PIV images using the Radon transform in free surface flows

Particle image velocimetry (PIV) processing of free surface flow images often requires the use of digital masks to overcome the problems caused by the interface. In cases where a large number of particle images are collected it is essential that the time-varying boundary between the two phases can be tracked automatically to produce the binary masks. The Radon transform-based technique presented in this paper allows the automatic detection of the air–water interface in a stream of particle images acquired from a single camera. It is applied to time-resolved PIV measurements in the liquid phase of a stratified multiphase flow in a circular pipe. Accuracy estimations are provided using synthetic and real wave profiles. An extension to the more complex case of an overturning wave is also discussed.     

Theory of non-isotropic spatial resolution in PIV

The spatial resolution of the PIV interrogation technique is discussed from an analytical standpoint and assessed with Monte Carlo numerical simulation of particle image motion. The PIV measurement error associated with lack of spatial resolution is modelled associating the cross-correlation operator to a moving average filter. The error associated with the "low-pass filtering" effect is investigated by adopting a second-order polynomial expression for the velocity spatial distribution. According to the present error analysis, the measurement error is proportional to the second-order spatial derivative of the velocity field and increases with the square of the window linear size. The strategy for the selection of the window size and properties (aspect ratio and orientation) so as to minimize the error is discussed. The principle is based on nonisotropic interrogation windows of elliptical shape, with a constant area and elongated in the direction of the largest curvature radius. The nonisotropic parameters are defined as eccentricity and orientation, which are based on the local eigenvalues/vectors of the Hessian tensor of the displacement spatial distribution. The technique is implemented in a recursive PIV interrogation method. The performance of nonisotropic interrogation technique is assessed by means of synthetic PIV images, which simulate three situations: first, a one-dimensional sinusoidal shear displacement, which allows comparison of the cross-correlation spatial response with the transfer function of linear filters. Second, the stream-wise exponential velocity decay is simulated, which simulates the particle tracers decelerating downstream of a shock wave and gives an example of a flow with main velocity differences aligned with the velocity direction. The results show that keeping the image density fixed, the error caused by insufficient spatial resolution can be reduced by a factor two when a preferential direction is found in the flow field. Finally, a Lamb–Oseen vortex flow is presented, which shows the complex pattern formed by the interrogation windows in a two-dimensional case. In this case, the improvement in interrogation performance is limited due to the isotropic nature of the velocity spatial fluctuation.     

A correlation-based continuous window-shift technique to reduce the peak-locking effect in digital PIV image evaluation

In this paper the peak-locking phenomenon is investigated in the evaluation of digital PIV recordings by using a correlation-based interrogation algorithm with a discrete window shift and a correlation-based tracking algorithm. Statistical analyses indicate that nonuniformly distributed bias errors are the main cause of the peak-locking effect, and the amplitude variation of the random error is also an important source of the peak locking. Simulations and experimental examples demonstrate that very strong peak-locking effects exist for the correlation-based interrogation algorithm with discrete window shift in the cases of large particle images, small interrogation windows, and very small particle images. Very strong peak-locking effects are also observed for the correlation-based tracking algorithm when the particle images are overexposed, binarized, or very small. These strong peak-locking effects can be avoided without loss of evaluation accuracy by using a continuous window-shift technique in combination with the correlation-based interrogation algorithm. Received: 2 July 2001 / Accepted: 28 November 2001     

Analysis of weighting windows for image deformation methods in PIV

The use of a weighting window (WW) in the evaluation of the cross-correlation coefficient and in the iterative procedure of image deformation method for particle image velocimetry (PIV) applications can be used to both stabilise the process and to increase the spatial resolution. The choice of the WW is a parameter that influences the complete PIV algorithm. Aim of this paper is to examine the influence of this aspect on both the accuracy and spatial resolution of the PIV algorithm. Results show an overall accordance between the theoretical approach and the simulation both with synthetic and real images. The choice of the combination of WW influences significantly the spatial resolution and accuracy of the PIV algorithm.

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两相流显微PIV/PTV系统的开发

开发了一个能同时测量两相流中两相速度和细颗粒尺寸分布的显微PIV/PTV系统,其硬件系统包括大功率连续激光器、显微镜、高速摄像机;软件系统由改进的球形颗粒图像识别算法、各种图像处理算法和各种先进的PIV/PTV算法组成。其中改进的圆弧识别算法能够进行更准确地进行曲线分割而能对充满噪音并相互重叠的颗粒图像给出较好的识别结果。应用该PIV系统,可以在微秒和微米数量级上捕获细颗粒/气泡图像,并能较准确地同时得到两相速度、颗粒尺寸和浓度分布。对焚香可吸入颗粒物进行了速度和尺寸的同时测量,得到了较满意的结果。     

A method for automatic estimation of instantaneous local uncertainty in particle image velocimetry measurements

The uncertainty of any measurement is the interval in which one believes the actual error lies. Particle image velocimetry (PIV) measurement error depends on the PIV algorithm used, a wide range of user inputs, flow characteristics, and the experimental setup. Since these factors vary in time and space, they lead to nonuniform error throughout the flow field. As such, a universal PIV uncertainty estimate is not adequate and can be misleading. This is of particular interest when PIV data are used for comparison with computational or experimental data. A method to estimate the uncertainty from sources detectable in the raw images and due to the PIV calculation of each individual velocity measurement is presented. The relationship between four error sources and their contribution to PIV error is first determined. The sources, or parameters, considered are particle image diameter, particle density, particle displacement, and velocity gradient, although this choice in parameters is arbitrary and may not be complete. This information provides a four-dimensional “uncertainty surface” specific to the PIV algorithm used. After PIV processing, our code “measures" the value of each of these parameters and estimates the velocity uncertainty due to the PIV algorithm for each vector in the flow field. The reliability of our methodology is validated using known flow fields so the actual error can be determined. Our analysis shows that, for most flows, the uncertainty distribution obtained using this method fits the confidence interval. An experiment is used to show that systematic uncertainties are accurately computed for a jet flow. The method is general and can be adapted to any PIV analysis, provided that the relevant error sources can be identified for a given experiment and the appropriate parameters can be quantified from the images obtained.     

Digital Image Correlation with Self-Adaptive Gaussian Windows

A novel subpixel registration algorithm with Gaussian windows is put forward for accurate deformation measurement in digital image correlation technique. Based on speckle image quality and potential deformation states, this algorithm can automatically minimize the influence of subset sizes by self-adaptively tuning the Gaussian window shapes with the aid of a so-called weighted sum-of-squared difference correlation criterion. Numerical results of synthetic speckle images undergoing in-plane sinusoidal displacement fields demonstrate that the proposed algorithm can significantly improve displacement and strain measurement accuracy especially in the case with relatively large deformation.     

Experimental and numerical study of ?ow structures of the second-mode instability

Flow structures of a Mach 6 transitional boundary layer over a 260 mm long flared cone are investigated by the particle image velocimetry(PIV). Particle images near the curved wall are initially transformed into surface-fitted orthogonal coordinates and spliced with their 180?-symmetric images to satisfy a no-slip condition at the wall.The results are then reversely transformed to the physical domain. Direct numerical simulation(DNS) is also performed to validate the experimental results. The experimental and numerical results are in agreement, indicating a strong dilatation process within the second-mode instability.     

Optical Metrology by Fringe Processing on Independent Windows Using a Genetic Algorithm

We present a method to retrieve the phase of a fringe pattern based on the window fringe pattern demodulation technique (WFPD). The overlapped phase similarity criterion is avoided in the proposed method, and it is substituted by a second order smoothness criterion. The fringe processing on independent windows (FPIW) method can measure physical quantities from closed and near sub-sampled fringe patterns by a simplified cost or fitness function. The fringe image is divided into a set of partially overlapping windows. In these sub-images the estimated phase is modelled as a parametric analytic-function, and its parameters are optimized using a genetic algorithm (GA). This analytic-function is used to estimate the phase in the area framed by the window. Phases from all windows are sequentially spliced to retrieve the whole phase field. A media filter is applied over the entire phase field to smooth the irregularities that appear in the junctures between windows.     

Development and validation of echo PIV

The combination of ultrasound echo images with digital particle image velocimetry (DPIV) methods has resulted in a two-dimensional, two-component velocity field measurement technique appropriate for opaque flow conditions including blood flow in clinical applications. Advanced PIV processing algorithms including an iterative scheme and window offsetting were used to increase the spatial resolution of the velocity measurement to a maximum of 1.8 mm×3.1 mm. Velocity validation tests in fully developed laminar pipe flow showed good agreement with both optical PIV measurements and the expected parabolic profile. A dynamic range of 1 to 60 cm/s has been obtained to date.     

Development of fiberscope PIV system by controlling diode laser illumination

Because of the inherent small size of optical fiberscopes, they provide access and relative handling ease in given closed vessels, which are hardly equipped with extra windows for conventional flow visualization. The use of an optical fiberscope in conjunction with a conventional particle image velocimetry/particle tracking velocimetry (PIV/PTV) system without optimization can lead to degraded transmission of images. The present study proposes a processing technique to filter background noise contained within the coarse bundle image by subtracting the original image of the bundle as reference image. Additionally, efforts were made to increase the reliability of vector processing using particle streak images via judicious pulse interval and duration adjustments. As an applications test we measured classic jet flow using the developed system and using established conventional measurement techniques. Our tests confirmed that our fiberscope PTV system provides vector fields with sufficient accuracy.     

Detection of Passive Scalar Interface Directly from PIV Particle Images in Inhomogeneous Turbulent Flows

This article proposes a technique to estimate the cross-sectional scalar interface (outer boundary) in an inhomogeneous turbulent flow from a conditioned particle image velocimetry (PIV) experiment, which is suitable for medium to high Reynolds numbers. The scalar interface is estimated directly by using conditioned PIV particle images which have distinguishably high particle seeding density in the area of interest, whereas conventionally in water based experiments, scalar interface is often determined from planar laser induced fluorescence (PLIF) or equivalent dye images. By comparing quantities in the vicinity of this scalar interface, it also shows that in terms of separate turbulent and non-turbulent regions, this technique could also replace the function of PLIF images in water experiments, with slightly lower spatial resolution. At the same time, if velocity information is also required simultaneously then the cost of a separate camera-laser system can be saved. The effect of particle field inhomogeneity on the PIV accuracy can be well reduced to an insignificant level by an image local normalisation treatment. This article shows that the interfacial layer could be detected fairly accurately by enhancing the particle images by wavelet based thresholding methods. The degree of detection accuracy is quantified by synthetic particle image analyses, where a scalar interface can be artificially pre-defined. The proposed technique is tested in two water based experiments but is expected to be particularly useful in gas-phase based experiments or some combustion applications, where liquid-phase dye cannot be applied.     

Non-intrusive temperature measurement using microscale visualization techniques

μPIV is a widely accepted tool for making accurate measurements in microscale flows. The particles that are used to seed the flow, due to their small size, undergo Brownian motion which adds a random noise component to the measurements. Brownian motion introduces an undesirable error in the velocity measurements, but also contains valuable temperature information. A PIV algorithm which detects both the location and broadening of the correlation peak can measure velocity as well as temperature simultaneously using the same set of images. The approach presented in this work eliminates the use of the calibration constant used in the literature (Hohreiter et al. in Meas Sci Technol 13(7):1072–1078, 2002), making the method system-independent, and reducing the uncertainty involved in the technique. The temperature in a stationary fluid was experimentally measured using this technique and compared to that obtained using the particle tracking thermometry method and a novel method, low image density PIV. The method of cross-correlation PIV was modified to measure the temperature of a moving fluid. A standard epi-fluorescence μPIV system was used for all the measurements. The experiments were conducted using spherical fluorescent polystyrene-latex particles suspended in water. Temperatures ranging from 20 to 80°C were measured. This method allows simultaneous non-intrusive temperature and velocity measurements in integrated cooling systems and lab-on-a-chip devices.     

Fundamentals of multiframe particle image velocimetry (PIV)

A sophisticated strategy for the evaluation of time-resolved PIV image sequences is presented which takes the temporal variation of the particle image pattern into account. The primary aim of the method is to increase the accuracy and dynamic range by locally adopting the particle image displacement for each interrogation window to overcome the largest drawback of PIV. This is required in order to resolve flow phenomena which have so far remained inaccessible. The method locally optimizes the temporal separation between the particle image pairs by taking first and second order effects into account. The validation of the evaluation method is performed with synthetically generated particle image sequences based on the solution of a direct numerical simulation. In addition, the performance of the evaluation approach is demonstrated by means of a real image sequence measured with a time-resolved PIV system.     

Influence of individual variations of particle image intensities on high-resolution PIV

Individual variations of intensity of tracer particles, e.g., due to out-of-plane displacements between exposures, strongly limit the achievable accuracy of correlation-based PIV processing. The RMS error originated by this effect correlates with the spatial resolution that can be achieved with the processing algorithm making especially high-resolution algorithms like iterative image deformation affected by this error. Both aspects are shown, the gain of resolution by iterative image deformation and the loss of accuracy due to individual variations of particle intensities.