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.     

An improved cross-correlation method for (digital) particle image velocimetry

An improved method that brings enhancement in accuracy for the interrogation of (digital) PIV images is described in this paper. This method is based on cross-correlation with discrete window offset, which makes use of a translation of the second interrogation window and rebuilds it considering rotation and shear. The displacement extracted from PIV images is predicted and corrected by means of an iterative procedure. In addition, the displacement vectors are validated at each intermediate of the iteration process. The present improved cross-correlation method is compared with the conventional one in accuracy by interrogation of synthetic and real (digital) PIV images and the interrogation results are discussed. The project supported by the National Natural Science Foundation of China (59936140 and 59876038)     

PIV measurement of flow around an arbitrarily moving body

This paper presents a PIV (particle image velocimetry) image processing method for measuring flow velocities around an arbitrarily moving body. This image processing technique uses a contour-texture analysis based on user-defined textons to determine the arbitrarily moving interface in the particle images. After the interface tracking procedure is performed, the particle images near the interface are transformed into Cartesian coordinates that are related to the distance from the interface. This transformed image always has a straight interface, so the interrogation windows can easily be arranged at certain distances from the interface. Accurate measurements near the interface can then be achieved by applying the window deformation algorithm in concert with PIV/IG (interface gradiometry). The displacement of each window is evaluated by using the window deformation algorithm and was found to result in acceptable errors except for the border windows. Quantitative evaluations of this method were performed by applying it to computer-generated images and actual PIV measurements.     

Background extraction from double-frame PIV images

This study presents a simple image pre-processing scheme to extract background information from double-frame particle image velocimetry (PIV) images. Everything that stays stagnant in the image (e.g., image background and light reflections from stationary objects) is assumed to be a source of disturbance and is removed by subtracting the second frame of the image pair from the first frame. This yields a single frame difference image, which is transferred back to a background extracted double-frame image. After the procedure the background in the image does not correlate with itself anymore and therefore a bias error in PIV analysis towards zero displacement is avoided. The simulations show that the procedure conserves the profile of tracer particle images when a displacement between the frames is larger than a particle image size. The performance of this procedure is emphasized with various examples, and extensions of the procedure are introduced. The extended procedure extracts background objects that move between the image frames, e.g. dispersed phase particles in a two-phase flow or laser light sheet reflections from moving objects.     

Improvements to PIV image analysis by recognizing the velocity gradients

Two iterative PIV image processing methods are introduced, which utilize displacement and deformation of the interrogation areas to maximize the correlation. The velocity gradients used for the window deformation are iteratively estimated directly from the images and no velocity values are required from neighbouring interrogation areas, as with numerical differentiation. The improved accuracy and resolution of the velocity gradient estimation compared to numerical differentiation is shown using synthetic images. The performance in a real application is shown using experimental reference images.     

A digital mask technique for reducing the bias error of the correlation-based PIV interrogation algorithm

 In this paper the bias phenomenon in the evaluation of PIV recordings by using the correlation-based interrogation algorithm is discussed, and a digital mask technique, that can effectively reduce the bias error, is introduced. The correlation-based interrogation algorithm, when masked with a Gaussian window function, can achieve a higher evaluation accuracy not only for PIV recordings of flows with small velocity gradients, but also for that of flows with large gradients. Received: 14 October 1998/Accepted: 20 July 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.     

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 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.     

Biases of PIV measurement of turbulent flow and the masked correlation-based interrogation algorithm

Influences of evaluation bias of the correlation-based interrogation algorithm on particle image velocimetry (PIV) measurement of turbulent flow are investigated. Experimental tests in the Iowa Institute of Hydraulic Research towing tank with a towed PIV system and a surface-piercing flat plate and simulations demonstrate that the experimentally determined mean velocity and Reynolds stress components are affected by the evaluation bias and the gradient of the evaluation bias, respectively. The evaluation bias and gradient of the evaluation bias can both be minimized effectively by using Gaussian digital masks on the interrogation window, so that the measurement uncertainty can be reduced. Received: 16 September 1999/Accepted: 7 February 2000     

Simultaneous measurements of velocity and density in buoyancy-driven mixing

A variant of the particle image velocimetry (PIV) technique is described for measuring velocity and density simultaneously in a turbulent Rayleigh-Taylor mixing layer. The velocity field is computed by the usual PIV technique of cross-correlating two consecutive images, and deducing particle displacements from correlation peaks of intensity fields. Different concentrations of seed particles are used in the two streams of different temperature (density) fluids, and a local measure of the density is obtained by spatially averaging over an interrogation window. Good agreement is reported between the first- and second-order statistics for density obtained from this technique and from a thermocouple. Velocity-density correlations computed by cross-correlating individual time series are presented. The errors in the density measurements are quantified and analyzed, and the issue of spatial resolution is also discussed. Our purpose for this paper is to introduce the PIV-S method and validate its accuracy against corresponding thermocouple measurements.     

A correlation-based central difference image correction (CDIC) method and application in a four-roll mill flow PIV measurement

An experiment is conducted in a four-roll mill to verify a novel particle image velocimetry (PIV) recording evaluation method that combines the advantages of central difference interrogation and an image correction technique. Simulations and experiments in the four-roll mill geometry demonstrate that the central difference image correction method described in this paper can not only avoid the bias error resulting from the curvature and high-velocity-gradient flow but also effectively reduce the random error resulting from particle image distortion. Two image correction schemes and two base algorithms are discussed. A four-point image correction scheme is suggested on the basis of the traditional correlation-based interrogation algorithm to enable a fast, high-accuracy evaluation of PIV recordings in complex flows. In addition, the PIV experiment accurately determines the velocity field in the four-roll mill and confirms the linear distributions of the velocity components and the roller speed.     

A comparative study of five different PIV interrogation algorithms

Five different particle image velocimetry (PIV) interrogation algorithms are tested with numerically generated particle images and two real data sets measured in turbulent flows with relatively small particle images of size 1.0–2.5 pixels. The size distribution of the particle images is analyzed for both the synthetic and the real data in order to evaluate the tendency for peak-locking occurrence. First, the accuracy of the algorithms in terms of mean bias and rms error is compared to simulated data. Then, the algorithms ability to handle the peak-locking effect in an accelerating flow through a 2:1 contraction is compared, and their ability to estimate the rms and Reynolds shear stress profiles in a near-wall region of a turbulent boundary layer (TBL) at Re=510 is analyzed. The results of the latter case are compared to direct numerical simulation (DNS) data of a TBL. The algorithms are: standard fast Fourier transform cross-correlation (FFT-CC), direct normalized cross-correlation (DNCC), iterative FFT-CC with discrete window shift (DWS), iterative FFT-CC with continuous window shift (CWS), and iterative FFT-CC CWS with image deformation (CWD). Gaussian three-point peak fitting for sub-pixel estimation is used in all the algorithms. According to the tests with the non-deformation algorithms, DNCC seems to give the best rms estimation by the wall, and the CWS methods give slightly smaller peak-locking observations than the other methods. With the CWS methods, a bias error compensation method for the bilinear image interpolation, based on the particle image size analysis, is developed and tested, giving the same performance as the image interpolation based on the cardinal function. With the CWD algorithms, the effect of the spatial filter size between the iteration loops is analyzed, and it is found to have a strong effect on the results. In the near-wall region, the turbulence intensity varies by up to 4%, depending on the chosen interrogation algorithm. In addition, the algorithms computational performance is tested.     

Error quantification of 3D homogeneous and isotropic turbulence measurements using 2D PIV

Particle image velocimetry (PIV) has become a popular non-intrusive tool for measuring various types of flows. However, when measuring three dimensional flows with 2D PIV, there is inherent measurement error due to out-of-plane motion. Errors in the measured velocity field propagate to turbulence statistics. Since this can distort the overall flow characteristics, it is important to understand the effect of this out-of-plane error. In this study, the effect of out-of-plane motion on turbulence statistics is quantified. Using forced isotropic turbulence direct numerical simulation (DNS) flow field data provided by the Johns Hopkins turbulence database (JHTDB), synthetic image tests are performed. Turbulence statistics such as turbulence kinetic energy, dissipation rate, Taylor microscale, Kolmogorov scale, and velocity correlations are calculated. Various test cases were simulated while controlling three main parameters which affect the out-of-plane motion: PIV interrogation window size, camera inter-frame time, and laser sheet thickness. The amount of out-of-plane motion was first quantified, and then the error variation according to these parameters was examined. This information can be useful when examining fully three dimensional flows such as homogeneous and isotropic turbulence via 2D PIV.     

Bias and precision errors of digital particle image velocimetry

The bias and precision errors of digital particle image velocimetry are quantified. Uniform displacement images are used to evaluate the uncertainty attributed to various sub-pixel peak finding algorithms. Bias errors are found to exist for all algorithms, and the presence of bias error tends to affect the precision error. The ability to “calibrate” out the bias error is explored using a rectangular free jet experiment. The calibration was effective in removing the bias error in the potential core and less effective in the shear layer. The bias error is found to functionally depend on the displacement gradients present in the interrogation region. The study stresses the need for in situ quantification of DPIV uncertainty. Received: 3 November 1998 / Accepted: 26 June 1999     

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.     

A new particle tracking algorithm based on deterministic annealing and alternative distance measures

We describe a new particle tracking algorithm for the interrogation of double frame single exposure data, which is obtained with particle image velocimetry. The new procedure is based on an algorithm which has recently been proposed by Gold et al. (Gold et al., 1998) for solving point matching problems in statistical pattern recognition. For a given interrogation window, the algorithm simultaneously extracts: (i) the correct correspondences between particles in both frames and (ii) an estimate of the local flow-field parameters. Contrary to previous methods, the algorithm determines not only the local velocity, but other local components of the flow field, for example rotation and shear. This makes the new interrogation method superior to standard methods in particular in regions with high velocity gradients (e.g. vortices or shear flows). We perform benchmarks with three standard particle image velocimetry (PIV) and particle tracking velocimetry (PTV) methods: cross-correlation, nearest neighbour search, and image relaxation. We show that the new algorithm requires less particles per interrogation window than cross-correlation and allows for much higher particle densities than the other PTV methods. Consequently, one may obtain the velocity field at high spatial resolution even in regions of very fast flows. Finally, we find that the new algorithm is more robust against out-of-plane noise than previously proposed methods. Received: 1 March 1999 / Accepted: 29 July 1999     

Iterative multigrid approach in PIV image processing with discrete window offset

 The features of an improved algorithm for the interrogation of (digital) particle image velocimetry (PIV) pictures are described. The method is based on cross-correlation. It makes use of a translation of the interrogation areas. Such a displacement is predicted and corrected by means of an iterative procedure. In addition, while iterating, the method allows a refinement of the size of the interrogation areas. The quality of the measured vectors is controlled with data validation criteria applied at each intermediate step of the iteration process. A brief section explains the expected improvements in terms of dynamic range and resolution. The accuracy is assessed analysing images with imposed displacement fields. The improved cross-correlation algorithm has been applied to the measurement of the turbulent flow past a backward facing step (BFS). A systematic comparison is presented with Direct Numerical Simulation (DNS) data available on the subject. Received: 7 October 1997/Accepted: 11 August 1998     

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     

PIV图像粒子像斑定位偏差综合评估试验及其测速误差评估

本文针对ＰＩＶ技术的直接测量法中图像的可读性和可测性，讨论了从模拟图像到数字图像，最后到粒子像斑中心位置的确定过程中的误差规律；并提出了一种称之为粒子像斑定位偏差综合评估的试验方法。