Robust evaluation of the dissimilarity between interrogation windows in image velocimetry

Image velocimetry techniques, which extract motion information by comparison of image regions, typically make use of cross-correlation to measure the degree of matching. In this work, a novel measure of the dissimilarity between interrogation windows is proposed which is based on a more robust estimator than cross-correlation. The method is validated on synthetic images and on two experimental data sets obtained from a periodically pulsed jet and a backward-facing step. The former is a basically laminar flow, whereas the latter is fully turbulent. Both of them are characterized by regions of high velocity gradients. The efficiency of the robust image velocimetry (RIV) is compared with a cross-correlation algorithm (PIV). The analysis of results shows that the RIV is less sensitive to the appearance and disappearance of particles, and to high velocity gradients and, in general, to noise, generating less spurious velocity vectors. As a consequence RIV resolves better the vorticity peaks at the center of the vortex rings generated by the pulsed jet, obtaining, for a given interrogation window size, a higher spatial resolution. Moreover, in the analysis of the flow field generated by the backward-facing step, the RIV performs better in the shear layer at the border of the recirculation region, leading to a more reliable estimation of Reynolds shear stress and horizontal velocity component.     

Spatially adaptive PIV interrogation based on data ensemble

This paper proposes a specific application of the approach recently proposed by the authors to achieve an autonomous and robust adaptive interrogation method for PIV data sets with the focus on the determination of mean velocity fields. Under circumstances such as suboptimal flow seeding distribution and large variations in the velocity field properties, neither multigrid techniques nor adaptive interrogation with criteria based on instantaneous conditions offer enough robustness for the flow field analysis. A method based on the data ensemble to select the adaptive interrogation parameters, namely, the window size, aspect ratio, orientation, and overlap factor is followed in this study. Interrogation windows are sized, shaped and spatially distributed on the basis of the average seeding density and the gradient of the velocity vector field. Compared to the instantaneous approach, the ensemble-based criterion adapts the windows in a more robust way especially for the implementation of non-isotropic windows (stretching and orientation), which yields a higher spatial resolution. If the procedure is applied recursively, the number of correlation samples can be optimized to satisfy a prescribed level of window overlap ratio. The relevance and applicability of the method are illustrated by an application to a shock-wave-boundary layer interaction problem. Furthermore, the application to a transonic airfoil wake verifies by means of a dual-resolution experiment that the spatial resolution in the wake can be increased by using non-isotropic interrogation windows.     

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)     

Second-order accurate particle image velocimetry

 An adaptive, second-order accurate particle image velocimetry (PIV) technique is presented. The technique uses two singly exposed images that are interrogated using a modified cross-correlation algorithm. Consequently, any of the equipment commonly available for conventional PIV (such as dual head Nd: YAG lasers, interline transfer CCD cameras, etc.) can be used with this more accurate algorithm. At the heart of the algorithm is a central difference approximation to the flow velocity (accurate to order Δt ²) versus the forward difference approximation (accurate to order Δt) common in PIV. An adaptive interrogation region-shifting algorithm is used to implement the central difference approximation. Adaptive shifting algorithms have been gaining popularity in recent years because they allow the spatial resolution of the PIV technique to be maximized. Adaptive shifting algorithms also have the virtue of helping to eliminate velocity bias errors. The second- order accuracy resulting from the central difference approximation can be obtained with relatively little additional computational effort compared to that required for a standard first-order accurate forward difference approximation. The adaptive central difference interrogation (CDI) algorithm has two main advantages over adaptive forward difference interrogation (FDI) algorithms: it is more accurate, especially at large time delays between camera exposures; and it provides a temporally symmetric view of the flow. By comparing measurements of flow around a single red blood cell made using both algorithms, the CDI technique is shown to perform better than conventional FDI-PIV interrogation algorithms near flow boundaries. Cylindrical Taylor–Couette flow images, both experimental and simulated, are used to demonstrate that the CDI algorithm is significantly more accurate than conventional PIV algorithms, especially as the time delay between exposures is increased. The results of the interrogations are shown to agree quite well with analytical predictions and confirm that the CDI algorithm is indeed second-order accurate while the conventional FDI algorithm is only first-order accurate. Received: 15 June 2000/Accepted: 2 February 2001     

Intensity Capping: a simple method to improve cross-correlation PIV results

A common source of error in particle image velocimetry (PIV) is the presence of bright spots within the images. These bright spots are characterized by grayscale intensities much greater than the mean intensity of the image and are typically generated by intense scattering from seed particles. The displacement of bright spots can dominate the cross-correlation calculation within an interrogation window, and may thereby bias the resulting velocity vector. An efficient and easy-to-implement image-enhancement procedure is described to improve PIV results when bright spots are present. The procedure, called Intensity Capping, imposes a user-specified upper limit to the grayscale intensity of the images. The displacement calculation then better represents the displacement of all particles in an interrogation window and the bias due to bright spots is reduced. Four PIV codes and a large set of experimental and simulated images were used to evaluate the performance of Intensity Capping. The results indicate that Intensity Capping can significantly increase the number of valid vectors from experimental image pairs and reduce displacement error in the analysis of simulated images. A comparison with other PIV image-enhancement techniques shows that Intensity Capping offers competitive performance, low computational cost, ease of implementation, and minimal modification to the images.     

PIV measurements of a microchannel flow

 A particle image velocimetry (PIV) system has been developed to measure velocity fields with order 1-μm spatial resolution. The technique uses 200 nm diameter flow-tracing particles, a pulsed Nd:YAG laser, an inverted epi-fluorescent microscope, and a cooled interline-transfer CCD camera to record high-resolution particle-image fields. The spatial resolution of the PIV technique is limited primarily by the diffraction-limited resolution of the recording optics. The accuracy of the PIV system was demonstrated by measuring the known flow field in a 30 μm×300 μm (nominal dimension) microchannel. The resulting velocity fields have a spatial resolution, defined by the size of the first window of the interrogation spot and out of plane resolution of 13.6 μm× 0.9 μm×1.8 μm, in the streamwise, wall-normal, and out of plane directions, respectively. By overlapping the interrogation spots by 50% to satisfy the Nyquist sampling criterion, a velocity-vector spacing of 450 nm in the wall-normal direction is achieved. These measurements are accurate to within 2% full-scale resolution, and are the highest spatially resolved PIV measurements published to date. Received: 29 October 1998/Accepted: 10 March 1999     

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.     

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 measurements of turbulent flow in planar mixing layer

A turbulent mixing layer consists of two different flow types, i.e. shear layer (shear-flow turbulence) and free stream regions (nearly homogeneous turbulence). The inherent non-uniform seeding tracer distributions observed around the interfaces between the shear layer and two free stream regions usually lead to a difficulty in particle image velocimetry (PIV) measurements. A parametric study on the application of PIV to the measurement of velocity field in a planar mixing layer is made by means of six factors, including interrogation window size, aspect ratio of interrogation window, interrogation window offset, threshold of data validation, sharpening spatial filters (Prewitt and Sobel masks), and smoothing spatial filter (median mask). The objective of this study is to obtain accurate turbulent measurements in both mean and fluctuating velocities using PIV under an appropriate parametric setting. The optimal levels, which are trade-off in between the accuracy and fine spatial resolution of velocity field measurements, are determined with the aid of the Taguchi method. It is shown that the PIV measurements made with this optimal set of parameters are in good agreement with the measurements made by a two-component hot-wire anemometer. Case independency of the proposed optimal set of parameters on the flow condition of the mixing layer is validated through the applications to two additional tests under the different experimental conditions in changing solely either velocity ratio of high-speed to low-speed free stream velocities or Reynolds number.     

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     

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 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.     

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.     

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.     

On improvement of PIV image interrogation near stationary interfaces

In this paper the problem posed by interfaces when present in PIV measurements is addressed. Different image pre-processing, processing and post-processing methodologies with the intention to minimize the interface effects are discussed and assessed using Monte Carlo simulations. Image treatment prior to the correlation process is shown to be incapable of fully removing the effects of the intensity pedestal across the object edge. The inherent assumption of periodicity in the signal causes the FFT-based correlation technique to perform the worst when the correlation window contains a signal truncation. Instead, an extended version of the masking technique introduced by Ronneberger et al. (Proceedings of the 9th international symposium on applications of laser techniques to fluid mechanics, Lisbon, 1998) is able to minimize the interface-correlation, resolving only the particle displacement peak. Once the displacement vector is obtained, the geometric center of the interrogation area is not the correct placement. Instead, the centre of mass position allows an unbiased representation of the wall flow (Usera et al. in Proceedings of the 12th international symposium on applications of laser techniques to fluid mechanics, Lisbon, 2004). The aforementioned concepts have been implemented in an adaptive interrogation methodology (Theunissen et al. in Meas Sci Technol 18:275–287, 2007) where additionally non-isotropic resolution and re-orientation of the correlation windows is applied near the interface, maximizing the wall-normal spatial resolution. The increase in resolution and robustness are demonstrated by application to a set of experimental images of a flat-plate, subsonic, turbulent boundary layer and a hypersonic flow over a double compression ramp.     

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     

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     

Dissipation rate estimation from PIV in zero-mean isotropic turbulence

Measuring the turbulent kinetic energy dissipation rate in an enclosed turbulence chamber that produces zero-mean flow is an experimental challenge. Traditional single-point dissipation rate measurement techniques are not applicable to flows with zero-mean velocity. Particle image velocimetry (PIV) affords calculation of the spatial derivative as well as the use of multi-point statistics to determine the dissipation rate. However, there is no consensus in the literature as to the best method to obtain dissipation rates from PIV measurements in such flows. We apply PIV in an enclosed zero-mean turbulent flow chamber and investigate five methods for dissipation rate estimation. We examine the influence of the PIV interrogation cell size on the performance of different dissipation rate estimation methods and evaluate correction factors that account for errors related to measurement uncertainty, finite spatial resolution, and low Reynolds number effects. We find the Re _λ corrected, second-order, longitudinal velocity structure function method to be the most robust method to estimate the dissipation rate in our zero-mean, gaseous flow system.     

Particle relaxation and its influence on the particle image velocimetry cross-correlation function

A study of some aspects of tracer particle responses to step changes in fluid velocity is presented. The effect of size distribution within a seed material on measured relaxation time is examined, with polydisperse particles of the same median diameter shown to possess a significantly higher relaxation time than their monodisperse counterparts when measured via a particle image velocimetry algorithm. The influence of a shock wave–induced velocity gradient within a PIV interrogation window on the correlation function is also examined using the noiseless cross-correlation function of Soria (Turbulence and coherent structures in fluids, plasmas and nonlinear media. World Scientific, Singapore, 2006). The presence of a shock is shown to introduce an artificial fluctuation into the measurement of velocity. This fluctuation is a function of the shock position, shock strength, spatial ratio and particle distribution. When the shock is located at the middle of the window, the magnitude of the fluctuation increases monotonically with increasing spatial ratio, increases asymptotically with shock strength, and decreases for increasing particle polydispersity. When the shock is located at the left-hand edge of the window, the magnitude of the artificial fluctuation is highest for intermediate spatial ratios, going to zero at infinitely high and low values. In this instance, particle polydispersity acts to increase the magnitude of fluctuations in measured velocity. In both cases, particle polydispersity serves to broaden the PDF of measured velocity. For the cases presented herein, with a shock located within the interrogation window, the root mean square of the artificial velocity fluctuations reaches values in excess of 30% of the freestream velocity.     

The development of high-speed particle image velocimetry (20 kHz) for large eddy simulation code refinement in bluff body flows

Flow interaction with a bluff body generates a highly complex flow field and has been the subject of much experimental and theoretical analysis. It has been shown that large eddy simulation (LES) modelling provides a more realistic analysis of the flow for such situations where the large scales of turbulence must be resolved. The inherent small-scale spatial velocity averaging in particle image velocimetry (PIV) is commensurate with the sub-grid scale modelling of LES and, therefore, offers potential as a code refinement technique. To demonstrate this potential, however, PIV must be performed with a temporal resolution of typically kHz and a spatial resolution of sub-mm² to be relevant for the vast majority of flows of engineering interest. This paper reports the development of a high-speed PIV system capable of operating at 20 kHz with a spatial resolution of 0.9 mm². This is the combined highest speed, highest resolution PIV data reported to date. The experiment chosen to demonstrate the system is the study of the steady flow interaction with circular and square cross-section obstacles. A Reynolds number of 3,900 is chosen for the cylinder flow to extend the database used by Breuer M. (1998 Int J Heat Fluid 19:512–521) in his extensive LES modelling of this flow. Data presented include a sequence of two-dimensional velocity and vorticity fields, including flow streamlines. Importantly, the random error, inherent in a PIV measurement, is discussed and a formula presented which allows the error to be estimated and regions of the flow identified where LES comparisons would be uncertain.