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.     

Coherent and turbulent process analysis in the flow past a circular cylinder at high Reynolds number

This article presents an experimental study of the turbulent flow past a circular cylinder at high Reynolds number by means of advanced optical measurements techniques. Following previous studies using standard PIV and stereoscopic PIV (3C PIV), TRPIV and 3C-TRPIV have been employed in low subsonic wind tunnel environment. The database consisting of statistical and time-dependent fields aims at providing a physical analysis of the coherent and turbulent part, as well as a proper basis for validation and improvement of recent turbulence modelling approaches for strongly detached flow at high Reynolds number. As the nonlinear interaction between the coherent and turbulent dynamics have to be taken into account in a model, particular attention is paid to a decomposition of the flow into a coherent and a turbulent part, and to the analysis of their dynamics. This is achieved both using phase averaging and Proper Orthogonal Decomposition. For phase averaging, the two first POD coefficients are used for the evaluation of the vortex shedding phase angle. Furthermore, selected results of a Detached Eddy Simulation which had been validated by means of the experiment, are also presented to contribute to the physical analysis. The present study's experimental data resolved in space and time allow the confirmation of the conditional averaging for the turbulent stresses evaluation, by alleviating their overestimation due to phase jitter that occurs between the trigger signal and the velocity, when the phase angle is determined from a wall pressure signal. A more accurate physical analysis of the flow is achieved, particularly regarding the occurrence of irregular vortex shedding.     

A kilohertz frame rate cinemagraphic PIV system for laboratory-scale turbulent and unsteady flows

A kilohertz frame rate cinemagraphic particle image velocimetry (PIV) system has been developed for acquiring time-resolved image sequences of laboratory-scale gas and liquid-phase turbulent flows. Up to 8000 instantaneous PIV images per second are obtained, with sequence lengths exceeding 4000 images. The two-frame cross-correlation method employed precludes directional ambiguity and has a higher signal-to-noise ratio than single-frame autocorrelation or cross-correlation methods, facilitating acquisition of long uninterrupted sequences of valid PIV images. Low and high velocities can be measured simultaneously with similar accuracy by adaptively cross-correlating images with the appropriate time delay. Seed particle illumination is provided by two frequency-doubled Nd:YAG lasers producing Q-switched pulses at the camera frame rate. PIV images are acquired using a 16 mm high-speed rotating prism camera. Frame-to-frame registration is accomplished by imaging two pairs of crossed lines onto each frame and aligning the digitized image sequence to these markers using image processing algorithms. No flow disturbance is created by the markers because only their image is projected to the PIV imaging plane, with the physical projection device residing outside the flow field. The frame-to-frame alignment uncertainty contributes 2% to the overall velocity measurement uncertainty, which is otherwise comparable to similar film-based PIV methods. Received: 11 July 2000 / Accepted: 21 June 2001 Published online: 29 November 2001     

Spatial resolution and dissipation rate estimation in Taylor--Couette flow for tomographic PIV

This paper assesses the spatial resolution and accuracy of tomographic particle image velocimetry (PIV). In tomographic PIV the number of velocity vectors are of the order of the number of reconstructed particle images, and sometimes even exceeds this number when a high overlap fraction between adjacent interrogations is used. This raises the question of the actual spatial resolution of tomographic PIV in relation to the various flow scales. We use a Taylor--Couette flow of a fluid between two independently rotating cylinders and consider three flow regimes: laminar flow, Taylor vortex flow and fully turbulent flow. The laminar flow has no flow structures, and the measurement results are used to assess the measurement uncertainty and to validate the accuracy of the technique for measurements through the curved wall. In the Taylor vortex flow regime, the flow contains large-scale flow structures that are much larger than the size of the interrogation volumes and are fully resolved. The turbulent flow regime contains a range of flow scales. Measurements in the turbulent flow regime are carried out for a Reynolds number Re between 3,800 and 47,000. We use the measured torque on the cylinders to obtain an independent estimate of the energy dissipation rate and estimate of the Kolmogorov length scale. The data obtained by tomographic PIV are assessed by estimating the dissipation rate and comparing the result against the dissipation rate obtained from the measured torque. The turbulent flow data are evaluated for different sizes of the interrogation volumes and for different overlap ratios between adjacent interrogation locations. The results indicate that the turbulent flow measurements for the lowest Re could be (nearly) fully resolved. At the highest Re only a small fraction of the dissipation rate is resolved, still a reasonable estimate of the total dissipation rate could be obtained by means of using a sub-grid turbulence model. The resolution of tomographic PIV in these measurements is determined by the size of the interrogation volume. We propose a range of vector spacing for fully resolving the turbulent flow scales. It is noted that the use of a high overlap ratio, that is, 75?%, yields a substantial improvement for the estimation of the dissipation rate in comparison with data for 0 and 50?% overlap. This indicates that additional information on small-scale velocity gradients can be obtained by reducing the data spacing.     

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.     

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.     

On the accuracy of a MJPEG-based digital image compression PIV-system

 In this communication, the Digital Image Compression (DIC) – PIV system is introduced. The present system allows the measurement of mean and RMS velocities in turbulent flow fields, using JPEG digital image compression technique for on-line recording of thousands of images. The decompression and subsequent analysis of the images, performed by means of digital cross-correlation technique, is carried out off-line. Errors incurred by the application of the compression method are assessed and discussed. The effect of the compression is firstly analysed by linearly traversing (synthetic) computer-generated PIV-images at constant velocity. Secondly, accurate LDA measurements and data from direct numerical simulation (DNS) are used as a basis for the analysis in a low Reynolds number open water channel flow. The results show that excellent agreement between LDA and DIC–PIV measurements for mean and RMS velocities can be achieved using a compression factor up to 12. Received: 27 August 1996 / Accepted: 15 December 1998     

3-Component acceleration field measurement by dual-time stereoscopic particle image velocimetry

In this article, a multiplane stereo-particle image velocimetry (PIV) system was implemented and validated to measure the three-component acceleration field in a plane of turbulent flows. The employed technique relies on the use of two stereoscopic particle image velocimetry (SPIV) systems to measure pairs of velocity fields superimposed in space but shifted in time. The time delay between the two velocity fields enables the implementation of a finite difference scheme to compute temporal derivatives. The use of two synchronized SPIV systems allows us to overcome the limited acquisition rate of PIV systems when dealing with highly turbulent flows. Moreover, a methodology based on the analysis of the spectral error distribution is described here to determine the optimal time delay to compute time derivatives. The present dual-time SPIV arrangement and the proposed analysis method are applied to measure three-component acceleration fields in a cross section of a subsonic plane turbulent mixing layer.     

Measurement of fully-developed turbulent pipe flow with digital particle image velocimetry

A new and unique high-resolution image acquisition system for digital particle image velocimetry (DPIV) in turbulent flows is used for the measurement of fully-developed turbulent pipe flow at a Reynolds number of 5300. The flow conditions of the pipe flow match those of a direct numerical simulation (DNS) and of measurements with conventional (viz., photographic) PIV and with laser-Doppler velocimetry (LDV). This experiment allows a direct and detailed comparison of the conventional and digital implementations of the PIV method for a non-trivial unsteady flow. The results for the turbulence statistics and power spectra show that the level of accuracy for DPIV is comparable to that of conventional PIV, despite a considerable difference in the interrogation pixel resolution, i.e. 32 × 32 (DPIV) versus 256 × 256 (PIV). This result is in agreement with an earlier analytical prediction for the measurement accuracy. One of the advantages of DPIV over conventional PIV is that the interrogation of the DPIV images takes only a fraction of the time needed for the interrogation of the PIV photographs.     

Simultaneous velocity field measurements in two-phase flows for turbulent mixing of sprays by means of two-phase PIV

This paper describes a novel derivative of the PIV method for measuring the velocity fields of droplets and gas phases simultaneously using fluorescence images rather than Mie scattering images. Two-phase PIV allows the simultaneous and independent velocity field measurement of the liquid phase droplets and ambient gas in the case of two-phase flow mixing. For phase discrimination, each phase is labelled by a different fluorescent dye: the gas phase is seeded with small liquid droplets, tagged by an efficient fluorescent dye while the droplets of the liquid phases are tagged by a different fluorescent dye. For each phase, the wavelength shift of fluorescence is used to separate fluorescence from Mie scattering and to distinguish between the fluorescence of each phase. With the use of two cross-correlation PIV cameras and adequate optical filters, we obtain two double frame images, one for each phase. Thus standard PIV or PTV algorithms are used to obtain the simultaneous and independent velocity fields of the two phases. Because the two-phase PIV technique relies on the ability to produce two simultaneous and independent images of the two phases, the choice of the labelling dyes and of the associated optical filter sets is relevant for the image acquisition. Thus a spectroscopic study has been carried out to choose the optimal fluorescent dyes and the associated optical filters. The method has been evaluated in a simple two-phase flow: droplets of 30–40 μm diameter, produced by an ultrasonic nozzle are injected into a gas coflow seeded with small particles. Some initial results have been obtained which demonstrate the potential of the method.     

Rod-like particles matching algorithm based on SOM neural network in dispersed two-phase flow measurements

A matching algorithm based on self-organizing map (SOM) neural network is proposed for tracking rod-like particles in 2D optical measurements of dispersed two-phase flows. It is verified by both synthetic images of elongated particles mimicking 2D suspension flows and direct numerical simulations-based results of prolate particles dispersed in a turbulent channel flow. Furthermore, the potential benefit of this algorithm is evaluated by applying it to the experimental data of rod-like fibers tracking in wall turbulence. The study of the behavior of elongated particles suspended in turbulent flows has a practical importance and covers a wide range of applications in engineering and science. In experimental approach, particle tracking velocimetry of the dispersed phase has a key role together with particle image velocimetry of the carrier phase to obtain the velocities of both phases. The essential parts of particle tracking are to identify and match corresponding particles correctly in consecutive images. The present study is focused on the development of an algorithm for pairing non-spherical particles that have one major symmetry axis. The novel idea in the algorithm is to take the orientation of the particles into account for matching in addition to their positions. The method used is based on the SOM neural network that finds the most likely matching link in images on the basis of feature extraction and clustering. The fundamental concept is finding corresponding particles in the images with the nearest characteristics: position and orientation. The most effective aspect of this two-frame matching algorithm is that it does not require any preliminary knowledge of neither the flow field nor the particle behavior. Furthermore, using one additional characteristic of the non-spherical particles, namely their orientation, in addition to its coordinate vector, the pairing is improved both for more reliable matching at higher concentrations of dispersed particles and for higher robustness against loss of particle pairs between image frames.     

Vector post-processing algorithm for phase discrimination of two-phase PIV

A simple phase separation method using vector post-processing techniques is evaluated to measure velocity fields in a bubble plume. To provide for validation, fluorescent seeding is used, and two sets of synoptic images are obtained: mixed-phase images containing bubbles and fluorescent particles, and fluid-phase images containing only fluorescent particles. A third dataset is derived by applying a digital mask to remove bubbles from the mixed-phase images. All datasets are processed using cross-correlation particle image velocimetry (PIV). The resulting vector maps for the raw, mixed-phase data contain both bubble and continuous-phase velocity vectors. To separate the phases, a vector post-processing algorithm applies a maximum velocity threshold for the continuous-phase velocities coupled with the vector median filter to identify remaining bubble-velocity vectors and remove them from the mixed-phase velocity field. To validate the phase separation algorithm, the post-processed fluid-phase vectors are compared to PIV results obtained from both the optically separated and digitally masked data. The comparison among these methods shows that the post-processed mixed-phase data have small errors in regions near some bubbles, but for dilute environmental flows (low void fraction and slip velocity approximately equal to the entrained fluid velocity), the algorithm predicts well both instantaneous and time average statistical quantities. The method is reliable for flows having 10% or less of the field of view occupied by bubbles. The resulting instantaneous data provide information on plume wandering and eddy-size distributions within the bubble plume. By comparison among the datasets, it is shown that the patchiness of the vector-post processed and image masked data limit the diameter of identifiable eddy structures to the average distance between bubbles in the image, and that both datasets give identical probability density functions of eddy size. The optically filtered data have better data coverage and predict a greater probability of larger eddies as compared to the other two datasets.     

Measurement of the conditioned turbulence and temperature field of a premixed Bunsen burner by planar laser Rayleigh scattering and stereo particle image velocimetry

The turbulence and temperature field of Bunsen-type turbulent lean methane/air flames has been investigated using planar laser Rayleigh scattering (PLRS) and stereo particle image velocimetry (stereo PIV). Temporally averaged reaction progress variable plots have been computed from PLRS measurements in order to provide a basis with regards to the verification of computational fluid dynamics (CFD) models. Turbulence was characterised by stereo PIV in one plane for all three velocity components. Averaged velocity fields have been calculated, as well as Reynolds-decomposed fluctuation vector fields. Conditioned root mean square (RMS) values of the turbulent fluctuations in terms of unburnt and burnt gas could be determined by making use of the information gained from a threshold setting procedure in the PIV raw images. Furthermore, several length scales were measured indirectly from PIV vector plots. In this context, all integral length scales being accessible with stereo PIV were computed separately for the burnt and unburnt regions and were compared to each other. It could be observed that all integral length scales increased in the burnt zone. Additionally, the conditioned Taylor and Kolmogorov lengths have been extracted from the PIV field data, derived either from the zero-radius curvature of the correlation function or from common turbulence theory relations.     

波浪环境中垂直射流紊动特性的实验研究

利用粒子图像测速技术PIV(particle imagevelocimetry)对有限水深规则波浪环境下垂直射流紊动特性进行了实验研究. 应用相位分析法从测量数据中分离出速度脉动项,用4种不同波高的波浪研究波高对射流紊动特性的影响,对紊动量的分布以及大小进行了分析. 结果表明波高对射流的紊动特性有显著影响,并且对流项对波高的变化较紊动扩散项更为敏感,紊动扩散项量值约是对流项的$1/8\sim1/3$, 在时均化的N-S方程中起的作用不可忽略.      

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。     

Measurements in an urban-type boundary layer

Wind tunnel measurements of the boundary layer flow over a very rough surface comprising a staggered array of cubes are presented and discussed. Attention is concentrated on the near-wall region, including the canopy region below the tops of the roughness elements. Particle image velocimetry (PIV) and laser Doppler anemometry were used to identify the dominant features of the mean and turbulent flow and these are compared with the better-known features of the flow above the roughness. Spatial correlation data, extracted from the PIV images, are used to provide information about eddy structures and it is shown that these differ in some crucial respects from those typical of more classical boundary layers. The implications of the results are discussed in terms of their relevance to flows within the urban environment.     

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     

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.     

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.     

Comparison of PIV data using multiple configurations and processing techniques

Particle image velocimetry (PIV) data have been acquired using three different experimental configurations in the far-field of the interaction created by a transverse supersonic jet exhausting from a flat plate into a transonic crossflow. The configurations included two-component PIV in the centerline streamwise plane at two overlapping stations, as well as stereoscopic PIV in both the same streamwise plane and in the crossplane. All measurement planes intersected at a common line. Data from both two-component measurement stations and the stereoscopic streamwise configuration agreed to within the estimated uncertainty, but data from the crossplane exhibited reduced velocity and turbulent stress magnitudes by a small but significant degree. Subsequent reprocessing of the data in nominally the same manner using a newer software package brought all values into close agreement with each other, but produced substantially higher turbulent stresses. The error source associated with the choice of software was traced to the use of image deformation in the newer software to treat velocity gradients, which is shown by synthetic PIV tests to yield a more accurate result for turbulence measurements even for gradients within the recommended limits for classical PIV. These detailed comparisons of replicate data suggest that routine methods of uncertainty quantification used for a turbulent PIV experiment may not fully capture the actual error sources.